diff --git a/changelog b/changelog index e684837..f766cd4 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,99 @@ +20130804 tpd src/axiom-website/patches.html 20130804.01.tpd.patch +20130804 tpd src/axiom-website/CATS/index.html +20130804 tpd src/axiom-website/CATS/rich1a.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich1a.input.pdf +20130804 tpd src/axiom-website/CATS/rich1b.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich1b.input.pdf +20130804 tpd src/axiom-website/CATS/rich3a.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3a.input.pdf +20130804 tpd src/axiom-website/CATS/rich3c.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3c.input.pdf +20130804 tpd src/axiom-website/CATS/rich3d.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3d.input.pdf +20130804 tpd src/axiom-website/CATS/rich3e.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3e.input.pdf +20130804 tpd src/axiom-website/CATS/rich3f.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3f.input.pdf +20130804 tpd src/axiom-website/CATS/rich3g.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3g.input.pdf +20130804 tpd src/axiom-website/CATS/rich3h.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3h.input.pdf +20130804 tpd src/axiom-website/CATS/rich3i.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3i.input.pdf +20130804 tpd src/axiom-website/CATS/rich3j.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3j.input.pdf +20130804 tpd src/axiom-website/CATS/rich3k.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3k.input.pdf +20130804 tpd src/axiom-website/CATS/rich3l.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3l.input.pdf +20130804 tpd src/axiom-website/CATS/rich3m.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3m.input.pdf +20130804 tpd src/axiom-website/CATS/rich3n.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3n.input.pdf +20130804 tpd src/axiom-website/CATS/rich3o.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3o.input.pdf +20130804 tpd src/axiom-website/CATS/rich3p.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3p.input.pdf +20130804 tpd src/axiom-website/CATS/rich3q.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3q.input.pdf +20130804 tpd src/axiom-website/CATS/rich3r.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3r.input.pdf +20130804 tpd src/axiom-website/CATS/rich3s.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3s.input.pdf +20130804 tpd src/axiom-website/CATS/rich3t.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich3t.input.pdf +20130804 tpd src/axiom-website/CATS/rich4a.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4a.input.pdf +20130804 tpd src/axiom-website/CATS/rich4b.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4b.input.pdf +20130804 tpd src/axiom-website/CATS/rich4c.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4c.input.pdf +20130804 tpd src/axiom-website/CATS/rich4d.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4d.input.pdf +20130804 tpd src/axiom-website/CATS/rich4e.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4e.input.pdf +20130804 tpd src/axiom-website/CATS/rich4f.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4f.input.pdf +20130804 tpd src/axiom-website/CATS/rich4g.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4g.input.pdf +20130804 tpd src/axiom-website/CATS/rich4h.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4h.input.pdf +20130804 tpd src/axiom-website/CATS/rich4i.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4i.input.pdf +20130804 tpd src/axiom-website/CATS/rich4j.input.pamphlet +20130804 tpd src/axiom-website/CATS/rich4j.input.pdf +20130804 tpd src/input/Makefile.pamphlet +20130804 tpd src/input/rich1a.input.pamphlet +20130804 tpd src/input/rich1b.input.pamphlet +20130804 tpd src/input/rich3a.input.pamphlet +20130804 tpd src/input/rich3c.input.pamphlet +20130804 tpd src/input/rich3d.input.pamphlet +20130804 tpd src/input/rich3e.input.pamphlet +20130804 tpd src/input/rich3f.input.pamphlet +20130804 tpd src/input/rich3g.input.pamphlet +20130804 tpd src/input/rich3h.input.pamphlet +20130804 tpd src/input/rich3i.input.pamphlet +20130804 tpd src/input/rich3j.input.pamphlet +20130804 tpd src/input/rich3k.input.pamphlet +20130804 tpd src/input/rich3l.input.pamphlet +20130804 tpd src/input/rich3m.input.pamphlet +20130804 tpd src/input/rich3n.input.pamphlet +20130804 tpd src/input/rich3o.input.pamphlet +20130804 tpd src/input/rich3p.input.pamphlet +20130804 tpd src/input/rich3q.input.pamphlet +20130804 tpd src/input/rich3r.input.pamphlet +20130804 tpd src/input/rich3s.input.pamphlet +20130804 tpd src/input/rich3t.input.pamphlet +20130804 tpd src/input/rich4a.input.pamphlet +20130804 tpd src/input/rich4b.input.pamphlet +20130804 tpd src/input/rich4c.input.pamphlet +20130804 tpd src/input/rich4d.input.pamphlet +20130804 tpd src/input/rich4e.input.pamphlet +20130804 tpd src/input/rich4f.input.pamphlet +20130804 tpd src/input/rich4g.input.pamphlet +20130804 tpd src/input/rich4h.input.pamphlet +20130804 tpd src/input/rich4i.input.pamphlet +20130804 tpd src/input/rich4j.input.pamphlet 20130727 tpd src/axiom-website/patches.html 20130727.01.tpd.patch 20130727 tpd src/axiom-website/CATS/index.html add rich3c 20130727 tpd src/axiom-website/CATS/rich3c.input added diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index 7303013..cc3cf50 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -293,10 +293,12 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d x)^n (part 2) source pdf
+ (a+b x)^m (A+B x) (d+e x)^p source pdf
(a+b x)^m (c+d)^n (e+f x)^p (part 1) + source pdf
(a+b x)^m (c+d)^n (e+f x)^p (part 2) @@ -305,6 +307,88 @@ They have been rewritten using Axiom syntax. (a+b x)^m (c+d)^n (e+f x)^p (part 3) source pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 4) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 5) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 6) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 7) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 8) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 9) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 10) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 11) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 12) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 13) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 14) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 15) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 16) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 17) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 18) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 19) + source + pdf
+ (a+b x)^m (c+d)^n (e+f x)^p (part 20) + source + pdf
+ + x^m (a+b x^n)^p (part 1) + source + pdf
+ x^m (a+b x^n)^p (part 2) + source + pdf
+ x^m (a+b x^n)^p (part 3) + source + pdf
+ x^m (a+b x^n)^p (part 4) + source + pdf
+ x^m (a+b x^n)^p (part 5) + source + pdf
+ x^m (a+b x^n)^p (part 6) + source + pdf
+ x^m (a+b x^n)^p (part 7) + source + pdf
+ x^m (a+b x^n)^p (part 8) + source + pdf
+ x^m (a+b x^n)^p (part 9) + source + pdf
+ x^m (a+b x^n)^p (part 10) + source + pdf


Rich



diff --git a/src/axiom-website/CATS/rich1a.input.pamphlet b/src/axiom-website/CATS/rich1a.input.pamphlet index 06f6586..b6a7a8b 100644 --- a/src/axiom-website/CATS/rich1a.input.pamphlet +++ b/src/axiom-website/CATS/rich1a.input.pamphlet @@ -33369,7 +33369,7 @@ r0000:=-2/3*(a+b*x)^(3/2)/(a*x^(3/2)) --R Type: Expression(Integer) --E 2555 ---S 2556 of 3333 +--S 2556 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33381,7 +33381,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2556 ---S 2557 of 3333 +--S 2557 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33426,7 +33426,7 @@ r0000:=-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2)) --R Type: Expression(Integer) --E 2560 ---S 2561 of 3333 +--S 2561 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33442,7 +33442,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2561 ---S 2562 of 3333 +--S 2562 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33489,7 +33489,7 @@ r0000:=-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2565 ---S 2566 of 3333 +--S 2566 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33505,7 +33505,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2566 ---S 2567 of 3333 +--S 2567 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33756,7 +33756,7 @@ r0000:=-2/3*(a-b*x)^(3/2)/(a*x^(3/2)) --R Type: Expression(Integer) --E 2595 ---S 2596 of 3333 +--S 2596 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33768,7 +33768,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2596 ---S 2597 of 3333 +--S 2597 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33813,7 +33813,7 @@ r0000:=-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2)) --R Type: Expression(Integer) --E 2600 ---S 2601 of 3333 +--S 2601 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33829,7 +33829,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2601 ---S 2602 of 3333 +--S 2602 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33876,7 +33876,7 @@ r0000:=-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2605 ---S 2606 of 3333 +--S 2606 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33892,7 +33892,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2606 ---S 2607 of 3333 +--S 2607 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34138,7 +34138,7 @@ r0000:=-1/3*(2+b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2635 ---S 2636 of 3333 +--S 2636 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34150,7 +34150,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2636 ---S 2637 of 3333 +--S 2637 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34195,7 +34195,7 @@ r0000:=-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2640 ---S 2641 of 3333 +--S 2641 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34207,7 +34207,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2641 ---S 2642 of 3333 +--S 2642 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34253,7 +34253,7 @@ r0000:=-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-_ --R Type: Expression(Integer) --E 2645 ---S 2646 of 3333 +--S 2646 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34269,7 +34269,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2646 ---S 2647 of 3333 +--S 2647 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34515,7 +34515,7 @@ r0000:=-1/3*(2-b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2675 ---S 2676 of 3333 +--S 2676 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34527,7 +34527,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2676 ---S 2677 of 3333 +--S 2677 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34572,7 +34572,7 @@ r0000:=-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2680 ---S 2681 of 3333 +--S 2681 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34584,7 +34584,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2681 ---S 2682 of 3333 +--S 2682 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36903,7 +36903,7 @@ r0000:=-2*sqrt(a+b*x)/(a*sqrt(x)) --R Type: Expression(Integer) --E 2950 ---S 2951 of 3333 +--S 2951 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -36914,7 +36914,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2951 ---S 2952 of 3333 +--S 2952 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36957,7 +36957,7 @@ r0000:=-2/3*sqrt(a+b*x)/(a*x^(3/2))+4/3*b*sqrt(a+b*x)/(a^2*sqrt(x)) --R Type: Expression(Integer) --E 2955 ---S 2956 of 3333 +--S 2956 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -36969,7 +36969,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2956 ---S 2957 of 3333 +--S 2957 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36984,7 +36984,7 @@ m0000:=a0000 - r0000 --S 2958 of 3333 d0000:=D(m0000,x) --R ---R +--R --R (5) 0 --R Type: Expression(Integer) --E 2958 @@ -37077,7 +37077,7 @@ r0000:=-2/7*sqrt(a+b*x)/(a*x^(7/2))+12/35*b*sqrt(a+b*x)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2965 ---S 2966 of 3333 +--S 2966 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37093,7 +37093,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2966 ---S 2967 of 3333 +--S 2967 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37264,7 +37264,7 @@ r0000:=2*sqrt(x)/(a*sqrt(a+b*x)) --R Type: Expression(Integer) --E 2985 ---S 2986 of 3333 +--S 2986 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37276,7 +37276,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2986 ---S 2987 of 3333 +--S 2987 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37381,7 +37381,7 @@ r0000:=2/(a*x^(3/2)*sqrt(a+b*x))-8/3*sqrt(a+b*x)/(a^2*x^(3/2))+_ --R Type: Expression(Integer) --E 2995 ---S 2996 of 3333 +--S 2996 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37400,7 +37400,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2996 ---S 2997 of 3333 +--S 2997 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37446,7 +37446,7 @@ r0000:=2/(a*x^(5/2)*sqrt(a+b*x))-12/5*sqrt(a+b*x)/(a^2*x^(5/2))+_ --R Type: Expression(Integer) --E 3000 ---S 3001 of 3333 +--S 3001 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37477,7 +37477,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3001 ---S 3002 of 3333 +--S 3002 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37613,7 +37613,7 @@ r0000:=2/3*x^(3/2)/(a*(a+b*x)^(3/2)) --R Type: Expression(Integer) --E 3015 ---S 3016 of 3333 +--S 3016 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37632,7 +37632,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3016 ---S 3017 of 3333 +--S 3017 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37676,7 +37676,7 @@ r0000:=2/3*sqrt(x)/(a*(a+b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a+b*x)) --R Type: Expression(Integer) --E 3020 ---S 3021 of 3333 +--S 3021 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37695,7 +37695,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3021 ---S 3022 of 3333 +--S 3022 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37741,7 +37741,7 @@ r0000:=2/3/(a*(a+b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a+b*x))-_ --R Type: Expression(Integer) --E 3025 ---S 3026 of 3333 +--S 3026 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37772,7 +37772,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3026 ---S 3027 of 3333 +--S 3027 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37818,7 +37818,7 @@ r0000:=2/3/(a*x^(3/2)*(a+b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a+b*x))-_ --R Type: Expression(Integer) --E 3030 ---S 3031 of 3333 ok to fail, random algorithm +--S 3031 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37867,7 +37867,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3031 ---S 3032 of 3333 ok to fail, random algorithm +--S 3032 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -40512,7 +40512,7 @@ r0000:=1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-_ --R Type: Expression(Integer) --E 3285 ---S 3286 of 3333 +--S 3286 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -40528,7 +40528,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3286 ---S 3287 of 3333 +--S 3287 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -40658,7 +40658,7 @@ r0000:=1/3*x^(3/2)/(2-b*x)^(3/2) --R Type: Expression(Integer) --E 3300 ---S 3301 of 3333 ok to fail, random algorithm +--S 3301 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -40673,7 +40673,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3301 ---S 3302 of 3333 ok to fail, random algorithm +--S 3302 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R diff --git a/src/axiom-website/CATS/rich1a.input.pdf b/src/axiom-website/CATS/rich1a.input.pdf index 4366ac0..1cfad11 100644 Binary files a/src/axiom-website/CATS/rich1a.input.pdf and b/src/axiom-website/CATS/rich1a.input.pdf differ diff --git a/src/axiom-website/CATS/rich1b.input.pamphlet b/src/axiom-website/CATS/rich1b.input.pamphlet index 7234288..1f09a0d 100644 --- a/src/axiom-website/CATS/rich1b.input.pamphlet +++ b/src/axiom-website/CATS/rich1b.input.pamphlet @@ -49865,7 +49865,7 @@ r0000:=2*asinh(sqrt(b*x)/sqrt(2))/b --R Type: Expression(Integer) --E 1964 ---S 1965 of 2952 +--S 1965 of 2952 ok to fail, (non-algebraic residues) a0000:=integrate(t0000,x) --R --R @@ -49876,7 +49876,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 1965 ---S 1966 of 2952 +--S 1966 of 2952 m0000:=a0000 - r0000 --R --R diff --git a/src/axiom-website/CATS/rich1b.input.pdf b/src/axiom-website/CATS/rich1b.input.pdf index 079dacf..ff54c9e 100644 Binary files a/src/axiom-website/CATS/rich1b.input.pdf and b/src/axiom-website/CATS/rich1b.input.pdf differ diff --git a/src/axiom-website/CATS/rich3a.input.pamphlet b/src/axiom-website/CATS/rich3a.input.pamphlet index fc946de..29348ed 100644 --- a/src/axiom-website/CATS/rich3a.input.pamphlet +++ b/src/axiom-website/CATS/rich3a.input.pamphlet @@ -28,16 +28,16 @@ There are: )set message auto off )clear all ---S 1 of 1092 +--S 1 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x) --R --R --R 3 2 n --R (1) (d x + c x )(b x + a) --R Type: Expression(Integer) ---E 1 +--E 1 ---S 2 of 1092 +--S 2 of 1092 r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+_ (b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -75,9 +75,9 @@ r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 2 +--E 2 ---S 3 of 1092 +--S 3 of 1092 a0:=integrate(t0,x) --R --R @@ -100,9 +100,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 3 +--E 3 ---S 4 of 1092 +--S 4 of 1092 m0:=a0-r0 --R --R @@ -152,28 +152,28 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 4 +--E 4 ---S 5 of 1092 +--S 5 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 5 +--E 5 )clear all ---S 6 of 1092 +--S 6 of 1092 t0:=x*(a+b*x)^n*(c+d*x) --R --R --R 2 n --R (1) (d x + c x)(b x + a) --R Type: Expression(Integer) ---E 6 +--E 6 ---S 7 of 1092 +--S 7 of 1092 r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ (b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n)) --R @@ -191,9 +191,9 @@ r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 7 +--E 7 ---S 8 of 1092 +--S 8 of 1092 a0:=integrate(t0,x) --R --R @@ -213,9 +213,9 @@ a0:=integrate(t0,x) --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Union(Expression(Integer),...) ---E 8 +--E 8 ---S 9 of 1092 +--S 9 of 1092 m0:=a0-r0 --R --R @@ -244,28 +244,28 @@ m0:=a0-r0 --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 9 +--E 9 ---S 10 of 1092 +--S 10 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 10 +--E 10 )clear all ---S 11 of 1092 +--S 11 of 1092 t0:=(a+b*x)^n*(c+d*x) --R --R --R n --R (1) (d x + c)(b x + a) --R Type: Expression(Integer) ---E 11 +--E 11 ---S 12 of 1092 +--S 12 of 1092 r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) --R --R @@ -275,9 +275,9 @@ r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Expression(Integer) ---E 12 +--E 12 ---S 13 of 1092 +--S 13 of 1092 a0:=integrate(t0,x) --R --R @@ -291,9 +291,9 @@ a0:=integrate(t0,x) --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Union(Expression(Integer),...) ---E 13 +--E 13 ---S 14 of 1092 +--S 14 of 1092 m0:=a0-r0 --R --R @@ -310,19 +310,19 @@ m0:=a0-r0 --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Expression(Integer) ---E 14 +--E 14 ---S 15 of 1092 +--S 15 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 15 +--E 15 )clear all ---S 16 of 1092 +--S 16 of 1092 t0:=(a+b*x)^n*(c+d*x)/x --R --R @@ -331,28 +331,28 @@ t0:=(a+b*x)^n*(c+d*x)/x --R (1) ------------------- --R x --R Type: Expression(Integer) ---E 16 +--E 16 ---S 17 of 1092 +--S 17 of 1092 --r0:=d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*_ -- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 17 +--E 17 ---S 18 of 1092 +--S 18 of 1092 --a0:=integrate(t0,x) ---E 18 +--E 18 ---S 19 of 1092 +--S 19 of 1092 --m0:=a0-r0 ---E 19 +--E 19 ---S 20 of 1092 +--S 20 of 1092 --d0:=D(m0,x) ---E 20 +--E 20 )clear all ---S 21 of 1092 +--S 21 of 1092 t0:=x^m*(a+b*x)*(c+d*x)^5 --R --R @@ -366,9 +366,9 @@ t0:=x^m*(a+b*x)*(c+d*x)^5 --R m --R x --R Type: Expression(Integer) ---E 21 +--E 21 ---S 22 of 1092 +--S 22 of 1092 r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ 5*c^3*d*(b*c+2*a*d)*x^(3+m)/(3+m)+10*c^2*d^2*(b*c+a*d)*_ x^(4+m)/(4+m)+5*c*d^3*(2*b*c+a*d)*x^(5+m)/(5+m)+_ @@ -466,9 +466,9 @@ r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Expression(Integer) ---E 22 +--E 22 ---S 23 of 1092 +--S 23 of 1092 a0:=integrate(t0,x) --R --R @@ -568,9 +568,9 @@ a0:=integrate(t0,x) --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Union(Expression(Integer),...) ---E 23 +--E 23 ---S 24 of 1092 +--S 24 of 1092 m0:=a0-r0 --R --R @@ -766,19 +766,19 @@ m0:=a0-r0 --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Expression(Integer) ---E 24 +--E 24 ---S 25 of 1092 +--S 25 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 25 +--E 25 )clear all ---S 26 of 1092 +--S 26 of 1092 t0:=x^3*(a+b*x)*(c+d*x)^5 --R --R @@ -789,9 +789,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 26 +--E 26 ---S 27 of 1092 +--S 27 of 1092 r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ 10/7*c^2*d^2*(b*c+a*d)*x^7+5/8*c*d^3*(2*b*c+a*d)*x^8+_ 1/9*d^4*(5*b*c+a*d)*x^9+1/10*b*d^5*x^10 @@ -810,9 +810,9 @@ r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ --R - a c x --R 4 --R Type: Polynomial(Fraction(Integer)) ---E 27 +--E 27 ---S 28 of 1092 +--S 28 of 1092 a0:=integrate(t0,x) --R --R @@ -829,27 +829,27 @@ a0:=integrate(t0,x) --R - a c x --R 4 --R Type: Polynomial(Fraction(Integer)) ---E 28 +--E 28 ---S 29 of 1092 +--S 29 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Polynomial(Fraction(Integer)) ---E 29 +--E 29 ---S 30 of 1092 +--S 30 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Polynomial(Fraction(Integer)) ---E 30 +--E 30 )clear all ---S 31 of 1092 +--S 31 of 1092 t0:=x^2*(a+b*x)*(c+d*x)^5 --R --R @@ -860,9 +860,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 31 +--E 31 ---S 32 of 1092 +--S 32 of 1092 r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ 1/8*(3*b*c-a*d)*(c+d*x)^8/d^4+1/9*b*(c+d*x)^9/d^4 --R @@ -883,9 +883,9 @@ r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 32 +--E 32 ---S 33 of 1092 +--S 33 of 1092 a0:=integrate(t0,x) --R --R @@ -902,9 +902,9 @@ a0:=integrate(t0,x) --R - a c x --R 3 --R Type: Polynomial(Fraction(Integer)) ---E 33 +--E 33 ---S 34 of 1092 +--S 34 of 1092 m0:=a0-r0 --R --R @@ -915,19 +915,19 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 34 +--E 34 ---S 35 of 1092 +--S 35 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 35 +--E 35 )clear all ---S 36 of 1092 +--S 36 of 1092 t0:=x*(a+b*x)*(c+d*x)^5 --R --R @@ -938,9 +938,9 @@ t0:=x*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 4 3 2 4 3 4 5 2 5 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 36 +--E 36 ---S 37 of 1092 +--S 37 of 1092 r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ 1/8*b*(c+d*x)^8/d^3 --R @@ -961,9 +961,9 @@ r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 37 +--E 37 ---S 38 of 1092 +--S 38 of 1092 a0:=integrate(t0,x) --R --R @@ -980,9 +980,9 @@ a0:=integrate(t0,x) --R - a c x --R 2 --R Type: Polynomial(Fraction(Integer)) ---E 38 +--E 38 ---S 39 of 1092 +--S 39 of 1092 m0:=a0-r0 --R --R @@ -993,19 +993,19 @@ m0:=a0-r0 --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 39 +--E 39 ---S 40 of 1092 +--S 40 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 40 +--E 40 )clear all ---S 41 of 1092 +--S 41 of 1092 t0:=(a+b*x)*(c+d*x)^5 --R --R @@ -1016,9 +1016,9 @@ t0:=(a+b*x)*(c+d*x)^5 --R 2 3 3 2 3 3 2 4 2 4 5 5 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c --R Type: Polynomial(Integer) ---E 41 +--E 41 ---S 42 of 1092 +--S 42 of 1092 r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 --R --R @@ -1038,9 +1038,9 @@ r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 --R 2 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 42 +--E 42 ---S 43 of 1092 +--S 43 of 1092 a0:=integrate(t0,x) --R --R @@ -1056,9 +1056,9 @@ a0:=integrate(t0,x) --R 5 --R a c x --R Type: Polynomial(Fraction(Integer)) ---E 43 +--E 43 ---S 44 of 1092 +--S 44 of 1092 m0:=a0-r0 --R --R @@ -1069,19 +1069,19 @@ m0:=a0-r0 --R 2 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 44 +--E 44 ---S 45 of 1092 +--S 45 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 45 +--E 45 )clear all ---S 46 of 1092 +--S 46 of 1092 t0:=(a+b*x)*(c+d*x)^5/x --R --R @@ -1094,9 +1094,9 @@ t0:=(a+b*x)*(c+d*x)^5/x --R / --R x --R Type: Fraction(Polynomial(Integer)) ---E 46 +--E 46 ---S 47 of 1092 +--S 47 of 1092 r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ 5/4*a*c*d^4*x^4+1/5*a*d^5*x^5+1/6*b*(c+d*x)^6/d+a*c^5*log(x) --R @@ -1113,9 +1113,9 @@ r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ --R / --R 60d --R Type: Expression(Integer) ---E 47 +--E 47 ---S 48 of 1092 +--S 48 of 1092 a0:=integrate(t0,x) --R --R @@ -1131,9 +1131,9 @@ a0:=integrate(t0,x) --R / --R 60 --R Type: Union(Expression(Integer),...) ---E 48 +--E 48 ---S 49 of 1092 +--S 49 of 1092 m0:=a0-r0 --R --R @@ -1142,19 +1142,19 @@ m0:=a0-r0 --R (4) - ---- --R 6d --R Type: Expression(Integer) ---E 49 +--E 49 ---S 50 of 1092 +--S 50 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 50 +--E 50 )clear all ---S 51 of 1092 +--S 51 of 1092 t0:=(a+b*x)*(c+d*x)^5/x^2 --R --R @@ -1168,9 +1168,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^2 --R 2 --R x --R Type: Fraction(Polynomial(Integer)) ---E 51 +--E 51 ---S 52 of 1092 +--S 52 of 1092 r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ 5/3*c*d^3*(2*b*c+a*d)*x^3+1/4*d^4*(5*b*c+a*d)*x^4+_ 1/5*b*d^5*x^5+c^4*(b*c+5*a*d)*log(x) @@ -1188,9 +1188,9 @@ r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ --R / --R 60x --R Type: Expression(Integer) ---E 52 +--E 52 ---S 53 of 1092 +--S 53 of 1092 a0:=integrate(t0,x) --R --R @@ -1206,27 +1206,27 @@ a0:=integrate(t0,x) --R / --R 60x --R Type: Union(Expression(Integer),...) ---E 53 +--E 53 ---S 54 of 1092 +--S 54 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 54 +--E 54 ---S 55 of 1092 +--S 55 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 55 +--E 55 )clear all ---S 56 of 1092 +--S 56 of 1092 t0:=(a+b*x)*(c+d*x)^5/x^3 --R --R @@ -1240,9 +1240,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^3 --R 3 --R x --R Type: Fraction(Polynomial(Integer)) ---E 56 +--E 56 ---S 57 of 1092 +--S 57 of 1092 r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ 5/2*c*d^3*(2*b*c+a*d)*x^2+1/3*d^4*(5*b*c+a*d)*x^3+_ 1/4*b*d^5*x^4+5*c^3*d*(b*c+2*a*d)*log(x) @@ -1261,9 +1261,9 @@ r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ --R 2 --R 12x --R Type: Expression(Integer) ---E 57 +--E 57 ---S 58 of 1092 +--S 58 of 1092 a0:=integrate(t0,x) --R --R @@ -1280,27 +1280,27 @@ a0:=integrate(t0,x) --R 2 --R 12x --R Type: Union(Expression(Integer),...) ---E 58 +--E 58 ---S 59 of 1092 +--S 59 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 59 +--E 59 ---S 60 of 1092 +--S 60 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 60 +--E 60 )clear all ---S 61 of 1092 +--S 61 of 1092 t0:=x*(a+b*x)*(c+d*x)^16 --R --R @@ -1329,9 +1329,9 @@ t0:=x*(a+b*x)*(c+d*x)^16 --R 14 2 15 3 15 16 2 16 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 61 +--E 61 ---S 62 of 1092 +--S 62 of 1092 r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ 1/19*b*(c+d*x)^19/d^3 --R @@ -1374,9 +1374,9 @@ r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 62 +--E 62 ---S 63 of 1092 +--S 63 of 1092 a0:=integrate(t0,x) --R --R @@ -1411,9 +1411,9 @@ a0:=integrate(t0,x) --R (30a c d + 4b c d)x + (-- a c d + - b c )x + - a c x --R 3 3 2 --R Type: Polynomial(Fraction(Integer)) ---E 63 +--E 63 ---S 64 of 1092 +--S 64 of 1092 m0:=a0-r0 --R --R @@ -1424,19 +1424,19 @@ m0:=a0-r0 --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 64 +--E 64 ---S 65 of 1092 +--S 65 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 65 +--E 65 )clear all ---S 66 of 1092 +--S 66 of 1092 t0:=x^2*(a+b*x)*(c+d*x)^16 --R --R @@ -1465,9 +1465,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^16 --R 14 2 15 4 15 16 3 16 2 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 66 +--E 66 ---S 67 of 1092 +--S 67 of 1092 r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ 1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4 --R @@ -1512,9 +1512,9 @@ r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 67 +--E 67 ---S 68 of 1092 +--S 68 of 1092 a0:=integrate(t0,x) --R --R @@ -1551,9 +1551,9 @@ a0:=integrate(t0,x) --R (24a c d + -- b c d)x + (4a c d + - b c )x + - a c x --R 5 4 3 --R Type: Polynomial(Fraction(Integer)) ---E 68 +--E 68 ---S 69 of 1092 +--S 69 of 1092 m0:=a0-r0 --R --R @@ -1564,19 +1564,19 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 69 +--E 69 ---S 70 of 1092 +--S 70 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 70 +--E 70 )clear all ---S 71 of 1092 +--S 71 of 1092 t0:=x^3*(a+b*x)*(c+d*x)^16 --R --R @@ -1605,9 +1605,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^16 --R 14 2 15 5 15 16 4 16 3 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 71 +--E 71 ---S 72 of 1092 +--S 72 of 1092 r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ 3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+_ 1/21*b*(c+d*x)^21/d^5 @@ -1653,9 +1653,9 @@ r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 72 +--E 72 ---S 73 of 1092 +--S 73 of 1092 a0:=integrate(t0,x) --R --R @@ -1692,9 +1692,9 @@ a0:=integrate(t0,x) --R (20a c d + - b c d)x + (-- a c d + - b c )x + - a c x --R 3 5 5 4 --R Type: Polynomial(Fraction(Integer)) ---E 73 +--E 73 ---S 74 of 1092 +--S 74 of 1092 m0:=a0-r0 --R --R @@ -1705,28 +1705,28 @@ m0:=a0-r0 --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 74 +--E 74 ---S 75 of 1092 +--S 75 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 75 +--E 75 )clear all ---S 76 of 1092 +--S 76 of 1092 t0:=x^2*(2+x)^5*(2+3*x) --R --R --R 8 7 6 5 4 3 2 --R (1) 3x + 32x + 140x + 320x + 400x + 256x + 64x --R Type: Polynomial(Integer) ---E 76 +--E 76 ---S 77 of 1092 +--S 77 of 1092 r0:=1/3*x^3*(2+x)^6 --R --R @@ -1734,9 +1734,9 @@ r0:=1/3*x^3*(2+x)^6 --R (2) - x + 4x + 20x + --- x + 80x + 64x + -- x --R 3 3 3 --R Type: Polynomial(Fraction(Integer)) ---E 77 +--E 77 ---S 78 of 1092 +--S 78 of 1092 a0:=integrate(t0,x) --R --R @@ -1744,36 +1744,36 @@ a0:=integrate(t0,x) --R (3) - x + 4x + 20x + --- x + 80x + 64x + -- x --R 3 3 3 --R Type: Polynomial(Fraction(Integer)) ---E 78 +--E 78 ---S 79 of 1092 +--S 79 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Polynomial(Fraction(Integer)) ---E 79 +--E 79 ---S 80 of 1092 +--S 80 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Polynomial(Fraction(Integer)) ---E 80 +--E 80 )clear all ---S 81 of 1092 +--S 81 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x)^2 --R --R --R 2 4 3 2 2 n --R (1) (d x + 2c d x + c x )(b x + a) --R Type: Expression(Integer) ---E 81 +--E 81 ---S 82 of 1092 +--S 82 of 1092 r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ (a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*_ (a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ @@ -1838,9 +1838,9 @@ r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 82 +--E 82 ---S 83 of 1092 +--S 83 of 1092 a0:=integrate(t0,x) --R --R @@ -1898,9 +1898,9 @@ a0:=integrate(t0,x) --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Union(Expression(Integer),...) ---E 83 +--E 83 ---S 84 of 1092 +--S 84 of 1092 m0:=a0-r0 --R --R @@ -2009,28 +2009,28 @@ m0:=a0-r0 --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 84 +--E 84 ---S 85 of 1092 +--S 85 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 85 +--E 85 )clear all ---S 86 of 1092 +--S 86 of 1092 t0:=x*(a+b*x)^n*(c+d*x)^2 --R --R --R 2 3 2 2 n --R (1) (d x + 2c d x + c x)(b x + a) --R Type: Expression(Integer) ---E 86 +--E 86 ---S 87 of 1092 +--S 87 of 1092 r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ (a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/_ (b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -2070,9 +2070,9 @@ r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 87 +--E 87 ---S 88 of 1092 +--S 88 of 1092 a0:=integrate(t0,x) --R --R @@ -2115,9 +2115,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 88 +--E 88 ---S 89 of 1092 +--S 89 of 1092 m0:=a0-r0 --R --R @@ -2190,28 +2190,28 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 89 +--E 89 ---S 90 of 1092 +--S 90 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 90 +--E 90 )clear all ---S 91 of 1092 +--S 91 of 1092 t0:=(a+b*x)^n*(c+d*x)^2 --R --R --R 2 2 2 n --R (1) (d x + 2c d x + c )(b x + a) --R Type: Expression(Integer) ---E 91 +--E 91 ---S 92 of 1092 +--S 92 of 1092 r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ (b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n)) --R @@ -2238,9 +2238,9 @@ r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 92 +--E 92 ---S 93 of 1092 +--S 93 of 1092 a0:=integrate(t0,x) --R --R @@ -2263,9 +2263,9 @@ a0:=integrate(t0,x) --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Union(Expression(Integer),...) ---E 93 +--E 93 ---S 94 of 1092 +--S 94 of 1092 m0:=a0-r0 --R --R @@ -2303,19 +2303,19 @@ m0:=a0-r0 --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 94 +--E 94 ---S 95 of 1092 +--S 95 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 95 +--E 95 )clear all ---S 96 of 1092 +--S 96 of 1092 t0:=(a+b*x)^n*(c+d*x)^2/x --R --R @@ -2324,29 +2324,29 @@ t0:=(a+b*x)^n*(c+d*x)^2/x --R (1) ------------------------------ --R x --R Type: Expression(Integer) ---E 96 +--E 96 ---S 97 of 1092 +--S 97 of 1092 --r0:=-d*(a*d-b*c*(3+n))*(a+b*x)^(1+n)/(b^2*(1+n)*(2+n))+_ -- d*(a+b*x)^(1+n)*(c+d*x)/(b*(2+n))-c^2*(a+b*x)^(1+n)*_ -- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 97 +--E 97 ---S 98 of 1092 +--S 98 of 1092 --a0:=integrate(t0,x) ---E 98 +--E 98 ---S 99 of 1092 +--S 99 of 1092 --m0:=a0-r0 ---E 99 +--E 99 ---S 100 of 1092 +--S 100 of 1092 --d0:=D(m0,x) ---E 100 +--E 100 )clear all ---S 101 of 1092 +--S 101 of 1092 t0:=x^m*(a+b*x)^2*(c+d*x)^5 --R --R @@ -2363,9 +2363,9 @@ t0:=x^m*(a+b*x)^2*(c+d*x)^5 --R m --R x --R Type: Expression(Integer) ---E 101 +--E 101 ---S 102 of 1092 +--S 102 of 1092 r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+_ 5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+_ @@ -2531,9 +2531,9 @@ r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Expression(Integer) ---E 102 +--E 102 ---S 103 of 1092 +--S 103 of 1092 a0:=integrate(t0,x) --R --R @@ -2699,9 +2699,9 @@ a0:=integrate(t0,x) --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Union(Expression(Integer),...) ---E 103 +--E 103 ---S 104 of 1092 +--S 104 of 1092 m0:=a0-r0 --R --R @@ -3023,19 +3023,19 @@ m0:=a0-r0 --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Expression(Integer) ---E 104 +--E 104 ---S 105 of 1092 +--S 105 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 105 +--E 105 )clear all ---S 106 of 1092 +--S 106 of 1092 t0:=x^3*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3088,9 +3088,9 @@ t0:=x^3*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 5 2 15 16 4 2 16 3 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 106 +--E 106 ---S 107 of 1092 +--S 107 of 1092 r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ (b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+_ 3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ @@ -3169,9 +3169,9 @@ r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ --R 6 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 107 +--E 107 ---S 108 of 1092 +--S 108 of 1092 a0:=integrate(t0,x) --R --R @@ -3239,9 +3239,9 @@ a0:=integrate(t0,x) --R (20a c d + -- a b c d + - b c )x + (-- a c d + - a b c )x + - a c x --R 3 6 5 5 4 --R Type: Polynomial(Fraction(Integer)) ---E 108 +--E 108 ---S 109 of 1092 +--S 109 of 1092 m0:=a0-r0 --R --R @@ -3252,19 +3252,19 @@ m0:=a0-r0 --R 6 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 109 +--E 109 ---S 110 of 1092 +--S 110 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 110 +--E 110 )clear all ---S 111 of 1092 +--S 111 of 1092 t0:=x^2*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3317,9 +3317,9 @@ t0:=x^2*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 4 2 15 16 3 2 16 2 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 111 +--E 111 ---S 112 of 1092 +--S 112 of 1092 r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ (c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-_ 1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5 @@ -3394,9 +3394,9 @@ r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 112 +--E 112 ---S 113 of 1092 +--S 113 of 1092 a0:=integrate(t0,x) --R --R @@ -3462,9 +3462,9 @@ a0:=integrate(t0,x) --R (24a c d + -- a b c d + - b c )x + (4a c d + - a b c )x + - a c x --R 5 5 2 3 --R Type: Polynomial(Fraction(Integer)) ---E 113 +--E 113 ---S 114 of 1092 +--S 114 of 1092 m0:=a0-r0 --R --R @@ -3475,19 +3475,19 @@ m0:=a0-r0 --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 114 +--E 114 ---S 115 of 1092 +--S 115 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 115 +--E 115 )clear all ---S 116 of 1092 +--S 116 of 1092 t0:=x*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3540,9 +3540,9 @@ t0:=x*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 3 2 15 16 2 2 16 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 116 +--E 116 ---S 117 of 1092 +--S 117 of 1092 r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ (c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+_ 1/20*b^2*(c+d*x)^20/d^4 @@ -3616,9 +3616,9 @@ r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 117 +--E 117 ---S 118 of 1092 +--S 118 of 1092 a0:=integrate(t0,x) --R --R @@ -3683,9 +3683,9 @@ a0:=integrate(t0,x) --R (30a c d + 8a b c d + - b c )x + (-- a c d + - a b c )x + - a c x --R 4 3 3 2 --R Type: Polynomial(Fraction(Integer)) ---E 118 +--E 118 ---S 119 of 1092 +--S 119 of 1092 m0:=a0-r0 --R --R @@ -3696,28 +3696,28 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 119 +--E 119 ---S 120 of 1092 +--S 120 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 120 +--E 120 )clear all ---S 121 of 1092 +--S 121 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x)^3 --R --R --R 3 5 2 4 2 3 3 2 n --R (1) (d x + 3c d x + 3c d x + c x )(b x + a) --R Type: Expression(Integer) ---E 121 +--E 121 ---S 122 of 1092 +--S 122 of 1092 r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ (b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*_ (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+_ @@ -3828,9 +3828,9 @@ r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Expression(Integer) ---E 122 +--E 122 ---S 123 of 1092 +--S 123 of 1092 a0:=integrate(t0,x) --R --R @@ -3921,9 +3921,9 @@ a0:=integrate(t0,x) --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Union(Expression(Integer),...) ---E 123 +--E 123 ---S 124 of 1092 +--S 124 of 1092 m0:=a0-r0 --R --R @@ -4113,28 +4113,28 @@ m0:=a0-r0 --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Expression(Integer) ---E 124 +--E 124 ---S 125 of 1092 +--S 125 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 125 +--E 125 )clear all ---S 126 of 1092 +--S 126 of 1092 t0:=x*(a+b*x)^n*(c+d*x)^3 --R --R --R 3 4 2 3 2 2 3 n --R (1) (d x + 3c d x + 3c d x + c x)(b x + a) --R Type: Expression(Integer) ---E 126 +--E 126 ---S 127 of 1092 +--S 127 of 1092 r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ (a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/_ (b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ @@ -4208,9 +4208,9 @@ r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 127 +--E 127 ---S 128 of 1092 +--S 128 of 1092 a0:=integrate(t0,x) --R --R @@ -4277,9 +4277,9 @@ a0:=integrate(t0,x) --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Union(Expression(Integer),...) ---E 128 +--E 128 ---S 129 of 1092 +--S 129 of 1092 m0:=a0-r0 --R --R @@ -4412,28 +4412,28 @@ m0:=a0-r0 --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 129 +--E 129 ---S 130 of 1092 +--S 130 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 130 +--E 130 )clear all ---S 131 of 1092 +--S 131 of 1092 t0:=(a+b*x)^n*(c+d*x)^3 --R --R --R 3 3 2 2 2 3 n --R (1) (d x + 3c d x + 3c d x + c )(b x + a) --R Type: Expression(Integer) ---E 131 +--E 131 ---S 132 of 1092 +--S 132 of 1092 r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ (a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/_ (b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -4479,9 +4479,9 @@ r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 132 +--E 132 ---S 133 of 1092 +--S 133 of 1092 a0:=integrate(t0,x) --R --R @@ -4530,9 +4530,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 133 +--E 133 ---S 134 of 1092 +--S 134 of 1092 m0:=a0-r0 --R --R @@ -4620,19 +4620,19 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 134 +--E 134 ---S 135 of 1092 +--S 135 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 135 +--E 135 )clear all ---S 136 of 1092 +--S 136 of 1092 t0:=(a+b*x)^n*(c+d*x)^3/x --R --R @@ -4641,30 +4641,30 @@ t0:=(a+b*x)^n*(c+d*x)^3/x --R (1) ---------------------------------------- --R x --R Type: Expression(Integer) ---E 136 +--E 136 ---S 137 of 1092 +--S 137 of 1092 --r0:=3*c^2*d*(a+b*x)^(1+n)/(b*(1+n))-3*a*c*d^2*(a+b*x)^(1+n)/(b^2*(1+n))+_ -- a^2*d^3*(a+b*x)^(1+n)/(b^3*(1+n))+3*c*d^2*(a+b*x)^(2+n)/(b^2*(2+n))-_ -- 2*a*d^3*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-_ -- c^3*(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 137 +--E 137 ---S 138 of 1092 +--S 138 of 1092 --a0:=integrate(t0,x) ---E 138 +--E 138 ---S 139 of 1092 +--S 139 of 1092 --m0:=a0-r0 ---E 139 +--E 139 ---S 140 of 1092 +--S 140 of 1092 --d0:=D(m0,x) ---E 140 +--E 140 )clear all ---S 141 of 1092 +--S 141 of 1092 t0:=x^m*(c+d*x)/(a+b*x) --R --R @@ -4673,28 +4673,28 @@ t0:=x^m*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Expression(Integer) ---E 141 +--E 141 ---S 142 of 1092 +--S 142 of 1092 --r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b*(1+m)) ---E 142 +--E 142 ---S 143 of 1092 +--S 143 of 1092 --a0:=integrate(t0,x) ---E 143 +--E 143 ---S 144 of 1092 +--S 144 of 1092 --m0:=a0-r0 ---E 144 +--E 144 ---S 145 of 1092 +--S 145 of 1092 --d0:=D(m0,x) ---E 145 +--E 145 )clear all ---S 146 of 1092 +--S 146 of 1092 t0:=x^4*(c+d*x)/(a+b*x) --R --R @@ -4703,9 +4703,9 @@ t0:=x^4*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 146 +--E 146 ---S 147 of 1092 +--S 147 of 1092 r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ 1/4*(b*c-a*d)*x^4/b^2+1/5*d*x^5/b+a^4*(b*c-a*d)*log(a+b*x)/b^6 --R @@ -4720,9 +4720,9 @@ r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 147 +--E 147 ---S 148 of 1092 +--S 148 of 1092 a0:=integrate(t0,x) --R --R @@ -4736,27 +4736,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 148 +--E 148 ---S 149 of 1092 +--S 149 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 149 +--E 149 ---S 150 of 1092 +--S 150 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 150 +--E 150 )clear all ---S 151 of 1092 +--S 151 of 1092 t0:=x^3*(c+d*x)/(a+b*x) --R --R @@ -4765,9 +4765,9 @@ t0:=x^3*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 151 +--E 151 ---S 152 of 1092 +--S 152 of 1092 r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ 1/4*d*x^4/b-a^3*(b*c-a*d)*log(a+b*x)/b^5 --R @@ -4782,9 +4782,9 @@ r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 152 +--E 152 ---S 153 of 1092 +--S 153 of 1092 a0:=integrate(t0,x) --R --R @@ -4798,27 +4798,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 153 +--E 153 ---S 154 of 1092 +--S 154 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 154 +--E 154 ---S 155 of 1092 +--S 155 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 155 +--E 155 )clear all ---S 156 of 1092 +--S 156 of 1092 t0:=x^2*(c+d*x)/(a+b*x) --R --R @@ -4827,9 +4827,9 @@ t0:=x^2*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 156 +--E 156 ---S 157 of 1092 +--S 157 of 1092 r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ a^2*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -4844,9 +4844,9 @@ r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ --R 4 --R 6b --R Type: Expression(Integer) ---E 157 +--E 157 ---S 158 of 1092 +--S 158 of 1092 a0:=integrate(t0,x) --R --R @@ -4860,27 +4860,27 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 158 +--E 158 ---S 159 of 1092 +--S 159 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 159 +--E 159 ---S 160 of 1092 +--S 160 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 160 +--E 160 )clear all ---S 161 of 1092 +--S 161 of 1092 t0:=x*(c+d*x)/(a+b*x) --R --R @@ -4889,9 +4889,9 @@ t0:=x*(c+d*x)/(a+b*x) --R (1) ---------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 161 +--E 161 ---S 162 of 1092 +--S 162 of 1092 r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 --R --R @@ -4901,9 +4901,9 @@ r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 --R 3 --R 2b --R Type: Expression(Integer) ---E 162 +--E 162 ---S 163 of 1092 +--S 163 of 1092 a0:=integrate(t0,x) --R --R @@ -4913,27 +4913,27 @@ a0:=integrate(t0,x) --R 3 --R 2b --R Type: Union(Expression(Integer),...) ---E 163 +--E 163 ---S 164 of 1092 +--S 164 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 164 +--E 164 ---S 165 of 1092 +--S 165 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 165 +--E 165 )clear all ---S 166 of 1092 +--S 166 of 1092 t0:=(c+d*x)/(a+b*x) --R --R @@ -4941,9 +4941,9 @@ t0:=(c+d*x)/(a+b*x) --R (1) ------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 166 +--E 166 ---S 167 of 1092 +--S 167 of 1092 r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 --R --R @@ -4952,9 +4952,9 @@ r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 --R 2 --R b --R Type: Expression(Integer) ---E 167 +--E 167 ---S 168 of 1092 +--S 168 of 1092 a0:=integrate(t0,x) --R --R @@ -4963,27 +4963,27 @@ a0:=integrate(t0,x) --R 2 --R b --R Type: Union(Expression(Integer),...) ---E 168 +--E 168 ---S 169 of 1092 +--S 169 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 169 +--E 169 ---S 170 of 1092 +--S 170 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 170 +--E 170 )clear all ---S 171 of 1092 +--S 171 of 1092 t0:=(c+d*x)/(x*(a+b*x)) --R --R @@ -4992,9 +4992,9 @@ t0:=(c+d*x)/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 171 +--E 171 ---S 172 of 1092 +--S 172 of 1092 r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) --R --R @@ -5002,9 +5002,9 @@ r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) --R (2) ------------------------------------ --R a b --R Type: Expression(Integer) ---E 172 +--E 172 ---S 173 of 1092 +--S 173 of 1092 a0:=integrate(t0,x) --R --R @@ -5012,27 +5012,27 @@ a0:=integrate(t0,x) --R (3) ------------------------------------ --R a b --R Type: Union(Expression(Integer),...) ---E 173 +--E 173 ---S 174 of 1092 +--S 174 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 174 +--E 174 ---S 175 of 1092 +--S 175 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 175 +--E 175 )clear all ---S 176 of 1092 +--S 176 of 1092 t0:=(c+d*x)/(x^2*(a+b*x)) --R --R @@ -5041,9 +5041,9 @@ t0:=(c+d*x)/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 176 +--E 176 ---S 177 of 1092 +--S 177 of 1092 r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 --R --R @@ -5052,9 +5052,9 @@ r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 --R 2 --R a x --R Type: Expression(Integer) ---E 177 +--E 177 ---S 178 of 1092 +--S 178 of 1092 a0:=integrate(t0,x) --R --R @@ -5063,27 +5063,27 @@ a0:=integrate(t0,x) --R 2 --R a x --R Type: Union(Expression(Integer),...) ---E 178 +--E 178 ---S 179 of 1092 +--S 179 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 179 +--E 179 ---S 180 of 1092 +--S 180 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 180 +--E 180 )clear all ---S 181 of 1092 +--S 181 of 1092 t0:=(c+d*x)/(x^3*(a+b*x)) --R --R @@ -5092,9 +5092,9 @@ t0:=(c+d*x)/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 181 +--E 181 ---S 182 of 1092 +--S 182 of 1092 r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ b*(b*c-a*d)*log(a+b*x)/a^3 --R @@ -5109,9 +5109,9 @@ r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ --R 3 2 --R 2a x --R Type: Expression(Integer) ---E 182 +--E 182 ---S 183 of 1092 +--S 183 of 1092 a0:=integrate(t0,x) --R --R @@ -5125,27 +5125,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a x --R Type: Union(Expression(Integer),...) ---E 183 +--E 183 ---S 184 of 1092 +--S 184 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 184 +--E 184 ---S 185 of 1092 +--S 185 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 185 +--E 185 )clear all ---S 186 of 1092 +--S 186 of 1092 t0:=(c+d*x)/(x^4*(a+b*x)) --R --R @@ -5154,9 +5154,9 @@ t0:=(c+d*x)/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 186 +--E 186 ---S 187 of 1092 +--S 187 of 1092 r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ b^2*(b*c-a*d)*log(x)/a^4+b^2*(b*c-a*d)*log(a+b*x)/a^4 --R @@ -5171,9 +5171,9 @@ r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 187 +--E 187 ---S 188 of 1092 +--S 188 of 1092 a0:=integrate(t0,x) --R --R @@ -5187,27 +5187,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 188 +--E 188 ---S 189 of 1092 +--S 189 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 189 +--E 189 ---S 190 of 1092 +--S 190 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 190 +--E 190 )clear all ---S 191 of 1092 +--S 191 of 1092 t0:=(c+d*x)/(x^5*(a+b*x)) --R --R @@ -5216,9 +5216,9 @@ t0:=(c+d*x)/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 191 +--E 191 ---S 192 of 1092 +--S 192 of 1092 r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ b^2*(b*c-a*d)/(a^4*x)+b^3*(b*c-a*d)*log(x)/a^5-_ b^3*(b*c-a*d)*log(a+b*x)/a^5 @@ -5234,9 +5234,9 @@ r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 192 +--E 192 ---S 193 of 1092 +--S 193 of 1092 a0:=integrate(t0,x) --R --R @@ -5250,27 +5250,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 193 +--E 193 ---S 194 of 1092 +--S 194 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 194 +--E 194 ---S 195 of 1092 +--S 195 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 195 +--E 195 )clear all ---S 196 of 1092 +--S 196 of 1092 t0:=x^m*(c+d*x)^2/(a+b*x) --R --R @@ -5279,29 +5279,29 @@ t0:=x^m*(c+d*x)^2/(a+b*x) --R (1) ---------------------- --R b x + a --R Type: Expression(Integer) ---E 196 +--E 196 ---S 197 of 1092 +--S 197 of 1092 --r0:=-d*(a*d*(2+m)-b*c*(3+m))*x^(1+m)/(b^2*(1+m)*(2+m))+_ -- d*x^(1+m)*(c+d*x)/(b*(2+m))+(b*c-a*d)^2*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^2*(1+m)) ---E 197 +--E 197 ---S 198 of 1092 +--S 198 of 1092 --a0:=integrate(t0,x) ---E 198 +--E 198 ---S 199 of 1092 +--S 199 of 1092 --m0:=a0-r0 ---E 199 +--E 199 ---S 200 of 1092 +--S 200 of 1092 --d0:=D(m0,x) ---E 200 +--E 200 )clear all ---S 201 of 1092 +--S 201 of 1092 t0:=x^4*(c+d*x)^2/(a+b*x) --R --R @@ -5310,9 +5310,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 201 +--E 201 ---S 202 of 1092 +--S 202 of 1092 r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ 1/3*a*(b*c-a*d)^2*x^3/b^4+1/4*(b*c-a*d)^2*x^4/b^3+_ 1/5*d*(2*b*c-a*d)*x^5/b^2+1/6*d^2*x^6/b+a^4*(b*c-a*d)^2*log(a+b*x)/b^7 @@ -5334,9 +5334,9 @@ r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ --R 7 --R 60b --R Type: Expression(Integer) ---E 202 +--E 202 ---S 203 of 1092 +--S 203 of 1092 a0:=integrate(t0,x) --R --R @@ -5356,27 +5356,27 @@ a0:=integrate(t0,x) --R 7 --R 60b --R Type: Union(Expression(Integer),...) ---E 203 +--E 203 ---S 204 of 1092 +--S 204 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 204 +--E 204 ---S 205 of 1092 +--S 205 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 205 +--E 205 )clear all ---S 206 of 1092 +--S 206 of 1092 t0:=x^3*(c+d*x)^2/(a+b*x) --R --R @@ -5385,9 +5385,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 206 +--E 206 ---S 207 of 1092 +--S 207 of 1092 r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ 1/3*(b*c-a*d)^2*x^3/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/5*d^2*x^5/b-_ a^3*(b*c-a*d)^2*log(a+b*x)/b^6 @@ -5406,9 +5406,9 @@ r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 207 +--E 207 ---S 208 of 1092 +--S 208 of 1092 a0:=integrate(t0,x) --R --R @@ -5425,27 +5425,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 208 +--E 208 ---S 209 of 1092 +--S 209 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 209 +--E 209 ---S 210 of 1092 +--S 210 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 210 +--E 210 )clear all ---S 211 of 1092 +--S 211 of 1092 t0:=x^2*(c+d*x)^2/(a+b*x) --R --R @@ -5454,9 +5454,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 211 +--E 211 ---S 212 of 1092 +--S 212 of 1092 r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ 1/4*d^2*x^4/b+a^2*(b*c-a*d)^2*log(a+b*x)/b^5 --R @@ -5474,9 +5474,9 @@ r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 212 +--E 212 ---S 213 of 1092 +--S 213 of 1092 a0:=integrate(t0,x) --R --R @@ -5493,27 +5493,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 213 +--E 213 ---S 214 of 1092 +--S 214 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 214 +--E 214 ---S 215 of 1092 +--S 215 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 215 +--E 215 )clear all ---S 216 of 1092 +--S 216 of 1092 t0:=x*(c+d*x)^2/(a+b*x) --R --R @@ -5522,9 +5522,9 @@ t0:=x*(c+d*x)^2/(a+b*x) --R (1) -------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 216 +--E 216 ---S 217 of 1092 +--S 217 of 1092 r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ a*(b*c-a*d)^2*log(a+b*x)/b^4 --R @@ -5539,9 +5539,9 @@ r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ --R 4 --R 6b --R Type: Expression(Integer) ---E 217 +--E 217 ---S 218 of 1092 +--S 218 of 1092 a0:=integrate(t0,x) --R --R @@ -5555,27 +5555,27 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 218 +--E 218 ---S 219 of 1092 +--S 219 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 219 +--E 219 ---S 220 of 1092 +--S 220 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 220 +--E 220 )clear all ---S 221 of 1092 +--S 221 of 1092 t0:=(c+d*x)^2/(a+b*x) --R --R @@ -5584,9 +5584,9 @@ t0:=(c+d*x)^2/(a+b*x) --R (1) ------------------ --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 221 +--E 221 ---S 222 of 1092 +--S 222 of 1092 r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 --R --R @@ -5600,9 +5600,9 @@ r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 --R 3 --R 2b --R Type: Expression(Integer) ---E 222 +--E 222 ---S 223 of 1092 +--S 223 of 1092 a0:=integrate(t0,x) --R --R @@ -5613,9 +5613,9 @@ a0:=integrate(t0,x) --R 3 --R 2b --R Type: Union(Expression(Integer),...) ---E 223 +--E 223 ---S 224 of 1092 +--S 224 of 1092 m0:=a0-r0 --R --R @@ -5624,19 +5624,19 @@ m0:=a0-r0 --R (4) - -- --R 2b --R Type: Expression(Integer) ---E 224 +--E 224 ---S 225 of 1092 +--S 225 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 225 +--E 225 )clear all ---S 226 of 1092 +--S 226 of 1092 t0:=(c+d*x)^2/(x*(a+b*x)) --R --R @@ -5646,9 +5646,9 @@ t0:=(c+d*x)^2/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 226 +--E 226 ---S 227 of 1092 +--S 227 of 1092 r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) --R --R @@ -5658,9 +5658,9 @@ r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) --R 2 --R a b --R Type: Expression(Integer) ---E 227 +--E 227 ---S 228 of 1092 +--S 228 of 1092 a0:=integrate(t0,x) --R --R @@ -5670,27 +5670,27 @@ a0:=integrate(t0,x) --R 2 --R a b --R Type: Union(Expression(Integer),...) ---E 228 +--E 228 ---S 229 of 1092 +--S 229 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 229 +--E 229 ---S 230 of 1092 +--S 230 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 230 +--E 230 )clear all ---S 231 of 1092 +--S 231 of 1092 t0:=(c+d*x)^2/(x^2*(a+b*x)) --R --R @@ -5700,9 +5700,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 231 +--E 231 ---S 232 of 1092 +--S 232 of 1092 r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) --R --R @@ -5713,9 +5713,9 @@ r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) --R 2 --R a b x --R Type: Expression(Integer) ---E 232 +--E 232 ---S 233 of 1092 +--S 233 of 1092 a0:=integrate(t0,x) --R --R @@ -5726,27 +5726,27 @@ a0:=integrate(t0,x) --R 2 --R a b x --R Type: Union(Expression(Integer),...) ---E 233 +--E 233 ---S 234 of 1092 +--S 234 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 234 +--E 234 ---S 235 of 1092 +--S 235 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 235 +--E 235 )clear all ---S 236 of 1092 +--S 236 of 1092 t0:=(c+d*x)^2/(x^3*(a+b*x)) --R --R @@ -5756,9 +5756,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 236 +--E 236 ---S 237 of 1092 +--S 237 of 1092 r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ (b*c-a*d)^2*log(a+b*x)/a^3 --R @@ -5773,9 +5773,9 @@ r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ --R 3 2 --R 2a x --R Type: Expression(Integer) ---E 237 +--E 237 ---S 238 of 1092 +--S 238 of 1092 a0:=integrate(t0,x) --R --R @@ -5789,27 +5789,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a x --R Type: Union(Expression(Integer),...) ---E 238 +--E 238 ---S 239 of 1092 +--S 239 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 239 +--E 239 ---S 240 of 1092 +--S 240 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 240 +--E 240 )clear all ---S 241 of 1092 +--S 241 of 1092 t0:=(c+d*x)^2/(x^4*(a+b*x)) --R --R @@ -5819,9 +5819,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 241 +--E 241 ---S 242 of 1092 +--S 242 of 1092 r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ b*(b*c-a*d)^2*log(x)/a^4+b*(b*c-a*d)^2*log(a+b*x)/a^4 --R @@ -5839,9 +5839,9 @@ r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 242 +--E 242 ---S 243 of 1092 +--S 243 of 1092 a0:=integrate(t0,x) --R --R @@ -5858,27 +5858,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 243 +--E 243 ---S 244 of 1092 +--S 244 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 244 +--E 244 ---S 245 of 1092 +--S 245 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 245 +--E 245 )clear all ---S 246 of 1092 +--S 246 of 1092 t0:=(c+d*x)^2/(x^5*(a+b*x)) --R --R @@ -5888,9 +5888,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 246 +--E 246 ---S 247 of 1092 +--S 247 of 1092 r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ 1/2*(b*c-a*d)^2/(a^3*x^2)+b*(b*c-a*d)^2/(a^4*x)+_ b^2*(b*c-a*d)^2*log(x)/a^5-b^2*(b*c-a*d)^2*log(a+b*x)/a^5 @@ -5912,9 +5912,9 @@ r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 247 +--E 247 ---S 248 of 1092 +--S 248 of 1092 a0:=integrate(t0,x) --R --R @@ -5934,27 +5934,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 248 +--E 248 ---S 249 of 1092 +--S 249 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 249 +--E 249 ---S 250 of 1092 +--S 250 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 250 +--E 250 )clear all ---S 251 of 1092 +--S 251 of 1092 t0:=(c+d*x)^2/(x^6*(a+b*x)) --R --R @@ -5964,9 +5964,9 @@ t0:=(c+d*x)^2/(x^6*(a+b*x)) --R 7 6 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 251 +--E 251 ---S 252 of 1092 +--S 252 of 1092 r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ 1/3*(b*c-a*d)^2/(a^3*x^3)+1/2*b*(b*c-a*d)^2/(a^4*x^2)-_ b^2*(b*c-a*d)^2/(a^5*x)-b^3*(b*c-a*d)^2*log(x)/a^6+_ @@ -5992,9 +5992,9 @@ r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ --R 6 5 --R 60a x --R Type: Expression(Integer) ---E 252 +--E 252 ---S 253 of 1092 +--S 253 of 1092 a0:=integrate(t0,x) --R --R @@ -6017,27 +6017,27 @@ a0:=integrate(t0,x) --R 6 5 --R 60a x --R Type: Union(Expression(Integer),...) ---E 253 +--E 253 ---S 254 of 1092 +--S 254 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 254 +--E 254 ---S 255 of 1092 +--S 255 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 255 +--E 255 )clear all ---S 256 of 1092 +--S 256 of 1092 t0:=x^m*(c+d*x)^3/(a+b*x) --R --R @@ -6046,29 +6046,29 @@ t0:=x^m*(c+d*x)^3/(a+b*x) --R (1) -------------------------------- --R b x + a --R Type: Expression(Integer) ---E 256 +--E 256 ---S 257 of 1092 +--S 257 of 1092 --r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^(1+m)/(b^3*(1+m))+_ -- d^2*(3*b*c-a*d)*x^(2+m)/(b^2*(2+m))+d^3*x^(3+m)/(b*(3+m))+_ -- (b*c-a*d)^3*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^3*(1+m)) ---E 257 +--E 257 ---S 258 of 1092 +--S 258 of 1092 --a0:=integrate(t0,x) ---E 258 +--E 258 ---S 259 of 1092 +--S 259 of 1092 --m0:=a0-r0 ---E 259 +--E 259 ---S 260 of 1092 +--S 260 of 1092 --d0:=D(m0,x) ---E 260 +--E 260 )clear all ---S 261 of 1092 +--S 261 of 1092 t0:=x^4*(c+d*x)^3/(a+b*x) --R --R @@ -6077,9 +6077,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 261 +--E 261 ---S 262 of 1092 +--S 262 of 1092 r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ x^3/b^5+1/4*(b*c-a*d)^3*x^4/b^4+1/5*d*(3*b^2*c^2-_ 3*a*b*c*d+a^2*d^2)*x^5/b^3+1/6*d^2*(3*b*c-a*d)*x^6/b^2+_ @@ -6111,9 +6111,9 @@ r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ --R 8 --R 420b --R Type: Expression(Integer) ---E 262 +--E 262 ---S 263 of 1092 +--S 263 of 1092 a0:=integrate(t0,x) --R --R @@ -6142,27 +6142,27 @@ a0:=integrate(t0,x) --R 8 --R 420b --R Type: Union(Expression(Integer),...) ---E 263 +--E 263 ---S 264 of 1092 +--S 264 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 264 +--E 264 ---S 265 of 1092 +--S 265 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 265 +--E 265 )clear all ---S 266 of 1092 +--S 266 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x) --R --R @@ -6171,9 +6171,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 266 +--E 266 ---S 267 of 1092 +--S 267 of 1092 r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ 1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_ 1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/6*d^3*x^6/b-a^3*(b*c-a*d)^3*log(a+b*x)/b^7 @@ -6198,9 +6198,9 @@ r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ --R 7 --R 60b --R Type: Expression(Integer) ---E 267 +--E 267 ---S 268 of 1092 +--S 268 of 1092 a0:=integrate(t0,x) --R --R @@ -6223,27 +6223,27 @@ a0:=integrate(t0,x) --R 7 --R 60b --R Type: Union(Expression(Integer),...) ---E 268 +--E 268 ---S 269 of 1092 +--S 269 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 269 +--E 269 ---S 270 of 1092 +--S 270 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 270 +--E 270 )clear all ---S 271 of 1092 +--S 271 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x) --R --R @@ -6252,9 +6252,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 271 +--E 271 ---S 272 of 1092 +--S 272 of 1092 r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ 1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_ 1/4*d^2*(3*b*c-a*d)*x^4/b^2+1/5*d^3*x^5/b+a^2*(b*c-a*d)^3*log(a+b*x)/b^6 @@ -6276,9 +6276,9 @@ r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 272 +--E 272 ---S 273 of 1092 +--S 273 of 1092 a0:=integrate(t0,x) --R --R @@ -6298,27 +6298,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 273 +--E 273 ---S 274 of 1092 +--S 274 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 274 +--E 274 ---S 275 of 1092 +--S 275 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 275 +--E 275 )clear all ---S 276 of 1092 +--S 276 of 1092 t0:=x*(c+d*x)^3/(a+b*x) --R --R @@ -6327,9 +6327,9 @@ t0:=x*(c+d*x)^3/(a+b*x) --R (1) ------------------------------ --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 276 +--E 276 ---S 277 of 1092 +--S 277 of 1092 r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ 1/3*d^2*(3*b*c-a*d)*x^3/b^2+1/4*d^3*x^4/b-a*(b*c-a*d)^3*log(a+b*x)/b^5 --R @@ -6347,9 +6347,9 @@ r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 277 +--E 277 ---S 278 of 1092 +--S 278 of 1092 a0:=integrate(t0,x) --R --R @@ -6366,27 +6366,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 278 +--E 278 ---S 279 of 1092 +--S 279 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 279 +--E 279 ---S 280 of 1092 +--S 280 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 280 +--E 280 )clear all ---S 281 of 1092 +--S 281 of 1092 t0:=(c+d*x)^3/(a+b*x) --R --R @@ -6395,9 +6395,9 @@ t0:=(c+d*x)^3/(a+b*x) --R (1) ---------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 281 +--E 281 ---S 282 of 1092 +--S 282 of 1092 r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ 1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4 --R @@ -6415,9 +6415,9 @@ r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ --R 4 --R 6b --R Type: Expression(Integer) ---E 282 +--E 282 ---S 283 of 1092 +--S 283 of 1092 a0:=integrate(t0,x) --R --R @@ -6431,9 +6431,9 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 283 +--E 283 ---S 284 of 1092 +--S 284 of 1092 m0:=a0-r0 --R --R @@ -6443,19 +6443,19 @@ m0:=a0-r0 --R 2 --R 6b --R Type: Expression(Integer) ---E 284 +--E 284 ---S 285 of 1092 +--S 285 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 285 +--E 285 )clear all ---S 286 of 1092 +--S 286 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)) --R --R @@ -6465,9 +6465,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 286 +--E 286 ---S 287 of 1092 +--S 287 of 1092 r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ c^3*log(x)/a-(b*c-a*d)^3*log(a+b*x)/(a*b^3) --R @@ -6482,9 +6482,9 @@ r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ --R 3 --R 2a b --R Type: Expression(Integer) ---E 287 +--E 287 ---S 288 of 1092 +--S 288 of 1092 a0:=integrate(t0,x) --R --R @@ -6498,27 +6498,27 @@ a0:=integrate(t0,x) --R 3 --R 2a b --R Type: Union(Expression(Integer),...) ---E 288 +--E 288 ---S 289 of 1092 +--S 289 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 289 +--E 289 ---S 290 of 1092 +--S 290 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 290 +--E 290 )clear all ---S 291 of 1092 +--S 291 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)) --R --R @@ -6528,9 +6528,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 291 +--E 291 ---S 292 of 1092 +--S 292 of 1092 r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ (b*c-a*d)^3*log(a+b*x)/(a^2*b^2) --R @@ -6545,9 +6545,9 @@ r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ --R 2 2 --R a b x --R Type: Expression(Integer) ---E 292 +--E 292 ---S 293 of 1092 +--S 293 of 1092 a0:=integrate(t0,x) --R --R @@ -6561,27 +6561,27 @@ a0:=integrate(t0,x) --R 2 2 --R a b x --R Type: Union(Expression(Integer),...) ---E 293 +--E 293 ---S 294 of 1092 +--S 294 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 294 +--E 294 ---S 295 of 1092 +--S 295 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 295 +--E 295 )clear all ---S 296 of 1092 +--S 296 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)) --R --R @@ -6591,9 +6591,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 296 +--E 296 ---S 297 of 1092 +--S 297 of 1092 r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(x)/a^3-(b*c-a*d)^3*log(a+b*x)/(a^3*b) --R @@ -6608,9 +6608,9 @@ r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ --R 3 2 --R 2a b x --R Type: Expression(Integer) ---E 297 +--E 297 ---S 298 of 1092 +--S 298 of 1092 a0:=integrate(t0,x) --R --R @@ -6624,27 +6624,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a b x --R Type: Union(Expression(Integer),...) ---E 298 +--E 298 ---S 299 of 1092 +--S 299 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 299 +--E 299 ---S 300 of 1092 +--S 300 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 300 +--E 300 )clear all ---S 301 of 1092 +--S 301 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)) --R --R @@ -6654,9 +6654,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 301 +--E 301 ---S 302 of 1092 +--S 302 of 1092 r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x)-_ (b*c-a*d)^3*log(x)/a^4+(b*c-a*d)^3*log(a+b*x)/a^4 @@ -6675,9 +6675,9 @@ r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 302 +--E 302 ---S 303 of 1092 +--S 303 of 1092 a0:=integrate(t0,x) --R --R @@ -6694,27 +6694,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 303 +--E 303 ---S 304 of 1092 +--S 304 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 304 +--E 304 ---S 305 of 1092 +--S 305 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 305 +--E 305 )clear all ---S 306 of 1092 +--S 306 of 1092 t0:=(c+d*x)^3/(x^5*(a+b*x)) --R --R @@ -6724,9 +6724,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 306 +--E 306 ---S 307 of 1092 +--S 307 of 1092 r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ 1/2*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^2)+_ (b*c-a*d)^3/(a^4*x)+b*(b*c-a*d)^3*log(x)/a^5-b*(b*c-a*d)^3*log(a+b*x)/a^5 @@ -6748,9 +6748,9 @@ r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 307 +--E 307 ---S 308 of 1092 +--S 308 of 1092 a0:=integrate(t0,x) --R --R @@ -6770,27 +6770,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 308 +--E 308 ---S 309 of 1092 +--S 309 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 309 +--E 309 ---S 310 of 1092 +--S 310 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 310 +--E 310 )clear all ---S 311 of 1092 +--S 311 of 1092 t0:=(c+d*x)^3/(x^6*(a+b*x)) --R --R @@ -6800,9 +6800,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x)) --R 7 6 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 311 +--E 311 ---S 312 of 1092 +--S 312 of 1092 r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ 1/3*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^3)+_ 1/2*(b*c-a*d)^3/(a^4*x^2)-b*(b*c-a*d)^3/(a^5*x)-_ @@ -6828,9 +6828,9 @@ r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ --R 6 5 --R 60a x --R Type: Expression(Integer) ---E 312 +--E 312 ---S 313 of 1092 +--S 313 of 1092 a0:=integrate(t0,x) --R --R @@ -6853,27 +6853,27 @@ a0:=integrate(t0,x) --R 6 5 --R 60a x --R Type: Union(Expression(Integer),...) ---E 313 +--E 313 ---S 314 of 1092 +--S 314 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 314 +--E 314 ---S 315 of 1092 +--S 315 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 315 +--E 315 )clear all ---S 316 of 1092 +--S 316 of 1092 t0:=(c+d*x)^3/(x^7*(a+b*x)) --R --R @@ -6883,9 +6883,9 @@ t0:=(c+d*x)^3/(x^7*(a+b*x)) --R 8 7 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 316 +--E 316 ---S 317 of 1092 +--S 317 of 1092 r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ 1/4*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^4)+_ 1/3*(b*c-a*d)^3/(a^4*x^3)-1/2*b*(b*c-a*d)^3/(a^5*x^2)+_ @@ -6915,9 +6915,9 @@ r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ --R 7 6 --R 60a x --R Type: Expression(Integer) ---E 317 +--E 317 ---S 318 of 1092 +--S 318 of 1092 a0:=integrate(t0,x) --R --R @@ -6943,27 +6943,27 @@ a0:=integrate(t0,x) --R 7 6 --R 60a x --R Type: Union(Expression(Integer),...) ---E 318 +--E 318 ---S 319 of 1092 +--S 319 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 319 +--E 319 ---S 320 of 1092 +--S 320 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 320 +--E 320 )clear all ---S 321 of 1092 +--S 321 of 1092 t0:=x^m/((a+b*x)*(c+d*x)) --R --R @@ -6973,28 +6973,28 @@ t0:=x^m/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Expression(Integer) ---E 321 +--E 321 ---S 322 of 1092 +--S 322 of 1092 --r0:=b*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)*(1+m))-_ -- d*x^(1+m)*hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)*(1+m)) ---E 322 +--E 322 ---S 323 of 1092 +--S 323 of 1092 --a0:=integrate(t0,x) ---E 323 +--E 323 ---S 324 of 1092 +--S 324 of 1092 --m0:=a0-r0 ---E 324 +--E 324 ---S 325 of 1092 +--S 325 of 1092 --d0:=D(m0,x) ---E 325 +--E 325 )clear all ---S 326 of 1092 +--S 326 of 1092 t0:=x^5/((a+b*x)*(c+d*x)) --R --R @@ -7004,9 +7004,9 @@ t0:=x^5/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 326 +--E 326 ---S 327 of 1092 +--S 327 of 1092 r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ 1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*x^2/(b^3*d^3)-_ 1/3*(b*c+a*d)*x^3/(b^2*d^2)+1/4*x^4/(b*d)-_ @@ -7023,9 +7023,9 @@ r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ --R 5 6 6 5 --R 12a b d - 12b c d --R Type: Expression(Integer) ---E 327 +--E 327 ---S 328 of 1092 +--S 328 of 1092 a0:=integrate(t0,x) --R --R @@ -7039,27 +7039,27 @@ a0:=integrate(t0,x) --R 5 6 6 5 --R 12a b d - 12b c d --R Type: Union(Expression(Integer),...) ---E 328 +--E 328 ---S 329 of 1092 +--S 329 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 329 +--E 329 ---S 330 of 1092 +--S 330 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 330 +--E 330 )clear all ---S 331 of 1092 +--S 331 of 1092 t0:=x^4/((a+b*x)*(c+d*x)) --R --R @@ -7069,9 +7069,9 @@ t0:=x^4/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 331 +--E 331 ---S 332 of 1092 +--S 332 of 1092 r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ 1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/3*x^3/(b*d)+_ a^4*log(a+b*x)/(b^4*(b*c-a*d))-c^4*log(c+d*x)/(d^4*(b*c-a*d)) @@ -7087,9 +7087,9 @@ r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ --R 4 5 5 4 --R 6a b d - 6b c d --R Type: Expression(Integer) ---E 332 +--E 332 ---S 333 of 1092 +--S 333 of 1092 a0:=integrate(t0,x) --R --R @@ -7103,27 +7103,27 @@ a0:=integrate(t0,x) --R 4 5 5 4 --R 6a b d - 6b c d --R Type: Union(Expression(Integer),...) ---E 333 +--E 333 ---S 334 of 1092 +--S 334 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 334 +--E 334 ---S 335 of 1092 +--S 335 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 335 +--E 335 )clear all ---S 336 of 1092 +--S 336 of 1092 t0:=x^3/((a+b*x)*(c+d*x)) --R --R @@ -7133,9 +7133,9 @@ t0:=x^3/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 336 +--E 336 ---S 337 of 1092 +--S 337 of 1092 r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ c^3*log(c+d*x)/(d^3*(b*c-a*d)) --R @@ -7150,9 +7150,9 @@ r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ --R 3 4 4 3 --R 2a b d - 2b c d --R Type: Expression(Integer) ---E 337 +--E 337 ---S 338 of 1092 +--S 338 of 1092 a0:=integrate(t0,x) --R --R @@ -7166,27 +7166,27 @@ a0:=integrate(t0,x) --R 3 4 4 3 --R 2a b d - 2b c d --R Type: Union(Expression(Integer),...) ---E 338 +--E 338 ---S 339 of 1092 +--S 339 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 339 +--E 339 ---S 340 of 1092 +--S 340 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 340 +--E 340 )clear all ---S 341 of 1092 +--S 341 of 1092 t0:=x^2/((a+b*x)*(c+d*x)) --R --R @@ -7196,9 +7196,9 @@ t0:=x^2/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 341 +--E 341 ---S 342 of 1092 +--S 342 of 1092 r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) --R --R @@ -7208,9 +7208,9 @@ r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) --R 2 3 3 2 --R a b d - b c d --R Type: Expression(Integer) ---E 342 +--E 342 ---S 343 of 1092 +--S 343 of 1092 a0:=integrate(t0,x) --R --R @@ -7220,27 +7220,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 --R a b d - b c d --R Type: Union(Expression(Integer),...) ---E 343 +--E 343 ---S 344 of 1092 +--S 344 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 344 +--E 344 ---S 345 of 1092 +--S 345 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 345 +--E 345 )clear all ---S 346 of 1092 +--S 346 of 1092 t0:=x/((a+b*x)*(c+d*x)) --R --R @@ -7249,9 +7249,9 @@ t0:=x/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 346 +--E 346 ---S 347 of 1092 +--S 347 of 1092 r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) --R --R @@ -7260,9 +7260,9 @@ r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) --R 2 2 --R a b d - b c d --R Type: Expression(Integer) ---E 347 +--E 347 ---S 348 of 1092 +--S 348 of 1092 a0:=integrate(t0,x) --R --R @@ -7271,27 +7271,27 @@ a0:=integrate(t0,x) --R 2 2 --R a b d - b c d --R Type: Union(Expression(Integer),...) ---E 348 +--E 348 ---S 349 of 1092 +--S 349 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 349 +--E 349 ---S 350 of 1092 +--S 350 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 350 +--E 350 )clear all ---S 351 of 1092 +--S 351 of 1092 t0:=1/((a+b*x)*(c+d*x)) --R --R @@ -7300,9 +7300,9 @@ t0:=1/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 351 +--E 351 ---S 352 of 1092 +--S 352 of 1092 r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) --R --R @@ -7310,9 +7310,9 @@ r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) --R (2) --------------------------- --R a d - b c --R Type: Expression(Integer) ---E 352 +--E 352 ---S 353 of 1092 +--S 353 of 1092 a0:=integrate(t0,x) --R --R @@ -7320,27 +7320,27 @@ a0:=integrate(t0,x) --R (3) --------------------------- --R a d - b c --R Type: Union(Expression(Integer),...) ---E 353 +--E 353 ---S 354 of 1092 +--S 354 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 354 +--E 354 ---S 355 of 1092 +--S 355 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 355 +--E 355 )clear all ---S 356 of 1092 +--S 356 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)) --R --R @@ -7349,9 +7349,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)) --R 3 2 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 356 +--E 356 ---S 357 of 1092 +--S 357 of 1092 r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) --R --R @@ -7360,9 +7360,9 @@ r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) --R 2 2 --R a c d - a b c --R Type: Expression(Integer) ---E 357 +--E 357 ---S 358 of 1092 +--S 358 of 1092 a0:=integrate(t0,x) --R --R @@ -7371,27 +7371,27 @@ a0:=integrate(t0,x) --R 2 2 --R a c d - a b c --R Type: Union(Expression(Integer),...) ---E 358 +--E 358 ---S 359 of 1092 +--S 359 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 359 +--E 359 ---S 360 of 1092 +--S 360 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 360 +--E 360 )clear all ---S 361 of 1092 +--S 361 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)) --R --R @@ -7400,9 +7400,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)) --R 4 3 2 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 361 +--E 361 ---S 362 of 1092 +--S 362 of 1092 r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ b^2*log(a+b*x)/(a^2*(b*c-a*d))-d^2*log(c+d*x)/(c^2*(b*c-a*d)) --R @@ -7417,9 +7417,9 @@ r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ --R 3 2 2 3 --R (a c d - a b c )x --R Type: Expression(Integer) ---E 362 +--E 362 ---S 363 of 1092 +--S 363 of 1092 a0:=integrate(t0,x) --R --R @@ -7433,27 +7433,27 @@ a0:=integrate(t0,x) --R 3 2 2 3 --R (a c d - a b c )x --R Type: Union(Expression(Integer),...) ---E 363 +--E 363 ---S 364 of 1092 +--S 364 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 364 +--E 364 ---S 365 of 1092 +--S 365 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 365 +--E 365 )clear all ---S 366 of 1092 +--S 366 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)) --R --R @@ -7462,9 +7462,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)) --R 5 4 3 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 366 +--E 366 ---S 367 of 1092 +--S 367 of 1092 r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ log(x)/(a^3*c^3)-b^3*log(a+b*x)/(a^3*(b*c-a*d))+_ d^3*log(c+d*x)/(c^3*(b*c-a*d)) @@ -7480,9 +7480,9 @@ r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ --R 4 3 3 4 2 --R (2a c d - 2a b c )x --R Type: Expression(Integer) ---E 367 +--E 367 ---S 368 of 1092 +--S 368 of 1092 a0:=integrate(t0,x) --R --R @@ -7496,27 +7496,27 @@ a0:=integrate(t0,x) --R 4 3 3 4 2 --R (2a c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 368 +--E 368 ---S 369 of 1092 +--S 369 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 369 +--E 369 ---S 370 of 1092 +--S 370 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 370 +--E 370 )clear all ---S 371 of 1092 +--S 371 of 1092 t0:=1/(x^4*(a+b*x)*(c+d*x)) --R --R @@ -7525,9 +7525,9 @@ t0:=1/(x^4*(a+b*x)*(c+d*x)) --R 6 5 4 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 371 +--E 371 ---S 372 of 1092 +--S 372 of 1092 r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ (-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*_ log(x)/(a^4*c^4)+b^4*log(a+b*x)/(a^4*(b*c-a*d))-_ @@ -7544,9 +7544,9 @@ r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ --R 5 4 4 5 3 --R (6a c d - 6a b c )x --R Type: Expression(Integer) ---E 372 +--E 372 ---S 373 of 1092 +--S 373 of 1092 a0:=integrate(t0,x) --R --R @@ -7560,27 +7560,27 @@ a0:=integrate(t0,x) --R 5 4 4 5 3 --R (6a c d - 6a b c )x --R Type: Union(Expression(Integer),...) ---E 373 +--E 373 ---S 374 of 1092 +--S 374 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 374 +--E 374 ---S 375 of 1092 +--S 375 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 375 +--E 375 )clear all ---S 376 of 1092 +--S 376 of 1092 t0:=x^m/((a+b*x)*(c+d*x)^2) --R --R @@ -7590,30 +7590,30 @@ t0:=x^m/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Expression(Integer) ---E 376 +--E 376 ---S 377 of 1092 +--S 377 of 1092 --r0:=-d*x^(1+m)/(c*(b*c-a*d)*(c+d*x))+b^2*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^2*(1+m))-b*d*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^2*(1+m))+d*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)*(1+m)) ---E 377 +--E 377 ---S 378 of 1092 +--S 378 of 1092 --a0:=integrate(t0,x) ---E 378 +--E 378 ---S 379 of 1092 +--S 379 of 1092 --m0:=a0-r0 ---E 379 +--E 379 ---S 380 of 1092 +--S 380 of 1092 --d0:=D(m0,x) ---E 380 +--E 380 )clear all ---S 381 of 1092 +--S 381 of 1092 t0:=x^m/((1-a*x)^2*(1+a*x)) --R --R @@ -7623,30 +7623,30 @@ t0:=x^m/((1-a*x)^2*(1+a*x)) --R 3 3 2 2 --R a x - a x - a x + 1 --R Type: Expression(Integer) ---E 381 +--E 381 ---S 382 of 1092 +--S 382 of 1092 --r0:=1/2*x^(1+m)/(1-a*x)+1/4*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-a*x)/(1+m)+1/4*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,a*x)/(1+m)-1/2*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,a*x)/(1+m) ---E 382 +--E 382 ---S 383 of 1092 +--S 383 of 1092 --a0:=integrate(t0,x) ---E 383 +--E 383 ---S 384 of 1092 +--S 384 of 1092 --m0:=a0-r0 ---E 384 +--E 384 ---S 385 of 1092 +--S 385 of 1092 --d0:=D(m0,x) ---E 385 +--E 385 )clear all ---S 386 of 1092 +--S 386 of 1092 t0:=x^5/((a+b*x)*(c+d*x)^2) --R --R @@ -7656,9 +7656,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 386 +--E 386 ---S 387 of 1092 +--S 387 of 1092 r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ 1/2*(2*b*c+a*d)*x^2/(b^2*d^3)+1/3*x^3/(b*d^2)-_ c^5/(d^5*(b*c-a*d)*(c+d*x))-a^5*log(a+b*x)/(b^4*(b*c-a*d)^2)-_ @@ -7684,9 +7684,9 @@ r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ --R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 --R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d --R Type: Expression(Integer) ---E 387 +--E 387 ---S 388 of 1092 +--S 388 of 1092 a0:=integrate(t0,x) --R --R @@ -7709,27 +7709,27 @@ a0:=integrate(t0,x) --R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 --R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d --R Type: Union(Expression(Integer),...) ---E 388 +--E 388 ---S 389 of 1092 +--S 389 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 389 +--E 389 ---S 390 of 1092 +--S 390 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 390 +--E 390 )clear all ---S 391 of 1092 +--S 391 of 1092 t0:=x^4/((a+b*x)*(c+d*x)^2) --R --R @@ -7739,9 +7739,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 391 +--E 391 ---S 392 of 1092 +--S 392 of 1092 r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ c^4/(d^4*(b*c-a*d)*(c+d*x))+a^4*log(a+b*x)/(b^3*(b*c-a*d)^2)+_ c^3*(3*b*c-4*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^2) @@ -7763,9 +7763,9 @@ r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ --R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 --R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d --R Type: Expression(Integer) ---E 392 +--E 392 ---S 393 of 1092 +--S 393 of 1092 a0:=integrate(t0,x) --R --R @@ -7785,27 +7785,27 @@ a0:=integrate(t0,x) --R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 --R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d --R Type: Union(Expression(Integer),...) ---E 393 +--E 393 ---S 394 of 1092 +--S 394 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 394 +--E 394 ---S 395 of 1092 +--S 395 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 395 +--E 395 )clear all ---S 396 of 1092 +--S 396 of 1092 t0:=x^3/((a+b*x)*(c+d*x)^2) --R --R @@ -7815,9 +7815,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 396 +--E 396 ---S 397 of 1092 +--S 397 of 1092 r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ a^3*log(a+b*x)/(b^2*(b*c-a*d)^2)-c^2*(2*b*c-3*a*d)*log(c+d*x)/_ (d^3*(b*c-a*d)^2) @@ -7836,9 +7836,9 @@ r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ --R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 397 +--E 397 ---S 398 of 1092 +--S 398 of 1092 a0:=integrate(t0,x) --R --R @@ -7855,27 +7855,27 @@ a0:=integrate(t0,x) --R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 398 +--E 398 ---S 399 of 1092 +--S 399 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 399 +--E 399 ---S 400 of 1092 +--S 400 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 400 +--E 400 )clear all ---S 401 of 1092 +--S 401 of 1092 t0:=x^2/((a+b*x)*(c+d*x)^2) --R --R @@ -7885,9 +7885,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 401 +--E 401 ---S 402 of 1092 +--S 402 of 1092 r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ c*(b*c-2*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^2) --R @@ -7902,9 +7902,9 @@ r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ --R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 402 +--E 402 ---S 403 of 1092 +--S 403 of 1092 a0:=integrate(t0,x) --R --R @@ -7918,27 +7918,27 @@ a0:=integrate(t0,x) --R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 403 +--E 403 ---S 404 of 1092 +--S 404 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 404 +--E 404 ---S 405 of 1092 +--S 405 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 405 +--E 405 )clear all ---S 406 of 1092 +--S 406 of 1092 t0:=x/((a+b*x)*(c+d*x)^2) --R --R @@ -7947,9 +7947,9 @@ t0:=x/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 406 +--E 406 ---S 407 of 1092 +--S 407 of 1092 r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 --R --R @@ -7960,9 +7960,9 @@ r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 --R 2 4 3 2 2 2 2 3 2 2 2 3 --R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 407 +--E 407 ---S 408 of 1092 +--S 408 of 1092 a0:=integrate(t0,x) --R --R @@ -7973,27 +7973,27 @@ a0:=integrate(t0,x) --R 2 4 3 2 2 2 2 3 2 2 2 3 --R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 408 +--E 408 ---S 409 of 1092 +--S 409 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 409 +--E 409 ---S 410 of 1092 +--S 410 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 410 +--E 410 )clear all ---S 411 of 1092 +--S 411 of 1092 t0:=1/((a+b*x)*(c+d*x)^2) --R --R @@ -8002,9 +8002,9 @@ t0:=1/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 411 +--E 411 ---S 412 of 1092 +--S 412 of 1092 r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 --R --R @@ -8013,9 +8013,9 @@ r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 --R 2 3 2 2 2 2 2 2 2 3 --R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c --R Type: Expression(Integer) ---E 412 +--E 412 ---S 413 of 1092 +--S 413 of 1092 a0:=integrate(t0,x) --R --R @@ -8024,27 +8024,27 @@ a0:=integrate(t0,x) --R 2 3 2 2 2 2 2 2 2 3 --R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c --R Type: Union(Expression(Integer),...) ---E 413 +--E 413 ---S 414 of 1092 +--S 414 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 414 +--E 414 ---S 415 of 1092 +--S 415 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 415 +--E 415 )clear all ---S 416 of 1092 +--S 416 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)^2) --R --R @@ -8053,9 +8053,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^2) --R 2 4 2 3 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 416 +--E 416 ---S 417 of 1092 +--S 417 of 1092 r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ b^2*log(a+b*x)/(a*(b*c-a*d)^2)+d*(2*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^2) --R @@ -8076,9 +8076,9 @@ r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ --R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 --R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c --R Type: Expression(Integer) ---E 417 +--E 417 ---S 418 of 1092 +--S 418 of 1092 a0:=integrate(t0,x) --R --R @@ -8098,27 +8098,27 @@ a0:=integrate(t0,x) --R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 --R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c --R Type: Union(Expression(Integer),...) ---E 418 +--E 418 ---S 419 of 1092 +--S 419 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 419 +--E 419 ---S 420 of 1092 +--S 420 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 420 +--E 420 )clear all ---S 421 of 1092 +--S 421 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)^2) --R --R @@ -8127,9 +8127,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^2) --R 2 5 2 4 2 3 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 421 +--E 421 ---S 422 of 1092 +--S 422 of 1092 r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ (b*c+2*a*d)*log(x)/(a^2*c^3)+b^3*log(a+b*x)/(a^2*(b*c-a*d)^2)-_ d^2*(3*b*c-2*a*d)*log(c+d*x)/(c^3*(b*c-a*d)^2) @@ -8151,9 +8151,9 @@ r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ --R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 --R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x --R Type: Expression(Integer) ---E 422 +--E 422 ---S 423 of 1092 +--S 423 of 1092 a0:=integrate(t0,x) --R --R @@ -8173,27 +8173,27 @@ a0:=integrate(t0,x) --R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 --R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x --R Type: Union(Expression(Integer),...) ---E 423 +--E 423 ---S 424 of 1092 +--S 424 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 424 +--E 424 ---S 425 of 1092 +--S 425 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 425 +--E 425 )clear all ---S 426 of 1092 +--S 426 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)^2) --R --R @@ -8202,9 +8202,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^2) --R 2 6 2 5 2 4 2 3 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 426 +--E 426 ---S 427 of 1092 +--S 427 of 1092 r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ d^3/(c^3*(b*c-a*d)*(c+d*x))+(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*log(x)/_ (a^3*c^4)-b^4*log(a+b*x)/(a^3*(b*c-a*d)^2)+d^3*(4*b*c-3*a*d)*_ @@ -8230,9 +8230,9 @@ r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ --R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 --R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x --R Type: Expression(Integer) ---E 427 +--E 427 ---S 428 of 1092 +--S 428 of 1092 a0:=integrate(t0,x) --R --R @@ -8255,27 +8255,27 @@ a0:=integrate(t0,x) --R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 --R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x --R Type: Union(Expression(Integer),...) ---E 428 +--E 428 ---S 429 of 1092 +--S 429 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 429 +--E 429 ---S 430 of 1092 +--S 430 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 430 +--E 430 )clear all ---S 431 of 1092 +--S 431 of 1092 t0:=x^m/((a+b*x)*(c+d*x)^3) --R --R @@ -8286,9 +8286,9 @@ t0:=x^m/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Expression(Integer) ---E 431 +--E 431 ---S 432 of 1092 +--S 432 of 1092 --r0:=-1/2*d*x^(1+m)/(c*(b*c-a*d)*(c+d*x)^2)-_ -- b*d*x^(1+m)/(c*(b*c-a*d)^2*(c+d*x))-_ -- 1/2*d*(1-m)*x^(1+m)/(c^2*(b*c-a*d)*(c+d*x))+_ @@ -8298,23 +8298,23 @@ t0:=x^m/((a+b*x)*(c+d*x)^3) -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)^2*(1+m))+_ -- 1/2*d*(1-m)*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^3*(b*c-a*d)*(1+m)) ---E 432 +--E 432 ---S 433 of 1092 +--S 433 of 1092 --a0:=integrate(t0,x) ---E 433 +--E 433 ---S 434 of 1092 +--S 434 of 1092 --m0:=a0-r0 ---E 434 +--E 434 ---S 435 of 1092 +--S 435 of 1092 --d0:=D(m0,x) ---E 435 +--E 435 )clear all ---S 436 of 1092 +--S 436 of 1092 t0:=x^6/((a+b*x)*(c+d*x)^3) --R --R @@ -8325,9 +8325,9 @@ t0:=x^6/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 436 +--E 436 ---S 437 of 1092 +--S 437 of 1092 r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ 1/2*(3*b*c+a*d)*x^2/(b^2*d^4)+1/3*x^3/(b*d^3)+_ 1/2*c^6/(d^6*(b*c-a*d)*(c+d*x)^2)-_ @@ -8378,9 +8378,9 @@ r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ --R 2 5 3 8 6 4 7 7 5 6 --R - 18a b c d + 18a b c d - 6b c d --R Type: Expression(Integer) ---E 437 +--E 437 ---S 438 of 1092 +--S 438 of 1092 a0:=integrate(t0,x) --R --R @@ -8426,27 +8426,27 @@ a0:=integrate(t0,x) --R 2 5 3 8 6 4 7 7 5 6 --R - 18a b c d + 18a b c d - 6b c d --R Type: Union(Expression(Integer),...) ---E 438 +--E 438 ---S 439 of 1092 +--S 439 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 439 +--E 439 ---S 440 of 1092 +--S 440 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 440 +--E 440 )clear all ---S 441 of 1092 +--S 441 of 1092 t0:=x^5/((a+b*x)*(c+d*x)^3) --R --R @@ -8457,9 +8457,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 441 +--E 441 ---S 442 of 1092 +--S 442 of 1092 r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ 1/2*c^5/(d^5*(b*c-a*d)*(c+d*x)^2)+c^4*(4*b*c-5*a*d)/_ (d^5*(b*c-a*d)^2*(c+d*x))-a^5*log(a+b*x)/(b^3*(b*c-a*d)^3)+_ @@ -8505,9 +8505,9 @@ r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ --R 5 4 6 6 5 5 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 442 +--E 442 ---S 443 of 1092 +--S 443 of 1092 a0:=integrate(t0,x) --R --R @@ -8550,27 +8550,27 @@ a0:=integrate(t0,x) --R 5 4 6 6 5 5 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 443 +--E 443 ---S 444 of 1092 +--S 444 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 444 +--E 444 ---S 445 of 1092 +--S 445 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 445 +--E 445 )clear all ---S 446 of 1092 +--S 446 of 1092 t0:=x^4/((a+b*x)*(c+d*x)^3) --R --R @@ -8581,9 +8581,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 446 +--E 446 ---S 447 of 1092 +--S 447 of 1092 r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ c^3*(3*b*c-4*a*d)/(d^4*(b*c-a*d)^2*(c+d*x))+_ a^4*log(a+b*x)/(b^2*(b*c-a*d)^3)-_ @@ -8623,9 +8623,9 @@ r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ --R 4 4 5 5 5 4 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 447 +--E 447 ---S 448 of 1092 +--S 448 of 1092 a0:=integrate(t0,x) --R --R @@ -8662,27 +8662,27 @@ a0:=integrate(t0,x) --R 4 4 5 5 5 4 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 448 +--E 448 ---S 449 of 1092 +--S 449 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 449 +--E 449 ---S 450 of 1092 +--S 450 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 450 +--E 450 )clear all ---S 451 of 1092 +--S 451 of 1092 t0:=x^3/((a+b*x)*(c+d*x)^3) --R --R @@ -8693,9 +8693,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 451 +--E 451 ---S 452 of 1092 +--S 452 of 1092 r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ (d^3*(b*c-a*d)^2*(c+d*x))-a^3*log(a+b*x)/(b*(b*c-a*d)^3)+_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^3) @@ -8725,9 +8725,9 @@ r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ --R 3 4 4 4 5 3 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 452 +--E 452 ---S 453 of 1092 +--S 453 of 1092 a0:=integrate(t0,x) --R --R @@ -8755,27 +8755,27 @@ a0:=integrate(t0,x) --R 3 4 4 4 5 3 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 453 +--E 453 ---S 454 of 1092 +--S 454 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 454 +--E 454 ---S 455 of 1092 +--S 455 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 455 +--E 455 )clear all ---S 456 of 1092 +--S 456 of 1092 t0:=x^2/((a+b*x)*(c+d*x)^3) --R --R @@ -8786,9 +8786,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 456 +--E 456 ---S 457 of 1092 +--S 457 of 1092 r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ (d^2*(b*c-a*d)^2*(c+d*x))+a^2*log(a+b*x)/(b*c-a*d)^3-_ a^2*log(c+d*x)/(b*c-a*d)^3 @@ -8813,9 +8813,9 @@ r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ --R 2 4 3 3 5 2 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 457 +--E 457 ---S 458 of 1092 +--S 458 of 1092 a0:=integrate(t0,x) --R --R @@ -8838,27 +8838,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 5 2 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 458 +--E 458 ---S 459 of 1092 +--S 459 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 459 +--E 459 ---S 460 of 1092 +--S 460 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 460 +--E 460 )clear all ---S 461 of 1092 +--S 461 of 1092 t0:=x/((a+b*x)*(c+d*x)^3) --R --R @@ -8868,9 +8868,9 @@ t0:=x/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 461 +--E 461 ---S 462 of 1092 +--S 462 of 1092 r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ a*b*log(a+b*x)/(b*c-a*d)^3+a*b*log(c+d*x)/(b*c-a*d)^3 --R @@ -8894,9 +8894,9 @@ r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ --R 2 4 2 3 5 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 462 +--E 462 ---S 463 of 1092 +--S 463 of 1092 a0:=integrate(t0,x) --R --R @@ -8919,27 +8919,27 @@ a0:=integrate(t0,x) --R 2 4 2 3 5 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 463 +--E 463 ---S 464 of 1092 +--S 464 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 464 +--E 464 ---S 465 of 1092 +--S 465 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 465 +--E 465 )clear all ---S 466 of 1092 +--S 466 of 1092 t0:=1/((a+b*x)*(c+d*x)^3) --R --R @@ -8949,9 +8949,9 @@ t0:=1/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 466 +--E 466 ---S 467 of 1092 +--S 467 of 1092 r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3 --R @@ -8975,9 +8975,9 @@ r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ --R 2 4 3 5 --R 6a b c d - 2b c --R Type: Expression(Integer) ---E 467 +--E 467 ---S 468 of 1092 +--S 468 of 1092 a0:=integrate(t0,x) --R --R @@ -9000,27 +9000,27 @@ a0:=integrate(t0,x) --R 2 4 3 5 --R 6a b c d - 2b c --R Type: Union(Expression(Integer),...) ---E 468 +--E 468 ---S 469 of 1092 +--S 469 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 469 +--E 469 ---S 470 of 1092 +--S 470 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 470 +--E 470 )clear all ---S 471 of 1092 +--S 471 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)^3) --R --R @@ -9033,9 +9033,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^3) --R 3 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 471 +--E 471 ---S 472 of 1092 +--S 472 of 1092 r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ (c^2*(b*c-a*d)^2*(c+d*x))+log(x)/(a*c^3)-_ b^3*log(a+b*x)/(a*(b*c-a*d)^3)+d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_ @@ -9077,9 +9077,9 @@ r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ --R 2 2 7 3 8 --R 6a b c d - 2a b c --R Type: Expression(Integer) ---E 472 +--E 472 ---S 473 of 1092 +--S 473 of 1092 a0:=integrate(t0,x) --R --R @@ -9118,27 +9118,27 @@ a0:=integrate(t0,x) --R 2 2 7 3 8 --R 6a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 473 +--E 473 ---S 474 of 1092 +--S 474 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 474 +--E 474 ---S 475 of 1092 +--S 475 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 475 +--E 475 )clear all ---S 476 of 1092 +--S 476 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)^3) --R --R @@ -9151,9 +9151,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^3) --R 3 2 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 476 +--E 476 ---S 477 of 1092 +--S 477 of 1092 r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ d^2*(3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x))-(b*c+3*a*d)*_ log(x)/(a^2*c^4)+b^4*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ @@ -9204,9 +9204,9 @@ r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ --R 5 6 3 4 7 2 3 2 8 2 3 9 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 477 +--E 477 ---S 478 of 1092 +--S 478 of 1092 a0:=integrate(t0,x) --R --R @@ -9254,27 +9254,27 @@ a0:=integrate(t0,x) --R 5 6 3 4 7 2 3 2 8 2 3 9 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 478 +--E 478 ---S 479 of 1092 +--S 479 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 479 +--E 479 ---S 480 of 1092 +--S 480 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 480 +--E 480 )clear all ---S 481 of 1092 +--S 481 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)^3) --R --R @@ -9287,9 +9287,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^3) --R 3 3 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 481 +--E 481 ---S 482 of 1092 +--S 482 of 1092 r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ (c+d*x)^2)-d^3*(4*b*c-3*a*d)/(c^4*(b*c-a*d)^2*(c+d*x))+_ (b^2*c^2+3*a*b*c*d+6*a^2*d^2)*log(x)/(a^3*c^5)-b^5*_ @@ -9344,9 +9344,9 @@ r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ --R 6 7 3 5 8 2 4 2 9 3 3 10 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 482 +--E 482 ---S 483 of 1092 +--S 483 of 1092 a0:=integrate(t0,x) --R --R @@ -9397,27 +9397,27 @@ a0:=integrate(t0,x) --R 6 7 3 5 8 2 4 2 9 3 3 10 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 483 +--E 483 ---S 484 of 1092 +--S 484 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 484 +--E 484 ---S 485 of 1092 +--S 485 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 485 +--E 485 )clear all ---S 486 of 1092 +--S 486 of 1092 t0:=x^4*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9427,9 +9427,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 486 +--E 486 ---S 487 of 1092 +--S 487 of 1092 r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ 1/3*(b*c-3*a*d)*(b*c-a*d)*x^3/b^4+1/2*d*(b*c-a*d)*x^4/b^3+_ 1/5*d^2*x^5/b^2-a^4*(b*c-a*d)^2/(b^7*(a+b*x))-_ @@ -9460,9 +9460,9 @@ r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ --R 8 7 --R 30b x + 30a b --R Type: Expression(Integer) ---E 487 +--E 487 ---S 488 of 1092 +--S 488 of 1092 a0:=integrate(t0,x) --R --R @@ -9490,27 +9490,27 @@ a0:=integrate(t0,x) --R 8 7 --R 30b x + 30a b --R Type: Union(Expression(Integer),...) ---E 488 +--E 488 ---S 489 of 1092 +--S 489 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 489 +--E 489 ---S 490 of 1092 +--S 490 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 490 +--E 490 )clear all ---S 491 of 1092 +--S 491 of 1092 t0:=x^3*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9520,9 +9520,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 491 +--E 491 ---S 492 of 1092 +--S 492 of 1092 r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ 2/3*d*(b*c-a*d)*x^3/b^3+1/4*d^2*x^4/b^2+_ a^3*(b*c-a*d)^2/(b^6*(a+b*x))+a^2*(3*b*c-5*a*d)*(b*c-a*d)*log(a+b*x)/b^6 @@ -9546,9 +9546,9 @@ r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ --R 7 6 --R 12b x + 12a b --R Type: Expression(Integer) ---E 492 +--E 492 ---S 493 of 1092 +--S 493 of 1092 a0:=integrate(t0,x) --R --R @@ -9570,27 +9570,27 @@ a0:=integrate(t0,x) --R 7 6 --R 12b x + 12a b --R Type: Union(Expression(Integer),...) ---E 493 +--E 493 ---S 494 of 1092 +--S 494 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 494 +--E 494 ---S 495 of 1092 +--S 495 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 495 +--E 495 )clear all ---S 496 of 1092 +--S 496 of 1092 t0:=x^2*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9600,9 +9600,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 496 +--E 496 ---S 497 of 1092 +--S 497 of 1092 r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ a^2*(b*c-a*d)^2/(b^5*(a+b*x))-2*a*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 --R @@ -9622,9 +9622,9 @@ r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ --R 6 5 --R 3b x + 3a b --R Type: Expression(Integer) ---E 497 +--E 497 ---S 498 of 1092 +--S 498 of 1092 a0:=integrate(t0,x) --R --R @@ -9643,27 +9643,27 @@ a0:=integrate(t0,x) --R 6 5 --R 3b x + 3a b --R Type: Union(Expression(Integer),...) ---E 498 +--E 498 ---S 499 of 1092 +--S 499 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 499 +--E 499 ---S 500 of 1092 +--S 500 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 500 +--E 500 )clear all ---S 501 of 1092 +--S 501 of 1092 t0:=x*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9673,9 +9673,9 @@ t0:=x*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 501 +--E 501 ---S 502 of 1092 +--S 502 of 1092 r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ (b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -9693,9 +9693,9 @@ r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ --R 5 4 --R 2b x + 2a b --R Type: Expression(Integer) ---E 502 +--E 502 ---S 503 of 1092 +--S 503 of 1092 a0:=integrate(t0,x) --R --R @@ -9712,27 +9712,27 @@ a0:=integrate(t0,x) --R 5 4 --R 2b x + 2a b --R Type: Union(Expression(Integer),...) ---E 503 +--E 503 ---S 504 of 1092 +--S 504 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 504 +--E 504 ---S 505 of 1092 +--S 505 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 505 +--E 505 )clear all ---S 506 of 1092 +--S 506 of 1092 t0:=(c+d*x)^2/(a+b*x)^2 --R --R @@ -9742,9 +9742,9 @@ t0:=(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 506 +--E 506 ---S 507 of 1092 +--S 507 of 1092 r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 --R --R @@ -9758,9 +9758,9 @@ r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 --R 4 3 --R b x + a b --R Type: Expression(Integer) ---E 507 +--E 507 ---S 508 of 1092 +--S 508 of 1092 a0:=integrate(t0,x) --R --R @@ -9774,27 +9774,27 @@ a0:=integrate(t0,x) --R 4 3 --R b x + a b --R Type: Union(Expression(Integer),...) ---E 508 +--E 508 ---S 509 of 1092 +--S 509 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 509 +--E 509 ---S 510 of 1092 +--S 510 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 510 +--E 510 )clear all ---S 511 of 1092 +--S 511 of 1092 t0:=(c+d*x)^2/(x*(a+b*x)^2) --R --R @@ -9804,9 +9804,9 @@ t0:=(c+d*x)^2/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 511 +--E 511 ---S 512 of 1092 +--S 512 of 1092 r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) --R --R @@ -9820,9 +9820,9 @@ r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) --R 2 3 3 2 --R a b x + a b --R Type: Expression(Integer) ---E 512 +--E 512 ---S 513 of 1092 +--S 513 of 1092 a0:=integrate(t0,x) --R --R @@ -9836,27 +9836,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 --R a b x + a b --R Type: Union(Expression(Integer),...) ---E 513 +--E 513 ---S 514 of 1092 +--S 514 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 514 +--E 514 ---S 515 of 1092 +--S 515 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 515 +--E 515 )clear all ---S 516 of 1092 +--S 516 of 1092 t0:=(c+d*x)^2/(x^2*(a+b*x)^2) --R --R @@ -9866,9 +9866,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 516 +--E 516 ---S 517 of 1092 +--S 517 of 1092 r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ log(x)/a^3+2*c*(b*c-a*d)*log(a+b*x)/a^3 --R @@ -9886,9 +9886,9 @@ r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ --R 3 2 2 4 --R a b x + a b x --R Type: Expression(Integer) ---E 517 +--E 517 ---S 518 of 1092 +--S 518 of 1092 a0:=integrate(t0,x) --R --R @@ -9905,27 +9905,27 @@ a0:=integrate(t0,x) --R 3 2 2 4 --R a b x + a b x --R Type: Union(Expression(Integer),...) ---E 518 +--E 518 ---S 519 of 1092 +--S 519 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 519 +--E 519 ---S 520 of 1092 +--S 520 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 520 +--E 520 )clear all ---S 521 of 1092 +--S 521 of 1092 t0:=(c+d*x)^2/(x^3*(a+b*x)^2) --R --R @@ -9935,9 +9935,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 521 +--E 521 ---S 522 of 1092 +--S 522 of 1092 r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ (b*c-a*d)*(3*b*c-a*d)*log(x)/a^4-(b*c-a*d)*(3*b*c-a*d)*log(a+b*x)/a^4 --R @@ -9957,9 +9957,9 @@ r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ --R 4 3 5 2 --R 2a b x + 2a x --R Type: Expression(Integer) ---E 522 +--E 522 ---S 523 of 1092 +--S 523 of 1092 a0:=integrate(t0,x) --R --R @@ -9978,27 +9978,27 @@ a0:=integrate(t0,x) --R 4 3 5 2 --R 2a b x + 2a x --R Type: Union(Expression(Integer),...) ---E 523 +--E 523 ---S 524 of 1092 +--S 524 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 524 +--E 524 ---S 525 of 1092 +--S 525 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 525 +--E 525 )clear all ---S 526 of 1092 +--S 526 of 1092 t0:=(c+d*x)^2/(x^4*(a+b*x)^2) --R --R @@ -10008,9 +10008,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 526 +--E 526 ---S 527 of 1092 +--S 527 of 1092 r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ (a^4*x)-b*(b*c-a*d)^2/(a^4*(a+b*x))-2*b*(b*c-a*d)*(2*b*c-a*d)*_ log(x)/a^5+2*b*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 @@ -10039,9 +10039,9 @@ r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ --R 5 4 6 3 --R 3a b x + 3a x --R Type: Expression(Integer) ---E 527 +--E 527 ---S 528 of 1092 +--S 528 of 1092 a0:=integrate(t0,x) --R --R @@ -10068,27 +10068,27 @@ a0:=integrate(t0,x) --R 5 4 6 3 --R 3a b x + 3a x --R Type: Union(Expression(Integer),...) ---E 528 +--E 528 ---S 529 of 1092 +--S 529 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 529 +--E 529 ---S 530 of 1092 +--S 530 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 530 +--E 530 )clear all ---S 531 of 1092 +--S 531 of 1092 t0:=(c+d*x)^2/(x^5*(a+b*x)^2) --R --R @@ -10098,9 +10098,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x)^2) --R 2 7 6 2 5 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 531 +--E 531 ---S 532 of 1092 +--S 532 of 1092 r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ (3*b*c-a*d)/(a^4*x^2)+2*b*(b*c-a*d)*(2*b*c-a*d)/(a^5*x)+_ b^2*(b*c-a*d)^2/(a^5*(a+b*x))+b^2*(5*b*c-3*a*d)*(b*c-a*d)*_ @@ -10133,9 +10133,9 @@ r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ --R 6 5 7 4 --R 12a b x + 12a x --R Type: Expression(Integer) ---E 532 +--E 532 ---S 533 of 1092 +--S 533 of 1092 a0:=integrate(t0,x) --R --R @@ -10165,27 +10165,27 @@ a0:=integrate(t0,x) --R 6 5 7 4 --R 12a b x + 12a x --R Type: Union(Expression(Integer),...) ---E 533 +--E 533 ---S 534 of 1092 +--S 534 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 534 +--E 534 ---S 535 of 1092 +--S 535 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 535 +--E 535 )clear all ---S 536 of 1092 +--S 536 of 1092 t0:=x^4*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10195,9 +10195,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 536 +--E 536 ---S 537 of 1092 +--S 537 of 1092 r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ (b*c-a*d)^2*x^2/b^6+1/3*(b*c-4*a*d)*(b*c-a*d)^2*x^3/b^5+_ 3/4*d*(b*c-a*d)^2*x^4/b^4+1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+_ @@ -10238,9 +10238,9 @@ r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ --R 9 8 --R 60b x + 60a b --R Type: Expression(Integer) ---E 537 +--E 537 ---S 538 of 1092 +--S 538 of 1092 a0:=integrate(t0,x) --R --R @@ -10277,27 +10277,27 @@ a0:=integrate(t0,x) --R 9 8 --R 60b x + 60a b --R Type: Union(Expression(Integer),...) ---E 538 +--E 538 ---S 539 of 1092 +--S 539 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 539 +--E 539 ---S 540 of 1092 +--S 540 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 540 +--E 540 )clear all ---S 541 of 1092 +--S 541 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10307,9 +10307,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 541 +--E 541 ---S 542 of 1092 +--S 542 of 1092 r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ x^2/b^5+d*(b*c-a*d)^2*x^3/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_ 1/5*d^3*x^5/b^2+a^3*(b*c-a*d)^3/(b^7*(a+b*x))+_ @@ -10343,9 +10343,9 @@ r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ --R 8 7 --R 20b x + 20a b --R Type: Expression(Integer) ---E 542 +--E 542 ---S 543 of 1092 +--S 543 of 1092 a0:=integrate(t0,x) --R --R @@ -10376,27 +10376,27 @@ a0:=integrate(t0,x) --R 8 7 --R 20b x + 20a b --R Type: Union(Expression(Integer),...) ---E 543 +--E 543 ---S 544 of 1092 +--S 544 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 544 +--E 544 ---S 545 of 1092 +--S 545 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 545 +--E 545 )clear all ---S 546 of 1092 +--S 546 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10406,9 +10406,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 546 +--E 546 ---S 547 of 1092 +--S 547 of 1092 r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ 1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/4*d^3*x^4/b^2-a^2*_ (b*c-a*d)^3/(b^6*(a+b*x))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*log(a+b*x)/b^6 @@ -10438,9 +10438,9 @@ r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ --R 7 6 --R 12b x + 12a b --R Type: Expression(Integer) ---E 547 +--E 547 ---S 548 of 1092 +--S 548 of 1092 a0:=integrate(t0,x) --R --R @@ -10468,27 +10468,27 @@ a0:=integrate(t0,x) --R 7 6 --R 12b x + 12a b --R Type: Union(Expression(Integer),...) ---E 548 +--E 548 ---S 549 of 1092 +--S 549 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 549 +--E 549 ---S 550 of 1092 +--S 550 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 550 +--E 550 )clear all ---S 551 of 1092 +--S 551 of 1092 t0:=x*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10498,7 +10498,7 @@ t0:=x*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 551 +--E 551 --S 552 of 1092 r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ @@ -10528,7 +10528,7 @@ r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ --R Type: Expression(Integer) --E 552 ---S 553 of 1092 +--S 553 of 1092 a0:=integrate(t0,x) --R --R @@ -10553,27 +10553,27 @@ a0:=integrate(t0,x) --R 6 5 --R 6b x + 6a b --R Type: Union(Expression(Integer),...) ---E 553 +--E 553 ---S 554 of 1092 +--S 554 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 554 +--E 554 ---S 555 of 1092 +--S 555 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 555 +--E 555 )clear all ---S 556 of 1092 +--S 556 of 1092 t0:=(c+d*x)^3/(a+b*x)^2 --R --R @@ -10583,9 +10583,9 @@ t0:=(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 556 +--E 556 ---S 557 of 1092 +--S 557 of 1092 r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ 3*d*(b*c-a*d)^2*log(a+b*x)/b^4 --R @@ -10605,9 +10605,9 @@ r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ --R 5 4 --R 2b x + 2a b --R Type: Expression(Integer) ---E 557 +--E 557 ---S 558 of 1092 +--S 558 of 1092 a0:=integrate(t0,x) --R --R @@ -10626,27 +10626,27 @@ a0:=integrate(t0,x) --R 5 4 --R 2b x + 2a b --R Type: Union(Expression(Integer),...) ---E 558 +--E 558 ---S 559 of 1092 +--S 559 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 559 +--E 559 ---S 560 of 1092 +--S 560 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 560 +--E 560 )clear all ---S 561 of 1092 +--S 561 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)^2) --R --R @@ -10656,9 +10656,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 561 +--E 561 ---S 562 of 1092 +--S 562 of 1092 r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ (b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x)/(a^2*b^3) --R @@ -10678,9 +10678,9 @@ r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ --R 2 4 3 3 --R a b x + a b --R Type: Expression(Integer) ---E 562 +--E 562 ---S 563 of 1092 +--S 563 of 1092 a0:=integrate(t0,x) --R --R @@ -10699,27 +10699,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 --R a b x + a b --R Type: Union(Expression(Integer),...) ---E 563 +--E 563 ---S 564 of 1092 +--S 564 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 564 +--E 564 ---S 565 of 1092 +--S 565 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 565 +--E 565 )clear all ---S 566 of 1092 +--S 566 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)^2) --R --R @@ -10729,9 +10729,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 566 +--E 566 ---S 567 of 1092 +--S 567 of 1092 r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ log(x)/a^3+(b*c-a*d)^2*(2*b*c+a*d)*log(a+b*x)/(a^3*b^2) --R @@ -10751,9 +10751,9 @@ r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ --R 3 3 2 4 2 --R a b x + a b x --R Type: Expression(Integer) ---E 567 +--E 567 ---S 568 of 1092 +--S 568 of 1092 a0:=integrate(t0,x) --R --R @@ -10772,27 +10772,27 @@ a0:=integrate(t0,x) --R 3 3 2 4 2 --R a b x + a b x --R Type: Union(Expression(Integer),...) ---E 568 +--E 568 ---S 569 of 1092 +--S 569 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 569 +--E 569 ---S 570 of 1092 +--S 570 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 570 +--E 570 )clear all ---S 571 of 1092 +--S 571 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)^2) --R --R @@ -10802,9 +10802,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 571 +--E 571 ---S 572 of 1092 +--S 572 of 1092 r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ (a^3*b*(a+b*x))+3*c*(b*c-a*d)^2*log(x)/a^4-3*c*(b*c-a*d)^2*log(a+b*x)/a^4 --R @@ -10835,9 +10835,9 @@ r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ --R 4 2 3 5 2 --R 2a b x + 2a b x --R Type: Expression(Integer) ---E 572 +--E 572 ---S 573 of 1092 +--S 573 of 1092 a0:=integrate(t0,x) --R --R @@ -10867,27 +10867,27 @@ a0:=integrate(t0,x) --R 4 2 3 5 2 --R 2a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 573 +--E 573 ---S 574 of 1092 +--S 574 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 574 +--E 574 ---S 575 of 1092 +--S 575 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 575 +--E 575 )clear all ---S 576 of 1092 +--S 576 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)^2) --R --R @@ -10897,9 +10897,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 576 +--E 576 ---S 577 of 1092 +--S 577 of 1092 r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ (a^4*x)-(b*c-a*d)^3/(a^4*(a+b*x))-(b*c-a*d)^2*(4*b*c-a*d)*log(x)/_ a^5+(b*c-a*d)^2*(4*b*c-a*d)*log(a+b*x)/a^5 @@ -10931,9 +10931,9 @@ r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ --R 5 4 6 3 --R 6a b x + 6a x --R Type: Expression(Integer) ---E 577 +--E 577 ---S 578 of 1092 +--S 578 of 1092 a0:=integrate(t0,x) --R --R @@ -10963,27 +10963,27 @@ a0:=integrate(t0,x) --R 5 4 6 3 --R 6a b x + 6a x --R Type: Union(Expression(Integer),...) ---E 578 +--E 578 ---S 579 of 1092 +--S 579 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 579 +--E 579 ---S 580 of 1092 +--S 580 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 580 +--E 580 )clear all ---S 581 of 1092 +--S 581 of 1092 t0:=(c+d*x)^3/(x^5*(a+b*x)^2) --R --R @@ -10993,9 +10993,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x)^2) --R 2 7 6 2 5 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 581 +--E 581 ---S 582 of 1092 +--S 582 of 1092 r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ 3/2*c*(b*c-a*d)^2/(a^4*x^2)+(b*c-a*d)^2*(4*b*c-a*d)/_ (a^5*x)+b*(b*c-a*d)^3/(a^5*(a+b*x))+b*(5*b*c-2*a*d)*_ @@ -11031,9 +11031,9 @@ r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ --R 6 5 7 4 --R 12a b x + 12a x --R Type: Expression(Integer) ---E 582 +--E 582 ---S 583 of 1092 +--S 583 of 1092 a0:=integrate(t0,x) --R --R @@ -11066,27 +11066,27 @@ a0:=integrate(t0,x) --R 6 5 7 4 --R 12a b x + 12a x --R Type: Union(Expression(Integer),...) ---E 583 +--E 583 ---S 584 of 1092 +--S 584 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 584 +--E 584 ---S 585 of 1092 +--S 585 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 585 +--E 585 )clear all ---S 586 of 1092 +--S 586 of 1092 t0:=(c+d*x)^3/(x^6*(a+b*x)^2) --R --R @@ -11096,9 +11096,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x)^2) --R 2 8 7 2 6 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 586 +--E 586 ---S 587 of 1092 +--S 587 of 1092 r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ (a^4*x^3)+1/2*(b*c-a*d)^2*(4*b*c-a*d)/(a^5*x^2)-_ b*(5*b*c-2*a*d)*(b*c-a*d)^2/(a^6*x)-b^2*(b*c-a*d)^3/_ @@ -11138,9 +11138,9 @@ r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ --R 7 6 8 5 --R 20a b x + 20a x --R Type: Expression(Integer) ---E 587 +--E 587 ---S 588 of 1092 +--S 588 of 1092 a0:=integrate(t0,x) --R --R @@ -11176,27 +11176,27 @@ a0:=integrate(t0,x) --R 7 6 8 5 --R 20a b x + 20a x --R Type: Union(Expression(Integer),...) ---E 588 +--E 588 ---S 589 of 1092 +--S 589 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 589 +--E 589 ---S 590 of 1092 +--S 590 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 590 +--E 590 )clear all ---S 591 of 1092 +--S 591 of 1092 t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 --R --R @@ -11206,9 +11206,9 @@ t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 --R 2 --R x + 2x + 1 --R Type: Expression(Integer) ---E 591 +--E 591 ---S 592 of 1092 +--S 592 of 1092 r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ 125*sqrt(x)/(1+x) --R @@ -11218,9 +11218,9 @@ r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ --R (2) -------------------------------------------------------------- --R 5x + 5 --R Type: Expression(Integer) ---E 592 +--E 592 ---S 593 of 1092 +--S 593 of 1092 r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ 1/5*(62-513*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x) --R @@ -11230,9 +11230,9 @@ r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ --R (3) -------------------------------------------------------------- --R 5x + 5 --R Type: Expression(Integer) ---E 593 +--E 593 ---S 594 of 1092 +--S 594 of 1092 a0:=integrate(t0,x) --R --R @@ -11241,43 +11241,43 @@ a0:=integrate(t0,x) --R (4) -------------------------------------------------------------- --R 5x + 5 --R Type: Union(Expression(Integer),...) ---E 594 +--E 594 ---S 595 of 1092 +--S 595 of 1092 m0a:=a0-r0a --R --R --R (5) 0 --R Type: Expression(Integer) ---E 595 +--E 595 ---S 596 of 1092 +--S 596 of 1092 d0:=D(m0a,x) --R --R --R (6) 0 --R Type: Expression(Integer) ---E 596 +--E 596 ---S 597 of 1092 +--S 597 of 1092 m0b:=a0-r0b --R --R --R (7) 0 --R Type: Expression(Integer) ---E 597 +--E 597 ---S 598 of 1092 +--S 598 of 1092 d0:=D(m0b,x) --R --R --R (8) 0 --R Type: Expression(Integer) ---E 598 +--E 598 )clear all ---S 599 of 1092 +--S 599 of 1092 t0:=x^6/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11291,9 +11291,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 599 +--E 599 ---S 600 of 1092 +--S 600 of 1092 r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ 1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-_ c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/_ @@ -11344,9 +11344,9 @@ r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ --R 2 7 3 6 8 4 5 --R 9a b c d - 3a b c d --R Type: Expression(Integer) ---E 600 +--E 600 ---S 601 of 1092 +--S 601 of 1092 a0:=integrate(t0,x) --R --R @@ -11394,27 +11394,27 @@ a0:=integrate(t0,x) --R 2 7 3 6 8 4 5 --R 9a b c d - 3a b c d --R Type: Union(Expression(Integer),...) ---E 601 +--E 601 ---S 602 of 1092 +--S 602 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 602 +--E 602 ---S 603 of 1092 +--S 603 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 603 +--E 603 )clear all ---S 604 of 1092 +--S 604 of 1092 t0:=x^5/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11428,9 +11428,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 604 +--E 604 ---S 605 of 1092 +--S 605 of 1092 r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ (a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*_ log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/_ @@ -11478,9 +11478,9 @@ r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ --R 2 6 3 5 7 4 4 --R 6a b c d - 2a b c d --R Type: Expression(Integer) ---E 605 +--E 605 ---S 606 of 1092 +--S 606 of 1092 a0:=integrate(t0,x) --R --R @@ -11525,27 +11525,27 @@ a0:=integrate(t0,x) --R 2 6 3 5 7 4 4 --R 6a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 606 +--E 606 ---S 607 of 1092 +--S 607 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 607 +--E 607 ---S 608 of 1092 +--S 608 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 608 +--E 608 )clear all ---S 609 of 1092 +--S 609 of 1092 t0:=x^4/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11559,9 +11559,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 609 +--E 609 ---S 610 of 1092 +--S 610 of 1092 r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ 2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-_ 2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3) @@ -11605,9 +11605,9 @@ r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ --R 2 5 3 4 6 4 3 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 610 +--E 610 ---S 611 of 1092 +--S 611 of 1092 a0:=integrate(t0,x) --R --R @@ -11649,27 +11649,27 @@ a0:=integrate(t0,x) --R 2 5 3 4 6 4 3 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 611 +--E 611 ---S 612 of 1092 +--S 612 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 612 +--E 612 ---S 613 of 1092 +--S 613 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 613 +--E 613 )clear all ---S 614 of 1092 +--S 614 of 1092 t0:=x^3/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11683,9 +11683,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 614 +--E 614 ---S 615 of 1092 +--S 615 of 1092 r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+_ c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3) @@ -11720,9 +11720,9 @@ r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ --R 2 4 3 3 5 4 2 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 615 +--E 615 ---S 616 of 1092 +--S 616 of 1092 a0:=integrate(t0,x) --R --R @@ -11755,27 +11755,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 5 4 2 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 616 +--E 616 ---S 617 of 1092 +--S 617 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 617 +--E 617 ---S 618 of 1092 +--S 618 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 618 +--E 618 )clear all ---S 619 of 1092 +--S 619 of 1092 t0:=x^2/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11789,9 +11789,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 619 +--E 619 ---S 620 of 1092 +--S 620 of 1092 r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ 2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3 --R @@ -11815,9 +11815,9 @@ r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ --R 2 3 3 2 4 4 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 620 +--E 620 ---S 621 of 1092 +--S 621 of 1092 a0:=integrate(t0,x) --R --R @@ -11840,27 +11840,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 4 4 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 621 +--E 621 ---S 622 of 1092 +--S 622 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 622 +--E 622 ---S 623 of 1092 +--S 623 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 623 +--E 623 )clear all ---S 624 of 1092 +--S 624 of 1092 t0:=x/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11873,9 +11873,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 624 +--E 624 ---S 625 of 1092 +--S 625 of 1092 r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ (b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3 --R @@ -11903,9 +11903,9 @@ r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ --R 3 4 --R - a b c --R Type: Expression(Integer) ---E 625 +--E 625 ---S 626 of 1092 +--S 626 of 1092 a0:=integrate(t0,x) --R --R @@ -11932,27 +11932,27 @@ a0:=integrate(t0,x) --R 3 4 --R - a b c --R Type: Union(Expression(Integer),...) ---E 626 +--E 626 ---S 627 of 1092 +--S 627 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 627 +--E 627 ---S 628 of 1092 +--S 628 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 628 +--E 628 )clear all ---S 629 of 1092 +--S 629 of 1092 t0:=1/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11965,9 +11965,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 629 +--E 629 ---S 630 of 1092 +--S 630 of 1092 r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ 2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3 --R @@ -11991,9 +11991,9 @@ r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ --R 3 4 --R - a b c --R Type: Expression(Integer) ---E 630 +--E 630 ---S 631 of 1092 +--S 631 of 1092 a0:=integrate(t0,x) --R --R @@ -12016,27 +12016,27 @@ a0:=integrate(t0,x) --R 3 4 --R - a b c --R Type: Union(Expression(Integer),...) ---E 631 +--E 631 ---S 632 of 1092 +--S 632 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 632 +--E 632 ---S 633 of 1092 +--S 633 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 633 +--E 633 )clear all ---S 634 of 1092 +--S 634 of 1092 t0:=1/(x*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12049,9 +12049,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 2 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 634 +--E 634 ---S 635 of 1092 +--S 635 of 1092 r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3) @@ -12097,9 +12097,9 @@ r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ --R 3 3 6 --R - a b c --R Type: Expression(Integer) ---E 635 +--E 635 ---S 636 of 1092 +--S 636 of 1092 a0:=integrate(t0,x) --R --R @@ -12143,27 +12143,27 @@ a0:=integrate(t0,x) --R 3 3 6 --R - a b c --R Type: Union(Expression(Integer),...) ---E 636 +--E 636 ---S 637 of 1092 +--S 637 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 637 +--E 637 ---S 638 of 1092 +--S 638 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 638 +--E 638 )clear all ---S 639 of 1092 +--S 639 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12176,9 +12176,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) --R 2 2 3 2 2 2 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 639 +--E 639 ---S 640 of 1092 +--S 640 of 1092 r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_ 2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+_ @@ -12231,9 +12231,9 @@ r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ --R 7 4 3 6 5 2 5 2 6 4 3 7 --R (a c d - 3a b c d + 3a b c d - a b c )x --R Type: Expression(Integer) ---E 640 +--E 640 ---S 641 of 1092 +--S 641 of 1092 a0:=integrate(t0,x) --R --R @@ -12283,27 +12283,27 @@ a0:=integrate(t0,x) --R 7 4 3 6 5 2 5 2 6 4 3 7 --R (a c d - 3a b c d + 3a b c d - a b c )x --R Type: Union(Expression(Integer),...) ---E 641 +--E 641 ---S 642 of 1092 +--S 642 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 642 +--E 642 ---S 643 of 1092 +--S 643 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 643 +--E 643 )clear all ---S 644 of 1092 +--S 644 of 1092 t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12316,9 +12316,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) --R 2 2 4 2 2 3 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 644 +--E 644 ---S 645 of 1092 +--S 645 of 1092 r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+_ (3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*_ @@ -12375,9 +12375,9 @@ r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ --R 8 5 3 7 6 2 6 2 7 5 3 8 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 645 +--E 645 ---S 646 of 1092 +--S 646 of 1092 a0:=integrate(t0,x) --R --R @@ -12430,27 +12430,27 @@ a0:=integrate(t0,x) --R 8 5 3 7 6 2 6 2 7 5 3 8 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 646 +--E 646 ---S 647 of 1092 +--S 647 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 647 +--E 647 ---S 648 of 1092 +--S 648 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 648 +--E 648 )clear all ---S 649 of 1092 +--S 649 of 1092 t0:=x^7/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12464,9 +12464,9 @@ t0:=x^7/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 649 +--E 649 ---S 650 of 1092 +--S 650 of 1092 r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ (b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/_ (d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*_ @@ -12570,9 +12570,9 @@ r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ --R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 --R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d --R Type: Expression(Integer) ---E 650 +--E 650 ---S 651 of 1092 +--S 651 of 1092 a0:=integrate(t0,x) --R --R @@ -12672,27 +12672,27 @@ a0:=integrate(t0,x) --R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 --R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d --R Type: Union(Expression(Integer),...) ---E 651 +--E 651 ---S 652 of 1092 +--S 652 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 652 +--E 652 ---S 653 of 1092 +--S 653 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 653 +--E 653 )clear all ---S 654 of 1092 +--S 654 of 1092 t0:=x^6/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12706,9 +12706,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 654 +--E 654 ---S 655 of 1092 +--S 655 of 1092 r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ (a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/_ (d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/_ @@ -12786,9 +12786,9 @@ r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ --R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 655 +--E 655 ---S 656 of 1092 +--S 656 of 1092 a0:=integrate(t0,x) --R --R @@ -12862,27 +12862,27 @@ a0:=integrate(t0,x) --R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 656 +--E 656 ---S 657 of 1092 +--S 657 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 657 +--E 657 ---S 658 of 1092 +--S 658 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 658 +--E 658 )clear all ---S 659 of 1092 +--S 659 of 1092 t0:=x^5/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12896,9 +12896,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 659 +--E 659 ---S 660 of 1092 +--S 660 of 1092 r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ (c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+_ a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*_ @@ -12966,9 +12966,9 @@ r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ --R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 660 +--E 660 ---S 661 of 1092 +--S 661 of 1092 a0:=integrate(t0,x) --R --R @@ -13033,27 +13033,27 @@ a0:=integrate(t0,x) --R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 661 +--E 661 ---S 662 of 1092 +--S 662 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 662 +--E 662 ---S 663 of 1092 +--S 663 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 663 +--E 663 )clear all ---S 664 of 1092 +--S 664 of 1092 t0:=x^4/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13067,9 +13067,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 664 +--E 664 ---S 665 of 1092 +--S 665 of 1092 r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ 2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*_ log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*_ @@ -13120,9 +13120,9 @@ r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ --R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 665 +--E 665 ---S 666 of 1092 +--S 666 of 1092 a0:=integrate(t0,x) --R --R @@ -13170,27 +13170,27 @@ a0:=integrate(t0,x) --R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 666 +--E 666 ---S 667 of 1092 +--S 667 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 667 +--E 667 ---S 668 of 1092 +--S 668 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 668 +--E 668 )clear all ---S 669 of 1092 +--S 669 of 1092 t0:=x^3/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13204,9 +13204,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 669 +--E 669 ---S 670 of 1092 +--S 670 of 1092 r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/_ (b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4 @@ -13250,9 +13250,9 @@ r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 670 +--E 670 ---S 671 of 1092 +--S 671 of 1092 a0:=integrate(t0,x) --R --R @@ -13294,27 +13294,27 @@ a0:=integrate(t0,x) --R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 671 +--E 671 ---S 672 of 1092 +--S 672 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 672 +--E 672 ---S 673 of 1092 +--S 673 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 673 +--E 673 )clear all ---S 674 of 1092 +--S 674 of 1092 t0:=x^2/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13328,9 +13328,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 674 +--E 674 ---S 675 of 1092 +--S 675 of 1092 r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ 2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+_ a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4 @@ -13371,9 +13371,9 @@ r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 675 +--E 675 ---S 676 of 1092 +--S 676 of 1092 a0:=integrate(t0,x) --R --R @@ -13412,27 +13412,27 @@ a0:=integrate(t0,x) --R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 676 +--E 676 ---S 677 of 1092 +--S 677 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 677 +--E 677 ---S 678 of 1092 +--S 678 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 678 +--E 678 )clear all ---S 679 of 1092 +--S 679 of 1092 t0:=x/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13445,9 +13445,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 679 +--E 679 ---S 680 of 1092 +--S 680 of 1092 r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ ((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-_ b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4 @@ -13488,9 +13488,9 @@ r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 680 +--E 680 ---S 681 of 1092 +--S 681 of 1092 a0:=integrate(t0,x) --R --R @@ -13529,27 +13529,27 @@ a0:=integrate(t0,x) --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 681 +--E 681 ---S 682 of 1092 +--S 682 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 682 +--E 682 ---S 683 of 1092 +--S 683 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 683 +--E 683 )clear all ---S 684 of 1092 +--S 684 of 1092 t0:=1/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13562,9 +13562,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 684 +--E 684 ---S 685 of 1092 +--S 685 of 1092 r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ 2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_ 3*b^2*d*log(c+d*x)/(b*c-a*d)^4 @@ -13602,9 +13602,9 @@ r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 685 +--E 685 ---S 686 of 1092 +--S 686 of 1092 a0:=integrate(t0,x) --R --R @@ -13640,27 +13640,27 @@ a0:=integrate(t0,x) --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 686 +--E 686 ---S 687 of 1092 +--S 687 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 687 +--E 687 ---S 688 of 1092 +--S 688 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 688 +--E 688 )clear all ---S 689 of 1092 +--S 689 of 1092 t0:=1/(x*(a+b*x)^2*(c+d*x)^3) --R --R @@ -13673,9 +13673,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 3 2 2 3 2 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 689 +--E 689 ---S 690 of 1092 +--S 690 of 1092 r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-_ b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-_ @@ -13740,9 +13740,9 @@ r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ --R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 690 +--E 690 ---S 691 of 1092 +--S 691 of 1092 a0:=integrate(t0,x) --R --R @@ -13804,27 +13804,27 @@ a0:=integrate(t0,x) --R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 691 +--E 691 ---S 692 of 1092 +--S 692 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 692 +--E 692 ---S 693 of 1092 +--S 693 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 693 +--E 693 )clear all ---S 694 of 1092 +--S 694 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) --R --R @@ -13837,9 +13837,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 4 2 2 3 3 2 3 2 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 694 +--E 694 ---S 695 of 1092 +--S 695 of 1092 r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ 1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/_ (c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+_ @@ -13926,112 +13926,23 @@ r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ --R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Expression(Integer) ---E 695 +--E 695 ---S 696 of 1092 -a0:=integrate(t0,x) ---R ---R ---R (3) ---R 5 7 4 2 6 3 3 2 5 4 ---R (6a b d - 20a b c d + 20a b c d )x ---R + ---R 6 7 5 6 4 2 2 5 3 3 3 4 3 ---R (6a d - 8a b c d - 20a b c d + 40a b c d )x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 ---R (12a c d - 34a b c d + 20a b c d + 20a b c d )x ---R + ---R 6 2 5 5 3 4 4 2 4 3 ---R (6a c d - 20a b c d + 20a b c d )x ---R * ---R log(d x + c) ---R + ---R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 ---R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x ---R + ---R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 ---R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x ---R * ---R log(b x + a) ---R + ---R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 ---R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x ---R + ---R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 ---R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d ---R + ---R 5 5 2 6 6 ---R 16a b c d - 8b c d ---R * ---R 3 ---R x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 ---R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d ---R + ---R 5 6 6 7 ---R 2a b c d - 4b c ---R * ---R 2 ---R x ---R + ---R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 ---R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x ---R * ---R log(x) ---R + ---R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 ---R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 ---R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d ---R + ---R 5 6 ---R - 8a b c d ---R * ---R 2 ---R x ---R + ---R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 ---R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x ---R + ---R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 ---R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c ---R / ---R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 ---R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x ---R + ---R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 ---R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x ---R + ---R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 ---R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x ---R + ---R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 ---R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x ---R Type: Union(Expression(Integer),...) ---E 696 +--S 696 of 1092 +--a0:=integrate(t0,x) +--E 696 ---S 697 of 1092 -m0:=a0-r0 ---R ---R ---R (4) 0 ---R Type: Expression(Integer) ---E 697 +--S 697 of 1092 +--m0:=a0-r0 +--E 697 ---S 698 of 1092 -d0:=D(m0,x) ---R ---R ---R (5) 0 ---R Type: Expression(Integer) ---E 698 +--S 698 of 1092 +--d0:=D(m0,x) +--E 698 )clear all ---S 699 of 1092 +--S 699 of 1092 t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) --R --R @@ -14044,9 +13955,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 5 2 2 3 4 2 3 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 699 +--E 699 ---S 700 of 1092 +--S 700 of 1092 r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ (a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/_ (c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/_ @@ -14142,9 +14053,9 @@ r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ --R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Expression(Integer) ---E 700 +--E 700 ---S 701 of 1092 +--S 701 of 1092 a0:=integrate(t0,x) --R --R @@ -14236,27 +14147,27 @@ a0:=integrate(t0,x) --R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Union(Expression(Integer),...) ---E 701 +--E 701 ---S 702 of 1092 +--S 702 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 702 +--E 702 ---S 703 of 1092 +--S 703 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 703 +--E 703 )clear all ---S 704 of 1092 +--S 704 of 1092 t0:=x^2/((-1+x)^2*(1+x)^2) --R --R @@ -14266,9 +14177,9 @@ t0:=x^2/((-1+x)^2*(1+x)^2) --R 4 2 --R x - 2x + 1 --R Type: Fraction(Polynomial(Integer)) ---E 704 +--E 704 ---S 705 of 1092 +--S 705 of 1092 r0:=1/2*x/(1-x^2)-1/2*atanh(x) --R --R @@ -14278,9 +14189,9 @@ r0:=1/2*x/(1-x^2)-1/2*atanh(x) --R 2 --R 2x - 2 --R Type: Expression(Integer) ---E 705 +--E 705 ---S 706 of 1092 +--S 706 of 1092 a0:=integrate(t0,x) --R --R @@ -14290,9 +14201,9 @@ a0:=integrate(t0,x) --R 2 --R 4x - 4 --R Type: Union(Expression(Integer),...) ---E 706 +--E 706 ---S 707 of 1092 +--S 707 of 1092 m0:=a0-r0 --R --R @@ -14300,19 +14211,19 @@ m0:=a0-r0 --R (4) ------------------------------------- --R 4 --R Type: Expression(Integer) ---E 707 +--E 707 ---S 708 of 1092 +--S 708 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 708 +--E 708 )clear all ---S 709 of 1092 +--S 709 of 1092 t0:=b^2*x^m/(b+a*x^2)^2 --R --R @@ -14322,28 +14233,28 @@ t0:=b^2*x^m/(b+a*x^2)^2 --R 2 4 2 2 --R a x + 2a b x + b --R Type: Expression(Integer) ---E 709 +--E 709 ---S 710 of 1092 +--S 710 of 1092 --r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ -- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) ---E 710 +--E 710 ---S 711 of 1092 +--S 711 of 1092 --a0:=integrate(t0,x) ---E 711 +--E 711 ---S 712 of 1092 +--S 712 of 1092 --m0:=a0-r0 ---E 712 +--E 712 ---S 713 of 1092 +--S 713 of 1092 --d0:=D(m0,x) ---E 713 +--E 713 )clear all ---S 714 of 1092 +--S 714 of 1092 t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) --R --R @@ -14353,28 +14264,28 @@ t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) --R 2 4 2 2 --R a x + 2a b x + b --R Type: Expression(Integer) ---E 714 +--E 714 ---S 715 of 1092 +--S 715 of 1092 --r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ -- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) ---E 715 +--E 715 ---S 716 of 1092 +--S 716 of 1092 --a0:=integrate(t0,x) ---E 716 +--E 716 ---S 717 of 1092 +--S 717 of 1092 --m0:=a0-r0 ---E 717 +--E 717 ---S 718 of 1092 +--S 718 of 1092 --d0:=D(m0,x) ---E 718 +--E 718 )clear all ---S 719 of 1092 +--S 719 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14384,9 +14295,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 719 +--E 719 ---S 720 of 1092 +--S 720 of 1092 r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ 3/2*d*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+d^2*(b*c-a*d)*x^3/b^4+_ 1/4*d^3*x^4/b^3+1/2*a^3*(b*c-a*d)^3/(b^7*(a+b*x)^2)-_ @@ -14424,9 +14335,9 @@ r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ --R 9 2 8 2 7 --R 4b x + 8a b x + 4a b --R Type: Expression(Integer) ---E 720 +--E 720 ---S 721 of 1092 +--S 721 of 1092 a0:=integrate(t0,x) --R --R @@ -14460,27 +14371,27 @@ a0:=integrate(t0,x) --R 9 2 8 2 7 --R 4b x + 8a b x + 4a b --R Type: Union(Expression(Integer),...) ---E 721 +--E 721 ---S 722 of 1092 +--S 722 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 722 +--E 722 ---S 723 of 1092 +--S 723 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 723 +--E 723 )clear all ---S 724 of 1092 +--S 724 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14490,9 +14401,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 724 +--E 724 ---S 725 of 1092 +--S 725 of 1092 r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ 1/3*d^3*x^3/b^3-1/2*a^2*(b*c-a*d)^3/(b^6*(a+b*x)^2)+_ a*(2*b*c-5*a*d)*(b*c-a*d)^2/(b^6*(a+b*x))+(b*c-a*d)*_ @@ -14526,9 +14437,9 @@ r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ --R 8 2 7 2 6 --R 6b x + 12a b x + 6a b --R Type: Expression(Integer) ---E 725 +--E 725 ---S 726 of 1092 +--S 726 of 1092 a0:=integrate(t0,x) --R --R @@ -14559,27 +14470,27 @@ a0:=integrate(t0,x) --R 8 2 7 2 6 --R 6b x + 12a b x + 6a b --R Type: Union(Expression(Integer),...) ---E 726 +--E 726 ---S 727 of 1092 +--S 727 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 727 +--E 727 ---S 728 of 1092 +--S 728 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 728 +--E 728 )clear all ---S 729 of 1092 +--S 729 of 1092 t0:=x*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14589,9 +14500,9 @@ t0:=x*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 729 +--E 729 ---S 730 of 1092 +--S 730 of 1092 r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ (b^5*(a+b*x)^2)-(b*c-4*a*d)*(b*c-a*d)^2/(b^5*(a+b*x))+_ 3*d*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 @@ -14618,9 +14529,9 @@ r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ --R 7 2 6 2 5 --R 2b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 730 +--E 730 ---S 731 of 1092 +--S 731 of 1092 a0:=integrate(t0,x) --R --R @@ -14645,27 +14556,27 @@ a0:=integrate(t0,x) --R 7 2 6 2 5 --R 2b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 731 +--E 731 ---S 732 of 1092 +--S 732 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 732 +--E 732 ---S 733 of 1092 +--S 733 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 733 +--E 733 )clear all ---S 734 of 1092 +--S 734 of 1092 t0:=(c+d*x)^3/(a+b*x)^3 --R --R @@ -14675,9 +14586,9 @@ t0:=(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 734 +--E 734 ---S 735 of 1092 +--S 735 of 1092 r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ (b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -14700,9 +14611,9 @@ r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ --R 6 2 5 2 4 --R 2b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 735 +--E 735 ---S 736 of 1092 +--S 736 of 1092 a0:=integrate(t0,x) --R --R @@ -14724,27 +14635,27 @@ a0:=integrate(t0,x) --R 6 2 5 2 4 --R 2b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 736 +--E 736 ---S 737 of 1092 +--S 737 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 737 +--E 737 ---S 738 of 1092 +--S 738 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 738 +--E 738 )clear all ---S 739 of 1092 +--S 739 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)^3) --R --R @@ -14754,9 +14665,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^3) --R 3 4 2 3 2 2 3 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 739 +--E 739 ---S 740 of 1092 +--S 740 of 1092 r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ (a^2*b^3*(a+b*x))+c^3*log(x)/a^3-(c^3/a^3-d^3/b^3)*log(a+b*x) --R @@ -14776,9 +14687,9 @@ r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ --R 3 5 2 4 4 5 3 --R 2a b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 740 +--E 740 ---S 741 of 1092 +--S 741 of 1092 a0:=integrate(t0,x) --R --R @@ -14797,27 +14708,27 @@ a0:=integrate(t0,x) --R 3 5 2 4 4 5 3 --R 2a b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 741 +--E 741 ---S 742 of 1092 +--S 742 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 742 +--E 742 ---S 743 of 1092 +--S 743 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 743 +--E 743 )clear all ---S 744 of 1092 +--S 744 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)^3) --R --R @@ -14827,9 +14738,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^3) --R 3 5 2 4 2 3 3 2 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 744 +--E 744 ---S 745 of 1092 +--S 745 of 1092 r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ (2*b*c+a*d)/(a^3*b^2*(a+b*x))-3*c^2*(b*c-a*d)*log(x)/a^4+_ 3*c^2*(b*c-a*d)*log(a+b*x)/a^4 @@ -14861,9 +14772,9 @@ r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ --R 4 4 3 5 3 2 6 2 --R 2a b x + 4a b x + 2a b x --R Type: Expression(Integer) ---E 745 +--E 745 ---S 746 of 1092 +--S 746 of 1092 a0:=integrate(t0,x) --R --R @@ -14893,27 +14804,27 @@ a0:=integrate(t0,x) --R 4 4 3 5 3 2 6 2 --R 2a b x + 4a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 746 +--E 746 ---S 747 of 1092 +--S 747 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 747 +--E 747 ---S 748 of 1092 +--S 748 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 748 +--E 748 )clear all ---S 749 of 1092 +--S 749 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)^3) --R --R @@ -14923,9 +14834,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^3) --R 3 6 2 5 2 4 3 3 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 749 +--E 749 ---S 750 of 1092 +--S 750 of 1092 r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ (a^3*b*(a+b*x)^2)+3*c*(b*c-a*d)^2/(a^4*(a+b*x))+3*c*(b*c-a*d)*_ (2*b*c-a*d)*log(x)/a^5-3*c*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 @@ -14966,9 +14877,9 @@ r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ --R 5 3 4 6 2 3 7 2 --R 2a b x + 4a b x + 2a b x --R Type: Expression(Integer) ---E 750 +--E 750 ---S 751 of 1092 +--S 751 of 1092 a0:=integrate(t0,x) --R --R @@ -15007,27 +14918,27 @@ a0:=integrate(t0,x) --R 5 3 4 6 2 3 7 2 --R 2a b x + 4a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 751 +--E 751 ---S 752 of 1092 +--S 752 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 752 +--E 752 ---S 753 of 1092 +--S 753 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 753 +--E 753 )clear all ---S 754 of 1092 +--S 754 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)^3) --R --R @@ -15037,9 +14948,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^3) --R 3 7 2 6 2 5 3 4 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 754 +--E 754 ---S 755 of 1092 +--S 755 of 1092 r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ (2*b*c-a*d)/(a^5*x)-1/2*(b*c-a*d)^3/(a^4*(a+b*x)^2)-(b*c-a*d)^2*_ (4*b*c-a*d)/(a^5*(a+b*x))-(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ @@ -15081,9 +14992,9 @@ r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ --R 6 2 5 7 4 8 3 --R 6a b x + 12a b x + 6a x --R Type: Expression(Integer) ---E 755 +--E 755 ---S 756 of 1092 +--S 756 of 1092 a0:=integrate(t0,x) --R --R @@ -15122,27 +15033,27 @@ a0:=integrate(t0,x) --R 6 2 5 7 4 8 3 --R 6a b x + 12a b x + 6a x --R Type: Union(Expression(Integer),...) ---E 756 +--E 756 ---S 757 of 1092 +--S 757 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 757 +--E 757 ---S 758 of 1092 +--S 758 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 758 +--E 758 )clear all ---S 759 of 1092 +--S 759 of 1092 t0:=x^7/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15159,9 +15070,9 @@ t0:=x^7/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 759 +--E 759 ---S 760 of 1092 +--S 760 of 1092 r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ (a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/_ (d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-_ @@ -15292,9 +15203,9 @@ r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ --R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 760 +--E 760 ---S 761 of 1092 +--S 761 of 1092 a0:=integrate(t0,x) --R --R @@ -15421,27 +15332,27 @@ a0:=integrate(t0,x) --R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 761 +--E 761 ---S 762 of 1092 +--S 762 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 762 +--E 762 ---S 763 of 1092 +--S 763 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 763 +--E 763 )clear all ---S 764 of 1092 +--S 764 of 1092 t0:=x^6/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15458,9 +15369,9 @@ t0:=x^6/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 764 +--E 764 ---S 765 of 1092 +--S 765 of 1092 r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ (b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-_ 3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-_ @@ -15576,9 +15487,9 @@ r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ --R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 765 +--E 765 ---S 766 of 1092 +--S 766 of 1092 a0:=integrate(t0,x) --R --R @@ -15690,27 +15601,27 @@ a0:=integrate(t0,x) --R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 766 +--E 766 ---S 767 of 1092 +--S 767 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 767 +--E 767 ---S 768 of 1092 +--S 768 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 768 +--E 768 )clear all ---S 769 of 1092 +--S 769 of 1092 t0:=x^5/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15727,9 +15638,9 @@ t0:=x^5/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 769 +--E 769 ---S 770 of 1092 +--S 770 of 1092 r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ (b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+_ c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-_ @@ -15828,9 +15739,9 @@ r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ --R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 770 +--E 770 ---S 771 of 1092 +--S 771 of 1092 a0:=integrate(t0,x) --R --R @@ -15925,27 +15836,27 @@ a0:=integrate(t0,x) --R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 771 +--E 771 ---S 772 of 1092 +--S 772 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 772 +--E 772 ---S 773 of 1092 +--S 773 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 773 +--E 773 )clear all ---S 774 of 1092 +--S 774 of 1092 t0:=x^4/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15962,9 +15873,9 @@ t0:=x^4/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 774 +--E 774 ---S 775 of 1092 +--S 775 of 1092 r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ (a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/_ (d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-_ @@ -16032,9 +15943,9 @@ r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ --R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 775 +--E 775 ---S 776 of 1092 +--S 776 of 1092 a0:=integrate(t0,x) --R --R @@ -16099,27 +16010,27 @@ a0:=integrate(t0,x) --R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 776 +--E 776 ---S 777 of 1092 +--S 777 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 777 +--E 777 ---S 778 of 1092 +--S 778 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 778 +--E 778 )clear all ---S 779 of 1092 +--S 779 of 1092 t0:=x^3/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16136,9 +16047,9 @@ t0:=x^3/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 779 +--E 779 ---S 780 of 1092 +--S 780 of 1092 r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ 1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-_ 3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/_ @@ -16209,9 +16120,9 @@ r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ --R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 780 +--E 780 ---S 781 of 1092 +--S 781 of 1092 a0:=integrate(t0,x) --R --R @@ -16279,27 +16190,27 @@ a0:=integrate(t0,x) --R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 781 +--E 781 ---S 782 of 1092 +--S 782 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 782 +--E 782 ---S 783 of 1092 +--S 783 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 783 +--E 783 )clear all ---S 784 of 1092 +--S 784 of 1092 t0:=x^2/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16316,9 +16227,9 @@ t0:=x^2/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 784 +--E 784 ---S 785 of 1092 +--S 785 of 1092 r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ 1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+_ (b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+_ @@ -16390,9 +16301,9 @@ r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 785 +--E 785 ---S 786 of 1092 +--S 786 of 1092 a0:=integrate(t0,x) --R --R @@ -16461,27 +16372,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 786 +--E 786 ---S 787 of 1092 +--S 787 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 787 +--E 787 ---S 788 of 1092 +--S 788 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 788 +--E 788 )clear all ---S 789 of 1092 +--S 789 of 1092 t0:=x/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16497,9 +16408,9 @@ t0:=x/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 789 +--E 789 ---S 790 of 1092 +--S 790 of 1092 r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ 1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-_ 3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*_ @@ -16559,9 +16470,9 @@ r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 790 +--E 790 ---S 791 of 1092 +--S 791 of 1092 a0:=integrate(t0,x) --R --R @@ -16618,27 +16529,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 791 +--E 791 ---S 792 of 1092 +--S 792 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 792 +--E 792 ---S 793 of 1092 +--S 793 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 793 +--E 793 )clear all ---S 794 of 1092 +--S 794 of 1092 t0:=1/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16654,9 +16565,9 @@ t0:=1/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 794 +--E 794 ---S 795 of 1092 +--S 795 of 1092 r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ 1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_ 6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5 @@ -16715,9 +16626,9 @@ r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 795 +--E 795 ---S 796 of 1092 +--S 796 of 1092 a0:=integrate(t0,x) --R --R @@ -16774,27 +16685,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 796 +--E 796 ---S 797 of 1092 +--S 797 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 797 +--E 797 ---S 798 of 1092 +--S 798 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 798 +--E 798 )clear all ---S 799 of 1092 +--S 799 of 1092 t0:=1/(x*(a+b*x)^3*(c+d*x)^3) --R --R @@ -16810,9 +16721,9 @@ t0:=1/(x*(a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 2 3 3 --R (3a c d + 3a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 799 +--E 799 ---S 800 of 1092 +--S 800 of 1092 r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ (a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/_ (c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-_ @@ -16946,9 +16857,9 @@ r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ --R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 800 +--E 800 ---S 801 of 1092 +--S 801 of 1092 a0:=integrate(t0,x) --R --R @@ -17078,27 +16989,27 @@ a0:=integrate(t0,x) --R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 801 +--E 801 ---S 802 of 1092 +--S 802 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 802 +--E 802 ---S 803 of 1092 +--S 803 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 803 +--E 803 )clear all ---S 804 of 1092 +--S 804 of 1092 t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) --R --R @@ -17114,9 +17025,9 @@ t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 3 2 --R (3a c d + 3a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 804 +--E 804 ---S 805 of 1092 +--S 805 of 1092 r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ (a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*_ (c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-_ @@ -17278,9 +17189,9 @@ r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ --R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 --R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x --R Type: Expression(Integer) ---E 805 +--E 805 ---S 806 of 1092 +--S 806 of 1092 a0:=integrate(t0,x) --R --R @@ -17437,27 +17348,27 @@ a0:=integrate(t0,x) --R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 --R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 806 +--E 806 ---S 807 of 1092 +--S 807 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 807 +--E 807 ---S 808 of 1092 +--S 808 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 808 +--E 808 )clear all ---S 809 of 1092 +--S 809 of 1092 t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) --R --R @@ -17467,9 +17378,9 @@ t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) --R 2 +-------+ --R x \|d x + c --R Type: Expression(Integer) ---E 809 +--E 809 ---S 810 of 1092 +--S 810 of 1092 r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ a^2*sqrt(c+d*x)/(c*x) --R @@ -17483,9 +17394,9 @@ r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ --R +-+ --R c d x\|c --R Type: Expression(Integer) ---E 810 +--E 810 ---S 811 of 1092 +--S 811 of 1092 a0:=integrate(t0,x) --R --R @@ -17510,9 +17421,9 @@ a0:=integrate(t0,x) --R +---+ --R c d x\|- c --R Type: Union(List(Expression(Integer)),...) ---E 811 +--E 811 ---S 812 of 1092 +--S 812 of 1092 m0a:=a0.1-r0 --R --R @@ -17531,17 +17442,17 @@ m0a:=a0.1-r0 --R +-+ --R 2c\|c --R Type: Expression(Integer) ---E 812 +--E 812 ---S 813 of 1092 +--S 813 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 813 +--E 813 ---S 814 of 1092 +--S 814 of 1092 m0b:=a0.2-r0 --R --R @@ -17560,19 +17471,19 @@ m0b:=a0.2-r0 --R +---+ +-+ --R c\|- c \|c --R Type: Expression(Integer) ---E 814 +--E 814 ---S 815 of 1092 +--S 815 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 815 +--E 815 )clear all ---S 816 of 1092 +--S 816 of 1092 t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) --R --R @@ -17582,9 +17493,9 @@ t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 816 +--E 816 ---S 817 of 1092 +--S 817 of 1092 r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ sqrt(c)/a^3-(4*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ sqrt(b*c-a*d)/(a^3*sqrt(b))-2*(b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x)) @@ -17609,9 +17520,9 @@ r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ --R 3 2 4 +-+ --R (a b x + a x)\|b --R Type: Expression(Integer) ---E 817 +--E 817 ---S 818 of 1092 +--S 818 of 1092 a0:=integrate(t0,x) --R --R @@ -17713,9 +17624,9 @@ a0:=integrate(t0,x) --R a b x + a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 818 +--E 818 ---S 819 of 1092 +--S 819 of 1092 m0a:=a0.1-r0 --R --R @@ -17752,17 +17663,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 2a \|b --R Type: Expression(Integer) ---E 819 +--E 819 ---S 820 of 1092 +--S 820 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 820 +--E 820 ---S 821 of 1092 +--S 821 of 1092 m0b:=a0.2-r0 --R --R @@ -17795,19 +17706,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R 2a \|b --R Type: Expression(Integer) ---E 821 +--E 821 ---S 822 of 1092 +--S 822 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 822 +--E 822 )clear all ---S 823 of 1092 +--S 823 of 1092 t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) --R --R @@ -17817,9 +17728,9 @@ t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 823 +--E 823 ---S 824 of 1092 +--S 824 of 1092 r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-_ 2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x)) @@ -17844,9 +17755,9 @@ r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ --R 3 2 4 +-----------+ +-+ --R (a b x + a x)\|- a d + b c \|c --R Type: Expression(Integer) ---E 824 +--E 824 ---S 825 of 1092 +--S 825 of 1092 a0:=integrate(t0,x) --R --R @@ -17956,9 +17867,9 @@ a0:=integrate(t0,x) --R (a b x + a x)\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 825 +--E 825 ---S 826 of 1092 +--S 826 of 1092 m0a:=a0.1-r0 --R --R @@ -17995,17 +17906,17 @@ m0a:=a0.1-r0 --R 3 +-----------+ +-+ --R 2a \|- a d + b c \|c --R Type: Expression(Integer) ---E 826 +--E 826 ---S 827 of 1092 +--S 827 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 827 +--E 827 ---S 828 of 1092 +--S 828 of 1092 m0b:=a0.2-r0 --R --R @@ -18038,19 +17949,19 @@ m0b:=a0.2-r0 --R 3 +-----------+ +-+ --R 2a \|- a d + b c \|c --R Type: Expression(Integer) ---E 828 +--E 828 ---S 829 of 1092 +--S 829 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 829 +--E 829 )clear all ---S 830 of 1092 +--S 830 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) --R --R @@ -18059,9 +17970,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) --R 2 4 3 2 2 +-------+ --R (b x + 2a b x + a x )\|d x + c --R Type: Expression(Integer) ---E 830 +--E 830 ---S 831 of 1092 +--S 831 of 1092 r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ (4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*_ (b*c-a*d)^(3/2))-b*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*c*(b*c-a*d)*(a+b*x))-_ @@ -18093,9 +18004,9 @@ r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ --R 4 3 2 2 2 5 4 2 +-----------+ +-+ --R ((a b c d - a b c )x + (a c d - a b c )x)\|- a d + b c \|c --R Type: Expression(Integer) ---E 831 +--E 831 ---S 832 of 1092 +--S 832 of 1092 a0:=integrate(t0,x) --R --R @@ -18211,9 +18122,9 @@ a0:=integrate(t0,x) --R ((a b c d - a b c )x + (a c d - a b c )x)\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 832 +--E 832 ---S 833 of 1092 +--S 833 of 1092 m0a:=a0.1-r0 --R --R @@ -18250,17 +18161,17 @@ m0a:=a0.1-r0 --R 4 3 2 +-----------+ +-+ --R (2a c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 833 +--E 833 ---S 834 of 1092 +--S 834 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 834 +--E 834 ---S 835 of 1092 +--S 835 of 1092 m0b:=a0.2-r0 --R --R @@ -18298,19 +18209,19 @@ m0b:=a0.2-r0 --R 4 3 2 +-----------+ +-+ --R (2a c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 835 +--E 835 ---S 836 of 1092 +--S 836 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 836 +--E 836 )clear all ---S 837 of 1092 +--S 837 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) --R --R @@ -18319,9 +18230,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) --R 2 5 2 4 2 3 2 2 +-------+ --R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c --R Type: Expression(Integer) ---E 837 +--E 837 ---S 838 of 1092 +--S 838 of 1092 r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ (4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a^3*(b*c-a*d)^(5/2))-d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/_ @@ -18366,9 +18277,9 @@ r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ --R +-----------+ +-+ +-------+ --R \|- a d + b c \|c \|d x + c --R Type: Expression(Integer) ---E 838 +--E 838 ---S 839 of 1092 +--S 839 of 1092 a0:=integrate(t0,x) --R --R @@ -18550,9 +18461,9 @@ a0:=integrate(t0,x) --R \|- c \|d x + c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 839 +--E 839 ---S 840 of 1092 +--S 840 of 1092 m0a:=a0.1-r0 --R --R @@ -18592,17 +18503,17 @@ m0a:=a0.1-r0 --R 5 2 2 4 3 3 2 4 +-----------+ +-+ --R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 840 +--E 840 ---S 841 of 1092 +--S 841 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 841 +--E 841 ---S 842 of 1092 +--S 842 of 1092 m0b:=a0.2-r0 --R --R @@ -18643,19 +18554,19 @@ m0b:=a0.2-r0 --R 5 2 2 4 3 3 2 4 +-----------+ +-+ --R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 842 +--E 842 ---S 843 of 1092 +--S 843 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 843 +--E 843 )clear all ---S 844 of 1092 +--S 844 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) --R --R @@ -18671,9 +18582,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) --R +-------+ --R \|d x + c --R Type: Expression(Integer) ---E 844 +--E 844 ---S 845 of 1092 +--S 845 of 1092 r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ (c+d*x)^(3/2))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+_ (-1)/(a*c*x*(a+b*x)*(c+d*x)^(3/2))+(4*b*c+5*a*d)*atanh(sqrt(c+d*x)/_ @@ -18737,9 +18648,9 @@ r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ --R +-----------+ +-+ +-------+ --R \|- a d + b c \|c \|d x + c --R Type: Expression(Integer) ---E 845 +--E 845 ---S 846 of 1092 +--S 846 of 1092 a0:=integrate(t0,x) --R --R @@ -19001,9 +18912,9 @@ a0:=integrate(t0,x) --R \|- c \|d x + c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 846 +--E 846 ---S 847 of 1092 +--S 847 of 1092 m0a:=a0.1-r0 --R --R @@ -19046,17 +18957,17 @@ m0a:=a0.1-r0 --R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ --R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 847 +--E 847 ---S 848 of 1092 +--S 848 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 848 +--E 848 ---S 849 of 1092 +--S 849 of 1092 m0b:=a0.2-r0 --R --R @@ -19100,19 +19011,19 @@ m0b:=a0.2-r0 --R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ --R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 849 +--E 849 ---S 850 of 1092 +--S 850 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 850 +--E 850 )clear all ---S 851 of 1092 +--S 851 of 1092 t0:=x^3*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19121,9 +19032,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x) --R (1) --------------------------------- --R b x + a --R Type: Expression(Integer) ---E 851 +--E 851 ---S 852 of 1092 +--S 852 of 1092 r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ 495*a^2*b*c*d^2-693*a^3*d^3)*(c+d*x)^(5/2)/(b^4*d^3)-2/693*_ (20*b^2*c^2+55*a*b*c*d-99*a^2*d^2)*x*(c+d*x)^(5/2)/(b^3*d^2)+_ @@ -19166,9 +19077,9 @@ r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ --R 6 3 +-+ --R 3465b d \|b --R Type: Expression(Integer) ---E 852 +--E 852 ---S 853 of 1092 +--S 853 of 1092 a0:=integrate(t0,x) --R --R @@ -19244,9 +19155,9 @@ a0:=integrate(t0,x) --R 3465b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 853 +--E 853 ---S 854 of 1092 +--S 854 of 1092 m0a:=a0.1-r0 --R --R @@ -19272,17 +19183,17 @@ m0a:=a0.1-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 854 +--E 854 ---S 855 of 1092 +--S 855 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 855 +--E 855 ---S 856 of 1092 +--S 856 of 1092 m0b:=a0.2-r0 --R --R @@ -19304,19 +19215,19 @@ m0b:=a0.2-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 856 +--E 856 ---S 857 of 1092 +--S 857 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 857 +--E 857 )clear all ---S 858 of 1092 +--S 858 of 1092 t0:=x^2*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19325,9 +19236,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x) --R (1) --------------------------------- --R b x + a --R Type: Expression(Integer) ---E 858 +--E 858 ---S 859 of 1092 +--S 859 of 1092 r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ 2/63*(2*b*c+9*a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*x*(c+d*x)^(7/2)/(b*d)-_ 2*a^2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/_ @@ -19362,9 +19273,9 @@ r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ --R 5 2 +-+ --R 315b d \|b --R Type: Expression(Integer) ---E 859 +--E 859 ---S 860 of 1092 +--S 860 of 1092 a0:=integrate(t0,x) --R --R @@ -19428,9 +19339,9 @@ a0:=integrate(t0,x) --R 315b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 860 +--E 860 ---S 861 of 1092 +--S 861 of 1092 m0a:=a0.1-r0 --R --R @@ -19456,17 +19367,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 861 +--E 861 ---S 862 of 1092 +--S 862 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 862 +--E 862 ---S 863 of 1092 +--S 863 of 1092 m0b:=a0.2-r0 --R --R @@ -19488,19 +19399,19 @@ m0b:=a0.2-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 863 +--E 863 ---S 864 of 1092 +--S 864 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 864 +--E 864 )clear all ---S 865 of 1092 +--S 865 of 1092 t0:=x*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19509,9 +19420,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x) --R (1) -------------------------------- --R b x + a --R Type: Expression(Integer) ---E 865 +--E 865 ---S 866 of 1092 +--S 866 of 1092 r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ 2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_ sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4 @@ -19539,9 +19450,9 @@ r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ --R 4 +-+ --R 105b d\|b --R Type: Expression(Integer) ---E 866 +--E 866 ---S 867 of 1092 +--S 867 of 1092 a0:=integrate(t0,x) --R --R @@ -19599,9 +19510,9 @@ a0:=integrate(t0,x) --R 105b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 867 +--E 867 ---S 868 of 1092 +--S 868 of 1092 m0a:=a0.1-r0 --R --R @@ -19627,17 +19538,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 868 +--E 868 ---S 869 of 1092 +--S 869 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 869 +--E 869 ---S 870 of 1092 +--S 870 of 1092 m0b:=a0.2-r0 --R --R @@ -19659,19 +19570,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 870 +--E 870 ---S 871 of 1092 +--S 871 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 871 +--E 871 )clear all ---S 872 of 1092 +--S 872 of 1092 t0:=(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19680,9 +19591,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x) --R (1) ------------------------------ --R b x + a --R Type: Expression(Integer) ---E 872 +--E 872 ---S 873 of 1092 +--S 873 of 1092 r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*_ sqrt(c+d*x)/b^3 @@ -19704,9 +19615,9 @@ r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ --R 3 +-+ --R 15b \|b --R Type: Expression(Integer) ---E 873 +--E 873 ---S 874 of 1092 +--S 874 of 1092 a0:=integrate(t0,x) --R --R @@ -19752,9 +19663,9 @@ a0:=integrate(t0,x) --R 15b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 874 +--E 874 ---S 875 of 1092 +--S 875 of 1092 m0a:=a0.1-r0 --R --R @@ -19780,17 +19691,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 875 +--E 875 ---S 876 of 1092 +--S 876 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 876 +--E 876 ---S 877 of 1092 +--S 877 of 1092 m0b:=a0.2-r0 --R --R @@ -19812,19 +19723,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 877 +--E 877 ---S 878 of 1092 +--S 878 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 878 +--E 878 )clear all ---S 879 of 1092 +--S 879 of 1092 t0:=(c+d*x)^(5/2)/(x*(a+b*x)) --R --R @@ -19834,9 +19745,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Expression(Integer) ---E 879 +--E 879 ---S 880 of 1092 +--S 880 of 1092 r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2 @@ -19861,9 +19772,9 @@ r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ --R 2 +-+ --R 3a b \|b --R Type: Expression(Integer) ---E 880 +--E 880 ---S 881 of 1092 +--S 881 of 1092 a0:=integrate(t0,x) --R --R @@ -19956,9 +19867,9 @@ a0:=integrate(t0,x) --R 3a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 881 +--E 881 ---S 882 of 1092 +--S 882 of 1092 m0a:=a0.1-r0 --R --R @@ -19995,17 +19906,17 @@ m0a:=a0.1-r0 --R 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 882 +--E 882 ---S 883 of 1092 +--S 883 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 883 +--E 883 ---S 884 of 1092 +--S 884 of 1092 m0b:=a0.2-r0 --R --R @@ -20038,19 +19949,19 @@ m0b:=a0.2-r0 --R 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 884 +--E 884 ---S 885 of 1092 +--S 885 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 885 +--E 885 )clear all ---S 886 of 1092 +--S 886 of 1092 t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) --R --R @@ -20060,9 +19971,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Expression(Integer) ---E 886 +--E 886 ---S 887 of 1092 +--S 887 of 1092 r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ atanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+_ @@ -20088,9 +19999,9 @@ r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ --R 2 +-+ --R a b x\|b --R Type: Expression(Integer) ---E 887 +--E 887 ---S 888 of 1092 +--S 888 of 1092 a0:=integrate(t0,x) --R --R @@ -20183,9 +20094,9 @@ a0:=integrate(t0,x) --R a b x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 888 +--E 888 ---S 889 of 1092 +--S 889 of 1092 m0a:=a0.1-r0 --R --R @@ -20222,17 +20133,17 @@ m0a:=a0.1-r0 --R 2 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 889 +--E 889 ---S 890 of 1092 +--S 890 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 890 +--E 890 ---S 891 of 1092 +--S 891 of 1092 m0b:=a0.2-r0 --R --R @@ -20265,19 +20176,19 @@ m0b:=a0.2-r0 --R 2 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 891 +--E 891 ---S 892 of 1092 +--S 892 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 892 +--E 892 )clear all ---S 893 of 1092 +--S 893 of 1092 t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) --R --R @@ -20287,9 +20198,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Expression(Integer) ---E 893 +--E 893 ---S 894 of 1092 +--S 894 of 1092 r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*_ @@ -20316,9 +20227,9 @@ r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ --R 3 2 +-+ --R 4a x \|b --R Type: Expression(Integer) ---E 894 +--E 894 ---S 895 of 1092 +--S 895 of 1092 a0:=integrate(t0,x) --R --R @@ -20414,9 +20325,9 @@ a0:=integrate(t0,x) --R 4a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 895 +--E 895 ---S 896 of 1092 +--S 896 of 1092 m0a:=a0.1-r0 --R --R @@ -20453,17 +20364,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 896 +--E 896 ---S 897 of 1092 +--S 897 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 897 +--E 897 ---S 898 of 1092 +--S 898 of 1092 m0b:=a0.2-r0 --R --R @@ -20496,19 +20407,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 898 +--E 898 ---S 899 of 1092 +--S 899 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 899 +--E 899 )clear all ---S 900 of 1092 +--S 900 of 1092 t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) --R --R @@ -20518,9 +20429,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Expression(Integer) ---E 900 +--E 900 ---S 901 of 1092 +--S 901 of 1092 r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*_ @@ -20553,9 +20464,9 @@ r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ --R 4 3 +-+ --R 24a x \|c --R Type: Expression(Integer) ---E 901 +--E 901 ---S 902 of 1092 +--S 902 of 1092 a0:=integrate(t0,x) --R --R @@ -20681,9 +20592,9 @@ a0:=integrate(t0,x) --R 24a x \|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 902 +--E 902 ---S 903 of 1092 +--S 903 of 1092 m0a:=a0.1-r0 --R --R @@ -20721,17 +20632,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 903 +--E 903 ---S 904 of 1092 +--S 904 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 904 +--E 904 ---S 905 of 1092 +--S 905 of 1092 m0b:=a0.2-r0 --R --R @@ -20766,19 +20677,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 905 +--E 905 ---S 906 of 1092 +--S 906 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 906 +--E 906 )clear all ---S 907 of 1092 +--S 907 of 1092 t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -20788,9 +20699,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 907 +--E 907 ---S 908 of 1092 +--S 908 of 1092 r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ 180*a*b*c*d-693*a^2*d^2)*(c+d*x)^(5/2)/(b^4*d^2)+_ 1/63*(10*b*c-99*a*d)*x*(c+d*x)^(5/2)/(b^3*d)+11/9*x^2*(c+d*x)^(5/2)/_ @@ -20833,9 +20744,9 @@ r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ --R 7 2 6 2 +-+ --R (315b d x + 315a b d )\|b --R Type: Expression(Integer) ---E 908 +--E 908 ---S 909 of 1092 +--S 909 of 1092 a0:=integrate(t0,x) --R --R @@ -20912,9 +20823,9 @@ a0:=integrate(t0,x) --R 315b d x + 315a b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 909 +--E 909 ---S 910 of 1092 +--S 910 of 1092 m0a:=a0.1-r0 --R --R @@ -20940,17 +20851,17 @@ m0a:=a0.1-r0 --R 6 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 910 +--E 910 ---S 911 of 1092 +--S 911 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 911 +--E 911 ---S 912 of 1092 +--S 912 of 1092 m0b:=a0.2-r0 --R --R @@ -20972,19 +20883,19 @@ m0b:=a0.2-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 912 +--E 912 ---S 913 of 1092 +--S 913 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 913 +--E 913 )clear all ---S 914 of 1092 +--S 914 of 1092 t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -20994,9 +20905,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 914 +--E 914 ---S 915 of 1092 +--S 915 of 1092 r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ (c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-_ a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*_ @@ -21035,9 +20946,9 @@ r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ --R 6 5 +-+ --R (105b d x + 105a b d)\|b --R Type: Expression(Integer) ---E 915 +--E 915 ---S 916 of 1092 +--S 916 of 1092 a0:=integrate(t0,x) --R --R @@ -21108,9 +21019,9 @@ a0:=integrate(t0,x) --R 105b d x + 105a b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 916 +--E 916 ---S 917 of 1092 +--S 917 of 1092 m0a:=a0.1-r0 --R --R @@ -21136,17 +21047,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 917 +--E 917 ---S 918 of 1092 +--S 918 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 918 +--E 918 ---S 919 of 1092 +--S 919 of 1092 m0b:=a0.2-r0 --R --R @@ -21168,19 +21079,19 @@ m0b:=a0.2-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 919 +--E 919 ---S 920 of 1092 +--S 920 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 920 +--E 920 )clear all ---S 921 of 1092 +--S 921 of 1092 t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -21190,9 +21101,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 921 +--E 921 ---S 922 of 1092 +--S 922 of 1092 r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ (b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*_ (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+_ @@ -21224,9 +21135,9 @@ r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ --R 5 4 +-+ --R (15b x + 15a b )\|b --R Type: Expression(Integer) ---E 922 +--E 922 ---S 923 of 1092 +--S 923 of 1092 a0:=integrate(t0,x) --R --R @@ -21285,9 +21196,9 @@ a0:=integrate(t0,x) --R 15b x + 15a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 923 +--E 923 ---S 924 of 1092 +--S 924 of 1092 m0a:=a0.1-r0 --R --R @@ -21313,17 +21224,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 924 +--E 924 ---S 925 of 1092 +--S 925 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 925 +--E 925 ---S 926 of 1092 +--S 926 of 1092 m0b:=a0.2-r0 --R --R @@ -21345,19 +21256,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 926 +--E 926 ---S 927 of 1092 +--S 927 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 927 +--E 927 )clear all ---S 928 of 1092 +--S 928 of 1092 t0:=(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -21367,9 +21278,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 928 +--E 928 ---S 929 of 1092 +--S 929 of 1092 r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*_ sqrt(c+d*x)/b^3 @@ -21394,9 +21305,9 @@ r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ --R 4 3 +-+ --R (3b x + 3a b )\|b --R Type: Expression(Integer) ---E 929 +--E 929 ---S 930 of 1092 +--S 930 of 1092 a0:=integrate(t0,x) --R --R @@ -21447,9 +21358,9 @@ a0:=integrate(t0,x) --R 3b x + 3a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 930 +--E 930 ---S 931 of 1092 +--S 931 of 1092 m0a:=a0.1-r0 --R --R @@ -21475,17 +21386,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 931 +--E 931 ---S 932 of 1092 +--S 932 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 932 +--E 932 ---S 933 of 1092 +--S 933 of 1092 m0b:=a0.2-r0 --R --R @@ -21507,19 +21418,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 933 +--E 933 ---S 934 of 1092 +--S 934 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 934 +--E 934 )clear all ---S 935 of 1092 +--S 935 of 1092 t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) --R --R @@ -21529,9 +21440,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 935 +--E 935 ---S 936 of 1092 +--S 936 of 1092 r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ atanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_ @@ -21560,9 +21471,9 @@ r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ --R 2 3 3 2 +-+ --R (a b x + a b )\|b --R Type: Expression(Integer) ---E 936 +--E 936 ---S 937 of 1092 +--S 937 of 1092 a0:=integrate(t0,x) --R --R @@ -21660,9 +21571,9 @@ a0:=integrate(t0,x) --R a b x + a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 937 +--E 937 ---S 938 of 1092 +--S 938 of 1092 m0a:=a0.1-r0 --R --R @@ -21699,17 +21610,17 @@ m0a:=a0.1-r0 --R 2 2 +-+ --R 2a b \|b --R Type: Expression(Integer) ---E 938 +--E 938 ---S 939 of 1092 +--S 939 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 939 +--E 939 ---S 940 of 1092 +--S 940 of 1092 m0b:=a0.2-r0 --R --R @@ -21742,19 +21653,19 @@ m0b:=a0.2-r0 --R 2 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 940 +--E 940 ---S 941 of 1092 +--S 941 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 941 +--E 941 )clear all ---S 942 of 1092 +--S 942 of 1092 t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) --R --R @@ -21764,9 +21675,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 942 +--E 942 ---S 943 of 1092 +--S 943 of 1092 r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-_ c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x)) @@ -21797,9 +21708,9 @@ r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ --R 3 2 2 4 +-+ --R (a b x + a b x)\|b --R Type: Expression(Integer) ---E 943 +--E 943 ---S 944 of 1092 +--S 944 of 1092 r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))+_ @@ -21831,9 +21742,9 @@ r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ --R 3 2 2 4 +-+ --R (a b x + a b x)\|b --R Type: Expression(Integer) ---E 944 +--E 944 ---S 945 of 1092 +--S 945 of 1092 a0:=integrate(t0,x) --R --R @@ -21943,9 +21854,9 @@ a0:=integrate(t0,x) --R a b x + a b x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 945 +--E 945 ---S 946 of 1092 +--S 946 of 1092 m0a:=a0.1-r0a --R --R @@ -21982,17 +21893,17 @@ m0a:=a0.1-r0a --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 946 +--E 946 ---S 947 of 1092 +--S 947 of 1092 d0a:=D(m0a,x) --R --R --R (6) 0 --R Type: Expression(Integer) ---E 947 +--E 947 ---S 948 of 1092 +--S 948 of 1092 m0b:=a0.1-r0b --R --R @@ -22029,17 +21940,17 @@ m0b:=a0.1-r0b --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 948 +--E 948 ---S 949 of 1092 +--S 949 of 1092 d0b:=D(m0b,x) --R --R --R (8) 0 --R Type: Expression(Integer) ---E 949 +--E 949 ---S 950 of 1092 +--S 950 of 1092 m0c:=a0.2-r0a --R --R @@ -22072,17 +21983,17 @@ m0c:=a0.2-r0a --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 950 +--E 950 ---S 951 of 1092 +--S 951 of 1092 d0c:=D(m0c,x) --R --R --R (10) 0 --R Type: Expression(Integer) ---E 951 +--E 951 ---S 952 of 1092 +--S 952 of 1092 m0d:=a0.2-r0b --R --R @@ -22115,19 +22026,19 @@ m0d:=a0.2-r0b --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 952 +--E 952 ---S 953 of 1092 +--S 953 of 1092 d0d:=D(m0d,x) --R --R --R (12) 0 --R Type: Expression(Integer) ---E 953 +--E 953 )clear all ---S 954 of 1092 +--S 954 of 1092 t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) --R --R @@ -22137,9 +22048,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 954 +--E 954 ---S 955 of 1092 +--S 955 of 1092 r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ (a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/_ sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*_ @@ -22178,9 +22089,9 @@ r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ --R 4 3 5 2 +-+ --R (4a b x + 4a x )\|b --R Type: Expression(Integer) ---E 955 +--E 955 ---S 956 of 1092 +--S 956 of 1092 a0:=integrate(t0,x) --R --R @@ -22314,9 +22225,9 @@ a0:=integrate(t0,x) --R 4a b x + 4a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 956 +--E 956 ---S 957 of 1092 +--S 957 of 1092 m0a:=a0.1-r0 --R --R @@ -22353,17 +22264,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 957 +--E 957 ---S 958 of 1092 +--S 958 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 958 +--E 958 ---S 959 of 1092 +--S 959 of 1092 m0b:=a0.2-r0 --R --R @@ -22396,19 +22307,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 959 +--E 959 ---S 960 of 1092 +--S 960 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 960 +--E 960 )clear all ---S 961 of 1092 +--S 961 of 1092 t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) --R --R @@ -22418,9 +22329,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 961 +--E 961 ---S 962 of 1092 +--S 962 of 1092 r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ (a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_ sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-_ @@ -22467,9 +22378,9 @@ r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ --R 5 4 6 3 +-+ --R (24a b x + 24a x )\|c --R Type: Expression(Integer) ---E 962 +--E 962 ---S 963 of 1092 +--S 963 of 1092 a0:=integrate(t0,x) --R --R @@ -22635,9 +22546,9 @@ a0:=integrate(t0,x) --R (24a b x + 24a x )\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 963 +--E 963 ---S 964 of 1092 +--S 964 of 1092 m0a:=a0.1-r0 --R --R @@ -22678,17 +22589,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 964 +--E 964 ---S 965 of 1092 +--S 965 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 965 +--E 965 ---S 966 of 1092 +--S 966 of 1092 m0b:=a0.2-r0 --R --R @@ -22726,28 +22637,28 @@ m0b:=a0.2-r0 --R 5 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 966 +--E 966 ---S 967 of 1092 +--S 967 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 967 +--E 967 )clear all ---S 968 of 1092 +--S 968 of 1092 t0:=x^3*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R 3 +-------+ +-------+ --R (1) x \|b x + a \|d x + c --R Type: Expression(Integer) ---E 968 +--E 968 ---S 969 of 1092 +--S 969 of 1092 r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-_ 1/960*(105*b^3*c^3-5*a*b^2*c^2*d-17*a^2*b*c*d^2-35*a^3*d^3)*_ @@ -22786,32 +22697,32 @@ r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ --R 4 4 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 969 +--E 969 ---S 970 of 1092 +--S 970 of 1092 --a0:=integrate(t0,x) ---E 970 +--E 970 ---S 971 of 1092 +--S 971 of 1092 --m0:=a0-r0 ---E 971 +--E 971 ---S 972 of 1092 +--S 972 of 1092 --d0:=D(m0,x) ---E 972 +--E 972 )clear all ---S 973 of 1092 +--S 973 of 1092 t0:=x^2*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R 2 +-------+ +-------+ --R (1) x \|b x + a \|d x + c --R Type: Expression(Integer) ---E 973 +--E 973 ---S 974 of 1092 +--S 974 of 1092 r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ (a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*_ (4*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ @@ -22845,32 +22756,32 @@ r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ --R 3 3 +-+ +-+ --R 192b d \|b \|d --R Type: Expression(Integer) ---E 974 +--E 974 ---S 975 of 1092 +--S 975 of 1092 --a0:=integrate(t0,x) ---E 975 +--E 975 ---S 976 of 1092 +--S 976 of 1092 --m0:=a0-r0 ---E 976 +--E 976 ---S 977 of 1092 +--S 977 of 1092 --d0:=D(m0,x) ---E 977 +--E 977 )clear all ---S 978 of 1092 +--S 978 of 1092 t0:=x*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R +-------+ +-------+ --R (1) x\|b x + a \|d x + c --R Type: Expression(Integer) ---E 978 +--E 978 ---S 979 of 1092 +--S 979 of 1092 r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ 1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*_ @@ -22893,32 +22804,32 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ --R 2 2 +-+ +-+ --R 24b d \|b \|d --R Type: Expression(Integer) ---E 979 +--E 979 ---S 980 of 1092 +--S 980 of 1092 --a0:=integrate(t0,x) ---E 980 +--E 980 ---S 981 of 1092 +--S 981 of 1092 --m0:=a0-r0 ---E 981 +--E 981 ---S 982 of 1092 +--S 982 of 1092 --d0:=D(m0,x) ---E 982 +--E 982 )clear all ---S 983 of 1092 +--S 983 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x) --R --R --R +-------+ +-------+ --R (1) \|b x + a \|d x + c --R Type: Expression(Integer) ---E 983 +--E 983 ---S 984 of 1092 +--S 984 of 1092 r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ (b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*_ sqrt(a+b*x)*sqrt(c+d*x)/(b*d) @@ -22937,23 +22848,23 @@ r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ --R +-+ +-+ --R 4b d\|b \|d --R Type: Expression(Integer) ---E 984 +--E 984 ---S 985 of 1092 +--S 985 of 1092 --a0:=integrate(t0,x) ---E 985 +--E 985 ---S 986 of 1092 +--S 986 of 1092 --m0:=a0-r0 ---E 986 +--E 986 ---S 987 of 1092 +--S 987 of 1092 --d0:=D(m0,x) ---E 987 +--E 987 )clear all ---S 988 of 1092 +--S 988 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x --R --R @@ -22962,9 +22873,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x --R (1) -------------------- --R x --R Type: Expression(Integer) ---E 988 +--E 988 ---S 989 of 1092 +--S 989 of 1092 r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ (b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ (sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x) @@ -22983,23 +22894,23 @@ r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ --R +-+ +-+ --R \|b \|d --R Type: Expression(Integer) ---E 989 +--E 989 ---S 990 of 1092 (non-algebraic residues) +--S 990 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 990 +--E 990 ---S 991 of 1092 +--S 991 of 1092 --m0:=a0-r0 ---E 991 +--E 991 ---S 992 of 1092 +--S 992 of 1092 --d0:=D(m0,x) ---E 992 +--E 992 )clear all ---S 993 of 1092 +--S 993 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 --R --R @@ -23009,9 +22920,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 993 +--E 993 ---S 994 of 1092 +--S 994 of 1092 r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (sqrt(a)*sqrt(c))+2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x @@ -23033,23 +22944,23 @@ r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R +-+ +-+ --R x\|a \|c --R Type: Expression(Integer) ---E 994 +--E 994 ---S 995 of 1092 +--S 995 of 1092 --a0:=integrate(t0,x) ---E 995 +--E 995 ---S 996 of 1092 +--S 996 of 1092 --m0:=a0-r0 ---E 996 +--E 996 ---S 997 of 1092 +--S 997 of 1092 --d0:=D(m0,x) ---E 997 +--E 997 )clear all ---S 998 of 1092 +--S 998 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 --R --R @@ -23059,9 +22970,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 998 +--E 998 ---S 999 of 1092 +--S 999 of 1092 r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-_ 1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x) @@ -23080,23 +22991,23 @@ r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R 2 +-+ +-+ --R 4a c x \|a \|c --R Type: Expression(Integer) ---E 999 +--E 999 ---S 1000 of 1092 +--S 1000 of 1092 --a0:=integrate(t0,x) ---E 1000 +--E 1000 ---S 1001 of 1092 +--S 1001 of 1092 --m0:=a0-r0 ---E 1001 +--E 1001 ---S 1002 of 1092 +--S 1002 of 1092 --d0:=D(m0,x) ---E 1002 +--E 1002 )clear all ---S 1003 of 1092 +--S 1003 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 --R --R @@ -23106,9 +23017,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 --R 4 --R x --R Type: Expression(Integer) ---E 1003 +--E 1003 ---S 1004 of 1092 +--S 1004 of 1092 r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/x^3-_ 1/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+_ @@ -23131,23 +23042,23 @@ r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ --R 2 2 3 +-+ +-+ --R 24a c x \|a \|c --R Type: Expression(Integer) ---E 1004 +--E 1004 ---S 1005 of 1092 +--S 1005 of 1092 --a0:=integrate(t0,x) ---E 1005 +--E 1005 ---S 1006 of 1092 +--S 1006 of 1092 --m0:=a0-r0 ---E 1006 +--E 1006 ---S 1007 of 1092 +--S 1007 of 1092 --d0:=D(m0,x) ---E 1007 +--E 1007 )clear all ---S 1008 of 1092 +--S 1008 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 --R --R @@ -23157,9 +23068,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 --R 5 --R x --R Type: Expression(Integer) ---E 1008 +--E 1008 ---S 1009 of 1092 +--S 1009 of 1092 r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ 1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*_ @@ -23190,23 +23101,23 @@ r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ --R 3 3 4 +-+ +-+ --R 192a c x \|a \|c --R Type: Expression(Integer) ---E 1009 +--E 1009 ---S 1010 of 1092 +--S 1010 of 1092 --a0:=integrate(t0,x) ---E 1010 +--E 1010 ---S 1011 of 1092 +--S 1011 of 1092 --m0:=a0-r0 ---E 1011 +--E 1011 ---S 1012 of 1092 +--S 1012 of 1092 --d0:=D(m0,x) ---E 1012 +--E 1012 )clear all ---S 1013 of 1092 +--S 1013 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 --R --R @@ -23216,9 +23127,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 --R 6 --R x --R Type: Expression(Integer) ---E 1013 +--E 1013 ---S 1014 of 1092 +--S 1014 of 1092 r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-_ 1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*_ @@ -23258,32 +23169,32 @@ r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ --R 4 4 5 +-+ +-+ --R 1920a c x \|a \|c --R Type: Expression(Integer) ---E 1014 +--E 1014 ---S 1015 of 1092 +--S 1015 of 1092 --a0:=integrate(t0,x) ---E 1015 +--E 1015 ---S 1016 of 1092 +--S 1016 of 1092 --m0:=a0-r0 ---E 1016 +--E 1016 ---S 1017 of 1092 +--S 1017 of 1092 --d0:=D(m0,x) ---E 1017 +--E 1017 )clear all ---S 1018 of 1092 +--S 1018 of 1092 t0:=x^2*(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R 3 2 +-------+ +-------+ --R (1) (d x + c x )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1018 +--E 1018 ---S 1019 of 1092 +--S 1019 of 1092 r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ (b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+_ 1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*_ @@ -23322,32 +23233,32 @@ r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ --R 4 3 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 1019 +--E 1019 ---S 1020 of 1092 +--S 1020 of 1092 --a0:=integrate(t0,x) ---E 1020 +--E 1020 ---S 1021 of 1092 +--S 1021 of 1092 --m0:=a0-r0 ---E 1021 +--E 1021 ---S 1022 of 1092 +--S 1022 of 1092 --d0:=D(m0,x) ---E 1022 +--E 1022 )clear all ---S 1023 of 1092 +--S 1023 of 1092 t0:=x*(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R 2 +-------+ +-------+ --R (1) (d x + c x)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1023 +--E 1023 ---S 1024 of 1092 +--S 1024 of 1092 r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-_ @@ -23380,32 +23291,32 @@ r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ --R 3 2 +-+ +-+ --R 192b d \|b \|d --R Type: Expression(Integer) ---E 1024 +--E 1024 ---S 1025 of 1092 +--S 1025 of 1092 --a0:=integrate(t0,x) ---E 1025 +--E 1025 ---S 1026 of 1092 +--S 1026 of 1092 --m0:=a0-r0 ---E 1026 +--E 1026 ---S 1027 of 1092 +--S 1027 of 1092 --d0:=D(m0,x) ---E 1027 +--E 1027 )clear all ---S 1028 of 1092 +--S 1028 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R +-------+ +-------+ --R (1) (d x + c)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1028 +--E 1028 ---S 1029 of 1092 +--S 1029 of 1092 r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*_ (a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*_ @@ -23428,23 +23339,23 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ --R 2 +-+ +-+ --R 24b d\|b \|d --R Type: Expression(Integer) ---E 1029 +--E 1029 ---S 1030 of 1092 +--S 1030 of 1092 --a0:=integrate(t0,x) ---E 1030 +--E 1030 ---S 1031 of 1092 +--S 1031 of 1092 --m0:=a0-r0 ---E 1031 +--E 1031 ---S 1032 of 1092 +--S 1032 of 1092 --d0:=D(m0,x) ---E 1032 +--E 1032 )clear all ---S 1033 of 1092 +--S 1033 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x --R --R @@ -23453,9 +23364,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x --R (1) ----------------------------- --R x --R Type: Expression(Integer) ---E 1033 +--E 1033 ---S 1034 of 1092 +--S 1034 of 1092 r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+_ @@ -23481,23 +23392,23 @@ r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ --R +-+ +-+ --R 4b\|b \|d --R Type: Expression(Integer) ---E 1034 +--E 1034 ---S 1035 of 1092 (non-algebraic residues) +--S 1035 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1035 +--E 1035 ---S 1036 of 1092 +--S 1036 of 1092 --m0:=a0-r0 ---E 1036 +--E 1036 ---S 1037 of 1092 +--S 1037 of 1092 --d0:=D(m0,x) ---E 1037 +--E 1037 )clear all ---S 1038 of 1092 +--S 1038 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 --R --R @@ -23507,9 +23418,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 1038 +--E 1038 ---S 1039 of 1092 +--S 1039 of 1092 r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ sqrt(c)/sqrt(a)+(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_ (sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*_ @@ -23535,23 +23446,23 @@ r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ --R +-+ +-+ --R x\|a \|b --R Type: Expression(Integer) ---E 1039 +--E 1039 ---S 1040 of 1092 (non-algebraic residues) +--S 1040 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1040 +--E 1040 ---S 1041 of 1092 +--S 1041 of 1092 --m0:=a0-r0 ---E 1041 +--E 1041 ---S 1042 of 1092 +--S 1042 of 1092 --d0:=D(m0,x) ---E 1042 +--E 1042 )clear all ---S 1043 of 1092 +--S 1043 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 --R --R @@ -23561,9 +23472,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 1043 +--E 1043 ---S 1044 of 1092 +--S 1044 of 1092 r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ 1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_ @@ -23590,23 +23501,23 @@ r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ --R 2 +-+ +-+ --R 4a x \|a \|c --R Type: Expression(Integer) ---E 1044 +--E 1044 ---S 1045 of 1092 (non-algebraic residues) +--S 1045 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1045 +--E 1045 ---S 1046 of 1092 +--S 1046 of 1092 --m0:=a0-r0 ---E 1046 +--E 1046 ---S 1047 of 1092 +--S 1047 of 1092 --d0:=D(m0,x) ---E 1047 +--E 1047 )clear all ---S 1048 of 1092 +--S 1048 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 --R --R @@ -23616,9 +23527,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 --R 4 --R x --R Type: Expression(Integer) ---E 1048 +--E 1048 ---S 1049 of 1092 +--S 1049 of 1092 r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-_ 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*_ @@ -23641,23 +23552,23 @@ r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R 2 3 +-+ +-+ --R 24a c x \|a \|c --R Type: Expression(Integer) ---E 1049 +--E 1049 ---S 1050 of 1092 +--S 1050 of 1092 --a0:=integrate(t0,x) ---E 1050 +--E 1050 ---S 1051 of 1092 +--S 1051 of 1092 --m0:=a0-r0 ---E 1051 +--E 1051 ---S 1052 of 1092 +--S 1052 of 1092 --d0:=D(m0,x) ---E 1052 +--E 1052 )clear all ---S 1053 of 1092 +--S 1053 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 --R --R @@ -23667,9 +23578,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 --R 5 --R x --R Type: Expression(Integer) ---E 1053 +--E 1053 ---S 1054 of 1092 +--S 1054 of 1092 r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/4*(c+d*x)^(3/2)*_ sqrt(a+b*x)/x^4-1/24*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+_ @@ -23700,23 +23611,23 @@ r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ --R 3 2 4 +-+ +-+ --R 192a c x \|a \|c --R Type: Expression(Integer) ---E 1054 +--E 1054 ---S 1055 of 1092 +--S 1055 of 1092 --a0:=integrate(t0,x) ---E 1055 +--E 1055 ---S 1056 of 1092 +--S 1056 of 1092 --m0:=a0-r0 ---E 1056 +--E 1056 ---S 1057 of 1092 +--S 1057 of 1092 --d0:=D(m0,x) ---E 1057 +--E 1057 )clear all ---S 1058 of 1092 +--S 1058 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 --R --R @@ -23726,9 +23637,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 --R 6 --R x --R Type: Expression(Integer) ---E 1058 +--E 1058 ---S 1059 of 1092 +--S 1059 of 1092 r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_ 1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*_ @@ -23768,32 +23679,32 @@ r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ --R 4 3 5 +-+ +-+ --R 1920a c x \|a \|c --R Type: Expression(Integer) ---E 1059 +--E 1059 ---S 1060 of 1092 +--S 1060 of 1092 --a0:=integrate(t0,x) ---E 1060 +--E 1060 ---S 1061 of 1092 +--S 1061 of 1092 --m0:=a0-r0 ---E 1061 +--E 1061 ---S 1062 of 1092 +--S 1062 of 1092 --d0:=D(m0,x) ---E 1062 +--E 1062 )clear all ---S 1063 of 1092 +--S 1063 of 1092 t0:=x^2*(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 4 3 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c x )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1063 +--E 1063 ---S 1064 of 1092 +--S 1064 of 1092 r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ (c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*_ @@ -23840,32 +23751,32 @@ r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ --R 5 3 +-+ +-+ --R 7680b d \|b \|d --R Type: Expression(Integer) ---E 1064 +--E 1064 ---S 1065 of 1092 +--S 1065 of 1092 --a0:=integrate(t0,x) ---E 1065 +--E 1065 ---S 1066 of 1092 +--S 1066 of 1092 --m0:=a0-r0 ---E 1066 +--E 1066 ---S 1067 of 1092 +--S 1067 of 1092 --d0:=D(m0,x) ---E 1067 +--E 1067 )clear all ---S 1068 of 1092 +--S 1068 of 1092 t0:=x*(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 3 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c x)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1068 +--E 1068 ---S 1069 of 1092 +--S 1069 of 1092 r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ 1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+_ 1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*_ @@ -23906,32 +23817,32 @@ r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ --R 4 2 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 1069 +--E 1069 ---S 1070 of 1092 +--S 1070 of 1092 --a0:=integrate(t0,x) ---E 1070 +--E 1070 ---S 1071 of 1092 +--S 1071 of 1092 --m0:=a0-r0 ---E 1071 +--E 1071 ---S 1072 of 1092 +--S 1072 of 1092 --d0:=D(m0,x) ---E 1072 +--E 1072 )clear all ---S 1073 of 1092 +--S 1073 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1073 +--E 1073 ---S 1074 of 1092 +--S 1074 of 1092 r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ (c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*_ @@ -23964,23 +23875,23 @@ r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ --R 3 +-+ +-+ --R 192b d\|b \|d --R Type: Expression(Integer) ---E 1074 +--E 1074 ---S 1075 of 1092 +--S 1075 of 1092 --a0:=integrate(t0,x) ---E 1075 +--E 1075 ---S 1076 of 1092 +--S 1076 of 1092 --m0:=a0-r0 ---E 1076 +--E 1076 ---S 1077 of 1092 +--S 1077 of 1092 --d0:=D(m0,x) ---E 1077 +--E 1077 )clear all ---S 1078 of 1092 +--S 1078 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x --R --R @@ -23989,9 +23900,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x --R (1) ---------------------------------------- --R x --R Type: Expression(Integer) ---E 1078 +--E 1078 ---S 1079 of 1092 +--S 1079 of 1092 r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ 1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+_ @@ -24021,23 +23932,23 @@ r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ --R 2 +-+ +-+ --R 24b \|b \|d --R Type: Expression(Integer) ---E 1079 +--E 1079 ---S 1080 of 1092 (non-algebraic residues) +--S 1080 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1080 +--E 1080 ---S 1081 of 1092 +--S 1081 of 1092 --m0:=a0-r0 ---E 1081 +--E 1081 ---S 1082 of 1092 +--S 1082 of 1092 --d0:=D(m0,x) ---E 1082 +--E 1082 )clear all ---S 1083 of 1092 +--S 1083 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 --R --R @@ -24047,9 +23958,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 1083 +--E 1083 ---S 1084 of 1092 +--S 1084 of 1092 r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*_ @@ -24076,23 +23987,23 @@ r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R +-+ +-+ --R 4b x\|a \|b --R Type: Expression(Integer) ---E 1084 +--E 1084 ---S 1085 of 1092 (non-algebraic residues) +--S 1085 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1085 +--E 1085 ---S 1086 of 1092 +--S 1086 of 1092 --m0:=a0-r0 ---E 1086 +--E 1086 ---S 1087 of 1092 +--S 1087 of 1092 --d0:=D(m0,x) ---E 1087 +--E 1087 )clear all ---S 1088 of 1092 +--S 1088 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 --R --R @@ -24102,9 +24013,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 1088 +--E 1088 ---S 1089 of 1092 +--S 1089 of 1092 r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-_ @@ -24132,17 +24043,17 @@ r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ --R 2 +-+ +-+ --R 4a x \|a \|b --R Type: Expression(Integer) ---E 1089 +--E 1089 ---S 1090 of 1092 (non-algebraic residues) +--S 1090 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1090 +--E 1090 ---S 1091 of 1092 +--S 1091 of 1092 --m0:=a0-r0 ---E 1091 +--E 1091 ---S 1092 of 1092 +--S 1092 of 1092 --d0:=D(m0,x) --E 1092 diff --git a/src/axiom-website/CATS/rich3a.input.pdf b/src/axiom-website/CATS/rich3a.input.pdf index 4bb733e..9e0e1fb 100644 Binary files a/src/axiom-website/CATS/rich3a.input.pdf and b/src/axiom-website/CATS/rich3a.input.pdf differ diff --git a/src/axiom-website/CATS/rich3c.input.pamphlet b/src/axiom-website/CATS/rich3c.input.pamphlet index 88bdf31..e55f406 100644 --- a/src/axiom-website/CATS/rich3c.input.pamphlet +++ b/src/axiom-website/CATS/rich3c.input.pamphlet @@ -4200,7 +4200,7 @@ r0:=sqrt(-1+x)*sqrt(1+x) --R Type: Expression(Integer) --E 267 ---S 268 of 500 +--S 268 of 500 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R @@ -4209,7 +4209,7 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 268 ---S 269 of 500 +--S 269 of 500 ok to fail, differs by a constant m0:=a0-r0 --R --R diff --git a/src/axiom-website/CATS/rich3c.input.pdf b/src/axiom-website/CATS/rich3c.input.pdf index 5182c84..8f08e4b 100644 Binary files a/src/axiom-website/CATS/rich3c.input.pdf and b/src/axiom-website/CATS/rich3c.input.pdf differ diff --git a/src/axiom-website/CATS/rich3d.input.pamphlet b/src/axiom-website/CATS/rich3d.input.pamphlet new file mode 100644 index 0000000..12ebaa2 --- /dev/null +++ b/src/axiom-website/CATS/rich3d.input.pamphlet @@ -0,0 +1,5940 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 95 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 5 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3d.output +)spool rich3d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^2) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 2 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 1 + +--S 2 of 500 +--r0:=(-3/37-18/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(%i*x)^(-1-1/6*%i)*_ +-- hypergeometric(1/6*%i,1+1/6*%i,2+1/6*%i,1/2*%i*(2-2*%i*x+%i*(%i+x))/x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^3) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 3 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 6 + +--S 7 of 500 +--r0:=(2/37-1/111*%i)*2^(-1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(3-18*%i+_ +-- 37*x+(3+19*%i)*x^2-2*%i*x^2*_ +-- hypergeometric(1,1+1/6*%i,2+1/6*%i,(%i+x)/(%i-x)))/_ +-- ((%i-x)*x^2*(1+1/2*%i*(%i+x))^(1/6*%i)) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x) +--R +--R +--R 2 m +--R (1) (- 10x - x + 3)(3x + 2) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-7/27*(2+3*x)^(1+m)/(1+m)+37/27*(2+3*x)^(2+m)/(2+m)-_ + 10/27*(2+3*x)^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 m + 3 2 m + 2 +--R (- 10m - 30m - 20)(3x + 2) + (37m + 148m + 111)(3x + 2) +--R + +--R 2 m + 1 +--R (- 7m - 35m - 42)(3x + 2) +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 +--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x +--R + +--R 2 2 +--R (63m + 591m + 486)x + 54m + 282m + 200 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 +--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x +--R + +--R 2 2 +--R (63m + 591m + 486)x + 54m + 282m + 200 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 2 m + 3 2 m + 2 +--R (10m + 30m + 20)(3x + 2) + (- 37m - 148m - 111)(3x + 2) +--R + +--R 2 m + 1 +--R (7m + 35m + 42)(3x + 2) +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 65610x - 356481x - 831789x - 1065312x - 771120x - 247968x +--R + +--R 4 3 2 +--R 62496x + 98304x + 42752x + 8960x + 768 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11 +--R +--R +--R (2) +--R 65610 11 356481 10 9 8 7 6 +--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x +--R 11 10 +--R + +--R 62496 5 4 42752 3 2 756736 +--R ----- x + 24576x + ----- x + 4480x + 768x + ------ +--R 5 3 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 65610 11 356481 10 9 8 7 6 +--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x +--R 11 10 +--R + +--R 62496 5 4 42752 3 2 +--R ----- x + 24576x + ----- x + 4480x + 768x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 756736 +--R (4) - ------ +--R 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 21870x - 104247x - 207765x - 216594x - 112644x - 7560x + 25872x +--R + +--R 2 +--R 15520x + 3904x + 384 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=-7/216*(2+3*x)^8+37/243*(2+3*x)^9-1/27*(2+3*x)^10 +--R +--R +--R (2) +--R 10 9 207765 8 7 6 5 4 +--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x +--R 8 +--R + +--R 15520 3 2 7712 +--R ----- x + 1952x + 384x + ---- +--R 3 243 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 207765 8 7 6 5 4 +--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x +--R 8 +--R + +--R 15520 3 2 +--R ----- x + 1952x + 384x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 7712 +--R (4) - ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x + 1664x +--R + +--R 192 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=-1/27*(2+3*x)^7+37/216*(2+3*x)^8-10/243*(2+3*x)^9 +--R +--R +--R (2) +--R 9 29889 8 7 6 5 4 5264 3 2 +--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x +--R 8 3 +--R + +--R 4384 +--R 192x + ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 29889 8 7 6 5 4 5264 3 2 +--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x +--R 8 3 +--R + +--R 192x +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 4384 +--R (4) - ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=96*x+344*x^2+1600/3*x^3+30*x^4-1170*x^5-3627/2*x^6-8343/7*x^7-1215/4*x^8 +--R +--R +--R 1215 8 8343 7 3627 6 5 4 1600 3 2 +--R (2) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x +--R 4 7 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1215 8 8343 7 3627 6 5 4 1600 3 2 +--R (3) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x +--R 4 7 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) - 810x - 2241x - 2133x - 528x + 392x + 272x + 48 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=48*x+136*x^2+392/3*x^3-132*x^4-2133/5*x^5-747/2*x^6-810/7*x^7 +--R +--R +--R 810 7 747 6 2133 5 4 392 3 2 +--R (2) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x +--R 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 810 7 747 6 2133 5 4 392 3 2 +--R (3) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x +--R 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) - 270x - 567x - 333x + 46x + 100x + 24 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=24*x+50*x^2+46/3*x^3-333/4*x^4-567/5*x^5-45*x^6 +--R +--R +--R 6 567 5 333 4 46 3 2 +--R (2) - 45x - --- x - --- x + -- x + 50x + 24x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 567 5 333 4 46 3 2 +--R (3) - 45x - --- x - --- x + -- x + 50x + 24x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) - 90x - 129x - 25x + 32x + 12 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=12*x+16*x^2-25/3*x^3-129/4*x^4-18*x^5 +--R +--R +--R 5 129 4 25 3 2 +--R (2) - 18x - --- x - -- x + 16x + 12x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 129 4 25 3 2 +--R (3) - 18x - --- x - -- x + 16x + 12x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x) +--R +--R +--R 3 2 +--R (1) - 30x - 23x + 7x + 6 +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 500 +r0:=6*x+7/2*x^2-23/3*x^3-15/2*x^4 +--R +--R +--R 15 4 23 3 7 2 +--R (2) - -- x - -- x + - x + 6x +--R 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 15 4 23 3 7 2 +--R (3) - -- x - -- x + - x + 6x +--R 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)*(3+5*x) +--R +--R +--R 2 +--R (1) - 10x - x + 3 +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 500 +r0:=3*x-1/2*x^2-10/3*x^3 +--R +--R +--R 10 3 1 2 +--R (2) - -- x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 10 3 1 2 +--R (3) - -- x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x) +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) -------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=17/9*x-5/3*x^2-7/27*log(2+3*x) +--R +--R +--R 2 +--R - 7log(3x + 2) - 45x + 51x +--R (2) --------------------------- +--R 27 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 7log(3x + 2) - 45x + 51x +--R (3) --------------------------- +--R 27 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) -------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=-10/9*x+7/27/(2+3*x)+37/27*log(2+3*x) +--R +--R +--R 2 +--R (111x + 74)log(3x + 2) - 90x - 60x + 7 +--R (2) --------------------------------------- +--R 81x + 54 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (111x + 74)log(3x + 2) - 90x - 60x + 7 +--R (3) --------------------------------------- +--R 81x + 54 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=7/54/(2+3*x)^2+(-37/27)/(2+3*x)-10/27*log(2+3*x) +--R +--R +--R 2 +--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141 +--R (2) --------------------------------------------- +--R 2 +--R 486x + 648x + 216 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141 +--R (3) --------------------------------------------- +--R 2 +--R 486x + 648x + 216 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=7/81/(2+3*x)^3+(-37/54)/(2+3*x)^2+10/27/(2+3*x) +--R +--R +--R 10 2 43 16 +--R -- x + --- x + ---- +--R 81 486 2187 +--R (2) -------------------- +--R 3 2 4 8 +--R x + 2x + - x + -- +--R 3 27 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 540x + 387x + 32 +--R (3) ------------------------------ +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=7/108/(2+3*x)^4+(-37/81)/(2+3*x)^3+5/27/(2+3*x)^2 +--R +--R +--R 5 2 23 35 +--R --- x + ---- x - ----- +--R 243 2187 26244 +--R (2) ---------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 540x + 276x - 35 +--R (3) ------------------------------------------- +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=7/135/(2+3*x)^5+(-37/108)/(2+3*x)^4+10/81/(2+3*x)^3 +--R +--R +--R 10 2 49 113 +--R ---- x + ----- x - ------ +--R 2187 26244 196830 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 1800x + 735x - 226 +--R (3) -------------------------------------------------------------- +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^2 +--R +--R +--R 3 2 m +--R (1) (- 50x - 35x + 12x + 9)(3x + 2) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=7/81*(2+3*x)^(1+m)/(1+m)-8/9*(2+3*x)^(2+m)/(2+m)+_ + 65/27*(2+3*x)^(3+m)/(3+m)-50/81*(2+3*x)^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (- 50m - 300m - 550m - 300)(3x + 2) +--R + +--R 3 2 m + 3 +--R (195m + 1365m + 2730m + 1560)(3x + 2) +--R + +--R 3 2 m + 2 +--R (- 72m - 576m - 1368m - 864)(3x + 2) +--R + +--R 3 2 m + 1 +--R (7m + 63m + 182m + 168)(3x + 2) +--R / +--R 4 3 2 +--R 81m + 810m + 2835m + 4050m + 1944 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 +--R (- 1350m - 8100m - 14850m - 8100)x +--R + +--R 3 2 3 +--R (- 1845m - 9315m - 15030m - 7560)x +--R + +--R 3 2 2 3 2 +--R (- 306m + 1242m + 5436m + 3888)x + (459m + 4539m + 9870m + 5832)x +--R + +--R 3 2 +--R 162m + 1314m + 2644m + 1520 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 4 3 2 +--R 27m + 270m + 945m + 1350m + 648 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 +--R (- 4050m - 24300m - 44550m - 24300)x +--R + +--R 3 2 3 +--R (- 5535m - 27945m - 45090m - 22680)x +--R + +--R 3 2 2 +--R (- 918m + 3726m + 16308m + 11664)x +--R + +--R 3 2 3 2 +--R (1377m + 13617m + 29610m + 17496)x + 486m + 3942m + 7932m + 4560 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 3 2 m + 4 +--R (50m + 300m + 550m + 300)(3x + 2) +--R + +--R 3 2 m + 3 +--R (- 195m - 1365m - 2730m - 1560)(3x + 2) +--R + +--R 3 2 m + 2 +--R (72m + 576m + 1368m + 864)(3x + 2) +--R + +--R 3 2 m + 1 +--R (- 7m - 63m - 182m - 168)(3x + 2) +--R / +--R 4 3 2 +--R 81m + 810m + 2835m + 4050m + 1944 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 328050x - 1979235x - 5228388x - 7821927x - 7051536x - 3553200x +--R + +--R 5 4 3 2 +--R - 431424x + 679008x + 508672x + 173056x + 30720x + 2304 +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 500 +r0:=7/729*(2+3*x)^9-4/45*(2+3*x)^10+65/297*(2+3*x)^11-25/486*(2+3*x)^12 +--R +--R +--R (2) +--R 54675 12 1979235 11 2614194 10 9 8 7 +--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x +--R 2 11 5 +--R + +--R 6 679008 5 4 173056 3 2 6070784 +--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x + ------- +--R 5 3 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 54675 12 1979235 11 2614194 10 9 8 7 +--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x +--R 2 11 5 +--R + +--R 6 679008 5 4 173056 3 2 +--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R 6070784 +--R (4) - ------- +--R 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 109350x - 586845x - 1351566x - 1706265x - 1213002x - 375732x +--R + +--R 4 3 2 +--R 106680x + 155216x + 66080x + 13632x + 1152 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=7/648*(2+3*x)^8-8/81*(2+3*x)^9+13/54*(2+3*x)^10-50/891*(2+3*x)^11 +--R +--R +--R (2) +--R 109350 11 117369 10 9 1706265 8 7 6 +--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x +--R 11 2 8 +--R + +--R 5 4 66080 3 2 74656 +--R 21336x + 38804x + ----- x + 6816x + 1152x + ----- +--R 3 891 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 109350 11 117369 10 9 1706265 8 7 6 +--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x +--R 11 2 8 +--R + +--R 5 4 66080 3 2 +--R 21336x + 38804x + ----- x + 6816x + 1152x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 74656 +--R (4) - ----- +--R 891 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 36450x - 171315x - 336312x - 344547x - 174636x - 8820x + 41440x +--R + +--R 2 +--R 24112x + 5952x + 576 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=576*x+2976*x^2+24112/3*x^3+10360*x^4-1764*x^5-29106*x^6-_ + 49221*x^7-42039*x^8-19035*x^9-3645*x^10 +--R +--R +--R (2) +--R 10 9 8 7 6 5 4 +--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x +--R + +--R 24112 3 2 +--R ----- x + 2976x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 6 5 4 +--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x +--R + +--R 24112 3 2 +--R ----- x + 2976x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 12150x - 49005x - 79434x - 61893x - 16950x + 8360x + 8240x + 2544x +--R + +--R 288 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=288*x+1272*x^2+8240/3*x^3+2090*x^4-3390*x^5-20631/2*x^6-79434/7*x^7-_ + 49005/8*x^8-1350*x^9 +--R +--R +--R (2) +--R 9 49005 8 79434 7 20631 6 5 4 8240 3 +--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x +--R 8 7 2 3 +--R + +--R 2 +--R 1272x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 49005 8 79434 7 20631 6 5 4 8240 3 +--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x +--R 8 7 2 3 +--R + +--R 2 +--R 1272x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=144*x+528*x^2+2536/3*x^3+94*x^4-9039/5*x^5-2898*x^6-13635/7*x^7-2025/4*x^8 +--R +--R +--R (2) +--R 2025 8 13635 7 6 9039 5 4 2536 3 2 +--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x +--R 4 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2025 8 13635 7 6 9039 5 4 2536 3 2 +--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x +--R 4 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) - 1350x - 3645x - 3366x - 769x + 638x + 420x + 72 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=72*x+210*x^2+638/3*x^3-769/4*x^4-3366/5*x^5-1215/2*x^6-1350/7*x^7 +--R +--R +--R 1350 7 1215 6 3366 5 769 4 638 3 2 +--R (2) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x +--R 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1350 7 1215 6 3366 5 769 4 638 3 2 +--R (3) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x +--R 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) - 450x - 915x - 512x + 85x + 156x + 36 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6 +--R +--R +--R 6 5 4 85 3 2 +--R (2) - 75x - 183x - 128x + -- x + 78x + 36x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 85 3 2 +--R (3) - 75x - 183x - 128x + -- x + 78x + 36x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--R (1) - 150x - 205x - 34x + 51x + 18 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=18*x+51/2*x^2-34/3*x^3-205/4*x^4-30*x^5 +--R +--R +--R 5 205 4 34 3 51 2 +--R (2) - 30x - --- x - -- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 205 4 34 3 51 2 +--R (3) - 30x - --- x - -- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)*(3+5*x)^2 +--R +--R +--R 3 2 +--R (1) - 50x - 35x + 12x + 9 +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 500 +r0:=9*x+6*x^2-35/3*x^3-25/2*x^4 +--R +--R +--R 25 4 35 3 2 +--R (2) - -- x - -- x + 6x + 9x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 25 4 35 3 2 +--R (3) - -- x - -- x + 6x + 9x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x) +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=118/27*x-5/18*x^2-50/9*x^3+7/81*log(2+3*x) +--R +--R +--R 3 2 +--R 14log(3x + 2) - 900x - 45x + 708x +--R (2) ----------------------------------- +--R 162 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 14log(3x + 2) - 900x - 45x + 708x +--R (3) ----------------------------------- +--R 162 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=95/27*x-25/9*x^2+(-7/81)/(2+3*x)-8/9*log(2+3*x) +--R +--R +--R 3 2 +--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7 +--R (2) ---------------------------------------------------- +--R 243x + 162 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7 +--R (3) ---------------------------------------------------- +--R 243x + 162 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=-50/27*x+(-7/162)/(2+3*x)^2+8/9/(2+3*x)+65/27*log(2+3*x) +--R +--R +--R 2 3 2 +--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281 +--R (2) ----------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281 +--R (3) ----------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-7/243)/(2+3*x)^3+4/9/(2+3*x)^2+(-65/27)/(2+3*x)-50/81*log(2+3*x) +--R +--R +--R 3 2 2 +--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131 +--R (2) --------------------------------------------------------------------- +--R 3 2 +--R 6561x + 13122x + 8748x + 1944 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131 +--R (3) --------------------------------------------------------------------- +--R 3 2 +--R 6561x + 13122x + 8748x + 1944 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=7/12*(3+5*x)^3/(2+3*x)^4+3/4*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 125 4 2300 3 515 2 38 25 +--R --- x + ---- x + --- x + -- x + -- +--R 36 243 54 9 36 +--R (2) ------------------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 600x + 810x + 312x + 25 +--R (3) -------------------------------------- +--R 4 3 2 +--R 2916x + 7776x + 7776x + 3456x + 576 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R 125 +--R (4) - --- +--R 36 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-7/405)/(2+3*x)^5+2/9/(2+3*x)^4+(-65/81)/(2+3*x)^3+25/81/(2+3*x)^2 +--R +--R +--R 25 3 85 2 58 127 +--R --- x + ---- x + ---- x - ----- +--R 729 2187 6561 98415 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 3375x + 3825x + 870x - 127 +--R (3) --------------------------------------------------------- +--R 5 4 3 2 +--R 98415x + 328050x + 437400x + 291600x + 97200x + 12960 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-7/486)/(2+3*x)^6+8/45/(2+3*x)^5+(-65/108)/(2+3*x)^4+50/243/(2+3*x)^3 +--R +--R +--R 50 3 205 2 97 1021 +--R ---- x + ----- x + ----- x - ------- +--R 6561 26244 98415 1771470 +--R (2) ---------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 27000x + 27675x + 3492x - 2042 +--R / +--R 6 5 4 3 2 +--R 3542940x + 14171760x + 23619600x + 20995200x + 10497600x + 2799360x +--R + +--R 311040 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=(-1/81)/(2+3*x)^7+4/27/(2+3*x)^6+(-13/27)/(2+3*x)^5+25/162/(2+3*x)^4 +--R +--R +--R 25 3 4 2 2 11 +--R ----- x + ---- x + ----- x - ----- +--R 13122 2187 19683 59049 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 225x + 216x + 12x - 22 +--R / +--R 7 6 5 4 3 2 +--R 118098x + 551124x + 1102248x + 1224720x + 816480x + 326592x +--R + +--R 72576x + 6912 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^3 +--R +--R +--R 4 3 2 m +--R (1) (- 250x - 325x - 45x + 81x + 27)(3x + 2) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-7/243*(2+3*x)^(1+m)/(1+m)+107/243*(2+3*x)^(2+m)/(2+m)-_ + 185/81*(2+3*x)^(3+m)/(3+m)+1025/243*(2+3*x)^(4+m)/(4+m)-_ + 250/243*(2+3*x)^(5+m)/(5+m) +--R +--R +--R (2) +--R 4 3 2 m + 5 +--R (- 250m - 2500m - 8750m - 12500m - 6000)(3x + 2) +--R + +--R 4 3 2 m + 4 +--R (1025m + 11275m + 42025m + 62525m + 30750)(3x + 2) +--R + +--R 4 3 2 m + 3 +--R (- 555m - 6660m - 27195m - 43290m - 22200)(3x + 2) +--R + +--R 4 3 2 m + 2 +--R (107m + 1391m + 6313m + 11449m + 6420)(3x + 2) +--R + +--R 4 3 2 m + 1 +--R (- 7m - 98m - 497m - 1078m - 840)(3x + 2) +--R / +--R 5 4 3 2 +--R 243m + 3645m + 20655m + 54675m + 66582m + 29160 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 5 +--R (- 20250m - 202500m - 708750m - 1012500m - 486000)x +--R + +--R 4 3 2 4 +--R (- 39825m - 370575m - 1227825m - 1686825m - 789750)x +--R + +--R 4 3 2 3 +--R (- 21195m - 148140m - 368955m - 387810m - 145800)x +--R + +--R 4 3 2 2 +--R (4131m + 96093m + 455229m + 756927m + 393660)x +--R + +--R 4 3 2 4 3 +--R (6561m + 86346m + 343215m + 526038m + 262440)x + 1458m + 17496m +--R + +--R 2 +--R 66366m + 99240m + 48800 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 5 4 3 2 +--R 81m + 1215m + 6885m + 18225m + 22194m + 9720 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 2 5 +--R (- 60750m - 607500m - 2126250m - 3037500m - 1458000)x +--R + +--R 4 3 2 4 +--R (- 119475m - 1111725m - 3683475m - 5060475m - 2369250)x +--R + +--R 4 3 2 3 +--R (- 63585m - 444420m - 1106865m - 1163430m - 437400)x +--R + +--R 4 3 2 2 +--R (12393m + 288279m + 1365687m + 2270781m + 1180980)x +--R + +--R 4 3 2 4 +--R (19683m + 259038m + 1029645m + 1578114m + 787320)x + 4374m +--R + +--R 3 2 +--R 52488m + 199098m + 297720m + 146400 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 4 3 2 m + 5 +--R (250m + 2500m + 8750m + 12500m + 6000)(3x + 2) +--R + +--R 4 3 2 m + 4 +--R (- 1025m - 11275m - 42025m - 62525m - 30750)(3x + 2) +--R + +--R 4 3 2 m + 3 +--R (555m + 6660m + 27195m + 43290m + 22200)(3x + 2) +--R + +--R 4 3 2 m + 2 +--R (- 107m - 1391m - 6313m - 11449m - 6420)(3x + 2) +--R + +--R 4 3 2 m + 1 +--R (7m + 98m + 497m + 1078m + 840)(3x + 2) +--R / +--R 5 4 3 2 +--R 243m + 3645m + 20655m + 54675m + 66582m + 29160 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 +--R - 1640250x - 10880325x - 32079645x - 54794799x - 58723461x +--R + +--R 7 6 5 4 3 2 +--R - 38920608x - 12816720x + 2100768x + 4580384x + 2391296x + 672768x +--R + +--R 103680x + 6912 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=-7/2187*(2+3*x)^9+107/2430*(2+3*x)^10-185/891*(2+3*x)^11+_ + 1025/2916*(2+3*x)^12-250/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 1640250 13 3626775 12 32079645 11 54794799 10 9 +--R - ------- x - ------- x - -------- x - -------- x - 6524829x +--R 13 4 11 10 +--R + +--R 8 7 6 4580384 5 4 3 +--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x +--R 5 +--R + +--R 2 640642048 +--R 51840x + 6912x + --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1640250 13 3626775 12 32079645 11 54794799 10 9 +--R - ------- x - ------- x - -------- x - -------- x - 6524829x +--R 13 4 11 10 +--R + +--R 8 7 6 4580384 5 4 3 +--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x +--R 5 +--R + +--R 2 +--R 51840x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 640642048 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 546750x - 3262275x - 8518365x - 12586023x - 11183805x - 5517666x +--R + +--R 5 4 3 2 +--R - 593796x + 1096120x + 796048x + 266400x + 46656x + 3456 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=3456*x+23328*x^2+88800*x^3+199012*x^4+219224*x^5-98966*x^6-_ + 788238*x^7-11183805/8*x^8-1398447*x^9-1703673/2*x^10-_ + 3262275/11*x^11-91125/2*x^12 +--R +--R +--R (2) +--R 91125 12 3262275 11 1703673 10 9 11183805 8 +--R - ----- x - ------- x - ------- x - 1398447x - -------- x +--R 2 11 2 8 +--R + +--R 7 6 5 4 3 2 +--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 91125 12 3262275 11 1703673 10 9 11183805 8 +--R - ----- x - ------- x - ------- x - 1398447x - -------- x +--R 2 11 2 8 +--R + +--R 7 6 5 4 3 2 +--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 182250x - 965925x - 2195505x - 2731671x - 1906821x - 568008x +--R + +--R 4 3 2 +--R 180740x + 244880x + 102096x + 20736x + 1728 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=1728*x+10368*x^2+34032*x^3+61220*x^4+36148*x^5-94668*x^6-_ + 272403*x^7-2731671/8*x^8-243945*x^9-193185/2*x^10-182250/11*x^11 +--R +--R +--R (2) +--R 182250 11 193185 10 9 2731671 8 7 6 +--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x +--R 11 2 8 +--R + +--R 5 4 3 2 +--R 36148x + 61220x + 34032x + 10368x + 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 182250 11 193185 10 9 2731671 8 7 6 +--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x +--R 11 2 8 +--R + +--R 5 4 3 2 +--R 36148x + 61220x + 34032x + 10368x + 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 60750x - 281475x - 544185x - 547767x - 270429x - 9050x + 66280x +--R + +--R 2 +--R 37440x + 9072x + 864 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=864*x+4536*x^2+12480*x^3+16570*x^4-1810*x^5-90143/2*x^6-_ + 547767/7*x^7-544185/8*x^8-31275*x^9-6075*x^10 +--R +--R +--R (2) +--R 10 9 544185 8 547767 7 90143 6 5 4 +--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x +--R 8 7 2 +--R + +--R 3 2 +--R 12480x + 4536x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 544185 8 547767 7 90143 6 5 4 +--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x +--R 8 7 2 +--R + +--R 3 2 +--R 12480x + 4536x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x +--R + +--R 3888x + 432 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=432*x+1944*x^2+4296*x^3+3452*x^4-25237/5*x^5-32453/2*x^6-_ + 127845/7*x^7-80325/8*x^8-2250*x^9 +--R +--R +--R (2) +--R 9 80325 8 127845 7 32453 6 25237 5 4 3 +--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x +--R 8 7 2 5 +--R + +--R 2 +--R 1944x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 80325 8 127845 7 32453 6 25237 5 4 3 +--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x +--R 8 7 2 5 +--R + +--R 2 +--R 1944x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-_ + 22275/7*x^7-3375/4*x^8 +--R +--R +--R (2) +--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2 +--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x +--R 4 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2 +--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x +--R 4 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) - 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=108*x+324*x^2+345*x^3-1111/4*x^4-1061*x^5-1975/2*x^6-2250/7*x^7 +--R +--R +--R 2250 7 1975 6 5 1111 4 3 2 +--R (2) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x +--R 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2250 7 1975 6 5 1111 4 3 2 +--R (3) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x +--R 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R (1) - 750x - 1475x - 785x + 153x + 243x + 54 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=54*x+243/2*x^2+51*x^3-785/4*x^4-295*x^5-125*x^6 +--R +--R +--R 6 5 785 4 3 243 2 +--R (2) - 125x - 295x - --- x + 51x + --- x + 54x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 785 4 3 243 2 +--R (3) - 125x - 295x - --- x + 51x + --- x + 54x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)*(3+5*x)^3 +--R +--R +--R 4 3 2 +--R (1) - 250x - 325x - 45x + 81x + 27 +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 500 +r0:=27*x+81/2*x^2-15*x^3-325/4*x^4-50*x^5 +--R +--R +--R 5 325 4 3 81 2 +--R (2) - 50x - --- x - 15x + -- x + 27x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 325 4 3 81 2 +--R (3) - 50x - --- x - 15x + -- x + 27x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x) +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1097/81*x+545/54*x^2-475/27*x^3-125/6*x^4-7/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x +--R (2) --------------------------------------------------- +--R 486 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x +--R (3) --------------------------------------------------- +--R 486 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=55/9*x+25/54*x^2-250/27*x^3+7/243/(2+3*x)+107/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14 +--R (2) ---------------------------------------------------------------- +--R 1458x + 972 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14 +--R (3) ---------------------------------------------------------------- +--R 1458x + 972 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=175/27*x-125/27*x^2+7/486/(2+3*x)^2+(-107/243)/(2+3*x)-185/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x +--R + +--R 11958x - 421 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x +--R + +--R 11958x - 421 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=-250/81*x+7/729/(2+3*x)^3+(-107/486)/(2+3*x)^2+185/81/(2+3*x)+_ + 1025/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x +--R + +--R 2 +--R - 132030x + 2997x + 12692 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x +--R + +--R 2 +--R - 132030x + 2997x + 12692 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=7/972/(2+3*x)^4+(-107/729)/(2+3*x)^3+185/162/(2+3*x)^2+_ + (-1025/243)/(2+3*x)-250/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2) +--R + +--R 3 2 +--R - 332100x - 634230x - 404124x - 85915 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2) +--R + +--R 3 2 +--R - 332100x - 634230x - 404124x - 85915 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=7/15*(3+5*x)^4/(2+3*x)^5+5/12*(3+5*x)^4/(2+3*x)^4 +--R +--R +--R 3125 5 5375 4 2425 3 2 119 13 +--R ---- x + ---- x + ---- x + 10x + --- x + -- +--R 972 486 162 36 30 +--R (2) ----------------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 405000x + 803250x + 559800x + 153795x + 11758 +--R (3) ----------------------------------------------------------------- +--R 5 4 3 2 +--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R 3125 +--R (4) - ---- +--R 972 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=7/18*(3+5*x)^4/(2+3*x)^6+29/45*(3+5*x)^4/(2+3*x)^5+_ + 29/36*(3+5*x)^4/(2+3*x)^4 +--R +--R +--R 18125 6 18125 5 30250 4 8975 3 665 2 664 49 +--R ----- x + ----- x + ----- x + ---- x + --- x + --- x + -- +--R 2916 729 729 243 36 135 90 +--R (2) -------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 607500x + 1066500x + 587925x + 78048x - 13198 +--R / +--R 6 5 4 3 2 +--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x +--R + +--R 933120 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R 18125 +--R (4) - ----- +--R 2916 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=1/243/(2+3*x)^7+(-107/1458)/(2+3*x)^6+37/81/(2+3*x)^5+_ + (-1025/972)/(2+3*x)^4+250/729/(2+3*x)^3 +--R +--R +--R 250 4 4925 3 1147 2 107 922 +--R ----- x + ------ x + ------ x + ------- x - ------- +--R 19683 236196 118098 1062882 1594323 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 81000x + 132975x + 61938x + 642x - 3688 +--R / +--R 7 6 5 4 3 +--R 6377292x + 29760696x + 59521392x + 66134880x + 44089920x +--R + +--R 2 +--R 17635968x + 3919104x + 373248 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(5-2*x)^6*(2+3*x)^3*(-16+33*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 57024x - 768960x + 4070736x - 10051008x + 8647828x + 8983380x +--R + +--R 4 3 2 +--R - 19081125x - 196250x + 11962500x - 75000x - 2000000 +--R Type: Polynomial(Integer) +--E 271 + +--S 272 of 500 +r0:=-1/2*(5-2*x)^7*(2+3*x)^4 +--R +--R +--R (2) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x - 625000 +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 625000 +--R Type: Polynomial(Fraction(Integer)) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x) +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=-2/15*(2+3*x)^(1+m)/(1+m)-11/5*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x) +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=1666663/78125*x+1777779/31250*x^2+152469/3125*x^3-_ + 152469/2500*x^4-106677/625*x^5-7047/50*x^6-1458/35*x^7+_ + 11/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x +--R + +--R 3 2 +--R 533641500x + 622222650x + 233332820x +--R / +--R 10937500 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x +--R + +--R 3 2 +--R 533641500x + 622222650x + 233332820x +--R / +--R 10937500 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=166663/15625*x+127779/6250*x^2+2469/625*x^3-17469/500*x^4-_ + 5427/125*x^5-81/5*x^6+11/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x +--R + +--R 2 +--R 6388950x + 3333260x +--R / +--R 312500 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x +--R + +--R 2 +--R 6388950x + 3333260x +--R / +--R 312500 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x) +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=16663/3125*x+7779/1250*x^2-531/125*x^3-1269/100*x^4-_ + 162/25*x^5+11/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x +--R (2) ------------------------------------------------------------------- +--R 62500 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x +--R (3) ------------------------------------------------------------------- +--R 62500 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x) +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=1663/625*x+279/250*x^2-81/25*x^3-27/10*x^4+11/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x +--R (2) --------------------------------------------------- +--R 6250 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x +--R (3) --------------------------------------------------- +--R 6250 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x) +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ---------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=163/125*x-21/50*x^2-6/5*x^3+11/625*log(3+5*x) +--R +--R +--R 3 2 +--R 22log(5x + 3) - 1500x - 525x + 1630x +--R (2) -------------------------------------- +--R 1250 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 22log(5x + 3) - 1500x - 525x + 1630x +--R (3) -------------------------------------- +--R 1250 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x) +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) ------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=13/25*x-3/5*x^2+11/125*log(3+5*x) +--R +--R +--R 2 +--R 11log(5x + 3) - 75x + 65x +--R (2) -------------------------- +--R 125 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 11log(5x + 3) - 75x + 65x +--R (3) -------------------------- +--R 125 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)/(3+5*x) +--R +--R +--R - 2x + 1 +--R (1) -------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=-2/5*x+11/25*log(3+5*x) +--R +--R +--R 11log(5x + 3) - 10x +--R (2) ------------------- +--R 25 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R 11log(5x + 3) - 10x +--R (3) ------------------- +--R 25 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=-7/3*log(2+3*x)+11/5*log(3+5*x) +--R +--R +--R 33log(5x + 3) - 35log(3x + 2) +--R (2) ----------------------------- +--R 15 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R 33log(5x + 3) - 35log(3x + 2) +--R (3) ----------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=7/3/(2+3*x)-11*log(2+3*x)+11*log(3+5*x) +--R +--R +--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7 +--R (2) --------------------------------------------------- +--R 9x + 6 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7 +--R (3) --------------------------------------------------- +--R 9x + 6 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=7/6/(2+3*x)^2+11/(2+3*x)-55*log(2+3*x)+55*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2) +--R + +--R 198x + 139 +--R / +--R 2 +--R 54x + 72x + 24 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2) +--R + +--R 198x + 139 +--R / +--R 2 +--R 54x + 72x + 24 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=7/9/(2+3*x)^3+11/2/(2+3*x)^2+55/(2+3*x)-275*log(2+3*x)+275*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (133650x + 267300x + 178200x + 39600)log(5x + 3) +--R + +--R 3 2 2 +--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x +--R + +--R 4172 +--R / +--R 3 2 +--R 486x + 972x + 648x + 144 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (133650x + 267300x + 178200x + 39600)log(5x + 3) +--R + +--R 3 2 2 +--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x +--R + +--R 4172 +--R / +--R 3 2 +--R 486x + 972x + 648x + 144 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=7/12/(2+3*x)^4+11/3/(2+3*x)^3+55/2/(2+3*x)^2+275/(2+3*x)-_ + 1375*log(2+3*x)+1375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2) +--R + +--R 3 2 +--R 89100x + 181170x + 122892x + 27815 +--R / +--R 4 3 2 +--R 972x + 2592x + 2592x + 1152x + 192 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2) +--R + +--R 3 2 +--R 89100x + 181170x + 122892x + 27815 +--R / +--R 4 3 2 +--R 972x + 2592x + 2592x + 1152x + 192 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=7/15/(2+3*x)^5+11/4/(2+3*x)^4+55/3/(2+3*x)^3+275/2/(2+3*x)^2+_ + 1375/(2+3*x)-6875*log(2+3*x)+6875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x +--R + +--R 4400000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x +--R + +--R - 4400000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2227500x + 6014250x + 6091800x + 2743565x + 463586 +--R / +--R 5 4 3 2 +--R 4860x + 16200x + 21600x + 14400x + 4800x + 640 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x +--R + +--R 4400000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x +--R + +--R - 4400000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2227500x + 6014250x + 6091800x + 2743565x + 463586 +--R / +--R 5 4 3 2 +--R 4860x + 16200x + 21600x + 14400x + 4800x + 640 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=7/18/(2+3*x)^6+11/5/(2+3*x)^5+55/4/(2+3*x)^4+275/3/(2+3*x)^3+_ + 1375/2/(2+3*x)^2+6875/(2+3*x)-34375*log(2+3*x)+34375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 4510687500x + 18042750000x + 30071250000x + 26730000000x +--R + +--R 2 +--R 13365000000x + 3564000000x + 396000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x +--R + +--R 2 +--R - 13365000000x - 3564000000x - 396000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x +--R + +--R 41722762 +--R / +--R 6 5 4 3 2 +--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 4510687500x + 18042750000x + 30071250000x + 26730000000x +--R + +--R 2 +--R 13365000000x + 3564000000x + 396000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x +--R + +--R 2 +--R - 13365000000x - 3564000000x - 396000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x +--R + +--R 41722762 +--R / +--R 6 5 4 3 2 +--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^2 +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-11/5*(2+3*x)^(1+m)/(3+5*x)+1/5*(2-33*m)*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x +--R + +--R 128 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=5555478/390625*x+5740767/156250*x^2+92592/3125*x^3-_ + 513783/12500*x^4-336798/3125*x^5-21627/250*x^6-_ + 4374/175*x^7+(-11/1953125)/(3+5*x)+229/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 +--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x +--R + +--R 6 5 4 3 +--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x +--R + +--R 2 +--R 9916639950x + 2333300760x - 308 +--R / +--R 273437500x + 164062500 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x +--R + +--R 6 5 4 3 +--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x +--R + +--R 2 +--R 9916639950x + 2333300760x - 308 +--R / +--R 273437500x + 164062500 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=555489/78125*x+40743/3125*x^2+5553/3125*x^3-14094/625*x^4-_ + 16767/625*x^5-243/25*x^6+(-11/390625)/(3+5*x)+196/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x +--R + +--R 4 3 2 +--R - 22955625x + 27546750x + 29165850x + 8332335x - 11 +--R / +--R 1953125x + 1171875 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x +--R + +--R 4 3 2 +--R - 22955625x + 27546750x + 29165850x + 8332335x - 11 +--R / +--R 1953125x + 1171875 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=444/125*x+24093/6250*x^2-1854/625*x^3-3969/500*x^4-_ + 486/125*x^5+(-11/78125)/(3+5*x)+163/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x +--R + +--R 3 2 +--R 3242250x + 9163950x + 3330000x - 44 +--R / +--R 1562500x + 937500 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x +--R + +--R 3 2 +--R 3242250x + 9163950x + 3330000x - 44 +--R / +--R 1562500x + 937500 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=5511/3125*x+378/625*x^2-261/125*x^3-81/50*x^4+(-11/15625)/(3+5*x)+_ + 26/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x +--R + +--R 165330x - 22 +--R / +--R 156250x + 93750 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x +--R + +--R 165330x - 22 +--R / +--R 156250x + 93750 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=522/625*x-81/250*x^2-18/25*x^3+(-11/3125)/(3+5*x)+97/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22 +--R (2) ------------------------------------------------------------------- +--R 31250x + 18750 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22 +--R (3) ------------------------------------------------------------------- +--R 31250x + 18750 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ---------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=33/125*x-9/25*x^2+(-11/625)/(3+5*x)+64/625*log(3+5*x) +--R +--R +--R 3 2 +--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11 +--R (2) ---------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11 +--R (3) ---------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=-6/25*x+(-11/125)/(3+5*x)+31/125*log(3+5*x) +--R +--R +--R 2 +--R (155x + 93)log(5x + 3) - 150x - 90x - 11 +--R (2) ----------------------------------------- +--R 625x + 375 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (155x + 93)log(5x + 3) - 150x - 90x - 11 +--R (3) ----------------------------------------- +--R 625x + 375 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)/(3+5*x)^2 +--R +--R +--R - 2x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-11/25)/(3+5*x)-2/25*log(3+5*x) +--R +--R +--R (- 10x - 6)log(5x + 3) - 11 +--R (2) --------------------------- +--R 125x + 75 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 10x - 6)log(5x + 3) - 11 +--R (3) --------------------------- +--R 125x + 75 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-11/5)/(3+5*x)+7*log(2+3*x)-7*log(3+5*x) +--R +--R +--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11 +--R (2) -------------------------------------------------------- +--R 25x + 15 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11 +--R (3) -------------------------------------------------------- +--R 25x + 15 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-7)/(2+3*x)+(-11)/(3+5*x)+68*log(2+3*x)-68*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2) +--R + +--R - 68x - 43 +--R / +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2) +--R + +--R - 68x - 43 +--R / +--R 2 +--R 15x + 19x + 6 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-7/2)/(2+3*x)^2+(-68)/(2+3*x)+(-55)/(3+5*x)+505*log(2+3*x)-505*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3) +--R + +--R 3 2 2 +--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277 +--R / +--R 3 2 +--R 90x + 174x + 112x + 24 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3) +--R + +--R 3 2 2 +--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277 +--R / +--R 3 2 +--R 90x + 174x + 112x + 24 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-7/3)/(2+3*x)^3+(-34)/(2+3*x)^2+(-505)/(2+3*x)+(-275)/(3+5*x)+_ + 3350*log(2+3*x)-3350*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3) +--R + +--R 4 3 2 +--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2) +--R + +--R 3 2 +--R - 90450x - 177885x - 116513x - 25413 +--R / +--R 4 3 2 +--R 405x + 1053x + 1026x + 444x + 72 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3) +--R + +--R 4 3 2 +--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2) +--R + +--R 3 2 +--R - 90450x - 177885x - 116513x - 25413 +--R / +--R 4 3 2 +--R 405x + 1053x + 1026x + 444x + 72 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-7/4)/(2+3*x)^4+(-68/3)/(2+3*x)^3+(-505/2)/(2+3*x)^2+_ + (-3350)/(2+3*x)+(-1375)/(3+5*x)+20875*log(2+3*x)-20875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x +--R + +--R - 12024000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x +--R + +--R 12024000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855 +--R / +--R 5 4 3 2 +--R 4860x + 15876x + 20736x + 13536x + 4416x + 576 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x +--R + +--R - 12024000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x +--R + +--R 12024000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855 +--R / +--R 5 4 3 2 +--R 4860x + 15876x + 20736x + 13536x + 4416x + 576 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-7/5)/(2+3*x)^5+(-17)/(2+3*x)^4+(-505/3)/(2+3*x)^3+_ + (-1675)/(2+3*x)^2+(-20875)/(2+3*x)+(-6875)/(3+5*x)+_ + 125000*log(2+3*x)-125000*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x +--R + +--R 2 +--R - 6300000000x - 1650000000x - 180000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 2278125000x + 8960625000x + 14681250000x + 12825000000x +--R + +--R 2 +--R 6300000000x + 1650000000x + 180000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x +--R + +--R - 18964893 +--R / +--R 6 5 4 3 2 +--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x +--R + +--R 2 +--R - 6300000000x - 1650000000x - 180000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 2278125000x + 8960625000x + 14681250000x + 12825000000x +--R + +--R 2 +--R 6300000000x + 1650000000x + 180000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x +--R + +--R - 18964893 +--R / +--R 6 5 4 3 2 +--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-7/6)/(2+3*x)^6+(-68/5)/(2+3*x)^5+(-505/4)/(2+3*x)^4+_ + (-3350/3)/(2+3*x)^3+(-20875/2)/(2+3*x)^2+(-125000)/(2+3*x)+_ + (-34375)/(3+5*x)+728125*log(2+3*x)-728125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x +--R + +--R 3 2 +--R - 346005000000x - 136305000000x - 29824000000x - 2796000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R 53080312500x + 244169437500x + 481261500000x + 526871250000x +--R + +--R 3 2 +--R 346005000000x + 136305000000x + 29824000000x + 2796000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x +--R + +--R 2 +--R - 10128331755x - 2676272018x - 294588002 +--R / +--R 7 6 5 4 3 2 +--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x +--R + +--R 3840 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x +--R + +--R 3 2 +--R - 346005000000x - 136305000000x - 29824000000x - 2796000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R 53080312500x + 244169437500x + 481261500000x + 526871250000x +--R + +--R 3 2 +--R 346005000000x + 136305000000x + 29824000000x + 2796000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x +--R + +--R 2 +--R - 10128331755x - 2676272018x - 294588002 +--R / +--R 7 6 5 4 3 2 +--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x +--R + +--R 3840 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^3 +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-11/10*(2+3*x)^(1+m)/(3+5*x)^2+1/10*(37-33*m)*(2+3*x)^(1+m)/(3+5*x)+_ +-- 3/10*(37-33*m)*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x +--R + +--R 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=1851147/390625*x+129654/15625*x^2+2052/3125*x^3-181521/12500*x^4-_ + 51759/3125*x^5-729/125*x^6+(-11/3906250)/(3+5*x)^2+_ + (-229/1953125)/(3+5*x)+2037/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x +--R + +--R 6 5 4 3 2 +--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x +--R + +--R 333201880x - 2770 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x +--R + +--R 6 5 4 3 2 +--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x +--R + +--R 333201880x - 2770 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=36936/15625*x+297/125*x^2-6399/3125*x^3-12393/2500*x^4-_ + 1458/625*x^5+(-11/781250)/(3+5*x)^2+(-196/390625)/(3+5*x)+_ + 1449/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x +--R + +--R 5 4 3 2 +--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374 +--R / +--R 2 +--R 39062500x + 46875000x + 14062500 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x +--R + +--R 5 4 3 2 +--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374 +--R / +--R 2 +--R 39062500x + 46875000x + 14062500 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=3636/3125*x+1971/6250*x^2-837/625*x^3-243/250*x^4+_ + (-11/156250)/(3+5*x)^2+(-163/78125)/(3+5*x)+192/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 4 +--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x +--R + +--R 3 2 +--R 4140000x + 5897475x + 1634570x - 989 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 4 +--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x +--R + +--R 3 2 +--R 4140000x + 5897475x + 1634570x - 989 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=1647/3125*x-297/1250*x^2-54/125*x^3+(-11/31250)/(3+5*x)^2+_ + (-26/3125)/(3+5*x)+114/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x +--R + +--R 2 +--R 427275x + 146930x - 791 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x +--R + +--R 2 +--R 427275x + 146930x - 791 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=81/625*x-27/125*x^2+(-11/6250)/(3+5*x)^2+(-97/3125)/(3+5*x)+_ + 279/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x +--R + +--R 6320x - 593 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x +--R + +--R 6320x - 593 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=-18/125*x+(-11/1250)/(3+5*x)^2+(-64/625)/(3+5*x)+87/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395 +--R (2) ------------------------------------------------------------------ +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395 +--R (3) ------------------------------------------------------------------ +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=(-11/250)/(3+5*x)^2+(-31/125)/(3+5*x)-6/125*log(3+5*x) +--R +--R +--R 2 +--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197 +--R (2) ---------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197 +--R (3) ---------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)/(3+5*x)^3 +--R +--R +--R - 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=-1/22*(1-2*x)^2/(3+5*x)^2 +--R +--R +--R 2 2 2 1 +--R - --- x + --- x - --- +--R 275 275 550 +--R (2) ---------------------- +--R 2 6 9 +--R x + - x + -- +--R 5 25 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 20x + 1 +--R (3) -------------------- +--R 2 +--R 1250x + 1500x + 450 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) --- +--R 275 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-11/10)/(3+5*x)^2+7/(3+5*x)-21*log(2+3*x)+21*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2) +--R + +--R 350x + 199 +--R / +--R 2 +--R 250x + 300x + 90 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2) +--R + +--R 350x + 199 +--R / +--R 2 +--R 250x + 300x + 90 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=21/(2+3*x)+(-11/2)/(3+5*x)^2+68/(3+5*x)-309*log(2+3*x)+309*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (46350x + 86520x + 53766x + 11124)log(5x + 3) +--R + +--R 3 2 2 +--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172 +--R / +--R 3 2 +--R 150x + 280x + 174x + 36 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (46350x + 86520x + 53766x + 11124)log(5x + 3) +--R + +--R 3 2 2 +--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172 +--R / +--R 3 2 +--R 150x + 280x + 174x + 36 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=21/2/(2+3*x)^2+309/(2+3*x)+(-55/2)/(3+5*x)^2+505/(3+5*x)-_ + 3060*log(2+3*x)+3060*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2) +--R + +--R 3 2 +--R 91800x + 174420x + 110296x + 23213 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2) +--R + +--R 3 2 +--R 91800x + 174420x + 110296x + 23213 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=7/(2+3*x)^3+309/2/(2+3*x)^2+3060/(2+3*x)+(-275/2)/(3+5*x)^2+3350/(3+5*x)-_ + 25350*log(2+3*x)+25350*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x +--R + +--R 3650400 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x +--R + +--R - 3650400 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2281500x + 5855850x + 5631080x + 2404363x + 384608 +--R / +--R 5 4 3 2 +--R 1350x + 4320x + 5526x + 3532x + 1128x + 144 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x +--R + +--R 3650400 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x +--R + +--R - 3650400 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2281500x + 5855850x + 5631080x + 2404363x + 384608 +--R / +--R 5 4 3 2 +--R 1350x + 4320x + 5526x + 3532x + 1128x + 144 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=21/4/(2+3*x)^4+103/(2+3*x)^3+1530/(2+3*x)^2+25350/(2+3*x)+_ + (-1375/2)/(3+5*x)^2+20875/(3+5*x)-189375*log(2+3*x)+189375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 1533937500x + 5931225000x + 9551317500x + 8199180000x +--R + +--R 2 +--R 3957180000x + 1018080000x + 109080000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x +--R + +--R 2 +--R - 3957180000x - 1018080000x - 109080000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x +--R + +--R 11492725 +--R / +--R 6 5 4 3 2 +--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 1533937500x + 5931225000x + 9551317500x + 8199180000x +--R + +--R 2 +--R 3957180000x + 1018080000x + 109080000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x +--R + +--R 2 +--R - 3957180000x - 1018080000x - 109080000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x +--R + +--R 11492725 +--R / +--R 6 5 4 3 2 +--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3d.input.pdf b/src/axiom-website/CATS/rich3d.input.pdf new file mode 100644 index 0000000..727fc1b Binary files /dev/null and b/src/axiom-website/CATS/rich3d.input.pdf differ diff --git a/src/axiom-website/CATS/rich3e.input.pamphlet b/src/axiom-website/CATS/rich3e.input.pamphlet new file mode 100644 index 0000000..9146b9c --- /dev/null +++ b/src/axiom-website/CATS/rich3e.input.pamphlet @@ -0,0 +1,6307 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 249 integrals in this file. +\item 249 supplied "optimal results". +\item 230 matching answers. +\item 24 cases where Axiom supplied 2 results. +\item 34 cases that Axiom failed to integrate. +\item 6 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3e.output +)spool rich3e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=21/5/(2+3*x)^5+309/4/(2+3*x)^4+1020/(2+3*x)^3+12675/(2+3*x)^2+_ + 189375/(2+3*x)+(-6875/2)/(3+5*x)^2+125000/(3+5*x)-_ + 1321875*log(2+3*x)+1321875*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x +--R + +--R 3 2 +--R 986647500000x + 382815000000x + 82485000000x + 7614000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x +--R + +--R 3 2 +--R - 986647500000x - 382815000000x - 82485000000x - 7614000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 10707187500x + 41758031250x + 67828050000x + 58733814375x +--R + +--R 2 +--R 28595335800x + 7421662135x + 802214966 +--R / +--R 7 6 5 4 3 2 +--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x +--R + +--R 62400x + 5760 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x +--R + +--R 3 2 +--R 986647500000x + 382815000000x + 82485000000x + 7614000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x +--R + +--R 3 2 +--R - 986647500000x - 382815000000x - 82485000000x - 7614000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 10707187500x + 41758031250x + 67828050000x + 58733814375x +--R + +--R 2 +--R 28595335800x + 7421662135x + 802214966 +--R / +--R 7 6 5 4 3 2 +--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x +--R + +--R 62400x + 5760 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 131220x + 647352x + 1307097x + 1298835x + 476928x - 275184x +--R + +--R 5 4 3 2 +--R - 372960x - 134112x + 12800x + 24832x + 7424x + 768 +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 500 +r0:=-49/729*(2+3*x)^9+91/270*(2+3*x)^10-16/99*(2+3*x)^11+5/243*(2+3*x)^12 +--R +--R +--R (2) +--R 12 647352 11 1307097 10 9 8 7 +--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x +--R 11 10 +--R + +--R 6 134112 5 4 24832 3 2 2566144 +--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x + ------- +--R 5 3 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 647352 11 1307097 10 9 8 7 +--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x +--R 11 10 +--R + +--R 6 134112 5 4 24832 3 2 +--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R 2566144 +--R (4) - ------- +--R 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 43740x + 186624x + 311283x + 225423x + 8694x - 97524x - 59304x +--R + +--R 3 2 +--R - 5168x + 7712x + 3136x + 384 +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 500 +r0:=-49/648*(2+3*x)^8+91/243*(2+3*x)^9-8/45*(2+3*x)^10+20/891*(2+3*x)^11 +--R +--R +--R (2) +--R 43740 11 93312 10 9 225423 8 7 6 59304 5 +--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x +--R 11 5 8 5 +--R + +--R 4 7712 3 2 485216 +--R - 1292x + ---- x + 1568x + 384x + ------ +--R 3 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 43740 11 93312 10 9 225423 8 7 6 59304 5 +--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x +--R 11 5 8 5 +--R + +--R 4 7712 3 2 +--R - 1292x + ---- x + 1568x + 384x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R 485216 +--R (4) - ------ +--R 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x + 1936x +--R + +--R 1280x + 192 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=192*x+640*x^2+1936/3*x^3-1372*x^4-4284*x^5-2772*x^6+4185*x^7+_ + 68769/8*x^8+5832*x^9+1458*x^10 +--R +--R +--R (2) +--R 10 9 68769 8 7 6 5 4 1936 3 +--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x +--R 8 3 +--R + +--R 2 +--R 640x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 68769 8 7 6 5 4 1936 3 +--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x +--R 8 3 +--R + +--R 2 +--R 640x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=96*x+248*x^2+224/3*x^3-770*x^4-1218*x^5+273/2*x^6+1917*x^7+1782*x^8+540*x^9 +--R +--R +--R (2) +--R 9 8 7 273 6 5 4 224 3 2 +--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 273 6 5 4 224 3 2 +--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=48*x+88*x^2-152/3*x^3-328*x^4-1077/5*x^5+675/2*x^6+3672/7*x^7+405/2*x^8 +--R +--R +--R 405 8 3672 7 675 6 1077 5 4 152 3 2 +--R (2) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x +--R 2 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R 405 8 3672 7 675 6 1077 5 4 152 3 2 +--R (3) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x +--R 2 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) 540x + 864x + 99x - 425x - 154x + 52x + 24 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7 +--R +--R +--R 540 7 6 99 5 425 4 154 3 2 +--R (2) --- x + 144x + -- x - --- x - --- x + 26x + 24x +--R 7 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 540 7 6 99 5 425 4 154 3 2 +--R (3) --- x + 144x + -- x - --- x - --- x + 26x + 24x +--R 7 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) 180x + 168x - 79x - 89x + 8x + 12 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=12*x+4*x^2-89/3*x^3-79/4*x^4+168/5*x^5+30*x^6 +--R +--R +--R 6 168 5 79 4 89 3 2 +--R (2) 30x + --- x - -- x - -- x + 4x + 12x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 168 5 79 4 89 3 2 +--R (3) 30x + --- x - -- x - -- x + 4x + 12x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) 60x + 16x - 37x - 5x + 6 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5 +--R +--R +--R 5 4 37 3 5 2 +--R (2) 12x + 4x - -- x - - x + 6x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 37 3 5 2 +--R (3) 12x + 4x - -- x - - x + 6x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^2*(3+5*x) +--R +--R +--R 3 2 +--R (1) 20x - 8x - 7x + 3 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=3*x-7/2*x^2-8/3*x^3+5*x^4 +--R +--R +--R 4 8 3 7 2 +--R (2) 5x - - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 8 3 7 2 +--R (3) 5x - - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x) +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=65/27*x-32/9*x^2+20/9*x^3-49/81*log(2+3*x) +--R +--R +--R 3 2 +--R - 49log(3x + 2) + 180x - 288x + 195x +--R (2) -------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 49log(3x + 2) + 180x - 288x + 195x +--R (3) -------------------------------------- +--R 81 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=-104/27*x+10/9*x^2+49/81/(2+3*x)+91/27*log(2+3*x) +--R +--R +--R 3 2 +--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49 +--R (2) --------------------------------------------------- +--R 243x + 162 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49 +--R (3) --------------------------------------------------- +--R 243x + 162 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=20/27*x+49/162/(2+3*x)^2+(-91/27)/(2+3*x)-16/9*log(2+3*x) +--R +--R +--R 2 3 2 +--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043 +--R (2) --------------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=49/243/(2+3*x)^3+(-91/54)/(2+3*x)^2+16/9/(2+3*x)+20/81*log(2+3*x) +--R +--R +--R 3 2 2 +--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916 +--R (2) ------------------------------------------------------------------ +--R 3 2 +--R 13122x + 26244x + 17496x + 3888 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916 +--R (3) ------------------------------------------------------------------ +--R 3 2 +--R 13122x + 26244x + 17496x + 3888 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=1/84*(1-2*x)^3/(2+3*x)^4-23/294*(1-2*x)^3/(2+3*x)^3 +--R +--R +--R 92 4 244 3 16 2 31 85 +--R ---- x - ----- x - ---- x + ---- x - ----- +--R 3969 11907 3969 3969 47628 +--R (2) --------------------------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 2160x - 1728x - 516x - 167 +--R (3) ------------------------------------------- +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R 92 +--R (4) - ---- +--R 3969 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=49/405/(2+3*x)^5+(-91/108)/(2+3*x)^4+16/27/(2+3*x)^3+(-10/81)/(2+3*x)^2 +--R +--R +--R 10 3 4 2 5 49 +--R - --- x - --- x + ---- x - ----- +--R 729 729 8748 65610 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 1800x - 720x + 75x - 98 +--R (3) ----------------------------------------------------------- +--R 5 4 3 2 +--R 131220x + 437400x + 583200x + 388800x + 129600x + 17280 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=49/486/(2+3*x)^6+(-91/135)/(2+3*x)^5+4/9/(2+3*x)^4+(-20/243)/(2+3*x)^3 +--R +--R +--R 20 3 4 2 47 311 +--R - ---- x - ---- x + ----- x - ------- +--R 6561 6561 98415 1771470 +--R (2) ---------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R - 5400x - 1080x + 846x - 311 +--R / +--R 6 5 4 3 2 +--R 1771470x + 7085880x + 11809800x + 10497600x + 5248800x + 1399680x +--R + +--R 155520 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--R 20x - 8x - 7x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=7/81/(2+3*x)^7+(-91/162)/(2+3*x)^6+16/45/(2+3*x)^5+(-5/81)/(2+3*x)^4 +--R +--R +--R 5 3 2 2 97 44 +--R - ---- x - ----- x + ------ x - ------ +--R 6561 32805 590490 885735 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R - 1350x - 108x + 291x - 88 +--R / +--R 7 6 5 4 3 2 +--R 1771470x + 8266860x + 16533720x + 18370800x + 12247200x + 4898880x +--R + +--R 1088640x + 103680 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R 656100x + 3630420x + 8477541x + 10415466x + 6281145x + 54864x +--R + +--R 6 5 4 3 2 +--R - 2690352x - 1789440x - 338336x + 162560x + 111616x + 26112x + 2304 +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 500 +r0:=49/2187*(2+3*x)^9-259/1215*(2+3*x)^10+503/891*(2+3*x)^11-_ + 185/729*(2+3*x)^12+100/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 656100 13 12 8477541 11 5207733 10 9 8 +--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x +--R 13 11 5 +--R + +--R 7 6 338336 5 4 111616 3 2 +--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x +--R 5 3 +--R + +--R 264616448 +--R --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 656100 13 12 8477541 11 5207733 10 9 8 +--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x +--R 13 11 5 +--R + +--R 7 6 338336 5 4 111616 3 2 +--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 264616448 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 218700x + 1064340x + 2116287x + 2060964x + 719739x - 461538x +--R + +--R 5 4 3 2 +--R - 589092x - 203752x + 23056x + 38816x + 11328x + 1152 +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 500 +r0:=1152*x+5664*x^2+38816/3*x^3+5764*x^4-203752/5*x^5-98182*x^6-65934*x^7+_ + 719739/8*x^8+228996*x^9+2116287/10*x^10+1064340/11*x^11+18225*x^12 +--R +--R +--R (2) +--R 12 1064340 11 2116287 10 9 719739 8 7 +--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x +--R 11 10 8 +--R + +--R 6 203752 5 4 38816 3 2 +--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 1064340 11 2116287 10 9 719739 8 7 +--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x +--R 11 10 8 +--R + +--R 6 203752 5 4 38816 3 2 +--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 72900x + 306180x + 501309x + 352782x + 4725x - 156996x - 91700x +--R + +--R 3 2 +--R - 6784x + 12208x + 4800x + 576 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=576*x+2400*x^2+12208/3*x^3-1696*x^4-18340*x^5-26166*x^6+675*x^7+_ + 176391/4*x^8+55701*x^9+30618*x^10+72900/11*x^11 +--R +--R +--R (2) +--R 72900 11 10 9 176391 8 7 6 5 +--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x +--R 11 4 +--R + +--R 4 12208 3 2 +--R - 1696x + ----- x + 2400x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 72900 11 10 9 176391 8 7 6 5 +--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x +--R 11 4 +--R + +--R 4 12208 3 2 +--R - 1696x + ----- x + 2400x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x +--R + +--R 2 +--R 3152x + 1968x + 288 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=288*x+984*x^2+3152/3*x^3-2030*x^4-6734*x^5-9331/2*x^6+6336*x^7+_ + 109863/8*x^8+9540*x^9+2430*x^10 +--R +--R +--R (2) +--R 10 9 109863 8 7 9331 6 5 4 3152 3 +--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x +--R 8 2 3 +--R + +--R 2 +--R 984x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 109863 8 7 9331 6 5 4 3152 3 +--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x +--R 8 2 3 +--R + +--R 2 +--R 984x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=144*x+384*x^2+424/3*x^3-1174*x^4-9791/5*x^5+115*x^6+21141/7*x^7+_ + 5805/2*x^8+900*x^9 +--R +--R +--R (2) +--R 9 5805 8 21141 7 6 9791 5 4 424 3 2 +--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x +--R 2 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 5805 8 21141 7 6 9791 5 4 424 3 2 +--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x +--R 2 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+_ + 675/2*x^8 +--R +--R +--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2 +--R (2) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x +--R 2 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2 +--R (3) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x +--R 2 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) 900x + 1380x + 109x - 682x - 227x + 84x + 36 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=36*x+42*x^2-227/3*x^3-341/2*x^4+109/5*x^5+230*x^6+900/7*x^7 +--R +--R +--R 900 7 6 109 5 341 4 227 3 2 +--R (2) --- x + 230x + --- x - --- x - --- x + 42x + 36x +--R 7 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 900 7 6 109 5 341 4 227 3 2 +--R (3) --- x + 230x + --- x - --- x - --- x + 42x + 36x +--R 7 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) 300x + 260x - 137x - 136x + 15x + 18 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=18*x+15/2*x^2-136/3*x^3-137/4*x^4+52*x^5+50*x^6 +--R +--R +--R 6 5 137 4 136 3 15 2 +--R (2) 50x + 52x - --- x - --- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 137 4 136 3 15 2 +--R (3) 50x + 52x - --- x - --- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^2*(3+5*x)^2 +--R +--R +--R 4 3 2 +--R (1) 100x + 20x - 59x - 6x + 9 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=9*x-3*x^2-59/3*x^3+5*x^4+20*x^5 +--R +--R +--R 5 4 59 3 2 +--R (2) 20x + 5x - -- x - 3x + 9x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 59 3 2 +--R (3) 20x + 5x - -- x - 3x + 9x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x) +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=340/81*x-251/54*x^2-140/27*x^3+25/3*x^4+49/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x +--R (2) ------------------------------------------------ +--R 486 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x +--R (3) ------------------------------------------------ +--R 486 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=143/27*x-170/27*x^2+100/27*x^3+(-49/243)/(2+3*x)-518/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49 +--R (2) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49 +--R (3) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=-20/3*x+50/27*x^2+(-49/486)/(2+3*x)^2+518/243/(2+3*x)+503/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x +--R + +--R - 9852x + 2023 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x +--R + +--R - 9852x + 2023 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=100/81*x+(-49/729)/(2+3*x)^3+259/243/(2+3*x)^2+(-503/81)/(2+3*x)-_ + 740/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x +--R + +--R 2 +--R - 8343x - 44793x - 16603 +--R / +--R 3 2 +--R 19683x + 39366x + 26244x + 5832 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x +--R + +--R 2 +--R - 8343x - 44793x - 16603 +--R / +--R 3 2 +--R 19683x + 39366x + 26244x + 5832 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-49/972)/(2+3*x)^4+518/729/(2+3*x)^3+(-503/162)/(2+3*x)^2+_ + 740/243/(2+3*x)+100/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x +--R + +--R 2 +--R 398034x + 217248x + 38821 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 3 +--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x +--R + +--R 2 +--R 398034x + 217248x + 38821 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=(-49/1215)/(2+3*x)^5+259/486/(2+3*x)^4+(-503/243)/(2+3*x)^3+_ + 370/243/(2+3*x)^2+(-100/243)/(2+3*x) +--R +--R +--R 100 4 430 3 683 2 1285 2014 +--R - --- x - ---- x - ---- x - ----- x - ------ +--R 729 2187 6561 39366 295245 +--R (2) ----------------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 81000x - 116100x - 61470x - 19275x - 4028 +--R (3) -------------------------------------------------------------- +--R 5 4 3 2 +--R 590490x + 1968300x + 2624400x + 1749600x + 583200x + 77760 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-49/1458)/(2+3*x)^6+518/1215/(2+3*x)^5+(-503/324)/(2+3*x)^4+_ + 740/729/(2+3*x)^3+(-50/243)/(2+3*x)^2 +--R +--R +--R 50 4 460 3 389 2 227 4099 +--R - ---- x - ----- x - ----- x - ------ x - ------- +--R 2187 19683 78732 295245 5314410 +--R (2) ---------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 243000x - 248400x - 52515x - 8172x - 8198 +--R / +--R 6 5 4 3 2 +--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x +--R + +--R 933120 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-7/243)/(2+3*x)^7+259/729/(2+3*x)^6+(-503/405)/(2+3*x)^5+_ + 185/243/(2+3*x)^4+(-100/729)/(2+3*x)^3 +--R +--R +--R 100 4 245 3 41 2 487 1423 +--R - ----- x - ----- x + ------ x + ------- x - ------- +--R 19683 59049 295245 2657205 7971615 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 40500x - 33075x + 1107x + 1461x - 1423 +--R / +--R 7 6 5 4 3 +--R 7971615x + 37200870x + 74401740x + 82668600x + 55112400x +--R + +--R 2 +--R 22044960x + 4898880x + 466560 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^2*(2+3*x)^10*(3+5*x)^3 +--R +--R +--R (1) +--R 15 14 13 12 11 +--R 29524500x + 220449600x + 734077485x + 1417418757x + 1707104403x +--R + +--R 10 9 8 7 6 +--R 1233925083x + 360437040x - 236139300x - 320907744x - 154612896x +--R + +--R 5 4 3 2 +--R - 21254656x + 15928960x + 10576640x + 3002112x + 442368x + 27648 +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 500 +r0:=-49/8019*(2+3*x)^11+763/8748*(2+3*x)^12-4099/9477*(2+3*x)^13+_ + 8285/10206*(2+3*x)^14-760/2187*(2+3*x)^15+125/2916*(2+3*x)^16 +--R +--R +--R (2) +--R 7381125 16 15 734077485 14 1417418757 13 569034801 12 +--R ------- x + 14696640x + --------- x + ---------- x + --------- x +--R 4 14 13 4 +--R + +--R 1233925083 11 10 9 8 154612896 7 +--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x +--R 11 7 +--R + +--R 10627328 6 5 4 3 2 +--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x +--R 3 +--R + +--R 3336045568 +--R ---------- +--R 2189187 +--R Type: Polynomial(Fraction(Integer)) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7381125 16 15 734077485 14 1417418757 13 569034801 12 +--R ------- x + 14696640x + --------- x + ---------- x + --------- x +--R 4 14 13 4 +--R + +--R 1233925083 11 10 9 8 154612896 7 +--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x +--R 11 7 +--R + +--R 10627328 6 5 4 3 2 +--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R 3336045568 +--R (4) - ---------- +--R 2189187 +--R Type: Polynomial(Fraction(Integer)) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^2*(2+3*x)^9*(3+5*x)^3 +--R +--R +--R (1) +--R 14 13 12 11 10 +--R 9841500x + 66922200x + 200077695x + 339087789x + 342976275x +--R + +--R 9 8 7 6 5 4 +--R 182657511x - 1625994x - 77629104x - 55216512x - 14726624x + 2732864x +--R + +--R 3 2 +--R 3487744x + 1200384x + 200448x + 13824 +--R Type: Polynomial(Integer) +--E 181 + +--S 182 of 500 +r0:=-49/7290*(2+3*x)^10+763/8019*(2+3*x)^11-4099/8748*(2+3*x)^12+_ + 8285/9477*(2+3*x)^13-1900/5103*(2+3*x)^14+100/2187*(2+3*x)^15 +--R +--R +--R (2) +--R 15 33461100 14 200077695 13 113029263 12 342976275 11 +--R 656100x + -------- x + --------- x + --------- x + --------- x +--R 7 13 4 11 +--R + +--R 182657511 10 9 8 55216512 7 7363312 6 +--R --------- x - 180666x - 9703638x - -------- x - ------- x +--R 10 7 3 +--R + +--R 2732864 5 4 3 2 9067849216 +--R ------- x + 871936x + 400128x + 100224x + 13824x + ---------- +--R 5 10945935 +--R Type: Polynomial(Fraction(Integer)) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 33461100 14 200077695 13 113029263 12 342976275 11 +--R 656100x + -------- x + --------- x + --------- x + --------- x +--R 7 13 4 11 +--R + +--R 182657511 10 9 8 55216512 7 7363312 6 +--R --------- x - 180666x - 9703638x - -------- x - ------- x +--R 10 7 3 +--R + +--R 2732864 5 4 3 2 +--R ------- x + 871936x + 400128x + 100224x + 13824x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R 9067849216 +--R (4) - ---------- +--R 10945935 +--R Type: Polynomial(Fraction(Integer)) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^3 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R 3280500x + 20120400x + 53278965x + 77509953x + 62652123x +--R + +--R 8 7 6 5 4 3 +--R 19117755x - 13287168x - 17018256x - 7060000x - 202208x + 1045760x +--R + +--R 2 +--R 465408x + 89856x + 6912 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=6912*x+44928*x^2+155136*x^3+261440*x^4-202208/5*x^5-3530000/3*x^6-_ + 17018256/7*x^7-1660896*x^8+2124195*x^9+62652123/10*x^10+_ + 77509953/11*x^11+17759655/4*x^12+20120400/13*x^13+1640250/7*x^14 +--R +--R +--R (2) +--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10 +--R ------- x + -------- x + -------- x + -------- x + -------- x +--R 7 13 4 11 10 +--R + +--R 9 8 17018256 7 3530000 6 202208 5 4 +--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x +--R 7 3 5 +--R + +--R 3 2 +--R 155136x + 44928x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10 +--R ------- x + -------- x + -------- x + -------- x + -------- x +--R 7 13 4 11 10 +--R + +--R 9 8 17018256 7 3530000 6 202208 5 4 +--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x +--R 7 3 5 +--R + +--R 3 2 +--R 155136x + 44928x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R 1093500x + 5977800x + 13774455x + 16653681x + 9781587x - 148473x +--R + +--R 6 5 4 3 2 +--R - 4330074x - 2786036x - 495976x + 263248x + 173088x + 39744x + 3456 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=3456*x+19872*x^2+57696*x^3+65812*x^4-495976/5*x^5-1393018/3*x^6-_ + 618582*x^7-148473/8*x^8+1086843*x^9+16653681/10*x^10+_ + 13774455/11*x^11+498150*x^12+1093500/13*x^13 +--R +--R +--R (2) +--R 1093500 13 12 13774455 11 16653681 10 9 +--R ------- x + 498150x + -------- x + -------- x + 1086843x +--R 13 11 10 +--R + +--R 148473 8 7 1393018 6 495976 5 4 3 +--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x +--R 8 3 5 +--R + +--R 2 +--R 19872x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1093500 13 12 13774455 11 16653681 10 9 +--R ------- x + 498150x + -------- x + -------- x + 1086843x +--R 13 11 10 +--R + +--R 148473 8 7 1393018 6 495976 5 4 3 +--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x +--R 8 3 5 +--R + +--R 2 +--R 19872x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 364500x + 1749600x + 3425085x + 3267837x + 1081971x - 770805x +--R + +--R 5 4 3 2 +--R - 929488x - 309020x + 40688x + 60624x + 17280x + 1728 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=1728*x+8640*x^2+20208*x^3+10172*x^4-61804*x^5-464744/3*x^6-_ + 110115*x^7+1081971/8*x^8+363093*x^9+685017/2*x^10+1749600/11*x^11+_ + 30375*x^12 +--R +--R +--R (2) +--R 12 1749600 11 685017 10 9 1081971 8 7 +--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x +--R 11 2 8 +--R + +--R 464744 6 5 4 3 2 +--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 1749600 11 685017 10 9 1081971 8 7 +--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x +--R 11 2 8 +--R + +--R 464744 6 5 4 3 2 +--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 121500x + 502200x + 806895x + 551349x - 6909x - 252329x - 141610x +--R + +--R 3 2 +--R - 8600x + 19296x + 7344x + 864 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=864*x+3672*x^2+6432*x^3-2150*x^4-28322*x^5-252329/6*x^6-987*x^7+_ + 551349/8*x^8+89655*x^9+50220*x^10+121500/11*x^11 +--R +--R +--R (2) +--R 121500 11 10 9 551349 8 7 252329 6 5 +--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x +--R 11 8 6 +--R + +--R 4 3 2 +--R - 2150x + 6432x + 3672x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 121500 11 10 9 551349 8 7 252329 6 5 +--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x +--R 11 8 6 +--R + +--R 4 3 2 +--R - 2150x + 6432x + 3672x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=432*x+1512*x^2+1704*x^3-2992*x^4-52853/5*x^5-46885/6*x^6+66873/7*x^7+_ + 175365/8*x^8+15600*x^9+4050*x^10 +--R +--R +--R (2) +--R 10 9 175365 8 66873 7 46885 6 52853 5 4 +--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x +--R 8 7 6 5 +--R + +--R 3 2 +--R 1704x + 1512x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 175365 8 66873 7 46885 6 52853 5 4 +--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x +--R 8 7 6 5 +--R + +--R 3 2 +--R 1704x + 1512x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+_ + 4725*x^8+1500*x^9 +--R +--R +--R (2) +--R 9 8 33255 7 121 6 15709 5 7145 4 3 2 +--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x +--R 7 6 5 4 +--R + +--R 216x +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 33255 7 121 6 15709 5 7145 4 3 2 +--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x +--R 7 6 5 4 +--R + +--R 216x +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8 +--R +--R +--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2 +--R (2) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x +--R 2 7 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2 +--R (3) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x +--R 2 7 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) 1500x + 2200x + 95x - 1091x - 333x + 135x + 54 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=54*x+135/2*x^2-111*x^3-1091/4*x^4+19*x^5+1100/3*x^6+1500/7*x^7 +--R +--R +--R 1500 7 1100 6 5 1091 4 3 135 2 +--R (2) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x +--R 7 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1500 7 1100 6 5 1091 4 3 135 2 +--R (3) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x +--R 7 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^2*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R (1) 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 500 +r0:=27*x+27/2*x^2-69*x^3-235/4*x^4+80*x^5+250/3*x^6 +--R +--R +--R 250 6 5 235 4 3 27 2 +--R (2) --- x + 80x - --- x - 69x + -- x + 27x +--R 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R 250 6 5 235 4 3 27 2 +--R (3) --- x + 80x - --- x - 69x + -- x + 27x +--R 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x) +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*log(2+3*x) +--R +--R +--R 5 4 3 2 +--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x +--R (2) -------------------------------------------------------------- +--R 1458 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x +--R (3) -------------------------------------------------------------- +--R 1458 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=1271/243*x-305/54*x^2-800/81*x^3+125/9*x^4+49/729/(2+3*x)+_ + 763/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98 +--R ----------------------------------------------------------------------------- +--R 4374x + 2916 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98 +--R ----------------------------------------------------------------------------- +--R 4374x + 2916 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=895/81*x-100/9*x^2+500/81*x^3+49/1458/(2+3*x)^2+(-763/729)/(2+3*x)-_ + 4099/729*log(2+3*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x +--R + +--R 2 +--R 128520x + 59862x - 3003 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x +--R + +--R 2 +--R 128520x + 59862x - 3003 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=-2800/243*x+250/81*x^2+49/2187/(2+3*x)^3+(-763/1458)/(2+3*x)^2+_ + 4099/729/(2+3*x)+8285/729*log(2+3*x) +--R +--R +--R (2) +--R 3 2 5 +--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x +--R + +--R 4 3 2 +--R - 631800x - 2235600x - 1485054x - 114939x + 93896 +--R / +--R 3 2 +--R 118098x + 236196x + 157464x + 34992 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 +--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x +--R + +--R 4 3 2 +--R - 631800x - 2235600x - 1485054x - 114939x + 93896 +--R / +--R 3 2 +--R 118098x + 236196x + 157464x + 34992 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=500/243*x+49/2916/(2+3*x)^4+(-763/2187)/(2+3*x)^3+4099/1458/(2+3*x)^2+_ + (-8285/729)/(2+3*x)-3800/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2) +--R + +--R 5 4 3 2 +--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2) +--R + +--R 5 4 3 2 +--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=49/3645/(2+3*x)^5+(-763/2916)/(2+3*x)^4+4099/2187/(2+3*x)^3+_ + (-8285/1458)/(2+3*x)^2+3800/729/(2+3*x)+500/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218 +--R / +--R 5 4 3 2 +--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218 +--R / +--R 5 4 3 2 +--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=49/4374/(2+3*x)^6+(-763/3645)/(2+3*x)^5+4099/2916/(2+3*x)^4+_ + (-8285/2187)/(2+3*x)^3+1900/729/(2+3*x)^2+(-500/729)/(2+3*x) +--R +--R +--R 500 5 3100 4 22685 3 39781 2 41968 116741 +--R - ---- x - ---- x - ----- x - ------ x - ------ x - -------- +--R 2187 6561 59049 236196 885735 15943230 +--R (2) ---------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 7290000x - 15066000x - 12249900x - 5370435x - 1510848x - 233482 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=7/729/(2+3*x)^7+(-763/4374)/(2+3*x)^6+4099/3645/(2+3*x)^5+_ + (-8285/2916)/(2+3*x)^4+3800/2187/(2+3*x)^3+(-250/729)/(2+3*x)^2 +--R +--R +--R 250 5 3700 4 23255 3 12077 2 35089 19072 +--R - ---- x - ----- x - ------ x - ------- x - -------- x - -------- +--R 6561 59049 708588 1771470 15943230 23914845 +--R (2) --------------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 3645000x - 5994000x - 3139425x - 652158x - 210534x - 76288 +--R / +--R 7 6 5 4 3 +--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x +--R + +--R 2 +--R 264539520x + 58786560x + 5598720 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-_ + 20577159/62500*x^4-7315947/15625*x^5+130383/1250*x^6+_ + 672867/875*x^7+16767/25*x^8+972/5*x^9+121/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x +--R + +--R 6 5 4 3 +--R 28521281250x - 128029072500x - 90025070625x + 4645056500x +--R + +--R 2 +--R 28194449150x + 11666661020x +--R / +--R 273437500 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x +--R + +--R 6 5 4 3 +--R 28521281250x - 128029072500x - 90025070625x + 4645056500x +--R + +--R 2 +--R 28194449150x + 11666661020x +--R / +--R 273437500 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-_ + 1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175*x^7+_ + 729/10*x^8+121/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x +--R + +--R 5 4 3 2 +--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x +--R / +--R 54687500 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x +--R + +--R 5 4 3 2 +--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x +--R / +--R 54687500 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+_ + 7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x +--R + +--R 3 2 +--R - 254943500x + 106949150x + 116661020x +--R / +--R 10937500 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x +--R + +--R 3 2 +--R - 254943500x + 106949150x + 116661020x +--R / +--R 10937500 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=83293/15625*x+5569/6250*x^2-7841/625*x^3-3159/500*x^4+1728/125*x^5+_ + 54/5*x^6+121/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x +--R + +--R 1665860x +--R / +--R 312500 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x +--R + +--R 1665860x +--R / +--R 312500 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x) +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=8293/3125*x-1931/1250*x^2-591/125*x^3+54/25*x^4+108/25*x^5+_ + 121/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x +--R (2) ----------------------------------------------------------------- +--R 31250 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x +--R (3) ----------------------------------------------------------------- +--R 31250 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x) +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=793/625*x-431/250*x^2-16/25*x^3+9/5*x^4+121/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x +--R (2) --------------------------------------------------- +--R 6250 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x +--R (3) --------------------------------------------------- +--R 6250 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x) +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=43/125*x-28/25*x^2+4/5*x^3+121/625*log(3+5*x) +--R +--R +--R 3 2 +--R 121log(5x + 3) + 500x - 700x + 215x +--R (2) ------------------------------------- +--R 625 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 121log(5x + 3) + 500x - 700x + 215x +--R (3) ------------------------------------- +--R 625 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^2/(3+5*x) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-32/25*x+2/5*x^2+121/125*log(3+5*x) +--R +--R +--R 2 +--R 121log(5x + 3) + 50x - 160x +--R (2) ---------------------------- +--R 125 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 121log(5x + 3) + 50x - 160x +--R (3) ---------------------------- +--R 125 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=4/15*x-49/9*log(2+3*x)+121/25*log(3+5*x) +--R +--R +--R 1089log(5x + 3) - 1225log(3x + 2) + 60x +--R (2) --------------------------------------- +--R 225 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1089log(5x + 3) - 1225log(3x + 2) + 60x +--R (3) --------------------------------------- +--R 225 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=49/9/(2+3*x)-217/9*log(2+3*x)+121/5*log(3+5*x) +--R +--R +--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245 +--R (2) ------------------------------------------------------------- +--R 135x + 90 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245 +--R (3) ------------------------------------------------------------- +--R 135x + 90 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=49/18/(2+3*x)^2+217/9/(2+3*x)-121*log(2+3*x)+121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (19602x + 26136x + 8712)log(5x + 3) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917 +--R / +--R 2 +--R 162x + 216x + 72 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (19602x + 26136x + 8712)log(5x + 3) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917 +--R / +--R 2 +--R 162x + 216x + 72 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=49/27/(2+3*x)^3+217/18/(2+3*x)^2+121/(2+3*x)-605*log(2+3*x)+605*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3) +--R + +--R 3 2 2 +--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x +--R + +--R 80361x + 27536 +--R / +--R 3 2 +--R 1458x + 2916x + 1944x + 432 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3) +--R + +--R 3 2 2 +--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x +--R + +--R 80361x + 27536 +--R / +--R 3 2 +--R 1458x + 2916x + 1944x + 432 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=49/36/(2+3*x)^4+217/27/(2+3*x)^3+121/2/(2+3*x)^2+605/(2+3*x)-_ + 3025*log(2+3*x)+3025*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2) +--R + +--R 3 2 +--R 1764180x + 3587166x + 2433252x + 550739 +--R / +--R 4 3 2 +--R 8748x + 23328x + 23328x + 10368x + 1728 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2) +--R + +--R 3 2 +--R 1764180x + 3587166x + 2433252x + 550739 +--R / +--R 4 3 2 +--R 8748x + 23328x + 23328x + 10368x + 1728 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=49/45/(2+3*x)^5+217/36/(2+3*x)^4+121/3/(2+3*x)^3+605/2/(2+3*x)^2+_ + 3025/(2+3*x)-15125*log(2+3*x)+15125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x +--R + +--R 87120000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 661567500x - 2205225000x - 2940300000x - 1960200000x +--R + +--R - 653400000x - 87120000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006 +--R / +--R 5 4 3 2 +--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x +--R + +--R 87120000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 661567500x - 2205225000x - 2940300000x - 1960200000x +--R + +--R - 653400000x - 87120000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006 +--R / +--R 5 4 3 2 +--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=49/54/(2+3*x)^6+217/45/(2+3*x)^5+121/4/(2+3*x)^4+605/3/(2+3*x)^3+_ + 3025/2/(2+3*x)^2+15125/(2+3*x)-75625*log(2+3*x)+75625*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 29770537500x + 119082150000x + 198470250000x + 176418000000x +--R + +--R 2 +--R 88209000000x + 23522400000x + 2613600000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x +--R + +--R 2 +--R - 88209000000x - 23522400000x - 2613600000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x +--R + +--R 275370238 +--R / +--R 6 5 4 3 2 +--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 29770537500x + 119082150000x + 198470250000x + 176418000000x +--R + +--R 2 +--R 88209000000x + 23522400000x + 2613600000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x +--R + +--R 2 +--R - 88209000000x - 23522400000x - 2613600000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x +--R + +--R 275370238 +--R / +--R 6 5 4 3 2 +--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=7/9/(2+3*x)^7+217/54/(2+3*x)^6+121/5/(2+3*x)^5+605/4/(2+3*x)^4+_ + 3025/3/(2+3*x)^3+15125/2/(2+3*x)^2+75625/(2+3*x)-378125*log(2+3*x)+_ + 378125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x +--R + +--R 3 2 +--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 446558062500x - 2083937625000x - 4167875250000x +--R + +--R 4 3 2 +--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x +--R + +--R - 26136000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 29770537500x + 120074501250x + 201822192000x + 180948267225x +--R + +--R 2 +--R 91271440062x + 24557875626x + 2753702432 +--R / +--R 7 6 5 4 3 2 +--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x +--R + +--R 725760x + 69120 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x +--R + +--R 3 2 +--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 446558062500x - 2083937625000x - 4167875250000x +--R + +--R 4 3 2 +--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x +--R + +--R - 26136000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 29770537500x + 120074501250x + 201822192000x + 180948267225x +--R + +--R 2 +--R 91271440062x + 24557875626x + 2753702432 +--R / +--R 7 6 5 4 3 2 +--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x +--R + +--R 725760x + 69120 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=27776932/1953125*x+17592879/781250*x^2-1512378/78125*x^3-_ + 213867/2500*x^4-656424/15625*x^5+116397/1250*x^6+_ + 107892/875*x^7+2187/50*x^8+(-121/9765625)/(3+5*x)+2497/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 +--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x +--R + +--R 7 6 5 4 +--R 228457968750x + 18948431250x - 151420775625x - 96641724375x +--R + +--R 3 2 +--R 14907569250x + 37916375350x + 11666311440x - 3388 +--R / +--R 1367187500x + 820312500 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x +--R + +--R 7 6 5 4 +--R 228457968750x + 18948431250x - 151420775625x - 96641724375x +--R + +--R 3 2 +--R 14907569250x + 37916375350x + 11666311440x - 3388 +--R / +--R 1367187500x + 820312500 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=2777053/390625*x+463086/78125*x^2-48771/3125*x^3-_ + 157599/6250*x^4+28917/3125*x^5+4374/125*x^6+2916/175*x^7+_ + (-121/1953125)/(3+5*x)+2134/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x +--R + +--R 5 4 3 2 +--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x +--R + +--R - 1694 +--R / +--R 136718750x + 82031250 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x +--R + +--R 5 4 3 2 +--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x +--R + +--R - 1694 +--R / +--R 136718750x + 82031250 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=277174/78125*x+1893/6250*x^2-25332/3125*x^3-8721/2500*x^4+_ + 5508/625*x^5+162/25*x^6+(-121/390625)/(3+5*x)+1771/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x +--R + +--R 4 3 2 +--R - 79681875x - 35631750x + 29137150x + 16630440x - 484 +--R / +--R 7812500x + 4687500 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x +--R + +--R 4 3 2 +--R - 79681875x - 35631750x + 29137150x + 16630440x - 484 +--R / +--R 7812500x + 4687500 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=5459/3125*x-3621/3125*x^2-1809/625*x^3+189/125*x^4+324/125*x^5+_ + (-121/78125)/(3+5*x)+1408/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x +--R + +--R 2 +--R 410800x + 409425x - 121 +--R / +--R 390625x + 234375 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x +--R + +--R 2 +--R 410800x + 409425x - 121 +--R / +--R 390625x + 234375 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=2416/3125*x-1449/1250*x^2-36/125*x^3+27/25*x^4+(-121/15625)/(3+5*x)+_ + 209/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x +--R + +--R 72480x - 242 +--R / +--R 156250x + 93750 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x +--R + +--R 72480x - 242 +--R / +--R 156250x + 93750 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=37/625*x-78/125*x^2+12/25*x^3+(-121/3125)/(3+5*x)+682/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121 +--R (2) ----------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121 +--R (3) ----------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=-92/125*x+6/25*x^2+(-121/625)/(3+5*x)+319/625*log(3+5*x) +--R +--R +--R 3 2 +--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121 +--R (2) ------------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121 +--R (3) ------------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^2/(3+5*x)^2 +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=4/25*x+(-121/125)/(3+5*x)-44/125*log(3+5*x) +--R +--R +--R 2 +--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121 +--R (2) --------------------------------------------- +--R 625x + 375 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121 +--R (3) --------------------------------------------- +--R 625x + 375 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-121/25)/(3+5*x)+49/3*log(2+3*x)-407/25*log(3+5*x) +--R +--R +--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363 +--R (2) ------------------------------------------------------------- +--R 375x + 225 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363 +--R (3) ------------------------------------------------------------- +--R 375x + 225 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-49/3)/(2+3*x)+(-121/5)/(3+5*x)+154*log(2+3*x)-154*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 34650x - 43890x - 13860)log(5x + 3) +--R + +--R 2 +--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461 +--R / +--R 2 +--R 225x + 285x + 90 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 34650x - 43890x - 13860)log(5x + 3) +--R + +--R 2 +--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461 +--R / +--R 2 +--R 225x + 285x + 90 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-49/6)/(2+3*x)^2+(-154)/(2+3*x)+(-121)/(3+5*x)+1133*log(2+3*x)-_ + 1133*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3) +--R + +--R 3 2 2 +--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x +--R + +--R - 8595 +--R / +--R 3 2 +--R 270x + 522x + 336x + 72 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3) +--R + +--R 3 2 2 +--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x +--R + +--R - 8595 +--R / +--R 3 2 +--R 270x + 522x + 336x + 72 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-49/9)/(2+3*x)^3+(-77)/(2+3*x)^2+(-1133)/(2+3*x)+(-605)/(3+5*x)+_ + 7480*log(2+3*x)-7480*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3) +--R + +--R 4 3 2 +--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2) +--R + +--R 3 2 +--R - 605880x - 1191564x - 780464x - 170229 +--R / +--R 4 3 2 +--R 1215x + 3159x + 3078x + 1332x + 216 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3) +--R + +--R 4 3 2 +--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2) +--R + +--R 3 2 +--R - 605880x - 1191564x - 780464x - 170229 +--R / +--R 4 3 2 +--R 1215x + 3159x + 3078x + 1332x + 216 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-49/12)/(2+3*x)^4+(-154/3)/(2+3*x)^3+(-1133/2)/(2+3*x)^2+_ + (-7480)/(2+3*x)+(-3025)/(3+5*x)+46475*log(2+3*x)-46475*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x +--R + +--R - 8923200 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x +--R + +--R 8923200 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153 +--R / +--R 5 4 3 2 +--R 1620x + 5292x + 6912x + 4512x + 1472x + 192 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x +--R + +--R - 8923200 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x +--R + +--R 8923200 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153 +--R / +--R 5 4 3 2 +--R 1620x + 5292x + 6912x + 4512x + 1472x + 192 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-49/15)/(2+3*x)^5+(-77/2)/(2+3*x)^4+(-1133/3)/(2+3*x)^3+_ + (-3740)/(2+3*x)^2+(-46475)/(2+3*x)+(-15125)/(3+5*x)+_ + 277750*log(2+3*x)-277750*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x +--R + +--R 2 +--R - 27997200000x - 7332600000x - 799920000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 10123987500x + 39821017500x + 65243475000x + 56994300000x +--R + +--R 2 +--R 27997200000x + 7332600000x + 799920000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x +--R + +--R - 84279984 +--R / +--R 6 5 4 3 2 +--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x +--R + +--R 2 +--R - 27997200000x - 7332600000x - 799920000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 10123987500x + 39821017500x + 65243475000x + 56994300000x +--R + +--R 2 +--R 27997200000x + 7332600000x + 799920000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x +--R + +--R - 84279984 +--R / +--R 6 5 4 3 2 +--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-49/18)/(2+3*x)^6+(-154/5)/(2+3*x)^5+(-1133/4)/(2+3*x)^4+_ + (-7480/3)/(2+3*x)^3+(-46475/2)/(2+3*x)^2+(-277750)/(2+3*x)+_ + (-75625)/(3+5*x)+1615625*log(2+3*x)-1615625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 1060011562500x - 4876053187500x - 9610771500000x +--R + +--R 4 3 2 +--R - 10521596250000x - 6909705000000x - 2722005000000x +--R + +--R - 595584000000x - 55836000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 1060011562500x + 4876053187500x + 9610771500000x +--R + +--R 4 3 2 +--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x +--R + +--R 55836000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x +--R + +--R 2 +--R - 202262350455x - 53445037346x - 5882909754 +--R / +--R 7 6 5 4 3 2 +--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x +--R + +--R 368640x + 34560 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 1060011562500x - 4876053187500x - 9610771500000x +--R + +--R 4 3 2 +--R - 10521596250000x - 6909705000000x - 2722005000000x +--R + +--R - 595584000000x - 55836000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 1060011562500x + 4876053187500x + 9610771500000x +--R + +--R 4 3 2 +--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x +--R + +--R 55836000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x +--R + +--R 2 +--R - 202262350455x - 53445037346x - 5882909754 +--R / +--R 7 6 5 4 3 2 +--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x +--R + +--R 368640x + 34560 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-7/3)/(2+3*x)^7+(-77/3)/(2+3*x)^6+(-1133/5)/(2+3*x)^5+_ + (-1870)/(2+3*x)^4+(-46475/3)/(2+3*x)^3+(-138875)/(2+3*x)^2+_ + (-1615625)/(2+3*x)+(-378125)/(3+5*x)+9212500*log(2+3*x)-9212500*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 1511080312500x - 7958356312500x - 18334441125000x +--R + +--R 5 4 3 +--R - 24132512250000x - 19849252500000x - 10446975000000x +--R + +--R 2 +--R - 3435894000000x - 645612000000x - 53064000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 1511080312500x + 7958356312500x + 18334441125000x +--R + +--R 5 4 3 +--R 24132512250000x + 19849252500000x + 10446975000000x +--R + +--R 2 +--R 3435894000000x + 645612000000x + 53064000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x +--R + +--R 3 2 +--R - 676227617505x - 268408563588x - 59178013234x - 5590850403 +--R / +--R 8 7 6 5 4 3 +--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x +--R + +--R 2 +--R 372960x + 70080x + 5760 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 1511080312500x - 7958356312500x - 18334441125000x +--R + +--R 5 4 3 +--R - 24132512250000x - 19849252500000x - 10446975000000x +--R + +--R 2 +--R - 3435894000000x - 645612000000x - 53064000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 1511080312500x + 7958356312500x + 18334441125000x +--R + +--R 5 4 3 +--R 24132512250000x + 19849252500000x + 10446975000000x +--R + +--R 2 +--R 3435894000000x + 645612000000x + 53064000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x +--R + +--R 3 2 +--R - 676227617505x - 268408563588x - 59178013234x - 5590850403 +--R / +--R 8 7 6 5 4 3 +--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x +--R + +--R 2 +--R 372960x + 70080x + 5760 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^2*(2+3*x)^8/(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=92582457/9765625*x+55559043/3906250*x^2-5350194/390625*x^3-_ + 1700919/31250*x^4-74601/3125*x^5+376407/6250*x^6+332424/4375*x^7+_ + 6561/250*x^8+(-121/97656250)/(3+5*x)^2+(-572/9765625)/(3+5*x)+_ + 5888/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 10 +--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x +--R + +--R 9 8 7 6 +--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x +--R + +--R 5 4 3 2 +--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x +--R + +--R 58326747710x - 120967 +--R / +--R 2 +--R 17089843750x + 20507812500x + 6152343750 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 +--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x +--R + +--R 9 8 7 6 +--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x +--R + +--R 5 4 3 2 +--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x +--R + +--R 58326747710x - 120967 +--R / +--R 2 +--R 17089843750x + 20507812500x + 6152343750 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=9251661/1953125*x+1390203/390625*x^2-162612/15625*x^3-_ + 193833/12500*x^4+104247/15625*x^5+13608/625*x^6+8748/875*x^7+_ + (-121/19531250)/(3+5*x)^2+(-2497/9765625)/(3+5*x)+21949/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 9 +--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x +--R + +--R 8 7 6 5 +--R 230850000000x + 248816812500x + 2308753125x - 181926753750x +--R + +--R 4 3 2 +--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x +--R + +--R 8 7 6 5 +--R 230850000000x + 248816812500x + 2308753125x - 181926753750x +--R + +--R 4 3 2 +--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=920502/390625*x+189/15625*x^2-16299/3125*x^3-23571/12500*x^4+_ + 17496/3125*x^5+486/125*x^6+(-121/3906250)/(3+5*x)^2+_ + (-2134/1953125)/(3+5*x)+15547/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x +--R + +--R 6 5 4 3 2 +--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x +--R + +--R 165647680x - 25850 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x +--R + +--R 6 5 4 3 2 +--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x +--R + +--R 165647680x - 25850 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=17796/15625*x-5301/6250*x^2-5499/3125*x^3+648/625*x^4+972/625*x^5+_ + (-121/781250)/(3+5*x)^2+(-1771/390625)/(3+5*x)+10234/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x +--R + +--R 5 4 3 2 +--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x +--R + +--R 5 4 3 2 +--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=1419/3125*x-4779/6250*x^2-72/625*x^3+81/125*x^4+(-121/156250)/(3+5*x)^2+_ + (-1408/78125)/(3+5*x)+1202/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 +--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x +--R + +--R 4 3 2 +--R - 2615625x - 1972500x + 1053225x + 624470x - 8569 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x +--R + +--R 4 3 2 +--R - 2615625x - 1972500x + 1053225x + 624470x - 8569 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=-153/3125*x-216/625*x^2+36/125*x^3+(-121/31250)/(3+5*x)^2+_ + (-209/3125)/(3+5*x)+23/125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 3 2 +--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x +--R + +--R - 24220x - 6391 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 2 +--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x +--R + +--R - 24220x - 6391 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=-264/625*x+18/125*x^2+(-121/6250)/(3+5*x)^2+(-682/3125)/(3+5*x)+_ + 829/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x +--R + +--R - 30580x - 4213 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x +--R + +--R - 30580x - 4213 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=12/125*x+(-121/1250)/(3+5*x)^2+(-319/625)/(3+5*x)-128/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035 +--R (2) --------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^2/(3+5*x)^3 +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=(-121/250)/(3+5*x)^2+44/125/(3+5*x)+4/125*log(3+5*x) +--R +--R +--R 2 +--R (200x + 240x + 72)log(5x + 3) + 440x + 143 +--R (2) ------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (200x + 240x + 72)log(5x + 3) + 440x + 143 +--R (3) ------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-121/50)/(3+5*x)^2+407/25/(3+5*x)-49*log(2+3*x)+49*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321 +--R / +--R 2 +--R 1250x + 1500x + 450 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321 +--R / +--R 2 +--R 1250x + 1500x + 450 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=49/(2+3*x)+(-121/10)/(3+5*x)^2+154/(3+5*x)-707*log(2+3*x)+707*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (530250x + 989800x + 615090x + 127260)log(5x + 3) +--R + +--R 3 2 2 +--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x +--R + +--R 13408 +--R / +--R 3 2 +--R 750x + 1400x + 870x + 180 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (530250x + 989800x + 615090x + 127260)log(5x + 3) +--R + +--R 3 2 2 +--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x +--R + +--R 13408 +--R / +--R 3 2 +--R 750x + 1400x + 870x + 180 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=49/2/(2+3*x)^2+707/(2+3*x)+(-121/2)/(3+5*x)^2+1133/(3+5*x)-_ + 6934*log(2+3*x)+6934*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3) +--R + +--R 4 3 2 +--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2) +--R + +--R 3 2 +--R 208020x + 395238x + 249932x + 52601 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3) +--R + +--R 4 3 2 +--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2) +--R + +--R 3 2 +--R 208020x + 395238x + 249932x + 52601 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=49/3/(2+3*x)^3+707/2/(2+3*x)^2+6934/(2+3*x)+(-605/2)/(3+5*x)^2+_ + 7480/(3+5*x)-57110*log(2+3*x)+57110*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x +--R + +--R 24671520 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x +--R + +--R - 24671520 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404 +--R / +--R 5 4 3 2 +--R 4050x + 12960x + 16578x + 10596x + 3384x + 432 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x +--R + +--R 24671520 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x +--R + +--R - 24671520 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404 +--R / +--R 5 4 3 2 +--R 4050x + 12960x + 16578x + 10596x + 3384x + 432 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=49/4/(2+3*x)^4+707/3/(2+3*x)^3+3467/(2+3*x)^2+57110/(2+3*x)+_ + (-3025/2)/(3+5*x)^2+46475/(3+5*x)-424975*log(2+3*x)+424975*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 10326892500x + 39930651000x + 64302117300x + 55199152800x +--R + +--R 2 +--R 26640832800x + 6853996800x + 734356800 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x +--R + +--R 2 +--R - 26640832800x - 6853996800x - 734356800 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x +--R + +--R 77372211 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 10326892500x + 39930651000x + 64302117300x + 55199152800x +--R + +--R 2 +--R 26640832800x + 6853996800x + 734356800 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x +--R + +--R 2 +--R - 26640832800x - 6853996800x - 734356800 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x +--R + +--R 77372211 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3e.input.pdf b/src/axiom-website/CATS/rich3e.input.pdf new file mode 100644 index 0000000..aa0dc30 Binary files /dev/null and b/src/axiom-website/CATS/rich3e.input.pdf differ diff --git a/src/axiom-website/CATS/rich3f.input.pamphlet b/src/axiom-website/CATS/rich3f.input.pamphlet new file mode 100644 index 0000000..1311f46 --- /dev/null +++ b/src/axiom-website/CATS/rich3f.input.pamphlet @@ -0,0 +1,6798 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 99 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 1 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3f.output +)spool rich3f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=49/5/(2+3*x)^5+707/4/(2+3*x)^4+6934/3/(2+3*x)^3+28555/(2+3*x)^2+_ + 424975/(2+3*x)+(-15125/2)/(3+5*x)^2+277750/(3+5*x)-_ + 2958125*log(2+3*x)+2958125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 1078236562500x + 4888005750000x + 9493273912500x +--R + +--R 4 3 2 +--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x +--R + +--R 51116400000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 1078236562500x - 4888005750000x - 9493273912500x +--R + +--R 4 3 2 +--R - 10239253875000x - 6623833500000x - 2570019000000x +--R + +--R - 553761000000x - 51116400000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 71882437500x + 280341506250x + 455361930000x + 394308004875x +--R + +--R 2 +--R 191974077080x + 49825144515x + 5385650262 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 1078236562500x + 4888005750000x + 9493273912500x +--R + +--R 4 3 2 +--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x +--R + +--R 51116400000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 1078236562500x - 4888005750000x - 9493273912500x +--R + +--R 4 3 2 +--R - 10239253875000x - 6623833500000x - 2570019000000x +--R + +--R - 553761000000x - 51116400000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 71882437500x + 280341506250x + 455361930000x + 394308004875x +--R + +--R 2 +--R 191974077080x + 49825144515x + 5385650262 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=49/6/(2+3*x)^6+707/5/(2+3*x)^5+3467/2/(2+3*x)^4+57110/3/(2+3*x)^3+_ + 424975/2/(2+3*x)^2+2958125/(2+3*x)+(-75625/2)/(3+5*x)^2+_ + 1615625/(3+5*x)-19637500*log(2+3*x)+19637500*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 3578934375000x + 18610458750000x + 42326863875000x +--R + +--R 5 4 3 +--R 54993640500000x + 44643892500000x + 23187960000000x +--R + +--R 2 +--R 7525090000000x + 1395048000000x + 113112000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 3578934375000x - 18610458750000x - 42326863875000x +--R + +--R 5 4 3 +--R - 54993640500000x - 44643892500000x - 23187960000000x +--R + +--R 2 +--R - 7525090000000x - 1395048000000x - 113112000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x +--R + +--R 3 2 +--R 1509746867100x + 590188362770x + 128130976648x + 11917538647 +--R / +--R 8 7 6 5 4 3 +--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x +--R + +--R 2 +--R 383200x + 71040x + 5760 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 3578934375000x + 18610458750000x + 42326863875000x +--R + +--R 5 4 3 +--R 54993640500000x + 44643892500000x + 23187960000000x +--R + +--R 2 +--R 7525090000000x + 1395048000000x + 113112000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 3578934375000x - 18610458750000x - 42326863875000x +--R + +--R 5 4 3 +--R - 54993640500000x - 44643892500000x - 23187960000000x +--R + +--R 2 +--R - 7525090000000x - 1395048000000x - 113112000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x +--R + +--R 3 2 +--R 1509746867100x + 590188362770x + 128130976648x + 11917538647 +--R / +--R 8 7 6 5 4 3 +--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x +--R + +--R 2 +--R 383200x + 71040x + 5760 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=7/(2+3*x)^7+707/6/(2+3*x)^6+6934/5/(2+3*x)^5+28555/2/(2+3*x)^4+_ + 424975/3/(2+3*x)^3+2958125/2/(2+3*x)^2+19637500/(2+3*x)+_ + (-378125/2)/(3+5*x)^2+9212500/(3+5*x)-125825000*log(2+3*x)+_ + 125825000*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 68794818750000x + 403596270000000x + 1052102094750000x +--R + +--R 6 5 4 +--R 1599505015500000x + 1562882391000000x + 1017823590000000x +--R + +--R 3 2 +--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 68794818750000x - 403596270000000x - 1052102094750000x +--R + +--R 6 5 4 +--R - 1599505015500000x - 1562882391000000x - 1017823590000000x +--R + +--R 3 2 +--R - 441796740000000x - 123248104000000x - 20051472000000x +--R + +--R - 1449504000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x +--R + +--R 4 3 2 +--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x +--R + +--R 152720488888 +--R / +--R 9 8 7 6 5 4 +--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x +--R + +--R 3 2 +--R 3511200x + 979520x + 159360x + 11520 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 68794818750000x + 403596270000000x + 1052102094750000x +--R + +--R 6 5 4 +--R 1599505015500000x + 1562882391000000x + 1017823590000000x +--R + +--R 3 2 +--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 68794818750000x - 403596270000000x - 1052102094750000x +--R + +--R 6 5 4 +--R - 1599505015500000x - 1562882391000000x - 1017823590000000x +--R + +--R 3 2 +--R - 441796740000000x - 123248104000000x - 20051472000000x +--R + +--R - 1449504000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x +--R + +--R 4 3 2 +--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x +--R + +--R 152720488888 +--R / +--R 9 8 7 6 5 4 +--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x +--R + +--R 3 2 +--R 3511200x + 979520x + 159360x + 11520 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 262440x - 1163484x - 1966842x - 1290573x + 344979x + 1027296x +--R + +--R 6 5 4 3 2 +--R 470736x - 104736x - 159712x - 36864x + 9984x + 5888x + 768 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=-343/2187*(2+3*x)^9+2009/2430*(2+3*x)^10-518/891*(2+3*x)^11+_ + 107/729*(2+3*x)^12-40/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 262440 13 12 1966842 11 1290573 10 9 8 +--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x +--R 13 11 10 +--R + +--R 7 6 159712 5 4 3 2 114328576 +--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x + --------- +--R 5 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 262440 13 12 1966842 11 1290573 10 9 8 +--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x +--R 13 11 10 +--R + +--R 7 6 159712 5 4 3 2 +--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 114328576 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 87480x - 329508x - 435942x - 139563x + 208035x + 203742x +--R + +--R 5 4 3 2 +--R 21084x - 48968x - 20592x + 1440x + 2368x + 384 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=384*x+1184*x^2+480*x^3-5148*x^4-48968/5*x^5+3514*x^6+29106*x^7+_ + 208035/8*x^8-15507*x^9-217971/5*x^10-329508/11*x^11-7290*x^12 +--R +--R +--R (2) +--R 12 329508 11 217971 10 9 208035 8 7 +--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x +--R 11 5 8 +--R + +--R 6 48968 5 4 3 2 +--R 3514x - ----- x - 5148x + 480x + 1184x + 384x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 329508 11 217971 10 9 208035 8 7 +--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x +--R 11 5 8 +--R + +--R 6 48968 5 4 3 2 +--R 3514x - ----- x - 5148x + 480x + 1184x + 384x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 29160x - 90396x - 85050x + 10179x + 62559x + 26208x - 10444x +--R + +--R 3 2 +--R - 9360x - 624x + 896x + 192 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=192*x+448*x^2-208*x^3-2340*x^4-10444/5*x^5+4368*x^6+8937*x^7+_ + 10179/8*x^8-9450*x^9-45198/5*x^10-29160/11*x^11 +--R +--R +--R (2) +--R 29160 11 45198 10 9 10179 8 7 6 10444 5 +--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x +--R 11 5 8 5 +--R + +--R 4 3 2 +--R - 2340x - 208x + 448x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 29160 11 45198 10 9 10179 8 7 6 10444 5 +--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x +--R 11 5 8 5 +--R + +--R 4 3 2 +--R - 2340x - 208x + 448x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 9720x - 23652x - 12582x + 11781x + 12999x + 70x - 3528x - 768x +--R + +--R 304x + 96 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=96*x+152*x^2-256*x^3-882*x^4+14*x^5+4333/2*x^6+1683*x^7-6291/4*x^8-_ + 2628*x^9-972*x^10 +--R +--R +--R (2) +--R 10 9 6291 8 7 4333 6 5 4 3 +--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x +--R 4 2 +--R + +--R 2 +--R 152x + 96x +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 6291 8 7 4333 6 5 4 3 +--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x +--R 4 2 +--R + +--R 2 +--R 152x + 96x +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 3240x - 5724x - 378x + 4179x + 1547x - 1008x - 504x + 80x + 48 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=48*x+40*x^2-168*x^3-252*x^4+1547/5*x^5+1393/2*x^6-54*x^7-1431/2*x^8-360*x^9 +--R +--R +--R (2) +--R 9 1431 8 7 1393 6 1547 5 4 3 2 +--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x +--R 2 2 5 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 1431 8 7 1393 6 1547 5 4 3 2 +--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x +--R 2 2 5 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 1080x - 1188x + 666x + 949x - 117x - 258x + 4x + 24 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=24*x+2*x^2-86*x^3-117/4*x^4+949/5*x^5+111*x^6-1188/7*x^7-135*x^8 +--R +--R +--R 8 1188 7 6 949 5 117 4 3 2 +--R (2) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 1188 7 6 949 5 117 4 3 2 +--R (3) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) - 360x - 156x + 326x + 99x - 105x - 16x + 12 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7 +--R +--R +--R 360 7 6 326 5 99 4 3 2 +--R (2) - --- x - 26x + --- x + -- x - 35x - 8x + 12x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 360 7 6 326 5 99 4 3 2 +--R (3) - --- x - 26x + --- x + -- x - 35x - 8x + 12x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) - 120x + 28x + 90x - 27x - 17x + 6 +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 500 +r0:=6*x-17/2*x^2-9*x^3+45/2*x^4+28/5*x^5-20*x^6 +--R +--R +--R 6 28 5 45 4 3 17 2 +--R (2) - 20x + -- x + -- x - 9x - -- x + 6x +--R 5 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 28 5 45 4 3 17 2 +--R (3) - 20x + -- x + -- x - 9x - -- x + 6x +--R 5 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^3*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) - 40x + 36x + 6x - 13x + 3 +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 500 +r0:=3*x-13/2*x^2+2*x^3+9*x^4-8*x^5 +--R +--R +--R 5 4 3 13 2 +--R (2) - 8x + 9x + 2x - -- x + 3x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 13 2 +--R (3) - 8x + 9x + 2x - -- x + 3x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x) +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=293/81*x-161/27*x^2+188/27*x^3-10/3*x^4-343/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x +--R (2) ------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x +--R (3) ------------------------------------------------- +--R 243 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=-286/27*x+134/27*x^2-40/27*x^3+343/243/(2+3*x)+2009/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343 +--R (2) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343 +--R (3) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=116/27*x-20/27*x^2+343/486/(2+3*x)^2+(-2009/243)/(2+3*x)-518/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x +--R + +--R - 3702x - 7693 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x +--R + +--R - 3702x - 7693 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=-40/81*x+343/729/(2+3*x)^3+(-2009/486)/(2+3*x)^2+518/81/(2+3*x)+_ + 428/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x +--R + +--R 2 +--R 57996x + 88047x + 25928 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x +--R + +--R 2 +--R 57996x + 88047x + 25928 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=343/972/(2+3*x)^4+(-2009/729)/(2+3*x)^3+259/81/(2+3*x)^2+_ + (-428/243)/(2+3*x)-40/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x +--R + +--R 2 +--R - 193428x - 97116x - 18835 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 3 +--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x +--R + +--R 2 +--R - 193428x - 97116x - 18835 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=1/105*(1-2*x)^4/(2+3*x)^5-173/2940*(1-2*x)^4/(2+3*x)^4 +--R +--R +--R 692 5 64 4 38 3 58 2 5 53 +--R - ----- x + ---- x - ----- x - ----- x + ---- x - ------ +--R 59535 3969 11907 11907 1764 119070 +--R (2) ------------------------------------------------------------ +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 64800x + 57240x + 34920x + 16905x + 1282 +--R (3) ----------------------------------------------------------------- +--R 5 4 3 2 +--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R 692 +--R (4) ----- +--R 59535 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=1/126*(1-2*x)^4/(2+3*x)^6-103/2205*(1-2*x)^4/(2+3*x)^5-_ + 103/30870*(1-2*x)^4/(2+3*x)^4 +--R +--R +--R (2) +--R 824 6 3296 5 44 4 316 3 659 2 349 +--R - ------- x - ------- x + ---- x - ------ x - ------ x + ------ x +--R 1250235 1250235 9261 250047 500094 416745 +--R + +--R 113 +--R - ------ +--R 833490 +--R / +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 48600x + 14040x + 3375x + 7218x - 413 +--R / +--R 6 5 4 3 2 +--R 5314410x + 21257640x + 35429400x + 31492800x + 15746400x + 4199040x +--R + +--R 466560 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 824 +--R (4) ------- +--R 1250235 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=49/243/(2+3*x)^7+(-2009/1458)/(2+3*x)^6+518/405/(2+3*x)^5+_ + (-107/243)/(2+3*x)^4+40/729/(2+3*x)^3 +--R +--R +--R 40 4 1 3 56 2 1531 302 +--R ----- x - ----- x - ------ x + ------- x - ------- +--R 19683 59049 295245 5314410 7971615 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 32400x - 270x - 3024x + 4593x - 604 +--R / +--R 7 6 5 4 3 +--R 15943230x + 74401740x + 148803480x + 165337200x + 110224800x +--R + +--R 2 +--R 44089920x + 9797760x + 933120 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R - 1312200x - 6604740x - 13324662x - 12353391x - 2146824x +--R + +--R 8 7 6 5 4 3 2 +--R 6171417x + 5435568x + 888528x - 1112768x - 663456x - 60672x + 59392x +--R + +--R 21504x + 2304 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=2304*x+10752*x^2+59392/3*x^3-15168*x^4-663456/5*x^5-556384/3*x^6+_ + 888528/7*x^7+679446*x^8+685713*x^9-1073412/5*x^10-_ + 12353391/11*x^11-2220777/2*x^12-6604740/13*x^13-656100/7*x^14 +--R +--R +--R (2) +--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10 +--R - ------ x - ------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 5 +--R + +--R 9 8 888528 7 556384 6 663456 5 4 +--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x +--R 7 3 5 +--R + +--R 59392 3 2 +--R ----- x + 10752x + 2304x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10 +--R - ------ x - ------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 5 +--R + +--R 9 8 888528 7 556384 6 663456 5 4 +--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x +--R 7 3 5 +--R + +--R 59392 3 2 +--R ----- x + 10752x + 2304x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 437400x - 1909980x - 3168234x - 2005641x + 621486x + 1642815x +--R + +--R 6 5 4 3 2 +--R 716646x - 181588x - 249864x - 54576x + 16160x + 9024x + 1152 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=1152*x+4512*x^2+16160/3*x^3-13644*x^4-249864/5*x^5-90794/3*x^6+_ + 102378*x^7+1642815/8*x^8+69054*x^9-2005641/10*x^10-3168234/11*x^11-_ + 159165*x^12-437400/13*x^13 +--R +--R +--R (2) +--R 437400 13 12 3168234 11 2005641 10 9 1642815 8 +--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x +--R 13 11 10 8 +--R + +--R 7 90794 6 249864 5 4 16160 3 2 +--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 437400 13 12 3168234 11 2005641 10 9 1642815 8 +--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x +--R 13 11 10 8 +--R + +--R 7 90794 6 249864 5 4 16160 3 2 +--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 145800x - 539460x - 696438x - 204255x + 343332x + 318717x +--R + +--R 5 4 3 2 +--R 26404x - 78132x - 31200x + 2608x + 3648x + 576 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=576*x+1824*x^2+2608/3*x^3-7800*x^4-78132/5*x^5+13202/3*x^6+45531*x^7+_ + 85833/2*x^8-22695*x^9-348219/5*x^10-539460/11*x^11-12150*x^12 +--R +--R +--R (2) +--R 12 539460 11 348219 10 9 85833 8 7 +--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x +--R 11 5 2 +--R + +--R 13202 6 78132 5 4 2608 3 2 +--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 539460 11 348219 10 9 85833 8 7 +--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x +--R 11 5 2 +--R + +--R 13202 6 78132 5 4 2608 3 2 +--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 48600x - 147420x - 133866x + 21159x + 100338x + 39347x - 17430x +--R + +--R 3 2 +--R - 14424x - 784x + 1392x + 288 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=288*x+696*x^2-784/3*x^3-3606*x^4-3486*x^5+39347/6*x^6+14334*x^7+_ + 21159/8*x^8-14874*x^9-14742*x^10-48600/11*x^11 +--R +--R +--R (2) +--R 48600 11 10 9 21159 8 7 39347 6 5 +--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x +--R 11 8 6 +--R + +--R 4 784 3 2 +--R - 3606x - --- x + 696x + 288x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 48600 11 10 9 21159 8 7 39347 6 5 +--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x +--R 11 8 6 +--R + +--R 4 784 3 2 +--R - 3606x - --- x + 696x + 288x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 16200x - 38340x - 19062x + 19761x + 20272x - 399x - 5544x - 1112x +--R + +--R 480x + 144 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=144*x+240*x^2-1112/3*x^3-1386*x^4-399/5*x^5+10136/3*x^6+2823*x^7-_ + 9531/4*x^8-4260*x^9-1620*x^10 +--R +--R +--R (2) +--R 10 9 9531 8 7 10136 6 399 5 4 +--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x +--R 4 3 5 +--R + +--R 1112 3 2 +--R - ---- x + 240x + 144x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 9531 8 7 10136 6 399 5 4 +--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x +--R 4 3 5 +--R + +--R 1112 3 2 +--R - ---- x + 240x + 144x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 5400x - 9180x - 234x + 6743x + 2262x - 1641x - 754x + 132x + 72 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-_ + 2295/2*x^8-600*x^9 +--R +--R +--R (2) +--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2 +--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x +--R 2 7 6 5 4 3 +--R + +--R 72x +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2 +--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x +--R 2 7 6 5 4 3 +--R + +--R 72x +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 1800x - 1860x + 1162x + 1473x - 228x - 395x + 12x + 36 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8 +--R +--R +--R 8 1860 7 581 6 1473 5 4 395 3 2 +--R (2) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x +--R 7 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 1860 7 581 6 1473 5 4 395 3 2 +--R (3) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x +--R 7 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) - 600x - 220x + 534x + 135x - 166x - 21x + 18 +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 500 +r0:=18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7 +--R +--R +--R 600 7 110 6 534 5 135 4 166 3 21 2 +--R (2) - --- x - --- x + --- x + --- x - --- x - -- x + 18x +--R 7 3 5 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 600 7 110 6 534 5 135 4 166 3 21 2 +--R (3) - --- x - --- x + --- x + --- x - --- x - -- x + 18x +--R 7 3 5 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^3*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) - 200x + 60x + 138x - 47x - 24x + 9 +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 500 +r0:=9*x-12*x^2-47/3*x^3+69/2*x^4+12*x^5-100/3*x^6 +--R +--R +--R 100 6 5 69 4 47 3 2 +--R (2) - --- x + 12x + -- x - -- x - 12x + 9x +--R 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 100 6 5 69 4 47 3 2 +--R (3) - --- x + 12x + -- x - -- x - 12x + 9x +--R 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x) +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*log(2+3*x) +--R +--R +--R 5 4 3 2 +--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x +--R (2) ------------------------------------------------------------- +--R 1458 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x +--R (3) ------------------------------------------------------------- +--R 1458 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=2323/243*x-313/27*x^2+980/81*x^3-50/9*x^4+(-343/729)/(2+3*x)-_ + 3724/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x +--R + +--R 13938x - 343 +--R / +--R 2187x + 1458 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x +--R + +--R 13938x - 343 +--R / +--R 2187x + 1458 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=-1546/81*x+230/27*x^2-200/81*x^3+(-343/1458)/(2+3*x)^2+3724/729/(2+3*x)+_ + 11599/729*log(2+3*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x +--R + +--R 2 +--R - 284256x - 88968x + 14553 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x +--R + +--R 2 +--R - 284256x - 88968x + 14553 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1780/243*x-100/81*x^2+(-343/2187)/(2+3*x)^3+1862/729/(2+3*x)^2+_ + (-11599/729)/(2+3*x)-8198/729*log(2+3*x) +--R +--R +--R (2) +--R 3 2 5 +--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x +--R + +--R 4 3 2 +--R 286740x + 767880x + 241947x - 272646x - 128359 +--R / +--R 3 2 +--R 59049x + 118098x + 78732x + 17496 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 +--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x +--R + +--R 4 3 2 +--R 286740x + 767880x + 241947x - 272646x - 128359 +--R / +--R 3 2 +--R 59049x + 118098x + 78732x + 17496 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=-200/243*x+(-343/2916)/(2+3*x)^4+3724/2187/(2+3*x)^3+_ + (-11599/1458)/(2+3*x)^2+8198/729/(2+3*x)+2180/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2) +--R + +--R 5 4 3 2 +--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2) +--R + +--R 5 4 3 2 +--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-343/3645)/(2+3*x)^5+931/729/(2+3*x)^4+(-11599/2187)/(2+3*x)^3+_ + 4099/729/(2+3*x)^2+(-2180/729)/(2+3*x)-200/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399 +--R / +--R 5 4 3 2 +--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399 +--R / +--R 5 4 3 2 +--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=(-343/4374)/(2+3*x)^6+3724/3645/(2+3*x)^5+(-11599/2916)/(2+3*x)^4+_ + 8198/2187/(2+3*x)^3+(-1090/729)/(2+3*x)^2+200/729/(2+3*x) +--R +--R +--R 200 5 910 4 6038 3 13345 2 15289 19643 +--R ---- x + ---- x + ----- x + ------ x + ------ x + -------- +--R 2187 6561 59049 236196 885735 15943230 +--R (2) -------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2916000x + 4422600x + 3260520x + 1801575x + 550404x + 39286 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=(-49/729)/(2+3*x)^7+1862/2187/(2+3*x)^6+(-11599/3645)/(2+3*x)^5+_ + 4099/1458/(2+3*x)^4+(-2180/2187)/(2+3*x)^3+100/729/(2+3*x)^2 +--R +--R +--R 100 5 820 4 1417 3 2686 2 10232 1763 +--R ---- x + ----- x + ------ x + ------ x + ------- x - -------- +--R 6561 59049 354294 885735 7971615 23914845 +--R (2) ----------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 729000x + 664200x + 191295x + 145044x + 61392x - 3526 +--R / +--R 7 6 5 4 3 +--R 47829690x + 223205220x + 446410440x + 496011600x + 330674400x +--R + +--R 2 +--R 132269760x + 29393280x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R - 2187000x - 10862100x - 21571110x - 19532907x - 2909493x +--R + +--R 8 7 6 5 4 3 +--R 10078533x + 8511675x + 1241998x - 1794084x - 1022472x - 82928x +--R + +--R 2 +--R 93600x + 32832x + 3456 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=3456*x+16416*x^2+31200*x^3-20732*x^4-1022472/5*x^5-299014*x^6+_ + 1241998/7*x^7+8511675/8*x^8+1119837*x^9-2909493/10*x^10-_ + 19532907/11*x^11-3595185/2*x^12-10862100/13*x^13-1093500/7*x^14 +--R +--R +--R (2) +--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10 +--R - ------- x - -------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 10 +--R + +--R 9 8511675 8 1241998 7 6 1022472 5 4 +--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x +--R 8 7 5 +--R + +--R 3 2 +--R 31200x + 16416x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10 +--R - ------- x - -------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 10 +--R + +--R 9 8511675 8 1241998 7 6 1022472 5 4 +--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x +--R 8 7 5 +--R + +--R 3 2 +--R 31200x + 16416x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 729000x - 3134700x - 5100570x - 3110589x + 1103895x + 2623581x +--R + +--R 6 5 4 3 2 +--R 1088171x - 311448x - 390396x - 80560x + 26064x + 13824x + 1728 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=1728*x+6912*x^2+8688*x^3-20140*x^4-390396/5*x^5-51908*x^6+_ + 155453*x^7+2623581/8*x^8+122655*x^9-3110589/10*x^10-5100570/11*x^11-_ + 261225*x^12-729000/13*x^13 +--R +--R +--R (2) +--R 729000 13 12 5100570 11 3110589 10 9 +--R - ------ x - 261225x - ------- x - ------- x + 122655x +--R 13 11 10 +--R + +--R 2623581 8 7 6 390396 5 4 3 2 +--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x +--R 8 5 +--R + +--R 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 729000 13 12 5100570 11 3110589 10 9 +--R - ------ x - 261225x - ------- x - ------- x + 122655x +--R 13 11 10 +--R + +--R 2623581 8 7 6 390396 5 4 3 2 +--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x +--R 8 5 +--R + +--R 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 243000x - 882900x - 1111590x - 295803x + 565167x + 497749x +--R + +--R 5 4 3 2 +--R 30891x - 124410x - 47192x + 4608x + 5616x + 864 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=864*x+2808*x^2+1536*x^3-11798*x^4-24882*x^5+10297/2*x^6+_ + 71107*x^7+565167/8*x^8-32867*x^9-111159*x^10-882900/11*x^11-20250*x^12 +--R +--R +--R (2) +--R 12 882900 11 10 9 565167 8 7 +--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x +--R 11 8 +--R + +--R 10297 6 5 4 3 2 +--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 882900 11 10 9 565167 8 7 +--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x +--R 11 8 +--R + +--R 10297 6 5 4 3 2 +--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 81000x - 240300x - 210330x + 41619x + 160643x + 58821x - 28917x +--R + +--R 3 2 +--R - 22192x - 936x + 2160x + 432 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+_ + 41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^11 +--R +--R +--R (2) +--R 81000 11 10 9 41619 8 7 19607 6 28917 5 +--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x +--R 11 8 2 5 +--R + +--R 4 3 2 +--R - 5548x - 312x + 1080x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 81000 11 10 9 41619 8 7 19607 6 28917 5 +--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x +--R 11 8 2 5 +--R + +--R 4 3 2 +--R - 5548x - 312x + 1080x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 27000x - 62100x - 28710x + 33013x + 31539x - 1419x - 8693x +--R + +--R 2 +--R - 1602x + 756x + 216 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-_ + 14355/4*x^8-6900*x^9-2700*x^10 +--R +--R +--R (2) +--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4 +--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x +--R 4 7 2 5 4 +--R + +--R 3 2 +--R - 534x + 378x + 216x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4 +--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x +--R 4 7 2 5 4 +--R + +--R 3 2 +--R - 534x + 378x + 216x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 9000x - 14700x + 230x + 10851x + 3279x - 2659x - 1125x + 216x + 108 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-_ + 3675/2*x^8-1000*x^9 +--R +--R +--R (2) +--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2 +--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x +--R 2 7 2 5 4 +--R + +--R 108x +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2 +--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x +--R 2 7 2 5 4 +--R + +--R 108x +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 3000x - 2900x + 2010x + 2277x - 425x - 603x + 27x + 54 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8 +--R +--R +--R 8 2900 7 6 2277 5 425 4 3 27 2 +--R (2) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x +--R 7 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 2900 7 6 2277 5 425 4 3 27 2 +--R (3) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x +--R 7 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^3*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*x^7 +--R +--R +--R 1000 7 6 5 179 4 3 27 2 +--R (2) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x +--R 7 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1000 7 6 5 179 4 3 27 2 +--R (3) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x +--R 7 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x) +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-_ + 343/2187*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x +--R + +--R 60078x +--R / +--R 4374 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x +--R + +--R 60078x +--R / +--R 4374 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=2287/729*x-5287/486*x^2-190/81*x^3+775/27*x^4-200/9*x^5+343/2187/(2+3*x)+_ + 1813/729*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x +--R + +--R 2 +--R - 54000x + 27444x + 686 +--R / +--R 13122x + 8748 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x +--R + +--R 2 +--R - 54000x + 27444x + 686 +--R / +--R 13122x + 8748 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=16253/729*x-1795/81*x^2+1700/81*x^3-250/27*x^4+343/4374/(2+3*x)^2+_ + (-1813/729)/(2+3*x)-10073/729*log(2+3*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x +--R + +--R 4 3 2 +--R 67230x + 81702x + 782496x + 357438x - 21413 +--R / +--R 2 +--R 39366x + 52488x + 17496 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x +--R + +--R 4 3 2 +--R 67230x + 81702x + 782496x + 357438x - 21413 +--R / +--R 2 +--R 39366x + 52488x + 17496 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=-24970/729*x+3550/243*x^2-1000/243*x^3+343/6561/(2+3*x)^3+_ + (-1813/1458)/(2+3*x)^2+10073/729/(2+3*x)+66193/2187*log(2+3*x) +--R +--R +--R (2) +--R 3 2 6 +--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x +--R + +--R 5 4 3 2 +--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308 +--R / +--R 3 2 +--R 354294x + 708588x + 472392x + 104976 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 6 +--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x +--R + +--R 5 4 3 2 +--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308 +--R / +--R 3 2 +--R 354294x + 708588x + 472392x + 104976 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=9100/729*x-500/243*x^2+343/8748/(2+3*x)^4+(-1813/2187)/(2+3*x)^3+_ + 10073/1458/(2+3*x)^2+(-66193/2187)/(2+3*x)-14390/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x +--R + +--R - 630195 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x +--R + +--R - 630195 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=-1000/729*x+343/10935/(2+3*x)^5+(-1813/2916)/(2+3*x)^4+_ + 10073/2187/(2+3*x)^3+(-66193/4374)/(2+3*x)^2+14390/729/(2+3*x)+_ + 3700/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x +--R + +--R 2368000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x +--R + +--R 19824285x + 3090594 +--R / +--R 5 4 3 2 +--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x +--R + +--R 2368000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x +--R + +--R 19824285x + 3090594 +--R / +--R 5 4 3 2 +--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=343/13122/(2+3*x)^6+(-1813/3645)/(2+3*x)^5+10073/2916/(2+3*x)^4+_ + (-66193/6561)/(2+3*x)^3+7195/729/(2+3*x)^2+(-3700/729)/(2+3*x)-_ + 1000/2187*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x +--R + +--R - 11520000x - 1280000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x +--R + +--R - 11520000x - 1280000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=49/2187/(2+3*x)^7+(-1813/4374)/(2+3*x)^6+10073/3645/(2+3*x)^5+_ + (-66193/8748)/(2+3*x)^4+14390/2187/(2+3*x)^3+(-1850/729)/(2+3*x)^2+_ + 1000/2187/(2+3*x) +--R +--R +--R (2) +--R 1000 6 2150 5 18890 4 146287 3 160381 2 331697 33326 +--R ---- x + ---- x + ----- x + ------ x + ------- x + -------- x + -------- +--R 6561 6561 59049 708588 1771470 15943230 23914845 +--R ----------------------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 14580000x + 31347000x + 30601800x + 19748745x + 8660574x + 1990182x +--R + +--R 133304 +--R / +--R 7 6 5 4 3 +--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x +--R + +--R 2 +--R 264539520x + 58786560x + 5598720 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=41666223/1953125*x+11111259/781250*x^2-17453753/234375*x^3-_ + 5848749/62500*x^4+2212083/15625*x^5+331713/1250*x^6-40338/875*x^7-_ + 13851/50*x^8-648/5*x^9+1331/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x +--R + +--R 6 5 4 3 +--R 217686656250x + 116134357500x - 76764830625x - 61088135500x +--R + +--R 2 +--R 11666821950x + 17499813660x +--R / +--R 820312500 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x +--R + +--R 6 5 4 3 +--R 217686656250x + 116134357500x - 76764830625x - 61088135500x +--R + +--R 2 +--R 11666821950x + 17499813660x +--R / +--R 820312500 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=4166223/390625*x-138741/156250*x^2-1703753/46875*x^3-73749/12500*x^4+_ + 243333/3125*x^5+4419/125*x^6-11988/175*x^7-243/5*x^8+_ + 1331/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x +--R + +--R 5 4 3 2 +--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x +--R / +--R 164062500 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x +--R + +--R 5 4 3 2 +--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x +--R / +--R 164062500 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=416223/78125*x-138741/31250*x^2-128753/9375*x^3+31251/2500*x^4+_ + 14958/625*x^5-306/25*x^6-648/35*x^7+1331/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x +--R + +--R 3 2 +--R - 450635500x - 145678050x + 174813660x +--R / +--R 32812500 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x +--R + +--R 3 2 +--R - 450635500x - 145678050x + 174813660x +--R / +--R 32812500 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=41223/15625*x-26241/6250*x^2-5003/1875*x^3+2313/250*x^4+_ + 108/125*x^5-36/5*x^6+1331/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x +--R + +--R 2 +--R - 1968075x + 1236690x +--R / +--R 468750 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x +--R + +--R 2 +--R - 1968075x + 1236690x +--R / +--R 468750 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x) +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=3723/3125*x-3741/1250*x^2+622/375*x^3+69/25*x^4-72/25*x^5+_ + 1331/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x +--R (2) --------------------------------------------------------------------- +--R 93750 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x +--R (3) --------------------------------------------------------------------- +--R 93750 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x) +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x +--R (2) ---------------------------------------------------- +--R 9375 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x +--R (3) ---------------------------------------------------- +--R 9375 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^3/(3+5*x) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=-402/125*x+42/25*x^2-8/15*x^3+1331/625*log(3+5*x) +--R +--R +--R 3 2 +--R 3993log(5x + 3) - 1000x + 3150x - 6030x +--R (2) ----------------------------------------- +--R 1875 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 3993log(5x + 3) - 1000x + 3150x - 6030x +--R (3) ----------------------------------------- +--R 1875 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=332/225*x-4/15*x^2-343/27*log(2+3*x)+1331/125*log(3+5*x) +--R +--R +--R 2 +--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x +--R (2) --------------------------------------------------- +--R 3375 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x +--R (3) --------------------------------------------------- +--R 3375 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-8/45*x+343/27/(2+3*x)-1421/27*log(2+3*x)+1331/25*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x +--R + +--R - 240x + 8575 +--R / +--R 2025x + 1350 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x +--R + +--R - 240x + 8575 +--R / +--R 2025x + 1350 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=343/54/(2+3*x)^2+1421/27/(2+3*x)-7189/27*log(2+3*x)+1331/5*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (646866x + 862488x + 287496)log(5x + 3) +--R + +--R 2 +--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135 +--R / +--R 2 +--R 2430x + 3240x + 1080 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (646866x + 862488x + 287496)log(5x + 3) +--R + +--R 2 +--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135 +--R / +--R 2 +--R 2430x + 3240x + 1080 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=343/81/(2+3*x)^3+1421/54/(2+3*x)^2+7189/27/(2+3*x)-1331*log(2+3*x)+_ + 1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x +--R + +--R 530397x + 181748 +--R / +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x +--R + +--R 530397x + 181748 +--R / +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=343/108/(2+3*x)^4+1421/81/(2+3*x)^3+7189/54/(2+3*x)^2+1331/(2+3*x)-_ + 6655*log(2+3*x)+6655*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 11643588x + 23675382x + 16059444x + 3634885 +--R / +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 11643588x + 23675382x + 16059444x + 3634885 +--R / +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=343/135/(2+3*x)^5+1421/108/(2+3*x)^4+7189/81/(2+3*x)^3+1331/2/(2+3*x)^2+_ + 6655/(2+3*x)-33275*log(2+3*x)+33275*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 13099036500x + 43663455000x + 58217940000x + 38811960000x +--R + +--R 12937320000x + 1724976000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x +--R + +--R - 12937320000x - 1724976000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346 +--R / +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13099036500x + 43663455000x + 58217940000x + 38811960000x +--R + +--R 12937320000x + 1724976000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x +--R + +--R - 12937320000x - 1724976000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346 +--R / +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=343/162/(2+3*x)^6+1421/135/(2+3*x)^5+7189/108/(2+3*x)^4+_ + 1331/3/(2+3*x)^3+6655/2/(2+3*x)^2+33275/(2+3*x)-166375*log(2+3*x)+_ + 166375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x +--R + +--R 2 +--R 582179400000x + 155247840000x + 17249760000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x +--R + +--R 2 +--R - 582179400000x - 155247840000x - 17249760000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 13099036500x + 44100089550x + 59401704780x + 40016101275x +--R + +--R 13482032616x + 1817443594 +--R / +--R 6 5 4 3 2 +--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x +--R + +--R 103680 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x +--R + +--R 2 +--R 582179400000x + 155247840000x + 17249760000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x +--R + +--R 2 +--R - 582179400000x - 155247840000x - 17249760000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 13099036500x + 44100089550x + 59401704780x + 40016101275x +--R + +--R 13482032616x + 1817443594 +--R / +--R 6 5 4 3 2 +--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x +--R + +--R 103680 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=49/27/(2+3*x)^7+1421/162/(2+3*x)^6+7189/135/(2+3*x)^5+1331/4/(2+3*x)^4+_ + 6655/3/(2+3*x)^3+33275/2/(2+3*x)^2+166375/(2+3*x)-_ + 831875*log(2+3*x)+831875*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2947283212500x + 13753988325000x + 27507976650000x +--R + +--R 4 3 2 +--R 30564418500000x + 20376279000000x + 8150511600000x +--R + +--R 1811224800000x + 172497600000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2947283212500x - 13753988325000x - 27507976650000x +--R + +--R 4 3 2 +--R - 30564418500000x - 20376279000000x - 8150511600000x +--R + +--R - 1811224800000x - 172497600000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x +--R + +--R 2 +--R 602391504582x + 162081979026x + 18174436072 +--R / +--R 7 6 5 4 3 2 +--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x +--R + +--R 2177280x + 207360 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 2947283212500x + 13753988325000x + 27507976650000x +--R + +--R 4 3 2 +--R 30564418500000x + 20376279000000x + 8150511600000x +--R + +--R 1811224800000x + 172497600000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2947283212500x - 13753988325000x - 27507976650000x +--R + +--R 4 3 2 +--R - 30564418500000x - 20376279000000x - 8150511600000x +--R + +--R - 1811224800000x - 172497600000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x +--R + +--R 2 +--R 602391504582x + 162081979026x + 18174436072 +--R / +--R 7 6 5 4 3 2 +--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x +--R + +--R 2177280x + 207360 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=13880997/1953125*x-461623/390625*x^2-1836723/78125*x^3-5643/3125*x^4+_ + 774981/15625*x^5+12231/625*x^6-37908/875*x^7-729/25*x^8+_ + (-1331/9765625)/(3+5*x)+23232/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 +--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x +--R + +--R 7 6 5 4 +--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x +--R + +--R 3 2 +--R - 5225318000x + 2186822400x + 1457504685x - 9317 +--R / +--R 341796875x + 205078125 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x +--R + +--R 7 6 5 4 +--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x +--R + +--R 3 2 +--R - 5225318000x + 2186822400x + 1457504685x - 9317 +--R / +--R 341796875x + 205078125 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=1382328/390625*x-507023/156250*x^2-26594/3125*x^3+108387/12500*x^4+_ + 44982/3125*x^5-1026/125*x^6-1944/175*x^7+(-1331/1953125)/(3+5*x)+_ + 19239/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 +--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x +--R + +--R 6 5 4 3 2 +--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x +--R + +--R 580577760x - 37268 +--R / +--R 273437500x + 164062500 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x +--R + +--R 6 5 4 3 2 +--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x +--R + +--R 580577760x - 37268 +--R / +--R 273437500x + 164062500 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=133659/78125*x-1816/625*x^2-4217/3125*x^3+7317/1250*x^4+108/625*x^5-_ + 108/25*x^6+(-1331/390625)/(3+5*x)+15246/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x +--R + +--R 4 3 2 +--R 8448125x - 14512750x - 127050x + 4009770x - 2662 +--R / +--R 3906250x + 2343750 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x +--R + +--R 4 3 2 +--R 8448125x - 14512750x - 127050x + 4009770x - 2662 +--R / +--R 3906250x + 2343750 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=1998/3125*x-12077/6250*x^2+786/625*x^3+189/125*x^4-216/125*x^5+_ + (-1331/78125)/(3+5*x)+11253/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x +--R + +--R 3 2 +--R - 920125x - 406275x + 299700x - 2662 +--R / +--R 781250x + 468750 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x +--R + +--R 3 2 +--R - 920125x - 406275x + 299700x - 2662 +--R / +--R 781250x + 468750 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=-1179/3125*x-427/625*x^2+164/125*x^3-18/25*x^4+(-1331/15625)/(3+5*x)+_ + 1452/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x +--R + +--R - 17685x - 1331 +--R / +--R 78125x + 46875 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x +--R + +--R - 17685x - 1331 +--R / +--R 78125x + 46875 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=-1098/625*x+122/125*x^2-8/25*x^3+(-1331/3125)/(3+5*x)+3267/3125*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331 +--R ----------------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331 +--R ----------------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^3/(3+5*x)^2 +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=108/125*x-4/25*x^2+(-1331/625)/(3+5*x)-726/625*log(3+5*x) +--R +--R +--R 3 2 +--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331 +--R (2) ----------------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331 +--R (3) ----------------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=-8/75*x+(-1331/125)/(3+5*x)+343/9*log(2+3*x)-4719/125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x +--R + +--R - 360x - 11979 +--R / +--R 5625x + 3375 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x +--R + +--R - 360x - 11979 +--R / +--R 5625x + 3375 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=(-343/9)/(2+3*x)+(-1331/25)/(3+5*x)+3136/9*log(2+3*x)-8712/25*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 1176120x - 1489752x - 470448)log(5x + 3) +--R + +--R 2 +--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683 +--R / +--R 2 +--R 3375x + 4275x + 1350 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 1176120x - 1489752x - 470448)log(5x + 3) +--R + +--R 2 +--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683 +--R / +--R 2 +--R 3375x + 4275x + 1350 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=(-343/18)/(2+3*x)^2+(-3136/9)/(2+3*x)+(-1331/5)/(3+5*x)+_ + 2541*log(2+3*x)-2541*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3) +--R + +--R 3 2 2 +--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x +--R + +--R - 891911x - 289137 +--R / +--R 3 2 +--R 4050x + 7830x + 5040x + 1080 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3) +--R + +--R 3 2 2 +--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x +--R + +--R - 891911x - 289137 +--R / +--R 3 2 +--R 4050x + 7830x + 5040x + 1080 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-343/27)/(2+3*x)^3+(-1568/9)/(2+3*x)^2+(-2541)/(2+3*x)+_ + (-1331)/(3+5*x)+16698*log(2+3*x)-16698*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R - 4057614x - 7979967x - 5226815x - 1140033 +--R / +--R 4 3 2 +--R 3645x + 9477x + 9234x + 3996x + 648 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R - 4057614x - 7979967x - 5226815x - 1140033 +--R / +--R 4 3 2 +--R 3645x + 9477x + 9234x + 3996x + 648 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-343/36)/(2+3*x)^4+(-3136/27)/(2+3*x)^3+(-2541/2)/(2+3*x)^2+_ + (-16698)/(2+3*x)+(-6655)/(3+5*x)+103455*log(2+3*x)-103455*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x +--R + +--R - 4111715520x - 536310720 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 4525121700x + 14782064220x + 19307185920x + 12603301920x +--R + +--R 4111715520x + 536310720 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975 +--R / +--R 5 4 3 2 +--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x +--R + +--R - 4111715520x - 536310720 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 4525121700x + 14782064220x + 19307185920x + 12603301920x +--R + +--R 4111715520x + 536310720 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975 +--R / +--R 5 4 3 2 +--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-343/45)/(2+3*x)^5+(-784/9)/(2+3*x)^4+(-847)/(2+3*x)^3+_ + (-8349)/(2+3*x)^2+(-103455)/(2+3*x)+(-33275)/(3+5*x)+_ + 617100*log(2+3*x)-617100*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x +--R + +--R 2 +--R - 93305520000x - 24437160000x - 2665872000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 33739942500x + 132710440500x + 217435185000x + 189943380000x +--R + +--R 2 +--R 93305520000x + 24437160000x + 2665872000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x +--R + +--R - 280877649 +--R / +--R 6 5 4 3 2 +--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x +--R + +--R 2 +--R - 93305520000x - 24437160000x - 2665872000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 33739942500x + 132710440500x + 217435185000x + 189943380000x +--R + +--R 2 +--R 93305520000x + 24437160000x + 2665872000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x +--R + +--R - 280877649 +--R / +--R 6 5 4 3 2 +--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-343/54)/(2+3*x)^6+(-3136/45)/(2+3*x)^5+(-2541/4)/(2+3*x)^4+_ + (-5566)/(2+3*x)^3+(-103455/2)/(2+3*x)^2+(-617100)/(2+3*x)+_ + (-166375)/(3+5*x)+3584625*log(2+3*x)-3584625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 7055617387500x - 32455839982500x - 63970930980000x +--R + +--R 4 3 2 +--R - 70033535550000x - 45992172600000x - 18118128600000x +--R + +--R - 3964308480000x - 371653920000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 7055617387500x + 32455839982500x + 63970930980000x +--R + +--R 4 3 2 +--R 70033535550000x + 45992172600000x + 18118128600000x +--R + +--R 3964308480000x + 371653920000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x +--R + +--R 2 +--R - 1346292632205x - 355739265638x - 39157648662 +--R / +--R 7 6 5 4 3 2 +--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x +--R + +--R 1105920x + 103680 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 7055617387500x - 32455839982500x - 63970930980000x +--R + +--R 4 3 2 +--R - 70033535550000x - 45992172600000x - 18118128600000x +--R + +--R - 3964308480000x - 371653920000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 7055617387500x + 32455839982500x + 63970930980000x +--R + +--R 4 3 2 +--R 70033535550000x + 45992172600000x + 18118128600000x +--R + +--R 3964308480000x + 371653920000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x +--R + +--R 2 +--R - 1346292632205x - 355739265638x - 39157648662 +--R / +--R 7 6 5 4 3 2 +--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x +--R + +--R 1105920x + 103680 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-49/9)/(2+3*x)^7+(-1568/27)/(2+3*x)^6+(-2541/5)/(2+3*x)^5+_ + (-8349/2)/(2+3*x)^4+(-34485)/(2+3*x)^3+(-308550)/(2+3*x)^2+_ + (-3584625)/(2+3*x)+(-831875)/(3+5*x)+20418750*log(2+3*x)-_ + 20418750*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 60285338437500x - 317502782437500x - 731462106375000x +--R + +--R 5 4 3 +--R - 962779182750000x - 791896297500000x - 416787525000000x +--R + +--R 2 +--R - 137076786000000x - 25757028000000x - 2117016000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 60285338437500x + 317502782437500x + 731462106375000x +--R + +--R 5 4 3 +--R 962779182750000x + 791896297500000x + 416787525000000x +--R + +--R 2 +--R 137076786000000x + 25757028000000x + 2117016000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 +--R - 4019022562500x - 18621471206250x - 36972030521250x +--R + +--R 4 3 2 +--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x +--R + +--R - 223049897418 +--R / +--R 8 7 6 5 4 +--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x +--R + +--R 3 2 +--R 20412000x + 6713280x + 1261440x + 103680 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 60285338437500x - 317502782437500x - 731462106375000x +--R + +--R 5 4 3 +--R - 962779182750000x - 791896297500000x - 416787525000000x +--R + +--R 2 +--R - 137076786000000x - 25757028000000x - 2117016000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 60285338437500x + 317502782437500x + 731462106375000x +--R + +--R 5 4 3 +--R 962779182750000x + 791896297500000x + 416787525000000x +--R + +--R 2 +--R 137076786000000x + 25757028000000x + 2117016000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 +--R - 4019022562500x - 18621471206250x - 36972030521250x +--R + +--R 4 3 2 +--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x +--R + +--R - 223049897418 +--R / +--R 8 7 6 5 4 +--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x +--R + +--R 3 2 +--R 20412000x + 6713280x + 1261440x + 103680 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^3*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 17496x - 55404x - 53946x + 4455x + 38934x + 17388x - 6216x +--R + +--R 3 2 +--R - 6064x - 480x + 576x + 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=46214407/9765625*x-2300646/1953125*x^2-5918904/390625*x^3+_ + 6507/62500*x^4+491913/15625*x^5+33291/3125*x^6-119556/4375*x^7-_ + 2187/125*x^8+(-1331/97656250)/(3+5*x)^2+(-1089/1953125)/(3+5*x)+_ + 47289/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 10 +--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x +--R + +--R 9 8 7 6 +--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x +--R + +--R 5 4 3 2 +--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x +--R + +--R 58226341320x - 2305534 +--R / +--R 2 +--R 34179687500x + 41015625000x + 12304687500 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 +--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x +--R + +--R 9 8 7 6 +--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x +--R + +--R 5 4 3 2 +--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x +--R + +--R 58226341320x - 2305534 +--R / +--R 2 +--R 34179687500x + 41015625000x + 12304687500 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=4571416/1953125*x-915777/390625*x^2-81747/15625*x^3+74223/12500*x^4+_ + 134622/15625*x^5-3402/625*x^6-5832/875*x^7+(-1331/19531250)/(3+5*x)^2+_ + (-23232/9765625)/(3+5*x)+166749/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 9 +--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x +--R + +--R 8 7 6 5 +--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x +--R + +--R 4 3 2 +--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x +--R + +--R 8 7 6 5 +--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x +--R + +--R 4 3 2 +--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=424432/390625*x-62097/31250*x^2-393/625*x^3+22977/6250*x^4-_ + 324/3125*x^5-324/125*x^6+(-1331/3906250)/(3+5*x)^2+_ + (-19239/1953125)/(3+5*x)+109032/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x +--R + +--R 6 5 4 3 2 +--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x +--R + +--R 38006490x - 116765 +--R / +--R 2 +--R 97656250x + 117187500x + 35156250 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x +--R + +--R 6 5 4 3 2 +--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x +--R + +--R 38006490x - 116765 +--R / +--R 2 +--R 97656250x + 117187500x + 35156250 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=4691/15625*x-7617/6250*x^2+2826/3125*x^3+513/625*x^4-648/625*x^5+_ + (-1331/781250)/(3+5*x)^2+(-15246/390625)/(3+5*x)+63294/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x +--R + +--R 5 4 3 2 +--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x +--R + +--R 5 4 3 2 +--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=-1303/3125*x-927/3125*x^2+468/625*x^3-54/125*x^4+_ + (-1331/156250)/(3+5*x)^2+(-11253/78125)/(3+5*x)+5907/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 +--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x +--R + +--R 4 3 2 +--R 1743750x - 1966250x - 2371650x - 698880x - 68849 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x +--R + +--R 4 3 2 +--R 1743750x - 1966250x - 2371650x - 698880x - 68849 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=-2978/3125*x+354/625*x^2-24/125*x^3+(-1331/31250)/(3+5*x)^2+_ + (-1452/3125)/(3+5*x)+1551/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x +--R + +--R 2 +--R - 734100x - 340620x - 44891 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x +--R + +--R 2 +--R - 734100x - 340620x - 44891 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=316/625*x-12/125*x^2+(-1331/6250)/(3+5*x)^2+(-3267/3125)/(3+5*x)-_ + 2046/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x +--R + +--R - 4230x - 20933 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x +--R + +--R - 4230x - 20933 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^3/(3+5*x)^3 +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=-8/125*x+(-1331/1250)/(3+5*x)^2+726/625/(3+5*x)+132/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025 +--R (2) ------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025 +--R (3) ------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=(-1331/250)/(3+5*x)^2+4719/125/(3+5*x)-343/3*log(2+3*x)+_ + 14289/125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2143350x + 2572020x + 771606)log(5x + 3) +--R + +--R 2 +--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949 +--R / +--R 2 +--R 18750x + 22500x + 6750 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2143350x + 2572020x + 771606)log(5x + 3) +--R + +--R 2 +--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949 +--R / +--R 2 +--R 18750x + 22500x + 6750 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=343/3/(2+3*x)+(-1331/50)/(3+5*x)^2+8712/25/(3+5*x)-1617*log(2+3*x)+_ + 1617*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3) +--R + +--R 3 2 2 +--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x +--R + +--R 1495689x + 459996 +--R / +--R 3 2 +--R 11250x + 21000x + 13050x + 2700 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3) +--R + +--R 3 2 2 +--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x +--R + +--R 1495689x + 459996 +--R / +--R 3 2 +--R 11250x + 21000x + 13050x + 2700 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=343/6/(2+3*x)^2+1617/(2+3*x)+(-1331/10)/(3+5*x)^2+2541/(3+5*x)-_ + 15708*log(2+3*x)+15708*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 7068600x + 13430348x + 8492784x + 1787403 +--R / +--R 4 3 2 +--R 6750x + 17100x + 16230x + 6840x + 1080 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 7068600x + 13430348x + 8492784x + 1787403 +--R / +--R 4 3 2 +--R 6750x + 17100x + 16230x + 6840x + 1080 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=343/9/(2+3*x)^3+1617/2/(2+3*x)^2+15708/(2+3*x)+(-1331/2)/(3+5*x)^2+_ + 16698/(3+5*x)-128634*log(2+3*x)+128634*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1562903100x + 5001289920x + 6397483356x + 4089017592x +--R + +--R 1305892368x + 166709664 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x +--R + +--R - 1305892368x - 166709664 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616 +--R / +--R 5 4 3 2 +--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1562903100x + 5001289920x + 6397483356x + 4089017592x +--R + +--R 1305892368x + 166709664 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x +--R + +--R - 1305892368x - 166709664 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616 +--R / +--R 5 4 3 2 +--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=343/12/(2+3*x)^4+539/(2+3*x)^3+7854/(2+3*x)^2+128634/(2+3*x)+_ + (-6655/2)/(3+5*x)^2+103455/(3+5*x)-953535*log(2+3*x)+953535*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 23170900500x + 89594148600x + 144277473780x + 123852754080x +--R + +--R 2 +--R 59775202080x + 15378612480x + 1647708480 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x +--R + +--R 2 +--R - 59775202080x - 15378612480x - 1647708480 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x +--R + +--R 173603415 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 23170900500x + 89594148600x + 144277473780x + 123852754080x +--R + +--R 2 +--R 59775202080x + 15378612480x + 1647708480 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x +--R + +--R 2 +--R - 59775202080x - 15378612480x - 1647708480 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x +--R + +--R 173603415 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=343/15/(2+3*x)^5+1617/4/(2+3*x)^4+5236/(2+3*x)^3+64317/(2+3*x)^2+_ + 953535/(2+3*x)+(-33275/2)/(3+5*x)^2+617100/(3+5*x)-_ + 6618975*log(2+3*x)+6618975*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2412616387500x + 10937194290000x + 21241746949500x +--R + +--R 4 3 2 +--R 22910920065000x + 14821208820000x + 5750565480000x +--R + +--R 1239072120000x + 114375888000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2412616387500x - 10937194290000x - 21241746949500x +--R + +--R 4 3 2 +--R - 22910920065000x - 14821208820000x - 5750565480000x +--R + +--R - 1239072120000x - 114375888000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x +--R + +--R 2 +--R 429553050280x + 111486629505x + 12050702538 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 2412616387500x + 10937194290000x + 21241746949500x +--R + +--R 4 3 2 +--R 22910920065000x + 14821208820000x + 5750565480000x +--R + +--R 1239072120000x + 114375888000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2412616387500x - 10937194290000x - 21241746949500x +--R + +--R 4 3 2 +--R - 22910920065000x - 14821208820000x - 5750565480000x +--R + +--R - 1239072120000x - 114375888000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x +--R + +--R 2 +--R 429553050280x + 111486629505x + 12050702538 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=343/18/(2+3*x)^6+1617/5/(2+3*x)^5+3927/(2+3*x)^4+42878/(2+3*x)^3+_ + 953535/2/(2+3*x)^2+6618975/(2+3*x)+(-166375/2)/(3+5*x)^2+_ + 3584625/(3+5*x)-43848750*log(2+3*x)+43848750*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 71922912187500x + 373999143375000x + 850608308137500x +--R + +--R 5 4 3 +--R 1105162141050000x + 897171734250000x + 465989436000000x +--R + +--R 2 +--R 151225569000000x + 28035136800000x + 2273119200000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 71922912187500x - 373999143375000x - 850608308137500x +--R + +--R 5 4 3 +--R - 1105162141050000x - 897171734250000x - 465989436000000x +--R + +--R 2 +--R - 151225569000000x - 28035136800000x - 2273119200000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x +--R + +--R 3 2 +--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063 +--R / +--R 8 7 6 5 4 3 +--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x +--R + +--R 2 +--R 3448800x + 639360x + 51840 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 71922912187500x + 373999143375000x + 850608308137500x +--R + +--R 5 4 3 +--R 1105162141050000x + 897171734250000x + 465989436000000x +--R + +--R 2 +--R 151225569000000x + 28035136800000x + 2273119200000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 71922912187500x - 373999143375000x - 850608308137500x +--R + +--R 5 4 3 +--R - 1105162141050000x - 897171734250000x - 465989436000000x +--R + +--R 2 +--R - 151225569000000x - 28035136800000x - 2273119200000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x +--R + +--R 3 2 +--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063 +--R / +--R 8 7 6 5 4 3 +--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x +--R + +--R 2 +--R 3448800x + 639360x + 51840 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=49/3/(2+3*x)^7+539/2/(2+3*x)^6+15708/5/(2+3*x)^5+64317/2/(2+3*x)^4+_ + 317845/(2+3*x)^3+6618975/2/(2+3*x)^2+43848750/(2+3*x)+_ + (-831875/2)/(3+5*x)^2+20418750/(3+5*x)-280500000*log(2+3*x)+_ + 280500000*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 460090125000000x + 2699195400000000x + 7036311645000000x +--R + +--R 6 5 4 +--R 10697265810000000x + 10452338820000000x + 6807061800000000x +--R + +--R 3 2 +--R 2954674800000000x + 824266080000000x + 134101440000000x +--R + +--R 9694080000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 460090125000000x - 2699195400000000x - 7036311645000000x +--R + +--R 6 5 4 +--R - 10697265810000000x - 10452338820000000x - 6807061800000000x +--R + +--R 3 2 +--R - 2954674800000000x - 824266080000000x - 134101440000000x +--R + +--R - 9694080000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R 30672675000000x + 160520332500000x + 367435926000000x +--R + +--R 5 4 3 +--R 480493891350000x + 392612784696000x + 205262100529200x +--R + +--R 2 +--R 67053019228048x + 12513316868859x + 1021373267628 +--R / +--R 9 8 7 6 5 4 +--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x +--R + +--R 3 2 +--R 10533600x + 2938560x + 478080x + 34560 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 460090125000000x + 2699195400000000x + 7036311645000000x +--R + +--R 6 5 4 +--R 10697265810000000x + 10452338820000000x + 6807061800000000x +--R + +--R 3 2 +--R 2954674800000000x + 824266080000000x + 134101440000000x +--R + +--R 9694080000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 460090125000000x - 2699195400000000x - 7036311645000000x +--R + +--R 6 5 4 +--R - 10697265810000000x - 10452338820000000x - 6807061800000000x +--R + +--R 3 2 +--R - 2954674800000000x - 824266080000000x - 134101440000000x +--R + +--R - 9694080000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R 30672675000000x + 160520332500000x + 367435926000000x +--R + +--R 5 4 3 +--R 480493891350000x + 392612784696000x + 205262100529200x +--R + +--R 2 +--R 67053019228048x + 12513316868859x + 1021373267628 +--R / +--R 9 8 7 6 5 4 +--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x +--R + +--R 3 2 +--R 10533600x + 2938560x + 478080x + 34560 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^m*(3+5*x)/(1-2*x) +--R +--R +--R m +--R (- 5x - 3)(3x + 2) +--R (1) ------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=-5/6*(2+3*x)^(1+m)/(1+m)+11/14*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3f.input.pdf b/src/axiom-website/CATS/rich3f.input.pdf new file mode 100644 index 0000000..a20d0ea Binary files /dev/null and b/src/axiom-website/CATS/rich3f.input.pdf differ diff --git a/src/axiom-website/CATS/rich3g.input.pamphlet b/src/axiom-website/CATS/rich3g.input.pamphlet new file mode 100644 index 0000000..fe9418d --- /dev/null +++ b/src/axiom-website/CATS/rich3g.input.pamphlet @@ -0,0 +1,6855 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3g.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 95 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 5 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3g.output +)spool rich3g.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x +--R + +--R 3 2 +--R - 225792x - 63744x - 10496x - 768 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=-63019595/512*x-60332619/512*x^2-17391129/128*x^3-37722699/256*x^4-_ + 21272139/160*x^5-2929689/32*x^6-353565/8*x^7-422091/32*x^8-_ + 3645/2*x^9-63412811/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 317064055log(- 2x + 1) - 9331200x - 67534560x - 226281600x +--R + +--R 6 5 4 3 2 +--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x +--R + +--R - 630195950x +--R / +--R 5120 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 317064055log(2x - 1) - 9331200x - 67534560x - 226281600x +--R + +--R 6 5 4 3 2 +--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x +--R + +--R - 630195950x +--R / +--R 5120 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 63412811log(2x - 1) + 63412811log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=-8960669/256*x-8362653/256*x^2-2257119/64*x^3-4352157/128*x^4-_ + 2053917/80*x^5-218943/16*x^6-126117/28*x^7-10935/16*x^8-_ + 9058973/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 317064055log(- 2x + 1) - 12247200x - 80714880x - 245216160x +--R + +--R 5 4 3 2 +--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x +--R / +--R 17920 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 317064055log(2x - 1) - 12247200x - 80714880x - 245216160x +--R + +--R 5 4 3 2 +--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x +--R / +--R 17920 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R - 9058973log(2x - 1) + 9058973log(- 2x + 1) +--R (4) ------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=-1269563/128*x-1138491/128*x^2-279657/32*x^3-458811/64*x^4-_ + 169371/40*x^5-12393/8*x^6-3645/14*x^7-1294139/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 45294865log(- 2x + 1) - 2332800x - 13880160x - 37939104x +--R + +--R 4 3 2 +--R - 64233540x - 78303960x - 79694370x - 88869410x +--R / +--R 8960 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 45294865log(2x - 1) - 2332800x - 13880160x - 37939104x - 64233540x +--R + +--R 3 2 +--R - 78303960x - 79694370x - 88869410x +--R / +--R 8960 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R - 1294139log(2x - 1) + 1294139log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=-178733/64*x-150573/64*x^2-32271/16*x^3-42093/32*x^4-10773/20*x^5-_ + 405/4*x^6-184877/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 924385log(- 2x + 1) - 64800x - 344736x - 841860x - 1290840x +--R + +--R 2 +--R - 1505730x - 1787330x +--R / +--R 640 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 924385log(2x - 1) - 64800x - 344736x - 841860x - 1290840x +--R + +--R 2 +--R - 1505730x - 1787330x +--R / +--R 640 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R - 184877log(2x - 1) + 184877log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=-24875/32*x-18987/32*x^2-3321/8*x^3-3051/16*x^4-81/2*x^5-_ + 26411/64*log(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 26411log(- 2x + 1) - 2592x - 12204x - 26568x - 37974x - 49750x +--R (2) -------------------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 26411log(2x - 1) - 2592x - 12204x - 26568x - 37974x - 49750x +--R (3) ------------------------------------------------------------------ +--R 64 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R - 26411log(2x - 1) + 26411log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x) +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=-3389/16*x-2205/16*x^2-279/4*x^3-135/8*x^4-3773/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 3773log(- 2x + 1) - 540x - 2232x - 4410x - 6778x +--R (2) ----------------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 3773log(2x - 1) - 540x - 2232x - 4410x - 6778x +--R (3) --------------------------------------------------- +--R 32 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R - 3773log(2x - 1) + 3773log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x) +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=-443/8*x-219/8*x^2-15/2*x^3-539/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 539log(- 2x + 1) - 120x - 438x - 886x +--R (2) ----------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 539log(2x - 1) - 120x - 438x - 886x +--R (3) --------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R - 539log(2x - 1) + 539log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x) +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ---------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=-53/4*x-15/4*x^2-77/8*log(1-2*x) +--R +--R +--R 2 +--R - 77log(- 2x + 1) - 30x - 106x +--R (2) ------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 77log(2x - 1) - 30x - 106x +--R (3) ----------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R - 77log(2x - 1) + 77log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)/(1-2*x) +--R +--R +--R - 5x - 3 +--R (1) -------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=-5/2*x-11/4*log(1-2*x) +--R +--R +--R - 11log(- 2x + 1) - 10x +--R (2) ----------------------- +--R 4 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 11log(2x - 1) - 10x +--R (3) --------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) ----------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=-11/14*log(1-2*x)-1/21*log(2+3*x) +--R +--R +--R - 2log(3x + 2) - 33log(- 2x + 1) +--R (2) -------------------------------- +--R 42 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 2log(3x + 2) - 33log(2x - 1) +--R (3) ------------------------------ +--R 42 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 14 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) -------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=1/21/(2+3*x)-11/49*log(1-2*x)+11/49*log(2+3*x) +--R +--R +--R (99x + 66)log(3x + 2) + (- 99x - 66)log(- 2x + 1) + 7 +--R (2) ----------------------------------------------------- +--R 441x + 294 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (99x + 66)log(3x + 2) + (- 99x - 66)log(2x - 1) + 7 +--R (3) --------------------------------------------------- +--R 441x + 294 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 49 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=1/42/(2+3*x)^2+(-11/49)/(2+3*x)-22/343*log(1-2*x)+22/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(- 2x + 1) +--R + +--R - 1386x - 875 +--R / +--R 2 +--R 18522x + 24696x + 8232 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(2x - 1) +--R + +--R - 1386x - 875 +--R / +--R 2 +--R 18522x + 24696x + 8232 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 22log(2x - 1) + 22log(- 2x + 1) +--R (4) --------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=1/63/(2+3*x)^3+(-11/98)/(2+3*x)^2+(-22/343)/(2+3*x)-_ + 44/2401*log(1-2*x)+44/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (21384x + 42768x + 28512x + 6336)log(3x + 2) +--R + +--R 3 2 2 +--R (- 21384x - 42768x - 28512x - 6336)log(- 2x + 1) - 24948x - 47817x +--R + +--R - 20104 +--R / +--R 3 2 +--R 1166886x + 2333772x + 1555848x + 345744 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (21384x + 42768x + 28512x + 6336)log(3x + 2) +--R + +--R 3 2 2 +--R (- 21384x - 42768x - 28512x - 6336)log(2x - 1) - 24948x - 47817x - 20104 +--R / +--R 3 2 +--R 1166886x + 2333772x + 1555848x + 345744 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 44log(2x - 1) + 44log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=1/84/(2+3*x)^4+(-11/147)/(2+3*x)^3+(-11/343)/(2+3*x)^2+_ + (-44/2401)/(2+3*x)-88/16807*log(1-2*x)+88/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(- 2x + 1) - 33264x +--R + +--R 2 +--R - 85932x - 85316x - 27741 +--R / +--R 4 3 2 +--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(2x - 1) - 33264x +--R + +--R 2 +--R - 85932x - 85316x - 27741 +--R / +--R 4 3 2 +--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 88log(2x - 1) + 88log(- 2x + 1) +--R (4) --------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^6) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=1/105/(2+3*x)^5+(-11/196)/(2+3*x)^4+(-22/1029)/(2+3*x)^3+_ + (-22/2401)/(2+3*x)^2+(-88/16807)/(2+3*x)-176/117649*log(1-2*x)+_ + 176/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582 +--R / +--R 5 4 3 2 +--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x +--R + +--R 225886080 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582 +--R / +--R 5 4 3 2 +--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x +--R + +--R 225886080 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 176log(2x - 1) + 176log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R - 5x - 3 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=1/126/(2+3*x)^6+(-11/245)/(2+3*x)^5+(-11/686)/(2+3*x)^4+_ + (-44/7203)/(2+3*x)^3+(-44/16807)/(2+3*x)^2+(-176/117649)/(2+3*x)-_ + 352/823543*log(1-2*x)+352/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x +--R + +--R 18247680x + 2027520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x +--R + +--R - 18247680x - 2027520 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x +--R + +--R - 21096187 +--R / +--R 6 5 4 3 +--R 54032656230x + 216130624920x + 360217708200x + 320193518400x +--R + +--R 2 +--R 160096759200x + 42692469120x + 4743607680 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x +--R + +--R 18247680x + 2027520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x +--R + +--R - 18247680x - 2027520 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x +--R + +--R - 21096187 +--R / +--R 6 5 4 3 +--R 54032656230x + 216130624920x + 360217708200x + 320193518400x +--R + +--R 2 +--R 160096759200x + 42692469120x + 4743607680 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 352log(2x - 1) + 352log(- 2x + 1) +--R (4) ----------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R - 5x - 3 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=1/147/(2+3*x)^7+(-11/294)/(2+3*x)^6+(-22/1715)/(2+3*x)^5+_ + (-11/2401)/(2+3*x)^4+(-88/50421)/(2+3*x)^3+(-88/117649)/(2+3*x)^2+_ + (-352/823543)/(2+3*x)-704/5764801*log(1-2*x)+704/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x +--R + +--R 2 +--R 127733760x + 28385280x + 2703360 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x +--R + +--R 2 +--R - 127733760x - 28385280x - 2703360 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x +--R + +--R - 177159213x - 40677476 +--R / +--R 7 6 5 4 +--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x +--R + +--R 3 2 +--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x +--R + +--R 2 +--R 127733760x + 28385280x + 2703360 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x +--R + +--R 2 +--R - 127733760x - 28385280x - 2703360 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x +--R + +--R - 177159213x - 40677476 +--R / +--R 7 6 5 4 +--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x +--R + +--R 3 2 +--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 704log(2x - 1) + 704log(- 2x + 1) +--R (4) ----------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^m*(3+5*x)^2/(1-2*x) +--R +--R +--R 2 m +--R (- 25x - 30x - 9)(3x + 2) +--R (1) --------------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=-5/36*(64+33*m)*(2+3*x)^(1+m)/((1+m)*(2+m))-_ +-- 5/6*(2+3*x)^(1+m)*(3+5*x)/(2+m)+121/28*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 164025x - 1071630x - 3150009x - 5485968x - 6268752x - 4910976x +--R + +--R 4 3 2 +--R - 2671200x - 996096x - 243712x - 35328x - 2304 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-_ + 487203129/512*x^4-316246329/320*x^5-53031699/64*x^6-8399295/16*x^7-_ + 14907321/64*x^8-256365/4*x^9-32805/4*x^10-697540921/2048*log(1-2*x) +--R +--R +--R (2) +--R 10 9 8 +--R - 3487704605log(- 2x + 1) - 83980800x - 656294400x - 2385171360x +--R + +--R 7 6 5 4 +--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x +--R + +--R 3 2 +--R - 8196045560x - 6770936890x - 6951816250x +--R / +--R 10240 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 +--R - 3487704605log(2x - 1) - 83980800x - 656294400x - 2385171360x +--R + +--R 7 6 5 4 +--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x +--R + +--R 3 2 +--R - 8196045560x - 6770936890x - 6951816250x +--R / +--R 10240 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R - 697540921log(2x - 1) + 697540921log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 2048 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x +--R + +--R 3 2 +--R - 351120x - 97952x - 15936x - 1152 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=-99058879/512*x-94979263/512*x^2-27480469/128*x^3-59969727/256*x^4-_ + 34084287/160*x^5-4736853/32*x^6-4040847/56*x^7-696195/32*x^8-_ + 6075/2*x^9-99648703/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 3487704605log(- 2x + 1) - 108864000x - 779738400x - 2586142080x +--R + +--R 6 5 4 3 +--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x +--R + +--R 2 +--R - 6648548410x - 6934121530x +--R / +--R 35840 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 3487704605log(2x - 1) - 108864000x - 779738400x - 2586142080x +--R + +--R 6 5 4 3 +--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x +--R + +--R 2 +--R - 6648548410x - 6934121530x +--R / +--R 35840 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R - 99648703log(2x - 1) + 99648703log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x +--R + +--R - 7104x - 576 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=-14088073/256*x-13178761/256*x^2-3575427/64*x^3-6947721/128*x^4-_ + 3310281/80*x^5-356643/16*x^6-207765/28*x^7-18225/16*x^8-_ + 14235529/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 498243515log(- 2x + 1) - 20412000x - 132969600x - 399440160x +--R + +--R 5 4 3 2 +--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x +--R / +--R 17920 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 498243515log(2x - 1) - 20412000x - 132969600x - 399440160x +--R + +--R 5 4 3 2 +--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x +--R / +--R 17920 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R - 14235529log(2x - 1) + 14235529log(- 2x + 1) +--R (4) --------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=-1996783/128*x-1797103/128*x^2-444581/32*x^3-736623/64*x^4-_ + 275103/40*x^5-20385/8*x^6-6075/14*x^7-2033647/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 71177645log(- 2x + 1) - 3888000x - 22831200x - 61623072x +--R + +--R 4 3 2 +--R - 103127220x - 124482680x - 125797210x - 139774810x +--R / +--R 8960 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 71177645log(2x - 1) - 3888000x - 22831200x - 61623072x - 103127220x +--R + +--R 3 2 +--R - 124482680x - 125797210x - 139774810x +--R / +--R 8960 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R - 2033647log(2x - 1) + 2033647log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=-281305/64*x-238297/64*x^2-51571/16*x^3-68121/32*x^4-3537/4*x^5-_ + 675/4*x^6-290521/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 290521log(- 2x + 1) - 21600x - 113184x - 272484x - 412568x +--R + +--R 2 +--R - 476594x - 562610x +--R / +--R 128 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 290521log(2x - 1) - 21600x - 113184x - 272484x - 412568x - 476594x +--R + +--R - 562610x +--R / +--R 128 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R - 290521log(2x - 1) + 290521log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=-39199/32*x-30175/32*x^2-5349/8*x^3-4995/16*x^4-135/2*x^5-_ + 41503/64*log(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 41503log(- 2x + 1) - 4320x - 19980x - 42792x - 60350x - 78398x +--R (2) -------------------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 41503log(2x - 1) - 4320x - 19980x - 42792x - 60350x - 78398x +--R (3) ------------------------------------------------------------------ +--R 64 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R - 41503log(2x - 1) + 41503log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x) +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=-5353/16*x-3529/16*x^2-455/4*x^3-225/8*x^4-5929/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 5929log(- 2x + 1) - 900x - 3640x - 7058x - 10706x +--R (2) ------------------------------------------------------ +--R 32 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 5929log(2x - 1) - 900x - 3640x - 7058x - 10706x +--R (3) ---------------------------------------------------- +--R 32 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R - 5929log(2x - 1) + 5929log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x) +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=-703/8*x-355/8*x^2-25/2*x^3-847/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 847log(- 2x + 1) - 200x - 710x - 1406x +--R (2) ------------------------------------------ +--R 16 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 847log(2x - 1) - 200x - 710x - 1406x +--R (3) ---------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R - 847log(2x - 1) + 847log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^2/(1-2*x) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=-85/4*x-25/4*x^2-121/8*log(1-2*x) +--R +--R +--R 2 +--R - 121log(- 2x + 1) - 50x - 170x +--R (2) -------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 121log(2x - 1) - 50x - 170x +--R (3) ------------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=-25/6*x-121/28*log(1-2*x)+1/63*log(2+3*x) +--R +--R +--R 4log(3x + 2) - 1089log(- 2x + 1) - 1050x +--R (2) ---------------------------------------- +--R 252 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4log(3x + 2) - 1089log(2x - 1) - 1050x +--R (3) -------------------------------------- +--R 252 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 28 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=(-1/63)/(2+3*x)-121/98*log(1-2*x)-68/441*log(2+3*x) +--R +--R +--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(- 2x + 1) - 14 +--R (2) -------------------------------------------------------------- +--R 2646x + 1764 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(2x - 1) - 14 +--R (3) ------------------------------------------------------------ +--R 2646x + 1764 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 98 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=(-1/126)/(2+3*x)^2+68/441/(2+3*x)-121/343*log(1-2*x)+121/343*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (19602x + 26136x + 8712)log(3x + 2) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(- 2x + 1) + 2856x + 1855 +--R / +--R 2 +--R 55566x + 74088x + 24696 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (19602x + 26136x + 8712)log(3x + 2) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(2x - 1) + 2856x + 1855 +--R / +--R 2 +--R 55566x + 74088x + 24696 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=(-1/189)/(2+3*x)^3+34/441/(2+3*x)^2+(-121/343)/(2+3*x)-_ + 242/2401*log(1-2*x)+242/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (176418x + 352836x + 235224x + 52272)log(3x + 2) +--R + +--R 3 2 2 +--R (- 176418x - 352836x - 235224x - 52272)log(- 2x + 1) - 205821x +--R + +--R - 259434x - 81823 +--R / +--R 3 2 +--R 1750329x + 3500658x + 2333772x + 518616 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (176418x + 352836x + 235224x + 52272)log(3x + 2) +--R + +--R 3 2 2 +--R (- 176418x - 352836x - 235224x - 52272)log(2x - 1) - 205821x - 259434x +--R + +--R - 81823 +--R / +--R 3 2 +--R 1750329x + 3500658x + 2333772x + 518616 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 242log(2x - 1) + 242log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-1/252)/(2+3*x)^4+68/1323/(2+3*x)^3+(-121/686)/(2+3*x)^2+(-242/2401)/_ + (2+3*x)-484/16807*log(1-2*x)+484/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2) +--R + +--R 4 3 2 +--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(- 2x + 1) +--R + +--R 3 2 +--R - 4939704x - 12760902x - 10148376x - 2564891 +--R / +--R 4 3 2 +--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2) +--R + +--R 4 3 2 +--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(2x - 1) +--R + +--R 3 2 +--R - 4939704x - 12760902x - 10148376x - 2564891 +--R / +--R 4 3 2 +--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 484log(2x - 1) + 484log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^6) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=(-1/315)/(2+3*x)^5+17/441/(2+3*x)^4+(-121/1029)/(2+3*x)^3+(-121/2401)/_ + (2+3*x)^2+(-484/16807)/(2+3*x)-968/117649*log(1-2*x)+968/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x +--R + +--R 1393920 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x +--R + +--R - 1393920 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617 +--R / +--R 5 4 3 2 +--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x +--R + +--R 169414560 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x +--R + +--R 1393920 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x +--R + +--R - 1393920 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617 +--R / +--R 5 4 3 2 +--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x +--R + +--R 169414560 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 968log(2x - 1) + 968log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-1/378)/(2+3*x)^6+68/2205/(2+3*x)^5+(-121/1372)/(2+3*x)^4+_ + (-242/7203)/(2+3*x)^3+(-242/16807)/(2+3*x)^2+(-968/117649)/(2+3*x)-_ + 1936/823543*log(1-2*x)+1936/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 762125760x + 3048503040x + 5080838400x + 4516300800x +--R + +--R 2 +--R 2258150400x + 602173440x + 66908160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 762125760x - 3048503040x - 5080838400x - 4516300800x +--R + +--R 2 +--R - 2258150400x - 602173440x - 66908160 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x +--R + +--R - 469699846 +--R / +--R 6 5 4 3 +--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x +--R + +--R 2 +--R 960580555200x + 256154814720x + 28461646080 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 762125760x + 3048503040x + 5080838400x + 4516300800x +--R + +--R 2 +--R 2258150400x + 602173440x + 66908160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 762125760x - 3048503040x - 5080838400x - 4516300800x +--R + +--R 2 +--R - 2258150400x - 602173440x - 66908160 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x +--R + +--R - 469699846 +--R / +--R 6 5 4 3 +--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x +--R + +--R 2 +--R 960580555200x + 256154814720x + 28461646080 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 1936log(2x - 1) + 1936log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-1/441)/(2+3*x)^7+34/1323/(2+3*x)^6+(-121/1715)/(2+3*x)^5+_ + (-121/4802)/(2+3*x)^4+(-484/50421)/(2+3*x)^3+(-484/117649)/(2+3*x)^2+_ + (-1936/823543)/(2+3*x)-3872/5764801*log(1-2*x)+3872/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 2286377280x + 10669760640x + 21339521280x + 23710579200x +--R + +--R 3 2 +--R 15807052800x + 6322821120x + 1405071360x + 133816320 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x +--R + +--R 3 2 +--R - 15807052800x - 6322821120x - 1405071360x - 133816320 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x +--R + +--R 2 +--R - 18847440612x - 7688480856x - 1354700662 +--R / +--R 7 6 5 4 +--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x +--R + +--R 3 2 +--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 2286377280x + 10669760640x + 21339521280x + 23710579200x +--R + +--R 3 2 +--R 15807052800x + 6322821120x + 1405071360x + 133816320 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x +--R + +--R 3 2 +--R - 15807052800x - 6322821120x - 1405071360x - 133816320 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x +--R + +--R 2 +--R - 18847440612x - 7688480856x - 1354700662 +--R / +--R 7 6 5 4 +--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x +--R + +--R 3 2 +--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R - 3872log(2x - 1) + 3872log(- 2x + 1) +--R (4) ------------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^m*(3+5*x)^3/(1-2*x) +--R +--R +--R 3 2 m +--R (- 125x - 225x - 135x - 27)(3x + 2) +--R (1) -------------------------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=-5135/216*(2+3*x)^(1+m)/(1+m)-725/108*(2+3*x)^(2+m)/(2+m)-_ +-- 125/54*(2+3*x)^(3+m)/(3+m)+1331/56*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 273375x - 1767825x - 5143095x - 8864559x - 10024182x - 7770924x +--R + +--R 4 3 2 +--R - 4182360x - 1543120x - 373536x - 53568x - 3456 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=-1092596789/1024*x-1065169973/1024*x^2-969544757/768*x^3-_ + 772025397/512*x^4-504354357/320*x^5-85228263/64*x^6-_ + 95297877/112*x^7-24381405/64*x^8-423225/4*x^9-54675/4*x^10-_ + 1096135733/2048*log(1-2*x) +--R +--R +--R (2) +--R 10 9 +--R - 115094251965log(- 2x + 1) - 2939328000x - 22752576000x +--R + +--R 8 7 6 5 +--R - 81921520800x - 182971923840x - 286366963680x - 338926127904x +--R + +--R 4 3 2 +--R - 324250666740x - 271472531960x - 223685694330x - 229445325690x +--R / +--R 215040 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 +--R - 115094251965log(2x - 1) - 2939328000x - 22752576000x - 81921520800x +--R + +--R 7 6 5 4 +--R - 182971923840x - 286366963680x - 338926127904x - 324250666740x +--R + +--R 3 2 +--R - 271472531960x - 223685694330x - 229445325690x +--R / +--R 215040 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R - 1096135733log(2x - 1) + 1096135733log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 2048 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x +--R + +--R 3 2 +--R - 545840x - 150480x - 24192x - 1728 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=-155706083/512*x-149512931/512*x^2-130251491/384*x^3-95317731/256*x^4-_ + 54600291/160*x^5-7656993/32*x^6-6596235/56*x^7-1148175/32*x^8-_ + 10125/2*x^9-156590819/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 16442035995log(- 2x + 1) - 544320000x - 3857868000x - 12664771200x +--R + +--R 6 5 4 3 +--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x +--R + +--R 2 +--R - 31397715510x - 32698277430x +--R / +--R 107520 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 16442035995log(2x - 1) - 544320000x - 3857868000x - 12664771200x +--R + +--R 6 5 4 3 +--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x +--R + +--R 2 +--R - 31397715510x - 32698277430x +--R / +--R 107520 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R - 156590819log(2x - 1) + 156590819log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 +--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x +--R + +--R 2 +--R - 59040x - 10800x - 864 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=-22148933/256*x-20766533/256*x^2-16987973/192*x^3-11088453/128*x^4-_ + 5333733/80*x^5-580815/16*x^6-342225/28*x^7-30375/16*x^8-_ + 22370117/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 2348862285log(- 2x + 1) - 102060000x - 657072000x - 1951538400x +--R + +--R 5 4 3 2 +--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x +--R / +--R 53760 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 2348862285log(2x - 1) - 102060000x - 657072000x - 1951538400x +--R + +--R 5 4 3 2 +--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x +--R / +--R 53760 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R - 22370117log(2x - 1) + 22370117log(- 2x + 1) +--R (4) --------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=-3140435/128*x-2836307/128*x^2-2119763/96*x^3-1182291/64*x^4-_ + 89343/8*x^5-33525/8*x^6-10125/14*x^7-3195731/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 67110351log(- 2x + 1) - 3888000x - 22528800x - 60038496x +--R + +--R 4 3 2 +--R - 99312444x - 118706728x - 119124894x - 131898270x +--R / +--R 5376 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 67110351log(2x - 1) - 3888000x - 22528800x - 60038496x - 99312444x +--R + +--R 3 2 +--R - 118706728x - 119124894x - 131898270x +--R / +--R 5376 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R - 3195731log(2x - 1) + 3195731log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=-442709/64*x-377045/64*x^2-247157/48*x^3-110205/32*x^4-5805/4*x^5-_ + 1125/4*x^6-456533/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 1369599log(- 2x + 1) - 108000x - 557280x - 1322460x - 1977256x +--R + +--R 2 +--R - 2262270x - 2656254x +--R / +--R 384 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 1369599log(2x - 1) - 108000x - 557280x - 1322460x - 1977256x +--R + +--R 2 +--R - 2262270x - 2656254x +--R / +--R 384 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R - 456533log(2x - 1) + 456533log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=-61763/32*x-47939/32*x^2-25835/24*x^3-8175/16*x^4-225/2*x^5-_ + 65219/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 195657log(- 2x + 1) - 21600x - 98100x - 206680x - 287634x - 370578x +--R ------------------------------------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 195657log(2x - 1) - 21600x - 98100x - 206680x - 287634x - 370578x +--R ----------------------------------------------------------------------- +--R 192 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R - 65219log(2x - 1) + 65219log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x) +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=-8453/16*x-5645/16*x^2-2225/12*x^3-375/8*x^4-9317/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 27951log(- 2x + 1) - 4500x - 17800x - 33870x - 50718x +--R (2) ---------------------------------------------------------- +--R 96 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 27951log(2x - 1) - 4500x - 17800x - 33870x - 50718x +--R (3) -------------------------------------------------------- +--R 96 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R - 9317log(2x - 1) + 9317log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^3/(1-2*x) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=-1115/8*x-575/8*x^2-125/6*x^3-1331/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 3993log(- 2x + 1) - 1000x - 3450x - 6690x +--R (2) --------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 3993log(2x - 1) - 1000x - 3450x - 6690x +--R (3) ------------------------------------------- +--R 48 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=-1225/36*x-125/12*x^2-1331/56*log(1-2*x)-1/189*log(2+3*x) +--R +--R +--R 2 +--R - 8log(3x + 2) - 35937log(- 2x + 1) - 15750x - 51450x +--R (2) ------------------------------------------------------ +--R 1512 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 8log(3x + 2) - 35937log(2x - 1) - 15750x - 51450x +--R (3) ---------------------------------------------------- +--R 1512 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 56 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=-125/18*x+1/189/(2+3*x)-1331/196*log(1-2*x)+103/1323*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(- 2x + 1) - 110250x +--R + +--R - 73500x + 28 +--R / +--R 15876x + 10584 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(2x - 1) - 110250x +--R + +--R - 73500x + 28 +--R / +--R 15876x + 10584 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 196 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1/378/(2+3*x)^2+(-103/1323)/(2+3*x)-1331/686*log(1-2*x)-_ + 3469/9261*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 62442x - 83256x - 27752)log(3x + 2) +--R + +--R 2 +--R (- 323433x - 431244x - 143748)log(- 2x + 1) - 4326x - 2835 +--R / +--R 2 +--R 166698x + 222264x + 74088 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 62442x - 83256x - 27752)log(3x + 2) +--R + +--R 2 +--R (- 323433x - 431244x - 143748)log(2x - 1) - 4326x - 2835 +--R / +--R 2 +--R 166698x + 222264x + 74088 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 686 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=1/567/(2+3*x)^3+(-103/2646)/(2+3*x)^2+3469/9261/(2+3*x)-_ + 1331/2401*log(1-2*x)+1331/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(- 2x + 1) + 1311282x +--R + +--R 1702953x + 553196 +--R / +--R 3 2 +--R 10501974x + 21003948x + 14002632x + 3111696 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(2x - 1) + 1311282x +--R + +--R 1702953x + 553196 +--R / +--R 3 2 +--R 10501974x + 21003948x + 14002632x + 3111696 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=1/756/(2+3*x)^4+(-103/3969)/(2+3*x)^3+3469/18522/(2+3*x)^2+_ + (-1331/2401)/(2+3*x)-2662/16807*log(1-2*x)+2662/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808) +--R * +--R log(- 2x + 1) +--R + +--R 3 2 +--R - 81505116x - 153831258x - 96858804x - 20345549 +--R / +--R 4 3 2 +--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808) +--R * +--R log(2x - 1) +--R + +--R 3 2 +--R - 81505116x - 153831258x - 96858804x - 20345549 +--R / +--R 4 3 2 +--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 2662log(2x - 1) + 2662log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^6) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=1/945/(2+3*x)^5+(-103/5292)/(2+3*x)^4+3469/27783/(2+3*x)^3+_ + (-1331/4802)/(2+3*x)^2+(-2662/16807)/(2+3*x)-_ + 5324/117649*log(1-2*x)+5324/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 2095845840x + 6986152800x + 9314870400x + 6209913600x +--R + +--R 2069971200x + 275996160 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x +--R + +--R - 2069971200x - 275996160 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446 +--R / +--R 5 4 3 2 +--R 46313705340x + 154379017800x + 205838690400x + 137225793600x +--R + +--R 45741931200x + 6098924160 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2095845840x + 6986152800x + 9314870400x + 6209913600x +--R + +--R 2069971200x + 275996160 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x +--R + +--R - 2069971200x - 275996160 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446 +--R / +--R 5 4 3 2 +--R 46313705340x + 154379017800x + 205838690400x + 137225793600x +--R + +--R 45741931200x + 6098924160 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 5324log(2x - 1) + 5324log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=1/1134/(2+3*x)^6+(-103/6615)/(2+3*x)^5+3469/37044/(2+3*x)^4+_ + (-1331/7203)/(2+3*x)^3+(-1331/16807)/(2+3*x)^2+_ + (-5324/117649)/(2+3*x)-10648/823543*log(1-2*x)+10648/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 12575075040x + 50300300160x + 83833833600x + 74518963200x +--R + +--R 2 +--R 37259481600x + 9935861760x + 1103984640 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x +--R + +--R 2 +--R - 37259481600x - 9935861760x - 1103984640 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x +--R + +--R - 32070746736x - 5135298434 +--R / +--R 6 5 4 3 +--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x +--R + +--R 2 +--R 2881741665600x + 768464444160x + 85384938240 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 12575075040x + 50300300160x + 83833833600x + 74518963200x +--R + +--R 2 +--R 37259481600x + 9935861760x + 1103984640 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x +--R + +--R 2 +--R - 37259481600x - 9935861760x - 1103984640 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x +--R + +--R - 32070746736x - 5135298434 +--R / +--R 6 5 4 3 +--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x +--R + +--R 2 +--R 2881741665600x + 768464444160x + 85384938240 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 10648log(2x - 1) + 10648log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=1/1323/(2+3*x)^7+(-103/7938)/(2+3*x)^6+3469/46305/(2+3*x)^5+_ + (-1331/9604)/(2+3*x)^4+(-2662/50421)/(2+3*x)^3+(-2662/117649)/(2+3*x)^2+_ + (-10648/823543)/(2+3*x)-21296/5764801*log(1-2*x)+21296/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 75450450240x + 352102101120x + 704204202240x + 782449113600x +--R + +--R 3 2 +--R 521632742400x + 208653096960x + 46367354880x + 4415938560 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x +--R + +--R 3 2 +--R - 521632742400x - 208653096960x - 46367354880x - 4415938560 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x +--R + +--R 2 +--R - 583053133446x - 206160259998x - 30169587896 +--R / +--R 7 6 5 +--R 20424344054940x + 95313605589720x + 190627211179440x +--R + +--R 4 3 2 +--R 211808012421600x + 141205341614400x + 56482136645760x +--R + +--R 12551585921280x + 1195389135360 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 75450450240x + 352102101120x + 704204202240x + 782449113600x +--R + +--R 3 2 +--R 521632742400x + 208653096960x + 46367354880x + 4415938560 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x +--R + +--R 3 2 +--R - 521632742400x - 208653096960x - 46367354880x - 4415938560 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x +--R + +--R 2 +--R - 583053133446x - 206160259998x - 30169587896 +--R / +--R 7 6 5 +--R 20424344054940x + 95313605589720x + 190627211179440x +--R + +--R 4 3 2 +--R 211808012421600x + 141205341614400x + 56482136645760x +--R + +--R 12551585921280x + 1195389135360 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R - 21296log(2x - 1) + 21296log(- 2x + 1) +--R (4) --------------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(a+b*x)^3/((c+d*x)*(e+f*x)) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +--R d f x + (c f + d e)x + c e +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=-b^2*(b*d*e+b*c*f-3*a*d*f)*x/(d^2*f^2)+1/2*b^3*x^2/(d*f)-_ + (b*c-a*d)^3*log(c+d*x)/(d^3*(d*e-c*f))+_ + (b*e-a*f)^3*log(e+f*x)/(f^3*(d*e-c*f)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 2 3 3 3 +--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c) +--R + +--R 3 2 3 3 3 2 2 +--R (b c d f - b d e f )x +--R + +--R 2 2 3 2 3 2 3 2 3 3 2 +--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x +--R / +--R 3 4 4 3 +--R 2c d f - 2d e f +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 2 3 3 3 +--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c) +--R + +--R 3 2 3 3 3 2 2 +--R (b c d f - b d e f )x +--R + +--R 2 2 3 2 3 2 3 2 3 3 2 +--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x +--R / +--R 3 4 4 3 +--R 2c d f - 2d e f +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)) +--R +--R +--R m +--R (3x + 2) +--R (1) - ------------ +--R 2 +--R 10x + x - 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=2/77*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-5/11*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=-40089855591/10000000*x-7136193339/2000000*x^2-345533877/100000*x^3-_ + 111146499/40000*x^4-8018271/5000*x^5-114453/200*x^6-6561/70*x^7-_ + 5764801/2816*log(1-2*x)+1/4296875*log(3+5*x) +--R +--R +--R (2) +--R 7 +--R 1792log(5x + 3) - 15763127734375log(- 2x + 1) - 721710000000x +--R + +--R 6 5 4 +--R - 4406440500000x - 12348137340000x - 21395701057500x +--R + +--R 3 2 +--R - 26606108529000x - 27474344355150x - 30869188805070x +--R / +--R 7700000000 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +--R 1792log(5x + 3) - 15763127734375log(2x - 1) - 721710000000x +--R + +--R 6 5 4 +--R - 4406440500000x - 12348137340000x - 21395701057500x +--R + +--R 3 2 +--R - 26606108529000x - 27474344355150x - 30869188805070x +--R / +--R 7700000000 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 2816 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=-1127138733/1000000*x-187738857/200000*x^2-7889751/10000*x^3-_ + 2006937/4000*x^4-99873/500*x^5-729/20*x^6-823543/1408*log(1-2*x)+_ + 1/859375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 +--R 128log(5x + 3) - 64339296875log(- 2x + 1) - 4009500000x - 21972060000x +--R + +--R 4 3 2 +--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x +--R / +--R 110000000 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 +--R 128log(5x + 3) - 64339296875log(2x - 1) - 4009500000x - 21972060000x +--R + +--R 4 3 2 +--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x +--R / +--R 110000000 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1408 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=-31289679/100000*x-4693491/20000*x^2-159813/1000*x^3-_ + 28431/400*x^4-729/50*x^5-117649/704*log(1-2*x)+1/171875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 +--R 64log(5x + 3) - 1838265625log(- 2x + 1) - 160380000x - 781852500x +--R + +--R 3 2 +--R - 1757943000x - 2581420050x - 3441864690x +--R / +--R 11000000 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 +--R 64log(5x + 3) - 1838265625log(2x - 1) - 160380000x - 781852500x +--R + +--R 3 2 +--R - 1757943000x - 2581420050x - 3441864690x +--R / +--R 11000000 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 704 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=-848277/10000*x-107433/2000*x^2-2619/100*x^3-243/40*x^4-_ + 16807/352*log(1-2*x)+1/34375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 +--R 32log(5x + 3) - 52521875log(- 2x + 1) - 6682500x - 28809000x +--R + +--R 2 +--R - 59088150x - 93310470x +--R / +--R 1100000 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 32log(5x + 3) - 52521875log(2x - 1) - 6682500x - 28809000x - 59088150x +--R + +--R - 93310470x +--R / +--R 1100000 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 352 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=-21951/1000*x-2079/200*x^2-27/10*x^3-2401/176*log(1-2*x)+1/6875*log(3+5*x) +--R +--R +--R 3 2 +--R 16log(5x + 3) - 1500625log(- 2x + 1) - 297000x - 1143450x - 2414610x +--R (2) ---------------------------------------------------------------------- +--R 110000 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 16log(5x + 3) - 1500625log(2x - 1) - 297000x - 1143450x - 2414610x +--R (3) -------------------------------------------------------------------- +--R 110000 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 176 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ----------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=-513/100*x-27/20*x^2-343/88*log(1-2*x)+1/1375*log(3+5*x) +--R +--R +--R 2 +--R 8log(5x + 3) - 42875log(- 2x + 1) - 14850x - 56430x +--R (2) ---------------------------------------------------- +--R 11000 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 8log(5x + 3) - 42875log(2x - 1) - 14850x - 56430x +--R (3) -------------------------------------------------- +--R 11000 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 88 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=-9/10*x-49/44*log(1-2*x)+1/275*log(3+5*x) +--R +--R +--R 4log(5x + 3) - 1225log(- 2x + 1) - 990x +--R (2) --------------------------------------- +--R 1100 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4log(5x + 3) - 1225log(2x - 1) - 990x +--R (3) ------------------------------------- +--R 1100 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 44 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ------------ +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-7/22*log(1-2*x)+1/55*log(3+5*x) +--R +--R +--R 2log(5x + 3) - 35log(- 2x + 1) +--R (2) ------------------------------ +--R 110 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2log(5x + 3) - 35log(2x - 1) +--R (3) ---------------------------- +--R 110 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - 7log(2x - 1) + 7log(- 2x + 1) +--R (4) ------------------------------- +--R 22 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------ +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=-1/11*log(1-2*x)+1/11*log(3+5*x) +--R +--R +--R log(5x + 3) - log(- 2x + 1) +--R (2) --------------------------- +--R 11 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) - log(2x - 1) +--R (3) ------------------------- +--R 11 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 11 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - -------------------- +--R 3 2 +--R 30x + 23x - 7x - 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=-2/77*log(1-2*x)-3/7*log(2+3*x)+5/11*log(3+5*x) +--R +--R +--R 35log(5x + 3) - 33log(3x + 2) - 2log(- 2x + 1) +--R (2) ---------------------------------------------- +--R 77 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R 35log(5x + 3) - 33log(3x + 2) - 2log(2x - 1) +--R (3) -------------------------------------------- +--R 77 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 2log(2x - 1) + 2log(- 2x + 1) +--R (4) ------------------------------- +--R 77 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------ +--R 4 3 2 +--R 90x + 129x + 25x - 32x - 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=3/7/(2+3*x)-4/539*log(1-2*x)-111/49*log(2+3*x)+25/11*log(3+5*x) +--R +--R +--R (2) +--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2) +--R + +--R (- 12x - 8)log(- 2x + 1) + 231 +--R / +--R 1617x + 1078 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2) +--R + +--R (- 12x - 8)log(2x - 1) + 231 +--R / +--R 1617x + 1078 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 539 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------- +--R 5 4 3 2 +--R 270x + 567x + 333x - 46x - 100x - 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=3/14/(2+3*x)^2+111/49/(2+3*x)-8/3773*log(1-2*x)-3897/343*log(2+3*x)+_ + 125/11*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (771750x + 1029000x + 343000)log(5x + 3) +--R + +--R 2 +--R (- 771606x - 1028808x - 342936)log(3x + 2) +--R + +--R 2 +--R (- 144x - 192x - 64)log(- 2x + 1) + 51282x + 35805 +--R / +--R 2 +--R 67914x + 90552x + 30184 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (771750x + 1029000x + 343000)log(5x + 3) +--R + +--R 2 +--R (- 771606x - 1028808x - 342936)log(3x + 2) +--R + +--R 2 +--R (- 144x - 192x - 64)log(2x - 1) + 51282x + 35805 +--R / +--R 2 +--R 67914x + 90552x + 30184 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 3773 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 6 5 4 3 2 +--R 810x + 2241x + 2133x + 528x - 392x - 272x - 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=1/7/(2+3*x)^3+111/98/(2+3*x)^2+3897/343/(2+3*x)-16/26411*log(1-2*x)-_ + 136419/2401*log(2+3*x)+625/11*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3) +--R + +--R 3 2 +--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2) +--R + +--R 3 2 2 +--R (- 864x - 1728x - 1152x - 256)log(- 2x + 1) + 5401242x + 7381143x +--R + +--R 2527756 +--R / +--R 3 2 +--R 1426194x + 2852388x + 1901592x + 422576 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3) +--R + +--R 3 2 +--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2) +--R + +--R 3 2 2 +--R (- 864x - 1728x - 1152x - 256)log(2x - 1) + 5401242x + 7381143x +--R + +--R 2527756 +--R / +--R 3 2 +--R 1426194x + 2852388x + 1901592x + 422576 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 26411 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2430x + 8343x + 10881x + 5850x - 120x - 1600x - 688x - 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=3/28/(2+3*x)^4+37/49/(2+3*x)^3+3897/686/(2+3*x)^2+136419/2401/(2+3*x)-_ + 32/184877*log(1-2*x)-4774713/16807*log(2+3*x)+3125/11*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 17017087500x + 45378900000x + 45378900000x + 20168400000x +--R + +--R 3361400000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x +--R + +--R - 3361397952 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(- 2x + 1) +--R + +--R 3 2 +--R 1134460404x + 2306729502x + 1564700676x + 354136321 +--R / +--R 4 3 2 +--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 17017087500x + 45378900000x + 45378900000x + 20168400000x +--R + +--R 3361400000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x +--R + +--R - 3361397952 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(2x - 1) + 1134460404x +--R + +--R 2 +--R 2306729502x + 1564700676x + 354136321 +--R / +--R 4 3 2 +--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 184877 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 7290x + 29889x + 49329x + 39312x + 11340x - 5040x - 5264x +--R + +--R - 1664x - 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=3/35/(2+3*x)^5+111/196/(2+3*x)^4+1299/343/(2+3*x)^3+_ + 136419/4802/(2+3*x)^2+4774713/16807/(2+3*x)-64/1294139*log(1-2*x)-_ + 167115051/117649*log(2+3*x)+15625/11*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 8933970937500x + 29779903125000x + 39706537500000x +--R + +--R 2 +--R 26471025000000x + 8823675000000x + 1176490000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8933970626460x - 29779902088200x - 39706536117600x +--R + +--R 2 +--R - 26471024078400x - 8823674692800x - 1176489959040 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x +--R + +--R 123954940494 +--R / +--R 5 4 3 2 +--R 6289515540x + 20965051800x + 27953402400x + 18635601600x +--R + +--R 6211867200x + 828248960 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 8933970937500x + 29779903125000x + 39706537500000x +--R + +--R 2 +--R 26471025000000x + 8823675000000x + 1176490000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8933970626460x - 29779902088200x - 39706536117600x +--R + +--R 2 +--R - 26471024078400x - 8823674692800x - 1176489959040 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x +--R + +--R 123954940494 +--R / +--R 5 4 3 2 +--R 6289515540x + 20965051800x + 27953402400x + 18635601600x +--R + +--R 6211867200x + 828248960 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 1294139 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=1/((1-2*x)*(2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 21870x + 104247x + 207765x + 216594x + 112644x + 7560x - 25872x +--R + +--R 2 +--R - 15520x - 3904x - 384 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=1/14/(2+3*x)^6+111/245/(2+3*x)^5+3897/1372/(2+3*x)^4+_ + 45473/2401/(2+3*x)^3+4774713/33614/(2+3*x)^2+_ + 167115051/117649/(2+3*x)-128/9058973*log(1-2*x)-_ + 5849026977/823543*log(2+3*x)+78125/11*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 938066948437500x + 3752267793750000x + 6253779656250000x +--R + +--R 3 2 +--R 5558915250000000x + 2779457625000000x + 741188700000000x +--R + +--R 82354300000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 938066946571260x - 3752267786285040x - 6253779643808400x +--R + +--R 3 2 +--R - 5558915238940800x - 2779457619470400x - 741188698525440x +--R + +--R - 82354299836160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x +--R + +--R - 1474560x - 163840 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 62537794385220x + 210543906566070x + 283597312285980x +--R + +--R 2 +--R 191046007176255x + 64366302153384x + 8676887688546 +--R / +--R 6 5 4 3 +--R 132079826340x + 528319305360x + 880532175600x + 782695267200x +--R + +--R 2 +--R 391347633600x + 104359368960x + 11595485440 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 938066948437500x + 3752267793750000x + 6253779656250000x +--R + +--R 3 2 +--R 5558915250000000x + 2779457625000000x + 741188700000000x +--R + +--R 82354300000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 938066946571260x - 3752267786285040x - 6253779643808400x +--R + +--R 3 2 +--R - 5558915238940800x - 2779457619470400x - 741188698525440x +--R + +--R - 82354299836160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x +--R + +--R - 1474560x - 163840 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 62537794385220x + 210543906566070x + 283597312285980x +--R + +--R 2 +--R 191046007176255x + 64366302153384x + 8676887688546 +--R / +--R 6 5 4 3 +--R 132079826340x + 528319305360x + 880532175600x + 782695267200x +--R + +--R 2 +--R 391347633600x + 104359368960x + 11595485440 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 9058973 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^2) +--R +--R +--R m +--R (3x + 2) +--R (1) - --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-5/11*(2+3*x)^(1+m)/(3+5*x)+4/847*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-10/121*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-15/11*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=-3579885909/5000000*x-118543581/200000*x^2-24660207/50000*x^3-_ + 6194313/20000*x^4-303993/2500*x^5-2187/100*x^6+(-1/4296875)/(3+5*x)-_ + 5764801/15488*log(1-2*x)+266/47265625*log(3+5*x) +--R +--R +--R (2) +--R (170240x + 102144)log(5x + 3) +--R + +--R 7 +--R (- 11259376953125x - 6755626171875)log(- 2x + 1) - 661567500000x +--R + +--R 6 5 4 +--R - 4075255800000x - 11575887592500x - 20540764282500x +--R + +--R 3 2 +--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408 +--R / +--R 30250000000x + 18150000000 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (170240x + 102144)log(5x + 3) +--R + +--R 7 +--R (- 11259376953125x - 6755626171875)log(2x - 1) - 661567500000x +--R + +--R 6 5 4 +--R - 4075255800000x - 11575887592500x - 20540764282500x +--R + +--R 3 2 +--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408 +--R / +--R 30250000000x + 18150000000 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 15488 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=-19846971/100000*x-14750667/100000*x^2-495477/5000*x^3-86751/2000*x^4-_ + 2187/250*x^5+(-1/859375)/(3+5*x)-823543/7744*log(1-2*x)+_ + 233/9453125*log(3+5*x) +--R +--R +--R (2) +--R (74560x + 44736)log(5x + 3) +--R + +--R 6 +--R (- 321696484375x - 193017890625)log(- 2x + 1) - 26462700000x +--R + +--R 5 4 3 2 +--R - 147088507500x - 378490117500x - 626065827750x - 868095478800x +--R + +--R - 360222523650x - 704 +--R / +--R 3025000000x + 1815000000 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (74560x + 44736)log(5x + 3) + (- 321696484375x - 193017890625)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 26462700000x - 147088507500x - 378490117500x - 626065827750x +--R + +--R 2 +--R - 868095478800x - 360222523650x - 704 +--R / +--R 3025000000x + 1815000000 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 7744 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=-2682909/50000*x-335097/10000*x^2-8019/500*x^3-729/200*x^4+_ + (-1/171875)/(3+5*x)-117649/3872*log(1-2*x)+8/75625*log(3+5*x) +--R +--R +--R (2) +--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x +--R + +--R - 9738959670x - 352 +--R / +--R 302500000x + 181500000 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(2x - 1) +--R + +--R 5 4 3 2 +--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x +--R + +--R - 9738959670x - 352 +--R / +--R 302500000x + 181500000 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 3872 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=-69039/5000*x-6399/1000*x^2-81/50*x^3+(-1/34375)/(3+5*x)-_ + 16807/1936*log(1-2*x)+167/378125*log(3+5*x) +--R +--R +--R (2) +--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(- 2x + 1) +--R + +--R 4 3 2 +--R - 49005000x - 222972750x - 533827800x - 250611570x - 176 +--R / +--R 30250000x + 18150000 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(2x - 1) +--R + +--R 4 3 2 +--R - 49005000x - 222972750x - 533827800x - 250611570x - 176 +--R / +--R 30250000x + 18150000 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=-1593/500*x-81/100*x^2+(-1/6875)/(3+5*x)-2401/968*log(1-2*x)+_ + 134/75625*log(3+5*x) +--R +--R +--R (2) +--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(- 2x + 1) +--R + +--R 3 2 +--R - 2450250x - 11107800x - 5782590x - 88 +--R / +--R 3025000x + 1815000 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(2x - 1) - 2450250x +--R + +--R 2 +--R - 11107800x - 5782590x - 88 +--R / +--R 3025000x + 1815000 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 968 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ----------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=-27/50*x+(-1/1375)/(3+5*x)-343/484*log(1-2*x)+101/15125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(- 2x + 1) - 163350x +--R + +--R - 98010x - 44 +--R / +--R 302500x + 181500 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(2x - 1) - 163350x +--R + +--R - 98010x - 44 +--R / +--R 302500x + 181500 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 484 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=(-1/275)/(3+5*x)-49/242*log(1-2*x)+68/3025*log(3+5*x) +--R +--R +--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(- 2x + 1) - 22 +--R (2) ------------------------------------------------------------ +--R 30250x + 18150 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(2x - 1) - 22 +--R (3) ---------------------------------------------------------- +--R 30250x + 18150 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 242 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-1/55)/(3+5*x)-7/121*log(1-2*x)+7/121*log(3+5*x) +--R +--R +--R (175x + 105)log(5x + 3) + (- 175x - 105)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------------- +--R 3025x + 1815 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (175x + 105)log(5x + 3) + (- 175x - 105)log(2x - 1) - 11 +--R (3) -------------------------------------------------------- +--R 3025x + 1815 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R - 7log(2x - 1) + 7log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-1/11)/(3+5*x)-2/121*log(1-2*x)+2/121*log(3+5*x) +--R +--R +--R (10x + 6)log(5x + 3) + (- 10x - 6)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------- +--R 605x + 363 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x + 6)log(5x + 3) + (- 10x - 6)log(2x - 1) - 11 +--R (3) -------------------------------------------------- +--R 605x + 363 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R - 2log(2x - 1) + 2log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 4 3 2 +--R 150x + 205x + 34x - 51x - 18 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-5/11)/(3+5*x)-4/847*log(1-2*x)+9/7*log(2+3*x)-155/121*log(3+5*x) +--R +--R +--R (2) +--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2) +--R + +--R (- 20x - 12)log(- 2x + 1) - 385 +--R / +--R 4235x + 2541 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2) +--R + +--R (- 20x - 12)log(2x - 1) - 385 +--R / +--R 4235x + 2541 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 847 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------------- +--R 5 4 3 2 +--R 450x + 915x + 512x - 85x - 156x - 36 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-9/7)/(2+3*x)+(-25/11)/(3+5*x)-8/5929*log(1-2*x)+648/49*log(2+3*x)-_ + 1600/121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 1176000x - 1489600x - 470400)log(5x + 3) +--R + +--R 2 +--R (1176120x + 1489752x + 470448)log(3x + 2) +--R + +--R 2 +--R (- 120x - 152x - 48)log(- 2x + 1) - 78540x - 49819 +--R / +--R 2 +--R 88935x + 112651x + 35574 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 1176000x - 1489600x - 470400)log(5x + 3) +--R + +--R 2 +--R (1176120x + 1489752x + 470448)log(3x + 2) +--R + +--R 2 +--R (- 120x - 152x - 48)log(2x - 1) - 78540x - 49819 +--R / +--R 2 +--R 88935x + 112651x + 35574 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 5929 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 6 5 4 3 2 +--R 1350x + 3645x + 3366x + 769x - 638x - 420x - 72 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-9/14)/(2+3*x)^2+(-648/49)/(2+3*x)+(-125/11)/(3+5*x)-_ + 16/41503*log(1-2*x)+34371/343*log(2+3*x)-12125/121*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3) +--R + +--R 3 2 +--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2) +--R + +--R 3 2 2 +--R (- 1440x - 2784x - 1792x - 384)log(- 2x + 1) - 24954930x - 32442333x +--R + +--R - 10519355 +--R / +--R 3 2 +--R 3735270x + 7221522x + 4648336x + 996072 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3) +--R + +--R 3 2 +--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2) +--R + +--R 3 2 2 +--R (- 1440x - 2784x - 1792x - 384)log(2x - 1) - 24954930x - 32442333x +--R + +--R - 10519355 +--R / +--R 3 2 +--R 3735270x + 7221522x + 4648336x + 996072 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 41503 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 4050x + 13635x + 17388x + 9039x - 376x - 2536x - 1056x - 144 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-3/7)/(2+3*x)^3+(-324/49)/(2+3*x)^2+(-34371/343)/(2+3*x)+_ + (-625/11)/(3+5*x)-32/290521*log(1-2*x)+1612242/2401*log(2+3*x)-_ + 81250/121*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x +--R + +--R - 4681950000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 26335973070x + 68473529982x + 66717798444x + 28872029736x +--R + +--R 4681950768 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 4320x - 11232x - 10944x - 4736x - 768)log(- 2x + 1) - 1755736290x +--R + +--R 2 +--R - 3452950809x - 2261654241x - 493301347 +--R / +--R 4 3 2 +--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x +--R + +--R - 4681950000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 26335973070x + 68473529982x + 66717798444x + 28872029736x +--R + +--R 4681950768 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 4320x - 11232x - 10944x - 4736x - 768)log(2x - 1) - 1755736290x +--R + +--R 2 +--R - 3452950809x - 2261654241x - 493301347 +--R / +--R 4 3 2 +--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 290521 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 12150x + 49005x + 79434x + 61893x + 16950x - 8360x - 8240x +--R + +--R - 2544x - 288 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-9/28)/(2+3*x)^4+(-216/49)/(2+3*x)^3+(-34371/686)/(2+3*x)^2+_ + (-1612242/2401)/(2+3*x)+(-3125/11)/(3+5*x)-64/2033647*log(1-2*x)+_ + 70752609/16807*log(2+3*x)-509375/121*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R - 13868926312500x - 45305159287500x - 59174085600000x +--R + +--R 2 +--R - 38627528100000x - 12601888600000x - 1643724600000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R 13868926416180x + 45305159626188x + 59174086042368x +--R + +--R 2 +--R 38627528388768x + 12601888694208x + 1643724612288 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x +--R + +--R - 173183872939 +--R / +--R 5 4 3 2 +--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x +--R + +--R 390460224 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 13868926312500x - 45305159287500x - 59174085600000x +--R + +--R 2 +--R - 38627528100000x - 12601888600000x - 1643724600000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R 13868926416180x + 45305159626188x + 59174086042368x +--R + +--R 2 +--R 38627528388768x + 12601888694208x + 1643724612288 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288)log(2x - 1) +--R + +--R 4 3 2 +--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x +--R + +--R - 173183872939 +--R / +--R 5 4 3 2 +--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x +--R + +--R 390460224 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 2033647 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 36450x + 171315x + 336312x + 344547x + 174636x + 8820x - 41440x +--R + +--R 2 +--R - 24112x - 5952x - 576 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-9/35)/(2+3*x)^5+(-162/49)/(2+3*x)^4+(-11457/343)/(2+3*x)^3+_ + (-806121/2401)/(2+3*x)^2+(-70752609/16807)/(2+3*x)+_ + (-15625/11)/(3+5*x)-128/14235529*log(1-2*x)+2977686468/117649*_ + log(2+3*x)-3062500/121*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 2188822879687500x - 8609369993437500x - 14105747446875000x +--R + +--R 3 2 +--R - 12322262137500000x - 6053041050000000x - 1585320275000000x +--R + +--R - 172944030000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 2188822880465100x + 8609369996496060x + 14105747451886200x +--R + +--R 3 2 +--R 12322262141877600x + 6053041052150400x + 1585320275563200x +--R + +--R 172944030061440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x +--R + +--R - 61440 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R - 145921526219700x - 481541037023970x - 635461225889490x +--R + +--R 2 +--R - 419169494735145x - 138206158563165x - 18221473659389 +--R / +--R 6 5 4 3 +--R 86480838675x + 340157965455x + 557320960350x + 486855091800x +--R + +--R 2 +--R 239156887200x + 62636327600x + 6833053920 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 2188822879687500x - 8609369993437500x - 14105747446875000x +--R + +--R 3 2 +--R - 12322262137500000x - 6053041050000000x - 1585320275000000x +--R + +--R - 172944030000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 2188822880465100x + 8609369996496060x + 14105747451886200x +--R + +--R 3 2 +--R 12322262141877600x + 6053041052150400x + 1585320275563200x +--R + +--R 172944030061440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x +--R + +--R - 61440 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R - 145921526219700x - 481541037023970x - 635461225889490x +--R + +--R 2 +--R - 419169494735145x - 138206158563165x - 18221473659389 +--R / +--R 6 5 4 3 +--R 86480838675x + 340157965455x + 557320960350x + 486855091800x +--R + +--R 2 +--R 239156887200x + 62636327600x + 6833053920 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 14235529 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^3) +--R +--R +--R m +--R (3x + 2) +--R (1) - ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-5/22*(2+3*x)^(1+m)/(3+5*x)^2-10/121*(2+3*x)^(1+m)/(3+5*x)+_ +-- 15/22*(1-m)*(2+3*x)^(1+m)/(3+5*x)+8/9317*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-20/1331*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-30/121*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)+45/22*(1-m)*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=-62934003/500000*x-9268263/100000*x^2-1535517/25000*x^3-_ + 264627/10000*x^4-6561/1250*x^5+(-1/8593750)/(3+5*x)^2+_ + (-266/47265625)/(3+5*x)-5764801/85184*log(1-2*x)+_ + 31024/519921875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (49638400x + 59566080x + 17869824)log(5x + 3) +--R + +--R 2 +--R (- 56296884765625x - 67556261718750x - 20266878515625)log(- 2x + 1) +--R + +--R 7 6 5 +--R - 4366345500000x - 27253273162500x - 79082602830000x +--R + +--R 4 3 2 +--R - 146338473723750x - 215620841031750x - 153403867608750x +--R + +--R - 37694322033170x - 565664 +--R / +--R 2 +--R 831875000000x + 998250000000x + 299475000000 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (49638400x + 59566080x + 17869824)log(5x + 3) +--R + +--R 2 +--R (- 56296884765625x - 67556261718750x - 20266878515625)log(2x - 1) +--R + +--R 7 6 5 +--R - 4366345500000x - 27253273162500x - 79082602830000x +--R + +--R 4 3 2 +--R - 146338473723750x - 215620841031750x - 153403867608750x +--R + +--R - 37694322033170x - 565664 +--R / +--R 2 +--R 831875000000x + 998250000000x + 299475000000 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^3) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=-339309/10000*x-1044657/50000*x^2-24543/2500*x^3-2187/1000*x^4+_ + (-1/1718750)/(3+5*x)^2+(-233/9453125)/(3+5*x)-_ + 823543/42592*log(1-2*x)+4667/20796875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (18668000x + 22401600x + 6720480)log(5x + 3) +--R + +--R 2 +--R (- 1608482421875x - 1930178906250x - 579053671875)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x +--R + +--R 2 +--R - 4012849402650x - 1016146037830x - 247984 +--R / +--R 2 +--R 83187500000x + 99825000000x + 29947500000 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (18668000x + 22401600x + 6720480)log(5x + 3) +--R + +--R 2 +--R (- 1608482421875x - 1930178906250x - 579053671875)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x +--R + +--R 2 +--R - 4012849402650x - 1016146037830x - 247984 +--R / +--R 2 +--R 83187500000x + 99825000000x + 29947500000 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 42592 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=-216999/25000*x-19683/5000*x^2-243/250*x^3+(-1/343750)/(3+5*x)^2+_ + (-8/75625)/(3+5*x)-117649/21296*log(1-2*x)+3347/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (6694000x + 8032800x + 2409840)log(5x + 3) +--R + +--R 2 +--R (- 45956640625x - 55147968750x - 16544390625)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 8085825000x - 42450581250x - 114414423750x - 98436833550x +--R + +--R - 25994486210x - 106568 +--R / +--R 2 +--R 8318750000x + 9982500000x + 2994750000 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (6694000x + 8032800x + 2409840)log(5x + 3) +--R + +--R 2 5 +--R (- 45956640625x - 55147968750x - 16544390625)log(2x - 1) - 8085825000x +--R + +--R 4 3 2 +--R - 42450581250x - 114414423750x - 98436833550x - 25994486210x - 106568 +--R / +--R 2 +--R 8318750000x + 9982500000x + 2994750000 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=-4941/2500*x-243/500*x^2+(-1/68750)/(3+5*x)^2+(-167/378125)/(3+5*x)-_ + 16807/10648*log(1-2*x)+11224/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2244800x + 2693760x + 808128)log(5x + 3) +--R + +--R 2 4 +--R (- 1313046875x - 1575656250x - 472696875)log(- 2x + 1) - 404291250x +--R + +--R 3 2 +--R - 2129267250x - 2118486150x - 591955870x - 44572 +--R / +--R 2 +--R 831875000x + 998250000x + 299475000 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2244800x + 2693760x + 808128)log(5x + 3) +--R + +--R 2 4 +--R (- 1313046875x - 1575656250x - 472696875)log(2x - 1) - 404291250x +--R + +--R 3 2 +--R - 2129267250x - 2118486150x - 591955870x - 44572 +--R / +--R 2 +--R 831875000x + 998250000x + 299475000 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=-81/250*x+(-1/13750)/(3+5*x)^2+(-134/75625)/(3+5*x)-_ + 2401/5324*log(1-2*x)+6802/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (680200x + 816240x + 244872)log(5x + 3) +--R + +--R 2 3 +--R (- 37515625x - 45018750x - 13505625)log(- 2x + 1) - 26952750x +--R + +--R 2 +--R - 32343300x - 9732470x - 17930 +--R / +--R 2 +--R 83187500x + 99825000x + 29947500 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (680200x + 816240x + 244872)log(5x + 3) +--R + +--R 2 3 +--R (- 37515625x - 45018750x - 13505625)log(2x - 1) - 26952750x +--R + +--R 2 +--R - 32343300x - 9732470x - 17930 +--R / +--R 2 +--R 83187500x + 99825000x + 29947500 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=(-1/2750)/(3+5*x)^2+(-101/15125)/(3+5*x)-343/2662*log(1-2*x)+_ + 3469/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (173450x + 208140x + 62442)log(5x + 3) +--R + +--R 2 +--R (- 1071875x - 1286250x - 385875)log(- 2x + 1) - 11110x - 6787 +--R / +--R 2 +--R 8318750x + 9982500x + 2994750 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (173450x + 208140x + 62442)log(5x + 3) +--R + +--R 2 +--R (- 1071875x - 1286250x - 385875)log(2x - 1) - 11110x - 6787 +--R / +--R 2 +--R 8318750x + 9982500x + 2994750 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 2662 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=(-1/550)/(3+5*x)^2+(-68/3025)/(3+5*x)-49/1331*log(1-2*x)+49/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(- 2x + 1) - 7480x - 4609 +--R / +--R 2 +--R 1663750x + 1996500x + 598950 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(2x - 1) - 7480x - 4609 +--R / +--R 2 +--R 1663750x + 1996500x + 598950 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=(-1/110)/(3+5*x)^2+(-7/121)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (3500x + 4200x + 1260)log(5x + 3) +--R + +--R 2 +--R (- 3500x - 4200x - 1260)log(- 2x + 1) - 3850x - 2431 +--R / +--R 2 +--R 332750x + 399300x + 119790 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (3500x + 4200x + 1260)log(5x + 3) + (- 3500x - 4200x - 1260)log(2x - 1) +--R + +--R - 3850x - 2431 +--R / +--R 2 +--R 332750x + 399300x + 119790 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R - 14log(2x - 1) + 14log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=1/((1-2*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-1/22)/(3+5*x)^2+(-2/121)/(3+5*x)-4/1331*log(1-2*x)+4/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(- 2x + 1) +--R + +--R - 220x - 253 +--R / +--R 2 +--R 66550x + 79860x + 23958 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(2x - 1) - 220x +--R + +--R - 253 +--R / +--R 2 +--R 66550x + 79860x + 23958 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 5 4 3 2 +--R 750x + 1475x + 785x - 153x - 243x - 54 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=(-5/22)/(3+5*x)^2+155/121/(3+5*x)-8/9317*log(1-2*x)-27/7*log(2+3*x)+_ + 5135/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (1797250x + 2156700x + 647010)log(5x + 3) +--R + +--R 2 +--R (- 1796850x - 2156220x - 646866)log(3x + 2) +--R + +--R 2 +--R (- 400x - 480x - 144)log(- 2x + 1) + 119350x + 67375 +--R / +--R 2 +--R 465850x + 559020x + 167706 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1797250x + 2156700x + 647010)log(5x + 3) +--R + +--R 2 +--R (- 1796850x - 2156220x - 646866)log(3x + 2) +--R + +--R 2 +--R (- 400x - 480x - 144)log(2x - 1) + 119350x + 67375 +--R / +--R 2 +--R 465850x + 559020x + 167706 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 9317 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 6 5 4 3 2 +--R 2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=27/7/(2+3*x)+(-25/22)/(3+5*x)^2+1600/121/(3+5*x)-16/65219*log(1-2*x)-_ + 2889/49*log(2+3*x)+78475/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3) +--R + +--R 3 2 +--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2400x - 4480x - 2784x - 576)log(- 2x + 1) + 38449950x + 47420065x +--R + +--R 14580412 +--R / +--R 3 2 +--R 9782850x + 18261320x + 11348106x + 2347884 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3) +--R + +--R 3 2 +--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2400x - 4480x - 2784x - 576)log(2x - 1) + 38449950x + 47420065x +--R + +--R 14580412 +--R / +--R 3 2 +--R 9782850x + 18261320x + 11348106x + 2347884 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 65219 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=27/14/(2+3*x)^2+2889/49/(2+3*x)+(-125/22)/(3+5*x)^2+12125/121/(3+5*x)-_ + 32/456533*log(1-2*x)-204228/343*log(2+3*x)+792500/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 122322375000x + 309883350000x + 294117355000x + 123953340000x +--R + +--R 19571580000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x +--R + +--R - 19571577696 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(- 2x + 1) +--R + +--R 3 2 +--R 8154808200x + 15494126340x + 9797832352x + 2062044985 +--R / +--R 4 3 2 +--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 122322375000x + 309883350000x + 294117355000x + 123953340000x +--R + +--R 19571580000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x +--R + +--R - 19571577696 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(2x - 1) + 8154808200x +--R + +--R 2 +--R 15494126340x + 9797832352x + 2062044985 +--R / +--R 4 3 2 +--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 20250x + 80325x + 127845x + 97359x + 25237x - 13808x - 12888x +--R + +--R - 3888x - 432 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=9/7/(2+3*x)^3+2889/98/(2+3*x)^2+204228/343/(2+3*x)+(-625/22)/(3+5*x)^2+_ + 81250/121/(3+5*x)-64/3195731*log(1-2*x)-11984706/2401*log(2+3*x)+_ + 6643750/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 21534719062500x + 68911101000000x + 88148783362500x +--R + +--R 2 +--R 56341205725000x + 17993454150000x + 2297036700000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 21534718976100x - 68911100723520x - 88148783008836x +--R + +--R 2 +--R - 56341205498952x - 17993454077808x - 2297036690784 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(- 2x + 1) +--R + +--R 4 3 2 +--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x +--R + +--R 242016815656 +--R / +--R 5 4 3 2 +--R 4314236850x + 13805557920x + 17659609506x + 11287321892x +--R + +--R 3604784568x + 460185264 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 21534719062500x + 68911101000000x + 88148783362500x +--R + +--R 2 +--R 56341205725000x + 17993454150000x + 2297036700000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 21534718976100x - 68911100723520x - 88148783008836x +--R + +--R 2 +--R - 56341205498952x - 17993454077808x - 2297036690784 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(2x - 1) +--R + +--R 4 3 2 +--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x +--R + +--R 242016815656 +--R / +--R 5 4 3 2 +--R 4314236850x + 13805557920x + 17659609506x + 11287321892x +--R + +--R 3604784568x + 460185264 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3g.input.pdf b/src/axiom-website/CATS/rich3g.input.pdf new file mode 100644 index 0000000..7f8f6b9 Binary files /dev/null and b/src/axiom-website/CATS/rich3g.input.pdf differ diff --git a/src/axiom-website/CATS/rich3h.input.pamphlet b/src/axiom-website/CATS/rich3h.input.pamphlet new file mode 100644 index 0000000..147824c --- /dev/null +++ b/src/axiom-website/CATS/rich3h.input.pamphlet @@ -0,0 +1,7356 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3h.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 97 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3h.output +)spool rich3h.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 60750x + 281475x + 544185x + 547767x + 270429x + 9050x - 66280x +--R + +--R 2 +--R - 37440x - 9072x - 864 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=27/28/(2+3*x)^4+963/49/(2+3*x)^3+102114/343/(2+3*x)^2+_ + 11984706/2401/(2+3*x)+(-3125/22)/(3+5*x)^2+509375/121/(3+5*x)-_ + 128/22370117*log(1-2*x)-631722537/16807*log(2+3*x)+_ + 50028125/1331*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 6810663844687500x + 26334566866125000x + 42407733539587500x +--R + +--R 3 2 +--R 36404259483900000x + 17569831073900000x + 4520262818400000x +--R + +--R 484313873400000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 6810663843650700x - 26334566862116040x - 42407733533131692x +--R + +--R 3 2 +--R - 36404259478358112x - 17569831071225312x - 4520262817711872x +--R + +--R - 484313873326272 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x +--R + +--R - 73728 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 454044255102900x + 1468076424167430x + 1897568655019884x +--R + +--R 2 +--R 1225594367568417x + 395538240141506x + 51027557612801 +--R / +--R 6 5 4 3 +--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x +--R + +--R 2 +--R 467445964832x + 120261748992x + 12885187392 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 6810663844687500x + 26334566866125000x + 42407733539587500x +--R + +--R 3 2 +--R 36404259483900000x + 17569831073900000x + 4520262818400000x +--R + +--R 484313873400000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 6810663843650700x - 26334566862116040x - 42407733533131692x +--R + +--R 3 2 +--R - 36404259478358112x - 17569831071225312x - 4520262817711872x +--R + +--R - 484313873326272 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x +--R + +--R - 73728 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 454044255102900x + 1468076424167430x + 1897568655019884x +--R + +--R 2 +--R 1225594367568417x + 395538240141506x + 51027557612801 +--R / +--R 6 5 4 3 +--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x +--R + +--R 2 +--R 467445964832x + 120261748992x + 12885187392 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=63412811/1024/(1-2*x)+91609881/256*x+122887143/512*x^2+5892813/32*x^3+_ + 32991057/256*x^4+5859459/80*x^5+976617/32*x^6+56862/7*x^7+_ + 32805/32*x^8+246239357/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (17236754990x - 8618377495)log(- 2x + 1) + 73483200x + 545525280x +--R + +--R 7 6 5 4 3 +--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x +--R + +--R 2 +--R 17048666670x - 12825383340x - 2219448385 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (17236754990x - 8618377495)log(2x - 1) + 73483200x + 545525280x +--R + +--R 7 6 5 4 3 +--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x +--R + +--R 2 +--R 17048666670x - 12825383340x - 2219448385 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R 246239357log(2x - 1) - 246239357log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=9058973/512/(1-2*x)+22333965/256*x+873207/16*x^2+2399985/64*x^3+_ + 1423899/64*x^4+793881/80*x^5+11421/4*x^6+10935/28*x^7+_ + 15647317/256*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (2190624380x - 1095312190)log(- 2x + 1) + 13996800x + 95333760x +--R + +--R 6 5 4 3 2 +--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x +--R + +--R - 1563377550x - 317064055 +--R / +--R 35840x - 17920 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (2190624380x - 1095312190)log(2x - 1) + 13996800x + 95333760x +--R + +--R 6 5 4 3 2 +--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x +--R + +--R - 1563377550x - 317064055 +--R / +--R 35840x - 17920 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R 15647317log(2x - 1) - 15647317log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R (1) --------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=1294139/256/(1-2*x)+661617/32*x+1507977/128*x^2+111501/16*x^3+_ + 210195/64*x^4+5103/5*x^5+1215/8*x^6+3916031/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (39160310x - 19580155)log(- 2x + 1) + 388800x + 2418336x + 7101432x +--R + +--R 4 3 2 +--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695 +--R / +--R 2560x - 1280 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (39160310x - 19580155)log(2x - 1) + 388800x + 2418336x + 7101432x +--R + +--R 4 3 2 +--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695 +--R / +--R 2560x - 1280 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 3916031log(2x - 1) - 3916031log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=184877/128/(1-2*x)+301467/64*x+75447/32*x^2+18027/16*x^3+2997/8*x^4+_ + 243/4*x^5+60025/16*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (960400x - 480200)log(- 2x + 1) + 15552x + 88128x + 240480x + 459360x +--R + +--R 2 +--R 904080x - 602934x - 184877 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (960400x - 480200)log(2x - 1) + 15552x + 88128x + 240480x + 459360x +--R + +--R 2 +--R 904080x - 602934x - 184877 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 60025log(2x - 1) - 60025log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=26411/64/(1-2*x)+16203/16*x+13419/32*x^2+144*x^3+405/16*x^4+_ + 57281/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (114562x - 57281)log(- 2x + 1) + 3240x + 16812x + 44460x + 102786x +--R + +--R - 64812x - 26411 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (114562x - 57281)log(2x - 1) + 3240x + 16812x + 44460x + 102786x +--R + +--R - 64812x - 26411 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 57281log(2x - 1) - 57281log(- 2x + 1) +--R (4) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=3773/32/(1-2*x)+3177/16*x+243/4*x^2+45/4*x^3+3283/16*log(1-2*x) +--R +--R +--R 4 3 2 +--R (13132x - 6566)log(- 2x + 1) + 720x + 3528x + 10764x - 6354x - 3773 +--R (2) ---------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (13132x - 6566)log(2x - 1) + 720x + 3528x + 10764x - 6354x - 3773 +--R (3) -------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R 3283log(2x - 1) - 3283log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^2 +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ---------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=539/16/(1-2*x)+33*x+45/8*x^2+707/16*log(1-2*x) +--R +--R +--R 3 2 +--R (1414x - 707)log(- 2x + 1) + 180x + 966x - 528x - 539 +--R (2) ------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (1414x - 707)log(2x - 1) + 180x + 966x - 528x - 539 +--R (3) ----------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R 707log(2x - 1) - 707log(- 2x + 1) +--R (4) --------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^2 +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) -------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=77/8/(1-2*x)+15/4*x+17/2*log(1-2*x) +--R +--R +--R 2 +--R (136x - 68)log(- 2x + 1) + 60x - 30x - 77 +--R (2) ------------------------------------------ +--R 16x - 8 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (136x - 68)log(2x - 1) + 60x - 30x - 77 +--R (3) ---------------------------------------- +--R 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R 17log(2x - 1) - 17log(- 2x + 1) +--R (4) ------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/(1-2*x)^2 +--R +--R +--R 5x + 3 +--R (1) ------------ +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=11/4/(1-2*x)+5/4*log(1-2*x) +--R +--R +--R (10x - 5)log(- 2x + 1) - 11 +--R (2) --------------------------- +--R 8x - 4 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x - 5)log(2x - 1) - 11 +--R (3) ------------------------- +--R 8x - 4 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R 5log(2x - 1) - 5log(- 2x + 1) +--R (4) ----------------------------- +--R 4 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=11/14/(1-2*x)+1/49*log(1-2*x)-1/49*log(2+3*x) +--R +--R +--R (- 4x + 2)log(3x + 2) + (4x - 2)log(- 2x + 1) - 77 +--R (2) -------------------------------------------------- +--R 196x - 98 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 4x + 2)log(3x + 2) + (4x - 2)log(2x - 1) - 77 +--R (3) ------------------------------------------------ +--R 196x - 98 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R log(2x - 1) - log(- 2x + 1) +--R (4) --------------------------- +--R 49 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 5x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=11/49/(1-2*x)+1/49/(2+3*x)-31/343*log(1-2*x)+31/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(- 2x + 1) - 217x +--R + +--R - 161 +--R / +--R 2 +--R 2058x + 343x - 686 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(2x - 1) - 217x - 161 +--R ---------------------------------------------------------------------------- +--R 2 +--R 2058x + 343x - 686 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 31log(2x - 1) + 31log(- 2x + 1) +--R (4) --------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=22/343/(1-2*x)+1/98/(2+3*x)^2+(-31/343)/(2+3*x)-128/2401*log(1-2*x)+_ + 128/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (4608x + 3840x - 1024x - 1024)log(3x + 2) +--R + +--R 3 2 2 +--R (- 4608x - 3840x + 1024x + 1024)log(- 2x + 1) - 5376x - 4032x - 413 +--R / +--R 3 2 +--R 86436x + 72030x - 19208x - 19208 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (4608x + 3840x - 1024x - 1024)log(3x + 2) +--R + +--R 3 2 2 +--R (- 4608x - 3840x + 1024x + 1024)log(2x - 1) - 5376x - 4032x - 413 +--R / +--R 3 2 +--R 86436x + 72030x - 19208x - 19208 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 5x + 3 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=44/2401/(1-2*x)+1/147/(2+3*x)^3+(-31/686)/(2+3*x)^2+(-128/2401)/(2+3*x)-_ + 388/16807*log(1-2*x)+388/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2) +--R + +--R 4 3 2 +--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(- 2x + 1) +--R + +--R 3 2 +--R - 146664x - 207774x - 48209x + 15148 +--R / +--R 4 3 2 +--R 5445468x + 8168202x + 1815156x - 2016840x - 806736 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(2x - 1) - 146664x +--R + +--R 2 +--R - 207774x - 48209x + 15148 +--R / +--R 4 3 2 +--R 5445468x + 8168202x + 1815156x - 2016840x - 806736 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 388log(2x - 1) + 388log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 5x + 3 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=88/16807/(1-2*x)+1/196/(2+3*x)^4+(-31/1029)/(2+3*x)^3+_ + (-64/2401)/(2+3*x)^2+(-388/16807)/(2+3*x)-1040/117649*log(1-2*x)+_ + 1040/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2358720x - 4914000x - 3003000x + 64610x + 370853 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2358720x - 4914000x - 3003000x + 64610x + 370853 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 1040log(2x - 1) + 1040log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=176/117649/(1-2*x)+1/245/(2+3*x)^5+(-31/1372)/(2+3*x)^4+_ + (-128/7203)/(2+3*x)^3+(-194/16807)/(2+3*x)^2+_ + (-1040/117649)/(2+3*x)-2608/823543*log(1-2*x)+2608/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x +--R + +--R - 27540480x - 5007360 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x +--R + +--R 27540480x + 5007360 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x +--R + +--R 14729806 +--R / +--R 6 5 4 3 +--R 24014513880x + 68041122660x + 66706983000x + 17788528800x +--R + +--R 2 +--R - 11859019200x - 8696614080x - 1581202560 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x +--R + +--R - 27540480x - 5007360 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x +--R + +--R 27540480x + 5007360 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x +--R + +--R 14729806 +--R / +--R 6 5 4 3 +--R 24014513880x + 68041122660x + 66706983000x + 17788528800x +--R + +--R 2 +--R - 11859019200x - 8696614080x - 1581202560 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 2608log(2x - 1) + 2608log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 5x + 3 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=352/823543/(1-2*x)+1/294/(2+3*x)^6+(-31/1715)/(2+3*x)^5+_ + (-32/2401)/(2+3*x)^4+(-388/50421)/(2+3*x)^3+_ + (-520/117649)/(2+3*x)^2+(-2608/823543)/(2+3*x)-_ + 128/117649*log(1-2*x)+128/117649*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 2 +--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x +--R + +--R - 81920 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 2 +--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x +--R + +--R 81920 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x +--R + +--R 343917 +--R / +--R 7 6 5 4 2 +--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x +--R + +--R - 527067520x - 75295360 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 2 +--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x +--R + +--R - 81920 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 2 +--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x +--R + +--R 81920 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x +--R + +--R 343917 +--R / +--R 7 6 5 4 2 +--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x +--R + +--R - 527067520x - 75295360 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=697540921/2048/(1-2*x)+2330515357/1024*x+413355417/256*x^2+_ + 346239417/256*x^3+275757561/256*x^4+235268793/320*x^5+_ + 396738*x^6+17378631/112*x^7+1235655/32*x^8+18225/4*x^9+_ + 1512848491/1024*log(1-2*x) +--R +--R +--R (2) +--R 10 9 +--R (211798788740x - 105899394370)log(- 2x + 1) + 653184000x + 5209142400x +--R + +--R 8 7 6 5 +--R 19476780480x + 45754035840x + 76962239424x + 101724024528x +--R + +--R 4 3 2 +--R 116681956440x + 134531996760x + 210532633220x - 163136074990x +--R + +--R - 24413932235 +--R / +--R 143360x - 71680 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 +--R (211798788740x - 105899394370)log(2x - 1) + 653184000x + 5209142400x +--R + +--R 8 7 6 5 +--R 19476780480x + 45754035840x + 76962239424x + 101724024528x +--R + +--R 4 3 2 +--R 116681956440x + 134531996760x + 210532633220x - 163136074990x +--R + +--R - 24413932235 +--R / +--R 143360x - 71680 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R 1512848491log(2x - 1) - 1512848491log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=99648703/1024/(1-2*x)+9077405/16*x+195497697/512*x^2+18842715/64*x^3+_ + 53086563/256*x^4+4750569/40*x^5+1597239/32*x^6+375435/28*x^7+_ + 54675/32*x^8+389535839/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (27267508730x - 13633754365)log(- 2x + 1) + 122472000x + 899877600x +--R + +--R 7 6 5 4 +--R 3097258560x + 6724111968x + 10607727816x + 13671721980x +--R + +--R 3 2 +--R 16817757180x + 26981935610x - 20333387200x - 3487704605 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (27267508730x - 13633754365)log(2x - 1) + 122472000x + 899877600x +--R + +--R 7 6 5 4 +--R 3097258560x + 6724111968x + 10607727816x + 13671721980x +--R + +--R 3 2 +--R 16817757180x + 26981935610x - 20333387200x - 3487704605 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 389535839log(2x - 1) - 389535839log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=14235529/512/(1-2*x)+35458963/256*x+11140101/128*x^2+3851307/64*x^3+_ + 575775/16*x^4+1295919/80*x^5+37665/8*x^6+18225/28*x^7+_ + 12386759/128*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (3468292520x - 1734146260)log(- 2x + 1) + 23328000x + 157075200x +--R + +--R 6 5 4 3 2 +--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x +--R + +--R - 2482127410x - 498243515 +--R / +--R 35840x - 17920 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (3468292520x - 1734146260)log(2x - 1) + 23328000x + 157075200x +--R + +--R 6 5 4 3 2 +--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x +--R + +--R - 2482127410x - 498243515 +--R / +--R 35840x - 17920 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R 12386759log(2x - 1) - 12386759log(- 2x + 1) +--R (4) ------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=2033647/256/(1-2*x)+2104901/64*x+2412699/128*x^2+89913/8*x^3+_ + 342333/64*x^4+6723/4*x^5+2025/8*x^6+6206585/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (12413170x - 6206585)log(- 2x + 1) + 129600x + 795744x + 2308392x +--R + +--R 4 3 2 +--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647 +--R / +--R 512x - 256 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (12413170x - 6206585)log(2x - 1) + 129600x + 795744x + 2308392x +--R + +--R 4 3 2 +--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647 +--R / +--R 512x - 256 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 6206585log(2x - 1) - 6206585log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=290521/128/(1-2*x)+480841/64*x+15159/4*x^2+29277/16*x^3+9855/16*x^4+_ + 405/4*x^5+381073/64*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 +--R (1524292x - 762146)log(- 2x + 1) + 25920x + 144720x + 389592x +--R + +--R 3 2 +--R 735960x + 1438276x - 961682x - 290521 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (1524292x - 762146)log(2x - 1) + 25920x + 144720x + 389592x + 735960x +--R + +--R 2 +--R 1438276x - 961682x - 290521 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R 381073log(2x - 1) - 381073log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=41503/64/(1-2*x)+12973/8*x+21717/32*x^2+945/4*x^3+675/16*x^4+_ + 91091/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (182182x - 91091)log(- 2x + 1) + 5400x + 27540x + 71748x + 164134x +--R + +--R - 103784x - 41503 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (182182x - 91091)log(2x - 1) + 5400x + 27540x + 71748x + 164134x +--R + +--R - 103784x - 41503 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R 91091log(2x - 1) - 91091log(- 2x + 1) +--R (4) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=5929/32/(1-2*x)+5119/16*x+795/8*x^2+75/4*x^3+1309/4*log(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (20944x - 10472)log(- 2x + 1) + 1200x + 5760x + 17296x - 10238x - 5929 +--R ------------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (20944x - 10472)log(2x - 1) + 1200x + 5760x + 17296x - 10238x - 5929 +--R ----------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R 1309log(2x - 1) - 1309log(- 2x + 1) +--R (4) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ----------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=847/16/(1-2*x)+215/4*x+75/8*x^2+1133/16*log(1-2*x) +--R +--R +--R 3 2 +--R (2266x - 1133)log(- 2x + 1) + 300x + 1570x - 860x - 847 +--R (2) --------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (2266x - 1133)log(2x - 1) + 300x + 1570x - 860x - 847 +--R (3) ------------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R 1133log(2x - 1) - 1133log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=121/8/(1-2*x)+25/4*x+55/4*log(1-2*x) +--R +--R +--R 2 +--R (220x - 110)log(- 2x + 1) + 100x - 50x - 121 +--R (2) --------------------------------------------- +--R 16x - 8 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (220x - 110)log(2x - 1) + 100x - 50x - 121 +--R (3) ------------------------------------------- +--R 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R 55log(2x - 1) - 55log(- 2x + 1) +--R (4) ------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=121/28/(1-2*x)+407/196*log(1-2*x)+1/147*log(2+3*x) +--R +--R +--R (8x - 4)log(3x + 2) + (2442x - 1221)log(- 2x + 1) - 2541 +--R (2) -------------------------------------------------------- +--R 1176x - 588 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (8x - 4)log(3x + 2) + (2442x - 1221)log(2x - 1) - 2541 +--R (3) ------------------------------------------------------ +--R 1176x - 588 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R 407log(2x - 1) - 407log(- 2x + 1) +--R (4) --------------------------------- +--R 196 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=121/98/(1-2*x)+(-1/147)/(2+3*x)+22/343*log(1-2*x)-22/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(- 2x + 1) +--R + +--R - 7651x - 5068 +--R / +--R 2 +--R 12348x + 2058x - 4116 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(2x - 1) +--R + +--R - 7651x - 5068 +--R / +--R 2 +--R 12348x + 2058x - 4116 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R 22log(2x - 1) - 22log(- 2x + 1) +--R (4) ------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=121/343/(1-2*x)+(-1/294)/(2+3*x)^2+22/343/(2+3*x)-319/2401*log(1-2*x)+_ + 319/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (34452x + 28710x - 7656x - 7656)log(3x + 2) +--R + +--R 3 2 2 +--R (- 34452x - 28710x + 7656x + 7656)log(- 2x + 1) - 40194x - 60158x +--R + +--R - 22127 +--R / +--R 3 2 +--R 259308x + 216090x - 57624x - 57624 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (34452x + 28710x - 7656x - 7656)log(3x + 2) +--R + +--R 3 2 2 +--R (- 34452x - 28710x + 7656x + 7656)log(2x - 1) - 40194x - 60158x - 22127 +--R / +--R 3 2 +--R 259308x + 216090x - 57624x - 57624 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 319log(2x - 1) + 319log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=242/2401/(1-2*x)+(-1/441)/(2+3*x)^3+11/343/(2+3*x)^2+_ + (-319/2401)/(2+3*x)-1364/16807*log(1-2*x)+1364/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2) +--R + +--R 4 3 2 +--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(- 2x + 1) +--R + +--R 3 2 +--R - 773388x - 1095633x - 464303x - 50939 +--R / +--R 4 3 2 +--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2) +--R + +--R 4 3 2 +--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(2x - 1) +--R + +--R 3 2 +--R - 773388x - 1095633x - 464303x - 50939 +--R / +--R 4 3 2 +--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 1364log(2x - 1) + 1364log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=484/16807/(1-2*x)+(-1/588)/(2+3*x)^4+22/1029/(2+3*x)^3+_ + (-319/4802)/(2+3*x)^2+(-1364/16807)/(2+3*x)-4180/117649*log(1-2*x)+_ + 4180/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 4180log(2x - 1) + 4180log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=968/117649/(1-2*x)+(-1/735)/(2+3*x)^5+11/686/(2+3*x)^4+_ + (-319/7203)/(2+3*x)^3+(-682/16807)/(2+3*x)^2+(-4180/117649)/(2+3*x)-_ + 11264/823543*log(1-2*x)+11264/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x +--R + +--R - 19824640x - 3604480 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x +--R + +--R 19824640x + 3604480 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708 +--R / +--R 6 5 4 3 +--R 4002418980x + 11340187110x + 11117830500x + 2964754800x +--R + +--R 2 +--R - 1976503200x - 1449435680x - 263533760 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x +--R + +--R - 19824640x - 3604480 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x +--R + +--R 19824640x + 3604480 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708 +--R / +--R 6 5 4 3 +--R 4002418980x + 11340187110x + 11117830500x + 2964754800x +--R + +--R 2 +--R - 1976503200x - 1449435680x - 263533760 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 11264log(2x - 1) + 11264log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1936/823543/(1-2*x)+(-1/882)/(2+3*x)^6+22/1715/(2+3*x)^5+_ + (-319/9604)/(2+3*x)^4+(-1364/50421)/(2+3*x)^3+(-2090/117649)/(2+3*x)^2+_ + (-11264/823543)/(2+3*x)-4048/823543*log(1-2*x)+4048/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 1062357120x + 3718249920x + 4957666560x + 2754259200x +--R + +--R 2 +--R - 734469120x - 326430720x - 46632960 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x +--R + +--R 2 +--R 734469120x + 326430720x + 46632960 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x +--R + +--R 426120352x + 132853546 +--R / +--R 7 6 5 4 +--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x +--R + +--R 2 +--R - 149423641920x - 66410507520x - 9487215360 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 1062357120x + 3718249920x + 4957666560x + 2754259200x +--R + +--R 2 +--R - 734469120x - 326430720x - 46632960 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x +--R + +--R 2 +--R 734469120x + 326430720x + 46632960 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x +--R + +--R 426120352x + 132853546 +--R / +--R 7 6 5 4 +--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x +--R + +--R 2 +--R - 149423641920x - 66410507520x - 9487215360 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 4048log(2x - 1) + 4048log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^8) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R / +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=3872/5764801/(1-2*x)+(-1/1029)/(2+3*x)^7+11/1029/(2+3*x)^6+_ + (-319/12005)/(2+3*x)^5+(-341/16807)/(2+3*x)^4+(-4180/352947)/(2+3*x)^3+_ + (-5632/823543)/(2+3*x)^2+(-4048/823543)/(2+3*x)-_ + 68288/40353607*log(1-2*x)+68288/40353607*log(2+3*x) +--R +--R +--R (2) +--R 8 7 6 5 +--R 4480375680x + 18668232000x + 31362629760x + 25554735360x +--R + +--R 4 3 2 +--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x +--R + +--R 4 3 2 +--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x +--R + +--R 3 2 +--R - 10470141297x + 1282240575x + 2289114821x + 535775051 +--R / +--R 8 7 6 5 +--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x +--R + +--R 4 3 2 +--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x +--R + +--R - 77478925440 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 4480375680x + 18668232000x + 31362629760x + 25554735360x +--R + +--R 4 3 2 +--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x +--R + +--R 4 3 2 +--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 4 +--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x +--R + +--R 3 2 +--R - 10470141297x + 1282240575x + 2289114821x + 535775051 +--R / +--R 8 7 6 5 +--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x +--R + +--R 4 3 2 +--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x +--R + +--R - 77478925440 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 68288log(2x - 1) + 68288log(- 2x + 1) +--R (4) --------------------------------------- +--R 40353607 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^8*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=7672950131/4096/(1-2*x)+7277894263/512*x+21573106793/2048*x^2+_ + 2416569641/256*x^3+8502681987/1024*x^4+260574273/40*x^5+_ + 544462047/128*x^6+242570133/112*x^7+101721015/128*x^8+_ + 370575/2*x^9+164025/8*x^10+36770371407/4096*log(1-2*x) +--R +--R +--R (2) +--R 11 +--R (2573925998490x - 1286962999245)log(- 2x + 1) + 5878656000x +--R + +--R 10 9 8 7 +--R 50186304000x + 201292257600x + 507052003680x + 909105215040x +--R + +--R 6 5 4 3 +--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x +--R + +--R 2 +--R 2565503311770x - 2037810393640x - 268553254585 +--R / +--R 286720x - 143360 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 +--R (2573925998490x - 1286962999245)log(2x - 1) + 5878656000x +--R + +--R 10 9 8 7 +--R 50186304000x + 201292257600x + 507052003680x + 909105215040x +--R + +--R 6 5 4 3 +--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x +--R + +--R 2 +--R 2565503311770x - 2037810393640x - 268553254585 +--R / +--R 286720x - 143360 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R 36770371407log(2x - 1) - 36770371407log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 4096 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=1096135733/2048/(1-2*x)+3690540955/1024*x+1312685491/512*x^2+_ + 551942075/256*x^3+220950207/128*x^4+379446471/320*x^5+_ + 20626947/32*x^6+28463805/112*x^7+127575/2*x^8+30375/4*x^9+_ + 298946109/128*log(1-2*x) +--R +--R +--R (2) +--R 10 +--R (334819642080x - 167409821040)log(- 2x + 1) + 1088640000x +--R + +--R 9 8 7 6 +--R 8600256000x + 31861382400x + 74191887360x + 123787657728x +--R + +--R 5 4 3 2 +--R 162468222336x + 185355446080x + 213008156480x + 332899764960x +--R + +--R - 258337866850x - 38364750655 +--R / +--R 143360x - 71680 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 +--R (334819642080x - 167409821040)log(2x - 1) + 1088640000x + 8600256000x +--R + +--R 8 7 6 5 +--R 31861382400x + 74191887360x + 123787657728x + 162468222336x +--R + +--R 4 3 2 +--R 185355446080x + 213008156480x + 332899764960x - 258337866850x +--R + +--R - 38364750655 +--R / +--R 143360x - 71680 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R 298946109log(2x - 1) - 298946109log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=156590819/1024/(1-2*x)+230244479/256*x+310976027/512*x^2+7530189/16*x^3+_ + 85406805/256*x^4+15403257/80*x^5+2611845/32*x^6+309825/14*x^7+_ + 91125/32*x^8+616195041/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (43133652870x - 21566826435)log(- 2x + 1) + 204120000x + 1484244000x +--R + +--R 7 6 5 4 +--R 5057380800x + 10876051872x + 17013246264x + 21778294020x +--R + +--R 3 2 +--R 26669020420x + 42700132230x - 32234227060x - 5480678665 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (43133652870x - 21566826435)log(2x - 1) + 204120000x + 1484244000x +--R + +--R 7 6 5 4 +--R 5057380800x + 10876051872x + 17013246264x + 21778294020x +--R + +--R 3 2 +--R 26669020420x + 42700132230x - 32234227060x - 5480678665 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R 616195041log(2x - 1) - 616195041log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=22370117/512/(1-2*x)+56291737/256*x+8881301/64*x^2+6179077/64*x^3+_ + 3724389/64*x^4+423009/16*x^5+15525/2*x^6+30375/28*x^7+_ + 39220335/256*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (1098169380x - 549084690)log(- 2x + 1) + 7776000x + 51753600x +--R + +--R 6 5 4 3 2 +--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x +--R + +--R - 788084318x - 156590819 +--R / +--R 7168x - 3584 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (1098169380x - 549084690)log(2x - 1) + 7776000x + 51753600x +--R + +--R 6 5 4 3 2 +--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x +--R + +--R - 788084318x - 156590819 +--R / +--R 7168x - 3584 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 39220335log(2x - 1) - 39220335log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=3195731/256/(1-2*x)+209243/4*x+3859469/128*x^2+289951/16*x^3+_ + 557415/64*x^4+5535/2*x^5+3375/8*x^6+9836211/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (19672422x - 9836211)log(- 2x + 1) + 216000x + 1308960x + 3750840x +--R + +--R 4 3 2 +--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731 +--R / +--R 512x - 256 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (19672422x - 9836211)log(2x - 1) + 216000x + 1308960x + 3750840x +--R + +--R 4 3 2 +--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731 +--R / +--R 512x - 256 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R 9836211log(2x - 1) - 9836211log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=456533/128/(1-2*x)+766807/64*x+194881/32*x^2+47535/16*x^3+_ + 2025/2*x^4+675/4*x^5+302379/32*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 +--R (2419032x - 1209516)log(- 2x + 1) + 43200x + 237600x + 630960x +--R + +--R 3 2 +--R 1178768x + 2287704x - 1533614x - 456533 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (2419032x - 1209516)log(2x - 1) + 43200x + 237600x + 630960x +--R + +--R 3 2 +--R 1178768x + 2287704x - 1533614x - 456533 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R 302379log(2x - 1) - 302379log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=65219/64/(1-2*x)+41537/16*x+35135/32*x^2+775/2*x^3+1125/16*x^4+_ + 144837/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (289674x - 144837)log(- 2x + 1) + 9000x + 45100x + 115740x + 262026x +--R + +--R - 166148x - 65219 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (289674x - 144837)log(2x - 1) + 9000x + 45100x + 115740x + 262026x +--R + +--R - 166148x - 65219 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R 144837log(2x - 1) - 144837log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=9317/32/(1-2*x)+8245/16*x+325/2*x^2+125/4*x^3+8349/16*log(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (33396x - 16698)log(- 2x + 1) + 2000x + 9400x + 27780x - 16490x - 9317 +--R ------------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (33396x - 16698)log(2x - 1) + 2000x + 9400x + 27780x - 16490x - 9317 +--R ----------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R 8349log(2x - 1) - 8349log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=1331/16/(1-2*x)+175/2*x+125/8*x^2+1815/16*log(1-2*x) +--R +--R +--R 3 2 +--R (3630x - 1815)log(- 2x + 1) + 500x + 2550x - 1400x - 1331 +--R (2) ----------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (3630x - 1815)log(2x - 1) + 500x + 2550x - 1400x - 1331 +--R (3) --------------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R 1815log(2x - 1) - 1815log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=1331/56/(1-2*x)+125/12*x+1089/49*log(1-2*x)-1/441*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(- 2x + 1) + 73500x +--R + +--R - 36750x - 83853 +--R / +--R 7056x - 3528 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(2x - 1) + 73500x - 36750x +--R + +--R - 83853 +--R / +--R 7056x - 3528 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R 1089log(2x - 1) - 1089log(- 2x + 1) +--R (4) ----------------------------------- +--R 49 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=1331/196/(1-2*x)+1/441/(2+3*x)+4719/1372*log(1-2*x)+101/3087*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (2424x + 404x - 808)log(3x + 2) +--R + +--R 2 +--R (254826x + 42471x - 84942)log(- 2x + 1) - 251503x - 167734 +--R / +--R 2 +--R 74088x + 12348x - 24696 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (2424x + 404x - 808)log(3x + 2) + (254826x + 42471x - 84942)log(2x - 1) +--R + +--R - 251503x - 167734 +--R / +--R 2 +--R 74088x + 12348x - 24696 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R 4719log(2x - 1) - 4719log(- 2x + 1) +--R (4) ----------------------------------- +--R 1372 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=1331/686/(1-2*x)+1/882/(2+3*x)^2+(-101/3087)/(2+3*x)+_ + 363/2401*log(1-2*x)-363/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2) +--R + +--R 3 2 2 +--R (117612x + 98010x - 26136x - 26136)log(- 2x + 1) - 763161x - 1007552x +--R + +--R - 332633 +--R / +--R 3 2 +--R 777924x + 648270x - 172872x - 172872 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2) +--R + +--R 3 2 2 +--R (117612x + 98010x - 26136x - 26136)log(2x - 1) - 763161x - 1007552x +--R + +--R - 332633 +--R / +--R 3 2 +--R 777924x + 648270x - 172872x - 172872 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R 363log(2x - 1) - 363log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1331/2401/(1-2*x)+1/1323/(2+3*x)^3+(-101/6174)/(2+3*x)^2+_ + 363/2401/(2+3*x)-3267/16807*log(1-2*x)+3267/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2) +--R + +--R 4 3 2 +--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(- 2x + 1) +--R + +--R 3 2 +--R - 11114334x - 25199244x - 18674579x - 4544792 +--R / +--R 4 3 2 +--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2) +--R + +--R 4 3 2 +--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(2x - 1) +--R + +--R 3 2 +--R - 11114334x - 25199244x - 18674579x - 4544792 +--R / +--R 4 3 2 +--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 3267log(2x - 1) + 3267log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=2662/16807/(1-2*x)+1/1764/(2+3*x)^4+(-101/9261)/(2+3*x)^3+_ + 363/4802/(2+3*x)^2+(-3267/16807)/(2+3*x)-14520/117649*log(1-2*x)+_ + 14520/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x +--R + +--R - 25090560 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x +--R + +--R 25090560 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787 +--R / +--R 5 4 3 2 +--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x +--R + +--R - 203297472 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x +--R + +--R - 25090560 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x +--R + +--R 25090560 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787 +--R / +--R 5 4 3 2 +--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x +--R + +--R - 203297472 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 14520log(2x - 1) + 14520log(- 2x + 1) +--R (4) --------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=5324/117649/(1-2*x)+1/2205/(2+3*x)^5+(-101/12348)/(2+3*x)^4+_ + 121/2401/(2+3*x)^3+(-3267/33614)/(2+3*x)^2+(-14520/117649)/(2+3*x)-_ + 45012/823543*log(1-2*x)+45012/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 3937649760x + 11156674320x + 10937916000x + 2916777600x +--R + +--R 2 +--R - 1944518400x - 1425980160x - 259269120 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x +--R + +--R 2 +--R 1944518400x + 1425980160x + 259269120 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x +--R + +--R - 181895609x + 165794902 +--R / +--R 6 5 4 3 +--R 72043541640x + 204123367980x + 200120949000x + 53365586400x +--R + +--R 2 +--R - 35577057600x - 26089842240x - 4743607680 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 3937649760x + 11156674320x + 10937916000x + 2916777600x +--R + +--R 2 +--R - 1944518400x - 1425980160x - 259269120 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x +--R + +--R 2 +--R 1944518400x + 1425980160x + 259269120 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x +--R + +--R - 181895609x + 165794902 +--R / +--R 6 5 4 3 +--R 72043541640x + 204123367980x + 200120949000x + 53365586400x +--R + +--R 2 +--R - 35577057600x - 26089842240x - 4743607680 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 45012log(2x - 1) + 45012log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=10648/823543/(1-2*x)+1/2646/(2+3*x)^6+(-101/15435)/(2+3*x)^5+_ + 363/9604/(2+3*x)^4+(-1089/16807)/(2+3*x)^3+(-7260/117649)/(2+3*x)^2+_ + (-45012/823543)/(2+3*x)-17424/823543*log(1-2*x)+17424/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 13718263680x + 48013922880x + 64018563840x + 35565868800x +--R + +--R 2 +--R - 9484231680x - 4215214080x - 602173440 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x +--R + +--R 2 +--R 9484231680x + 4215214080x + 602173440 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x +--R + +--R 2 +--R - 6211643067x + 3228815828x + 1017833894 +--R / +--R 7 6 5 4 +--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x +--R + +--R 2 +--R - 448270925760x - 199231522560x - 28461646080 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 13718263680x + 48013922880x + 64018563840x + 35565868800x +--R + +--R 2 +--R - 9484231680x - 4215214080x - 602173440 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x +--R + +--R 2 +--R 9484231680x + 4215214080x + 602173440 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x +--R + +--R 2 +--R - 6211643067x + 3228815828x + 1017833894 +--R / +--R 7 6 5 4 +--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x +--R + +--R 2 +--R - 448270925760x - 199231522560x - 28461646080 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 17424log(2x - 1) + 17424log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^8) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=21296/5764801/(1-2*x)+1/3087/(2+3*x)^7+(-101/18522)/(2+3*x)^6+_ + 363/12005/(2+3*x)^5+(-3267/67228)/(2+3*x)^4+(-4840/117649)/(2+3*x)^3+_ + (-22506/823543)/(2+3*x)^2+(-17424/823543)/(2+3*x)-_ + 307824/40353607*log(1-2*x)+307824/40353607*log(2+3*x) +--R +--R +--R (2) +--R 8 7 6 5 +--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x +--R + +--R 4 3 2 +--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x +--R + +--R - 21276794880 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R - 727067975040x - 3029449896000x - 5089475825280x +--R + +--R 5 4 3 2 +--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x +--R + +--R 180852756480x + 21276794880 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x +--R + +--R 3 2 +--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928 +--R / +--R 8 7 6 +--R 95313605589720x + 397140023290500x + 667195239128040x +--R + +--R 5 4 3 +--R 543640565215440x + 164739565216800x - 65895826086720x +--R + +--R 2 +--R - 73217584540800x - 23708551184640x - 2789241315840 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x +--R + +--R 4 3 2 +--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x +--R + +--R - 21276794880 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R - 727067975040x - 3029449896000x - 5089475825280x +--R + +--R 5 4 3 2 +--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x +--R + +--R 180852756480x + 21276794880 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 4 +--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x +--R + +--R 3 2 +--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928 +--R / +--R 8 7 6 +--R 95313605589720x + 397140023290500x + 667195239128040x +--R + +--R 5 4 3 +--R 543640565215440x + 164739565216800x - 65895826086720x +--R + +--R 2 +--R - 73217584540800x - 23708551184640x - 2789241315840 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 307824log(2x - 1) + 307824log(- 2x + 1) +--R (4) ----------------------------------------- +--R 40353607 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(a+b*x)^m/(e+f*x)^2 +--R +--R +--R m +--R (b x + a) +--R (1) ------------------ +--R 2 2 2 +--R f x + 2e f x + e +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=(a+b*x)^(1+m)/((b*e-a*f)*(e+f*x))-b*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(1+m)) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(a+b*x)^m/((c+d*x)*(e+f*x)^2) +--R +--R +--R m +--R (b x + a) +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R d f x + (c f + 2d e f)x + (2c e f + d e )x + c e +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+d^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*_ +-- (d*e-c*f)^2*(1+m))-d*f*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)*(d*e-c*f)^2*(1+m))+b*f*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)^2*(d*e-c*f)*(1+m)) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(a+b*x)^m/((c+d*x)^2*(e+f*x)^2) +--R +--R +--R (1) +--R m +--R (b x + a) +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R d f x + (2c d f + 2d e f)x + (c f + 4c d e f + d e )x +--R + +--R 2 2 2 2 +--R (2c e f + 2c d e )x + c e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=d^2*(a+b*x)^(1+m)/((b*c-a*d)*(d*e-c*f)^2*(c+d*x))+_ +-- f^2*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x))-_ +-- 2*d^2*f*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*(d*e-c*f)^3*(1+m))-b*d^2*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)^2*(d*e-c*f)^2*(1+m))+2*d*f^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)*(d*e-c*f)^3*(1+m))-b*f^2*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)^2*(d*e-c*f)^2*(1+m)) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=5764801/2816/(1-2*x)+2041906293/250000*x+1839811401/400000*x^2+_ + 26773659/10000*x^3+9899091/8000*x^4+94041/250*x^5+2187/40*x^6+_ + 188591347/30976*log(1-2*x)+1/9453125*log(3+5*x) +--R +--R +--R (2) +--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x +--R + +--R 3 2 +--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375 +--R / +--R 4840000000x - 2420000000 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(2x - 1) +--R + +--R 7 6 5 4 +--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x +--R + +--R 3 2 +--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375 +--R / +--R 4840000000x - 2420000000 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R 188591347log(2x - 1) - 188591347log(- 2x + 1) +--R (4) --------------------------------------------- +--R 30976 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=823543/1408/(1-2*x)+370109547/200000*x+18237069/20000*x^2+_ + 853659/2000*x^3+13851/100*x^4+2187/100*x^5+5764801/3872*log(1-2*x)+_ + 1/1890625*log(3+5*x) +--R +--R +--R (2) +--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 10585080000x + 61746300000x + 173066058000x + 338044330800x +--R + +--R 2 +--R 674996568840x - 447832551870x - 141546453125 +--R / +--R 484000000x - 242000000 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(2x - 1) +--R + +--R 6 5 4 3 +--R 10585080000x + 61746300000x + 173066058000x + 338044330800x +--R + +--R 2 +--R 674996568840x - 447832551870x - 141546453125 +--R / +--R 484000000x - 242000000 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R 5764801log(2x - 1) - 5764801log(- 2x + 1) +--R (4) ----------------------------------------- +--R 3872 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=117649/704/(1-2*x)+3946293/10000*x+639819/4000*x^2+2673/50*x^3+_ + 729/80*x^4+2739541/7744*log(1-2*x)+1/378125*log(3+5*x) +--R +--R +--R (2) +--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x +--R + +--R - 4044184375 +--R / +--R 48400000x - 24200000 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(2x - 1) +--R + +--R 5 4 3 2 +--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x +--R + +--R - 4044184375 +--R / +--R 48400000x - 24200000 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R 2739541log(2x - 1) - 2739541log(- 2x + 1) +--R (4) ----------------------------------------- +--R 7744 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=16807/352/(1-2*x)+152793/2000*x+567/25*x^2+81/20*x^3+_ + 156065/1936*log(1-2*x)+1/75625*log(3+5*x) +--R +--R +--R (2) +--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(- 2x + 1) +--R + +--R 4 3 2 +--R 19602000x + 99970200x + 314873460x - 184879530x - 115548125 +--R / +--R 4840000x - 2420000 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(2x - 1) + 19602000x +--R + +--R 3 2 +--R 99970200x + 314873460x - 184879530x - 115548125 +--R / +--R 4840000x - 2420000 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R 156065log(2x - 1) - 156065log(- 2x + 1) +--R (4) --------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=2401/176/(1-2*x)+621/50*x+81/40*x^2+33271/1936*log(1-2*x)+_ + 1/15125*log(3+5*x) +--R +--R +--R (2) +--R 3 +--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(- 2x + 1) + 980100x +--R + +--R 2 +--R 5521230x - 3005640x - 3301375 +--R / +--R 484000x - 242000 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(2x - 1) + 980100x +--R + +--R 2 +--R 5521230x - 3005640x - 3301375 +--R / +--R 484000x - 242000 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R 33271log(2x - 1) - 33271log(- 2x + 1) +--R (4) ------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=343/88/(1-2*x)+27/20*x+392/121*log(1-2*x)+1/3025*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (16x - 8)log(5x + 3) + (156800x - 78400)log(- 2x + 1) + 65340x - 32670x +--R + +--R - 94325 +--R / +--R 48400x - 24200 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (16x - 8)log(5x + 3) + (156800x - 78400)log(2x - 1) + 65340x - 32670x +--R + +--R - 94325 +--R / +--R 48400x - 24200 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R 392log(2x - 1) - 392log(- 2x + 1) +--R (4) --------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=49/44/(1-2*x)+217/484*log(1-2*x)+1/605*log(3+5*x) +--R +--R +--R (8x - 4)log(5x + 3) + (2170x - 1085)log(- 2x + 1) - 2695 +--R (2) -------------------------------------------------------- +--R 4840x - 2420 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (8x - 4)log(5x + 3) + (2170x - 1085)log(2x - 1) - 2695 +--R (3) ------------------------------------------------------ +--R 4840x - 2420 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R 217log(2x - 1) - 217log(- 2x + 1) +--R (4) --------------------------------- +--R 484 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=7/22/(1-2*x)-1/121*log(1-2*x)+1/121*log(3+5*x) +--R +--R +--R (4x - 2)log(5x + 3) + (- 4x + 2)log(- 2x + 1) - 77 +--R (2) -------------------------------------------------- +--R 484x - 242 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (4x - 2)log(5x + 3) + (- 4x + 2)log(2x - 1) - 77 +--R (3) ------------------------------------------------ +--R 484x - 242 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 121 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=1/11/(1-2*x)-5/121*log(1-2*x)+5/121*log(3+5*x) +--R +--R +--R (10x - 5)log(5x + 3) + (- 10x + 5)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------- +--R 242x - 121 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x - 5)log(5x + 3) + (- 10x + 5)log(2x - 1) - 11 +--R (3) -------------------------------------------------- +--R 242x - 121 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - 5log(2x - 1) + 5log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 4 3 2 +--R 60x + 16x - 37x - 5x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=2/77/(1-2*x)-136/5929*log(1-2*x)-9/49*log(2+3*x)+25/121*log(3+5*x) +--R +--R +--R (2) +--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2) +--R + +--R (- 272x + 136)log(- 2x + 1) - 154 +--R / +--R 11858x - 5929 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2) +--R + +--R (- 272x + 136)log(2x - 1) - 154 +--R / +--R 11858x - 5929 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 136log(2x - 1) + 136log(- 2x + 1) +--R (4) ----------------------------------- +--R 5929 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 180x + 168x - 79x - 89x + 8x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=4/539/(1-2*x)+9/49/(2+3*x)-404/41503*log(1-2*x)-_ + 351/343*log(2+3*x)+125/121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (257250x + 42875x - 85750)log(5x + 3) +--R + +--R 2 +--R (- 254826x - 42471x + 84942)log(3x + 2) +--R + +--R 2 +--R (- 2424x - 404x + 808)log(- 2x + 1) + 14322x - 8239 +--R / +--R 2 +--R 249018x + 41503x - 83006 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (257250x + 42875x - 85750)log(5x + 3) +--R + +--R 2 +--R (- 254826x - 42471x + 84942)log(3x + 2) +--R + +--R 2 +--R (- 2424x - 404x + 808)log(2x - 1) + 14322x - 8239 +--R / +--R 2 +--R 249018x + 41503x - 83006 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 404log(2x - 1) + 404log(- 2x + 1) +--R (4) ----------------------------------- +--R 41503 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 540x + 864x + 99x - 425x - 154x + 52x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=8/3773/(1-2*x)+9/98/(2+3*x)^2+351/343/(2+3*x)-1072/290521*log(1-2*x)-_ + 12393/2401*log(2+3*x)+625/121*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3) +--R + +--R 3 2 +--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2) +--R + +--R 3 2 2 +--R (- 38592x - 32160x + 8576x + 8576)log(- 2x + 1) + 3556476x + 686532x +--R + +--R - 1247477 +--R / +--R 3 2 +--R 10458756x + 8715630x - 2324168x - 2324168 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3) +--R + +--R 3 2 +--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2) +--R + +--R 3 2 2 +--R (- 38592x - 32160x + 8576x + 8576)log(2x - 1) + 3556476x + 686532x +--R + +--R - 1247477 +--R / +--R 3 2 +--R 10458756x + 8715630x - 2324168x - 2324168 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 1072log(2x - 1) + 1072log(- 2x + 1) +--R (4) ------------------------------------- +--R 290521 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=16/26411/(1-2*x)+3/49/(2+3*x)^3+351/686/(2+3*x)^2+12393/2401/(2+3*x)-_ + 2672/2033647*log(1-2*x)-434043/16807*log(2+3*x)+3125/121*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x +--R + +--R 840307248 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(- 2x + 1) +--R + +--R 3 2 +--R 377820828x + 327259548x - 81484557x - 88405856 +--R / +--R 4 3 2 +--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x +--R + +--R 840307248 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(2x - 1) +--R + +--R 3 2 +--R 377820828x + 327259548x - 81484557x - 88405856 +--R / +--R 4 3 2 +--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 2672log(2x - 1) + 2672log(- 2x + 1) +--R (4) ------------------------------------- +--R 2033647 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 8 7 6 5 4 3 2 +--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=32/184877/(1-2*x)+9/196/(2+3*x)^4+117/343/(2+3*x)^3+_ + 12393/4802/(2+3*x)^2+434043/16807/(2+3*x)-6400/14235529*log(1-2*x)-_ + 15192225/117649*log(2+3*x)+15625/121*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x +--R + +--R - 470596000000x - 117649000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 1191191977800x - 2580915951900x - 1588255970400x +--R + +--R 2 +--R 176472885600x + 470594361600x + 117648590400 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441 +--R / +--R 5 4 3 2 +--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x +--R + +--R - 911073856 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x +--R + +--R - 470596000000x - 117649000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 1191191977800x - 2580915951900x - 1588255970400x +--R + +--R 2 +--R 176472885600x + 470594361600x + 117648590400 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441 +--R / +--R 5 4 3 2 +--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x +--R + +--R - 911073856 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 6400log(2x - 1) + 6400log(- 2x + 1) +--R (4) ------------------------------------- +--R 14235529 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^6*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x +--R + +--R 2 +--R 1936x + 1280x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=64/1294139/(1-2*x)+9/245/(2+3*x)^5+351/1372/(2+3*x)^4+_ + 4131/2401/(2+3*x)^3+434043/33614/(2+3*x)^2+15192225/117649/(2+3*x)-_ + 14912/99648703*log(1-2*x)-531729603/823543*log(2+3*x)+78125/121*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 625377965625000x + 1771904235937500x + 1737161015625000x +--R + +--R 3 2 +--R 463242937500000x - 308828625000000x - 226474325000000x +--R + +--R - 41177150000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 625377820680360x - 1771903825261020x - 1737160613001000x +--R + +--R 3 2 +--R - 463242830133600x + 308828553422400x + 226474272509760x +--R + +--R 41177140456320 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x +--R + +--R 52490240x + 9543680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x +--R + +--R - 16998574124301x - 4338387945122 +--R / +--R 6 5 4 3 +--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x +--R + +--R 2 +--R - 478313774400x - 350763434560x - 63775169920 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 625377965625000x + 1771904235937500x + 1737161015625000x +--R + +--R 3 2 +--R 463242937500000x - 308828625000000x - 226474325000000x +--R + +--R - 41177150000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 625377820680360x - 1771903825261020x - 1737160613001000x +--R + +--R 3 2 +--R - 463242830133600x + 308828553422400x + 226474272509760x +--R + +--R 41177140456320 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x +--R + +--R 52490240x + 9543680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x +--R + +--R - 16998574124301x - 4338387945122 +--R / +--R 6 5 4 3 +--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x +--R + +--R 2 +--R - 478313774400x - 350763434560x - 63775169920 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 14912log(2x - 1) + 14912log(- 2x + 1) +--R (4) --------------------------------------- +--R 99648703 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=5764801/15488/(1-2*x)+231915717/200000*x+14171517/25000*x^2+_ + 2626101/10000*x^3+168399/2000*x^4+6561/500*x^5+(-1/9453125)/(3+5*x)+_ + 79883671/85184*log(1-2*x)+268/103984375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (343040x + 34304x - 102912)log(5x + 3) +--R + +--R 2 +--R (124818235937500x + 12481823593750x - 37445470781250)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x +--R + +--R 3 2 +--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717 +--R / +--R 2 +--R 133100000000x + 13310000000x - 39930000000 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (343040x + 34304x - 102912)log(5x + 3) +--R + +--R 2 +--R (124818235937500x + 12481823593750x - 37445470781250)log(2x - 1) +--R + +--R 7 6 5 4 +--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x +--R + +--R 3 2 +--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717 +--R / +--R 2 +--R 133100000000x + 13310000000x - 39930000000 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R 79883671log(2x - 1) - 79883671log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=823543/7744/(1-2*x)+6156243/25000*x+1974861/20000*x^2+16281/500*x^3+_ + 2187/400*x^4+(-1/1890625)/(3+5*x)+18941489/85184*log(1-2*x)+_ + 47/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (150400x + 15040x - 45120)log(5x + 3) +--R + +--R 2 +--R (2959607656250x + 295960765625x - 887882296875)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x +--R + +--R 2 +--R - 66522621330x - 1691007398993x - 424639358671 +--R / +--R 2 +--R 13310000000x + 1331000000x - 3993000000 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (150400x + 15040x - 45120)log(5x + 3) +--R + +--R 2 +--R (2959607656250x + 295960765625x - 887882296875)log(2x - 1) +--R + +--R 6 5 4 3 +--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x +--R + +--R 2 +--R - 66522621330x - 1691007398993x - 424639358671 +--R / +--R 2 +--R 13310000000x + 1331000000x - 3993000000 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R 18941489log(2x - 1) - 18941489log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=117649/3872/(1-2*x)+473607/10000*x+13851/1000*x^2+243/100*x^3+_ + (-1/378125)/(3+5*x)+67228/1331*log(1-2*x)+202/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (64640x + 6464x - 19392)log(5x + 3) +--R + +--R 2 5 +--R (67228000000x + 6722800000x - 20168400000)log(- 2x + 1) + 3234330000x +--R + +--R 4 3 2 +--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773 +--R / +--R 2 +--R 1331000000x + 133100000x - 399300000 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (64640x + 6464x - 19392)log(5x + 3) +--R + +--R 2 5 +--R (67228000000x + 6722800000x - 20168400000)log(2x - 1) + 3234330000x +--R + +--R 4 3 2 +--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773 +--R / +--R 2 +--R 1331000000x + 133100000x - 399300000 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R 67228log(2x - 1) - 67228log(- 2x + 1) +--R (4) ------------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=16807/1936/(1-2*x)+3807/500*x+243/200*x^2+(-1/75625)/(3+5*x)+_ + 228095/21296*log(1-2*x)+169/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (27040x + 2704x - 8112)log(5x + 3) +--R + +--R 2 4 +--R (1425593750x + 142559375x - 427678125)log(- 2x + 1) + 161716500x +--R + +--R 3 2 +--R 1029595050x + 52827390x - 881767997x - 346644199 +--R / +--R 2 +--R 133100000x + 13310000x - 39930000 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (27040x + 2704x - 8112)log(5x + 3) +--R + +--R 2 4 +--R (1425593750x + 142559375x - 427678125)log(2x - 1) + 161716500x +--R + +--R 3 2 +--R 1029595050x + 52827390x - 881767997x - 346644199 +--R / +--R 2 +--R 133100000x + 13310000x - 39930000 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R 228095log(2x - 1) - 228095log(- 2x + 1) +--R (4) --------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=2401/968/(1-2*x)+81/100*x+(-1/15125)/(3+5*x)+10633/5324*log(1-2*x)+_ + 136/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (10880x + 1088x - 3264)log(5x + 3) +--R + +--R 2 3 2 +--R (26582500x + 2658250x - 7974750)log(- 2x + 1) + 10781100x + 1078110x +--R + +--R - 19741381x - 9904037 +--R / +--R 2 +--R 13310000x + 1331000x - 3993000 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (10880x + 1088x - 3264)log(5x + 3) +--R + +--R 2 3 2 +--R (26582500x + 2658250x - 7974750)log(2x - 1) + 10781100x + 1078110x +--R + +--R - 19741381x - 9904037 +--R / +--R 2 +--R 13310000x + 1331000x - 3993000 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R 10633log(2x - 1) - 10633log(- 2x + 1) +--R (4) ------------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=343/484/(1-2*x)+(-1/3025)/(3+5*x)+1421/5324*log(1-2*x)+103/33275*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (4120x + 412x - 1236)log(5x + 3) +--R + +--R 2 +--R (355250x + 35525x - 106575)log(- 2x + 1) - 471713x - 282931 +--R / +--R 2 +--R 1331000x + 133100x - 399300 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (4120x + 412x - 1236)log(5x + 3) +--R + +--R 2 +--R (355250x + 35525x - 106575)log(2x - 1) - 471713x - 282931 +--R / +--R 2 +--R 1331000x + 133100x - 399300 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R 1421log(2x - 1) - 1421log(- 2x + 1) +--R (4) ----------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=49/242/(1-2*x)+(-1/605)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(- 2x + 1) +--R + +--R - 13519x - 8063 +--R / +--R 2 +--R 133100x + 13310x - 39930 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(2x - 1) +--R + +--R - 13519x - 8063 +--R / +--R 2 +--R 133100x + 13310x - 39930 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R - 14log(2x - 1) + 14log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 3x + 2 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=7/121/(1-2*x)+(-1/121)/(3+5*x)-37/1331*log(1-2*x)+37/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(- 2x + 1) +--R + +--R - 407x - 220 +--R / +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(2x - 1) - 407x +--R + +--R - 220 +--R / +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R - 37log(2x - 1) + 37log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=2/121/(1-2*x)+(-5/121)/(3+5*x)-20/1331*log(1-2*x)+20/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(- 2x + 1) - 220x - 11 +--R ----------------------------------------------------------------------------- +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(2x - 1) - 220x - 11 +--R --------------------------------------------------------------------------- +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R - 20log(2x - 1) + 20log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 300x + 260x - 137x - 136x + 15x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=4/847/(1-2*x)+(-25/121)/(3+5*x)-412/65219*log(1-2*x)+27/49*log(2+3*x)-_ + 725/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 355250x - 35525x + 106575)log(5x + 3) +--R + +--R 2 +--R (359370x + 35937x - 107811)log(3x + 2) +--R + +--R 2 +--R (- 4120x - 412x + 1236)log(- 2x + 1) - 28490x + 12551 +--R / +--R 2 +--R 652190x + 65219x - 195657 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 355250x - 35525x + 106575)log(5x + 3) +--R + +--R 2 +--R (359370x + 35937x - 107811)log(3x + 2) +--R + +--R 2 +--R (- 4120x - 412x + 1236)log(2x - 1) - 28490x + 12551 +--R / +--R 2 +--R 652190x + 65219x - 195657 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R - 412log(2x - 1) + 412log(- 2x + 1) +--R (4) ----------------------------------- +--R 65219 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 900x + 1380x + 109x - 682x - 227x + 84x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=8/5929/(1-2*x)+(-27/49)/(2+3*x)+(-125/121)/(3+5*x)-_ + 1088/456533*log(1-2*x)+1998/343*log(2+3*x)-7750/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3) +--R + +--R 3 2 +--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2) +--R + +--R 3 2 2 +--R (- 32640x - 25024x + 7616x + 6528)log(- 2x + 1) - 5354580x - 734888x +--R + +--R 1694231 +--R / +--R 3 2 +--R 13695990x + 10500259x - 3195731x - 2739198 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3) +--R + +--R 3 2 +--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2) +--R + +--R 3 2 2 +--R (- 32640x - 25024x + 7616x + 6528)log(2x - 1) - 5354580x - 734888x +--R + +--R 1694231 +--R / +--R 3 2 +--R 13695990x + 10500259x - 3195731x - 2739198 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R - 1088log(2x - 1) + 1088log(- 2x + 1) +--R (4) ------------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=16/41503/(1-2*x)+(-27/98)/(2+3*x)^2+(-1998/343)/(2+3*x)+_ + (-625/121)/(3+5*x)-2704/3195731*log(1-2*x)+107109/2401*log(2+3*x)-_ + 59375/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x +--R + +--R 3421425000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 25661174220x + 36781016382x + 7128103950x - 9123973056x +--R + +--R - 3421489896 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(- 2x + 1) +--R + +--R 3 2 +--R - 1711280340x - 1369336584x + 390771227x + 360692563 +--R / +--R 4 3 2 +--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x +--R + +--R 3421425000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 25661174220x + 36781016382x + 7128103950x - 9123973056x +--R + +--R - 3421489896 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(2x - 1) +--R + +--R 3 2 +--R - 1711280340x - 1369336584x + 390771227x + 360692563 +--R / +--R 4 3 2 +--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R - 2704log(2x - 1) + 2704log(- 2x + 1) +--R (4) ------------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=32/290521/(1-2*x)+(-9/49)/(2+3*x)^3+(-999/343)/(2+3*x)^2+_ + (-107109/2401)/(2+3*x)+(-3125/121)/(3+5*x)-6464/22370117*log(1-2*x)+_ + 5050944/16807*log(2+3*x)-400000/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R - 1815156000000x - 3811827600000x - 2238692400000x +--R + +--R 2 +--R 309248800000x + 672280000000x + 161347200000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x +--R + +--R - 672280646400x - 161347355136 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x +--R + +--R 17000329577 +--R / +--R 5 4 3 2 +--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x +--R + +--R - 536882808 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 1815156000000x - 3811827600000x - 2238692400000x +--R + +--R 2 +--R 309248800000x + 672280000000x + 161347200000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x +--R + +--R - 672280646400x - 161347355136 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x +--R + +--R 17000329577 +--R / +--R 5 4 3 2 +--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x +--R + +--R - 536882808 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R - 6464log(2x - 1) + 6464log(- 2x + 1) +--R (4) ------------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x +--R + +--R 2 +--R 3152x + 1968x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=64/2033647/(1-2*x)+(-27/196)/(2+3*x)^4+(-666/343)/(2+3*x)^3+_ + (-107109/4802)/(2+3*x)^2+(-5050944/16807)/(2+3*x)+(-15625/121)/(3+5*x)-_ + 15040/156590819*log(1-2*x)+222359715/117649*log(2+3*x)-_ + 2515625/1331*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 958912880625000x - 2652992303062500x - 2525137252312500x +--R + +--R 3 2 +--R - 625069137000000x + 464066480500000x + 322005313000000x +--R + +--R 56824467000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 958912929354600x + 2652992437881060x + 2525137380633780x +--R + +--R 3 2 +--R 625069168764480x - 464066504082720x - 322005329363520x +--R + +--R - 56824469887680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x +--R + +--R 16363520x + 2887680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R - 63927582226200x - 136378873350720x - 81993113952750x +--R + +--R 2 +--R 10222048359600x + 24455908667575x + 5987073080219 +--R / +--R 6 5 4 3 +--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x +--R + +--R 2 +--R - 245534404192x - 170370811072x - 30065437248 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 958912880625000x - 2652992303062500x - 2525137252312500x +--R + +--R 3 2 +--R - 625069137000000x + 464066480500000x + 322005313000000x +--R + +--R 56824467000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 958912929354600x + 2652992437881060x + 2525137380633780x +--R + +--R 3 2 +--R 625069168764480x - 464066504082720x - 322005329363520x +--R + +--R - 56824469887680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x +--R + +--R 16363520x + 2887680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R - 63927582226200x - 136378873350720x - 81993113952750x +--R + +--R 2 +--R 10222048359600x + 24455908667575x + 5987073080219 +--R / +--R 6 5 4 3 +--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x +--R + +--R 2 +--R - 245534404192x - 170370811072x - 30065437248 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R - 15040log(2x - 1) + 15040log(- 2x + 1) +--R (4) --------------------------------------- +--R 156590819 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=5764801/85184/(1-2*x)+7680987/50000*x+6093711/100000*x^2+12393/625*x^3+_ + 6561/2000*x^4+(-1/18906250)/(3+5*x)^2+(-268/103984375)/(3+5*x)+_ + 130943337/937024*log(1-2*x)+6312/228765625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3) +--R + +--R 3 2 +--R 511497410156250x + 358048187109375x - 122759378437500x +--R + +--R - 92069533828125 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R 12007450125000x + 80983580287500x + 270968124487500x +--R + +--R 4 3 2 +--R 698838044478750x + 327005737947900x - 298950055409445x +--R + +--R - 249835373577966x - 44587132164487 +--R / +--R 3 2 +--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3) +--R + +--R 3 2 +--R 511497410156250x + 358048187109375x - 122759378437500x +--R + +--R - 92069533828125 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R 12007450125000x + 80983580287500x + 270968124487500x +--R + +--R 4 3 2 +--R 698838044478750x + 327005737947900x - 298950055409445x +--R + +--R - 249835373577966x - 44587132164487 +--R / +--R 3 2 +--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R 130943337log(2x - 1) - 130943337log(- 2x + 1) +--R (4) --------------------------------------------- +--R 937024 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=823543/42592/(1-2*x)+1467477/50000*x+21141/2500*x^2+729/500*x^3+_ + (-1/3781250)/(3+5*x)^2+(-47/4159375)/(3+5*x)+7411887/234256*log(1-2*x)+_ + 4761/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3) +--R + +--R 3 2 +--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750) +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x +--R + +--R 2 +--R - 6674047531965x - 6180073448472x - 1273917828029 +--R / +--R 3 2 +--R 366025000000x + 256217500000x - 87846000000x - 65884500000 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3) +--R + +--R 3 2 +--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750) +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x +--R + +--R 2 +--R - 6674047531965x - 6180073448472x - 1273917828029 +--R / +--R 3 2 +--R 366025000000x + 256217500000x - 87846000000x - 65884500000 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R 7411887log(2x - 1) - 7411887log(- 2x + 1) +--R (4) ----------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=117649/21296/(1-2*x)+2916/625*x+729/1000*x^2+(-1/756250)/(3+5*x)^2+_ + (-202/4159375)/(3+5*x)+1563051/234256*log(1-2*x)+17139/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3) +--R + +--R 3 2 +--R (244226718750x + 170958703125x - 58614412500x - 43960809375) +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 26683222500x + 189450879750x + 113136863400x - 146893374705x +--R + +--R - 152064641058x - 36397551751 +--R / +--R 3 2 +--R 36602500000x + 25621750000x - 8784600000x - 6588450000 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3) +--R + +--R 3 2 +--R (244226718750x + 170958703125x - 58614412500x - 43960809375)log(2x - 1) +--R + +--R 5 4 3 2 +--R 26683222500x + 189450879750x + 113136863400x - 146893374705x +--R + +--R - 152064641058x - 36397551751 +--R / +--R 3 2 +--R 36602500000x + 25621750000x - 8784600000x - 6588450000 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R 1563051log(2x - 1) - 1563051log(- 2x + 1) +--R (4) ----------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=16807/10648/(1-2*x)+243/500*x+(-1/151250)/(3+5*x)^2+_ + (-169/831875)/(3+5*x)+36015/29282*log(1-2*x)+11562/9150625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3) +--R + +--R 3 2 +--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(- 2x + 1) +--R + +--R 4 3 2 +--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025 +--R / +--R 3 2 +--R 3660250000x + 2562175000x - 878460000x - 658845000 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3) +--R + +--R 3 2 +--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(2x - 1) +--R + +--R 4 3 2 +--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025 +--R / +--R 3 2 +--R 3660250000x + 2562175000x - 878460000x - 658845000 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R 36015log(2x - 1) - 36015log(- 2x + 1) +--R (4) ------------------------------------- +--R 29282 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=2401/5324/(1-2*x)+(-1/30250)/(3+5*x)^2+(-136/166375)/(3+5*x)+_ + 9261/58564*log(1-2*x)+7074/1830125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (1414800x + 990360x - 339552x - 254664)log(5x + 3) +--R + +--R 3 2 +--R (57881250x + 40516875x - 13891500x - 10418625)log(- 2x + 1) +--R + +--R 2 +--R - 82594215x - 99047718x - 29694181 +--R / +--R 3 2 +--R 366025000x + 256217500x - 87846000x - 65884500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1414800x + 990360x - 339552x - 254664)log(5x + 3) +--R + +--R 3 2 2 +--R (57881250x + 40516875x - 13891500x - 10418625)log(2x - 1) - 82594215x +--R + +--R - 99047718x - 29694181 +--R / +--R 3 2 +--R 366025000x + 256217500x - 87846000x - 65884500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R 9261log(2x - 1) - 9261log(- 2x + 1) +--R (4) ----------------------------------- +--R 58564 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=343/2662/(1-2*x)+(-1/6050)/(3+5*x)^2+(-103/33275)/(3+5*x)-_ + 147/14641*log(1-2*x)+147/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (367500x + 257250x - 88200x - 66150)log(5x + 3) +--R + +--R 3 2 2 +--R (- 367500x - 257250x + 88200x + 66150)log(- 2x + 1) - 2380785x +--R + +--R - 2832258x - 842006 +--R / +--R 3 2 +--R 36602500x + 25621750x - 8784600x - 6588450 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (367500x + 257250x - 88200x - 66150)log(5x + 3) +--R + +--R 3 2 2 +--R (- 367500x - 257250x + 88200x + 66150)log(2x - 1) - 2380785x +--R + +--R - 2832258x - 842006 +--R / +--R 3 2 +--R 36602500x + 25621750x - 8784600x - 6588450 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R - 147log(2x - 1) + 147log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=49/1331/(1-2*x)+(-1/1210)/(3+5*x)^2+(-14/1331)/(3+5*x)-_ + 273/14641*log(1-2*x)+273/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (136500x + 95550x - 32760x - 24570)log(5x + 3) +--R + +--R 3 2 2 +--R (- 136500x - 95550x + 32760x + 24570)log(- 2x + 1) - 150150x - 163482x +--R + +--R - 43769 +--R / +--R 3 2 +--R 7320500x + 5124350x - 1756920x - 1317690 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (136500x + 95550x - 32760x - 24570)log(5x + 3) +--R + +--R 3 2 2 +--R (- 136500x - 95550x + 32760x + 24570)log(2x - 1) - 150150x - 163482x +--R + +--R - 43769 +--R / +--R 3 2 +--R 7320500x + 5124350x - 1756920x - 1317690 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R - 273log(2x - 1) + 273log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 3x + 2 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=14/1331/(1-2*x)+(-1/242)/(3+5*x)^2+(-37/1331)/(3+5*x)-_ + 144/14641*log(1-2*x)+144/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (14400x + 10080x - 3456x - 2592)log(5x + 3) +--R + +--R 3 2 2 +--R (- 14400x - 10080x + 3456x + 2592)log(- 2x + 1) - 15840x - 10296x - 209 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (14400x + 10080x - 3456x - 2592)log(5x + 3) +--R + +--R 3 2 2 +--R (- 14400x - 10080x + 3456x + 2592)log(2x - 1) - 15840x - 10296x - 209 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R - 144log(2x - 1) + 144log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=4/1331/(1-2*x)+(-5/242)/(3+5*x)^2+(-20/1331)/(3+5*x)-_ + 60/14641*log(1-2*x)+60/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (6000x + 4200x - 1440x - 1080)log(5x + 3) +--R + +--R 3 2 2 +--R (- 6000x - 4200x + 1440x + 1080)log(- 2x + 1) - 6600x - 4290x + 1133 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (6000x + 4200x - 1440x - 1080)log(5x + 3) +--R + +--R 3 2 2 +--R (- 6000x - 4200x + 1440x + 1080)log(2x - 1) - 6600x - 4290x + 1133 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R - 60log(2x - 1) + 60log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 1500x + 2200x + 95x - 1091x - 333x + 135x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=8/9317/(1-2*x)+(-25/242)/(3+5*x)^2+725/1331/(3+5*x)-_ + 1104/717409*log(1-2*x)-81/49*log(2+3*x)+24225/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3) +--R + +--R 3 2 +--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2) +--R + +--R 3 2 2 +--R (- 110400x - 77280x + 26496x + 19872)log(- 2x + 1) + 7784700x +--R + +--R 448140x - 2207513 +--R / +--R 3 2 +--R 71740900x + 50218630x - 17217816x - 12913362 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3) +--R + +--R 3 2 +--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2) +--R + +--R 3 2 2 +--R (- 110400x - 77280x + 26496x + 19872)log(2x - 1) + 7784700x + 448140x +--R + +--R - 2207513 +--R / +--R 3 2 +--R 71740900x + 50218630x - 17217816x - 12913362 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R - 1104log(2x - 1) + 1104log(- 2x + 1) +--R (4) ------------------------------------- +--R 717409 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=16/65219/(1-2*x)+81/49/(2+3*x)+(-125/242)/(3+5*x)^2+7750/1331/(3+5*x)-_ + 2736/5021863*log(1-2*x)-8829/343*log(2+3*x)+376875/14641*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 38780437500x + 52999931250x + 8790232500x - 13185348750x +--R + +--R - 4653652500 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x +--R + +--R 4653554004 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(- 2x + 1) +--R + +--R 3 2 +--R 2584404900x + 1894703580x - 614007471x - 489983648 +--R / +--R 4 3 2 +--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 38780437500x + 52999931250x + 8790232500x - 13185348750x +--R + +--R - 4653652500 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x +--R + +--R 4653554004 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(2x - 1) +--R + +--R 3 2 +--R 2584404900x + 1894703580x - 614007471x - 489983648 +--R / +--R 4 3 2 +--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R - 2736log(2x - 1) + 2736log(- 2x + 1) +--R (4) ------------------------------------- +--R 5021863 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=32/456533/(1-2*x)+81/98/(2+3*x)^2+8829/343/(2+3*x)+(-625/242)/(3+5*x)^2+_ + 59375/1331/(3+5*x)-6528/35153041*log(1-2*x)-_ + 630342/2401*log(2+3*x)+3843750/14641*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 8305959375000x + 16888784062500x + 9450336000000x +--R + +--R 2 +--R - 1568903437500x - 2879399250000x - 664476750000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8305953499800x - 16888772116260x - 9450329315328x +--R + +--R 2 +--R 1568902327740x + 2879397213264x + 664476279984 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 553723770600x + 775209508920x + 139245535506x - 192629430378x +--R + +--R - 70007419097 +--R / +--R 5 4 3 2 +--R 31637736900x + 64330065030x + 35996713984x - 5976016970x +--R + +--R - 10967748792x - 2531018952 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 8305959375000x + 16888784062500x + 9450336000000x +--R + +--R 2 +--R - 1568903437500x - 2879399250000x - 664476750000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8305953499800x - 16888772116260x - 9450329315328x +--R + +--R 2 +--R 1568902327740x + 2879397213264x + 664476279984 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 553723770600x + 775209508920x + 139245535506x - 192629430378x +--R + +--R - 70007419097 +--R / +--R 5 4 3 2 +--R 31637736900x + 64330065030x + 35996713984x - 5976016970x +--R + +--R - 10967748792x - 2531018952 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R - 6528log(2x - 1) + 6528log(- 2x + 1) +--R (4) ------------------------------------- +--R 35153041 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=64/3195731/(1-2*x)+27/49/(2+3*x)^3+8829/686/(2+3*x)^2+_ + 630342/2401/(2+3*x)+(-3125/242)/(3+5*x)^2+400000/1331/(3+5*x)-_ + 15168/246071287*log(1-2*x)-37214802/16807*log(2+3*x)+_ + 32418750/14641*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 1471127214375000x + 3972043478812500x + 3668010521175000x +--R + +--R 3 2 +--R 837997650262500x - 695243824275000x - 457684022250000x +--R + +--R - 78460118100000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 1471127173421400x - 3972043368237780x - 3668010419064024x +--R + +--R 3 2 +--R - 837997626934116x + 695243804920632x + 457684009508880x +--R + +--R 78460115915808 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x +--R + +--R 12741120x + 2184192 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 98075099845800x + 202688513402760x + 116200773740898x +--R + +--R 2 +--R - 17675352484482x - 35145131488467x - 8266584593036 +--R / +--R 6 5 4 3 +--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x +--R + +--R 2 +--R - 313986962212x - 206699881080x - 35434265328 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 1471127214375000x + 3972043478812500x + 3668010521175000x +--R + +--R 3 2 +--R 837997650262500x - 695243824275000x - 457684022250000x +--R + +--R - 78460118100000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 1471127173421400x - 3972043368237780x - 3668010419064024x +--R + +--R 3 2 +--R - 837997626934116x + 695243804920632x + 457684009508880x +--R + +--R 78460115915808 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x +--R + +--R 12741120x + 2184192 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 98075099845800x + 202688513402760x + 116200773740898x +--R + +--R 2 +--R - 17675352484482x - 35145131488467x - 8266584593036 +--R / +--R 6 5 4 3 +--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x +--R + +--R 2 +--R - 313986962212x - 206699881080x - 35434265328 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R - 15168log(2x - 1) + 15168log(- 2x + 1) +--R (4) --------------------------------------- +--R 246071287 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x +--R + +--R 3 2 +--R - 225792x - 63744x - 10496x - 768 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=63412811/2048/(1-2*x)^2+(-246239357/1024)/(1-2*x)-120864213/256*x-_ + 118841283/512*x^2-16042509/128*x^3-7568235/128*x^4-213597/10*x^5-_ + 162567/32*x^6-32805/56*x^7-106237047/256*log(1-2*x) +--R +--R +--R (2) +--R 2 +--R (- 118985492640x + 118985492640x - 29746373160)log(- 2x + 1) +--R + +--R 9 8 7 6 +--R - 167961600x - 1288638720x - 4709643264x - 11192743296x +--R + +--R 5 4 3 2 +--R - 20513437056x - 34854109920x - 77800605120x + 118730138940x +--R + +--R 631530340x - 15017306605 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 118985492640x + 118985492640x - 29746373160)log(2x - 1) - 167961600x +--R + +--R 8 7 6 5 +--R - 1288638720x - 4709643264x - 11192743296x - 20513437056x +--R + +--R 4 3 2 +--R - 34854109920x - 77800605120x + 118730138940x + 631530340x - 15017306605 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R - 106237047log(2x - 1) + 106237047log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=9058973/1024/(1-2*x)^2+(-15647317/256)/(1-2*x)-24960933/256*x-_ + 10989621/256*x^2-631611/32*x^3-235467/32*x^4-147987/80*x^5-_ + 3645/16*x^6-23647449/256*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 1891795920x + 1891795920x - 472948980)log(- 2x + 1) - 4665600x +--R + +--R 7 6 5 4 3 +--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x +--R + +--R 2 +--R 1777082220x + 126674020x - 267651475 +--R / +--R 2 +--R 20480x - 20480x + 5120 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 1891795920x + 1891795920x - 472948980)log(2x - 1) - 4665600x +--R + +--R 7 6 5 4 3 +--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x +--R + +--R 2 +--R 1777082220x + 126674020x - 267651475 +--R / +--R 2 +--R 20480x - 20480x + 5120 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R - 23647449log(2x - 1) + 23647449log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=1294139/512/(1-2*x)^2+(-3916031/256)/(1-2*x)-2431647/128*x-_ + 461835/64*x^2-10611/4*x^3-44469/64*x^4-729/8*x^5-5078115/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 6 +--R (- 40624920x + 40624920x - 10156230)log(- 2x + 1) - 186624x - 1236384x +--R + +--R 5 4 3 2 +--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 40624920x + 40624920x - 10156230)log(2x - 1) - 186624x - 1236384x +--R + +--R 5 4 3 2 +--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R - 5078115log(2x - 1) + 5078115log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=184877/256/(1-2*x)^2+(-60025/16)/(1-2*x)-109089/32*x-16821/16*x^2-_ + 4401/16*x^3-1215/32*x^4-519645/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 4157160x + 4157160x - 1039290)log(- 2x + 1) - 38880x - 242784x +--R + +--R 4 3 2 +--R - 804600x - 2484720x + 3221712x + 1048088x - 775523 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 4157160x + 4157160x - 1039290)log(2x - 1) - 38880x - 242784x +--R + +--R 4 3 2 +--R - 804600x - 2484720x + 3221712x + 1048088x - 775523 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R - 519645log(2x - 1) + 519645log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/axiom-website/CATS/rich3h.input.pdf b/src/axiom-website/CATS/rich3h.input.pdf new file mode 100644 index 0000000..74ea9fe Binary files /dev/null and b/src/axiom-website/CATS/rich3h.input.pdf differ diff --git a/src/axiom-website/CATS/rich3i.input.pamphlet b/src/axiom-website/CATS/rich3i.input.pamphlet new file mode 100644 index 0000000..8e4ecb1 --- /dev/null +++ b/src/axiom-website/CATS/rich3i.input.pamphlet @@ -0,0 +1,7464 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3i.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 92 matching answers. +\item 8 cases where Axiom differed from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3i.output +)spool rich3i.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=26411/128/(1-2*x)^2+(-57281/64)/(1-2*x)-540*x-3861/32*x^2-_ + 135/8*x^3-24843/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (- 397488x + 397488x - 99372)log(- 2x + 1) - 8640x - 53136x - 216864x +--R + +--R 2 +--R 261036x + 160004x - 88151 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 397488x + 397488x - 99372)log(2x - 1) - 8640x - 53136x - 216864x +--R + +--R 2 +--R 261036x + 160004x - 88151 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 24843log(2x - 1) + 24843log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=3773/64/(1-2*x)^2+(-3283/16)/(1-2*x)-1107/16*x-135/16*x^2-1071/8*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 34272x + 34272x - 8568)log(- 2x + 1) - 2160x - 15552x + 17172x +--R + +--R 21836x - 9359 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 34272x + 34272x - 8568)log(2x - 1) - 2160x - 15552x + 17172x +--R + +--R 21836x - 9359 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R - 1071log(2x - 1) + 1071log(- 2x + 1) +--R (4) ------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=539/32/(1-2*x)^2+(-707/16)/(1-2*x)-45/8*x-309/16*log(1-2*x) +--R +--R +--R 2 3 2 +--R (- 2472x + 2472x - 618)log(- 2x + 1) - 720x + 720x + 2648x - 875 +--R (2) ------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 2472x + 2472x - 618)log(2x - 1) - 720x + 720x + 2648x - 875 +--R (3) ----------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R - 309log(2x - 1) + 309log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^3 +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=77/16/(1-2*x)^2+(-17/2)/(1-2*x)-15/8*log(1-2*x) +--R +--R +--R 2 +--R (- 120x + 120x - 30)log(- 2x + 1) + 272x - 59 +--R (2) ---------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 120x + 120x - 30)log(2x - 1) + 272x - 59 +--R (3) -------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R - 15log(2x - 1) + 15log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)/(1-2*x)^3 +--R +--R +--R - 5x - 3 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=1/22*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 25 2 15 9 +--R -- x + -- x + -- +--R 88 44 88 +--R (2) ----------------- +--R 2 1 +--R x - x + - +--R 4 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R 20x + 1 +--R (3) -------------- +--R 2 +--R 32x - 32x + 8 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 25 +--R (4) - -- +--R 88 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) -------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=11/28/(1-2*x)^2+(-1/49)/(1-2*x)+3/343*log(1-2*x)-3/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(- 2x + 1) + 56x + 511 +--R --------------------------------------------------------------------------- +--R 2 +--R 5488x - 5488x + 1372 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(2x - 1) + 56x + 511 +--R ------------------------------------------------------------------------- +--R 2 +--R 5488x - 5488x + 1372 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 3log(2x - 1) - 3log(- 2x + 1) +--R (4) ----------------------------- +--R 343 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=11/98/(1-2*x)^2+31/343/(1-2*x)+3/343/(2+3*x)-87/2401*log(1-2*x)+_ + 87/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (2088x - 696x - 870x + 348)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2088x + 696x + 870x - 348)log(- 2x + 1) - 2436x + 1015x + 1988 +--R / +--R 3 2 +--R 57624x - 19208x - 24010x + 9604 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (2088x - 696x - 870x + 348)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2088x + 696x + 870x - 348)log(2x - 1) - 2436x + 1015x + 1988 +--R / +--R 3 2 +--R 57624x - 19208x - 24010x + 9604 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R - 87log(2x - 1) + 87log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=11/343/(1-2*x)^2+128/2401/(1-2*x)+3/686/(2+3*x)^2+(-87/2401)/(2+3*x)-_ + 558/16807*log(1-2*x)+558/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(- 2x + 1) - 46872x +--R + +--R 2 +--R - 11718x + 25606x + 9191 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(2x - 1) - 46872x +--R + +--R 2 +--R - 11718x + 25606x + 9191 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R - 558log(2x - 1) + 558log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=22/2401/(1-2*x)^2+388/16807/(1-2*x)+1/343/(2+3*x)^3+_ + (-87/4802)/(2+3*x)^2+(-558/16807)/(2+3*x)-2280/117649*log(1-2*x)+_ + 2280/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 574560x - 526680x + 218120x + 236075x + 21616 +--R / +--R 5 4 3 2 +--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480)log(2x - 1) +--R + +--R 4 3 2 +--R - 574560x - 526680x + 218120x + 236075x + 21616 +--R / +--R 5 4 3 2 +--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R - 2280log(2x - 1) + 2280log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=44/16807/(1-2*x)^2+1040/117649/(1-2*x)+3/1372/(2+3*x)^4+_ + (-29/2401)/(2+3*x)^3+(-279/16807)/(2+3*x)^2+(-2280/117649)/(2+3*x)-_ + 7680/823543*log(1-2*x)+7680/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x +--R + +--R 491520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x +--R + +--R - 983040x - 491520 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925 +--R / +--R 6 5 4 3 2 +--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x +--R + +--R 105413504x + 52706752 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x +--R + +--R 491520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x +--R + +--R - 983040x - 491520 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925 +--R / +--R 6 5 4 3 2 +--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x +--R + +--R 105413504x + 52706752 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R - 7680log(2x - 1) + 7680log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^6) +--R +--R +--R (1) +--R - 5x - 3 +--R / +--R 9 8 7 6 5 4 3 2 +--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x +--R + +--R - 192x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=88/117649/(1-2*x)^2+2608/823543/(1-2*x)+3/1715/(2+3*x)^5+_ + (-87/9604)/(2+3*x)^4+(-186/16807)/(2+3*x)^3+(-1140/117649)/(2+3*x)^2+_ + (-7680/823543)/(2+3*x)-3312/823543*log(1-2*x)+3312/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x +--R + +--R 2 +--R - 7418880x + 7418880x + 2119680 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x +--R + +--R 2 +--R 7418880x - 7418880x - 2119680 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x +--R + +--R 7943257x - 2669758 +--R / +--R 7 6 5 4 +--R 16009675920x + 37355910480x + 21790947780x - 10376641800x +--R + +--R 3 2 +--R - 13835522400x - 1844736320x + 1844736320x + 527067520 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x +--R + +--R 2 +--R - 7418880x + 7418880x + 2119680 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x +--R + +--R 2 +--R 7418880x - 7418880x - 2119680 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x +--R + +--R 7943257x - 2669758 +--R / +--R 7 6 5 4 +--R 16009675920x + 37355910480x + 21790947780x - 10376641800x +--R + +--R 3 2 +--R - 13835522400x - 1844736320x + 1844736320x + 527067520 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R - 3312log(2x - 1) + 3312log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x +--R + +--R 3 2 +--R - 351120x - 97952x - 15936x - 1152 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=99648703/2048/(1-2*x)^2+(-389535839/1024)/(1-2*x)-48280011/64*x-_ + 190742391/512*x^2-25895367/128*x^3-12299769/128*x^4-2798631/80*x^5-_ + 268515/32*x^6-54675/56*x^7-84589631/128*log(1-2*x) +--R +--R +--R (2) +--R 2 +--R (- 189480773440x + 189480773440x - 47370193360)log(- 2x + 1) +--R + +--R 9 8 7 6 +--R - 279936000x - 2125958400x - 7694383104x - 18122662656x +--R + +--R 5 4 3 2 +--R - 32961712896x - 55697987520x - 123980115840x + 189590514540x +--R + +--R 461405140x - 23779804125 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 189480773440x + 189480773440x - 47370193360)log(2x - 1) - 279936000x +--R + +--R 8 7 6 5 +--R - 2125958400x - 7694383104x - 18122662656x - 32961712896x +--R + +--R 4 3 2 +--R - 55697987520x - 123980115840x + 189590514540x + 461405140x +--R + +--R - 23779804125 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 84589631log(2x - 1) + 84589631log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x +--R + +--R - 7104x - 576 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=14235529/1024/(1-2*x)^2+(-12386759/128)/(1-2*x)-39980457/256*x-_ + 17700255/256*x^2-1024389/32*x^3-770067/64*x^4-48843/16*x^5-_ + 6075/16*x^6-18859855/128*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 603515360x + 603515360x - 150878840)log(- 2x + 1) - 1555200x +--R + +--R 7 6 5 4 3 +--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x +--R + +--R 2 +--R 568886292x + 38266316x - 84858543 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 603515360x + 603515360x - 150878840)log(2x - 1) - 1555200x +--R + +--R 7 6 5 4 3 +--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x +--R + +--R 2 +--R 568886292x + 38266316x - 84858543 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 18859855log(2x - 1) + 18859855log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=2033647/512/(1-2*x)^2+(-6206585/256)/(1-2*x)-3907293/128*x-_ + 747297/64*x^2-69273/16*x^3-73305/64*x^4-1215/8*x^5-8117095/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 6 +--R (- 64936760x + 64936760x - 16234190)log(- 2x + 1) - 311040x - 2034720x +--R + +--R 5 4 3 2 +--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 64936760x + 64936760x - 16234190)log(2x - 1) - 311040x - 2034720x +--R + +--R 5 4 3 2 +--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 8117095log(2x - 1) + 8117095log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=290521/256/(1-2*x)^2+(-381073/64)/(1-2*x)-176055/32*x-_ + 54783/32*x^2-7245/16*x^3-2025/32*x^4-832951/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 6663608x + 6663608x - 1665902)log(- 2x + 1) - 64800x - 398880x +--R + +--R 4 3 2 +--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 6663608x + 6663608x - 1665902)log(2x - 1) - 64800x - 398880x +--R + +--R 4 3 2 +--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 832951log(2x - 1) + 832951log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=41503/128/(1-2*x)^2+(-91091/64)/(1-2*x)-14031/16*x-6345/32*x^2-_ + 225/8*x^3-39977/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 +--R (- 639632x + 639632x - 159908)log(- 2x + 1) - 14400x - 87120x +--R + +--R 3 2 +--R - 351072x + 423612x + 252116x - 140679 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 639632x + 639632x - 159908)log(2x - 1) - 14400x - 87120x - 351072x +--R + +--R 2 +--R 423612x + 252116x - 140679 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 39977log(2x - 1) + 39977log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=5929/64/(1-2*x)^2+(-1309/4)/(1-2*x)-1815/16*x-225/16*x^2-3467/16*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 55472x + 55472x - 13868)log(- 2x + 1) - 3600x - 25440x + 28140x +--R + +--R 34628x - 15015 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 55472x + 55472x - 13868)log(2x - 1) - 3600x - 25440x + 28140x +--R + +--R 34628x - 15015 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 3467log(2x - 1) + 3467log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=847/32/(1-2*x)^2+(-1133/16)/(1-2*x)-75/8*x-505/16*log(1-2*x) +--R +--R +--R (2) +--R 2 3 2 +--R (- 4040x + 4040x - 1010)log(- 2x + 1) - 1200x + 1200x + 4232x - 1419 +--R ----------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 4040x + 4040x - 1010)log(2x - 1) - 1200x + 1200x + 4232x - 1419 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R - 505log(2x - 1) + 505log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=121/16/(1-2*x)^2+(-55/4)/(1-2*x)-25/8*log(1-2*x) +--R +--R +--R 2 +--R (- 200x + 200x - 50)log(- 2x + 1) + 440x - 99 +--R (2) ---------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 200x + 200x - 50)log(2x - 1) + 440x - 99 +--R (3) -------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R - 25log(2x - 1) + 25log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=121/56/(1-2*x)^2+(-407/196)/(1-2*x)-1/343*log(1-2*x)+1/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(- 2x + 1) + 11396x + 231 +--R ---------------------------------------------------------------------------- +--R 2 +--R 10976x - 10976x + 2744 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(2x - 1) + 11396x + 231 +--R -------------------------------------------------------------------------- +--R 2 +--R 10976x - 10976x + 2744 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 343 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=121/196/(1-2*x)^2+(-22/343)/(1-2*x)+(-1/343)/(2+3*x)+_ + 64/2401*log(1-2*x)-64/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 3072x + 1024x + 1280x - 512)log(3x + 2) +--R + +--R 3 2 2 +--R (3072x - 1024x - 1280x + 512)log(- 2x + 1) + 3584x + 18515x + 10598 +--R / +--R 3 2 +--R 115248x - 38416x - 48020x + 19208 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 3072x + 1024x + 1280x - 512)log(3x + 2) +--R + +--R 3 2 2 +--R (3072x - 1024x - 1280x + 512)log(2x - 1) + 3584x + 18515x + 10598 +--R / +--R 3 2 +--R 115248x - 38416x - 48020x + 19208 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 64log(2x - 1) - 64log(- 2x + 1) +--R (4) ------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=121/686/(1-2*x)^2+319/2401/(1-2*x)+(-1/686)/(2+3*x)^2+_ + 64/2401/(2+3*x)-829/16807*log(1-2*x)+829/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(- 2x + 1) - 69636x +--R + +--R 2 +--R - 17409x + 84728x + 43323 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(2x - 1) - 69636x +--R + +--R 2 +--R - 17409x + 84728x + 43323 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R - 829log(2x - 1) + 829log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=121/2401/(1-2*x)^2+1364/16807/(1-2*x)+(-1/1029)/(2+3*x)^3+_ + 32/2401/(2+3*x)^2+(-829/16807)/(2+3*x)-5750/117649*log(1-2*x)+_ + 5750/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2173500x - 1992375x + 825125x + 1260700x + 310877 +--R / +--R 5 4 3 2 +--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2173500x - 1992375x + 825125x + 1260700x + 310877 +--R / +--R 5 4 3 2 +--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R - 5750log(2x - 1) + 5750log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=242/16807/(1-2*x)^2+4180/117649/(1-2*x)+(-1/1372)/(2+3*x)^4+_ + 64/7203/(2+3*x)^3+(-829/33614)/(2+3*x)^2+(-5750/117649)/(2+3*x)-_ + 24040/823543*log(1-2*x)+24040/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x +--R + +--R 9231360x + 4615680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x +--R + +--R - 9231360x - 4615680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x +--R + +--R 9231360x + 4615680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x +--R + +--R - 9231360x - 4615680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R - 24040log(2x - 1) + 24040log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^6) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R / +--R 9 8 7 6 5 4 3 2 +--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x +--R + +--R - 192x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=484/117649/(1-2*x)^2+11264/823543/(1-2*x)+(-1/1715)/(2+3*x)^5+_ + 16/2401/(2+3*x)^4+(-829/50421)/(2+3*x)^3+(-2875/117649)/(2+3*x)^2+_ + (-24040/823543)/(2+3*x)-11696/823543*log(1-2*x)+11696/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x +--R + +--R 2 +--R - 19649280x + 19649280x + 5614080 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x +--R + +--R 2 +--R 19649280x - 19649280x - 5614080 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x +--R + +--R 29616692x - 1806623 +--R / +--R 7 6 5 4 +--R 12007256940x + 28016932860x + 16343210835x - 7782481350x +--R + +--R 3 2 +--R - 10376641800x - 1383552240x + 1383552240x + 395300640 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x +--R + +--R 2 +--R - 19649280x + 19649280x + 5614080 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x +--R + +--R 2 +--R 19649280x - 19649280x - 5614080 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x +--R + +--R 29616692x - 1806623 +--R / +--R 7 6 5 4 +--R 12007256940x + 28016932860x + 16343210835x - 7782481350x +--R + +--R 3 2 +--R - 10376641800x - 1383552240x + 1383552240x + 395300640 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R - 11696log(2x - 1) + 11696log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x +--R + +--R 3 2 +--R - 545840x - 150480x - 24192x - 1728 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=156590819/2048/(1-2*x)^2+(-616195041/1024)/(1-2*x)-308539921/256*x-_ + 306103815/512*x^2-41793093/128*x^3-19986237/128*x^4-_ + 229149/4*x^5-443475/32*x^6-91125/56*x^7-33674025/32*log(1-2*x) +--R +--R +--R (2) +--R 2 9 +--R (- 60343852800x + 60343852800x - 15085963200)log(- 2x + 1) - 93312000x +--R + +--R 8 7 6 5 +--R - 701395200x - 2513700864x - 5867430912x - 10590741504x +--R + +--R 4 3 2 +--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841 +--R / +--R 2 +--R 57344x - 57344x + 14336 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 60343852800x + 60343852800x - 15085963200)log(2x - 1) - 93312000x +--R + +--R 8 7 6 5 +--R - 701395200x - 2513700864x - 5867430912x - 10590741504x +--R + +--R 4 3 2 +--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841 +--R / +--R 2 +--R 57344x - 57344x + 14336 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R - 33674025log(2x - 1) + 33674025log(- 2x + 1) +--R (4) --------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 +--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x +--R + +--R 2 +--R - 59040x - 10800x - 864 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=22370117/1024/(1-2*x)^2+(-39220335/256)/(1-2*x)-64029233/256*x-_ + 28504029/256*x^2-1661133/32*x^3-629505/32*x^4-80595/16*x^5-_ + 10125/16*x^6-60160485/256*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 962567760x + 962567760x - 240641940)log(- 2x + 1) - 2592000x +--R + +--R 7 6 5 4 3 +--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x +--R + +--R 2 +--R 910451612x + 57645748x - 134511223 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 962567760x + 962567760x - 240641940)log(2x - 1) - 2592000x +--R + +--R 7 6 5 4 3 +--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x +--R + +--R 2 +--R 910451612x + 57645748x - 134511223 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R - 60160485log(2x - 1) + 60160485log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=3195731/512/(1-2*x)^2+(-9836211/256)/(1-2*x)-6277415/128*x-_ + 1208973/64*x^2-7065*x^3-120825/64*x^4-2025/8*x^5-12973191/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 +--R (- 103785528x + 103785528x - 25946382)log(- 2x + 1) - 518400x +--R + +--R 6 5 4 3 2 +--R - 3348000x - 10732320x - 25184616x - 65368784x + 90766856x +--R + +--R 14235184x - 16476691 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 103785528x + 103785528x - 25946382)log(2x - 1) - 518400x - 3348000x +--R + +--R 5 4 3 2 +--R - 10732320x - 25184616x - 65368784x + 90766856x + 14235184x - 16476691 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R - 12973191log(2x - 1) + 12973191log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=456533/256/(1-2*x)^2+(-302379/32)/(1-2*x)-284071/32*x-44595/16*x^2-_ + 11925/16*x^3-3375/32*x^4-1334949/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 10679592x + 10679592x - 2669898)log(- 2x + 1) - 108000x - 655200x +--R + +--R 4 3 2 +--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 10679592x + 10679592x - 2669898)log(2x - 1) - 108000x - 655200x +--R + +--R 4 3 2 +--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 1334949log(2x - 1) + 1334949log(- 2x + 1) +--R (4) ------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=65219/128/(1-2*x)^2+(-144837/64)/(1-2*x)-5695/4*x-10425/32*x^2-_ + 375/8*x^3-64317/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 +--R (- 1029072x + 1029072x - 257268)log(- 2x + 1) - 24000x - 142800x +--R + +--R 3 2 +--R - 568160x + 687260x + 397108x - 224455 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 +--R (- 1029072x + 1029072x - 257268)log(2x - 1) - 24000x - 142800x +--R + +--R 3 2 +--R - 568160x + 687260x + 397108x - 224455 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 64317log(2x - 1) + 64317log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=9317/64/(1-2*x)^2+(-8349/16)/(1-2*x)-2975/16*x-375/16*x^2-2805/8*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 89760x + 89760x - 22440)log(- 2x + 1) - 6000x - 41600x + 46100x +--R + +--R 54892x - 24079 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 89760x + 89760x - 22440)log(2x - 1) - 6000x - 41600x + 46100x +--R + +--R 54892x - 24079 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 2805log(2x - 1) + 2805log(- 2x + 1) +--R (4) ------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=1331/32/(1-2*x)^2+(-1815/16)/(1-2*x)-125/8*x-825/16*log(1-2*x) +--R +--R +--R (2) +--R 2 3 2 +--R (- 6600x + 6600x - 1650)log(- 2x + 1) - 2000x + 2000x + 6760x - 2299 +--R ----------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 6600x + 6600x - 1650)log(2x - 1) - 2000x + 2000x + 6760x - 2299 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 825log(2x - 1) + 825log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1331/112/(1-2*x)^2+(-1089/49)/(1-2*x)-14289/2744*log(1-2*x)-_ + 1/1029*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 64x + 64x - 16)log(3x + 2) +--R + +--R 2 +--R (- 342936x + 342936x - 85734)log(- 2x + 1) + 731808x - 170247 +--R / +--R 2 +--R 65856x - 65856x + 16464 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 64x + 64x - 16)log(3x + 2) +--R + +--R 2 +--R (- 342936x + 342936x - 85734)log(2x - 1) + 731808x - 170247 +--R / +--R 2 +--R 65856x - 65856x + 16464 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 14289log(2x - 1) + 14289log(- 2x + 1) +--R (4) --------------------------------------- +--R 2744 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=1331/392/(1-2*x)^2+(-4719/1372)/(1-2*x)+1/1029/(2+3*x)-_ + 33/2401*log(1-2*x)+33/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (9504x - 3168x - 3960x + 1584)log(3x + 2) +--R + +--R 3 2 2 +--R (- 9504x + 3168x + 3960x - 1584)log(- 2x + 1) + 1189412x + 784945x +--R + +--R - 5026 +--R / +--R 3 2 +--R 691488x - 230496x - 288120x + 115248 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (9504x - 3168x - 3960x + 1584)log(3x + 2) +--R + +--R 3 2 2 +--R (- 9504x + 3168x + 3960x - 1584)log(2x - 1) + 1189412x + 784945x - 5026 +--R / +--R 3 2 +--R 691488x - 230496x - 288120x + 115248 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 33log(2x - 1) + 33log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=1331/1372/(1-2*x)^2+(-363/2401)/(1-2*x)+1/2058/(2+3*x)^2+_ + (-33/2401)/(2+3*x)+1023/16807*log(1-2*x)-1023/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2) +--R + +--R 4 3 2 3 +--R (441936x + 147312x - 282348x - 49104x + 49104)log(- 2x + 1) + 515592x +--R + +--R 2 +--R 2229773x + 2239384x + 655214 +--R / +--R 4 3 2 +--R 7260624x + 2420208x - 4638732x - 806736x + 806736 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2) +--R + +--R 4 3 2 3 +--R (441936x + 147312x - 282348x - 49104x + 49104)log(2x - 1) + 515592x +--R + +--R 2 +--R 2229773x + 2239384x + 655214 +--R / +--R 4 3 2 +--R 7260624x + 2420208x - 4638732x - 806736x + 806736 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R 1023log(2x - 1) - 1023log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=1331/4802/(1-2*x)^2+3267/16807/(1-2*x)+1/3087/(2+3*x)^3+_ + (-33/4802)/(2+3*x)^2+1023/16807/(2+3*x)-7755/117649*log(1-2*x)+_ + 7755/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076 +--R / +--R 5 4 3 2 +--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076 +--R / +--R 5 4 3 2 +--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R - 7755log(2x - 1) + 7755log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=1331/16807/(1-2*x)^2+14520/117649/(1-2*x)+1/4116/(2+3*x)^4+_ + (-11/2401)/(2+3*x)^3+1023/33614/(2+3*x)^2+(-7755/117649)/(2+3*x)-_ + 59070/823543*log(1-2*x)+59070/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x +--R + +--R 22682880x + 11341440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x +--R + +--R - 22682880x - 11341440 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x +--R + +--R 27940465 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x +--R + +--R 22682880x + 11341440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x +--R + +--R - 22682880x - 11341440 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x +--R + +--R 27940465 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R - 59070log(2x - 1) + 59070log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=5764801/5632/(1-2*x)^2+(-188591347/30976)/(1-2*x)-2941619571/400000*x-_ + 110180817/40000*x^2-124416/125*x^3-408969/1600*x^4-6561/200*x^5-_ + 2644396573/340736*log(1-2*x)+1/20796875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2048x - 2048x + 512)log(5x + 3) +--R + +--R 2 +--R (- 330549571625000x + 330549571625000x - 82637392906250)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x +--R + +--R 3 2 +--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625 +--R / +--R 2 +--R 42592000000x - 42592000000x + 10648000000 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2048x - 2048x + 512)log(5x + 3) +--R + +--R 2 +--R (- 330549571625000x + 330549571625000x - 82637392906250)log(2x - 1) +--R + +--R 7 6 5 4 +--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x +--R + +--R 3 2 +--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625 +--R / +--R 2 +--R 42592000000x - 42592000000x + 10648000000 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R - 2644396573log(2x - 1) + 2644396573log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 340736 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=823543/2816/(1-2*x)^2+(-5764801/3872)/(1-2*x)-26161299/20000*x-_ + 792423/2000*x^2-40581/400*x^3-2187/160*x^4-269063263/170368*_ + log(1-2*x)+1/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (1024x - 1024x + 256)log(5x + 3) +--R + +--R 2 +--R (- 6726581575000x + 6726581575000x - 1681645393750)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x +--R + +--R 2 +--R 5149424229840x + 1777812991240x - 1273918078125 +--R / +--R 2 +--R 4259200000x - 4259200000x + 1064800000 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1024x - 1024x + 256)log(5x + 3) +--R + +--R 2 +--R (- 6726581575000x + 6726581575000x - 1681645393750)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x +--R + +--R 2 +--R 5149424229840x + 1777812991240x - 1273918078125 +--R / +--R 2 +--R 4259200000x - 4259200000x + 1064800000 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R - 269063263log(2x - 1) + 269063263log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 170368 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=117649/1408/(1-2*x)^2+(-2739541/7744)/(1-2*x)-102303/500*x-35721/800*x^2-_ + 243/40*x^3-12761315/42592*log(1-2*x)+1/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (512x - 512x + 128)log(5x + 3) +--R + +--R 2 +--R (- 127613150000x + 127613150000x - 31903287500)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x +--R + +--R 53550930620x - 28771483125 +--R / +--R 2 +--R 425920000x - 425920000x + 106480000 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (512x - 512x + 128)log(5x + 3) +--R + +--R 2 +--R (- 127613150000x + 127613150000x - 31903287500)log(2x - 1) +--R + +--R 5 4 3 2 +--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x +--R + +--R 53550930620x - 28771483125 +--R / +--R 2 +--R 425920000x - 425920000x + 106480000 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R - 12761315log(2x - 1) + 12761315log(- 2x + 1) +--R (4) --------------------------------------------- +--R 42592 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=16807/704/(1-2*x)^2+(-156065/1936)/(1-2*x)-10287/400*x-243/80*x^2-_ + 543655/10648*log(1-2*x)+1/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (256x - 256x + 64)log(5x + 3) +--R + +--R 2 4 +--R (- 2174620000x + 2174620000x - 543655000)log(- 2x + 1) - 129373200x +--R + +--R 3 2 +--R - 965986560x + 1063016460x + 1442875060x - 604151625 +--R / +--R 2 +--R 42592000x - 42592000x + 10648000 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (256x - 256x + 64)log(5x + 3) +--R + +--R 2 4 +--R (- 2174620000x + 2174620000x - 543655000)log(2x - 1) - 129373200x +--R + +--R 3 2 +--R - 965986560x + 1063016460x + 1442875060x - 604151625 +--R / +--R 2 +--R 42592000x - 42592000x + 10648000 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R - 543655log(2x - 1) + 543655log(- 2x + 1) +--R (4) ----------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=2401/352/(1-2*x)^2+(-33271/1936)/(1-2*x)-81/40*x-_ + 153811/21296*log(1-2*x)+1/33275*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (128x - 128x + 32)log(5x + 3) +--R + +--R 2 3 2 +--R (- 30762200x + 30762200x - 7690550)log(- 2x + 1) - 8624880x + 8624880x +--R + +--R 34441880x - 11036025 +--R / +--R 2 +--R 4259200x - 4259200x + 1064800 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (128x - 128x + 32)log(5x + 3) +--R + +--R 2 3 2 +--R (- 30762200x + 30762200x - 7690550)log(2x - 1) - 8624880x + 8624880x +--R + +--R 34441880x - 11036025 +--R / +--R 2 +--R 4259200x - 4259200x + 1064800 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R - 153811log(2x - 1) + 153811log(- 2x + 1) +--R (4) ----------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=343/176/(1-2*x)^2+(-392/121)/(1-2*x)-7189/10648*log(1-2*x)+_ + 1/6655*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (64x - 64x + 16)log(5x + 3) +--R + +--R 2 +--R (- 287560x + 287560x - 71890)log(- 2x + 1) + 689920x - 137445 +--R / +--R 2 +--R 425920x - 425920x + 106480 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (64x - 64x + 16)log(5x + 3) + (- 287560x + 287560x - 71890)log(2x - 1) +--R + +--R 689920x - 137445 +--R / +--R 2 +--R 425920x - 425920x + 106480 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R - 7189log(2x - 1) + 7189log(- 2x + 1) +--R (4) ------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=49/88/(1-2*x)^2+(-217/484)/(1-2*x)-1/1331*log(1-2*x)+1/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(- 2x + 1) + 9548x + 1155 +--R ---------------------------------------------------------------------------- +--R 2 +--R 42592x - 42592x + 10648 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(2x - 1) + 9548x + 1155 +--R -------------------------------------------------------------------------- +--R 2 +--R 42592x - 42592x + 10648 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=7/44/(1-2*x)^2+1/121/(1-2*x)-5/1331*log(1-2*x)+5/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(- 2x + 1) - 88x + 891 +--R --------------------------------------------------------------------------- +--R 2 +--R 21296x - 21296x + 5324 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(2x - 1) - 88x + 891 +--R ------------------------------------------------------------------------- +--R 2 +--R 21296x - 21296x + 5324 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R - 5log(2x - 1) + 5log(- 2x + 1) +--R (4) ------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=1/((1-2*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=1/22/(1-2*x)^2+5/121/(1-2*x)-25/1331*log(1-2*x)+25/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(- 2x + 1) +--R + +--R - 220x + 231 +--R / +--R 2 +--R 10648x - 10648x + 2662 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(2x - 1) - 220x +--R + +--R 231 +--R / +--R 2 +--R 10648x - 10648x + 2662 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R - 25log(2x - 1) + 25log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------ +--R 5 4 3 2 +--R 120x - 28x - 90x + 27x + 17x - 6 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1/77/(1-2*x)^2+136/5929/(1-2*x)-6938/456533*log(1-2*x)-_ + 27/343*log(2+3*x)+125/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (171500x - 171500x + 42875)log(5x + 3) +--R + +--R 2 +--R (- 143748x + 143748x - 35937)log(3x + 2) +--R + +--R 2 +--R (- 27752x + 27752x - 6938)log(- 2x + 1) - 20944x + 16401 +--R / +--R 2 +--R 1826132x - 1826132x + 456533 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (171500x - 171500x + 42875)log(5x + 3) +--R + +--R 2 +--R (- 143748x + 143748x - 35937)log(3x + 2) +--R + +--R 2 +--R (- 27752x + 27752x - 6938)log(2x - 1) - 20944x + 16401 +--R / +--R 2 +--R 1826132x - 1826132x + 456533 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 6938log(2x - 1) + 6938log(- 2x + 1) +--R (4) ------------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------- +--R 6 5 4 3 2 +--R 360x + 156x - 326x - 99x + 105x + 16x - 12 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=2/539/(1-2*x)^2+404/41503/(1-2*x)+27/343/(2+3*x)-_ + 27208/3195731*log(1-2*x)-1107/2401*log(2+3*x)+625/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3) +--R + +--R 3 2 +--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2) +--R + +--R 3 2 2 +--R (- 326496x + 108832x + 136040x - 54416)log(- 2x + 1) + 819588x +--R + +--R - 1001770x + 337491 +--R / +--R 3 2 +--R 38348772x - 12782924x - 15978655x + 6391462 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3) +--R + +--R 3 2 +--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2) +--R + +--R 3 2 2 +--R (- 326496x + 108832x + 136040x - 54416)log(2x - 1) + 819588x +--R + +--R - 1001770x + 337491 +--R / +--R 3 2 +--R 38348772x - 12782924x - 15978655x + 6391462 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 27208log(2x - 1) + 27208log(- 2x + 1) +--R (4) --------------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 1080x + 1188x - 666x - 949x + 117x + 258x - 4x - 24 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=4/3773/(1-2*x)^2+1072/290521/(1-2*x)+27/686/(2+3*x)^2+1107/2401/(2+3*x)-_ + 89792/22370117*log(1-2*x)-39393/16807*log(2+3*x)+3125/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(- 2x + 1) +--R + +--R 3 2 +--R 244562472x - 77517132x - 108953306x + 43866669 +--R / +--R 4 3 2 +--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(2x - 1) +--R + +--R 3 2 +--R 244562472x - 77517132x - 108953306x + 43866669 +--R / +--R 4 3 2 +--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 89792log(2x - 1) + 89792log(- 2x + 1) +--R (4) --------------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R - --------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 3240x + 5724x + 378x - 4179x - 1547x + 1008x + 504x - 80x - 48 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=8/26411/(1-2*x)^2+2672/2033647/(1-2*x)+9/343/(2+3*x)^3+_ + 1107/4802/(2+3*x)^2+39393/16807/(2+3*x)-267760/156590819*log(1-2*x)-_ + 1380915/117649*log(2+3*x)+15625/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 397065375000x + 397065375000x - 165443906250x - 213238812500x +--R + +--R 14706125000x + 29412250000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x +--R + +--R - 14703982920x - 29407965840 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x +--R + +--R - 4284160 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924 +--R / +--R 5 4 3 2 +--R 33823616904x + 33823616904x - 14093173710x - 18164535004x +--R + +--R 1252726552x + 2505453104 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 397065375000x + 397065375000x - 165443906250x - 213238812500x +--R + +--R 14706125000x + 29412250000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x +--R + +--R - 14703982920x - 29407965840 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x +--R + +--R - 4284160 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924 +--R / +--R 5 4 3 2 +--R 33823616904x + 33823616904x - 14093173710x - 18164535004x +--R + +--R 1252726552x + 2505453104 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 267760log(2x - 1) + 267760log(- 2x + 1) +--R (4) ----------------------------------------- +--R 156590819 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=5764801/30976/(1-2*x)^2+(-79883671/85184)/(1-2*x)-81001863/100000*x-_ + 4863159/20000*x^2-123201/2000*x^3-6561/800*x^4+(-1/20796875)/(3+5*x)-_ + 1845559863/1874048*log(1-2*x)+54/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (1382400x - 552960x - 483840x + 207360)log(5x + 3) +--R + +--R 3 2 +--R - 1153474914375000x + 461389965750000x + 403716220031250x +--R + +--R - 173021237156250 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R - 9605960100000x - 68309049600000x - 252583384185000x +--R + +--R 4 3 2 +--R - 811024095717000x + 468362848619160x + 838544848893576x +--R + +--R - 32898384865071x - 132062840768441 +--R / +--R 3 2 +--R 1171280000000x - 468512000000x - 409948000000x + 175692000000 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1382400x - 552960x - 483840x + 207360)log(5x + 3) +--R + +--R 3 2 +--R - 1153474914375000x + 461389965750000x + 403716220031250x +--R + +--R - 173021237156250 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R - 9605960100000x - 68309049600000x - 252583384185000x +--R + +--R 4 3 2 +--R - 811024095717000x + 468362848619160x + 838544848893576x +--R + +--R - 32898384865071x - 132062840768441 +--R / +--R 3 2 +--R 1171280000000x - 468512000000x - 409948000000x + 175692000000 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 1845559863log(2x - 1) + 1845559863log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 1874048 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=823543/15488/(1-2*x)^2+(-18941489/85184)/(1-2*x)-1258983/10000*x-_ + 108621/4000*x^2-729/200*x^3+(-1/4159375)/(3+5*x)-_ + 87177909/468512*log(1-2*x)+237/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (606720x - 242688x - 212352x + 91008)log(5x + 3) +--R + +--R 3 2 +--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500) +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x +--R + +--R 2 +--R 17706353292408x + 647305946397x - 2972475517033 +--R / +--R 3 2 +--R 117128000000x - 46851200000x - 40994800000x + 17569200000 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (606720x - 242688x - 212352x + 91008)log(5x + 3) +--R + +--R 3 2 +--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500) +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x +--R + +--R 2 +--R 17706353292408x + 647305946397x - 2972475517033 +--R / +--R 3 2 +--R 117128000000x - 46851200000x - 40994800000x + 17569200000 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R - 87177909log(2x - 1) + 87177909log(- 2x + 1) +--R (4) --------------------------------------------- +--R 468512 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=117649/7744/(1-2*x)^2+(-67228/1331)/(1-2*x)-31347/2000*x-729/400*x^2+_ + (-1/831875)/(3+5*x)-7383075/234256*log(1-2*x)+204/9150625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (261120x - 104448x - 91392x + 39168)log(5x + 3) +--R + +--R 3 2 +--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500) +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x +--R + +--R 46529265321x - 62049343829 +--R / +--R 3 2 +--R 11712800000x - 4685120000x - 4099480000x + 1756920000 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (261120x - 104448x - 91392x + 39168)log(5x + 3) +--R + +--R 3 2 +--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500) +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x +--R + +--R 46529265321x - 62049343829 +--R / +--R 3 2 +--R 11712800000x - 4685120000x - 4099480000x + 1756920000 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R - 7383075log(2x - 1) + 7383075log(- 2x + 1) +--R (4) ------------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=16807/3872/(1-2*x)^2+(-228095/21296)/(1-2*x)-243/200*x+_ + (-1/166375)/(3+5*x)-1034145/234256*log(1-2*x)+171/1830125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (109440x - 43776x - 38304x + 16416)log(5x + 3) +--R + +--R 3 2 +--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(- 2x + 1) +--R + +--R 4 3 2 +--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477 +--R / +--R 3 2 +--R 1171280000x - 468512000x - 409948000x + 175692000 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (109440x - 43776x - 38304x + 16416)log(5x + 3) +--R + +--R 3 2 +--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(2x - 1) +--R + +--R 4 3 2 +--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477 +--R / +--R 3 2 +--R 1171280000x - 468512000x - 409948000x + 175692000 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R - 1034145log(2x - 1) + 1034145log(- 2x + 1) +--R (4) ------------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=2401/1936/(1-2*x)^2+(-10633/5324)/(1-2*x)+(-1/33275)/(3+5*x)-_ + 47481/117128*log(1-2*x)+138/366025*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (44160x - 17664x - 15456x + 6624)log(5x + 3) +--R + +--R 3 2 +--R (- 47481000x + 18992400x + 16618350x - 7122150)log(- 2x + 1) +--R + +--R 2 +--R 116962296x + 48012129x - 13300001 +--R / +--R 3 2 +--R 117128000x - 46851200x - 40994800x + 17569200 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (44160x - 17664x - 15456x + 6624)log(5x + 3) +--R + +--R 3 2 +--R (- 47481000x + 18992400x + 16618350x - 7122150)log(2x - 1) +--R + +--R 2 +--R 116962296x + 48012129x - 13300001 +--R / +--R 3 2 +--R 117128000x - 46851200x - 40994800x + 17569200 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R - 47481log(2x - 1) + 47481log(- 2x + 1) +--R (4) --------------------------------------- +--R 117128 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=343/968/(1-2*x)^2+(-1421/5324)/(1-2*x)+(-1/6655)/(3+5*x)-_ + 21/14641*log(1-2*x)+21/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (16800x - 6720x - 5880x + 2520)log(5x + 3) +--R + +--R 3 2 2 +--R (- 16800x + 6720x + 5880x - 2520)log(- 2x + 1) + 1562748x + 1194237x +--R + +--R 153527 +--R / +--R 3 2 +--R 11712800x - 4685120x - 4099480x + 1756920 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (16800x - 6720x - 5880x + 2520)log(5x + 3) +--R + +--R 3 2 2 +--R (- 16800x + 6720x + 5880x - 2520)log(2x - 1) + 1562748x + 1194237x +--R + +--R 153527 +--R / +--R 3 2 +--R 11712800x - 4685120x - 4099480x + 1756920 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R - 21log(2x - 1) + 21log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=49/484/(1-2*x)^2+14/1331/(1-2*x)+(-1/1331)/(3+5*x)-_ + 72/14641*log(1-2*x)+72/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (5760x - 2304x - 2016x + 864)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5760x + 2304x + 2016x - 864)log(- 2x + 1) - 6336x + 29205x + 19591 +--R / +--R 3 2 +--R 1171280x - 468512x - 409948x + 175692 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5760x - 2304x - 2016x + 864)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5760x + 2304x + 2016x - 864)log(2x - 1) - 6336x + 29205x + 19591 +--R / +--R 3 2 +--R 1171280x - 468512x - 409948x + 175692 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R - 72log(2x - 1) + 72log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=7/242/(1-2*x)^2+37/1331/(1-2*x)+(-5/1331)/(3+5*x)-_ + 195/14641*log(1-2*x)+195/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (7800x - 3120x - 2730x + 1170)log(5x + 3) +--R + +--R 3 2 2 +--R (- 7800x + 3120x + 2730x - 1170)log(- 2x + 1) - 8580x + 3861x + 4873 +--R / +--R 3 2 +--R 585640x - 234256x - 204974x + 87846 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (7800x - 3120x - 2730x + 1170)log(5x + 3) +--R + +--R 3 2 2 +--R (- 7800x + 3120x + 2730x - 1170)log(2x - 1) - 8580x + 3861x + 4873 +--R / +--R 3 2 +--R 585640x - 234256x - 204974x + 87846 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R - 195log(2x - 1) + 195log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=1/121/(1-2*x)^2+20/1331/(1-2*x)+(-25/1331)/(3+5*x)-_ + 150/14641*log(1-2*x)+150/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (3000x - 1200x - 1050x + 450)log(5x + 3) +--R + +--R 3 2 2 +--R (- 3000x + 1200x + 1050x - 450)log(- 2x + 1) - 3300x + 1485x + 748 +--R / +--R 3 2 +--R 292820x - 117128x - 102487x + 43923 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (3000x - 1200x - 1050x + 450)log(5x + 3) +--R + +--R 3 2 2 +--R (- 3000x + 1200x + 1050x - 450)log(2x - 1) - 3300x + 1485x + 748 +--R / +--R 3 2 +--R 292820x - 117128x - 102487x + 43923 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R - 150log(2x - 1) + 150log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------ +--R 6 5 4 3 2 +--R 600x + 220x - 534x - 135x + 166x + 21x - 18 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=2/847/(1-2*x)^2+412/65219/(1-2*x)+(-125/1331)/(3+5*x)-_ + 28296/5021863*log(1-2*x)+81/343*log(2+3*x)-3375/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3) +--R + +--R 3 2 +--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2) +--R + +--R 3 2 2 +--R (- 565920x + 226368x + 198072x - 84888)log(- 2x + 1) - 2203740x +--R + +--R 1914066x - 340879 +--R / +--R 3 2 +--R 100437260x - 40174904x - 35153041x + 15065589 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3) +--R + +--R 3 2 +--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2) +--R + +--R 3 2 2 +--R (- 565920x + 226368x + 198072x - 84888)log(2x - 1) - 2203740x +--R + +--R 1914066x - 340879 +--R / +--R 3 2 +--R 100437260x - 40174904x - 35153041x + 15065589 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R - 28296log(2x - 1) + 28296log(- 2x + 1) +--R (4) --------------------------------------- +--R 5021863 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 1800x + 1860x - 1162x - 1473x + 228x + 395x - 12x - 36 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=4/5929/(1-2*x)^2+1088/456533/(1-2*x)+(-81/343)/(2+3*x)+_ + (-625/1331)/(3+5*x)-92496/35153041*log(1-2*x)+_ + 6156/2401*log(2+3*x)-37500/14641*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(- 2x + 1) +--R + +--R 3 2 +--R - 366624720x + 130867968x + 141681540x - 57273139 +--R / +--R 4 3 2 +--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(2x - 1) +--R + +--R 3 2 +--R - 366624720x + 130867968x + 141681540x - 57273139 +--R / +--R 4 3 2 +--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R - 92496log(2x - 1) + 92496log(- 2x + 1) +--R (4) --------------------------------------- +--R 35153041 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R - ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 5400x + 9180x + 234x - 6743x - 2262x + 1641x + 754x - 132x - 72 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=8/41503/(1-2*x)^2+2704/3195731/(1-2*x)+(-81/686)/(2+3*x)^2+_ + (-6156/2401)/(2+3*x)+(-3125/1331)/(3+5*x)-_ + 274224/246071287*log(1-2*x)+333639/16807*log(2+3*x)-_ + 290625/14641*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x +--R + +--R - 78152550000x - 117228825000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x +--R + +--R 78156937584x + 117235406376 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x +--R + +--R - 6581376 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x +--R + +--R - 12361039691 +--R / +--R 5 4 3 2 +--R 88585663320x + 82679952432x - 38879263346x - 43800689086x +--R + +--R 3937140592x + 5905710888 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x +--R + +--R - 78152550000x - 117228825000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x +--R + +--R 78156937584x + 117235406376 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x +--R + +--R - 6581376 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x +--R + +--R - 12361039691 +--R / +--R 5 4 3 2 +--R 88585663320x + 82679952432x - 38879263346x - 43800689086x +--R + +--R 3937140592x + 5905710888 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - 274224log(2x - 1) + 274224log(- 2x + 1) +--R (4) ----------------------------------------- +--R 246071287 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 16200x + 38340x + 19062x - 19761x - 20272x + 399x + 5544x +--R + +--R 2 +--R 1112x - 480x - 144 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=16/290521/(1-2*x)^2+6464/22370117/(1-2*x)+(-27/343)/(2+3*x)^3+_ + (-3078/2401)/(2+3*x)^2+(-333639/16807)/(2+3*x)+_ + (-15625/1331)/(3+5*x)-761760/1722499009*log(1-2*x)+_ + 15820110/117649*log(2+3*x)-1968750/14641*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 125075593125000x - 200120949000000x - 22930525406250x +--R + +--R 3 2 +--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 125076004475400x + 200121607160640x + 22930600820490x +--R + +--R 3 2 +--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x +--R + +--R - 39611520x - 18282240 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x +--R + +--R - 342379099755x - 585732955423 +--R / +--R 6 5 4 3 +--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x +--R + +--R 2 +--R - 265264847386x + 89569948468x + 41339976216 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 125075593125000x - 200120949000000x - 22930525406250x +--R + +--R 3 2 +--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 125076004475400x + 200121607160640x + 22930600820490x +--R + +--R 3 2 +--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x +--R + +--R - 39611520x - 18282240 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x +--R + +--R - 342379099755x - 585732955423 +--R / +--R 6 5 4 3 +--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x +--R + +--R 2 +--R - 265264847386x + 89569948468x + 41339976216 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - 761760log(2x - 1) + 761760log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1722499009 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^9/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 19683x - 118098x - 314928x - 489888x - 489888x - 326592x +--R + +--R 3 2 +--R - 145152x - 41472x - 6912x - 512 +--R / +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=40353607/340736/(1-2*x)^2+(-17294403/29282)/(1-2*x)-_ + 50150097/100000*x-7459857/50000*x^2-373977/10000*x^3-_ + 19683/4000*x^4+(-1/207968750)/(3+5*x)^2+(-303/1143828125)/(3+5*x)-_ + 12657032367/20614528*log(1-2*x)+8202/2516421875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 197766130734375000x - 39553226146875000x + 116682017133281250x +--R + +--R 11865967844062500x - 17798951766093750 +--R * +--R log(- 2x + 1) +--R + +--R 8 7 6 +--R - 1584983416500000x - 12362870648700000x - 49530731765625000x +--R + +--R 5 4 3 +--R - 163943640232020000x - 3373337816263800x + 192223824266320440x +--R + +--R 2 +--R 81487109015452107x - 25922683108313662x - 13688249752028357 +--R / +--R 4 3 2 +--R 322102000000000x + 64420400000000x - 190040180000000x +--R + +--R - 19326120000000x + 28989180000000 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 197766130734375000x - 39553226146875000x + 116682017133281250x +--R + +--R 11865967844062500x - 17798951766093750 +--R * +--R log(2x - 1) +--R + +--R 8 7 6 +--R - 1584983416500000x - 12362870648700000x - 49530731765625000x +--R + +--R 5 4 3 +--R - 163943640232020000x - 3373337816263800x + 192223824266320440x +--R + +--R 2 +--R 81487109015452107x - 25922683108313662x - 13688249752028357 +--R / +--R 4 3 2 +--R 322102000000000x + 64420400000000x - 190040180000000x +--R + +--R - 19326120000000x + 28989180000000 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 12657032367log(2x - 1) + 12657032367log(- 2x + 1) +--R (4) --------------------------------------------------- +--R 20614528 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=5764801/170368/(1-2*x)^2+(-130943337/937024)/(1-2*x)-242028/3125*x-_ + 330237/20000*x^2-2187/1000*x^3+(-1/41593750)/(3+5*x)^2+_ + (-54/45753125)/(3+5*x)-595421589/5153632*log(1-2*x)+_ + 1284/100656875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 3721384931250000x - 744276986250000x + 2195617109437500x +--R + +--R 223283095875000x - 334924643812500 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R - 70443707400000x - 545938732350000x - 2559454702200000x +--R + +--R 4 3 2 +--R - 180911181221100x + 3748001092791780x + 1949701238862399x +--R + +--R - 437687139939434x - 307014257976349 +--R / +--R 4 3 2 +--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x +--R + +--R 2898918000000 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 3721384931250000x - 744276986250000x + 2195617109437500x +--R + +--R 223283095875000x - 334924643812500 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R - 70443707400000x - 545938732350000x - 2559454702200000x +--R + +--R 4 3 2 +--R - 180911181221100x + 3748001092791780x + 1949701238862399x +--R + +--R - 437687139939434x - 307014257976349 +--R / +--R 4 3 2 +--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x +--R + +--R 2898918000000 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 595421589log(2x - 1) + 595421589log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 5153632 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=823543/85184/(1-2*x)^2+(-7411887/234256)/(1-2*x)-95499/10000*x-_ + 2187/2000*x^2+(-1/8318750)/(3+5*x)^2+(-237/45753125)/(3+5*x)-_ + 25059237/1288408*log(1-2*x)+24279/503284375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3) +--R + +--R 4 3 2 +--R - 62648092500000x - 12529618500000x + 36962374575000x +--R + +--R 3758885550000x - 5638328325000 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x +--R + +--R 2 +--R 44983390879251x - 5655984161146x - 6369590895041 +--R / +--R 4 3 2 +--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x +--R + +--R 289891800000 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3) +--R + +--R 4 3 2 +--R - 62648092500000x - 12529618500000x + 36962374575000x +--R + +--R 3758885550000x - 5638328325000 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x +--R + +--R 2 +--R 44983390879251x - 5655984161146x - 6369590895041 +--R / +--R 4 3 2 +--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x +--R + +--R 289891800000 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 25059237log(2x - 1) + 25059237log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1288408 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=117649/42592/(1-2*x)^2+(-1563051/234256)/(1-2*x)-729/1000*x+_ + (-1/1663750)/(3+5*x)^2+(-204/9150625)/(3+5*x)-_ + 6950895/2576816*log(1-2*x)+17547/100656875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3) +--R + +--R 4 3 2 +--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x +--R + +--R - 78197568750 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x +--R + +--R - 12119848070x - 113352927985 +--R / +--R 4 3 2 +--R 322102000000x + 64420400000x - 190040180000x - 19326120000x +--R + +--R 28989180000 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3) +--R + +--R 4 3 2 +--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x +--R + +--R - 78197568750 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x +--R + +--R - 12119848070x - 113352927985 +--R / +--R 4 3 2 +--R 322102000000x + 64420400000x - 190040180000x - 19326120000x +--R + +--R 28989180000 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 6950895log(2x - 1) + 6950895log(- 2x + 1) +--R (4) ------------------------------------------- +--R 2576816 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=16807/21296/(1-2*x)^2+(-36015/29282)/(1-2*x)+(-1/332750)/(3+5*x)^2+_ + (-171/1830125)/(3+5*x)-313845/1288408*log(1-2*x)+11904/20131375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3) +--R + +--R 4 3 2 +--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250) +--R * +--R log(- 2x + 1) +--R + +--R 3 2 +--R 19807648080x + 20221158771x + 2872410794x - 1277723381 +--R / +--R 4 3 2 +--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3) +--R + +--R 4 3 2 +--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250) +--R * +--R log(2x - 1) +--R + +--R 3 2 +--R 19807648080x + 20221158771x + 2872410794x - 1277723381 +--R / +--R 4 3 2 +--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 313845log(2x - 1) + 313845log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1288408 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=2401/10648/(1-2*x)^2+(-9261/58564)/(1-2*x)+(-1/66550)/(3+5*x)^2+_ + (-138/366025)/(3+5*x)-294/161051*log(1-2*x)+294/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(- 2x + 1) +--R + +--R 3 2 +--R 254434620x + 359945091x + 156855094x + 19488359 +--R / +--R 4 3 2 +--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(2x - 1) +--R + +--R 3 2 +--R 254434620x + 359945091x + 156855094x + 19488359 +--R / +--R 4 3 2 +--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 294log(2x - 1) + 294log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=343/5324/(1-2*x)^2+147/14641/(1-2*x)+(-1/13310)/(3+5*x)^2+_ + (-21/14641)/(3+5*x)-777/161051*log(1-2*x)+777/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(- 2x + 1) +--R + +--R 3 2 +--R - 1709400x + 4091967x + 6646838x + 2144593 +--R / +--R 4 3 2 +--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(2x - 1) +--R + +--R 3 2 +--R - 1709400x + 4091967x + 6646838x + 2144593 +--R / +--R 4 3 2 +--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R - 777log(2x - 1) + 777log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=49/2662/(1-2*x)^2+273/14641/(1-2*x)+(-1/2662)/(3+5*x)^2+_ + (-72/14641)/(3+5*x)-1509/161051*log(1-2*x)+1509/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3) +--R + +--R 4 3 2 +--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(- 2x + 1) +--R + +--R 3 2 +--R - 331980x - 49797x + 261514x + 102542 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(2x - 1) - 331980x +--R + +--R 2 +--R - 49797x + 261514x + 102542 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R - 1509log(2x - 1) + 1509log(- 2x + 1) +--R (4) ------------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=7/1331/(1-2*x)^2+144/14641/(1-2*x)+(-5/2662)/(3+5*x)^2+_ + (-195/14641)/(3+5*x)-1110/161051*log(1-2*x)+1110/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3) +--R + +--R 4 3 2 +--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(- 2x + 1) +--R + +--R 3 2 +--R - 244200x - 36630x + 121286x + 30283 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(2x - 1) - 244200x +--R + +--R 2 +--R - 36630x + 121286x + 30283 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R - 1110log(2x - 1) + 1110log(- 2x + 1) +--R (4) ------------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=1/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=2/1331/(1-2*x)^2+60/14641/(1-2*x)+(-25/2662)/(3+5*x)^2+_ + (-150/14641)/(3+5*x)-600/161051*log(1-2*x)+600/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(- 2x + 1) - 132000x +--R + +--R 2 +--R - 19800x + 65560x + 3311 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(2x - 1) - 132000x +--R + +--R 2 +--R - 19800x + 65560x + 3311 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R - 600log(2x - 1) + 600log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 3000x + 2900x - 2010x - 2277x + 425x + 603x - 27x - 54 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=4/9317/(1-2*x)^2+1104/717409/(1-2*x)+(-125/2662)/(3+5*x)^2+_ + 3375/14641/(3+5*x)-95232/55240493*log(1-2*x)-243/343*log(2+3*x)+_ + 114375/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(- 2x + 1) +--R + +--R 3 2 +--R 500854200x - 229258260x - 154059598x + 73172407 +--R / +--R 4 3 2 +--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(2x - 1) +--R + +--R 3 2 +--R 500854200x - 229258260x - 154059598x + 73172407 +--R / +--R 4 3 2 +--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R - 95232log(2x - 1) + 95232log(- 2x + 1) +--R (4) --------------------------------------- +--R 55240493 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 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52624397700000x +--R + +--R 22553313300000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 563831434029600x - 864541532178720x - 68286251454696x +--R + +--R 3 2 +--R 427258931120208x + 142210817249688x - 52624267176096x +--R + +--R - 22553257361184 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 1398470400x - 2144321280x - 169370304x + 1059729792x +--R + +--R 2 +--R 352725312x - 130523904x - 55938816 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 37587223951200x + 33827604204240x - 16859483294808x - 17801732753112x +--R + +--R 1786038929444x + 2376093430249 +--R / +--R 6 5 4 3 +--R 4872211482600x + 7470724273320x + 590078946226x - 3692053590148x +--R + +--R 2 +--R - 1228880007278x + 454739738376x + 194888459304 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 563832832500000x + 864543676500000x + 68286420825000x +--R + +--R 3 2 +--R - 427259990850000x - 142211169975000x + 52624397700000x +--R + +--R 22553313300000 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Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 10 9 8 7 6 5 +--R 81000x + 240300x + 210330x - 41619x - 160643x - 58821x +--R + +--R 4 3 2 +--R 28917x + 22192x + 936x - 2160x - 432 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=32/3195731/(1-2*x)^2+15168/246071287/(1-2*x)+81/343/(2+3*x)^3+_ + 26973/4802/(2+3*x)^2+1944972/16807/(2+3*x)+(-15625/2662)/(3+5*x)^2+_ + 1968750/14641/(3+5*x)-2054400/18947489099*log(1-2*x)-_ + 115534350/117649*log(2+3*x)+158156250/161051*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 100477393143750000x + 221050264916250000x + 114879152827687500x +--R + +--R 4 3 2 +--R - 68026916543250000x - 76102321844062500x - 7517197561125000x +--R + +--R 10271022410250000x + 2679397150500000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 100477382049990000x - 221050240509978000x - 114879140143821900x +--R + +--R 4 3 2 +--R 68026909032363600x + 76102313441566500x + 7517196731147400x +--R + +--R - 10271021276221200x - 2679396854666400 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 11093760000x - 24406272000x - 12683865600x + 7510886400x +--R + +--R 3 2 +--R 8402496000x + 829977600x - 1134028800x - 295833600 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 +--R 6698479933530000x + 10494278110701000x + 1014683641656300x +--R + +--R 3 2 +--R - 5175447127123350x - 1796782743686700x + 635595472278305x +--R + +--R 282301665291184 +--R / +--R 7 6 5 +--R 102316441134600x + 225096170496120x + 116981797697226x +--R + +--R 4 3 2 +--R - 69272020145944x - 77495230414910x - 7654785595996x + 10459013982648x +--R + +--R 2728438430256 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 100477393143750000x + 221050264916250000x + 114879152827687500x +--R + +--R 4 3 2 +--R - 68026916543250000x - 76102321844062500x - 7517197561125000x +--R + +--R 10271022410250000x + 2679397150500000 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------------------------------------------- +--R 18947489099 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^6*(3+5*x)*sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1294139/384*(1-2*x)^(3/2)+3916031/640*(1-2*x)^(5/2)-_ + 725445/128*(1-2*x)^(7/2)+406455/128*(1-2*x)^(9/2)-_ + 1580985/1408*(1-2*x)^(11/2)+409941/1664*(1-2*x)^(13/2)-_ + 19683/640*(1-2*x)^(15/2)+3645/2176*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x +--R + +--R 3 2 +--R 72883440x + 5339712x - 16666112x - 23667392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x +--R + +--R 3 2 +--R 72883440x + 5339712x - 16666112x - 23667392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)^5*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-184877/192*(1-2*x)^(3/2)+12005/8*(1-2*x)^(5/2)-74235/64*(1-2*x)^(7/2)+_ + 4165/8*(1-2*x)^(9/2)-97335/704*(1-2*x)^(11/2)+81/4*(1-2*x)^(13/2)-_ + 81/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 33 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 33 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^4*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-26411/96*(1-2*x)^(3/2)+57281/160*(1-2*x)^(5/2)-3549/16*(1-2*x)^(7/2)+_ + 1197/16*(1-2*x)^(9/2)-4671/352*(1-2*x)^(11/2)+405/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^3*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-3773/48*(1-2*x)^(3/2)+3283/40*(1-2*x)^(5/2)-153/4*(1-2*x)^(7/2)+_ + 69/8*(1-2*x)^(9/2)-135/176*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1 +--R (2) -------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1 +--R (3) -------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^2*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-539/24*(1-2*x)^(3/2)+707/40*(1-2*x)^(5/2)-309/56*(1-2*x)^(7/2)+_ + 5/8*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-77/12*(1-2*x)^(3/2)+17/5*(1-2*x)^(5/2)-15/28*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (450x + 753x + 257x - 373)\|- 2x + 1 +--R (2) --------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (450x + 753x + 257x - 373)\|- 2x + 1 +--R (3) --------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(3+5*x)*sqrt(1-2*x) +--R +--R +--R +--------+ +--R (1) (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-11/6*(1-2*x)^(3/2)+1/2*(1-2*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (6x + 5x - 4)\|- 2x + 1 +--R (2) ------------------------- +--R 3 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (6x + 5x - 4)\|- 2x + 1 +--R (3) ------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-5/9*(1-2*x)^(3/2)+2/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 2/9*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--------+ +--R 2\|7 atanh(---------------) + (10x - 7)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------ +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +--------+ +--R \|7 log(---------------------------------) + (10x - 7)\|3 \|- 2x + 1 +--R 3x + 2 +--R (3) --------------------------------------------------------------------- +--R +-+ +--R 9\|3 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(---------------------------------) - 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/21*(1-2*x)^(3/2)/(2+3*x)-8*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 8/7*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (- 72x - 48)atanh(---------------) + (10x + 7)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) -------------------------------------------------------------- +--R +--+ +--R (9x + 6)\|21 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (36x + 24)log(-----------------------------) + (10x + 7)\|21 \|- 2x + 1 +--R 3x + 2 +--R ------------------------------------------------------------------------ +--R +--+ +--R (9x + 6)\|21 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4log(-----------------------------) + 8atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------- +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 12x + 20)\|21 + (12x - 20)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 8x + 4)\|3 \|7 \|21 + 168x - 84 +--R / +--R 2 +--------+ 3 2 +--+ +--R (126x + 21x - 42)\|- 2x + 1 + (18x - 27x - 11x + 10)\|21 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1/42*(1-2*x)^(3/2)/(2+3*x)^2+23/21*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-23/42*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--+ +--------+ +--R (414x + 552x + 184)atanh(---------------) + (- 71x - 45)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R 2 +--+ +--R (378x + 504x + 168)\|21 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (207x + 276x + 92)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 71x - 45)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (378x + 504x + 168)\|21 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23log(-------------------------------) - 46atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 42\|21 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (46x - 23)\|3 \|7 \|21 - 966x + 483 +--R / +--R 2 +--------+ 3 2 +--+ +--R (5292x + 882x - 1764)\|- 2x + 1 + (- 756x + 1134x + 462x - 420)\|21 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=1/63*(1-2*x)^(3/2)/(2+3*x)^3+34/441*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-17/63*sqrt(1-2*x)/(2+3*x)^2+17/441*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (918x + 1836x + 1224x + 272)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (153x - 167x - 163)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (11907x + 23814x + 15876x + 3528)\|21 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (459x + 918x + 612x + 136)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (153x - 167x - 163)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (11907x + 23814x + 15876x + 3528)\|21 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 17log(-------------------------------) - 34atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 441\|21 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (34x - 17)\|3 \|7 \|21 - 714x + 357 +--R / +--R 2 +--------+ +--R (55566x + 9261x - 18522)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 7938x + 11907x + 4851x - 4410)\|21 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=1/84*(1-2*x)^(3/2)/(2+3*x)^4+5/1372*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-5/28*sqrt(1-2*x)/(2+3*x)^3+5/392*sqrt(1-2*x)/(2+3*x)^2+_ + 15/2744*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 +-+ \|3 \|- 2x + 1 +--R (2430x + 6480x + 6480x + 2880x + 480)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (1215x + 3240x + 3240x + 1440x + 240)\|3 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 5\|3 log(---------------------------------) - 10\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 2744\|7 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=1/105*(1-2*x)^(3/2)/(2+3*x)^5+2/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-2/15*sqrt(1-2*x)/(2+3*x)^4+2/315*sqrt(1-2*x)/(2+3*x)^3+_ + 1/441*sqrt(1-2*x)/(2+3*x)^2+1/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 5 4 3 2 \|3 \|- 2x + 1 +--R (2430x + 8100x + 10800x + 7200x + 2400x + 320)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1215x + 4050x + 5400x + 3600x + 1200x + 160) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 18522x + 27783x + 11319x - 10290)\|21 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^4*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-290521/192*(1-2*x)^(3/2)+381073/160*(1-2*x)^(5/2)-118993/64*_ + (1-2*x)^(7/2)+40453/48*(1-2*x)^(9/2)-159111/704*(1-2*x)^(11/2)+_ + 13905/416*(1-2*x)^(13/2)-135/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x +--R + +--R - 426024x - 734904 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x +--R + +--R - 426024x - 734904 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^3*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-41503/96*(1-2*x)^(3/2)+91091/160*(1-2*x)^(5/2)-5711/16*(1-2*x)^(7/2)+_ + 1949/16*(1-2*x)^(9/2)-7695/352*(1-2*x)^(11/2)+675/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^2*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-5929/48*(1-2*x)^(3/2)+1309/10*(1-2*x)^(5/2)-3467/56*(1-2*x)^(7/2)+_ + 85/6*(1-2*x)^(9/2)-225/176*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-847/24*(1-2*x)^(3/2)+1133/40*(1-2*x)^(5/2)-505/56*(1-2*x)^(7/2)+_ + 25/24*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-121/12*(1-2*x)^(3/2)+11/2*(1-2*x)^(5/2)-25/28*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (150x + 237x + 74x - 115)\|- 2x + 1 +--R (2) -------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (150x + 237x + 74x - 115)\|- 2x + 1 +--R (3) -------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-28/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(3/2)*(3+5*x)-2/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+2/27*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+ +--R - 2\|7 atanh(---------------) + (90x + 65x - 53)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 2 +-+ +--------+ +--R \|7 log(-------------------------------) + (90x + 65x - 53)\|3 \|- 2x + 1 +--R 3x + 2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(-------------------------------) + 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-25/27*(1-2*x)^(3/2)-1/63*(1-2*x)^(3/2)/(2+3*x)+142/27*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-142/189*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 2 +--+ +--------+ +--R (426x + 284)atanh(---------------) + (150x - 35x - 91)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R (81x + 54)\|21 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R (213x + 142)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (150x - 35x - 91)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (81x + 54)\|21 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 71log(-------------------------------) - 142atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491 +--R / +--R 2 +--------+ 3 2 +--+ +--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/126*(1-2*x)^(3/2)/(2+3*x)^2+139/882*(1-2*x)^(3/2)/(2+3*x)-_ + 863/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+863/441*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 15534x - 20712x - 6904)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (2100x + 2941x + 1025)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1134x + 1512x + 504)\|21 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (7767x + 10356x + 3452)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (2100x + 2941x + 1025)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1134x + 1512x + 504)\|21 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 863log(-----------------------------) + 1726atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 126\|21 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2589x + 4315)\|21 + (2589x - 4315)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1726x + 863)\|3 \|7 \|21 + 36246x - 18123 +--R / +--R 2 +--------+ 3 2 +--+ +--R (15876x + 2646x - 5292)\|- 2x + 1 + (2268x - 3402x - 1386x + 1260)\|21 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-1/189*(1-2*x)^(3/2)/(2+3*x)^3+23/294*(1-2*x)^(3/2)/(2+3*x)^2+_ + 2381/1323*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 2381/2646*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (128574x + 257148x + 171432x + 38096)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (71442x + 142884x + 95256x + 21168)\|21 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (64287x + 128574x + 85716x + 19048)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (71442x + 142884x + 95256x + 21168)\|21 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2381log(-------------------------------) - 4762atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 2646\|21 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001 +--R / +--R 2 +--------+ +--R (333396x + 55566x - 111132)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 47628x + 71442x + 29106x - 26460)\|21 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-1/252*(1-2*x)^(3/2)/(2+3*x)^4+275/5292*(1-2*x)^(3/2)/(2+3*x)^3+_ + 4625/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 4625/10584*sqrt(1-2*x)/(2+3*x)^2+4625/74088*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (749250x + 1998000x + 1998000x + 888000x + 148000) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (374625x + 999000x + 999000x + 444000x + 74000) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4625log(-------------------------------) - 9250atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 74088\|21 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13875x + 23125)\|21 + (13875x - 23125)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (9250x - 4625)\|3 \|7 \|21 - 194250x + 97125 +--R / +--R 2 +--------+ +--R (9335088x + 1555848x - 3111696)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 1333584x + 2000376x + 814968x - 740880)\|21 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3i.input.pdf b/src/axiom-website/CATS/rich3i.input.pdf new file mode 100644 index 0000000..a5d5df8 Binary files /dev/null and b/src/axiom-website/CATS/rich3i.input.pdf differ diff --git a/src/axiom-website/CATS/rich3j.input.pamphlet b/src/axiom-website/CATS/rich3j.input.pamphlet new file mode 100644 index 0000000..7bfb8f5 --- /dev/null +++ b/src/axiom-website/CATS/rich3j.input.pamphlet @@ -0,0 +1,9134 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3j.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 55 matching answers. +\item 45 cases where Axiom differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3j.output +)spool rich3j.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-1/315*(1-2*x)^(3/2)/(2+3*x)^5+7/180*(1-2*x)^(3/2)/(2+3*x)^4+_ + 31/1764*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 31/108*sqrt(1-2*x)/(2+3*x)^3+31/1512*sqrt(1-2*x)/(2+3*x)^2+_ + 31/3528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (75330x + 251100x + 334800x + 223200x + 74400x + 9920) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (37665x + 125550x + 167400x + 111600x + 37200x + 4960) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 31log(-------------------------------) - 62atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3528\|21 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 93x + 155)\|21 + (93x - 155)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (62x - 31)\|3 \|7 \|21 - 1302x + 651 +--R / +--R 2 +--------+ +--R (444528x + 74088x - 148176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 63504x + 95256x + 38808x - 35280)\|21 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-1/378*(1-2*x)^(3/2)/(2+3*x)^6+137/4410*(1-2*x)^(3/2)/(2+3*x)^5+_ + 1613/518616*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1613/7560*sqrt(1-2*x)/(2+3*x)^4+1613/158760*sqrt(1-2*x)/(2+3*x)^3+_ + 1613/444528*sqrt(1-2*x)/(2+3*x)^2+1613/1037232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 11758770x + 47035080x + 78391800x + 69681600x + 34840800x +--R + +--R 9290880x + 1032320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 3780710640x + 15122842560x + 25204737600x + 22404211200x +--R + +--R 2 +--R 11202105600x + 2987228160x + 331914240 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 5879385x + 23517540x + 39195900x + 34840800x + 17420400x +--R + +--R 4645440x + 516160 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 3780710640x + 15122842560x + 25204737600x + 22404211200x +--R + +--R 2 +--R 11202105600x + 2987228160x + 331914240 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1613log(-------------------------------) - 3226atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 1037232\|21 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 4839x + 8065)\|21 + (4839x - 8065)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (3226x - 1613)\|3 \|7 \|21 - 67746x + 33873 +--R / +--R 2 +--------+ +--R (130691232x + 21781872x - 43563744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 18670176x + 28005264x + 11409552x - 10372320)\|21 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^4*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-3195731/384*(1-2*x)^(3/2)+9836211/640*(1-2*x)^(5/2)-_ + 1853313/128*(1-2*x)^(7/2)+9504551/1152*(1-2*x)^(9/2)-_ + 4177401/1408*(1-2*x)^(11/2)+1101465/1664*(1-2*x)^(13/2)-_ + 10755/128*(1-2*x)^(15/2)+10125/2176*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x +--R + +--R 3 2 +--R 514265240x + 26582592x - 124054192x - 171312832 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x +--R + +--R 3 2 +--R 514265240x + 26582592x - 124054192x - 171312832 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^3*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-456533/192*(1-2*x)^(3/2)+302379/80*(1-2*x)^(5/2)-_ + 190707/64*(1-2*x)^(7/2)+98209/72*(1-2*x)^(9/2)-_ + 260055/704*(1-2*x)^(11/2)+11475/208*(1-2*x)^(13/2)-225/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x +--R + +--R 2 +--R 2166357x - 2030662x - 3420622 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x +--R + +--R 2 +--R 2166357x - 2030662x - 3420622 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^2*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-65219/96*(1-2*x)^(3/2)+144837/160*(1-2*x)^(5/2)-_ + 64317/112*(1-2*x)^(7/2)+28555/144*(1-2*x)^(9/2)-_ + 12675/352*(1-2*x)^(11/2)+1125/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x +--R + +--R - 8261156 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x +--R + +--R - 8261156 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (375x + 925x + 855x + 351x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-9317/48*(1-2*x)^(3/2)+8349/40*(1-2*x)^(5/2)-2805/28*(1-2*x)^(7/2)+_ + 1675/72*(1-2*x)^(9/2)-375/176*(1-2*x)^(11/2) +--R +--R +--R (2) +--R 5 4 3 2 +--------+ +--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1 +--R ------------------------------------------------------------------------ +--R 3465 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--------+ +--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1 +--R ------------------------------------------------------------------------ +--R 3465 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-1331/24*(1-2*x)^(3/2)+363/8*(1-2*x)^(5/2)-825/56*(1-2*x)^(7/2)+_ + 125/72*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 63 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=2/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-6946/945*sqrt(1-2*x)-_ + 47/315*(3+5*x)^2*sqrt(1-2*x)+2/21*(3+5*x)^3*sqrt(1-2*x)-_ + 1/567*(1333+1877*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 14\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(---------------------------------) - 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-212/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-124/27*sqrt(1-2*x)+_ + 7/9*(3+5*x)^2*sqrt(1-2*x)-1/3*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)-_ + 10/81*(5+34*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (- 636x - 424)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (243x + 162)\|21 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R (318x + 212)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (243x + 162)\|21 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 106log(-----------------------------) + 212atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 81\|21 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 318x + 530)\|21 + (318x - 530)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 212x + 106)\|3 \|7 \|21 + 4452x - 2226 +--R / +--R 2 +--------+ 3 2 +--+ +--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=7559/567*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+115/27*sqrt(1-2*x)-_ + 5/1134*(643-2815*x)*sqrt(1-2*x)-53/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-_ + 1/6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (136062x + 181416x + 60472)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (10206x + 13608x + 4536)\|21 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (68031x + 90708x + 30236)log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (10206x + 13608x + 4536)\|21 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 7559log(-------------------------------) - 15118atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 1134\|21 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739 +--R / +--R 2 +--------+ +--R (142884x + 23814x - 47628)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 20412x + 30618x + 12474x - 11340)\|21 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-92996/3969*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+23710/3969*sqrt(1-2*x)-_ + 3796/3969*(3+5*x)*sqrt(1-2*x)/(2+3*x)-53/189*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2510892x - 5021784x - 3347856x - 743968)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (107163x + 214326x + 142884x + 31752)\|21 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1255446x + 2510892x + 1673928x + 371984) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (107163x + 214326x + 142884x + 31752)\|21 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 46498log(-----------------------------) + 92996atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3969\|21 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 139494x + 232490)\|21 + (139494x - 232490)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 92996x + 46498)\|3 \|7 \|21 + 1952916x - 976458 +--R / +--R 2 +--------+ +--R (500094x + 83349x - 166698)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (71442x - 107163x - 43659x + 39690)\|21 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=328715/111132*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-48005/111132*_ + sqrt(1-2*x)/(2+3*x)-7625/31752*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2-_ + 53/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-1/12*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 4 3 2 +--R (53251830x + 142004880x + 142004880x + 63113280x + 10518880) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (26625915x + 71002440x + 71002440x + 31556640x + 5259440) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 328715log(-------------------------------) - 657430atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +--+ +--R 222264\|21 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 986145x + 1643575)\|21 + (986145x - 1643575)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (657430x - 328715)\|3 \|7 \|21 - 13806030x + 6903015 +--R / +--R 2 +--------+ +--R (28005264x + 4667544x - 9335088)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 4000752x + 6001128x + 2444904x - 2222640)\|21 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=11237/55566*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 475/5292*sqrt(1-2*x)/(2+3*x)^2+11237/111132*sqrt(1-2*x)/(2+3*x)-_ + 547/5670*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3-53/630*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 5 4 3 2 +--R 27305910x + 91019700x + 121359600x + 80906400x + 26968800x +--R + +--R 3595840 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x +--R + +--R 17781120 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13652955x + 45509850x + 60679800x + 40453200x + 13484400x +--R + +--R 1797920 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x +--R + +--R 17781120 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 11237log(-------------------------------) - 22474atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 111132\|21 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 33711x + 56185)\|21 + (33711x - 56185)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (22474x - 11237)\|3 \|7 \|21 - 471954x + 235977 +--R / +--R 2 +--------+ +--R (14002632x + 2333772x - 4667544)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2000376x + 3000564x + 1222452x - 1111320)\|21 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=43957/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1861/59535*sqrt(1-2*x)/(2+3*x)^3+43957/1333584*sqrt(1-2*x)/(2+_ + 3*x)^2+43957/3111696*sqrt(1-2*x)/(2+3*x)-7691/158760*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)^4-53/945*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5-_ + 1/18*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R (2) +--R 6 5 4 3 +--R 320446530x + 1281786120x + 2136310200x + 1898942400x +--R + +--R 2 +--R 949471200x + 253192320x + 28132480 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x +--R + +--R - 36741296 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 11342131920x + 45368527680x + 75614212800x + 67212633600x +--R + +--R 2 +--R 33606316800x + 8961684480x + 995742720 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 160223265x + 640893060x + 1068155100x + 949471200x + 474735600x +--R + +--R 126596160x + 14066240 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x +--R + +--R - 36741296 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 11342131920x + 45368527680x + 75614212800x + 67212633600x +--R + +--R 2 +--R 33606316800x + 8961684480x + 995742720 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 43957log(-------------------------------) - 87914atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 3111696\|21 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 131871x + 219785)\|21 + (131871x - 219785)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (87914x - 43957)\|3 \|7 \|21 - 1846194x + 923097 +--R / +--R 2 +--------+ +--R (392073696x + 65345616x - 130691232)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=47434/9529569*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 13676/972405*sqrt(1-2*x)/(2+3*x)^4+47434/2917215*_ + sqrt(1-2*x)/(2+3*x)^3+23717/4084101*sqrt(1-2*x)/(2+3*x)^2+_ + 23717/9529569*sqrt(1-2*x)/(2+3*x)-3862/138915*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)^5-53/1323*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6-_ + 1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R (2) +--R 7 6 5 4 +--R 518690790x + 2420557020x + 4841114040x + 5379015600x +--R + +--R 3 2 +--R 3586010400x + 1434404160x + 318756480x + 30357760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x +--R + +--R - 361589428x - 88036937 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x +--R + +--R 3 2 +--R 720435416400x + 288174166560x + 64038703680x + 6098924160 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 259345395x + 1210278510x + 2420557020x + 2689507800x +--R + +--R 3 2 +--R 1793005200x + 717202080x + 159378240x + 15178880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x +--R + +--R - 361589428x - 88036937 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x +--R + +--R 3 2 +--R 720435416400x + 288174166560x + 64038703680x + 6098924160 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23717log(-------------------------------) - 47434atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 9529569\|21 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 71151x + 118585)\|21 + (71151x - 118585)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (47434x - 23717)\|3 \|7 \|21 - 996114x + 498057 +--R / +--R 2 +--------+ +--R (1200725694x + 200120949x - 400241898)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 171532242x + 257298363x + 104825259x - 95295690)\|21 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-93922/28125*_ + sqrt(1-2*x)-107/225*(2+3*x)*sqrt(1-2*x)-184/1875*(2+3*x)^2*_ + sqrt(1-2*x)-17/1575*(2+3*x)^3*sqrt(1-2*x)+2/45*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 14\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 21875\|5 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 21875\|5 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 922/625*sqrt(1-2*x)-3/125*(2+3*x)^2*sqrt(1-2*x)+2/35*(2+3*x)^3*_ + sqrt(1-2*x)-1/625*(236+375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 14\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 4375\|5 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 4375\|5 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-8/25*(1-2*x)^(3/2)-3/25*(1-2*x)^(3/2)*(2+3*x)-2/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+2/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 2\|11 atanh(---------------) + (90x + 95x - 68)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 2 +-+ +--------+ +--R \|11 log(--------------------------------) + (90x + 95x - 68)\|5 \|- 2x + 1 +--R 5x + 3 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-1/5*(1-2*x)^(3/2)-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/25*_ + sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 2\|11 atanh(---------------) + (10x - 3)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R \|11 log(--------------------------------) + (10x - 3)\|5 \|- 2x + 1 +--R 5x + 3 +--R (3) --------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=sqrt(1-2*x)/(3+5*x) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/5*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 2\|11 atanh(---------------) + 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R \|11 log(--------------------------------) + 2\|5 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3) +--R +--R +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2\|5 \|7 atanh(---------------) - 2\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +-+ +--R \|3 \|5 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R \|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R \|5 \|7 log(---------------------------------) +--R 3x + 2 +--R / +--R +-+ +-+ +--R \|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R \|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R \|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 2\|5 \|7 atanh(---------------) + 2\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R \|3 \|5 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=68*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (204x + 136)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--+ +--------+ +--R (- 6x - 4)\|21 \|55 atanh(---------------) + \|21 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +--+ +--R (3x + 2)\|21 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (3x + 2)\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (102x + 68)log(-------------------------------) + \|21 \|- 2x + 1 +--R 3x + 2 +--R / +--R +--+ +--R (3x + 2)\|21 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-------------------------------) - 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (45x - 117x + 22x + 80)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 340x - 34x + 102)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 210x - 441x + 168 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ 2 +-+ +--+ +--R (75x - 365x + 592x - 320)\|21 + (6930x + 1155x - 2310)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2550x + 6800x - 1802x - 4080)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 30x + 113x - 129x + 40)\|21 +--R + +--R 3 2 +-+ +--+ +--R (630x - 903x - 378x + 336)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1020x - 1598x - 476x + 510)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 990x + 1485x + 605x - 550)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1700x + 2550x + 782x - 816)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1050x - 3885x + 4368x - 1344 +--R / +--R 4 3 2 +--+ +--+ 4 3 2 +--R (90x - 81x - 136x + 17x + 30)\|21 \|55 - 3150x + 2625x + 4599x +--R + +--R - 546x - 1008 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (1260x + 336x - 777x - 105x + 126)\|55 +--R + +--R 5 4 3 2 +--+ +--R (450x - 1125x - 32x + 1173x + 14x - 240)\|21 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=793/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+1/2*sqrt(1-2*x)/(2+3*x)^2+69/14*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (14274x + 19032x + 6344)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 1260x - 1680x - 560)\|7 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (207x + 145)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +--R (126x + 168x + 56)\|7 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R 2 +-+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (630x + 840x + 280)\|7 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (7137x + 9516x + 3172)\|3 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R (207x + 145)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +--R (126x + 168x + 56)\|7 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +-+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 70\|7 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 793\|3 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 1586\|3 atanh(---------------) + 140\|7 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +-+ +--+ +-+ +--+ +--R ((75x - 245x + 200)\|5 \|7 \|11 + (- 3850x + 1925)\|3 )\|55 +--R + +--R +-+ +-+ +--+ 2 +-+ +--R (3850x - 1925)\|3 \|5 \|11 + (- 4125x + 13475x - 11000)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ 2 +-+ +--+ +--R ((350x - 735x + 280)\|3 \|5 \|11 + (1650x - 3575x + 1375)\|7 )\|55 +--R + +--R 2 +-+ +-+ +--+ 2 +-+ +--R (- 1650x + 3575x - 1375)\|5 \|7 \|11 + (- 19250x + 40425x - 15400)\|3 +--R / +--R 3 2 +-+ +--+ +--R (30x - 47x - 14x + 15)\|7 \|55 +--R + +--R 3 2 +-+ +--R (- 350x + 525x + 161x - 168)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--+ +--R (140x - 56x - 49x + 21)\|3 \|55 +--R + +--R 4 3 2 +-+ +--R (150x - 475x + 306x + 187x - 120)\|7 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=83264/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+1/3*sqrt(1-2*x)/(2+3*x)^3+52/21*_ + sqrt(1-2*x)/(2+3*x)^2+1207/49*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (2248128x + 4496256x + 2997504x + 666112)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 66150x - 132300x - 88200x - 19600)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (10863x + 14848x + 5087)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (1323x + 2646x + 1764x + 392)\|21 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (33075x + 66150x + 44100x + 9800)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (1124064x + 2248128x + 1498752x + 333056) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (10863x + 14848x + 5087)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (1323x + 2646x + 1764x + 392)\|21 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1225\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 41632log(-------------------------------) - 83264atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2450\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (55125x - 143325x + 26950x + 98000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 416320x - 41632x + 124896)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 253470x - 540603x + 206934 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (90525x - 443525x + 724246x - 394160)\|21 +--R + +--R 2 +-+ +--+ +--R (8489250x + 1414875x - 2829750)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 3122400x + 8326400x - 2206496x - 4995840)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 36210x + 137579x - 158277x + 49270)\|21 +--R + +--R 3 2 +-+ +--+ +--R (771750x - 1106175x - 463050x + 411600)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1248960x - 1956704x - 582848x + 624480)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1212750x + 1819125x + 741125x - 673750)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2081600x + 3122400x + 957536x - 999168)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1267350x - 4730775x + 5359494x - 1655472 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (4410x - 3969x - 6664x + 833x + 1470)\|21 \|55 - 154350x +--R + +--R 3 2 +--R 128625x + 225351x - 26754x - 49392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (61740x + 16464x - 38073x - 5145x + 6174)\|55 +--R + +--R 5 4 3 2 +--+ +--R (22050x - 55125x - 1568x + 57477x + 686x - 11760)\|21 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^5*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=11656955/1372*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-250*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/4*sqrt(1-2*x)/(2+3*x)^4+_ + 139/84*sqrt(1-2*x)/(2+3*x)^3+14555/1176*sqrt(1-2*x)/(2+3*x)^2+_ + 337955/2744*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1888426710x + 5035804560x + 5035804560x + 2238135360x + 373022560) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 55566000x - 148176000x - 148176000x - 65856000x - 10976000)\|21 +--R * +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (222264x + 592704x + 592704x + 263424x + 43904)\|21 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--+ +--R (27783000x + 74088000x + 74088000x + 32928000x + 5488000)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (944213355x + 2517902280x + 2517902280x + 1119067680x + 186511280) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (222264x + 592704x + 592704x + 263424x + 43904)\|21 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 343000\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 11656955log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 23313910atanh(---------------) + 686000\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2744\|21 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (15435000x - 40131000x + 7546000x + 27440000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 116569550x - 11656955x + 34970865)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 70970550x - 151368945x + 57941835 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (25346625x - 124186000x + 202788615x - 110365400)\|21 +--R + +--R 2 +-+ +--+ +--R (2376990000x + 396165000x - 792330000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 874271625x + 2331391000x - 617818615x - 1398834600)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 10138650x + 38521885x - 44317630x + 13795675)\|21 +--R + +--R 3 2 +-+ +--+ +--R (216090000x - 309729000x - 129654000x + 115248000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (349708650x - 547876885x - 163197370x + 174854325)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 339570000x + 509355000x + 207515000x - 188650000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 582847750x + 874271625x + 268109965x - 279766920)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 354852750x - 1324609125x + 1500660735x - 463534680 +--R / +--R 4 3 2 +--+ +--+ +--R (246960x - 222264x - 373184x + 46648x + 82320)\|21 \|55 +--R + +--R 4 3 2 +--R - 8643600x + 7203000x + 12619656x - 1498224x - 2765952 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (3457440x + 921984x - 2132088x - 288120x + 345744)\|55 +--R + +--R 5 4 3 2 +--+ +--R (1234800x - 3087000x - 87808x + 3218712x + 38416x - 658560)\|21 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-328/15625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-35128/15625*_ + sqrt(1-2*x)-172/3125*(2+3*x)^2*sqrt(1-2*x)+64/2625*(2+3*x)^3*_ + sqrt(1-2*x)+11/75*(2+3*x)^4*sqrt(1-2*x)-1/5*(2+3*x)^5*_ + sqrt(1-2*x)/(3+5*x)-4/15625*(2216+3625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 11480x - 6888)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072) +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (546875x + 328125)\|55 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (5740x + 3444)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072) +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (546875x + 328125)\|55 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 164log(-----------------------------) + 328atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 15625\|55 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 820x + 1312)\|55 + (820x - 1312)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 328x + 164)\|5 \|11 \|55 + 18040x - 9020 +--R / +--R 2 +--------+ +--R (8593750x + 859375x - 2578125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (781250x - 1171875x - 359375x + 375000)\|55 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=-262/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3018/3125*sqrt(1-2*x)-_ + 3/25*(2+3*x)*sqrt(1-2*x)+12/625*(2+3*x)^2*sqrt(1-2*x)+_ + 27/175*(2+3*x)^3*sqrt(1-2*x)-1/5*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 9170x - 5502)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (109375x + 65625)\|55 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (4585x + 2751)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (109375x + 65625)\|55 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 131log(-----------------------------) + 262atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3125\|55 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 655x + 1048)\|55 + (655x - 1048)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 262x + 131)\|5 \|11 \|55 + 14410x - 7205 +--R / +--R 2 +--------+ +--R (1718750x + 171875x - 515625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (156250x - 234375x - 71875x + 75000)\|55 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-196/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-294/625*sqrt(1-2*x)+_ + 21/125*(2+3*x)^2*sqrt(1-2*x)-1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 980x - 588)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (3125x + 1875)\|55 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (490x + 294)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (3125x + 1875)\|55 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 98log(-----------------------------) + 196atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 625\|55 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 490x + 784)\|55 + (490x - 784)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 196x + 98)\|5 \|11 \|55 + 10780x - 5390 +--R / +--R 2 +--------+ +--R (343750x + 34375x - 103125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (31250x - 46875x - 14375x + 15000)\|55 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-3/25*(1-2*x)^(3/2)-1/275*(1-2*x)^(3/2)/(3+5*x)-_ + 26/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+26/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R (- 130x - 78)atanh(---------------) + (30x + 15x - 2)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (65x + 39)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (30x + 15x - 2)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (125x + 75)\|55 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 13log(-----------------------------) + 26atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 65x + 104)\|55 + (65x - 104)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 26x + 13)\|5 \|11 \|55 + 1430x - 715 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-1/55*(1-2*x)^(3/2)/(3+5*x)-64/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+64/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 320x - 192)atanh(---------------) + (30x + 17)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (160x + 96)log(-----------------------------) + (30x + 17)\|55 \|- 2x + 1 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 32log(-----------------------------) + 64atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 160x + 256)\|55 + (160x - 256)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 64x + 32)\|5 \|11 \|55 + 3520x - 1760 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/5*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (10x + 6)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------- +--R +--+ +--R (25x + 15)\|55 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (5x + 3)log(-------------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) --------------------------------------------------------------- +--R +--+ +--R (25x + 15)\|55 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55 +--R + +--R - 110x + 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2750x + 275x - 825)\|- 2x + 1 + (- 250x + 375x + 115x - 120)\|55 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=-2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)+68*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 +--R (- 10x - 6)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (340x + 204)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +--+ +--R (5x + 3)\|55 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5 +--R (5x + 3)\|21 \|55 log(-------------------------) +--R 3x + 2 +--R + +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (170x + 102)log(-------------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R / +--R +--+ +--R (5x + 3)\|55 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5 +--R \|21 \|55 log(-------------------------) +--R 3x + 2 +--R + +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--R 34log(-------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R 2\|21 \|55 atanh(---------------) - 68atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 204x - 34x + 68)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (75x - 200x + 53x + 120)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 45x + 222x - 365x + 200 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 330x + 715x - 275)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 1530x + 3978x - 748x - 2720)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (11550x + 1155x - 3465)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30x - 113x + 129x - 40)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 612x + 918x + 374x - 340)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1050x + 1575x + 483x - 504)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (1020x - 1462x - 612x + 544)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1650x - 2585x - 770x + 825)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 990x + 3795x - 4400x + 1375 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (150x - 125x - 219x + 26x + 48)\|21 \|55 - 4950x + 4455x +--R + +--R 2 +--R 7480x - 935x - 1650 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (450x - 1125x - 32x + 1173x + 14x - 240)\|55 +--R + +--R 4 3 2 +--+ +--R (3300x + 880x - 2035x - 275x + 330)\|21 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-138*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+134*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-10*sqrt(1-2*x)/(3+5*x)+sqrt(1-2*x)/_ + ((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (- 2070x - 2622x - 828)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (2010x + 2546x + 804)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (- 30x - 19)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (15x + 19x + 6)\|7 \|11 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (1035x + 1311x + 414)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (1005x + 1273x + 402)\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R (- 30x - 19)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (15x + 19x + 6)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 69\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 67\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 138\|3 \|11 atanh(---------------) - 134\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-7209/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1000*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-1045/14*sqrt(1-2*x)/(3+5*x)+_ + 1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+52/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 648810x - 1254366x - 807408x - 173016)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|5 \|- 2x + 1 +--R (630000x + 1218000x + 784000x + 168000)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (630x + 1218x + 784x + 168)\|7 \|11 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (324405x + 627183x + 403704x + 86508)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--R (315000x + 609000x + 392000x + 84000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (630x + 1218x + 784x + 168)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7209\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7000\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 14418\|3 \|11 atanh(---------------) - 14000\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 14\|7 \|11 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-335579/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+6650*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-48645/98*sqrt(1-2*x)/_ + (3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+139/42*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+7261/147*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +--R (- 90606330x - 235576458x - 229536036x - 99331384x - 16107792)\|3 +--R * +--R +-+ +--------+ +--R +--+ \|3 \|- 2x + 1 +--R \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (87979500x + 228746700x + 222881400x + 96451600x + 15640800)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--+ +--R (45303165x + 117788229x + 114768018x + 49665692x + 8053896)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (43989750x + 114373350x + 111440700x + 48225800x + 7820400)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 335579\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 325850\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 671158\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 651700\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 98\|7 \|11 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-12803/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-10017/34375*_ + sqrt(1-2*x)+21/550*(2+3*x)*sqrt(1-2*x)+1428/6875*(2+3*x)^2*_ + sqrt(1-2*x)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-131/550*_ + (2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 640150x - 768180x - 230454)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1718750x + 2062500x + 618750)\|55 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (320075x + 384090x + 115227)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1718750x + 2062500x + 618750)\|55 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 12803log(-----------------------------) + 25606atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 68750\|55 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 64015x + 102424)\|55 + (64015x - 102424)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 25606x + 12803)\|5 \|11 \|55 + 1408330x - 704165 +--R / +--R 2 +--------+ +--R (37812500x + 3781250x - 11343750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3437500x - 5156250x - 1581250x + 1650000)\|55 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-1267/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+623/1375*sqrt(1-2*x)-_ + 7/2750*(46-225*x)*sqrt(1-2*x)-1/10*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 49/275*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 63350x - 76020x - 22806)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (68750x + 82500x + 24750)\|55 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (31675x + 38010x + 11403)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (68750x + 82500x + 24750)\|55 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 1267log(-----------------------------) + 2534atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 2750\|55 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 6335x + 10136)\|55 + (6335x - 10136)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2534x + 1267)\|5 \|11 \|55 + 139370x - 69685 +--R / +--R 2 +--------+ +--R (1512500x + 151250x - 453750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (137500x - 206250x - 63250x + 66000)\|55 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-1/550*(1-2*x)^(3/2)/(3+5*x)^2-133/6050*(1-2*x)^(3/2)/(3+5*x)-_ + 409/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+409/3025*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 20450x - 24540x - 7362)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (1980x + 2245x + 632)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (10225x + 12270x + 3681)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (1980x + 2245x + 632)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 409log(-----------------------------) + 818atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 550\|55 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 2045x + 3272)\|55 + (2045x - 3272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 818x + 409)\|5 \|11 \|55 + 44990x - 22495 +--R / +--R 2 +--------+ +--R (302500x + 30250x - 90750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (27500x - 41250x - 12650x + 13200)\|55 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-1/110*(1-2*x)^(3/2)/(3+5*x)^2+67/275*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-67/550*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (3350x + 4020x + 1206)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 325x - 206)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (1675x + 2010x + 603)log(-------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 325x - 206)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 67log(-------------------------------) - 134atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 550\|55 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (134x - 67)\|5 \|11 \|55 - 7370x + 3685 +--R / +--R 2 +--------+ +--R (302500x + 30250x - 90750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 27500x + 41250x + 12650x - 13200)\|55 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=1/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/10*sqrt(1-2*x)/(3+5*x)^2+_ + 1/110*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (50x + 60x + 18)atanh(---------------) + (5x - 8)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R 2 +--+ +--R (2750x + 3300x + 990)\|55 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (25x + 30x + 9)log(-------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (5x - 8)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2750x + 3300x + 990)\|55 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 110\|55 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55 +--R + +--R - 110x + 55 +--R / +--R 2 +--------+ +--R (60500x + 6050x - 18150)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 5500x + 8250x + 2530x - 2640)\|55 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-2243/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-1/2*sqrt(1-2*x)/(3+5*x)^2+67/22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ +--+ \|3 \|- 2x + 1 +--R (3300x + 3960x + 1188)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 112150x - 134580x - 40374)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (335x + 190)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (550x + 660x + 198)\|55 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (56075x + 67290x + 20187)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R (1650x + 1980x + 594)\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (335x + 190)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (550x + 660x + 198)\|55 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 2243log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 66\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 132\|21 \|55 atanh(---------------) + 4486atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 22\|55 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 13458x - 2243x + 4486)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (4950x - 13200x + 3498x + 7920)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 3015x + 14769x - 24112x + 13120 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 22110x + 47135x - 18040)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 100935x + 262431x - 49346x - 179440)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (762300x + 76230x - 228690)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2010x + 7501x - 8496x + 2624)\|21 +--R + +--R 3 2 +-+ +--+ +--R (40374x - 60561x - 24673x + 22430)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (69300x - 103950x - 31878x + 33264)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 67290x + 96449x + 40374x - 35888)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 108900x + 170610x + 50820x - 54450)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 66330x - 251955x + 289795x - 90200 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (3300x - 2750x - 4818x + 572x + 1056)\|21 \|55 - 108900x +--R + +--R 3 2 +--R 98010x + 164560x - 20570x - 36300 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 9900x + 24750x + 704x - 25806x - 308x + 5280)\|55 +--R + +--R 4 3 2 +--+ +--R (- 72600x - 19360x + 44770x + 6050x - 7260)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=624*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-6665/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-15/2*sqrt(1-2*x)/_ + (3+5*x)^2+sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+995/22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (1029600x + 1921920x + 1194336x + 247104)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 999750x - 1866200x - 1159710x - 239940)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (1650x + 3080x + 1914x + 396)\|7 \|11 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (499875x + 933100x + 579855x + 119970)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (514800x + 960960x + 597168x + 123552)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (1650x + 3080x + 1914x + 396)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 6665\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 6864\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 13728\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 13330\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 22\|7 \|11 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=43467/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-66325/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1045/14*_ + sqrt(1-2*x)/(3+5*x)^2+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 139/14*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+34655/77*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--R (215161650x + 545076180x + 517344234x + 218030472x + 34425864)\|3 +--R * +--R +-+ +--------+ +--R +--+ \|3 \|- 2x + 1 +--R \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--R (- 208923750x - 529273500x - 502345550x - 211709400x - 33427800)\|5 +--R * +--R +-+ +--------+ +--R +-+ \|5 \|- 2x + 1 +--R \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (104461875x + 264636750x + 251172775x + 105854700x + 16713900)\|5 +--R * +--R +-+ +--------+ +--+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--R (107580825x + 272538090x + 258672117x + 109015236x + 17212932)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 464275\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 478137\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 956274\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 928550\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 154\|7 \|11 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=2528082/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 551075/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_ + 182335/294*sqrt(1-2*x)/(3+5*x)^2+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+_ + 29/7*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+4042/49*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^2)+4031135/1078*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 37542017700x + 120134456640x + 153671992452x + 98221041864x +--R + +--R 31368441456x + 4004481888 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 36453611250x - 116651556000x - 149216782050x - 95373448100x +--R + +--R - 30459017400x - 3888385200 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 18226805625x + 58325778000x + 74608391025x + 47686724050x +--R + +--R 15229508700x + 1944192600 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 18771008850x + 60067228320x + 76835996226x + 49110520932x +--R + +--R 15684220728x + 2002240944 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 27002675\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 27808902\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 55617804\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 54005350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1078\|7 \|11 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x +--R + +--R 1664x + 192 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-1294139/640*(1-2*x)^(5/2)+559433/128*(1-2*x)^(7/2)-_ + 564235/128*(1-2*x)^(9/2)+3658095/1408*(1-2*x)^(11/2)-_ + 1580985/1664*(1-2*x)^(13/2)+136647/640*(1-2*x)^(15/2)-_ + 59049/2176*(1-2*x)^(17/2)+3645/2432*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x +--R + +--R 4 3 2 +--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 230945 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x +--R + +--R 4 3 2 +--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 230945 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-184877/320*(1-2*x)^(5/2)+8575/8*(1-2*x)^(7/2)-173215/192*(1-2*x)^(9/2)+_ + 37485/88*(1-2*x)^(11/2)-97335/832*(1-2*x)^(13/2)+_ + 351/20*(1-2*x)^(15/2)-1215/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x +--R + +--R 3 2 +--R 19014940x + 9775332x + 488008x - 3012632 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x +--R + +--R 3 2 +--R 19014940x + 9775332x + 488008x - 3012632 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 810x - 2241x - 2133x - 528x + 392x + 272x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-26411/160*(1-2*x)^(5/2)+8183/32*(1-2*x)^(7/2)-8281/48*(1-2*x)^(9/2)+_ + 10773/176*(1-2*x)^(11/2)-4671/416*(1-2*x)^(13/2)+27/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x +--R + +--R 36368x - 66592 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x +--R + +--R 36368x - 66592 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=-3773/80*(1-2*x)^(5/2)+469/8*(1-2*x)^(7/2)-119/4*(1-2*x)^(9/2)+_ + 621/88*(1-2*x)^(11/2)-135/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 715 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 715 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-539/40*(1-2*x)^(5/2)+101/8*(1-2*x)^(7/2)-103/24*(1-2*x)^(9/2)+_ + 45/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1 +--R (2) ------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1 +--R (3) ------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-77/20*(1-2*x)^(5/2)+17/7*(1-2*x)^(7/2)-5/12*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1 +--R (2) ------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1 +--R (3) ------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x) +--R +--R +--R 2 +--------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-11/10*(1-2*x)^(5/2)+5/14*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (- 100x - 4x + 79x - 26)\|- 2x + 1 +--R (2) ------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 100x - 4x + 79x - 26)\|- 2x + 1 +--R (3) ------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x) +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-2/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(5/2)+14/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)-14/27*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+ +--R 14\|7 atanh(---------------) + (- 36x + 40x - 25)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--------+ +--R (- 36x + 40x - 25)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 27\|3 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=76/189*(1-2*x)^(3/2)+1/21*(1-2*x)^(5/2)/(2+3*x)-76/27*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+76/27*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 228x - 152)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--------+ +--R (- 60x + 212x + 175)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (81x + 54)\|3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (114x + 76)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--------+ +--R (- 60x + 212x + 175)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (81x + 54)\|3 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 38\|7 log(-------------------------------) + 76\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=1/42*(1-2*x)^(5/2)/(2+3*x)^2-71/126*(1-2*x)^(3/2)/(2+3*x)+_ + 71/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-71/63*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (1278x + 1704x + 568)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 235x - 101)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (162x + 216x + 72)\|21 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (639x + 852x + 284)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 235x - 101)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (162x + 216x + 72)\|21 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 71log(-------------------------------) - 142atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 18\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2268x + 378x - 756)\|- 2x + 1 + (- 324x + 486x + 198x - 180)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=1/63*(1-2*x)^(5/2)/(2+3*x)^3-52/189*(1-2*x)^(3/2)/(2+3*x)^2-_ + 104/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+52/189*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2808x - 5616x - 3744x - 832)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (792x + 664x + 107)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (5103x + 10206x + 6804x + 1512)\|21 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (1404x + 2808x + 1872x + 416)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (792x + 664x + 107)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (5103x + 10206x + 6804x + 1512)\|21 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 52log(-----------------------------) + 104atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 189\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 156x + 260)\|21 + (156x - 260)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 104x + 52)\|3 \|7 \|21 + 2184x - 1092 +--R / +--R 2 +--------+ 3 2 +--+ +--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=1/84*(1-2*x)^(5/2)/(2+3*x)^4-137/756*(1-2*x)^(3/2)/(2+3*x)^3-_ + 137/5292*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+137/1512*_ + sqrt(1-2*x)/(2+3*x)^2-137/10584*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (- 22194x - 59184x - 59184x - 26304x - 4384)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (11097x + 29592x + 29592x + 13152x + 2192) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 137log(-----------------------------) + 274atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 10584\|21 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 411x + 685)\|21 + (411x - 685)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 274x + 137)\|3 \|7 \|21 + 5754x - 2877 +--R / +--R 2 +--------+ +--R (1333584x + 222264x - 444528)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (190512x - 285768x - 116424x + 105840)\|21 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=1/105*(1-2*x)^(5/2)/(2+3*x)^5-17/126*(1-2*x)^(3/2)/(2+3*x)^4-_ + 17/6174*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+17/378*_ + sqrt(1-2*x)/(2+3*x)^3-17/5292*sqrt(1-2*x)/(2+3*x)^2-17/12348*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 41310x - 137700x - 183600x - 122400x - 40800x - 5440) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (20655x + 68850x + 91800x + 61200x + 20400x + 2720) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 17log(-----------------------------) + 34atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 12348\|21 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 34x + 17)\|3 \|7 \|21 + 714x - 357 +--R / +--R 2 +--------+ +--R (1555848x + 259308x - 518616)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (222264x - 333396x - 135828x + 123480)\|21 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-290521/320*(1-2*x)^(5/2)+54439/32*(1-2*x)^(7/2)-832951/576*_ + (1-2*x)^(9/2)+121359/176*(1-2*x)^(11/2)-159111/832*(1-2*x)^(13/2)+_ + 927/32*(1-2*x)^(15/2)-2025/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x +--R + +--R 3 2 +--R 90028420x + 44740356x + 1821784x - 13931096 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x +--R + +--R 3 2 +--R 90028420x + 44740356x + 1821784x - 13931096 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=-41503/160*(1-2*x)^(5/2)+13013/32*(1-2*x)^(7/2)-39977/144*(1-2*x)^(9/2)+_ + 17541/176*(1-2*x)^(11/2)-7695/416*(1-2*x)^(13/2)+45/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x +--R + +--R 155842x - 307478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x +--R + +--R 155842x - 307478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=-5929/80*(1-2*x)^(5/2)+187/2*(1-2*x)^(7/2)-3467/72*(1-2*x)^(9/2)+_ + 255/22*(1-2*x)^(11/2)-225/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x +--R + +--R - 117478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x +--R + +--R - 117478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-847/40*(1-2*x)^(5/2)+1133/56*(1-2*x)^(7/2)-505/72*(1-2*x)^(9/2)+_ + 75/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1 +--R (2) ---------------------------------------------------------------------- +--R 3465 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1 +--R (3) ---------------------------------------------------------------------- +--R 3465 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-121/20*(1-2*x)^(5/2)+55/14*(1-2*x)^(7/2)-25/36*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1 +--R (2) ----------------------------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1 +--R (3) ----------------------------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2/81*(1-2*x)^(3/2)-26/63*(1-2*x)^(5/2)-5/21*(1-2*x)^(5/2)*(3+5*x)-_ + 14/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+14/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 98\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 49\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(-------------------------------) + 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-146/567*(1-2*x)^(3/2)-5/9*(1-2*x)^(5/2)-1/63*(1-2*x)^(5/2)/(2+3*x)+_ + 146/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-146/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (438x + 292)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (219x + 146)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 73\|7 log(---------------------------------) - 146\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=2873/3969*(1-2*x)^(3/2)-1/126*(1-2*x)^(5/2)/(2+3*x)^2+_ + 47/294*(1-2*x)^(5/2)/(2+3*x)-2873/81*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+2873/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 51714x - 68952x - 22984)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1458x + 1944x + 648)\|21 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (25857x + 34476x + 11492)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1458x + 1944x + 648)\|21 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2873log(-----------------------------) + 5746atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 162\|21 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 8619x + 14365)\|21 + (8619x - 14365)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 5746x + 2873)\|3 \|7 \|21 + 120666x - 60333 +--R / +--R 2 +--------+ 3 2 +--+ +--R (20412x + 3402x - 6804)\|- 2x + 1 + (2916x - 4374x - 1782x + 1620)\|21 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/189*(1-2*x)^(5/2)/(2+3*x)^3+209/2646*(1-2*x)^(5/2)/(2+3*x)^2-_ + 7559/7938*(1-2*x)^(3/2)/(2+3*x)+7559/567*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-7559/3969*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (408186x + 816372x + 544248x + 120944)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (30618x + 61236x + 40824x + 9072)\|21 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (204093x + 408186x + 272124x + 60472) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (30618x + 61236x + 40824x + 9072)\|21 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 7559log(-------------------------------) - 15118atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 1134\|21 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739 +--R / +--R 2 +--------+ +--R (142884x + 23814x - 47628)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 20412x + 30618x + 12474x - 11340)\|21 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1/252*(1-2*x)^(5/2)/(2+3*x)^4+277/5292*(1-2*x)^(5/2)/(2+3*x)^3-_ + 14423/31752*(1-2*x)^(3/2)/(2+3*x)^2-14423/15876*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+14423/31752*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 2336526x - 6230736x - 6230736x - 2769216x - 461536) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1168263x + 3115368x + 3115368x + 1384608x + 230768) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 14423log(-----------------------------) + 28846atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 31752\|21 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 43269x + 72115)\|21 + (43269x - 72115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 28846x + 14423)\|3 \|7 \|21 + 605766x - 302883 +--R / +--R 2 +--------+ +--R (4000752x + 666792x - 1333584)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (571536x - 857304x - 349272x + 317520)\|21 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-1/315*(1-2*x)^(5/2)/(2+3*x)^5+23/588*(1-2*x)^(5/2)/(2+3*x)^4-_ + 4693/15876*(1-2*x)^(3/2)/(2+3*x)^3-4693/111132*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+4693/31752*sqrt(1-2*x)/(2+3*x)^2-_ + 4693/222264*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 11403990x - 38013300x - 50684400x - 33789600x - 11263200x +--R + +--R - 1501760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x +--R + +--R 35562240 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (5701995x + 19006650x + 25342200x + 16894800x + 5631600x + 750880) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x +--R + +--R 35562240 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4693log(-----------------------------) + 9386atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 222264\|21 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 14079x + 23465)\|21 + (14079x - 23465)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 9386x + 4693)\|3 \|7 \|21 + 197106x - 98553 +--R / +--R 2 +--------+ +--R (28005264x + 4667544x - 9335088)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (4000752x - 6001128x - 2444904x + 2222640)\|21 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-1/378*(1-2*x)^(5/2)/(2+3*x)^6+59/1890*(1-2*x)^(5/2)/(2+3*x)^5-_ + 991/4536*(1-2*x)^(3/2)/(2+3*x)^4-991/222264*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+991/13608*sqrt(1-2*x)/(2+3*x)^3-_ + 991/190512*sqrt(1-2*x)/(2+3*x)^2-991/444528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 7224390x - 28897560x - 48162600x - 42811200x - 21405600x +--R + +--R - 5708160x - 634240 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 3612195x + 14448780x + 24081300x + 21405600x + 10702800x +--R + +--R 2854080x + 317120 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 991log(-----------------------------) + 1982atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2973x + 4955)\|21 + (2973x - 4955)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1982x + 991)\|3 \|7 \|21 + 41622x - 20811 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8001504x - 12002256x - 4889808x + 4445280)\|21 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x +--R + +--R 3888x + 432 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-3195731/640*(1-2*x)^(5/2)+1405173/128*(1-2*x)^(7/2)-_ + 4324397/384*(1-2*x)^(9/2)+9504551/1408*(1-2*x)^(11/2)-_ + 4177401/1664*(1-2*x)^(13/2)+73431/128*(1-2*x)^(15/2)-_ + 161325/2176*(1-2*x)^(17/2)+10125/2432*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 +--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x +--R + +--R 5 4 3 2 +--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x +--R + +--R - 369438704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 692835 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 +--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x +--R + +--R 5 4 3 2 +--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x +--R + +--R - 369438704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 692835 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-456533/320*(1-2*x)^(5/2)+43197/16*(1-2*x)^(7/2)-_ + 444983/192*(1-2*x)^(9/2)+98209/88*(1-2*x)^(11/2)-_ + 260055/832*(1-2*x)^(13/2)+765/16*(1-2*x)^(15/2)-3375/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x +--R + +--R 3 2 +--R 47302655x + 22736811x + 717734x - 7158706 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x +--R + +--R 3 2 +--R 47302655x + 22736811x + 717734x - 7158706 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-65219/160*(1-2*x)^(5/2)+20691/32*(1-2*x)^(7/2)-_ + 21439/48*(1-2*x)^(9/2)+28555/176*(1-2*x)^(11/2)-975/32*(1-2*x)^(13/2)+_ + 75/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x +--R + +--R - 12136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 165 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x +--R + +--R - 12136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 165 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 750x - 1475x - 785x + 153x + 243x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-9317/80*(1-2*x)^(5/2)+8349/56*(1-2*x)^(7/2)-935/12*(1-2*x)^(9/2)+_ + 1675/88*(1-2*x)^(11/2)-375/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x +--R + +--R - 421301 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x +--R + +--R - 421301 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 15015 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-1331/40*(1-2*x)^(5/2)+1815/56*(1-2*x)^(7/2)-275/24*(1-2*x)^(9/2)+_ + 125/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=2/27*(1-2*x)^(3/2)*(3+5*x)^3+14/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-72742/14175*sqrt(1-2*x)-919/4725*(3+5*x)^2*_ + sqrt(1-2*x)+26/315*(3+5*x)^3*sqrt(1-2*x)-1/8505*(14711+17779*x)*_ + sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 98\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 1701\|3 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 49\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 1701\|3 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 243\|3 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)-8/9*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-1832/315*sqrt(1-2*x)+2/63*(4-239*x)*sqrt(1-2*x)+_ + 67/35*(3+5*x)^2*sqrt(1-2*x)-2/7*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 168x - 112)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (189x + 126)\|3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (84x + 56)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (189x + 126)\|3 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 4\|7 log(-------------------------------) + 8\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2+887/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+13*sqrt(1-2*x)-5/54*(67-343*x)*sqrt(1-2*x)-_ + 31/3*(3+5*x)^2*sqrt(1-2*x)+6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (15966x + 21288x + 7096)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 2 +--+ +--------+ +--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (486x + 648x + 216)\|21 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (7983x + 10644x + 3548)log(-------------------------------) +--R 3x + 2 +--R + +--R 4 2 +--+ +--------+ +--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (486x + 648x + 216)\|21 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 887log(-------------------------------) - 1774atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 54\|21 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2661x + 4435)\|21 + (2661x - 4435)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1774x - 887)\|3 \|7 \|21 - 37254x + 18627 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6804x + 1134x - 2268)\|- 2x + 1 + (- 972x + 1458x + 594x - 540)\|21 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3-36038/567*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-830/27*sqrt(1-2*x)+5/567*(1163-7265*x)*_ + sqrt(1-2*x)+251/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)+2*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 973026x - 1946052x - 1297368x - 288304)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (15309x + 30618x + 20412x + 4536)\|21 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (486513x + 973026x + 648684x + 144152) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (15309x + 30618x + 20412x + 4536)\|21 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 18019log(-----------------------------) + 36038atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 567\|21 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 54057x + 90095)\|21 + (54057x - 90095)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 36038x + 18019)\|3 \|7 \|21 + 756798x - 378399 +--R / +--R 2 +--------+ +--R (71442x + 11907x - 23814)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (10206x - 15309x - 6237x + 5670)\|21 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4+13243/588*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-5305/588*sqrt(1-2*x)+337/392*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)+13/56*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+_ + (3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 4 3 2 +--R (2145366x + 5720976x + 5720976x + 2542656x + 423776) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1072683x + 2860488x + 2860488x + 1271328x + 211888) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 13243log(-------------------------------) - 26486atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 39729x + 66215)\|21 + (39729x - 66215)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (26486x - 13243)\|3 \|7 \|21 - 556206x + 278103 +--R / +--R 2 +--------+ +--R (148176x + 24696x - 49392)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 21168x + 31752x + 12936x - 11760)\|21 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5-13892/9261*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+1/1323*(136-19*x)*sqrt(1-2*x)/(2+3*x)^2-_ + 3335/3087*sqrt(1-2*x)/(2+3*x)-67/315*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3+_ + 3/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 16878780x - 56262600x - 75016800x - 50011200x - 16670400x +--R + +--R - 2222720 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (8439390x + 28131300x + 37508400x + 25005600x + 8335200x + 1111360) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 6946log(-----------------------------) + 13892atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 9261\|21 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 20838x + 34730)\|21 + (20838x - 34730)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 13892x + 6946)\|3 \|7 \|21 + 291732x - 145866 +--R / +--R 2 +--------+ +--R (1166886x + 194481x - 388962)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (166698x - 250047x - 101871x + 92610)\|21 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6-15313/222264*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/158760*(9323-8405*x)*_ + sqrt(1-2*x)/(2+3*x)^3-43207/63504*sqrt(1-2*x)/(2+3*x)^2-_ + 15313/444528*sqrt(1-2*x)/(2+3*x)-653/2520*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^4+2/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 111631770x - 446527080x - 744211800x - 661521600x - 330760800x +--R + +--R - 88202880x - 9800320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x +--R + +--R - 1660816 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 55815885x + 223263540x + 372105900x + 330760800x + 165380400x +--R + +--R 44101440x + 4900160 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x +--R + +--R - 1660816 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 15313log(-----------------------------) + 30626atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 45939x + 76565)\|21 + (45939x - 76565)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 30626x + 15313)\|3 \|7 \|21 + 643146x - 321573 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8001504x - 12002256x - 4889808x + 4445280)\|21 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7-4369/605052*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/61740*(2201-2675*x)*_ + sqrt(1-2*x)/(2+3*x)^4-5471/13230*sqrt(1-2*x)/(2+3*x)^3-_ + 4369/518616*sqrt(1-2*x)/(2+3*x)^2-4369/1210104*sqrt(1-2*x)/_ + (2+3*x)-173/735*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5+2/7*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 95550030x - 445900140x - 891800280x - 990889200x - 660592800x +--R + +--R 2 +--R - 264237120x - 58719360x - 5592320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x +--R + +--R - 606784x - 7033976 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 13232487240x + 61751607120x + 123503214240x + 137225793600x +--R + +--R 3 2 +--R 91483862400x + 36593544960x + 8131898880x + 774466560 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 47775015x + 222950070x + 445900140x + 495444600x + 330296400x +--R + +--R 2 +--R 132118560x + 29359680x + 2796160 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x +--R + +--R - 606784x - 7033976 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 13232487240x + 61751607120x + 123503214240x + 137225793600x +--R + +--R 3 2 +--R 91483862400x + 36593544960x + 8131898880x + 774466560 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4369log(-----------------------------) + 8738atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 1210104\|21 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13107x + 21845)\|21 + (13107x - 21845)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 8738x + 4369)\|3 \|7 \|21 + 183498x - 91749 +--R / +--R 2 +--------+ +--R (152473104x + 25412184x - 50824368)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (21781872x - 32672808x - 13311144x + 12101040)\|21 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^6/(3+5*x) +--R +--R +--R 7 6 5 4 2 +--------+ +--R (- 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^6-22/390625*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-16097737918/1508203125*sqrt(1-2*x)-18395813/12065625*(2+3*x)*_ + sqrt(1-2*x)-32816296/100546875*(2+3*x)^2*sqrt(1-2*x)-_ + 6469823/84459375*(2+3*x)^3*sqrt(1-2*x)-36202/2413125*(2+3*x)^4*_ + sqrt(1-2*x)+683/53625*(2+3*x)^5*sqrt(1-2*x)+2/195*(2+3*x)^6*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 66066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x +--R + +--R 3 2 +--R 61883481375x + 56176961670x + 9645684935x - 15379193944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 1173046875\|5 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33033\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 7 6 5 4 +--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x +--R + +--R 3 2 +--R 61883481375x + 56176961670x + 9645684935x - 15379193944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 1173046875\|5 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 390625\|5 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^5-22/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-158985118/33515625*sqrt(1-2*x)-2803796/20109375*(2+3*x)^2*_ + sqrt(1-2*x)-467323/16891875*(2+3*x)^3*sqrt(1-2*x)+_ + 6673/482625*(2+3*x)^4*sqrt(1-2*x)+158/10725*(2+3*x)^5*sqrt(1-2*x)-_ + 1/100546875*(119316702+198601625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 66066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x +--R + +--R 2 +--R 4276774170x + 1321809935x - 1180568944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33033\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x +--R + +--R 2 +--R 4276774170x + 1321809935x - 1180568944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^4-22/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-10083686/4640625*sqrt(1-2*x)-11401/37125*(2+3*x)*_ + sqrt(1-2*x)-17792/309375*(2+3*x)^2*sqrt(1-2*x)+3629/259875*(2+3*x)^3*_ + sqrt(1-2*x)+166/7425*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x +--R + +--R - 7095688 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x +--R + +--R - 7095688 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^3-22/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-10826/9375*sqrt(1-2*x)+53/5625*(2+3*x)^2*sqrt(1-2*x)+_ + 58/1575*(2+3*x)^3*sqrt(1-2*x)-1/28125*(8664+12625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 462\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 231\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=2/375*(1-2*x)^(3/2)-18/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(5/2)*(2+3*x)-_ + 22/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 462\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 231\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=2/75*(1-2*x)^(3/2)-3/25*(1-2*x)^(5/2)-22/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+22/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 66\|11 atanh(---------------) + (- 180x + 160x + 31)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +--R 375\|5 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 180x + 160x + 31)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 375\|5 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2/15*(1-2*x)^(3/2)-22/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 22/25*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 66\|11 atanh(---------------) + (- 20x + 76)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------- +--R +-+ +--R 75\|5 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R 33\|11 log(--------------------------------) + (- 20x + 76)\|5 \|- 2x + 1 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +-+ +--R 75\|5 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-22/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+14/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)-4/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 70\|5 \|7 atanh(---------------) - 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R + +--R +-+ +-+ +--------+ +--R - 4\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +-+ +--------+ +--R 35\|5 \|7 log(---------------------------------) - 4\|3 \|5 \|- 2x + 1 +--R 3x + 2 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 35\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 70\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x)/(6+9*x),(1-2*x)^(3/2)/(2+3*x)-_ + 22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+2/3*sqrt(1-2*x) +--R +--R +--R (2) +--R [ +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (192x + 128)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R , +--R +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (192x + 128)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (99x + 66)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (96x + 64)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R 7\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 32\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 64\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 3\|3 \|5 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=1/2*(1-2*x)^(3/2)/(2+3*x)^2+2243/3*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+67/6*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (40374x + 53832x + 17944)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 1188x - 1584x - 528)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (195x + 137)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (54x + 72x + 24)\|21 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R 2 +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (594x + 792x + 264)\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (20187x + 26916x + 8972)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (195x + 137)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (54x + 72x + 24)\|21 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 66\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2243log(-------------------------------) - 4486atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 132\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 6\|21 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (2970x - 7722x + 1452x + 5280)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 22430x - 2243x + 6729)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 13650x - 29127x + 11151 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4 3 2 +--+ +--R (2700x - 6750x - 192x + 7038x + 84x - 1440)\|21 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=1/3*(1-2*x)^(3/2)/(2+3*x)^3+78506/21*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-110*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+17/3*_ + sqrt(1-2*x)/(2+3*x)^2+1138/21*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (2119662x + 4239324x + 2826216x + 628048)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 62370x - 124740x - 83160x - 18480)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (10242x + 13999x + 4797)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (567x + 1134x + 756x + 168)\|21 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (31185x + 62370x + 41580x + 9240)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (1059831x + 2119662x + 1413108x + 314024) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (10242x + 13999x + 4797)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (567x + 1134x + 756x + 168)\|21 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1155\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39253log(-------------------------------) - 78506atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2310\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (51975x - 135135x + 25410x + 92400)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 392530x - 39253x + 117759)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 238980x - 509712x + 195111 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (85350x - 418175x + 682859x - 371640)\|21 +--R + +--R 2 +-+ +--+ +--R (8004150x + 1334025x - 2668050)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2943975x + 7850600x - 2080409x - 4710360)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 34140x + 129716x - 149233x + 46455)\|21 +--R + +--R 3 2 +-+ +--+ +--R (727650x - 1042965x - 436590x + 388080)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1177590x - 1844891x - 549542x + 588795)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1143450x + 1715175x + 698775x - 635250)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1962650x + 2943975x + 902819x - 942072)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1194900x - 4460400x + 5053251x - 1560888 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (1890x - 1701x - 2856x + 357x + 630)\|21 \|55 - 66150x + 55125x +--R + +--R 2 +--R 96579x - 11466x - 21168 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (26460x + 7056x - 16317x - 2205x + 2646)\|55 +--R + +--R 5 4 3 2 +--+ +--R (9450x - 23625x - 672x + 24633x + 294x - 5040)\|21 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 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* +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (890258283x + 2374022088x + 2374022088x + 1055120928x + 175853488) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (8603361x + 17494905x + 11868230x + 2686470)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 323400\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 10990843log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 21981686atanh(---------------) + 646800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (14553000x - 37837800x + 7114800x + 25872000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 109908430x - 10990843x + 32972529)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 66915030x - 142719297x + 54630891 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (23898225x - 117089600x + 191200679x - 104058840)\|21 +--R + +--R 2 +-+ +--+ +--R (2241162000x + 373527000x - 747054000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 824313225x + 2198168600x - 582514679x - 1318901160)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 9559290x + 36320621x - 41785198x + 13007355)\|21 +--R + +--R 3 2 +-+ +--+ +--R (203742000x - 292030200x - 122245200x + 108662400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (329725290x - 516569621x - 153871802x + 164862645)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 320166000x + 480249000x + 195657000x - 177870000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 549542150x + 824313225x + 252789389x - 263780232)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 334575150x - 1248916725x + 1414908831x - 437047128 +--R / +--R 4 3 2 +--+ +--+ +--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55 +--R + +--R 4 3 2 +--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (1481760x + 395136x - 913752x - 123480x + 148176)\|55 +--R + +--R 5 4 3 2 +--+ +--R (529200x - 1323000x - 37632x + 1379448x + 16464x - 282240)\|21 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^6*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Expression(Integer) +--E 471 + 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Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3438146250x + 11460487500x + 15280650000x + 10187100000x +--R + +--R 3395700000x + 452760000 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 116846400555x + 389488001850x + 519317335800x + 346211557200x +--R + +--R 115403852400x + 15387180320 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1129191435x + 3049001415x + 3088510878x + 1391064622x + 235067382) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (2500470x + 8334900x + 11113200x + 7408800x + 2469600x + 329280)\|21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 2829750\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 96169877log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 192339754atanh(---------------) + 5659500\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (127338750x - 331080750x + 62254500x + 226380000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 961698770x - 96169877x + 288509631)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 585506670x - 1248793833x + 478020249 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (209109525x - 1024534150x + 1673005981x - 910514760)\|21 +--R + +--R 2 +-+ +--+ +--R (19610167500x + 3268361250x - 6536722500)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 7212740775x + 19233975400x - 5097003481x - 11540385240)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 83643810x + 317805469x - 365620472x + 113814345)\|21 +--R + +--R 3 2 +-+ +--+ +--R (1782742500x - 2555264250x - 1069645500x + 950796000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (2885096310x - 4519984219x - 1346378278x + 1442548155)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 2801452500x + 4202178750x + 1711998750x - 1556362500)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4808493850x + 7212740775x + 2211907171x - 2308077048)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 2927533350x - 10928022525x + 12380451909x - 3824161992 +--R / +--R 4 3 2 +--+ +--+ +--R (185220x - 166698x - 279888x + 34986x + 61740)\|21 \|55 +--R + +--R 4 3 2 +--R - 6482700x + 5402250x + 9464742x - 1123668x - 2074464 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (2593080x + 691488x - 1599066x - 216090x + 259308)\|55 +--R + +--R 5 4 3 2 +--+ +--R (926100x - 2315250x - 65856x + 2414034x + 28812x - 493920)\|21 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)-324/78125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-1270604/859375*sqrt(1-2*x)-9388/515625*_ + (2+3*x)^2*sqrt(1-2*x)+33406/433125*(2+3*x)^3*sqrt(1-2*x)+_ + 4019/12375*(2+3*x)^4*sqrt(1-2*x)-26/275*(2+3*x)^5*sqrt(1-2*x)-_ + 2/2578125*(491178+769625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 124740x - 74844)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x +--R + +--R 2532130x - 23061496 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (30078125x + 18046875)\|5 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (62370x + 37422)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x +--R + +--R 2532130x - 23061496 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (30078125x + 18046875)\|5 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 162\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 324\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)-258/15625*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-110938/140625*sqrt(1-2*x)-83/1125*(2+3*x)*_ + sqrt(1-2*x)+764/9375*(2+3*x)^2*sqrt(1-2*x)+2707/7875*(2+3*x)^3*_ + sqrt(1-2*x)-22/225*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 9030x - 5418)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (546875x + 328125)\|5 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (4515x + 2709)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (546875x + 328125)\|5 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 129\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 258\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)-192/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-1418/3125*sqrt(1-2*x)+2/25*(2+3*x)*_ + sqrt(1-2*x)+237/625*(2+3*x)^2*sqrt(1-2*x)-18/175*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 6720x - 4032)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (109375x + 65625)\|5 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (3360x + 2016)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (109375x + 65625)\|5 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 96\|11 log(--------------------------------) + 192\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=42/1375*(1-2*x)^(3/2)-9/125*(1-2*x)^(5/2)-1/275*(1-2*x)^(5/2)/(3+5*x)-_ + 126/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+126/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 630x - 378)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (3125x + 1875)\|5 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (315x + 189)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (3125x + 1875)\|5 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 63\|11 log(--------------------------------) + 126\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=4/55*(1-2*x)^(3/2)-1/55*(1-2*x)^(5/2)/(3+5*x)-12/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+12/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R (- 60x - 36)\|11 atanh(---------------) + (- 20x + 60x + 41)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R (125x + 75)\|5 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (30x + 18)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 20x + 60x + 41)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (125x + 75)\|5 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 6\|11 log(--------------------------------) + 12\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/axiom-website/CATS/rich3j.input.pdf b/src/axiom-website/CATS/rich3j.input.pdf new file mode 100644 index 0000000..adf65d6 Binary files /dev/null and b/src/axiom-website/CATS/rich3j.input.pdf differ diff --git a/src/axiom-website/CATS/rich3k.input.pamphlet b/src/axiom-website/CATS/rich3k.input.pamphlet new file mode 100644 index 0000000..5349e5c --- /dev/null +++ b/src/axiom-website/CATS/rich3k.input.pamphlet @@ -0,0 +1,9833 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3k.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 61 matching answers. +\item 39 results where Axiom differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3k.output +)spool rich3k.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^2 +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-1/5*(1-2*x)^(3/2)/(3+5*x)+6/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-6/25*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R (30x + 18)\|11 atanh(---------------) + (- 20x - 23)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +-+ +--R (125x + 75)\|5 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (15x + 9)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R (- 20x - 23)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (125x + 75)\|5 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 3\|11 log(----------------------------------) - 6\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-(1-2*x)^(3/2)/(3+5*x)+72/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)_ + -14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2/5*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (- 350x - 210)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (360x + 216)\|3 \|11 atanh(---------------) - 11\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (25x + 15)\|3 \|5 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (175x + 105)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (180x + 108)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R - 11\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (25x + 15)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 35\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 36\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 70\|5 \|7 atanh(---------------) - 72\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 5\|3 \|5 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x))+138*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-134*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 2010x - 2546x - 804)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (2070x + 2622x + 828)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (- 68x - 43)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (15x + 19x + 6)\|3 \|5 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (1005x + 1273x + 402)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1035x + 1311x + 414)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (- 68x - 43)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (15x + 19x + 6)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 67\|5 \|7 log(-------------------------------) +--R 3x + 2 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+--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ \|3 \|- 2x + 1 +--R (- 207990x - 402114x - 258832x - 55464)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +--+ \|5 \|- 2x + 1 +--R (18360x + 35496x + 22848x + 4896)\|7 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +--R (90x + 174x + 112x + 24)\|7 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (103995x + 201057x + 129416x + 27732)\|3 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (9180x + 17748x + 11424x + 2448)\|7 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +--R (90x + 174x + 112x + 24)\|7 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2311\|3 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +-+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 204\|7 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 4622\|3 atanh(---------------) - 408\|7 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 2\|7 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +-+ +--+ +-+ +--+ +--R ((1530x - 4998x + 4080)\|5 \|7 \|11 + (- 78540x + 39270)\|3 )\|55 +--R + +--R +-+ +-+ +--+ 2 +-+ +--R (78540x - 39270)\|3 \|5 \|11 + (- 84150x + 274890x - 224400)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ +--R (- 7140x + 14994x - 5712)\|3 \|5 \|11 +--R + +--R 2 +-+ 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3231900x + 1398600x + 226800)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 418995x - 824092x - 539819x - 117752)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1890x + 4914x + 4788x + 2072x + 336)\|21 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 321161log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 9450\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 642322atanh(---------------) - 18900\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 14\|21 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (425250x - 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5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 666792000x + 2178187200x + 2844979200x + 1857139200x + 605875200x +--R + +--R 79027200 +--R * +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (- 218994705x - 576721848x - 569295605x - 249642200x - 41029970) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (158760x + 518616x + 677376x + 442176x + 144256x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 55953383log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 1646400\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 111906766atanh(---------------) - 3292800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 392\|21 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (74088000x - 192628800x + 36220800x + 131712000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 559533830x - 55953383x + 167860149)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 340658430x - 726570957x + 278120871 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (121663725x - 596092600x + 973385299x - 529754040)\|21 +--R + +--R 2 +-+ +--+ +--R (11409552000x + 1901592000x - 3803184000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4196503725x + 11190676600x - 2965529299x - 6714405960)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (48665490x - 184905001x + 212724638x - 66219255)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 1037232000x + 1486699200x + 622339200x - 553190400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1678601490x + 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+--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2-12279/15625*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+2571/15625*sqrt(1-2*x)-3/31250*(1618-4125*x)*_ + sqrt(1-2*x)+1404/3125*(2+3*x)^2*sqrt(1-2*x)+2643/1750*(2+3*x)^3*_ + sqrt(1-2*x)-129/50*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 4297650x - 5157180x - 1547154)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--+ +--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (5468750x + 6562500x + 1968750)\|55 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (2148825x + 2578590x + 773577)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--+ +--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (5468750x + 6562500x + 1968750)\|55 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 12279log(-----------------------------) + 24558atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 31250\|55 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 61395x + 98232)\|55 + (61395x - 98232)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 24558x + 12279)\|5 \|11 \|55 + 1350690x - 675345 +--R / +--R 2 +--------+ +--R (17187500x + 1718750x - 5156250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1562500x - 2343750x - 718750x + 750000)\|55 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2-5943/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+273/3125*sqrt(1-2*x)+21/50*(2+3*x)*_ + sqrt(1-2*x)+693/625*(2+3*x)^2*sqrt(1-2*x)-48/25*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 297150x - 356580x - 106974)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (156250x + 187500x + 56250)\|55 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (148575x + 178290x + 53487)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (156250x + 187500x + 56250)\|55 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 5943log(-----------------------------) + 11886atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 6250\|55 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 29715x + 47544)\|55 + (29715x - 47544)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 11886x + 5943)\|5 \|11 \|55 + 653730x - 326865 +--R / +--R 2 +--------+ +--R (3437500x + 343750x - 1031250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (312500x - 468750x - 143750x + 150000)\|55 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=119/3025*(1-2*x)^(3/2)-1/550*(1-2*x)^(5/2)/(3+5*x)^2-131/6050*_ + (1-2*x)^(5/2)/(3+5*x)-357/125*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+357/1375*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 17850x - 21420x - 6426)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6250x + 7500x + 2250)\|55 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (8925x + 10710x + 3213)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6250x + 7500x + 2250)\|55 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 357log(-----------------------------) + 714atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 250\|55 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1785x + 2856)\|55 + (1785x - 2856)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 714x + 357)\|5 \|11 \|55 + 39270x - 19635 +--R / +--R 2 +--------+ +--R (137500x + 13750x - 41250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (12500x - 18750x - 5750x + 6000)\|55 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-1/110*(1-2*x)^(5/2)/(3+5*x)^2-13/110*(1-2*x)^(3/2)/(3+5*x)+_ + 39/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-39/275*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (1950x + 2340x + 702)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 205x - 82)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (975x + 1170x + 351)log(-------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 205x - 82)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 39log(-------------------------------) - 78atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 50\|55 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 195x + 312)\|55 + (195x - 312)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (78x - 39)\|5 \|11 \|55 - 4290x + 2145 +--R / +--R 2 +--------+ +--R (27500x + 2750x - 8250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2500x + 3750x + 1150x - 1200)\|55 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^3 +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-1/10*(1-2*x)^(3/2)/(3+5*x)^2-3/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+3/50*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (- 150x - 180x - 54)atanh(---------------) + (25x + 4)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (75x + 90x + 27)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (25x + 4)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 3log(-----------------------------) + 6atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 50\|55 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165 +--R / +--R 2 +--------+ 3 2 +--+ +--R (27500x + 2750x - 8250)\|- 2x + 1 + (2500x - 3750x - 1150x + 1200)\|55 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-1/2*(1-2*x)^(3/2)/(3+5*x)^2+14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-_ + 2379/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+69/10*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ +--+ \|3 \|- 2x + 1 +--R (3500x + 4200x + 1260)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 118950x - 142740x - 42822)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (355x + 202)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (250x + 300x + 90)\|55 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (59475x + 71370x + 21411)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R (1750x + 2100x + 630)\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (355x + 202)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (250x + 300x + 90)\|55 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 2379log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 70\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 140\|21 \|55 atanh(---------------) + 4758atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 10\|55 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 14274x - 2379x + 4758)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (5250x - 14000x + 3710x + 8400)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 3195x + 15657x - 25572x + 13920 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 23430x + 49995x - 19140)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 107055x + 278343x - 52338x - 190320)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (808500x + 80850x - 242550)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2130x + 7953x - 9012x + 2784)\|21 +--R + +--R 3 2 +-+ +--+ +--R (42822x - 64233x - 26169x + 23790)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (73500x - 110250x - 33810x + 35280)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 71370x + 102297x + 42822x - 38064)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 115500x + 180950x + 53900x - 57750)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 70290x - 267135x + 307395x - 95700 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (1500x - 1250x - 2190x + 260x + 480)\|21 \|55 - 49500x + 44550x +--R + +--R 2 +--R 74800x - 9350x - 16500 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 4500x + 11250x + 320x - 11730x - 140x + 2400)\|55 +--R + +--R 4 3 2 +--+ +--R (- 33000x - 8800x + 20350x + 2750x - 3300)\|21 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2)+204*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(21)-6933*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 33/2*sqrt(1-2*x)/(3+5*x)^2+207/2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|3 \|- 2x + 1 +--R (30600x + 57120x + 35496x + 7344)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 \|5 \|- 2x + 1 +--R (- 1039950x - 1941240x - 1206342x - 249588)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (3105x + 3830x + 1178)\|55 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (150x + 280x + 174x + 36)\|55 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (519975x + 970620x + 603171x + 124794) +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--+ +--R (15300x + 28560x + 17748x + 3672)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|21 \|- 2x + 1 + 3x - 5 +--R log(---------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (3105x + 3830x + 1178)\|55 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (150x + 280x + 174x + 36)\|55 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 6933log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 204\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 408\|21 \|55 atanh(---------------) + 13866atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2\|55 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 41598x - 6933x + 13866)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (15300x - 40800x + 10812x + 24480)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 9315x + 45639x - 74526x + 40560 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 68310x + 145695x - 55770)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 311985x + 811161x - 152526x - 554640)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (2356200x + 235620x - 706860)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 6210x + 23181x - 26262x + 8112)\|21 +--R + +--R 3 2 +-+ +--+ +--R (124794x - 187191x - 76263x + 69330)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (214200x - 321300x - 98532x + 102816)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 207990x + 298119x + 124794x - 110928)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 336600x + 527340x + 157080x - 168300)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 204930x - 778635x + 895785x - 278850 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (300x - 250x - 438x + 52x + 96)\|21 \|55 - 9900x + 8910x +--R + +--R 2 +--R 14960x - 1870x - 3300 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 900x + 2250x + 64x - 2346x - 28x + 480)\|55 +--R + +--R 4 3 2 +--+ +--R (- 6600x - 1760x + 4070x + 550x - 660)\|21 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2)+14073*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-13665*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)-1015/6*sqrt(1-2*x)/(3+5*x)^2+137/6*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^2)+1020*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (6332850x + 16043220x + 15226986x + 6417288x + 1013256)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (- 6149250x - 15578100x - 14785530x - 6231240x - 983880)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (3074625x + 7789050x + 7392765x + 3115620x + 491940)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 13665\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 14073\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 28146\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 27330\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 2\|7 \|11 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2)+813716/7*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-112875*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)-176065/126*sqrt(1-2*x)/(3+5*x)^2+86/9*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+1301/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 117955/14*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1098516600x + 3515253120x + 4496594616x + 2874044912x +--R + +--R 917871648x + 117175104 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 1066668750x - 3413340000x - 4366230750x - 2790721500x +--R + +--R - 891261000x - 113778000 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 533334375x + 1706670000x + 2183115375x + 1395360750x + 445630500x +--R + +--R 56889000 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 549258300x + 1757626560x + 2248297308x + 1437022456x + 458935824x +--R + +--R 58587552 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 790125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 813716\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1627432\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1580250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 14\|7 \|11 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x +--R + +--R 2 +--R 1936x + 1280x + 192 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-184877/128*(1-2*x)^(7/2)+3916031/1152*(1-2*x)^(9/2)-_ + 5078115/1408*(1-2*x)^(11/2)+3658095/1664*(1-2*x)^(13/2)-_ + 105399/128*(1-2*x)^(15/2)+409941/2176*(1-2*x)^(17/2)-_ + 59049/2432*(1-2*x)^(19/2)+1215/896*(1-2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 +--R 4040613720x + 15971057388x + 23013359226x + 10299128697x +--R + +--R 6 5 4 3 +--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x +--R + +--R 2 +--R 1656222432x + 235056064x - 323646080 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2909907 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 +--R 4040613720x + 15971057388x + 23013359226x + 10299128697x +--R + +--R 6 5 4 3 +--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x +--R + +--R 2 +--R 1656222432x + 235056064x - 323646080 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2909907 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-26411/64*(1-2*x)^(7/2)+60025/72*(1-2*x)^(9/2)-519645/704*(1-2*x)^(11/2)+_ + 37485/104*(1-2*x)^(13/2)-6489/64*(1-2*x)^(15/2)+1053/68*(1-2*x)^(17/2)-_ + 1215/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x +--R + +--R 4 3 2 +--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 415701 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x +--R + +--R 4 3 2 +--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 415701 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-3773/32*(1-2*x)^(7/2)+57281/288*(1-2*x)^(9/2)-24843/176*(1-2*x)^(11/2)+_ + 10773/208*(1-2*x)^(13/2)-1557/160*(1-2*x)^(15/2)+405/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x +--R + +--R 3 2 +--R - 2705920x + 9403464x + 3351776x - 1899184 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x +--R + +--R 3 2 +--R - 2705920x + 9403464x + 3351776x - 1899184 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-539/16*(1-2*x)^(7/2)+3283/72*(1-2*x)^(9/2)-1071/44*(1-2*x)^(11/2)+_ + 621/104*(1-2*x)^(13/2)-9/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x +--R + +--R - 9038 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x +--R + +--R - 9038 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=-77/8*(1-2*x)^(7/2)+707/72*(1-2*x)^(9/2)-309/88*(1-2*x)^(11/2)+_ + 45/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1 +--R --------------------------------------------------------------------------- +--R 1287 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1 +--R --------------------------------------------------------------------------- +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=-11/4*(1-2*x)^(7/2)+17/9*(1-2*x)^(9/2)-15/44*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1 +--R (2) --------------------------------------------------------- +--R 99 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1 +--R (3) --------------------------------------------------------- +--R 99 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=-11/14*(1-2*x)^(7/2)+5/18*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1 +--R (2) ---------------------------------------------- +--R 63 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1 +--R (3) ---------------------------------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=-14/81*(1-2*x)^(3/2)-2/45*(1-2*x)^(5/2)-5/21*(1-2*x)^(7/2)+_ + 98/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-98/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 3430\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1715\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 2835\|3 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=80/81*(1-2*x)^(3/2)+16/63*(1-2*x)^(5/2)+1/21*(1-2*x)^(7/2)/(2+3*x)-_ + 560/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+560/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 1680x - 1120)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (840x + 560)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 280\|7 log(-------------------------------) + 560\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-365/567*(1-2*x)^(3/2)+1/42*(1-2*x)^(7/2)/(2+3*x)^2-_ + 73/126*(1-2*x)^(5/2)/(2+3*x)+365/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-365/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (6570x + 8760x + 2920)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (3285x + 4380x + 1460)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 365\|7 log(---------------------------------) - 730\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=1/63*(1-2*x)^(7/2)/(2+3*x)^3-53/189*(1-2*x)^(5/2)/(2+3*x)^2+_ + 265/567*(1-2*x)^(3/2)/(2+3*x)-530/81*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+530/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 14310x - 28620x - 19080x - 4240)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (2187x + 4374x + 2916x + 648)\|21 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (7155x + 14310x + 9540x + 2120)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (2187x + 4374x + 2916x + 648)\|21 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 265log(-----------------------------) + 530atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 81\|21 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 795x + 1325)\|21 + (795x - 1325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 530x + 265)\|3 \|7 \|21 + 11130x - 5565 +--R / +--R 2 +--------+ 3 2 +--+ +--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=1/84*(1-2*x)^(7/2)/(2+3*x)^4-139/756*(1-2*x)^(5/2)/(2+3*x)^3+_ + 695/4536*(1-2*x)^(3/2)/(2+3*x)^2+695/2268*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-695/4536*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (112590x + 300240x + 300240x + 133440x + 22240)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (56295x + 150120x + 150120x + 66720x + 11120) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 695log(-------------------------------) - 1390atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 4536\|21 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2085x + 3475)\|21 + (2085x - 3475)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1390x - 695)\|3 \|7 \|21 - 29190x + 14595 +--R / +--R 2 +--------+ +--R (571536x + 95256x - 190512)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 81648x + 122472x + 49896x - 45360)\|21 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=1/105*(1-2*x)^(7/2)/(2+3*x)^5-43/315*(1-2*x)^(5/2)/(2+3*x)^4+_ + 43/567*(1-2*x)^(3/2)/(2+3*x)^3+43/3969*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-43/1134*sqrt(1-2*x)/(2+3*x)^2+43/7938*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (104490x + 348300x + 464400x + 309600x + 103200x + 13760) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (52245x + 174150x + 232200x + 154800x + 51600x + 6880) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 43log(-------------------------------) - 86atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 7938\|21 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 129x + 215)\|21 + (129x - 215)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (86x - 43)\|3 \|7 \|21 - 1806x + 903 +--R / +--R 2 +--------+ +--R (1000188x + 166698x - 333396)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 142884x + 214326x + 87318x - 79380)\|21 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=1/126*(1-2*x)^(7/2)/(2+3*x)^6-41/378*(1-2*x)^(5/2)/(2+3*x)^5+_ + 205/4536*(1-2*x)^(3/2)/(2+3*x)^4+205/222264*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-205/13608*sqrt(1-2*x)/(2+3*x)^3+_ + 205/190512*sqrt(1-2*x)/(2+3*x)^2+205/444528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 298890x + 1195560x + 1992600x + 1771200x + 885600x + 236160x +--R + +--R 26240 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x +--R + +--R 256048128x + 28449792 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 149445x + 597780x + 996300x + 885600x + 442800x + 118080x +--R + +--R 13120 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x +--R + +--R 256048128x + 28449792 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 205log(-------------------------------) - 410atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 615x + 1025)\|21 + (615x - 1025)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (410x - 205)\|3 \|7 \|21 - 8610x + 4305 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 8001504x + 12002256x + 4889808x - 4445280)\|21 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-41503/64*(1-2*x)^(7/2)+381073/288*(1-2*x)^(9/2)-_ + 832951/704*(1-2*x)^(11/2)+121359/208*(1-2*x)^(13/2)-_ + 53037/320*(1-2*x)^(15/2)+13905/544*(1-2*x)^(17/2)-2025/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x +--R + +--R 4 3 2 +--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x +--R + +--R 4 3 2 +--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2078505 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-5929/32*(1-2*x)^(7/2)+91091/288*(1-2*x)^(9/2)-_ + 39977/176*(1-2*x)^(11/2)+17541/208*(1-2*x)^(13/2)-_ + 513/32*(1-2*x)^(15/2)+675/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 +--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x +--R + +--R 2 +--R 2934177x + 993442x - 581846 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 21879 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 +--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x +--R + +--R 2 +--R 2934177x + 993442x - 581846 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 21879 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=-847/16*(1-2*x)^(7/2)+1309/18*(1-2*x)^(9/2)-3467/88*(1-2*x)^(11/2)+_ + 255/26*(1-2*x)^(13/2)-15/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x +--R + +--R - 13826 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x +--R + +--R - 13826 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-121/8*(1-2*x)^(7/2)+1133/72*(1-2*x)^(9/2)-505/88*(1-2*x)^(11/2)+_ + 75/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R 1287 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-121/28*(1-2*x)^(7/2)+55/18*(1-2*x)^(9/2)-25/44*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1 +--R (2) -------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1 +--R (3) -------------------------------------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=14/243*(1-2*x)^(3/2)+2/135*(1-2*x)^(5/2)-40/189*(1-2*x)^(7/2)-_ + 5/27*(1-2*x)^(7/2)*(3+5*x)-98/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)+98/243*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 3430\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 8505\|3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1715\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 8505\|3 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(-------------------------------) + 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 243\|3 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-50/81*(1-2*x)^(3/2)-10/63*(1-2*x)^(5/2)-25/63*(1-2*x)^(7/2)-_ + 1/63*(1-2*x)^(7/2)/(2+3*x)+350/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-350/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (7350x + 4900)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (1701x + 1134)\|3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (3675x + 2450)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (1701x + 1134)\|3 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 175\|7 log(---------------------------------) - 350\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=1055/567*(1-2*x)^(3/2)+211/441*(1-2*x)^(5/2)-1/126*(1-2*x)^(7/2)/_ + (2+3*x)^2+143/882*(1-2*x)^(7/2)/(2+3*x)-1055/81*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+1055/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (- 18990x - 25320x - 8440)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (9495x + 12660x + 4220)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 1055\|7 log(-------------------------------) + 2110\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-4435/3969*(1-2*x)^(3/2)-1/189*(1-2*x)^(7/2)/(2+3*x)^3+_ + 211/2646*(1-2*x)^(7/2)/(2+3*x)^2-887/882*(1-2*x)^(5/2)/(2+3*x)+_ + 4435/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4435/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (239490x + 478980x + 319320x + 70960)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (4374x + 8748x + 5832x + 1296)\|21 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (119745x + 239490x + 159660x + 35480) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (4374x + 8748x + 5832x + 1296)\|21 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4435log(-------------------------------) - 8870atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 162\|21 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13305x + 22175)\|21 + (13305x - 22175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (8870x - 4435)\|3 \|7 \|21 - 186270x + 93135 +--R / +--R 2 +--------+ +--R (20412x + 3402x - 6804)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2916x + 4374x + 1782x - 1620)\|21 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-1/252*(1-2*x)^(7/2)/(2+3*x)^4+31/588*(1-2*x)^(7/2)/(2+3*x)^3-_ + 4993/10584*(1-2*x)^(5/2)/(2+3*x)^2+24965/31752*(1-2*x)^(3/2)/(2+3*x)-_ + 24965/2268*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+24965/15876*sqrt(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 4044330x - 10784880x - 10784880x - 4793280x - 798880) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (2022165x + 5392440x + 5392440x + 2396640x + 399440) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 24965log(-----------------------------) + 49930atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 4536\|21 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 74895x + 124825)\|21 + (74895x - 124825)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 49930x + 24965)\|3 \|7 \|21 + 1048530x - 524265 +--R / +--R 2 +--------+ +--R (571536x + 95256x - 190512)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (81648x - 122472x - 49896x + 45360)\|21 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-1/315*(1-2*x)^(7/2)/(2+3*x)^5+347/8820*(1-2*x)^(7/2)/(2+3*x)^4-_ + 8051/26460*(1-2*x)^(5/2)/(2+3*x)^3+8051/31752*(1-2*x)^(3/2)/(2+3*x)^2+_ + 8051/15876*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 8051/31752*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 19563930x + 65213100x + 86950800x + 57967200x + 19322400x +--R + +--R 2576320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x +--R + +--R 5080320 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (9781965x + 32606550x + 43475400x + 28983600x + 9661200x + 1288160) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x +--R + +--R 5080320 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 8051log(-------------------------------) - 16102atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 31752\|21 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 24153x + 40255)\|21 + (24153x - 40255)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (16102x - 8051)\|3 \|7 \|21 - 338142x + 169071 +--R / +--R 2 +--------+ +--R (4000752x + 666792x - 1333584)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 571536x + 857304x + 349272x - 317520)\|21 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1/378*(1-2*x)^(7/2)/(2+3*x)^6+83/2646*(1-2*x)^(7/2)/(2+3*x)^5-_ + 263/1176*(1-2*x)^(5/2)/(2+3*x)^4+1315/10584*(1-2*x)^(3/2)/(2+3*x)^3+_ + 1315/74088*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1315/21168*sqrt(1-2*x)/(2+3*x)^2+1315/148176*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 1917270x + 7669080x + 12781800x + 11361600x + 5680800x +--R + +--R 1514880x + 168320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x +--R + +--R 85349376x + 9483264 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 958635x + 3834540x + 6390900x + 5680800x + 2840400x + 757440x +--R + +--R 84160 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x +--R + +--R 85349376x + 9483264 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1315log(-------------------------------) - 2630atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 148176\|21 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 3945x + 6575)\|21 + (3945x - 6575)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (2630x - 1315)\|3 \|7 \|21 - 55230x + 27615 +--R / +--R 2 +--------+ +--R (18670176x + 3111696x - 6223392)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2667168x + 4000752x + 1629936x - 1481760)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-1/441*(1-2*x)^(7/2)/(2+3*x)^7+23/882*(1-2*x)^(7/2)/(2+3*x)^6-_ + 467/2646*(1-2*x)^(5/2)/(2+3*x)^5+2335/31752*(1-2*x)^(3/2)/(2+3*x)^4+_ + 2335/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 2335/95256*sqrt(1-2*x)/(2+3*x)^3+2335/1333584*sqrt(1-2*x)/(2+3*x)^2+_ + 2335/3111696*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 10213290x + 47662020x + 95324040x + 105915600x + 70610400x +--R + +--R 2 +--R 28244160x + 6276480x + 597760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x +--R + +--R 1415408x - 1107536 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 6805279152x + 31757969376x + 63515938752x + 70573265280x +--R + +--R 3 2 +--R 47048843520x + 18819537408x + 4182119424x + 398297088 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 5106645x + 23831010x + 47662020x + 52957800x + 35305200x +--R + +--R 2 +--R 14122080x + 3138240x + 298880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x +--R + +--R 1415408x - 1107536 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 6805279152x + 31757969376x + 63515938752x + 70573265280x +--R + +--R 3 2 +--R 47048843520x + 18819537408x + 4182119424x + 398297088 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2335log(-------------------------------) - 4670atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3111696\|21 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7005x + 11675)\|21 + (7005x - 11675)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4670x - 2335)\|3 \|7 \|21 - 98070x + 49035 +--R / +--R 2 +--------+ +--R (392073696x + 65345616x - 130691232)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-456533/128*(1-2*x)^(7/2)+3278737/384*(1-2*x)^(9/2)-_ + 1179381/128*(1-2*x)^(11/2)+9504551/1664*(1-2*x)^(13/2)-_ + 1392467/640*(1-2*x)^(15/2)+1101465/2176*(1-2*x)^(17/2)-_ + 161325/2432*(1-2*x)^(19/2)+3375/896*(1-2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 +--R 1700595000x + 6471211500x + 8880844050x + 3513142893x +--R + +--R 6 5 4 3 2 +--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x +--R + +--R 74758064x - 115708576 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 440895 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 +--R 1700595000x + 6471211500x + 8880844050x + 3513142893x +--R + +--R 6 5 4 3 2 +--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x +--R + +--R 74758064x - 115708576 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 440895 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x +--R + +--R 216 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-65219/64*(1-2*x)^(7/2)+100793/48*(1-2*x)^(9/2)-_ + 121359/64*(1-2*x)^(11/2)+98209/104*(1-2*x)^(13/2)-_ + 17337/64*(1-2*x)^(15/2)+675/16*(1-2*x)^(17/2)-3375/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 4 +--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x +--R + +--R 3 2 +--R 281231x + 406155x + 84038x - 76018 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 741 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 4 +--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x +--R + +--R 3 2 +--R 281231x + 406155x + 84038x - 76018 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 741 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-9317/32*(1-2*x)^(7/2)+16093/32*(1-2*x)^(9/2)-5847/16*(1-2*x)^(11/2)+_ + 28555/208*(1-2*x)^(13/2)-845/32*(1-2*x)^(15/2)+1125/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x +--R + +--R 14864x - 9004 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 221 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 2 +--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x +--R + +--R 14864x - 9004 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 221 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-1331/16*(1-2*x)^(7/2)+2783/24*(1-2*x)^(9/2)-255/4*(1-2*x)^(11/2)+_ + 1675/104*(1-2*x)^(13/2)-25/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--------+ +--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 39 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--------+ +--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 39 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-1331/56*(1-2*x)^(7/2)+605/24*(1-2*x)^(9/2)-75/8*(1-2*x)^(11/2)+_ + 125/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 273 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 273 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=34/405*(1-2*x)^(3/2)*(3+5*x)^3+2/33*(1-2*x)^(5/2)*(3+5*x)^3+_ + 98/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 1012658/212625*sqrt(1-2*x)-25631/70875*(3+5*x)^2*sqrt(1-2*x)+_ + 514/4725*(3+5*x)^3*sqrt(1-2*x)-1/127575*(227389+191021*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 37730\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R 280665\|3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 18865\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R 280665\|3 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 729\|3 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-22/81*(1-2*x)^(3/2)*(3+5*x)^3-1/3*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)-_ + 1540/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+_ + 138578/127575*sqrt(1-2*x)-416152/127575*(3+5*x)*sqrt(1-2*x)+_ + 65153/14175*(3+5*x)^2*sqrt(1-2*x)-682/945*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 32340x - 21560)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (15309x + 10206)\|3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (16170x + 10780)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (15309x + 10206)\|3 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 770\|7 log(-------------------------------) + 1540\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 729\|3 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2+55/9*(1-2*x)^(3/2)*_ + (3+5*x)^3/(2+3*x)+935/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 78947/2835*sqrt(1-2*x)+89771/5670*(3+5*x)*sqrt(1-2*x)-_ + 7997/315*(3+5*x)^2*sqrt(1-2*x)+88/21*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (117810x + 157080x + 52360)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (10206x + 13608x + 4536)\|3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (58905x + 78540x + 26180)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (10206x + 13608x + 4536)\|3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 935\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 1870\|7 atanh(---------------) +--R +-+ +--R \|7 +--R / +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3+55/27*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^2-41360/243*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 12166/243*sqrt(1-2*x)-8294/243*(3+5*x)*sqrt(1-2*x)+_ + 1441/27*(3+5*x)^2*sqrt(1-2*x)-275/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 1116720x - 2233440x - 1488960x - 330880)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--------+ +--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (6561x + 13122x + 8748x + 1944)\|21 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (558360x + 1116720x + 744480x + 165440) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--------+ +--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (6561x + 13122x + 8748x + 1944)\|21 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 20680log(-----------------------------) + 41360atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 243\|21 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 62040x + 103400)\|21 + (62040x - 103400)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 41360x + 20680)\|3 \|7 \|21 + 868560x - 434280 +--R / +--R 2 +--------+ +--R (30618x + 5103x - 10206)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (4374x - 6561x - 2673x + 2430)\|21 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4+55/54*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^3+645865/6804*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 224675/6804*sqrt(1-2*x)+252725/13608*(3+5*x)*sqrt(1-2*x)-_ + 2255/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-55/24*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R 4 3 2 +--R (104630130x + 279013680x + 279013680x + 124006080x + 20667680) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (52315065x + 139506840x + 139506840x + 62003040x + 10333840) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 645865log(-------------------------------) - 1291730atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +--+ +--R 13608\|21 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1937595x + 3229325)\|21 + (1937595x - 3229325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1291730x - 645865)\|3 \|7 \|21 - 27126330x + 13563165 +--R / +--R 2 +--------+ +--R (1714608x + 285768x - 571536)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 244944x + 367416x + 149688x - 136080)\|21 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5+11/18*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^4-146971/7938*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 715/7938*sqrt(1-2*x)-13387/15876*(3+5*x)*sqrt(1-2*x)/(2+3*x)-_ + 209/756*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+11/9*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 357139530x - 1190465100x - 1587286800x - 1058191200x +--R + +--R - 352730400x - 47030720 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x +--R + +--R 7933096 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 178569765x + 595232550x + 793643400x + 529095600x + 176365200x +--R + +--R 23515360 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x +--R + +--R 7933096 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 146971log(-----------------------------) + 293942atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 15876\|21 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 440913x + 734855)\|21 + (440913x - 734855)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 293942x + 146971)\|3 \|7 \|21 + 6172782x - 3086391 +--R / +--R 2 +--------+ +--R (2000376x + 333396x - 666792)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (285768x - 428652x - 174636x + 158760)\|21 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-121/4536*(1-2*x)^(3/2)/(2+3*x)^4+33275/95256*(1-2*x)^(3/2)/(2+3*x)^3-_ + 1/18*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6+11/27*(1-2*x)^(3/2)*_ + (3+5*x)^3/(2+3*x)^5+559625/666792*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-559625/190512*sqrt(1-2*x)/(2+3*x)^2+559625/1333584*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 815933250x + 3263733000x + 5439555000x + 4835160000x +--R + +--R 2 +--R 2417580000x + 644688000x + 71632000 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x +--R + +--R - 13847024 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x +--R + +--R 768144384x + 85349376 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 407966625x + 1631866500x + 2719777500x + 2417580000x +--R + +--R 2 +--R 1208790000x + 322344000x + 35816000 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x +--R + +--R - 13847024 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x +--R + +--R 768144384x + 85349376 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 559625log(-------------------------------) - 1119250atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +--+ +--R 1333584\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1678875x + 2798125)\|21 + (1678875x - 2798125)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1119250x - 559625)\|3 \|7 \|21 - 23504250x + 11752125 +--R / +--R 2 +--------+ +--R (168031584x + 28005264x - 56010528)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 24004512x + 36006768x + 14669424x - 13335840)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7+55/189*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^6+33935/1166886*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 11/166698*(3833-4355*x)*sqrt(1-2*x)/(2+3*x)^3-153505/47628*_ + sqrt(1-2*x)/(2+3*x)^2+33935/2333772*sqrt(1-2*x)/(2+3*x)-_ + 3223/2646*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+11/7*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 7 6 5 4 +--R 148431690x + 692681220x + 1385362440x + 1539291600x +--R + +--R 3 2 +--R 1026194400x + 410477760x + 91217280x + 8687360 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x +--R + +--R - 12384752x - 4005436 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 5103959364x + 23818477032x + 47636954064x + 52929948960x +--R + +--R 3 2 +--R 35286632640x + 14114653056x + 3136589568x + 298722816 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 74215845x + 346340610x + 692681220x + 769645800x + 513097200x +--R + +--R 2 +--R 205238880x + 45608640x + 4343680 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x +--R + +--R - 12384752x - 4005436 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 5103959364x + 23818477032x + 47636954064x + 52929948960x +--R + +--R 3 2 +--R 35286632640x + 14114653056x + 3136589568x + 298722816 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 33935log(-------------------------------) - 67870atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 2333772\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 101805x + 169675)\|21 + (101805x - 169675)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (67870x - 33935)\|3 \|7 \|21 - 1425270x + 712635 +--R / +--R 2 +--------+ +--R (294055272x + 49009212x - 98018424)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 42007896x + 63011844x + 25671492x - 23337720)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=298/10725*(1-2*x)^(3/2)*(2+3*x)^4+2/65*(1-2*x)^(5/2)*(2+3*x)^4-_ + 242/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 601617098/301640625*sqrt(1-2*x)-669943/2413125*(2+3*x)*_ + sqrt(1-2*x)-829256/20109375*(2+3*x)^2*sqrt(1-2*x)+_ + 861947/16891875*(2+3*x)^3*sqrt(1-2*x)+4138/482625*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 726726\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 2338875000x + 2842087500x - 1540428750x - 2556079875x +--R + +--R 2 +--R 399578370x + 960784285x - 289133384 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363363\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R 2338875000x + 2842087500x - 1540428750x - 2556079875x +--R + +--R 2 +--R 399578370x + 960784285x - 289133384 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=34/825*(1-2*x)^(3/2)*(2+3*x)^3+2/55*(1-2*x)^(5/2)*(2+3*x)^3-242/15625*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-207982/171875*_ + sqrt(1-2*x)+6221/103125*(2+3*x)^2*sqrt(1-2*x)+706/28875*_ + (2+3*x)^3*sqrt(1-2*x)-1/515625*(177948+223375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 55902\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318) +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 27951\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318) +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=22/1875*(1-2*x)^(3/2)+2/625*(1-2*x)^(5/2)-44/525*(1-2*x)^(7/2)-_ + 1/15*(1-2*x)^(7/2)*(2+3*x)-242/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+242/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=22/375*(1-2*x)^(3/2)+2/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(7/2)-_ + 242/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=22/75*(1-2*x)^(3/2)+2/25*(1-2*x)^(5/2)-242/125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 726\|11 atanh(---------------) + (120x - 340x + 866)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +--R 375\|5 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (120x - 340x + 866)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 375\|5 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-4/45*(1-2*x)^(3/2)-242/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)+98/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-272/225*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2450\|5 \|7 atanh(---------------) - 2178\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R + +--R +-+ +-+ +--------+ +--R (40x - 292)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1089\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (40x - 292)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1089\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 2450\|5 \|7 atanh(---------------) + 2178\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=2/3*(1-2*x)^(3/2)+(1-2*x)^(5/2)/(2+3*x)-242/5*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+140/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)+26/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (2100x + 1400)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R (- 2178x - 1452)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (8x + 87)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (45x + 30)\|3 \|5 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1089x + 726)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (1050x + 700)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (8x + 87)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (45x + 30)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 350\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 700\|5 \|7 atanh(---------------) + 726\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=1/2*(1-2*x)^(5/2)/(2+3*x)^2+65/6*(1-2*x)^(3/2)/(2+3*x)-_ + 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 235*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (12690x + 16920x + 5640)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 13068x - 17424x - 5808)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (427x + 301)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (54x + 72x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (6534x + 8712x + 2904)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (6345x + 8460x + 2820)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (427x + 301)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (54x + 72x + 24)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 242\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 235\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 470\|5 \|7 atanh(---------------) + 484\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=1/3*(1-2*x)^(5/2)/(2+3*x)^3+50/9*(1-2*x)^(3/2)/(2+3*x)^2+_ + 74020/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1105/9*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (1998540x + 3997080x + 2664720x + 592160)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 58806x - 117612x - 78408x - 17424)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (9657x + 13198x + 4523)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (243x + 486x + 324x + 72)\|21 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (29403x + 58806x + 39204x + 8712)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (999270x + 1998540x + 1332360x + 296080) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (9657x + 13198x + 4523)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (243x + 486x + 324x + 72)\|21 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1089\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 37010log(-------------------------------) - 74020atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2178\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 9\|21 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (49005x - 127413x + 23958x + 87120)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 370100x - 37010x + 111030)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 225330x - 480585x + 183960 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (80475x - 394285x + 643840x - 350400)\|21 +--R + +--R 2 +-+ +--+ +--R (7546770x + 1257795x - 2515590)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2775750x + 7402000x - 1961530x - 4441200)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 32190x + 122305x - 140705x + 43800)\|21 +--R + +--R 3 2 +-+ +--+ +--R (686070x - 983367x - 411642x + 365904)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1110300x - 1739470x - 518140x + 555150)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1078110x + 1617165x + 658845x - 598950)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1850500x + 2775750x + 851230x - 888240)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1126650x - 4205565x + 4764480x - 1471680 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (810x - 729x - 1224x + 153x + 270)\|21 \|55 - 28350x + 23625x +--R + +--R 2 +--R 41391x - 4914x - 9072 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (11340x + 3024x - 6993x - 945x + 1134)\|55 +--R + +--R 5 4 3 2 +--+ +--R (4050x - 10125x - 288x + 10557x + 126x - 2160)\|21 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 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674589762000x - 282386412000x + 251010144000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 3 2 +--R (761665426050x - 1193275834145x - 355443865490x + 380832713025) +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--R (- 739583460000x + 1109375190000x + 451967670000x - 410879700000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 3 2 +--R - 1269442376750x + 1904163565125x + 583943493305x +--R + +--R - 609332340840 +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 772868811750x - 2884997957625x + 3268439300595x - 1009578762360 +--R / +--R 4 3 2 +--+ +--+ +--R (4445280x - 4000752x - 6717312x + 839664x + 1481760)\|21 \|55 +--R + +--R 4 3 2 +--R - 155584800x + 129654000x + 227153808x - 26968032x - 49787136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (62233920x + 16595712x - 38377584x - 5186160x + 6223392)\|55 +--R + +--R 5 4 3 2 +--R (22226400x - 55566000x - 1580544x + 57936816x + 691488x - 11854080) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-26/275*(1-2*x)^(3/2)*(2+3*x)^4-1/5*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)-_ + 2794/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 20103122/23203125*sqrt(1-2*x)-7327/185625*(2+3*x)*sqrt(1-2*x)+_ + 312916/1546875*(2+3*x)^2*sqrt(1-2*x)+975383/1299375*(2+3*x)^3*_ + sqrt(1-2*x)-8318/37125*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 3227070x - 1936242)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x +--R + +--R 50081215x - 15982128 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (90234375x + 54140625)\|5 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1613535x + 968121)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x +--R + +--R 50081215x - 15982128 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (90234375x + 54140625)\|5 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1397\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 2794\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-22/225*(1-2*x)^(3/2)*(2+3*x)^3-1/5*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)-_ + 2068/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 224794/421875*sqrt(1-2*x)+796/3375*(2+3*x)*sqrt(1-2*x)+_ + 23357/28125*(2+3*x)^2*sqrt(1-2*x)-1898/7875*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 217140x - 130284)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (1640625x + 984375)\|5 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (108570x + 65142)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (1640625x + 984375)\|5 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1034\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 2068\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=122/1875*(1-2*x)^(3/2)+122/6875*(1-2*x)^(5/2)-9/175*(1-2*x)^(7/2)-_ + 1/275*(1-2*x)^(7/2)/(3+5*x)-1342/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)+1342/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 140910x - 84546)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (328125x + 196875)\|5 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (70455x + 42273)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (328125x + 196875)\|5 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 671\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 1342\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=56/375*(1-2*x)^(3/2)+56/1375*(1-2*x)^(5/2)-1/55*(1-2*x)^(7/2)/(3+5*x)-_ + 616/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+616/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 9240x - 5544)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (9375x + 5625)\|5 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (4620x + 2772)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (9375x + 5625)\|5 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 308\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 616\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2/15*(1-2*x)^(3/2)-1/5*(1-2*x)^(5/2)/(3+5*x)+22/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-22/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R (330x + 198)\|11 atanh(---------------) + (40x - 260x - 243)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R (375x + 225)\|5 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (165x + 99)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (40x - 260x - 243)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (375x + 225)\|5 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 11\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 22\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-2/5*(1-2*x)^(3/2)-(1-2*x)^(5/2)/(3+5*x)+836/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-98/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-58/75*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (- 12250x - 7350)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R (12540x + 7524)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (40x - 339)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (375x + 225)\|3 \|5 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (6125x + 3675)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (6270x + 3762)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (40x - 339)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (375x + 225)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1254\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2450\|5 \|7 atanh(---------------) - 2508\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 75\|3 \|5 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-22*(1-2*x)^(3/2)/(3+5*x)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x))+_ + 1562/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 910/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-136/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 68250x - 86450x - 27300)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (70290x + 89034x + 28116)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (225x + 285x + 90)\|3 \|5 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (34125x + 43225x + 13650)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (35145x + 44517x + 14058)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (225x + 285x + 90)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 2275\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2343\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 4550\|5 \|7 atanh(---------------) - 4686\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x))+50/3*(1-2*x)^(3/2)/((2+3*x)*_ + (3+5*x))+2288*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 6665/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2189/6*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 599850x - 1159710x - 746480x - 159960)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +--+ \|5 \|- 2x + 1 +--R (617760x + 1194336x + 768768x + 164736)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (270x + 522x + 336x + 72)\|3 \|5 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (299925x + 579855x + 373240x + 79980)\|5 \|7 +--R * +--R +-+ +--------+ +-+ +--R 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (308880x + 597168x + 384384x + 82368)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (270x + 522x + 336x + 72)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 6665\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 6864\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 13330\|5 \|7 atanh(---------------) - 13728\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 6\|3 \|5 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x))+15/2*(1-2*x)^(3/2)/((2+3*x)^2*_ + (3+5*x))-307295/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 3014*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 44545/18*sqrt(1-2*x)/(3+5*x)+2260/9*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R (- 82969650x - 215721090x - 210189780x - 90959320x - 14750160) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--+ +--R (2441340x + 6347484x + 6184728x + 2676432x + 434016)\|21 \|55 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (810x + 2106x + 2052x + 888x + 144)\|21 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (41484825x + 107860545x + 105094890x + 45479660x + 7375080) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--+ +--R (1220670x + 3173742x + 3092364x + 1338216x + 217008)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (810x + 2106x + 2052x + 888x + 144)\|21 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 307295log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 9042\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 614590atanh(---------------) - 18084\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 6\|21 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (406890x - 1057914x + 198924x + 723360)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 3072950x - 307295x + 921885)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 1870890x - 3990315x + 1527435 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (668175x - 3273730x + 5345815x - 2909400)\|21 +--R + +--R 2 +-+ +--+ +--R (62661060x + 10443510x - 20887020)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 23047125x + 61459000x - 16286635x - 36875400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (267270x - 1015495x + 1168280x - 363675)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 5696460x + 8164926x + 3417876x - 3038112)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 9218850x + 14442865x + 4302130x - 4609425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (8951580x - 13427370x - 5470410x + 4973100)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (15364750x - 23047125x - 7067785x + 7375080)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 9354450x + 34918695x - 39559695x + 12219480 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (540x - 486x - 816x + 102x + 180)\|21 \|55 - 18900x + 15750x +--R + +--R 2 +--R 27594x - 3276x - 6048 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 7560x - 2016x + 4662x + 630x - 756)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 2700x + 6750x + 192x - 7038x - 84x + 1440)\|21 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x))+85/18*(1-2*x)^(3/2)/((2+3*x)^3*_ + (3+5*x))-53384095/84*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 18700*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 7738475/504*sqrt(1-2*x)/(3+5*x)+22765/216*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+288770/189*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 43241116950x - 141254315370x - 184495432320x - 120434518320x +--R + +--R - 39290693920x - 5124873120 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 1272348000x + 4156336800x + 5428684800x + 3543724800x +--R + +--R 1156108800x + 150796800 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R 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290304x + 189504x + 61824x + 8064)\|21 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 53384095log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 1570800\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 106768190atanh(---------------) - 3141600\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 168\|21 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (70686000x - 183783600x + 34557600x + 125664000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 533840950x - 53384095x + 160152285)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 325015950x - 693208005x + 265350015 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (116077125x - 568721000x + 928689035x - 505428600)\|21 +--R + +--R 2 +-+ +--+ +--R (10885644000x + 1814274000x - 3628548000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4003807125x + 10676819000x - 2829357035x - 6406091400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (46430850x - 176414465x + 202956670x - 63178575)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 989604000x + 1418432400x + 593762400x - 527788800)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1601522850x + 2509052465x + 747377330x - 800761425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (1555092000x - 2332638000x - 950334000x + 863940000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (2669204750x - 4003807125x - 1227834185x + 1281218280)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 1625079750x + 6066167625x - 6872414115x + 2122800120 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (15120x - 13608x - 22848x + 2856x + 5040)\|21 \|55 - 529200x +--R + +--R 3 2 +--R 441000x + 772632x - 91728x - 169344 +--R * 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174698351810100x +--R + +--R 3 2 +--R - 152610054454800x - 74966342539200x - 19634042093600x +--R + +--R - 2141895501120 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 +--R 797649930000x + 3137423058000x + 5140410660000x + 4490473680000x +--R + +--R 2 +--R 2205846720000x + 577721760000x + 63024192000 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 130986207675x - 432275892930x - 570477768855x - 376323861626x +--R + +--R - 124085884254x - 16360698684 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 7144200x + 28100520x + 46040400x + 40219200x + 19756800x +--R + +--R 5174400x + 564480 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 13554182468025x + 53313117707565x + 87349175905050x +--R + +--R 3 2 +--R 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+--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 65650200\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R 4462282294atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R - 131300400\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +--R (2954259000x - 7681073400x + 1444304400x + 5252016000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 22311411470x - 2231141147x + 6693423441)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 13583754870x - 28972016913x + 11090069739 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (4851341025x - 23769192400x + 38813738791x - 21123942360)\|21 +--R + +--R 2 +-+ +--+ +--R (454955886000x + 75825981000x - 151651962000)\|5 \|11 +--R + +--R 3 2 +--R (- 167335586025x + 446228229400x - 118250480791x - 267736937640) +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1940536410x - 7373086909x + 8482394942x - 2640492795)\|21 +--R + +--R 3 2 +-+ +--R (- 41359626000x + 59282130600x + 24815775600x - 22058467200)\|5 +--R * +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 66934234410x + 104863633909x + 31235976058x - 33467117205)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (64993698000x - 97490547000x - 39718371000x + 36107610000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (111557057350x - 167335586025x - 51316246381x + 53547387528)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 67918774350x + 253530123525x - 287226483999x + 88720557912 +--R / +--R 4 3 2 +--+ +--+ +--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55 +--R + +--R 4 3 2 +--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 1481760x - 395136x + 913752x + 123480x - 148176)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 529200x + 1323000x + 37632x - 1379448x - 16464x + 282240)\|21 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2-127/50*(1-2*x)^(3/2)*(2+3*x)^4/_ + (3+5*x)-11763/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 50557/78125*sqrt(1-2*x)-1/468750*(118254-449875*x)*sqrt(1-2*x)+_ + 44804/46875*(2+3*x)^2*sqrt(1-2*x)+250829/78750*(2+3*x)^3*_ + sqrt(1-2*x)-1117/1125*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 4117050x - 4940460x - 1482138)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x +--R + +--R 6891315x + 871208 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (27343750x + 32812500x + 9843750)\|5 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (2058525x + 2470230x + 741069)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x +--R + +--R 6891315x + 871208 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (27343750x + 32812500x + 9843750)\|5 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 11763\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 23526\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 156250\|5 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2-47/25*(1-2*x)^(3/2)*(2+3*x)^3/_ + (3+5*x)-5559/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 5839/15625*sqrt(1-2*x)+223/250*(2+3*x)*sqrt(1-2*x)+_ + 7149/3125*(2+3*x)^2*sqrt(1-2*x)-636/875*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 1945650x - 2334780x - 700434)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +-+ +--R (5468750x + 6562500x + 1968750)\|5 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (972825x + 1167390x + 350217)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +-+ +--R (5468750x + 6562500x + 1968750)\|5 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 5559\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 11118\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 31250\|5 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=511/6875*(1-2*x)^(3/2)+1533/75625*(1-2*x)^(5/2)-1/550*(1-2*x)^(7/2)/_ + (3+5*x)^2-129/6050*(1-2*x)^(7/2)/(3+5*x)-1533/3125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1533/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 76650x - 91980x - 27594)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (156250x + 187500x + 56250)\|5 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (38325x + 45990x + 13797)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (156250x + 187500x + 56250)\|5 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1533\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 3066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 6250\|5 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-21/275*(1-2*x)^(3/2)-1/110*(1-2*x)^(7/2)/(3+5*x)^2-_ + 63/550*(1-2*x)^(5/2)/(3+5*x)+63/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-63/125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (3150x + 3780x + 1134)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (6250x + 7500x + 2250)\|5 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1575x + 1890x + 567)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (6250x + 7500x + 2250)\|5 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 63\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 126\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 250\|5 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/10*(1-2*x)^(5/2)/(3+5*x)^2+1/10*(1-2*x)^(3/2)/(3+5*x)-_ + 3/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+3/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 150x - 180x - 54)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (80x + 195x + 64)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1250x + 1500x + 450)\|5 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (75x + 90x + 27)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (80x + 195x + 64)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1250x + 1500x + 450)\|5 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 3\|11 log(--------------------------------) + 6\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/2*(1-2*x)^(5/2)/(3+5*x)^2+71/10*(1-2*x)^(3/2)/(3+5*x)-_ + 2523/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 98*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+73/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (122500x + 147000x + 44100)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 126150x - 151380x - 45414)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (4125x + 2354)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (1250x + 1500x + 450)\|3 \|5 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (63075x + 75690x + 22707)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (61250x + 73500x + 22050)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (4125x + 2354)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (1250x + 1500x + 450)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2523\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 2450\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 4900\|5 \|7 atanh(---------------) + 5046\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 50\|3 \|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-33/2*(1-2*x)^(3/2)/(3+5*x)^2+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2)-_ + 7209/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 1400*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+2299/10*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|3 \|- 2x + 1 +--R (1050000x + 1960000x + 1218000x + 252000)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--+ +--R (- 1081350x - 2018520x - 1254366x - 259524)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (750x + 1400x + 870x + 180)\|3 \|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (540675x + 1009260x + 627183x + 129762)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +-+ +--R (525000x + 980000x + 609000x + 126000)\|5 \|7 +--R * +--R +-+ +--------+ +-+ +--R - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (750x + 1400x + 870x + 180)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7209\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7000\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R - 14000\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R 14418\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R 10\|3 \|5 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2)+45/2*(1-2*x)^(3/2)/((2+3*x)*_ + (3+5*x)^2)-14073*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 4555*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-737/2*sqrt(1-2*x)/_ + (3+5*x)^2+2311*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (2049750x + 5192700x + 4928510x + 2077080x + 327960)\|5 \|21 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 6332850x - 16043220x - 15226986x - 6417288x - 1013256)\|11 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (450x + 1140x + 1082x + 456x + 72)\|5 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|11 +--R * +--R +--+ +--------+ +-+ +--R 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (1024875x + 2596350x + 2464255x + 1038540x + 163980)\|5 \|21 +--R * +--R +--+ +--------+ +--R - \|21 \|- 2x + 1 + 3x - 5 +--R log(---------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (450x + 1140x + 1082x + 456x + 72)\|5 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 14073\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +-+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 4555\|5 \|21 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--+ \|5 \|- 2x + 1 +--R - 9110\|5 \|21 atanh(---------------) + 28146\|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 2\|5 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +--R (- 956550x + 478275)\|11 +--R + +--R 2 +-+ +-+ +-+ +--R (68325x - 223195x + 182200)\|3 \|5 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R +-+ +-+ +--+ +--R (956550x - 478275)\|3 \|7 \|11 +--R + +--R 2 +-+ +--R (- 1434825x + 4687095x - 3826200)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ +--R (- 136650x + 296075x - 113875)\|3 \|7 \|11 +--R + +--R 2 +-+ +--R (- 956550x + 2008755x - 765240)\|5 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--+ +--R (2869650x - 6217575x + 2391375)\|11 +--R + +--R 2 +-+ +-+ +-+ +--R (956550x - 2008755x + 765240)\|3 \|5 \|7 +--R / +--R 3 2 +-+ +--+ +--R (60x - 86x - 36x + 32)\|5 \|21 +--R + +--R 3 2 +--+ +--R (- 180x + 270x + 110x - 100)\|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--+ +--R (- 120x + 40x + 50x - 20)\|11 \|21 +--R + +--R 4 3 2 +-+ +--R (- 180x + 558x - 322x - 276x + 160)\|5 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2)+85/9*(1-2*x)^(3/2)/((2+3*x)^2*_ + (3+5*x)^2)+785570*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 23115*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-169975/54*_ + sqrt(1-2*x)/(3+5*x)^2+11470/27*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 113875/6*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1060519500x + 3393662400x + 4341059820x + 2774633240x +--R + +--R 886122960x + 113122080 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 31205250x - 99856800x - 127733490x - 81642180x - 26073720x +--R + +--R - 3328560 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 15602625x + 49928400x + 63866745x + 40821090x + 13036860x +--R + +--R 1664280 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 530259750x + 1696831200x + 2170529910x + 1387316620x + 443061480x +--R + +--R 56561040 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 23115\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 785570log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 1571140atanh(---------------) + 46230\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2\|21 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (1040175x - 2704455x + 508530x + 1849200)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 7855700x - 785570x + 2356710)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 4782750x - 10200855x + 3904740 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (1708125x - 8368975x + 13666060x - 7437600)\|21 +--R + +--R 2 +-+ +--+ +--R (160186950x + 26697825x - 53395650)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 58917750x + 157114000x - 41635210x - 94268400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 683250x + 2596015x - 2986595x + 929700)\|21 +--R + +--R 3 2 +-+ +--+ +--R (14562450x - 20872845x - 8737470x + 7766640)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (23567100x - 36921790x - 10997980x + 11783550)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 22883850x + 34325775x + 13984575x - 12713250)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 39278500x + 58917750x + 18068110x - 18853680)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 23913750x - 89266275x + 101130540x - 31237920 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (180x - 162x - 272x + 34x + 60)\|21 \|55 - 6300x + 5250x +--R + +--R 2 +--R 9198x - 1092x - 2016 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (2520x + 672x - 1554x - 210x + 252)\|55 +--R + +--R 5 4 3 2 +--+ +--R (900x - 2250x - 64x + 2346x + 28x - 480)\|21 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2)+205/36*(1-2*x)^(3/2)/((2+3*x)^3*_ + (3+5*x)^2)+163363895/28*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 171675*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 8836825/378*sqrt(1-2*x)/(3+5*x)^2+34525/216*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+522385/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 23680975/168*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 661623774750x + 2558278595700x + 4119710704110x + 3536501598960x +--R + +--R 2 +--R 1706825974960x + 439122149760x + 47048801760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 +--R - 19467945000x - 75276054000x - 121220404200x - 104059771200x +--R + +--R 2 +--R - 50222491200x - 12920947200x - 1384387200 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 3196931625x + 10337268075x + 13362164665x + 8630749831x +--R + +--R 2785562634x + 359378534 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--+ +--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 9733972500x + 37638027000x + 60610202100x + 52029885600x +--R + +--R 2 +--R 25111245600x + 6460473600x + 692193600 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R 330811887375x + 1279139297850x + 2059855352055x + 1768250799480x +--R + +--R 2 +--R 853412987480x + 219561074880x + 23524400880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 3196931625x + 10337268075x + 13362164665x + 8630749831x +--R + +--R 2785562634x + 359378534 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--+ +--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 4806900\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 163363895log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 326727790atanh(---------------) + 9613800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 56\|21 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (216310500x - 562407300x + 105751800x + 384552000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 1633638950x - 163363895x + 490091685)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 994600950x - 2121327705x + 812013615 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (355214625x - 1740377500x + 2841937435x - 1546692600)\|21 +--R + +--R 2 +-+ +--+ +--R (33311817000x + 5551969500x - 11103939000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 12252292125x + 32672779000x - 8658286435x - 19603667400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 142085850x + 539856565x - 621079970x + 193336575)\|21 +--R + +--R 3 2 +-+ +--+ +--R (3028347000x - 4340630700x - 1817008200x + 1615118400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (4900916850x - 7678103065x - 2287094530x + 2450458425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 4758831000x + 7138246500x + 2908174500x - 2643795000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 8168194750x + 12252292125x + 3757369585x - 3920733480)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 4973004750x - 18563446125x + 21030689715x - 6496108920 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (5040x - 4536x - 7616x + 952x + 1680)\|21 \|55 - 176400x +--R + +--R 3 2 +--R 147000x + 257544x - 30576x - 56448 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (70560x + 18816x - 43512x - 5880x + 7056)\|55 +--R + +--R 5 4 3 2 +--+ +--R (25200x - 63000x - 1792x + 65688x + 784x - 13440)\|21 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^5*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=60025/24*(1-2*x)^(3/2)-103929/64*(1-2*x)^(5/2)+5355/8*(1-2*x)^(7/2)-_ + 10815/64*(1-2*x)^(9/2)+1053/44*(1-2*x)^(11/2)-_ + 1215/832*(1-2*x)^(13/2)-184877/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x +--R + +--R - 638648 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x +--R + +--R - 638648 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^4*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=57281/96*(1-2*x)^(3/2)-24843/80*(1-2*x)^(5/2)+1539/16*(1-2*x)^(7/2)-_ + 519/32*(1-2*x)^(9/2)+405/352*(1-2*x)^(11/2)-26411/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^3*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=3283/24*(1-2*x)^(3/2)-1071/20*(1-2*x)^(5/2)+621/56*(1-2*x)^(7/2)-_ + 15/16*(1-2*x)^(9/2)-3773/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1 +--R (2) --------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1 +--R (3) --------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^2*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ---------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=707/24*(1-2*x)^(3/2)-309/40*(1-2*x)^(5/2)+45/56*(1-2*x)^(7/2)-_ + 539/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1 +--R (2) -------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1 +--R (3) -------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) -------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=17/3*(1-2*x)^(3/2)-3/4*(1-2*x)^(5/2)-77/4*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (- 9x - 25x - 43)\|- 2x + 1 +--R (2) ----------------------------- +--R 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (- 9x - 25x - 43)\|- 2x + 1 +--R (3) ----------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(3+5*x)/sqrt(1-2*x) +--R +--R +--R 5x + 3 +--R (1) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=5/6*(1-2*x)^(3/2)-11/2*sqrt(1-2*x) +--R +--R +--R +--------+ +--R (- 5x - 14)\|- 2x + 1 +--R (2) ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R (- 5x - 14)\|- 2x + 1 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=2/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/3*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R 2atanh(---------------) - 5\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R log(-------------------------------) - 5\|21 \|- 2x + 1 +--R 3x + 2 +--R (3) -------------------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (378x + 63x - 126)\|- 2x + 1 + (- 54x + 81x + 33x - 30)\|21 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-68/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/21*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (- 204x - 136)atanh(---------------) + \|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------- +--R +--+ +--R (63x + 42)\|21 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (102x + 68)log(-----------------------------) + \|21 \|- 2x + 1 +--R 3x + 2 +--R (3) ---------------------------------------------------------------- +--R +--+ +--R (63x + 42)\|21 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-67/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/42*sqrt(1-2*x)/(2+3*x)^2-_ + 67/294*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 1206x - 1608x - 536)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +--+ +--------+ +--R (- 201x - 127)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (603x + 804x + 268)log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 201x - 127)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 67log(-----------------------------) + 134atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 294\|21 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 134x + 67)\|3 \|7 \|21 + 2814x - 1407 +--R / +--R 2 +--------+ +--R (37044x + 6174x - 12348)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (5292x - 7938x - 3234x + 2940)\|21 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-100/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 1/63*sqrt(1-2*x)/(2+3*x)^3-50/441*sqrt(1-2*x)/(2+3*x)^2-_ + 50/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2700x - 5400x - 3600x - 800)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 450x - 950x - 417)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (27783x + 55566x + 37044x + 8232)\|21 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (1350x + 2700x + 1800x + 400)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 450x - 950x - 417)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (27783x + 55566x + 37044x + 8232)\|21 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 50log(-----------------------------) + 100atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 150x + 250)\|21 + (150x - 250)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 100x + 50)\|3 \|7 \|21 + 2100x - 1050 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18522x - 27783x - 11319x + 10290)\|21 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-95/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 1/84*sqrt(1-2*x)/(2+3*x)^4-19/252*sqrt(1-2*x)/(2+3*x)^3-_ + 95/3528*sqrt(1-2*x)/(2+3*x)^2-95/8232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (- 15390x - 41040x - 41040x - 18240x - 3040)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7695x + 20520x + 20520x + 9120x + 1520) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 95log(-----------------------------) + 190atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 8232\|21 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 285x + 475)\|21 + (285x - 475)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 190x + 95)\|3 \|7 \|21 + 3990x - 1995 +--R / +--R 2 +--------+ +--R (1037232x + 172872x - 345744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (148176x - 222264x - 90552x + 82320)\|21 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=6206585/384*(1-2*x)^(3/2)-1623419/128*(1-2*x)^(5/2)+_ + 842415/128*(1-2*x)^(7/2)-285565/128*(1-2*x)^(9/2)+_ + 672003/1408*(1-2*x)^(11/2)-97605/1664*(1-2*x)^(13/2)+_ + 405/128*(1-2*x)^(15/2)-2033647/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x +--R + +--R - 3152152x - 3275704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x +--R + +--R - 3152152x - 3275704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3k.input.pdf b/src/axiom-website/CATS/rich3k.input.pdf new file mode 100644 index 0000000..9354f79 Binary files /dev/null and b/src/axiom-website/CATS/rich3k.input.pdf differ diff --git a/src/axiom-website/CATS/rich3l.input.pamphlet b/src/axiom-website/CATS/rich3l.input.pamphlet new file mode 100644 index 0000000..86bc6fd --- /dev/null +++ b/src/axiom-website/CATS/rich3l.input.pamphlet @@ -0,0 +1,8152 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3l.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 50 matching answers. +\item 51 cases where the Axiom result differs from Rubi +\item 1 case where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3l.output +)spool rich3l.output +)set message test on +)set message auto off +)clear all + +--S 1 of 502 +t0:=(2+3*x)^4*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 502 +r0:=381073/96*(1-2*x)^(3/2)-832951/320*(1-2*x)^(5/2)+17337/16*(1-2*x)^(7/2)-_ + 17679/64*(1-2*x)^(9/2)+13905/352*(1-2*x)^(11/2)-2025/832*(1-2*x)^(13/2)-_ + 290521/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x +--R + +--R - 4994536 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x +--R + +--R - 4994536 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 502 +t0:=(2+3*x)^3*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 502 +r0:=91091/96*(1-2*x)^(3/2)-39977/80*(1-2*x)^(5/2)+17541/112*(1-2*x)^(7/2)-_ + 855/32*(1-2*x)^(9/2)+675/352*(1-2*x)^(11/2)-41503/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--------+ +--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--------+ +--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 502 +t0:=(2+3*x)^2*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 502 +r0:=1309/6*(1-2*x)^(3/2)-3467/40*(1-2*x)^(5/2)+255/14*(1-2*x)^(7/2)-_ + 25/16*(1-2*x)^(9/2)-5929/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1 +--R (2) ---------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1 +--R (3) ---------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 502 +t0:=(2+3*x)*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ----------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 502 +r0:=1133/24*(1-2*x)^(3/2)-101/8*(1-2*x)^(5/2)+75/56*(1-2*x)^(7/2)-_ + 847/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1 +--R (2) ------------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1 +--R (3) ------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 502 +t0:=(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 502 +r0:=55/6*(1-2*x)^(3/2)-5/4*(1-2*x)^(5/2)-121/4*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (- 15x - 40x - 67)\|- 2x + 1 +--R (2) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (- 15x - 40x - 67)\|- 2x + 1 +--R (3) ------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 502 +t0:=(3+5*x)^2/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 502 +r0:=-2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/9*(13+5*x)*sqrt(1-2*x),_ + -2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50/9*sqrt(1-2*x)-_ + 5/9*(3+5*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R [--------------------------------------------------------, +--R +--+ +--R 9\|21 +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R --------------------------------------------------------] +--R +--+ +--R 9\|21 +--R Type: Tuple(Expression(Integer)) +--E 27 + +--S 28 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R log(-----------------------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R 3x + 2 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R 9\|21 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 9\|21 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (1134x + 189x - 378)\|- 2x + 1 + (162x - 243x - 99x + 90)\|21 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 502 +t0:=(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 502 +r0:=46/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-25/9*sqrt(1-2*x)-_ + 1/63*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (138x + 92)atanh(---------------) + (- 175x - 117)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--R (63x + 42)\|21 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R (69x + 46)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 175x - 117)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (63x + 42)\|21 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23log(-------------------------------) - 46atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (46x - 23)\|3 \|7 \|21 - 966x + 483 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (- 378x + 567x + 231x - 210)\|21 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 502 +t0:=(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 502 +r0:=-257/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/126*sqrt(1-2*x)/(2+3*x)^2+137/882*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 13878x - 18504x - 6168)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +--+ +--------+ +--R (137x + 89)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (6939x + 9252x + 3084)log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (137x + 89)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 257log(-----------------------------) + 514atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 98\|21 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 771x + 1285)\|21 + (771x - 1285)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 514x + 257)\|3 \|7 \|21 + 10794x - 5397 +--R / +--R 2 +--------+ 3 2 +--+ +--R (12348x + 2058x - 4116)\|- 2x + 1 + (1764x - 2646x - 1078x + 980)\|21 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 502 +t0:=(3+5*x)^2/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 502 +r0:=-2245/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/189*sqrt(1-2*x)/(2+3*x)^3+205/2646*sqrt(1-2*x)/(2+3*x)^2-_ + 2245/6174*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 121230x - 242460x - 161640x - 35920)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (166698x + 333396x + 222264x + 49392)\|21 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (60615x + 121230x + 80820x + 17960)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (166698x + 333396x + 222264x + 49392)\|21 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2245log(-----------------------------) + 4490atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6174\|21 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 4490x + 2245)\|3 \|7 \|21 + 94290x - 47145 +--R / +--R 2 +--------+ +--R (777924x + 129654x - 259308)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (111132x - 166698x - 67914x + 61740)\|21 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 502 +t0:=(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 502 +r0:=-635/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/252*sqrt(1-2*x)/(2+3*x)^4+13/252*sqrt(1-2*x)/(2+3*x)^3-_ + 635/3528*sqrt(1-2*x)/(2+3*x)^2-635/8232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 102870x - 274320x - 274320x - 121920x - 20320) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (51435x + 137160x + 137160x + 60960x + 10160) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 635log(-----------------------------) + 1270atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 8232\|21 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1905x + 3175)\|21 + (1905x - 3175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1270x + 635)\|3 \|7 \|21 + 26670x - 13335 +--R / +--R 2 +--------+ +--R (1037232x + 172872x - 345744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (148176x - 222264x - 90552x + 82320)\|21 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 502 +t0:=(3+5*x)^2/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 502 +r0:=-117/9604*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1/315*sqrt(1-2*x)/(2+3*x)^5+341/8820*sqrt(1-2*x)/(2+3*x)^4-_ + 117/980*sqrt(1-2*x)/(2+3*x)^3-117/2744*sqrt(1-2*x)/(2+3*x)^2-_ + 351/19208*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 852930x - 2843100x - 3790800x - 2527200x - 842400x - 112320)\|3 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x +--R + +--R 9219840 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (426465x + 1421550x + 1895400x + 1263600x + 421200x + 56160)\|3 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x +--R + +--R 9219840 +--R * +--R +-+ +--R \|7 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 117\|3 log(-------------------------------) + 234\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 19208\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 502 +t0:=(2+3*x)^4*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 502 +r0:=3278737/128*(1-2*x)^(3/2)-12973191/640*(1-2*x)^(5/2)+_ + 1357793/128*(1-2*x)^(7/2)-1392467/384*(1-2*x)^(9/2)+_ + 1101465/1408*(1-2*x)^(11/2)-161325/1664*(1-2*x)^(13/2)+_ + 675/128*(1-2*x)^(15/2)-3195731/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x +--R + +--R 2 +--R - 31962552x - 24706048x - 25632688 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x +--R + +--R 2 +--R - 31962552x - 24706048x - 25632688 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 502 +t0:=(2+3*x)^3*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 502 +r0:=100793/16*(1-2*x)^(3/2)-1334949/320*(1-2*x)^(5/2)+_ + 98209/56*(1-2*x)^(7/2)-28895/64*(1-2*x)^(9/2)+_ + 11475/176*(1-2*x)^(11/2)-3375/832*(1-2*x)^(13/2)-456533/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x +--R + +--R - 17147586x - 18228666 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5005 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x +--R + +--R - 17147586x - 18228666 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5005 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 502 +t0:=(2+3*x)^2*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 502 +r0:=48279/32*(1-2*x)^(3/2)-64317/80*(1-2*x)^(5/2)+28555/112*(1-2*x)^(7/2)-_ + 4225/96*(1-2*x)^(9/2)+1125/352*(1-2*x)^(11/2)-65219/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1155 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 502 +t0:=(2+3*x)*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 502 +r0:=2783/8*(1-2*x)^(3/2)-561/4*(1-2*x)^(5/2)+1675/56*(1-2*x)^(7/2)-_ + 125/48*(1-2*x)^(9/2)-9317/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1 +--R (2) ----------------------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1 +--R (3) ----------------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 502 +t0:=(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 502 +r0:=605/8*(1-2*x)^(3/2)-165/8*(1-2*x)^(5/2)+125/56*(1-2*x)^(7/2)-_ + 1331/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 125x - 390x - 575x - 764)\|- 2x + 1 +--R (2) ----------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 125x - 390x - 575x - 764)\|- 2x + 1 +--R (3) ----------------------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 502 +t0:=(3+5*x)^3/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 502 +r0:=2/27*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-218/9*sqrt(1-2*x)-_ + 1/3*(3+5*x)^2*sqrt(1-2*x)-5/27*(41+61*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 2 +--+ +--------+ +--R 2atanh(---------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 2 +--+ +--------+ +--R log(-------------------------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1 +--R 3x + 2 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 502 +t0:=(3+5*x)^3/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 502 +r0:=-208/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1570/189*sqrt(1-2*x)-_ + 38/189*(3+5*x)*sqrt(1-2*x)/(2+3*x)-5/9*(3+5*x)^2*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (- 624x - 416)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (567x + 378)\|21 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R (312x + 208)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (567x + 378)\|21 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 104log(-----------------------------) + 208atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 189\|21 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 312x + 520)\|21 + (312x - 520)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 208x + 104)\|3 \|7 \|21 + 4368x - 2184 +--R / +--R 2 +--------+ 3 2 +--+ +--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 502 +t0:=(3+5*x)^3/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 502 +r0:=2381/441*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/126*(7-25*x)*_ + sqrt(1-2*x)/(2+3*x)^2-274/147*sqrt(1-2*x)/(2+3*x)-_ + 5/3*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (42858x + 57144x + 19048)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (7938x + 10584x + 3528)\|21 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (21429x + 28572x + 9524)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (7938x + 10584x + 3528)\|21 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2381log(-------------------------------) - 4762atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 882\|21 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001 +--R / +--R 2 +--------+ +--R (111132x + 18522x - 37044)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 15876x + 23814x + 9702x - 8820)\|21 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 502 +t0:=(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 502 +r0:=-78710/9261*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+10600/9261*_ + sqrt(1-2*x)-3385/9261*(3+5*x)*sqrt(1-2*x)/(2+3*x)-50/441*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2125170x - 4250340x - 2833560x - 629680)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (31680x + 41155x + 13373)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (250047x + 500094x + 333396x + 74088)\|21 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1062585x + 2125170x + 1416780x + 314840) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (31680x + 41155x + 13373)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (250047x + 500094x + 333396x + 74088)\|21 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39355log(-----------------------------) + 78710atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 9261\|21 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 118065x + 196775)\|21 + (118065x - 196775)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 78710x + 39355)\|3 \|7 \|21 + 1652910x - 826455 +--R / +--R 2 +--------+ +--R (1166886x + 194481x - 388962)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (166698x - 250047x - 101871x + 92610)\|21 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 502 +t0:=(3+5*x)^3/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 502 +r0:=-42995/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 3275/12348*sqrt(1-2*x)/(2+3*x)-1/18*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-_ + 1/28*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4+5/10584*(79+29*x)*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R 4 3 2 +--R (- 6965190x - 18573840x - 18573840x - 8255040x - 1375840) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3482595x + 9286920x + 9286920x + 4127520x + 687920) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 42995log(-----------------------------) + 85990atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 74088\|21 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 128985x + 214975)\|21 + (128985x - 214975)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 85990x + 42995)\|3 \|7 \|21 + 1805790x - 902895 +--R / +--R 2 +--------+ +--R (9335088x + 1555848x - 3111696)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1333584x - 2000376x - 814968x + 740880)\|21 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 502 +t0:=(3+5*x)^3/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 502 +r0:=-5293/21609*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 61/882*sqrt(1-2*x)/(2+3*x)^2-5293/43218*sqrt(1-2*x)/(2+3*x)-_ + 8/245*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^5+1/15435*(353+295*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 12861990x - 42873300x - 57164400x - 38109600x - 12703200x +--R + +--R - 1693760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x +--R + +--R 6914880 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (6430995x + 21436650x + 28582200x + 19054800x + 6351600x + 846880) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x +--R + +--R 6914880 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 5293log(-----------------------------) + 10586atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 43218\|21 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 15879x + 26465)\|21 + (15879x - 26465)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 10586x + 5293)\|3 \|7 \|21 + 222306x - 111153 +--R / +--R 2 +--------+ +--R (5445468x + 907578x - 1815156)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (777924x - 1166886x - 475398x + 432180)\|21 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 502 +t0:=(a+b*x)^2/((c+d*x)^2*sqrt(e+f*x)) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|f x + e +--R Type: Expression(Integer) +--E 111 + +--S 112 of 502 +r0:=(b*c-a*d)*(4*b*d*e-3*b*c*f-a*d*f)*atanh(sqrt(d)*sqrt(e+f*x)/_ + sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))+2*b^2*sqrt(e+f*x)/_ + (d^2*f)-(b*c-a*d)^2*sqrt(e+f*x)/(d^2*(d*e-c*f)*(c+d*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 2 2 +--R ((- a d - 2a b c d + 3b c d)f + (4a b d - 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- a c d - 2a b c d + 3b c )f + (4a b c d - 4b c d)e f +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R + +--R 2 2 2 2 2 2 2 2 +--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e) +--R * +--R +-----------+ +-+ +-------+ +--R \|- c f + d e \|d \|f x + e +--R / +--R 3 2 4 2 2 2 3 +-----------+ +-+ +--R ((c d f - d e f)x + c d f - c d e f)\|- c f + d e \|d +--R Type: Expression(Integer) +--E 112 + +--S 113 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 2 2 +--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e +--R log(----------------------------------------------------------------) +--R d x + c +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4b c d f - 4b d e)x + (2a d - 4a b c d + 6b c )f - 4b c d e) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- c d f + d e \|f x + e +--R / +--R +-------------+ +--R 3 2 4 2 2 2 3 | 2 +--R ((2c d f - 2d e f)x + 2c d f - 2c d e f)\|- c d f + d e +--R , +--R +--R 2 3 2 2 2 2 3 2 2 +--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R atan(------------------------) +--R c f - d e +--R + +--R 2 2 2 2 2 2 2 2 +--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R / +--R +-----------+ +--R 3 2 4 2 2 2 3 | 2 +--R ((c d f - d e f)x + c d f - c d e f)\|c d f - d e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 113 + +--S 114 of 502 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +-----------+ +-+ +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e +--R log(----------------------------------------------------------------) +--R d x + c +--R + +--R +-------------+ +--R 2 2 2 2 2 2 | 2 +--R ((2a d + 4a b c d - 6b c )f + (- 8a b d + 8b c d)e)\|- c d f + d e +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R / +--R +-------------+ +--R 2 3 | 2 +-----------+ +-+ +--R (2c d f - 2d e)\|- c d f + d e \|- c f + d e \|d +--R Type: Expression(Integer) +--E 114 + +--S 115 of 502 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 502 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 2 2 2 2 | 2 +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|c d f - d e +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R + +--R 2 2 2 2 2 2 +-----------+ +-+ +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R atan(------------------------) +--R c f - d e +--R / +--R +-----------+ +--R 2 3 +-----------+ +-+ | 2 +--R (c d f - d e)\|- c f + d e \|d \|c d f - d e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 502 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 502 +t0:=(2+3*x)^5/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 118 + +--S 119 of 502 +r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 125702/3125*sqrt(1-2*x)-748/625*(2+3*x)^2*sqrt(1-2*x)-_ + 149/525*(2+3*x)^3*sqrt(1-2*x)-1/15*(2+3*x)^4*sqrt(1-2*x)-_ + 1/3125*(31426+52375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R - 14atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 21875\|55 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 7log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 21875\|55 +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 3125\|55 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (1718750x + 171875x - 515625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (156250x - 234375x - 71875x + 75000)\|55 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 502 +t0:=(2+3*x)^4/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 502 +r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7878/625*sqrt(1-2*x)-_ + 9/5*(2+3*x)*sqrt(1-2*x)-48/125*(2+3*x)^2*sqrt(1-2*x)-_ + 3/35*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R - 14atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 4375\|55 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 7log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 4375\|55 +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 625\|55 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (343750x + 34375x - 103125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (31250x - 46875x - 14375x + 15000)\|55 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 502 +t0:=(2+3*x)^3/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 502 +r0:=-2/125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-542/125*sqrt(1-2*x)-_ + 3/25*(2+3*x)^2*sqrt(1-2*x)-1/125*(136+225*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R - 2atanh(---------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--R 125\|55 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 2 +--+ +--------+ +--R log(-----------------------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1 +--R 5x + 3 +--R --------------------------------------------------------------------------- +--R +--+ +--R 125\|55 +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 125\|55 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (68750x + 6875x - 20625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6250x - 9375x - 2875x + 3000)\|55 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 502 +t0:=(2+3*x)^2/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 133 + +--S 134 of 502 +r0:=-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-38/25*sqrt(1-2*x)-_ + 1/5*(2+3*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 15x - 48)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R log(-----------------------------) + (- 15x - 48)\|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Union(Expression(Integer),...) +--E 135 + +--S 136 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 502 +t0:=(2+3*x)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 138 + +--S 139 of 502 +r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/5*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) - 3\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------- +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R log(-----------------------------) - 3\|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------ +--R +--+ +--R 5\|55 +--R Type: Union(Expression(Integer),...) +--E 140 + +--S 141 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2750x + 275x - 825)\|- 2x + 1 + (250x - 375x - 115x + 120)\|55 +--R Type: Expression(Integer) +--E 142 + +)clear all + +--S 143 of 502 +t0:=1/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 502 +r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R 2atanh(---------------) +--R +--+ +--R \|11 +--R (2) - ----------------------- +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R (3) ---------------------------------- +--R +--+ +--R \|55 +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (550x + 55x - 165)\|- 2x + 1 + (50x - 75x - 23x + 24)\|55 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 502 +t0:=1/((2+3*x)*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--------+ +--R (15x + 19x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 502 +r0:=2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11) +--R +--R +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 2\|3 \|11 atanh(---------------) - 2\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2\|3 \|11 atanh(---------------) + 2\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 152 + +)clear all + +--S 153 of 502 +t0:=1/((2+3*x)^2*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 2 +--------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 502 +r0:=72/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+3/7*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R (216x + 144)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+ +--R (- 210x - 140)\|5 \|7 atanh(---------------) + 3\|7 \|11 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R (21x + 14)\|7 \|11 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (105x + 70)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (108x + 72)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R 3\|7 \|11 \|- 2x + 1 +--R / +--R +-+ +--+ +--R (21x + 14)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 36\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 72\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 7\|7 \|11 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 502 +t0:=1/((2+3*x)^3*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 502 +r0:=2523/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+3/14*sqrt(1-2*x)/(2+3*x)^2+_ + 219/98*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (45414x + 60552x + 20184)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (- 44100x - 58800x - 19600)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (657x + 459)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (882x + 1176x + 392)\|7 \|11 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (22050x + 29400x + 9800)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (22707x + 30276x + 10092)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R (657x + 459)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (882x + 1176x + 392)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2450\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2523\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 5046\|3 \|11 atanh(---------------) + 4900\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 98\|7 \|11 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 502 +t0:=1/((2+3*x)^4*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 502 +r0:=88310/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1/7*sqrt(1-2*x)/(2+3*x)^3+_ + 55/49*sqrt(1-2*x)/(2+3*x)^2+3840/343*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (2384370x + 4768740x + 3179160x + 706480)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 2315250x - 4630500x - 3087000x - 686000)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (9261x + 18522x + 12348x + 2744)\|7 \|11 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (1157625x + 2315250x + 1543500x + 343000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (1192185x + 2384370x + 1589580x + 353240)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (9261x + 18522x + 12348x + 2744)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 42875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 44155\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 88310\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 85750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 343\|7 \|11 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 502 +t0:=1/((2+3*x)^5*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 502 +r0:=36045/28*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1250*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 3/28*sqrt(1-2*x)/(2+3*x)^4+3/4*sqrt(1-2*x)/(2+3*x)^3+_ + 45/8*sqrt(1-2*x)/(2+3*x)^2+3135/56*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (5839290x + 15571440x + 15571440x + 6920640x + 1153440)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (- 5670000x - 15120000x - 15120000x - 6720000x - 1120000)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (2835000x + 7560000x + 7560000x + 3360000x + 560000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (2919645x + 7785720x + 7785720x + 3460320x + 576720)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35000\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 36045\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 72090\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 70000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 56\|7 \|11 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 502 +t0:=(2+3*x)^6/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 502 +r0:=-398/171875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 4434698/171875*sqrt(1-2*x)-26352/34375*(2+3*x)^2*sqrt(1-2*x)-_ + 1717/9625*(2+3*x)^3*sqrt(1-2*x)+8/825*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-_ + 1/15*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)-1/171875*(1108774+_ + 1847625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 13930x - 8358)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x +--R + +--R - 135011752 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (6015625x + 3609375)\|55 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (6965x + 4179)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x +--R + +--R - 135011752 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (6015625x + 3609375)\|55 +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 199log(-----------------------------) + 398atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 171875\|55 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 995x + 1592)\|55 + (995x - 1592)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 398x + 199)\|5 \|11 \|55 + 21890x - 10945 +--R / +--R 2 +--------+ +--R (94531250x + 9453125x - 28359375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8593750x - 12890625x - 3953125x + 4125000)\|55 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 502 +t0:=(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 502 +r0:=-332/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 278748/34375*sqrt(1-2*x)-318/275*(2+3*x)*sqrt(1-2*x)-_ + 1668/6875*(2+3*x)^2*sqrt(1-2*x)+26/1925*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)-3/35*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 11620x - 6972)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +--+ +--R (1203125x + 721875)\|55 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (5810x + 3486)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +--+ +--R (1203125x + 721875)\|55 +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 166log(-----------------------------) + 332atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 34375\|55 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 830x + 1328)\|55 + (830x - 1328)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 332x + 166)\|5 \|11 \|55 + 18260x - 9130 +--R / +--R 2 +--------+ +--R (18906250x + 1890625x - 5671875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1718750x - 2578125x - 790625x + 825000)\|55 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 502 +t0:=(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 502 +r0:=-266/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 19166/6875*sqrt(1-2*x)+28/1375*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)-_ + 3/25*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)-7/6875*(694+1125*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 1330x - 798)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (34375x + 20625)\|55 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (665x + 399)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (34375x + 20625)\|55 +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 133log(-----------------------------) + 266atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 6875\|55 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 665x + 1064)\|55 + (665x - 1064)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 266x + 133)\|5 \|11 \|55 + 14630x - 7315 +--R / +--R 2 +--------+ +--R (3781250x + 378125x - 1134375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (343750x - 515625x - 158125x + 165000)\|55 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 502 +t0:=(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 502 +r0:=-8/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-54/55*sqrt(1-2*x)+_ + 2/55*(2+3*x)*sqrt(1-2*x)/(3+5*x)-1/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R (- 40x - 24)atanh(---------------) + (- 99x - 396x - 202)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (20x + 12)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 99x - 396x - 202)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (275x + 165)\|55 +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4log(-----------------------------) + 8atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 20x + 32)\|55 + (20x - 32)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 8x + 4)\|5 \|11 \|55 + 440x - 220 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 502 +t0:=(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 502 +r0:=-134/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-9/25*sqrt(1-2*x)-_ + 1/275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 670x - 402)atanh(---------------) + (- 495x - 298)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------------- +--R +--+ +--R (1375x + 825)\|55 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (335x + 201)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 495x - 298)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (1375x + 825)\|55 +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 67log(-----------------------------) + 134atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 275\|55 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 134x + 67)\|5 \|11 \|55 + 7370x - 3685 +--R / +--R 2 +--------+ +--R (151250x + 15125x - 45375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (13750x - 20625x - 6325x + 6600)\|55 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 502 +t0:=(2+3*x)/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 502 +r0:=-68/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/55*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 340x - 204)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (170x + 102)log(-----------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 502 +t0:=1/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/11*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 10x - 6)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +--+ +--R (55x + 33)\|55 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (5x + 3)log(-----------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------------- +--R +--+ +--R (55x + 33)\|55 +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 11\|55 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 502 +t0:=1/((2+3*x)*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 2 +--------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 502 +r0:=-6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-5/11*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R (- 330x - 198)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+ +--R (320x + 192)\|5 \|7 atanh(---------------) - 5\|7 \|11 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R (55x + 33)\|7 \|11 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (165x + 99)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (160x + 96)\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R - 5\|7 \|11 \|- 2x + 1 +--R / +--R +-+ +--+ +--R (55x + 33)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 33\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 32\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 66\|3 \|11 atanh(---------------) - 64\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 11\|7 \|11 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 502 +t0:=1/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 502 +r0:=-426/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+650/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-340/77*sqrt(1-2*x)/(3+5*x)+3/7*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (- 70290x - 89034x - 28116)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (68250x + 86450x + 27300)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (- 1020x - 647)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (1155x + 1463x + 462)\|7 \|11 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (35145x + 44517x + 14058)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--R (34125x + 43225x + 13650)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R (- 1020x - 647)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (1155x + 1463x + 462)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2343\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2275\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 4686\|3 \|11 atanh(---------------) - 4550\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 77\|7 \|11 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 502 +t0:=1/((2+3*x)^3*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 502 +r0:=-22479/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+4900/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35845/1078*_ + sqrt(1-2*x)/(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 162/49*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 22254210x - 43024806x - 27694128x - 5934456)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (21609000x + 41777400x + 26891200x + 5762400)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (48510x + 93786x + 60368x + 12936)\|7 \|11 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (11127105x + 21512403x + 13847064x + 2967228)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--R (10804500x + 20888700x + 13445600x + 2881200)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (48510x + 93786x + 60368x + 12936)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 247269\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 240100\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 494538\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 480200\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1078\|7 \|11 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 502 +t0:=1/((2+3*x)^4*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 502 +r0:=-1051695/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+32750/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1676975/7546*_ + sqrt(1-2*x)/(3+5*x)+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+_ + 145/98*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+7585/343*sqrt(1-2*x)/_ + ((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 3123534150x - 8121188790x - 7912953180x - 3424318920x +--R + +--R - 555294960 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (3032977500x + 7885741500x + 7683543000x + 3325042000x + 539196000) +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1561767075x + 4060594395x + 3956476590x + 1712159460x + 277647480) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1516488750x + 3942870750x + 3841771500x + 1662521000x + 269598000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 11568645\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 11233250\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 23137290\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 22466500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 7546\|7 \|11 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 502 +t0:=(2+3*x)^6/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 502 +r0:=-33069/1890625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 9865791/1890625*sqrt(1-2*x)-22437/30250*(2+3*x)*sqrt(1-2*x)-_ + 56556/378125*(2+3*x)^2*sqrt(1-2*x)+59/3850*(2+3*x)^4*_ + sqrt(1-2*x)/(3+5*x)^2-3/35*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2+_ + 309/211750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 11574150x - 13888980x - 4166694)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 551306250x - 2690374500x - 6078090150x - 9876010320x +--R + +--R - 7254126105x - 1804176536 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (661718750x + 794062500x + 238218750)\|55 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (5787075x + 6944490x + 2083347)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 551306250x - 2690374500x - 6078090150x - 9876010320x +--R + +--R - 7254126105x - 1804176536 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (661718750x + 794062500x + 238218750)\|55 +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 33069log(-----------------------------) + 66138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3781250\|55 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 165345x + 264552)\|55 + (165345x - 264552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 66138x + 33069)\|5 \|11 \|55 + 3637590x - 1818795 +--R / +--R 2 +--------+ +--R (2079687500x + 207968750x - 623906250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (189062500x - 283593750x - 86968750x + 90750000)\|55 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 502 +t0:=(2+3*x)^5/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 502 +r0:=-22113/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 674163/378125*sqrt(1-2*x)+61/2750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 3/25*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2+504/75625*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)-189/756250*(1842+2875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 1105650x - 1326780x - 398034)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (18906250x + 22687500x + 6806250)\|55 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (552825x + 663390x + 199017)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (18906250x + 22687500x + 6806250)\|55 +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 22113log(-----------------------------) + 44226atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 756250\|55 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 110565x + 176904)\|55 + (110565x - 176904)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 44226x + 22113)\|5 \|11 \|55 + 2432430x - 1216215 +--R / +--R 2 +--------+ +--R (415937500x + 41593750x - 124781250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37812500x - 56718750x - 17393750x + 18150000)\|55 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 502 +t0:=(2+3*x)^4/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 502 +r0:=-2667/15125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 9513/15125*sqrt(1-2*x)+21/550*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2-_ + 1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2+21/1210*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 133350x - 160020x - 48006)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (756250x + 907500x + 272250)\|55 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (66675x + 80010x + 24003)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (756250x + 907500x + 272250)\|55 +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2667log(-----------------------------) + 5334atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 30250\|55 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 13335x + 21336)\|55 + (13335x - 21336)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5334x + 2667)\|5 \|11 \|55 + 293370x - 146685 +--R / +--R 2 +--------+ +--R (16637500x + 1663750x - 4991250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1512500x - 2268750x - 695750x + 726000)\|55 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 502 +t0:=(2+3*x)^3/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 502 +r0:=-1347/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+13/110*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x)^2-3/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 201/3025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 67350x - 80820x - 24246)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (33675x + 40410x + 12123)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 1347log(-----------------------------) + 2694atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6050\|55 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 6735x + 10776)\|55 + (6735x - 10776)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2694x + 1347)\|5 \|11 \|55 + 148170x - 74085 +--R / +--R 2 +--------+ +--R (3327500x + 332750x - 998250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (302500x - 453750x - 139150x + 145200)\|55 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 502 +t0:=(2+3*x)^2/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 502 +r0:=-2313/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/550*sqrt(1-2*x)/_ + (3+5*x)^2-27/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 115650x - 138780x - 41634)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 675x - 416)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (57825x + 69390x + 20817)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 675x - 416)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2313log(-----------------------------) + 4626atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6050\|55 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 11565x + 18504)\|55 + (11565x - 18504)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 4626x + 2313)\|5 \|11 \|55 + 254430x - 127215 +--R / +--R 2 +--------+ +--R (3327500x + 332750x - 998250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (302500x - 453750x - 139150x + 145200)\|55 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 502 +t0:=(2+3*x)/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 502 +r0:=-69/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*sqrt(1-2*x)/_ + (3+5*x)^2-69/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 3450x - 4140x - 1242)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 345x - 218)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (30250x + 36300x + 10890)\|55 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (1725x + 2070x + 621)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 345x - 218)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (30250x + 36300x + 10890)\|55 +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 69log(-----------------------------) + 138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1210\|55 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795 +--R / +--R 2 +--------+ +--R (665500x + 66550x - 199650)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (60500x - 90750x - 27830x + 29040)\|55 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 502 +t0:=1/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 502 +r0:=-3/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/22*sqrt(1-2*x)/_ + (3+5*x)^2-3/242*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (- 150x - 180x - 54)atanh(---------------) + (- 15x - 20)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R 2 +--+ +--R (6050x + 7260x + 2178)\|55 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (75x + 90x + 27)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 15x - 20)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6050x + 7260x + 2178)\|55 +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 3log(-----------------------------) + 6atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 242\|55 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165 +--R / +--R 2 +--------+ +--R (133100x + 13310x - 39930)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (12100x - 18150x - 5566x + 5808)\|55 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 502 +t0:=1/((2+3*x)*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (375x + 925x + 855x + 351x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 502 +r0:=18*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2115/121*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-5/22*sqrt(1-2*x)/(3+5*x)^2+_ + 315/242*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (108900x + 130680x + 39204)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (- 105750x - 126900x - 38070)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (1575x + 890)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (6050x + 7260x + 2178)\|7 \|11 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (52875x + 63450x + 19035)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (54450x + 65340x + 19602)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R (1575x + 890)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (6050x + 7260x + 2178)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2115\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2178\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 4356\|3 \|11 atanh(---------------) + 4230\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 242\|7 \|11 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 502 +t0:=1/((2+3*x)^2*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 502 +r0:=1908/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-32025/121*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-505/154*sqrt(1-2*x)/(3+5*x)^2+_ + 3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+33465/1694*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (34630200x + 64643040x + 40171032x + 8311248)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 33626250x - 62769000x - 39006450x - 8070300)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (127050x + 237160x + 147378x + 30492)\|7 \|11 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (16813125x + 31384500x + 19503225x + 4035150)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (17315100x + 32321520x + 20085516x + 4155624)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (127050x + 237160x + 147378x + 30492)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 224175\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 230868\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 461736\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 448350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1694\|7 \|11 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 502 +t0:=1/((2+3*x)^3*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1 +--R Type: Expression(Integer) +--E 273 + +--S 274 of 502 +r0:=134217/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-321825/121*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35495/1078*_ + sqrt(1-2*x)/(3+5*x)^2+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 429/98*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1177080/5929*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 7308115650x + 18513892980x + 17571958074x + 7405557192x +--R + +--R 1169298504 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 7096241250x - 17977144500x - 17062517850x - 7190857800x +--R + +--R - 1135398600 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3548120625x + 8988572250x + 8531258925x + 3595428900x + 567699300) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (3654057825x + 9256946490x + 8785979037x + 3702778596x + 584649252) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 15769425\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 16240257\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 32480514\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 31538850\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 11858\|7 \|11 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 502 +t0:=1/((2+3*x)^4*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 502 +r0:=7852680/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 2689875/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_ + 2076675/7546*sqrt(1-2*x)/(3+5*x)^2+1/7*sqrt(1-2*x)/((2+3*x)^3*_ + (3+5*x)^2)+90/49*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 12555/343*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+137735775/83006*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1282735278000x + 4104752889600x + 5250663071280x + 3356015556960x +--R + +--R 1071796587840x + 136825096320 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 +--R - 1245546618750x - 3985749180000x - 5098437492750x +--R + +--R 2 +--R - 3258719005500x - 1040723397000x - 132858306000 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R 18594329625x + 47728484550x + 45899434890x + 19599448500x +--R + +--R 3135381218 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x +--R + +--R 5976432 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 622773309375x + 1992874590000x + 2549218746375x + 1629359502750x +--R + +--R 520361698500x + 66429153000 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 641367639000x + 2052376444800x + 2625331535640x + 1678007778480x +--R + +--R 535898293920x + 68412548160 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R 18594329625x + 47728484550x + 45899434890x + 19599448500x +--R + +--R 3135381218 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x +--R + +--R 5976432 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 922627125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 950174280\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1900348560\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1845254250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 502 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 502 +r0:=-7882483/128*(1-2*x)^(3/2)+4084101/128*(1-2*x)^(5/2)-_ + 787185/64*(1-2*x)^(7/2)+422919/128*(1-2*x)^(9/2)-_ + 821583/1408*(1-2*x)^(11/2)+101331/1664*(1-2*x)^(13/2)-_ + 729/256*(1-2*x)^(15/2)+9058973/256/sqrt(1-2*x)+15647317/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 8 7 6 5 4 3 +--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x +--R + +--R 2 +--R - 8106616x - 16881328x + 16936240 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 +--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x +--R + +--R 2 +--R - 8106616x - 16881328x + 16936240 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 502 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 502 +r0:=-1692705/128*(1-2*x)^(3/2)+731619/128*(1-2*x)^(5/2)-_ + 225855/128*(1-2*x)^(7/2)+45549/128*(1-2*x)^(9/2)-_ + 59049/1408*(1-2*x)^(11/2)+3645/1664*(1-2*x)^(13/2)+_ + 1294139/128/sqrt(1-2*x)+3916031/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x +--R + +--R - 4512448x + 4539904 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x +--R + +--R - 4512448x + 4539904 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 502 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 502 +r0:=-173215/64*(1-2*x)^(3/2)+7497/8*(1-2*x)^(5/2)-13905/64*(1-2*x)^(7/2)+_ + 117/4*(1-2*x)^(9/2)-1215/704*(1-2*x)^(11/2)+_ + 184877/64/sqrt(1-2*x)+60025/8*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760 +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 502 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760 +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 502 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 502 +r0:=-8281/16*(1-2*x)^(3/2)+10773/80*(1-2*x)^(5/2)-4671/224*(1-2*x)^(7/2)+_ + 45/32*(1-2*x)^(9/2)+26411/32/sqrt(1-2*x)+57281/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456 +--R (2) ------------------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456 +--R (3) ------------------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 502 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 502 +r0:=-357/4*(1-2*x)^(3/2)+621/40*(1-2*x)^(5/2)-135/112*(1-2*x)^(7/2)+_ + 3773/16/sqrt(1-2*x)+3283/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 675x - 2997x - 6987x - 19154x + 19994 +--R (2) ------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 675x - 2997x - 6987x - 19154x + 19994 +--R (3) ------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 502 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 502 +r0:=-103/8*(1-2*x)^(3/2)+9/8*(1-2*x)^(5/2)+539/8/sqrt(1-2*x)+707/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 9x - 38x - 132x + 144 +--R (2) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x - 38x - 132x + 144 +--R (3) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 502 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 502 +r0:=-5/4*(1-2*x)^(3/2)+77/4/sqrt(1-2*x)+17*sqrt(1-2*x) +--R +--R +--R 2 +--R - 5x - 29x + 35 +--R (2) ---------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5x - 29x + 35 +--R (3) ---------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 502 +t0:=(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R - 5x - 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 502 +r0:=11/2/sqrt(1-2*x)+5/2*sqrt(1-2*x) +--R +--R +--R - 5x + 8 +--R (2) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 502 +a0:=integrate(t0,x) +--R +--R +--R - 5x + 8 +--R (3) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 502 +r0:=2/7*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R 2\|- 2x + 1 atanh(---------------) + 11\|21 +--R +-+ +--R \|7 +--R (2) -------------------------------------------- +--R +--+ +--------+ +--R 7\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R \|- 2x + 1 log(-------------------------------) + 11\|21 +--R 3x + 2 +--R (3) --------------------------------------------------------- +--R +--+ +--------+ +--R 7\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 7\|21 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (882x + 147x - 294)\|- 2x + 1 + (- 126x + 189x + 77x - 70)\|21 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 502 +r0:=-64/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+64/147/sqrt(1-2*x)+_ + 1/21/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (- 192x - 128)\|- 2x + 1 atanh(---------------) + (64x + 45)\|21 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (147x + 98)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R (96x + 64)\|- 2x + 1 log(-----------------------------) + (64x + 45)\|21 +--R 3x + 2 +--R ------------------------------------------------------------------------- +--R +--+ +--------+ +--R (147x + 98)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 32log(-----------------------------) + 64atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 96x + 160)\|21 + (96x - 160)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 64x + 32)\|3 \|7 \|21 + 1344x - 672 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 502 +r0:=-65/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/42/((2+3*x)^2*_ + sqrt(1-2*x))+65/147/((2+3*x)*sqrt(1-2*x))-195/686*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 1170x - 1560x - 520)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--R (1170x + 1105x + 233)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 8232x + 2744)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (585x + 780x + 260)\|3 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (1170x + 1105x + 233)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 8232x + 2744)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 65\|3 log(-------------------------------) + 130\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 502 +r0:=-10/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/63/((2+3*x)^3*_ + sqrt(1-2*x))+4/9/((2+3*x)^2*sqrt(1-2*x))-5/21*sqrt(1-2*x)/_ + (2+3*x)^2-5/49*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (- 270x - 540x - 360x - 80)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (90x + 145x + 57x + 1)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (135x + 270x + 180x + 40)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (90x + 145x + 57x + 1)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 5log(-----------------------------) + 10atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 15x + 25)\|21 + (15x - 25)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 10x + 5)\|3 \|7 \|21 + 210x - 105 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 502 +r0:=-655/9604*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/84/((2+3*x)^4*_ + sqrt(1-2*x))+131/294/((2+3*x)^3*sqrt(1-2*x))-131/588*_ + sqrt(1-2*x)/(2+3*x)^3-655/8232*sqrt(1-2*x)/(2+3*x)^2-_ + 655/19208*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 106110x - 282960x - 282960x - 125760x - 20960)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (35370x + 80565x + 60391x + 10742x - 2566)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (53055x + 141480x + 141480x + 62880x + 10480)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (35370x + 80565x + 60391x + 10742x - 2566)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 655log(-----------------------------) + 1310atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 19208\|21 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1965x + 3275)\|21 + (1965x - 3275)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1310x + 655)\|3 \|7 \|21 + 27510x - 13755 +--R / +--R 2 +--------+ +--R (2420208x + 403368x - 806736)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (345744x - 518616x - 211288x + 192080)\|21 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^6) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------------------------- +--R 7 6 5 4 2 +--------+ +--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 502 +r0:=-123/16807*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/105/((2+3*x)^5*_ + sqrt(1-2*x))+328/735/((2+3*x)^4*sqrt(1-2*x))-369/1715*sqrt(1-2*x)/_ + (2+3*x)^4-123/1715*sqrt(1-2*x)/(2+3*x)^3-123/4802*sqrt(1-2*x)/_ + (2+3*x)^2-369/33614*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 298890x - 996300x - 1328400x - 885600x - 295200x - 39360)\|3 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7 +--R / +--R 5 4 3 2 +--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x +--R + +--R 5378240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (149445x + 498150x + 664200x + 442800x + 147600x + 19680)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7 +--R / +--R 5 4 3 2 +--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x +--R + +--R 5378240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 123\|3 log(-------------------------------) + 246\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 33614\|7 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 502 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 502 +r0:=-8117095/384*(1-2*x)^(3/2)+1179381/128*(1-2*x)^(5/2)-_ + 367155/128*(1-2*x)^(7/2)+74667/128*(1-2*x)^(9/2)-_ + 97605/1408*(1-2*x)^(11/2)+6075/1664*(1-2*x)^(13/2)+_ + 2033647/128/sqrt(1-2*x)+6206585/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x +--R + +--R - 21370088x + 21493640 +--R / +--R +--------+ +--R 429\|- 2x + 1 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x +--R + +--R - 21370088x + 21493640 +--R / +--R +--------+ +--R 429\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 502 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 502 +r0:=-832951/192*(1-2*x)^(3/2)+121359/80*(1-2*x)^(5/2)-_ + 159111/448*(1-2*x)^(7/2)+1545/32*(1-2*x)^(9/2)-_ + 2025/704*(1-2*x)^(11/2)+290521/64/sqrt(1-2*x)+381073/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x +--R + +--R 15380984 +--R / +--R +--------+ +--R 1155\|- 2x + 1 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x +--R + +--R 15380984 +--R / +--R +--------+ +--R 1155\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 502 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 502 +r0:=-39977/48*(1-2*x)^(3/2)+17541/80*(1-2*x)^(5/2)-_ + 7695/224*(1-2*x)^(7/2)+75/32*(1-2*x)^(9/2)+_ + 41503/32/sqrt(1-2*x)+91091/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286 +--R (2) ---------------------------------------------------------- +--R +--------+ +--R 105\|- 2x + 1 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286 +--R (3) ---------------------------------------------------------- +--R +--------+ +--R 105\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 502 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 502 +r0:=-3467/24*(1-2*x)^(3/2)+51/2*(1-2*x)^(5/2)-225/112*(1-2*x)^(7/2)+_ + 5929/16/sqrt(1-2*x)+1309/2*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 675x - 2934x - 6721x - 18230x + 18986 +--R (2) ------------------------------------------ +--R +--------+ +--R 21\|- 2x + 1 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 675x - 2934x - 6721x - 18230x + 18986 +--R (3) ------------------------------------------ +--R +--------+ +--R 21\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 502 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 502 +r0:=-505/24*(1-2*x)^(3/2)+15/8*(1-2*x)^(5/2)+847/8/sqrt(1-2*x)+_ + 1133/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 45x - 185x - 631x + 685 +--R (2) --------------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 45x - 185x - 631x + 685 +--R (3) --------------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 502 +t0:=(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 502 +r0:=-25/12*(1-2*x)^(3/2)+121/4/sqrt(1-2*x)+55/2*sqrt(1-2*x) +--R +--R +--R 2 +--R - 25x - 140x + 167 +--R (2) ------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 25x - 140x + 167 +--R (3) ------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 502 +r0:=-2/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/sqrt(1-2*x)+_ + 25/6*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 175x + 269)\|21 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------- +--R +--+ +--------+ +--R 21\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 175x + 269)\|21 +--R 3x + 2 +--R (3) ------------------------------------------------------------------- +--R +--+ +--------+ +--R 21\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 502 +r0:=134/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)*_ + sqrt(1-2*x))-1091/294*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (402x + 268)\|- 2x + 1 atanh(---------------) + (1091x + 725)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (201x + 134)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--R (1091x + 725)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 67log(-------------------------------) - 134atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (134x - 67)\|3 \|7 \|21 - 2814x + 1407 +--R / +--R 2 +--------+ +--R (18522x + 3087x - 6174)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2646x + 3969x + 1617x - 1470)\|21 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 502 +r0:=-2045/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^2*_ + sqrt(1-2*x))-545/147*sqrt(1-2*x)/(2+3*x)^2-2045/2058*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (- 36810x - 49080x - 16360)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (12270x + 17305x + 6067)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (18405x + 24540x + 8180)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (12270x + 17305x + 6067)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2045log(-----------------------------) + 4090atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6135x + 10225)\|21 + (6135x - 10225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 4090x + 2045)\|3 \|7 \|21 + 85890x - 42945 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37044x - 55566x - 22638x + 20580)\|21 +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 502 +r0:=-905/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^3*_ + sqrt(1-2*x))-467/126*sqrt(1-2*x)/(2+3*x)^3-905/882*_ + sqrt(1-2*x)/(2+3*x)^2-905/2058*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (- 48870x - 97740x - 65160x - 14480)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (16290x + 26245x + 13747x + 2316)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (24435x + 48870x + 32580x + 7240)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (16290x + 26245x + 13747x + 2316)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 905log(-----------------------------) + 1810atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1810x + 905)\|3 \|7 \|21 + 38010x - 19005 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37044x - 55566x - 22638x + 20580)\|21 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 502 +r0:=-9145/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^4*_ + sqrt(1-2*x))-2179/588*sqrt(1-2*x)/(2+3*x)^4-1829/1764*_ + sqrt(1-2*x)/(2+3*x)^3-9145/24696*sqrt(1-2*x)/(2+3*x)^2-_ + 9145/57624*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 1481490x - 3950640x - 3950640x - 1755840x - 292640)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (740745x + 1975320x + 1975320x + 877920x + 146320)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 9145log(-----------------------------) + 18290atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 57624\|21 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 27435x + 45725)\|21 + (27435x - 45725)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 18290x + 9145)\|3 \|7 \|21 + 384090x - 192045 +--R / +--R 2 +--------+ +--R (7260624x + 1210104x - 2420208)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1037232x - 1555848x - 633864x + 576240)\|21 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 502 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 502 +r0:=-4324397/128*(1-2*x)^(3/2)+9504551/640*(1-2*x)^(5/2)-_ + 4177401/896*(1-2*x)^(7/2)+122385/128*(1-2*x)^(9/2)-_ + 161325/1408*(1-2*x)^(11/2)+10125/1664*(1-2*x)^(13/2)+_ + 3195731/128/sqrt(1-2*x)+9836211/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x +--R + +--R 2 +--R - 184884496x - 393552752x + 395714912 +--R / +--R +--------+ +--R 5005\|- 2x + 1 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x +--R + +--R 2 +--R - 184884496x - 393552752x + 395714912 +--R / +--R +--------+ +--R 5005\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 502 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 502 +r0:=-444983/64*(1-2*x)^(3/2)+98209/40*(1-2*x)^(5/2)-260055/448*(1-2*x)^(7/2)+_ + 1275/16*(1-2*x)^(9/2)-3375/704*(1-2*x)^(11/2)+456533/64/sqrt(1-2*x)+_ + 302379/16*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x +--R + +--R 8096086 +--R / +--R +--------+ +--R 385\|- 2x + 1 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x +--R + +--R 8096086 +--R / +--R +--------+ +--R 385\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 502 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 502 +r0:=-21439/16*(1-2*x)^(3/2)+5711/16*(1-2*x)^(5/2)-12675/224*(1-2*x)^(7/2)+_ + 125/32*(1-2*x)^(9/2)+65219/32/sqrt(1-2*x)+144837/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700 +--R (2) ---------------------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700 +--R (3) ---------------------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 502 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 502 +r0:=-935/4*(1-2*x)^(3/2)+335/8*(1-2*x)^(5/2)-375/112*(1-2*x)^(7/2)+_ + 9317/16/sqrt(1-2*x)+8349/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 375x - 1595x - 3590x - 9637x + 10015 +--R (2) ----------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 375x - 1595x - 3590x - 9637x + 10015 +--R (3) ----------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 502 +t0:=(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 502 +r0:=-275/8*(1-2*x)^(3/2)+25/8*(1-2*x)^(5/2)+1331/8/sqrt(1-2*x)+_ + 1815/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 25x - 100x - 335x + 362 +--R (2) --------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 25x - 100x - 335x + 362 +--R (3) --------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 502 +r0:=2/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+737/63*(3+5*x)/sqrt(1-2*x)-_ + 5/9*(3+5*x)^2/sqrt(1-2*x)+3680/63*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 2 +--+ +--R 2\|- 2x + 1 atanh(---------------) + (- 875x - 4725x + 5576)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R 63\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 875x - 4725x + 5576)\|21 +--R / +--R +--+ +--------+ +--R 63\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 63\|21 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (7938x + 1323x - 2646)\|- 2x + 1 + (- 1134x + 1701x + 693x - 630)\|21 +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 502 +r0:=-68/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+374/21*(3+5*x)/((2+3*x)*_ + sqrt(1-2*x))-5/3*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))+386/147*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R (- 204x - 136)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 6125x + 4968x + 6035)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (102x + 68)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 6125x + 4968x + 6035)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714 +--R / +--R 2 +--------+ 3 2 +--+ +--R (18522x + 3087x - 6174)\|- 2x + 1 + (2646x - 3969x - 1617x + 1470)\|21 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 502 +r0:=2245/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_ + ((2+3*x)^2*sqrt(1-2*x))+650/343*sqrt(1-2*x)+5/98*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-5/2058*(61+65*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (40410x + 53880x + 17960)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (72280x + 95895x + 31811)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (20205x + 26940x + 8980)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (72280x + 95895x + 31811)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2245log(-------------------------------) - 4490atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4490x - 2245)\|3 \|7 \|21 - 94290x + 47145 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 37044x + 55566x + 22638x - 20580)\|21 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 502 +r0:=-9320/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_ + ((2+3*x)^3*sqrt(1-2*x))+590/3087*sqrt(1-2*x)/(2+3*x)+_ + 40/441*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2+1/21*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 251640x - 503280x - 335520x - 74560)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (83880x + 178015x + 125154x + 29177)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (125820x + 251640x + 167760x + 37280)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (83880x + 178015x + 125154x + 29177)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4660log(-----------------------------) + 9320atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 3087\|21 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13980x + 23300)\|21 + (13980x - 23300)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 9320x + 4660)\|3 \|7 \|21 + 195720x - 97860 +--R / +--R 2 +--------+ +--R (388962x + 64827x - 129654)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (55566x - 83349x - 33957x + 30870)\|21 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 502 +r0:=-39185/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 2/7*(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x))+375/2744*sqrt(1-2*x)/(2+3*x)^2-_ + 39185/57624*sqrt(1-2*x)/(2+3*x)+47/588*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3+_ + 9/196*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 6347970x - 16927920x - 16927920x - 7523520x - 1253920)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (3173985x + 8463960x + 8463960x + 3761760x + 626960)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39185log(-----------------------------) + 78370atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 57624\|21 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 117555x + 195925)\|21 + (117555x - 195925)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 78370x + 39185)\|3 \|7 \|21 + 1645770x - 822885 +--R / +--R 2 +--------+ +--R (7260624x + 1210104x - 2420208)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1037232x - 1555848x - 633864x + 576240)\|21 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 502 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 502 +r0:=-2/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+406/165*(2+3*x)^4/_ + sqrt(1-2*x)-1/15*(2+3*x)^5/sqrt(1-2*x)+19886122/34375*sqrt(1-2*x)+_ + 22727/275*(2+3*x)*sqrt(1-2*x)+121752/6875*(2+3*x)^2*sqrt(1-2*x)+_ + 8117/1925*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 14\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x +--R + +--R 213097384 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R 240625\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R 7\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x +--R + +--R 213097384 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R 240625\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 34375\|55 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (18906250x + 1890625x - 5671875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1718750x - 2578125x - 790625x + 825000)\|55 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 502 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 502 +r0:=-2/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+139/55*(2+3*x)^3/_ + sqrt(1-2*x)-3/35*(2+3*x)^4/sqrt(1-2*x)+1050298/6875*sqrt(1-2*x)+_ + 6252/1375*(2+3*x)^2*sqrt(1-2*x)+1/6875*(262574+437625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 14\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55 +--R / +--R +--+ +--------+ +--R 48125\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R 7\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55 +--R / +--R +--+ +--------+ +--R 48125\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 6875\|55 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (3781250x + 378125x - 1134375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (343750x - 515625x - 158125x + 165000)\|55 +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 502 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 502 +r0:=-2/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+728/275*(2+3*x)^2/_ + sqrt(1-2*x)-3/25*(2+3*x)^3/sqrt(1-2*x)+50922/1375*sqrt(1-2*x)+_ + 291/55*(2+3*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 2\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 4455x - 19800x - 71379x + 78712)\|55 +--R / +--R +--+ +--------+ +--R 1375\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R \|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 4455x - 19800x - 71379x + 78712)\|55 +--R / +--R +--+ +--------+ +--R 1375\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 1375\|55 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (756250x + 75625x - 226875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (68750x - 103125x - 31625x + 33000)\|55 +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 502 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 502 +r0:=-2/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+161/55*(2+3*x)/_ + sqrt(1-2*x)-1/5*(2+3*x)^2/sqrt(1-2*x)+2412/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 2 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 495x - 3069x + 3802)\|55 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +--------+ +--R 275\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 2 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 495x - 3069x + 3802)\|55 +--R 5x + 3 +--R ----------------------------------------------------------------------------- +--R +--+ +--------+ +--R 275\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 275\|55 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (151250x + 15125x - 45375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (13750x - 20625x - 6325x + 6600)\|55 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 502 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 502 +r0:=-2/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/sqrt(1-2*x)+_ + 9/10*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 99x + 172)\|55 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------- +--R +--+ +--------+ +--R 55\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 99x + 172)\|55 +--R 5x + 3 +--R (3) ------------------------------------------------------------------ +--R +--+ +--------+ +--R 55\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 502 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + 7\|55 +--R +--+ +--R \|11 +--R (2) --------------------------------------------- +--R +--+ +--------+ +--R 11\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R \|- 2x + 1 log(-----------------------------) + 7\|55 +--R 5x + 3 +--R (3) ------------------------------------------------------ +--R +--+ +--------+ +--R 11\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 11\|55 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 502 +t0:=1/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|5 \|- 2x + 1 atanh(---------------) + 2\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--------+ +--R 11\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 502 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--+ +--R \|5 \|- 2x + 1 log(---------------------------------) + 2\|11 +--R 5x + 3 +--R (3) -------------------------------------------------------------- +--R +--+ +--------+ +--R 11\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R \|5 log(---------------------------------) + 2\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 11\|11 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 502 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------- +--R 3 2 +--------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 502 +r0:=6/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+4/77/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R 66\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +-+ +--+ +--R - 70\|5 \|7 \|- 2x + 1 atanh(---------------) + 4\|7 \|11 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--------+ +--R 77\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ +--+ +--R 33\|3 \|11 \|- 2x + 1 log(---------------------------------) + 4\|7 \|11 +--R 3x + 2 +--R / +--R +-+ +--+ +--------+ +--R 77\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 33\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 66\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 77\|7 \|11 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 502 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 4 3 2 +--------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 502 +r0:=228/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((2+3*x)*_ + sqrt(1-2*x))+87/539*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (7524x + 5016)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 7350x - 4900)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (- 174x + 115)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (1617x + 1078)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (3675x + 2450)\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (3762x + 2508)\|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--R (- 174x + 115)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (1617x + 1078)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1225\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1254\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2508\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 539\|7 \|11 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 502 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3l.input.pdf b/src/axiom-website/CATS/rich3l.input.pdf new file mode 100644 index 0000000..b47f7e7 Binary files /dev/null and b/src/axiom-website/CATS/rich3l.input.pdf differ diff --git a/src/axiom-website/CATS/rich3m.input.pamphlet b/src/axiom-website/CATS/rich3m.input.pamphlet new file mode 100644 index 0000000..ade3647 --- /dev/null +++ b/src/axiom-website/CATS/rich3m.input.pamphlet @@ -0,0 +1,8548 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3m.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 55 matching answers. +\item 37 cases where Axiom supplied 2 results. +\item 8 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3m.output +)spool rich3m.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=8025/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*sqrt(1-2*x))+75/1078*sqrt(1-2*x)/(2+3*x)^2+_ + 7575/7546*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (1588950x + 2118600x + 706200)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 1543500x - 2058000x - 686000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 45450x - 8625x + 16067)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (771750x + 1029000x + 343000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (794475x + 1059300x + 353100)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 45450x - 8625x + 16067)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 85750\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 88275\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 176550\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 171500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 7546\|7 \|11 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=40140/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^3*sqrt(1-2*x))+3/77*sqrt(1-2*x)/(2+3*x)^3+_ + 270/539*sqrt(1-2*x)/(2+3*x)^2+19185/3773*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--------+ +--R (11921580x + 23843160x + 15895440x + 3532320)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (- 11576250x - 23152500x - 15435000x - 3430000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (5788125x + 11576250x + 7717500x + 1715000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (5960790x + 11921580x + 7947720x + 1766160)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 214375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 220770\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 441540\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 428750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 3773\|7 \|11 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-402/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 139/55*(2+3*x)^4/((3+5*x)*sqrt(1-2*x))-3/35*(2+3*x)^5/((3+5*x)*_ + sqrt(1-2*x))+36473898/378125*sqrt(1-2*x)+217152/75625*(2+3*x)^2*_ + sqrt(1-2*x)-4839/21175*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+_ + 3/378125*(3039458+5065875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 14070x - 8442)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x +--R + +--R 1143572552 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (13234375x + 7940625)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (7035x + 4221)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x +--R + +--R 1143572552 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (13234375x + 7940625)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 201log(-----------------------------) + 402atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 378125\|55 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1005x + 1608)\|55 + (1005x - 1608)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 402x + 201)\|5 \|11 \|55 + 22110x - 11055 +--R / +--R 2 +--------+ +--R (207968750x + 20796875x - 62390625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18906250x - 28359375x - 8696875x + 9075000)\|55 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-336/75625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 728/275*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-3/25*(2+3*x)^4/((3+5*x)*_ + sqrt(1-2*x))+1763496/75625*sqrt(1-2*x)+2016/605*(2+3*x)*_ + sqrt(1-2*x)-3612/15125*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 1680x - 1008)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55 +--R / +--R +--+ +--------+ +--R (378125x + 226875)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (840x + 504)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55 +--R / +--R +--+ +--------+ +--R (378125x + 226875)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 168log(-----------------------------) + 336atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 75625\|55 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 840x + 1344)\|55 + (840x - 1344)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 336x + 168)\|5 \|11 \|55 + 18480x - 9240 +--R / +--R 2 +--------+ +--R (41593750x + 4159375x - 12478125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3781250x - 5671875x - 1739375x + 1815000)\|55 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-54/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 161/55*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 1/5*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))+_ + 15648/3025*sqrt(1-2*x)+3/3025*(436+815*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 270x - 162)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 16335x - 114345x + 68661x + 78832)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (135x + 81)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 16335x - 114345x + 68661x + 78832)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 27log(-----------------------------) + 54atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 135x + 216)\|55 + (135x - 216)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 54x + 27)\|5 \|11 \|55 + 2970x - 1485 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-204/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 238/55*(2+3*x)/((3+5*x)*sqrt(1-2*x))-3/5*(2+3*x)^2/_ + ((3+5*x)*sqrt(1-2*x))-1158/3025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 1020x - 612)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 16335x + 19806x + 17762)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (510x + 306)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (- 16335x + 19806x + 17762)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 102log(-----------------------------) + 204atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 510x + 816)\|55 + (510x - 816)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 204x + 102)\|5 \|11 \|55 + 11220x - 5610 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-138/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 49/22/((3+5*x)*sqrt(1-2*x))-1227/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 690x - 414)\|- 2x + 1 atanh(---------------) + (1227x + 734)\|55 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +--------+ +--R (3025x + 1815)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (345x + 207)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (1227x + 734)\|55 +--R / +--R +--+ +--------+ +--R (3025x + 1815)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 69log(-----------------------------) + 138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 605\|55 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795 +--R / +--R 2 +--------+ +--R (332750x + 33275x - 99825)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30250x - 45375x - 13915x + 14520)\|55 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-72/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 72/605/sqrt(1-2*x)+(-1/55)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 360x - 216)\|- 2x + 1 atanh(---------------) + (72x + 41)\|55 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (605x + 363)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R (180x + 108)\|- 2x + 1 log(-----------------------------) + (72x + 41)\|55 +--R 5x + 3 +--R --------------------------------------------------------------------------- +--R +--+ +--------+ +--R (605x + 363)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 36log(-----------------------------) + 72atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 121\|55 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 180x + 288)\|55 + (180x - 288)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 72x + 36)\|5 \|11 \|55 + 3960x - 1980 +--R / +--R 2 +--------+ +--R (66550x + 6655x - 19965)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6050x - 9075x - 2783x + 2904)\|55 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-6/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 2/11/((3+5*x)*sqrt(1-2*x))-15/121*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 30x - 18)\|5 \|- 2x + 1 atanh(---------------) + (30x + 7)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (605x + 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (15x + 9)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (30x + 7)\|11 +--R / +--R +--+ +--------+ +--R (605x + 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 3\|5 log(---------------------------------) + 6\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - -------------------------------------------- +--R 4 3 2 +--------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-18/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 300/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((3+5*x)*sqrt(1-2*x))-195/847*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (- 10890x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (10500x + 6300)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (390x - 151)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (4235x + 2541)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (5445x + 3267)\|3 \|11 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (5250x + 3150)\|5 \|7 \|- 2x + 1 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--R (390x - 151)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (4235x + 2541)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1089\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1050\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 2178\|3 \|11 atanh(---------------) - 2100\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 847\|7 \|11 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-1314/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 3150/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)*(3+5*x)*sqrt(1-2*x))-11610/5929*sqrt(1-2*x)/(3+5*x)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (- 2384910x - 3020886x - 953964)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (2315250x + 2932650x + 926100)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (69660x + 9696x - 21955)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--+ +--------+ +--R (1192455x + 1510443x + 476982)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (1157625x + 1466325x + 463050)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--R (69660x + 9696x - 21955)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 79497\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 77175\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 158994\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 154350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 5929\|7 \|11 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-70065/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 24000/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_ + 1229325/83006*sqrt(1-2*x)/(3+5*x)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 5520/3773*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 763007850x - 1475148510x - 949520880x - 203468760)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (740880000x + 1432368000x + 921984000x + 197568000)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (381503925x + 737574255x + 474760440x + 101734380)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (370440000x + 716184000x + 460992000x + 98784000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 8477865\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 8232000\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 16955730\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 16464000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=-33873/4159375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 728/275*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))-_ + 3/25*(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x))+_ + 61055253/4159375*sqrt(1-2*x)+139671/66550*(2+3*x)*sqrt(1-2*x)-_ + 7219/30250*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 125916/831875*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 1693650x - 2032380x - 609714)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 242574750x - 1423105200x - 5682717810x - 762244410x +--R + +--R 4150263077x + 1702670584 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +--R (846825x + 1016190x + 304857)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 242574750x - 1423105200x - 5682717810x - 762244410x +--R + +--R 4150263077x + 1702670584 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 33873log(-----------------------------) + 67746atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 8318750\|55 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 169365x + 270984)\|55 + (169365x - 270984)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 67746x + 33873)\|5 \|11 \|55 + 3726030x - 1863015 +--R / +--R 2 +--------+ +--R (4575312500x + 457531250x - 1372593750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (415937500x - 623906250x - 191331250x + 199650000)\|55 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-4557/166375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 161/55*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_ + 1/5*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))+_ + 538608/166375*sqrt(1-2*x)-1589/6050*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 147/332750*(612+1145*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 227850x - 273420x - 82026)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55 +--R / +--R 2 +--+ +--------+ +--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (113925x + 136710x + 41013)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55 +--R / +--R 2 +--+ +--------+ +--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4557log(-----------------------------) + 9114atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 332750\|55 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 22785x + 36456)\|55 + (22785x - 36456)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 9114x + 4557)\|5 \|11 \|55 + 501270x - 250635 +--R / +--R 2 +--------+ +--R (183012500x + 18301250x - 54903750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (16637500x - 24956250x - 7653250x + 7986000)\|55 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=-111/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 238/55*(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))-3/5*(2+3*x)^3/((3+5*x)^2*_ + sqrt(1-2*x))-1/6050*(346-195*x)*sqrt(1-2*x)/(3+5*x)^2-_ + 15759/33275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 27750x - 33300x - 9990)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 215622x + 149298x + 411911x + 146824)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (13875x + 16650x + 4995)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 215622x + 149298x + 411911x + 146824)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 111log(-----------------------------) + 222atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 2662\|55 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 555x + 888)\|55 + (555x - 888)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 222x + 111)\|5 \|11 \|55 + 12210x - 6105 +--R / +--R 2 +--------+ +--R (1464100x + 146410x - 439230)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (133100x - 199650x - 61226x + 63888)\|55 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-7143/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 2/11*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))+_ + 3408/33275*sqrt(1-2*x)-5/242*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 3/13310*(24+71*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 357150x - 428580x - 128574)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (430800x + 514727x + 153724)\|55 +--R / +--R 2 +--+ +--------+ +--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (178575x + 214290x + 64287)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (430800x + 514727x + 153724)\|55 +--R / +--R 2 +--+ +--------+ +--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 7143log(-----------------------------) + 14286atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 66550\|55 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 35715x + 57144)\|55 + (35715x - 57144)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 14286x + 7143)\|5 \|11 \|55 + 785730x - 392865 +--R / +--R 2 +--------+ +--R (36602500x + 3660250x - 10980750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3327500x - 4991250x - 1530650x + 1597200)\|55 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-2589/6655*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/((3+5*x)^2*_ + sqrt(1-2*x))-613/605*sqrt(1-2*x)/(3+5*x)^2-2589/13310*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 129450x - 155340x - 46602)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (25890x + 29561x + 8392)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (64725x + 77670x + 23301)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (25890x + 29561x + 8392)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2589log(-----------------------------) + 5178atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 13310\|55 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 12945x + 20712)\|55 + (12945x - 20712)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5178x + 2589)\|5 \|11 \|55 + 284790x - 142395 +--R / +--R 2 +--------+ +--R (7320500x + 732050x - 2196150)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (665500x - 998250x - 306130x + 319440)\|55 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-213/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-1/110)/((3+5*x)^2*_ + sqrt(1-2*x))+71/605/((3+5*x)*sqrt(1-2*x))-213/2662*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 10650x - 12780x - 3834)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (2130x + 1775x + 274)\|55 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (5325x + 6390x + 1917)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (2130x + 1775x + 274)\|55 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 213log(-----------------------------) + 426atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 2662\|55 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1065x + 1704)\|55 + (1065x - 1704)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 426x + 213)\|5 \|11 \|55 + 23430x - 11715 +--R / +--R 2 +--------+ +--R (1464100x + 146410x - 439230)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (133100x - 199650x - 61226x + 63888)\|55 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-15/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/((3+5*x)^2*_ + sqrt(1-2*x))-25/242*sqrt(1-2*x)/(3+5*x)^2-75/2662*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 750x - 900x - 270)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (750x + 625x - 16)\|11 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (375x + 450x + 135)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (750x + 625x - 16)\|11 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 15\|5 log(---------------------------------) + 30\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 2662\|11 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (750x + 1475x + 785x - 153x - 243x - 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=54/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-9975/1331*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((3+5*x)^2*_ + sqrt(1-2*x))-215/1694*sqrt(1-2*x)/(3+5*x)^2+10245/18634*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (3593700x + 4312440x + 1293732)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 3491250x - 4189500x - 1256850)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 102450x - 5515x + 29338)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (1745625x + 2094750x + 628425)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (1796850x + 2156220x + 646866)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 102450x - 5515x + 29338)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 69825\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 71874\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 143748\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 139650\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 18634\|7 \|11 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=5832/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 153825/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-_ + 17095/11858*sqrt(1-2*x)/(3+5*x)^2+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1124835/130438*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (1164358800x + 2173469760x + 1350656208x + 279446112)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 1130613750x - 2110479000x - 1311511950x - 271347300)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (565306875x + 1055239500x + 655755975x + 135673650)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (582179400x + 1086734880x + 675328104x + 139723056)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7537425\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7762392\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 15524784\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 15074850\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 130438\|7 \|11 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=414315/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1561125/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x))-_ + 1205525/83006*sqrt(1-2*x)/(3+5*x)^2+75/1078*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+14505/7546*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 39968475/456533*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 248153969250x + 628656722100x + 596672432730x + 251462688840x +--R + +--R 39704635080 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 240959643750x - 610431097500x - 579374076750x - 244172439000x +--R + +--R - 38553543000 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x +--R + +--R 909821467 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +-+ +--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 120479821875x + 305215548750x + 289687038375x + 122086219500x +--R + +--R 19276771500 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R 124076984625x + 314328361050x + 298336216365x + 125731344420x +--R + +--R 19852317540 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x +--R + +--R 909821467 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +-+ +--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 535465875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 551453265\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1102906530\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1070931750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 913066\|7 \|11 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=184877/192/(1-2*x)^(3/2)+12495/8*(1-2*x)^(3/2)-19467/64*(1-2*x)^(5/2)+_ + 1053/28*(1-2*x)^(7/2)-135/64*(1-2*x)^(9/2)+(-60025/8)/sqrt(1-2*x)-_ + 519645/64*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696 +--R (2) ------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696 +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=26411/96/(1-2*x)^(3/2)+3591/16*(1-2*x)^(3/2)-4671/160*(1-2*x)^(5/2)+_ + 405/224*(1-2*x)^(7/2)+(-57281/32)/sqrt(1-2*x)-24843/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408 +--R (2) --------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408 +--R (3) --------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=3773/48/(1-2*x)^(3/2)+207/8*(1-2*x)^(3/2)-27/16*(1-2*x)^(5/2)+_ + (-3283/8)/sqrt(1-2*x)-1071/4*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 81x + 459x + 2403x - 5250x + 1726 +--R (2) ------------------------------------ +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 81x + 459x + 2403x - 5250x + 1726 +--R (3) ------------------------------------ +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=539/24/(1-2*x)^(3/2)+15/8*(1-2*x)^(3/2)+(-707/8)/sqrt(1-2*x)-_ + 309/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 45x + 396x - 960x + 308 +--R (2) ------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 45x + 396x - 960x + 308 +--R (3) ------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=77/12/(1-2*x)^(3/2)+(-17)/sqrt(1-2*x)-15/4*sqrt(1-2*x) +--R +--R +--R 2 +--R 45x - 147x + 43 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 45x - 147x + 43 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=11/6/(1-2*x)^(3/2)+(-5/2)/sqrt(1-2*x) +--R +--R +--R - 15x + 2 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 15x + 2 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=11/21/(1-2*x)^(3/2)+2/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + (-2/49)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|3 \|- 2x + 1 +-+ +--R (12x - 6)\|3 \|- 2x + 1 atanh(---------------) + (- 12x - 71)\|7 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (6x - 3)\|3 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--R (- 12x - 71)\|7 +--R / +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R \|3 log(---------------------------------) - 2\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 49\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=20/147/(1-2*x)^(3/2)+1/21/((1-2*x)^(3/2)*(2+3*x))-_ + 60/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+60/343/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 1080x - 180x + 360)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--R (1080x - 240x - 689)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (540x + 90x - 180)\|3 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (1080x - 240x - 689)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 30\|3 log(-------------------------------) + 60\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 343\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=5/49/(1-2*x)^(3/2)+1/42/((1-2*x)^(3/2)*(2+3*x)^2)+_ + (-3/14)/((1-2*x)^(3/2)*(2+3*x))-45/343*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+45/343/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 4860x - 4050x + 1080x + 1080)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--R (4860x + 2160x - 2277x - 1087)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (2430x + 2025x - 540x - 540)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--R (4860x + 2160x - 2277x - 1087)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 45\|3 log(-------------------------------) + 90\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/63/((1-2*x)^(3/2)*(2+3*x)^3)+64/441/((1-2*x)^(3/2)*(2+3*x)^2)-_ + 160/2401*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/147/((2+3*x)^2*_ + sqrt(1-2*x))-80/343*sqrt(1-2*x)/(2+3*x)^2-240/2401*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--------+ +--R (- 25920x - 38880x - 8640x + 9600x + 3840)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--R (25920x + 28800x - 4464x - 11280x - 2237)\|7 +--R / +--R 4 3 2 +-+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--------+ +--R (12960x + 19440x + 4320x - 4800x - 1920)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (25920x + 28800x - 4464x - 11280x - 2237)\|7 +--R / +--R 4 3 2 +-+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 80\|3 log(-------------------------------) + 160\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 2401\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 5x + 3 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=1/84/((1-2*x)^(3/2)*(2+3*x)^4)+43/294/((1-2*x)^(3/2)*(2+3*x)^3)-_ + 1935/67228*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+387/686/((2+3*x)^3*_ + sqrt(1-2*x))-387/1372*sqrt(1-2*x)/(2+3*x)^3-1935/19208*_ + sqrt(1-2*x)/(2+3*x)^2-5805/134456*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 1880820x - 4075110x - 2507760x + 278640x + 743040x + 185760)\|3 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (940410x + 2037555x + 1253880x - 139320x - 371520x - 92880)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 1935\|3 log(-------------------------------) + 3870\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 134456\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=2033647/384/(1-2*x)^(3/2)+1965635/128*(1-2*x)^(3/2)-_ + 514017/128*(1-2*x)^(5/2)+672003/896*(1-2*x)^(7/2)-_ + 10845/128*(1-2*x)^(9/2)+6075/1408*(1-2*x)^(11/2)+_ + (-6206585/128)/sqrt(1-2*x)-8117095/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x +--R + +--R - 65622552x + 21852008 +--R / +--R +--------+ +--R (462x - 231)\|- 2x + 1 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x +--R + +--R - 65622552x + 21852008 +--R / +--R +--------+ +--R (462x - 231)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=290521/192/(1-2*x)^(3/2)+40453/16*(1-2*x)^(3/2)-_ + 159111/320*(1-2*x)^(5/2)+13905/224*(1-2*x)^(7/2)-_ + 225/64*(1-2*x)^(9/2)+(-381073/32)/sqrt(1-2*x)-832951/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=41503/96/(1-2*x)^(3/2)+5847/16*(1-2*x)^(3/2)-_ + 1539/32*(1-2*x)^(5/2)+675/224*(1-2*x)^(7/2)+(-91091/32)/sqrt(1-2*x)-_ + 39977/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442 +--R (2) ------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442 +--R (3) ------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=5929/48/(1-2*x)^(3/2)+85/2*(1-2*x)^(3/2)-45/16*(1-2*x)^(5/2)+_ + (-1309/2)/sqrt(1-2*x)-3467/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 135x + 750x + 3873x - 8430x + 2774 +--R (2) ------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 135x + 750x + 3873x - 8430x + 2774 +--R (3) ------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=847/24/(1-2*x)^(3/2)+25/8*(1-2*x)^(3/2)+(-1133/8)/sqrt(1-2*x)-_ + 505/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 75x + 645x - 1551x + 499 +--R (2) -------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 75x + 645x - 1551x + 499 +--R (3) -------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=121/12/(1-2*x)^(3/2)+(-55/2)/sqrt(1-2*x)-25/4*sqrt(1-2*x) +--R +--R +--R 2 +--R 75x - 240x + 71 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 75x - 240x + 71 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=121/42/(1-2*x)^(3/2)-2/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + (-407/98)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 1221x + 187)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 1221x + 187)\|21 +--R 3x + 2 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x))+130/343*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+(-130/1029)/sqrt(1-2*x)+(-365/294)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (2340x + 390x - 780)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 780x - 2685x - 1427)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (1170x + 195x - 390)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 780x - 2685x - 1427)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 65log(-------------------------------) - 130atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 343\|21 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 195x + 325)\|21 + (195x - 325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (130x - 65)\|3 \|7 \|21 - 2730x + 1365 +--R / +--R 2 +--------+ +--R (43218x + 7203x - 14406)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 6174x + 9261x + 3773x - 3430)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^2)-85/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)+(-26/21)/((2+3*x)^2*sqrt(1-2*x))+85/147/((2+3*x)*_ + sqrt(1-2*x))-255/686*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 9180x - 7650x + 2040x + 2040)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--R (9180x + 4080x - 7731x - 4231)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (4590x + 3825x - 1020x - 1020)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--R (9180x + 4080x - 7731x - 4231)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 85\|3 log(-------------------------------) + 170\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^3)-1415/2401*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+(-1091/882)/((2+3*x)^3*sqrt(1-2*x))+566/441/((2+3*x)^2*_ + sqrt(1-2*x))-1415/2058*sqrt(1-2*x)/(2+3*x)^2-1415/4802*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 458460x - 687690x - 152820x + 169800x + 67920)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (152820x + 169800x - 26319x - 83655x - 23872)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (229230x + 343845x + 76410x - 84900x - 33960)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (152820x + 169800x - 26319x - 83655x - 23872)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1415log(-----------------------------) + 2830atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 4802\|21 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 4245x + 7075)\|21 + (4245x - 7075)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 2830x + 1415)\|3 \|7 \|21 + 59430x - 29715 +--R / +--R 2 +--------+ +--R (605052x + 100842x - 201684)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (86436x - 129654x - 52822x + 48020)\|21 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^4)-20465/67228*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+(-727/588)/((2+3*x)^4*sqrt(1-2*x))+_ + 4093/2058/((2+3*x)^3*sqrt(1-2*x))-4093/4116*sqrt(1-2*x)/(2+3*x)^3-_ + 20465/57624*sqrt(1-2*x)/(2+3*x)^2-20465/134456*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 19891980x - 43099290x - 26522640x + 2946960x + 7858560x +--R + +--R 1964640 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (9945990x + 21549645x + 13261320x - 1473480x - 3929280x - 982320) +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 20465log(-----------------------------) + 40930atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 134456\|21 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 61395x + 102325)\|21 + (61395x - 102325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 40930x + 20465)\|3 \|7 \|21 + 859530x - 429765 +--R / +--R 2 +--------+ +--R (16941456x + 2823576x - 5647152)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (2420208x - 3630312x - 1479016x + 1344560)\|21 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R / +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=22370117/768/(1-2*x)^(3/2)+52725715/384*(1-2*x)^(3/2)-_ + 2887773/64*(1-2*x)^(5/2)+10121229/896*(1-2*x)^(7/2)-_ + 246315/128*(1-2*x)^(9/2)+277425/1408*(1-2*x)^(11/2)-_ + 30375/3328*(1-2*x)^(13/2)+(-39220335/128)/sqrt(1-2*x)-_ + 60160485/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x +--R + +--R 3 2 +--R 905206628x + 2892917004x - 5818266408x + 1938557272 +--R / +--R +--------+ +--R (6006x - 3003)\|- 2x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x +--R + +--R 3 2 +--R 905206628x + 2892917004x - 5818266408x + 1938557272 +--R / +--R +--------+ +--R (6006x - 3003)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=3195731/384/(1-2*x)^(3/2)+9504551/384*(1-2*x)^(3/2)-_ + 4177401/640*(1-2*x)^(5/2)+1101465/896*(1-2*x)^(7/2)-_ + 17925/128*(1-2*x)^(9/2)+10125/1408*(1-2*x)^(11/2)+_ + (-9836211/128)/sqrt(1-2*x)-12973191/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x +--R + +--R 2 +--R 258342648x - 522173856x + 173891632 +--R / +--R +--------+ +--R (2310x - 1155)\|- 2x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x +--R + +--R 2 +--R 258342648x - 522173856x + 173891632 +--R / +--R +--------+ +--R (2310x - 1155)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=456533/192/(1-2*x)^(3/2)+98209/24*(1-2*x)^(3/2)-52011/64*(1-2*x)^(5/2)+_ + 11475/112*(1-2*x)^(7/2)-375/64*(1-2*x)^(9/2)+(-302379/16)/sqrt(1-2*x)-_ + 1334949/64*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074 +--R (2) ---------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074 +--R (3) ---------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=65219/96/(1-2*x)^(3/2)+28555/48*(1-2*x)^(3/2)-2535/32*(1-2*x)^(5/2)+_ + 1125/224*(1-2*x)^(7/2)+(-144837/32)/sqrt(1-2*x)-64317/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264 +--R (2) -------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264 +--R (3) -------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=9317/48/(1-2*x)^(3/2)+1675/24*(1-2*x)^(3/2)-75/16*(1-2*x)^(5/2)+_ + (-8349/8)/sqrt(1-2*x)-2805/4*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 225x + 1225x + 6240x - 13533x + 4457 +--R (2) --------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 225x + 1225x + 6240x - 13533x + 4457 +--R (3) --------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=1331/24/(1-2*x)^(3/2)+125/24*(1-2*x)^(3/2)+(-1815/8)/sqrt(1-2*x)-_ + 825/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 125x + 1050x - 2505x + 808 +--R (2) ---------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 125x + 1050x - 2505x + 808 +--R (3) ---------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=253/21*(3+5*x)/(1-2*x)^(3/2)-5/3*(3+5*x)^2/(1-2*x)^(3/2)+_ + 2/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-2948/49)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 2 +--+ +--R (4x - 2)\|- 2x + 1 atanh(---------------) + (6125x - 19193x + 5736)\|21 +--R +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (2x - 1)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (6125x - 19193x + 5736)\|21 +--R / +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ +--R (18522x + 3087x - 6174)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2646x + 3969x + 1617x - 1470)\|21 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x))-200/1029*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-15/49*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))-_ + 750/343*sqrt(1-2*x)-50/1029*(3+5*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (- 1200x - 200x + 400)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 42475x - 21050x + 4839)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (600x + 100x - 200)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 42475x - 21050x + 4839)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 100log(-----------------------------) + 200atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 300x + 500)\|21 + (300x - 500)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 200x + 100)\|3 \|7 \|21 + 4200x - 2100 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18522x - 27783x - 11319x + 10290)\|21 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2)+905/1029*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+1/7*(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x))-_ + 5/294*(1+x)*sqrt(1-2*x)/(2+3*x)^2+50/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (32580x + 27150x - 7240x - 7240)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (- 10860x - 33410x - 29593x - 8103)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (16290x + 13575x - 3620x - 3620)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (- 10860x - 33410x - 29593x - 8103)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 905log(-------------------------------) - 1810atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1810x - 905)\|3 \|7 \|21 - 38010x + 19005 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 37044x + 55566x + 22638x - 20580)\|21 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3)-7510/7203*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+29/49*(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x))+_ + 125/1029*sqrt(1-2*x)/(2+3*x)^2-3755/7203*sqrt(1-2*x)/(2+3*x)+_ + 4/49*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 405540x - 608310x - 135180x + 150200x + 60080)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (135180x + 150200x - 83306x - 150295x - 45383)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (202770x + 304155x + 67590x - 75100x - 30040)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (135180x + 150200x - 83306x - 150295x - 45383)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 3755log(-----------------------------) + 7510atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 7203\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 11265x + 18775)\|21 + (11265x - 18775)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 7510x + 3755)\|3 \|7 \|21 + 157710x - 78855 +--R / +--R 2 +--------+ +--R (907578x + 151263x - 302526)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (129654x - 194481x - 79233x + 72030)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4)-177635/201684*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+51/49*(3+5*x)^2/((2+3*x)^4*_ + sqrt(1-2*x))+692/3087*sqrt(1-2*x)/(2+3*x)^3-177635/172872*_ + sqrt(1-2*x)/(2+3*x)^2-177635/403368*sqrt(1-2*x)/(2+3*x)+_ + 601/4116*(3+5*x)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 57553740x - 124699770x - 76738320x + 8526480x + 22737280x +--R + +--R 5684320 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x +--R + +--R - 2094250 +--R * +--R +--+ +--R \|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 28776870x + 62349885x + 38369160x - 4263240x - 11368640x +--R + +--R - 2842160 +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x +--R + +--R - 2094250 +--R * +--R +--+ +--R \|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 177635log(-----------------------------) + 355270atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 403368\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 532905x + 888175)\|21 + (532905x - 888175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 355270x + 177635)\|3 \|7 \|21 + 7460670x - 3730335 +--R / +--R 2 +--------+ +--R (50824368x + 8470728x - 16941456)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (7260624x - 10890936x - 4437048x + 4033680)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^6) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R (2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5)-163474/352947*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+73/49*(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x))+_ + 3912/12005*sqrt(1-2*x)/(2+3*x)^4-163474/108045*sqrt(1-2*x)/(2+3*x)^3-_ + 81737/151263*sqrt(1-2*x)/(2+3*x)^2-81737/352947*sqrt(1-2*x)/(2+3*x)+_ + 1082/5145*(3+5*x)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 +--R - 397241820x - 1125518490x - 1103449500x - 294253200x +--R + +--R 2 +--R 196168800x + 143857120x + 26155840 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x +--R + +--R - 42553376x - 5615203 +--R * +--R +--+ +--R \|21 +--R / +--R 6 5 4 3 2 +--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x +--R + +--R - 310593360x - 56471520 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 198620910x + 562759245x + 551724750x + 147126600x - 98084400x +--R + +--R - 71928560x - 13077920 +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x +--R + +--R - 42553376x - 5615203 +--R * +--R +--+ +--R \|21 +--R / +--R 6 5 4 3 2 +--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x +--R + +--R - 310593360x - 56471520 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 81737log(-----------------------------) + 163474atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 352947\|21 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 245211x + 408685)\|21 + (245211x - 408685)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 163474x + 81737)\|3 \|7 \|21 + 3432954x - 1716477 +--R / +--R 2 +--------+ +--R (44471322x + 7411887x - 14823774)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6353046x - 9529569x - 3882417x + 3529470)\|21 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=172/165*(2+3*x)^4/(1-2*x)^(3/2)-3/35*(2+3*x)^5/(1-2*x)^(3/2)-2/75625*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7561/605*(2+3*x)^3/_ + sqrt(1-2*x)-55573878/75625*sqrt(1-2*x)-63513/605*(2+3*x)*_ + sqrt(1-2*x)-340248/15125*(2+3*x)^2*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 84x + 42)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x +--R + +--R 1780047848 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (3176250x - 1588125)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (42x - 21)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x +--R + +--R 1780047848 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (3176250x - 1588125)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 75625\|55 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (41593750x + 4159375x - 12478125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3781250x - 5671875x - 1739375x + 1815000)\|55 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=959/825*(2+3*x)^3/(1-2*x)^(3/2)-3/25*(2+3*x)^4/(1-2*x)^(3/2)-2/15125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-31612/3025*(2+3*x)^2/_ + sqrt(1-2*x)-2276102/15125*sqrt(1-2*x)-1/15125*(569026+948375*x)*_ + sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55 +--R / +--R +--+ +--------+ +--R (90750x - 45375)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55 +--R / +--R +--+ +--------+ +--R (90750x - 45375)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 15125\|55 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (8318750x + 831875x - 2495625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (756250x - 1134375x - 347875x + 363000)\|55 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=238/165*(2+3*x)^2/(1-2*x)^(3/2)-1/5*(2+3*x)^3/(1-2*x)^(3/2)-_ + 2/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 7/605*(1426+2377*x)/sqrt(1-2*x)-80818/3025*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (49005x + 450846x - 1111431x + 354344)\|55 +--R / +--R +--+ +--------+ +--R (18150x - 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (49005x + 450846x - 1111431x + 354344)\|55 +--R / +--R +--+ +--------+ +--R (18150x - 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=469/165*(2+3*x)/(1-2*x)^(3/2)-3/5*(2+3*x)^2/(1-2*x)^(3/2)-_ + 2/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-5152/605)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 2 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (9801x - 33321x + 9494)\|55 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (3630x - 1815)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (9801x - 33321x + 9494)\|55 +--R / +--R +--+ +--------+ +--R (3630x - 1815)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 605\|55 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (332750x + 33275x - 99825)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30250x - 45375x - 13915x + 14520)\|55 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=49/66/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + (-217/242)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 651x + 56)\|55 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 651x + 56)\|55 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 121\|55 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (66550x + 6655x - 19965)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6050x - 9075x - 2783x + 2904)\|55 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=7/33/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 2/121/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 12x + 6)\|5 \|- 2x + 1 atanh(---------------) + (12x - 83)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (6x - 3)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (12x - 83)\|11 +--R / +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R \|5 log(---------------------------------) + 2\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2/33/(1-2*x)^(3/2)-10/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 10/121/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 60x + 30)\|5 \|- 2x + 1 atanh(---------------) + (60x - 52)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (30x - 15)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (60x - 52)\|11 +--R / +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 5\|5 log(---------------------------------) + 10\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=4/231/(1-2*x)^(3/2)+18/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 50/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/5929/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (13068x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 14700x + 7350)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (1632x - 1124)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (35574x - 17787)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (7350x - 3675)\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (6534x - 3267)\|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--R (1632x - 1124)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (35574x - 17787)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1225\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1089\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2178\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 5929\|7 \|11 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x))+720/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 360/5929/((2+3*x)*sqrt(1-2*x))+2055/41503*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (1568160x + 261360x - 522720)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 1543500x - 257250x + 514500)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 24660x + 39780x - 15881)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (771750x + 128625x - 257250)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (784080x + 130680x - 261360)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 24660x + 39780x - 15881)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 42875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 43560\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 87120\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 85750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 41503\|7 \|11 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2)+3645/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-1250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 64/847/((2+3*x)^2*sqrt(1-2*x))+45/11858*sqrt(1-2*x)/(2+3*x)^2+_ + 36885/83006*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--------+ +--R (47632860x + 39694050x - 10585080x - 10585080)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (- 46305000x - 38587500x + 10290000x + 10290000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (23152500x + 19293750x - 5145000x - 5145000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (23816430x + 19847025x - 5292540x - 5292540)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 428750\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 441045\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 882090\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 857500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^3)+127710/2401*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-6250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+536/5929/((2+3*x)^3*sqrt(1-2*x))-93/5929*_ + sqrt(1-2*x)/(2+3*x)^3+8955/41503*sqrt(1-2*x)/(2+3*x)^2+_ + 669990/290521*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (2503371420x + 3755057130x + 834457140x - 927174600x - 370869840) +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (- 2431012500x - 3646518750x - 810337500x + 900375000x + 360150000) +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1215506250x + 1823259375x + 405168750x - 450187500x - 180075000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (1251685710x + 1877528565x + 417228570x - 463587300x - 185434920) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7503125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7726455\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 15452910\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 15006250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 290521\|7 \|11 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=959/825*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x))-3/25*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x))-406/831875*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-93611/9075*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-_ + 77849506/831875*sqrt(1-2*x)+154448/166375*(2+3*x)^2*sqrt(1-2*x)/_ + (3+5*x)-7/831875*(2780354+4633875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 12180x - 1218x + 3654)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x +--R + +--R 1035652776 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6090x + 609x - 1827)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x +--R + +--R 1035652776 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 203log(-----------------------------) + 406atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 831875\|55 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1015x + 1624)\|55 + (1015x - 1624)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 406x + 203)\|5 \|11 \|55 + 22330x - 11165 +--R / +--R 2 +--------+ +--R (457531250x + 45753125x - 137259375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (41593750x - 62390625x - 19133125x + 19965000)\|55 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=238/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-1/5*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x))-68/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-15442/1815*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 532452/33275*sqrt(1-2*x)+1014/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 2040x - 204x + 612)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (1020x + 102x - 306)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 33275\|55 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870 +--R / +--R 2 +--------+ +--R (18301250x + 1830125x - 5490375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1663750x - 2495625x - 765325x + 798600)\|55 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=469/165*(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x))-3/5*(2+3*x)^3/((1-2*x)^(3/2)*_ + (3+5*x))-274/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 7/1815*(3944+7323*x)/((3+5*x)*sqrt(1-2*x))-26988/33275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 8220x - 822x + 2466)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (1617165x - 4634229x - 1790101x + 943584)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (4110x + 411x - 1233)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (1617165x - 4634229x - 1790101x + 943584)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 137log(-----------------------------) + 274atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 33275\|55 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 685x + 1096)\|55 + (685x - 1096)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 274x + 137)\|5 \|11 \|55 + 15070x - 7535 +--R / +--R 2 +--------+ +--R (18301250x + 1830125x - 5490375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1663750x - 2495625x - 765325x + 798600)\|55 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-208/6655*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-23/363*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 942/6655*sqrt(1-2*x)+6/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 6240x - 624x + 1872)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 106563x - 57832x + 3678)\|55 +--R / +--R 2 +--+ +--------+ +--R (199650x + 19965x - 59895)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (3120x + 312x - 936)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (- 106563x - 57832x + 3678)\|55 +--R / +--R 2 +--+ +--------+ +--R (199650x + 19965x - 59895)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 104log(-----------------------------) + 208atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 6655\|55 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 520x + 832)\|55 + (520x - 832)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 208x + 104)\|5 \|11 \|55 + 11440x - 5720 +--R / +--R 2 +--------+ +--R (3660250x + 366025x - 1098075)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (332750x - 499125x - 153065x + 159720)\|55 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x))-142/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+142/6655/sqrt(1-2*x)+(-1231/3630)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 4260x - 426x + 1278)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (852x - 2623x - 1866)\|55 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (2130x + 213x - 639)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (852x - 2623x - 1866)\|55 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 71log(-----------------------------) + 142atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1331\|55 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 355x + 568)\|55 + (355x - 568)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 142x + 71)\|5 \|11 \|55 + 7810x - 3905 +--R / +--R 2 +--------+ +--R (732050x + 73205x - 219615)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (66550x - 99825x - 30613x + 31944)\|55 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=76/1815/(1-2*x)^(3/2)+(-1/55)/((1-2*x)^(3/2)*(3+5*x))-_ + 76/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+76/1331/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 2280x - 228x + 684)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (2280x - 608x - 1113)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--------+ +--R (1140x + 114x - 342)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (2280x - 608x - 1113)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 38\|5 log(---------------------------------) + 76\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 1331\|11 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=10/363/(1-2*x)^(3/2)+(-1/11)/((1-2*x)^(3/2)*(3+5*x))-_ + 50/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+50/1331/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 1500x - 150x + 450)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (1500x - 400x - 417)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (750x + 75x - 225)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (1500x - 400x - 417)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 25\|5 log(---------------------------------) + 50\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 1331\|11 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x))-54/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)+1400/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 1096/17787/((3+5*x)*sqrt(1-2*x))-8185/65219*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (- 2156220x - 215622x + 646866)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (2058000x + 205800x - 617400)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (98220x - 74108x + 9111)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--+ +--------+ +--R (1078110x + 107811x - 323433)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (1029000x + 102900x - 308700)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--R (98220x - 74108x + 9111)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 35937\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 34300\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 71874\|3 \|11 atanh(---------------) - 68600\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 65219\|7 \|11 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))-4050/343*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+15250/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+1360/17787/((2+3*x)*(3+5*x)*sqrt(1-2*x))-_ + 399500/456533*sqrt(1-2*x)/(3+5*x)+1775/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 485149500x - 371947950x + 113201550x + 97029900)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (470767500x + 360921750x - 109845750x - 94153500)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--------+ +--R (242574750x + 185973975x - 56600775x - 48514950)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (235383750x + 180460875x - 54922875x - 47076750)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2695275\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2615375\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 5390550\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 5230750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 456533\|7 \|11 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x))-4455/49*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+117500/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+232/2541/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_ + 860525/130438*sqrt(1-2*x)/(3+5*x)-5/1694*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+3790/5929*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R (- 3201986700x - 4589514270x - 889440750x + 1138484160x + 426931560) +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (3109050000x + 4456305000x + 863625000x - 1105440000x - 414540000) +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1600993350x + 2294757135x + 444720375x - 569242080x - 213465780) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1554525000x + 2228152500x + 431812500x - 552720000x - 207270000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(-----------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 5929605\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 5757500\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 11859210\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 11515000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 130438\|7 \|11 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=238/165*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-1/5*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x)^2)-6937/1830125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-15197/1815*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_ + 18063843/1830125*sqrt(1-2*x)+149653/199650*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)^2+13755/29282*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 2081100x - 1456770x + 499464x + 374598)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x +--R + +--R 1463964312 +--R * +--R +--+ +--R \|55 +--R / +--R 3 2 +--+ +--------+ +--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (1040550x + 728385x - 249732x - 187299)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x +--R + +--R 1463964312 +--R * +--R +--+ +--R \|55 +--R / +--R 3 2 +--+ +--------+ +--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 6937log(-----------------------------) + 13874atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 3660250\|55 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 34685x + 55496)\|55 + (34685x - 55496)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 13874x + 6937)\|5 \|11 \|55 + 763070x - 381535 +--R / +--R 2 +--------+ +--R (2013137500x + 201313750x - 603941250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (183012500x - 274518750x - 84185750x + 87846000)\|55 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=469/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-3/5*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x)^2)-4693/366025*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-14966/1815*(2+3*x)^2/((3+5*x)^2*_ + sqrt(1-2*x))+29033/39930*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2+_ + 164309/366025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 1407900x - 985530x + 337896x + 253422)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (703950x + 492765x - 168948x - 126711)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4693log(-----------------------------) + 9386atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 732050\|55 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 23465x + 37544)\|55 + (23465x - 37544)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 9386x + 4693)\|5 \|11 \|55 + 516230x - 258115 +--R / +--R 2 +--------+ +--R (402627500x + 40262750x - 120788250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (36602500x - 54903750x - 16837150x + 17569200)\|55 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-14423/366025*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-19/363*(2+3*x)^3/_ + ((3+5*x)^2*sqrt(1-2*x))-29037/366025*sqrt(1-2*x)+_ + 31/7986*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+141/146410*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 4326900x - 3028830x + 1038456x + 778842)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 34712250x - 40823468x - 11479257x + 311208)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (2163450x + 1514415x - 519228x - 389421)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 34712250x - 40823468x - 11479257x + 311208)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 14423log(-----------------------------) + 28846atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 732050\|55 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 72115x + 115384)\|55 + (72115x - 115384)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 28846x + 14423)\|5 \|11 \|55 + 1586530x - 793265 +--R / +--R 2 +--------+ +--R (402627500x + 40262750x - 120788250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (36602500x - 54903750x - 16837150x + 17569200)\|55 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-7559/73205*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+47/363*(2+3*x)^2/_ + ((3+5*x)^2*sqrt(1-2*x))-101/7986*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2-_ + 683/73205*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 2267700x - 1587390x + 544248x + 408186)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (453540x - 639434x - 1242261x - 417036)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (1133850x + 793695x - 272124x - 204093)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (453540x - 639434x - 1242261x - 417036)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 7559log(-----------------------------) + 15118atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 146410\|55 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 37795x + 60472)\|55 + (37795x - 60472)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 15118x + 7559)\|5 \|11 \|55 + 831490x - 415745 +--R / +--R 2 +--------+ +--R (80525500x + 8052550x - 24157650)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (7320500x - 10980750x - 3367430x + 3513840)\|55 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^2)-2873/14641*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+(-614/1815)/((3+5*x)^2*sqrt(1-2*x))+_ + 2873/19965/((3+5*x)*sqrt(1-2*x))-2873/29282*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 861900x - 603330x + 206856x + 155142)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (172380x + 57460x - 107127x - 47568)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (430950x + 301665x - 103428x - 77571)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (172380x + 57460x - 107127x - 47568)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2873log(-----------------------------) + 5746atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 29282\|55 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 14365x + 22984)\|55 + (14365x - 22984)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5746x + 2873)\|5 \|11 \|55 + 316030x - 158015 +--R / +--R 2 +--------+ +--R (16105100x + 1610510x - 4831530)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1464100x - 2196150x - 673486x + 702768)\|55 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=73/3993/(1-2*x)^(3/2)+(-1/110)/((1-2*x)^(3/2)*(3+5*x)^2)+(-73/1210)/_ + ((1-2*x)^(3/2)*(3+5*x))-365/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+365/14641/sqrt(1-2*x) +--R +--R +--R (2) +--R 3 2 +-+ +--------+ +--R (- 109500x - 76650x + 26280x + 19710)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (109500x + 36500x - 47961x - 17466)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (54750x + 38325x - 13140x - 9855)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (109500x + 36500x - 47961x - 17466)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 365\|5 log(---------------------------------) + 730\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 29282\|11 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^2)-175/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+70/363/((3+5*x)^2*sqrt(1-2*x))-875/7986*sqrt(1-2*x)/_ + (3+5*x)^2-875/29282*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--------+ +--R (- 52500x - 36750x + 12600x + 9450)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (52500x + 17500x - 22995x - 4764)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (26250x + 18375x - 6300x - 4725)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (52500x + 17500x - 22995x - 4764)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 175\|5 log(---------------------------------) + 350\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 29282\|11 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^2)+162/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-47075/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+1376/17787/((3+5*x)^2*sqrt(1-2*x))-_ + 33535/391314*sqrt(1-2*x)/(3+5*x)^2+325835/1434818*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (711552600x + 498086820x - 170772624x - 128079468)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 692002500x - 484401750x + 166080600x + 124560450)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (346001250x + 242200875x - 83040300x - 62280225)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (355776300x + 249043410x - 85386312x - 64039734)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2306675\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2371842\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 4743684\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 4613350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1434818\|7 \|11 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)+17820/343*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-738625/14641*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1640/17787/_ + ((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-1759475/2739198*_ + sqrt(1-2*x)/(3+5*x)^2+1495/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 37771225/10043726*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 234812358000x + 320910222600x + 53224134480x - 79836201720x +--R + +--R - 28177482960 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 228013537500x - 311618501250x - 51683068500x + 77524602750x +--R + +--R 27361624500 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882) +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204) +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 114006768750x + 155809250625x + 25841534250x - 38762301375x +--R + +--R - 13680812250 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R 117406179000x + 160455111300x + 26612067240x - 39918100860x +--R + +--R - 14088741480 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882) +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204) +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 253348375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 260902620\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 521805240\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 506696750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 10043726\|7 \|11 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x +--R + +--R 216 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2)+182655/343*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-7570625/14641*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/2541/((2+3*x)^2*(3+5*x)^2*_ + sqrt(1-2*x))-17552275/2739198*sqrt(1-2*x)/(3+5*x)^2-_ + 115/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 69235/83006*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 193818700/5021863*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 7220480008500x + 14681642683950x + 8215301698560x +--R + +--R 2 +--R - 1363868446050x - 2503099736280x - 577638400680 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 +--R - 7011155812500x - 14256016818750x - 7977137280000x +--R + +--R 2 +--R 1324329431250x + 2430534015000x + 560892465000 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x +--R + +--R - 9944654283x - 13236365823 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 5 4 3 2 +--R 13559030100x + 27570027870x + 15427163136x - 2561150130x +--R + +--R - 4700463768x - 1084722408 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3505577906250x + 7128008409375x + 3988568640000x - 662164715625x +--R + +--R - 1215267007500x - 280446232500 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 3610240004250x + 7340821341975x + 4107650849280x - 681934223025x +--R + +--R - 1251549868140x - 288819200340 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x +--R + +--R - 9944654283x - 13236365823 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 5 4 3 2 +--R 13559030100x + 27570027870x + 15427163136x - 2561150130x +--R + +--R - 4700463768x - 1084722408 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2596724375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2674251855\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 5348503710\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 5193448750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 10043726\|7 \|11 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=4122385421/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 32497997/38400000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 186473/960000*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3731/80000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 17/3000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)+1/30*(2+3*x)^4*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-374762311/51200000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 4122385421asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 2218752000x + 2739830400x + 1468973920x + 45781940x +--R + +--R - 518122939 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 51200000\|10 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=39142411/1280000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 104377/320000*(3+5*x)^(3/2)*sqrt(1-2*x)-21/2000*(2+3*x)^2*_ + (3+5*x)^(3/2)*sqrt(1-2*x)+1/25*(2+3*x)^3*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-7/40000*(3+5*x)^(3/2)*(802+1245*x)*sqrt(1-2*x)-_ + 3558401/1280000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 39142411asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x + 17366400x + 14946720x + 3002540x - 4282349)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1280000\|10 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (9x + 12x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-37/160*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(2+3*x)*_ + (3+5*x)^(3/2)+158873/12800*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-1313/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+14443/12800*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 158873asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (28800x + 51680x + 22500x - 13327)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 12800\|10 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) (3x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(3+5*x)^(3/2)+4477/800*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-37/80*(1-2*x)^(3/2)*sqrt(3+5*x)+407/800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 4477asin(-------------) + (800x + 820x - 203)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 800\|10 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=121/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+11/40*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 121asin(-------------) + (20x + 1)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------- +--R +--+ +--R 40\|10 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 37/9*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 2\|7 \|10 atan(-------------) + 37asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R 3\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9\|10 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=37/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 2/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/3*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3 +--R (111x + 74)atan(-------------) + (- 6x - 4)\|7 \|10 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R - 3\|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (27x + 18)\|7 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=121/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/28*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (1089x + 1452x + 484)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (37x + 20)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (252x + 336x + 112)\|7 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 2178x - 2904x - 968)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ 2 +--R (1036x + 560)\|- 2x + 1 \|5x + 3 + 2205x + 2940x + 980 +--R / +--R 2 +--R 7056x + 9408x + 3136 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 484atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R - 242atan(-----------------------------------------------------) + 35\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=4477/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+37/252*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+3547/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (120879x + 241758x + 161172x + 35816)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (3547x + 4902x + 1648)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (10584x + 21168x + 14112x + 3136)\|7 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 120879x - 241758x - 161172x - 35816)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (49658x + 68628x + 23072)\|- 2x + 1 \|5x + 3 - 155736x - 311472x +--R + +--R - 207648x - 46144 +--R / +--R 3 2 +--R 148176x + 296352x + 197568x + 43904 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 8954atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 4477atan(--------------------------------------------------) - 824\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=794365/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+37/504*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+6005/14112*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2+625115/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1875345x + 3834760x + 2617388x + 594416)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (26254830x + 53686640x + 36643432x + 8321824)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 84258468x + 224689248x + 224689248x + 99861888x + 16643648 +--R / +--R 4 3 2 +--R 24893568x + 66382848x + 66382848x + 29503488x + 4917248 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1588730atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 794365atan(------------------------------------------------) + 148604\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 43904\|7 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=5591773/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+37/840*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4+403/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 14023/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1466281/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 6794004195x + 22646680650x + 30195574200x + 20130382800x +--R + +--R 6710127600x + 894683680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (197947935x + 536695650x + 546004068x + 247045192x + 41933792)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13588008390x + 45293361300x + 60391148400x + 40260765600x +--R + +--R 13420255200x + 1789367360 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R 5542542180x + 15027478200x + 15288113904x + 6917265376x +--R + +--R 1174146176 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 15603301917x - 52011006390x - 69348008520x - 46232005680x +--R + +--R - 15410668560x - 2054755808 +--R / +--R 5 4 3 2 +--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x +--R + +--R 196689920 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 111835460atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 55917730atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 9173017\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^7 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=588912203/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6+37/1260*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^5+10921/70560*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 126799/141120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 4429459/790272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 463266973/11063808*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R 2146584979935x + 8586339919740x + 14310566532900x +--R + +--R 3 2 +--R 12720503584800x + 6360251792400x + 1696067144640x + 188451904960 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 62541041355x + 211260697020x + 285550790544x + 193055073632x +--R + +--R 65287037520x + 8835086144 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 4480842240x + 17923368960x + 29872281600x + 26553139200x +--R + +--R 2 +--R 13276569600x + 3540418560x + 393379840 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 8586339919740x - 34345359678960x - 57242266131600x +--R + +--R 3 2 +--R - 50882014339200x - 25441007169600x - 6784268578560x - 753807619840 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 3502298315880x + 11830599033120x + 15990844270464x +--R + +--R 2 +--R 10811084123392x + 3656074101120x + 494764824064 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 13384741363497x + 53538965453988x + 89231609089980x + 79316985857760x +--R + +--R 2 +--R 39658492928880x + 10575598114368x + 1175066457152 +--R / +--R 6 5 4 3 +--R 250927165440x + 1003708661760x + 1672847769600x + 1486975795200x +--R + +--R 2 +--R 743487897600x + 198263439360x + 22029271040 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 23556488120atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 11778244060 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 2622916199\|7 +--R / +--R +-+ +--R 49172480\|7 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=70224051139/204800000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 580364059/153600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 10031801/19200000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 8223/64000*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 643/20000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 17/4200*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 1/35*(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 6384004649/204800000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1474705073919asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000000x + 950400000000x + 1480681728000x + 1161696585600x +--R + +--R 2 +--R 402838062880x - 72932734340x - 201521732121 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4300800000\|10 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3m.input.pdf b/src/axiom-website/CATS/rich3m.input.pdf new file mode 100644 index 0000000..a55bc17 Binary files /dev/null and b/src/axiom-website/CATS/rich3m.input.pdf differ diff --git a/src/axiom-website/CATS/rich3n.input.pamphlet b/src/axiom-website/CATS/rich3n.input.pamphlet new file mode 100644 index 0000000..a405749 --- /dev/null +++ b/src/axiom-website/CATS/rich3n.input.pamphlet @@ -0,0 +1,6816 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3n.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 35 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 65 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3n.output +)spool rich3n.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=1269748711/10240000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 10493791/7680000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 183701/960000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 7/1000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 1/30*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 49/80000*(3+5*x)^(5/2)*(146+225*x)*sqrt(1-2*x)-_ + 115431701/10240000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 3809246133asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 2163456000x + 2600899200x + 1349400160x + 21761620x +--R + +--R - 483864147 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 30720000\|10 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-9007/9600*(1-2*x)^(3/2)*(3+5*x)^(3/2)-153/800*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 11988317/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 99077/25600*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1089847/256000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 35964951asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x + 16790400x + 13913120x + 2552540x - 4015809)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 768000\|10 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-181/480*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_ + 240911/12800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 1991/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+21901/12800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 722733asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (144000x + 245600x + 99380x - 63387)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 38400\|10 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R +--------+ +------+ +--R (1) (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1331/160*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-11/16*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 121/160*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (800x + 740x - 207)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 480\|10 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=2/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 793/216*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)-41/72*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 16\|7 \|10 atan(-------------) + 793asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (180x - 15)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 216\|10 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=41/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_ + 107/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+10/9*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (- 321x - 214)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (123x + 82)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (45x + 33)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (81x + 54)\|2 \|7 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=4091/756*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 107/252*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (36819x + 49092x + 16364)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (- 2520x - 3360x - 1120)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (- 1593x - 1020)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (6804x + 9072x + 3024)\|7 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=1331/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 11/84*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 121/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (107811x + 215622x + 143748x + 31944)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (4223x + 4478x + 1152)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (31752x + 63504x + 42336x + 9408)\|7 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (107811x + 215622x + 143748x + 31944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (59122x + 62692x + 16128)\|- 2x + 1 \|5x + 3 - 129276x - 258552x +--R + +--R - 172368x - 38304 +--R / +--R 3 2 +--R 444528x + 889056x + 592704x + 131712 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 1331atan(------------------------------------------------------) - 228\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=153065/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 107/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 4355/42336*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 368045/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (37194795x + 99186120x + 99186120x + 44082720x + 7347120) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1104135x + 2269240x + 1512052x + 328464)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 185973975x - 495930600x - 495930600x - 220413600x - 36735600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (77289450x + 158846800x + 105843640x + 22992480)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 325918404x + 869115744x + 869115744x + 386273664x + 64378944 +--R / +--R 4 3 2 +--R 373403520x + 995742720x + 995742720x + 442552320x + 73758720 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1530650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 765325atan(-----------------------------------------------) + 191604\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 219520\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=783959/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-_ + 107/2520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 641/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 17981/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1852307/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 2857530555x + 9525101850x + 12700135800x + 8466757200x +--R + +--R 2822252400x + 376300320 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (83353815x + 226052850x + 230080132x + 103856008x + 17507808)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 14287652775x - 47625509250x - 63500679000x - 42333786000x +--R + +--R - 14111262000x - 1881501600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R 5834767050x + 15823699500x + 16105609240x + 7269920560x +--R + +--R 1225546560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 26058183732x + 86860612440x + 115814149920x + 77209433280x +--R + +--R 25736477760x + 3431530368 +--R / +--R 5 4 3 2 +--R 11202105600x + 37340352000x + 49787136000x + 33191424000x +--R + +--R 11063808000x + 1475174400 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 39197950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 19598975atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 5106444\|7 +--R / +--R +-+ +--R 2195200\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=64645339/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_ + 107/3780*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 4619/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 42461/423360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1460201/2370816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 152571047/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 706896781965x + 2827587127860x + 4712645213100x + 4189017967200x +--R + +--R 2 +--R 2094508983600x + 558535728960x + 62059525440 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 20597091345x + 69576897780x + 94045700016x + 63585046048x +--R + +--R 21497808880x + 2906375616 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 13442526720x + 53770106880x + 89616844800x + 79659417600x +--R + +--R 2 +--R 39829708800x + 10621255680x + 1180139520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 706896781965x - 2827587127860x - 4712645213100x +--R + +--R 3 2 +--R - 4189017967200x - 2094508983600x - 558535728960x - 62059525440 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 288359278830x + 974076568920x + 1316639800224x + 890190644672x +--R + +--R 300969324320x + 40689258624 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 926952173028x + 3707808692112x + 6179681153520x + 5493049914240x +--R + +--R 2 +--R 2746524957120x + 732406655232x + 81378517248 +--R / +--R 6 5 4 3 +--R 188195374080x + 752781496320x + 1254635827200x + 1115231846400x +--R + +--R 2 +--R 557615923200x + 148697579520x + 16521953280 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 646453390atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 323226695atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 60549492\|7 +--R / +--R +-+ +--R 12293120\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=1988505613369/1310720000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 16433930689/983040000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1493993699/614400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 18411711/51200000*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 58671/640000*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 753/32000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 17/5600*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 1/40*(2+3*x)^4*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 180773237579/1310720000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 41758617880749asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 +--R 6967296000000x + 30838579200000x + 57746856960000x +--R + +--R 4 3 2 +--R 58346097408000x + 32457421737600x + 6882844528480x +--R + +--R - 3991703112140x - 5973304472091 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 27525120000\|10 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=4343003753/8192000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 35892593/6144000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3262963/3840000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 8131/64000*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/200*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 1/35*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 3/20000*(3+5*x)^(7/2)*(414+635*x)*sqrt(1-2*x)-_ + 394818523/8192000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 91203078813asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 16588800000x + 62069760000x + 94673664000x + 72591427200x +--R + +--R 2 +--R 24336990560x - 4902803980x - 12531569067 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 172032000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-11759/3072*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1069/1280*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-13/80*(1-2*x)^(3/2)*(3+5*x)^(7/2)-1/20*(1-2*x)^(3/2)*_ + (2+3*x)*(3+5*x)^(7/2)+15651229/81920*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-129349/8192*(1-2*x)^(3/2)*sqrt(3+5*x)+1422839/81920*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 46953687asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (9216000x + 28108800x + 32887680x + 16507936x + 17884x - 6023169) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 245760\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=-2761/1920*(1-2*x)^(3/2)*(3+5*x)^(3/2)-251/800*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(3+5*x)^(7/2)+_ + 3674891/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 30371/5120*(1-2*x)^(3/2)*sqrt(3+5*x)+334081/51200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 11024673asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (2304000x + 5404800x + 4310240x + 718340x - 1254087)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 153600\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-55/96*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/8*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_ + 14641/512*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 605/256*(1-2*x)^(3/2)*sqrt(3+5*x)+1331/512*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (9600x + 15520x + 5836x - 4005)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1536\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=6553/2592*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/81*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-5/24*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+1/9*(3+5*x)^(5/2)*sqrt(1-2*x)-925/864*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R - 64\|2 \|7 atan(-------------) + 6553\|5 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (7200x + 5940x - 1803)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 2592\|2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=155/216*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+59/27*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/6*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-_ + 95/72*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (1416x + 944)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (465x + 310)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +------+ +--R (900x + 405x - 138)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (648x + 432)\|2 \|7 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2119/252*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-59/84*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 215/84*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ \|7 \|5x + 3 +--R (- 19071x - 25428x - 8476)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +-+ \|2 \|5x + 3 +--R (6300x + 8400x + 2800)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +------+ +--R (2100x + 3117x + 1140)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +-+ +--R (2268x + 3024x + 1008)\|2 \|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=250433/31752*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 50/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-59/252*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 6401/10584*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (6761691x + 13523382x + 9015588x + 2003464)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 529200x - 1058400x - 705600x - 156800)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 372537x - 477522x - 153168)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (857304x + 1714608x + 1143072x + 254016)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=73205/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 605/4704*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/168*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^3+1/4*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 6655/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (814395x + 1285720x + 654436x + 105552)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (11401530x + 18000080x + 9162104x + 1477728)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 14961996x - 39898656x - 39898656x - 17732736x - 2955456 +--R / +--R 4 3 2 +--R 74680704x + 199148544x + 199148544x + 88510464x + 14751744 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 146410atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 73205atan(------------------------------------------------) - 8796\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 43904\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=248897/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/840*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-103/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 947/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+67709/131712*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 907229565x + 3024098550x + 4032131400x + 2688087600x + 896029200x +--R + +--R 119470560 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (27422145x + 74915550x + 74550556x + 32206264x + 5112864)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1814459130x + 6048197100x + 8064262800x + 5376175200x +--R + +--R 1792058400x + 238941120 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R (767820060x + 2097635400x + 2087415568x + 901775392x + 143160192) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 1902464739x - 6341549130x - 8455398840x - 5636932560x - 1878977520x +--R + +--R - 250530336 +--R / +--R 5 4 3 2 +--R 4480842240x + 14936140800x + 19914854400x + 13276569600x +--R + +--R 4425523200x + 590069760 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4977940atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 2488970atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 372813\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=15036307/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/1260*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/18*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-6533/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 47279/1270080*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1057139/7112448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 106751933/99574272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 164422017045x + 657688068180x + 1096146780300x + 974352693600x +--R + +--R 2 +--R 487176346800x + 129913692480x + 14434854720 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 4803836985x + 16234789140x + 21960917808x + 14818971424x +--R + +--R 4978384240x + 665270208 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 13442526720x + 53770106880x + 89616844800x + 79659417600x +--R + +--R 2 +--R 39829708800x + 10621255680x + 1180139520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 822110085225x - 3288440340900x - 5480733901500x +--R + +--R 3 2 +--R - 4871763468000x - 2435881734000x - 649568462400x - 72174273600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 5 4 3 2 +--R 336268588950x + 1136435239800x + 1537264246560x + 1037327999680x +--R + +--R 348486896800x + 46568914560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 1485257318748x + 5941029274992x + 9901715458320x + 8801524851840x +--R + +--R 2 +--R 4400762425920x + 1173536646912x + 130392960768 +--R / +--R 6 5 4 3 +--R 940976870400x + 3763907481600x + 6273179136000x + 5576159232000x +--R + +--R 2 +--R 2788079616000x + 743487897600x + 82609766400 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 751815350atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 375907675atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 97018572\|7 +--R / +--R +-+ +--R 61465600\|7 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=3735929329/120472576*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/1764*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-1/21*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^7-6577/370440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 369409/20744640*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 2524471/41489280*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 84539611/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 8818415317/3252759552*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 122557161637845x + 571933420976610x + 1143866841953220x +--R + +--R 4 3 2 +--R 1270963157725800x + 847308771817200x + 338923508726880x +--R + +--R 75316335272640x + 7172984311680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 3571458203385x + 14445612678330x + 24351227238888x +--R + +--R 3 2 +--R 21898948566336x + 11077661454896x + 2987299350368x + 335335888512 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 +--R 3952102855680x + 18443146659840x + 36886293319680x +--R + +--R 4 3 2 +--R 40984770355200x + 27323180236800x + 10929272094720x + 2428727132160x +--R + +--R 231307345920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 122557161637845x - 571933420976610x - 1143866841953220x +--R + +--R 4 3 2 +--R - 1270963157725800x - 847308771817200x - 338923508726880x +--R + +--R - 75316335272640x - 7172984311680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 6 5 4 +--R 50000414847390x + 202238577496620x + 340917181344432x +--R + +--R 3 2 +--R 306585279928704x + 155087260368544x + 41822190905152x + 4694702439168 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 160426784913444x - 748658329596072x - 1497316659192144x +--R + +--R 4 3 2 +--R - 1663685176880160x - 1109123451253440x - 443649380501376x +--R + +--R - 98588751222528x - 9389404878336 +--R / +--R 7 6 5 +--R 55329439979520x + 258204053237760x + 516408106475520x +--R + +--R 4 3 2 +--R 573786784972800x + 382524523315200x + 153009809326080x +--R + +--R 34002179850240x + 3238302842880 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 37359293290atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 18679646645atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 3493082172\|7 +--R / +--R +-+ +--R 1204725760\|7 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=525371/64000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 46613/64000*sqrt(1-2*x)*sqrt(3+5*x)-7/400*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)+1/20*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/16000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 525371asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (86400x + 162720x + 76140x - 41789)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 64000\|10 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=3047/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-23/80*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-1/10*(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)+277/800*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3047asin(-------------) + (480x + 540x - 113)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 800\|10 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=451/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+41/200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 451asin(-------------) + (60x + 11)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------ +--R +--+ +--R 200\|10 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=11/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/5*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 11asin(-------------) + \|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--R 5\|10 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-2/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+2/3*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7) +--R +--R +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R 2\|5 \|7 atan(-------------) - 2\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R (2) ------------------------------------------------------- +--R +-+ +--R 3\|5 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=11*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (33x + 22)atan(-------------) + \|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------- +--R +-+ +--R (3x + 2)\|7 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 33x - 22)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R 14\|- 2x + 1 \|5x + 3 + 42x + 28 +--R / +--R 42x + 28 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 22atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 11atan(--------------------------------------------------) + 2\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=1177/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/2*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+103/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (10593x + 14124x + 4708)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (309x + 220)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (252x + 336x + 112)\|7 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 10593x - 14124x - 4708)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (4326x + 3080)\|- 2x + 1 \|5x + 3 + 13860x + 18480x + 6160 +--R / +--R 2 +--R 3528x + 4704x + 1568 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2354atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 1177atan(--------------------------------------------------) + 220\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 56\|7 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=68959/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+173/84*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+18083/1176*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (1861893x + 3723786x + 2482524x + 551672)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (54249x + 74754x + 25856)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (10584x + 21168x + 14112x + 3136)\|7 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 9309465x - 18618930x - 12412620x - 2758360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (3797430x + 5232780x + 1809920)\|- 2x + 1 \|5x + 3 + 17103744x +--R + +--R 2 +--R 34207488x + 22804992x + 5067776 +--R / +--R 3 2 +--R 740880x + 1481760x + 987840x + 219520 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 689590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 344795atan(-----------------------------------------------) + 90496\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 3920\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=16925425/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+81/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+14145/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1479375/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1370959425x + 3655891800x + 3655891800x + 1624840800x + 270806800) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (39943125x + 81668520x + 55729116x + 12696112)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 6854797125x - 18279459000x - 18279459000x - 8124204000x +--R + +--R - 1354034000 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (2796018750x + 5716796400x + 3901038120x + 888727840)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 12597717132x + 33593912352x + 33593912352x + 14930627712x + 2488437952 +--R / +--R 4 3 2 +--R 124467840x + 331914240x + 331914240x + 147517440x + 24586240 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 169254250atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 84627125atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 22218196\|7 +--R / +--R +-+ +--R 219520\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=10409/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(2+3*x)^3*_ + sqrt(1-2*x)/sqrt(3+5*x)-791/4000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 7/200*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+7/25*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 10409\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (7200x + 13140x + 3825x - 893)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 4000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=317/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(3/2)/_ + sqrt(3+5*x)-9/100*(1-2*x)^(3/2)*sqrt(3+5*x)+317/2200*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R 317\|5x + 3 asin(-------------) + (180x + 165x + 31)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------------- +--R +--+ +------+ +--R 200\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=29/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(3/2)/_ + sqrt(3+5*x)+29/275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--+ +--------+ +--R 29\|5x + 3 asin(-------------) + (15x + 7)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------- +--R +--+ +------+ +--R 25\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-2/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/5*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R - 2\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------ +--R +-+ +------+ +--R 5\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R - 2\|7 \|5x + 3 atan(-------------) - 2\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R (- 60x - 36)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +--------+ +------+ +--R - 24\|- 2x + 1 \|5x + 3 + 95x + 57 +--R / +--R 60x + 36 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 24\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 12\|7 atan(------------------------------------------------------) + 19 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R 12 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-103*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-15*sqrt(1-2*x)/_ + sqrt(3+5*x)+sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R (- 309x - 206)\|5x + 3 atan(-------------) + (- 45x - 29)\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ------------------------------------------------------------------------ +--R +-+ +------+ +--R (3x + 2)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 37080x - 46968x - 14832)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +--------+ +------+ 2 +--R (- 15120x - 9744)\|- 2x + 1 \|5x + 3 + 57855x + 73283x + 23142 +--R / +--R 2 +--R 5040x + 6384x + 2016 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 4944atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 2472atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R 551\|7 +--R / +--R +-+ +--R 48\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-17951/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 2615/28*sqrt(1-2*x)/sqrt(3+5*x)+1/2*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+173/28*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 161559x - 215412x - 71804)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 23535x - 30861x - 10100)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (252x + 336x + 112)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (9693540x + 18740844x + 12063072x + 2584944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 3953880x - 5184648x - 1696800)\|- 2x + 1 \|5x + 3 - 15112125x +--R + +--R 2 +--R - 29216775x - 18806200x - 4029900 +--R / +--R 3 2 +--R 211680x + 409248x + 263424x + 56448 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 430824atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 215412atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 47975\|7 +--R / +--R +-+ +--R 672\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1463447/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 639565/1176*sqrt(1-2*x)/sqrt(3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*_ + sqrt(3+5*x))+81/28*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 14101/392*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 39513069x - 79026138x - 52684092x - 11707576)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 5756085x - 11385261x - 7502166x - 1646704)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (10584x + 21168x + 14112x + 3136)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (592696035x + 1541009691x + 1501496622x + 649770468x + 105368184) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (- 241755570x - 478180962x - 315090972x - 69161568)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 778067640x + 2022975864x + 1971104688x + 852992672x + 138323136 +--R / +--R 4 3 2 +--R 2222640x + 5778864x + 5630688x + 2436672x + 395136 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 8780682atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 4390341atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 823352\|7 +--R / +--R +-+ +--R 2352\|7 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=35511/20000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^4*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-524/825*(2+3*x)^3*sqrt(1-2*x)/_ + sqrt(3+5*x)-23779/220000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 1043/11000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 623/1375*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (5859315x + 3515589)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (3564000x + 8999100x + 6384015x + 995870x - 218953)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3300000x + 1980000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=1071/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-392/825*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_ + 11557/11000*sqrt(1-2*x)*sqrt(3+5*x)-21/2750*(34-145*x)*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (176715x + 106029)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (89100x + 147015x + 75470x + 11567)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (165000x + 99000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-2/825*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/5*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-12/275*(1-2*x)^(3/2)/sqrt(3+5*x)+3/55*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (495x + 297)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (297x + 278x + 59)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (825x + 495)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-2/165*(1-2*x)^(3/2)/(3+5*x)^(3/2)-6/25*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)-6/25*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 990x - 594)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 970x - 604)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (4125x + 2475)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-2/33*(1-2*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (4x - 2)\|- 2x + 1 +--R (2) -------------------- +--R +------+ +--R (165x + 99)\|5x + 3 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (36x - 18)\|- 2x + 1 \|5x + 3 - 100x - 120x - 36 +--R (3) -------------------------------------------------- +--R 2 +--R 7425x + 8910x + 2673 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - --- +--R 297 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2/3*sqrt(1-2*x)/(3+5*x)^(3/2)+202/33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (990x + 594)\|7 \|5x + 3 atan(-------------) + (1010x + 584)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R +------+ +--R (165x + 99)\|5x + 3 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (22275x + 26730x + 8019)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (9090x + 5256)\|- 2x + 1 \|5x + 3 + 29200x + 35040x + 10512 +--R / +--R 2 +--R 7425x + 8910x + 2673 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 1782\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 891\|7 atan(------------------------------------------------) + 1168 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 297 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=519*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 25/3*sqrt(1-2*x)/(3+5*x)^(3/2)+sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2495/33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (256905x + 325413x + 102762)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (37425x + 46580x + 14453)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (495x + 627x + 198)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 11560725x - 21580020x - 13410441x - 2774574)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (4715550x + 5869080x + 1821078)\|- 2x + 1 \|5x + 3 + 15175650x +--R + +--R 2 +--R 28327880x + 17603754x + 3642156 +--R / +--R 3 2 +--R 311850x + 582120x + 361746x + 74844 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 308286atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 154143atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 28906\|7 +--R / +--R +-+ +--R 594\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=126513/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 6095/84*sqrt(1-2*x)/(3+5*x)^(3/2)+1/2*sqrt(1-2*x)/((2+3*x)^2*_ + (3+5*x)^(3/2))+243/28*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 608185/924*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +------+ +--R (187871805x + 363218823x + 233796024x + 50099148)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (27368325x + 52308690x + 33277877x + 7046540)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (41580x + 80388x + 51744x + 11088)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 8454231225x + 21417385770x + 20327729301x + 8566954308x +--R + +--R 1352676996 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +--R (3448408950x + 6590894940x + 4193012502x + 887864040)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R - 11098300500x - 28115694600x - 26685246980x - 11246277840x - 1775728080 +--R / +--R 4 3 2 +--R 26195400x + 66361680x + 62985384x + 26544672x + 4191264 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 75148722atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 37574361atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 7046540\|7 +--R / +--R +-+ +--R 16632\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=13246251/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 638165/1176*sqrt(1-2*x)/(3+5*x)^(3/2)+1/3*sqrt(1-2*x)/((2+3*x)^3*_ + (3+5*x)^(3/2))+313/84*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 25441/392*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 63678595/12936*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 59012048205x + 153431325333x + 149497188786x + 64694689884x +--R + +--R 10491030792 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 8596610325x + 22161651840x + 21406565457x + 9181937962x +--R + +--R 1475586688 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (1746360x + 4540536x + 4424112x + 1914528x + 310464)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 2655542169225x - 8497734941520x - 10870019279361x +--R + +--R 2 +--R - 6947685142002x - 2218853012508x - 283257831384 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 1083172900950x + 2792368131840x + 2697227247582x + 1156924183212x +--R + +--R 185923922688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 3486073550400x + 11155435361280x + 14269661066304x + 9120601318528x +--R + +--R 2912808122112x + 371847845376 +--R / +--R 5 4 3 2 +--R 1100206800x + 3520661760x + 4503513168x + 2878466976x + 919283904x +--R + +--R 117355392 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7868273094atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 3934136547atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 737793344\|7 +--R / +--R +-+ +--R 232848\|7 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1/30*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 452517373/25600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 3501533/19200000*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 791/120000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 29/1500*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 7/2400000*(3+5*x)^(3/2)*(28458+41105*x)*sqrt(1-2*x)-_ + 41137943/25600000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1357552119asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 691200000x - 1251072000x - 308534400x + 623566880x + 374573660x +--R + +--R - 81405921 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 76800000\|10 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-567/4000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*_ + (2+3*x)*(3+5*x)^(3/2)+5487713/640000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+45353/192000*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 4123/9600*(1-2*x)^(5/2)*sqrt(3+5*x)+498883/640000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 16463139asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 7286400x + 3141280x + 4872460x - 382101)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1920000\|10 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (- 6x - x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-3/40*(1-2*x)^(5/2)*(3+5*x)^(3/2)+30613/6400*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+253/1920*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 23/96*(1-2*x)^(5/2)*sqrt(3+5*x)+2783/6400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 91839asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 6880x + 23420x + 1959)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 19200\|10 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=1331/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/120*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-1/6*(1-2*x)^(5/2)*sqrt(3+5*x)+121/400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (- 800x + 580x + 273)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +--+ +--R 1200\|10 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-14/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 4091/540*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/6*(1-2*x)^(3/2)*sqrt(3+5*x)+107/180*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 280\|7 \|10 atan(-------------) + 4091asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (- 180x + 411)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 540\|10 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-107/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+41/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/_ + (2+3*x)-4/9*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (123x + 82)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R (- 321x - 214)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (- 18x - 33)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (81x + 54)\|5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=793/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/6*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^2+41/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (7137x + 9516x + 3172)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (144x + 192x + 64)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (405x + 228)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|7 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+_ + 1331/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 11/4*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-121/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (107811x + 215622x + 143748x + 31944)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (3103x + 4366x + 1488)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (4536x + 9072x + 6048x + 1344)\|7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (107811x + 215622x + 143748x + 31944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (43442x + 61124x + 20832)\|- 2x + 1 \|5x + 3 + 140616x + 281232x +--R + +--R 187488x + 41664 +--R / +--R 3 2 +--R 63504x + 127008x + 84672x + 18816 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1331atan(------------------------------------------------) + 248\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=240911/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+41/216*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+5413/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 568363/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (58541373x + 156110328x + 156110328x + 69382368x + 11563728) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1705089x + 3485960x + 2381420x + 541680)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 58541373x - 156110328x - 156110328x - 69382368x - 11563728)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (23871246x + 48803440x + 33339880x + 7583520)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 76783140x + 204755040x + 204755040x + 91002240x + 15167040 +--R / +--R 4 3 2 +--R 10668672x + 28449792x + 28449792x + 12644352x + 2107392 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 481822atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 240911atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 45140\|7 +--R / +--R +-+ +--R 6272\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=11988317/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+41/360*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4+7723/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 270463/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 28291441/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 43697415465x + 145658051550x + 194210735400x + 129473823600x +--R + +--R 43157941200x + 5754392160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (1273114845x + 3451770150x + 3511594796x + 1588955864x + 269759904) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 43697415465x - 145658051550x - 194210735400x - 129473823600x +--R + +--R - 43157941200x - 5754392160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 17823607830x + 48324782100x + 49162327144x + 22245382096x +--R + +--R 3776638656 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 57357699588x - 191192331960x - 254923109280x - 169948739520x +--R + +--R - 56649579840x - 7553277312 +--R / +--R 5 4 3 2 +--R 2240421120x + 7468070400x + 9957427200x + 6638284800x + 2212761600x +--R + +--R 295034880 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 119883170atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 59941585atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 11239996\|7 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=1/35*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+_ + 6219452877/102400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 17133479/25600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 870407/9600000*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 51/10000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+29/2100*(2+3*x)^3*_ + (3+5*x)^(5/2)*sqrt(1-2*x)-1/800000*(3+5*x)^(5/2)*_ + (35878+51675*x)*sqrt(1-2*x)-565404807/102400000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43536170139asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 27648000000x - 67968000000x - 46732032000x + 12527113600x +--R + +--R 2 +--R 28707557280x + 9288436460x - 3952411101 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 716800000\|10 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-3101/6400*(1-2*x)^(5/2)*(3+5*x)^(3/2)-259/2000*(1-2*x)^(5/2)*_ + (3+5*x)^(5/2)-1/20*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 136205223/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 375221/512000*(1-2*x)^(3/2)*sqrt(3+5*x)-34111/25600*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+12382293/5120000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 136205223asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 76800000x - 132864000x - 27804800x + 66492960x + 37288220x +--R + +--R - 8705457 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5120000\|10 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=-37/160*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_ + 1625151/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 4477/12800*(1-2*x)^(3/2)*sqrt(3+5*x)-407/640*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+147741/128000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1625151asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 768000x - 745600x + 364320x + 489340x - 46809)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 128000\|10 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-1/8*(1-2*x)^(5/2)*(3+5*x)^(3/2)+43923/6400*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+121/640*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 11/32*(1-2*x)^(5/2)*sqrt(3+5*x)+3993/6400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 16000x - 2400x + 11980x + 603)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6400\|10 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)+14/81*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+19573/6480*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)+37/180*(3+5*x)^(3/2)*sqrt(1-2*x)-1781/2160*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 1120\|7 \|10 atan(-------------) + 19573asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (- 7200x + 5940x + 813)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6480\|10 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)-37/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1649/108*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 107/36*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (- 444x - 296)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (4947x + 3298)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (- 180x + 315x + 318)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (324x + 216)\|10 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2+1649/108*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-37/27*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)+37/12*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)-205/36*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (14841x + 19788x + 6596)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (- 1332x - 1776x - 592)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 360x - 1035x - 516)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|7 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+19573/4536*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/81*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+37/36*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-661/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (528471x + 1056942x + 704628x + 156584)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (30240x + 60480x + 40320x + 8960)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (57123x + 65286x + 18528)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (122472x + 244944x + 163296x + 36288)\|7 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=1/4*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+_ + 43923/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)-121/224*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 11/8*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 3993/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3557763x + 9487368x + 9487368x + 4216608x + 702768) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (100159x + 213240x + 145940x + 32400)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3557763x + 9487368x + 9487368x + 4216608x + 702768)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (1402226x + 2985360x + 2043160x + 453600)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 4592700x - 12247200x - 12247200x - 5443200x - 907200 +--R / +--R 4 3 2 +--R 3556224x + 9483264x + 9483264x + 4214784x + 702464 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 87846atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 43923atan(------------------------------------------------) - 8100\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 6272\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5+_ + 1625151/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+37/120*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 5281/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 36149/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 3831323/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1974558465x + 6581861550x + 8775815400x + 5850543600x +--R + +--R 1950181200x + 260024160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (57469845x + 155783350x + 158785356x + 71866904x + 12157344)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1974558465x - 6581861550x - 8775815400x - 5850543600x +--R + +--R - 1950181200x - 260024160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R (804577830x + 2180966900x + 2222994984x + 1006136656x + 170202816) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 2584955268x - 8616517560x - 11488690080x - 7659126720x +--R + +--R - 2553042240x - 340405632 +--R / +--R 5 4 3 2 +--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x +--R + +--R 98344960 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16251510atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 8125755atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 1519668\|7 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6+19457889/175616*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+37/180*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5-7591/30240*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 37333/181440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1316353/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 137752591/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 70924005405x + 283696021620x + 472826702700x + 420290402400x +--R + +--R 2 +--R 210145201200x + 56038720320x + 6226524480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 2066288865x + 6979774260x + 9434103472x + 6379024416x +--R + +--R 2157325040x + 291805632 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x +--R + +--R 505774080x + 56197120 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 70924005405x + 283696021620x + 472826702700x + 420290402400x +--R + +--R 2 +--R 210145201200x + 56038720320x + 6226524480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 28928044110x + 97716839640x + 132077448608x + 89306341824x +--R + +--R 30202550560x + 4085278848 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 93067758756x - 372271035024x - 620451725040x - 551512644480x +--R + +--R 2 +--R - 275756322240x - 73535019264x - 8170557696 +--R / +--R 6 5 4 3 +--R 8961684480x + 35846737920x + 59744563200x + 53106278400x +--R + +--R 2 +--R 26553139200x + 7080837120x + 786759680 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 194578890atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 97289445atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 18237852\|7 +--R / +--R +-+ +--R 1756160\|7 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7+_ + 6219452877/17210368*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 37/252*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_ + 9901/52920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 341917/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 4014523/5927040*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 140331343/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 14677525921/464679936*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 68009717209995x + 317378680313310x + 634757360626620x +--R + +--R 4 3 2 +--R 705285956251800x + 470190637501200x + 188076255000480x +--R + +--R 41794723333440x + 3980449841280 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 1981465999335x + 8014272743430x + 13509190228248x +--R + +--R 3 2 +--R 12147806104256x + 6146173476816x + 1658923773088x + 186609267072 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x +--R + +--R 3 2 +--R 1301103820800x + 520441528320x + 115653672960x + 11014635520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 68009717209995x - 317378680313310x - 634757360626620x +--R + +--R 4 3 2 +--R - 705285956251800x - 470190637501200x - 188076255000480x +--R + +--R - 41794723333440x - 3980449841280 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 6 5 4 +--R 27740523990690x + 112199818408020x + 189128663195472x +--R + +--R 3 2 +--R 170069285459584x + 86046428675424x + 23224932823232x + 2612529739008 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 89275039675164x - 416616851817432x - 833233703634864x +--R + +--R 4 3 2 +--R - 925815226260960x - 617210150840640x - 246884060336256x +--R + +--R - 54863124519168x - 5225059478016 +--R / +--R 7 6 5 4 +--R 2634735237120x + 12295431106560x + 24590862213120x + 27323180236800x +--R + +--R 3 2 +--R 18215453491200x + 7286181396480x + 1619151421440x + 154204897280 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 62194528770atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 31097264385atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 5831539596\|7 +--R / +--R +-+ +--R 172103680\|7 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +------+ +--R (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=1/40*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+_ + 147858829437/655360000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 407324599/163840000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 37029509/102400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 803549/15360000*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 193/48000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 29/2800*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/1600000*(3+5*x)^(7/2)*(43298+62245*x)*sqrt(1-2*x)-_ + 13441711767/655360000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1035011806059asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R - 774144000000x - 2394316800000x - 2554199040000x - 592093952000x +--R + +--R 3 2 +--R 910419721600x + 749541131680x + 138459209260x - 116041578381 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4587520000\|10 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-8613/5120*(1-2*x)^(5/2)*(3+5*x)^(3/2)-783/1600*(1-2*x)^(5/2)*_ + (3+5*x)^(5/2)-47/400*(1-2*x)^(5/2)*(3+5*x)^(7/2)-_ + 3/70*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(7/2)+_ + 378308799/4096000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1042173/409600*(1-2*x)^(3/2)*sqrt(3+5*x)-94743/20480*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+34391709/4096000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 2648161593asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 1843200000x - 4387840000x - 2867456000x + 887043200x +--R + +--R 2 +--R 1789716960x + 549624420x - 247243887 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 28672000\|10 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-187/256*(1-2*x)^(5/2)*(3+5*x)^(3/2)-17/80*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_ + 1/20*(1-2*x)^(5/2)*(3+5*x)^(7/2)+8213601/204800*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+22627/20480*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-2057/1024*(1-2*x)^(5/2)*sqrt(3+5*x)+_ + 746691/204800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 8213601asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (- 5120000x - 8448000x - 1456000x + 4238560x + 2224900x - 555399) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 204800\|10 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-11/32*(1-2*x)^(5/2)*(3+5*x)^(3/2)-1/10*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_ + 483153/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1331/2560*(1-2*x)^(3/2)*sqrt(3+5*x)-121/128*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+43923/25600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 483153asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 256000x - 227200x + 124640x + 147140x - 16407)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 25600\|10 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)-14/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+648919/62208*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-53/192*(3+5*x)^(3/2)*sqrt(1-2*x)+23/216*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-15863/20736*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 3584\|7 \|10 atan(-------------) + 648919asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 259200x - 15840x + 175068x + 7167)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 62208\|10 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)-43/3888*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)+181/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+25/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 8/27*(3+5*x)^(5/2)*sqrt(1-2*x)-3065/1296*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (8688x + 5792)\|2 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R (- 129x - 86)\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (- 21600x + 5580x + 10539x - 2190)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (11664x + 7776)\|2 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2+1945/324*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-6829/324*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-35/4*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+181/36*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)+_ + 185/27*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ \|7 \|5x + 3 +--R (- 61461x - 81948x - 27316)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +-+ \|2 \|5x + 3 +--R (17505x + 23340x + 7780)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +-+ +--------+ +------+ +--R (- 2700x + 3285x + 8955x + 3696)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +-+ +--R (2916x + 3888x + 1296)\|2 \|7 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3+326717/13608*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-575/243*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+331/168*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)+181/108*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 39745/4536*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (8821359x + 17642718x + 11761812x + 2613736)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 869400x - 1738800x - 1159200x - 257600)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (- 226800x - 860373x - 825066x - 235248)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (367416x + 734832x + 489888x + 108864)\|7 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+1922677/762048*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+100/243*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-871/6048*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2+181/216*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 77269/254016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (155736837x + 415298232x + 415298232x + 184576992x + 30762832) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--+ +--R (25401600x + 67737600x + 67737600x + 30105600x + 5017600)\|7 \|10 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (39870441x + 69556680x + 40302540x + 7751280)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (61725888x + 164602368x + 164602368x + 73156608x + 12192768)\|7 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=1/5*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5+483153/43904*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-1331/3136*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-121/560*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 33/40*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-43923/43904*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (15899035x + 46076650x + 47906548x + 21437032x + 3507552)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R (222586490x + 645073100x + 670691672x + 300118448x + 49105728) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 745793244x - 2485977480x - 3314636640x - 2209757760x - 736585920x +--R + +--R - 98211456 +--R / +--R 5 4 3 2 +--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x +--R + +--R 98344960 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4831530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2415765atan(------------------------------------------------) - 438444\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6+4348377/175616*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2857/10080*_ + (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+181/540*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-126463/544320*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^3+852587/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 92126789/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 15849834165x + 63399336660x + 105665561100x + 93924943200x +--R + +--R 2 +--R 46962471600x + 12523325760x + 1391480640 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 460633945x + 1555340180x + 2108117296x + 1428134688x + 482263920x +--R + +--R 64829376 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x +--R + +--R 505774080x + 56197120 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 15849834165x - 63399336660x - 105665561100x - 93924943200x +--R + +--R 2 +--R - 46962471600x - 12523325760x - 1391480640 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 6448875230x + 21774762520x + 29513642144x + 19993885632x +--R + +--R 6751694880x + 907611264 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 20676519108x + 82706076432x + 137843460720x + 122527520640x +--R + +--R 2 +--R 61263760320x + 16337002752x + 1815222528 +--R / +--R 6 5 4 3 +--R 8961684480x + 35846737920x + 59744563200x + 53106278400x +--R + +--R 2 +--R 26553139200x + 7080837120x + 786759680 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 43483770atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 21741885atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 4051836\|7 +--R / +--R +-+ +--R 1756160\|7 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7+1104970911/17210368*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-12421/52920*_ + (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+181/756*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-1289227/8890560*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^4+6249601/53343360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 224018941/298722816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 23466191827/4182119424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 12082856911785x + 56386665588330x + 112773331176660x +--R + +--R 4 3 2 +--R 125303701307400x + 83535800871600x + 33414320348640x +--R + +--R 7425404521920x + 707181383040 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 351992877405x + 1423652835490x + 2399706883464x + 2158260396608x +--R + +--R 2 +--R 1092179419888x + 294736348384x + 33120084096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x +--R + +--R 3 2 +--R 1301103820800x + 520441528320x + 115653672960x + 11014635520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=18648399/3200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/25*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)-_ + 4802371/9600000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 511/60000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 29/1000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 7/800000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 18648399asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 7862400x + 2952480x + 5372860x - 314441)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 3200000\|10 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=109263/32000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 301/3200*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 119/800*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 3/40*(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)+9933/32000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 109263asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 9440x + 25020x + 3383)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 32000\|10 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1089/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 3/40*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 1/10*(1-2*x)^(5/2)*sqrt(3+5*x)+99/400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 1089asin(-------------) + (- 160x + 100x + 89)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 400\|10 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=363/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/10*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+33/100*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 363asin(-------------) + (- 20x + 43)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------- +--R +--+ +--R 100\|10 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=-103/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_ + 14/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2/15*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R 70\|5 \|7 atan(-------------) - 103\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R - 6\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 45\|5 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=4/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+29/9*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)+2/3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R (87x + 58)\|5 \|7 atan(-------------) + (12x + 8)\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R 21\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (27x + 18)\|5 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=363/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+33/4*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (3267x + 4356x + 1452)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (95x + 68)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (36x + 48x + 16)\|7 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 13068x - 17424x - 5808)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (5320x + 3808)\|- 2x + 1 \|5x + 3 + 20349x + 27132x + 9044 +--R / +--R 2 +--R 2016x + 2688x + 896 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2904atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 1452atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 323\|7 +--R / +--R +-+ +--R 32\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=21417/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3+_ + 169/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 16847/504*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (578259x + 1156518x + 771012x + 171336)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (16847x + 23214x + 8032)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (1512x + 3024x + 2016x + 448)\|7 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (578259x + 1156518x + 771012x + 171336)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (235858x + 324996x + 112448)\|- 2x + 1 \|5x + 3 - 759024x - 1518048x +--R + +--R - 1012032x - 224896 +--R / +--R 3 2 +--R 21168x + 42336x + 28224x + 6272 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 42834atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 21417atan(------------------------------------------------) - 4016\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=5274027/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_ + 239/72*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 39667/2016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 4148797/28224*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (427196187x + 1139189832x + 1139189832x + 506306592x + 84384432) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12446391x + 25448120x + 17365300x + 3956240)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 854392374x - 2278379664x - 2278379664x - 1012613184x - 168768864) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 3 2 +--------+ +------+ +--R (348498948x + 712547360x + 486228400x + 110774720)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 981394785x + 2617052760x + 2617052760x + 1163134560x + 193855760 +--R / +--R 4 3 2 +--R 7112448x + 18966528x + 18966528x + 8429568x + 1404928 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 21096108atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 10548054atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 1730855\|7 +--R / +--R +-+ +--R 12544\|7 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^6*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=333216939/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 103/40*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 23909/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 835409/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 87374783/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 404858580885x + 1349528602950x + 1799371470600x + 1199580980400x +--R + +--R 399860326800x + 53314710240 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 11795595705x + 31981229550x + 32535654204x + 14720806136x +--R + +--R 2499608096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 809717161770x - 2699057205900x - 3598742941200x +--R + +--R 2 +--R - 2399161960800x - 799720653600x - 106629420480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120 +--R + +--R 4 3 2 +--R 330276679740x + 895474427400x + 910998317712x + 412182571808x +--R + +--R 69989026688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 1727307307089x + 5757691023630x + 7676921364840x + 5117947576560x +--R + +--R 1705982525520x + 227464336736 +--R / +--R 5 4 3 2 +--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x +--R + +--R 196689920 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 6664338780atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 3332169390atan(------------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120 +--R + +--R +-+ +--R 1015465789\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=390621/160000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/5*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)-_ + 23779/160000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 1043/8000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 623/1000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 9/50*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 390621\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 432000x - 439200x + 287460x + 317125x + 46783)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 160000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=3927/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/275*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 119/2200*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 3/50*(1-2*x)^(5/2)*sqrt(3+5*x)+357/2000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 3927\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2400x - 180x + 2575x + 1021)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 2000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=33/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/55*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 1/22*(1-2*x)^(3/2)*sqrt(3+5*x)+3/20*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R 33\|5x + 3 asin(-------------) + (- 12x + 17x + 11)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +------+ +--R 20\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-33/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 2/5*(1-2*x)^(3/2)/sqrt(3+5*x)-6/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R - 33\|2 \|5x + 3 asin(-------------) + (- 10x - 28)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +------+ +--R 25\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=4/15*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 14/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2*(1-2*x)^(3/2)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R - 70\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 4\|2 \|5x + 3 asin(-------------) - 66\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +------+ +--R 15\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-33*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + (1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (- 99x - 66)\|7 \|5x + 3 atan(-------------) + (- 101x - 65)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 1485x - 1881x - 594)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (- 606x - 390)\|- 2x + 1 \|5x + 3 - 1950x - 2470x - 780 +--R / +--R 2 +--R 90x + 114x + 36 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 198\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R - 99\|7 atan(------------------------------------------------) - 130 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 6 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3n.input.pdf b/src/axiom-website/CATS/rich3n.input.pdf new file mode 100644 index 0000000..ec916dd Binary files /dev/null and b/src/axiom-website/CATS/rich3n.input.pdf differ diff --git a/src/axiom-website/CATS/rich3o.input.pamphlet b/src/axiom-website/CATS/rich3o.input.pamphlet new file mode 100644 index 0000000..fada68f --- /dev/null +++ b/src/axiom-website/CATS/rich3o.input.pamphlet @@ -0,0 +1,7197 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3o.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 36 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 64 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3o.output +)spool rich3o.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-5709/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x))-_ + 2495/12*sqrt(1-2*x)/sqrt(3+5*x)+169/12*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 51381x - 68508x - 22836)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 7485x - 9815x - 3212)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (36x + 48x + 16)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (3082860x + 5960196x + 3836448x + 822096)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 1257480x - 1648920x - 539616)\|- 2x + 1 \|5x + 3 - 4805955x +--R + +--R 2 +--R - 9291513x - 5980744x - 1281588 +--R / +--R 3 2 +--R 30240x + 58464x + 37632x + 8064 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 137016atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 68508atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 15257\|7 +--R / +--R +-+ +--R 96\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-463881/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x))-_ + 608185/504*sqrt(1-2*x)/sqrt(3+5*x)+_ + 239/36*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 13409/168*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 12524787x - 25049574x - 16699716x - 3711048)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 1824555x - 3608883x - 2378026x - 521968)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (1512x + 3024x + 2016x + 448)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 187871805x - 488466693x - 475941906x - 205963164x - 33399432)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 3 2 +--------+ +------+ +--R (- 76631310x - 151573086x - 99877092x - 21922656)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 215801145x + 561082977x + 546696234x + 236581996x + 38364648 +--R / +--R 4 3 2 +--R 317520x + 825552x + 804384x + 348096x + 56448 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 2783286atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R - 1391643atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R 228361\|7 +--R / +--R +-+ +--R 336\|7 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-145708761/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x))-_ + 63678595/9408*sqrt(1-2*x)/sqrt(3+5*x)+_ + 103/24*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_ + 8063/224*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 1403963/3136*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 11802409641x - 31473092376x - 31473092376x - 13988041056x +--R + +--R - 2331340176 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R - 1719322065x - 4546951839x - 4508028900x - 1985778980x +--R + +--R - 327908240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 177036144615x + 578318072409x + 755354217024x + 493078447224x +--R + +--R 160862472144x + 20982061584 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 72211526730x - 190971977238x - 189337213800x - 83402717160x +--R + +--R - 13772146080 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 325366951140x - 1062865373724x - 1388232324864x - 906207212064x +--R + +--R - 295642069184x - 38562009024 +--R / +--R 5 4 3 2 +--R 53343360x + 174254976x + 227598336x + 148571136x + 48470016x + 6322176 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 874252566atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 437126283atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 114767884\|7 +--R / +--R +-+ +--R 18816\|7 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2)+_ + 13153/10000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 128/25*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+_ + 1953/10000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 399/500*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 378/125*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (197295x + 118377)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 108000x - 83700x + 118395x + 129910x + 31171)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (150000x + 90000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-2/825*(1-2*x)^(5/2)/(3+5*x)^(3/2)+_ + 343/500*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 388/9075*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 343/18150*(1-2*x)^(3/2)*sqrt(3+5*x)+343/5500*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (5145x + 3087)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2700x + 1845x + 3610x + 901)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (7500x + 4500)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-2/165*(1-2*x)^(5/2)/(3+5*x)^(3/2)-_ + 19/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 38/165*(1-2*x)^(3/2)/sqrt(3+5*x)-38/275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 285x - 171)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (- 90x - 290x - 146)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-2/15*(1-2*x)^(3/2)/(3+5*x)^(3/2)+_ + 4/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+4/25*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R (60x + 36)\|2 \|5x + 3 asin(-------------) + (80x + 26)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-2/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+14*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+14*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (210x + 126)\|7 \|5x + 3 atan(-------------) + (214x + 124)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------------------- +--R +------+ +--R (15x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 9450x - 11340x - 3402)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (3852x + 2232)\|- 2x + 1 \|5x + 3 + 14725x + 17670x + 5301 +--R / +--R 2 +--R 1350x + 1620x + 486 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 756\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 378\|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 589 +--R / +--R 54 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2))+_ + 169*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 55/3*sqrt(1-2*x)/(3+5*x)^(3/2)+517/3*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (7605x + 9633x + 3042)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (7755x + 9652x + 2995)\|- 2x + 1 +--R / +--R 2 +------+ +--R (45x + 57x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (342225x + 638820x + 396981x + 82134)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (139590x + 173736x + 53910)\|- 2x + 1 \|5x + 3 + 449250x + 838600x +--R + +--R 521130x + 107820 +--R / +--R 3 2 +--R 4050x + 7560x + 4698x + 972 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 9126\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 4563\|7 atan(------------------------------------------------) + 5990 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 54 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 40787/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 655/4*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 239/12*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 17825/12*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +------+ \|7 \|5x + 3 +--R (5506245x + 10645407x + 6852216x + 1468332)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (802125x + 1533090x + 975325x + 206524)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (540x + 1044x + 672x + 144)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (247781025x + 627711930x + 595775709x + 251084772x + 39644964)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (101067750x + 193169340x + 122890950x + 26022024)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 325275300x + 824030760x + 782106388x + 329612304x + 52044048 +--R / +--R 4 3 2 +--R 340200x + 861840x + 817992x + 344736x + 54432 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2202498atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1101249atan(------------------------------------------------) + 206524\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 216\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 4246733/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 204595/168*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 103/12*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 24469/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 618645/56*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1719926865x + 4471809849x + 4357148058x + 1885549452x + 305764776) +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (250551225x + 645909120x + 623901861x + 267610802x + 43006496)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (22680x + 58968x + 57456x + 24864x + 4032)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 77396708925x - 247669468560x - 316810528533x - 202492722906x +--R + +--R - 64669250124x - 8255648952 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 31569454350x + 81384549120x + 78611634486x + 33718961052x +--R + +--R 5418818496 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 120653380575x + 386090817840x + 493874504487x + 315664992734x +--R + +--R 100812602436x + 12869693928 +--R / +--R 5 4 3 2 +--R 14288400x + 45722880x + 58487184x + 37382688x + 11938752x + 1524096 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 229323582atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 114661791atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 25535107\|7 +--R / +--R +-+ +--R 3024\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=17/700*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 1/35*(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 3735929329/256000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 26653009/192000000*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 35443/1200000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 919/105000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/24000000*(3+5*x)^(3/2)*(1730238+2099155*x)*_ + sqrt(1-2*x)-339629939/256000000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 78454515909asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 82944000000x + 97459200000x - 52468992000x - 85095638400x +--R + +--R 2 +--R 9906627680x + 29819034260x - 679278531 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5376000000\|10 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=-193/2000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*_ + (2+3*x)*(3+5*x)^(3/2)+105254149/12800000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+869869/3840000*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+79079/960000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 7189/32000*(1-2*x)^(7/2)*sqrt(3+5*x)+9568559/12800000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 315762447asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 230400000x + 94464000x - 237187200x - 61262560x + 102523580x +--R + +--R 9303927 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 38400000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-3/50*(1-2*x)^(7/2)*(3+5*x)^(3/2)+1742279/320000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+14399/96000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1309/24000*(1-2*x)^(5/2)*sqrt(3+5*x)-119/800*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+158389/320000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5226837asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (2304000x - 931200x - 1849760x + 1108180x + 355917)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 960000\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=14641/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 121/960*(1-2*x)^(3/2)*sqrt(3+5*x)+11/240*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-1/8*(1-2*x)^(7/2)*sqrt(3+5*x)+1331/3200*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (9600x - 12640x + 3020x + 4443)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9600\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-98/81*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 250433/16200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 59/180*(1-2*x)^(3/2)*sqrt(3+5*x)+1/9*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+6401/5400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 19600\|7 \|10 atan(-------------) + 250433asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (7200x - 17820x + 26313)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 16200\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=35/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2119/90*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)-1/3*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)-43/30*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (1050x + 700)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (- 6357x - 4238)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (60x - 237x - 348)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (270x + 180)\|10 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=118/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_ + 155/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 5/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)+19/18*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (1395x + 1860x + 620)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (4248x + 5664x + 1888)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (144x + 1305x + 708)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|5 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=32765/648*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 8/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 1/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+_ + 5/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 925/216*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (884655x + 1769310x + 1179540x + 262120)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 1728x - 3456x - 2304x - 512)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (23067x + 33318x + 11568)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (17496x + 34992x + 23328x + 5184)\|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=1/4*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+55/24*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^3+73205/448*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)+605/32*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 6655/448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (518715x + 1059032x + 723428x + 164688)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (108864x + 290304x + 290304x + 129024x + 21504)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 88944075x - 237184200x - 237184200x - 105415200x - 17569200)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (36310050x + 74132240x + 50639960x + 11528160)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 163411668x + 435764448x + 435764448x + 193673088x + 32278848 +--R / +--R 4 3 2 +--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 732050atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 366025atan(-----------------------------------------------) + 96068\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 4480\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=3674891/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+1/8*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^4+493/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 82937/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 8672663/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 13394977695x + 44649925650x + 59533234200x + 39688822800x +--R + +--R 13229607600x + 1763947680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (390269835x + 1058136330x + 1076423732x + 487066088x + 82697568)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x +--R + +--R 3010560 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 53579910780x - 178599702600x - 238132936800x - 158755291200x +--R + +--R - 52918430400x - 7055790720 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 21855110760x + 59255634480x + 60279728992x + 27275700928x +--R + +--R 4631063808 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 83521959381x + 278406531270x + 371208708360x + 247472472240x +--R + +--R 82490824080x + 10998776544 +--R / +--R 5 4 3 2 +--R 1280240640x + 4267468800x + 5689958400x + 3793305600x + 1264435200x +--R + +--R 168591360 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 146995640atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 73497820atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 16367227\|7 +--R / +--R +-+ +--R 250880\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=391280725/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+1/12*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^5+647/864*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 151621/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 26486645/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 2770202075/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 855730945575x + 3422923782300x + 5704872970500x + 5070998196000x +--R + +--R 2 +--R 2535499098000x + 676133092800x + 75125899200 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 24931818675x + 84218501340x + 113834022672x + 76960600672x +--R + +--R 26026519504x + 3522190656 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 1711461891150x - 6845847564600x - 11409745941000x +--R + +--R 3 2 +--R - 10141996392000x - 5070998196000x - 1352266185600x - 150251798400 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 5 4 3 2 +--R 698090922900x + 2358118037520x + 3187352634816x + 2154896818816x +--R + +--R 728742546112x + 98621338368 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 1965877694109x + 7863510776436x + 13105851294060x + 11649645594720x +--R + +--R 2 +--R 5824822797360x + 1553286079296x + 172587342144 +--R / +--R 6 5 4 3 +--R 10754021376x + 43016085504x + 71693475840x + 63727534080x +--R + +--R 2 +--R 31863767040x + 8497004544x + 944111616 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1565122900atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 782561450atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 128413201\|7 +--R / +--R +-+ +--R 702464\|7 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--------+ +------+ +--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=51/2800*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+1/40*(1-2*x)^(5/2)*_ + (2+3*x)^3*(3+5*x)^(5/2)+355329559167/8192000000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-978869309/2048000000*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-135322391/2304000000*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+16321/800000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 2477/504000*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-1/192000000*_ + (3+5*x)^(5/2)*(6543814+7759275*x)*sqrt(1-2*x)-_ + 32302687197/8192000000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 2487306914169asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R 3870720000000x + 7105536000000x + 808627200000x - 5264367872000x +--R + +--R 3 2 +--R - 2347326614400x + 1304824422880x + 942468770660x - 115416461871 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 57344000000\|10 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=-2287/8000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-263/2800*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 1104970911/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 3043997/5120000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 276727/1280000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 75471/128000*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 100451901/51200000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 7734796377asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 9216000000x + 10112000000x - 6123776000x - 8717155200x +--R + +--R 2 +--R 1291331040x + 2994263780x - 104420943 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 358400000\|10 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-63/400*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_ + 30438639/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 83853/256000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 7623/64000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 2079/6400*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 2767149/2560000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 30438639asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (25600000x + 8448000x - 25526400x - 5162720x + 10406460x + 717399) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2560000\|10 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-1/10*(1-2*x)^(7/2)*(3+5*x)^(3/2)+483153/64000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1331/6400*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+121/1600*(1-2*x)^(5/2)*sqrt(3+5*x)-33/160*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+43923/64000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 483153asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +------+ +--R (256000x - 124800x - 177440x + 116420x + 29673)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 64000\|10 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=181/1080*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)+_ + 98/243*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 1922677/777600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 7093/21600*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 390869/259200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 313600\|7 \|10 atan(-------------) + 1922677asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (1296000x - 1821600x + 692820x + 178797)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 777600\|10 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-8/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/3*(1-2*x)^(5/2)*_ + (3+5*x)^(3/2)/(2+3*x)-805/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+326717/9720*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-247/270*(3+5*x)^(3/2)*sqrt(1-2*x)+24251/3240*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (- 96600x - 64400)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (980151x + 653434)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (21600x - 41220x + 51831x + 65154)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (29160x + 19440)\|10 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2+115/36*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)+1945/324*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)-6829/162*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)+41/18*(3+5*x)^(3/2)*sqrt(1-2*x)-1649/108*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +--+ \|7 \|5x + 3 +--R (17505x + 23340x + 7780)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 \|2 \|5x + 3 +--R (- 122922x - 163896x - 54632)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (1080x - 3690x - 10413x - 4884)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +--+ +--R (2916x + 3888x + 1296)\|10 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3+115/108*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^2-215/1944*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)+362/243*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(10)+365/216*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-_ + 845/648*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (- 5805x - 11610x - 7740x - 1720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (78192x + 156384x + 104256x + 23168)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12960x + 103023x + 108702x + 30912)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (52488x + 104976x + 69984x + 15552)\|7 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+115/216*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^3+3244595/108864*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-40/243*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(10)+2675/864*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 97235/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (262812195x + 700832520x + 700832520x + 311481120x + 51913520) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--+ +--R (- 1451520x - 3870720x - 3870720x - 1720320x - 286720)\|7 \|10 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (5370975x + 12310776x + 8842644x + 2031504)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (8817984x + 23514624x + 23514624x + 10450944x + 1741824)\|7 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/5*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+11/8*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^4+483153/6272*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-1331/448*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2+121/16*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 43923/6272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (17153435x + 46327530x + 47166452x + 21361768x + 3620448)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +-+ +--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520)\|7 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R (240148090x + 648585420x + 660330328x + 299064752x + 50686272) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 769797756x - 2565992520x - 3421323360x - 2280882240x - 760294080x +--R + +--R - 101372544 +--R / +--R 5 4 3 2 +--R 106686720x + 355622400x + 474163200x + 316108800x + 105369600x +--R + +--R 14049280 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4831530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2415765atan(------------------------------------------------) - 452556\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 62720\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-1/18*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6+23/108*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^5+41068005/175616*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1459/864*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^4-241207/108864*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^3+8346895/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 872316385/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 29938575645x + 119754302580x + 199590504300x + 177413781600x +--R + +--R 2 +--R 88706890800x + 23655170880x + 2628352320 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 872316385x + 2946673460x + 3982356144x + 2692519968x + 910641904x +--R + +--R 123208128 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 128024064x + 512096256x + 853493760x + 758661120x + 379330560x +--R + +--R 101154816x + 11239424 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 29938575645x - 119754302580x - 199590504300x - 177413781600x +--R + +--R 2 +--R - 88706890800x - 23655170880x - 2628352320 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 12212429390x + 41253428440x + 55752986016x + 37695279552x +--R + +--R 12748986656x + 1724913792 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 39295692324x - 157182769296x - 261971282160x - 232863361920x +--R + +--R 2 +--R - 116431680960x - 31048448256x - 3449827584 +--R / +--R 6 5 4 3 +--R 1792336896x + 7169347584x + 11948912640x + 10621255680x +--R + +--R 2 +--R 5310627840x + 1416167424x + 157351936 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 82136010atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 41068005atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 7700508\|7 +--R / +--R +-+ +--R 351232\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7+115/756*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^6+1891543995/2458624*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1921/1512*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5-443563/254016*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^4+2199649/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 384136145/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 40175505215/597445632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 4136806717065x + 19305098012970x + 38610196025940x +--R + +--R 4 3 2 +--R 42900217806600x + 28600145204400x + 11440058081760x +--R + +--R 2542235129280x + 242117631360 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 120526515645x + 487483968610x + 821723878536x + 738910550592x +--R + +--R 2 +--R 373848853744x + 100906793184x + 11351210112 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 5377010688x + 25092716544x + 50185433088x + 55761592320x +--R + +--R 3 2 +--R 37174394880x + 14869757952x + 3304390656x + 314703872 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 8273613434130x + 38610196025940x + 77220392051880x +--R + +--R 4 3 2 +--R 85800435613200x + 57200290408800x + 22880116163520x +--R + +--R 5084470258560x + 484235262720 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 6 5 4 +--R 3374742438060x + 13649551121080x + 23008268599008x +--R + +--R 3 2 +--R 20689495416576x + 10467767904832x + 2825390209152x + 317833883136 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 9503357259627x - 44349000544926x - 88698001089852x +--R + +--R 4 3 2 +--R - 98553334544280x - 65702223029520x - 26280889211808x - 5840197602624x +--R + +--R - 556209295488 +--R / +--R 7 6 5 4 +--R 150556299264x + 702596063232x + 1405192126464x + 1561324584960x +--R + +--R 3 2 +--R 1040883056640x + 416353222656x + 92522938368x + 8811708416 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7566175980atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 3783087990atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 620769303\|7 +--R / +--R +-+ +--R 9834496\|7 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=17/1200*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+1/45*(1-2*x)^(5/2)*_ + (2+3*x)^3*(3+5*x)^(7/2)+932023556783/6553600000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 7702674023/4915200000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 700243093/3072000000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 122147797/4147200000*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 193049/12960000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 2197/756000*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/432000000*(3+5*x)^(7/2)*(7919314+9176285*x)*sqrt(1-2*x)-_ + 84729414253/6553600000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 19572494692443asin(-------------) +--R +--+ +--R \|11 +--R + +--R 8 7 6 +--R 41287680000000x + 102445056000000x + 59625676800000x +--R + +--R 5 4 3 +--R - 46327577600000x - 60250198784000x - 5712426076800x +--R + +--R 2 +--R 16445681555360x + 6397508631020x - 1496712721437 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 137625600000\|10 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-132451/153600*(1-2*x)^(7/2)*(3+5*x)^(3/2)-12041/38400*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-999/11200*(1-2*x)^(7/2)*(3+5*x)^(7/2)-3/80*_ + (1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(7/2)+21331366001/327680000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+176292281/98304000*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+16026571/24576000*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-1456961/819200*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 1939215091/327680000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 447958686021asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R 774144000000x + 1362124800000x + 97008640000x - 1013681408000x +--R + +--R 3 2 +--R - 413675529600x + 252700365920x + 169330465940x - 22414998339 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6881280000\|10 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-407/960*(1-2*x)^(7/2)*(3+5*x)^(3/2)-37/240*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(3+5*x)^(7/2)+_ + 65547757/2048000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 541717/614400*(1-2*x)^(3/2)*sqrt(3+5*x)+49247/153600*_ + (1-2*x)^(5/2)*sqrt(3+5*x)-4477/5120*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+5958887/2048000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1376502897asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 1843200000x + 1879040000x - 1272064000x - 1600483200x +--R + +--R 2 +--R 287177440x + 540576580x - 24901623 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 43008000\|10 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-11/48*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/12*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_ + 1771561/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 14641/30720*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1331/7680*(1-2*x)^(5/2)*sqrt(3+5*x)-121/256*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+161051/102400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5314683asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--+ +--R (5120000x + 1280000x - 4905600x - 748640x + 1895020x + 96003)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 307200\|10 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=37/360*(1-2*x)^(3/2)*(3+5*x)^(5/2)+1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_ + 98/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 109715471/9331200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 14557/28800*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 4783/32400*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1994287/3110400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 1254400\|7 \|10 atan(-------------) + 109715471asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 4 3 2 +--+ +--R (62208000x - 35510400x - 35831520x + 25518780x + 6495351)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9331200\|10 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-5/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)-1/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/_ + (2+3*x)+1295/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 660959/93312*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1453/288*(3+5*x)^(3/2)*sqrt(1-2*x)-247/324*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-155777/31104*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (497280x + 331520)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (- 1982877x - 1321918)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (777600x - 643680x - 181044x + 218547x - 136974)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R (279936x + 186624)\|10 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2+185/36*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)+81733/5832*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-21935/2916*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*_ + sqrt(7)-785/36*(3+5*x)^(3/2)*sqrt(1-2*x)+575/162*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+34145/1944*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (- 394830x - 526440x - 175480)\|2 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (735597x + 980796x + 326932)\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +------+ +--R (64800x - 86940x + 95193x + 361602x + 159612)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (52488x + 69984x + 23328)\|2 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3+185/108*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^2-21935/1458*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)+408665/5832*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+2075/72*(3+5*x)^(3/2)*sqrt(1-2*x)-10385/648*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)-48625/1944*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +-+ \|7 \|5x + 3 +--R (11033955x + 22067910x + 14711940x + 3269320)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +-+ \|2 \|5x + 3 +--R (- 2368980x - 4737960x - 3158640x - 701920)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +-+ +--------+ +--R (97200x - 280260x - 1261593x - 1173042x - 323952)\|2 \|7 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R 3 2 +-+ +-+ +--R (157464x + 314928x + 209952x + 46656)\|2 \|7 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4+185/216*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^3-3304795/326592*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1850/729*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)-3485/4032*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)+1165/2592*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 249575/108864*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 267688395x - 713835720x - 713835720x - 317260320x - 52876720) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (67132800x + 179020800x + 179020800x + 79564800x + 13260800)\|7 +--R * +--R +-+ +------+ +--R +--+ \|2 \|5x + 3 +--R \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--R (10886400x + 88425945x + 136691784x + 77996556x + 15279216)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (26453952x + 70543872x + 70543872x + 31352832x + 5225472)\|7 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+37/72*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^4+109715471/4572288*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-200/729*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)-32453/36288*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2+2543/1296*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 3248687/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 133304297265x + 444347657550x + 592463543400x + 394975695600x +--R + +--R 131658565200x + 17554475360 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 1524096000x - 5080320000x - 6773760000x - 4515840000x +--R + +--R - 1505280000x - 200704000 +--R * +--R +-+ +------+ +--R +-+ +--+ \|2 \|5x + 3 +--R \|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (1471239045x + 5428407510x + 6440871564x + 3132020376x + 542283936) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 5555329920x + 18517766400x + 24690355200x + 16460236800x +--R + +--R 5486745600x + 731566080 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=1/6*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+11/12*(1-2*x)^(3/2)*_ + (3+5*x)^(7/2)/(2+3*x)^5+8857805/175616*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-73205/37632*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2-1331/1344*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 121/32*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-805255/175616*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 19372019535x + 77488078140x + 129146796900x + 114797152800x +--R + +--R 2 +--R 57398576400x + 15306287040x + 1700698560 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 568572155x + 1905431420x + 2573967504x + 1743189856x + 589734736x +--R + +--R 79536960 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 19372019535x - 77488078140x - 129146796900x - 114797152800x +--R + +--R 2 +--R - 57398576400x - 15306287040x - 1700698560 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 7960010170x + 26676039880x + 36035545056x + 24404657984x +--R + +--R 8256286304x + 1113517440 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 25367319180x - 101469276720x - 169115461200x - 150324854400x +--R + +--R 2 +--R - 75162427200x - 20043313920x - 2227034880 +--R / +--R 6 5 4 3 +--R 5377010688x + 21508042752x + 35846737920x + 31863767040x +--R + +--R 2 +--R 15931883520x + 4248502272x + 472055808 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 17715610atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 8857805atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 1657020\|7 +--R / +--R +-+ +--R 351232\|7 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7+185/756*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^6+327738785/2458624*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-129911/84672*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^4+7163/4536*(3+5*x)^(5/2)*sqrt(1-2*x)/_ + (2+3*x)^5-5777249/4572288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 200146505/128024064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 20886641735/1792336896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2150294168385x + 10034706119130x + 20069412238260x +--R + +--R 4 3 2 +--R 22299346931400x + 14866231287600x + 5946492515040x +--R + +--R 1321442781120x + 125851693440 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 62659925205x + 253441751890x + 427105196104x + 384048502848x +--R + +--R 2 +--R 194338741616x + 52456780256x + 5897927808 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 16131032064x + 75278149632x + 150556299264x + 167284776960x +--R + +--R 3 2 +--R 111523184640x + 44609273856x + 9913171968x + 944111616 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 8601176673540x + 40138824476520x + 80277648953040x +--R + +--R 4 3 2 +--R 89197387725600x + 59464925150400x + 23785970060160x +--R + +--R 5285771124480x + 503406773760 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 6 5 4 +--R 3508955811480x + 14192738105840x + 23917890981824x +--R + +--R 3 2 +--R 21506716159488x + 10882969530496x + 2937579694336x + 330283957248 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 13402626245631x - 62545589146278x - 125091178292556x +--R + +--R 4 3 2 +--R - 138990198102840x - 92660132068560x - 37064052827424x +--R + +--R - 8236456183872x - 784424398464 +--R / +--R 7 6 5 4 +--R 903337795584x + 4215576379392x + 8431152758784x + 9367947509760x +--R + +--R 3 2 +--R 6245298339840x + 2498119335936x + 555137630208x + 52870250496 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2621910280atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 1310955140atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 291824553\|7 +--R / +--R +-+ +--R 19668992\|7 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9 +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 9 8 7 6 5 4 3 +--R 19683x + 118098x + 314928x + 489888x + 489888x + 326592x + 145152x +--R + +--R 2 +--R 41472x + 6912x + 512 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-1/24*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8+185/1008*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^7+106656830005/275365888*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-720833/508032*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5+47365/36288*(3+5*x)^(5/2)*sqrt(1-2*x)/_ + (2+3*x)^6-75045071/85349376*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 372439373/512096256*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 64983635965/14338695168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 6796051494355/200741732352*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 8 7 6 +--R 2099326384988415x + 11196407386604880x + 26124950568744720x +--R + +--R 5 4 3 +--R 34833267424992960x + 29027722854160800x + 15481452188885760x +--R + +--R 2 +--R 5160484062961920x + 982949345326080x + 81912445443840 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 7 6 5 +--R 61164463449195x + 288163475473440x + 581931572602156x +--R + +--R 4 3 2 +--R 652979564561296x + 439702534402320x + 177688060285568x +--R + +--R 39899303549504x + 3840133416192 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 +--R 5420026773504x + 28906809458688x + 67449222070272x +--R + +--R 5 4 3 +--R 89932296093696x + 74943580078080x + 39969909374976x +--R + +--R 2 +--R 13323303124992x + 2537772023808x + 211481001984 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 2099326384988415x + 11196407386604880x + 26124950568744720x +--R + +--R 5 4 3 +--R 34833267424992960x + 29027722854160800x + 15481452188885760x +--R + +--R 2 +--R 5160484062961920x + 982949345326080x + 81912445443840 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 7 6 5 +--R 856302488288730x + 4034288656628160x + 8147042016430184x +--R + +--R 4 3 2 +--R 9141713903858144x + 6155835481632480x + 2487632843997952x +--R + +--R 558590249693056x + 53761867826688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 8 7 6 +--R - 2755715740710156x - 14697150617120832x - 34293351439948608x +--R + +--R 5 4 3 +--R - 45724468586598144x - 38103723822165120x - 20321986038488064x +--R + +--R 2 +--R - 6773995346162688x - 1290284827840512x - 107523735653376 +--R / +--R 8 7 6 +--R 75880374829056x + 404695332421632x + 944289108983808x +--R + +--R 5 4 3 +--R 1259052145311744x + 1049210121093120x + 559578731249664x +--R + +--R 2 +--R 186526243749888x + 35528808333312x + 2960734027776 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 213313660010atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 106656830005atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 20000694876\|7 +--R / +--R +-+ +--R 550731776\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=12679836719/1280000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 149/6300*(1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)+1/35*(1-2*x)^(5/2)*_ + (2+3*x)^4*sqrt(3+5*x)-29880867787/34560000000*sqrt(1-2*x)*_ + sqrt(3+5*x)-280447621/1728000000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 5575081/216000000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 3090401/75600000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+_ + 5647/945000*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 266276571099asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000000x + 311731200000x - 147923712000x - 275707382400x +--R + +--R 2 +--R 23172376480x + 98827130860x - 920643741 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 26880000000\|10 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=368012183/64000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 17/500*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)+1/30*(1-2*x)^(5/2)*_ + (2+3*x)^3*sqrt(3+5*x)-800452163/1728000000*sqrt(1-2*x)*_ + sqrt(3+5*x)+499583/10800000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 3037/180000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-7/144000000*_ + (3860014+4790855*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1104036549asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 338688000x - 729302400x - 233839520x + 334643860x +--R + +--R 39899709 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 192000000\|10 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=6531217/1600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+53977/480000*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+4907/120000*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-369/4000*(1-2*x)^(7/2)*sqrt(3+5*x)-_ + 3/50*(1-2*x)^(7/2)*(2+3*x)*sqrt(3+5*x)+593747/1600000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 19593651asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x - 2217600x - 6256480x + 3384140x + 1498491)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4800000\|10 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=65219/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+539/4800*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+49/1200*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 3/40*(1-2*x)^(7/2)*sqrt(3+5*x)+5929/16000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 195657asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (28800x - 35360x + 2980x + 21537)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 48000\|10 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=1331/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/60*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+1/15*(1-2*x)^(5/2)*sqrt(3+5*x)+121/200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (160x - 380x + 513)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 600\|10 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=98/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 17687/1350*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/15*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-239/450*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 4900\|7 \|10 atan(-------------) - 17687asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (180x - 807)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1350\|10 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=346/135*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+175/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + (1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)+74/45*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (2625x + 1750)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +-+ +--------+ +------+ +--R (1038x + 692)\|2 asin(-------------) + (36x + 759)\|5 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +--R (405x + 270)\|5 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-8/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+3035/108*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)^2+95/12*(1-2*x)^(3/2)*sqrt(3+5*x)/_ + (2+3*x)+91/18*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (27315x + 36420x + 12140)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (- 288x - 384x - 128)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (5481x + 3948)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|5 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=6655/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)^3+55/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 605/8*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (539055x + 1078110x + 718740x + 159720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (15707x + 21638x + 7488)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (648x + 1296x + 864x + 192)\|7 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 2695275x - 5390550x - 3593700x - 798600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (1099490x + 1514660x + 524160)\|- 2x + 1 \|5x + 3 + 4953312x +--R + +--R 2 +--R 9906624x + 6604416x + 1467648 +--R / +--R 3 2 +--R 45360x + 90720x + 60480x + 13440 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 66550atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 33275atan(-----------------------------------------------) + 8736\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 80\|7 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=1643785/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4+235/72*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^3+38875/864*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+3879245/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (399439755x + 1065172680x + 1065172680x + 473410080x + 78901680) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (11637735x + 23794744x + 16236916x + 3699216)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (108864x + 290304x + 290304x + 129024x + 21504)\|7 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 1997198775x - 5325863400x - 5325863400x - 2367050400x +--R + +--R - 394508400 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (814641450x + 1665632080x + 1136584120x + 258945120)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 3670547076x + 9788125536x + 9788125536x + 4350278016x + 725046336 +--R / +--R 4 3 2 +--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16437850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 8218925atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 2157876\|7 +--R / +--R +-+ +--R 4480\|7 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=104040277/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 61/24*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_ + 14131/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 2347559/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 245529161/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 379226809665x + 1264089365550x + 1685452487400x + 1123634991600x +--R + +--R 374544997200x + 49939332960 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 11048812245x + 29956486710x + 30475811404x + 13788819736x +--R + +--R 2341358496 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x +--R + +--R 3010560 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 1896134048325x - 6320446827750x - 8427262437000x +--R + +--R 2 +--R - 5618174958000x - 1872724986000x - 249696664800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R 773416857150x + 2096954069700x + 2133306798280x + 965217381520x +--R + +--R 163895094720 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 3484819451484x + 11616064838280x + 15488086451040x + 10325390967360x +--R + +--R 3441796989120x + 458906265216 +--R / +--R 5 4 3 2 +--R 1600300800x + 5334336000x + 7112448000x + 4741632000x + 1580544000x +--R + +--R 210739200 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5202013850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 2601006925atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 682896228\|7 +--R / +--R +-+ +--R 313600\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^7*sqrt(3+5*x)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=13391796605/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+_ + 25/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 7445/288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 1729615/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 302171615/338688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 31603880465/4741632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R 29287859175135x + 117151436700540x + 195252394500900x +--R + +--R 3 2 +--R 173557684000800x + 86778842000400x + 23141024533440x + 2571224948160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 853304772555x + 2882422865340x + 3896029345680x + 2634024494432x +--R + +--R 890768460368x + 120549503808 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 117151436700540x - 468605746802160x - 781009578003600x +--R + +--R 3 2 +--R - 694230736003200x - 347115368001600x - 92564098133760x +--R + +--R - 10284899792640 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 47785067263080x + 161415680459040x + 218177643358080x +--R + +--R 2 +--R 147505371688192x + 49883033780608x + 6750772213248 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R 182626847511129x + 730507390044516x + 1217512316740860x +--R + +--R 3 2 +--R 1082233170436320x + 541116585218160x + 144297756058176x + 16033084006464 +--R / +--R 6 5 4 3 +--R 21508042752x + 86032171008x + 143386951680x + 127455068160x +--R + +--R 2 +--R 63727534080x + 16994009088x + 1888223232 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 107134372840atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 53567186420 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 11929377981\|7 +--R / +--R +-+ +--R 1404928\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=1298595837/320000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/5*(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x)-13/75*(1-2*x)^(3/2)*_ + (2+3*x)^4*sqrt(3+5*x)-320899019/2880000000*sqrt(1-2*x)*_ + sqrt(3+5*x)-7/240000000*(6000382-1842385*x)*sqrt(1-2*x)*_ + sqrt(3+5*x)+5421479/18000000*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)+1178663/900000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 4439/11250*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 1298595837\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 3456000000x + 4043520000x - 2530224000x - 3673002400x +--R + +--R 2 +--R 938891620x + 1366129125x + 168414751 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 320000000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=24319911/8000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*_ + (1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x)-22/125*(1-2*x)^(3/2)*_ + (2+3*x)^3*sqrt(3+5*x)-2987467/24000000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 386939/1200000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 205079/150000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 1019/2500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 24319911\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 34560000x + 12528000x - 39487200x - 4101140x + 20337375x +--R + +--R 6089453 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 8000000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=236313/80000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(7/2)/_ + sqrt(3+5*x)+651/8000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 651/22000*(1-2*x)^(5/2)*sqrt(3+5*x)-9/200*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+21483/80000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 236313\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (144000x - 77600x - 112620x + 134625x + 79699)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 80000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2541/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(7/2)/_ + sqrt(3+5*x)+7/100*(1-2*x)^(3/2)*sqrt(3+5*x)+7/275*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+231/1000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 2541\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (800x - 1340x + 1125x + 943)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 1000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-363/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)/_ + sqrt(3+5*x)-1/5*(1-2*x)^(3/2)*sqrt(3+5*x)-33/50*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R - 363\|5x + 3 asin(-------------) + (20x - 75x - 149)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +--+ +------+ +--R 50\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=338/225*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-98/9*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*(1-2*x)^(5/2)/sqrt(3+5*x)-_ + 4/5*(1-2*x)^(3/2)*sqrt(3+5*x)-128/75*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R - 2450\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 338\|2 \|5x + 3 asin(-------------) + (60x - 2142)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +------+ +--R 225\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-8/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-665/9*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-33*(1-2*x)^(3/2)/sqrt(3+5*x)+_ + (1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x))-202/15*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R (- 9975x - 6650)\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 24x - 16)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 10209x - 6561)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (135x + 90)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1815/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*_ + (1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+55/4*(1-2*x)^(3/2)/((2+3*x)*_ + sqrt(3+5*x))-1815/4*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (- 16335x - 21780x - 7260)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (- 16657x - 21843x - 7148)\|- 2x + 1 +--R / +--R 2 +------+ +--R (36x + 48x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 980100x - 1894860x - 1219680x - 261360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 399768x - 524232x - 171552)\|- 2x + 1 \|5x + 3 + 1527885x +--R + +--R 2 +--R 2953911x + 1901368x + 407436 +--R / +--R 3 2 +--R 4320x + 8352x + 5376x + 1152 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 43560\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 21780\|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 33953 +--R / +--R 96 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-147015/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x))+235/36*(1-2*x)^(3/2)/_ + ((2+3*x)^2*sqrt(3+5*x))-578245/216*sqrt(1-2*x)/sqrt(3+5*x)+_ + 39155/216*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 3969405x - 7938810x - 5292540x - 1176120)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 578245x - 1143741x - 753654x - 165424)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (216x + 432x + 288x + 64)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (59541075x + 154806795x + 150837390x + 65274660x + 10585080)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 3 2 +--------+ +------+ +--R (- 24286290x - 48037122x - 31653468x - 6947808)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 68392485x - 177820461x - 173260962x - 74978428x - 12158664 +--R / +--R 4 3 2 +--R 45360x + 117936x + 114912x + 49728x + 8064 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 882090atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R 441045atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R - 72373\|7 +--R / +--R +-+ +--R 48\|7 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-46095555/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x))+305/72*(1-2*x)^(3/2)/_ + ((2+3*x)^3*sqrt(3+5*x))-181304825/12096*sqrt(1-2*x)/sqrt(3+5*x)+_ + 71215/864*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+3997345/4032*_ + sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 3733739955x - 9956639880x - 9956639880x - 4425173280x +--R + +--R - 737528880 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (- 543914475x - 1438446565x - 1426133132x - 628209228x - 103735088) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (36288x + 96768x + 96768x + 43008x + 7168)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 280030496625x + 914766288975x + 1194796785600x + 779936790600x +--R + +--R 254447463600x + 33188799600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 114222039750x - 302073778650x - 299487957720x - 131923937880x +--R + +--R - 21784368480 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 514655705340x - 1681208637444x - 2195864342784x - 1433411445984x +--R + +--R - 467637776704x - 60996231744 +--R / +--R 5 4 3 2 +--R 38102400x + 124467840x + 162570240x + 106122240x + 34621440x + 4515840 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 1382866650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 691433325atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 181536404\|7 +--R / +--R +-+ +--R 13440\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-3538809681/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x))+25/8*(1-2*x)^(3/2)/_ + ((2+3*x)^4*sqrt(3+5*x))-4639661185/56448*sqrt(1-2*x)/sqrt(3+5*x)+_ + 7501/144*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+587477/1344*_ + sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+102293609/18816*sqrt(1-2*x)/_ + ((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 5 4 3 +--R - 4299653762415x - 14332179208050x - 19109572277400x +--R + +--R 2 +--R - 12739714851600x - 4246571617200x - 566209548960 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 +--R - 626354259975x - 2074037896035x - 2746600901250x +--R + +--R 2 +--R - 1818284414692x - 601741553688x - 79638637088 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 64494806436225x + 253679571982485x + 415633197033450x +--R + +--R 3 2 +--R 363081873270600x + 178356007922400x + 46712287789200x + 5095885940640 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 +--R - 26306878918950x - 87109591633470x - 115357237852500x +--R + +--R 2 +--R - 76367945417064x - 25273145254896x - 3344822757696 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R - 84665826054180x - 333018915813108x - 545624212349160x +--R + +--R 3 2 +--R - 476637242971680x - 234137593038720x - 61321750557760x - 6689645515392 +--R / +--R 6 5 4 3 2 +--R 1600300800x + 6294516480x + 10313049600x + 9009100800x + 4425523200x +--R + +--R 1159065600x + 126443520 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 106164290430atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 53082145215atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 9954829636\|7 +--R / +--R +-+ +--R 188160\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2)+_ + 88296593/40000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 508/75*(1-2*x)^(3/2)*(2+3*x)^4/sqrt(3+5*x)+_ + 59754401/40000000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/10000000*(191622-763085*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 525259/250000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 109323/12500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 1676/625*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (1324448895x + 794669337)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 1555200000x + 1626480000x - 1419228000x - 1405199700x +--R + +--R 2 +--R 865945995x + 980658710x + 210855251 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (600000000x + 360000000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2)+_ + 766843/400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 376/75*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)+_ + 195643/400000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 34069/20000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 16009/2500*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 247/125*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (11502645x + 6901587)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (6480000x + 972000x - 7724700x + 3074745x + 7876210x + 2322001) +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (6000000x + 3600000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-2/825*(1-2*x)^(7/2)/(3+5*x)^(3/2)+_ + 3619/5000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 76/1815*(1-2*x)^(7/2)/sqrt(3+5*x)+329/16500*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+329/45375*(1-2*x)^(5/2)*sqrt(3+5*x)+_ + 329/5000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (54285x + 32571)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (36000x - 35100x + 3585x + 40930x + 10633)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (75000x + 45000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-2/165*(1-2*x)^(7/2)/(3+5*x)^(3/2)-1001/250*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-182/825*(1-2*x)^(5/2)/sqrt(3+5*x)-_ + 91/825*(1-2*x)^(3/2)*sqrt(3+5*x)-91/250*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (- 15015x - 9009)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (900x - 2715x - 7970x - 3707)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3750x + 2250)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-2/15*(1-2*x)^(5/2)/(3+5*x)^(3/2)+22/25*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)+4/15*(1-2*x)^(3/2)/sqrt(3+5*x)+4/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (330x + 198)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (60x + 380x + 158)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-2/3*(1-2*x)^(5/2)/(3+5*x)^(3/2)-8/75*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)+98/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 218/15*(1-2*x)^(3/2)/sqrt(3+5*x)+148/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R (12250x + 7350)\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 40x - 24)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (12430x + 7216)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-55/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))+_ + 385*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+385*sqrt(1-2*x)/_ + sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (17325x + 21945x + 6930)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (17667x + 21988x + 6823)\|- 2x + 1 +--R / +--R 2 +------+ +--R (45x + 57x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (779625x + 1455300x + 904365x + 187110)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (318006x + 395784x + 122814)\|- 2x + 1 \|5x + 3 + 1023450x + 1910440x +--R + +--R 1187202x + 245628 +--R / +--R 3 2 +--R 4050x + 7560x + 4698x + 972 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 20790\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 10395\|7 atan(------------------------------------------------) + 13646 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 54 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2))+235/12*(1-2*x)^(3/2)/_ + ((2+3*x)*(3+5*x)^(3/2))+13145/4*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)-4279/12*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 40213/12*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +--R (1774575x + 3430845x + 2208360x + 473220)\|7 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--------+ +--R (1809585x + 3458634x + 2200321x + 465916)\|- 2x + 1 +--R / +--R 3 2 +------+ +--R (540x + 1044x + 672x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 79855875x - 202301550x - 192009015x - 80920620x - 12776940)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (32572530x + 62255412x + 39605778x + 8386488)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 104831100x + 265572120x + 252060556x + 106228848x + 16772976 +--R / +--R 4 3 2 +--R 48600x + 123120x + 116856x + 49248x + 7776 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 709830\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 354915\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 465916 +--R / +--R 216 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 305/36*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 1361195/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 196735/72*sqrt(1-2*x)/(3+5*x)^(3/2)+7975/24*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+1784635/72*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (551283975x + 1433338335x + 1396586070x + 604370580x + 98006040) +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (80308575x + 207031680x + 199977747x + 85776638x + 13784768)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (3240x + 8424x + 8208x + 3552x + 576)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 24807778875x + 79384892400x + 101546508195x + 64904499990x +--R + +--R 20728277460x + 2646163080 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R 10118880450x + 26085991680x + 25197196122x + 10807856388x +--R + +--R 1736880768 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 32566514400x + 104212846080x + 133305598944x + 85203651008x +--R + +--R 27211132032x + 3473761536 +--R / +--R 5 4 3 2 +--R 2041200x + 6531840x + 8355312x + 5340384x + 1705536x + 217728 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 73504530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 36752265atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 6892384\|7 +--R / +--R +-+ +--R 432\|7 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2))+125/24*(1-2*x)^(3/2)/_ + ((2+3*x)^3*(3+5*x)^(3/2))+519421265/448*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-25024175/1344*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 12595/96*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+2992825/1344*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+227000875/1344*_ + sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 631096836975x + 2061583000785x + 2692679837760x + 1757721560760x +--R + +--R 573441076560x + 74796662160 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 91935354375x + 298295199450x + 386933096475x + 250814924064x +--R + +--R 81243850516x + 10520317456 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--R (544320x + 1778112x + 2322432x + 1516032x + 494592x + 64512)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 28399357663875x + 109810849633650x + 176833333720395x +--R + +--R 3 2 +--R 151799825853720x + 73263330585720x + 18848758864320x + 2019509878320 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 +--R 11583854651250x + 37585195130700x + 48753570155850x +--R + +--R 2 +--R 31602680432064x + 10236725165016x + 1325559999456 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R - 37281374984700x - 144154649940840x - 232138694904732x +--R + +--R 3 2 +--R - 199275853251552x - 96176742182752x - 24743786656512x - 2651119998912 +--R / +--R 6 5 4 3 2 +--R 342921600x + 1325963520x + 2135258496x + 1832979456x + 884653056x +--R + +--R 227598336x + 24385536 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 28048748310atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 14024374155atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 2630079364\|7 +--R / +--R +-+ +--R 24192\|7 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=1/5*(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2))+89/24*(1-2*x)^(3/2)/_ + ((2+3*x)^4*(3+5*x)^(3/2))+46975917593/6272*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-754386765/6272*sqrt(1-2*x)/_ + (3+5*x)^(3/2)+10945/144*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 3329689/4032*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 270667969/18816*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 20529722435/18816*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 856136098132425x + 3367468652654205x + 5517321521297850x +--R + +--R 3 2 +--R 4819729145041800x + 2367586246687200x + 620082112227600x +--R + +--R 67645321333920 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 124718063792625x + 487807977825900x + 794682454662945x +--R + +--R 3 2 +--R 690189860794590x + 337048538999244x + 87747789308536x + 9514465420576 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 114307200x + 449608320x + 736646400x + 643507200x + 316108800x +--R + +--R 82790400x + 9031680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 77052248831918250x - 349303528038029400x - 678402244160133570x +--R + +--R 4 3 2 +--R - 731710985203845900x - 473348136034105200x - 183657047421592800x +--R + +--R - 39572512980343200x - 3652847352031680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 6 5 4 +--R 31428952075741500x + 122927610412126800x + 200259978575062140x +--R + +--R 3 2 +--R 173927844920236680x + 84936231827809488x + 22112442905751072x +--R + +--R 2397645285985152 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R 88506827939686275x + 401230953326577780x + 779253449548971159x +--R + +--R 4 3 2 +--R 840487062360576330x + 543716019540591240x + 210959484537721360x +--R + +--R 45455358546801840x + 4195879250474016 +--R / +--R 7 6 5 4 +--R 144027072000x + 652922726400x + 1268078353920x + 1367723750400x +--R + +--R 3 2 +--R 884788531200x + 343294156800x + 73969459200x + 6827950080 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 25366995500220atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 12683497750110 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 2081289310751\|7 +--R / +--R +-+ +--R 3386880\|7 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R (1) ------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=1067352517/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 96151531/2560000*sqrt(1-2*x)*sqrt(3+5*x)-25529/16000*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x)-313/800*(2+3*x)^3*sqrt(1-2*x)*_ + sqrt(3+5*x)-1/10*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/640000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1067352517asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 20736000x - 82339200x - 146144160x - 163168620x - 157419203)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2560000\|10 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R (1) -------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=677017/5120*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 11835/1024*sqrt(1-2*x)*sqrt(3+5*x)-2829/1280*(2+3*x)*_ + sqrt(1-2*x)*sqrt(3+5*x)-81/160*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)-1/8*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 677017asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 17280x - 57888x - 88092x - 97295)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5120\|10 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R (1) ------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=68959/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 181/400*(3+5*x)^(3/2)*sqrt(1-2*x)-1/10*(2+3*x)*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-6269/1600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 68959asin(-------------) + (- 2400x - 6660x - 9401)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 1600\|10 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (3x + 2)\|5x + 3 +--R (1) ----------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=1177/80*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-107/80*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 1177asin(-------------) + (- 60x - 143)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------- +--R +--+ +--R 80\|10 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=11/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 11asin(-------------) - \|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--R 2\|10 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-2/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10) +--R +--R +--R +-+ +------+ +-+ +------+ +--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3 +--R - 2atan(-------------) + \|7 \|10 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R (2) ----------------------------------------------------- +--R +-+ +--R 3\|7 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=11/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (33x + 22)atan(-------------) - \|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------- +--R +-+ +--R (21x + 14)\|7 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 33x - 22)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R - 14\|- 2x + 1 \|5x + 3 + 42x + 28 +--R / +--R 294x + 196 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 22atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 11atan(--------------------------------------------------) + 2\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=451/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+29/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (4059x + 5412x + 1804)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (87x + 44)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (4059x + 5412x + 1804)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (1218x + 616)\|- 2x + 1 \|5x + 3 + 2772x + 3696x + 1232 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 902atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 451atan(------------------------------------------------) + 44\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=15235/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 25/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 3895/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (411345x + 822690x + 548460x + 121880)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (11685x + 15930x + 5296)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 411345x - 822690x - 548460x - 121880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (163590x + 223020x + 74144)\|- 2x + 1 \|5x + 3 + 437913x + 875826x +--R + +--R 583884x + 129752 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 30470atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 15235atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 2317\|7 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=375265/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+1/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+305/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 32735/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (30396465x + 81057240x + 81057240x + 36025440x + 6004240) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (883845x + 1806120x + 1230876x + 278960)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 121585860x - 324228960x - 324228960x - 144101760x - 24016960)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 3 2 +--------+ +------+ +--R (49495320x + 101142720x + 68929056x + 15621760)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 187827255x + 500872680x + 500872680x + 222610080x + 37101680 +--R / +--R 4 3 2 +--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 3002120atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 1501060atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 331265\|7 +--R / +--R +-+ +--R 175616\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=333216939/512000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 875641/128000*(3+5*x)^(3/2)*sqrt(1-2*x)-5029/3200*(2+3*x)*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-309/800*(2+3*x)^2*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/10*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 30292449/512000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 333216939asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 26870400x - 46785120x - 51453140x - 49229901)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 512000\|10 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=5274027/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 14529/6400*(3+5*x)^(3/2)*sqrt(1-2*x)-251/800*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-3/40*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 479457/25600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5274027asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 144000x - 469600x - 698580x - 760653)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 25600\|10 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=21417/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-59/80*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/10*(3+5*x)^(5/2)*sqrt(1-2*x)-1947/320*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 21417asin(-------------) + (- 800x - 2140x - 2943)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--R 320\|10 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=363/16*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-33/16*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 363asin(-------------) + (- 20x - 45)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------- +--R +--+ +--R 16\|10 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=29/18*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/6*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3 +--R 4\|2 atan(-------------) + 29\|5 \|7 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R - 15\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R 18\|2 \|7 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-103/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 5/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/7*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)+5/21*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R (- 309x - 206)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +--+ \|2 \|5x + 3 +-+ +--------+ +------+ +--R (105x + 70)\|7 \|10 asin(-------------) + 3\|7 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +--R (189x + 126)\|7 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=363/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/14*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-33/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (3267x + 4356x + 1452)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (- 169x - 108)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 3267x - 4356x - 1452)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 2366x - 1512)\|- 2x + 1 \|5x + 3 - 6804x - 9072x - 3024 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 726atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 363atan(--------------------------------------------------) - 108\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=5445/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-95/1764*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+2195/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (147015x + 294030x + 196020x + 43560)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (2195x + 1830x + 288)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 147015x - 294030x - 196020x - 43560)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (30730x + 25620x + 4032)\|- 2x + 1 \|5x + 3 - 27216x - 54432x +--R + +--R - 36288x - 8064 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10890atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 5445atan(--------------------------------------------------) - 144\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=78045/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/28*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-13/504*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+85/14112*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 57595/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (6321645x + 16857720x + 16857720x + 7492320x + 1248720) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (172785x + 346760x + 226348x + 48240)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (25286580x + 67430880x + 67430880x + 29969280x + 4994880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ +--R (9675960x + 19418560x + 12675488x + 2701440)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 32480595x - 86614920x - 86614920x - 38495520x - 6415920 +--R / +--R 4 3 2 +--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 624360atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 312180atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 57285\|7 +--R / +--R +-+ +--R 175616\|7 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3o.input.pdf b/src/axiom-website/CATS/rich3o.input.pdf new file mode 100644 index 0000000..eb4dbda Binary files /dev/null and b/src/axiom-website/CATS/rich3o.input.pdf differ diff --git a/src/axiom-website/CATS/rich3p.input.pamphlet b/src/axiom-website/CATS/rich3p.input.pamphlet new file mode 100644 index 0000000..a65f92d --- /dev/null +++ b/src/axiom-website/CATS/rich3p.input.pamphlet @@ -0,0 +1,6785 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3p.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 49 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 51 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3p.output +)spool rich3p.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=2664057/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-29/1960*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-73/11760*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 6107/65856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+694229/921984*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3236829255x + 10789430850x + 14385907800x + 9590605200x +--R + +--R 3196868400x + 426249120 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (93720915x + 253769850x + 257531412x + 115804328x + 19437408)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 373403520x + 1244678400x + 1659571200x + 1106380800x + 368793600x +--R + +--R 49172480 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 6473658510x - 21578861700x - 28771815600x - 19181210400x +--R + +--R - 6393736800x - 852498240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 4 3 2 +--R (2624185620x + 7105555800x + 7210879536x + 3242521184x + 544247424) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 7232538033x + 24108460110x + 32144613480x + 21429742320x +--R + +--R 7143247440x + 952432992 +--R / +--R 5 4 3 2 +--R 10455298560x + 34850995200x + 46467993600x + 30978662400x +--R + +--R 10326220800x + 1376829440 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 53281140atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 26640570atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 4251933\|7 +--R / +--R +-+ +--R 6146560\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=2678359321/819200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 22135201/614400*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 382619/76800*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1569/1280*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 5/16*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1/12*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 243487211/819200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 8035077963asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 138240000x - 615168000x - 1229558400x - 1505007200x +--R + +--R - 1362715220x - 1202896557 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2457600\|10 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=104040277/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 859837/76800*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 78167/48000*(3+5*x)^(5/2)*sqrt(1-2*x)-963/4000*(3+5*x)^(7/2)*_ + sqrt(1-2*x)-3/50*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 9458207/102400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 312120831asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 26294400x - 44906720x - 48658820x - 46187289)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 307200\|10 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=328757/1024*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2717/768*(3+5*x)^(3/2)*sqrt(1-2*x)-247/480*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-3/40*(3+5*x)^(7/2)*sqrt(1-2*x)-29887/1024*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 986271asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 91360x - 132868x - 142713)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 3072\|10 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=1331/64*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-55/48*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)-605/64*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R 3993\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 800x - 2060x - 2763)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 192\|2 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=3035/432*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 455/144*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3 +--R - 32\|2 atan(-------------) + 3035\|5 \|7 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (- 900x - 1905)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R 432\|2 \|7 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=125/54*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+173/189*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/21*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/7*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-185/126*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (1038x + 692)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (2625x + 1750)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (- 1575x - 1056)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (1134x + 756)\|2 \|7 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-17687/5292*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 25/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 169/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-1/14*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^2+1195/1764*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (- 159183x - 212244x - 70748)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (44100x + 58800x + 19600)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (2781x + 1812)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (47628x + 63504x + 21168)\|7 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=6655/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 55/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^3-605/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (539055x + 1078110x + 718740x + 159720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 37685x - 48170x - 15408)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (222264x + 444528x + 296352x + 65856)\|7 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (539055x + 1078110x + 718740x + 159720)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (- 527590x - 674380x - 215712)\|- 2x + 1 \|5x + 3 + 1456056x +--R + +--R 2 +--R 2912112x + 1941408x + 431424 +--R / +--R 3 2 +--R 3111696x + 6223392x + 4148928x + 921984 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 13310atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 6655atan(------------------------------------------------) + 2568\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=6655/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 23/504*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-1/28*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^4-295/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 4315/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1617165x + 4312440x + 4312440x + 1916640x + 319440) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12945x + 6920x - 6484x - 3600)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3234330x + 8624880x + 8624880x + 3833280x + 638880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (362460x + 193760x - 181552x - 100800)\|- 2x + 1 \|5x + 3 + 893025x +--R + +--R 3 2 +--R 2381400x + 2381400x + 1058400x + 176400 +--R / +--R 4 3 2 +--R 21337344x + 56899584x + 56899584x + 25288704x + 4214784 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 26620atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 13310atan(---------------------------------------------------) + 525\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 12544\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=933031/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 157/5880*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-1721/105840*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 12371/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1948963/8297856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3400897995x + 11336326650x + 15115102200x + 10076734800x +--R + +--R 3358911600x + 447854880 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (87703335x + 231277650x + 222865988x + 93291272x + 14330592)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 1120210560x + 3734035200x + 4978713600x + 3319142400x + 1106380800x +--R + +--R 147517440 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 13603591980x - 45345306600x - 60460408800x - 40306939200x +--R + +--R - 13435646400x - 1791419520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 4911386760x + 12951548400x + 12480495328x + 5224311232x +--R + +--R 802513152 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 14473450089x + 48244833630x + 64326444840x + 42884296560x +--R + +--R 14294765520x + 1905968736 +--R / +--R 5 4 3 2 +--R 62731791360x + 209105971200x + 278807961600x + 185871974400x +--R + +--R 61957324800x + 8260976640 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 37321240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 18660620atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 2836263\|7 +--R / +--R +-+ +--R 12293120\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^7*sqrt(1-2*x)) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=52573169/8605184*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 17/980*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/42*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-3037/493920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 71369/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 958171/16595712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 122343637/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x +--R + +--R 2 +--R 1703370675600x + 454232180160x + 50470242240 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 16516390995x + 55658284380x + 74931979536x + 50261760608x +--R + +--R 16771747280x + 2225100096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 94097687040x + 376390748160x + 627317913600x + 557615923200x +--R + +--R 2 +--R 278807961600x + 74348789760x + 8260976640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x +--R + +--R 2 +--R 1703370675600x + 454232180160x + 50470242240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 231229473930x + 779215981320x + 1049047713504x + 703664648512x +--R + +--R 234804461920x + 31151401344 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 709667861868x + 2838671447472x + 4731119079120x + 4205439181440x +--R + +--R 2 +--R 2102719590720x + 560725224192x + 62302802688 +--R / +--R 6 5 4 3 +--R 1317367618560x + 5269470474240x + 8782450790400x + 7806622924800x +--R + +--R 2 +--R 3903311462400x + 1040883056640x + 115653672960 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 525731690atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 262865845atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 46356252\|7 +--R / +--R +-+ +--R 86051840\|7 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=10866247/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 949753/128000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 9079/6400*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 259/800*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 3/40*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 10866247asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 259200x - 891360x - 1387620x - 1555473)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 128000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=44437/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 799/320*sqrt(1-2*x)*sqrt(3+5*x)-1/10*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)-3/400*(114+185*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 44437asin(-------------) + (- 1440x - 4140x - 6003)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 1600\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=3827/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 333/400*sqrt(1-2*x)*sqrt(3+5*x)-3/20*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 3827asin(-------------) + (- 180x - 453)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--R 400\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=37/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/10*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 37asin(-------------) - 3\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------- +--R +--+ +--R 10\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=1/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5) +--R +--R +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R \|2 asin(-------------) +--R +--+ +--R \|11 +--R (2) ----------------------- +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=1/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------- +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R (3) - ------------------------------------------------------------------ +--R 7 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R / +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=1/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=37/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 3/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (111x + 74)atan(-------------) + 3\|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------- +--R +-+ +--R (21x + 14)\|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 111x - 74)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R 42\|- 2x + 1 \|5x + 3 - 126x - 84 +--R / +--R 294x + 196 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 74atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 37atan(--------------------------------------------------) - 6\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=1/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=3827/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 3/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+333/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (34443x + 45924x + 15308)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (999x + 708)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (34443x + 45924x + 15308)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (13986x + 9912)\|- 2x + 1 \|5x + 3 - 44604x - 59472x - 19824 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7654atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 3827atan(------------------------------------------------) - 708\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=1/((2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=222185/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+185/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+19415/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (5998995x + 11997990x + 7998660x + 1777480)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (174735x + 240750x + 83232)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 5998995x - 11997990x - 7998660x - 1777480)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (2446290x + 3370500x + 1165248)\|- 2x + 1 \|5x + 3 + 7865424x +--R + +--R 2 +--R 15730848x + 10487232x + 2330496 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 444370atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 222185atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 41616\|7 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=143283/8000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 7/550*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-1/10*(2+3*x)^3*_ + sqrt(1-2*x)/sqrt(3+5*x)-139839/88000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 63/22000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 1576113\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 237600x - 849420x - 1477575x - 632101)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 88000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=2493/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/44*(2+3*x)*_ + sqrt(1-2*x)/sqrt(3+5*x)-3/20*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_ + 2337/4400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 27423\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 5940x - 19305x - 9451)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 4400\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=123/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*sqrt(1-2*x)/_ + sqrt(3+5*x)-9/50*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--+ +--------+ +--R 1353\|5x + 3 asin(-------------) + (- 495x - 301)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +------+ +--R 550\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=3/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/55*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 33\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------- +--R +-+ +------+ +--R 55\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-2/11*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R 2\|- 2x + 1 +--R (2) - ------------ +--R +------+ +--R 11\|5x + 3 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ +--R - 6\|- 2x + 1 \|5x + 3 - 20x - 12 +--R (3) ---------------------------------- +--R 165x + 99 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 33 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=1/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (15x + 19x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=-6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/11*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R - 66\|5x + 3 atan(-------------) - 10\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------- +--R +-+ +------+ +--R 11\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R (495x + 297)\|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +--------+ +------+ +--R - 210\|- 2x + 1 \|5x + 3 - 980x - 588 +--R / +--R 1155x + 693 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 198atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R 99atan(-----------------------------------------------) - 28\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 33\|7 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=1/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-321/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 515/77*sqrt(1-2*x)/sqrt(3+5*x)+3/7*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R (- 10593x - 7062)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +--R (- 1545x - 997)\|7 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (231x + 154)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (158895x + 201267x + 63558)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 64890x - 41874)\|- 2x + 1 \|5x + 3 + 209370x + 265202x + 83748 +--R / +--R 2 +--R 48510x + 61446x + 19404 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 21186atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 10593atan(--------------------------------------------------) + 1994\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 462\|7 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=1/((2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-56421/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 90415/2156*sqrt(1-2*x)/sqrt(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+543/196*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 5585679x - 7447572x - 2482524)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 813735x - 1067061x - 349252)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (19404x + 25872x + 8624)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (335140740x + 647938764x + 417064032x + 89370864)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 136707480x - 179266248x - 58674336)\|- 2x + 1 \|5x + 3 - 522568305x +--R + +--R 2 +--R - 1010298723x - 650307224x - 139351548 +--R / +--R 3 2 +--R 16299360x + 31512096x + 20283648x + 4346496 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 14895144atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 7447572atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 1658947\|7 +--R / +--R +-+ +--R 51744\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=1/((2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------ +--R 5 4 3 2 +--------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-4616025/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 7396875/30184*sqrt(1-2*x)/sqrt(3+5*x)+1/7*sqrt(1-2*x)/_ + ((2+3*x)^3*sqrt(3+5*x))+255/196*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+44475/2744*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 1370959425x - 2741918850x - 1827945900x - 406210200)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 199715625x - 395028225x - 260298990x - 57135248)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (814968x + 1629936x + 1086624x + 241472)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 20564391375x - 53467417575x - 52096458150x - 22544666100x +--R + +--R - 3655891800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +--R (- 8388056250x - 16591185450x - 10932557580x - 2399680416)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 26996404680x + 70190652168x + 68390891856x + 29596058464x + 4799360832 +--R / +--R 4 3 2 +--R 171143280x + 444972528x + 433562976x + 187623744x + 30425472 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 304657650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R - 152328825atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 28567624\|7 +--R / +--R +-+ +--R 181104\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)^5/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=462357/40000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+29/1650*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 511/90750*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_ + 4802371/4840000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/1210000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (839177955x + 503506773)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 117612000x - 502791300x - 1030526145x - 795297410x - 199549721) +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (72600000x + 43560000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(2+3*x)^4/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=8127/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+91/3300*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-3/20*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 119/36300*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-80633/242000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (14750505x + 8850303)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2940300x - 11712195x - 10891910x - 2953931)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3630000x + 2178000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(2+3*x)^3/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=81/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+19/330*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-3/10*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 439/18150*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (147015x + 88209)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 49005x - 60010x - 18373)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (90750x + 54450)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^2/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=9/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/825*sqrt(1-2*x)/_ + (3+5*x)^(3/2)-404/9075*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (16335x + 9801)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 2020x - 1234)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (45375x + 27225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-2/165*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 206x - 128)\|- 2x + 1 +--R (2) ------------------------- +--R +------+ +--R (1815x + 1089)\|5x + 3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 1854x - 1152)\|- 2x + 1 \|5x + 3 - 6400x - 7680x - 2304 +--R (3) ------------------------------------------------------------ +--R 2 +--R 81675x + 98010x + 29403 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 256 +--R (4) - ---- +--R 3267 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-2/33*sqrt(1-2*x)/(3+5*x)^(3/2)-8/363*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 40x - 46)\|- 2x + 1 +--R (2) ----------------------- +--R +------+ +--R (1815x + 1089)\|5x + 3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 360x - 414)\|- 2x + 1 \|5x + 3 - 2300x - 2760x - 828 +--R (3) --------------------------------------------------------- +--R 2 +--R 81675x + 98010x + 29403 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 92 +--R (4) - ---- +--R 3267 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=1/((2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 3 2 +--------+ +------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=18*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/33*sqrt(1-2*x)/(3+5*x)^(3/2)+950/363*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R (32670x + 19602)\|5x + 3 atan(-------------) + (4750x + 2740)\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R +-+ +------+ +--R (1815x + 1089)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (735075x + 882090x + 264627)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (299250x + 172620)\|- 2x + 1 \|5x + 3 - 959000x - 1150800x - 345240 +--R / +--R 2 +--R 571725x + 686070x + 205821 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 58806atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 29403atan(------------------------------------------------) - 5480\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 3267\|7 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=1/((2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=1593/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 845/231*sqrt(1-2*x)/(3+5*x)^(3/2)+3/7*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^(3/2))+84235/2541*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (8673885x + 10986921x + 3469554)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (1263525x + 1572580x + 487909)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (38115x + 48279x + 15246)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 390324825x - 728606340x - 452776797x - 93677958)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (159204150x + 198145080x + 61476534)\|- 2x + 1 \|5x + 3 + 512304450x +--R + +--R 2 +--R 956301640x + 594273162x + 122953068 +--R / +--R 3 2 +--R 24012450x + 44823240x + 27854442x + 5762988 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10408662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 5204331atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 975818\|7 +--R / +--R +-+ +--R 45738\|7 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=1/((2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------ +--R 5 4 3 2 +--------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=392283/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 207895/6468*sqrt(1-2*x)/(3+5*x)^(3/2)+3/14*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^(3/2))+753/196*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^(3/2))+20743985/71148*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +------+ +--R (6407942805x + 12388689423x + 7974328824x + 1708784748)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (933479325x + 1784145090x + 1135041037x + 240342364)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (3201660x + 6189876x + 3984288x + 853776)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 288357426225x + 730505479770x + 693339411501x + 292202191908x +--R + +--R 46137188196 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--R (117618394950x + 224802281340x + 143015170662x + 30283137864) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 378539223300x - 958966032360x - 910176532468x - 383586412944x +--R + +--R - 60566275728 +--R / +--R 4 3 2 +--R 2017045800x + 5109849360x + 4849874568x + 2043939744x + 322727328 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2563177122atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 1281588561atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 240342364\|7 +--R / +--R +-+ +--R 1280664\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=1/((2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=41307885/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 21891025/90552*sqrt(1-2*x)/(3+5*x)^(3/2)+1/7*sqrt(1-2*x)/_ + ((2+3*x)^3*(3+5*x)^(3/2))+325/196*sqrt(1-2*x)/((2+3*x)^2*_ + (3+5*x)^(3/2))+79335/2744*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2184369575/996072*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 2024292904425x + 5263161551505x + 5128208691210x + 2219224813740x +--R + +--R 359874294120 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 294889892625x + 760212086400x + 734310313245x + 314968389410x +--R + +--R 50617099616 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (134469720x + 349621272x + 340656624x + 147418656x + 23905728)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 91093180699125x + 291498178237200x + 372874752995085x +--R + +--R 2 +--R 238326751280970x + 76113413206380x + 9716605941240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R 37156126470750x + 95786722886400x + 92523099468870x +--R + +--R 39686017065660x + 6377754551616 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 +--R - 104635035612450x - 334832113959840x - 428306079106962x +--R + +--R 2 +--R - 273756256135684x - 87428385311736x - 11161070465328 +--R / +--R 5 4 3 2 +--R 84715923600x + 271090955520x + 346770513936x + 221641957152x +--R + +--R 70784860608x + 9036365184 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 269905720590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 134952860295atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 22144981082\|7 +--R / +--R +-+ +--R 17929296\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-35439958001/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^5*_ + sqrt(3+5*x)/sqrt(1-2*x)+3192575743/5120000*sqrt(1-2*x)*_ + sqrt(3+5*x)+847637/32000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 10389/1600*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+33/20*(2+3*x)^4*_ + sqrt(1-2*x)*sqrt(3+5*x)+147/1280000*(1853322+3022165*x)*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 35439958001\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 124416000x - 613267200x - 1429191360x - 2297649240x +--R + +--R - 3810769458x + 5389783159 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 5120000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-92108287/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_ + sqrt(3+5*x)/sqrt(1-2*x)+8050753/51200*sqrt(1-2*x)*sqrt(3+5*x)+_ + 15395/512*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+2203/320*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x)+27/16*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 92108287\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 518400x - 2283840x - 5020200x - 9587886x + 14050073)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 51200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1463447/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_ + sqrt(3+5*x)/sqrt(1-2*x)+131833/3200*sqrt(1-2*x)*sqrt(3+5*x)+7/4*_ + (2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+3/160*(750+1223*x)*sqrt(1-2*x)*_ + sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 1463447\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 14400x - 57960x - 142686x + 224833)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 3200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-17951/160*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(3/2)/_ + sqrt(1-2*x)+9/40*(3+5*x)^(3/2)*sqrt(1-2*x)+17951/1760*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 17951\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (- 360x - 1518x + 2809)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 160\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 3x - 2)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-103/4*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(3/2)/_ + sqrt(1-2*x)+103/44*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 103\|- 2x + 1 asin(-------------) + (- 6x + 17)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------- +--R +--+ +--------+ +--R 4\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R - \|5 \|- 2x + 1 asin(-------------) + \|2 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +-+ +--------+ +--R \|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-2/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R - 2\|- 2x + 1 atan(-------------) + 2\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------- +--R +-+ +--------+ +--R 7\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R (4x - 2)\|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ +--R - 28\|- 2x + 1 \|5x + 3 + 98x - 49 +--R / +--R 196x - 98 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 4atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R 2atan(-----------------------------------------------------) + 7\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=29/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))-9/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (87x + 58)\|- 2x + 1 atan(-------------) + (18x + 5)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ----------------------------------------------------------------- +--R +-+ +--------+ +--R (147x + 98)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 1392x - 232x + 464)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (- 2016x - 560)\|- 2x + 1 \|5x + 3 + 3990x + 665x - 1330 +--R / +--R 2 +--R 32928x + 5488x - 10976 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 464atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 232atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 95\|7 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=1585/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-15/98*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+15/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (14265x + 19020x + 6340)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 90x + 405x + 212)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 142650x - 118875x + 31700x + 31700)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 2 +--R (6300x - 28350x - 14840)\|- 2x + 1 \|5x + 3 + 186984x + 155820x +--R + +--R - 41552x - 41552 +--R / +--R 3 2 +--R 1728720x + 1440600x - 384160x - 384160 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 15850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 7925atan(-----------------------------------------------) + 1484\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 13720\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=7435/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-1/7*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3-5/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 565/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (200745x + 401490x + 267660x + 59480)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 10170x - 8055x + 3114x + 2512)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (802980x + 1204470x + 267660x - 297400x - 118960)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (284760x + 225540x - 87192x - 70336)\|- 2x + 1 \|5x + 3 - 1127574x +--R + +--R 3 2 +--R - 1691361x - 375858x + 417620x + 167048 +--R / +--R 4 3 2 +--R 4148928x + 6223392x + 1382976x - 1536640x - 614656 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 29740atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 14870atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 2983\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1244755/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-27/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-13/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 835/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+107245/153664*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (100825155x + 268867080x + 268867080x + 119496480x + 19916080) +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 5791230x - 8897265x - 2075184x + 2239092x + 917264)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 403300620x + 873818010x + 537734160x - 59748240x - 159328640x +--R + +--R - 39832160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R (162154440x + 249123420x + 58105152x - 62694576x - 25683392) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 455077602x - 986001471x - 606770136x + 67418904x + 179783744x +--R + +--R 44945936 +--R / +--R 5 4 3 2 +--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x +--R + +--R - 68841472 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4979020atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 2489510atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 401303\|7 +--R / +--R +-+ +--R 614656\|7 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 405x - 1323x - 1728x - 1128x - 368x - 48)\|5x + 3 +--R (1) --------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-11199264087/1024000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_ + (3+5*x)^(3/2)/sqrt(1-2*x)+29429853/256000*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+169017/6400*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 10377/1600*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+33/20*(2+3*x)^3*_ + (3+5*x)^(3/2)*sqrt(1-2*x)+1018114917/1024000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 11199264087\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 41472000x - 200966400x - 461171520x - 732415080x - 1206337246x +--R + +--R 1702927233 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 1024000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 135x - 351x - 342x - 148x - 24)\|5x + 3 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-145708761/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_ + (3+5*x)^(3/2)/sqrt(1-2*x)+392979/12800*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+27/16*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 3/320*(3+5*x)^(3/2)*(1382+2199*x)*sqrt(1-2*x)+_ + 13246251/51200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 145708761\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 864000x - 3729600x - 8057880x - 15218818x + 22217679)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 51200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 45x - 87x - 56x - 12)\|5x + 3 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-463881/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(5/2)/_ + sqrt(1-2*x)+14057/1760*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 3/20*(3+5*x)^(5/2)*sqrt(1-2*x)+42171/640*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 463881\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 4800x - 18840x - 45538x + 71199)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 640\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 15x - 19x - 6)\|5x + 3 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-5709/32*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(5/2)/_ + sqrt(1-2*x)+173/88*(3+5*x)^(3/2)*sqrt(1-2*x)+519/32*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 2 +--+ +------+ +--R - 5709\|- 2x + 1 asin(-------------) + (- 120x - 490x + 891)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--------+ +--R 32\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-33/4*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(3/2)/_ + sqrt(1-2*x)+15/4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R - 33\|5 \|- 2x + 1 asin(-------------) + (- 10x + 27)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +--------+ +--R 4\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=-5/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 2/21*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R 2\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +-+ +-+ +------+ +--R - 35\|5 \|7 \|- 2x + 1 asin(-------------) + 33\|2 \|7 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--------+ +--R 21\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-33/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+3/49*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (- 99x - 66)\|- 2x + 1 atan(-------------) + (64x + 45)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R +-+ +--------+ +--R (147x + 98)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 198x - 33x + 66)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (- 896x - 630)\|- 2x + 1 \|5x + 3 - 3780x - 630x + 1260 +--R / +--R 2 +--R 4116x + 686x - 1372 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R - 33atan(------------------------------------------------) - 90\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 98\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=825/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x))+_ + 5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 425/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (7425x + 9900x + 3300)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (2550x + 2245x + 396)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 59400x - 49500x + 13200x + 13200)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 142800x - 125720x - 22176)\|- 2x + 1 \|5x + 3 + 237006x + 197505x +--R + +--R - 52668x - 52668 +--R / +--R 3 2 +--R 1382976x + 1152480x - 307328x - 307328 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 6600atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 3300atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 1881\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=2805/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x))+_ + 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 145/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 415/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (75735x + 151470x + 100980x + 22440)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (2490x + 6135x + 3782x + 576)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 151470x - 227205x - 50490x + 56100x + 22440)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 34860x - 85890x - 52948x - 8064)\|- 2x + 1 \|5x + 3 + 108864x +--R + +--R 3 2 +--R 163296x + 36288x - 40320x - 16128 +--R / +--R 4 3 2 +--R 2074464x + 3111696x + 691488x - 768320x - 307328 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5610atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 2805atan(--------------------------------------------------) + 288\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=279015/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x))+9/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-89/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 745/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+16985/153664*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (22600215x + 60267240x + 60267240x + 26785440x + 4464240)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 917190x - 1188045x + 60048x + 538276x + 163152)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 90400860x + 195868530x + 120534480x - 13392720x - 35713920x +--R + +--R - 8928480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--------+ +--R (25681320x + 33265260x - 1681344x - 15071728x - 4568256)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R - 80943786x - 175378203x - 107925048x + 11991672x + 31977792x + 7994448 +--R / +--R 5 4 3 2 +--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x +--R + +--R - 68841472 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1116060atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 558030atan(---------------------------------------------------) - 71379\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 614656\|7 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144)\|5x + 3 +--R ----------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-107121749031/1638400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + (2+3*x)^4*(3+5*x)^(5/2)/sqrt(1-2*x)+295101237/409600*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+5100983/51200*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 62751/2560*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)+999/160*(2+3*x)^2*_ + (3+5*x)^(5/2)*sqrt(1-2*x)+13/8*(2+3*x)^3*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+9738340821/1638400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 107121749031\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 276480000x - 1479168000x - 3687379200x - 5945485120x +--R + +--R 2 +--R - 7755469800x - 11734056318x + 16267424049 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 1638400\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|5x + 3 +--R (1) --------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=-3538809681/204800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + (2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)+9748787/51200*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+172209/6400*(3+5*x)^(5/2)*sqrt(1-2*x)+33/20*_ + (2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+3/1600*(3+5*x)^(5/2)*_ + (6602+10365*x)*sqrt(1-2*x)+321709971/204800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 3538809681\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 13824000x - 65836800x - 148751040x - 233394520x - 381820658x +--R + +--R 538018839 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 204800\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 225x - 570x - 541x - 228x - 36)\|5x + 3 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-9219111/2048*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22*(3+5*x)^(7/2)/sqrt(1-2*x)+25397/512*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+25397/3520*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 9/80*(3+5*x)^(7/2)*sqrt(1-2*x)+838101/2048*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 9219111\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 57600x - 243520x - 517096x - 966014x + 1405233)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 2048\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 75x - 140x - 87x - 18)\|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=-29403/128*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 7/11*(3+5*x)^(7/2)/sqrt(1-2*x)+405/32*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+81/44*(3+5*x)^(5/2)*sqrt(1-2*x)+13365/128*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R - 29403\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +------+ +--R (- 1600x - 6120x - 14526x + 22545)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R 128\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1815/32*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(5/2)/_ + sqrt(1-2*x)+25/8*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 825/32*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R - 1815\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (- 200x - 790x + 1413)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R 32\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------- +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-475/36*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_ + 2/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 505/84*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R - 8\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R - 3325\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (- 1050x + 2703)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R 252\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 169/441*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x))+_ + 3/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+160/147*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R (507x + 338)\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R (- 3675x - 2450)\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (3273x + 2175)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R (1323x + 882)\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-1815/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))+_ + 5/98*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 165/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (- 16335x - 21780x - 7260)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (8110x + 11525x + 4068)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (32670x + 27225x - 7260x - 7260)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 113540x - 161350x - 56952)\|- 2x + 1 \|5x + 3 - 512568x - 427140x +--R + +--R 113904x + 113904 +--R / +--R 3 2 +--R 345744x + 288120x - 76832x - 76832 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 3630atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 1815atan(--------------------------------------------------) - 4068\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2744\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=1815/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x))+_ + 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 155/1764*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 12335/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (49005x + 98010x + 65340x + 14520)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (24670x + 37405x + 17666x + 2448)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 490050x - 735075x - 163350x + 181500x + 72600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (- 1726900x - 2618350x - 1236620x - 171360)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 3238704x + 4858056x + 1079568x - 1199520x - 479808 +--R / +--R 4 3 2 +--R 10372320x + 15558480x + 3457440x - 3841600x - 1536640 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 18150atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 9075atan(-----------------------------------------------) + 8568\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 27440\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=168795/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x))+_ + 9/196*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+_ + 277/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 38365/98784*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 167155/1382976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (13672395x + 36459720x + 36459720x + 16204320x + 2700720)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (1002930x + 2578615x + 2184144x + 687828x + 53136)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 109379160x + 236988180x + 145838880x - 16204320x - 43211520x +--R + +--R - 10802880 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 4 3 2 +--R (- 56164080x - 144402440x - 122312064x - 38518368x - 2975616) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 71554266x - 155034243x - 95405688x + 10600632x + 28268352x + 7067088 +--R / +--R 5 4 3 2 +--R 1394039808x + 3020419584x + 1858719744x - 206524416x - 550731776x +--R + +--R - 137682944 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1350360atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 675180atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 63099\|7 +--R / +--R +-+ +--R 1229312\|7 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^6) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------------------------------- +--R 7 6 5 4 2 +--------+ +--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=3474273/2151296*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x))+11/245*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5+1019/13720*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 29297/82320*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-55277/460992*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+426781/6453888*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4221241695x + 14070805650x + 18761074200x + 12507382800x +--R + +--R 4169127600x + 555883680 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 115230870x - 180017865x + 19738914x + 164918884x + 95331368x +--R + +--R 16456032 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 5 4 3 2 +--R 2613824640x + 8712748800x + 11616998400x + 7744665600x +--R + +--R 2581555200x + 344207360 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 8442483390x + 23920369605x + 23451342750x + 6253691400x +--R + +--R 2 +--R - 4169127600x - 3057360240x - 555883680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 1613232180x + 2520250110x - 276344796x - 2308864376x +--R + +--R - 1334639152x - 230384448 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 6997927608x - 19827461556x - 19438687800x - 5183650080x +--R + +--R 2 +--R 3455766720x + 2534228928x + 460768896 +--R / +--R 6 5 4 3 +--R 73187089920x + 207363421440x + 203297472000x + 54212659200x +--R + +--R 2 +--R - 36141772800x - 26503966720x - 4818903040 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 34742730atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 17371365atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 2057004\|7 +--R / +--R +-+ +--R 21512960\|7 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-291096141/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 2191/880*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)-3/40*(2+3*x)^4*_ + sqrt(3+5*x)/sqrt(1-2*x)+288454593/2816000*sqrt(1-2*x)*_ + sqrt(3+5*x)+76587/17600*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 63/704000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 3202057551\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 17107200x - 76887360x - 171939240x - 332129358x + 488641609)\|10 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--------+ +--R 2816000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-184641/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 567/220*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-1/10*(2+3*x)^3*_ + sqrt(3+5*x)/sqrt(1-2*x)+35505/1408*sqrt(1-2*x)*sqrt(3+5*x)+_ + 8487/1760*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 2031051\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 19008x - 78408x - 196614x + 312365)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 7040\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-56421/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)-3/20*(2+3*x)^2*_ + sqrt(3+5*x)/sqrt(1-2*x)+54249/8800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 620631\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (- 11880x - 51678x + 97409)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 8800\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-321/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22*sqrt(3+5*x)/sqrt(1-2*x)+9/20*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 3531\|- 2x + 1 asin(-------------) + (- 198x + 589)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R 220\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-3*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 33\|- 2x + 1 asin(-------------) + 7\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +--+ +--------+ +--R 11\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=2/11*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R 2\|5x + 3 +--R (2) ------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ +--R - 2\|- 2x + 1 \|5x + 3 - 8x + 4 +--R (3) -------------------------------- +--R 22x - 11 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 11 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=6/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R 66\|- 2x + 1 atan(-------------) + 4\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ------------------------------------------------- +--R +-+ +--------+ +--R 77\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 66x + 33)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R - 28\|- 2x + 1 \|5x + 3 + 112x - 56 +--R / +--R 1078x - 539 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 33atan(--------------------------------------------------) + 8\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 77\|7 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=123/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))+87/539*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (4059x + 2706)\|- 2x + 1 atan(-------------) + (- 174x + 115)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (1617x + 1078)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (32472x + 5412x - 10824)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +--------+ +------+ 2 +--R (9744x - 6440)\|- 2x + 1 \|5x + 3 - 33810x - 5635x + 11270 +--R / +--R 2 +--R 181104x + 30184x - 60368 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10824atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 5412atan(---------------------------------------------------) - 805\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 4312\|7 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=12465/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+_ + 75/1078*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 11685/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (1234035x + 1645380x + 548460)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 70110x - 13785x + 25204)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (135828x + 181104x + 60368)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (4936140x + 4113450x - 1096920x - 1096920)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 2 +--------+ +------+ 3 +--R (1963080x + 385980x - 705712)\|- 2x + 1 \|5x + 3 - 5557482x +--R + +--R 2 +--R - 4631235x + 1234996x + 1234996 +--R / +--R 3 2 +--R 7606368x + 6338640x - 1690304x - 1690304 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 548460atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 274230atan(---------------------------------------------------) - 44107\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 60368\|7 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=102345/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))+_ + 3/77*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 915/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 98205/30184*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (30396465x + 60792930x + 40528620x + 9006360)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 1767690x - 1549935x + 377658x + 421184)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (814968x + 1629936x + 1086624x + 241472)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (60792930x + 91189395x + 20264310x - 22515900x - 9006360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (24747660x + 21699090x - 5287212x - 5896576)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 79603776x - 119405664x - 26534592x + 29482880x + 11793152 +--R / +--R 4 3 2 +--R 22819104x + 34228656x + 7606368x - 8451520x - 3380608 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2251590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1125795atan(------------------------------------------------) - 210592\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 60368\|7 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R (1) +--R 1 +--R - ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=24922335/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))+_ + 51/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 1269/4312*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 228645/120736*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 23958315/1690304*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R 22205800485x + 59215467960x + 59215467960x + 26317985760x +--R + +--R 4386330960 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (- 1293749010x - 1998242055x - 482249808x + 491393004x + 205593328) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (136914624x + 365105664x + 365105664x + 162269184x + 27044864)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 88823201940x - 192450270870x - 118430935920x + 13158992880x +--R + +--R 35090647680x + 8772661920 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 4 3 2 +--R 36224972280x + 55950777540x + 13502994624x - 13759004112x +--R + +--R - 5756613184 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 101999989854x + 220999978017x + 135999986472x - 15111109608x +--R + +--R - 40296292288x - 10074073072 +--R / +--R 5 4 3 2 +--R 7667218944x + 16612307712x + 10222958592x - 1135884288x - 3029024768x +--R + +--R - 757256192 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1096582740atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 548291370atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 89947081\|7 +--R / +--R +-+ +--R 6761216\|7 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-2911419/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 567/220*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 1/10*(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 2821/12100*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_ + 30791901/1936000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 294483/96800*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 352281699\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 15681600x - 75663720x - 208989990x + 169670279x + 162727423)\|10 +--R / +--R +--+ +--------+ +------+ +--R 1936000\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-35451/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3/20*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))+_ + 1/24200*(31586+54645*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 316941/96800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 4289571\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 392040x - 1992870x + 2323271x + 2026687)\|10 +--R / +--R +--+ +--------+ +------+ +--R 96800\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=-999/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 721/220*(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3/10*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3547/12100*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 120879\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 32670x + 82499x + 61243)\|10 +--R / +--R +--+ +--------+ +------+ +--R 12100\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-9/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22/(sqrt(1-2*x)*sqrt(3+5*x))-1229/1210*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--+ +--R - 1089\|- 2x + 1 \|5x + 3 asin(-------------) + (1229x + 733)\|10 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +------+ +--R 605\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=(-2/55)/(sqrt(1-2*x)*sqrt(3+5*x))+74/605*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 74x + 40 +--R (2) ----------------------- +--R +--------+ +------+ +--R 121\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 222x - 120)\|- 2x + 1 \|5x + 3 - 950x - 95x + 285 +--R (3) ------------------------------------------------------ +--R 2 +--R 3630x + 363x - 1089 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 95 +--R (4) - --- +--R 363 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2/11/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 40x + 2 +--R (2) ----------------------- +--R +--------+ +------+ +--R 121\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 120x - 6)\|- 2x + 1 \|5x + 3 - 40x - 4x + 12 +--R (3) ------------------------------------------------- +--R 2 +--R 3630x + 363x - 1089 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - --- +--R 363 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-18/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/(sqrt(1-2*x)*sqrt(3+5*x))-370/847*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +-+ +--R - 2178\|- 2x + 1 \|5x + 3 atan(-------------) + (740x - 326)\|7 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------------- +--R +-+ +--------+ +------+ +--R 847\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (32670x + 3267x - 9801)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 15540x + 6846)\|- 2x + 1 \|5x + 3 + 45640x + 4564x - 13692 +--R / +--R 2 +--R 177870x + 17787x - 53361 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 6534atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 3267atan(--------------------------------------------------) + 652\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2541\|7 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-999/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_ + 17735/5929*sqrt(1-2*x)/sqrt(3+5*x)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (- 362637x - 241758)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (106410x + 15821x - 34205)\|7 +--R / +--R +-+ +--------+ +------+ +--R (17787x + 11858)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (87032880x + 66725208x - 20307672x - 17406576)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 35753760x - 5315856x + 11492880)\|- 2x + 1 \|5x + 3 - 136477950x +--R + +--R 2 +--R - 104633095x + 31844855x + 27295590 +--R / +--R 3 2 +--R 59764320x + 45819312x - 13945008x - 11952864 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 5802192atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 2901096atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 649895\|7 +--R / +--R +-+ +--R 284592\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-177255/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))-_ + 3125575/166012*sqrt(1-2*x)/sqrt(3+5*x)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 18615/15092*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (- 193030695x - 257374260x - 85791420)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (56260350x + 45655035x - 12730165x - 12072596)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (1494108x + 1992144x + 664048)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5790920850x + 8300319885x + 1608589125x - 2058994080x - 772122780) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +--R (- 2362934700x - 1917511470x + 534666930x + 507049032)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R - 7605735480x - 10901554188x - 2112704300x + 2704261504x + 1014098064 +--R / +--R 4 3 2 +--R 627525360x + 899453016x + 174312600x - 223120128x - 83670048 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 128687130atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 64343565atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 12072596\|7 +--R / +--R +-+ +--R 996072\|7 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R - ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-2079585/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x))-_ + 36657025/332024*sqrt(1-2*x)/sqrt(3+5*x)+_ + 3/77*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_ + 1245/2156*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 220305/30184*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 6794004195x - 13588008390x - 9058672260x - 2013038280)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (1979479350x + 2925598635x + 622325745x - 723664682x - 283149136)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (8964648x + 17929296x + 11952864x + 2656192)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1019100629250x + 2140111321425x + 1256890776075x - 173624551650x +--R + +--R - 377444677500x - 90586722600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 415690663500x - 614375713350x - 130688406450x + 151969583220x +--R + +--R 59461318560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 1873031534640x - 3933366222744x - 2310072226056x + 319109076272x +--R + +--R 693715383200x + 166491691968 +--R / +--R 5 4 3 2 +--R 18825760800x + 39534097680x + 23218438320x - 3207351840x +--R + +--R - 6972504000x - 1673400960 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 7548893550atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 3774446775atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 991021976\|7 +--R / +--R +-+ +--R 9960720\|7 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-111321/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3/20*(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 17983/72600*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 7/3993000*(467578+809265*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 10952053/5324000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 2222523765x - 1333514259)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 194059800x - 1128781170x + 612106475x + 1785872944x + 632498543)\|10 +--R / +--R +--+ +--------+ +------+ +--R (79860000x + 47916000)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-621/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 721/220*(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3/10*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))+_ + 1/36300*(4706+11385*x)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 168781/399300*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 12398265x - 7438959)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 3234330x + 6746215x + 11581424x + 3821563)\|10 +--R / +--R +--+ +--------+ +------+ +--R (1996500x + 1197900)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-27/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 2/11*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 8/363*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 4/19965*(158+321*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 3103/33275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 539055x - 323433)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (649265x + 772408x + 229661)\|10 +--R / +--R +--+ +--------+ +------+ +--R (499125x + 299475)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=49/22/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3679/3630*sqrt(1-2*x)/(3+5*x)^(3/2)-4091/19965*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 8182x + 8912x + 2392 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 73638x - 80208x - 21528)\|- 2x + 1 \|5x + 3 - 209300x - 146510x +--R + +--R 50232x + 37674 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4186 +--R (4) - ----- +--R 35937 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=7/11/((3+5*x)^(3/2)*sqrt(1-2*x))-107/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 428/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 4280x + 2782x + 80 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 38520x - 25038x - 720)\|- 2x + 1 \|5x + 3 + 7000x + 4900x - 1680x +--R + +--R - 1260 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 140 +--R (4) ----- +--R 35937 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=2/11/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 160/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 1600x + 1040x - 194 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 14400x - 9360x + 1746)\|- 2x + 1 \|5x + 3 - 19400x - 13580x +--R + +--R 4656x + 3492 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 388 +--R (4) - ----- +--R 35937 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=54/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 410/2541*sqrt(1-2*x)/(3+5*x)^(3/2)+31030/27951*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (1078110x + 646866)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (- 310300x - 22010x + 90032)\|7 +--R / +--R +-+ +--------+ +------+ +--R (139755x + 83853)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 48514950x - 33960465x + 11643588x + 8732691)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (19548900x + 1386630x - 5672016)\|- 2x + 1 \|5x + 3 - 63022400x +--R + +--R 2 +--R - 44115680x + 15125376x + 11344032 +--R / +--R 3 2 +--R 88045650x + 61631955x - 21130956x - 15848217 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1940598atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 970299atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 180064\|7 +--R / +--R +-+ +--R 251559\|7 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3p.input.pdf b/src/axiom-website/CATS/rich3p.input.pdf new file mode 100644 index 0000000..1b9a93e Binary files /dev/null and b/src/axiom-website/CATS/rich3p.input.pdf differ diff --git a/src/axiom-website/CATS/rich3q.input.pamphlet b/src/axiom-website/CATS/rich3q.input.pamphlet new file mode 100644 index 0000000..ee96be1 --- /dev/null +++ b/src/axiom-website/CATS/rich3q.input.pamphlet @@ -0,0 +1,5581 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3q.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 34 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 25 cases that Axiom failed to integrate. +\item 41 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3q.output +)spool rich3q.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=4887/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))-_ + 28705/17787*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2841815/195657*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (292706865x + 370762029x + 117082746)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (- 85254450x - 63467215x + 20145298x + 16461125)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (2934855x + 3717483x + 1173942)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 26343617850x - 36002944395x - 5971220046x + 8956830069x +--R + +--R 3161234142 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (10742060700x + 7996869090x - 2538307548x - 2074101750)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 48395707500x + 66140800250x + 10969693700x - 16454540550x - 5807484900 +--R / +--R 4 3 2 +--R 3697917300x + 5053820310x + 838194588x - 1257291882x - 443750076 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 351248238atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 175624119atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 46091150\|7 +--R / +--R +-+ +--R 3521826\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R - -------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=1215945/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x))-_ + 7090175/498036*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 25545/15092*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 707286025/5478396*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (218487077325x + 422408349495x + 271895029560x + 58263220620) +--R * +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R \|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R - 63655742250x - 89836042575x - 16567908760x + 22311149965x +--R + +--R 8194676012 +--R * +--R +-+ +--R \|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (246527820x + 476620452x + 306790176x + 65740752)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 19663836959250x - 39983135150475x - 22373076718080x +--R + +--R 2 +--R 3714280314525x + 6816796812540x + 1573106956740 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 8020623523500x + 11319341364450x + 2087556503760x - 2811204895590x +--R + +--R - 1032529177512 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 +--R - 25813229437800x - 52486899856860x - 29369718827008x +--R + +--R 2 +--R 4875832227140x + 8948586205104x + 2065058355024 +--R / +--R 5 4 3 2 +--R 310625053200x + 631604274840x + 353422282752x - 58673621160x +--R + +--R - 107683351776x - 24850004256 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 87394830930atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 43697415465atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 8194676012\|7 +--R / +--R +-+ +--R 98611128\|7 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=13246251/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*(2+3*x)^4*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-299/66*(2+3*x)^3*sqrt(3+5*x)/_ + sqrt(1-2*x)-12735719/70400*sqrt(1-2*x)*sqrt(3+5*x)-_ + 121769/3520*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 697/88*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (874252566x - 437126283)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (2851200x + 15040080x + 52700868x - 183672928x + 66038637)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (422400x - 211200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R (1) -------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=126513/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/3*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-233/66*(2+3*x)^2*_ + sqrt(3+5*x)/sqrt(1-2*x)-25073/704*sqrt(1-2*x)*sqrt(3+5*x)-_ + 3/880*(3566+5815*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (8349858x - 4174929)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (71280x + 431244x - 1786144x + 625431)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (21120x - 10560)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=49/66*(3+5*x)^(3/2)/(1-2*x)^(3/2)+519/8*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-21/11*(3+5*x)^(3/2)/sqrt(1-2*x)-519/88*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (34254x - 17127)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (1188x - 7712x + 2481)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (528x - 264)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R (3x + 2)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=7/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)+3/2*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-3/2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R (198x - 99)\|5 \|- 2x + 1 asin(-------------) + (- 268x + 57)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (132x - 66)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=2/33*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 10x - 6)\|5x + 3 +--R (2) --------------------- +--R +--------+ +--R (66x - 33)\|- 2x + 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (10x + 6)\|- 2x + 1 \|5x + 3 - 48x + 48x - 12 +--R (3) ----------------------------------------------- +--R 2 +--R 132x - 132x + 33 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 11 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-6/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*sqrt(3+5*x)/_ + (1-2*x)^(3/2)+128/1617*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (- 396x + 198)\|- 2x + 1 atan(-------------) + (256x - 282)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R ------------------------------------------------------------------------ +--R +-+ +--------+ +--R (3234x - 1617)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (396x - 396x + 99)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 1792x + 1974)\|- 2x + 1 \|5x + 3 + 15792x - 15792x + 3948 +--R / +--R 2 +--R 45276x - 45276x + 11319 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 33atan(--------------------------------------------------) + 188\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 539\|7 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=75/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+260/1617*sqrt(3+5*x)/_ + ((2+3*x)*sqrt(1-2*x))-425/3773*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (14850x + 2475x - 4950)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (5100x - 1460x - 1623)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (67914x + 11319x - 22638)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 148500x + 49500x + 61875x - 24750)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (- 357000x + 102200x + 113610)\|- 2x + 1 \|5x + 3 + 1908648x +--R + +--R 2 +--R - 636216x - 795270x + 318108 +--R / +--R 3 2 +--R 9507960x - 3169320x - 3961650x + 1584660 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 8250atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 4125atan(-----------------------------------------------) + 7574\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 37730\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=765/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+8/33*sqrt(3+5*x)/_ + ((2+3*x)^2*sqrt(1-2*x))-145/1078*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2-415/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (454410x + 378675x - 100980x - 100980)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (14940x + 19380x - 8633x - 6708)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (814968x + 679140x - 181104x - 181104)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (908820x + 302940x - 580635x - 100980x + 100980)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 209160x - 271320x + 120862x + 93912)\|- 2x + 1 \|5x + 3 - 1690416x +--R + +--R 3 2 +--R - 563472x + 1079988x + 187824x - 187824 +--R / +--R 4 3 2 +--R 22819104x + 7606368x - 14578872x - 2535456x + 2535456 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16830atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 8415atan(------------------------------------------------) - 2236\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 30184\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=25365/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+_ + 524/1617*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_ + 89/539*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 745/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 16985/211288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (45200430x + 67800645x + 15066810x - 16740900x - 6696360)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 1834380x - 235980x + 1465461x + 39530x - 302352)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (34228656x + 51342984x + 11409552x - 12677280x - 5070912)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 452004300x - 452004300x + 188335125x + 242743050x - 16740900x +--R + +--R - 33481800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R (128406600x + 16518600x - 102582270x - 2767100x + 21164640) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 800023392x + 800023392x - 333343080x - 429642192x + 29630496x +--R + +--R 59260992 +--R / +--R 5 4 3 2 +--R 4792011840x + 4792011840x - 1996671600x - 2573487840x + 177481920x +--R + +--R 354963840 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2790150atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 1395075atan(-----------------------------------------------) + 352744\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 2112880\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=1/3*(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ + 1626211523/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 123/22*(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 47007627/281600*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 269967/7040*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3315/352*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1626211523/1126400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (9757269138x - 4878634569)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 15552000x + 83548800x + 236669040x + 633940524x - 2034703904x +--R + +--R 739060191 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (614400x - 307200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=1/3*(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ + 4246733/1280*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 101/22*(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 125989/3520*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/440*(3+5*x)^(3/2)*(6646+10575*x)*sqrt(1-2*x)-_ + 4246733/14080*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (25480398x - 12740199)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (86400x + 447120x + 1544724x - 5349344x + 1925361)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (7680x - 3840)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=49/66*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ + 40787/64*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 938/363*(3+5*x)^(5/2)/sqrt(1-2*x)-_ + 40787/5808*(3+5*x)^(3/2)*sqrt(1-2*x)-40787/704*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (244722x - 122361)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (2160x + 12780x - 52256x + 18351)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (384x - 192)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=7/33*(3+5*x)^(5/2)/(1-2*x)^(3/2)+169/8*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)-169/66*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 845/88*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1014x - 507)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (180x - 1136x + 369)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (48x - 24)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=1/3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+5/2*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-5/2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R (30x - 15)\|5 \|- 2x + 1 asin(-------------) + (- 40x + 9)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +-+ +--------+ +--R (12x - 6)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=2/21*(3+5*x)^(3/2)/(1-2*x)^(3/2)+2/49*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2/49*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (12x - 6)\|- 2x + 1 atan(-------------) + (- 82x - 36)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ------------------------------------------------------------------- +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 12x + 12x - 3)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ 2 +--R (574x + 252)\|- 2x + 1 \|5x + 3 + 1764x - 1764x + 441 +--R / +--R 2 +--R 4116x - 4116x + 1029 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R - atan(-----------------------------------------------------) + 21\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 49\|7 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x))-95/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/49*sqrt(3+5*x)/((2+3*x)*_ + sqrt(1-2*x))-55/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (- 1710x - 285x + 570)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (660x - 310x - 549)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 17100x + 5700x + 7125x - 2850)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7 +--R atan(---------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 46200x + 21700x + 38430)\|- 2x + 1 \|5x + 3 - 645624x + 215208x +--R + +--R 269010x - 107604 +--R / +--R 3 2 +--R 864360x - 288120x - 360150x + 144060 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7 +-+ +--R - 475atan(---------------------------------------------) - 2562\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700 +--R / +--R +-+ +--R 3430\|7 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2)+5/28*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+6/7*sqrt(3+5*x)/((2+3*x)^2*_ + sqrt(1-2*x))-5/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-5/28*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (270x + 225x - 60x - 60)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (180x + 60x - 91x - 36)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (1512x + 1260x - 336x - 336)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (2160x + 720x - 1380x - 240x + 240)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 10080x - 3360x + 5096x + 2016)\|- 2x + 1 \|5x + 3 - 43092x +--R + +--R 3 2 +--R - 14364x + 27531x + 4788x - 4788 +--R / +--R 4 3 2 +--R 169344x + 56448x - 108192x - 18816x + 18816 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 40atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 20atan(------------------------------------------------------) - 57\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 224\|7 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3)+_ + 9395/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+64/49*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_ + 27/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-285/1372*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-1395/19208*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (1521990x + 2282985x + 507330x - 563700x - 225480)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (150660x + 193860x - 17127x - 80510x - 19296)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (3043980x + 3043980x - 1268325x - 1634730x + 112740x + 225480)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--------+ +--R (- 2109240x - 2714040x + 239778x + 1127140x + 270144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R - 7293888x - 7293888x + 3039120x + 3917088x - 270144x - 540288 +--R / +--R 5 4 3 2 +--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 18790atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 9395atan(------------------------------------------------) - 3216\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 38416\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=1/3*(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ + 46975917593/409600*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-439/66*(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)-_ + 4270537963/3379200*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 24606179/140800*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 302699/7040*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 4819/440*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 4270537963/409600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (281855505558x - 140927752779)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000x + 1423526400x + 4002203520x + 8217694800x +--R + +--R 2 +--R 18987469764x - 58600061024x + 21368105901 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (2457600x - 1228800)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=1/3*(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+103884253/4096*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-373/66*(2+3*x)^2*_ + (3+5*x)^(5/2)/sqrt(1-2*x)-9444023/33792*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-278043/7040*(3+5*x)^(5/2)*sqrt(1-2*x)-1/1760*_ + (3+5*x)^(5/2)*(31978+50205*x)*sqrt(1-2*x)-9444023/4096*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (623305518x - 311652759)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 1036800x + 5477760x + 15301008x + 40614996x - 129940960x +--R + +--R 47216961 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (24576x - 12288)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=49/66*(3+5*x)^(7/2)/(1-2*x)^(3/2)+272239/256*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)-1183/363*(3+5*x)^(7/2)/sqrt(1-2*x)-_ + 123745/2112*(3+5*x)^(3/2)*sqrt(1-2*x)-24749/2904*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-123745/256*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1633434x - 816717)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +------+ +--R (28800x + 146160x + 497868x - 1713440x + 617319)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (1536x - 768)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=7/33*(3+5*x)^(7/2)/(1-2*x)^(3/2)+13145/64*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-239/66*(3+5*x)^(5/2)/sqrt(1-2*x)-5975/528*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-5975/64*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (78870x - 39435)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +------+ +--R (3600x + 20820x - 84064x + 29601)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (384x - 192)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=1/3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+275/8*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-25/6*(3+5*x)^(3/2)/sqrt(1-2*x)-125/8*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1650x - 825)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (300x - 1840x + 603)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (48x - 24)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=2/21*(3+5*x)^(5/2)/(1-2*x)^(3/2)+25/6*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-2/147*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)-76/147*(3+5*x)^(3/2)/sqrt(1-2*x)-185/98*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R (- 8x + 4)\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R (2450x - 1225)\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (- 3212x + 759)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R (588x - 294)\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))+55/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-10/147*(3+5*x)^(3/2)/((2+3*x)*_ + sqrt(1-2*x))-5/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (990x + 165x - 330)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 3090x - 3070x - 657)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (15840x - 5280x - 6600x + 2640)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (346080x + 343840x + 73584)\|- 2x + 1 \|5x + 3 - 1048572x + 349524x +--R + +--R 436905x - 174762 +--R / +--R 3 2 +--R 1382976x - 460992x - 576240x + 230496 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 880atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 440atan(------------------------------------------------------) - 4161\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2)-715/1372*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+8/21*(3+5*x)^(3/2)/((2+3*x)^2*_ + sqrt(1-2*x))+5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-285/1372*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (- 38610x - 32175x + 8580x + 8580)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (10260x + 1620x - 13627x - 6732)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 61740x - 16464x - 16464)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 308880x - 102960x + 197340x + 34320x - 34320)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 574560x - 90720x + 763112x + 376992)\|- 2x + 1 \|5x + 3 - 8058204x +--R + +--R 3 2 +--R - 2686068x + 5148297x + 895356x - 895356 +--R / +--R 4 3 2 +--R 8297856x + 2765952x - 5301408x - 921984x + 921984 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 5720atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 2860atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 10659\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3)+2585/19208*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+122/147*(3+5*x)^(3/2)/((2+3*x)^3*_ + sqrt(1-2*x))+17/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-2165/4116*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-15755/57624*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (418770x + 628155x + 139590x - 155100x - 62040)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (567180x + 552780x - 169221x - 304730x - 75888)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (837540x + 837540x - 348975x - 449790x + 31020x + 62040)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--------+ +--R (- 7940520x - 7738920x + 2369094x + 4266220x + 1062432)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R 28685664x + 28685664x - 11952360x - 15405264x + 1062432x + 2124864 +--R / +--R 5 4 3 2 +--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5170atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2585atan(------------------------------------------------) + 12648\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 38416\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4)+547745/1075648*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+188/147*(3+5*x)^(3/2)/_ + ((2+3*x)^4*sqrt(1-2*x))+247/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 2287/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-24335/76832*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2-139745/1075648*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 266204070x + 576775485x + 354938760x - 39437640x - 105167040x +--R + +--R - 26291760 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 45277380x + 82071900x + 25673409x - 27318504x - 18627988x +--R + +--R - 2906640 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 5 4 3 2 +--R 522764928x + 1132657344x + 697019904x - 77446656x - 206524416x +--R + +--R - 51631104 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 1064816280x + 1774693800x + 266204070x - 867628080x - 341792880x +--R + +--R 105167040x + 52583520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 5 4 3 2 +--R - 1267766640x - 2298013200x - 718855452x + 764918112x +--R + +--R 521583664x + 81385920 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 2 +--R - 2884113540x - 4806855900x - 721028385x + 2350018440x + 925764840x +--R + +--R - 284850720x - 142425360 +--R / +--R 6 5 4 3 +--R 29274835968x + 48791393280x + 7318708992x - 23853570048x +--R + +--R 2 +--R - 9396860928x + 2891341824x + 1445670912 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2190980atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 1095490atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 423885\|7 +--R / +--R +-+ +--R 4302592\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=8261577/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+721/660*(2+3*x)^3*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-1/10*(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 167363/14520*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-_ + 90052591/774400*sqrt(1-2*x)*sqrt(3+5*x)-3/193600*_ + (2561546+4177045*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (5997904902x - 2998952451)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (18817920x + 101146320x + 359461476x - 1261070176x + 452899509)\|10 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--------+ +--R (4646400x - 2323200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=392283/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^2*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-3/20*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 7/29040*(76466+124737*x)*sqrt(3+5*x)/sqrt(1-2*x)-_ + 4282637/193600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (284797458x - 142398729)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (2352240x + 14544684x - 61036064x + 21305631)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (1161600x - 580800)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=1593/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-3/10*(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 117929/14520*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (1156518x - 578259)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (39204x - 261664x + 83301)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (29040x - 14520)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=9/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/66*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-448/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R (6534x - 3267)\|- 2x + 1 asin(-------------) + (- 1792x + 357)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (1452x - 726)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=7/33*sqrt(3+5*x)/(1-2*x)^(3/2)-29/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (- 58x - 48)\|5x + 3 +--R (2) ----------------------- +--R +--------+ +--R (726x - 363)\|- 2x + 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (58x + 48)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84 +--R (3) -------------------------------------------------- +--R 2 +--R 1452x - 1452x + 363 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 28 +--R (4) --- +--R 121 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=1/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=2/33*sqrt(3+5*x)/(1-2*x)^(3/2)+20/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (40x - 42)\|5x + 3 +--R (2) ----------------------- +--R +--------+ +--R (726x - 363)\|- 2x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 40x + 42)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84 +--R (3) ---------------------------------------------------- +--R 2 +--R 1452x - 1452x + 363 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 28 +--R (4) --- +--R 121 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=18/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_ + sqrt(3+5*x)/(1-2*x)^(3/2)+676/17787*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (13068x - 6534)\|- 2x + 1 atan(-------------) + (1352x - 984)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (35574x - 17787)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 13068x + 13068x - 3267)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 9464x + 6888)\|- 2x + 1 \|5x + 3 + 55104x - 55104x + 13776 +--R / +--R 2 +--R 498036x - 498036x + 124509 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2178atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 1089atan(--------------------------------------------------) + 656\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5929\|7 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=405/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+940/17787*sqrt(3+5*x)/_ + ((2+3*x)*sqrt(1-2*x))+2195/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (882090x + 147015x - 294030)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 26340x + 39500x - 15321)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 14113440x + 4704480x + 5880600x - 2352240)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (2950080x - 4424000x + 1715952)\|- 2x + 1 \|5x + 3 + 24452316x +--R + +--R 2 +--R - 8150772x - 10188465x + 4075386 +--R / +--R 3 2 +--R 167340096x - 55780032x - 69725040x + 27890016 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 784080atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 392040atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 97033\|7 +--R / +--R +-+ +--R 664048\|7 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=5805/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+172/2541*_ + sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+85/11858*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+57595/166012*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (37929870x + 31608225x - 8428860x - 8428860)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 2073420x + 676860x + 945629x - 391476)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (8964648x + 7470540x - 1992144x - 1992144)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 303438960x - 101146320x + 193863780x + 33715440x - 33715440)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 3 2 +--------+ +------+ +--R (116111520x - 37904160x - 52955224x + 21922656)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 468596772x + 156198924x - 299381271x - 52066308x + 52066308 +--R / +--R 4 3 2 +--R 1004040576x + 334680192x - 641470368x - 111560064x + 111560064 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5619240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 2809620atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 619837\|7 +--R / +--R +-+ +--R 1328096\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=330255/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+1468/17787*_ + sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-73/5929*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+30535/166012*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2+3471145/2324168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (6473658510x + 9710487765x + 2157886170x - 2397651300x - 959060520) +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (- 374883660x - 140350860x + 244982277x + 48873610x - 44829024)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (376515216x + 564772824x + 125505072x - 139450080x - 55780032)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 12947317020x - 12947317020x + 5394715425x + 6953188770x +--R + +--R - 479530260x - 959060520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R (5248371240x + 1964912040x - 3429751878x - 684230540x + 627606336) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 20122628148x + 20122628148x - 8384428395x - 10806596598x + 745282524x +--R + +--R 1490565048 +--R / +--R 5 4 3 2 +--R 10542426048x + 10542426048x - 4392677520x - 5661673248x + 390460224x +--R + +--R 780920448 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 79921710atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 39960855atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 8872411\|7 +--R / +--R +-+ +--R 4648336\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=243189/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^3/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-3/20*(2+3*x)^4/((1-2*x)^(3/2)*_ + sqrt(3+5*x))-273749/29040*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))+_ + 270463/319440*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-28291441/2129600*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (1942107354x - 971053677)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (77623920x + 536898780x - 1790987404x - 525679641x + 435258129)\|10 +--R / +--R +--+ +--------+ +------+ +--R (12777600x - 6388800)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=4887/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)^2/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-3/10*(2+3*x)^3/((1-2*x)^(3/2)*_ + sqrt(3+5*x))-7/14520*(31106+53757*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 212417/798600*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (39027582x - 19513791)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (6468660x - 40488772x - 12657123x + 8379147)\|10 +--R / +--R +--+ +--------+ +------+ +--R (1597200x - 798600)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=27/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+2/33*(2+3*x)^3/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-58/363*(2+3*x)^2/(sqrt(1-2*x)*_ + sqrt(3+5*x))+50/3993*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_ + 3103/13310*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (215622x - 107811)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 298852x - 124263x + 33087)\|10 +--R / +--R +--+ +--------+ +------+ +--R (79860x - 39930)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=49/66/((1-2*x)^(3/2)*sqrt(3+5*x))+(-1237/3630)/(sqrt(1-2*x)*_ + sqrt(3+5*x))-793/19965*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R - 1586x - 2880x - 1128 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (1586x + 2880x + 1128)\|- 2x + 1 \|5x + 3 + 13160x - 5264x - 4606x + 1974 +--R ----------------------------------------------------------------------------- +--R 3 2 +--R 79860x - 31944x - 27951x + 11979 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 658 +--R (4) ---- +--R 3993 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=(-2/55)/((1-2*x)^(3/2)*sqrt(3+5*x))+82/1815*sqrt(3+5*x)/(1-2*x)^(3/2)+_ + 164/3993*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R 1640x - 738x - 888 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 1640x + 738x + 888)\|- 2x + 1 \|5x + 3 + 14060x - 5624x - 4921x + 2109 +--R ----------------------------------------------------------------------------- +--R 3 2 +--R 79860x - 31944x - 27951x + 11979 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 703 +--R (4) ---- +--R 3993 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=2/33/((1-2*x)^(3/2)*sqrt(3+5*x))+40/363/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 400/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 1600x - 720x - 282 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 3200x + 1440x + 564)\|- 2x + 1 \|5x + 3 + 6580x - 2632x - 2303x + 987 +--R ---------------------------------------------------------------------------- +--R 3 2 +--R 159720x - 63888x - 55902x + 23958 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 329 +--R (4) ---- +--R 7986 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-54/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*sqrt(3+5*x))+_ + 956/17787/(sqrt(1-2*x)*sqrt(3+5*x))-42230/195657*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (- 431244x + 215622)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (168920x - 147888x + 28326)\|7 +--R / +--R +-+ +--------+ +------+ +--R (391314x - 195657)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 4312440x + 1724976x + 1509354x - 646866)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 2364880x + 2070432x - 396564)\|- 2x + 1 \|5x + 3 + 4626580x +--R + +--R 2 +--R - 1850632x - 1619303x + 693987 +--R / +--R 3 2 +--R 54783960x - 21913584x - 19174386x + 8217594 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 431244atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R - 215622atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R 33047\|7 +--R / +--R +-+ +--R 391314\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=-3105/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))+_ + 1220/17787/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_ + 1840225/1369599*sqrt(1-2*x)/sqrt(3+5*x)+_ + 1915/41503*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (- 74389590x - 12398265x + 24796530)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (22082700x - 7613680x - 8760465x + 3499599)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (8217594x + 1369599x - 2739198)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 5951167200x - 1586977920x + 3669886440x + 495930600x - 595116720) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +--R (- 2473262400x + 852732160x + 981172080x - 391955088)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 9308933340x + 2482382224x - 5740508893x - 775744445x + 930893334 +--R / +--R 4 3 2 +--R 9203705280x + 2454321408x - 5675618256x - 766975440x + 920370528 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 198372240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 99186120atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R 22164127\|7 +--R / +--R +-+ +--R 21913584\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-79515/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x))+212/2541/((2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x))-46307675/5478396*sqrt(1-2*x)/sqrt(3+5*x)+_ + 5/11858*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 89945/166012*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 5715061110x - 4762550925x + 1270013580x + 1270013580)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (1667076300x + 520073880x - 1053213025x - 169466391x + 178740084)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (98611128x + 82175940x - 21913584x - 21913584)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 285753055500x + 266702851800x - 125413841025x - 141289010775x +--R + +--R 12700135800x + 19050203700 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 116695341000x - 36405171600x + 73724911750x + 11862647370x +--R + +--R - 12511805880 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 525495846960x - 490462790496x + 230634288388x + 259828502108x +--R + +--R - 23355370976x - 35033056464 +--R / +--R 5 4 3 2 +--R 69027789600x + 64425936960x - 30295529880x - 34130407080x +--R + +--R 3067901760x + 4601852640 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 3175033950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 1587516975atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 417060196\|7 +--R / +--R +-+ +--R 54783960\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=1673/1320*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/20*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x)^(3/2))+753543/8000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-89943/9680*(2+3*x)^3/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+1332779/1597200*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 9214471/17569200*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_ + 964268137/117128000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (330978691890x + 33097869189x - 99293607567)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 12807946800x + 97980793020x - 252342435560x - 274128335769x +--R + +--R 19932058554x + 44437106459 +--R * +--R +--+ +--R \|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (3513840000x + 351384000x - 1054152000)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1183/660*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/10*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x)^(3/2))+2997/200*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-38003/4840*(2+3*x)^2/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+111719/159720*(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 3831323/8784600*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (1316372310x + 131637231x - 394911693)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (213465780x - 1247811640x - 1260430251x + 19593966x + 168318961)\|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (87846000x + 8784600x - 26353800)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))+81/50*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-18/121*(2+3*x)^3/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+50/3993*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1058/219615*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-100159/732050*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ +------+ \|2 \|5x + 3 +--R (35577630x + 3557763x - 10673289)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 49702040x - 51334383x - 7883562x + 3014813)\|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (21961500x + 2196150x - 6588450)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))+49/121/((3+5*x)^(3/2)*_ + sqrt(1-2*x))-3679/19965*sqrt(1-2*x)/(3+5*x)^(3/2)-8182/_ + 219615*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R - 39146x - 124464x - 104088x - 26080 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (352314x + 1120176x + 936792x + 234720)\|- 2x + 1 \|5x + 3 + 5216000x +--R + +--R 3 2 +--R 1043200x - 3077440x - 312960x + 469440 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 52160 +--R (4) ------ +--R 395307 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^(3/2))+14/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 1649/7986*sqrt(1-2*x)/(3+5*x)^(3/2)-3298/43923*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 65960x + 9894x - 49200x - 18728 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ +--R (- 2968200x - 445230x + 2214000x + 842760)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 26219200x + 5243840x - 15469328x - 1573152x + 2359728 +--R / +--R 4 3 2 +--R 197653500x + 39530700x - 116615565x - 11859210x + 17788815 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 262192 +--R (4) ------- +--R 1976535 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=(-2/165)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+74/1815/((1-2*x)^(3/2)*_ + sqrt(3+5*x))+296/3993/(sqrt(1-2*x)*sqrt(3+5*x))-2960/43923*_ + sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 59200x + 8880x - 26418x - 5728 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (- 532800x - 79920x + 237762x + 51552)\|- 2x + 1 \|5x + 3 - 1145600x +--R + +--R 3 2 +--R - 229120x + 675904x + 68736x - 103104 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 11456 +--R (4) - ------ +--R 395307 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^(3/2))+20/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 400/3993*sqrt(1-2*x)/(3+5*x)^(3/2)-1600/43923*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 32000x + 4800x - 14280x - 722 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (- 288000x - 43200x + 128520x + 6498)\|- 2x + 1 \|5x + 3 + 144400x +--R + +--R 3 2 +--R 28880x - 85196x - 8664x + 12996 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 1444 +--R (4) ------ +--R 395307 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2))+162/49*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+412/5929/((3+5*x)^(3/2)*_ + sqrt(1-2*x))-19130/195657*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1001590/2152227*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ +------+ \|7 \|5x + 3 +--R (71155260x + 7115526x - 21346578)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (- 20031800x + 8854440x + 6468522x - 2981164)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (21522270x + 2152227x - 6456681)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 3201986700x - 640397340x + 1889172153x + 192119202x - 288178803) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (1262003400x - 557829720x - 407516886x + 187813332)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 4173629600x + 834725920x - 2462441464x - 250417776x + 375626664 +--R / +--R 4 3 2 +--R 13559030100x + 2711806020x - 7999827759x - 813541806x + 1220312709 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 64039734atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 32019867atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 5962328\|7 +--R / +--R +-+ +--R 19370043\|7 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))+14985/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+500/5929/((2+3*x)*(3+5*x)^(3/2)*_ + sqrt(1-2*x))-985525/1369599*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1635/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 95783075/15065589*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (19745584650x + 15138281565x - 4607303085x - 3949116930)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (- 5746984500x - 1402439900x + 3498236655x + 429626520x - 555141781)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (451967670x + 346508547x - 105459123x - 90393534)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1777102618500x + 1540155602700x - 811543529115x - 805619853720x +--R + +--R 88855130925x + 106626157110 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R 724120047000x + 176707427400x - 440777818530x - 54132941520x +--R + +--R 69947864406 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 2331595480200x - 2020716082840x + 1064761935958x + 1056989951024x +--R + +--R - 116579774010x - 139895728812 +--R / +--R 5 4 3 2 +--R 569479264200x + 493548695640x - 260062197318x - 258163933104x +--R + +--R 28473963210x + 34168755852 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 11847350790atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 5923675395atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 1110283562\|7 +--R / +--R +-+ +--R 271180602\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2))+538245/1372*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+12/121/((2+3*x)^2*(3+5*x)^(3/2)*_ + sqrt(1-2*x))-34551425/5478396*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 75/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 122295/166012*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 3443814775/60262356*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 2127720162150x + 3049732232415x + 591033378375x - 756522724320x +--R + +--R - 283696021620 +--R * +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R \|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 619886659500x - 564878517900x + 276089438305x + 297937101390x +--R + +--R - 28838387211x - 39900939556 +--R * +--R +-+ +--R \|7 +--R / +--R 4 3 2 +--R (5423612040x + 7773843924x + 1506558900x - 1928395392x - 723148272) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 765979258374000x - 1174501529506800x - 92768599069740x +--R + +--R 3 2 +--R 580442060234520x + 193196990723220x - 71491397448240x +--R + +--R - 30639170334960 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 312422876388000x + 284698773021600x - 139149076905720x +--R + +--R 2 +--R - 150160299100560x + 14534547154344x + 20110073536224 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R 1194035616213300x + 1830854611527060x + 144610980185833x +--R + +--R 3 2 +--R - 904813655841634x - 301162316533799x + 111443324179908x + 47761424648532 +--R / +--R 6 5 4 3 +--R 27335004681600x + 41913673845120x + 3310572789216x - 20713859103168x +--R + +--R 2 +--R - 6894495625248x + 2551267103616x + 1093400187264 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1702176129720atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 851088064860 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 189529462891\|7 +--R / +--R +-+ +--R 4338889632\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=167647/101250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2911577/50625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),_ +-- 33/35)/sqrt(35)-23/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)+2/45*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 1244/13125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 175111/236250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=796/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 55019/2250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/35*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-27/875*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-823/2625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=-1159/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 259/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/25*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-31/225*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=-37/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=-74/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-74/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 40/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+74/63*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=148/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4636/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+74/315*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+4636/2205*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=6368/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 220076/3087*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+74/735*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+3184/5145*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+220076/36015*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=21713939/3341250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1508889271/6682500*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 23/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+2/55*(2+3*x)^(5/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)-342971/866250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-543/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 11346991/3898125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=153319/60750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5327983/60750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/45*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1208/7875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 3/175*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 160297/141750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=2129/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 148831/4050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-31/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2/35*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2252/4725*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-974/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 119/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 41/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=362/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 49/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/3*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+40/27*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1150/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/9*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 214/189*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=1252/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 8314/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-214/945*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+8314/6615*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=17156/27783*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 475592/27783*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_ +-- 214/2205*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8578/46305*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+475592/324135*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(11/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=664744/583443*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 22738708/583443*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/27*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 214/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+8842/138915*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+332372/972405*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+22738708/6806835*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=472506679/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-16416987253/17374500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-23/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)+2/65*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 1865989/1126125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 564731/2252250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2014/53625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 493825477/40540500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=222527/22275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 30926081/89100*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/55*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 7031/11550*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 177/1925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 3/275*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 465127/103950*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=28109/7290*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 488149/3645*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-223/945*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 31/945*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/45*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-29357/17010*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=134/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 9013/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-1/7*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 131/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=-3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/3*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+4/3*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=-2209/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2960/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 118/63*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+2470/567*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-13834/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 31588/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-118/315*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 2/15*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-12758/6615*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=32176/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 173482/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-118/735*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-4282/15435*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+173482/108045*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=1136636/1750329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-27198452/1750329*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-118/1323*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-2/27*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-12934/138915*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+568318/2917215*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+27198452/20420505*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=38834192/44925111*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1305025844/44925111*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-118/2079*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(9/2)-2/33*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(11/2)-13022/305613*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(7/2)+627806/10696455*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+19417096/74875185*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+1305025844/524126295*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(a+b*x)^(1/2)/((c+d*x)^(1/2)*(e+f*x)^(1/2)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|d x + c \|f x + e +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=2*elliptic_e(asin(sqrt(f)*sqrt(c+d*x)/sqrt(-d*e+c*f)),-b*(d*e-c*f)/_ +-- ((b*c-a*d)*f))*sqrt(-d*e+c*f)*sqrt(a+b*x)*sqrt(d*(e+f*x)/_ +-- (d*e-c*f))/(d*sqrt(f)*sqrt(-d*(a+b*x)/(b*c-a*d))*sqrt(e+f*x)) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +--R +--R +--R (2) tpdhere +--R Type: Variable(tpdhere) +)clear all + +--S 436 of 500 +t0:=(a+b*x)^(1/2)/((c+d*x)^(3/2)*(e+f*x)^(1/2)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|d x + c \|f x + e +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-2*sqrt(a+b*x)*sqrt(e+f*x)/((d*e-c*f)*sqrt(c+d*x))+_ +-- 2*elliptic_e(asin(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d)),_ +-- (b*c-a*d)*f/(d*(b*e-a*f)))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/_ +-- (b*c-a*d))*sqrt(e+f*x)/((d*e-c*f)*sqrt(d)*sqrt(c+d*x)*_ +-- sqrt(b*(e+f*x)/(b*e-a*f))) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=859/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 61151/3750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-23/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2/35*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-859/4375*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=7/125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 146/125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 9/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) -------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=-31/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------ +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=-2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_ +-- 2*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=-136/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 136/21*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=184/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 6388/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+92/35*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+6388/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=226/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_ +-- sqrt(11/3)-203179/18750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(2+3*x)^(7/2)*sqrt(1-2*x)/_ +-- sqrt(3+5*x)+183/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 48/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2486/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-1409/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-91/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 36/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+13/625*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-19/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-56/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 8/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) -------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=4/5*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/5*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3q.input.pdf b/src/axiom-website/CATS/rich3q.input.pdf new file mode 100644 index 0000000..fa439a4 Binary files /dev/null and b/src/axiom-website/CATS/rich3q.input.pdf differ diff --git a/src/axiom-website/CATS/rich3r.input.pamphlet b/src/axiom-website/CATS/rich3r.input.pamphlet new file mode 100644 index 0000000..e83adb6 --- /dev/null +++ b/src/axiom-website/CATS/rich3r.input.pamphlet @@ -0,0 +1,3527 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3r.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 0 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3r.output +)spool rich3r.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +--r0:=-4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-20*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +--r0:=556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-80/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 92/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2780/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +--r0:=-3352/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 116464/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 416/105*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 19268/245*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 116464/147*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +--r0:=12601/103125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1473539/206250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/15*(2+3*x)^(9/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-118/165*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 5153/48125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 958/1925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 12601/240625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +--r0:=-47342/103125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-19033/103125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/15*(2+3*x)^(7/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-458/825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 2818/6875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2719/34375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +--r0:=-169/4125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 3206/4125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 326/825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 458/1375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +--r0:=458/825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1358/825*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/15*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 194/825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +--r0:=62/165*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/165*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-_ +-- 62/165*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=sqrt(1-2*x)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +--r0:=-136/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+28/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 136/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +--r0:=536/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 532/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-40/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+2660/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +--r0:=-36968/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5320/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+416/21*_ +-- sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-2780/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+184840/231*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +--r0:=296816/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-10312712/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 556/105*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 116044/735*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 155104/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 10312712/1617*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+17427983/16706250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 604915631/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+1103/259875*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ +-- 178/7425*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 124891/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 18177329/38981250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (- 6x - x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +--r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+83093/151875*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5684677/303750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+62/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 347/39375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 84134/354375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (- 2x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +--r0:=4289/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 118898/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/35*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 194/2625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2657/23625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +--r0:=-4157/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+4382/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+214/675*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1610/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)-16/27*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=724/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 98/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+82/27*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +--r0:=68/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 82/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3896/945*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +--r0:=17032/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-595324/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/21*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 82/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8516/6615*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+595324/46305*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +--r0:=1226552/83349*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-42623864/83349*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/27*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(9/2)+82/567*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(7/2)+13136/19845*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+613276/138915*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+42623864/972405*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+_ +-- 371279941/108590625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-51601293223/434362500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+601/160875*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+178/10725*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-11725073/56306250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-18034/625625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 776112041/506756250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+5199979/3341250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 90397364/1670625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+62/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 40703/433125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 23/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 5442127/7796250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +--r0:=70226/91125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4971289/182250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/45*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 839/23625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 194/4725*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 76163/212625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +--r0:=-31/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 29933/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 74/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1847/4725*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +--r0:=-2209/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+4144/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_ +-- 8/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+494/135*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_ +-- 8774/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 592/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+74/9*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 1150/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_ +-- 1184/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4418/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+74/45*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_ +-- 988/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_ +-- 124/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 119732/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+74/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_ +-- 3632/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 119732/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_ +-- 561808/250047*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-19885156/250047*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/189*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-8252/19845*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+280904/416745*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+19885156/2917215*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_ +-- 41599832/6417873*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1446357824/6417873*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/297*(3+5*x)^(3/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-12872/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 442076/1528065*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 20799916/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 1446357824/74875185*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +------+ +------+ +--R (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +--r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)+_ +-- 48128081531/3909262500*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-836091184171/1954631250*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+_ +-- 178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 380132617/506756250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 57509209/506756250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 199721/12065625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 50299451003/9121612500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 134992031/26061750*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-9380126059/52123500*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 62/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 2133359/6756750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 160084/3378375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 67/160875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 70536439/30405375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +--r0:=2810993/1202850*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-97540001/1202850*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2/55*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(2+3*x)-22576/155925*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2377/155925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 194/7425*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2930159/2806650*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +--r0:=14101/10935*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 886499/21870*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 499/2835*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 46/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 11908/25515*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=-835/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2894/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)+_ +-- 202/63*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 32/63*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1061/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-_ +-- 9587/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+21206/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+362/27*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 614/27*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2632/243*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-_ +-- 47422/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+116854/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+362/135*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_ +-- 9808/945*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 43214/1701*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_ +-- 290204/11907*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-962678/11907*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2108/6615*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+362/315*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+249448/138915*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 192 + +--S 193 of 500 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_ +-- 600868/750141*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-17830424/750141*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-1864/6615*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+362/567*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-558524/1250235*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+17830424/8751645*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 197 + +--S 198 of 500 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_ +-- 91496584/57760857*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-3316711588/57760857*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-13292/43659*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)+362/891*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-1366496/4584195*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+45748292/96268095*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+3316711588/673876665*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +--r0:=-2/39*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 7046965448/1752079329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-245282464136/1752079329*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-20992/81081*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(9/2)+362/1287*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(11/2)-2174468/11918907*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(7/2)+73596464/417161745*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+3523482724/2920132215*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+245282464136/20440925505*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +--r0:=87476/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6515539/506250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x)+403/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 178/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/590625*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +--r0:=487/5625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 46159/5625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/35*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_ +-- 62/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/13125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +--r0:=-2797/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-2828/3375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/25*(1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)+194/1125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +--r0:=272/135*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1442/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-4/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +--r0:=-74/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 56/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +--r0:=116/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 124/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 128/9*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +--r0:=512/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 268/45*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17804/315*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +--r0:=36136/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1255552/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 136/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18068/735*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1255552/5145*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +--r0:=12601/84375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1473539/168750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(7/2)/_ +-- sqrt(3+5*x)+5153/39375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 958/1575*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-8/45*(2+3*x)^(7/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-12601/196875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=-2719/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 47342/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_ +-- 2818/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 32/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2719/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-169/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-3206/1875*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/5*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-24/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 458/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=458/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1358/225*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-_ +-- 16/75*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +--r0:=62/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=136/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 28/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +--r0:=-536/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 532/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 268/9*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2660/9*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 282 + +--S 283 of 500 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +--r0:=-1064/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 36968/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 136/15*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+6116/35*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-36968/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 287 + +--S 288 of 500 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 500 +--m0:=a0-r0 +--E 289 + +--S 290 of 500 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +--r0:=-296816/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 10312712/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_ +-- 548/105*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+12276/245*_ +-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+1706144/1715*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-10312712/1029*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 292 + +--S 293 of 500 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 500 +--m0:=a0-r0 +--E 294 + +--S 295 of 500 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_ +-- 4801/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 25643/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-6*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 3872/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 622/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4801/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)+_ +-- 1973/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-15848/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-106/25*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 1558/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2264/3125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)+_ +-- 496/375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-1246/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-62/25*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 178/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=38/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 112/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-_ +-- 18/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=-148/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/3*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+48/5*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 112/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+556/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 1096/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1088/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 136/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-300*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+5440/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 8672/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 301304/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+548/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 111884/315*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 16616/7*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 301304/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=62/2145*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_ +-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_ +-- 67138787/72393750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1163388067/36196875*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+32717/1126125*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+34/2475*(2+3*x)^(5/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)-445024/9384375*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-69808931/168918750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=106/2475*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+2/55*(1-2*x)^(5/2)*_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)+4854274/8353125*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 326256461/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2866/86625*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ +-- 38729/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 4738087/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=284159/455625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6799613/455625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+326/4725*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 2/45*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 10214/118125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 110717/1063125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=16088/3375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 86741/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 118/525*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/21*(1-2*x)^(5/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+4282/7875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=31588/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-96838/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)-_ +-- 8/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1076/675*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2) +--E 361 + +--S 362 of 500 +--r0:=-4418/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+8288/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 10/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+196/81*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 362 + +--S 363 of 500 +--Ra0:=integrate(t0,x) +--R +--R +--R (1) t0 x +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 500 +--Rm0:=a0-r0 +--R +--R +--R (2) t0 x - r0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 500 +--Rd0:=D(m0,x) +--R +--R +--R (3) t0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=-12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+2/3*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+8*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=-36052/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5360/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/21*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+2/7*_ +-- (1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+524/189*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+36052/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=-7810384/35721*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+1124360/35721*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/27*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 10/63*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+832/567*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+112436/11907*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+7810384/83349*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=-247408648/305613*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+35604320/305613*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(11/2)+10/99*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 1900/2079*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 76492/14553*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 3560432/101871*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 247408648/713097*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*_ +-- (2+3*x)^(5/2)*(3+5*x)^(5/2)+25385346787/9773156250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1764163292393/19546312500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+142391/7239375*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-400516993/2533781250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-569519/28153125*(3+5*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-13267820528/11402015625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=106/3575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_ +-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_ +-- 880870681/651543750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-30660308017/651543750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+8318/482625*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-6794792/84459375*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+25603/1876875*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 923943703/1520268750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=11437073/15035625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-829177897/30071250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/7425*(1-2*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(2+3*x)+2/55*(1-2*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(2+3*x)-78797/3898125*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+30362/779625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 12996374/35083125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=-150217/273375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-4457606/273375*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+362/2835*(1-2*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x)+2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 14318/70875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 429479/637875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=145102/6075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 481339/6075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_ +-- 32/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)-_ +-- 2108/1575*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 124724/14175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+116854/3645*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 331954/3645*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+230/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)+_ +-- 788/135*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-43214/1215*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_ +-- 46/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_ +-- 19174/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+42412/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-316/27*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+5264/243*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)+_ +-- 46/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-_ +-- 11576/1701*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-16700/1701*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+608/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 4244/3969*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_ +-- 230/567*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_ +-- 3545996/107163*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+564040/107163*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+1532/567*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-104036/35721*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+3545996/250047*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_ +-- 230/891*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-_ +-- 780320008/8251551*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+112439720/8251551*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+12280/6237*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-325796/130977*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+11243972/2750517*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+780320008/19253619*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)+_ +-- 230/1287*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-_ +-- 75041008472/250297047*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+10799362480/250297047*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1300/891*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 3347620/1702701*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 23210828/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 1079936248/83432349*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 75041008472/584026443*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=106/4875*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 2/75*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 11371367372/2931946875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1580201444291/11727787500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+8038/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)-359748241/1520268750*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-26534891/760134375*(3+5*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+364267/36196875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 23763809947/13682418750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=469049629/234555750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-8120161139/117277875*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/10725*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(2+3*x)+2/65*(1-2*x)^(5/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-_ +-- 3872003/30405375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 121031/30405375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2314/111375*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 486785077/547296750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=2617892/1804275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-146222113/3608550*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(2+3*x)+2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 146963/467775*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 9698/93555*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1654421/4209975*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=-291227/32805*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-25111/32805*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_ +-- 40/81*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+_ +-- 64628/8505*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2108/1701*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 310399/76545*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_ +-- 153452/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-452399/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+370/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_ +-- 31298/567*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 5260/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 135334/5103*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+_ +-- 74/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_ +-- 136028/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-374366/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6464/81*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+_ +-- 11036/81*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 48478/729*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_ +-- 74/63*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-904798/15309*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 1534520/15309*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1844/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 62596/3969*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+_ +-- 1353340/35721*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)+_ +-- 370/567*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-_ +-- 100444/321489*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-5824540/321489*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-13316/35721*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+2776/1701*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-1241596/750141*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_ +-- 370/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_ +-- 584888452/24754653*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+104715680/24754653*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-55772/43659*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+36980/18711*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-17089252/8251551*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+584888452/57760857*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 370/1287*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-_ +-- 129922578224/2252673423*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+18761985160/2252673423*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2622980/1702701*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+_ +-- 60080/34749*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 54281308/35756721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 1876198516/750891141*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 129922578224/5256237987*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2) +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=-2/45*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)+_ +-- 74/351*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 363883755904/15768713961*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-12641611554328/15768713961*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 1085156/729729*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_ +-- 16636/11583*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_ +-- 112817764/107270163*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 3914701972/3754455705*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 181941877952/26281189935*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 12641611554328/183968329545*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=2865161/8353125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-231061879/16706250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+62/1485*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x)+2/55*(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_ +-- 181333/3898125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4258/155925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2865161/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3r.input.pdf b/src/axiom-website/CATS/rich3r.input.pdf new file mode 100644 index 0000000..24baa5a Binary files /dev/null and b/src/axiom-website/CATS/rich3r.input.pdf differ diff --git a/src/axiom-website/CATS/rich3s.input.pamphlet b/src/axiom-website/CATS/rich3s.input.pamphlet new file mode 100644 index 0000000..41adf97 --- /dev/null +++ b/src/axiom-website/CATS/rich3s.input.pamphlet @@ -0,0 +1,3401 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3s.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 0 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3s.output +)spool rich3s.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +--r0:=-21547/759375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-8024546/759375*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+106/1575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x)+2/45*(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_ +-- 8878/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 21547/1771875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +--r0:=-101902/50625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-408311/50625*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/2625*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+2/35*(1-2*x)^(5/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)+30922/118125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +--r0:=53194/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-246694/10125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-4/75*(1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)-1088/3375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +--r0:=-8314/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 8764/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+428/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +--r0:=-3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 476/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+40/3*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/sqrt(2+3*x)+232/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +--r0:=-16564/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 3352/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+52/9*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+3412/27*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +--r0:=-703480/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 101240/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+80/21*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+10580/189*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+703480/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +--r0:=-66055016/11907*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+9505840/11907*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(9/2)+20/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 7148/189*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 950584/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 66055016/27783*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(13/2)*sqrt(3+5*x)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R ------------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +--r0:=-23204503328/916839*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+3339309520/916839*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(11/2)+680/297*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 180020/6237*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 7173272/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 333930952/305613*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 23204503328/2139291*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +--r0:=703672/13921875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-264260033/27843750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(7/2)/_ +-- sqrt(3+5*x)-48/275*(1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)+_ +-- 2020841/6496875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 346636/259875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2972/7425*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 703672/32484375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +--r0:=-196499/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1509007/253125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(5/2)/_ +-- sqrt(3+5*x)-8/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_ +-- 167228/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 1972/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 196499/590625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +--r0:=-106772/28125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+53279/28125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-32/175*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)-_ +-- 1972/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 106772/65625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +--r0:=81164/16875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 218414/16875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-_ +-- 24/125*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-_ +-- 3028/5625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +--r0:=5594/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 5656/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)-388/225*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +--r0:=4636/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1036/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)-272/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +--r0:=17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 3584/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+260/9*(1-2*x)^(3/2)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-5764/9*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +--r0:=105584/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 21272/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+80/9*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(3/2)*sqrt(3+5*x))+10636/27*sqrt(1-2*x)/(sqrt(2+3*x)*_ +-- sqrt(3+5*x))-105584/27*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=1959032/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 281920/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+36/7*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(5/2)*sqrt(3+5*x))+7204/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_ +-- sqrt(3+5*x))+324104/147*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 9795160/441*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +--r0:=683150096/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-98310640/3969*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)/((2+3*x)^(9/2)*_ +-- sqrt(3+5*x))+680/189*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_ +-- 36284/567*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 813208/1323*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 113020952/9261*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 3415750480/27783*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_ +-- 500501/421875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1065118/421875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-442/75*(1-2*x)^(3/2)*(2+3*x)^(7/2)/sqrt(3+5*x)+_ +-- 373022/196875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 59662/7875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 524/225*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 500501/984375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)-_ +-- 33778/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 49321/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 62/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_ +-- 22866/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 284/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 33778/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)-_ +-- 6902/3125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_ +-- sqrt(3/11)+9206/3125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)-178/75*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-572/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 8874/3125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +--r0:=338/1125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 6412/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-46/75*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)-76/375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +--r0:=28/25*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 584/25*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2/3*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+152/15*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)+104/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +--r0:=-6388/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1288/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+2068/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +--r0:=2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 36968/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7448/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 400/9*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-5852/9*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+36968/9*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +--r0:=2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+12*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(3/2)*(3+5*x)^(3/2))-96808/3*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)+19504/3*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2420/3*sqrt(1-2*x)/((3+5*x)^(3/2)*_ +-- sqrt(2+3*x))-16016/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 96808/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +--r0:=2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))+136/21*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(5/2)*(3+5*x)^(3/2))-2234208/7*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+321520/7*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+12188/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2))+2488904/441*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 5544440/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+11171040/49*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +--r0:=1613/250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 56041/250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 104/175*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1/7*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-4839/1750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +--r0:=-1597/150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 161/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-23/25*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) ------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +--r0:=-34/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/3*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +--r0:=-elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)-2/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +--r0:=-62/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+62/147*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +--r0:=4/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 584/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+1752/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=317384/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 44109377/40500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-137/315*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 1/9*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-9547/5250*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-663409/47250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +--r0:=4517/450*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 78472/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 1/7*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-102/175*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-4721/1050*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +--r0:=-4451/270*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 448/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-67/45*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +--r0:=29/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 31/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 5/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 192 + +--S 193 of 500 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +--r0:=-37/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/7*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 197 + +--S 198 of 500 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +--r0:=272/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1030/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-202/441*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +--r0:=-808/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5594/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-194/2205*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+5594/15435*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(9/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +--r0:=1948/21609*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 184636/21609*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-62/1715*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+974/36015*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+184636/252105*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +--r0:=8787401429/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-610627101631/34749000*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-14303/12870*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-41/143*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1/13*(2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-138809831/4504500*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-221673/50050*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-2295970088/10135125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +--r0:=41741369/267300*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-725140729/133650*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-34/99*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-1/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 329683/34650*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1053/770*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 43624697/623700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +--r0:=118823/2430*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 8256877/4860*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-1/9*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1877/630*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/7*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-62092/2835*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +--r0:=-17587/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2531/162*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 20/21*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1/7*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-2645/378*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +--r0:=-4141/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 419/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-62/27*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +--r0:=-974/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 85/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/7*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-205/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +--r0:=-4157/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 3130/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-38/49*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(2+3*x)+2060/1323*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +--r0:=-35242/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 53194/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 334/2205*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-2/35*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-34154/46305*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(9/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=-203804/194481*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 816622/194481*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 326/5145*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-2/49*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-30922/324135*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+816622/2268945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(11/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-86188/4084101*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 32098184/4084101*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-106/3087*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_ +-- 2/63*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-8878/324135*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-43094/6806835*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+32098184/47647845*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(13/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R --------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=-924247516/314475777*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+114606440/314475777*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-310/14553*(3+5*x)^(3/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-2/77*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_ +-- 21290/2139291*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_ +-- 362666/14975037*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 11460644/104825259*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 924247516/733776813*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +--r0:=15553/3750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 270248/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 333/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-3/35*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-15553/8750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ------------------------ +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=-5161/750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 518/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 3/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-74/125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +--r0:=-37/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 282 + +--S 283 of 500 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +--r0:=-elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5) +--E 287 + +--S 288 of 500 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 500 +--m0:=a0-r0 +--E 289 + +--S 290 of 500 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------- +--R +--------+ +------+ +------+ +--R \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +--r0:=-2*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33) +--E 292 + +--S 293 of 500 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 500 +--m0:=a0-r0 +--E 294 + +--S 295 of 500 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 500 +t0:=1/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=-2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 6/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=1/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=-148/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+148/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=1/((2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=592/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 20644/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 6/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+296/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+20644/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=-61151/13750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+6013/6875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/11*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 69/1375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+6/55*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-2577/6875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=21/275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 438/275*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2/11*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-27/275*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-31/55*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/11*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)-2/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +------+ +------+ +--R (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 10/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=136/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 6/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-680/77*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=6388/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 920/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+288/49*sqrt(1-2*x)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-31940/539*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=1/((2+3*x)^(7/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=-12904/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 1344984/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+436/245*sqrt(1-2*x)/_ +-- ((2+3*x)^(3/2)*sqrt(3+5*x))+60684/1715*sqrt(1-2*x)/(sqrt(2+3*x)*_ +-- sqrt(3+5*x))-1344984/3773*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^(9/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-6515539/2268750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+612332/1134375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(2+3*x)^(9/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-602/1815*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 403/75625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+668/3025*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/378125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^(7/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=-46159/45375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+3409/45375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/33*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 94/363*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+536/3025*_ +-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/15125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^(5/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +--r0:=-2797/9075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2828/9075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-338/1815*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+404/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^(3/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=272/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1442/1815*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=sqrt(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=74/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 56/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-74/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=116/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 124/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 10/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+620/363*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------ +--R 3 2 +--------+ +------+ +------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=-17804/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2560/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 6/7*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-1340/231*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+89020/2541*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=-1255552/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+180680/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 428/49*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 94420/1617*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 6277760/17787*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=10156288/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 352875016/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 576/245*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 120324/1715*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 5307272/11319*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 352875016/124509*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=-2663/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_ +-- 4071079/1500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+2517/350*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+12/7*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 29293/875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 9x - 12x - 4)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=7279/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2933/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+9/5*(2+3*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)+419/50*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R (- 3x - 2)\|3x + 2 \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+2*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) - ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=4/7*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 10/7*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-12/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=-38/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 80/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-8/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+38/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-52/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5636/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-36/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-26/1715*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+5636/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (- 135x - 351x - 342x - 148x - 24)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-6478333/13500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 112543103/6750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+1397/210*_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+5/3*(2+3*x)^(5/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+24358/875*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+6770629/31500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 45x - 87x - 56x - 12)\|3x + 2 \|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=-18551/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1289089/300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+12/7*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+2511/350*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+9694/175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 15x - 19x - 6)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=4621/30*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 931/30*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+9/5*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+139/10*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R (- 5x - 3)\|3x + 2 \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=-67/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 133/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- (3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+10/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=34/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 5/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=31/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=458/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 970/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-458/1029*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=-916/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 338/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-458/1715*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+338/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=-10876/50421*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 189368/50421*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+16/343*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-2818/12005*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-5438/84035*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+189368/588245*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-128715331/44550*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+17888580643/178200*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(5/2)/_ +-- sqrt(1-2*x)+419/66*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+_ +-- 18/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+4066493/23100*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9741/385*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+269045681/207900*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (- 225x - 570x - 541x - 228x - 36)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-1228883/1620*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 42696881/1620*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+5/3*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+4853/105*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+93/14*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 1284329/3780*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 75x - 140x - 87x - 18)\|3x + 2 \|5x + 3 +--R (1) --------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=-1762/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 244879/36*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+167/14*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+12/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 3683/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 25x - 30x - 9)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=6599/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2659/54*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+3*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+397/18*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3s.input.pdf b/src/axiom-website/CATS/rich3s.input.pdf new file mode 100644 index 0000000..b101f17 Binary files /dev/null and b/src/axiom-website/CATS/rich3s.input.pdf differ diff --git a/src/axiom-website/CATS/rich3t.input.pamphlet b/src/axiom-website/CATS/rich3t.input.pamphlet new file mode 100644 index 0000000..8134e56 --- /dev/null +++ b/src/axiom-website/CATS/rich3t.input.pamphlet @@ -0,0 +1,5009 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3t.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 119 integrals in this file. +\item 119 supplied "optimal results". +\item 7 matching answers. +\item 3 cases where Axiom's result differs from Rubi +\item 1 case where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3t.output +)spool rich3t.output +)set message test on +)set message auto off +)clear all + +--S 1 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 597 +--r0:=4451/54*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 320/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+335/63*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 2 + +--S 3 of 597 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 597 +--m0:=a0-r0 +--E 4 + +--S 5 of 597 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 597 +--r0:=1159/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 185/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(2+3*x)+155/147*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 7 + +--S 8 of 597 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 597 +--m0:=a0-r0 +--E 9 + +--S 10 of 597 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 597 +--r0:=2797/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2020/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+598/3087*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 12 + +--S 13 of 597 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 597 +--m0:=a0-r0 +--E 14 + +--S 15 of 597 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 597 +--r0:=-31202/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 81164/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+1514/15435*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)-81164/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 17 + +--S 18 of 597 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 597 +--m0:=a0-r0 +--E 19 + +--S 20 of 597 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 597 +--r0:=-213544/151263*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+106558/151263*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_ +-- 16/343*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+986/12005*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-106772/252105*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-106558/1764735*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 22 + +--S 23 of 597 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 597 +--m0:=a0-r0 +--E 24 + +--S 25 of 597 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(11/2)) +--R +--R +--R (1) +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 597 +--r0:=-6036028/9529569*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-3929980/9529569*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/7*(3+5*x)^(5/2)/((2+3*x)^(9/2)*_ +-- sqrt(1-2*x))+20/441*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_ +-- 4930/64827*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-167228/453789*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-392998/3176523*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+6036028/22235661*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 27 + +--S 28 of 597 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 597 +--m0:=a0-r0 +--E 29 + +--S 30 of 597 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ---------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 597 +--r0:=-11291/2750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 168123/2750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2/11*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+_ +-- 312/275*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+3/11*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+14517/2750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 32 + +--S 33 of 597 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 597 +--m0:=a0-r0 +--E 34 + +--S 35 of 597 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 597 +--r0:=1597/110*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 161/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+69/55*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 37 + +--S 38 of 597 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 597 +--m0:=a0-r0 +--E 39 + +--S 40 of 597 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 597 +--r0:=34/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 7/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 42 + +--S 43 of 597 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 597 +--m0:=a0-r0 +--E 44 + +--S 45 of 597 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 597 +--r0:=elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 2/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 47 + +--S 48 of 597 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 597 +--m0:=a0-r0 +--E 49 + +--S 50 of 597 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 597 +t0:=1/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R +--------+ +------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 597 +--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)+4/77*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 52 + +--S 53 of 597 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 597 +--m0:=a0-r0 +--E 54 + +--S 55 of 597 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 2 +--------+ +------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 597 +--r0:=-62/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 57 + +--S 58 of 597 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 597 +--m0:=a0-r0 +--E 59 + +--S 60 of 597 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 597 +--r0:=60/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 1752/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 4/77*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+5256/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 62 + +--S 63 of 597 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 597 +--m0:=a0-r0 +--E 64 + +--S 65 of 597 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 597 +--r0:=6872/3773*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 244604/3773*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 4/77*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+10308/18865*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+733812/132055*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 67 + +--S 68 of 597 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 597 +--m0:=a0-r0 +--E 69 + +--S 70 of 597 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 597 +--r0:=2911577/75625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-1173529/151250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/(sqrt(1-2*x)*_ +-- sqrt(3+5*x))-4/121*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 10851/15125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+111/605*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+502941/151250*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 597 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 597 +--m0:=a0-r0 +--E 74 + +--S 75 of 597 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 597 +--r0:=55019/6050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 5572/3025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*(2+3*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)+2388/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 77 + +--S 78 of 597 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 597 +--m0:=a0-r0 +--E 79 + +--S 80 of 597 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 597 +--r0:=1159/605*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 259/605*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 82 + +--S 83 of 597 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 597 +--m0:=a0-r0 +--E 84 + +--S 85 of 597 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 597 +--r0:=37/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 28/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 4/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 87 + +--S 88 of 597 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 597 +--m0:=a0-r0 +--E 89 + +--S 90 of 597 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 597 +--r0:=-74/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 92 + +--S 93 of 597 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 597 +--m0:=a0-r0 +--E 94 + +--S 95 of 597 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 597 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 597 +--r0:=74/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 40/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 370/847*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 97 + +--S 98 of 597 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 597 +--m0:=a0-r0 +--E 99 + +--S 100 of 597 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 597 +--r0:=4636/847*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 740/847*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+186/539*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-23180/5929*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 102 + +--S 103 of 597 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 597 +--m0:=a0-r0 +--E 104 + +--S 105 of 597 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 597 +--r0:=220076/5929*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 31840/5929*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+54/539*_ +-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+9876/3773*sqrt(1-2*x)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-1100380/41503*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 107 + +--S 108 of 597 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 597 +--m0:=a0-r0 +--E 109 + +--S 110 of 597 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R - ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 597 +--r0:=-1341176/41503*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+46585232/41503*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 14928/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 2101332/132055*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 46585232/290521*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 112 + +--S 113 of 597 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 597 +--m0:=a0-r0 +--E 114 + +--S 115 of 597 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|3x + 2 +--R (1) ------------------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 597 +--r0:=604915631/24956250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-121995881/24956250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(11/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 1022/19965*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 380188/831875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4553/33275*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 17427983/8318750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 597 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 597 +--m0:=a0-r0 +--E 119 + +--S 120 of 597 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 597 +--r0:=5684677/998250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-581651/499125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 178/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+4421/33275*_ +-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+83093/166375*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 122 + +--S 123 of 597 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 597 +--m0:=a0-r0 +--E 124 + +--S 125 of 597 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 597 +--r0:=118898/99825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-30023/99825*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 758/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+4289/33275*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 127 + +--S 128 of 597 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 597 +--m0:=a0-r0 +--E 129 + +--S 130 of 597 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 597 +--r0:=4157/19965*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 4382/19965*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/(3+5*x)^(3/2)-626/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 132 + +--S 133 of 597 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 597 +--m0:=a0-r0 +--E 134 + +--S 135 of 597 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 597 +--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1610/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-494/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 137 + +--S 138 of 597 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 597 +--m0:=a0-r0 +--E 139 + +--S 140 of 597 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 597 +--r0:=-724/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 98/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-490/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 142 + +--S 143 of 597 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 597 +--m0:=a0-r0 +--E 144 + +--S 145 of 597 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 597 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 597 +--r0:=-3896/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 340/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+19480/27951*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 147 + +--S 148 of 597 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 597 +--m0:=a0-r0 +--E 149 + +--S 150 of 597 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 597 +--r0:=-595324/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+85160/27951*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x))+186/539*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 45040/17787*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 2976620/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 152 + +--S 153 of 597 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 597 +--m0:=a0-r0 +--E 154 + +--S 155 of 597 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R - ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 597 +--r0:=-42623864/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+6132760/195657*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((2+3*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 14496/3773*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 3205940/124509*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 213119320/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 157 + +--S 158 of 597 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 597 +--m0:=a0-r0 +--E 159 + +--S 160 of 597 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 +--R * +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 597 +--r0:=347423024/1369599*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-12071114168/1369599*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 19548/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 4115652/132055*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 181551856/871563*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 12071114168/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 162 + +--S 163 of 597 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 597 +--m0:=a0-r0 +--E 164 + +--S 165 of 597 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 597 +t0:=(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R (1) --------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 597 +--r0:=6478333/16500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 112543103/8250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+1/3*(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-166/33*_ +-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-139163/3850*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-1327/154*(2+3*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)-6478333/38500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 167 + +--S 168 of 597 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 597 +--m0:=a0-r0 +--E 169 + +--S 170 of 597 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 597 +t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 597 +--r0:=-1289089/3300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+129857/1650*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+1/3*(2+3*x)^(7/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-133/33*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 797/110*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-18551/550*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 172 + +--S 173 of 597 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 597 +--m0:=a0-r0 +--E 174 + +--S 175 of 597 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 597 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 597 +--r0:=-4621/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 931/66*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-100/33*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x)/sqrt(1-2*x)-133/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 597 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 597 +--m0:=a0-r0 +--E 179 + +--S 180 of 597 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 597 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 597 +--r0:=67/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 133/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 1/3*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-67/33*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 182 + +--S 183 of 597 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 597 +--m0:=a0-r0 +--E 184 + +--S 185 of 597 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 597 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 597 +--r0:=-34/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-68/231*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 187 + +--S 188 of 597 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 597 +--m0:=a0-r0 +--E 189 + +--S 190 of 597 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 597 +--r0:=31/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+62/1617*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 192 + +--S 193 of 597 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 597 +--m0:=a0-r0 +--E 194 + +--S 195 of 597 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 597 +--r0:=458/1617*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 970/1617*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+194/1617*sqrt(3+5*x)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 197 + +--S 198 of 597 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 597 +--m0:=a0-r0 +--E 199 + +--S 200 of 597 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 597 +--r0:=-338/11319*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 4580/11319*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+326/1617*sqrt(3+5*x)/_ +-- ((2+3*x)^(3/2)*sqrt(1-2*x))-458/3773*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+338/26411*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 597 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 597 +--m0:=a0-r0 +--E 204 + +--S 205 of 597 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 597 +--r0:=-10876/79233*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 189368/79233*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+458/1617*sqrt(3+5*x)/_ +-- ((2+3*x)^(5/2)*sqrt(1-2*x))-2818/18865*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)-5438/132055*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 189368/924385*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 597 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 597 +--m0:=a0-r0 +--E 209 + +--S 210 of 597 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 597 +t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 597 +--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+188443/300*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-6547351/300*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-56/11*_ +-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-1341/154*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)-140289/3850*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-2166399/7700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 212 + +--S 213 of 597 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 597 +--m0:=a0-r0 +--E 214 + +--S 215 of 597 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 597 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 597 +--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-37663/60*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1897/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 45/11*(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-807/110*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-6231/110*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 597 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 597 +--m0:=a0-r0 +--E 219 + +--S 220 of 597 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 597 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 597 +--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ +-- 137/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 68/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 34/11*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-225/22*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 597 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 597 +--m0:=a0-r0 +--E 224 + +--S 225 of 597 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 597 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 597 +--r0:=-139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-23/7*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 227 + +--S 228 of 597 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 597 +--m0:=a0-r0 +--E 229 + +--S 230 of 597 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 597 +--r0:=-37/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-13/49*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 232 + +--S 233 of 597 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 597 +--m0:=a0-r0 +--E 234 + +--S 235 of 597 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 597 +--r0:=19/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 40/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))+9/49*sqrt(3+5*x)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-19/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 237 + +--S 238 of 597 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 597 +--m0:=a0-r0 +--E 239 + +--S 240 of 597 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 597 +--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_ +-- 496/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-890/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+31/49*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-_ +-- 89/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-496/2401*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 242 + +--S 243 of 597 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 597 +--m0:=a0-r0 +--E 244 + +--S 245 of 597 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 597 +--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_ +-- 4528/7203*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 3946/7203*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 53/49*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_ +-- 779/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_ +-- 2264/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_ +-- 3946/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 247 + +--S 248 of 597 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 597 +--m0:=a0-r0 +--E 249 + +--S 250 of 597 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 597 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 597 +--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ +-- 2513419/540*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 174654791/1080*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-203/33*(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_ +-- 225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1310203/4620*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6277/154*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-1313411/630*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 252 + +--S 253 of 597 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 597 +--m0:=a0-r0 +--E 254 + +--S 255 of 597 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 597 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 597 +--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ +-- 4019/4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 69819/2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 170/33*(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_ +-- 28283/462*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1355/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 12601/28*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 257 + +--S 258 of 597 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 597 +--m0:=a0-r0 +--E 259 + +--S 260 of 597 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 597 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 597 +--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-_ +-- 12101/12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1219/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 137/33*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)-_ +-- 817/66*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 91*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 262 + +--S 263 of 597 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 597 +--m0:=a0-r0 +--E 264 + +--S 265 of 597 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 597 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 597 +--r0:=-4621/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 665/18*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-104/21*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(1-2*x)-695/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 267 + +--S 268 of 597 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 597 +--m0:=a0-r0 +--E 269 + +--S 270 of 597 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 597 +--r0:=-1597/42*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 115/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-_ +-- 109/147*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-_ +-- 120/49*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 597 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 597 +--m0:=a0-r0 +--E 274 + +--S 275 of 597 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 597 +--r0:=5/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 146/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))-43/147*(3+5*x)^(3/2)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-17/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 277 + +--S 278 of 597 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 597 +--m0:=a0-r0 +--E 279 + +--S 280 of 597 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+169/3087*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2290/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 23/147*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+19/1029*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-169/7203*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 282 + +--S 283 of 597 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 597 +--m0:=a0-r0 +--E 284 + +--S 285 of 597 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_ +-- 986/2401*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 9206/2401*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 89/147*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+143/1715*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-4437/12005*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-27618/84035*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 287 + +--S 288 of 597 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 597 +--m0:=a0-r0 +--E 289 + +--S 290 of 597 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(9/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))+_ +-- 98642/352947*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-337780/352947*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+155/147*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_ +-- 355/2401*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_ +-- 11433/16807*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_ +-- 33778/117649*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_ +-- 98642/823543*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 292 + +--S 293 of 597 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 597 +--m0:=a0-r0 +--E 294 + +--S 295 of 597 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 597 +--r0:=-44109377/181500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2221688/45375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-227/363*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 27271/6050*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-130/121*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-317384/15125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 597 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 597 +--m0:=a0-r0 +--E 299 + +--S 300 of 597 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 597 +--r0:=-78472/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+31619/3630*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-161/363*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 97/121*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-4517/1210*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 597 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 597 +--m0:=a0-r0 +--E 304 + +--S 305 of 597 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 597 +--r0:=-4451/726*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+448/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/33*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_ +-- 95/363*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-64/121*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 597 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 597 +--m0:=a0-r0 +--E 309 + +--S 310 of 597 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 597 +--r0:=29/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 31/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/33*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_ +-- 29/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 312 + +--S 313 of 597 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 597 +--m0:=a0-r0 +--E 314 + +--S 315 of 597 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 597 +--r0:=37/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+74/2541*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 317 + +--S 318 of 597 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 597 +--m0:=a0-r0 +--E 319 + +--S 320 of 597 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 597 +t0:=1/((1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 597 +--r0:=272/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1030/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+544/17787*_ +-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 322 + +--S 323 of 597 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 597 +--m0:=a0-r0 +--E 324 + +--S 325 of 597 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 597 +--r0:=-5594/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 4040/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+808/17787*_ +-- sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+5594/41503*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 327 + +--S 328 of 597 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 597 +--m0:=a0-r0 +--E 329 + +--S 330 of 597 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 597 +--r0:=-184636/124509*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+9740/124509*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_ +-- 1072/17787*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+_ +-- 974/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 184636/290521*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 332 + +--S 333 of 597 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 597 +--m0:=a0-r0 +--E 334 + +--S 335 of 597 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 597 +--r0:=699808/871563*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 26062156/871563*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+_ +-- 1336/17787*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_ +-- 806/207515*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 349904/1452605*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 26062156/10168235*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 337 + +--S 338 of 597 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 597 +--m0:=a0-r0 +--E 339 + +--S 340 of 597 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 597 +--r0:=-1508889271/9982500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+151997573/4991250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-223/363*(2+3*x)^(9/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 215/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 932783/332750*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 4439/6655*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 21713939/1663750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 597 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 597 +--m0:=a0-r0 +--E 344 + +--S 345 of 597 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 597 +--r0:=-5327983/199650*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+1073233/199650*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-157/363*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 149/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 3284/6655*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 153319/66550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 597 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 597 +--m0:=a0-r0 +--E 349 + +--S 350 of 597 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 597 +--r0:=-148831/39930*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+14903/19965*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-91/363*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 83/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 2129/6655*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 597 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 597 +--m0:=a0-r0 +--E 354 + +--S 355 of 597 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 597 +--r0:=-974/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 119/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-_ +-- 25/363*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 17/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 357 + +--S 358 of 597 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 597 +--m0:=a0-r0 +--E 359 + +--S 360 of 597 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 597 +--r0:=-362/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 49/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))+_ +-- 41/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 245/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 362 + +--S 363 of 597 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 597 +--m0:=a0-r0 +--E 364 + +--S 365 of 597 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 597 +--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1150/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+214/2541*sqrt(2+3*x)/_ +-- (sqrt(1-2*x)*sqrt(3+5*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 367 + +--S 368 of 597 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 597 +--m0:=a0-r0 +--E 369 + +--S 370 of 597 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 597 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 597 +--r0:=8314/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 6260/27951*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+_ +-- 824/17787*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 41570/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 372 + +--S 373 of 597 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 597 +--m0:=a0-r0 +--E 374 + +--S 375 of 597 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 597 +--r0:=475592/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-85780/195657*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x))+1088/17787/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+_ +-- 5314/41503*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 2377960/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 377 + +--S 378 of 597 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 597 +--m0:=a0-r0 +--E 379 + +--S 380 of 597 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 597 +--r0:=22738708/1369599*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-3323720/1369599*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x))+1352/17787/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 694/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 336536/290521*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 113693540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 382 + +--S 383 of 597 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 597 +--m0:=a0-r0 +--E 384 + +--S 385 of 597 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 597 +--r0:=-139423864/9587193*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4839325048/9587193*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x))+1616/17787/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 2206/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 499564/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 72709316/10168235*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 4839325048/67110351*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 387 + +--S 388 of 597 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 597 +--m0:=a0-r0 +--E 389 + +--S 390 of 597 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 597 +t0:=(2+3*x)^(13/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 597 +--r0:=2/33*(2+3*x)^(13/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 51601293223/549037500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)+2598959587/137259375*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 73/121*(2+3*x)^(11/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 215/3993*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 6503/219615*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 31887029/18301250*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 150812/366025*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 371279941/45753125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 597 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 597 +--m0:=a0-r0 +--E 394 + +--S 395 of 597 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 597 +--r0:=2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 90397364/5490375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+36399853/10980750*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-51/121*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+149/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 865/43923*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 110519/366025*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 5199979/3660250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 597 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 597 +--m0:=a0-r0 +--E 399 + +--S 400 of 597 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 597 +--r0:=2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 4971289/2196150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+491582/1098075*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-29/121*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+83/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 2147/219615*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 70226/366025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 597 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 597 +--m0:=a0-r0 +--E 404 + +--S 405 of 597 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 597 +--r0:=2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 29933/219615*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-217/219615*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-7/121*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 17/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-31/219615*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 407 + +--S 408 of 597 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 597 +--m0:=a0-r0 +--E 409 + +--S 410 of 597 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 597 +--r0:=2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 2209/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-4144/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+15/121*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 49/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2209/43923*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 412 + +--S 413 of 597 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 597 +--m0:=a0-r0 +--E 414 + +--S 415 of 597 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 597 +--r0:=2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 8774/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+592/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+37/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 575/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2960/43923*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 417 + +--S 418 of 597 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 597 +--m0:=a0-r0 +--E 419 + +--S 420 of 597 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 597 +--r0:=4418/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-5920/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+118/847*_ +-- sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-2470/27951*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-22090/307461*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 422 + +--S 423 of 597 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 597 +--m0:=a0-r0 +--E 424 + +--S 425 of 597 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 597 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 597 +--r0:=-119732/307461*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-620/307461*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 368/5929*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 18470/195657*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 598660/2152227*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 427 + +--S 428 of 597 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 597 +--m0:=a0-r0 +--E 429 + +--S 430 of 597 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 597 +--r0:=-19885156/2152227*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+2809040/2152227*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x))+456/5929/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+_ +-- 5034/41503*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 1523260/1369599*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 99425780/15065589*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 432 + +--S 433 of 597 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 597 +--m0:=a0-r0 +--E 434 + +--S 435 of 597 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 597 +--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 1446357824/15065589*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+207999160/15065589*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 544/5929/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 414/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 488436/290521*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 108842540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 7231789120/105459123*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 437 + +--S 438 of 597 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 597 +--m0:=a0-r0 +--E 439 + +--S 440 of 597 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72) +--R * +--R +--------+ +------+ +------+ +--R \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 597 +--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 11880958112/105459123*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-412810345784/105459123*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 632/5929/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 3606/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 649224/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 140700876/10168235*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 6208896328/67110351*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 412810345784/738213861*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 442 + +--S 443 of 597 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 597 +--m0:=a0-r0 +--E 444 + +--S 445 of 597 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 597 +t0:=(a+b*x)*(A+B*x)*sqrt(c+d*x)/x +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|d x + c +--R (1) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 446 + +--S 447 of 597 +r0:=-2/15*(2*b*B*c-5*A*b*d-2*a*B*d)*(c+d*x)^(3/2)/d^2+_ + 2/5*B*(a+b*x)*(c+d*x)^(3/2)/d-2*a*A*atanh(sqrt(c+d*x)/sqrt(c))*_ + sqrt(c)+2*a*A*sqrt(c+d*x) +--R +--R +--R (2) +--R +-------+ +--R 2 +-+ \|d x + c +--R - 30A a d \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 2 +--R 6B b d x + ((10A b + 10B a)d + 2B b c d)x + 30A a d +--R + +--R 2 +--R (10A b + 10B a)c d - 4B b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 15d +--R Type: Expression(Integer) +--E 447 + +--S 448 of 597 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 597 +--m0:=a0-r0 +--E 449 + +--S 450 of 597 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 597 +t0:=(A+B*x)*(c+d*x)*sqrt(a+b*x)/x +--R +--R +--R 2 +-------+ +--R (B d x + (A d + B c)x + A c)\|b x + a +--R (1) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 451 + +--S 452 of 597 +r0:=2/15*(5*b*B*c+2*A*b*d-2*a*B*d)*(a+b*x)^(3/2)/b^2+_ + 2/5*d*(a+b*x)^(3/2)*(A+B*x)/b-2*A*c*atanh(sqrt(a+b*x)/sqrt(a))*_ + sqrt(a)+2*A*c*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 2 +-+ \|b x + a +--R - 30A b c\|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 452 + +--S 453 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15A b c\|a log(----------------------------) +--R x +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R , +--R +--R +-------+ +--R 2 +---+ \|b x + a +--R - 30A b c\|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 453 + +--S 454 of 597 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) A c\|a log(----------------------------) + 2A c\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 597 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 597 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2A c\|a atanh(----------) - 2A c\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 597 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 597 +t0:=x^3*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 4 3 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 597 +r0:=-75/128*asin(1-2*a*x)/a^4-75/64*sqrt(a*x-a^2*x^2)/a^4-_ + 25/32*x*sqrt(a*x-a^2*x^2)/a^3-5/8*x^2*sqrt(a*x-a^2*x^2)/a^2-_ + 1/4*x^3*sqrt(a*x-a^2*x^2)/a +--R +--R +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (- 32a x - 80a x - 100a x - 150)\|- a x + a x + 75asin(2a x - 1) +--R (2) -------------------------------------------------------------------- +--R 4 +--R 128a +--R Type: Expression(Integer) +--E 459 + +--S 460 of 597 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 597 +--m0:=a0-r0 +--E 461 + +--S 462 of 597 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 597 +t0:=x^2*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 3 2 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 597 +r0:=-11/16*asin(1-2*a*x)/a^3-11/8*sqrt(a*x-a^2*x^2)/a^3-_ + 11/12*x*sqrt(a*x-a^2*x^2)/a^2-1/3*x^2*sqrt(a*x-a^2*x^2)/a +--R +--R +--R +------------+ +--R 2 2 | 2 2 +--R (- 16a x - 44a x - 66)\|- a x + a x + 33asin(2a x - 1) +--R (2) --------------------------------------------------------- +--R 3 +--R 48a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 597 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 597 +--m0:=a0-r0 +--E 466 + +--S 467 of 597 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 597 +t0:=x*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 2 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 597 +r0:=-7/8*asin(1-2*a*x)/a^2-5/4*sqrt(a*x)*sqrt(1-a*x)/a^2-_ + 1/2*(1+a*x)*sqrt(a*x)*sqrt(1-a*x)/a^2 +--R +--R +--R +---------+ +---+ +--R (- 4a x - 14)\|- a x + 1 \|a x + 7asin(2a x - 1) +--R (2) ------------------------------------------------- +--R 2 +--R 8a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 597 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 597 +--m0:=a0-r0 +--E 471 + +--S 472 of 597 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 597 +t0:=(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 473 + +--S 474 of 597 +r0:=-3/2*asin(1-2*a*x)/a-sqrt(a*x)*sqrt(1-a*x)/a +--R +--R +--R +---------+ +---+ +--R - 2\|- a x + 1 \|a x + 3asin(2a x - 1) +--R (2) --------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 474 + +--S 475 of 597 +--a0:=integrate(t0,x) +--E 475 + +--S 476 of 597 +--m0:=a0-r0 +--E 476 + +--S 477 of 597 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 of 597 +t0:=(1+a*x)/(x*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) ------------------- +--R +---------+ +---+ +--R x\|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 478 + +--S 479 of 597 +r0:=-asin(1-2*a*x)-2*sqrt(a*x-a^2*x^2)/(a*x) +--R +--R +--R +------------+ +--R | 2 2 +--R - 2\|- a x + a x + a x asin(2a x - 1) +--R (2) --------------------------------------- +--R a x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 597 +--a0:=integrate(t0,x) +--E 480 + +--S 481 of 597 +--m0:=a0-r0 +--E 481 + +--S 482 of 597 +--d0:=D(m0,x) +--E 482 + +)clear all + +--S 483 of 597 +t0:=(1+a*x)/(x^2*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 2 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 597 +r0:=-2/3*sqrt(a*x-a^2*x^2)/(a*x^2)-10/3*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R | 2 2 +--R (- 10a x - 2)\|- a x + a x +--R (2) ---------------------------- +--R 2 +--R 3a x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 597 +--a0:=integrate(t0,x) +--E 485 + +--S 486 of 597 +--m0:=a0-r0 +--E 486 + +--S 487 of 597 +--d0:=D(m0,x) +--E 487 + +)clear all + +--S 488 of 597 +t0:=(1+a*x)/(x^3*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 3 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 597 +r0:=-2/5*sqrt(a*x-a^2*x^2)/(a*x^3)-6/5*sqrt(a*x-a^2*x^2)/x^2-_ + 12/5*a*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 2 2 | 2 2 +--R (- 12a x - 6a x - 2)\|- a x + a x +--R (2) ------------------------------------ +--R 3 +--R 5a x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 597 +--a0:=integrate(t0,x) +--E 490 + +--S 491 of 597 +--m0:=a0-r0 +--E 491 + +--S 492 of 597 +--d0:=D(m0,x) +--E 492 + +)clear all + +--S 493 of 597 +t0:=(1+a*x)/(x^4*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 4 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 493 + +--S 494 of 597 +r0:=-2/7*sqrt(a*x-a^2*x^2)/(a*x^4)-26/35*sqrt(a*x-a^2*x^2)/x^3-_ + 104/105*a*sqrt(a*x-a^2*x^2)/x^2-208/105*a^2*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (- 208a x - 104a x - 78a x - 30)\|- a x + a x +--R (2) ------------------------------------------------- +--R 4 +--R 105a x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 597 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 +---------+ +---+ +--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x +--R + +--R 3 2 4 +--R (104a + 52a + 39a + 15)x +--R / +--R 4 +--R 105a x +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 597 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 +---------+ +---+ +--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x +--R + +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (208a x + 104a x + 78a x + 30)\|- a x + a x +--R + +--R 3 2 4 +--R (104a + 52a + 39a + 15)x +--R / +--R 4 +--R 105a x +--R Type: Expression(Integer) +--E 496 + +--S 497 of 597 +d0:=D(m0,x) +--R +--R +--R +------------+ +--R +---------+ +---+ | 2 2 +--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x +--R (5) -------------------------------------------------------- +--R +------------+ +--R 4 | 2 2 +---------+ +---+ +--R x \|- a x + a x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 597 +t0:=(1+a*x)/(x^5*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 5 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 498 + +--S 499 of 597 +r0:=-2/9*sqrt(a*x-a^2*x^2)/(a*x^5)-34/63*sqrt(a*x-a^2*x^2)/x^4-_ + 68/105*a*sqrt(a*x-a^2*x^2)/x^3-272/315*a^2*sqrt(a*x-a^2*x^2)/x^2-_ + 544/315*a^3*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 4 4 3 3 2 2 | 2 2 +--R (- 544a x - 272a x - 204a x - 170a x - 70)\|- a x + a x +--R (2) ------------------------------------------------------------ +--R 5 +--R 315a x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 597 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 +---------+ +---+ +--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x +--R + +--R 5 4 3 2 5 +--R (816a - 680a - 238a - 153a - 235a - 140)x +--R / +--R 5 +--R 630a x +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 597 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 +---------+ +---+ +--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x +--R + +--R +------------+ +--R 4 4 3 3 2 2 | 2 2 +--R (1088a x + 544a x + 408a x + 340a x + 140)\|- a x + a x +--R + +--R 5 4 3 2 5 +--R (816a - 680a - 238a - 153a - 235a - 140)x +--R / +--R 5 +--R 630a x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 597 +d0:=D(m0,x) +--R +--R +--R +------------+ +--R +---------+ +---+ | 2 2 +--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x +--R (5) -------------------------------------------------------- +--R +------------+ +--R 5 | 2 2 +---------+ +---+ +--R x \|- a x + a x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 597 +t0:=x^m*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R m n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 503 + +--S 504 of 597 +--r0:=b*x^(1+m)*(e+f*x)^n*_ +-- AppellF1(1+m,1,-n,2+m,-b*x/a,-f*x/e)/(a*(b*c-a*d)*(1+m)*_ +-- ((e+f*x)/e)^n)-d*x^(1+m)*(e+f*x)^n*_ +-- AppellF1(1+m,1,-n,2+m,-d*x/c,-f*x/e)/(c*(b*c-a*d)*(1+m)*_ +-- ((e+f*x)/e)^n) +--E 504 + +--S 505 of 597 +--a0:=integrate(t0,x) +--E 505 + +--S 506 of 597 +--m0:=a0-r0 +--E 506 + +--S 507 of 597 +--d0:=D(m0,x) +--E 507 + +)clear all + +--S 508 of 597 +t0:=x^4*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 4 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 508 + +--S 509 of 597 +--r0:=e^2*(e+f*x)^(1+n)/(b*d*f^3*(1+n))+(b*c+a*d)*e*(e+f*x)^(1+n)/_ +-- (b^2*d^2*f^2*(1+n))+(b^2*c^2+a*b*c*d+a^2*d^2)*(e+f*x)^(1+n)/_ +-- (b^3*d^3*f*(1+n))-2*e*(e+f*x)^(2+n)/(b*d*f^3*(2+n))-_ +-- (b*c+a*d)*(e+f*x)^(2+n)/(b^2*d^2*f^2*(2+n))+(e+f*x)^(3+n)/_ +-- (b*d*f^3*(3+n))-a^4*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b^3*(b*c-a*d)*(b*e-a*f)*(1+n))+c^4*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d^3*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 509 + +--S 510 of 597 +--a0:=integrate(t0,x) +--E 510 + +--S 511 of 597 +--m0:=a0-r0 +--E 511 + +--S 512 of 597 +--d0:=D(m0,x) +--E 512 + +)clear all + +--S 513 of 597 +t0:=x^3*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 3 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 513 + +--S 514 of 597 +--r0:=-e*(e+f*x)^(1+n)/(b*d*f^2*(1+n))-(b*c+a*d)*(e+f*x)^(1+n)/_ +-- (b^2*d^2*f*(1+n))+(e+f*x)^(2+n)/(b*d*f^2*(2+n))+a^3*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b^2*(b*c-a*d)*(b*e-a*f)*(1+n))-c^3*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d^2*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 514 + +--S 515 of 597 +--a0:=integrate(t0,x) +--E 515 + +--S 516 of 597 +--m0:=a0-r0 +--E 516 + +--S 517 of 597 +--d0:=D(m0,x) +--E 517 + +)clear all + +--S 518 of 597 +t0:=x^2*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 2 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 518 + +--S 519 of 597 +--r0:=(e+f*x)^(1+n)/(b*d*f*(1+n))-a^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b*(b*c-a*d)*(b*e-a*f)*(1+n))+c^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 519 + +--S 520 of 597 +--a0:=integrate(t0,x) +--E 520 + +--S 521 of 597 +--m0:=a0-r0 +--E 521 + +--S 522 of 597 +--d0:=D(m0,x) +--E 522 + +)clear all + +--S 523 of 597 +t0:=x*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 523 + +--S 524 of 597 +--r0:=a*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- ((b*c-a*d)*(b*e-a*f)*(1+n))-c*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- ((b*c-a*d)*(d*e-c*f)*(1+n)) +--E 524 + +--S 525 of 597 +--a0:=integrate(t0,x) +--E 525 + +--S 526 of 597 +--m0:=a0-r0 +--E 526 + +--S 527 of 597 +--d0:=D(m0,x) +--E 527 + +)clear all + +--S 528 of 597 +t0:=(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 528 + +--S 529 of 597 +--r0:=-b*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/_ +-- (b*e-a*f))/((b*c-a*d)*(b*e-a*f)*(1+n))+d*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- ((b*c-a*d)*(d*e-c*f)*(1+n)) +--E 529 + +--S 530 of 597 +--a0:=integrate(t0,x) +--E 530 + +--S 531 of 597 +--m0:=a0-r0 +--E 531 + +--S 532 of 597 +--d0:=D(m0,x) +--E 532 + +)clear all + +--S 533 of 597 +t0:=(e+f*x)^n/(x*(a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) ------------------------------ +--R 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 597 +--r0:=-(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a*c*e*(1+n))+_ +-- b^2*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (a*(b*c-a*d)*(b*e-a*f)*(1+n))-d^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (c*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 534 + +--S 535 of 597 +--a0:=integrate(t0,x) +--E 535 + +--S 536 of 597 +--m0:=a0-r0 +--E 536 + +--S 537 of 597 +--d0:=D(m0,x) +--E 537 + +)clear all + +--S 538 of 597 +t0:=(e+f*x)^n/(x^2*(a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) ------------------------------- +--R 4 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 597 +--r0:=-(e+f*x)^(1+n)/(a*c*e*x)+(b*c+a*d)*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a^2*c^2*e*(1+n))-_ +-- f*n*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/_ +-- (a*c*e^2*(1+n))-b^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,_ +-- 2+n,b*(e+f*x)/(b*e-a*f))/(a^2*(b*c-a*d)*(b*e-a*f)*(1+n))_ +-- +d^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,d*(e+f*x)/_ +-- (d*e-c*f))/(c^2*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 539 + +--S 540 of 597 +--a0:=integrate(t0,x) +--E 540 + +--S 541 of 597 +--m0:=a0-r0 +--E 541 + +--S 542 of 597 +--d0:=D(m0,x) +--E 542 + +)clear all + +--S 543 of 597 +t0:=(a+b*x)*(c+d*x)*(e+f*x)*(g+h*x) +--R +--R +--R (1) +--R 4 3 +--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x +--R + +--R 2 +--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x +--R + +--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g +--R Type: Polynomial(Integer) +--E 543 + +--S 544 of 597 +r0:=a*c*e*g*x+1/2*(b*c*e*g+a*(d*e*g+c*f*g+c*e*h))*x^2+_ + 1/3*(b*(d*e*g+c*f*g+c*e*h)+a*(d*f*g+d*e*h+c*f*h))*x^3+_ + 1/4*(a*d*f*h+b*(d*f*g+d*e*h+c*f*h))*x^4+1/5*b*d*f*h*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 1 4 +--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x +--R 5 4 4 4 4 +--R + +--R 1 1 1 1 1 1 3 +--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x +--R 3 3 3 3 3 3 +--R + +--R 1 1 1 1 2 +--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x +--R 2 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 544 + +--S 545 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 1 4 +--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x +--R 5 4 4 4 4 +--R + +--R 1 1 1 1 1 1 3 +--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x +--R 3 3 3 3 3 3 +--R + +--R 1 1 1 1 2 +--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x +--R 2 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 545 + +--S 546 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 546 + +--S 547 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 547 + +)clear all + +--S 548 of 597 +t0:=(a+b*x)*(c+d*x)*(e+f*x)/(g+h*x) +--R +--R +--R 3 2 +--R b d f x + ((a d + b c)f + b d e)x + (a c f + (a d + b c)e)x + a c e +--R (1) --------------------------------------------------------------------- +--R h x + g +--R Type: Fraction(Polynomial(Integer)) +--E 548 + +--S 549 of 597 +r0:=(b*(d*g-c*h)*(f*g-e*h)-a*h*(d*f*g-d*e*h-c*f*h))*x/h^3+_ + 1/2*(a*d*f*h-b*(d*f*g-d*e*h-c*f*h))*x^2/h^2+_ + 1/3*b*d*f*x^3/h-(b*g-a*h)*(d*g-c*h)*(f*g-e*h)*log(g+h*x)/h^4 +--R +--R +--R (2) +--R 3 2 +--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h +--R + +--R 2 3 +--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g +--R * +--R log(h x + g) +--R + +--R 3 3 3 2 2 +--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x +--R + +--R 3 2 +--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h +--R + +--R 2 +--R 6b d f g h +--R * +--R x +--R / +--R 4 +--R 6h +--R Type: Expression(Integer) +--E 549 + +--S 550 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h +--R + +--R 2 3 +--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g +--R * +--R log(h x + g) +--R + +--R 3 3 3 2 2 +--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x +--R + +--R 3 2 +--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h +--R + +--R 2 +--R 6b d f g h +--R * +--R x +--R / +--R 4 +--R 6h +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 597 +t0:=(a+b*x)*(c+d*x)/((e+f*x)*(g+h*x)) +--R +--R +--R 2 +--R b d x + (a d + b c)x + a c +--R (1) --------------------------- +--R 2 +--R f h x + (e h + f g)x + e g +--R Type: Fraction(Polynomial(Integer)) +--E 553 + +--S 554 of 597 +r0:=b*d*x/(f*h)+(b*e-a*f)*(d*e-c*f)*log(e+f*x)/(f^2*(f*g-e*h))-_ + (b*g-a*h)*(d*g-c*h)*log(g+h*x)/(h^2*(f*g-e*h)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )h log(f x + e) +--R + +--R 2 2 +--R (b d e f h - b d f g h)x +--R / +--R 2 3 3 2 +--R e f h - f g h +--R Type: Expression(Integer) +--E 554 + +--S 555 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )h log(f x + e) +--R + +--R 2 2 +--R (b d e f h - b d f g h)x +--R / +--R 2 3 3 2 +--R e f h - f g h +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 597 +t0:=(a+b*x)/((c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g +--R Type: Fraction(Polynomial(Integer)) +--E 558 + +--S 559 of 597 +r0:=-(b*c-a*d)*log(c+d*x)/((d*e-c*f)*(d*g-c*h))+_ + (b*e-a*f)*log(e+f*x)/((d*e-c*f)*(f*g-e*h))-_ + (b*g-a*h)*log(g+h*x)/((d*g-c*h)*(f*g-e*h)) +--R +--R +--R (2) +--R ((a c f - a d e)h + (- b c f + b d e)g)log(h x + g) +--R + +--R ((- a c f + b c e)h + (a d f - b d e)g)log(f x + e) +--R + +--R ((a d - b c)e h + (- a d + b c)f g)log(d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 +--R (c e f - c d e )h + (- c f + d e )g h + (c d f - d e f)g +--R Type: Expression(Integer) +--E 559 + +--S 560 of 597 +--a0:=integrate(t0,x) +--E 560 + +--S 561 of 597 +--m0:=a0-r0 +--E 561 + +--S 562 of 597 +--d0:=D(m0,x) +--E 562 + +)clear all + +--S 563 of 597 +t0:=1/((a+b*x)*(c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 +--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x +--R + +--R 2 +--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x +--R + +--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g +--R Type: Fraction(Polynomial(Integer)) +--E 563 + +--S 564 of 597 +r0:=b^2*log(a+b*x)/((b*c-a*d)*(b*e-a*f)*(b*g-a*h))-_ + d^2*log(c+d*x)/((b*c-a*d)*(d*e-c*f)*(d*g-c*h))+_ + f^2*log(e+f*x)/((b*e-a*f)*(d*e-c*f)*(f*g-e*h))-_ + h^2*log(g+h*x)/((b*g-a*h)*(d*g-c*h)*(f*g-e*h)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d)e )h +--R * +--R log(h x + g) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R ((- a c d + a b c )f h + (a d - b c )f g h + (- a b d + b c d)f g ) +--R * +--R log(f x + e) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d e f - a b d e )h + (- a d f + b d e )g h +--R + +--R 2 2 2 2 2 +--R (a b d f - b d e f)g +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- b c e f + b c d e )h + (b c f - b d e )g h +--R + +--R 2 2 2 2 2 +--R (- b c d f + b d e f)g +--R * +--R log(b x + a) +--R / +--R 3 2 2 3 2 3 2 2 3 2 +--R (a c d - a b c )e f + (- a c d + a b c )e f +--R + +--R 2 2 2 2 3 +--R (a b c d - a b c d)e +--R * +--R 3 +--R h +--R + +--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2 +--R ((- a c d + a b c )f + (a d - b c )e f + (- a b d + b c d)e )g h +--R + +--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2 +--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d )e )g h +--R + +--R 2 2 2 2 3 2 3 3 2 2 +--R (- a b c d + a b c d)f + (a b d - b c d)e f +--R + +--R 2 3 3 2 2 +--R (- a b d + b c d )e f +--R * +--R 3 +--R g +--R Type: Expression(Integer) +--E 564 + +--S 565 of 597 +--a0:=integrate(t0,x) +--E 565 + +--S 566 of 597 +--m0:=a0-r0 +--E 566 + +--S 567 of 597 +--d0:=D(m0,x) +--E 567 + +)clear all + +--S 568 of 597 +t0:=(a+b*x)^m*(c+d*x)*(e+f*x)*(g+h*x) +--R +--R +--R (1) +--R 3 2 +--R (d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g) +--R * +--R m +--R (b x + a) +--R Type: Expression(Integer) +--E 568 + +--S 569 of 597 +r0:=(b*c-a*d)*(b*e-a*f)*(b*g-a*h)*(a+b*x)^(1+m)/(b^4*(1+m))+_ + (3*a^2*d*f*h+b^2*(d*e*g+c*f*g+c*e*h)-_ + 2*a*b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(2+m)/(b^4*(2+m))-_ + (3*a*d*f*h-b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(3+m)/(b^4*(3+m))+_ + d*f*h*(a+b*x)^(4+m)/(b^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (d f h m + 6d f h m + 11d f h m + 6d f h)(b x + a) +--R + +--R 3 +--R (((- 3a d + b c)f + b d e)h + b d f g)m +--R + +--R 2 +--R (((- 21a d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R (((- 42a d + 14b c)f + 14b d e)h + 14b d f g)m +--R + +--R ((- 24a d + 8b c)f + 8b d e)h + 8b d f g +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 2 +--R ((3a d - 2a b c)f + (- 2a b d + b c)e)h +--R + +--R 2 2 +--R ((- 2a b d + b c)f + b d e)g +--R * +--R 3 +--R m +--R + +--R 2 2 +--R ((24a d - 16a b c)f + (- 16a b d + 8b c)e)h +--R + +--R 2 2 +--R ((- 16a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 +--R ((57a d - 38a b c)f + (- 38a b d + 19b c)e)h +--R + +--R 2 2 +--R ((- 38a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 2 2 +--R ((36a d - 24a b c)f + (- 24a b d + 12b c)e)h +--R + +--R 2 2 +--R ((- 24a b d + 12b c)f + 12b d e)g +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((- a d + a b c)f + (a b d - a b c)e)h +--R + +--R 2 2 2 3 +--R ((a b d - a b c)f + (- a b d + b c)e)g +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 +--R ((- 9a d + 9a b c)f + (9a b d - 9a b c)e)h +--R + +--R 2 2 2 3 +--R ((9a b d - 9a b c)f + (- 9a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 +--R ((- 26a d + 26a b c)f + (26a b d - 26a b c)e)h +--R + +--R 2 2 2 3 +--R ((26a b d - 26a b c)f + (- 26a b d + 26b c)e)g +--R * +--R m +--R + +--R 3 2 2 2 +--R ((- 24a d + 24a b c)f + (24a b d - 24a b c)e)h +--R + +--R 2 2 2 3 +--R ((24a b d - 24a b c)f + (- 24a b d + 24b c)e)g +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x +--R + +--R 3 4 4 4 3 +--R (((a b d + b c)f + b d e)h + b d f g)m +--R + +--R 3 4 4 4 2 +--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R 3 4 4 4 4 4 +--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m + (8b c f + 8b d e)h +--R + +--R 4 +--R 8b d f g +--R * +--R 3 +--R x +--R + +--R 3 3 4 3 4 4 3 +--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h +--R + +--R 3 4 4 +--R ((5a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h +--R + +--R 3 4 4 +--R ((4a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 4 4 4 +--R 12b c e h + (12b c f + 12b d e)g +--R * +--R 2 +--R x +--R + +--R 3 3 3 4 3 +--R (a b c e h + (a b c f + (a b d + b c)e)g)m +--R + +--R 2 2 2 2 3 +--R (- 2a b c f + (- 2a b d + 7a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 2 3 +--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g +--R * +--R m +--R + +--R 4 +--R 24b c e g +--R * +--R x +--R + +--R 3 3 2 2 2 2 2 2 3 2 +--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m +--R + +--R 3 3 2 2 +--R (2a b c f + (2a b d - 7a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g +--R * +--R m +--R + +--R 4 3 3 2 2 +--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g +--R * +--R m log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 597 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x +--R + +--R 3 4 4 4 3 +--R (((a b d + b c)f + b d e)h + b d f g)m +--R + +--R 3 4 4 4 2 +--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R 3 4 4 4 +--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m +--R + +--R 4 4 4 +--R (8b c f + 8b d e)h + 8b d f g +--R * +--R 3 +--R x +--R + +--R 3 3 4 3 4 4 3 +--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h +--R + +--R 3 4 4 +--R ((5a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h +--R + +--R 3 4 4 +--R ((4a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 4 4 4 +--R 12b c e h + (12b c f + 12b d e)g +--R * +--R 2 +--R x +--R + +--R 3 3 3 4 3 +--R (a b c e h + (a b c f + (a b d + b c)e)g)m +--R + +--R 2 2 2 2 3 +--R (- 2a b c f + (- 2a b d + 7a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 2 3 +--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g +--R * +--R m +--R + +--R 4 +--R 24b c e g +--R * +--R x +--R + +--R 3 3 2 2 2 2 2 2 3 2 +--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m +--R + +--R 3 3 2 2 +--R (2a b c f + (2a b d - 7a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g +--R * +--R m +--R + +--R 4 3 3 2 2 +--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g +--R * +--R m log(b x + a) +--R %e +--R + +--R 3 2 m + 4 +--R (- d f h m - 6d f h m - 11d f h m - 6d f h)(b x + a) +--R + +--R 3 +--R (((3a d - b c)f - b d e)h - b d f g)m +--R + +--R 2 +--R (((21a d - 7b c)f - 7b d e)h - 7b d f g)m +--R + +--R (((42a d - 14b c)f - 14b d e)h - 14b d f g)m +--R + +--R ((24a d - 8b c)f - 8b d e)h - 8b d f g +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 2 +--R ((- 3a d + 2a b c)f + (2a b d - b c)e)h +--R + +--R 2 2 +--R ((2a b d - b c)f - b d e)g +--R * +--R 3 +--R m +--R + +--R 2 2 +--R ((- 24a d + 16a b c)f + (16a b d - 8b c)e)h +--R + +--R 2 2 +--R ((16a b d - 8b c)f - 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 +--R ((- 57a d + 38a b c)f + (38a b d - 19b c)e)h +--R + +--R 2 2 +--R ((38a b d - 19b c)f - 19b d e)g +--R * +--R m +--R + +--R 2 2 +--R ((- 36a d + 24a b c)f + (24a b d - 12b c)e)h +--R + +--R 2 2 +--R ((24a b d - 12b c)f - 12b d e)g +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((a d - a b c)f + (- a b d + a b c)e)h +--R + +--R 2 2 2 3 +--R ((- a b d + a b c)f + (a b d - b c)e)g +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 +--R ((9a d - 9a b c)f + (- 9a b d + 9a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 9a b d + 9a b c)f + (9a b d - 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 +--R ((26a d - 26a b c)f + (- 26a b d + 26a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 26a b d + 26a b c)f + (26a b d - 26b c)e)g +--R * +--R m +--R + +--R 3 2 2 2 +--R ((24a d - 24a b c)f + (- 24a b d + 24a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 24a b d + 24a b c)f + (24a b d - 24b c)e)g +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 571 + +--S 572 of 597 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 3 3 3 3 2 +--R b d f h x + ((b c f + b d e)h + b d f g)x +--R + +--R 3 3 3 3 +--R (b c e h + (b c f + b d e)g)x + b c e g +--R * +--R m log(b x + a) +--R %e +--R + +--R m + 3 +--R - d f h (b x + a) +--R + +--R m + 2 +--R (((3a d - b c)f - b d e)h - b d f g)(b x + a) +--R + +--R 2 2 2 2 +--R (((- 3a d + 2a b c)f + (2a b d - b c)e)h + ((2a b d - b c)f - b d e)g) +--R * +--R m + 1 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((a d - a b c)f + (- a b d + a b c)e)h +--R + +--R 2 2 2 3 +--R ((- a b d + a b c)f + (a b d - b c)e)g +--R * +--R m +--R (b x + a) +--R / +--R 3 +--R b +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 597 +t0:=(a+b*x)^m*(c+d*x)*(e+f*x)/(g+h*x) +--R +--R +--R 2 m +--R (d f x + (c f + d e)x + c e)(b x + a) +--R (1) --------------------------------------- +--R h x + g +--R Type: Expression(Integer) +--E 573 + +--S 574 of 597 +--r0:=(b*d*e*h*(2+m)+f*(b*c*h-d*(a*h+b*g*(2+m))))*(a+b*x)^(1+m)/_ +-- (b^2*h^2*(1+m)*(2+m))+f*(a+b*x)^(1+m)*(c+d*x)/(b*h*(2+m))+_ +-- (d*g-c*h)*(f*g-e*h)*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,_ +-- -h*(a+b*x)/(b*g-a*h))/(h^2*(b*g-a*h)*(1+m)) +--E 574 + +--S 575 of 597 +--a0:=integrate(t0,x) +--E 575 + +--S 576 of 597 +--m0:=a0-r0 +--E 576 + +--S 577 of 597 +--d0:=D(m0,x) +--E 577 + +)clear all + +--S 578 of 597 +t0:=(a+b*x)^m*(c+d*x)/((e+f*x)*(g+h*x)) +--R +--R +--R m +--R (d x + c)(b x + a) +--R (1) --------------------------- +--R 2 +--R f h x + (e h + f g)x + e g +--R Type: Expression(Integer) +--E 578 + +--S 579 of 597 +--r0:=-(d*e-c*f)*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_ +-- (f*g-e*h)*(1+m))+(d*g-c*h)*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_ +-- (f*g-e*h)*(1+m)) +--E 579 + +--S 580 of 597 +--a0:=integrate(t0,x) +--E 580 + +--S 581 of 597 +--m0:=a0-r0 +--E 581 + +--S 582 of 597 +--d0:=D(m0,x) +--E 582 + +)clear all + +--S 583 of 597 +t0:=(a+b*x)^m/((c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R m +--R (b x + a) +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g +--R Type: Expression(Integer) +--E 583 + +--S 584 of 597 +--r0:=d^2*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*(d*e-c*f)*(d*g-c*h)*(1+m))-f^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_ +-- (d*e-c*f)*(f*g-e*h)*(1+m))+h^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_ +-- (d*g-c*h)*(f*g-e*h)*(1+m)) +--E 584 + +--S 585 of 597 +--a0:=integrate(t0,x) +--E 585 + +--S 586 of 597 +--m0:=a0-r0 +--E 586 + +--S 587 of 597 +--d0:=D(m0,x) +--E 587 + +)clear all + +--S 588 of 597 +t0:=x/((1+x)*(2+x)*(3+x)) +--R +--R +--R x +--R (1) ------------------ +--R 3 2 +--R x + 6x + 11x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 588 + +--S 589 of 597 +r0:=-1/2*log(1+x)+2*log(2+x)-3/2*log(3+x) +--R +--R +--R - 3log(x + 3) + 4log(x + 2) - log(x + 1) +--R (2) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 597 +a0:=integrate(t0,x) +--R +--R +--R - 3log(x + 3) + 4log(x + 2) - log(x + 1) +--R (3) ---------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 597 +t0:=(-x^2+x^3)/((-6+x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R x - x +--R (1) ----------------------------------- +--R 4 3 2 +--R 125x - 525x - 1215x - 783x - 162 +--R Type: Fraction(Polynomial(Integer)) +--E 593 + +--S 594 of 597 +r0:=(-12/1375)/(3+5*x)^2+201/15125/(3+5*x)+_ + 20/3993*log(6-x)+1493/499125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (37325x + 44790x + 13437)log(5x + 3) +--R + +--R 2 +--R (62500x + 75000x + 22500)log(- x + 6) + 33165x + 15543 +--R / +--R 2 +--R 12478125x + 14973750x + 4492125 +--R Type: Expression(Integer) +--E 594 + +--S 595 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (37325x + 44790x + 13437)log(5x + 3) +--R + +--R 2 +--R (62500x + 75000x + 22500)log(x - 6) + 33165x + 15543 +--R / +--R 2 +--R 12478125x + 14973750x + 4492125 +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 597 +m0:=a0-r0 +--R +--R +--R 20log(x - 6) - 20log(- x + 6) +--R (4) ----------------------------- +--R 3993 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich3t.input.pdf b/src/axiom-website/CATS/rich3t.input.pdf new file mode 100644 index 0000000..994820e Binary files /dev/null and b/src/axiom-website/CATS/rich3t.input.pdf differ diff --git a/src/axiom-website/CATS/rich4a.input.pamphlet b/src/axiom-website/CATS/rich4a.input.pamphlet new file mode 100644 index 0000000..45696d2 --- /dev/null +++ b/src/axiom-website/CATS/rich4a.input.pamphlet @@ -0,0 +1,20344 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 311 matching answers. +\item 59 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4a.output +)spool rich4a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1393 +t0:=x^m*(a+b*x^2) +--R +--R +--R 2 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1393 +r0:=a*x^(1+m)/(1+m)+b*x^(3+m)/(3+m) +--R +--R +--R m + 3 m + 1 +--R (b m + b)x + (a m + 3a)x +--R (2) ---------------------------------- +--R 2 +--R m + 4m + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 m log(x) +--R ((b m + b)x + (a m + 3a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 4m + 3 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 m log(x) m + 3 +--R ((b m + b)x + (a m + 3a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 3a)x +--R / +--R 2 +--R m + 4m + 3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1393 +t0:=x^4*(a+b*x^2) +--R +--R +--R 6 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1393 +r0:=1/5*a*x^5+1/7*b*x^7 +--R +--R +--R 1 7 1 5 +--R (2) - b x + - a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 5 +--R (3) - b x + - a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 1393 +t0:=x^3*(a+b*x^2) +--R +--R +--R 5 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1393 +r0:=1/4*a*x^4+1/6*b*x^6 +--R +--R +--R 1 6 1 4 +--R (2) - b x + - a x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 4 +--R (3) - b x + - a x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 1393 +t0:=x^2*(a+b*x^2) +--R +--R +--R 4 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1393 +r0:=1/3*a*x^3+1/5*b*x^5 +--R +--R +--R 1 5 1 3 +--R (2) - b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 3 +--R (3) - b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 1393 +t0:=x*(a+b*x^2) +--R +--R +--R 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1393 +r0:=1/2*a*x^2+1/4*b*x^4 +--R +--R +--R 1 4 1 2 +--R (2) - b x + - a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 2 +--R (3) - b x + - a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1393 +t0:=a+b*x^2 +--R +--R +--R 2 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1393 +r0:=a*x+1/3*b*x^3 +--R +--R +--R 1 3 +--R (2) - b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 +--R (3) - b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1393 +t0:=(a+b*x^2)/x +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1393 +r0:=1/2*b*x^2+a*log(x) +--R +--R +--R 2 +--R 2a log(x) + b x +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2a log(x) + b x +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1393 +t0:=(a+b*x^2)/x^2 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1393 +r0:=-a/x+b*x +--R +--R +--R 2 +--R b x - a +--R (2) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 37 + +--S 38 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x - a +--R (3) -------- +--R x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1393 +t0:=(a+b*x^2)/x^3 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1393 +r0:=-1/2*a/x^2+b*log(x) +--R +--R +--R 2 +--R 2b x log(x) - a +--R (2) --------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x log(x) - a +--R (3) --------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1393 +t0:=(a+b*x^2)/x^4 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1393 +r0:=-1/3*a/x^3-b/x +--R +--R +--R 2 1 +--R - b x - - a +--R 3 +--R (2) ------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3b x - a +--R (3) ----------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1393 +t0:=(a+b*x^2)/x^5 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1393 +r0:=-1/4*a/x^4-1/2*b/x^2 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 2 4 +--R (2) -------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2b x - a +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1393 +t0:=(a+b*x^2)/x^6 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1393 +r0:=-1/5*a/x^5-1/3*b/x^3 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 3 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5b x - 3a +--R (3) ------------ +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1393 +t0:=(a+b*x^2)/x^7 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1393 +r0:=-1/6*a/x^6-1/4*b/x^4 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 4 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3b x - 2a +--R (3) ------------ +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1393 +t0:=x^m*(a+b*x^2)^2 +--R +--R +--R 2 4 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1393 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(3+m)/(3+m)+b^2*x^(5+m)/(5+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 5 2 m + 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 8a m + 15a )x +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 5 2 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 +--R (a m + 8a m + 15a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 5 2 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 +--R (a m + 8a m + 15a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 5 2 m + 3 +--R (- b m - 4b m - 3b )x + (- 2a b m - 12a b m - 10a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 8a m - 15a )x +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1393 +t0:=x^5*(a+b*x^2)^2 +--R +--R +--R 2 9 7 2 5 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1393 +r0:=1/6*a^2*x^6+1/4*a*b*x^8+1/10*b^2*x^10 +--R +--R +--R 1 2 10 1 8 1 2 6 +--R (2) -- b x + - a b x + - a x +--R 10 4 6 +--R Type: Polynomial(Fraction(Integer)) +--E 72 + +--S 73 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 1 8 1 2 6 +--R (3) -- b x + - a b x + - a x +--R 10 4 6 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 1393 +t0:=x^4*(a+b*x^2)^2 +--R +--R +--R 2 8 6 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1393 +r0:=1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9 +--R +--R +--R 1 2 9 2 7 1 2 5 +--R (2) - b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 2 7 1 2 5 +--R (3) - b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1393 +t0:=x^3*(a+b*x^2)^2 +--R +--R +--R 2 7 5 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1393 +r0:=1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8 +--R +--R +--R 1 2 8 1 6 1 2 4 +--R (2) - b x + - a b x + - a x +--R 8 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 1 6 1 2 4 +--R (3) - b x + - a b x + - a x +--R 8 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1393 +t0:=x^2*(a+b*x^2)^2 +--R +--R +--R 2 6 4 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1393 +r0:=1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7 +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (2) - b x + - a b x + - a x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (3) - b x + - a b x + - a x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1393 +t0:=x*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1393 +r0:=1/6*(a+b*x^2)^3/b +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - b x + - a b x + - a b x + - a +--R 6 2 2 6 +--R (2) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 4 1 2 2 +--R (3) - b x + - a b x + - a x +--R 6 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1393 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - a +--R 6 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 94 + +--S 95 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +)clear all + +--S 96 of 1393 +t0:=(a+b*x^2)^2 +--R +--R +--R 2 4 2 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1393 +r0:=a^2*x+2/3*a*b*x^3+1/5*b^2*x^5 +--R +--R +--R 1 2 5 2 3 2 +--R (2) - b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 2 3 2 +--R (3) - b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1393 +t0:=(a+b*x^2)^2/x +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1393 +r0:=a*b*x^2+1/4*b^2*x^4+a^2*log(x) +--R +--R +--R 2 2 4 2 +--R 4a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1393 +t0:=(a+b*x^2)^2/x^2 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1393 +r0:=-a^2/x+2*a*b*x+1/3*b^2*x^3 +--R +--R +--R 2 4 2 2 +--R b x + 6a b x - 3a +--R (2) -------------------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 107 + +--S 108 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R b x + 6a b x - 3a +--R (3) -------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1393 +t0:=(a+b*x^2)^2/x^3 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1393 +r0:=-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*log(x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + b x - a +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + b x - a +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1393 +t0:=(a+b*x^2)^2/x^4 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1393 +r0:=-1/3*a^2/x^3-2*a*b/x+b^2*x +--R +--R +--R 2 4 2 1 2 +--R b x - 2a b x - - a +--R 3 +--R (2) --------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 3b x - 6a b x - a +--R (3) -------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1393 +t0:=(a+b*x^2)^2/x^5 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1393 +r0:=-1/4*a^2/x^4-a*b/x^2+b^2*log(x) +--R +--R +--R 2 4 2 2 +--R 4b x log(x) - 4a b x - a +--R (2) -------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 4b x log(x) - 4a b x - a +--R (3) -------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1393 +t0:=(a+b*x^2)^2/x^6 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1393 +r0:=-1/5*a^2/x^5-2/3*a*b/x^3-b^2/x +--R +--R +--R 2 4 2 2 1 2 +--R - b x - - a b x - - a +--R 3 5 +--R (2) ------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 15b x - 10a b x - 3a +--R (3) ------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1393 +t0:=(a+b*x^2)^2/x^7 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 1393 +r0:=-1/6*(a+b*x^2)^3/(a*x^6) +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 2 2 6 +--R (2) ------------------------------------- +--R 6 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 132 + +--S 133 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 3b x - 3a b x - a +--R (3) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1393 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R 6a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1393 +t0:=(a+b*x^2)^2/x^8 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 1393 +r0:=-1/7*a^2/x^7-2/5*a*b/x^5-1/3*b^2/x^3 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - b x - - a b x - - a +--R 3 5 7 +--R (2) -------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 35b x - 42a b x - 15a +--R (3) -------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1393 +t0:=(a+b*x^2)^2/x^9 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 1393 +r0:=-1/8*a^2/x^8-1/3*a*b/x^6-1/4*b^2/x^4 +--R +--R +--R 1 2 4 1 2 1 2 +--R - - b x - - a b x - - a +--R 4 3 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +--S 143 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 6b x - 8a b x - 3a +--R (3) ----------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1393 +t0:=(a+b*x^2)^2/x^10 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1393 +r0:=-1/9*a^2/x^9-2/7*a*b/x^7-1/5*b^2/x^5 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - b x - - a b x - - a +--R 5 7 9 +--R (2) -------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 63b x - 90a b x - 35a +--R (3) -------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1393 +t0:=x^m*(a+b*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1393 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(3+m)/(3+m)+3*a*b^2*x^(5+m)/(5+m)+_ + b^3*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 15a m + 71a m + 105a )x +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 15a m + 71a m + 105a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 15a m + 71a m + 105a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 7 +--R (- b m - 9b m - 23b m - 15b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (- 3a b m - 33a b m - 93a b m - 63a b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 39a b m - 141a b m - 105a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 15a m - 71a m - 105a )x +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1393 +t0:=x^9*(a+b*x^2)^3 +--R +--R +--R 3 15 2 13 2 11 3 9 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1393 +r0:=1/10*a^3*x^10+1/4*a^2*b*x^12+3/14*a*b^2*x^14+1/16*b^3*x^16 +--R +--R +--R 1 3 16 3 2 14 1 2 12 1 3 10 +--R (2) -- b x + -- a b x + - a b x + -- a x +--R 16 14 4 10 +--R Type: Polynomial(Fraction(Integer)) +--E 157 + +--S 158 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 16 3 2 14 1 2 12 1 3 10 +--R (3) -- b x + -- a b x + - a b x + -- a x +--R 16 14 4 10 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 159 + +--S 160 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 160 + +)clear all + +--S 161 of 1393 +t0:=x^7*(a+b*x^2)^3 +--R +--R +--R 3 13 2 11 2 9 3 7 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 1393 +r0:=1/8*a^3*x^8+3/10*a^2*b*x^10+1/4*a*b^2*x^12+1/14*b^3*x^14 +--R +--R +--R 1 3 14 1 2 12 3 2 10 1 3 8 +--R (2) -- b x + - a b x + -- a b x + - a x +--R 14 4 10 8 +--R Type: Polynomial(Fraction(Integer)) +--E 162 + +--S 163 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 1 2 12 3 2 10 1 3 8 +--R (3) -- b x + - a b x + -- a b x + - a x +--R 14 4 10 8 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 164 + +--S 165 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 165 + +)clear all + +--S 166 of 1393 +t0:=x^5*(a+b*x^2)^3 +--R +--R +--R 3 11 2 9 2 7 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 166 + +--S 167 of 1393 +r0:=1/6*a^3*x^6+3/8*a^2*b*x^8+3/10*a*b^2*x^10+1/12*b^3*x^12 +--R +--R +--R 1 3 12 3 2 10 3 2 8 1 3 6 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 12 10 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 167 + +--S 168 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 12 3 2 10 3 2 8 1 3 6 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 12 10 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 168 + +--S 169 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 169 + +--S 170 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 170 + +)clear all + +--S 171 of 1393 +t0:=x^3*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 171 + +--S 172 of 1393 +r0:=-1/8*a*(a+b*x^2)^4/b^2+1/10*(a+b*x^2)^5/b^2 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 10 8 2 4 40 +--R (2) ------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 10 3 2 8 1 2 6 1 3 4 +--R (3) -- b x + - a b x + - a b x + - a x +--R 10 8 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 173 + +--S 174 of 1393 +m0:=a0-r0 +--R +--R +--R 1 5 +--R -- a +--R 40 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 174 + +--S 175 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 175 + +)clear all + +--S 176 of 1393 +t0:=x*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 1393 +r0:=1/8*(a+b*x^2)^4/b +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - b x + - a b x + - a b x + - a b x + - a +--R 8 2 4 2 8 +--R (2) ---------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 8 1 2 6 3 2 4 1 3 2 +--R (3) - b x + - a b x + - a b x + - a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 1393 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 180 + +)clear all + +--S 181 of 1393 +t0:=(a+b*x^2)^3/x +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1393 +r0:=3/2*a^2*b*x^2+3/4*a*b^2*x^4+1/6*b^3*x^6+a^3*log(x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12a log(x) + 2b x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12a log(x) + 2b x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1393 +t0:=(a+b*x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1393 +r0:=-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*log(x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1393 +t0:=(a+b*x^2)^3/x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1393 +r0:=-1/4*a^3/x^4-3/2*a^2*b/x^2+1/2*b^3*x^2+3*a*b^2*log(x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2b x - 6a b x - a +--R (2) ------------------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2b x - 6a b x - a +--R (3) ------------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1393 +t0:=(a+b*x^2)^3/x^7 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1393 +r0:=-1/6*a^3/x^6-3/4*a^2*b/x^4-3/2*a*b^2/x^2+b^3*log(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12b x log(x) - 18a b x - 9a b x - 2a +--R (2) --------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12b x log(x) - 18a b x - 9a b x - 2a +--R (3) --------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1393 +t0:=(a+b*x^2)^3/x^9 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1393 +r0:=-1/8*(a+b*x^2)^4/(a*x^8) +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 8 2 4 2 8 +--R (2) ------------------------------------------------ +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1393 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) -- +--R 8a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1393 +t0:=(a+b*x^2)^3/x^11 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1393 +r0:=-1/10*a^3/x^10-3/8*a^2*b/x^8-1/2*a*b^2/x^6-1/4*b^3/x^4 +--R +--R +--R 1 3 6 1 2 4 3 2 2 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 4 2 8 10 +--R (2) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 207 + +--S 208 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ------------------------------------ +--R 10 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1393 +t0:=(a+b*x^2)^3/x^13 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1393 +r0:=-1/12*a^3/x^12-3/10*a^2*b/x^10-3/8*a*b^2/x^8-1/6*b^3/x^6 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - b x - - a b x - -- a b x - -- a +--R 6 8 10 12 +--R (2) --------------------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------- +--R 12 +--R 120x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1393 +t0:=(a+b*x^2)^3/x^15 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1393 +r0:=-1/14*a^3/x^14-1/4*a^2*b/x^12-3/10*a*b^2/x^10-1/8*b^3/x^8 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - b x - -- a b x - - a b x - -- a +--R 8 10 4 14 +--R (2) --------------------------------------- +--R 14 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------- +--R 14 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1393 +t0:=x^6*(a+b*x^2)^3 +--R +--R +--R 3 12 2 10 2 8 3 6 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1393 +r0:=1/7*a^3*x^7+1/3*a^2*b*x^9+3/11*a*b^2*x^11+1/13*b^3*x^13 +--R +--R +--R 1 3 13 3 2 11 1 2 9 1 3 7 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 13 11 3 7 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 3 2 11 1 2 9 1 3 7 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 13 11 3 7 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 1393 +t0:=x^4*(a+b*x^2)^3 +--R +--R +--R 3 10 2 8 2 6 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1393 +r0:=1/5*a^3*x^5+3/7*a^2*b*x^7+1/3*a*b^2*x^9+1/11*b^3*x^11 +--R +--R +--R 1 3 11 1 2 9 3 2 7 1 3 5 +--R (2) -- b x + - a b x + - a b x + - a x +--R 11 3 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 11 1 2 9 3 2 7 1 3 5 +--R (3) -- b x + - a b x + - a b x + - a x +--R 11 3 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 1393 +t0:=x^2*(a+b*x^2)^3 +--R +--R +--R 3 8 2 6 2 4 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1393 +r0:=1/3*a^3*x^3+3/5*a^2*b*x^5+3/7*a*b^2*x^7+1/9*b^3*x^9 +--R +--R +--R 1 3 9 3 2 7 3 2 5 1 3 3 +--R (2) - b x + - a b x + - a b x + - a x +--R 9 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 9 3 2 7 3 2 5 1 3 3 +--R (3) - b x + - a b x + - a b x + - a x +--R 9 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 1393 +t0:=(a+b*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1393 +r0:=a^3*x+a^2*b*x^3+3/5*a*b^2*x^5+1/7*b^3*x^7 +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (2) - b x + - a b x + a b x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 237 + +--S 238 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (3) - b x + - a b x + a b x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 239 + +--S 240 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 240 + +)clear all + +--S 241 of 1393 +t0:=(a+b*x^2)^3/x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1393 +r0:=-a^3/x+3*a^2*b*x+a*b^2*x^3+1/5*b^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 5a b x + 15a b x - 5a +--R (2) ------------------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 242 + +--S 243 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 5a b x + 15a b x - 5a +--R (3) ------------------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1393 +t0:=(a+b*x^2)^3/x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1393 +r0:=-1/3*a^3/x^3-3*a^2*b/x+3*a*b^2*x+1/3*b^3*x^3 +--R +--R +--R 1 3 6 2 4 2 2 1 3 +--R - b x + 3a b x - 3a b x - - a +--R 3 3 +--R (2) --------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 9a b x - 9a b x - a +--R (3) ----------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1393 +t0:=(a+b*x^2)^3/x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1393 +r0:=-1/5*a^3/x^5-a^2*b/x^3-3*a*b^2/x+b^3*x +--R +--R +--R 3 6 2 4 2 2 1 3 +--R b x - 3a b x - a b x - - a +--R 5 +--R (2) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 252 + +--S 253 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 5b x - 15a b x - 5a b x - a +--R (3) ------------------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1393 +t0:=(a+b*x^2)^3/x^8 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1393 +r0:=-1/7*a^3/x^7-3/5*a^2*b/x^5-a*b^2/x^3-b^3/x +--R +--R +--R 3 6 2 4 3 2 2 1 3 +--R - b x - a b x - - a b x - - a +--R 5 7 +--R (2) --------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 35a b x - 21a b x - 5a +--R (3) ------------------------------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1393 +t0:=(a+b*x^2)^3/x^10 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1393 +r0:=-1/9*a^3/x^9-3/7*a^2*b/x^7-3/5*a*b^2/x^5-1/3*b^3/x^3 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 3 5 7 9 +--R (2) ------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 105b x - 189a b x - 135a b x - 35a +--R (3) ---------------------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1393 +t0:=(a+b*x^2)^3/x^12 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1393 +r0:=-1/11*a^3/x^11-1/3*a^2*b/x^9-3/7*a*b^2/x^7-1/5*b^3/x^5 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 5 7 3 11 +--R (2) -------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 231b x - 495a b x - 385a b x - 105a +--R (3) ----------------------------------------- +--R 11 +--R 1155x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1393 +t0:=x^m*(a+b*x^2)^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1393 +r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(3+m)/(3+m)+10*a^3*b^2*x^(5+m)/(5+m)+_ + 10*a^2*b^3*x^(7+m)/(7+m)+5*a*b^4*x^(9+m)/(9+m)+b^5*x^(11+m)/(11+m) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m + 5775a b ) +--R * +--R m + 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R m + 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R m + 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R m + 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m +--R + +--R 4 +--R 5775a b +--R * +--R 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R * +--R m log(x) +--R %e +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 3 5 2 5 5 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m +--R + +--R 4 +--R 5775a b +--R * +--R 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R * +--R m log(x) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 11 +--R (- b m - 25b m - 230b m - 950b m - 1689b m - 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 135a b m - 1310a b m - 5610a b m - 10205a b m +--R + +--R 4 +--R - 5775a b +--R * +--R m + 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R - 10a b m - 290a b m - 3020a b m - 13660a b m - 25770a b m +--R + +--R 2 3 +--R - 14850a b +--R * +--R m + 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R - 10a b m - 310a b m - 3500a b m - 17300a b m - 34890a b m +--R + +--R 3 2 +--R - 20790a b +--R * +--R m + 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 165a b m - 2030a b m - 11310a b m - 26765a b m +--R + +--R 4 +--R - 17325a b +--R * +--R m + 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (- a m - 35a m - 470a m - 3010a m - 9129a m - 10395a )x +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1393 +t0:=x^11*(a+b*x^2)^5 +--R +--R +--R 5 21 4 19 2 3 17 3 2 15 4 13 5 11 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 276 + +--S 277 of 1393 +r0:=1/12*a^5*x^12+5/14*a^4*b*x^14+5/8*a^3*b^2*x^16+5/9*a^2*b^3*x^18+_ + 1/4*a*b^4*x^20+1/22*b^5*x^22 +--R +--R +--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12 +--R (2) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x +--R 22 4 9 8 14 12 +--R Type: Polynomial(Fraction(Integer)) +--E 277 + +--S 278 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12 +--R (3) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x +--R 22 4 9 8 14 12 +--R Type: Polynomial(Fraction(Integer)) +--E 278 + +--S 279 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 279 + +--S 280 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 280 + +)clear all + +--S 281 of 1393 +t0:=x^9*(a+b*x^2)^5 +--R +--R +--R 5 19 4 17 2 3 15 3 2 13 4 11 5 9 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 281 + +--S 282 of 1393 +r0:=1/10*a^5*x^10+5/12*a^4*b*x^12+5/7*a^3*b^2*x^14+5/8*a^2*b^3*x^16+_ + 5/18*a*b^4*x^18+1/20*b^5*x^20 +--R +--R +--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10 +--R (2) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x +--R 20 18 8 7 12 10 +--R Type: Polynomial(Fraction(Integer)) +--E 282 + +--S 283 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10 +--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x +--R 20 18 8 7 12 10 +--R Type: Polynomial(Fraction(Integer)) +--E 283 + +--S 284 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 284 + +--S 285 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 285 + +)clear all + +--S 286 of 1393 +t0:=x^7*(a+b*x^2)^5 +--R +--R +--R 5 17 4 15 2 3 13 3 2 11 4 9 5 7 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 286 + +--S 287 of 1393 +r0:=1/8*a^5*x^8+1/2*a^4*b*x^10+5/6*a^3*b^2*x^12+5/7*a^2*b^3*x^14+_ + 5/16*a*b^4*x^16+1/18*b^5*x^18 +--R +--R +--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8 +--R (2) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 18 16 7 6 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 287 + +--S 288 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8 +--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 18 16 7 6 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 288 + +--S 289 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 289 + +--S 290 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 290 + +)clear all + +--S 291 of 1393 +t0:=x^5*(a+b*x^2)^5 +--R +--R +--R 5 15 4 13 2 3 11 3 2 9 4 7 5 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 291 + +--S 292 of 1393 +r0:=1/12*a^2*(a+b*x^2)^6/b^3-1/7*a*(a+b*x^2)^7/b^3+1/16*(a+b*x^2)^8/b^3 +--R +--R +--R (2) +--R 1 8 16 5 7 14 5 2 6 12 3 5 10 5 4 4 8 1 5 3 6 1 8 +--R -- b x + -- a b x + - a b x + a b x + - a b x + - a b x + --- a +--R 16 14 6 8 6 336 +--R -------------------------------------------------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 16 5 4 14 5 2 3 12 3 2 10 5 4 8 1 5 6 +--R (3) -- b x + -- a b x + - a b x + a b x + - a b x + - a x +--R 16 14 6 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 293 + +--S 294 of 1393 +m0:=a0-r0 +--R +--R +--R 1 8 +--R --- a +--R 336 +--R (4) - ------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 294 + +--S 295 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 295 + +)clear all + +--S 296 of 1393 +t0:=x^3*(a+b*x^2)^5 +--R +--R +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 296 + +--S 297 of 1393 +r0:=-1/12*a*(a+b*x^2)^6/b^2+1/14*(a+b*x^2)^7/b^2 +--R +--R +--R (2) +--R 1 7 14 5 6 12 2 5 10 5 3 4 8 5 4 3 6 1 5 2 4 1 7 +--R -- b x + -- a b x + a b x + - a b x + - a b x + - a b x - -- a +--R 14 12 4 6 4 84 +--R ------------------------------------------------------------------------ +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 14 5 4 12 2 3 10 5 3 2 8 5 4 6 1 5 4 +--R (3) -- b x + -- a b x + a b x + - a b x + - a b x + - a x +--R 14 12 4 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 298 + +--S 299 of 1393 +m0:=a0-r0 +--R +--R +--R 1 7 +--R -- a +--R 84 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 299 + +--S 300 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 300 + +)clear all + +--S 301 of 1393 +t0:=x*(a+b*x^2)^5 +--R +--R +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 301 + +--S 302 of 1393 +r0:=1/12*(a+b*x^2)^6/b +--R +--R +--R (2) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x + - a b x + -- a +--R 12 2 4 3 4 2 12 +--R ------------------------------------------------------------------------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 12 1 4 10 5 2 3 8 5 3 2 6 5 4 4 1 5 2 +--R (3) -- b x + - a b x + - a b x + - a b x + - a b x + - a x +--R 12 2 4 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 303 + +--S 304 of 1393 +m0:=a0-r0 +--R +--R +--R 1 6 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 304 + +--S 305 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 305 + +)clear all + +--S 306 of 1393 +t0:=(a+b*x^2)^5/x +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1393 +r0:=5/2*a^4*b*x^2+5/2*a^3*b^2*x^4+5/3*a^2*b^3*x^6+5/8*a*b^4*x^8+_ + 1/10*b^5*x^10+a^5*log(x) +--R +--R +--R 5 5 10 4 8 2 3 6 3 2 4 4 2 +--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (2) -------------------------------------------------------------------- +--R 120 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 5 10 4 8 2 3 6 3 2 4 4 2 +--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (3) -------------------------------------------------------------------- +--R 120 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1393 +t0:=(a+b*x^2)^5/x^3 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1393 +r0:=-1/2*a^5/x^2+5*a^3*b^2*x^2+5/2*a^2*b^3*x^4+5/6*a*b^4*x^6+_ + 1/8*b^5*x^8+5*a^4*b*log(x) +--R +--R +--R 4 2 5 10 4 8 2 3 6 3 2 4 5 +--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 24x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 2 5 10 4 8 2 3 6 3 2 4 5 +--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (3) ----------------------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1393 +t0:=(a+b*x^2)^5/x^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1393 +r0:=-1/4*a^5/x^4-5/2*a^4*b/x^2+5*a^2*b^3*x^2+5/4*a*b^4*x^4+_ + 1/6*b^5*x^6+10*a^3*b^2*log(x) +--R +--R +--R 3 2 4 5 10 4 8 2 3 6 4 2 5 +--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (2) --------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 2 4 5 10 4 8 2 3 6 4 2 5 +--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (3) --------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1393 +t0:=(a+b*x^2)^5/x^7 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1393 +r0:=-1/6*a^5/x^6-5/4*a^4*b/x^4-5*a^3*b^2/x^2+5/2*a*b^4*x^2+_ + 1/4*b^5*x^4+10*a^2*b^3*log(x) +--R +--R +--R 2 3 6 5 10 4 8 3 2 4 4 2 5 +--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (2) --------------------------------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 3 6 5 10 4 8 3 2 4 4 2 5 +--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (3) --------------------------------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1393 +t0:=(a+b*x^2)^5/x^9 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1393 +r0:=-1/8*a^5/x^8-5/6*a^4*b/x^6-5/2*a^3*b^2/x^4-5*a^2*b^3/x^2+_ + 1/2*b^5*x^2+5*a*b^4*log(x) +--R +--R +--R 4 8 5 10 2 3 6 3 2 4 4 2 5 +--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (2) ----------------------------------------------------------------- +--R 8 +--R 24x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 8 5 10 2 3 6 3 2 4 4 2 5 +--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (3) ----------------------------------------------------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1393 +t0:=(a+b*x^2)^5/x^11 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1393 +r0:=-1/10*a^5/x^10-5/8*a^4*b/x^8-5/3*a^3*b^2/x^6-5/2*a^2*b^3/x^4-_ + 5/2*a*b^4/x^2+b^5*log(x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (2) -------------------------------------------------------------------- +--R 10 +--R 120x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (3) -------------------------------------------------------------------- +--R 10 +--R 120x +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1393 +t0:=(a+b*x^2)^5/x^13 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1393 +r0:=-1/12*(a+b*x^2)^6/(a*x^12) +--R +--R +--R (2) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R - -- b x - - a b x - - a b x - - a b x - - a b x - - a b x - -- a +--R 12 2 4 3 4 2 12 +--R -------------------------------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (3) -------------------------------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1393 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) --- +--R 12a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1393 +t0:=(a+b*x^2)^5/x^15 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1393 +r0:=-1/14*(a+b*x^2)^6/(a*x^14)+1/84*b*(a+b*x^2)^6/(a^2*x^12) +--R +--R +--R (2) +--R 1 7 14 1 2 5 10 5 3 4 8 5 4 3 6 5 2 4 5 6 2 1 7 +--R -- b x - - a b x - - a b x - - a b x - a b x - -- a b x - -- a +--R 84 4 6 4 12 14 +--R ----------------------------------------------------------------------- +--R 2 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (3) ------------------------------------------------------------ +--R 14 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1393 +m0:=a0-r0 +--R +--R +--R 7 +--R b +--R (4) - ---- +--R 2 +--R 84a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1393 +t0:=(a+b*x^2)^5/x^17 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1393 +r0:=-1/16*a^5/x^16-5/14*a^4*b/x^14-5/6*a^3*b^2/x^12-a^2*b^3/x^10-_ + 5/8*a*b^4/x^8-1/6*b^5/x^6 +--R +--R +--R 1 5 10 5 4 8 2 3 6 5 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - a b x - - a b x - -- a b x - -- a +--R 6 8 6 14 16 +--R (2) ------------------------------------------------------------ +--R 16 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a +--R (3) ---------------------------------------------------------------- +--R 16 +--R 336x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1393 +t0:=(a+b*x^2)^5/x^19 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1393 +r0:=-1/18*a^5/x^18-5/16*a^4*b/x^16-5/7*a^3*b^2/x^14-5/6*a^2*b^3/x^12-_ + 1/2*a*b^4/x^10-1/8*b^5/x^8 +--R +--R +--R 1 5 10 1 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - - a b x - - a b x - -- a b x - -- a +--R 8 2 6 7 16 18 +--R (2) -------------------------------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) ----------------------------------------------------------------- +--R 18 +--R 1008x +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1393 +t0:=(a+b*x^2)^5/x^21 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1393 +r0:=-1/20*a^5/x^20-5/18*a^4*b/x^18-5/8*a^3*b^2/x^16-5/7*a^2*b^3/x^14-_ + 5/12*a*b^4/x^12-1/10*b^5/x^10 +--R +--R +--R 1 5 10 5 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5 +--R - -- b x - -- a b x - - a b x - - a b x - -- a b x - -- a +--R 10 12 7 8 18 20 +--R (2) ---------------------------------------------------------------- +--R 20 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 357 + +--S 358 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a +--R (3) --------------------------------------------------------------------- +--R 20 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1393 +t0:=x^8*(a+b*x^2)^5 +--R +--R +--R 5 18 4 16 2 3 14 3 2 12 4 10 5 8 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 1393 +r0:=1/9*a^5*x^9+5/11*a^4*b*x^11+10/13*a^3*b^2*x^13+2/3*a^2*b^3*x^15+_ + 5/17*a*b^4*x^17+1/19*b^5*x^19 +--R +--R +--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9 +--R (2) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x +--R 19 17 3 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 362 + +--S 363 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9 +--R (3) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x +--R 19 17 3 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 1393 +t0:=x^6*(a+b*x^2)^5 +--R +--R +--R 5 16 4 14 2 3 12 3 2 10 4 8 5 6 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 366 + +--S 367 of 1393 +r0:=1/7*a^5*x^7+5/9*a^4*b*x^9+10/11*a^3*b^2*x^11+10/13*a^2*b^3*x^13+_ + 1/3*a*b^4*x^15+1/17*b^5*x^17 +--R +--R +--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7 +--R (2) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x +--R 17 3 13 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 367 + +--S 368 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7 +--R (3) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x +--R 17 3 13 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 368 + +--S 369 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 369 + +--S 370 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 370 + +)clear all + +--S 371 of 1393 +t0:=x^4*(a+b*x^2)^5 +--R +--R +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 371 + +--S 372 of 1393 +r0:=1/5*a^5*x^5+5/7*a^4*b*x^7+10/9*a^3*b^2*x^9+10/11*a^2*b^3*x^11+_ + 5/13*a*b^4*x^13+1/15*b^5*x^15 +--R +--R +--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5 +--R (2) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x +--R 15 13 11 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 372 + +--S 373 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5 +--R (3) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x +--R 15 13 11 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 373 + +--S 374 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 374 + +--S 375 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 375 + +)clear all + +--S 376 of 1393 +t0:=x^2*(a+b*x^2)^5 +--R +--R +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 376 + +--S 377 of 1393 +r0:=1/3*a^5*x^3+a^4*b*x^5+10/7*a^3*b^2*x^7+10/9*a^2*b^3*x^9+_ + 5/11*a*b^4*x^11+1/13*b^5*x^13 +--R +--R +--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3 +--R (2) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x +--R 13 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 377 + +--S 378 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3 +--R (3) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x +--R 13 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 378 + +--S 379 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 379 + +--S 380 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 380 + +)clear all + +--S 381 of 1393 +t0:=(a+b*x^2)^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 381 + +--S 382 of 1393 +r0:=a^5*x+5/3*a^4*b*x^3+2*a^3*b^2*x^5+10/7*a^2*b^3*x^7+5/9*a*b^4*x^9+_ + 1/11*b^5*x^11 +--R +--R +--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5 +--R (2) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x +--R 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 382 + +--S 383 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5 +--R (3) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x +--R 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 383 + +--S 384 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 384 + +--S 385 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 385 + +)clear all + +--S 386 of 1393 +t0:=(a+b*x^2)^5/x^2 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1393 +r0:=-a^5/x+5*a^4*b*x+10/3*a^3*b^2*x^3+2*a^2*b^3*x^5+5/7*a*b^4*x^7+1/9*b^5*x^9 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a +--R (2) ------------------------------------------------------------ +--R 63x +--R Type: Fraction(Polynomial(Integer)) +--E 387 + +--S 388 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a +--R (3) ------------------------------------------------------------ +--R 63x +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1393 +t0:=(a+b*x^2)^5/x^4 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1393 +r0:=-1/3*a^5/x^3-5*a^4*b/x+10*a^3*b^2*x+10/3*a^2*b^3*x^3+a*b^4*x^5+1/7*b^5*x^7 +--R +--R +--R 1 5 10 4 8 10 2 3 6 3 2 4 4 2 1 5 +--R - b x + a b x + -- a b x + 10a b x - 5a b x - - a +--R 7 3 3 +--R (2) -------------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 392 + +--S 393 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 21a b x + 70a b x + 210a b x - 105a b x - 7a +--R (3) ---------------------------------------------------------- +--R 3 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1393 +t0:=(a+b*x^2)^5/x^6 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1393 +r0:=-1/5*a^5/x^5-5/3*a^4*b/x^3-10*a^3*b^2/x+10*a^2*b^3*x+_ + 5/3*a*b^4*x^3+1/5*b^5*x^5 +--R +--R +--R 1 5 10 5 4 8 2 3 6 3 2 4 5 4 2 1 5 +--R - b x + - a b x + 10a b x - 10a b x - - a b x - - a +--R 5 3 3 5 +--R (2) ---------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x + 150a b x - 150a b x - 25a b x - 3a +--R (3) ---------------------------------------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1393 +t0:=(a+b*x^2)^5/x^8 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1393 +r0:=-1/7*a^5/x^7-a^4*b/x^5-10/3*a^3*b^2/x^3-10*a^2*b^3/x+5*a*b^4*x+1/3*b^5*x^3 +--R +--R +--R 1 5 10 4 8 2 3 6 10 3 2 4 4 2 1 5 +--R - b x + 5a b x - 10a b x - -- a b x - a b x - - a +--R 3 3 7 +--R (2) -------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 402 + +--S 403 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 105a b x - 210a b x - 70a b x - 21a b x - 3a +--R (3) ---------------------------------------------------------- +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1393 +t0:=(a+b*x^2)^5/x^10 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1393 +r0:=-1/9*a^5/x^9-5/7*a^4*b/x^7-2*a^3*b^2/x^5-10/3*a^2*b^3/x^3-5*a*b^4/x+b^5*x +--R +--R +--R 5 10 4 8 10 2 3 6 3 2 4 5 4 2 1 5 +--R b x - 5a b x - -- a b x - 2a b x - - a b x - - a +--R 3 7 9 +--R (2) ------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 407 + +--S 408 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 63b x - 315a b x - 210a b x - 126a b x - 45a b x - 7a +--R (3) ------------------------------------------------------------ +--R 9 +--R 63x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1393 +t0:=(a+b*x^2)^5/x^12 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1393 +r0:=-1/11*a^5/x^11-5/9*a^4*b/x^9-10/7*a^3*b^2/x^7-2*a^2*b^3/x^5-_ + 5/3*a*b^4/x^3-b^5/x +--R +--R +--R 5 10 5 4 8 2 3 6 10 3 2 4 5 4 2 1 5 +--R - b x - - a b x - 2a b x - -- a b x - - a b x - -- a +--R 3 7 9 11 +--R (2) ----------------------------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 412 + +--S 413 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 693b x - 1155a b x - 1386a b x - 990a b x - 385a b x - 63a +--R (3) ------------------------------------------------------------------- +--R 11 +--R 693x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1393 +t0:=(a+b*x^2)^5/x^14 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1393 +r0:=-1/13*a^5/x^13-5/11*a^4*b/x^11-10/9*a^3*b^2/x^9-10/7*a^2*b^3/x^7-_ + a*b^4/x^5-1/3*b^5/x^3 +--R +--R +--R 1 5 10 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5 +--R - - b x - a b x - -- a b x - -- a b x - -- a b x - -- a +--R 3 7 9 11 13 +--R (2) -------------------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 417 + +--S 418 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 3003b x - 9009a b x - 12870a b x - 10010a b x - 4095a b x - 693a +--R ------------------------------------------------------------------------- +--R 13 +--R 9009x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1393 +t0:=(a+b*x^2)^5/x^16 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1393 +r0:=-1/15*a^5/x^15-5/13*a^4*b/x^13-10/11*a^3*b^2/x^11-10/9*a^2*b^3/x^9-_ + 5/7*a*b^4/x^7-1/5*b^5/x^5 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - -- a b x - -- a b x - -- a b x - -- a +--R 5 7 9 11 13 15 +--R (2) ---------------------------------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 422 + +--S 423 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 9009b x - 32175a b x - 50050a b x - 40950a b x - 17325a b x - 3003a +--R ---------------------------------------------------------------------------- +--R 15 +--R 45045x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1393 +t0:=(a+b*x^2)^5/x^18 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1393 +r0:=-1/17*a^5/x^17-1/3*a^4*b/x^15-10/13*a^3*b^2/x^13-_ + 10/11*a^2*b^3/x^11-5/9*a*b^4/x^9-1/7*b^5/x^7 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 1 4 2 1 5 +--R - - b x - - a b x - -- a b x - -- a b x - - a b x - -- a +--R 7 9 11 13 3 17 +--R (2) --------------------------------------------------------------- +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 427 + +--S 428 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 21879b x - 85085a b x - 139230a b x - 117810a b x - 51051a b x +--R + +--R 5 +--R - 9009a +--R / +--R 17 +--R 153153x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1393 +t0:=(a+b*x^2)^5/x^20 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 1393 +r0:=-1/19*a^5/x^19-5/17*a^4*b/x^17-2/3*a^3*b^2/x^15-10/13*a^2*b^3/x^13-_ + 5/11*a*b^4/x^11-1/9*b^5/x^9 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 2 3 2 4 5 4 2 1 5 +--R - - b x - -- a b x - -- a b x - - a b x - -- a b x - -- a +--R 9 11 13 3 17 19 +--R (2) ---------------------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 46189b x - 188955a b x - 319770a b x - 277134a b x - 122265a b x +--R + +--R 5 +--R - 21879a +--R / +--R 19 +--R 415701x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1393 +t0:=x^m*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1393 +r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(3+m)/(3+m)+28*a^6*b^2*x^(5+m)/(5+m)+_ + 56*a^5*b^3*x^(7+m)/(7+m)+70*a^4*b^4*x^(9+m)/(9+m)+_ + 56*a^3*b^5*x^(11+m)/(11+m)+28*a^2*b^6*x^(13+m)/(13+m)+_ + 8*a*b^7*x^(15+m)/(15+m)+b^8*x^(17+m)/(17+m) +--R +--R +--R (2) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R m + 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R m + 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b +--R * +--R m + 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m + 15772064a b m +--R + +--R 3 5 3 3 5 2 3 5 3 5 +--R 82703600a b m + 242205264a b m + 349055280a b m + 175429800a b +--R * +--R m + 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m + 22248660a b m +--R + +--R 4 4 3 4 4 2 4 4 4 4 +--R 120007440a b m + 359864120a b m + 527864400a b m + 268017750a b +--R * +--R m + 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m + 20318144a b m +--R + +--R 5 3 3 5 3 2 5 3 5 3 +--R 113969296a b m + 354159792a b m + 534194640a b m + 275675400a b +--R * +--R m + 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m + 11730712a b m +--R + +--R 6 2 3 6 2 2 6 2 6 2 +--R 69444592a b m + 228749472a b m + 362909232a b m + 192972780a b +--R * +--R m + 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R m + 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b +--R * +--R 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 3 5 +--R 15772064a b m + 82703600a b m + 242205264a b m + 349055280a b m +--R + +--R 3 5 +--R 175429800a b +--R * +--R 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 +--R 22248660a b m + 120007440a b m + 359864120a b m + 527864400a b m +--R + +--R 4 4 +--R 268017750a b +--R * +--R 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 5 3 +--R 20318144a b m + 113969296a b m + 354159792a b m + 534194640a b m +--R + +--R 5 3 +--R 275675400a b +--R * +--R 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 6 2 +--R 11730712a b m + 69444592a b m + 228749472a b m + 362909232a b m +--R + +--R 6 2 +--R 192972780a b +--R * +--R 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m +--R + +--R 2 6 4 2 6 3 2 6 2 2 6 +--R 7063672a b m + 36270416a b m + 104457024a b m + 148715280a b m +--R + +--R 2 6 +--R 74220300a b +--R * +--R 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R 15772064a b m + 82703600a b m + 242205264a b m +--R + +--R 3 5 3 5 +--R 349055280a b m + 175429800a b +--R * +--R 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R 22248660a b m + 120007440a b m + 359864120a b m +--R + +--R 4 4 4 4 +--R 527864400a b m + 268017750a b +--R * +--R 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R 20318144a b m + 113969296a b m + 354159792a b m +--R + +--R 5 3 5 3 +--R 534194640a b m + 275675400a b +--R * +--R 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R 11730712a b m + 69444592a b m + 228749472a b m +--R + +--R 6 2 6 2 +--R 362909232a b m + 192972780a b +--R * +--R 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - b m - 64b m - 1708b m - 24640b m - 208054b m - 1038016b m +--R + +--R 8 2 8 8 +--R - 2924172b m - 4098240b m - 2027025b +--R * +--R m + 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 528a b m - 14448a b m - 212688a b m - 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R - 9222192a b m - 26230672a b m - 37013232a b m - 18378360a b +--R * +--R m + 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R - 28a b m - 1904a b m - 53536a b m - 806960a b m - 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R - 36270416a b m - 104457024a b m - 148715280a b m - 74220300a b +--R * +--R m + 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R - 56a b m - 3920a b m - 113456a b m - 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 3 5 +--R - 15772064a b m - 82703600a b m - 242205264a b m - 349055280a b m +--R + +--R 3 5 +--R - 175429800a b +--R * +--R m + 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R - 70a b m - 5040a b m - 150360a b m - 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 +--R - 22248660a b m - 120007440a b m - 359864120a b m - 527864400a b m +--R + +--R 4 4 +--R - 268017750a b +--R * +--R m + 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R - 56a b m - 4144a b m - 127568a b m - 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 5 3 +--R - 20318144a b m - 113969296a b m - 354159792a b m - 534194640a b m +--R + +--R 5 3 +--R - 275675400a b +--R * +--R m + 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R - 28a b m - 2128a b m - 67648a b m - 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 6 2 +--R - 11730712a b m - 69444592a b m - 228749472a b m - 362909232a b m +--R + +--R 6 2 +--R - 192972780a b +--R * +--R m + 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 624a b m - 20496a b m - 367920a b m - 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R - 24864336a b m - 89970544a b m - 160561680a b m - 91891800a b +--R * +--R m + 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - a m - 80a m - 2716a m - 50960a m - 575974a m - 3998960a m +--R + +--R 8 2 8 8 +--R - 16571484a m - 37237680a m - 34459425a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1393 +t0:=x^13*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 29 7 27 2 6 25 3 5 23 4 4 21 5 3 19 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 17 7 15 8 13 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 441 + +--S 442 of 1393 +r0:=1/14*a^8*x^14+1/2*a^7*b*x^16+14/9*a^6*b^2*x^18+14/5*a^5*b^3*x^20+_ + 35/11*a^4*b^4*x^22+7/3*a^3*b^5*x^24+14/13*a^2*b^6*x^26+_ + 2/7*a*b^7*x^28+1/30*b^8*x^30 +--R +--R +--R (2) +--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 30 7 13 3 11 5 +--R + +--R 14 6 2 18 1 7 16 1 8 14 +--R -- a b x + - a b x + -- a x +--R 9 2 14 +--R Type: Polynomial(Fraction(Integer)) +--E 442 + +--S 443 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 30 7 13 3 11 5 +--R + +--R 14 6 2 18 1 7 16 1 8 14 +--R -- a b x + - a b x + -- a x +--R 9 2 14 +--R Type: Polynomial(Fraction(Integer)) +--E 443 + +--S 444 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 444 + +--S 445 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 445 + +)clear all + +--S 446 of 1393 +t0:=x^11*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 27 7 25 2 6 23 3 5 21 4 4 19 5 3 17 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 15 7 13 8 11 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 446 + +--S 447 of 1393 +r0:=-1/18*a^5*(a+b*x^2)^9/b^6+1/4*a^4*(a+b*x^2)^10/b^6-_ + 5/11*a^3*(a+b*x^2)^11/b^6+5/12*a^2*(a+b*x^2)^12/b^6-_ + 5/26*a*(a+b*x^2)^13/b^6+1/28*(a+b*x^2)^14/b^6 +--R +--R +--R (2) +--R 1 14 28 4 13 26 7 2 12 24 28 3 11 22 7 4 10 20 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x +--R 28 13 6 11 2 +--R + +--R 28 5 9 18 7 6 8 16 4 7 7 14 1 8 6 12 1 14 +--R -- a b x + - a b x + - a b x + -- a b x - ----- a +--R 9 4 7 12 36036 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 28 4 7 26 7 2 6 24 28 3 5 22 7 4 4 20 28 5 3 18 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x +--R 28 13 6 11 2 9 +--R + +--R 7 6 2 16 4 7 14 1 8 12 +--R - a b x + - a b x + -- a x +--R 4 7 12 +--R Type: Polynomial(Fraction(Integer)) +--E 448 + +--S 449 of 1393 +m0:=a0-r0 +--R +--R +--R 1 14 +--R ----- a +--R 36036 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 449 + +--S 450 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 450 + +)clear all + +--S 451 of 1393 +t0:=x^9*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 25 7 23 2 6 21 3 5 19 4 4 17 5 3 15 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 13 7 11 8 9 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 451 + +--S 452 of 1393 +r0:=1/18*a^4*(a+b*x^2)^9/b^5-1/5*a^3*(a+b*x^2)^10/b^5+_ + 3/11*a^2*(a+b*x^2)^11/b^5-1/6*a*(a+b*x^2)^12/b^5+1/26*(a+b*x^2)^13/b^5 +--R +--R +--R (2) +--R 1 13 26 1 12 24 14 2 11 22 14 3 10 20 35 4 9 18 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x +--R 26 3 11 5 9 +--R + +--R 7 5 8 16 6 7 14 2 7 6 12 1 8 5 10 1 13 +--R - a b x + 2a b x + - a b x + -- a b x + ----- a +--R 2 3 10 12870 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 26 1 7 24 14 2 6 22 14 3 5 20 35 4 4 18 7 5 3 16 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 26 3 11 5 9 2 +--R + +--R 6 2 14 2 7 12 1 8 10 +--R 2a b x + - a b x + -- a x +--R 3 10 +--R Type: Polynomial(Fraction(Integer)) +--E 453 + +--S 454 of 1393 +m0:=a0-r0 +--R +--R +--R 1 13 +--R ----- a +--R 12870 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 454 + +--S 455 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 455 + +)clear all + +--S 456 of 1393 +t0:=x^7*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 23 7 21 2 6 19 3 5 17 4 4 15 5 3 13 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 11 7 9 8 7 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 456 + +--S 457 of 1393 +r0:=-1/18*a^3*(a+b*x^2)^9/b^4+3/20*a^2*(a+b*x^2)^10/b^4-_ + 3/22*a*(a+b*x^2)^11/b^4+1/24*(a+b*x^2)^12/b^4 +--R +--R +--R (2) +--R 1 12 24 4 11 22 7 2 10 20 28 3 9 18 35 4 8 16 5 7 14 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x +--R 24 11 5 9 8 +--R + +--R 7 6 6 12 4 7 5 10 1 8 4 8 1 12 +--R - a b x + - a b x + - a b x - ---- a +--R 3 5 8 3960 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 24 4 7 22 7 2 6 20 28 3 5 18 35 4 4 16 5 3 14 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x +--R 24 11 5 9 8 +--R + +--R 7 6 2 12 4 7 10 1 8 8 +--R - a b x + - a b x + - a x +--R 3 5 8 +--R Type: Polynomial(Fraction(Integer)) +--E 458 + +--S 459 of 1393 +m0:=a0-r0 +--R +--R +--R 1 12 +--R ---- a +--R 3960 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 459 + +--S 460 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 460 + +)clear all + +--S 461 of 1393 +t0:=x^5*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 21 7 19 2 6 17 3 5 15 4 4 13 5 3 11 6 2 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 7 8 5 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 461 + +--S 462 of 1393 +r0:=1/18*a^2*(a+b*x^2)^9/b^3-1/10*a*(a+b*x^2)^10/b^3+1/22*(a+b*x^2)^11/b^3 +--R +--R +--R (2) +--R 1 11 22 2 10 20 14 2 9 18 7 3 8 16 4 7 14 14 5 6 12 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x +--R 22 5 9 2 3 +--R + +--R 14 6 5 10 7 4 8 1 8 3 6 1 11 +--R -- a b x + a b x + - a b x + --- a +--R 5 6 990 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 22 2 7 20 14 2 6 18 7 3 5 16 4 4 14 14 5 3 12 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x +--R 22 5 9 2 3 +--R + +--R 14 6 2 10 7 8 1 8 6 +--R -- a b x + a b x + - a x +--R 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 463 + +--S 464 of 1393 +m0:=a0-r0 +--R +--R +--R 1 11 +--R --- a +--R 990 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 464 + +--S 465 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 465 + +)clear all + +--S 466 of 1393 +t0:=x^3*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 19 7 17 2 6 15 3 5 13 4 4 11 5 3 9 6 2 7 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 5 8 3 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 466 + +--S 467 of 1393 +r0:=-1/18*a*(a+b*x^2)^9/b^2+1/20*(a+b*x^2)^10/b^2 +--R +--R +--R (2) +--R 1 10 20 4 9 18 7 2 8 16 3 7 14 35 4 6 12 28 5 5 10 +--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x +--R 20 9 4 6 5 +--R + +--R 7 6 4 8 4 7 3 6 1 8 2 4 1 10 +--R - a b x + - a b x + - a b x - --- a +--R 2 3 4 180 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 20 4 7 18 7 2 6 16 3 5 14 35 4 4 12 28 5 3 10 +--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x +--R 20 9 4 6 5 +--R + +--R 7 6 2 8 4 7 6 1 8 4 +--R - a b x + - a b x + - a x +--R 2 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 468 + +--S 469 of 1393 +m0:=a0-r0 +--R +--R +--R 1 10 +--R --- a +--R 180 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 469 + +--S 470 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 470 + +)clear all + +--S 471 of 1393 +t0:=x*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 5 3 7 6 2 5 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 3 8 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 471 + +--S 472 of 1393 +r0:=1/18*(a+b*x^2)^9/b +--R +--R +--R (2) +--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8 +--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x +--R 18 2 3 +--R + +--R 14 6 3 6 7 2 4 1 8 2 1 9 +--R -- a b x + 2a b x + - a b x + -- a +--R 3 2 18 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 18 1 7 16 2 6 14 14 3 5 12 4 4 10 5 3 8 +--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x +--R 18 2 3 +--R + +--R 14 6 2 6 7 4 1 8 2 +--R -- a b x + 2a b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 473 + +--S 474 of 1393 +m0:=a0-r0 +--R +--R +--R 1 9 +--R -- a +--R 18 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 474 + +--S 475 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 475 + +)clear all + +--S 476 of 1393 +t0:=(a+b*x^2)^8/x +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1393 +r0:=4*a^7*b*x^2+7*a^6*b^2*x^4+28/3*a^5*b^3*x^6+35/4*a^4*b^4*x^8+_ + 28/5*a^3*b^5*x^10+7/3*a^2*b^6*x^12+4/7*a*b^7*x^14+_ + 1/16*b^8*x^16+a^8*log(x) +--R +--R +--R (2) +--R 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 1680 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 1680 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1393 +t0:=(a+b*x^2)^8/x^3 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1393 +r0:=-1/2*a^8/x^2+14*a^6*b^2*x^2+14*a^5*b^3*x^4+35/3*a^4*b^4*x^6+_ + 7*a^3*b^5*x^8+14/5*a^2*b^6*x^10+2/3*a*b^7*x^12+_ + 1/14*b^8*x^14+8*a^7*b*log(x) +--R +--R +--R (2) +--R 7 2 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 8 5 3 6 6 2 4 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 2 +--R 210x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 2 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 8 5 3 6 6 2 4 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 2 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1393 +t0:=(a+b*x^2)^8/x^5 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1393 +r0:=-1/4*a^8/x^4-4*a^7*b/x^2+28*a^5*b^3*x^2+35/2*a^4*b^4*x^4+_ + 28/3*a^3*b^5*x^6+7/2*a^2*b^6*x^8+4/5*a*b^7*x^10+_ + 1/12*b^8*x^12+28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 6 2 4 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 8 5 3 6 7 2 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 4 +--R 60x +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 4 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 8 5 3 6 7 2 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 4 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1393 +t0:=(a+b*x^2)^8/x^7 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1393 +r0:=-1/6*a^8/x^6-2*a^7*b/x^4-14*a^6*b^2/x^2+35*a^4*b^4*x^2+_ + 14*a^3*b^5*x^4+14/3*a^2*b^6*x^6+a*b^7*x^8+1/10*b^8*x^10+_ + 56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 5 3 6 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 8 6 2 4 7 2 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 6 +--R 30x +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 6 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 8 6 2 4 7 2 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 6 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1393 +t0:=(a+b*x^2)^8/x^9 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1393 +r0:=-1/8*a^8/x^8-4/3*a^7*b/x^6-7*a^6*b^2/x^4-28*a^5*b^3/x^2+_ + 28*a^3*b^5*x^2+7*a^2*b^6*x^4+4/3*a*b^7*x^6+1/8*b^8*x^8+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 4 4 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 8 +--R 24x +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1393 +t0:=(a+b*x^2)^8/x^11 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1393 +r0:=-1/10*a^8/x^10-a^7*b/x^8-14/3*a^6*b^2/x^6-14*a^5*b^3/x^4-_ + 35*a^4*b^4/x^2+14*a^2*b^6*x^2+2*a*b^7*x^4+1/6*b^8*x^6+56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 3 5 10 8 16 7 14 2 6 12 4 4 8 +--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 10 +--R 30x +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 10 8 16 7 14 2 6 12 4 4 8 +--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 10 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1393 +t0:=(a+b*x^2)^8/x^13 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1393 +r0:=-1/12*a^8/x^12-4/5*a^7*b/x^10-7/2*a^6*b^2/x^8-28/3*a^5*b^3/x^6-_ + 35/2*a^4*b^4/x^4-28*a^3*b^5/x^2+4*a*b^7*x^2+1/4*b^8*x^4+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 2 6 12 8 16 7 14 3 5 10 4 4 8 +--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 12 +--R 60x +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 12 8 16 7 14 3 5 10 4 4 8 +--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 12 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1393 +t0:=(a+b*x^2)^8/x^15 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1393 +r0:=-1/14*a^8/x^14-2/3*a^7*b/x^12-14/5*a^6*b^2/x^10-7*a^5*b^3/x^8-_ + 35/3*a^4*b^4/x^6-14*a^3*b^5/x^4-14*a^2*b^6/x^2+1/2*b^8*x^2+8*a*b^7*log(x) +--R +--R +--R (2) +--R 7 14 8 16 2 6 12 3 5 10 4 4 8 +--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 14 +--R 210x +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 8 16 2 6 12 3 5 10 4 4 8 +--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 14 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1393 +t0:=(a+b*x^2)^8/x^17 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1393 +r0:=-1/16*a^8/x^16-4/7*a^7*b/x^14-7/3*a^6*b^2/x^12-28/5*a^5*b^3/x^10-_ + 35/4*a^4*b^4/x^8-28/3*a^3*b^5/x^6-7*a^2*b^6/x^4-4*a*b^7/x^2+b^8*log(x) +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 16 +--R 1680x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 16 +--R 1680x +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1393 +t0:=(a+b*x^2)^8/x^19 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1393 +r0:=-1/18*(a+b*x^2)^9/(a*x^18) +--R +--R +--R (2) +--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8 +--R - -- b x - - a b x - 2a b x - -- a b x - 7a b x - 7a b x +--R 18 2 3 +--R + +--R 14 6 3 6 7 2 4 1 8 2 1 9 +--R - -- a b x - 2a b x - - a b x - -- a +--R 3 2 18 +--R / +--R 18 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 522 + +--S 523 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 4 7 2 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1393 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 18a +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1393 +t0:=(a+b*x^2)^8/x^21 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1393 +r0:=-1/20*(a+b*x^2)^9/(a*x^20)+1/180*b*(a+b*x^2)^9/(a^2*x^18) +--R +--R +--R (2) +--R 1 10 20 1 2 8 16 4 3 7 14 7 4 6 12 28 5 5 10 35 6 4 8 +--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 180 4 3 2 5 6 +--R + +--R 7 3 6 7 8 2 4 4 9 2 1 10 +--R - 4a b x - - a b x - - a b x - -- a +--R 4 9 20 +--R / +--R 2 20 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 527 + +--S 528 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 720a b x - 315a b x - 80a b x - 9a +--R / +--R 20 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1393 +m0:=a0-r0 +--R +--R +--R 10 +--R b +--R (4) - ----- +--R 2 +--R 180a +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1393 +t0:=(a+b*x^2)^8/x^23 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 23 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1393 +r0:=-1/22*(a+b*x^2)^9/(a*x^22)+1/110*b*(a+b*x^2)^9/(a^2*x^20)-_ + 1/990*b^2*(a+b*x^2)^9/(a^3*x^18) +--R +--R +--R (2) +--R 1 11 22 1 3 8 16 4 7 14 14 5 6 12 14 6 5 10 7 4 8 +--R - --- b x - - a b x - a b x - -- a b x - -- a b x - 5a b x +--R 990 6 5 3 +--R + +--R 7 8 3 6 14 9 2 4 2 10 2 1 11 +--R - - a b x - -- a b x - - a b x - -- a +--R 2 9 5 22 +--R / +--R 3 22 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 532 + +--S 533 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 3465a b x - 1540a b x - 396a b x - 45a +--R / +--R 22 +--R 990x +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1393 +m0:=a0-r0 +--R +--R +--R 11 +--R b +--R (4) ----- +--R 3 +--R 990a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1393 +t0:=(a+b*x^2)^8/x^25 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1393 +r0:=-1/24*(a+b*x^2)^9/(a*x^24)+1/88*b*(a+b*x^2)^9/(a^2*x^22)-_ + 1/440*b^2*(a+b*x^2)^9/(a^3*x^20)+1/3960*b^3*(a+b*x^2)^9/(a^4*x^18) +--R +--R +--R (2) +--R 1 12 24 1 4 8 16 4 5 7 14 7 6 6 12 7 5 10 35 8 4 8 +--R ---- b x - - a b x - - a b x - - a b x - 4a b x - -- a b x +--R 3960 8 5 3 8 +--R + +--R 28 9 3 6 7 10 2 4 4 11 2 1 12 +--R - -- a b x - - a b x - -- a b x - -- a +--R 9 5 11 24 +--R / +--R 4 24 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 537 + +--S 538 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 12320a b x - 5544a b x - 1440a b x - 165a +--R / +--R 24 +--R 3960x +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1393 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ------ +--R 4 +--R 3960a +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1393 +t0:=(a+b*x^2)^8/x^27 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 27 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1393 +r0:=-1/26*a^8/x^26-1/3*a^7*b/x^24-14/11*a^6*b^2/x^22-14/5*a^5*b^3/x^20-_ + 35/9*a^4*b^4/x^18-7/2*a^3*b^5/x^16-2*a^2*b^6/x^14-_ + 2/3*a*b^7/x^12-1/10*b^8/x^10 +--R +--R +--R (2) +--R 1 8 16 2 7 14 2 6 12 7 3 5 10 35 4 4 8 14 5 3 6 +--R - -- b x - - a b x - 2a b x - - a b x - -- a b x - -- a b x +--R 10 3 2 9 5 +--R + +--R 14 6 2 4 1 7 2 1 8 +--R - -- a b x - - a b x - -- a +--R 11 3 26 +--R / +--R 26 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 542 + +--S 543 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 36036a b x - 16380a b x - 4290a b x - 495a +--R / +--R 26 +--R 12870x +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1393 +t0:=(a+b*x^2)^8/x^29 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 29 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1393 +r0:=-1/28*a^8/x^28-4/13*a^7*b/x^26-7/6*a^6*b^2/x^24-28/11*a^5*b^3/x^22-_ + 7/2*a^4*b^4/x^20-28/9*a^3*b^5/x^18-7/4*a^2*b^6/x^16-_ + 4/7*a*b^7/x^14-1/12*b^8/x^12 +--R +--R +--R (2) +--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 7 4 4 8 28 5 3 6 +--R - -- b x - - a b x - - a b x - -- a b x - - a b x - -- a b x +--R 12 7 4 9 2 11 +--R + +--R 7 6 2 4 4 7 2 1 8 +--R - - a b x - -- a b x - -- a +--R 6 13 28 +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 547 + +--S 548 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 91728a b x - 42042a b x - 11088a b x - 1287a +--R / +--R 28 +--R 36036x +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1393 +t0:=(a+b*x^2)^8/x^31 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1393 +r0:=-1/30*a^8/x^30-2/7*a^7*b/x^28-14/13*a^6*b^2/x^26-7/3*a^5*b^3/x^24-_ + 35/11*a^4*b^4/x^22-14/5*a^3*b^5/x^20-14/9*a^2*b^6/x^18-_ + 1/2*a*b^7/x^16-1/14*b^8/x^14 +--R +--R +--R (2) +--R 1 8 16 1 7 14 14 2 6 12 14 3 5 10 35 4 4 8 7 5 3 6 +--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - - a b x +--R 14 2 9 5 11 3 +--R + +--R 14 6 2 4 2 7 2 1 8 +--R - -- a b x - - a b x - -- a +--R 13 7 30 +--R / +--R 30 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 552 + +--S 553 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 6435b x - 45045a b x - 140140a b x - 252252a b x - 286650a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 210210a b x - 97020a b x - 25740a b x - 3003a +--R / +--R 30 +--R 90090x +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1393 +t0:=(a+b*x^2)^8/x^33 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 33 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1393 +r0:=-1/32*a^8/x^32-4/15*a^7*b/x^30-a^6*b^2/x^28-28/13*a^5*b^3/x^26-_ + 35/12*a^4*b^4/x^24-28/11*a^3*b^5/x^22-7/5*a^2*b^6/x^20-_ + 4/9*a*b^7/x^18-1/16*b^8/x^16 +--R +--R +--R (2) +--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 35 4 4 8 28 5 3 6 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 16 9 5 11 12 13 +--R + +--R 6 2 4 4 7 2 1 8 +--R - a b x - -- a b x - -- a +--R 15 32 +--R / +--R 32 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 557 + +--S 558 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 12870b x - 91520a b x - 288288a b x - 524160a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 600600a b x - 443520a b x - 205920a b x - 54912a b x - 6435a +--R / +--R 32 +--R 205920x +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1393 +t0:=x^8*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 24 7 22 2 6 20 3 5 18 4 4 16 5 3 14 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 12 7 10 8 8 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 561 + +--S 562 of 1393 +r0:=1/9*a^8*x^9+8/11*a^7*b*x^11+28/13*a^6*b^2*x^13+56/15*a^5*b^3*x^15+_ + 70/17*a^4*b^4*x^17+56/19*a^3*b^5*x^19+4/3*a^2*b^6*x^21+_ + 8/23*a*b^7*x^23+1/25*b^8*x^25 +--R +--R +--R (2) +--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 25 23 3 19 17 15 +--R + +--R 28 6 2 13 8 7 11 1 8 9 +--R -- a b x + -- a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 562 + +--S 563 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 25 23 3 19 17 15 +--R + +--R 28 6 2 13 8 7 11 1 8 9 +--R -- a b x + -- a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 563 + +--S 564 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 564 + +--S 565 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 565 + +)clear all + +--S 566 of 1393 +t0:=x^6*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 22 7 20 2 6 18 3 5 16 4 4 14 5 3 12 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 10 7 8 8 6 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 566 + +--S 567 of 1393 +r0:=1/7*a^8*x^7+8/9*a^7*b*x^9+28/11*a^6*b^2*x^11+56/13*a^5*b^3*x^13+_ + 14/3*a^4*b^4*x^15+56/17*a^3*b^5*x^17+28/19*a^2*b^6*x^19+_ + 8/21*a*b^7*x^21+1/23*b^8*x^23 +--R +--R +--R (2) +--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 23 21 19 17 3 13 +--R + +--R 28 6 2 11 8 7 9 1 8 7 +--R -- a b x + - a b x + - a x +--R 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 567 + +--S 568 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 23 21 19 17 3 13 +--R + +--R 28 6 2 11 8 7 9 1 8 7 +--R -- a b x + - a b x + - a x +--R 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 568 + +--S 569 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 569 + +--S 570 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 570 + +)clear all + +--S 571 of 1393 +t0:=x^4*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 20 7 18 2 6 16 3 5 14 4 4 12 5 3 10 6 2 8 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 6 8 4 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 571 + +--S 572 of 1393 +r0:=1/5*a^8*x^5+8/7*a^7*b*x^7+28/9*a^6*b^2*x^9+56/11*a^5*b^3*x^11+_ + 70/13*a^4*b^4*x^13+56/15*a^3*b^5*x^15+28/17*a^2*b^6*x^17+_ + 8/19*a*b^7*x^19+1/21*b^8*x^21 +--R +--R +--R (2) +--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 21 19 17 15 13 11 +--R + +--R 28 6 2 9 8 7 7 1 8 5 +--R -- a b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 572 + +--S 573 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 21 19 17 15 13 11 +--R + +--R 28 6 2 9 8 7 7 1 8 5 +--R -- a b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 573 + +--S 574 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 574 + +--S 575 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 575 + +)clear all + +--S 576 of 1393 +t0:=x^2*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 18 7 16 2 6 14 3 5 12 4 4 10 5 3 8 6 2 6 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 4 8 2 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 576 + +--S 577 of 1393 +r0:=1/3*a^8*x^3+8/5*a^7*b*x^5+4*a^6*b^2*x^7+56/9*a^5*b^3*x^9+_ + 70/11*a^4*b^4*x^11+56/13*a^3*b^5*x^13+28/15*a^2*b^6*x^15+_ + 8/17*a*b^7*x^17+1/19*b^8*x^19 +--R +--R +--R (2) +--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 19 17 15 13 11 9 +--R + +--R 6 2 7 8 7 5 1 8 3 +--R 4a b x + - a b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 577 + +--S 578 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 19 17 15 13 11 9 +--R + +--R 6 2 7 8 7 5 1 8 3 +--R 4a b x + - a b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 578 + +--S 579 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 579 + +--S 580 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 580 + +)clear all + +--S 581 of 1393 +t0:=(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R Type: Polynomial(Integer) +--E 581 + +--S 582 of 1393 +r0:=a^8*x+8/3*a^7*b*x^3+28/5*a^6*b^2*x^5+8*a^5*b^3*x^7+_ + 70/9*a^4*b^4*x^9+56/11*a^3*b^5*x^11+28/13*a^2*b^6*x^13+_ + 8/15*a*b^7*x^15+1/17*b^8*x^17 +--R +--R +--R (2) +--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x +--R 17 15 13 11 9 +--R + +--R 28 6 2 5 8 7 3 8 +--R -- a b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 582 + +--S 583 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x +--R 17 15 13 11 9 +--R + +--R 28 6 2 5 8 7 3 8 +--R -- a b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 583 + +--S 584 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 584 + +--S 585 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 585 + +)clear all + +--S 586 of 1393 +t0:=(a+b*x^2)^8/x^2 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1393 +r0:=-a^8/x+8*a^7*b*x+28/3*a^6*b^2*x^3+56/5*a^5*b^3*x^5+10*a^4*b^4*x^7+_ + 56/9*a^3*b^5*x^9+28/11*a^2*b^6*x^11+8/13*a*b^7*x^13+1/15*b^8*x^15 +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 72072a b x + 60060a b x + 51480a b x - 6435a +--R / +--R 6435x +--R Type: Fraction(Polynomial(Integer)) +--E 587 + +--S 588 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 72072a b x + 60060a b x + 51480a b x - 6435a +--R / +--R 6435x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1393 +t0:=(a+b*x^2)^8/x^4 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1393 +r0:=-1/3*a^8/x^3-8*a^7*b/x+28*a^6*b^2*x+56/3*a^5*b^3*x^3+14*a^4*b^4*x^5+_ + 8*a^3*b^5*x^7+28/9*a^2*b^6*x^9+8/11*a*b^7*x^11+1/13*b^8*x^13 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6 +--R -- b x + -- a b x + -- a b x + 8a b x + 14a b x + -- a b x +--R 13 11 9 3 +--R + +--R 6 2 4 7 2 1 8 +--R 28a b x - 8a b x - - a +--R 3 +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 592 + +--S 593 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 99b x + 936a b x + 4004a b x + 10296a b x + 18018a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 24024a b x + 36036a b x - 10296a b x - 429a +--R / +--R 3 +--R 1287x +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1393 +t0:=(a+b*x^2)^8/x^6 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1393 +r0:=-1/5*a^8/x^5-8/3*a^7*b/x^3-28*a^6*b^2/x+56*a^5*b^3*x+70/3*a^4*b^4*x^3+_ + 56/5*a^3*b^5*x^5+4*a^2*b^6*x^7+8/9*a*b^7*x^9+1/11*b^8*x^11 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 5 3 6 +--R -- b x + - a b x + 4a b x + -- a b x + -- a b x + 56a b x +--R 11 9 5 3 +--R + +--R 6 2 4 8 7 2 1 8 +--R - 28a b x - - a b x - - a +--R 3 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 45b x + 440a b x + 1980a b x + 5544a b x + 11550a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 27720a b x - 13860a b x - 1320a b x - 99a +--R / +--R 5 +--R 495x +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1393 +t0:=(a+b*x^2)^8/x^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1393 +r0:=-1/7*a^8/x^7-8/5*a^7*b/x^5-28/3*a^6*b^2/x^3-56*a^5*b^3/x+70*a^4*b^4*x+_ + 56/3*a^3*b^5*x^3+28/5*a^2*b^6*x^5+8/7*a*b^7*x^7+1/9*b^8*x^9 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 56 3 5 10 4 4 8 5 3 6 +--R - b x + - a b x + -- a b x + -- a b x + 70a b x - 56a b x +--R 9 7 5 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - - a b x - - a +--R 3 5 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 602 + +--S 603 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 35b x + 360a b x + 1764a b x + 5880a b x + 22050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 17640a b x - 2940a b x - 504a b x - 45a +--R / +--R 7 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1393 +t0:=(a+b*x^2)^8/x^10 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1393 +r0:=-1/9*a^8/x^9-8/7*a^7*b/x^7-28/5*a^6*b^2/x^5-56/3*a^5*b^3/x^3-_ + 70*a^4*b^4/x+56*a^3*b^5*x+28/3*a^2*b^6*x^3+8/5*a*b^7*x^5+1/7*b^8*x^7 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6 +--R - b x + - a b x + -- a b x + 56a b x - 70a b x - -- a b x +--R 7 5 3 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - - a b x - - a +--R 5 7 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 607 + +--S 608 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 45b x + 504a b x + 2940a b x + 17640a b x - 22050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 5880a b x - 1764a b x - 360a b x - 35a +--R / +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1393 +t0:=(a+b*x^2)^8/x^12 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1393 +r0:=-1/11*a^8/x^11-8/9*a^7*b/x^9-4*a^6*b^2/x^7-56/5*a^5*b^3/x^5-_ + 70/3*a^4*b^4/x^3-56*a^3*b^5/x+28*a^2*b^6*x+8/3*a*b^7*x^3+1/5*b^8*x^5 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 3 5 10 70 4 4 8 56 5 3 6 +--R - b x + - a b x + 28a b x - 56a b x - -- a b x - -- a b x +--R 5 3 3 5 +--R + +--R 6 2 4 8 7 2 1 8 +--R - 4a b x - - a b x - -- a +--R 9 11 +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 99b x + 1320a b x + 13860a b x - 27720a b x - 11550a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 5544a b x - 1980a b x - 440a b x - 45a +--R / +--R 11 +--R 495x +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1393 +t0:=(a+b*x^2)^8/x^14 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1393 +r0:=-1/13*a^8/x^13-8/11*a^7*b/x^11-28/9*a^6*b^2/x^9-8*a^5*b^3/x^7-_ + 14*a^4*b^4/x^5-56/3*a^3*b^5/x^3-28*a^2*b^6/x+8*a*b^7*x+1/3*b^8*x^3 +--R +--R +--R (2) +--R 1 8 16 7 14 2 6 12 56 3 5 10 4 4 8 5 3 6 +--R - b x + 8a b x - 28a b x - -- a b x - 14a b x - 8a b x +--R 3 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 9 11 13 +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 10296a b x - 36036a b x - 24024a b x - 18018a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 10296a b x - 4004a b x - 936a b x - 99a +--R / +--R 13 +--R 1287x +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 1393 +t0:=(a+b*x^2)^8/x^16 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 1393 +r0:=-1/15*a^8/x^15-8/13*a^7*b/x^13-28/11*a^6*b^2/x^11-56/9*a^5*b^3/x^9-_ + 10*a^4*b^4/x^7-56/5*a^3*b^5/x^5-28/3*a^2*b^6/x^3-8*a*b^7/x+b^8*x +--R +--R +--R (2) +--R 8 16 7 14 28 2 6 12 56 3 5 10 4 4 8 56 5 3 6 +--R b x - 8a b x - -- a b x - -- a b x - 10a b x - -- a b x +--R 3 5 9 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 11 13 15 +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 622 + +--S 623 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 6435b x - 51480a b x - 60060a b x - 72072a b x - 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 40040a b x - 16380a b x - 3960a b x - 429a +--R / +--R 15 +--R 6435x +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 1393 +t0:=(a+b*x^2)^8/x^18 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 1393 +r0:=-1/17*a^8/x^17-8/15*a^7*b/x^15-28/13*a^6*b^2/x^13-56/11*a^5*b^3/x^11-_ + 70/9*a^4*b^4/x^9-8*a^3*b^5/x^7-28/5*a^2*b^6/x^5-8/3*a*b^7/x^3-b^8/x +--R +--R +--R (2) +--R 8 16 8 7 14 28 2 6 12 3 5 10 70 4 4 8 56 5 3 6 +--R - b x - - a b x - -- a b x - 8a b x - -- a b x - -- a b x +--R 3 5 9 11 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 13 15 17 +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 627 + +--S 628 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 109395b x - 291720a b x - 612612a b x - 875160a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 850850a b x - 556920a b x - 235620a b x - 58344a b x - 6435a +--R / +--R 17 +--R 109395x +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1393 +t0:=(a+b*x^2)^8/x^20 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 1393 +r0:=-1/19*a^8/x^19-8/17*a^7*b/x^17-28/15*a^6*b^2/x^15-56/13*a^5*b^3/x^13-_ + 70/11*a^4*b^4/x^11-56/9*a^3*b^5/x^9-4*a^2*b^6/x^7-_ + 8/5*a*b^7/x^5-1/3*b^8/x^3 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 56 5 3 6 +--R - - b x - - a b x - 4a b x - -- a b x - -- a b x - -- a b x +--R 3 5 9 11 13 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 15 17 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 692835b x - 3325608a b x - 8314020a b x - 12932920a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 13226850a b x - 8953560a b x - 3879876a b x - 978120a b x - 109395a +--R / +--R 19 +--R 2078505x +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1393 +t0:=x^m/(a+b*x^2) +--R +--R +--R m +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1393 +--r0:=x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a*(1+m)) +--E 637 + +--S 638 of 1393 +--a0:=integrate(t0,x) +--E 638 + +--S 639 of 1393 +--m0:=a0-r0 +--E 639 + +--S 640 of 1393 +--d0:=D(m0,x) +--E 640 + +)clear all + +--S 641 of 1393 +t0:=x^11/(a+b*x^2) +--R +--R +--R 11 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 1393 +r0:=1/2*a^4*x^2/b^5-1/4*a^3*x^4/b^4+1/6*a^2*x^6/b^3-1/8*a*x^8/b^2+_ + 1/10*x^10/b-1/2*a^5*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R ------------------------------------------------------------------------- +--R 6 +--R 120b +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R ------------------------------------------------------------------------- +--R 6 +--R 120b +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1393 +t0:=x^10/(a+b*x^2) +--R +--R +--R 10 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 646 + +--S 647 of 1393 +r0:=a^4*x/b^5-1/3*a^3*x^3/b^4+1/5*a^2*x^5/b^3-1/7*a*x^7/b^2+_ + 1/9*x^9/b-a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 +-+ x\|b +--R - 315a \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (35b x - 45a b x + 63a b x - 105a b x + 315a x)\|b +--R / +--R 5 +-+ +--R 315b \|b +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 | a \| b 4 9 3 7 2 2 5 +--R 315a |- - log(-----------------------) + 70b x - 90a b x + 126a b x +--R \| b 2 +--R b x + a +--R + +--R 3 3 4 +--R - 210a b x + 630a x +--R / +--R 5 +--R 630b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 4 |a \|b 4 9 3 7 2 2 5 3 3 4 +--R 315a |- atan(----) + 35b x - 45a b x + 63a b x - 105a b x + 315a x +--R \|b x +--R -----------------------------------------------------------------------] +--R 5 +--R 315b +--R Type: Union(List(Expression(Integer)),...) +--E 648 + +--S 649 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R a \|a atan(-----) + a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1393 +t0:=x^9/(a+b*x^2) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 653 + +--S 654 of 1393 +r0:=-1/2*a^3*x^2/b^4+1/4*a^2*x^4/b^3-1/6*a*x^6/b^2+1/8*x^8/b+_ + 1/2*a^4*log(a+b*x^2)/b^5 +--R +--R +--R 4 2 4 8 3 6 2 2 4 3 2 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) -------------------------------------------------------- +--R 5 +--R 24b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 2 4 8 3 6 2 2 4 3 2 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) -------------------------------------------------------- +--R 5 +--R 24b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1393 +t0:=x^8/(a+b*x^2) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 of 1393 +r0:=-a^3*x/b^4+1/3*a^2*x^3/b^3-1/5*a*x^5/b^2+1/7*x^7/b+_ + a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 3 7 2 5 2 3 3 +-+ +--R 105a \|a atan(-----) + (15b x - 21a b x + 35a b x - 105a x)\|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 | a \| b 3 7 2 5 2 3 +--R 105a |- - log(---------------------) + 30b x - 42a b x + 70a b x +--R \| b 2 +--R b x + a +--R + +--R 3 +--R - 210a x +--R / +--R 4 +--R 210b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 3 |a \|b 3 7 2 5 2 3 3 +--R - 105a |- atan(----) + 15b x - 21a b x + 35a b x - 105a x +--R \|b x +--R -------------------------------------------------------------] +--R 4 +--R 105b +--R Type: Union(List(Expression(Integer)),...) +--E 660 + +--S 661 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R a |- - \|b log(---------------------) - 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - a \|a atan(-----) - a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1393 +t0:=x^7/(a+b*x^2) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1393 +r0:=1/2*a^2*x^2/b^3-1/4*a*x^4/b^2+1/6*x^6/b-1/2*a^3*log(a+b*x^2)/b^4 +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ---------------------------------------------- +--R 4 +--R 12b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) ---------------------------------------------- +--R 4 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1393 +t0:=x^6/(a+b*x^2) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1393 +r0:=a^2*x/b^3-1/3*a*x^3/b^2+1/5*x^5/b-a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2) +--R +--R +--R +-+ +--R 2 +-+ x\|b 2 5 3 2 +-+ +--R - 15a \|a atan(-----) + (3b x - 5a b x + 15a x)\|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 | a \| b 2 5 3 2 +--R 15a |- - log(-----------------------) + 6b x - 10a b x + 30a x +--R \| b 2 +--R b x + a +--R [-----------------------------------------------------------------, +--R 3 +--R 30b +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 2 5 3 2 +--R 15a |- atan(----) + 3b x - 5a b x + 15a x +--R \|b x +--R --------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 672 + +--S 673 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R a \|a atan(-----) + a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1393 +t0:=x^5/(a+b*x^2) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 677 + +--S 678 of 1393 +r0:=-1/2*a*x^2/b^2+1/4*x^4/b+1/2*a^2*log(a+b*x^2)/b^3 +--R +--R +--R 2 2 2 4 2 +--R 2a log(b x + a) + b x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 4b +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 4 2 +--R 2a log(b x + a) + b x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1393 +t0:=x^4/(a+b*x^2) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 682 + +--S 683 of 1393 +r0:=-a*x/b^2+1/3*x^3/b+a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(5/2) +--R +--R +--R +-+ +--R +-+ x\|b 3 +-+ +--R 3a\|a atan(-----) + (b x - 3a x)\|b +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R | a \| b 3 +--R 3a |- - log(---------------------) + 2b x - 6a x +--R \| b 2 +--R b x + a +--R [-------------------------------------------------, +--R 2 +--R 6b +--R +-+ +--R |a +--R +-+ |- +--R |a \|b 3 +--R - 3a |- atan(----) + b x - 3a x +--R \|b x +--R --------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 684 + +--S 685 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R a |- - \|b log(---------------------) - 2a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - a\|a atan(-----) - a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1393 +t0:=x^3/(a+b*x^2) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1393 +r0:=1/2*x^2/b-1/2*a*log(a+b*x^2)/b^2 +--R +--R +--R 2 2 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1393 +t0:=x^2/(a+b*x^2) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1393 +r0:=x/b-atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R - \|a atan(-----) + x\|b +--R +-+ +--R \|a +--R (2) ------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | a 2 +-+ +--R +---+ - 2b x |- - + b x - a |a +--R | a \| b +-+ |- +--R |- - log(-----------------------) + 2x |a \|b +--R \| b 2 |- atan(----) + x +--R b x + a \|b x +--R (3) [---------------------------------------,------------------] +--R 2b b +--R Type: Union(List(Expression(Integer)),...) +--E 696 + +--S 697 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R |- - \|b log(-----------------------) + 2\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R \|a atan(-----) + |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1393 +t0:=x/(a+b*x^2) +--R +--R +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 1393 +r0:=1/2*log(a+b*x^2)/b +--R +--R +--R 2 +--R log(b x + a) +--R (2) ------------- +--R 2b +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x + a) +--R (3) ------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1393 +t0:=1/(a+b*x^2) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 of 1393 +r0:=atan(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R (2) ----------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +---+ +--R log(---------------------------) x\|a b +--R 2 atan(-------) +--R b x + a a +--R (3) [--------------------------------,-------------] +--R +-----+ +---+ +--R 2\|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 708 + +--S 709 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a b \|a \|b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1393 +t0:=1/(x*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------- +--R 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 713 + +--S 714 of 1393 +r0:=log(x)/a-1/2*log(a+b*x^2)/a +--R +--R +--R 2 +--R - log(b x + a) + 2log(x) +--R (2) ------------------------- +--R 2a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x + a) + 2log(x) +--R (3) ------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1393 +t0:=1/(x^2*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 4 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 of 1393 +r0:=(-1)/(a*x)-atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R - x\|b atan(-----) - \|a +--R +-+ +--R \|a +--R (2) ------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | b 2 +-+ +--R +---+ - 2a x |- - + b x - a |b +--R | b \| a +-+ a |- +--R x |- - log(-----------------------) - 2 |b \|a +--R \| a 2 x |- atan(-----) - 1 +--R b x + a \|a b x +--R (3) [---------------------------------------,--------------------] +--R 2a x a x +--R Type: Union(List(Expression(Integer)),...) +--E 720 + +--S 721 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R |- - \|a log(-----------------------) + 2\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R \|b atan(-----) + \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1393 +t0:=1/(x^3*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 725 + +--S 726 of 1393 +r0:=(-1/2)/(a*x^2)-b*log(x)/a^2+1/2*b*log(a+b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R b x log(b x + a) - 2b x log(x) - a +--R (2) ----------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x + a) - 2b x log(x) - a +--R (3) ----------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1393 +t0:=1/(x^4*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1393 +r0:=(-1/3)/(a*x^3)+b/(a^2*x)+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R 3b x \|b atan(-----) + (3b x - a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 | b \| a 2 +--R 3b x |- - log(---------------------) + 6b x - 2a +--R \| a 2 +--R b x + a +--R [--------------------------------------------------, +--R 2 3 +--R 6a x +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 +--R - 3b x |- atan(-----) + 3b x - a +--R \|a b x +--R ----------------------------------] +--R 2 3 +--R 3a x +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R b |- - \|a log(---------------------) - 2b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - b\|b atan(-----) - b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1393 +t0:=1/(x^5*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 737 + +--S 738 of 1393 +r0:=(-1/4)/(a*x^4)+1/2*b/(a^2*x^2)+b^2*log(x)/a^3-1/2*b^2*log(a+b*x^2)/a^3 +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a +--R (2) ------------------------------------------------- +--R 3 4 +--R 4a x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a +--R (3) ------------------------------------------------- +--R 3 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 739 + +--S 740 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1393 +t0:=1/(x^6*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 1393 +r0:=(-1/5)/(a*x^5)+1/3*b/(a^2*x^3)-b^2/(a^3*x)-_ + b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2) +--R +--R +--R +-+ +--R 2 5 +-+ x\|b 2 4 2 2 +-+ +--R - 15b x \|b atan(-----) + (- 15b x + 5a b x - 3a )\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------- +--R 3 5 +-+ +--R 15a x \|a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 2 5 | b \| a 2 4 2 2 +--R 15b x |- - log(-----------------------) - 30b x + 10a b x - 6a +--R \| a 2 +--R b x + a +--R [------------------------------------------------------------------, +--R 3 5 +--R 30a x +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 |b \|a 2 4 2 2 +--R 15b x |- atan(-----) - 15b x + 5a b x - 3a +--R \|a b x +--R ----------------------------------------------] +--R 3 5 +--R 15a x +--R Type: Union(List(Expression(Integer)),...) +--E 744 + +--S 745 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R b |- - \|a log(-----------------------) + 2b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R b \|b atan(-----) + b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1393 +t0:=1/(x^7*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 749 + +--S 750 of 1393 +r0:=(-1/6)/(a*x^6)+1/4*b/(a^2*x^4)-1/2*b^2/(a^3*x^2)-b^3*log(x)/a^4+_ + 1/2*b^3*log(a+b*x^2)/a^4 +--R +--R +--R 3 6 2 3 6 2 4 2 2 3 +--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a +--R (2) ----------------------------------------------------------- +--R 4 6 +--R 12a x +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 3 6 2 4 2 2 3 +--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a +--R (3) ----------------------------------------------------------- +--R 4 6 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1393 +t0:=1/(x^8*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 8 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1393 +r0:=(-1/7)/(a*x^7)+1/5*b/(a^2*x^5)-1/3*b^2/(a^3*x^3)+_ + b^3/(a^4*x)+b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R +-+ +--R 3 7 +-+ x\|b 3 6 2 4 2 2 3 +-+ +--R 105b x \|b atan(-----) + (105b x - 35a b x + 21a b x - 15a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 7 +-+ +--R 105a x \|a +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 7 | b \| a 3 6 2 4 2 2 +--R 105b x |- - log(---------------------) + 210b x - 70a b x + 42a b x +--R \| a 2 +--R b x + a +--R + +--R 3 +--R - 30a +--R / +--R 4 7 +--R 210a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 |b \|a 3 6 2 4 2 2 3 +--R - 105b x |- atan(-----) + 105b x - 35a b x + 21a b x - 15a +--R \|a b x +--R ---------------------------------------------------------------] +--R 4 7 +--R 105a x +--R Type: Union(List(Expression(Integer)),...) +--E 756 + +--S 757 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R b |- - \|a log(---------------------) - 2b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - b \|b atan(-----) - b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 1393 +t0:=1/(x^9*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 1393 +r0:=(-1/8)/(a*x^8)+1/6*b/(a^2*x^6)-1/4*b^2/(a^3*x^4)+1/2*b^3/(a^4*x^2)+_ + b^4*log(x)/a^5-1/2*b^4*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 2 4 8 3 6 2 2 4 3 2 4 +--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ------------------------------------------------------------------------- +--R 5 8 +--R 24a x +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 2 4 8 3 6 2 2 4 3 2 4 +--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ------------------------------------------------------------------------- +--R 5 8 +--R 24a x +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1393 +t0:=x^m/(a+b*x^2)^2 +--R +--R +--R m +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1393 +--r0:=1/2*x^(1+m)/(a*(a+b*x^2))+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a^2*(1+m)) +--E 767 + +--S 768 of 1393 +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1393 +--m0:=a0-r0 +--E 769 + +--S 770 of 1393 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1393 +t0:=x^13/(a+b*x^2)^2 +--R +--R +--R 13 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 771 + +--S 772 of 1393 +r0:=5/2*a^4*x^2/b^6-a^3*x^4/b^5+1/2*a^2*x^6/b^4-1/4*a*x^8/b^3+_ + 1/10*x^10/b^2-1/2*a^6/(b^7*(a+b*x^2))-3*a^5*log(a+b*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 4 5 2 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 2 7 +--R 20b x + 20a b +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 4 5 2 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 2 7 +--R 20b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1393 +t0:=x^12/(a+b*x^2)^2 +--R +--R +--R 12 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 776 + +--S 777 of 1393 +r0:=11/2*a^4*x/b^6-11/6*a^3*x^3/b^5+11/10*a^2*x^5/b^4-11/14*a*x^7/b^3+_ + 11/18*x^9/b^2-1/2*x^11/(b*(a+b*x^2))-_ + 11/2*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2) +--R +--R +--R (2) +--R +-+ +--R 4 2 5 +-+ x\|b +--R (- 3465a b x - 3465a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (70b x - 110a b x + 198a b x - 462a b x + 2310a b x + 3465a x)\|b +--R / +--R 7 2 6 +-+ +--R (630b x + 630a b )\|b +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 2 5 | a \| b 5 11 +--R (3465a b x + 3465a ) |- - log(-----------------------) + 140b x +--R \| b 2 +--R b x + a +--R + +--R 4 9 2 3 7 3 2 5 4 3 5 +--R - 220a b x + 396a b x - 924a b x + 4620a b x + 6930a x +--R / +--R 7 2 6 +--R 1260b x + 1260a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 4 2 5 |a \|b 5 11 4 9 2 3 7 +--R (3465a b x + 3465a ) |- atan(----) + 70b x - 110a b x + 198a b x +--R \|b x +--R + +--R 3 2 5 4 3 5 +--R - 462a b x + 2310a b x + 3465a x +--R / +--R 7 2 6 +--R 630b x + 630a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 778 + +--S 779 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R 11a |- - \|b log(-----------------------) + 22a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 6 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R 11a \|a atan(-----) + 11a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 6 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1393 +t0:=x^11/(a+b*x^2)^2 +--R +--R +--R 11 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1393 +r0:=-2*a^3*x^2/b^5+3/4*a^2*x^4/b^4-1/3*a*x^6/b^3+1/8*x^8/b^2+_ + 1/2*a^5/(b^6*(a+b*x^2))+5/2*a^4*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 2 5 +--R - 48a b x + 12a +--R / +--R 7 2 6 +--R 24b x + 24a b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 2 5 +--R - 48a b x + 12a +--R / +--R 7 2 6 +--R 24b x + 24a b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1393 +t0:=x^10/(a+b*x^2)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 788 + +--S 789 of 1393 +r0:=-9/2*a^3*x/b^5+3/2*a^2*x^3/b^4-9/10*a*x^5/b^3+9/14*x^7/b^2-_ + 1/2*x^9/(b*(a+b*x^2))+9/2*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 +-+ x\|b +--R (315a b x + 315a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (10b x - 18a b x + 42a b x - 210a b x - 315a x)\|b +--R / +--R 6 2 5 +-+ +--R (70b x + 70a b )\|b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 2 4 | a \| b 4 9 3 7 +--R (315a b x + 315a ) |- - log(---------------------) + 20b x - 36a b x +--R \| b 2 +--R b x + a +--R + +--R 2 2 5 3 3 4 +--R 84a b x - 420a b x - 630a x +--R / +--R 6 2 5 +--R 140b x + 140a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 3 2 4 |a \|b 4 9 3 7 2 2 5 +--R (- 315a b x - 315a ) |- atan(----) + 10b x - 18a b x + 42a b x +--R \|b x +--R + +--R 3 3 4 +--R - 210a b x - 315a x +--R / +--R 6 2 5 +--R 70b x + 70a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 790 + +--S 791 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R 9a |- - \|b log(---------------------) - 18a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - 9a \|a atan(-----) - 9a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1393 +t0:=x^9/(a+b*x^2)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1393 +r0:=3/2*a^2*x^2/b^4-1/2*a*x^4/b^3+1/6*x^6/b^2-1/2*a^4/(b^5*(a+b*x^2))-_ + 2*a^3*log(a+b*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 797 + +--S 798 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1393 +t0:=x^8/(a+b*x^2)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 800 + +--S 801 of 1393 +r0:=7/2*a^2*x/b^4-7/6*a*x^3/b^3+7/10*x^5/b^2-1/2*x^7/(b*(a+b*x^2))-_ + 7/2*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 3 +-+ x\|b +--R (- 105a b x - 105a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6b x - 14a b x + 70a b x + 105a x)\|b +--R / +--R 5 2 4 +-+ +--R (30b x + 30a b )\|b +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 2 3 | a \| b 3 7 +--R (105a b x + 105a ) |- - log(-----------------------) + 12b x +--R \| b 2 +--R b x + a +--R + +--R 2 5 2 3 3 +--R - 28a b x + 140a b x + 210a x +--R / +--R 5 2 4 +--R 60b x + 60a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 2 3 |a \|b 3 7 2 5 2 3 3 +--R (105a b x + 105a ) |- atan(----) + 6b x - 14a b x + 70a b x + 105a x +--R \|b x +--R ------------------------------------------------------------------------] +--R 5 2 4 +--R 30b x + 30a b +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 7a |- - \|b log(-----------------------) + 14a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 7a \|a atan(-----) + 7a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1393 +t0:=x^7/(a+b*x^2)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 807 + +--S 808 of 1393 +r0:=-a*x^2/b^3+1/4*x^4/b^2+1/2*a^3/(b^4*(a+b*x^2))+3/2*a^2*log(a+b*x^2)/b^4 +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) ------------------------------------------------------------- +--R 5 2 4 +--R 4b x + 4a b +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) ------------------------------------------------------------- +--R 5 2 4 +--R 4b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 809 + +--S 810 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +)clear all + +--S 812 of 1393 +t0:=x^6/(a+b*x^2)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 812 + +--S 813 of 1393 +r0:=-5/2*a*x/b^3+5/6*x^3/b^2-1/2*x^5/(b*(a+b*x^2))+_ + 5/2*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2) +--R +--R +--R +-+ +--R 2 2 +-+ x\|b 2 5 3 2 +-+ +--R (15a b x + 15a )\|a atan(-----) + (2b x - 10a b x - 15a x)\|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 4 2 3 +-+ +--R (6b x + 6a b )\|b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 2 | a \| b 2 5 3 2 +--R (15a b x + 15a ) |- - log(---------------------) + 4b x - 20a b x - 30a x +--R \| b 2 +--R b x + a +--R [---------------------------------------------------------------------------- +--R 4 2 3 +--R 12b x + 12a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 2 |a \|b 2 5 3 2 +--R (- 15a b x - 15a ) |- atan(----) + 2b x - 10a b x - 15a x +--R \|b x +--R ------------------------------------------------------------] +--R 4 2 3 +--R 6b x + 6a b +--R Type: Union(List(Expression(Integer)),...) +--E 814 + +--S 815 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 5a\|a atan(-----) - 5a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1393 +t0:=x^5/(a+b*x^2)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 819 + +--S 820 of 1393 +r0:=1/2*x^2/b^2-1/2*a^2/(b^3*(a+b*x^2))-a*log(a+b*x^2)/b^3 +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) --------------------------------------------------- +--R 4 2 3 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) --------------------------------------------------- +--R 4 2 3 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1393 +t0:=x^4/(a+b*x^2)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 824 + +--S 825 of 1393 +r0:=3/2*x/b^2-1/2*x^3/(b*(a+b*x^2))-3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(5/2) +--R +--R +--R +-+ +--R 2 +-+ x\|b 3 +-+ +--R (- 3b x - 3a)\|a atan(-----) + (2b x + 3a x)\|b +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 3 2 2 +-+ +--R (2b x + 2a b )\|b +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 | a \| b 3 +--R (3b x + 3a) |- - log(-----------------------) + 4b x + 6a x +--R \| b 2 +--R b x + a +--R [-------------------------------------------------------------, +--R 3 2 2 +--R 4b x + 4a b +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 3 +--R (3b x + 3a) |- atan(----) + 2b x + 3a x +--R \|b x +--R -----------------------------------------] +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(List(Expression(Integer)),...) +--E 826 + +--S 827 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 3 |- - \|b log(----------------------- + 6\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 3\|a atan(-----) + 3 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1393 +t0:=x^3/(a+b*x^2)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 831 + +--S 832 of 1393 +r0:=1/2*a/(b^2*(a+b*x^2))+1/2*log(a+b*x^2)/b^2 +--R +--R +--R 2 2 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 2 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1393 +t0:=x^2/(a+b*x^2)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 836 + +--S 837 of 1393 +r0:=-1/2*x/(b*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x + a)atan(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2b x + 2a b)\|a \|b +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (b x - a)\|- a b + 2a b x +-----+ +--R (b x + a)log(---------------------------) - 2x\|- a b +--R 2 +--R b x + a +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4b x + 4a b)\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (b x + a)atan(-------) - x\|a b +--R a +--R ---------------------------------] +--R 2 2 +---+ +--R (2b x + 2a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 838 + +--S 839 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1393 +t0:=x/(a+b*x^2)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1393 +r0:=(-1/2)/(b*(a+b*x^2)) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ---------- +--R 2 2 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 844 + +--S 845 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1393 +t0:=1/(a+b*x^2)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1393 +r0:=1/2*x/(a*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x + a)atan(-----) + x\|a \|b +--R +-+ +--R \|a +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x + 2a )\|a \|b +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (b x - a)\|- a b + 2a b x +-----+ +--R (b x + a)log(---------------------------) + 2x\|- a b +--R 2 +--R b x + a +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a b x + 4a )\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (b x + a)atan(-------) + x\|a b +--R a +--R ---------------------------------] +--R 2 2 +---+ +--R (2a b x + 2a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 850 + +--S 851 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1393 +t0:=1/(x*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 855 + +--S 856 of 1393 +r0:=1/2/(a*(a+b*x^2))+log(x)/a^2-1/2*log(a+b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2a +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1393 +t0:=1/(x^2*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 860 + +--S 861 of 1393 +r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a+b*x^2))-_ + 3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (- 3b x - 3a x)\|b atan(-----) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x + 2a x)\|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 | b \| a 2 +--R (3b x + 3a x) |- - log(-----------------------) - 6b x - 4a +--R \| a 2 +--R b x + a +--R [-------------------------------------------------------------, +--R 2 3 3 +--R 4a b x + 4a x +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 +--R (3b x + 3a x) |- atan(-----) - 3b x - 2a +--R \|a b x +--R ------------------------------------------] +--R 2 3 3 +--R 2a b x + 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 862 + +--S 863 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 3 |- - \|a log(----------------------- + 6\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 3\|b atan(-----) + 3\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 866 + +)clear all + +--S 867 of 1393 +t0:=1/(x^3*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 867 + +--S 868 of 1393 +r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a+b*x^2))-2*b*log(x)/a^3+b*log(a+b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 869 + +--S 870 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1393 +t0:=1/(x^4*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 6 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 872 + +--S 873 of 1393 +r0:=(-5/6)/(a^2*x^3)+5/2*b/(a^3*x)+1/2/(a*x^3*(a+b*x^2))+_ + 5/2*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2) +--R +--R +--R +-+ +--R 2 5 3 +-+ x\|b 2 4 2 2 +-+ +--R (15b x + 15a b x )\|b atan(-----) + (15b x + 10a b x - 2a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 5 4 3 +-+ +--R (6a b x + 6a x )\|a +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 2 5 3 | b \| a 2 4 2 +--R (15b x + 15a b x ) |- - log(---------------------) + 30b x + 20a b x +--R \| a 2 +--R b x + a +--R + +--R 2 +--R - 4a +--R / +--R 3 5 4 3 +--R 12a b x + 12a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 3 |b \|a 2 4 2 2 +--R (- 15b x - 15a b x ) |- atan(-----) + 15b x + 10a b x - 2a +--R \|a b x +--R --------------------------------------------------------------] +--R 3 5 4 3 +--R 6a b x + 6a x +--R Type: Union(List(Expression(Integer)),...) +--E 874 + +--S 875 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 5b\|b atan(-----) - 5b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 878 + +)clear all + +--S 879 of 1393 +t0:=1/(x^5*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 7 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 879 + +--S 880 of 1393 +r0:=(-3/4)/(a^2*x^4)+3/2*b/(a^3*x^2)+1/2/(a*x^4*(a+b*x^2))+_ + 3*b^2*log(x)/a^4-3/2*b^2*log(a+b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - a +--R / +--R 4 6 5 4 +--R 4a b x + 4a x +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - a +--R / +--R 4 6 5 4 +--R 4a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 881 + +--S 882 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 883 + +)clear all + +--S 884 of 1393 +t0:=1/(x^6*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 8 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 884 + +--S 885 of 1393 +r0:=(-7/10)/(a^2*x^5)+7/6*b/(a^3*x^3)-7/2*b^2/(a^4*x)+_ + 1/2/(a*x^5*(a+b*x^2))-7/2*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 +-+ x\|b +--R (- 105b x - 105a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 105b x - 70a b x + 14a b x - 6a )\|a +--R / +--R 4 7 5 5 +-+ +--R (30a b x + 30a x )\|a +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 7 2 5 | b \| a 3 6 +--R (105b x + 105a b x ) |- - log(-----------------------) - 210b x +--R \| a 2 +--R b x + a +--R + +--R 2 4 2 2 3 +--R - 140a b x + 28a b x - 12a +--R / +--R 4 7 5 5 +--R 60a b x + 60a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 2 5 |b \|a 3 6 2 4 2 2 3 +--R (105b x + 105a b x ) |- atan(-----) - 105b x - 70a b x + 14a b x - 6a +--R \|a b x +--R --------------------------------------------------------------------------] +--R 4 7 5 5 +--R 30a b x + 30a x +--R Type: Union(List(Expression(Integer)),...) +--E 886 + +--S 887 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 7b \|b atan(-----) + 7b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1393 +t0:=1/(x^7*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 11 9 2 7 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 891 + +--S 892 of 1393 +r0:=(-2/3)/(a^2*x^6)+b/(a^3*x^4)-2*b^2/(a^4*x^2)+1/2/(a*x^6*(a+b*x^2))-_ + 4*b^3*log(x)/a^5+2*b^3*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 4 8 3 6 3 6 +--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 8 6 6 +--R 6a b x + 6a x +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 4 8 3 6 3 6 +--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 8 6 6 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1393 +t0:=1/(x^8*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 12 10 2 8 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 896 + +--S 897 of 1393 +r0:=(-9/14)/(a^2*x^7)+9/10*b/(a^3*x^5)-3/2*b^2/(a^4*x^3)+9/2*b^3/(a^5*x)+_ + 1/2/(a*x^7*(a+b*x^2))+9/2*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 +-+ x\|b +--R (315b x + 315a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 210a b x - 42a b x + 18a b x - 10a )\|a +--R / +--R 5 9 6 7 +-+ +--R (70a b x + 70a x )\|a +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 4 9 3 7 | b \| a 4 8 +--R (315b x + 315a b x ) |- - log(---------------------) + 630b x +--R \| a 2 +--R b x + a +--R + +--R 3 6 2 2 4 3 2 4 +--R 420a b x - 84a b x + 36a b x - 20a +--R / +--R 5 9 6 7 +--R 140a b x + 140a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 4 9 3 7 |b \|a 4 8 3 6 2 2 4 +--R (- 315b x - 315a b x ) |- atan(-----) + 315b x + 210a b x - 42a b x +--R \|a b x +--R + +--R 3 2 4 +--R 18a b x - 10a +--R / +--R 5 9 6 7 +--R 70a b x + 70a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 898 + +--S 899 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - 9b \|b atan(-----) - 9b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1393 +t0:=1/(x^9*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 13 11 2 9 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 903 + +--S 904 of 1393 +r0:=(-5/8)/(a^2*x^8)+5/6*b/(a^3*x^6)-5/4*b^2/(a^4*x^4)+5/2*b^3/(a^5*x^2)+_ + 1/2/(a*x^8*(a+b*x^2))+5*b^4*log(x)/a^6-5/2*b^4*log(a+b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 5 10 4 8 +--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 60a b x + 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 10 7 8 +--R 24a b x + 24a x +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 5 10 4 8 +--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 60a b x + 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 10 7 8 +--R 24a b x + 24a x +--R Type: Union(Expression(Integer),...) +--E 905 + +--S 906 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1393 +t0:=x^m/(a+b*x^2)^3 +--R +--R +--R m +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1393 +--r0:=1/4*x^(1+m)/(a*(a+b*x^2)^2)+1/8*(3-m)*x^(1+m)/(a^2*(a+b*x^2))+_ +-- 1/8*(1-m)*(3-m)*x^(1+m)*hypergeometric(1,1/2*(1+m),_ +-- 1/2*(3+m),-b*x^2/a)/(a^3*(1+m)) +--E 909 + +--S 910 of 1393 +--a0:=integrate(t0,x) +--E 910 + +--S 911 of 1393 +--m0:=a0-r0 +--E 911 + +--S 912 of 1393 +--d0:=D(m0,x) +--E 912 + +)clear all + +--S 913 of 1393 +t0:=x^15/(a+b*x^2)^3 +--R +--R +--R 15 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1393 +r0:=15/2*a^4*x^2/b^7-5/2*a^3*x^4/b^6+a^2*x^6/b^5-3/8*a*x^8/b^4+_ + 1/10*x^10/b^3+1/4*a^7/(b^8*(a+b*x^2)^2)-7/2*a^6/(b^8*(a+b*x^2))-_ + 21/2*a^5*log(a+b*x^2)/b^8 +--R +--R +--R (2) +--R 5 2 4 6 2 7 2 7 14 6 12 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x +--R + +--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7 +--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 4 9 2 2 8 +--R 40b x + 80a b x + 40a b +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 6 2 7 2 7 14 6 12 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x +--R + +--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7 +--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 4 9 2 2 8 +--R 40b x + 80a b x + 40a b +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1393 +t0:=x^14/(a+b*x^2)^3 +--R +--R +--R 14 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1393 +r0:=143/8*a^4*x/b^7-143/24*a^3*x^3/b^6+143/40*a^2*x^5/b^5-_ + 143/56*a*x^7/b^4+143/72*x^9/b^3-1/4*x^13/(b*(a+b*x^2)^2)-_ + 13/8*x^11/(b^2*(a+b*x^2))-143/8*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(15/2) +--R +--R +--R (2) +--R +-+ +--R 4 2 4 5 2 6 +-+ x\|b +--R (- 45045a b x - 90090a b x - 45045a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 280b x - 520a b x + 1144a b x - 3432a b x + 24024a b x +--R + +--R 5 3 6 +--R 75075a b x + 45045a x +--R * +--R +-+ +--R \|b +--R / +--R 9 4 8 2 2 7 +-+ +--R (2520b x + 5040a b x + 2520a b )\|b +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 2 4 5 2 6 | a \| b +--R (45045a b x + 90090a b x + 45045a ) |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 560b x - 1040a b x + 2288a b x - 6864a b x + 48048a b x +--R + +--R 5 3 6 +--R 150150a b x + 90090a x +--R / +--R 9 4 8 2 2 7 +--R 5040b x + 10080a b x + 5040a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 4 2 4 5 2 6 |a \|b 6 13 +--R (45045a b x + 90090a b x + 45045a ) |- atan(----) + 280b x +--R \|b x +--R + +--R 5 11 2 4 9 3 3 7 4 2 5 5 3 +--R - 520a b x + 1144a b x - 3432a b x + 24024a b x + 75075a b x +--R + +--R 6 +--R 45045a x +--R / +--R 9 4 8 2 2 7 +--R 2520b x + 5040a b x + 2520a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 920 + +--S 921 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R 143a |- - \|b log(-----------------------) + 286a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 7 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R 143a \|a atan(-----) + 143a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------------- +--R 7 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1393 +t0:=x^13/(a+b*x^2)^3 +--R +--R +--R 13 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 925 + +--S 926 of 1393 +r0:=-5*a^3*x^2/b^6+3/2*a^2*x^4/b^5-1/2*a*x^6/b^4+1/8*x^8/b^3-_ + 1/4*a^6/(b^7*(a+b*x^2)^2)+3*a^5/(b^7*(a+b*x^2))+15/2*a^4*log(a+b*x^2)/b^7 +--R +--R +--R (2) +--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 4 8 2 2 7 +--R 8b x + 16a b x + 8a b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 4 8 2 2 7 +--R 8b x + 16a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 927 + +--S 928 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1393 +t0:=x^12/(a+b*x^2)^3 +--R +--R +--R 12 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 930 + +--S 931 of 1393 +r0:=-99/8*a^3*x/b^6+33/8*a^2*x^3/b^5-99/40*a*x^5/b^4+99/56*x^7/b^3-_ + 1/4*x^11/(b*(a+b*x^2)^2)-11/8*x^9/(b^2*(a+b*x^2))+_ + 99/8*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 4 2 5 +-+ x\|b +--R (3465a b x + 6930a b x + 3465a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (40b x - 88a b x + 264a b x - 1848a b x - 5775a b x - 3465a x)\|b +--R / +--R 8 4 7 2 2 6 +-+ +--R (280b x + 560a b x + 280a b )\|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 2 4 4 2 5 | a \| b +--R (3465a b x + 6930a b x + 3465a ) |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R 80b x - 176a b x + 528a b x - 3696a b x - 11550a b x - 6930a x +--R / +--R 8 4 7 2 2 6 +--R 560b x + 1120a b x + 560a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 3 2 4 4 2 5 |a \|b 5 11 4 9 +--R (- 3465a b x - 6930a b x - 3465a ) |- atan(----) + 40b x - 88a b x +--R \|b x +--R + +--R 2 3 7 3 2 5 4 3 5 +--R 264a b x - 1848a b x - 5775a b x - 3465a x +--R / +--R 8 4 7 2 2 6 +--R 280b x + 560a b x + 280a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 932 + +--S 933 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R 99a |- - \|b log(---------------------) - 198a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 6 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - 99a \|a atan(-----) - 99a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------------- +--R 6 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 936 + +)clear all + +--S 937 of 1393 +t0:=x^11/(a+b*x^2)^3 +--R +--R +--R 11 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 937 + +--S 938 of 1393 +r0:=3*a^2*x^2/b^5-3/4*a*x^4/b^4+1/6*x^6/b^3+1/4*a^5/(b^6*(a+b*x^2)^2)-_ + 5/2*a^4/(b^6*(a+b*x^2))-5*a^3*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x +--R + +--R 2 3 6 3 2 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27a +--R / +--R 8 4 7 2 2 6 +--R 12b x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x +--R + +--R 2 3 6 3 2 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27a +--R / +--R 8 4 7 2 2 6 +--R 12b x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 939 + +--S 940 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 941 + +)clear all + +--S 942 of 1393 +t0:=x^10/(a+b*x^2)^3 +--R +--R +--R 10 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 942 + +--S 943 of 1393 +r0:=63/8*a^2*x/b^5-21/8*a*x^3/b^4+63/40*x^5/b^3-1/4*x^9/(b*(a+b*x^2)^2)-_ + 9/8*x^7/(b^2*(a+b*x^2))-63/8*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 4 3 2 4 +-+ x\|b +--R (- 315a b x - 630a b x - 315a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (8b x - 24a b x + 168a b x + 525a b x + 315a x)\|b +--R / +--R 7 4 6 2 2 5 +-+ +--R (40b x + 80a b x + 40a b )\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 2 4 3 2 4 | a \| b +--R (315a b x + 630a b x + 315a ) |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +--R 16b x - 48a b x + 336a b x + 1050a b x + 630a x +--R / +--R 7 4 6 2 2 5 +--R 80b x + 160a b x + 80a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 2 4 3 2 4 |a \|b 4 9 3 7 +--R (315a b x + 630a b x + 315a ) |- atan(----) + 8b x - 24a b x +--R \|b x +--R + +--R 2 2 5 3 3 4 +--R 168a b x + 525a b x + 315a x +--R / +--R 7 4 6 2 2 5 +--R 40b x + 80a b x + 40a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 944 + +--S 945 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 63a |- - \|b log(-----------------------) + 126a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 63a \|a atan(-----) + 63a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1393 +t0:=x^9/(a+b*x^2)^3 +--R +--R +--R 9 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 949 + +--S 950 of 1393 +r0:=-3/2*a*x^2/b^4+1/4*x^4/b^3-1/4*a^4/(b^5*(a+b*x^2)^2)+_ + 2*a^3/(b^5*(a+b*x^2))+3*a^2*log(a+b*x^2)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7a +--R / +--R 7 4 6 2 2 5 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7a +--R / +--R 7 4 6 2 2 5 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1393 +t0:=x^8/(a+b*x^2)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 954 + +--S 955 of 1393 +r0:=-35/8*a*x/b^4+35/24*x^3/b^3-1/4*x^7/(b*(a+b*x^2)^2)-_ + 7/8*x^5/(b^2*(a+b*x^2))+35/8*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 3 +-+ x\|b +--R (105a b x + 210a b x + 105a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (8b x - 56a b x - 175a b x - 105a x)\|b +--R / +--R 6 4 5 2 2 4 +-+ +--R (24b x + 48a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 4 2 2 3 | a \| b +--R (105a b x + 210a b x + 105a ) |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 3 7 2 5 2 3 3 +--R 16b x - 112a b x - 350a b x - 210a x +--R / +--R 6 4 5 2 2 4 +--R 48b x + 96a b x + 48a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 4 2 2 3 |a \|b 3 7 2 5 +--R (- 105a b x - 210a b x - 105a ) |- atan(----) + 8b x - 56a b x +--R \|b x +--R + +--R 2 3 3 +--R - 175a b x - 105a x +--R / +--R 6 4 5 2 2 4 +--R 24b x + 48a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 35a\|a atan(-----) - 35a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1393 +t0:=x^7/(a+b*x^2)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1393 +r0:=1/2*x^2/b^3+1/4*a^3/(b^4*(a+b*x^2)^2)-3/2*a^2/(b^4*(a+b*x^2))-_ + 3/2*a*log(a+b*x^2)/b^4 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R --------------------------------------------------------------------------- +--R 6 4 5 2 2 4 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R --------------------------------------------------------------------------- +--R 6 4 5 2 2 4 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1393 +t0:=x^6/(a+b*x^2)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 1393 +r0:=15/8*x/b^3-1/4*x^5/(b*(a+b*x^2)^2)-5/8*x^3/(b^2*(a+b*x^2))-_ + 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 +-+ x\|b 2 5 3 2 +-+ +--R (- 15b x - 30a b x - 15a )\|a atan(-----) + (8b x + 25a b x + 15a x)\|b +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R 5 4 4 2 2 3 +-+ +--R (8b x + 16a b x + 8a b )\|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 4 2 2 | a \| b 2 5 +--R (15b x + 30a b x + 15a ) |- - log(-----------------------) + 16b x +--R \| b 2 +--R b x + a +--R + +--R 3 2 +--R 50a b x + 30a x +--R / +--R 5 4 4 2 2 3 +--R 16b x + 32a b x + 16a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 4 2 2 |a \|b 2 5 3 2 +--R (15b x + 30a b x + 15a ) |- atan(----) + 8b x + 25a b x + 15a x +--R \|b x +--R -------------------------------------------------------------------] +--R 5 4 4 2 2 3 +--R 8b x + 16a b x + 8a b +--R Type: Union(List(Expression(Integer)),...) +--E 968 + +--S 969 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 15 |- - \|b log(----------------------- + 30\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 15\|a atan(-----) + 15 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1393 +t0:=x^5/(a+b*x^2)^3 +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1393 +r0:=-1/4*a^2/(b^3*(a+b*x^2)^2)+a/(b^3*(a+b*x^2))+1/2*log(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ---------------------------------------------------- +--R 5 4 4 2 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ---------------------------------------------------- +--R 5 4 4 2 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1393 +t0:=x^4/(a+b*x^2)^3 +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 978 + +--S 979 of 1393 +r0:=-1/4*x^3/(b*(a+b*x^2)^2)-3/8*x/(b^2*(a+b*x^2))+_ + 3/8*atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x + 6a b x + 3a )atan(-----) + (- 5b x - 3a x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 4 4 3 2 2 2 +-+ +-+ +--R (8b x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (3b x + 6a b x + 3a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (- 10b x - 6a x)\|- a b +--R / +--R 4 4 3 2 2 2 +-----+ +--R (16b x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3b x + 6a b x + 3a )atan(-------) + (- 5b x - 3a x)\|a b +--R a +--R -------------------------------------------------------------] +--R 4 4 3 2 2 2 +---+ +--R (8b x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 980 + +--S 981 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1393 +t0:=x^3/(a+b*x^2)^3 +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 985 + +--S 986 of 1393 +r0:=1/4*x^4/(a*(a+b*x^2)^2) +--R +--R +--R 1 4 +--R - x +--R 4 +--R (2) --------------------- +--R 2 4 2 2 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 986 + +--S 987 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2b x - a +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 987 + +--S 988 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +)clear all + +--S 990 of 1393 +t0:=x^2/(a+b*x^2)^3 +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 990 + +--S 991 of 1393 +r0:=-1/4*x/(b*(a+b*x^2)^2)+1/8*x/(a*b*(a+b*x^2))+_ + 1/8*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (b x + 2a b x + a )atan(-----) + (b x - a x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x + 16a b x + 8a b)\|a \|b +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (b x + 2a b x + a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (2b x - 2a x)\|- a b +--R / +--R 3 4 2 2 2 3 +-----+ +--R (16a b x + 32a b x + 16a b)\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (b x + 2a b x + a )atan(-------) + (b x - a x)\|a b +--R a +--R -------------------------------------------------------] +--R 3 4 2 2 2 3 +---+ +--R (8a b x + 16a b x + 8a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 992 + +--S 993 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 996 + +)clear all + +--S 997 of 1393 +t0:=x/(a+b*x^2)^3 +--R +--R +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 997 + +--S 998 of 1393 +r0:=(-1/4)/(b*(a+b*x^2)^2) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - -------------------- +--R 3 4 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 998 + +--S 999 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 3 4 2 2 2 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 999 + +--S 1000 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1001 + +)clear all + +--S 1002 of 1393 +t0:=1/(a+b*x^2)^3 +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1002 + +--S 1003 of 1393 +r0:=1/4*x/(a*(a+b*x^2)^2)+3/8*x/(a^2*(a+b*x^2))+_ + 3/8*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x + 6a b x + 3a )atan(-----) + (3b x + 5a x)\|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x + 16a b x + 8a )\|a \|b +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (3b x + 6a b x + 3a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (6b x + 10a x)\|- a b +--R / +--R 2 2 4 3 2 4 +-----+ +--R (16a b x + 32a b x + 16a )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3b x + 6a b x + 3a )atan(-------) + (3b x + 5a x)\|a b +--R a +--R -----------------------------------------------------------] +--R 2 2 4 3 2 4 +---+ +--R (8a b x + 16a b x + 8a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1004 + +--S 1005 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1393 +t0:=1/(x*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 7 2 5 2 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1009 + +--S 1010 of 1393 +r0:=1/4/(a*(a+b*x^2)^2)+1/2/(a^2*(a+b*x^2))+log(x)/a^3-1/2*log(a+b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x) +--R + +--R 2 2 +--R 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x + 8a b x + 4a +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x) +--R + +--R 2 2 +--R 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x + 8a b x + 4a +--R Type: Union(Expression(Integer),...) +--E 1011 + +--S 1012 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1013 + +)clear all + +--S 1014 of 1393 +t0:=1/(x^2*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1014 + +--S 1015 of 1393 +r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a+b*x^2)^2)+5/8/(a^2*x*(a+b*x^2))-_ + 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|b +--R (- 15b x - 30a b x - 15a x)\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +--R (- 15b x - 25a b x - 8a )\|a +--R / +--R 3 2 5 4 3 5 +-+ +--R (8a b x + 16a b x + 8a x)\|a +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 2 5 3 2 | b \| a 2 4 +--R (15b x + 30a b x + 15a x) |- - log(-----------------------) - 30b x +--R \| a 2 +--R b x + a +--R + +--R 2 2 +--R - 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x + 32a b x + 16a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 3 2 |b \|a 2 4 2 2 +--R (15b x + 30a b x + 15a x) |- atan(-----) - 15b x - 25a b x - 8a +--R \|a b x +--R --------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x + 16a b x + 8a x +--R Type: Union(List(Expression(Integer)),...) +--E 1016 + +--S 1017 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 15 |- - \|a log(----------------------- + 30\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 15\|b atan(-----) + 15\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1393 +t0:=1/(x^3*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 1393 +r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a+b*x^2)^2)+3/4/(a^2*x^2*(a+b*x^2))-_ + 3*b*log(x)/a^4+3/2*b*log(a+b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 2 +--R (6b x + 12a b x + 6a b x )log(b x + a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (6b x + 12a b x + 6a b x )log(b x + a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1393 +t0:=1/(x^4*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 10 2 8 2 6 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 1393 +r0:=(-35/24)/(a^3*x^3)+35/8*b/(a^4*x)+1/4/(a*x^3*(a+b*x^2)^2)+_ + 7/8/(a^2*x^3*(a+b*x^2))+35/8*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 2 3 +-+ x\|b +--R (105b x + 210a b x + 105a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105b x + 175a b x + 56a b x - 8a )\|a +--R / +--R 4 2 7 5 5 6 3 +-+ +--R (24a b x + 48a b x + 24a x )\|a +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 7 2 5 2 3 | b \| a +--R (105b x + 210a b x + 105a b x ) |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 3 6 2 4 2 2 3 +--R 210b x + 350a b x + 112a b x - 16a +--R / +--R 4 2 7 5 5 6 3 +--R 48a b x + 96a b x + 48a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 2 5 2 3 |b \|a 3 6 +--R (- 105b x - 210a b x - 105a b x ) |- atan(-----) + 105b x +--R \|a b x +--R + +--R 2 4 2 2 3 +--R 175a b x + 56a b x - 8a +--R / +--R 4 2 7 5 5 6 3 +--R 24a b x + 48a b x + 24a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1028 + +--S 1029 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 35b\|b atan(-----) - 35b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1032 + +)clear all + +--S 1033 of 1393 +t0:=1/(x^5*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 11 2 9 2 7 3 5 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1033 + +--S 1034 of 1393 +r0:=(-3/2)/(a^3*x^4)+3*b/(a^4*x^2)+1/4/(a*x^4*(a+b*x^2)^2)+_ + 1/(a^2*x^4*(a+b*x^2))+6*b^2*log(x)/a^5-3*b^2*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 8 6 6 7 4 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 8 6 6 7 4 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1035 + +--S 1036 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1393 +t0:=1/(x^6*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 12 2 10 2 8 3 6 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1038 + +--S 1039 of 1393 +r0:=(-63/40)/(a^3*x^5)+21/8*b/(a^4*x^3)-63/8*b^2/(a^5*x)+_ + 1/4/(a*x^5*(a+b*x^2)^2)+9/8/(a^2*x^5*(a+b*x^2))-_ + 63/8*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 2 2 5 +-+ x\|b +--R (- 315b x - 630a b x - 315a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x - 525a b x - 168a b x + 24a b x - 8a )\|a +--R / +--R 5 2 9 6 7 7 5 +-+ +--R (40a b x + 80a b x + 40a x )\|a +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 4 9 3 7 2 2 5 | b \| a +--R (315b x + 630a b x + 315a b x ) |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x - 1050a b x - 336a b x + 48a b x - 16a +--R / +--R 5 2 9 6 7 7 5 +--R 80a b x + 160a b x + 80a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 4 9 3 7 2 2 5 |b \|a 4 8 3 6 +--R (315b x + 630a b x + 315a b x ) |- atan(-----) - 315b x - 525a b x +--R \|a b x +--R + +--R 2 2 4 3 2 4 +--R - 168a b x + 24a b x - 8a +--R / +--R 5 2 9 6 7 7 5 +--R 40a b x + 80a b x + 40a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 63b \|b atan(-----) + 63b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1393 +t0:=1/(x^7*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 13 2 11 2 9 3 7 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1045 + +--S 1046 of 1393 +r0:=(-5/3)/(a^3*x^6)+5/2*b/(a^4*x^4)-5*b^2/(a^5*x^2)+_ + 1/4/(a*x^6*(a+b*x^2)^2)+5/4/(a^2*x^6*(a+b*x^2))-_ + 10*b^3*log(x)/a^6+5*b^3*log(a+b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 3 6 2 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 10 4 8 2 3 6 4 8 2 3 6 +--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x +--R + +--R 3 2 4 4 2 5 +--R - 20a b x + 5a b x - 2a +--R / +--R 6 2 10 7 8 8 6 +--R 12a b x + 24a b x + 12a x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 2 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 10 4 8 2 3 6 4 8 2 3 6 +--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x +--R + +--R 3 2 4 4 2 5 +--R - 20a b x + 5a b x - 2a +--R / +--R 6 2 10 7 8 8 6 +--R 12a b x + 24a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1393 +t0:=1/(x^8*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 14 2 12 2 10 3 8 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1050 + +--S 1051 of 1393 +r0:=(-99/56)/(a^3*x^7)+99/40*b/(a^4*x^5)-33/8*b^2/(a^5*x^3)+_ + 99/8*b^3/(a^6*x)+1/4/(a*x^7*(a+b*x^2)^2)+11/8/(a^2*x^7*(a+b*x^2))+_ + 99/8*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(13/2) +--R +--R +--R (2) +--R +-+ +--R 5 11 4 9 2 3 7 +-+ x\|b +--R (3465b x + 6930a b x + 3465a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (3465b x + 5775a b x + 1848a b x - 264a b x + 88a b x - 40a )\|a +--R / +--R 6 2 11 7 9 8 7 +-+ +--R (280a b x + 560a b x + 280a x )\|a +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 5 11 4 9 2 3 7 | b \| a +--R (3465b x + 6930a b x + 3465a b x ) |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 6930b x + 11550a b x + 3696a b x - 528a b x + 176a b x - 80a +--R / +--R 6 2 11 7 9 8 7 +--R 560a b x + 1120a b x + 560a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 5 11 4 9 2 3 7 |b \|a 5 10 +--R (- 3465b x - 6930a b x - 3465a b x ) |- atan(-----) + 3465b x +--R \|a b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 5775a b x + 1848a b x - 264a b x + 88a b x - 40a +--R / +--R 6 2 11 7 9 8 7 +--R 280a b x + 560a b x + 280a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1052 + +--S 1053 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R 99b |- - \|a log(---------------------) - 198b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 6 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - 99b \|b atan(-----) - 99b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------------- +--R 6 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1056 + +)clear all + +--S 1057 of 1393 +t0:=1/(x^9*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 15 2 13 2 11 3 9 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1057 + +--S 1058 of 1393 +r0:=(-15/8)/(a^3*x^8)+5/2*b/(a^4*x^6)-15/4*b^2/(a^5*x^4)+_ + 15/2*b^3/(a^6*x^2)+1/4/(a*x^8*(a+b*x^2)^2)+3/2/(a^2*x^8*(a+b*x^2))+_ + 15*b^4*log(x)/a^7-15/2*b^4*log(a+b*x^2)/a^7 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 2 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 12 5 10 2 4 8 5 10 2 4 8 +--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R 20a b x - 5a b x + 2a b x - a +--R / +--R 7 2 12 8 10 9 8 +--R 8a b x + 16a b x + 8a x +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 2 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 12 5 10 2 4 8 5 10 2 4 8 +--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R 20a b x - 5a b x + 2a b x - a +--R / +--R 7 2 12 8 10 9 8 +--R 8a b x + 16a b x + 8a x +--R Type: Union(Expression(Integer),...) +--E 1059 + +--S 1060 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1061 + +)clear all + +--S 1062 of 1393 +t0:=x^25/(a+b*x^2)^10 +--R +--R +--R (1) +--R 25 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1062 + +--S 1063 of 1393 +r0:=55/2*a^2*x^2/b^12-5/2*a*x^4/b^11+1/6*x^6/b^10-_ + 1/18*a^12/(b^13*(a+b*x^2)^9)+3/4*a^11/(b^13*(a+b*x^2)^8)-_ + 33/7*a^10/(b^13*(a+b*x^2)^7)+55/3*a^9/(b^13*(a+b*x^2)^6)-_ + 99/2*a^8/(b^13*(a+b*x^2)^5)+99*a^7/(b^13*(a+b*x^2)^4)-_ + 154*a^6/(b^13*(a+b*x^2)^3)+198*a^5/(b^13*(a+b*x^2)^2)-_ + 495/2*a^4/(b^13*(a+b*x^2))-110*a^3*log(a+b*x^2)/b^13 +--R +--R +--R (2) +--R 3 9 18 4 8 16 5 7 14 6 6 12 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 10 8 4 8 9 3 6 10 2 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 2 12 +--R - 249480a b x - 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 4 8 16 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 18 21 16 2 20 14 3 19 12 4 18 10 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 18 4 8 16 5 7 14 6 6 12 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 10 8 4 8 9 3 6 10 2 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 2 12 +--R - 249480a b x - 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 4 8 16 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 18 21 16 2 20 14 3 19 12 4 18 10 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1064 + +--S 1065 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +)clear all + +--S 1067 of 1393 +t0:=x^23/(a+b*x^2)^10 +--R +--R +--R (1) +--R 23 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1067 + +--S 1068 of 1393 +r0:=-5*a*x^2/b^11+1/4*x^4/b^10+1/18*a^11/(b^12*(a+b*x^2)^9)-_ + 11/16*a^10/(b^12*(a+b*x^2)^8)+55/14*a^9/(b^12*(a+b*x^2)^7)-_ + 55/4*a^8/(b^12*(a+b*x^2)^6)+33*a^7/(b^12*(a+b*x^2)^5)-_ + 231/4*a^6/(b^12*(a+b*x^2)^4)+77*a^5/(b^12*(a+b*x^2)^3)-_ + 165/2*a^4/(b^12*(a+b*x^2)^2)+165/2*a^3/(b^12*(a+b*x^2))+_ + 55/2*a^2*log(a+b*x^2)/b^12 +--R +--R +--R (2) +--R 2 9 18 3 8 16 4 7 14 5 6 12 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 2 11 +--R 249480a b x + 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 4 10 2 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 18 20 16 2 19 14 3 18 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 17 10 5 16 8 6 15 6 7 14 4 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 8 13 2 9 12 +--R 9072a b x + 1008a b +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 18 3 8 16 4 7 14 5 6 12 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 2 11 +--R 249480a b x + 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 4 10 2 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 18 20 16 2 19 14 3 18 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 17 10 5 16 8 6 15 6 7 14 4 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 8 13 2 9 12 +--R 9072a b x + 1008a b +--R Type: Union(Expression(Integer),...) +--E 1069 + +--S 1070 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1393 +t0:=x^21/(a+b*x^2)^10 +--R +--R +--R (1) +--R 21 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1072 + +--S 1073 of 1393 +r0:=1/2*x^2/b^10-1/18*a^10/(b^11*(a+b*x^2)^9)+5/8*a^9/(b^11*(a+b*x^2)^8)-_ + 45/14*a^8/(b^11*(a+b*x^2)^7)+10*a^7/(b^11*(a+b*x^2)^6)-_ + 21*a^6/(b^11*(a+b*x^2)^5)+63/2*a^5/(b^11*(a+b*x^2)^4)-_ + 35*a^4/(b^11*(a+b*x^2)^3)+30*a^3/(b^11*(a+b*x^2)^2)-_ + 45/2*a^2/(b^11*(a+b*x^2))-5*a*log(a+b*x^2)/b^11 +--R +--R +--R (2) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 2 10 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x +--R + +--R 9 2 10 +--R - 41229a b x - 4861a +--R / +--R 20 18 19 16 2 18 14 3 17 12 4 16 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 2 10 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x +--R + +--R 9 2 10 +--R - 41229a b x - 4861a +--R / +--R 20 18 19 16 2 18 14 3 17 12 4 16 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1074 + +--S 1075 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1393 +t0:=x^19/(a+b*x^2)^10 +--R +--R +--R (1) +--R 19 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1393 +r0:=1/18*a^9/(b^10*(a+b*x^2)^9)-9/16*a^8/(b^10*(a+b*x^2)^8)+_ + 18/7*a^7/(b^10*(a+b*x^2)^7)-7*a^6/(b^10*(a+b*x^2)^6)+_ + 63/5*a^5/(b^10*(a+b*x^2)^5)-63/4*a^4/(b^10*(a+b*x^2)^4)+_ + 14*a^3/(b^10*(a+b*x^2)^3)-9*a^2/(b^10*(a+b*x^2)^2)+_ + 9/2*a/(b^10*(a+b*x^2))+1/2*log(a+b*x^2)/b^10 +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 9 +--R 22680a b x + 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 18 18 16 2 17 14 3 16 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 15 10 5 14 8 6 13 6 7 12 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 11 2 9 10 +--R 45360a b x + 5040a b +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 9 +--R 22680a b x + 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 18 18 16 2 17 14 3 16 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 15 10 5 14 8 6 13 6 7 12 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 11 2 9 10 +--R 45360a b x + 5040a b +--R Type: Union(Expression(Integer),...) +--E 1079 + +--S 1080 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +)clear all + +--S 1082 of 1393 +t0:=x^17/(a+b*x^2)^10 +--R +--R +--R (1) +--R 17 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1082 + +--S 1083 of 1393 +r0:=1/18*x^18/(a*(a+b*x^2)^9) +--R +--R +--R (2) +--R 1 18 +--R -- x +--R 18 +--R / +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 6 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 4 7 2 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 18 17 16 2 16 14 3 15 12 4 14 10 +--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x +--R + +--R 5 13 8 6 12 6 7 11 4 8 10 2 9 9 +--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b +--R Type: Union(Expression(Integer),...) +--E 1084 + +--S 1085 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------ +--R 9 +--R 18a b +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1086 + +)clear all + +--S 1087 of 1393 +t0:=x^15/(a+b*x^2)^10 +--R +--R +--R (1) +--R 15 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1087 + +--S 1088 of 1393 +r0:=1/18*x^16/(a*(a+b*x^2)^9)+1/144*x^16/(a^2*(a+b*x^2)^8) +--R +--R +--R (2) +--R 1 18 1 16 +--R --- b x + -- a x +--R 144 16 +--R / +--R 2 9 18 3 8 16 4 7 14 5 6 12 6 5 10 7 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 8 3 6 9 2 4 10 2 11 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 36b x - 84a b x - 126a b x - 126a b x - 84a b x - 36a b x +--R + +--R 6 2 7 +--R - 9a b x - a +--R / +--R 17 18 16 16 2 15 14 3 14 12 4 13 10 +--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x +--R + +--R 5 12 8 6 11 6 7 10 4 8 9 2 9 8 +--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b +--R Type: Union(Expression(Integer),...) +--E 1089 + +--S 1090 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------- +--R 2 8 +--R 144a b +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1091 + +)clear all + +--S 1092 of 1393 +t0:=x^13/(a+b*x^2)^10 +--R +--R +--R (1) +--R 13 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1092 + +--S 1093 of 1393 +r0:=1/18*x^14/(a*(a+b*x^2)^9)+1/72*x^14/(a^2*(a+b*x^2)^8)+_ + 1/504*x^14/(a^3*(a+b*x^2)^7) +--R +--R +--R (2) +--R 1 2 18 1 16 1 2 14 +--R --- b x + -- a b x + -- a x +--R 504 56 14 +--R / +--R 3 9 18 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R - 84b x - 126a b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 16 18 15 16 2 14 14 3 13 12 4 12 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 11 8 6 10 6 7 9 4 8 8 2 9 7 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1094 + +--S 1095 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------- +--R 3 7 +--R 504a b +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1096 + +)clear all + +--S 1097 of 1393 +t0:=x^11/(a+b*x^2)^10 +--R +--R +--R (1) +--R 11 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1097 + +--S 1098 of 1393 +r0:=1/18*x^12/(a*(a+b*x^2)^9)+1/48*x^12/(a^2*(a+b*x^2)^8)+_ + 1/168*x^12/(a^3*(a+b*x^2)^7)+1/1008*x^12/(a^4*(a+b*x^2)^6) +--R +--R +--R (2) +--R 1 3 18 1 2 16 1 2 14 1 3 12 +--R ---- b x + --- a b x + -- a b x + -- a x +--R 1008 112 28 12 +--R / +--R 4 9 18 5 8 16 6 7 14 7 6 12 8 5 10 9 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 10 3 6 11 2 4 12 2 13 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1098 + +--S 1099 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 126b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 15 18 14 16 2 13 14 3 12 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 11 10 5 10 8 6 9 6 7 8 4 8 7 2 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x + 9072a b x +--R + +--R 9 6 +--R 1008a b +--R Type: Union(Expression(Integer),...) +--E 1099 + +--S 1100 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - -------- +--R 4 6 +--R 1008a b +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1101 + +)clear all + +--S 1102 of 1393 +t0:=x^9/(a+b*x^2)^10 +--R +--R +--R (1) +--R 9 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1102 + +--S 1103 of 1393 +r0:=-1/18*a^4/(b^5*(a+b*x^2)^9)+1/4*a^3/(b^5*(a+b*x^2)^8)-_ + 3/7*a^2/(b^5*(a+b*x^2)^7)+1/3*a/(b^5*(a+b*x^2)^6)+_ + (-1/10)/(b^5*(a+b*x^2)^5) +--R +--R +--R (2) +--R 1 4 8 1 3 6 1 2 2 4 1 3 2 1 4 +--R - -- b x - -- a b x - -- a b x - --- a b x - ---- a +--R 10 15 35 140 1260 +--R / +--R 14 18 13 16 2 12 14 3 11 12 4 10 10 5 9 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 8 6 7 7 4 8 6 2 9 5 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 3 2 4 +--R - 126b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 14 18 13 16 2 12 14 3 11 12 +--R 1260b x + 11340a b x + 45360a b x + 105840a b x +--R + +--R 4 10 10 5 9 8 6 8 6 7 7 4 8 6 2 +--R 158760a b x + 158760a b x + 105840a b x + 45360a b x + 11340a b x +--R + +--R 9 5 +--R 1260a b +--R Type: Union(Expression(Integer),...) +--E 1104 + +--S 1105 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1106 + +)clear all + +--S 1107 of 1393 +t0:=x^7/(a+b*x^2)^10 +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1107 + +--S 1108 of 1393 +r0:=1/18*a^3/(b^4*(a+b*x^2)^9)-3/16*a^2/(b^4*(a+b*x^2)^8)+_ + 3/14*a/(b^4*(a+b*x^2)^7)+(-1/12)/(b^4*(a+b*x^2)^6) +--R +--R +--R (2) +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - -- b x - -- a b x - --- a b x - ---- a +--R 12 28 112 1008 +--R / +--R 13 18 12 16 2 11 14 3 10 12 4 9 10 5 8 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 7 6 7 6 4 8 5 2 9 4 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1108 + +--S 1109 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 3 +--R - 84b x - 36a b x - 9a b x - a +--R / +--R 13 18 12 16 2 11 14 3 10 12 4 9 10 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x + 127008a b x +--R + +--R 5 8 8 6 7 6 7 6 4 8 5 2 9 4 +--R 127008a b x + 84672a b x + 36288a b x + 9072a b x + 1008a b +--R Type: Union(Expression(Integer),...) +--E 1109 + +--S 1110 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1111 + +)clear all + +--S 1112 of 1393 +t0:=x^5/(a+b*x^2)^10 +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1112 + +--S 1113 of 1393 +r0:=-1/18*a^2/(b^3*(a+b*x^2)^9)+1/8*a/(b^3*(a+b*x^2)^8)+_ + (-1/14)/(b^3*(a+b*x^2)^7) +--R +--R +--R (2) +--R 1 2 4 1 2 1 2 +--R - -- b x - -- a b x - --- a +--R 14 56 504 +--R / +--R 12 18 11 16 2 10 14 3 9 12 4 8 10 5 7 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 6 6 7 5 4 8 4 2 9 3 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1113 + +--S 1114 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 +--R - 36b x - 9a b x - a +--R / +--R 12 18 11 16 2 10 14 3 9 12 4 8 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 7 8 6 6 6 7 5 4 8 4 2 9 3 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1114 + +--S 1115 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1116 + +)clear all + +--S 1117 of 1393 +t0:=x^3/(a+b*x^2)^10 +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1117 + +--S 1118 of 1393 +r0:=1/18*a/(b^2*(a+b*x^2)^9)+(-1/16)/(b^2*(a+b*x^2)^8) +--R +--R +--R (2) +--R 1 2 1 +--R - -- b x - --- a +--R 16 144 +--R / +--R 11 18 10 16 2 9 14 3 8 12 4 7 10 5 6 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 5 6 7 4 4 8 3 2 9 2 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1118 + +--S 1119 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R - 9b x - a +--R / +--R 11 18 10 16 2 9 14 3 8 12 4 7 10 +--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x +--R + +--R 5 6 8 6 5 6 7 4 4 8 3 2 9 2 +--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b +--R Type: Union(Expression(Integer),...) +--E 1119 + +--S 1120 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1121 + +)clear all + +--S 1122 of 1393 +t0:=x/(a+b*x^2)^10 +--R +--R +--R (1) +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1122 + +--S 1123 of 1393 +r0:=(-1/18)/(b*(a+b*x^2)^9) +--R +--R +--R (2) +--R - +--R 1 +--R -- +--R 18 +--R / +--R 10 18 9 16 2 8 14 3 7 12 4 6 10 5 5 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 4 6 7 3 4 8 2 2 9 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1123 + +--S 1124 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 10 18 9 16 2 8 14 3 7 12 4 6 10 +--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x +--R + +--R 5 5 8 6 4 6 7 3 4 8 2 2 9 +--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b +--R Type: Union(Expression(Integer),...) +--E 1124 + +--S 1125 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1126 + +)clear all + +--S 1127 of 1393 +t0:=1/(x*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 21 9 19 2 8 17 3 7 15 4 6 13 5 5 11 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1127 + +--S 1128 of 1393 +r0:=1/18/(a*(a+b*x^2)^9)+1/16/(a^2*(a+b*x^2)^8)+1/14/(a^3*(a+b*x^2)^7)+_ + 1/12/(a^4*(a+b*x^2)^6)+1/10/(a^5*(a+b*x^2)^5)+_ + 1/8/(a^6*(a+b*x^2)^4)+1/6/(a^7*(a+b*x^2)^3)+_ + 1/4/(a^8*(a+b*x^2)^2)+1/2/(a^9*(a+b*x^2))+log(x)/a^10-_ + 1/2*log(a+b*x^2)/a^10 +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 9 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 2 9 +--R 45360a b x + 5040a +--R * +--R log(x) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 18 11 8 16 12 7 14 13 6 12 +--R 5040a b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 14 5 10 15 4 8 16 3 6 17 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 18 2 19 +--R 45360a b x + 5040a +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 9 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 2 9 +--R 45360a b x + 5040a +--R * +--R log(x) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 18 11 8 16 12 7 14 13 6 12 +--R 5040a b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 14 5 10 15 4 8 16 3 6 17 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 18 2 19 +--R 45360a b x + 5040a +--R Type: Union(Expression(Integer),...) +--E 1129 + +--S 1130 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1131 + +)clear all + +--S 1132 of 1393 +t0:=1/(x^3*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 23 9 21 2 8 19 3 7 17 4 6 15 5 5 13 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 11 7 3 9 8 2 7 9 5 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1132 + +--S 1133 of 1393 +r0:=(-5)/(a^10*x^2)+1/18/(a*x^2*(a+b*x^2)^9)+5/72/(a^2*x^2*(a+b*x^2)^8)+_ + 5/56/(a^3*x^2*(a+b*x^2)^7)+5/42/(a^4*x^2*(a+b*x^2)^6)+_ + 1/6/(a^5*x^2*(a+b*x^2)^5)+1/4/(a^6*x^2*(a+b*x^2)^4)+_ + 5/12/(a^7*x^2*(a+b*x^2)^3)+5/6/(a^8*x^2*(a+b*x^2)^2)+_ + 5/2/(a^9*x^2*(a+b*x^2))-10*b*log(x)/a^11+5*b*log(a+b*x^2)/a^11 +--R +--R +--R (2) +--R 10 20 9 18 2 8 16 3 7 14 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 4 9 2 +--R 22680a b x + 2520a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 5040b x - 45360a b x - 181440a b x - 423360a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x +--R + +--R 8 2 4 9 2 +--R - 45360a b x - 5040a b x +--R * +--R log(x) +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x +--R + +--R 10 +--R - 252a +--R / +--R 11 9 20 12 8 18 13 7 16 14 6 14 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x +--R + +--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4 +--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x +--R + +--R 20 2 +--R 504a x +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 4 9 2 +--R 22680a b x + 2520a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 5040b x - 45360a b x - 181440a b x - 423360a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x +--R + +--R 8 2 4 9 2 +--R - 45360a b x - 5040a b x +--R * +--R log(x) +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x +--R + +--R 10 +--R - 252a +--R / +--R 11 9 20 12 8 18 13 7 16 14 6 14 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x +--R + +--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4 +--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x +--R + +--R 20 2 +--R 504a x +--R Type: Union(Expression(Integer),...) +--E 1134 + +--S 1135 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1136 + +)clear all + +--S 1137 of 1393 +t0:=1/(x^5*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 25 9 23 2 8 21 3 7 19 4 6 17 5 5 15 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 13 7 3 11 8 2 9 9 7 10 5 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1137 + +--S 1138 of 1393 +r0:=(-55/4)/(a^10*x^4)+55/2*b/(a^11*x^2)+1/18/(a*x^4*(a+b*x^2)^9)+_ + 11/144/(a^2*x^4*(a+b*x^2)^8)+55/504/(a^3*x^4*(a+b*x^2)^7)+_ + 55/336/(a^4*x^4*(a+b*x^2)^6)+11/42/(a^5*x^4*(a+b*x^2)^5)+_ + 11/24/(a^6*x^4*(a+b*x^2)^4)+11/12/(a^7*x^4*(a+b*x^2)^3)+_ + 55/24/(a^8*x^4*(a+b*x^2)^2)+55/6/(a^9*x^4*(a+b*x^2))+_ + 55*b^2*log(x)/a^12-55/2*b^2*log(a+b*x^2)/a^12 +--R +--R +--R (2) +--R 11 22 10 20 2 9 18 3 8 16 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 6 9 2 4 +--R - 249480a b x - 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 +--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x +--R + +--R 8 3 6 9 2 4 +--R 498960a b x + 55440a b x +--R * +--R log(x) +--R + +--R 10 20 2 9 18 3 8 16 4 7 14 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 4 10 2 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 22 13 8 20 14 7 18 15 6 16 +--R 1008a b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 16 5 14 17 4 12 18 3 10 19 2 8 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 20 6 21 4 +--R 9072a b x + 1008a x +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 22 10 20 2 9 18 3 8 16 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 6 9 2 4 +--R - 249480a b x - 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 +--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x +--R + +--R 8 3 6 9 2 4 +--R 498960a b x + 55440a b x +--R * +--R log(x) +--R + +--R 10 20 2 9 18 3 8 16 4 7 14 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 4 10 2 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 22 13 8 20 14 7 18 15 6 16 +--R 1008a b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 16 5 14 17 4 12 18 3 10 19 2 8 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 20 6 21 4 +--R 9072a b x + 1008a x +--R Type: Union(Expression(Integer),...) +--E 1139 + +--S 1140 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1393 +t0:=1/(x^7*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 27 9 25 2 8 23 3 7 21 4 6 19 5 5 17 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 15 7 3 13 8 2 11 9 9 10 7 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1393 +r0:=(-110/3)/(a^10*x^6)+55*b/(a^11*x^4)-110*b^2/(a^12*x^2)+_ + 1/18/(a*x^6*(a+b*x^2)^9)+1/12/(a^2*x^6*(a+b*x^2)^8)+_ + 11/84/(a^3*x^6*(a+b*x^2)^7)+55/252/(a^4*x^6*(a+b*x^2)^6)+_ + 11/28/(a^5*x^6*(a+b*x^2)^5)+11/14/(a^6*x^6*(a+b*x^2)^4)+_ + 11/6/(a^7*x^6*(a+b*x^2)^3)+11/2/(a^8*x^6*(a+b*x^2)^2)+_ + 55/2/(a^9*x^6*(a+b*x^2))-220*b^3*log(x)/a^13+110*b^3*log(a+b*x^2)/a^13 +--R +--R +--R (2) +--R 12 24 11 22 2 10 20 3 9 18 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 8 9 3 6 +--R 249480a b x + 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x +--R + +--R 8 4 8 9 3 6 +--R - 498960a b x - 55440a b x +--R * +--R log(x) +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 18 4 14 19 3 12 20 2 10 21 8 22 6 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 24 11 22 2 10 20 3 9 18 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 8 9 3 6 +--R 249480a b x + 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x +--R + +--R 8 4 8 9 3 6 +--R - 498960a b x - 55440a b x +--R * +--R log(x) +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 18 4 14 19 3 12 20 2 10 21 8 22 6 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1393 +t0:=x^24/(a+b*x^2)^10 +--R +--R +--R (1) +--R 24 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1393 +r0:=7436429/65536*a^2*x/b^12-7436429/196608*a*x^3/b^11+_ + 7436429/327680*x^5/b^10-1/18*x^23/(b*(a+b*x^2)^9)-_ + 23/288*x^21/(b^2*(a+b*x^2)^8)-23/192*x^19/(b^3*(a+b*x^2)^7)-_ + 437/2304*x^17/(b^4*(a+b*x^2)^6)-7429/23040*x^15/(b^5*(a+b*x^2)^5)-_ + 7429/12288*x^13/(b^6*(a+b*x^2)^4)-96577/73728*x^11/(b^7*(a+b*x^2)^3)-_ + 1062347/294912*x^9/(b^8*(a+b*x^2)^2)-_ + 1062347/65536*x^7/(b^9*(a+b*x^2))-_ + 7436429/65536*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(25/2) +--R +--R +--R (2) +--R 2 9 18 3 8 16 4 7 14 +--R - 334639305a b x - 3011753745a b x - 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R - 28109701620a b x - 42164552430a b x - 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R - 28109701620a b x - 12047014980a b x - 3011753745a b x +--R + +--R 11 +--R - 334639305a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 7323998514a b x + 19562592546a b x + 32314857354a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 34810986496a b x + 24648575094a b x + 11110024926a b x +--R + +--R 10 3 11 +--R 2900207310a b x + 334639305a x +--R * +--R +-+ +--R \|b +--R / +--R 21 18 20 16 2 19 14 +--R 2949120b x + 26542080a b x + 106168320a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 9 18 3 8 16 4 7 14 +--R 334639305a b x + 3011753745a b x + 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 11 +--R 334639305a +--R * +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b +--R |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 1179648b x - 9043968a b x + 189923328a b x + 2939264622a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 14647997028a b x + 39125185092a b x + 64629714708a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 69621972992a b x + 49297150188a b x + 22220049852a b x +--R + +--R 10 3 11 +--R 5800414620a b x + 669278610a x +--R / +--R 21 18 20 16 2 19 14 +--R 5898240b x + 53084160a b x + 212336640a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 495452160a b x + 743178240a b x + 743178240a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a b +--R , +--R +--R 2 9 18 3 8 16 4 7 14 +--R 334639305a b x + 3011753745a b x + 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 11 +--R 334639305a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 7323998514a b x + 19562592546a b x + 32314857354a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 34810986496a b x + 24648575094a b x + 11110024926a b x +--R + +--R 10 3 11 +--R 2900207310a b x + 334639305a x +--R / +--R 21 18 20 16 2 19 14 +--R 2949120b x + 26542080a b x + 106168320a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1149 + +--S 1150 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 7436429a |- - \|b log(-----------------------) + 14872858a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R --------------------------------------------------------------------------- +--R 12 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 7436429a \|a atan(-----) + 7436429a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------------ +--R 12 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1153 + +)clear all + +--S 1154 of 1393 +t0:=x^22/(a+b*x^2)^10 +--R +--R +--R (1) +--R 22 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1154 + +--S 1155 of 1393 +r0:=-1616615/65536*a*x/b^11+1616615/196608*x^3/b^10-_ + 1/18*x^21/(b*(a+b*x^2)^9)-7/96*x^19/(b^2*(a+b*x^2)^8)-_ + 19/192*x^17/(b^3*(a+b*x^2)^7)-323/2304*x^15/(b^4*(a+b*x^2)^6)-_ + 323/1536*x^13/(b^5*(a+b*x^2)^5)-4199/12288*x^11/(b^6*(a+b*x^2)^4)-_ + 46189/73728*x^9/(b^7*(a+b*x^2)^3)-46189/32768*x^7/(b^8*(a+b*x^2)^2)-_ + 323323/65536*x^5/(b^9*(a+b*x^2))+_ + 1616615/65536*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(23/2) +--R +--R +--R (2) +--R 9 18 2 8 16 3 7 14 +--R 14549535a b x + 130945815a b x + 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 850547502a b x - 1404993798a b x - 1513521152a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x +--R * +--R +-+ +--R \|b +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 4 16 10 5 15 8 6 14 6 7 13 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 8 12 2 9 11 +--R 5308416a b x + 589824a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 2 8 16 3 7 14 +--R 14549535a b x + 130945815a b x + 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R | a \| b +--R |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 393216b x - 8257536a b x - 127794114a b x - 636869436a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 1701095004a b x - 2809987596a b x - 3027042304a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 2143354356a b x - 966089124a b x - 252191940a b x - 29099070a x +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 1179648b x + 10616832a b x + 42467328a b x + 99090432a b x +--R + +--R 4 16 10 5 15 8 6 14 6 +--R 148635648a b x + 148635648a b x + 99090432a b x +--R + +--R 7 13 4 8 12 2 9 11 +--R 42467328a b x + 10616832a b x + 1179648a b +--R , +--R +--R 9 18 2 8 16 3 7 14 +--R - 14549535a b x - 130945815a b x - 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 850547502a b x - 1404993798a b x - 1513521152a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 4 16 10 5 15 8 6 14 6 7 13 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 8 12 2 9 11 +--R 5308416a b x + 589824a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1156 + +--S 1157 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 1616615a |- - \|b log(---------------------) - 3233230a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------------- +--R 11 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 1616615a\|a atan(-----) - 1616615a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------------ +--R 11 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1393 +t0:=x^20/(a+b*x^2)^10 +--R +--R +--R (1) +--R 20 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 1393 +r0:=230945/65536*x/b^10-1/18*x^19/(b*(a+b*x^2)^9)-_ + 19/288*x^17/(b^2*(a+b*x^2)^8)-323/4032*x^15/(b^3*(a+b*x^2)^7)-_ + 1615/16128*x^13/(b^4*(a+b*x^2)^6)-4199/32256*x^11/(b^5*(a+b*x^2)^5)-_ + 46189/258048*x^9/(b^6*(a+b*x^2)^4)-_ + 46189/172032*x^7/(b^7*(a+b*x^2)^3)-46189/98304*x^5/(b^8*(a+b*x^2)^2)-_ + 230945/196608*x^3/(b^9*(a+b*x^2))-_ + 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(21/2) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 1404993798a b x + 1513521152a b x + 1071677178a b x +--R + +--R 7 2 5 8 3 9 +--R 483044562a b x + 126095970a b x + 14549535a x +--R * +--R +-+ +--R \|b +--R / +--R 19 18 18 16 2 17 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b +--R |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 8257536b x + 127794114a b x + 636869436a b x + 1701095004a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 2809987596a b x + 3027042304a b x + 2143354356a b x +--R + +--R 7 2 5 8 3 9 +--R 966089124a b x + 252191940a b x + 29099070a x +--R / +--R 19 18 18 16 2 17 14 +--R 8257536b x + 74317824a b x + 297271296a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R , +--R +--R 9 18 8 16 2 7 14 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 1404993798a b x + 1513521152a b x + 1071677178a b x +--R + +--R 7 2 5 8 3 9 +--R 483044562a b x + 126095970a b x + 14549535a x +--R / +--R 19 18 18 16 2 17 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1163 + +--S 1164 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 230945 |- - \|b log(----------------------- + 461890\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 10 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 230945\|a atan(-----) + 230945 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------ +--R 10 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1167 + +)clear all + +--S 1168 of 1393 +t0:=x^18/(a+b*x^2)^10 +--R +--R +--R (1) +--R 18 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1168 + +--S 1169 of 1393 +r0:=-1/18*x^17/(b*(a+b*x^2)^9)-17/288*x^15/(b^2*(a+b*x^2)^8)-_ + 85/1344*x^13/(b^3*(a+b*x^2)^7)-1105/16128*x^11/(b^4*(a+b*x^2)^6)-_ + 2431/32256*x^9/(b^5*(a+b*x^2)^5)-2431/28672*x^7/(b^6*(a+b*x^2)^4)-_ + 2431/24576*x^5/(b^7*(a+b*x^2)^3)-12155/98304*x^3/(b^8*(a+b*x^2)^2)-_ + 12155/65536*x/(b^9*(a+b*x^2))+_ + 12155/65536*atan(x*sqrt(b)/sqrt(a))/(b^(19/2)*sqrt(a)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 3363003b x - 16759722a b x - 44765658a b x - 73947042a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 79659008a b x - 56404062a b x - 25423398a b x - 6636630a b x +--R + +--R 8 +--R - 765765a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 18 18 17 16 2 16 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 +--R - 6726006b x - 33519444a b x - 89531316a b x +--R + +--R 3 5 11 4 4 9 5 3 7 +--R - 147894084a b x - 159318016a b x - 112808124a b x +--R + +--R 6 2 5 7 3 8 +--R - 50846796a b x - 13273260a b x - 1531530a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 18 18 17 16 2 16 14 +--R 8257536b x + 74317824a b x + 297271296a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 +--R - 3363003b x - 16759722a b x - 44765658a b x +--R + +--R 3 5 11 4 4 9 5 3 7 +--R - 73947042a b x - 79659008a b x - 56404062a b x +--R + +--R 6 2 5 7 3 8 +--R - 25423398a b x - 6636630a b x - 765765a x +--R * +--R +---+ +--R \|a b +--R / +--R 18 18 17 16 2 16 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1170 + +--S 1171 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R ------------------------------------------------------------------------ +--R 9 +-----+ +-+ +-+ +--R 131072b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------------- +--R 9 +-+ +-+ +---+ +--R 65536b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1393 +t0:=x^16/(a+b*x^2)^10 +--R +--R +--R (1) +--R 16 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1175 + +--S 1176 of 1393 +r0:=-1/18*x^15/(b*(a+b*x^2)^9)-5/96*x^13/(b^2*(a+b*x^2)^8)-_ + 65/1344*x^11/(b^3*(a+b*x^2)^7)-715/16128*x^9/(b^4*(a+b*x^2)^6)-_ + 143/3584*x^7/(b^5*(a+b*x^2)^5)-143/4096*x^5/(b^6*(a+b*x^2)^4)-_ + 715/24576*x^3/(b^7*(a+b*x^2)^3)-715/32768*x/(b^8*(a+b*x^2)^2)+_ + 715/65536*x/(a*b^8*(a+b*x^2))+_ + 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(17/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 17 18 2 16 16 3 15 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x - 1971732a b x - 5266548a b x - 8699652a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 17 18 2 16 16 3 15 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 17 18 2 16 16 3 15 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1177 + +--S 1178 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------------- +--R 8 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 715\|a \|b atan(-------) - 715\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 8 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1181 + +)clear all + +--S 1182 of 1393 +t0:=x^14/(a+b*x^2)^10 +--R +--R +--R (1) +--R 14 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1182 + +--S 1183 of 1393 +r0:=-1/18*x^13/(b*(a+b*x^2)^9)-13/288*x^11/(b^2*(a+b*x^2)^8)-_ + 143/4032*x^9/(b^3*(a+b*x^2)^7)-143/5376*x^7/(b^4*(a+b*x^2)^6)-_ + 143/7680*x^5/(b^5*(a+b*x^2)^5)-143/12288*x^3/(b^6*(a+b*x^2)^4)-_ + 143/24576*x/(b^7*(a+b*x^2)^3)+143/98304*x/(a*b^7*(a+b*x^2)^2)+_ + 143/65536*x/(a^2*b^7*(a+b*x^2))+_ + 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(15/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x - 5266548a b x - 8699652a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 41287680a b x + 371589120a b x + 1486356480a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 3468165120a b x + 5202247680a b x + 5202247680a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 3468165120a b x + 1486356480a b x + 371589120a b x + 41287680a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1184 + +--S 1185 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 2 7 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 143\|a \|b atan(-------) - 143\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 2 7 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1188 + +)clear all + +--S 1189 of 1393 +t0:=x^12/(a+b*x^2)^10 +--R +--R +--R (1) +--R 12 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1189 + +--S 1190 of 1393 +r0:=-1/18*x^11/(b*(a+b*x^2)^9)-11/288*x^9/(b^2*(a+b*x^2)^8)-_ + 11/448*x^7/(b^3*(a+b*x^2)^7)-11/768*x^5/(b^4*(a+b*x^2)^6)-_ + 11/1536*x^3/(b^5*(a+b*x^2)^5)-11/4096*x/(b^6*(a+b*x^2)^4)+_ + 11/24576*x/(a*b^6*(a+b*x^2)^3)+55/98304*x/(a^2*b^6*(a+b*x^2)^2)+_ + 55/65536*x/(a^3*b^6*(a+b*x^2))+_ + 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(13/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x - 334602a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 6930b x + 60060a b x + 230076a b x - 669204a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 720896a b x - 510444a b x - 230076a b x - 60060a b x - 6930a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x - 334602a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +---+ +--R \|a b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1191 + +--S 1192 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------- +--R 3 6 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 55\|a \|b atan(-------) - 55\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 3 6 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1393 +t0:=x^10/(a+b*x^2)^10 +--R +--R +--R (1) +--R 10 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 1393 +r0:=-1/18*x^9/(b*(a+b*x^2)^9)-1/32*x^7/(b^2*(a+b*x^2)^8)-_ + 1/64*x^5/(b^3*(a+b*x^2)^7)-5/768*x^3/(b^4*(a+b*x^2)^6)-_ + 1/512*x/(b^5*(a+b*x^2)^5)+1/4096*x/(a*b^5*(a+b*x^2)^4)+_ + 7/24576*x/(a^2*b^5*(a+b*x^2)^3)+35/98304*x/(a^3*b^5*(a+b*x^2)^2)+_ + 35/65536*x/(a^4*b^5*(a+b*x^2))+_ + 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*b^(11/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 4 14 18 5 13 16 6 12 14 7 11 12 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 8 10 10 9 9 8 10 8 6 11 7 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 12 6 2 13 5 +--R 5308416a b x + 589824a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 630b x + 5460a b x + 20916a b x + 46404a b x - 65536a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 46404a b x - 20916a b x - 5460a b x - 630a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 4 14 18 5 13 16 6 12 14 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 7 11 12 8 10 10 9 9 8 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 10 8 6 11 7 4 12 6 2 13 5 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +---+ +--R \|a b +--R / +--R 4 14 18 5 13 16 6 12 14 +--R 589824a b x + 5308416a b x + 21233664a b x +--R + +--R 7 11 12 8 10 10 9 9 8 +--R 49545216a b x + 74317824a b x + 74317824a b x +--R + +--R 10 8 6 11 7 4 12 6 2 13 5 +--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1198 + +--S 1199 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 4 5 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 35\|a \|b atan(-------) - 35\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 4 5 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1202 + +)clear all + +--S 1203 of 1393 +t0:=x^8/(a+b*x^2)^10 +--R +--R +--R (1) +--R 8 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1203 + +--S 1204 of 1393 +r0:=-1/18*x^7/(b*(a+b*x^2)^9)-7/288*x^5/(b^2*(a+b*x^2)^8)-_ + 5/576*x^3/(b^3*(a+b*x^2)^7)-5/2304*x/(b^4*(a+b*x^2)^6)+_ + 1/4608*x/(a*b^4*(a+b*x^2)^5)+1/4096*x/(a^2*b^4*(a+b*x^2)^4)+_ + 7/24576*x/(a^3*b^4*(a+b*x^2)^3)+35/98304*x/(a^4*b^4*(a+b*x^2)^2)+_ + 35/65536*x/(a^5*b^4*(a+b*x^2))+_ + 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(11/2)*b^(9/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 5 13 18 6 12 16 7 11 14 8 10 12 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 9 9 10 10 8 8 11 7 6 12 6 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 13 5 2 14 4 +--R 5308416a b x + 589824a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 630b x + 5460a b x + 20916a b x + 46404a b x + 65536a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 46404a b x - 20916a b x - 5460a b x - 630a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 5 13 18 6 12 16 7 11 14 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 8 10 12 9 9 10 10 8 8 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 11 7 6 12 6 4 13 5 2 14 4 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +---+ +--R \|a b +--R / +--R 5 13 18 6 12 16 7 11 14 +--R 589824a b x + 5308416a b x + 21233664a b x +--R + +--R 8 10 12 9 9 10 10 8 8 +--R 49545216a b x + 74317824a b x + 74317824a b x +--R + +--R 11 7 6 12 6 4 13 5 2 14 4 +--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1205 + +--S 1206 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 5 4 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 35\|a \|b atan(-------) - 35\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 5 4 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1393 +t0:=x^6/(a+b*x^2)^10 +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1393 +r0:=-1/18*x^5/(b*(a+b*x^2)^9)-5/288*x^3/(b^2*(a+b*x^2)^8)-_ + 5/1344*x/(b^3*(a+b*x^2)^7)+5/16128*x/(a*b^3*(a+b*x^2)^6)+_ + 11/32256*x/(a^2*b^3*(a+b*x^2)^5)+11/28672*x/(a^3*b^3*(a+b*x^2)^4)+_ + 11/24576*x/(a^4*b^3*(a+b*x^2)^3)+55/98304*x/(a^5*b^3*(a+b*x^2)^2)+_ + 55/65536*x/(a^6*b^3*(a+b*x^2))+_ + 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(13/2)*b^(7/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x + 255222a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 6930b x + 60060a b x + 230076a b x + 510444a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 720896a b x + 669204a b x - 230076a b x - 60060a b x - 6930a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x + 255222a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +---+ +--R \|a b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1212 + +--S 1213 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------- +--R 6 3 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 55\|a \|b atan(-------) - 55\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 6 3 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1216 + +)clear all + +--S 1217 of 1393 +t0:=x^4/(a+b*x^2)^10 +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1393 +r0:=-1/18*x^3/(b*(a+b*x^2)^9)-1/96*x/(b^2*(a+b*x^2)^8)+_ + 1/1344*x/(a*b^2*(a+b*x^2)^7)+13/16128*x/(a^2*b^2*(a+b*x^2)^6)+_ + 143/161280*x/(a^3*b^2*(a+b*x^2)^5)+143/143360*x/(a^4*b^2*(a+b*x^2)^4)+_ + 143/122880*x/(a^5*b^2*(a+b*x^2)^3)+143/98304*x/(a^6*b^2*(a+b*x^2)^2)+_ + 143/65536*x/(a^7*b^2*(a+b*x^2))+_ + 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(15/2)*b^(5/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 13 5 6 14 4 4 15 3 2 16 2 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 9371648a b x + 8699652a b x + 5266548a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 41287680a b x + 371589120a b x + 1486356480a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 3468165120a b x + 5202247680a b x + 5202247680a b x +--R + +--R 13 5 6 14 4 4 15 3 2 +--R 3468165120a b x + 1486356480a b x + 371589120a b x +--R + +--R 16 2 +--R 41287680a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 13 5 6 14 4 4 15 3 2 16 2 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1219 + +--S 1220 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 7 2 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 143\|a \|b atan(-------) - 143\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 7 2 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1223 + +)clear all + +--S 1224 of 1393 +t0:=x^2/(a+b*x^2)^10 +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1224 + +--S 1225 of 1393 +r0:=-1/18*x/(b*(a+b*x^2)^9)+1/288*x/(a*b*(a+b*x^2)^8)+_ + 5/1344*x/(a^2*b*(a+b*x^2)^7)+65/16128*x/(a^3*b*(a+b*x^2)^6)+_ + 143/32256*x/(a^4*b*(a+b*x^2)^5)+143/28672*x/(a^5*b*(a+b*x^2)^4)+_ + 143/24576*x/(a^6*b*(a+b*x^2)^3)+715/98304*x/(a^7*b*(a+b*x^2)^2)+_ + 715/65536*x/(a^8*b*(a+b*x^2))+_ + 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(17/2)*b^(3/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 9371648a b x + 8699652a b x + 5266548a b x + 1971732a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1226 + +--S 1227 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------------- +--R 8 +-----+ +-+ +-+ +--R 131072a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 715\|a \|b atan(-------) - 715\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 8 +-+ +-+ +---+ +--R 65536a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1393 +t0:=1/(a+b*x^2)^10 +--R +--R +--R (1) +--R 1 +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 1393 +r0:=1/18*x/(a*(a+b*x^2)^9)+17/288*x/(a^2*(a+b*x^2)^8)+_ + 85/1344*x/(a^3*(a+b*x^2)^7)+1105/16128*x/(a^4*(a+b*x^2)^6)+_ + 2431/32256*x/(a^5*(a+b*x^2)^5)+2431/28672*x/(a^6*(a+b*x^2)^4)+_ + 2431/24576*x/(a^7*(a+b*x^2)^3)+12155/98304*x/(a^8*(a+b*x^2)^2)+_ + 12155/65536*x/(a^9*(a+b*x^2))+_ + 12155/65536*atan(x*sqrt(b)/sqrt(a))/(a^(19/2)*sqrt(b)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x +--R + +--R 8 +--R 3363003a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 1531530b x + 13273260a b x + 50846796a b x + 112808124a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 159318016a b x + 147894084a b x + 89531316a b x + 33519444a b x +--R + +--R 8 +--R 6726006a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x +--R + +--R 8 +--R 3363003a x +--R * +--R +---+ +--R \|a b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1233 + +--S 1234 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R ------------------------------------------------------------------------ +--R 9 +-----+ +-+ +-+ +--R 131072a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------------- +--R 9 +-+ +-+ +---+ +--R 65536a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1393 +t0:=1/(x^2*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 22 9 20 2 8 18 3 7 16 4 6 14 5 5 12 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1238 + +--S 1239 of 1393 +r0:=(-230945/65536)/(a^10*x)+1/18/(a*x*(a+b*x^2)^9)+_ + 19/288/(a^2*x*(a+b*x^2)^8)+323/4032/(a^3*x*(a+b*x^2)^7)+_ + 1615/16128/(a^4*x*(a+b*x^2)^6)+4199/32256/(a^5*x*(a+b*x^2)^5)+_ + 46189/258048/(a^6*x*(a+b*x^2)^4)+46189/172032/(a^7*x*(a+b*x^2)^3)+_ + 46189/98304/(a^8*x*(a+b*x^2)^2)+230945/196608/(a^9*x*(a+b*x^2))-_ + 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(21/2) +--R +--R +--R (2) +--R 9 19 8 17 2 7 15 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 126095970a b x - 483044562a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1071677178a b x - 1513521152a b x - 1404993798a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a +--R * +--R +-+ +--R \|a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 19 8 17 2 7 15 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x +--R * +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R | b \| a +--R |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 9 18 8 16 2 7 14 +--R - 29099070b x - 252191940a b x - 966089124a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 2143354356a b x - 3027042304a b x - 2809987596a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 1701095004a b x - 636869436a b x - 127794114a b x - 8257536a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a x +--R , +--R +--R 9 19 8 17 2 7 15 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 126095970a b x - 483044562a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1071677178a b x - 1513521152a b x - 1404993798a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1240 + +--S 1241 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 230945 |- - \|a log(----------------------- + 461890\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 10 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 230945\|b atan(-----) + 230945\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------- +--R 10 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1393 +t0:=1/(x^4*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 24 9 22 2 8 20 3 7 18 4 6 16 5 5 14 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 12 7 3 10 8 2 8 9 6 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1393 +r0:=(-1616615/196608)/(a^10*x^3)+1616615/65536*b/(a^11*x)+_ + 1/18/(a*x^3*(a+b*x^2)^9)+7/96/(a^2*x^3*(a+b*x^2)^8)+_ + 19/192/(a^3*x^3*(a+b*x^2)^7)+323/2304/(a^4*x^3*(a+b*x^2)^6)+_ + 323/1536/(a^5*x^3*(a+b*x^2)^5)+4199/12288/(a^6*x^3*(a+b*x^2)^4)+_ + 46189/73728/(a^7*x^3*(a+b*x^2)^3)+46189/32768/(a^8*x^3*(a+b*x^2)^2)+_ + 323323/65536/(a^9*x^3*(a+b*x^2))+_ + 1616615/65536*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(23/2) +--R +--R +--R (2) +--R 10 21 9 19 2 8 17 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 10 20 9 18 2 8 16 +--R 14549535b x + 126095970a b x + 483044562a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 1071677178a b x + 1513521152a b x + 1404993798a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x +--R + +--R 10 +--R - 196608a +--R * +--R +-+ +--R \|a +--R / +--R 11 9 21 12 8 19 13 7 17 14 6 15 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 15 5 13 16 4 11 17 3 9 18 2 7 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 19 5 20 3 +--R 5308416a b x + 589824a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 10 21 9 19 2 8 17 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x +--R * +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b \| a +--R |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 10 20 9 18 2 8 16 +--R 29099070b x + 252191940a b x + 966089124a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 2143354356a b x + 3027042304a b x + 2809987596a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 1701095004a b x + 636869436a b x + 127794114a b x + 8257536a b x +--R + +--R 10 +--R - 393216a +--R / +--R 11 9 21 12 8 19 13 7 17 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 14 6 15 15 5 13 16 4 11 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 17 3 9 18 2 7 19 5 20 3 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a x +--R , +--R +--R 10 21 9 19 2 8 17 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 +--R - 1222160940a b x - 523783260a b x - 130945815a b x +--R + +--R 9 3 +--R - 14549535a b x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 10 20 9 18 2 8 16 +--R 14549535b x + 126095970a b x + 483044562a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 1071677178a b x + 1513521152a b x + 1404993798a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x +--R + +--R 10 +--R - 196608a +--R / +--R 11 9 21 12 8 19 13 7 17 14 6 15 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 15 5 13 16 4 11 17 3 9 18 2 7 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 19 5 20 3 +--R 5308416a b x + 589824a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1247 + +--S 1248 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 1616615b |- - \|a log(---------------------) - 3233230b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------------- +--R 11 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 1616615b\|b atan(-----) - 1616615b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------------- +--R 11 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1393 +t0:=1/(x^6*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 26 9 24 2 8 22 3 7 20 4 6 18 5 5 16 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 14 7 3 12 8 2 10 9 8 10 6 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1252 + +--S 1253 of 1393 +r0:=(-7436429/327680)/(a^10*x^5)+7436429/196608*b/(a^11*x^3)-_ + 7436429/65536*b^2/(a^12*x)+1/18/(a*x^5*(a+b*x^2)^9)+_ + 23/288/(a^2*x^5*(a+b*x^2)^8)+23/192/(a^3*x^5*(a+b*x^2)^7)+_ + 437/2304/(a^4*x^5*(a+b*x^2)^6)+7429/23040/(a^5*x^5*(a+b*x^2)^5)+_ + 7429/12288/(a^6*x^5*(a+b*x^2)^4)+96577/73728/(a^7*x^5*(a+b*x^2)^3)+_ + 1062347/294912/(a^8*x^5*(a+b*x^2)^2)+_ + 1062347/65536/(a^9*x^5*(a+b*x^2))-_ + 7436429/65536*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(25/2) +--R +--R +--R (2) +--R 11 23 10 21 2 9 19 +--R - 334639305b x - 3011753745a b x - 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R - 28109701620a b x - 42164552430a b x - 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R - 28109701620a b x - 12047014980a b x - 3011753745a b x +--R + +--R 9 2 5 +--R - 334639305a b x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 11 22 10 20 2 9 18 +--R - 334639305b x - 2900207310a b x - 11110024926a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 24648575094a b x - 34810986496a b x - 32314857354a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 19562592546a b x - 7323998514a b x - 1469632311a b x +--R + +--R 9 2 4 10 2 11 +--R - 94961664a b x + 4521984a b x - 589824a +--R * +--R +-+ +--R \|a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 2949120a b x + 26542080a b x + 106168320a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 11 23 10 21 2 9 19 +--R 334639305b x + 3011753745a b x + 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 9 2 5 +--R 334639305a b x +--R * +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R | b \| a +--R |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 11 22 10 20 2 9 18 +--R - 669278610b x - 5800414620a b x - 22220049852a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 49297150188a b x - 69621972992a b x - 64629714708a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 39125185092a b x - 14647997028a b x - 2939264622a b x +--R + +--R 9 2 4 10 2 11 +--R - 189923328a b x + 9043968a b x - 1179648a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 5898240a b x + 53084160a b x + 212336640a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 495452160a b x + 743178240a b x + 743178240a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a x +--R , +--R +--R 11 23 10 21 2 9 19 +--R 334639305b x + 3011753745a b x + 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 9 2 5 +--R 334639305a b x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 11 22 10 20 2 9 18 +--R - 334639305b x - 2900207310a b x - 11110024926a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 24648575094a b x - 34810986496a b x - 32314857354a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 19562592546a b x - 7323998514a b x - 1469632311a b x +--R + +--R 9 2 4 10 2 11 +--R - 94961664a b x + 4521984a b x - 589824a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 2949120a b x + 26542080a b x + 106168320a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1254 + +--S 1255 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 7436429b |- - \|a log(-----------------------) + 14872858b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R --------------------------------------------------------------------------- +--R 12 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 7436429b \|b atan(-----) + 7436429b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------------- +--R 12 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1258 + +)clear all + +--S 1259 of 1393 +t0:=x^3/(a-b*x^2) +--R +--R +--R 3 +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1259 + +--S 1260 of 1393 +r0:=-1/2*x^2/b-1/2*a*log(a-b*x^2)/b^2 +--R +--R +--R 2 2 +--R - a log(- b x + a) - b x +--R (2) -------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - a log(b x - a) - b x +--R (3) ------------------------ +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1261 + +--S 1262 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - a log(b x - a) + a log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1263 + +)clear all + +--S 1264 of 1393 +t0:=x^2/(a-b*x^2) +--R +--R +--R 2 +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1264 + +--S 1265 of 1393 +r0:=-x/b+atanh(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R \|a atanh(-----) - x\|b +--R +-+ +--R \|a +--R (2) ------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R |a 2 +---+ +--R +-+ 2b x |- + b x + a | a +--R |a \|b +---+ |- - +--R |- log(-------------------) - 2x | a \| b +--R \|b 2 - |- - atan(------) - x +--R b x - a \| b x +--R (3) [---------------------------------,------------------------] +--R 2b b +--R Type: Union(List(Expression(Integer)),...) +--E 1266 + +--S 1267 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |a 2 +--R +-+ 2b x |- + b x + a +-+ +--R |a +-+ \|b +-+ x\|b +--R |- \|b log(-------------------) - 2\|a atanh(-----) +--R \|b 2 +-+ +--R b x - a \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | a +--R +-+ +---+ |- - +--R +-+ x\|b | a +-+ \| b +--R - \|a atanh(-----) - |- - \|b atan(------) +--R +-+ \| b x +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 1393 +t0:=x/(a-b*x^2) +--R +--R +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1271 + +--S 1272 of 1393 +r0:=-1/2*log(a-b*x^2)/b +--R +--R +--R 2 +--R log(- b x + a) +--R (2) - --------------- +--R 2b +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x - a) +--R (3) - ------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 1393 +t0:=1/(a-b*x^2) +--R +--R +--R 1 +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1276 + +--S 1277 of 1393 +r0:=atanh(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +---+ +--R (b x + a)\|a b + 2a b x +-----+ +--R log(-------------------------) x\|- a b +--R 2 atan(---------) +--R b x - a a +--R (3) [------------------------------,---------------] +--R +---+ +-----+ +--R 2\|a b \|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1278 + +--S 1279 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) - 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2\|a \|b \|a b +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - \|- a b atanh(-----) + \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1282 + +)clear all + +--S 1283 of 1393 +t0:=1/(x*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ---------- +--R 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1283 + +--S 1284 of 1393 +r0:=log(x)/a-1/2*log(a-b*x^2)/a +--R +--R +--R 2 +--R 2log(x) - log(- b x + a) +--R (2) ------------------------- +--R 2a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x - a) + 2log(x) +--R (3) ------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 1285 + +--S 1286 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1287 + +)clear all + +--S 1288 of 1393 +t0:=1/(x^2*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ----------- +--R 4 2 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1288 + +--S 1289 of 1393 +r0:=(-1)/(a*x)+atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R x\|b atanh(-----) - \|a +--R +-+ +--R \|a +--R (2) ------------------------ +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R |b 2 +---+ +--R +-+ 2a x |- + b x + a | b +--R |b \|a +---+ a |- - +--R x |- log(-------------------) - 2 | b \| a +--R \|a 2 - x |- - atan(-------) - 1 +--R b x - a \| a b x +--R (3) [---------------------------------,--------------------------] +--R 2a x a x +--R Type: Union(List(Expression(Integer)),...) +--E 1290 + +--S 1291 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R \|a |- log(-------------------) - 2\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - \|b atanh(-----) - |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) -------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1393 +t0:=1/(x^3*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ----------- +--R 5 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1393 +r0:=(-1/2)/(a*x^2)+b*log(x)/a^2-1/2*b*log(a-b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R 2b x log(x) - b x log(- b x + a) - a +--R (2) ------------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - b x log(b x - a) + 2b x log(x) - a +--R (3) ------------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1393 +t0:=x^3/(a-b*x^2)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1393 +r0:=1/2*a/(b^2*(a-b*x^2))+1/2*log(a-b*x^2)/b^2 +--R +--R +--R 2 2 +--R (b x - a)log(- b x + a) - a +--R (2) ----------------------------- +--R 3 2 2 +--R 2b x - 2a b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (b x - a)log(b x - a) - a +--R (3) --------------------------- +--R 3 2 2 +--R 2b x - 2a b +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R log(b x - a) - log(- b x + a) +--R (4) ------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1393 +t0:=x^2/(a-b*x^2)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1393 +r0:=1/2*x/(b*(a-b*x^2))-1/2*atanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (- b x + a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------ +--R 2 2 +-+ +-+ +--R (2b x - 2a b)\|a \|b +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 (b x + a)\|a b - 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4b x - 4a b)\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (- b x + a)atan(---------) - x\|- a b +--R a +--R ---------------------------------------] +--R 2 2 +-----+ +--R (2b x - 2a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1307 + +--S 1308 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1311 + +)clear all + +--S 1312 of 1393 +t0:=x/(a-b*x^2)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1312 + +--S 1313 of 1393 +r0:=1/2/(b*(a-b*x^2)) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ---------- +--R 2 2 +--R b x - a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1313 + +--S 1314 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2b x - 2a b +--R Type: Union(Expression(Integer),...) +--E 1314 + +--S 1315 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1316 + +)clear all + +--S 1317 of 1393 +t0:=1/(a-b*x^2)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1317 + +--S 1318 of 1393 +r0:=1/2*x/(a*(a-b*x^2))+1/2*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x - a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x - 2a )\|a \|b +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 (b x + a)\|a b + 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4a b x - 4a )\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (b x - a)atan(---------) - x\|- a b +--R a +--R -------------------------------------] +--R 2 2 +-----+ +--R (2a b x - 2a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1319 + +--S 1320 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) - 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - \|- a b atanh(-----) + \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1323 + +)clear all + +--S 1324 of 1393 +t0:=1/(x*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1324 + +--S 1325 of 1393 +r0:=1/2/(a*(a-b*x^2))+log(x)/a^2-1/2*log(a-b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R (2b x - 2a)log(x) + (- b x + a)log(- b x + a) - a +--R (2) ---------------------------------------------------- +--R 2 2 3 +--R 2a b x - 2a +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x + a)log(b x - a) + (2b x - 2a)log(x) - a +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 1326 + +--S 1327 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1328 + +)clear all + +--S 1329 of 1393 +t0:=1/(x^2*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1329 + +--S 1330 of 1393 +r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a-b*x^2))+_ + 3/2*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (3b x - 3a x)\|b atanh(-----) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x - 2a x)\|a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 |b \|a 2 +--R (3b x - 3a x) |- log(-------------------) - 6b x + 4a +--R \|a 2 +--R b x - a +--R [-------------------------------------------------------, +--R 2 3 3 +--R 4a b x - 4a x +--R +---+ +--R | b +--R +---+ a |- - +--R 3 | b \| a 2 +--R (- 3b x + 3a x) |- - atan(-------) - 3b x + 2a +--R \| a b x +--R ------------------------------------------------] +--R 2 3 3 +--R 2a b x - 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 1331 + +--S 1332 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 3\|a |- log(-------------------) - 6\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ----------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 3\|b atanh(-----) - 3 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) ---------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1335 + +)clear all + +--S 1336 of 1393 +t0:=1/(x^3*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1336 + +--S 1337 of 1393 +r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a-b*x^2))+2*b*log(x)/a^3-b*log(a-b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 4 2 2 2 2 +--R (4b x - 4a b x )log(x) + (- 2b x + 2a b x )log(- b x + a) - 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x - 2a x +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (- 2b x + 2a b x )log(b x - a) + (4b x - 4a b x )log(x) - 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x - 2a x +--R Type: Union(Expression(Integer),...) +--E 1338 + +--S 1339 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1340 + +)clear all + +--S 1341 of 1393 +t0:=x^3/(a-b*x^2)^3 +--R +--R +--R 3 +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1341 + +--S 1342 of 1393 +r0:=1/4*x^4/(a*(a-b*x^2)^2) +--R +--R +--R 1 4 +--R - x +--R 4 +--R (2) --------------------- +--R 2 4 2 2 3 +--R a b x - 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1342 + +--S 1343 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x - a +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4b x - 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 1343 + +--S 1344 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1345 + +)clear all + +--S 1346 of 1393 +t0:=x^2/(a-b*x^2)^3 +--R +--R +--R 2 +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1346 + +--S 1347 of 1393 +r0:=1/4*x/(b*(a-b*x^2)^2)-1/8*x/(a*b*(a-b*x^2))-_ + 1/8*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (- b x + 2a b x - a )atanh(-----) + (b x + a x)\|a \|b +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x - 16a b x + 8a b)\|a \|b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b - 2a b x 3 +---+ +--R (b x - 2a b x + a )log(-------------------------) + (2b x + 2a x)\|a b +--R 2 +--R b x - a +--R [--------------------------------------------------------------------------, +--R 3 4 2 2 2 3 +---+ +--R (16a b x - 32a b x + 16a b)\|a b +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (- b x + 2a b x - a )atan(---------) + (b x + a x)\|- a b +--R a +--R -------------------------------------------------------------] +--R 3 4 2 2 2 3 +-----+ +--R (8a b x - 16a b x + 8a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1348 + +--S 1349 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 16a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1352 + +)clear all + +--S 1353 of 1393 +t0:=x/(a-b*x^2)^3 +--R +--R +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1353 + +--S 1354 of 1393 +r0:=1/4/(b*(a-b*x^2)^2) +--R +--R +--R 1 +--R - +--R 4 +--R (2) -------------------- +--R 3 4 2 2 2 +--R b x - 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1354 + +--S 1355 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) ---------------------- +--R 3 4 2 2 2 +--R 4b x - 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 1355 + +--S 1356 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1357 + +)clear all + +--S 1358 of 1393 +t0:=1/(a-b*x^2)^3 +--R +--R +--R 1 +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1358 + +--S 1359 of 1393 +r0:=1/4*x/(a*(a-b*x^2)^2)+3/8*x/(a^2*(a-b*x^2))+_ + 3/8*atanh(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x - 6a b x + 3a )atanh(-----) + (- 3b x + 5a x)\|a \|b +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x - 16a b x + 8a )\|a \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b + 2a b x +--R (3b x - 6a b x + 3a )log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 +---+ +--R (- 6b x + 10a x)\|a b +--R / +--R 2 2 4 3 2 4 +---+ +--R (16a b x - 32a b x + 16a )\|a b +--R , +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (3b x - 6a b x + 3a )atan(---------) + (- 3b x + 5a x)\|- a b +--R a +--R -----------------------------------------------------------------] +--R 2 2 4 3 2 4 +-----+ +--R (8a b x - 16a b x + 8a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1360 + +--S 1361 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R 3\|a \|b log(-------------------------) - 6\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - 3\|- a b atanh(-----) + 3\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1393 +t0:=1/(x*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------ +--R 3 7 2 5 2 3 3 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1365 + +--S 1366 of 1393 +r0:=1/4/(a*(a-b*x^2)^2)+1/2/(a^2*(a-b*x^2))+log(x)/a^3-1/2*log(a-b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (4b x - 8a b x + 4a )log(x) + (- 2b x + 4a b x - 2a )log(- b x + a) +--R + +--R 2 2 +--R - 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x - 8a b x + 4a +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x + 4a b x - 2a )log(b x - a) + (4b x - 8a b x + 4a )log(x) +--R + +--R 2 2 +--R - 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x - 8a b x + 4a +--R Type: Union(Expression(Integer),...) +--E 1367 + +--S 1368 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1369 + +)clear all + +--S 1370 of 1393 +t0:=1/(x^2*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1370 + +--S 1371 of 1393 +r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a-b*x^2)^2)+5/8/(a^2*x*(a-b*x^2))+_ + 15/8*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|b 2 4 2 2 +-+ +--R (15b x - 30a b x + 15a x)\|b atanh(-----) + (- 15b x + 25a b x - 8a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 2 5 4 3 5 +-+ +--R (8a b x - 16a b x + 8a x)\|a +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 2 5 3 2 |b \|a 2 4 +--R (15b x - 30a b x + 15a x) |- log(-------------------) - 30b x +--R \|a 2 +--R b x - a +--R + +--R 2 2 +--R 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x - 32a b x + 16a x +--R , +--R +---+ +--R | b +--R +---+ a |- - +--R 2 5 3 2 | b \| a 2 4 2 2 +--R (- 15b x + 30a b x - 15a x) |- - atan(-------) - 15b x + 25a b x - 8a +--R \| a b x +--R --------------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x - 16a b x + 8a x +--R Type: Union(List(Expression(Integer)),...) +--E 1372 + +--S 1373 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 15\|a |- log(-------------------) - 30\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 15\|b atanh(-----) - 15 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) ------------------------------------------------ +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1376 + +)clear all + +--S 1377 of 1393 +t0:=1/(x^3*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1377 + +--S 1378 of 1393 +r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a-b*x^2)^2)+_ + 3/4/(a^2*x^2*(a-b*x^2))+3*b*log(x)/a^4-3/2*b*log(a-b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 +--R (12b x - 24a b x + 12a b x )log(x) +--R + +--R 3 6 2 4 2 2 2 2 4 2 2 3 +--R (- 6b x + 12a b x - 6a b x )log(- b x + a) - 6a b x + 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x - 8a b x + 4a x +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (- 6b x + 12a b x - 6a b x )log(b x - a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (12b x - 24a b x + 12a b x )log(x) - 6a b x + 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x - 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1379 + +--S 1380 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 3b log(b x - a) + 3b log(- b x + a) +--R (4) --------------------------------------- +--R 4 +--R 2a +--R Type: Expression(Integer) +--E 1380 + +--S 1381 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1381 + +)clear all + +--S 1382 of 1393 +t0:=x^3/(a-b*x^2)^5 +--R +--R +--R 3 +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1382 + +--S 1383 of 1393 +r0:=1/8*a/(b^2*(a-b*x^2)^4)+(-1/6)/(b^2*(a-b*x^2)^3) +--R +--R +--R 1 2 1 +--R - b x - -- a +--R 6 24 +--R (2) ----------------------------------------- +--R 6 8 5 6 2 4 4 3 3 2 4 2 +--R b x - 4a b x + 6a b x - 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1383 + +--S 1384 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 4b x - a +--R (3) ------------------------------------------------- +--R 6 8 5 6 2 4 4 3 3 2 4 2 +--R 24b x - 96a b x + 144a b x - 96a b x + 24a b +--R Type: Union(Expression(Integer),...) +--E 1384 + +--S 1385 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1386 + +)clear all + +--S 1387 of 1393 +t0:=x^2/(a-b*x^2)^5 +--R +--R +--R 2 +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1387 + +--S 1388 of 1393 +r0:=1/8*x/(b*(a-b*x^2)^4)-1/48*x/(a*b*(a-b*x^2)^3)-_ + 5/192*x/(a^2*b*(a-b*x^2)^2)-5/128*x/(a^3*b*(a-b*x^2))-_ + 5/128*atanh(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (15b x - 55a b x + 73a b x + 15a x)\|a \|b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|a \|b +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (15b x - 60a b x + 90a b x - 60a b x + 15a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b - 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (30b x - 110a b x + 146a b x + 30a x)\|a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a b)\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (15b x - 55a b x + 73a b x + 15a x)\|- a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1389 + +--S 1390 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R 5\|a \|b log(-------------------------) + 10\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +-+ +---+ +--R 256a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R 5\|- a b atanh(-----) - 5\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R 3 +-----+ +-+ +-+ +--R 128a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1393 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4a.input.pdf b/src/axiom-website/CATS/rich4a.input.pdf new file mode 100644 index 0000000..b71ccd1 Binary files /dev/null and b/src/axiom-website/CATS/rich4a.input.pdf differ diff --git a/src/axiom-website/CATS/rich4b.input.pamphlet b/src/axiom-website/CATS/rich4b.input.pamphlet new file mode 100644 index 0000000..bb0584e --- /dev/null +++ b/src/axiom-website/CATS/rich4b.input.pamphlet @@ -0,0 +1,25024 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 287 matching answers. +\item 6 cases where Axiom answer differs from Rubi +\item 47 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 9 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4b.output +)spool rich4b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1369 +t0:=x/(a-b*x^2)^5 +--R +--R +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 1369 +r0:=1/8/(b*(a-b*x^2)^4) +--R +--R +--R 1 +--R - +--R 8 +--R (2) ---------------------------------------- +--R 5 8 4 6 2 3 4 3 2 2 4 +--R b x - 4a b x + 6a b x - 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2 + +--S 3 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) --------------------------------------------- +--R 5 8 4 6 2 3 4 3 2 2 4 +--R 8b x - 32a b x + 48a b x - 32a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1369 +t0:=1/(a-b*x^2)^5 +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 1369 +r0:=1/8*x/(a*(a-b*x^2)^4)+7/48*x/(a^2*(a-b*x^2)^3)+_ + 35/192*x/(a^3*(a-b*x^2)^2)+35/128*x/(a^4*(a-b*x^2))+_ + 35/128*atanh(x*sqrt(b)/sqrt(a))/(a^(9/2)*sqrt(b)) +--R +--R +--R (2) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (- 105b x + 385a b x - 511a b x + 279a x)\|a \|b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|a \|b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (105b x - 420a b x + 630a b x - 420a b x + 105a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b + 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (- 210b x + 770a b x - 1022a b x + 558a x)\|a b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a )\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (- 105b x + 385a b x - 511a b x + 279a x)\|- a b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 8 + +--S 9 of 1369 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R 35\|a \|b log(-------------------------) - 70\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +-+ +---+ +--R 256a \|a \|b \|a b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - 35\|- a b atanh(-----) + 35\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------- +--R 4 +-----+ +-+ +-+ +--R 128a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1369 +t0:=1/(x*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 13 + +--S 14 of 1369 +r0:=1/8/(a*(a-b*x^2)^4)+1/6/(a^2*(a-b*x^2)^3)+1/4/(a^3*(a-b*x^2)^2)+_ + 1/2/(a^4*(a-b*x^2))+log(x)/a^5-1/2*log(a-b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 3 2 4 +--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x) +--R + +--R 4 8 3 6 2 2 4 3 2 4 2 +--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(- b x + a) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 12a b x + 42a b x - 52a b x + 25a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 3 2 4 2 +--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(b x - a) +--R + +--R 4 8 3 6 2 2 4 3 2 4 3 6 +--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R 42a b x - 52a b x + 25a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a +--R Type: Union(Expression(Integer),...) +--E 15 + +--S 16 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 5 +--R 2a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 17 + +)clear all + +--S 18 of 1369 +t0:=1/(x^2*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 18 + +--S 19 of 1369 +r0:=(-315/128)/(a^5*x)+1/8/(a*x*(a-b*x^2)^4)+3/16/(a^2*x*(a-b*x^2)^3)+_ + 21/64/(a^3*x*(a-b*x^2)^2)+105/128/(a^4*x*(a-b*x^2))+_ + 315/128*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ x\|b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x + 1155a b x - 1533a b x + 837a b x - 128a )\|a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +-+ +--R (128a b x - 512a b x + 768a b x - 512a b x + 128a x)\|a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 |b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x) |- +--R \|a +--R * +--R +-+ +--R |b 2 +--R 2a x |- + b x + a +--R \|a +--R log(-------------------) +--R 2 +--R b x - a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x + 2310a b x - 3066a b x + 1674a b x - 256a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 256a b x - 1024a b x + 1536a b x - 1024a b x + 256a x +--R , +--R +--R +---+ +--R 4 9 3 7 2 2 5 3 3 4 | b +--R (- 315b x + 1260a b x - 1890a b x + 1260a b x - 315a x) |- - +--R \| a +--R * +--R +---+ +--R | b +--R a |- - +--R \| a +--R atan(-------) +--R b x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 315b x + 1155a b x - 1533a b x + 837a b x - 128a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 128a b x - 512a b x + 768a b x - 512a b x + 128a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 20 + +--S 21 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 315\|a |- log(-------------------) - 630\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) --------------------------------------------------------- +--R 5 +-+ +--R 256a \|a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 315\|b atanh(-----) - 315 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) -------------------------------------------------- +--R 5 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 1369 +t0:=1/(x^3*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 of 1369 +r0:=(-5/2)/(a^5*x^2)+1/8/(a*x^2*(a-b*x^2)^4)+5/24/(a^2*x^2*(a-b*x^2)^3)+_ + 5/12/(a^3*x^2*(a-b*x^2)^2)+5/4/(a^4*x^2*(a-b*x^2))+_ + 5*b*log(x)/a^6-5/2*b*log(a-b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x) +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 2 +--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(- b x + a) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a +--R / +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 2 +--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(b x - a) +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a +--R / +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x +--R Type: Union(Expression(Integer),...) +--E 27 + +--S 28 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 5b log(b x - a) + 5b log(- b x + a) +--R (4) --------------------------------------- +--R 6 +--R 2a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 29 + +)clear all + +--S 30 of 1369 +t0:=1/(x*(1+b*x^2)) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 30 + +--S 31 of 1369 +r0:=-atanh(1+2*b*x^2) +--R +--R +--R 2 +--R (2) - atanh(2b x + 1) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x + 1) + 2log(x) +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 32 + +--S 33 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 34 + +)clear all + +--S 35 of 1369 +t0:=1/(x*(-1+b*x^2)) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 35 + +--S 36 of 1369 +r0:=atanh(1-2*b*x^2) +--R +--R +--R 2 +--R (2) - atanh(2b x - 1) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x - 1) - 2log(x) +--R (3) ----------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 37 + +--S 38 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R log(b x - 1) - 2log(x) + 2atanh(2b x - 1) +--R (4) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 38 + +--S 39 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 1369 +t0:=1/(x^3*(1+b*x^2)) +--R +--R +--R 1 +--R (1) --------- +--R 5 3 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 40 + +--S 41 of 1369 +r0:=(-1/2)/x^2+b*atanh(1+2*b*x^2) +--R +--R +--R 2 2 +--R 2b x atanh(2b x + 1) - 1 +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x + 1) - 2b x log(x) - 1 +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 42 + +--S 43 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R b log(b x + 1) - 2b log(x) - 2b atanh(2b x + 1) +--R (4) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 44 + +)clear all + +--S 45 of 1369 +t0:=1/(x^3*(-1+b*x^2)) +--R +--R +--R 1 +--R (1) --------- +--R 5 3 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 45 + +--S 46 of 1369 +r0:=1/2/x^2+b*atanh(1-2*b*x^2) +--R +--R +--R 2 2 +--R - 2b x atanh(2b x - 1) + 1 +--R (2) --------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x - 1) - 2b x log(x) + 1 +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 47 + +--S 48 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R b log(b x - 1) - 2b log(x) + 2b atanh(2b x - 1) +--R (4) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 49 + +)clear all + +--S 50 of 1369 +t0:=1/(-1+a+a*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +--R a x + a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 50 + +--S 51 of 1369 +r0:=-atanh(x*sqrt(a)/sqrt(1-a))/sqrt((1-a)*a) +--R +--R +--R +-+ +--R x\|a +--R atanh(----------) +--R +-------+ +--R \|- a + 1 +--R (2) - ----------------- +--R +--------+ +--R | 2 +--R \|- a + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +------+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x | 2 +--R log(---------------------------------------) x\|a - a +--R 2 atan(----------) +--R a x + a - 1 a - 1 +--R (3) [--------------------------------------------,----------------] +--R +--------+ +------+ +--R | 2 | 2 +--R 2\|- a + a \|a - a +--R Type: Union(List(Expression(Integer)),...) +--E 52 + +--S 53 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R 2 | 2 2 +-+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x x\|a +--R log(---------------------------------------) + 2atanh(----------) +--R 2 +-------+ +--R a x + a - 1 \|- a + 1 +--R (4) ----------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- a + a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1369 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-+ 2 | 2 +--R (2x\|- a + a - a x + a - 1)\|- a + 1 \|a + (a x - a + 1)\|- a + a +--R + +--R 2 +--R (2a - 2a)x +--R / +--R +--------+ +--R 2 4 2 | 2 3 2 3 3 2 +--R (a x - a + 2a - 1)\|- a + a + (2a - 2a )x + (2a - 4a + 2a)x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------+ +--R +------+ +-+ +--------+ | 2 +--R | 2 x\|a | 2 x\|a - a +--R \|a - a atanh(----------) + \|- a + a atan(----------) +--R +-------+ a - 1 +--R \|- a + 1 +--R (6) -------------------------------------------------------- +--R +--------+ +------+ +--R | 2 | 2 +--R \|- a + a \|a - a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1369 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +--------+ +--R | 2 +-------+ +-+ 2 +--R \|- a + a \|- a + 1 \|a + a - a +--R (7) ---------------------------------- +--R 3 2 2 3 2 +--R (a - a )x + a - 2a + a +--R Type: Expression(Integer) +--E 56 + +)clear all + +--S 57 of 1369 +t0:=1/(-c-d+(c-d)*x^2) +--R +--R +--R 1 +--R (1) - ----------------- +--R 2 +--R (d - c)x + d + c +--R Type: Fraction(Polynomial(Integer)) +--E 57 + +--S 58 of 1369 +r0:=-atanh(x*sqrt(c-d)/sqrt(c+d))/(sqrt(c-d)*sqrt(c+d)) +--R +--R +--R +-------+ +--R x\|- d + c +--R atanh(-----------) +--R +-----+ +--R \|d + c +--R (2) - ------------------ +--R +-------+ +-----+ +--R \|- d + c \|d + c +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 2 2 2 +-------+ +--R ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x | 2 2 +--R log(------------------------------------------------) x\|d - c +--R 2 atan(-----------) +--R (d - c)x + d + c d + c +--R [-----------------------------------------------------,- -----------------] +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 2\|- d + c \|d - c +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 2 2 2 +--R +-------+ +-----+ ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x +--R \|- d + c \|d + c log(------------------------------------------------) +--R 2 +--R (d - c)x + d + c +--R + +--R +---------+ +-------+ +--R | 2 2 x\|- d + c +--R 2\|- d + c atanh(-----------) +--R +-----+ +--R \|d + c +--R / +--R +---------+ +--R | 2 2 +-------+ +-----+ +--R 2\|- d + c \|- d + c \|d + c +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +--R +-------+ +-------+ | 2 2 +--R | 2 2 x\|- d + c +-------+ +-----+ x\|d - c +--R \|d - c atanh(-----------) - \|- d + c \|d + c atan(-----------) +--R +-----+ d + c +--R \|d + c +--R (6) ------------------------------------------------------------------ +--R +-------+ +--R +-------+ +-----+ | 2 2 +--R \|- d + c \|d + c \|d - c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1369 +t0:=1/(x*(1+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 5 3 +--R b x + 2b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 of 1369 +r0:=1/2/(1+b*x^2)-atanh(1+2*b*x^2) +--R +--R +--R 2 2 +--R (- 2b x - 2)atanh(2b x + 1) + 1 +--R (2) --------------------------------- +--R 2 +--R 2b x + 2 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x - 1)log(b x + 1) + (2b x + 2)log(x) + 1 +--R (3) ------------------------------------------------- +--R 2 +--R 2b x + 2 +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1369 +t0:=1/(x*(-1+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 5 3 +--R b x - 2b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 69 + +--S 70 of 1369 +r0:=1/2/(1-b*x^2)-atanh(1-2*b*x^2) +--R +--R +--R 2 2 +--R (2b x - 2)atanh(2b x - 1) - 1 +--R (2) ------------------------------- +--R 2 +--R 2b x - 2 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x + 1)log(b x - 1) + (2b x - 2)log(x) - 1 +--R (3) ------------------------------------------------- +--R 2 +--R 2b x - 2 +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - 1) + 2log(x) - 2atanh(2b x - 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1369 +t0:=x^m/(1+a*x^2/b)^2 +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1369 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 75 + +--S 76 of 1369 +--a0:=integrate(t0,x) +--E 76 + +--S 77 of 1369 +--m0:=a0-r0 +--E 77 + +--S 78 of 1369 +--d0:=D(m0,x) +--E 78 + +)clear all + +--S 79 of 1369 +t0:=x^m*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1369 +--r0:=x^(1+m)*sqrt(a+b*x^2)/(2+m)+a*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((2+3*m+m^2)*sqrt(a+b*x^2)) +--E 80 + +--S 81 of 1369 +--a0:=integrate(t0,x) +--E 81 + +--S 82 of 1369 +--m0:=a0-r0 +--E 82 + +--S 83 of 1369 +--d0:=D(m0,x) +--E 83 + +)clear all + +--S 84 of 1369 +t0:=x^7*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 7 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1369 +r0:=-1/3*a^3*(a+b*x^2)^(3/2)/b^4+3/5*a^2*(a+b*x^2)^(5/2)/b^4-_ + 3/7*a*(a+b*x^2)^(7/2)/b^4+1/9*(a+b*x^2)^(9/2)/b^4 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a +--R (2) -------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 16 2 3 14 3 2 12 4 10 5 8 +--R (- 315a b x - 4245a b x - 15666a b x - 21672a b x - 10080a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 18 4 16 2 3 14 3 2 12 4 10 +--R 35b x + 1440a b x + 9999a b x + 25242a b x + 26712a b x +--R + +--R 5 8 +--R 10080a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 86 + +--S 87 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (- 16a b x - 640a b x - 3840a b x - 7168a b x - 4096a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (144a b x + 1920a b x + 6912a b x + 9216a b x + 4096a )\|a +--R / +--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 88 + +)clear all + +--S 89 of 1369 +t0:=x^5*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 5 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1369 +r0:=1/3*a^2*(a+b*x^2)^(3/2)/b^3-2/5*a*(a+b*x^2)^(5/2)/b^3+_ + 1/7*(a+b*x^2)^(7/2)/b^3 +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (15b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) --------------------------------------------- +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 12 2 2 10 3 8 4 6 | 2 +--R (- 105a b x - 861a b x - 1820a b x - 1120a x )\|b x + a +--R + +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (15b x + 378a b x + 1631a b x + 2380a b x + 1120a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x +--R + +--R 2 2 4 3 2 4 +--R - 5880a b x - 11760a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 91 + +--S 92 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (8a b x + 192a b x + 640a b x + 512a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (- 56a b x - 448a b x - 896a b x - 512a )\|a +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +-+ | 2 6 6 +--R (105b x + 2520a b x + 8400a b x + 6720a b )\|a \|b x + a - 735a b x +--R + +--R 2 5 4 3 4 2 4 3 +--R - 5880a b x - 11760a b x - 6720a b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1369 +t0:=x^3*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 3 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1369 +r0:=-1/3*a*(a+b*x^2)^(3/2)/b^2+1/5*(a+b*x^2)^(5/2)/b^2 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (3b x + a b x - 2a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 2 6 3 4 | 2 +--R (- 15a b x - 65a b x - 60a x )\|b x + a +--R + +--R 3 10 2 8 2 6 3 4 +-+ +--R (3b x + 40a b x + 95a b x + 60a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+ +--R (- 2a b x - 24a b x - 32a )\|b x + a + (10a b x + 40a b x + 32a )\|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2 +--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x +--R + +--R 3 2 +--R - 240a b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 98 + +)clear all + +--S 99 of 1369 +t0:=x*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)/b +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (2) --------------------- +--R 3b +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a +--R (3) ------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (a b x + 4a )\|b x + a + (- 3a b x - 4a )\|a +--R (4) ------------------------------------------------- +--R +--------+ +--R 2 2 +-+ | 2 2 2 2 +--R (3b x + 12a b)\|a \|b x + a - 9a b x - 12a b +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 103 + +)clear all + +--S 104 of 1369 +t0:=sqrt(a+b*x^2)/x +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R +-+ \|b x + a | 2 +--R (2) - \|a atanh(-----------) + \|b x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a - a\|a )log(------------------) + b x \|a +--R x +--R (3) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (a\|b x + a - a\|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|b x + a | 2 +-+ +--R (a\|b x + a - a\|a )atanh(-----------) + a\|b x + a - a\|a +--R +-+ +--R \|a +--R / +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1369 +t0:=sqrt(a+b*x^2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1369 +r0:=-1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-1/2*sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 \|b x + a +-+ | 2 +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 2 +-+ +--R 2x \|a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|b x + a - \|a +--R (2a b x \|b x + a + (- b x - 2a b x )\|a )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4a x \|a \|b x + a - 2a b x - 4a x +--R Type: Union(Expression(Integer),...) +--E 111 + +--S 112 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R b log(------------------) + b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 113 + +)clear all + +--S 114 of 1369 +t0:=sqrt(a+b*x^2)/x^5 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1369 +r0:=1/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/4*sqrt(a+b*x^2)/x^4-_ + 1/8*b*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 4 +-+ +--R 8a x \|a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+ +--R ((- 4a b x - 8a b x )\|b x + a + (b x + 8a b x + 8a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (a b x + 10a b x + 24a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 4a b x - 20a b x - 32a b x - 16a )\|a +--R / +--R +--------+ +--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 116 + +--S 117 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1369 +t0:=sqrt(a+b*x^2)/x^7 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1369 +r0:=-1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/6*sqrt(a+b*x^2)/x^6-_ + 1/24*b*sqrt(a+b*x^2)/(a*x^4)+1/16*b^2*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R - 3b x atanh(-----------) + (3b x - 2a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 2 6 +-+ +--R 48a x \|a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (18a b x + 96a b x + 96a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (- 3b x - 54a b x - 144a b x - 96a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (- 3a b x - 52a b x - 100a b x + 144a b x + 448a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+ +--R (18a b x + 102a b x + 68a b x - 336a b x - 576a b x - 256a )\|a +--R / +--R +--------+ +--R 3 2 10 4 8 5 6 +-+ | 2 3 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 4 2 10 5 8 6 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 121 + +--S 122 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R b log(------------------) + b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------ +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1369 +t0:=x^4*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 4 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1369 +r0:=1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 1/16*a^2*x*sqrt(a+b*x^2)/b^2+1/24*a*x^3*sqrt(a+b*x^2)/b+_ + 1/6*x^5*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R 3a atanh(-----------) + (8b x + 2a b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------------------- +--R 2 +-+ +--R 48b \|b +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x +--R + +--R 5 2 6 +--R - 144a b x - 96a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x)\|b +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +-+ +--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (36a b x + 192a b x + 192a )\|a \|b x + a - 6a b x - 108a b x +--R + +--R 5 2 6 +--R - 288a b x - 192a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x) +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 126 + +--S 127 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R - a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R - a \|- b atanh(-----------) + 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R -------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 16b \|- b \|b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1369 +t0:=x^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1369 +r0:=-1/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 1/8*a*x*sqrt(a+b*x^2)/b+1/4*x^3*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R - a atanh(-----------) + (2b x + a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 8b\|b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8a )\|a \|b x + a - a b x - 8a b x - 8a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 17a b x - 24a b x - 8a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 28a b x + 28a b x + 8a x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32b x + 64a b)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b)\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16a )\|a \|b x + a + 2a b x + 16a b x + 16a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 17a b x - 24a b x - 8a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 28a b x + 28a b x + 8a x)\|- b \|a +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32b x + 64a b)\|- b \|a \|b x + a +--R + +--R 3 4 2 2 2 +---+ +--R (- 8b x - 64a b x - 64a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 133 + +--S 134 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 8b\|b +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R a \|- b atanh(-----------) - 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 8b\|- b \|b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 1369 +t0:=sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1369 +r0:=1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+1/2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R x\|b +-+ | 2 +--R a atanh(-----------) + x\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2a\|a \|b x + a - a b x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|b x + a + (- 2b x - 4a)\|b +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- b \|b x + a - \|- b \|a +--R (4a\|a \|b x + a - 2a b x - 4a )atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- b \|a \|b x + a + (- 2b x - 4a)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 140 + +--S 141 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - a\|- b atanh(-----------) + 2a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1369 +t0:=sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)-sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R +-+ x\|b | 2 +--R x\|b atanh(-----------) - \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|b \|b x + a - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R / +--R +--------+ +--R | 2 +-+ +--R x\|b x + a - x\|a +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|b x + a - \|a +--R (2x\|- b \|b x + a - 2x\|- b \|a )atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R / +--R +--------+ +--R | 2 +-+ +--R x\|b x + a - x\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 147 + +--S 148 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R (6) - \|b atanh(-----------) + 2\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 151 + +)clear all + +--S 152 of 1369 +t0:=sqrt(a+b*x^2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1369 +r0:=-1/3*(a+b*x^2)^(3/2)/(a*x^3) +--R +--R +--R +--------+ +--R 2 | 2 +--R (- b x - a)\|b x + a +--R (2) ----------------------- +--R 3 +--R 3a x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (3b x + 7a b x + 4a )\|a \|b x + a - b x - 6a b x - 9a b x - 4a +--R ----------------------------------------------------------------------- +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a +--R Type: Union(Expression(Integer),...) +--E 154 + +--S 155 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1369 +t0:=sqrt(a+b*x^2)/x^6 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1369 +r0:=-1/5*(a+b*x^2)^(3/2)/(a*x^5)+2/15*b*(a+b*x^2)^(3/2)/(a^2*x^3) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x - a b x - 3a )\|b x + a +--R (2) --------------------------------- +--R 2 5 +--R 15a x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (- 10b x - 35a b x + 3a b x + 76a b x + 48a )\|a \|b x + a + 2b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 25a b x + 40a b x - 35a b x - 100a b x - 48a +--R / +--R +--------+ +--R 2 2 9 3 7 4 5 | 2 +--R (15a b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 2 9 3 7 4 5 +-+ +--R (- 75a b x - 300a b x - 240a x )\|a +--R Type: Union(Expression(Integer),...) +--E 159 + +--S 160 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 161 + +)clear all + +--S 162 of 1369 +t0:=sqrt(a+b*x^2)/x^8 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1369 +r0:=-1/7*(a+b*x^2)^(3/2)/(a*x^7)+4/35*b*(a+b*x^2)^(3/2)/(a^2*x^5)-_ + 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^3) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (- 8b x + 4a b x - 3a b x - 15a )\|b x + a +--R (2) ----------------------------------------------- +--R 3 7 +--R 105a x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 56b x + 420a b x + 693a b x + 337a b x + 920a b x + 1872a b x +--R + +--R 6 +--R 960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 8b x - 196a b x - 735a b x - 826a b x - 623a b x - 1736a b x +--R + +--R 6 2 7 +--R - 2352a b x - 960a +--R / +--R +--------+ +--R 3 3 13 4 2 11 5 9 6 7 | 2 +--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a +--R + +--R 3 3 13 4 2 11 5 9 6 7 +-+ +--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a +--R Type: Union(Expression(Integer),...) +--E 164 + +--S 165 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 166 + +)clear all + +--S 167 of 1369 +t0:=sqrt(a+b*x^2)/x^10 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1369 +r0:=-1/9*(a+b*x^2)^(3/2)/(a*x^9)+2/21*b*(a+b*x^2)^(3/2)/(a^2*x^7)-_ + 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^5)+16/315*b^3*(a+b*x^2)^(3/2)/(a^4*x^3) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x - 8a b x + 6a b x - 5a b x - 35a )\|b x + a +--R (2) -------------------------------------------------------- +--R 4 9 +--R 315a x +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 144b x - 1848a b x - 6006a b x - 6435a b x - 1165a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 4952a b x + 16464a b x + 21440a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 648a b x + 4158a b x + 9009a b x + 7200a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 243a b x - 11064a b x - 26064a b x - 25920a b x - 8960a +--R / +--R 4 4 17 5 3 15 6 2 13 7 11 8 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 4 17 5 3 15 6 2 13 7 11 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 169 + +--S 170 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 1369 +t0:=x^m*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 m | 2 +--R (1) (b x + a)x \|b x + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1369 +--r0:=x^(1+m)*(a+b*x^2)^(3/2)/(4+m)+3*a*x^(1+m)*sqrt(a+b*x^2)/(8+6*m+m^2)+_ +-- 3*a^2*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 173 + +--S 174 of 1369 +--a0:=integrate(t0,x) +--E 174 + +--S 175 of 1369 +--m0:=a0-r0 +--E 175 + +--S 176 of 1369 +--d0:=D(m0,x) +--E 176 + +)clear all + +--S 177 of 1369 +t0:=x^7*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 9 7 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1369 +r0:=-1/5*a^3*(a+b*x^2)^(5/2)/b^4+3/7*a^2*(a+b*x^2)^(7/2)/b^4-_ + 1/3*a*(a+b*x^2)^(9/2)/b^4+1/11*(a+b*x^2)^(11/2)/b^4 +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (105b x + 140a b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 20 2 5 18 3 4 16 4 3 14 +--R - 1155a b x - 24640a b x - 160215a b x - 469194a b x +--R + +--R 5 2 12 6 10 7 8 +--R - 694848a b x - 510048a b x - 147840a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 22 6 20 2 5 18 3 4 16 4 3 14 +--R 105b x + 6545a b x + 73645a b x + 334059a b x + 762102a b x +--R + +--R 5 2 12 6 10 7 8 +--R 931392a b x + 583968a b x + 147840a x +--R * +--R +-+ +--R \|a +--R / +--R 5 10 4 8 2 3 6 3 2 4 +--R 1155b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 4 2 5 +--R 2661120a b x + 1182720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 5 2 6 +--R - 3252480a b x - 1182720a +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R - 16a b x - 960a b x - 8960a b x - 28672a b x - 36864a b x +--R + +--R 11 +--R - 16384a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R 176a b x + 3520a b x + 19712a b x + 45056a b x + 45056a b x +--R + +--R 11 +--R 16384a +--R * +--R +-+ +--R \|a +--R / +--R 9 10 8 8 2 7 6 3 6 4 +--R 1155b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 4 5 2 5 4 +--R 2661120a b x + 1182720a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 10 2 8 8 3 7 6 4 6 4 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 5 5 2 6 4 +--R - 3252480a b x - 1182720a b +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 181 + +)clear all + +--S 182 of 1369 +t0:=x^5*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 7 5 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1369 +r0:=1/5*a^2*(a+b*x^2)^(5/2)/b^3-2/7*a*(a+b*x^2)^(7/2)/b^3+_ + 1/9*(a+b*x^2)^(9/2)/b^3 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 50a b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 16 2 4 14 3 3 12 4 2 10 +--R - 315a b x - 4650a b x - 21147a b x - 42084a b x +--R + +--R 5 8 6 6 +--R - 38640a b x - 13440a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 18 5 16 2 4 14 3 3 12 4 2 10 +--R 35b x + 1485a b x + 11853a b x + 38199a b x + 59724a b x +--R + +--R 5 8 6 6 +--R 45360a b x + 13440a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 184 + +--S 185 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (8a b x + 320a b x + 1920a b x + 3584a b x + 2048a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (- 72a b x - 960a b x - 3456a b x - 4608a b x - 2048a )\|a +--R / +--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 8 2 6 6 3 5 4 4 4 2 5 3 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 1369 +t0:=x^3*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 5 3 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1369 +r0:=-1/5*a*(a+b*x^2)^(5/2)/b^2+1/7*(a+b*x^2)^(7/2)/b^2 +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (5b x + 8a b x + a b x - 2a )\|b x + a +--R (2) ------------------------------------------- +--R 2 +--R 35b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2 +--R (- 35a b x - 336a b x - 1015a b x - 1260a b x - 560a x )\|b x + a +--R + +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+ +--R (5b x + 133a b x + 721a b x + 1575a b x + 1540a b x + 560a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (35b x + 840a b x + 2800a b x + 2240a )\|a \|b x + a - 245a b x +--R + +--R 2 2 4 3 2 4 +--R - 1960a b x - 3920a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 189 + +--S 190 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (- 2a b x - 48a b x - 160a b x - 128a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (14a b x + 112a b x + 224a b x + 128a )\|a +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +-+ | 2 5 6 +--R (35b x + 840a b x + 2800a b x + 2240a b )\|a \|b x + a - 245a b x +--R + +--R 2 4 4 3 3 2 4 2 +--R - 1960a b x - 3920a b x - 2240a b +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 191 + +)clear all + +--S 192 of 1369 +t0:=x*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 3 | 2 +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1369 +r0:=1/5*(a+b*x^2)^(5/2)/b +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (2) -------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 8 2 2 6 3 4 4 2 | 2 +--R (- 5a b x - 30a b x - 60a b x - 40a x )\|b x + a +--R + +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ +--R (b x + 15a b x + 55a b x + 80a b x + 40a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (5b x + 60a b x + 80a )\|a \|b x + a - 25a b x - 100a b x - 80a +--R Type: Union(Expression(Integer),...) +--E 194 + +--S 195 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+ +--R (a b x + 12a b x + 16a )\|b x + a + (- 5a b x - 20a b x - 16a )\|a +--R ------------------------------------------------------------------------- +--R +--------+ +--R 3 4 2 2 2 +-+ | 2 3 4 2 2 2 3 +--R (5b x + 60a b x + 80a b)\|a \|b x + a - 25a b x - 100a b x - 80a b +--R Type: Expression(Integer) +--E 195 + +--S 196 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 196 + +)clear all + +--S 197 of 1369 +t0:=(a+b*x^2)^(3/2)/x +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)-a^(3/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R +-+ \|b x + a 2 | 2 +--R - 3a\|a atanh(-----------) + (b x + 4a)\|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (- 3a b x - 12a b x )\|b x + a + (b x + 9a b x + 12a b x )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 199 + +--S 200 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 2 3 | 2 2 2 3 +-+ \|b x + a +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (4a b x + 16a )\|b x + a + (- 12a b x - 16a )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 1369 +t0:=(a+b*x^2)^(3/2)/x^3 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1369 +r0:=-1/2*(a+b*x^2)^(3/2)/x^2-3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))*_ + sqrt(a)+3/2*b*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 | 2 +--R - 3b x \|a atanh(-----------) + (2b x - a)\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|b x + a + (- 9a b x - 12a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 4a b x + 3a b x + 4a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2b x + 3a b x - 5a b x - 4a )\|a +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2b x + 8a x )\|a \|b x + a - 6a b x - 8a x +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a b x + 8a b)\|b x + a + (- 6a b x - 8a b)\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (2b x + 8a)\|a \|b x + a - 6a b x - 8a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 206 + +)clear all + +--S 207 of 1369 +t0:=(a+b*x^2)^(3/2)/x^5 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1369 +r0:=-1/4*(a+b*x^2)^(3/2)/x^4-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_ + 3/8*b*sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R - 3b x atanh(-----------) + (- 5b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 4 +-+ +--R 8x \|a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|b x + a +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3b x - 24a b x - 24a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (5a b x + 42a b x + 56a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 20a b x - 68a b x - 64a b x - 16a )\|a +--R / +--R +--------+ +--R 6 2 4 +-+ | 2 2 8 2 6 3 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 211 + +)clear all + +--S 212 of 1369 +t0:=(a+b*x^2)^(3/2)/x^7 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1369 +r0:=-1/6*(a+b*x^2)^(3/2)/x^6+1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 1/8*b*sqrt(a+b*x^2)/x^4-1/16*b^2*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R 3b x atanh(-----------) + (- 3b x - 14a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 6 +-+ +--R 48a x \|a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (- 18a b x - 96a b x - 96a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (3b x + 54a b x + 144a b x + 96a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+ +--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256a )\|a +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 +-+ | 2 2 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 3 2 10 4 8 5 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1369 +t0:=(a+b*x^2)^(3/2)/x^9 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1369 +r0:=-1/8*(a+b*x^2)^(3/2)/x^8-3/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/16*b*sqrt(a+b*x^2)/x^6-1/64*b^2*sqrt(a+b*x^2)/(a*x^4)+_ + 3/128*b^3*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 \|b x + a +--R - 3b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 +--R (3b x - 2a b x - 24a b x - 16a )\|a \|b x + a +--R / +--R 2 8 +-+ +--R 128a x \|a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 2 6 12 3 5 10 4 4 8 | 2 +--R (24a b x + 240a b x + 576a b x + 384a b x )\|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+ +--R (- 3b x - 96a b x - 480a b x - 768a b x - 384a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 3a b x - 94a b x - 392a b x + 336a b x + 4480a b x +--R + +--R 6 2 4 7 2 8 +--R 8960a b x + 7168a b x + 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 24a b x + 248a b x + 448a b x - 1824a b x - 8192a b x +--R + +--R 6 2 4 7 2 8 +--R - 12288a b x - 8192a b x - 2048a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 3 14 4 2 12 5 10 6 8 +-+ | 2 +--R (1024a b x + 10240a b x + 24576a b x + 16384a x )\|a \|b x + a +--R + +--R 3 4 16 4 3 14 5 2 12 6 10 7 8 +--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a x +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 4 \|b x + a - \|a 4 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 221 + +)clear all + +--S 222 of 1369 +t0:=x^4*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 6 4 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1369 +r0:=1/8*x^5*(a+b*x^2)^(3/2)+3/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/128*a^3*x*sqrt(a+b*x^2)/b^2+1/64*a^2*x^3*sqrt(a+b*x^2)/b+_ + 1/16*a*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 x\|b 3 7 2 5 2 3 3 +-+ | 2 +--R 3a atanh(-----------) + (16b x + 24a b x + 2a b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 4 4 8 +--R (24a b x + 240a b x + 576a b x + 384a )\|a \|b x + a - 3a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 96a b x - 480a b x - 768a b x - 384a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x +--R + +--R 5 2 5 6 3 7 +--R - 3104a b x + 512a b x + 384a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x +--R + +--R 5 2 5 6 3 7 +--R 2896a b x - 704a b x - 384a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2 +--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|a \|b \|b x + a +--R + +--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+ +--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|b +--R , +--R +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (48a b x + 480a b x + 1152a b x + 768a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 6a b x - 192a b x - 960a b x - 1536a b x - 768a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x +--R + +--R 5 2 5 6 3 7 +--R - 3104a b x + 512a b x + 384a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x +--R + +--R 5 2 5 6 3 7 +--R 2896a b x - 704a b x - 384a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2 +--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|- b \|a \|b x + a +--R + +--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+ +--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 224 + +--S 225 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 4 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 128b \|- b \|b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1369 +t0:=x^2*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 4 2 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1369 +r0:=1/6*x^3*(a+b*x^2)^(3/2)-1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 1/16*a^2*x*sqrt(a+b*x^2)/b+1/8*a*x^3*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R - 3a atanh(-----------) + (8b x + 14a b x + 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 48b\|b +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x +--R + +--R 5 2 6 +--R - 144a b x - 96a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a x) +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 3 4 2 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b)\|a \|b \|b x + a +--R + +--R 4 6 3 4 2 2 2 3 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (- 36a b x - 192a b x - 192a )\|a \|b x + a + 6a b x +--R + +--R 4 2 4 5 2 6 +--R 108a b x + 288a b x + 192a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x) +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 3 4 2 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b)\|- b \|a \|b x + a +--R + +--R 4 6 3 4 2 2 2 3 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 231 + +--S 232 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 16b\|b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R a \|- b atanh(-----------) - 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 16b\|- b \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1369 +t0:=(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1369 +r0:=1/4*x*(a+b*x^2)^(3/2)+3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_ + 3/8*a*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R 3a atanh(-----------) + (2b x + 5a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 8\|b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 21a b x - 56a b x - 40a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 44a b x + 76a b x + 40a x)\|a \|b +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32b x + 64a)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a )\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 21a b x - 56a b x - 40a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 44a b x + 76a b x + 40a x)\|- b \|a +--R / +--R +--------+ +--R 2 +---+ +-+ | 2 2 4 2 2 +---+ +--R (32b x + 64a)\|- b \|a \|b x + a + (- 8b x - 64a b x - 64a )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 238 + +--S 239 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 8\|b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 8\|- b \|b +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1369 +t0:=(a+b*x^2)^(3/2)/x^2 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1369 +r0:=-(a+b*x^2)^(3/2)/x+3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_ + 3/2*b*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R +-+ x\|b 2 | 2 +--R 3a x\|b atanh(-----------) + (b x - 2a)\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12a x)\|b \|b x + a + (- 9a b x - 12a x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a +--R , +--R +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24a x)\|- b \|b x + a + (- 18a b x - 24a x)\|- b \|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 245 + +--S 246 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 3a\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - 3a\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R - 3a\|b atanh(-----------) + 6a\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1369 +t0:=(a+b*x^2)^(3/2)/x^4 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1369 +r0:=-1/3*(a+b*x^2)^(3/2)/x^3+b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-_ + b*sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R 3 +-+ x\|b 2 | 2 +--R 3b x \|b atanh(-----------) + (- 4b x - a)\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------ +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3b x + 12a b x )\|b \|b x + a + (- 9b x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a +--R , +--R +--R +--------+ +--R 2 5 3 +---+ | 2 +--R (6b x + 24a b x )\|- b \|b x + a +--R + +--R 2 5 3 +---+ +-+ +--R (- 18b x - 24a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 252 + +--S 253 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R (6) - b\|b atanh(-----------) + 2b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 256 + +)clear all + +--S 257 of 1369 +t0:=(a+b*x^2)^(3/2)/x^6 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1369 +r0:=-1/5*(a+b*x^2)^(5/2)/(a*x^5) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (- b x - 2a b x - a )\|b x + a +--R (2) ---------------------------------- +--R 5 +--R 5a x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (5b x + 30a b x + 61a b x + 52a b x + 16a )\|a \|b x + a - b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16a +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80a x )\|b x + a +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80a x )\|a +--R Type: Union(Expression(Integer),...) +--E 259 + +--S 260 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 1369 +t0:=(a+b*x^2)^(3/2)/x^8 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1369 +r0:=-1/7*(a+b*x^2)^(5/2)/(a*x^7)+2/35*b*(a+b*x^2)^(5/2)/(a^2*x^5) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x - a b x - 8a b x - 5a )\|b x + a +--R (2) ------------------------------------------- +--R 2 7 +--R 35a x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R - 14b x - 105a b x - 112a b x + 467a b x + 1240a b x +--R + +--R 5 2 6 +--R 1072a b x + 320a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 2b x + 49a b x + 175a b x - 21a b x - 973a b x - 1736a b x +--R + +--R 6 2 7 +--R - 1232a b x - 320a +--R / +--R +--------+ +--R 2 3 13 3 2 11 4 9 5 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a x )\|b x + a +--R + +--R 2 3 13 3 2 11 4 9 5 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a x )\|a +--R Type: Union(Expression(Integer),...) +--E 264 + +--S 265 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 266 + +)clear all + +--S 267 of 1369 +t0:=(a+b*x^2)^(3/2)/x^10 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1369 +r0:=-1/9*(a+b*x^2)^(5/2)/(a*x^9)+4/63*b*(a+b*x^2)^(5/2)/(a^2*x^7)-_ + 8/315*b^2*(a+b*x^2)^(5/2)/(a^3*x^5) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (- 8b x + 4a b x - 3a b x - 50a b x - 35a )\|b x + a +--R (2) ---------------------------------------------------------- +--R 3 9 +--R 315a x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 72b x + 924a b x + 3003a b x + 3690a b x + 7355a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 26504a b x + 44688a b x + 32960a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R - 8b x - 324a b x - 2079a b x - 4557a b x - 5805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 16731a b x - 45288a b x - 60048a b x - 37440a b x - 8960a +--R / +--R 3 4 17 4 3 15 5 2 13 6 11 7 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 4 17 4 3 15 5 2 13 6 11 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 269 + +--S 270 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 271 + +)clear all + +--S 272 of 1369 +t0:=(a+b*x^2)^(3/2)/x^12 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1369 +r0:=-1/11*(a+b*x^2)^(5/2)/(a*x^11)+2/33*b*(a+b*x^2)^(5/2)/(a^2*x^9)-_ + 8/231*b^2*(a+b*x^2)^(5/2)/(a^3*x^7)+16/1155*b^3*(a+b*x^2)^(5/2)/(a^4*x^5) +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (16b x - 8a b x + 6a b x - 5a b x - 140a b x - 105a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 11 +--R 1155a x +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 +--R - 176b x - 3432a b x - 18018a b x - 36465a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 27280a b x + 27363a b x + 200956a b x + 531536a b x +--R + +--R 8 2 4 9 2 10 +--R 695040a b x + 439040a b x + 107520a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 16b x + 968a b x + 9438a b x + 33033a b x + 49995a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4 +--R 22847a b x - 90629a b x - 403084a b x - 830896a b x - 901120a b x +--R + +--R 10 2 11 +--R - 492800a b x - 107520a +--R / +--R 4 5 21 5 4 19 6 3 17 7 2 15 +--R 1155a b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 8 13 9 11 +--R 2661120a b x + 1182720a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 21 5 4 19 6 3 17 7 2 15 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 8 13 9 11 +--R - 3252480a b x - 1182720a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 274 + +--S 275 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 1369 +t0:=x^m*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 m | 2 +--R (1) (b x + 2a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1369 +--r0:=5*a*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m))+x^(1+m)*(a+b*x^2)^(5/2)/_ +-- (6+m)+15*a^2*x^(1+m)*sqrt(a+b*x^2)/((6+m)*(8+6*m+m^2))+15*_ +-- a^3*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((6+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 278 + +--S 279 of 1369 +--a0:=integrate(t0,x) +--E 279 + +--S 280 of 1369 +--m0:=a0-r0 +--E 280 + +--S 281 of 1369 +--d0:=D(m0,x) +--E 281 + +)clear all + +--S 282 of 1369 +t0:=x^7*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 11 9 2 7 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1369 +r0:=-1/7*a^3*(a+b*x^2)^(7/2)/b^4+1/3*a^2*(a+b*x^2)^(9/2)/b^4-_ + 3/11*a*(a+b*x^2)^(11/2)/b^4+1/13*(a+b*x^2)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (231b x + 567a b x + 371a b x + 5a b x - 6a b x + 8a b x - 16a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 2 7 22 3 6 20 4 5 18 +--R - 3003a b x - 91455a b x - 883883a b x - 4092517a b x +--R + +--R 5 4 16 6 3 14 7 2 12 +--R - 10586862a b x - 16226496a b x - 14702688a b x +--R + +--R 8 10 9 8 +--R - 7303296a b x - 1537536a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 26 8 24 2 7 22 3 6 20 +--R 231b x + 20202a b x + 326690a b x + 2214784a b x +--R + +--R 4 5 18 5 4 16 6 3 14 7 2 12 +--R 8033311a b x + 17258670a b x + 22761024a b x + 18162144a b x +--R + +--R 8 10 9 8 +--R 8072064a b x + 1537536a x +--R * +--R +-+ +--R \|a +--R / +--R 6 12 5 10 2 4 8 3 3 6 +--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 4 2 4 5 2 6 +--R 34594560a b x + 33825792a b x + 12300288a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 5 2 4 6 2 7 +--R - 49969920a b x - 39975936a b x - 12300288a +--R Type: Union(Expression(Integer),...) +--E 284 + +--S 285 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R - 16a b x - 1344a b x - 17920a b x - 86016a b x +--R + +--R 11 2 4 12 2 13 +--R - 184320a b x - 180224a b x - 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 208a b x + 5824a b x + 46592a b x + 159744a b x +--R + +--R 11 2 4 12 2 13 +--R 266240a b x + 212992a b x + 65536a +--R * +--R +-+ +--R \|a +--R / +--R 10 12 9 10 2 8 8 3 7 6 +--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 4 6 4 5 5 2 6 4 +--R 34594560a b x + 33825792a b x + 12300288a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 10 12 2 9 10 3 8 8 4 7 6 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 5 6 4 6 5 2 7 4 +--R - 49969920a b x - 39975936a b x - 12300288a b +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 286 + +)clear all + +--S 287 of 1369 +t0:=x^5*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1369 +r0:=1/7*a^2*(a+b*x^2)^(7/2)/b^3-2/9*a*(a+b*x^2)^(9/2)/b^3+_ + 1/11*(a+b*x^2)^(11/2)/b^3 +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (63b x + 161a b x + 113a b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 20 2 6 18 3 5 16 4 4 14 +--R - 693a b x - 15631a b x - 114279a b x - 400653a b x +--R + +--R 5 3 12 6 2 10 7 8 8 6 +--R - 770616a b x - 838992a b x - 487872a b x - 118272a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 22 7 20 2 6 18 3 5 16 4 4 14 +--R 63b x + 4004a b x + 48994a b x + 254892a b x + 706959a b x +--R + +--R 5 3 12 6 2 10 7 8 8 6 +--R 1136520a b x + 1068144a b x + 547008a b x + 118272a x +--R * +--R +-+ +--R \|a +--R / +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x +--R + +--R 5 +--R 709632a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 5 2 6 +--R - 1951488a b x - 709632a +--R Type: Union(Expression(Integer),...) +--E 289 + +--S 290 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R 8a b x + 480a b x + 4480a b x + 14336a b x + 18432a b x +--R + +--R 11 +--R 8192a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R - 88a b x - 1760a b x - 9856a b x - 22528a b x - 22528a b x +--R + +--R 11 +--R - 8192a +--R * +--R +-+ +--R \|a +--R / +--R 8 10 7 8 2 6 6 3 5 4 4 4 2 +--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x +--R + +--R 5 3 +--R 709632a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 10 2 7 8 3 6 6 4 5 4 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 5 4 2 6 3 +--R - 1951488a b x - 709632a b +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 1369 +t0:=x^3*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1369 +r0:=-1/7*a*(a+b*x^2)^(7/2)/b^2+1/9*(a+b*x^2)^(9/2)/b^2 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (7b x + 19a b x + 15a b x + a b x - 2a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 16 2 5 14 3 4 12 4 3 10 5 2 8 +--R - 63a b x - 1011a b x - 5439a b x - 14049a b x - 19320a b x +--R + +--R 6 6 7 4 +--R - 13776a b x - 4032a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 18 6 16 2 5 14 3 4 12 4 3 10 +--R 7b x + 306a b x + 2754a b x + 10752a b x + 22239a b x +--R + +--R 5 2 8 6 6 7 4 +--R 25704a b x + 15792a b x + 4032a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a +--R Type: Union(Expression(Integer),...) +--E 294 + +--S 295 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (- 2a b x - 80a b x - 480a b x - 896a b x - 512a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (18a b x + 240a b x + 864a b x + 1152a b x + 512a )\|a +--R / +--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+ +--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 2 5 6 3 4 4 4 3 2 5 2 +--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a b +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 296 + +)clear all + +--S 297 of 1369 +t0:=x*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 5 3 2 | 2 +--R (1) (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1369 +r0:=1/7*(a+b*x^2)^(7/2)/b +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R (2) ------------------------------------------ +--R 7b +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2 +--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4 +--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x +--R + +--R 6 2 +--R 224a x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (7b x + 168a b x + 560a b x + 448a )\|a \|b x + a - 49a b x +--R + +--R 2 2 4 3 2 4 +--R - 392a b x - 784a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (a b x + 24a b x + 80a b x + 64a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (- 7a b x - 56a b x - 112a b x - 64a )\|a +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +-+ | 2 4 6 +--R (7b x + 168a b x + 560a b x + 448a b)\|a \|b x + a - 49a b x +--R + +--R 2 3 4 3 2 2 4 +--R - 392a b x - 784a b x - 448a b +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 301 + +)clear all + +--S 302 of 1369 +t0:=(a+b*x^2)^(5/2)/x +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1369 +r0:=1/3*a*(a+b*x^2)^(3/2)+1/5*(a+b*x^2)^(5/2)-_ + a^(5/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15a \|a atanh(-----------) + (3b x + 11a b x + 23a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 | 2 +--R (- 15a b x - 115a b x - 360a b x - 360a b x )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+ +--R (3b x + 50a b x + 250a b x + 540a b x + 360a b x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (23a b x + 276a b x + 368a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 115a b x - 460a b x - 368a )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 1369 +t0:=(a+b*x^2)^(5/2)/x^3 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1369 +r0:=5/6*b*(a+b*x^2)^(3/2)-1/2*(a+b*x^2)^(5/2)/x^2-_ + 5/2*a^(3/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+5/2*a*b*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15a b x \|a atanh(-----------) + (2b x + 14a b x - 3a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 3 6 3 2 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|b x + a +--R + +--R 2 3 6 3 2 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (2b x + 40a b x + 165a b x + 105a b x - 84a b x - 48a )\|a +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6b x + 72a b x + 96a x )\|a \|b x + a - 30a b x - 120a b x - 96a x +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (15a b x + 180a b x + 240a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (15a b x + 180a b x + 240a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (14a b x + 168a b x + 224a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 70a b x - 280a b x - 224a b)\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (6b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 311 + +)clear all + +--S 312 of 1369 +t0:=(a+b*x^2)^(5/2)/x^5 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1369 +r0:=-5/8*b*(a+b*x^2)^(3/2)/x^2-1/4*(a+b*x^2)^(5/2)/x^4-_ + 15/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+15/8*b^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15b x \|a atanh(-----------) + (8b x - 9a b x - 2a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 2 3 6 3 2 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|b x + a +--R + +--R 4 8 2 3 6 3 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (8b x + 55a b x - 55a b x - 278a b x - 200a b x - 32a )\|a +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8b x + 96a b x + 128a x )\|a \|b x + a - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128a x +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (15a b x + 180a b x + 240a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 75a b x - 300a b x - 240a b )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (15a b x + 180a b x + 240a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 75a b x - 300a b x - 240a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (8a b x + 96a b x + 128a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 40a b x - 160a b x - 128a b )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (8b x + 96a b x + 128a )\|a \|b x + a - 40a b x - 160a b x - 128a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1369 +t0:=(a+b*x^2)^(5/2)/x^7 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1369 +r0:=-5/24*b*(a+b*x^2)^(3/2)/x^4-1/6*(a+b*x^2)^(5/2)/x^6-_ + 5/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-5/16*b^2*sqrt(a+b*x^2)/x^2 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R - 15b x atanh(-----------) + (- 33b x - 26a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 6 +-+ +--R 48x \|a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (90a b x + 480a b x + 480a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (- 15b x - 270a b x - 720a b x - 480a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (33a b x + 620a b x + 2060a b x + 2448a b x + 1216a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x +--R + +--R 6 +--R - 256a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 2 10 2 8 3 6 +-+ | 2 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 2 2 10 3 8 4 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R 5b log(------------------) + 5b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1369 +t0:=(a+b*x^2)^(5/2)/x^9 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1369 +r0:=-5/48*b*(a+b*x^2)^(3/2)/x^6-1/8*(a+b*x^2)^(5/2)/x^8+_ + 5/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 5/64*b^2*sqrt(a+b*x^2)/x^4-5/128*b^3*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 \|b x + a +--R 15b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 +--R (- 15b x - 118a b x - 136a b x - 48a )\|a \|b x + a +--R / +--R 8 +-+ +--R 384a x \|a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 2 6 12 3 5 10 4 4 8 | 2 +--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+ +--R (15b x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 6 2 4 7 2 8 +--R 57600a b x + 29696a b x + 6144a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 6 2 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 2 3 14 3 2 12 4 10 5 8 +-+ | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a +--R + +--R 2 4 16 3 3 14 4 2 12 5 10 6 8 +--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 4 \|b x + a - \|a 4 \|b x + a +--R - 5b log(------------------) - 5b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +)clear all + +--S 327 of 1369 +t0:=(a+b*x^2)^(5/2)/x^11 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1369 +r0:=-1/16*b*(a+b*x^2)^(3/2)/x^8-1/10*(a+b*x^2)^(5/2)/x^10-_ + 3/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/32*b^2*sqrt(a+b*x^2)/x^6-1/128*b^3*sqrt(a+b*x^2)/(a*x^4)+_ + 3/256*b^4*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 5 10 \|b x + a +--R - 15b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (15b x - 10a b x - 248a b x - 336a b x - 128a )\|a \|b x + a +--R / +--R 2 10 +-+ +--R 1280a x \|a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 150a b x + 2400a b x + 10080a b x + 15360a b x +--R + +--R 5 5 10 +--R 7680a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 15b x - 750a b x - 6000a b x - 16800a b x +--R + +--R 4 6 12 5 5 10 +--R - 19200a b x - 7680a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R - 15a b x - 740a b x - 5252a b x - 64a b x + 108128a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 423680a b x + 750080a b x + 700416a b x + 335872a b x + 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R 150a b x + 2450a b x + 8300a b x - 28400a b x - 258656a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R - 729600a b x - 1062400a b x - 860160a b x - 368640a b x - 65536a +--R * +--R +-+ +--R \|a +--R / +--R 3 4 18 4 3 16 5 2 14 6 12 +--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 7 10 +--R 655360a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 5 20 4 4 18 5 3 16 6 2 14 +--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 7 12 8 10 +--R - 1638400a b x - 655360a x +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 5 \|b x + a - \|a 5 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 256a \|a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 331 + +)clear all + +--S 332 of 1369 +t0:=x^4*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 8 6 2 4 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1369 +r0:=1/16*a*x^5*(a+b*x^2)^(3/2)+1/10*x^5*(a+b*x^2)^(5/2)+_ + 3/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/256*a^4*x*sqrt(a+b*x^2)/b^2+1/128*a^3*x^3*sqrt(a+b*x^2)/b+_ + 1/32*a^2*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 5 x\|b +--R 15a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (128b x + 336a b x + 248a b x + 10a b x - 15a x)\|b \|b x + a +--R / +--R 2 +-+ +--R 1280b \|b +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (150a b x + 2400a b x + 10080a b x + 15360a b x + 7680a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 15a b x - 750a b x - 6000a b x - 16800a b x - 19200a b x +--R + +--R 10 +--R - 7680a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 6736a b x - 68248a b x - 290170a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x +--R + +--R 8 3 9 +--R 14080a b x + 7680a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 25120a b x + 166096a b x + 538900a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x +--R + +--R 8 3 9 +--R - 17920a b x - 7680a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 8 5 6 2 4 4 3 3 2 +--R 12800b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 4 2 +--R 655360a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 7 10 6 8 2 5 6 3 4 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 3 2 5 2 +--R - 1638400a b x - 655360a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (300a b x + 4800a b x + 20160a b x + 30720a b x + 15360a ) +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 30a b x - 1500a b x - 12000a b x - 33600a b x - 38400a b x +--R + +--R 10 +--R - 15360a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 6736a b x - 68248a b x - 290170a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x +--R + +--R 8 3 9 +--R 14080a b x + 7680a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 25120a b x + 166096a b x + 538900a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x +--R + +--R 8 3 9 +--R - 17920a b x - 7680a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 6 8 5 6 2 4 4 3 3 2 +--R 12800b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 4 2 +--R 655360a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 7 10 6 8 2 5 6 3 4 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 3 2 5 2 +--R - 1638400a b x - 655360a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 334 + +--S 335 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 5 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 5 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 256b \|b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 5 +---+ x\|b 5 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 256b \|- b \|b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1369 +t0:=x^2*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 6 4 2 2 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1369 +r0:=5/48*a*x^3*(a+b*x^2)^(3/2)+1/8*x^3*(a+b*x^2)^(5/2)-_ + 5/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 5/128*a^3*x*sqrt(a+b*x^2)/b+5/64*a^2*x^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 4 x\|b +--R - 15a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (48b x + 136a b x + 118a b x + 15a x)\|b \|b x + a +--R / +--R +-+ +--R 384b\|b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (120a b x + 1200a b x + 2880a b x + 1920a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 15a b x - 480a b x - 2400a b x - 3840a b x - 1920a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x +--R + +--R 5 2 5 6 3 7 +--R - 50016a b x - 18944a b x - 1920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x +--R + +--R 5 2 5 6 3 7 +--R 59248a b x + 19904a b x + 1920a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +-+ +-+ | 2 +--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|a \|b \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|b +--R , +--R +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (- 240a b x - 2400a b x - 5760a b x - 3840a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 30a b x + 960a b x + 4800a b x + 7680a b x + 3840a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x +--R + +--R 5 2 5 6 3 7 +--R - 50016a b x - 18944a b x - 1920a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x +--R + +--R 5 2 5 6 3 7 +--R 59248a b x + 19904a b x + 1920a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +---+ +-+ | 2 +--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|- b \|a \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +---+ +--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 341 + +--S 342 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 4 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 x\|b +--R 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 128b\|b +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a +--R 5a \|- b atanh(-----------) - 10a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R -------------------------------------------------------------------------- +--R +---+ +-+ +--R 128b\|- b \|b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1369 +t0:=(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (1) (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1369 +r0:=5/24*a*x*(a+b*x^2)^(3/2)+1/6*x*(a+b*x^2)^(5/2)+_ + 5/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+5/16*a^2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R 15a atanh(-----------) + (8b x + 26a b x + 33a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 48\|b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (90a b x + 480a b x + 480a )\|a \|b x + a - 15a b x +--R + +--R 4 2 4 5 2 6 +--R - 270a b x - 720a b x - 480a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x +--R + +--R 5 +--R - 1056a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x +--R + +--R 5 +--R 1056a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 2 4 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a )\|a \|b \|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a )\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (180a b x + 960a b x + 960a )\|a \|b x + a - 30a b x +--R + +--R 4 2 4 5 2 6 +--R - 540a b x - 1440a b x - 960a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x +--R + +--R 5 +--R - 1056a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x +--R + +--R 5 +--R 1056a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 2 4 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a )\|- b \|a \|b x + a +--R + +--R 3 6 2 4 2 2 3 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 348 + +--S 349 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R - 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 16\|b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R - 5a \|- b atanh(-----------) + 10a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ---------------------------------------------------------------------------- +--R +---+ +-+ +--R 16\|- b \|b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1369 +t0:=(a+b*x^2)^(5/2)/x^2 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1369 +r0:=5/4*b*x*(a+b*x^2)^(3/2)-(a+b*x^2)^(5/2)/x+_ + 15/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+15/8*a*b*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 +-+ x\|b 2 4 2 2 | 2 +--R 15a x\|b atanh(-----------) + (2b x + 9a b x - 8a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ---------------------------------------------------------------- +--R 8x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240a x)\|b \|b x + a +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240a x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8b x + 96a b x + 128a x)\|b x + a +--R + +--R 2 5 3 2 +-+ +--R (- 40b x - 160a b x - 128a x)\|a +--R , +--R +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480a x)\|- b \|b x + a +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480a x)\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8b x + 96a b x + 128a x)\|b x + a +--R + +--R 2 5 3 2 +-+ +--R (- 40b x - 160a b x - 128a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 355 + +--S 356 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 15a \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 +-+ x\|b +--R - 15a \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a +--R - 15a \|b atanh(-----------) + 30a \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ----------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 359 + +)clear all + +--S 360 of 1369 +t0:=(a+b*x^2)^(5/2)/x^4 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1369 +r0:=-5/3*b*(a+b*x^2)^(3/2)/x-1/3*(a+b*x^2)^(5/2)/x^3+_ + 5/2*a*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+5/2*b^2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 +-+ x\|b 2 4 2 2 | 2 +--R 15a b x \|b atanh(-----------) + (3b x - 14a b x - 2a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) -------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|b \|b x + a +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6b x + 72a b x + 96a x )\|b x + a +--R + +--R 2 7 5 2 3 +-+ +--R (- 30b x - 120a b x - 96a x )\|a +--R , +--R +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- b \|b x + a +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6b x + 72a b x + 96a x )\|b x + a +--R + +--R 2 7 5 2 3 +-+ +--R (- 30b x - 120a b x - 96a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 362 + +--S 363 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 5a b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - 5a b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R - 5a b\|b atanh(-----------) + 10a b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 1369 +t0:=(a+b*x^2)^(5/2)/x^6 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1369 +r0:=-1/3*b*(a+b*x^2)^(3/2)/x^3-1/5*(a+b*x^2)^(5/2)/x^5+_ + b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^2*sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R 2 5 +-+ x\|b 2 4 2 2 | 2 +--R 15b x \|b atanh(-----------) + (- 23b x - 11a b x - 3a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------------------------- +--R 5 +--R 15x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15b x + 180a b x + 240a b x )\|b \|b x + a +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 9 7 2 5 +-+ +--R (- 75b x - 300a b x - 240a x )\|a +--R , +--R +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30b x + 360a b x + 480a b x )\|- b \|b x + a +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150b x - 600a b x - 480a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 9 7 2 5 +-+ +--R (- 75b x - 300a b x - 240a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 369 + +--S 370 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 +-+ x\|b +--R - b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a +--R (6) - b \|b atanh(-----------) + 2b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1369 +t0:=(a+b*x^2)^(5/2)/x^8 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1369 +r0:=-1/7*(a+b*x^2)^(7/2)/(a*x^7) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (- b x - 3a b x - 3a b x - a )\|b x + a +--R (2) -------------------------------------------- +--R 7 +--R 7a x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 7b x + 77a b x + 301a b x + 575a b x + 584a b x + 304a b x +--R + +--R 6 +--R 64a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - b x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64a +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448a x )\|b x + a +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448a x )\|a +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1369 +t0:=(a+b*x^2)^(5/2)/x^10 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1369 +r0:=-1/9*(a+b*x^2)^(7/2)/(a*x^9)+2/63*b*(a+b*x^2)^(7/2)/(a^2*x^7) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (2b x - a b x - 15a b x - 19a b x - 7a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 9 +--R 63a x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 18b x - 231a b x - 609a b x + 1251a b x + 8887a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 17944a b x + 17808a b x + 8896a b x + 1792a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2b x + 81a b x + 504a b x + 462a b x - 4266a b x - 16119a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 25848a b x - 22032a b x - 9792a b x - 1792a +--R / +--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +--R (63a b x + 2520a b x + 15120a b x + 28224a b x + 16128a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +-+ +--R (- 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a x )\|a +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1369 +t0:=(a+b*x^2)^(5/2)/x^12 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1369 +r0:=-1/11*(a+b*x^2)^(7/2)/(a*x^11)+4/99*b*(a+b*x^2)^(7/2)/(a^2*x^9)-_ + 8/693*b^2*(a+b*x^2)^(7/2)/(a^3*x^7) +--R +--R +--R (2) +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 8b x + 4a b x - 3a b x - 113a b x - 161a b x - 63a )\|b x + a +--R ------------------------------------------------------------------------ +--R 3 11 +--R 693a x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 88b x + 1716a b x + 9009a b x + 19503a b x + 41591a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 180705a b x + 534772a b x + 852272a b x + 746496a b x +--R + +--R 9 2 10 +--R 342272a b x + 64512a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R - 8b x - 484a b x - 4719a b x - 16632a b x - 32274a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 97240a b x - 376607a b x - 886468a b x - 1186768a b x +--R + +--R 9 2 4 10 2 11 +--R - 909568a b x - 374528a b x - 64512a +--R / +--R 3 5 21 4 4 19 5 3 17 6 2 15 +--R 693a b x + 41580a b x + 388080a b x + 1241856a b x +--R + +--R 7 13 8 11 +--R 1596672a b x + 709632a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 5 21 4 4 19 5 3 17 6 2 15 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 7 13 8 11 +--R - 1951488a b x - 709632a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1369 +t0:=(a+b*x^2)^(5/2)/x^14 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 14 +--R x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1369 +r0:=-1/13*(a+b*x^2)^(7/2)/(a*x^13)+6/143*b*(a+b*x^2)^(7/2)/(a^2*x^11)-_ + 8/429*b^2*(a+b*x^2)^(7/2)/(a^3*x^9)+16/3003*b^3*(a+b*x^2)^(7/2)/(a^4*x^7) +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (16b x - 8a b x + 6a b x - 5a b x - 371a b x - 567a b x - 231a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 13 +--R 3003a x +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 24 11 22 2 10 20 3 9 18 +--R - 208b x - 5720a b x - 43758a b x - 138567a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 197197a b x + 17199a b x + 1280783a b x + 5475348a b x +--R + +--R 8 4 8 9 3 6 10 2 4 11 2 +--R 12549024a b x + 16700416a b x + 12911360a b x + 5397504a b x +--R + +--R 12 +--R 946176a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 13 26 12 24 2 11 22 3 10 20 4 9 18 +--R 16b x + 1352a b x + 18590a b x + 94809a b x + 224796a b x +--R + +--R 5 8 16 6 7 14 7 6 12 8 5 10 +--R 230230a b x - 362726a b x - 3117439a b x - 10284300a b x +--R + +--R 9 4 8 10 3 6 11 2 4 12 2 +--R - 19585696a b x - 22540544a b x - 15491840a b x - 5870592a b x +--R + +--R 13 +--R - 946176a +--R / +--R 4 6 25 5 5 23 6 4 21 7 3 19 +--R 3003a b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 8 2 17 9 15 10 13 +--R 34594560a b x + 33825792a b x + 12300288a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 6 25 5 5 23 6 4 21 7 3 19 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 8 2 17 9 15 10 13 +--R - 49969920a b x - 39975936a b x - 12300288a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1369 +t0:=(a+b*x^2)^(5/2)/x^16 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 16 +--R x +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1369 +r0:=-1/15*(a+b*x^2)^(7/2)/(a*x^15)+8/195*b*(a+b*x^2)^(7/2)/(a^2*x^13)-_ + 16/715*b^2*(a+b*x^2)^(7/2)/(a^3*x^11)+_ + 64/6435*b^3*(a+b*x^2)^(7/2)/(a^4*x^9)-_ + 128/45045*b^4*(a+b*x^2)^(7/2)/(a^5*x^7) +--R +--R +--R (2) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 128b x + 64a b x - 48a b x + 40a b x - 35a b x - 4473a b x +--R + +--R 6 2 7 +--R - 7161a b x - 3003a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 5 15 +--R 45045a x +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 28 13 26 2 12 24 3 11 22 +--R 1920b x + 70720a b x + 739024a b x + 3325608a b x +--R + +--R 4 10 20 5 9 18 6 8 16 7 7 14 +--R 7436429a b x + 8518055a b x + 7017255a b x + 31888581a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R 174491952a b x + 540852576a b x + 1004347520a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R 1146763520a b x + 790013952a b x + 301830144a b x + 49201152a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 15 30 14 28 2 13 26 3 12 24 +--R - 128b x - 14400a b x - 265200a b x - 1847560a b x +--R + +--R 4 11 22 5 10 20 6 9 18 7 8 16 +--R - 6235515a b x - 11159148a b x - 11079250a b x - 15095700a b x +--R + +--R 8 7 14 9 6 12 10 5 10 +--R - 85709115a b x - 367431760a b x - 938611872a b x +--R + +--R 11 4 8 12 3 6 13 2 4 +--R - 1495920000a b x - 1507116800a b x - 934778880a b x +--R + +--R 14 2 15 +--R - 326430720a b x - 49201152a +--R / +--R 5 7 29 6 6 27 7 5 25 8 4 23 +--R 45045a b x + 5045040a b x + 90810720a b x + 605404800a b x +--R + +--R 9 3 21 10 2 19 11 17 +--R 1902700800a b x + 3044321280a b x + 2398556160a b x +--R + +--R 12 15 +--R 738017280a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 7 29 6 6 27 7 5 25 +--R - 675675a b x - 25225200a b x - 272432160a b x +--R + +--R 8 4 23 9 3 21 10 2 19 +--R - 1297296000a b x - 3171168000a b x - 4151347200a b x +--R + +--R 11 17 12 15 +--R - 2767564800a b x - 738017280a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1369 +t0:=(a+b*x^2)^(5/2)/x^18 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 18 +--R x +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1369 +r0:=-1/17*(a+b*x^2)^(7/2)/(a*x^17)+2/51*b*(a+b*x^2)^(7/2)/(a^2*x^15)-_ + 16/663*b^2*(a+b*x^2)^(7/2)/(a^3*x^13)+_ + 32/2431*b^3*(a+b*x^2)^(7/2)/(a^4*x^11)-_ + 128/21879*b^4*(a+b*x^2)^(7/2)/(a^5*x^9)+_ + 256/153153*b^5*(a+b*x^2)^(7/2)/(a^6*x^7) +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 256b x - 128a b x + 96a b x - 80a b x + 70a b x - 63a b x +--R + +--R 6 2 4 7 2 8 +--R - 12705a b x - 21021a b x - 9009a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 6 17 +--R 153153a x +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 32 15 30 2 14 28 3 13 26 +--R - 4352b x - 206720a b x - 2821728a b x - 16997552a b x +--R + +--R 4 12 24 5 11 22 6 10 20 +--R - 53117350a b x - 91265265a b x - 84612927a b x +--R + +--R 7 9 18 8 8 16 9 7 14 +--R - 26796675a b x + 158507217a b x + 1163856848a b x +--R + +--R 10 6 12 11 5 10 12 4 8 +--R 4663848992a b x + 11445343104a b x + 17876348672a b x +--R + +--R 13 3 6 14 2 4 15 2 +--R 17866512384a b x + 11078774784a b x + 3886891008a b x +--R + +--R 16 +--R 590413824a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 17 34 16 32 2 15 30 3 14 28 +--R 256b x + 36992a b x + 878560a b x + 7994896a b x +--R + +--R 4 13 26 5 12 24 6 11 22 +--R 36119798a b x + 90299495a b x + 129279696a b x +--R + +--R 7 10 20 8 9 18 9 8 16 +--R 101136162a b x - 7854510a b x - 490730449a b x +--R + +--R 10 7 14 11 6 12 12 5 10 +--R - 2717211728a b x - 8930043424a b x - 18706939264a b x +--R + +--R 13 4 8 14 3 6 15 2 4 +--R - 25644625664a b x - 22956939264a b x - 12948418560a b x +--R + +--R 16 2 17 +--R - 4182097920a b x - 590413824a +--R / +--R 6 8 33 7 7 31 8 6 29 +--R 153153a b x + 22054032a b x + 514594080a b x +--R + +--R 9 5 27 10 4 25 11 3 23 +--R 4528427904a b x + 19407548160a b x + 44853000192a b x +--R + +--R 12 2 21 13 19 14 17 +--R 57085636608a b x + 37638881280a b x + 10037035008a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 33 7 7 31 8 6 29 +--R - 2603601a b x - 124972848a b x - 1749619872a b x +--R + +--R 9 5 27 10 4 25 11 3 23 +--R - 10997610624a b x - 36658702080a b x - 69318273024a b x +--R + +--R 12 2 21 13 19 14 17 +--R - 74650447872a b x - 42657398784a b x - 10037035008a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1369 +t0:=x^m*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 m | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1369 +--r0:=315*a^3*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m)*(8+m)*(10+m))+_ +-- 63*a^2*x^(1+m)*(a+b*x^2)^(5/2)/((6+m)*(8+m)*(10+m))+_ +-- 9*a*x^(1+m)*(a+b*x^2)^(7/2)/(80+18*m+m^2)+x^(1+m)*_ +-- (a+b*x^2)^(9/2)/(10+m)+945*a^4*x^(1+m)*sqrt(a+b*x^2)/_ +-- ((6+m)*(8+m)*(10+m)*(8+6*m+m^2))+945*a^5*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((6+m)*(8+m)*(10+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 405 + +--S 406 of 1369 +--a0:=integrate(t0,x) +--E 406 + +--S 407 of 1369 +--m0:=a0-r0 +--E 407 + +--S 408 of 1369 +--d0:=D(m0,x) +--E 408 + +)clear all + +--S 409 of 1369 +t0:=x^15*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 23 3 21 2 2 19 3 17 4 15 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1369 +r0:=-1/11*a^7*(a+b*x^2)^(11/2)/b^8+7/13*a^6*(a+b*x^2)^(13/2)/b^8-_ + 7/5*a^5*(a+b*x^2)^(15/2)/b^8+35/17*a^4*(a+b*x^2)^(17/2)/b^8-_ + 35/19*a^3*(a+b*x^2)^(19/2)/b^8+a^2*(a+b*x^2)^(21/2)/b^8-_ + 7/23*a*(a+b*x^2)^(23/2)/b^8+1/25*(a+b*x^2)^(25/2)/b^8 +--R +--R +--R (2) +--R 12 24 11 22 2 10 20 3 9 18 +--R 1062347b x + 4665089a b x + 7759752a b x + 5810090a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8 +--R 1659515a b x + 429a b x - 462a b x + 504a b x - 560a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R 640a b x - 768a b x + 1024a b x - 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 48 2 15 46 3 14 44 +--R - 26558675a b x - 2878729425a b x - 97395972960a b x +--R + +--R 4 13 42 5 12 40 +--R - 1609225902570a b x - 15696010222035a b x +--R + +--R 6 11 38 7 10 36 +--R - 100124312670525a b x - 444286575778650a b x +--R + +--R 8 9 34 9 8 32 +--R - 1425766406694360a b x - 3390169039300720a b x +--R + +--R 10 7 30 11 6 28 +--R - 6054288088284160a b x - 8157338113996800a b x +--R + +--R 12 5 26 13 4 24 +--R - 8256379402444800a b x - 6184960931901440a b x +--R + +--R 14 3 22 15 2 20 +--R - 3328737290977280a b x - 1218036417495040a b x +--R + +--R 16 18 17 16 +--R - 271525694668800a b x - 27848789196800a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 17 50 16 48 2 15 46 +--R 1062347b x + 337179700a b x + 18813934425a b x +--R + +--R 3 14 44 4 13 42 5 12 40 +--R 435911726250a b x + 5537985721125a b x + 44226266816160a b x +--R + +--R 6 11 38 7 10 36 +--R 240242576724975a b x + 932460385321650a b x +--R + +--R 8 9 34 9 8 32 +--R 2668614201361000a b x + 5742120965670000a b x +--R + +--R 10 7 30 11 6 28 +--R 9385626998420480a b x + 11679727644825600a b x +--R + +--R 12 5 26 13 4 24 +--R 10999050000998400a b x + 7712957537792000a b x +--R + +--R 14 3 22 15 2 20 +--R 3905555337216000a b x + 1350318166179840a b x +--R + +--R 16 18 17 16 +--R 285450089267200a b x + 27848789196800a x +--R * +--R +-+ +--R \|a +--R / +--R 12 24 11 22 2 10 20 +--R 26558675b x + 8286306600a b x + 425363738800a b x +--R + +--R 3 9 18 4 8 16 5 7 14 +--R 8507274776000a b x + 87503397696000a b x + 528909426073600a b x +--R + +--R 6 6 12 7 5 10 +--R 2019472354099200a b x + 5059776887193600a b x +--R + +--R 8 4 8 9 3 6 +--R 8432961478656000a b x + 9259722407936000a b x +--R + +--R 10 2 4 11 2 12 +--R 6433070304460800a b x + 2562088606105600a b x + 445580627148800a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 12 24 2 11 22 3 10 20 +--R - 663966875a b x - 69052555000a b x - 2126818694000a b x +--R + +--R 4 9 18 5 8 16 +--R - 30383124200000a b x - 243064993600000a b x +--R + +--R 6 7 14 7 6 12 +--R - 1202066877440000a b x - 3883600680960000a b x +--R + +--R 8 5 10 9 4 8 +--R - 8432961478656000a b x - 12401413939200000a b x +--R + +--R 10 3 6 11 2 4 +--R - 12183845273600000a b x - 7658417029120000a b x +--R + +--R 12 2 13 +--R - 2784878919680000a b x - 445580627148800a +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 12 24 14 11 22 15 10 20 +--R - 2048a b x - 638976a b x - 32800768a b x +--R + +--R 16 9 18 17 8 16 18 7 14 +--R - 656015360a b x - 6747586560a b x - 40785412096a b x +--R + +--R 19 6 12 20 5 10 21 4 8 +--R - 155726118912a b x - 390170935296a b x - 650284892160a b x +--R + +--R 22 3 6 23 2 4 24 2 +--R - 714038312960a b x - 496068722688a b x - 197568495616a b x +--R + +--R 25 +--R - 34359738368a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 13 12 24 14 11 22 15 10 20 +--R 51200a b x + 5324800a b x + 164003840a b x +--R + +--R 16 9 18 17 8 16 18 7 14 +--R 2342912000a b x + 18743296000a b x + 92694118400a b x +--R + +--R 19 6 12 20 5 10 21 4 8 +--R 299473305600a b x + 650284892160a b x + 956301312000a b x +--R + +--R 22 3 6 23 2 4 24 2 +--R 939524096000a b x + 590558003200a b x + 214748364800a b x +--R + +--R 25 +--R 34359738368a +--R * +--R +-+ +--R \|a +--R / +--R 20 24 19 22 2 18 20 +--R 26558675b x + 8286306600a b x + 425363738800a b x +--R + +--R 3 17 18 4 16 16 +--R 8507274776000a b x + 87503397696000a b x +--R + +--R 5 15 14 6 14 12 +--R 528909426073600a b x + 2019472354099200a b x +--R + +--R 7 13 10 8 12 8 +--R 5059776887193600a b x + 8432961478656000a b x +--R + +--R 9 11 6 10 10 4 +--R 9259722407936000a b x + 6433070304460800a b x +--R + +--R 11 9 2 12 8 +--R 2562088606105600a b x + 445580627148800a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 20 24 2 19 22 3 18 20 +--R - 663966875a b x - 69052555000a b x - 2126818694000a b x +--R + +--R 4 17 18 5 16 16 +--R - 30383124200000a b x - 243064993600000a b x +--R + +--R 6 15 14 7 14 12 +--R - 1202066877440000a b x - 3883600680960000a b x +--R + +--R 8 13 10 9 12 8 +--R - 8432961478656000a b x - 12401413939200000a b x +--R + +--R 10 11 6 11 10 4 +--R - 12183845273600000a b x - 7658417029120000a b x +--R + +--R 12 9 2 13 8 +--R - 2784878919680000a b x - 445580627148800a b +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1369 +t0:=x^13*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 21 3 19 2 2 17 3 15 4 13 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1369 +r0:=1/11*a^6*(a+b*x^2)^(11/2)/b^7-6/13*a^5*(a+b*x^2)^(13/2)/b^7+_ + a^4*(a+b*x^2)^(15/2)/b^7-20/17*a^3*(a+b*x^2)^(17/2)/b^7+_ + 15/19*a^2*(a+b*x^2)^(19/2)/b^7-2/7*a*(a+b*x^2)^(21/2)/b^7+_ + 1/23*(a+b*x^2)^(23/2)/b^7 +--R +--R +--R (2) +--R 11 22 10 20 2 9 18 3 8 16 +--R 323323b x + 1431859a b x + 2406690a b x + 1826110a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6 +--R 530959a b x + 231a b x - 252a b x + 280a b x - 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+t0:=x^5*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 13 3 11 2 2 9 3 7 4 5 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1369 +r0:=1/11*a^2*(a+b*x^2)^(11/2)/b^3-2/13*a*(a+b*x^2)^(13/2)/b^3+_ + 1/15*(a+b*x^2)^(15/2)/b^3 +--R +--R +--R (2) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 143b x + 671a b x + 1218a b x + 1030a b x + 355a b x + 3a b x +--R + +--R 6 2 7 +--R - 4a b x + 8a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 3 +--R 2145b +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 28 2 10 26 3 9 24 4 8 22 +--R - 2145a b x - 90145a b x - 1258894a b x - 8874138a b x +--R + +--R 5 7 20 6 6 18 7 5 16 +--R - 37340589a b x - 101923965a b x - 188185140a b x +--R + +--R 8 4 14 9 3 12 10 2 10 +--R - 238572048a b x - 205810176a b x - 116083968a b x +--R + +--R 11 8 12 6 +--R - 38804480a b x - 5857280a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 12 30 11 28 2 10 26 3 9 24 +--R 143b x + 16830a b x + 381345a b x + 3776760a b x +--R + +--R 4 8 22 5 7 20 6 6 18 +--R 21041865a b x + 74123478a b x + 175464575a b x +--R + +--R 7 5 16 8 4 14 9 3 12 +--R 287644500a b x + 329163120a b x + 259367680a b x +--R + +--R 10 2 10 11 8 12 6 +--R 134754048a b x + 41733120a b x + 5857280a x +--R * +--R +-+ +--R \|a +--R / +--R 7 14 6 12 2 5 10 3 4 8 +--R 2145b x + 240240a b x + 4324320a b x + 28828800a b x +--R + +--R 4 3 6 5 2 4 6 2 7 +--R 90604800a b x + 144967680a b x + 114216960a b x + 35143680a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 +--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 151008000a b x - 197683200a b x - 131788800a b x - 35143680a +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 7 14 9 6 12 10 5 10 11 4 8 12 3 6 +--R 8a b x + 896a b x + 16128a b x + 107520a b x + 337920a b x +--R + +--R 13 2 4 14 2 15 +--R 540672a b x + 425984a b x + 131072a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 7 14 9 6 12 10 5 10 11 4 8 +--R - 120a b x - 4480a b x - 48384a b x - 230400a b x +--R + +--R 12 3 6 13 2 4 14 2 15 +--R - 563200a b x - 737280a b x - 491520a b x - 131072a +--R * +--R +-+ +--R \|a +--R / +--R 10 14 9 12 2 8 10 3 7 8 +--R 2145b x + 240240a b x + 4324320a b x + 28828800a b x +--R + +--R 4 6 6 5 5 4 6 4 2 7 3 +--R 90604800a b x + 144967680a b x + 114216960a b x + 35143680a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 10 14 2 9 12 3 8 10 4 7 8 +--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x +--R + +--R 5 6 6 6 5 4 7 4 2 8 3 +--R - 151008000a b x - 197683200a b x - 131788800a b x - 35143680a b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1369 +t0:=x^3*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 11 3 9 2 2 7 3 5 4 3 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1369 +r0:=-1/11*a*(a+b*x^2)^(11/2)/b^2+1/13*(a+b*x^2)^(13/2)/b^2 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (11b x + 53a b x + 100a b x + 90a b x + 35a b x + a b x - 2a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 24 2 9 22 3 8 20 4 7 18 +--R - 143a b x - 4693a b x - 52624a b x - 301730a b x +--R + +--R 5 6 16 6 5 14 7 4 12 8 3 10 +--R - 1036607a b x - 2301585a b x - 3415412a b x - 3397680a b x +--R + +--R 9 2 8 10 6 11 4 +--R - 2196480a b x - 841984a b x - 146432a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 11 26 10 24 2 9 22 3 8 20 4 7 18 +--R 11b x + 988a b x + 17849a b x + 143858a b x + 658229a b x +--R + +--R 5 6 16 6 5 14 7 4 12 8 3 10 +--R 1907048a b x + 3692975a b x + 4886596a b x + 4399824a b x +--R + +--R 9 2 8 10 6 11 4 +--R 2599168a b x + 915200a b x + 146432a x +--R * +--R +-+ +--R \|a +--R / +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x +--R + +--R 5 2 6 +--R 1610752a b x + 585728a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 +--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x +--R + +--R 5 2 4 6 2 7 +--R - 2379520a b x - 1903616a b x - 585728a +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4 +--R - 2a b x - 168a b x - 2240a b x - 10752a b x - 23040a b x +--R + +--R 12 2 13 +--R - 22528a b x - 8192a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4 +--R 26a b x + 728a b x + 5824a b x + 19968a b x + 33280a b x +--R + +--R 12 2 13 +--R 26624a b x + 8192a +--R * +--R +-+ +--R \|a +--R / +--R 8 12 7 10 2 6 8 3 5 6 4 4 4 +--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x +--R + +--R 5 3 2 6 2 +--R 1610752a b x + 585728a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 12 2 7 10 3 6 8 4 5 6 +--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x +--R + +--R 5 4 4 6 3 2 7 2 +--R - 2379520a b x - 1903616a b x - 585728a b +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1369 +t0:=x*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1369 +r0:=1/11*(a+b*x^2)^(11/2)/b +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a +--R (2) ----------------------------------------------------------------- +--R 11b +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 20 2 8 18 3 7 16 4 6 14 5 5 12 +--R - 11a b x - 275a b x - 2442a b x - 11286a b x - 31471a b x +--R + +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R - 56694a b x - 67760a b x - 53152a b x - 25344a b x - 5632a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 22 9 20 2 8 18 3 7 16 4 6 14 +--R b x + 66a b x + 935a b x + 6072a b x + 22671a b x +--R + +--R 5 5 12 6 4 10 7 3 8 8 2 6 9 4 +--R 53834a b x + 85294a b x + 91520a b x + 65120a b x + 28160a b x +--R + +--R 10 2 +--R 5632a x +--R * +--R +-+ +--R \|a +--R / +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R 11b x + 660a b x + 6160a b x + 19712a b x + 25344a b x +--R + +--R 5 +--R 11264a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R - 121a b x - 2420a b x - 13552a b x - 30976a b x - 30976a b x +--R + +--R 6 +--R - 11264a +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 11 +--R (a b x + 60a b x + 560a b x + 1792a b x + 2304a b x + 1024a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R - 11a b x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 11 +--R - 1024a +--R * +--R +-+ +--R \|a +--R / +--R 6 10 5 8 2 4 6 3 3 4 4 2 2 +--R 11b x + 660a b x + 6160a b x + 19712a b x + 25344a b x +--R + +--R 5 +--R 11264a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 10 2 5 8 3 4 6 4 3 4 5 2 2 +--R - 121a b x - 2420a b x - 13552a b x - 30976a b x - 30976a b x +--R + +--R 6 +--R - 11264a b +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1369 +t0:=(a+b*x^2)^(9/2)/x +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1369 +r0:=1/3*a^3*(a+b*x^2)^(3/2)+1/5*a^2*(a+b*x^2)^(5/2)+1/7*a*(a+b*x^2)^(7/2)+_ + 1/9*(a+b*x^2)^(9/2)-a^(9/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+_ + a^4*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 +-+ \|b x + a +--R - 315a \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 185a b x + 408a b x + 506a b x + 563a )\|b x + a +--R / +--R 315 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 315a b x - 5865a b x - 40992a b x - 153594a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 357000a b x - 546000a b x - 504000a b x - 201600a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1620a b x + 17793a b x + 93114a b x + 287469a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 579600a b x + 772800a b x + 604800a b x + 201600a b x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (563a b x + 22520a b x + 135120a b x + 252224a b x + 144128a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (- 5067a b x - 67560a b x - 243216a b x - 324288a b x - 144128a )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1369 +t0:=(a+b*x^2)^(9/2)/x^3 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1369 +r0:=3/2*a^2*b*(a+b*x^2)^(3/2)+9/10*a*b*(a+b*x^2)^(5/2)+_ + 9/14*b*(a+b*x^2)^(7/2)-1/2*(a+b*x^2)^(9/2)/x^2-_ + 9/2*a^(7/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+9/2*a^3*b*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 3 2 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 2 +--R 70x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 8 2 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 2 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 90a b x - 1722a b x - 12684a b x - 52640a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 134085a b x - 175000a b x - 74480a b x + 20160a b x + 8960a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 468a b x + 5334a b x + 29904a b x + 103005a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 211365a b x + 214200a b x + 65520a b x - 24640a b x - 8960a +--R * +--R +-+ +--R \|a +--R / +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 10 2 3 8 3 2 6 4 4 5 2 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a x +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (388a b x + 15520a b x + 93120a b x + 173824a b x + 99328a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +-+ +--R (- 3492a b x - 46560a b x - 167616a b x - 223488a b x - 99328a b)\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1369 +t0:=(a+b*x^2)^(9/2)/x^5 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1369 +r0:=21/8*a*b^2*(a+b*x^2)^(3/2)+63/40*b^2*(a+b*x^2)^(5/2)-_ + 9/8*b*(a+b*x^2)^(7/2)/x^2-1/4*(a+b*x^2)^(9/2)/x^4-_ + 63/8*a^(5/2)*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))+63/8*a^2*b^2*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 2 2 4 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 4 +--R 40x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 12 4 5 10 5 4 8 6 3 6 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 7 2 4 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 4 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R - 72a b x - 1464a b x - 12480a b x - 51075a b x - 79310a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 13280a b x + 53280a b x + 27520a b x + 2560a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 384a b x + 4824a b x + 30315a b x + 86745a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 90990a b x - 10080a b x - 66720a b x - 28800a b x - 2560a +--R * +--R +-+ +--R \|a +--R / +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 12 2 3 10 3 2 8 4 6 5 4 +--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a x +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (288a b x + 11520a b x + 69120a b x + 129024a b x + 73728a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +-+ +--R (- 2592a b x - 34560a b x - 124416a b x - 165888a b x - 73728a b )\|a +--R / +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1369 +t0:=(a+b*x^2)^(9/2)/x^7 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1369 +r0:=35/16*b^3*(a+b*x^2)^(3/2)-21/16*b^2*(a+b*x^2)^(5/2)/x^2-_ + 3/8*b*(a+b*x^2)^(7/2)/x^4-1/6*(a+b*x^2)^(9/2)/x^6-_ + 105/16*a^(3/2)*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))+_ + 105/16*a*b^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 3 6 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 6 +--R 48x +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 14 3 6 12 4 5 10 5 4 8 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 6 3 6 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 6 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 144a b x - 3584a b x - 22067a b x - 28902a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 46632a b x + 117600a b x + 74496a b x + 17408a b x + 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 864a b x + 10971a b x + 37473a b x + 16254a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 97128a b x - 152800a b x - 82944a b x - 18432a b x - 2048a +--R * +--R +-+ +--R \|a +--R / +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 14 2 3 12 3 2 10 4 8 5 6 +--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a x +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (208a b x + 8320a b x + 49920a b x + 93184a b x + 53248a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +-+ +--R (- 1872a b x - 24960a b x - 89856a b x - 119808a b x - 53248a b )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1369 +t0:=(a+b*x^2)^(9/2)/x^9 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1369 +r0:=-105/128*b^3*(a+b*x^2)^(3/2)/x^2-21/64*b^2*(a+b*x^2)^(5/2)/x^4-_ + 3/16*b*(a+b*x^2)^(7/2)/x^6-1/8*(a+b*x^2)^(9/2)/x^8-_ + 315/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+_ + 315/128*b^4*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 +-+ \|b x + a +--R - 315b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 8 +--R 128x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 5 4 8 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 8 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 1024a b x - 7315a b x + 16314a b x + 150008a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 288624a b x + 244096a b x + 111360a b x + 31744a b x + 4096a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 128b x + 3771a b x + 6945a b x - 66930a b x - 269640a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 398576a b x - 296064a b x - 126720a b x - 33792a b x - 4096a +--R * +--R +-+ +--R \|a +--R / +--R 4 16 3 14 2 2 12 3 10 4 8 +-+ +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 16 2 3 14 3 2 12 4 10 5 8 +--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a x +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (128a b x + 5120a b x + 30720a b x + 57344a b x + 32768a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +-+ +--R (- 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a b )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1369 +t0:=(a+b*x^2)^(9/2)/x^11 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1369 +r0:=-21/128*b^3*(a+b*x^2)^(3/2)/x^4-21/160*b^2*(a+b*x^2)^(5/2)/x^6-_ + 9/80*b*(a+b*x^2)^(7/2)/x^8-1/10*(a+b*x^2)^(9/2)/x^10-_ + 63/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_ + 63/256*b^4*sqrt(a+b*x^2)/x^2 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 5 10 \|b x + a +--R - 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|a \|b x + a +--R / +--R 10 +-+ +--R 1280x \|a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 3150a b x + 50400a b x + 211680a b x + 322560a b x +--R + +--R 5 5 10 +--R 161280a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 315b x - 15750a b x - 126000a b x - 352800a b x +--R + +--R 4 6 12 5 5 10 +--R - 403200a b x - 161280a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 965a b x + 49740a b x + 461868a b x + 1745856a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 3484128a b x + 4202240a b x + 3299840a b x + 1683456a b x +--R + +--R 9 2 10 +--R 499712a b x + 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 9650a b x - 178950a b x - 1069860a b x - 3115440a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 5260256a b x - 5670400a b x - 4083200a b x - 1925120a b x +--R + +--R 9 2 10 +--R - 532480a b x - 65536a +--R * +--R +-+ +--R \|a +--R / +--R 4 18 2 3 16 3 2 14 4 12 +--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 5 10 +--R 655360a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 20 2 4 18 3 3 16 4 2 14 +--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 5 12 6 10 +--R - 1638400a b x - 655360a x +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 5 \|b x + a - \|a 5 \|b x + a +--R 63b log(------------------) + 63b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 256\|a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1369 +t0:=(a+b*x^2)^(9/2)/x^13 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1369 +r0:=-7/128*b^3*(a+b*x^2)^(3/2)/x^6-21/320*b^2*(a+b*x^2)^(5/2)/x^8-_ + 3/40*b*(a+b*x^2)^(7/2)/x^10-1/12*(a+b*x^2)^(9/2)/x^12+_ + 21/1024*b^6*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 21/512*b^4*sqrt(a+b*x^2)/x^4-21/1024*b^5*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 6 12 \|b x + a +--R 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R / +--R 12 +-+ +--R 15360a x \|a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 3780a b x - 88200a b x - 564480a b x - 1451520a b x +--R + +--R 5 7 14 6 6 12 +--R - 1612800a b x - 645120a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R 315b x + 22680a b x + 264600a b x + 1128960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 +--R 2177280a b x + 1935360a b x + 645120a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R 315a b x + 27590a b x + 629552a b x + 6088608a b x +--R + +--R 5 7 14 6 6 12 7 5 10 +--R 30258240a b x + 87499392a b x + 158714880a b x +--R + +--R 8 4 8 9 3 6 10 2 4 11 2 +--R 187787264a b x + 145965056a b x + 72253440a b x + 20709376a b x +--R + +--R 12 +--R 2621440a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 3780a b x - 150900a b x - 2223584a b x - 15673392a b x +--R + +--R 5 7 14 6 6 12 7 5 10 +--R - 61796736a b x - 150196352a b x - 238141440a b x +--R + +--R 8 4 8 9 3 6 10 2 4 +--R - 252930048a b x - 179666944a b x - 82280448a b x +--R + +--R 11 2 12 +--R - 22020096a b x - 2621440a +--R * +--R +-+ +--R \|a +--R / +--R 2 5 22 3 4 20 4 3 18 5 2 16 +--R 184320a b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 6 14 7 12 +--R 78643200a b x + 31457280a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 6 24 3 5 22 4 4 20 5 3 18 +--R - 15360a b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 6 2 16 7 14 8 12 +--R - 106168320a b x - 94371840a b x - 31457280a x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 6 \|b x + a - \|a 6 \|b x + a +--R - 21b log(------------------) - 21b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------ +--R +-+ +--R 1024a\|a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1369 +t0:=(a+b*x^2)^(9/2)/x^15 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 15 +--R x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1369 +r0:=-3/128*b^3*(a+b*x^2)^(3/2)/x^8-3/80*b^2*(a+b*x^2)^(5/2)/x^10-_ + 3/56*b*(a+b*x^2)^(7/2)/x^12-1/14*(a+b*x^2)^(9/2)/x^14-_ + 9/2048*b^7*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 3/256*b^4*sqrt(a+b*x^2)/x^6-3/1024*b^5*sqrt(a+b*x^2)/(a*x^4)+_ + 9/2048*b^6*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 7 14 \|b x + a +--R - 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 2 6 +--R - 24320a b x - 5120a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R / +--R 2 14 +-+ +--R 71680a x \|a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 26 2 12 24 3 11 22 4 10 20 +--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R 8870400a b x + 7741440a b x + 2580480a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 14 28 13 26 2 12 24 3 11 22 +--R - 315b x - 30870a b x - 493920a b x - 2963520a b x +--R + +--R 4 10 20 5 9 18 6 8 16 +--R - 8467200a b x - 12418560a b x - 9031680a b x +--R + +--R 7 7 14 +--R - 2580480a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 13 26 2 12 24 3 11 22 4 10 20 +--R - 315a b x - 30660a b x - 459172a b x - 1206720a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R 19596320a b x + 192185856a b x + 820357632a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R 2073143296a b x + 3392184320a b x + 3709009920a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R 2704539648a b x + 1267204096a b x + 346030080a b x + 41943040a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 13 26 2 12 24 3 11 22 4 10 20 +--R 4410a b x + 142590a b x + 1115828a b x - 1924720a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R - 72509024a b x - 463341312a b x - 1587302912a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R - 3433744384a b x - 4975452160a b x - 4922867712a b x +--R + +--R 11 3 6 12 2 4 13 2 +--R - 3297509376a b x - 1434976256a b x - 367001600a b x +--R + +--R 14 +--R - 41943040a +--R * +--R +-+ +--R \|a +--R / +--R 3 6 26 4 5 24 5 4 22 +--R 1003520a b x + 32112640a b x + 289013760a b x +--R + +--R 6 3 20 7 2 18 8 16 +--R 1101004800a b x + 2018508800a b x + 1761607680a b x +--R + +--R 9 14 +--R 587202560a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 28 4 6 26 5 5 24 6 4 22 +--R - 71680a b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 7 3 20 8 2 18 9 16 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 10 14 +--R - 587202560a x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 7 \|b x + a - \|a 7 \|b x + a +--R 9b log(------------------) + 9b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 2048a \|a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1369 +t0:=x^6*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 14 3 12 2 2 10 3 8 4 6 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1369 +r0:=3/256*a^3*x^7*(a+b*x^2)^(3/2)+3/128*a^2*x^7*(a+b*x^2)^(5/2)+_ + 9/224*a*x^7*(a+b*x^2)^(7/2)+1/16*x^7*(a+b*x^2)^(9/2)-_ + 45/32768*a^8*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+_ + 45/32768*a^7*x*sqrt(a+b*x^2)/b^3-15/16384*a^6*x^3*_ + 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15 2 16 +--R - 41287680a b x - 10321920a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 15 31 14 29 2 13 27 +--R - 14336b x - 1901568a b x - 47173888a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R - 502530176a b x - 2975022960a b x - 11035277480a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R - 27310058286a b x - 46527167547a b x - 55047454848a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R - 44639228800a b x - 23770343424a b x - 7526059520a b x +--R + +--R 12 3 7 13 2 5 14 3 +--R - 1103085568a b x - 45072384a b x - 34406400a b x +--R + +--R 15 +--R - 10321920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 15 31 14 29 2 13 27 +--R 229376b x + 10928128a b x + 172937216a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R 1386100736a b x + 6676770560a b x + 21084247936a b x +--R + +--R 6 9 19 7 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- 26611200a b x - 70963200a b x - 100638720a b x +--R + +--R 14 2 15 +--R - 72253440a b x - 20643840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 8 16 9 7 14 10 6 12 11 5 10 +--R 630a b x + 80640a b x + 1693440a b x + 13547520a b x +--R + +--R 12 4 8 13 3 6 14 2 4 +--R 53222400a b x + 113541120a b x + 134184960a b x +--R + +--R 15 2 16 +--R 82575360a b x + 20643840a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 15 31 14 29 2 13 27 +--R - 14336b x - 1901568a b x - 47173888a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R - 502530176a b x - 2975022960a b x - 11035277480a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R - 27310058286a b x - 46527167547a b x - 55047454848a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R - 44639228800a b x - 23770343424a b x - 7526059520a b x +--R + +--R 12 3 7 13 2 5 14 3 +--R - 1103085568a b x - 45072384a b x - 34406400a b x +--R + +--R 15 +--R - 10321920a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 15 31 14 29 2 13 27 +--R 229376b x + 10928128a b x + 172937216a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R 1386100736a b x + 6676770560a b x + 21084247936a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R 45737690208a b x + 69692308560a b x + 74823758928a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R 55651554400a b x + 27397242752a b x + 8073715456a b x +--R + +--R 12 3 7 13 2 5 14 3 15 +--R 1121966080a b x + 60985344a b x + 39567360a b x + 10321920a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 10 14 9 12 2 8 10 +--R 3670016b x + 154140672a b x + 1849688064a b x +--R + +--R 3 7 8 4 6 6 5 5 4 +--R 9688842240a b x + 25836912640a b x + 36641439744a b x +--R + +--R 6 4 2 7 3 +--R 26306674688a b x + 7516192768a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 11 16 10 14 2 9 12 +--R - 229376b x - 29360128a b x - 616562688a b x +--R + +--R 3 8 10 4 7 8 5 6 6 +--R - 4932501504a b x - 19377684480a b x - 41339060224a b x +--R + +--R 6 5 4 7 4 2 8 3 +--R - 48855252992a b x - 30064771072a b x - 7516192768a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 491 + +--S 492 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 8 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 45a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 8 x\|b +--R 45a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 3 +-+ +--R 32768b \|b +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 8 +---+ x\|b 8 +-+ \|- b \|b x + a - \|- b \|a +--R 45a \|- b atanh(-----------) - 90a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 32768b \|- b \|b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1369 +t0:=x^4*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 12 3 10 2 2 8 3 6 4 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1369 +r0:=3/128*a^3*x^5*(a+b*x^2)^(3/2)+3/80*a^2*x^5*(a+b*x^2)^(5/2)+_ + 3/56*a*x^5*(a+b*x^2)^(7/2)+1/14*x^5*(a+b*x^2)^(9/2)+_ + 9/2048*a^7*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 9/2048*a^6*x*sqrt(a+b*x^2)/b^2+3/1024*a^5*x^3*sqrt(a+b*x^2)/b+_ + 3/256*a^4*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 7 x\|b +--R 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 5120b x + 24320a b x + 44928a b x + 39056a b x + 14168a b x +--R + +--R 5 3 6 +--R 210a b x - 315a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R / +--R 2 +-+ +--R 71680b \|b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x +--R + +--R 11 2 4 12 2 13 +--R 8870400a b x + 7741440a b x + 2580480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 7 14 8 6 12 9 5 10 10 4 8 +--R - 315a b x - 30870a b x - 493920a b x - 2963520a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R - 8467200a b x - 12418560a b x - 9031680a b x - 2580480a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 13 27 12 25 2 11 23 3 10 21 +--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x +--R + +--R 4 9 19 5 8 17 6 7 15 +--R - 440716920a b x - 1340883586a b x - 2702931497a b x +--R + +--R 7 6 13 8 5 11 9 4 9 +--R - 3693903786a b x - 3409466400a b x - 2049104320a b x +--R + +--R 10 3 7 11 2 5 12 3 13 +--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 13 27 12 25 2 11 23 +--R 71680b x + 2705920a b x + 34802432a b x +--R + +--R 3 10 21 4 9 19 5 8 17 +--R 229544160a b x + 913955504a b x + 2381177932a b x +--R + +--R 6 7 15 7 6 13 8 5 11 +--R 4226517442a b x + 5183442054a b x + 4350339840a b x +--R + +--R 9 4 9 10 3 7 11 2 5 +--R 2398031552a b x + 781569536a b x + 106333696a b x +--R + +--R 12 3 13 +--R - 8601600a b x - 2580480a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 12 7 10 2 6 8 3 5 6 +--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x +--R + +--R 4 4 4 5 3 2 6 2 +--R 2018508800a b x + 1761607680a b x + 587202560a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 9 14 8 12 2 7 10 3 6 8 +--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 4 5 6 5 4 4 6 3 2 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 7 2 +--R - 587202560a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 8820a b x + 282240a b x + 2540160a b x + 9676800a b x +--R + +--R 11 2 4 12 2 13 +--R 17740800a b x + 15482880a b x + 5160960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 7 14 8 6 12 9 5 10 10 4 8 +--R - 630a b x - 61740a b x - 987840a b x - 5927040a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R - 16934400a b x - 24837120a b x - 18063360a b x - 5160960a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 13 27 12 25 2 11 23 3 10 21 +--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x +--R + +--R 4 9 19 5 8 17 6 7 15 +--R - 440716920a b x - 1340883586a b x - 2702931497a b x +--R + +--R 7 6 13 8 5 11 9 4 9 +--R - 3693903786a b x - 3409466400a b x - 2049104320a b x +--R + +--R 10 3 7 11 2 5 12 3 13 +--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 13 27 12 25 2 11 23 +--R 71680b x + 2705920a b x + 34802432a b x +--R + +--R 3 10 21 4 9 19 5 8 17 +--R 229544160a b x + 913955504a b x + 2381177932a b x +--R + +--R 6 7 15 7 6 13 8 5 11 +--R 4226517442a b x + 5183442054a b x + 4350339840a b x +--R + +--R 9 4 9 10 3 7 11 2 5 +--R 2398031552a b x + 781569536a b x + 106333696a b x +--R + +--R 12 3 13 +--R - 8601600a b x - 2580480a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 8 12 7 10 2 6 8 3 5 6 +--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x +--R + +--R 4 4 4 5 3 2 6 2 +--R 2018508800a b x + 1761607680a b x + 587202560a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 9 14 8 12 2 7 10 3 6 8 +--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 4 5 6 5 4 4 6 3 2 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 7 2 +--R - 587202560a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 498 + +--S 499 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 7 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 9a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 7 x\|b +--R - 9a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 2048b \|b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 7 +---+ x\|b 7 +-+ \|- b \|b x + a - \|- b \|a +--R - 9a \|- b atanh(-----------) + 18a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ---------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2048b \|- b \|b +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1369 +t0:=x^2*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 10 3 8 2 2 6 3 4 4 2 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1369 +r0:=7/128*a^3*x^3*(a+b*x^2)^(3/2)+21/320*a^2*x^3*(a+b*x^2)^(5/2)+_ + 3/40*a*x^3*(a+b*x^2)^(7/2)+1/12*x^3*(a+b*x^2)^(9/2)-_ + 21/1024*a^6*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 21/1024*a^5*x*sqrt(a+b*x^2)/b+21/512*a^4*x^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 6 x\|b +--R - 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 1280b x + 6272a b x + 12144a b x + 11432a b x + 4910a b x +--R + +--R 5 +--R 315a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R / +--R +-+ +--R 15360b\|b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3780a b x + 88200a b x + 564480a b x + 1451520a b x +--R + +--R 10 2 11 +--R 1612800a b x + 645120a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 6 12 7 5 10 8 4 8 9 3 6 +--R - 315a b x - 22680a b x - 264600a b x - 1128960a b x +--R + +--R 10 2 4 11 2 12 +--R - 2177280a b x - 1935360a b x - 645120a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R - 42355182a b x - 104697195a b x - 170215304a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R - 184337816a b x - 130176000a b x - 55757056a b x +--R + +--R 10 3 11 +--R - 11991040a b x - 645120a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 81152072a b x + 173035260a b x + 249146268a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 243180424a b x + 156595968a b x + 61671936a b x +--R + +--R 10 3 11 +--R 12313600a b x + 645120a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 10 5 8 2 4 6 3 3 4 +--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 4 2 2 5 +--R 78643200a b x + 31457280a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 7 12 6 10 2 5 8 3 4 6 +--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 4 3 4 5 2 2 6 +--R - 106168320a b x - 94371840a b x - 31457280a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R - 7560a b x - 176400a b x - 1128960a b x - 2903040a b x +--R + +--R 10 2 11 +--R - 3225600a b x - 1290240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 6 12 7 5 10 8 4 8 9 3 6 +--R 630a b x + 45360a b x + 529200a b x + 2257920a b x +--R + +--R 10 2 4 11 2 12 +--R 4354560a b x + 3870720a b x + 1290240a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R - 42355182a b x - 104697195a b x - 170215304a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R - 184337816a b x - 130176000a b x - 55757056a b x +--R + +--R 10 3 11 +--R - 11991040a b x - 645120a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 81152072a b x + 173035260a b x + 249146268a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 243180424a b x + 156595968a b x + 61671936a b x +--R + +--R 10 3 11 +--R 12313600a b x + 645120a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 6 10 5 8 2 4 6 3 3 4 +--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 4 2 2 5 +--R 78643200a b x + 31457280a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 7 12 6 10 2 5 8 3 4 6 +--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 4 3 4 5 2 2 6 +--R - 106168320a b x - 94371840a b x - 31457280a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 505 + +--S 506 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 6 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 21a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 6 x\|b +--R 21a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 1024b\|b +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 6 +---+ x\|b 6 +-+ \|- b \|b x + a - \|- b \|a +--R 21a \|- b atanh(-----------) - 42a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 1024b\|- b \|b +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 509 + +)clear all + +--S 510 of 1369 +t0:=(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1369 +r0:=21/128*a^3*x*(a+b*x^2)^(3/2)+21/160*a^2*x*(a+b*x^2)^(5/2)+_ + 9/80*a*x*(a+b*x^2)^(7/2)+1/10*x*(a+b*x^2)^(9/2)+_ + 63/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_ + 63/256*a^4*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 5 x\|b +--R 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (128b x + 656a b x + 1368a b x + 1490a b x + 965a x)\|b \|b x + a +--R / +--R +-+ +--R 1280\|b +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 3150a b x + 50400a b x + 211680a b x + 322560a b x +--R + +--R 9 +--R 161280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 315a b x - 15750a b x - 126000a b x - 352800a b x +--R + +--R 9 2 10 +--R - 403200a b x - 161280a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 7056a b x - 85368a b x - 475650a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x +--R + +--R 8 3 9 +--R - 1998080a b x - 494080a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 28320a b x + 231696a b x + 1010340a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x +--R + +--R 8 3 9 +--R 2245120a b x + 494080a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 4 8 3 6 2 2 4 3 2 4 +--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 2 5 +--R - 1638400a b x - 655360a +--R * +--R +-+ +--R \|b +--R , +--R +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 6300a b x + 100800a b x + 423360a b x + 645120a b x +--R + +--R 9 +--R 322560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 630a b x - 31500a b x - 252000a b x - 705600a b x +--R + +--R 9 2 10 +--R - 806400a b x - 322560a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 7056a b x - 85368a b x - 475650a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x +--R + +--R 8 3 9 +--R - 1998080a b x - 494080a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 28320a b x + 231696a b x + 1010340a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x +--R + +--R 8 3 9 +--R 2245120a b x + 494080a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a ) +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 2 5 +--R - 1638400a b x - 655360a +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 512 + +--S 513 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 5 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 63a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 5 x\|b +--R - 63a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 256\|b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 +---+ x\|b +--R - 63a \|- b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R 5 +-+ \|- b \|b x + a - \|- b \|a +--R 126a \|b atan(------------------------------) +--R b x +--R / +--R +---+ +-+ +--R 256\|- b \|b +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 1369 +t0:=(a+b*x^2)^(9/2)/x^2 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1369 +r0:=105/64*a^2*b*x*(a+b*x^2)^(3/2)+21/16*a*b*x*(a+b*x^2)^(5/2)+_ + 9/8*b*x*(a+b*x^2)^(7/2)-(a+b*x^2)^(9/2)/x+_ + 315/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_ + 315/128*a^3*b*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 4 +-+ x\|b +--R 315a x\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x + 88a b x + 210a b x + 325a b x - 128a )\|b x + a +--R / +--R 128x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 144b x - 2712a b x - 19362a b x - 75357a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a +--R / +--R 4 9 3 7 2 2 5 3 3 4 +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a +--R , +--R +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 8 +--R 161280a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 8 +--R - 161280a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 144b x - 2712a b x - 19362a b x - 75357a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a +--R / +--R 4 9 3 7 2 2 5 3 3 4 +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 519 + +--S 520 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 4 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 315a \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 +-+ x\|b +--R - 315a \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 128 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 4 +-+ x\|b 4 +---+ \|b x + a - \|a +--R - 315a \|b atanh(-----------) + 630a \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1369 +t0:=(a+b*x^2)^(9/2)/x^4 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1369 +r0:=35/8*a*b^2*x*(a+b*x^2)^(3/2)+7/2*b^2*x*(a+b*x^2)^(5/2)-_ + 3*b*(a+b*x^2)^(7/2)/x-1/3*(a+b*x^2)^(9/2)/x^3+_ + 105/16*a^3*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_ + 105/16*a^2*b^2*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 3 3 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (8b x + 50a b x + 165a b x - 208a b x - 16a )\|b x + a +--R / +--R 3 +--R 48x +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 7 3 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 3 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 16064a b x + 84480a b x + 62464a b x + 4096a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a +--R / +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a +--R , +--R +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 7 3 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 7 3 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 16064a b x + 84480a b x + 62464a b x + 4096a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a +--R / +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 526 + +--S 527 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 105a b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 +-+ x\|b +--R - 105a b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 16 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a +--R - 105a b\|b atanh(-----------) + 210a b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) --------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1369 +t0:=(a+b*x^2)^(9/2)/x^6 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1369 +r0:=21/4*b^3*x*(a+b*x^2)^(3/2)-21/5*b^2*(a+b*x^2)^(5/2)/x-_ + 3/5*b*(a+b*x^2)^(7/2)/x^3-1/5*(a+b*x^2)^(9/2)/x^5+_ + 63/8*a^2*b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_ + 63/8*a*b^3*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 5 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (10b x + 85a b x - 288a b x - 56a b x - 8a )\|b x + a +--R / +--R 5 +--R 40x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 6 2 5 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 2 5 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 169280a b x + 109440a b x + 18944a b x + 2048a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a +--R / +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a +--R , +--R +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 6 2 5 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 6 2 5 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 169280a b x + 109440a b x + 18944a b x + 2048a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a +--R / +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 533 + +--S 534 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 63a b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 2 +-+ x\|b +--R - 63a b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 2 +-+ x\|b 2 2 +---+ \|b x + a - \|a +--R - 63a b \|b atanh(-----------) + 126a b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1369 +t0:=(a+b*x^2)^(9/2)/x^8 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1369 +r0:=-3*b^3*(a+b*x^2)^(3/2)/x-3/5*b^2*(a+b*x^2)^(5/2)/x^3-_ + 9/35*b*(a+b*x^2)^(7/2)/x^5-1/7*(a+b*x^2)^(9/2)/x^7+_ + 9/2*a*b^(7/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+9/2*b^4*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 3 7 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x - 388a b x - 156a b x - 58a b x - 10a )\|b x + a +--R / +--R 7 +--R 70x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 15 2 6 13 3 5 11 4 4 9 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 5 3 7 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 2 6 13 3 5 11 4 4 9 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 3 7 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 315b x - 708a b x + 32844a b x + 166698a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a +--R / +--R 4 15 3 13 2 2 11 3 9 4 7 +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 15 3 13 2 2 11 3 9 4 7 +-+ +--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a +--R , +--R +--R 7 15 2 6 13 3 5 11 4 4 9 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 5 3 7 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 2 6 13 3 5 11 4 4 9 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 5 3 7 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 315b x - 708a b x + 32844a b x + 166698a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a +--R / +--R 4 15 3 13 2 2 11 3 9 4 7 +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 15 3 13 2 2 11 3 9 4 7 +-+ +--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 540 + +--S 541 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 9a b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 +-+ x\|b +--R - 9a b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a +--R - 9a b \|b atanh(-----------) + 18a b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1369 +t0:=(a+b*x^2)^(9/2)/x^10 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1369 +r0:=-1/3*b^3*(a+b*x^2)^(3/2)/x^3-1/5*b^2*(a+b*x^2)^(5/2)/x^5-_ + 1/7*b*(a+b*x^2)^(7/2)/x^7-1/9*(a+b*x^2)^(9/2)/x^9+_ + b^(9/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^4*sqrt(a+b*x^2)/x +--R +--R +--R (2) +--R +-+ +--R 4 9 +-+ x\|b +--R 315b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (- 563b x - 506a b x - 408a b x - 185a b x - 35a )\|b x + a +--R / +--R 9 +--R 315x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 4 4 9 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 2835b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 4 4 9 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R 5067b x + 72114a b x + 307608a b x + 593505a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 634355a b x + 448664a b x + 226128a b x + 67520a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R - 563b x - 23589a b x - 178794a b x - 545937a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 866340a b x - 834291a b x - 553848a b x - 258768a b x +--R + +--R 8 2 9 +--R - 72000a b x - 8960a +--R / +--R 4 17 3 15 2 2 13 3 11 4 9 +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 17 3 15 2 2 13 3 11 +--R - 2835b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 4 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R , +--R +--R 8 17 7 15 2 6 13 3 5 11 +--R 630b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 4 4 9 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 5670b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 4 4 9 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R 5067b x + 72114a b x + 307608a b x + 593505a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 634355a b x + 448664a b x + 226128a b x + 67520a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R - 563b x - 23589a b x - 178794a b x - 545937a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 866340a b x - 834291a b x - 553848a b x - 258768a b x +--R + +--R 8 2 9 +--R - 72000a b x - 8960a +--R / +--R 4 17 3 15 2 2 13 3 11 4 9 +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 17 3 15 2 2 13 3 11 +--R - 2835b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 4 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 547 + +--S 548 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 4 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 +-+ x\|b +--R - b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 4 +-+ x\|b 4 +---+ \|b x + a - \|a +--R (6) - b \|b atanh(-----------) + 2b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 551 + +)clear all + +--S 552 of 1369 +t0:=(a+b*x^2)^(9/2)/x^12 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1369 +r0:=-1/11*(a+b*x^2)^(11/2)/(a*x^11) +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|b x + a +--R (2) ------------------------------------------------------------------- +--R 11 +--R 11a x +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 11b x + 275a b x + 2442a b x + 11286a b x + 31471a b x +--R + +--R 5 5 10 6 4 8 7 3 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1739922632448a b x - 5694292251648a b x +--R + +--R 12 4 29 13 3 27 +--R - 11680599490560a b x - 15129157435392a b x +--R + +--R 14 2 25 15 23 16 21 +--R - 12014330904576a b x - 5339702624256a b x - 1017086214144a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 579 + +--S 580 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 581 + +)clear all + +--S 582 of 1369 +t0:=(a+b*x^2)^(9/2)/x^24 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 24 +--R x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1369 +r0:=-1/23*(a+b*x^2)^(11/2)/(a*x^23)+4/161*b*(a+b*x^2)^(11/2)/(a^2*x^21)-_ + 40/3059*b^2*(a+b*x^2)^(11/2)/(a^3*x^19)+_ + 320/52003*b^3*(a+b*x^2)^(11/2)/(a^4*x^17)-_ + 128/52003*b^4*(a+b*x^2)^(11/2)/(a^5*x^15)+_ + 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8 16 15 7 14 +--R 170212073470272a b x + 319842513071872a b x +--R + +--R 16 6 12 17 5 10 +--R 443676599296000a b x + 454256483090432a b x +--R + +--R 18 4 8 19 3 6 +--R 339251670810624a b x + 179812413800448a b x +--R + +--R 20 2 4 21 2 22 +--R 64121040535552a b x + 13803312906240a b x + 1356114952192a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 23 46 22 44 2 21 42 3 20 40 +--R - 1024b x - 270848a b x - 11849600a b x - 202628160a b x +--R + +--R 4 19 38 5 18 36 6 17 34 +--R - 1783851480a b x - 9216565980a b x - 29953839435a b x +--R + +--R 7 16 32 8 15 30 9 14 28 +--R - 63364422286a b x - 88059985805a b x - 85139238184a b x +--R + +--R 10 13 26 11 12 24 12 11 22 +--R - 172487832517a b x - 1389299606422a b x - 9097536087003a b x +--R + +--R 13 10 20 14 9 18 +--R - 40522439458872a b x - 127747340088848a b x +--R + +--R 15 8 16 16 7 14 +--R - 293619192660032a b x - 500570144755968a b x +--R + +--R 17 6 12 18 5 10 +--R - 637481553092608a b x - 604911221161984a b x +--R + +--R 19 4 8 20 3 6 21 2 4 +--R - 421952481460224a b x - 210232277139456a b x - 70853182619648a b x +--R + +--R 22 2 23 +--R - 14481370382336a b x - 1356114952192a +--R / +--R 7 11 45 8 10 43 9 9 41 +--R 7436429a b x + 1963217256a b x + 85072747760a b x +--R + +--R 10 8 39 11 7 37 +--R 1429222162368a b x + 12250475677440a b x +--R + +--R 12 6 35 13 5 33 +--R 60980145594368a b x + 188484086382592a b x +--R + +--R 14 4 31 15 3 29 +--R 372825665372160a b x + 472245842804736a b x +--R + +--R 16 2 27 17 25 +--R 370388896317440a b x + 163750880477184a b x +--R + +--R 18 23 +--R 31190643900416a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 11 45 8 10 43 9 9 41 +--R - 171037867a b x - 15051332296a b x - 391334639696a b x +--R + +--R 10 8 39 11 7 37 +--R - 4696015676352a b x - 31306771175680a b x +--R + +--R 12 6 35 13 5 33 +--R - 127503940788224a b x - 333471845138432a b x +--R + +--R 14 4 31 15 3 29 +--R - 571666020237312a b x - 638920846147584a b x +--R + +--R 16 2 27 17 25 +--R - 448365506068480a b x - 179346202427392a b x +--R + +--R 18 23 +--R - 31190643900416a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 584 + +--S 585 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 586 + +)clear all + +--S 587 of 1369 +t0:=x^5*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 5 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1369 +r0:=27/64*(9+4*x^2)^(3/2)-9/160*(9+4*x^2)^(5/2)+1/448*(9+4*x^2)^(7/2) +--R +--R +--R +-------+ +--R 6 4 2 | 2 +--R (40x + 18x - 54x + 243)\|4x + 9 +--R (2) ------------------------------------ +--R 280 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 11 9 7 5 +--R - 327680x - 1437696x - 1589760x - 1310256x - 6062364x +--R + +--R 3 +--R - 8266860x - 2480058x +--R * +--R +-------+ +--R | 2 +--R \|4x + 9 +--R + +--R 14 12 10 8 6 4 +--R 655360x + 3612672x + 5999616x + 4844448x + 14451696x + 28934010x +--R + +--R 2 +--R 17360406x + 1594323 +--R / +--R +-------+ +--R 6 4 2 | 2 7 +--R (1146880x + 3225600x + 2177280x + 204120)\|4x + 9 - 2293760x +--R + +--R 5 3 +--R - 9031680x - 10160640x - 2857680x +--R Type: Union(Expression(Integer),...) +--E 589 + +--S 590 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 1369 +t0:=x^4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 4 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1369 +r0:=729/512*asinh(2/3*x)-81/256*x*sqrt(9+4*x^2)+_ + 3/32*x^3*sqrt(9+4*x^2)+1/6*x^5*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 5 3 | 2 2x +--R (256x + 144x - 486x)\|4x + 9 + 2187asinh(--) +--R 3 +--R (2) ------------------------------------------------ +--R 1536 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 3 | 2 6 +--R (- 2239488x - 5038848x - 2125764x)\|4x + 9 + 4478976x +--R + +--R 4 2 +--R 15116544x + 12754584x + 1594323 +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R 11 9 7 5 3 +--R (- 524288x - 2064384x - 1492992x + 2332800x + 2729376x + 354294x) +--R * +--R +-------+ +--R | 2 +--R \|4x + 9 +--R + +--R 12 10 8 6 4 2 +--R 1048576x + 5308416x + 6967296x - 3172608x - 10707552x - 4251528x +--R / +--R +-------+ +--R 5 3 | 2 6 4 +--R (1572864x + 3538944x + 1492992x)\|4x + 9 - 3145728x - 10616832x +--R + +--R 2 +--R - 8957952x - 1119744 +--R Type: Union(Expression(Integer),...) +--E 594 + +--S 595 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 729log(\|4x + 9 - 2x) - 729asinh(--) +--R 3 +--R (4) ---------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 596 + +)clear all + +--S 597 of 1369 +t0:=x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1369 +r0:=-3/16*(9+4*x^2)^(3/2)+1/80*(9+4*x^2)^(5/2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (8x + 6x - 27)\|4x + 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 4096x - 14592x - 1296x + 34020x + 21870x)\|4x + 9 + 8192x +--R + +--R 8 6 4 2 +--R 38400x + 30240x - 77760x - 109350x - 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 599 + +--S 600 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 601 + +)clear all + +--S 602 of 1369 +t0:=x^2*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1369 +r0:=-81/64*asinh(2/3*x)+9/32*x*sqrt(9+4*x^2)+1/4*x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 2x +--R (16x + 18x)\|4x + 9 - 81asinh(--) +--R 3 +--R (2) ------------------------------------ +--R 64 +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((5184x + 5832x)\|4x + 9 - 10368x - 23328x - 6561) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 6 +--R (- 2048x - 6912x - 6480x - 1458x)\|4x + 9 + 4096x + 18432x +--R + +--R 4 2 +--R 25920x + 11664x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (4096x + 4608x)\|4x + 9 - 8192x - 18432x - 5184 +--R Type: Union(Expression(Integer),...) +--E 604 + +--S 605 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 81log(\|4x + 9 - 2x) + 81asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 64 +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 1369 +t0:=x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) x\|4x + 9 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1369 +r0:=1/12*(9+4*x^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x + 9)\|4x + 9 +--R (2) ------------------- +--R 12 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 128x - 504x - 486x)\|4x + 9 + 256x + 1296x + 1944x + 729 +--R (3) ------------------------------------------------------------------ +--R +-------+ +--R 2 | 2 3 +--R (192x + 108)\|4x + 9 - 384x - 648x +--R Type: Union(Expression(Integer),...) +--E 609 + +--S 610 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 611 + +)clear all + +--S 612 of 1369 +t0:=sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) \|4x + 9 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1369 +r0:=9/4*asinh(2/3*x)+1/2*x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 2x +--R 2x\|4x + 9 + 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 4 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 36x\|4x + 9 + 72x + 81)log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x - 18x)\|4x + 9 + 32x + 72x +--R / +--R +-------+ +--R | 2 2 +--R 16x\|4x + 9 - 32x - 36 +--R Type: Union(Expression(Integer),...) +--E 614 + +--S 615 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 9log(\|4x + 9 - 2x) - 9asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 616 + +)clear all + +--S 617 of 1369 +t0:=sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1369 +r0:=-3*atanh(1/3*sqrt(9+4*x^2))+sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +-------+ +--R \|4x + 9 | 2 +--R (2) - 3atanh(----------) + \|4x + 9 +--R 3 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 | 2 +--R (- 3\|4x + 9 + 6x)log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +-------+ +--R | 2 | 2 | 2 2 +--R (3\|4x + 9 - 6x)log(\|4x + 9 - 2x - 3) - 2x\|4x + 9 + 4x + 9 +--R / +--R +-------+ +--R | 2 +--R \|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 619 + +--S 620 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 3log(\|4x + 9 - 2x + 3) + 3log(\|4x + 9 - 2x - 3) + 3atanh(----------) +--R 3 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1369 +t0:=sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1369 +r0:=2*asinh(2/3*x)-sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 2x +--R - \|4x + 9 + 2x asinh(--) +--R 3 +--R (2) --------------------------- +--R x +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 2x\|4x + 9 + 4x )log(\|4x + 9 - 2x) - 9 +--R (3) ---------------------------------------------- +--R +-------+ +--R | 2 2 +--R x\|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 624 + +--S 625 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R (4) - 2log(\|4x + 9 - 2x) - 2asinh(--) - 2 +--R 3 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 1369 +t0:=sqrt(9+4*x^2)/x^3 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1369 +r0:=-2/3*atanh(1/3*sqrt(9+4*x^2))-1/2*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x + 9 | 2 +--R - 4x atanh(----------) - 3\|4x + 9 +--R 3 +--R (2) ------------------------------------ +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x + 27)\|4x + 9 - 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 24x \|4x + 9 - 48x - 54x +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------) +--R 3 +--R ---------------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 1369 +t0:=sqrt(9+4*x^2)/x^4 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1369 +r0:=-1/27*(9+4*x^2)^(3/2)/x^3 +--R +--R +--R +-------+ +--R 2 | 2 +--R (- 4x - 9)\|4x + 9 +--R (2) --------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 | 2 4 2 +--R (16x + 18x)\|4x + 9 - 32x - 72x - 27 +--R (3) ----------------------------------------- +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x + 9x )\|4x + 9 - 32x - 54x +--R Type: Union(Expression(Integer),...) +--E 634 + +--S 635 of 1369 +m0:=a0-r0 +--R +--R +--R 8 +--R (4) - -- +--R 27 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1369 +t0:=sqrt(9+4*x^2)/x^5 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1369 +r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/4*sqrt(9+4*x^2)/x^4-1/18*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x + 9 2 | 2 +--R 8x atanh(----------) + (- 6x - 27)\|4x + 9 +--R 3 +--R (2) --------------------------------------------- +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (768x + 5184x + 8262x + 2187)\|4x + 9 - 1536x - 12096x - 27216x +--R + +--R - 17496x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (6912x + 7776x )\|4x + 9 - 13824x - 31104x - 8748x +--R Type: Union(Expression(Integer),...) +--E 639 + +--S 640 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------) +--R 3 +--R -------------------------------------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 641 + +)clear all + +--S 642 of 1369 +t0:=x^5*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 5 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1369 +r0:=-27/64*(9-4*x^2)^(3/2)+9/160*(9-4*x^2)^(5/2)-1/448*(9-4*x^2)^(7/2) +--R +--R +--R +---------+ +--R 6 4 2 | 2 +--R (40x - 18x - 54x - 243)\|- 4x + 9 +--R (2) -------------------------------------- +--R 280 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 12 10 8 6 | 2 14 12 +--R (- 420x + 7749x - 36855x + 51030x )\|- 4x + 9 - 80x + 4536x +--R + +--R 10 8 6 +--R - 44037x + 144585x - 153090x +--R / +--R +---------+ +--R 6 4 2 | 2 6 4 +--R (140x - 7560x + 56700x - 102060)\|- 4x + 9 - 2940x + 52920x +--R + +--R 2 +--R - 238140x + 306180 +--R Type: Union(Expression(Integer),...) +--E 644 + +--S 645 of 1369 +m0:=a0-r0 +--R +--R +--R 729 +--R (4) - --- +--R 280 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 646 + +)clear all + +--S 647 of 1369 +t0:=x^4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 4 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1369 +r0:=729/512*asin(2/3*x)-81/256*x*sqrt(9-4*x^2)-_ + 3/32*x^3*sqrt(9-4*x^2)+1/6*x^5*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 5 3 | 2 2x +--R (256x - 144x - 486x)\|- 4x + 9 + 2187asin(--) +--R 3 +--R (2) ------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 4 2 | 2 6 4 +--R (- 19683x + 236196x - 531441)\|- 4x + 9 - 4374x + 177147x +--R + +--R 2 +--R - 1062882x + 1594323 +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 11 9 7 5 3 | 2 +--R (256x - 10512x + 67554x - 108621x - 65610x + 177147x)\|- 4x + 9 +--R + +--R 11 9 7 5 3 +--R - 4608x + 68256x - 277020x + 295245x + 314928x - 531441x +--R / +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (6912x - 82944x + 186624)\|- 4x + 9 + 1536x - 62208x + 373248x +--R + +--R - 559872 +--R Type: Union(Expression(Integer),...) +--E 649 + +--S 650 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 1458atan(----------------) - 729asin(--) +--R 2x 3 +--R (4) ------------------------------------------ +--R 512 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1369 +t0:=x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1369 +r0:=-3/16*(9-4*x^2)^(3/2)+1/80*(9-4*x^2)^(5/2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (8x - 6x - 27)\|- 4x + 9 +--R (2) ---------------------------- +--R 40 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 8 6 4 | 2 10 8 6 4 +--R (- 60x + 585x - 1215x )\|- 4x + 9 - 16x + 480x - 2565x + 3645x +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 | 2 4 2 +--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860 +--R Type: Union(Expression(Integer),...) +--E 654 + +--S 655 of 1369 +m0:=a0-r0 +--R +--R +--R 81 +--R (4) - -- +--R 40 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 656 + +)clear all + +--S 657 of 1369 +t0:=x^2*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1369 +r0:=81/64*asin(2/3*x)-9/32*x*sqrt(9-4*x^2)+1/4*x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 2x +--R (16x - 18x)\|- 4x + 9 + 81asin(--) +--R 3 +--R (2) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +--R ((- 486x + 2187)\|- 4x + 9 - 162x + 2916x - 6561) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 7 5 3 | 2 7 5 3 +--R (16x - 306x + 972x - 729x)\|- 4x + 9 - 192x + 1512x - 3402x + 2187x +--R / +--R +---------+ +--R 2 | 2 4 2 +--R (192x - 864)\|- 4x + 9 + 64x - 1152x + 2592 +--R Type: Union(Expression(Integer),...) +--E 659 + +--S 660 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 162atan(----------------) - 81asin(--) +--R 2x 3 +--R (4) ---------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 661 + +)clear all + +--S 662 of 1369 +t0:=x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) x\|- 4x + 9 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1369 +r0:=-1/12*(9-4*x^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x - 9)\|- 4x + 9 +--R (2) --------------------- +--R 12 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (- 18x + 81x )\|- 4x + 9 - 8x + 108x - 243x +--R (3) ------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (6x - 54)\|- 4x + 9 - 54x + 162 +--R Type: Union(Expression(Integer),...) +--E 664 + +--S 665 of 1369 +m0:=a0-r0 +--R +--R +--R 9 +--R (4) - - +--R 4 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1369 +t0:=sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) \|- 4x + 9 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1369 +r0:=9/4*asin(2/3*x)+1/2*x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 2x +--R 2x\|- 4x + 9 + 9asin(--) +--R 3 +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R | 2 2 \|- 4x + 9 - 3 +--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +--R (2x - 9x)\|- 4x + 9 - 12x + 27x +--R / +--R +---------+ +--R | 2 2 +--R 6\|- 4x + 9 + 4x - 18 +--R Type: Union(Expression(Integer),...) +--E 669 + +--S 670 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 18atan(----------------) - 9asin(--) +--R 2x 3 +--R (4) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 671 + +)clear all + +--S 672 of 1369 +t0:=sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1369 +r0:=-3*atanh(1/3*sqrt(9-4*x^2))+sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +---------+ +--R \|- 4x + 9 | 2 +--R (2) - 3atanh(------------) + \|- 4x + 9 +--R 3 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|- 4x + 9 - 3 2 +--R (3\|- 4x + 9 - 9)log(----------------) - 4x +--R x +--R (3) ---------------------------------------------- +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R Type: Union(Expression(Integer),...) +--E 674 + +--S 675 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R (4) 3log(----------------) + 3atanh(------------) + 3 +--R x 3 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1369 +t0:=sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1369 +r0:=-2*asin(2/3*x)-sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 2x +--R - \|- 4x + 9 - 2x asin(--) +--R 3 +--R (2) ---------------------------- +--R x +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +---------+ +--R | 2 \|- 4x + 9 - 3 | 2 2 +--R (4x\|- 4x + 9 - 12x)atan(----------------) + 3\|- 4x + 9 + 4x - 9 +--R 2x +--R (3) ---------------------------------------------------------------------- +--R +---------+ +--R | 2 +--R x\|- 4x + 9 - 3x +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R (4) 4atan(----------------) + 2asin(--) +--R 2x 3 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1369 +t0:=sqrt(9-4*x^2)/x^3 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1369 +r0:=2/3*atanh(1/3*sqrt(9-4*x^2))-1/2*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x + 9 | 2 +--R 4x atanh(------------) - 3\|- 4x + 9 +--R 3 +--R (2) -------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 4 2 \|- 4x + 9 - 3 +--R (- 12x \|- 4x + 9 - 8x + 36x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 6x + 27)\|- 4x + 9 + 36x - 81 +--R / +--R +---------+ +--R 2 | 2 4 2 +--R 18x \|- 4x + 9 + 12x - 54x +--R Type: Union(Expression(Integer),...) +--E 684 + +--S 685 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R - 2log(----------------) - 2atanh(------------) +--R x 3 +--R (4) ----------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +)clear all + +--S 687 of 1369 +t0:=sqrt(9-4*x^2)/x^4 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1369 +r0:=-1/27*(9-4*x^2)^(3/2)/x^3 +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x - 9)\|- 4x + 9 +--R (2) --------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (- 36x + 189x - 243)\|- 4x + 9 - 16x + 216x - 729x + 729 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +--R (27x - 243x )\|- 4x + 9 - 243x + 729x +--R Type: Union(Expression(Integer),...) +--E 689 + +--S 690 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 691 + +)clear all + +--S 692 of 1369 +t0:=sqrt(9-4*x^2)/x^5 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1369 +r0:=2/27*atanh(1/3*sqrt(9-4*x^2))-1/4*sqrt(9-4*x^2)/x^4+1/18*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x + 9 2 | 2 +--R 8x atanh(------------) + (6x - 27)\|- 4x + 9 +--R 3 +--R (2) ----------------------------------------------- +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +--R ((- 48x + 216x )\|- 4x + 9 - 16x + 288x - 648x ) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R log(----------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 2 +--R (12x - 270x + 1458x - 2187)\|- 4x + 9 - 144x + 1620x - 5832x + 6561 +--R / +--R +---------+ +--R 6 4 | 2 8 6 4 +--R (648x - 2916x )\|- 4x + 9 + 216x - 3888x + 8748x +--R Type: Union(Expression(Integer),...) +--E 694 + +--S 695 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R - 2log(----------------) - 2atanh(------------) +--R x 3 +--R (4) ----------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1369 +t0:=x^5*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 5 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1369 +r0:=27/64*(-9+4*x^2)^(3/2)+9/160*(-9+4*x^2)^(5/2)+1/448*(-9+4*x^2)^(7/2) +--R +--R +--R +-------+ +--R 6 4 2 | 2 +--R (40x - 18x - 54x - 243)\|4x - 9 +--R (2) ------------------------------------ +--R 280 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 11 9 7 5 +--R - 327680x + 1437696x - 1589760x + 1310256x - 6062364x +--R + +--R 3 +--R 8266860x - 2480058x +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 +--R + +--R 14 12 10 8 6 4 +--R 655360x - 3612672x + 5999616x - 4844448x + 14451696x - 28934010x +--R + +--R 2 +--R 17360406x - 1594323 +--R / +--R +-------+ +--R 6 4 2 | 2 7 +--R (1146880x - 3225600x + 2177280x - 204120)\|4x - 9 - 2293760x +--R + +--R 5 3 +--R 9031680x - 10160640x + 2857680x +--R Type: Union(Expression(Integer),...) +--E 699 + +--S 700 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 701 + +)clear all + +--S 702 of 1369 +t0:=x^4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 4 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1369 +r0:=-729/512*atanh(2*x/sqrt(-9+4*x^2))-81/256*x*sqrt(-9+4*x^2)-_ + 3/32*x^3*sqrt(-9+4*x^2)+1/6*x^5*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 5 3 | 2 +--R - 2187atanh(----------) + (256x - 144x - 486x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 3 | 2 6 4 +--R (2239488x - 5038848x + 2125764x)\|4x - 9 - 4478976x + 15116544x +--R + +--R 2 +--R - 12754584x + 1594323 +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R 11 9 7 5 3 +--R (- 524288x + 2064384x - 1492992x - 2332800x + 2729376x - 354294x) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 +--R + +--R 12 10 8 6 4 2 +--R 1048576x - 5308416x + 6967296x + 3172608x - 10707552x + 4251528x +--R / +--R +-------+ +--R 5 3 | 2 6 4 +--R (1572864x - 3538944x + 1492992x)\|4x - 9 - 3145728x + 10616832x +--R + +--R 2 +--R - 8957952x + 1119744 +--R Type: Union(Expression(Integer),...) +--E 704 + +--S 705 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 729log(\|4x - 9 - 2x) + 729atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ---------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 706 + +)clear all + +--S 707 of 1369 +t0:=x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1369 +r0:=3/16*(-9+4*x^2)^(3/2)+1/80*(-9+4*x^2)^(5/2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (8x - 6x - 27)\|4x - 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 4096x + 14592x - 1296x - 34020x + 21870x)\|4x - 9 + 8192x +--R + +--R 8 6 4 2 +--R - 38400x + 30240x + 77760x - 109350x + 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 709 + +--S 710 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 1369 +t0:=x^2*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1369 +r0:=-81/64*atanh(2*x/sqrt(-9+4*x^2))-9/32*x*sqrt(-9+4*x^2)+_ + 1/4*x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 3 | 2 +--R - 81atanh(----------) + (16x - 18x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((5184x - 5832x)\|4x - 9 - 10368x + 23328x - 6561) +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 6 +--R (- 2048x + 6912x - 6480x + 1458x)\|4x - 9 + 4096x - 18432x +--R + +--R 4 2 +--R 25920x - 11664x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (4096x - 4608x)\|4x - 9 - 8192x + 18432x - 5184 +--R Type: Union(Expression(Integer),...) +--E 714 + +--S 715 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 81log(\|4x - 9 - 2x) + 81atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) -------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 716 + +)clear all + +--S 717 of 1369 +t0:=x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) x\|4x - 9 +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1369 +r0:=1/12*(-9+4*x^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x - 9)\|4x - 9 +--R (2) ------------------- +--R 12 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 128x + 504x - 486x)\|4x - 9 + 256x - 1296x + 1944x - 729 +--R (3) ------------------------------------------------------------------ +--R +-------+ +--R 2 | 2 3 +--R (192x - 108)\|4x - 9 - 384x + 648x +--R Type: Union(Expression(Integer),...) +--E 719 + +--S 720 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 721 + +)clear all + +--S 722 of 1369 +t0:=sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) \|4x - 9 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1369 +r0:=-9/4*atanh(2*x/sqrt(-9+4*x^2))+1/2*x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x | 2 +--R - 9atanh(----------) + 2x\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (36x\|4x - 9 - 72x + 81)log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x + 18x)\|4x - 9 + 32x - 72x +--R / +--R +-------+ +--R | 2 2 +--R 16x\|4x - 9 - 32x + 36 +--R Type: Union(Expression(Integer),...) +--E 724 + +--S 725 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 9log(\|4x - 9 - 2x) + 9atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 1369 +t0:=sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1369 +r0:=-3*atan(1/3*sqrt(-9+4*x^2))+sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +-------+ +--R \|4x - 9 | 2 +--R (2) - 3atan(----------) + \|4x - 9 +--R 3 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R +-------+ | 2 +-------+ +--R | 2 \|4x - 9 - 2x | 2 2 +--R (- 6\|4x - 9 + 12x)atan(---------------) - 2x\|4x - 9 + 4x - 9 +--R 3 +--R (3) ------------------------------------------------------------------- +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 729 + +--S 730 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R (4) 3atan(----------) - 6atan(---------------) +--R 3 3 +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 731 + +)clear all + +--S 732 of 1369 +t0:=sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1369 +r0:=2*atanh(2*x/sqrt(-9+4*x^2))-sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R 2x | 2 +--R 2x atanh(----------) - \|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 2x\|4x - 9 + 4x )log(\|4x - 9 - 2x) + 9 +--R (3) ---------------------------------------------- +--R +-------+ +--R | 2 2 +--R x\|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 734 + +--S 735 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R (4) - 2log(\|4x - 9 - 2x) - 2atanh(----------) - 2 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1369 +t0:=sqrt(-9+4*x^2)/x^3 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1369 +r0:=2/3*atan(1/3*sqrt(-9+4*x^2))-1/2*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x - 9 | 2 +--R 4x atan(----------) - 3\|4x - 9 +--R 3 +--R (2) --------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-------+ | 2 +--R 3 | 2 4 2 \|4x - 9 - 2x +--R (32x \|4x - 9 - 64x + 72x )atan(---------------) +--R 3 +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x - 27)\|4x - 9 - 48x + 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 24x \|4x - 9 - 48x + 54x +--R Type: Union(Expression(Integer),...) +--E 739 + +--S 740 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1369 +t0:=sqrt(-9+4*x^2)/x^4 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1369 +r0:=1/27*(-9+4*x^2)^(3/2)/x^3 +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x - 9)\|4x - 9 +--R (2) ------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 | 2 4 2 +--R (16x - 18x)\|4x - 9 - 32x + 72x - 27 +--R (3) ----------------------------------------- +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x - 9x )\|4x - 9 - 32x + 54x +--R Type: Union(Expression(Integer),...) +--E 744 + +--S 745 of 1369 +m0:=a0-r0 +--R +--R +--R 8 +--R (4) -- +--R 27 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 1369 +t0:=sqrt(-9+4*x^2)/x^5 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1369 +r0:=2/27*atan(1/3*sqrt(-9+4*x^2))-1/4*sqrt(-9+4*x^2)/x^4+_ + 1/18*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x - 9 2 | 2 +--R 8x atan(----------) + (6x - 27)\|4x - 9 +--R 3 +--R (2) ------------------------------------------ +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x ) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R atan(---------------) +--R 3 +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x + 5184x - 8262x + 2187)\|4x - 9 + 1536x - 12096x + 27216x +--R + +--R - 17496x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (6912x - 7776x )\|4x - 9 - 13824x + 31104x - 8748x +--R Type: Union(Expression(Integer),...) +--E 749 + +--S 750 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 751 + +)clear all + +--S 752 of 1369 +t0:=x^5*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 5 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1369 +r0:=-27/64*(-9-4*x^2)^(3/2)-9/160*(-9-4*x^2)^(5/2)-1/448*(-9-4*x^2)^(7/2) +--R +--R +--R +---------+ +--R 6 4 2 | 2 +--R (40x + 18x - 54x + 243)\|- 4x - 9 +--R (2) -------------------------------------- +--R 280 +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 12 10 8 6 | 2 +--R (420x + 7749x + 36855x + 51030x )\|- 4x - 9 +--R + +--R 14 12 10 8 6 +---+ +--R (- 80x - 4536x - 44037x - 144585x - 153090x )\|- 1 +--R / +--R +---------+ +--R 6 4 2 +---+ | 2 6 4 +--R (140x + 7560x + 56700x + 102060)\|- 1 \|- 4x - 9 + 2940x + 52920x +--R + +--R 2 +--R 238140x + 306180 +--R Type: Union(Expression(Integer),...) +--E 754 + +--S 755 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 6 4 2 | 2 +--R (- 729x - 39366x - 295245x - 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (15309x + 275562x + 1240029x + 1594323)\|- 1 +--R / +--R +---------+ +--R 6 4 2 +---+ | 2 6 +--R (280x + 15120x + 113400x + 204120)\|- 1 \|- 4x - 9 + 5880x +--R + +--R 4 2 +--R 105840x + 476280x + 612360 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 of 1369 +t0:=x^4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 4 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1369 +r0:=-729/512*atan(2*x/sqrt(-9-4*x^2))-81/256*x*sqrt(-9-4*x^2)+_ + 3/32*x^3*sqrt(-9-4*x^2)+1/6*x^5*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 5 3 | 2 +--R - 2187atan(------------) + (256x + 144x - 486x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 4 2 | 2 +--R (- 19683x - 236196x - 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (4374x + 177147x + 1062882x + 1594323)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 4 2 | 2 +--R (19683x + 236196x + 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (- 4374x - 177147x - 1062882x - 1594323)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 11 9 7 5 3 | 2 +--R (512x + 21024x + 135108x + 217242x - 131220x - 354294x)\|- 4x - 9 +--R + +--R 11 9 7 5 3 +---+ +--R (- 9216x - 136512x - 554040x - 590490x + 629856x + 1062882x)\|- 1 +--R / +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (13824x + 165888x + 373248)\|- 1 \|- 4x - 9 + 3072x + 124416x +--R + +--R 2 +--R 746496x + 1119744 +--R Type: Union(Expression(Integer),...) +--E 759 + +--S 760 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 +--R (- 6561x - 78732x - 177147)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (1458x + 59049x + 354294x + 531441)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 4 2 | 2 +--R (6561x + 78732x + 177147)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (- 1458x - 59049x - 354294x - 531441)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (6561x + 78732x + 177147)\|- 1 \|- 4x - 9 + 1458x + 59049x +--R + +--R 2 +--R 354294x + 531441 +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (4608x + 55296x + 124416)\|- 1 \|- 4x - 9 + 1024x + 41472x +--R + +--R 2 +--R 248832x + 373248 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 761 + +)clear all + +--S 762 of 1369 +t0:=x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1369 +r0:=3/16*(-9-4*x^2)^(3/2)+1/80*(-9-4*x^2)^(5/2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (8x + 6x - 27)\|- 4x - 9 +--R (2) ---------------------------- +--R 40 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 8 6 4 | 2 +--R (60x + 585x + 1215x )\|- 4x - 9 +--R + +--R 10 8 6 4 +---+ +--R (- 16x - 480x - 2565x - 3645x )\|- 1 +--R / +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860 +--R Type: Union(Expression(Integer),...) +--E 764 + +--S 765 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 4 2 +---+ +--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1 +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720 +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 766 + +)clear all + +--S 767 of 1369 +t0:=x^2*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1369 +r0:=81/64*atan(2*x/sqrt(-9-4*x^2))+9/32*x*sqrt(-9-4*x^2)+1/4*x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 3 | 2 +--R 81atan(------------) + (16x + 18x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ----------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 7 5 3 | 2 +--R (32x + 612x + 1944x + 1458x)\|- 4x - 9 +--R + +--R 7 5 3 +---+ +--R (- 384x - 3024x - 6804x - 4374x)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184 +--R Type: Union(Expression(Integer),...) +--E 769 + +--S 770 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 +---+ | 2 4 2 +--R ((- 486x - 2187)\|- 1 \|- 4x - 9 - 162x - 2916x - 6561) +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184 +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 771 + +)clear all + +--S 772 of 1369 +t0:=x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) x\|- 4x - 9 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1369 +r0:=-1/12*(-9-4*x^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x + 9)\|- 4x - 9 +--R (2) --------------------- +--R 12 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +---+ +--R (18x + 81x )\|- 4x - 9 + (- 8x - 108x - 243x )\|- 1 +--R (3) --------------------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (6x + 54)\|- 1 \|- 4x - 9 + 54x + 162 +--R Type: Union(Expression(Integer),...) +--E 774 + +--S 775 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1 +--R (4) --------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (4x + 36)\|- 1 \|- 4x - 9 + 36x + 108 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 776 + +)clear all + +--S 777 of 1369 +t0:=sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) \|- 4x - 9 +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1369 +r0:=-9/4*atan(2*x/sqrt(-9-4*x^2))+1/2*x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x | 2 +--R - 9atan(------------) + 2x\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (4x + 18x)\|- 4x - 9 + (- 24x - 54x)\|- 1 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 12\|- 1 \|- 4x - 9 + 8x + 36 +--R Type: Union(Expression(Integer),...) +--E 779 + +--S 780 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 2x +--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 12\|- 1 \|- 4x - 9 + 8x + 36 +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 781 + +)clear all + +--S 782 of 1369 +t0:=sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1369 +r0:=-3*atan(1/3*sqrt(-9-4*x^2))+sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +---------+ +--R \|- 4x - 9 | 2 +--R (2) - 3atan(------------) + \|- 4x - 9 +--R 3 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 +---+ \|- 4x - 9 - 3\|- 1 2 +---+ +--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------) - 4x \|- 1 +--R x +--R (3) ------------------------------------------------------------------ +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Union(Expression(Integer),...) +--E 784 + +--S 785 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---------+ +--R +---+ | 2 \|- 4x - 9 | 2 +---+ +--R (3\|- 1 \|- 4x - 9 + 9)atan(------------) - 3\|- 4x - 9 + 9\|- 1 +--R 3 +--R / +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 786 + +)clear all + +--S 787 of 1369 +t0:=sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1369 +r0:=-2*atan(2*x/sqrt(-9-4*x^2))-sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R 2x | 2 +--R - 2x atan(------------) - \|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R x +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1 +--R (2x\|- 1 \|- 4x - 9 + 6x)log(-----------------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1 +--R (- 2x\|- 1 \|- 4x - 9 - 6x)log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 +--R 3\|- 1 \|- 4x - 9 + 4x + 9 +--R / +--R +---------+ +--R | 2 +---+ +--R x\|- 4x - 9 - 3x\|- 1 +--R Type: Union(Expression(Integer),...) +--E 789 + +--S 790 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1 +--R (2\|- 1 \|- 4x - 9 + 6)log(-----------------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1 +--R (- 2\|- 1 \|- 4x - 9 - 6)log(-------------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ 2x +--R (2\|- 4x - 9 - 6\|- 1 )atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 791 + +)clear all + +--S 792 of 1369 +t0:=sqrt(-9-4*x^2)/x^3 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1369 +r0:=-2/3*atan(1/3*sqrt(-9-4*x^2))-1/2*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x - 9 | 2 +--R - 4x atan(------------) - 3\|- 4x - 9 +--R 3 +--R (2) --------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 6x - 27)\|- 4x - 9 + (36x + 81)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R 18x \|- 1 \|- 4x - 9 + 12x + 54x +--R Type: Union(Expression(Integer),...) +--E 794 + +--S 795 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R +---+ | 2 2 \|- 4x - 9 +--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------) +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 9\|- 1 \|- 4x - 9 + 6x + 27 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 796 + +)clear all + +--S 797 of 1369 +t0:=sqrt(-9-4*x^2)/x^4 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1369 +r0:=1/27*(-9-4*x^2)^(3/2)/x^3 +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 4x - 9)\|- 4x - 9 +--R (2) ----------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 +---+ | 2 6 4 2 +--R (36x + 189x + 243)\|- 1 \|- 4x - 9 + 16x + 216x + 729x + 729 +--R (3) ------------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +---+ +--R (27x + 243x )\|- 4x - 9 + (- 243x - 729x )\|- 1 +--R Type: Union(Expression(Integer),...) +--E 799 + +--S 800 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 801 + +)clear all + +--S 802 of 1369 +t0:=sqrt(-9-4*x^2)/x^5 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1369 +r0:=2/27*atan(1/3*sqrt(-9-4*x^2))-1/4*sqrt(-9-4*x^2)/x^4-_ + 1/18*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x - 9 2 | 2 +--R 8x atan(------------) + (- 6x - 27)\|- 4x - 9 +--R 3 +--R (2) ------------------------------------------------ +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +---+ +--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 +--R (- 12x - 270x - 1458x - 2187)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (144x + 1620x + 5832x + 6561)\|- 1 +--R / +--R +---------+ +--R 6 4 +---+ | 2 8 6 4 +--R (648x + 2916x )\|- 1 \|- 4x - 9 + 216x + 3888x + 8748x +--R Type: Union(Expression(Integer),...) +--E 804 + +--S 805 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 +---+ | 2 4 2 \|- 4x - 9 +--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------) +--R 3 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (162x + 729)\|- 1 \|- 4x - 9 + 54x + 972x + 2187 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1369 +t0:=x^m/(a+b*x^2)^(1/2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1369 +--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2)) +--E 808 + +--S 809 of 1369 +--a0:=integrate(t0,x) +--E 809 + +--S 810 of 1369 +--m0:=a0-r0 +--E 810 + +--S 811 of 1369 +--d0:=D(m0,x) +--E 811 + +)clear all + +--S 812 of 1369 +t0:=x^5/sqrt(a+b*x^2) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1369 +r0:=8/15*a^2*sqrt(a+b*x^2)/b^3-4/15*a*x^2*sqrt(a+b*x^2)/b^2+_ + 1/5*x^4*sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (3b x - 4a b x + 8a )\|b x + a +--R (2) ---------------------------------- +--R 3 +--R 15b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 8 2 6 | 2 2 10 8 2 6 +-+ +--R (- 15a b x - 40a x )\|b x + a + (3b x + 35a b x + 40a x )\|a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 814 + +--S 815 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (8a b x + 96a b x + 128a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 40a b x - 160a b x - 128a )\|a +--R / +--R +--------+ +--R 5 4 4 2 2 3 +-+ | 2 5 4 2 4 2 +--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x +--R + +--R 3 3 +--R - 240a b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 816 + +)clear all + +--S 817 of 1369 +t0:=x^4/sqrt(a+b*x^2) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1369 +r0:=3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/8*a*x*sqrt(a+b*x^2)/b^2+1/4*x^3*sqrt(a+b*x^2)/b +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R 3a atanh(-----------) + (2b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 13a b x + 8a b x + 24a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 12a b x - 20a b x - 24a x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32b x + 64a b )\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b )\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 13a b x + 8a b x + 24a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 12a b x - 20a b x - 24a x)\|- b \|a +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32b x + 64a b )\|- b \|a \|b x + a +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8b x - 64a b x - 64a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 819 + +--S 820 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 8b \|- b \|b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1369 +t0:=x^3/sqrt(a+b*x^2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1369 +r0:=-2/3*a*sqrt(a+b*x^2)/b^2+1/3*x^2*sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x - 2a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3a x \|b x + a + (b x + 3a x )\|a +--R (3) --------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 826 + +--S 827 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (- 2a b x - 8a )\|b x + a + (6a b x + 8a )\|a +--R (4) -------------------------------------------------- +--R +--------+ +--R 3 2 2 +-+ | 2 3 2 2 2 +--R (3b x + 12a b )\|a \|b x + a - 9a b x - 12a b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 828 + +)clear all + +--S 829 of 1369 +t0:=x^2/sqrt(a+b*x^2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1369 +r0:=-1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*x*sqrt(a+b*x^2)/b +--R +--R +--R +-+ +--------+ +--R x\|b +-+ | 2 +--R - a atanh(-----------) + x\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2a\|a \|b x + a - a b x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4a\|a \|b x + a + 2a b x + 4a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 831 + +--S 832 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R a\|- b atanh(-----------) - 2a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2b\|- b \|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1369 +t0:=x/sqrt(a+b*x^2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1369 +r0:=sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|a +--R (3) ------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 2 +-+ +--R a\|b x + a - a\|a +--R (4) ---------------------- +--R +--------+ +--R +-+ | 2 +--R b\|a \|b x + a - a b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1369 +t0:=1/sqrt(a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R [-------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R 2atan(------------------------------) +--R b x +--R -------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 843 + +--S 844 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1369 +t0:=1/(x*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 2 +--R x\|b x + a +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|b x + a - \|a +--R \|a log(------------------) +--R x +--R (3) --------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R log(------------------) + atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1369 +t0:=1/(x^2*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1369 +r0:=-sqrt(a+b*x^2)/(a*x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) - ----------- +--R a x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R (3) -------------------------- +--R +--------+ +--R | 2 +-+ +--R a x\|b x + a - a x\|a +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1369 +t0:=1/(x^3*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1369 +r0:=1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/2*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 \|b x + a +-+ | 2 +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 2 +-+ +--R 2a x \|a +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|b x + a - \|a +--R (- 2a b x \|b x + a + (b x + 2a b x )\|a )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 4 3 2 +--R 4a x \|a \|b x + a - 2a b x - 4a x +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1369 +t0:=1/(x^4*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1369 +r0:=-1/3*sqrt(a+b*x^2)/(a*x^3)+2/3*b*sqrt(a+b*x^2)/(a^2*x) +--R +--R +--R +--------+ +--R 2 | 2 +--R (2b x - a)\|b x + a +--R (2) ---------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 6b x - 5a b x + 4a )\|a \|b x + a + 2b x + 9a b x + 3a b x - 4a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1369 +t0:=1/(x^5*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1369 +r0:=-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/4*sqrt(a+b*x^2)/(a*x^4)+3/8*b*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 4 +-+ +--R 8a x \|a +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|b x + a +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3b x - 24a b x - 24a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (- 3a b x - 22a b x - 8a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 4 +-+ +--R (12a b x + 28a b x - 16a )\|a +--R / +--R +--------+ +--R 3 6 4 4 +-+ | 2 3 2 8 4 6 5 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1369 +t0:=x^m/(a+b*x^2)^(3/2) +--R +--R +--R m +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1369 +--r0:=x^(1+m)/(a*sqrt(a+b*x^2))-m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a*(1+m)*sqrt(a+b*x^2)) +--E 874 + +--S 875 of 1369 +--a0:=integrate(t0,x) +--E 875 + +--S 876 of 1369 +--m0:=a0-r0 +--E 876 + +--S 877 of 1369 +--d0:=D(m0,x) +--E 877 + +)clear all + +--S 878 of 1369 +t0:=x^5/(a+b*x^2)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)/b^3-a^2/(b^3*sqrt(a+b*x^2))-2*a*sqrt(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R b x - 4a b x - 8a +--R (2) -------------------- +--R +--------+ +--R 3 | 2 +--R 3b \|b x + a +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4a x \|b x + a + (b x + 4a x )\|a +--R (3) --------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (3b x + 24a b x + 24a )\|a \|b x + a - 12a b x - 36a b x - 24a +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R (- 32a b x - 64a )\|a \|b x + a + 8a b x + 64a b x + 64a +--R (4) ------------------------------------------------------------------ +--R +--------+ +--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+ +--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1369 +t0:=x^4/(a+b*x^2)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1369 +r0:=-3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + x^3/(b*sqrt(a+b*x^2))+3/2*x*sqrt(a+b*x^2)/b^2 +--R +--R +--R +--------+ +-+ +--R | 2 x\|b 3 +-+ +--R - 3a\|b x + a atanh(-----------) + (b x + 3a x)\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 +--R 2b \|b \|b x + a +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((9a b x + 12a )\|a \|b x + a - 3a b x - 15a b x - 12a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (- b x - 7a b x - 12a x)\|b \|b x + a +--R + +--R 2 5 3 2 +-+ +-+ +--R (3b x + 13a b x + 12a x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (6b x + 8a b )\|a \|b \|b x + a + (- 2b x - 10a b x - 8a b )\|b +--R , +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((- 18a b x - 24a )\|a \|b x + a + 6a b x + 30a b x + 24a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (- b x - 7a b x - 12a x)\|- b \|b x + a +--R + +--R 2 5 3 2 +---+ +-+ +--R (3b x + 13a b x + 12a x)\|- b \|a +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+ +--R (6b x + 8a b )\|- b \|a \|b x + a + (- 2b x - 10a b x - 8a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 885 + +--S 886 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 3a\|- b atanh(-----------) - 6a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 889 + +)clear all + +--S 890 of 1369 +t0:=x^3/(a+b*x^2)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1369 +r0:=a/(b^2*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^2 +--R +--R +--R 2 +--R b x + 2a +--R (2) ------------- +--R +--------+ +--R 2 | 2 +--R b \|b x + a +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R x \|a +--R (3) ------------------------------------------ +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (b x + 2a)\|a \|b x + a - 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 892 + +--S 893 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +-+ | 2 2 2 +--R 4a\|a \|b x + a - 2a b x - 4a +--R (4) --------------------------------------- +--R +--------+ +--R 2 | 2 3 2 2 +-+ +--R 2a b \|b x + a + (- b x - 2a b )\|a +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1369 +t0:=x^2/(a+b*x^2)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)-x/(b*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +-+ +--R | 2 x\|b +-+ +--R \|b x + a atanh(-----------) - x\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------- +--R +--------+ +--R +-+ | 2 +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R x\|b \|b x + a - x\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R b\|a \|b \|b x + a + (- b x - a b)\|b +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 \|- b \|b x + a - \|- b \|a +--R (2\|a \|b x + a - 2b x - 2a)atan(------------------------------) +--R b x +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R x\|- b \|b x + a - x\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R b\|- b \|a \|b x + a + (- b x - a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 897 + +--S 898 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R b\|- b \|b +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 901 + +)clear all + +--S 902 of 1369 +t0:=x/(a+b*x^2)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1369 +r0:=(-1)/(b*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (2) - ------------ +--R +--------+ +--R | 2 +--R b\|b x + a +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|a +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R a\|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 904 + +--S 905 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +--R - \|a \|b x + a + a +--R (4) ------------------------ +--R +--------+ +--R | 2 +-+ +--R a b\|b x + a - a b\|a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1369 +t0:=1/(a+b*x^2)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1369 +r0:=x/(a*sqrt(a+b*x^2)) +--R +--R +--R x +--R (2) ------------ +--R +--------+ +--R | 2 +--R a\|b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R - x\|b x + a + x\|a +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R a\|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 909 + +--S 910 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 911 + +)clear all + +--S 912 of 1369 +t0:=1/(x*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R 3 | 2 +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+1/(a*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-+ +--R - \|b x + a atanh(-----------) + \|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 2 +--R a\|a \|b x + a +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a + (- b x - a)\|a )log(------------------) - b x \|a +--R x +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 3 +--R a \|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 914 + +--S 915 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (\|b x + a - \|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|b x + a | 2 +-+ +--R (\|b x + a - \|a )atanh(-----------) + \|b x + a - \|a +--R +-+ +--R \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R a\|a \|b x + a - a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 916 + +)clear all + +--S 917 of 1369 +t0:=1/(x^2*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 4 2 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1369 +r0:=1/(a*x*sqrt(a+b*x^2))-2*sqrt(a+b*x^2)/(a^2*x) +--R +--R +--R 2 +--R - 2b x - a +--R (2) -------------- +--R +--------+ +--R 2 | 2 +--R a x\|b x + a +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 4 2 2 +--R (4b x + 2a)\|a \|b x + a - 2b x - 5a b x - 2a +--R (3) --------------------------------------------------- +--R +--------+ +--R 2 3 3 | 2 2 3 3 +-+ +--R (a b x + 2a x)\|b x + a + (- 2a b x - 2a x)\|a +--R Type: Union(Expression(Integer),...) +--E 919 + +--S 920 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1369 +t0:=1/(x^3*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 5 3 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1369 +r0:=3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_ + 1/(a*x^2*sqrt(a+b*x^2))-3/2*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 \|b x + a 2 +-+ +--R 3b x \|b x + a atanh(-----------) + (- 3b x - a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 2 +-+ | 2 +--R 2a x \|a \|b x + a +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R ((- 9a b x - 12a b x )\|b x + a + (3b x + 15a b x + 12a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 3a b x + 5a b x + 4a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2b x + a b x - 7a b x - 4a )\|a +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 3 2 6 4 4 5 2 +--R (6a b x + 8a x )\|a \|b x + a - 2a b x - 10a b x - 8a x +--R Type: Union(Expression(Integer),...) +--E 924 + +--S 925 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 2 | 2 2 2 +-+ \|b x + a +--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (- 2b x - 8a b)\|b x + a + (6b x + 8a b)\|a +--R / +--R +--------+ +--R 2 2 3 +-+ | 2 3 2 4 +--R (2a b x + 8a )\|a \|b x + a - 6a b x - 8a +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 926 + +)clear all + +--S 927 of 1369 +t0:=1/(x^4*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 6 4 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1369 +r0:=1/(a*x^3*sqrt(a+b*x^2))-4/3*sqrt(a+b*x^2)/(a^2*x^3)+_ + 8/3*b*sqrt(a+b*x^2)/(a^3*x) +--R +--R +--R 2 4 2 2 +--R 8b x + 4a b x - a +--R (2) -------------------- +--R +--------+ +--R 3 3 | 2 +--R 3a x \|b x + a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (- 32b x - 80a b x - 28a b x + 8a )\|a \|b x + a + 8b x + 68a b x +--R + +--R 2 2 4 3 2 4 +--R 95a b x + 24a b x - 8a +--R / +--R +--------+ +--R 3 2 7 4 5 5 3 | 2 +--R (3a b x + 24a b x + 24a x )\|b x + a +--R + +--R 3 2 7 4 5 5 3 +-+ +--R (- 12a b x - 36a b x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 929 + +--S 930 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 931 + +)clear all + +--S 932 of 1369 +t0:=x^m/(a+b*x^2)^(5/2) +--R +--R +--R m +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1369 +--r0:=1/3*x^(1+m)/(a*(a+b*x^2)^(3/2))+1/3*(2-m)*x^(1+m)/_ +-- (a^2*sqrt(a+b*x^2))-1/3*(2-m)*m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a^2*(1+m)*sqrt(a+b*x^2)) +--E 933 + +--S 934 of 1369 +--a0:=integrate(t0,x) +--E 934 + +--S 935 of 1369 +--m0:=a0-r0 +--E 935 + +--S 936 of 1369 +--d0:=D(m0,x) +--E 936 + +)clear all + +--S 937 of 1369 +t0:=x^6/(a+b*x^2)^(5/2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1369 +r0:=-1/3*x^5/(b*(a+b*x^2)^(3/2))-5/2*a*atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(7/2)-5/3*x^3/(b^2*sqrt(a+b*x^2))+_ + 5/2*x*sqrt(a+b*x^2)/b^3 +--R +--R +--R (2) +--R +--------+ +-+ +--R 2 2 | 2 x\|b +--R (- 15a b x - 15a )\|b x + a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 5 3 2 +-+ +--R (3b x + 20a b x + 15a x)\|b +--R / +--R +--------+ +--R 4 2 3 +-+ | 2 +--R (6b x + 6a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|b \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|a \|b +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2 +--R (30b x + 150a b x + 216a b x + 96a b )\|a \|b \|b x + a +--R + +--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+ +--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|b +--R , +--R +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 150a b x - 750a b x - 1080a b x - 480a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|- b \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|- b \|a +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2 +--R (30b x + 150a b x + 216a b x + 96a b )\|- b \|a \|b x + a +--R + +--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+ +--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 939 + +--S 940 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 5a\|- b atanh(-----------) - 10a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R 3 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 943 + +)clear all + +--S 944 of 1369 +t0:=x^5/(a+b*x^2)^(5/2) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1369 +r0:=-1/3*a^2/(b^3*(a+b*x^2)^(3/2))+2*a/(b^3*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R 3b x + 12a b x + 8a +--R (2) -------------------------- +--R +--------+ +--R 4 2 3 | 2 +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4a x \|b x + a + (3b x + 4a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (3b x + 27a b x + 48a b x + 24a )\|a \|b x + a - 12a b x - 48a b x +--R + +--R 3 2 4 +--R - 60a b x - 24a +--R Type: Union(Expression(Integer),...) +--E 946 + +--S 947 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R (32a b x + 64a )\|a \|b x + a - 8a b x - 64a b x - 64a +--R (4) ------------------------------------------------------------------ +--R +--------+ +--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+ +--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1369 +t0:=x^4/(a+b*x^2)^(5/2) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1369 +r0:=-1/3*x^3/(b*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + x/(b^2*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +-+ +--R 2 | 2 x\|b 3 +-+ +--R (3b x + 3a)\|b x + a atanh(-----------) + (- 4b x - 3a x)\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R 3 2 2 +-+ | 2 +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (9b x + 21a b x + 12a )\|a \|b x + a - 3b x - 18a b x +--R + +--R 2 2 3 +--R - 27a b x - 12a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (4b x + 19a b x + 12a x)\|b \|b x + a +--R + +--R 2 5 3 2 +-+ +-+ +--R (- 12b x - 25a b x - 12a x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (9b x + 21a b x + 12a b )\|a \|b \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +-+ +--R (- 3b x - 18a b x - 27a b x - 12a b )\|b +--R , +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (18b x + 42a b x + 24a )\|a \|b x + a - 6b x - 36a b x +--R + +--R 2 2 3 +--R - 54a b x - 24a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (4b x + 19a b x + 12a x)\|- b \|b x + a +--R + +--R 2 5 3 2 +---+ +-+ +--R (- 12b x - 25a b x - 12a x)\|- b \|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (9b x + 21a b x + 12a b )\|- b \|a \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +---+ +--R (- 3b x - 18a b x - 27a b x - 12a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 951 + +--S 952 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 2 +---+ +-+ +--R b \|- b \|b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 1369 +t0:=x^3/(a+b*x^2)^(5/2) +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1369 +r0:=1/3*a/(b^2*(a+b*x^2)^(3/2))+(-1)/(b^2*sqrt(a+b*x^2)) +--R +--R +--R 2 +--R - 3b x - 2a +--R (2) -------------------------- +--R +--------+ +--R 3 2 2 | 2 +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3a x \|b x + a + (2b x + 3a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (- 2b x - 8a)\|a \|b x + a + 6a b x + 8a +--R (4) -------------------------------------------------------- +--R +--------+ +--R 3 2 2 2 | 2 3 2 2 2 +-+ +--R (3a b x + 12a b )\|b x + a + (- 9a b x - 12a b )\|a +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1369 +t0:=x^2/(a+b*x^2)^(5/2) +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1369 +r0:=1/3*x^3/(a*(a+b*x^2)^(3/2)) +--R +--R +--R 3 +--R x +--R (2) -------------------------- +--R +--------+ +--R 2 2 | 2 +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (- b x - 4a x )\|b x + a + (3b x + 4a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1369 +t0:=x/(a+b*x^2)^(5/2) +--R +--R +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1369 +r0:=(-1/3)/(b*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - ------------------------- +--R +--------+ +--R 2 2 | 2 +--R (3b x + 3a b)\|b x + a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (- b x - 4a)\|a \|b x + a + 3a b x + 4a +--R (4) ------------------------------------------------------ +--R +--------+ +--R 2 2 2 3 | 2 2 2 2 3 +-+ +--R (3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1369 +t0:=1/(a+b*x^2)^(5/2) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1369 +r0:=1/3*x/(a*(a+b*x^2)^(3/2))+2/3*x/(a^2*sqrt(a+b*x^2)) +--R +--R +--R 3 +--R 2b x + 3a x +--R (2) -------------------------- +--R +--------+ +--R 2 2 3 | 2 +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 5 3 2 | 2 2 5 3 2 +-+ +--R (- 2b x - 11a b x - 12a x)\|b x + a + (6b x + 17a b x + 12a x)\|a +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1369 +t0:=1/(x*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +--------+ +--R 2 5 3 2 | 2 +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1369 +r0:=1/3/(a*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_ + 1/(a^2*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 \|b x + a 2 +-+ +--R (- 3b x - 3a)\|b x + a atanh(-----------) + (3b x + 4a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 2 2 3 +-+ | 2 +--R (3a b x + 3a )\|a \|b x + a +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (9a b x + 21a b x + 12a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3b x - 18a b x - 27a b x - 12a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (9a b x + 12a b x )\|b x + a + (- 4b x - 15a b x - 12a b x )\|a +--R / +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 5 2 6 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 +-+ \|b x + a - \|a +--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 | 2 2 +-+ +--R (4b x + 16a)\|b x + a + (- 12b x - 16a)\|a +--R / +--R +--------+ +--R 2 2 3 +-+ | 2 3 2 4 +--R (3a b x + 12a )\|a \|b x + a - 9a b x - 12a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1369 +t0:=1/(x^2*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 6 4 2 2 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1369 +r0:=1/3/(a*x*(a+b*x^2)^(3/2))+4/3/(a^2*x*sqrt(a+b*x^2))-_ + 8/3*sqrt(a+b*x^2)/(a^3*x) +--R +--R +--R 2 4 2 2 +--R - 8b x - 12a b x - 3a +--R (2) --------------------------- +--R +--------+ +--R 3 3 4 | 2 +--R (3a b x + 3a x)\|b x + a +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (32b x + 112a b x + 108a b x + 24a )\|a \|b x + a - 8b x - 76a b x +--R + +--R 2 2 4 3 2 4 +--R - 163a b x - 120a b x - 24a +--R / +--R +--------+ +--R 3 3 7 4 2 5 5 3 6 | 2 +--R (3a b x + 27a b x + 48a b x + 24a x)\|b x + a +--R + +--R 3 3 7 4 2 5 5 3 6 +-+ +--R (- 12a b x - 48a b x - 60a b x - 24a x)\|a +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1369 +t0:=1/(x^3*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1369 +r0:=1/3/(a*x^2*(a+b*x^2)^(3/2))+5/2*b*atanh(sqrt(a+b*x^2)/_ + sqrt(a))/a^(7/2)+5/3/(a^2*x^2*sqrt(a+b*x^2))-_ + 5/2*sqrt(a+b*x^2)/(a^3*x^2) +--R +--R +--R (2) +--R +--------+ +--R +--------+ | 2 +--R 2 4 2 | 2 \|b x + a +--R (15b x + 15a b x )\|b x + a atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +--R (- 15b x - 20a b x - 3a )\|a +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 +--R (6a b x + 6a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 | 2 +--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+ +--R (15b x + 210a b x + 615a b x + 660a b x + 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (14b x + 121a b x + 174a b x - 39a b x - 156a b x - 48a )\|a +--R / +--R +--------+ +--R 4 3 8 5 2 6 6 4 7 2 +-+ | 2 4 4 10 +--R (30a b x + 150a b x + 216a b x + 96a x )\|a \|b x + a - 6a b x +--R + +--R 5 3 8 6 2 6 7 4 8 2 +--R - 84a b x - 246a b x - 264a b x - 96a x +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 15b x - 180a b x - 240a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (75b x + 300a b x + 240a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 15b x - 180a b x - 240a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (75b x + 300a b x + 240a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 14b x - 168a b x - 224a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (70b x + 280a b x + 224a b)\|a +--R / +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6 +--R (6a b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1369 +t0:=1/(x^4*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 8 6 2 4 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1369 +r0:=1/3/(a*x^3*(a+b*x^2)^(3/2))+2/(a^2*x^3*sqrt(a+b*x^2))-_ + 8/3*sqrt(a+b*x^2)/(a^3*x^3)+16/3*b*sqrt(a+b*x^2)/(a^4*x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 16b x + 24a b x + 6a b x - a +--R (2) -------------------------------- +--R +--------+ +--R 4 5 5 3 | 2 +--R (3a b x + 3a x )\|b x + a +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (- 96b x - 656a b x - 1316a b x - 954a b x - 160a b x + 32a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 16b x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x +--R + +--R 6 +--R - 32a +--R / +--R +--------+ +--R 4 4 11 5 3 9 6 2 7 7 5 8 3 | 2 +--R (3a b x + 57a b x + 198a b x + 240a b x + 96a x )\|b x + a +--R + +--R 4 4 11 5 3 9 6 2 7 7 5 8 3 +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a x )\|a +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1369 +t0:=x^m/(a+b*x^2)^(9/2) +--R +--R +--R m +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1369 +--r0:=1/7*x^(1+m)/(a*(a+b*x^2)^(7/2))+1/35*(6-m)*x^(1+m)/_ +-- (a^2*(a+b*x^2)^(5/2))+1/105*(4-m)*(6-m)*x^(1+m)/_ +-- (a^3*(a+b*x^2)^(3/2))+1/105*(2-m)*(4-m)*(6-m)*x^(1+m)/_ +-- (a^4*sqrt(a+b*x^2))-1/105*(2-m)*(4-m)*(6-m)*m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a^4*(1+m)*sqrt(a+b*x^2)) +--E 997 + +--S 998 of 1369 +--a0:=integrate(t0,x) +--E 998 + +--S 999 of 1369 +--m0:=a0-r0 +--E 999 + +--S 1000 of 1369 +--d0:=D(m0,x) +--E 1000 + +)clear all + +--S 1001 of 1369 +t0:=x^10/(a+b*x^2)^(9/2) +--R +--R +--R 10 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1369 +r0:=-1/7*x^9/(b*(a+b*x^2)^(7/2))-9/35*x^7/(b^2*(a+b*x^2)^(5/2))-_ + 3/5*x^5/(b^3*(a+b*x^2)^(3/2))-9/2*a*atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(11/2)-3*x^3/(b^4*sqrt(a+b*x^2))+_ + 9/2*x*sqrt(a+b*x^2)/b^5 +--R +--R +--R (2) +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (- 315a b x - 945a b x - 945a b x - 315a )\|b x + a +--R * +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (35b x + 528a b x + 1218a b x + 1050a b x + 315a x)\|b +--R / +--R +--------+ +--R 8 6 7 4 2 6 2 3 5 +-+ | 2 +--R (70b x + 210a b x + 210a b x + 70a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 14 2 6 12 3 5 10 4 4 8 +--R 2835a b x + 46305a b x + 257985a b x + 705915a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 1071000a b x + 922320a b x + 423360a b x + 80640a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 315a b x - 13860a b x - 127890a b x - 520380a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 1149435a b x - 1484280a b x - 1123920a b x - 463680a b x +--R + +--R 9 +--R - 80640a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 35b x - 1928a b x - 30738a b x - 192170a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 8952a b x + 89442a b x + 403866a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x +--R + +--R 8 +--R 80640a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 12 14 11 12 2 10 10 3 9 8 +--R 630b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 4 8 6 5 7 4 6 6 2 7 5 +--R 238000a b x + 204960a b x + 94080a b x + 17920a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 13 16 12 14 2 11 12 3 10 10 +--R - 70b x - 3080a b x - 28420a b x - 115640a b x +--R + +--R 4 9 8 5 8 6 6 7 4 7 6 2 +--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x +--R + +--R 8 5 +--R - 17920a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 7 14 2 6 12 3 5 10 4 4 8 +--R - 5670a b x - 92610a b x - 515970a b x - 1411830a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 2142000a b x - 1844640a b x - 846720a b x - 161280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 630a b x + 27720a b x + 255780a b x + 1040760a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 2298870a b x + 2968560a b x + 2247840a b x + 927360a b x +--R + +--R 9 +--R 161280a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 35b x - 1928a b x - 30738a b x - 192170a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 8952a b x + 89442a b x + 403866a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x +--R + +--R 8 +--R 80640a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 12 14 11 12 2 10 10 3 9 8 +--R 630b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 4 8 6 5 7 4 6 6 2 7 5 +--R 238000a b x + 204960a b x + 94080a b x + 17920a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 13 16 12 14 2 11 12 3 10 10 +--R - 70b x - 3080a b x - 28420a b x - 115640a b x +--R + +--R 4 9 8 5 8 6 6 7 4 7 6 2 +--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x +--R + +--R 8 5 +--R - 17920a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1003 + +--S 1004 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 9a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 9a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 9a\|- b atanh(-----------) - 18a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R 5 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1007 + +)clear all + +--S 1008 of 1369 +t0:=x^9/(a+b*x^2)^(9/2) +--R +--R +--R 9 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1369 +r0:=-1/7*a^4/(b^5*(a+b*x^2)^(7/2))+4/5*a^3/(b^5*(a+b*x^2)^(5/2))-_ + 2*a^2/(b^5*(a+b*x^2)^(3/2))+4*a/(b^5*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^5 +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R 35b x + 280a b x + 560a b x + 448a b x + 128a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 8 6 7 4 2 6 2 3 5 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 14 2 12 3 10 | 2 +--R (- 152a b x - 560a b x - 448a x )\|b x + a +--R + +--R 3 16 2 14 2 12 3 10 +-+ +--R (35b x + 376a b x + 784a b x + 448a x )\|a +--R / +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R 35b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x +--R + +--R 5 2 4 6 2 7 +--R 45920a b x + 22400a b x + 4480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x +--R + +--R 6 2 4 7 2 8 +--R - 56560a b x - 24640a b x - 4480a +--R Type: Union(Expression(Integer),...) +--E 1010 + +--S 1011 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (1024a b x + 10240a b x + 24576a b x + 16384a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a +--R / +--R +--------+ +--R 8 6 2 7 4 3 6 2 4 5 | 2 +--R (280a b x + 2800a b x + 6720a b x + 4480a b )\|b x + a +--R + +--R 9 8 8 6 2 7 4 3 6 2 4 5 +-+ +--R (- 35b x - 1120a b x - 5600a b x - 8960a b x - 4480a b )\|a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1369 +t0:=x^8/(a+b*x^2)^(9/2) +--R +--R +--R 8 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1369 +r0:=-1/7*x^7/(b*(a+b*x^2)^(7/2))-1/5*x^5/(b^2*(a+b*x^2)^(5/2))-_ + 1/3*x^3/(b^3*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(9/2)-x/(b^4*sqrt(a+b*x^2)) +--R +--R +--R (2) +--R +--------+ +-+ +--R 3 6 2 4 2 2 3 | 2 x\|b +--R (105b x + 315a b x + 315a b x + 105a )\|b x + a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 176b x - 406a b x - 350a b x - 105a x)\|b +--R / +--R +--------+ +--R 7 6 6 4 2 5 2 3 4 +-+ | 2 +--R (105b x + 315a b x + 315a b x + 105a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 12 5 10 2 4 8 3 3 6 +--R 735b x + 8085a b x + 31605a b x + 60375a b x +--R + +--R 4 2 4 5 2 6 +--R 61320a b x + 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 5 2 4 6 2 7 +--R - 76440a b x - 35280a b x - 6720a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x +--R + +--R 5 3 6 +--R 30800a b x + 6720a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 +--R - 1232b x - 12698a b x - 44898a b x - 77071a b x +--R + +--R 4 2 5 5 3 6 +--R - 71064a b x - 34160a b x - 6720a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 10 12 9 10 2 8 8 3 7 6 4 6 4 +--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 5 5 2 6 4 +--R 31920a b x + 6720a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 11 14 10 12 2 9 10 3 8 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 7 6 5 6 4 6 5 2 7 4 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 6 12 5 10 2 4 8 3 3 6 +--R 1470b x + 16170a b x + 63210a b x + 120750a b x +--R + +--R 4 2 4 5 2 6 +--R 122640a b x + 63840a b x + 13440a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 +--R - 210b x - 5880a b x - 38220a b x - 111720a b x +--R + +--R 4 3 6 5 2 4 6 2 7 +--R - 174930a b x - 152880a b x - 70560a b x - 13440a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x +--R + +--R 5 3 6 +--R 30800a b x + 6720a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 +--R - 1232b x - 12698a b x - 44898a b x - 77071a b x +--R + +--R 4 2 5 5 3 6 +--R - 71064a b x - 34160a b x - 6720a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 10 12 9 10 2 8 8 3 7 6 4 6 4 +--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 5 5 2 6 4 +--R 31920a b x + 6720a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 11 14 10 12 2 9 10 3 8 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 7 6 5 6 4 6 5 2 7 4 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 4 +---+ +-+ +--R b \|- b \|b +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1369 +t0:=x^7/(a+b*x^2)^(9/2) +--R +--R +--R 7 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1369 +r0:=1/7*a^3/(b^4*(a+b*x^2)^(7/2))-3/5*a^2/(b^4*(a+b*x^2)^(5/2))+_ + a/(b^4*(a+b*x^2)^(3/2))+(-1)/(b^4*sqrt(a+b*x^2)) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 70a b x - 56a b x - 16a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 7 6 6 4 2 5 2 3 4 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 12 2 10 3 8 | 2 +--R (- 77a b x - 322a b x - 280a x )\|b x + a +--R + +--R 3 14 2 12 2 10 3 8 +-+ +--R (16b x + 203a b x + 462a b x + 280a x )\|a +--R / +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 6 2 7 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 6 2 4 7 2 8 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1022 + +--S 1023 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 16b x - 384a b x - 1280a b x - 1024a )\|a \|b x + a + 112a b x +--R + +--R 2 2 4 3 2 4 +--R 896a b x + 1792a b x + 1024a +--R / +--R +--------+ +--R 7 6 2 6 4 3 5 2 4 4 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a +--R + +--R 7 6 2 6 4 3 5 2 4 4 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +)clear all + +--S 1025 of 1369 +t0:=x^6/(a+b*x^2)^(9/2) +--R +--R +--R 6 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1369 +r0:=1/7*x^7/(a*(a+b*x^2)^(7/2)) +--R +--R +--R 7 +--R x +--R (2) ------------------------------------------------ +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (7a b x + 21a b x + 21a b x + 7a )\|b x + a +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 13 2 11 2 9 3 7 | 2 +--R (- b x - 24a b x - 80a b x - 64a x )\|b x + a +--R + +--R 3 13 2 11 2 9 3 7 +-+ +--R (7b x + 56a b x + 112a b x + 64a x )\|a +--R / +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x +--R + +--R 6 2 7 +--R 2128a b x + 448a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x +--R + +--R 6 2 4 7 2 8 +--R - 5096a b x - 2352a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 1027 + +--S 1028 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +)clear all + +--S 1030 of 1369 +t0:=x^5/(a+b*x^2)^(9/2) +--R +--R +--R 5 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1369 +r0:=-1/7*a^2/(b^3*(a+b*x^2)^(7/2))+2/5*a/(b^3*(a+b*x^2)^(5/2))+_ + (-1/3)/(b^3*(a+b*x^2)^(3/2)) +--R +--R +--R 2 4 2 2 +--R - 35b x - 28a b x - 8a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 | 2 +--R (105b x + 315a b x + 315a b x + 105a b )\|b x + a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 12 2 2 10 3 8 4 6 | 2 +--R (- 56a b x - 581a b x - 1540a b x - 1120a x )\|b x + a +--R + +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (8b x + 224a b x + 1211a b x + 2100a b x + 1120a x )\|a +--R / +--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 7 2 8 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 7 2 4 8 2 9 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 8b x - 192a b x - 640a b x - 512a )\|a \|b x + a + 56a b x +--R + +--R 2 2 4 3 2 4 +--R 448a b x + 896a b x + 512a +--R / +--R +--------+ +--R 2 6 6 3 5 4 4 4 2 5 3 | 2 +--R (105a b x + 2520a b x + 8400a b x + 6720a b )\|b x + a +--R + +--R 2 6 6 3 5 4 4 4 2 5 3 +-+ +--R (- 735a b x - 5880a b x - 11760a b x - 6720a b )\|a +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1369 +t0:=x^4/(a+b*x^2)^(9/2) +--R +--R +--R 4 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1369 +r0:=1/7*x^5/(a*(a+b*x^2)^(7/2))+2/35*x^5/(a^2*(a+b*x^2)^(5/2)) +--R +--R +--R 7 5 +--R 2b x + 7a x +--R (2) ---------------------------------------------------- +--R +--------+ +--R 2 3 6 3 2 4 4 2 5 | 2 +--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 13 3 11 2 2 9 3 7 4 5 | 2 +--R (- 2b x - 55a b x - 328a b x - 688a b x - 448a x )\|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (14b x + 161a b x + 616a b x + 912a b x + 448a x )\|a +--R / +--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 7 2 8 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 7 2 4 8 2 9 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1369 +t0:=x^3/(a+b*x^2)^(9/2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1369 +r0:=1/7*a/(b^2*(a+b*x^2)^(7/2))+(-1/5)/(b^2*(a+b*x^2)^(5/2)) +--R +--R +--R 2 +--R - 7b x - 2a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2 +--R (- 14a b x - 154a b x - 595a b x - 980a b x - 560a x )\|b x + a +--R + +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+ +--R (2b x + 56a b x + 364a b x + 1015a b x + 1260a b x + 560a x )\|a +--R / +--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 8 2 9 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 8 2 4 9 2 10 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 2b x - 48a b x - 160a b x - 128a )\|a \|b x + a + 14a b x +--R + +--R 2 2 4 3 2 4 +--R 112a b x + 224a b x + 128a +--R / +--R +--------+ +--R 3 5 6 4 4 4 5 3 2 6 2 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a +--R + +--R 3 5 6 4 4 4 5 3 2 6 2 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1369 +t0:=x^2/(a+b*x^2)^(9/2) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1369 +r0:=1/7*x^3/(a*(a+b*x^2)^(7/2))+4/35*x^3/(a^2*(a+b*x^2)^(5/2))+_ + 8/105*x^3/(a^3*(a+b*x^2)^(3/2)) +--R +--R +--R 2 7 5 2 3 +--R 8b x + 28a b x + 35a x +--R (2) ------------------------------------------------------ +--R +--------+ +--R 3 3 6 4 2 4 5 2 6 | 2 +--R (105a b x + 315a b x + 315a b x + 105a )\|b x + a +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 13 4 11 2 3 9 3 2 7 4 5 +--R - 8b x - 220a b x - 1347a b x - 3592a b x - 4592a b x +--R + +--R 5 3 +--R - 2240a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 13 4 11 2 3 9 3 2 7 4 5 +--R 56b x + 644a b x + 2709a b x + 5608a b x + 5712a b x +--R + +--R 5 3 +--R 2240a x +--R * +--R +-+ +--R \|a +--R / +--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 8 2 9 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 8 2 4 9 2 10 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1369 +t0:=x/(a+b*x^2)^(9/2) +--R +--R +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1369 +r0:=(-1/7)/(b*(a+b*x^2)^(7/2)) +--R +--R +--R 1 +--R (2) - ----------------------------------------------- +--R +--------+ +--R 4 6 3 4 2 2 2 3 | 2 +--R (7b x + 21a b x + 21a b x + 7a b)\|b x + a +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2 +--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4 +--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x +--R + +--R 6 2 +--R 224a x +--R * +--R +-+ +--R \|a +--R / +--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4 +--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x +--R + +--R 9 2 10 +--R 2128a b x + 448a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x +--R + +--R 9 2 4 10 2 11 +--R - 5096a b x - 2352a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (- b x - 24a b x - 80a b x - 64a )\|a \|b x + a + 7a b x + 56a b x +--R + +--R 3 2 4 +--R 112a b x + 64a +--R / +--R +--------+ +--R 4 4 6 5 3 4 6 2 2 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448a b)\|b x + a +--R + +--R 4 4 6 5 3 4 6 2 2 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448a b)\|a +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1369 +t0:=1/(a+b*x^2)^(9/2) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1369 +r0:=1/7*x/(a*(a+b*x^2)^(7/2))+6/35*x/(a^2*(a+b*x^2)^(5/2))+_ + 8/35*x/(a^3*(a+b*x^2)^(3/2))+16/35*x/(a^4*sqrt(a+b*x^2)) +--R +--R +--R 3 7 2 5 2 3 3 +--R 16b x + 56a b x + 70a b x + 35a x +--R (2) ---------------------------------------------------- +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R - 16b x - 440a b x - 2694a b x - 7219a b x - 10024a b x +--R + +--R 5 3 6 +--R - 7280a b x - 2240a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 112b x + 1288a b x + 5418a b x + 11461a b x + 13384a b x +--R + +--R 5 3 6 +--R 8400a b x + 2240a x +--R * +--R +-+ +--R \|a +--R / +--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 9 2 10 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 9 2 4 10 2 11 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1369 +t0:=1/(x*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1369 +r0:=1/7/(a*(a+b*x^2)^(7/2))+1/5/(a^2*(a+b*x^2)^(5/2))+_ + 1/3/(a^3*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/_ + a^(9/2)+1/(a^4*sqrt(a+b*x^2)) +--R +--R +--R (2) +--R +--------+ +--R +--------+ | 2 +--R 3 6 2 4 2 2 3 | 2 \|b x + a +--R (- 105b x - 315a b x - 315a b x - 105a )\|b x + a atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105b x + 350a b x + 406a b x + 176a )\|a +--R / +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (105a b x + 315a b x + 315a b x + 105a )\|a \|b x + a +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 2 5 10 3 4 8 4 3 6 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x +--R + +--R 5 2 4 6 2 7 +--R 61320a b x + 31920a b x + 6720a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 3 6 5 2 4 6 2 7 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 1127a b x + 10682a b x + 35770a b x + 56560a b x + 43680a b x +--R + +--R 6 2 +--R 13440a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R - 176b x - 4193a b x - 23702a b x - 59430a b x - 76720a b x +--R + +--R 5 2 4 6 2 +--R - 50400a b x - 13440a b x +--R * +--R +-+ +--R \|a +--R / +--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 10 2 11 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 9 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 10 2 4 11 2 12 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (176b x + 4224a b x + 14080a b x + 11264a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 1232b x - 9856a b x - 19712a b x - 11264a )\|a +--R / +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6 +--R (105a b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x +--R + +--R 6 2 4 7 2 8 +--R - 5880a b x - 11760a b x - 6720a +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1369 +t0:=1/(x^2*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R +--------+ +--R 4 10 3 8 2 2 6 3 4 4 2 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1369 +r0:=1/7/(a*x*(a+b*x^2)^(7/2))+8/35/(a^2*x*(a+b*x^2)^(5/2))+_ + 16/35/(a^3*x*(a+b*x^2)^(3/2))+64/35/(a^4*x*sqrt(a+b*x^2))-_ + 128/35*sqrt(a+b*x^2)/(a^5*x) +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - 128b x - 448a b x - 560a b x - 280a b x - 35a +--R (2) ----------------------------------------------------- +--R +--------+ +--R 5 3 7 6 2 5 7 3 8 | 2 +--R (35a b x + 105a b x + 105a b x + 35a x)\|b x + a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R 1024b x + 13824a b x + 64896a b x + 149440a b x + 187544a b x +--R + +--R 5 2 4 6 2 7 +--R 128240a b x + 42560a b x + 4480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 128b x - 4544a b x - 35376a b x - 122648a b x - 229667a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 246624a b x - 148960a b x - 44800a b x - 4480a +--R / +--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7 +--R 35a b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x +--R + +--R 10 2 5 11 3 12 +--R 45920a b x + 22400a b x + 4480a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7 +--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x +--R + +--R 10 2 5 11 3 12 +--R - 56560a b x - 24640a b x - 4480a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1369 +t0:=1/(x^3*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R +--------+ +--R 4 11 3 9 2 2 7 3 5 4 3 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1369 +r0:=1/7/(a*x^2*(a+b*x^2)^(7/2))+9/35/(a^2*x^2*(a+b*x^2)^(5/2))+_ + 3/5/(a^3*x^2*(a+b*x^2)^(3/2))+9/2*b*atanh(sqrt(a+b*x^2)/_ + sqrt(a))/a^(11/2)+3/(a^4*x^2*sqrt(a+b*x^2))-9/2*sqrt(a+b*x^2)/(a^5*x^2) +--R +--R +--R (2) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 | 2 +--R (315b x + 945a b x + 945a b x + 315a b x )\|b x + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x - 1050a b x - 1218a b x - 528a b x - 35a )\|a +--R / +--R +--------+ +--R 5 3 8 6 2 6 7 4 8 2 +-+ | 2 +--R (70a b x + 210a b x + 210a b x + 70a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 2835a b x - 46305a b x - 257985a b x - 705915a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 1071000a b x - 922320a b x - 423360a b x - 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 315b x + 13860a b x + 127890a b x + 520380a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 1149435a b x + 1484280a b x + 1123920a b x + 463680a b x +--R + +--R 8 2 +--R 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 3177a b x - 43386a b x - 198954a b x - 427140a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 454685a b x - 193480a b x + 35280a b x + 51520a b x + 8960a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 388b x + 14237a b x + 110278a b x + 367934a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 629860a b x + 552965a b x + 181720a b x - 59920a b x +--R + +--R 8 2 9 +--R - 56000a b x - 8960a +--R * +--R +-+ +--R \|a +--R / +--R 6 7 16 7 6 14 8 5 12 9 4 10 +--R 630a b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 10 3 8 11 2 6 12 4 13 2 +--R 238000a b x + 204960a b x + 94080a b x + 17920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 8 18 7 7 16 8 6 14 9 5 12 10 4 10 +--R - 70a b x - 3080a b x - 28420a b x - 115640a b x - 255430a b x +--R + +--R 11 3 8 12 2 6 13 4 14 2 +--R - 329840a b x - 249760a b x - 103040a b x - 17920a x +--R Type: Union(Expression(Integer),...) +--E 1072 + +--S 1073 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 388b x - 15520a b x - 93120a b x - 173824a b x - 99328a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (3492b x + 46560a b x + 167616a b x + 223488a b x + 99328a b)\|a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (70a b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1074 + +)clear all + +--S 1075 of 1369 +t0:=1/(x^4*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------- +--R +--------+ +--R 4 12 3 10 2 2 8 3 6 4 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1369 +r0:=1/7/(a*x^3*(a+b*x^2)^(7/2))+2/7/(a^2*x^3*(a+b*x^2)^(5/2))+_ + 16/21/(a^3*x^3*(a+b*x^2)^(3/2))+32/7/(a^4*x^3*sqrt(a+b*x^2))-_ + 128/21*sqrt(a+b*x^2)/(a^5*x^3)+256/21*b*sqrt(a+b*x^2)/(a^6*x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 256b x + 896a b x + 1120a b x + 560a b x + 70a b x - 7a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 6 3 9 7 2 7 8 5 9 3 | 2 +--R (21a b x + 63a b x + 63a b x + 21a x )\|b x + a +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2560b x - 49920a b x - 326592a b x - 1049056a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 1891516a b x - 1993082a b x - 1192800a b x - 353696a b x +--R + +--R 8 2 9 +--R - 28672a b x + 3584a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 256b x + 13696a b x + 148320a b x + 701680a b x + 1807270a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 2759845a b x + 2547202a b x + 1365840a b x + 368480a b x +--R + +--R 9 2 10 +--R 26880a b x - 3584a +--R / +--R 6 8 19 7 7 17 8 6 15 9 5 13 +--R 21a b x + 1113a b x + 11613a b x + 51891a b x +--R + +--R 10 4 11 11 3 9 12 2 7 13 5 +--R 123690a b x + 170352a b x + 136416a b x + 59136a b x +--R + +--R 14 3 +--R 10752a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 19 7 7 17 8 6 15 9 5 13 +--R - 210a b x - 4200a b x - 28812a b x - 98952a b x +--R + +--R 10 4 11 11 3 9 12 2 7 13 5 +--R - 195090a b x - 231840a b x - 164640a b x - 64512a b x +--R + +--R 14 3 +--R - 10752a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1077 + +--S 1078 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1079 + +)clear all + +--S 1080 of 1369 +t0:=x^5/sqrt(9+4*x^2) +--R +--R +--R 5 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1369 +r0:=27/40*sqrt(9+4*x^2)-3/20*x^2*sqrt(9+4*x^2)+1/20*x^4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (2x - 6x + 27)\|4x + 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 1024x + 192x - 6804x - 34020x - 21870x)\|4x + 9 + 2048x +--R + +--R 8 6 4 2 +--R 1920x + 11880x + 85050x + 109350x + 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 1082 + +--S 1083 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1084 + +)clear all + +--S 1085 of 1369 +t0:=x^4/sqrt(9+4*x^2) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1369 +r0:=243/256*asinh(2/3*x)-27/128*x*sqrt(9+4*x^2)+1/16*x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 2x +--R (16x - 54x)\|4x + 9 + 243asinh(--) +--R 3 +--R (2) ------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((- 15552x - 17496x)\|4x + 9 + 31104x + 69984x + 19683) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 4 +--R (- 2048x + 2304x + 14256x + 4374x)\|4x + 9 + 4096x - 36288x +--R + +--R 2 +--R - 34992x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (16384x + 18432x)\|4x + 9 - 32768x - 73728x - 20736 +--R Type: Union(Expression(Integer),...) +--E 1087 + +--S 1088 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 243log(\|4x + 9 - 2x) - 243asinh(--) +--R 3 +--R (4) ---------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1369 +t0:=x^3/sqrt(9+4*x^2) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1369 +r0:=-3/8*sqrt(9+4*x^2)+1/12*x^2*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2x - 9)\|4x + 9 +--R (2) ------------------- +--R 24 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 64x + 180x + 486x)\|4x + 9 + 128x - 216x - 1458x - 729 +--R (3) ---------------------------------------------------------------- +--R +-------+ +--R 2 | 2 3 +--R (384x + 216)\|4x + 9 - 768x - 1296x +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1369 +t0:=x^2/sqrt(9+4*x^2) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1369 +r0:=-9/16*asinh(2/3*x)+1/8*x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 2x +--R 2x\|4x + 9 - 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (36x\|4x + 9 - 72x - 81)log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x - 18x)\|4x + 9 + 32x + 72x +--R / +--R +-------+ +--R | 2 2 +--R 64x\|4x + 9 - 128x - 144 +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 9log(\|4x + 9 - 2x) + 9asinh(--) +--R 3 +--R (4) ---------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1369 +t0:=x/sqrt(9+4*x^2) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1369 +r0:=1/4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (2) ---------- +--R 4 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R - 2x\|4x + 9 + 4x + 9 +--R (3) ------------------------ +--R +-------+ +--R | 2 +--R 4\|4x + 9 - 8x +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1369 +t0:=1/sqrt(9+4*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1369 +r0:=1/2*asinh(2/3*x) +--R +--R +--R 2x +--R asinh(--) +--R 3 +--R (2) --------- +--R 2 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R (3) - -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - log(\|4x + 9 - 2x) - asinh(--) +--R 3 +--R (4) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1369 +t0:=1/(x*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 2 +--R x\|4x + 9 +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1369 +r0:=-1/3*atanh(1/3*sqrt(9+4*x^2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R atanh(----------) +--R 3 +--R (2) - ----------------- +--R 3 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3) +--R (3) ----------------------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3) + atanh(----------) +--R 3 +--R ------------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1369 +t0:=1/(x^2*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1369 +r0:=-1/9*sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (2) - ---------- +--R 9x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------- +--R +-------+ +--R | 2 2 +--R x\|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1369 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - - +--R 9 +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1369 +t0:=1/(x^3*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1369 +r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/18*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x + 9 | 2 +--R 4x atanh(----------) - 3\|4x + 9 +--R 3 +--R (2) ---------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x + 27)\|4x + 9 - 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 216x \|4x + 9 - 432x - 486x +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------) +--R 3 +--R -------------------------------------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1369 +t0:=1/(x^4*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1369 +r0:=-1/27*sqrt(9+4*x^2)/x^3+8/243*sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R 2 | 2 +--R (8x - 9)\|4x + 9 +--R (2) ------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R 2x\|4x + 9 - 4x - 3 +--R (3) ------------------------------------ +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x + 9x )\|4x + 9 - 32x - 54x +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1369 +m0:=a0-r0 +--R +--R +--R 16 +--R (4) --- +--R 243 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1369 +t0:=1/(x^5*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1369 +r0:=-2/81*atanh(1/3*sqrt(9+4*x^2))-1/36*sqrt(9+4*x^2)/x^4+_ + 1/54*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x + 9 2 | 2 +--R - 8x atanh(----------) + (6x - 9)\|4x + 9 +--R 3 +--R (2) -------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x - 576x + 2106x + 729)\|4x + 9 + 1536x + 2880x - 3888x +--R + +--R - 5832x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (20736x + 23328x )\|4x + 9 - 41472x - 93312x - 26244x +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------) +--R 3 +--R ---------------------------------------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1369 +t0:=x^5/sqrt(9-4*x^2) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1369 +r0:=-27/40*sqrt(9-4*x^2)-3/20*x^2*sqrt(9-4*x^2)-1/20*x^4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (- 2x - 6x - 27)\|- 4x + 9 +--R (2) ------------------------------ +--R 40 +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 8 6 | 2 10 8 6 +--R (15x - 90x )\|- 4x + 9 + 4x - 105x + 270x +--R (3) --------------------------------------------------------- +--R +---------+ +--R 4 2 | 2 4 2 +--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860 +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1369 +m0:=a0-r0 +--R +--R +--R 81 +--R (4) - -- +--R 40 +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1369 +t0:=x^4/sqrt(9-4*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1369 +r0:=243/256*asin(2/3*x)-27/128*x*sqrt(9-4*x^2)-1/16*x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 2x +--R (- 16x - 54x)\|- 4x + 9 + 243asin(--) +--R 3 +--R (2) ---------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +--R ((- 1458x + 6561)\|- 4x + 9 - 486x + 8748x - 19683) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 7 5 3 | 2 7 5 3 +--R (- 16x + 234x + 324x - 2187x)\|- 4x + 9 + 192x - 648x - 2430x +--R + +--R 6561x +--R / +--R +---------+ +--R 2 | 2 4 2 +--R (768x - 3456)\|- 4x + 9 + 256x - 4608x + 10368 +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 486atan(----------------) - 243asin(--) +--R 2x 3 +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1369 +t0:=x^3/sqrt(9-4*x^2) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1369 +r0:=-3/8*sqrt(9-4*x^2)-1/12*x^2*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2x - 9)\|- 4x + 9 +--R (2) ----------------------- +--R 24 +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 2 6 4 +--R 9x \|- 4x + 9 + 4x - 27x +--R (3) -------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (12x - 108)\|- 4x + 9 - 108x + 324 +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1369 +m0:=a0-r0 +--R +--R +--R 9 +--R (4) - - +--R 8 +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1369 +t0:=x^2/sqrt(9-4*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1369 +r0:=9/16*asin(2/3*x)-1/8*x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 2x +--R - 2x\|- 4x + 9 + 9asin(--) +--R 3 +--R (2) ---------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R | 2 2 \|- 4x + 9 - 3 +--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +--R (- 2x + 9x)\|- 4x + 9 + 12x - 27x +--R / +--R +---------+ +--R | 2 2 +--R 24\|- 4x + 9 + 16x - 72 +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 18atan(----------------) - 9asin(--) +--R 2x 3 +--R (4) -------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1369 +t0:=x/sqrt(9-4*x^2) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1369 +r0:=-1/4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (2) - ------------ +--R 4 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R x +--R (3) ---------------- +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R (4) - - +--R 4 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1369 +t0:=1/sqrt(9-4*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1369 +r0:=1/2*asin(2/3*x) +--R +--R +--R 2x +--R asin(--) +--R 3 +--R (2) -------- +--R 2 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R (3) - atan(----------------) +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 2atan(----------------) - asin(--) +--R 2x 3 +--R (4) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1369 +t0:=1/(x*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 2 +--R x\|- 4x + 9 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1369 +r0:=-1/3*atanh(1/3*sqrt(9-4*x^2)) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R atanh(------------) +--R 3 +--R (2) - ------------------- +--R 3 +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R log(----------------) +--R x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R log(----------------) + atanh(------------) +--R x 3 +--R (4) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1369 +t0:=1/(x^2*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1369 +r0:=-1/9*sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (2) - ------------ +--R 9x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 2 +--R 3\|- 4x + 9 + 4x - 9 +--R (3) ----------------------- +--R +---------+ +--R | 2 +--R 9x\|- 4x + 9 - 27x +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1369 +t0:=1/(x^3*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1369 +r0:=-2/27*atanh(1/3*sqrt(9-4*x^2))-1/18*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x + 9 | 2 +--R - 4x atanh(------------) - 3\|- 4x + 9 +--R 3 +--R (2) ---------------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 4 2 \|- 4x + 9 - 3 +--R (12x \|- 4x + 9 + 8x - 36x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 6x + 27)\|- 4x + 9 + 36x - 81 +--R / +--R +---------+ +--R 2 | 2 4 2 +--R 162x \|- 4x + 9 + 108x - 486x +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R 2log(----------------) + 2atanh(------------) +--R x 3 +--R (4) --------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1369 +t0:=1/(x^4*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1369 +r0:=-1/27*sqrt(9-4*x^2)/x^3-8/243*sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 8x - 9)\|- 4x + 9 +--R (2) ----------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (72x - 135x - 243)\|- 4x + 9 + 32x - 324x + 243x + 729 +--R (3) ------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +--R (243x - 2187x )\|- 4x + 9 - 2187x + 6561x +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1369 +t0:=1/(x^5*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 5 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1369 +r0:=-2/81*atanh(1/3*sqrt(9-4*x^2))-1/36*sqrt(9-4*x^2)/x^4-_ + 1/54*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x + 9 2 | 2 +--R - 8x atanh(------------) + (- 6x - 9)\|- 4x + 9 +--R 3 +--R (2) -------------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 6 4 | 2 8 6 4 \|- 4x + 9 - 3 +--R ((48x - 216x )\|- 4x + 9 + 16x - 288x + 648x )log(----------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 +--R (- 12x + 198x - 162x - 729)\|- 4x + 9 + 144x - 756x + 2187 +--R / +--R +---------+ +--R 6 4 | 2 8 6 4 +--R (1944x - 8748x )\|- 4x + 9 + 648x - 11664x + 26244x +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R 2log(----------------) + 2atanh(------------) +--R x 3 +--R (4) --------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1369 +t0:=x^5/sqrt(-9+4*x^2) +--R +--R +--R 5 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1369 +r0:=27/40*sqrt(-9+4*x^2)+3/20*x^2*sqrt(-9+4*x^2)+1/20*x^4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (2x + 6x + 27)\|4x - 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 1024x - 192x - 6804x + 34020x - 21870x)\|4x - 9 + 2048x +--R + +--R 8 6 4 2 +--R - 1920x + 11880x - 85050x + 109350x - 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1369 +t0:=x^4/sqrt(-9+4*x^2) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1369 +r0:=243/256*atanh(2*x/sqrt(-9+4*x^2))+27/128*x*sqrt(-9+4*x^2)+_ + 1/16*x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 3 | 2 +--R 243atanh(----------) + (16x + 54x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((- 15552x + 17496x)\|4x - 9 + 31104x - 69984x + 19683) +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 4 +--R (- 2048x - 2304x + 14256x - 4374x)\|4x - 9 + 4096x - 36288x +--R + +--R 2 +--R 34992x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (16384x - 18432x)\|4x - 9 - 32768x + 73728x - 20736 +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 243log(\|4x - 9 - 2x) - 243atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------------ +--R 256 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1369 +t0:=x^3/sqrt(-9+4*x^2) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1369 +r0:=3/8*sqrt(-9+4*x^2)+1/12*x^2*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2x + 9)\|4x - 9 +--R (2) ------------------- +--R 24 +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 64x - 180x + 486x)\|4x - 9 + 128x + 216x - 1458x + 729 +--R (3) ---------------------------------------------------------------- +--R +-------+ +--R 2 | 2 3 +--R (384x - 216)\|4x - 9 - 768x + 1296x +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1369 +t0:=x^2/sqrt(-9+4*x^2) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1369 +r0:=9/16*atanh(2*x/sqrt(-9+4*x^2))+1/8*x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x | 2 +--R 9atanh(----------) + 2x\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 36x\|4x - 9 + 72x - 81)log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x + 18x)\|4x - 9 + 32x - 72x +--R / +--R +-------+ +--R | 2 2 +--R 64x\|4x - 9 - 128x + 144 +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 9log(\|4x - 9 - 2x) - 9atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) -------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1369 +t0:=x/sqrt(-9+4*x^2) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1369 +r0:=1/4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------- +--R 4 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R - 2x\|4x - 9 + 4x - 9 +--R (3) ------------------------ +--R +-------+ +--R | 2 +--R 4\|4x - 9 - 8x +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1369 +t0:=1/sqrt(-9+4*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1369 +r0:=1/2*atanh(2*x/sqrt(-9+4*x^2)) +--R +--R +--R 2x +--R atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ----------------- +--R 2 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R (3) - -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - log(\|4x - 9 - 2x) - atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1369 +t0:=1/(x*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 2 +--R x\|4x - 9 +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1369 +r0:=1/3*atan(1/3*sqrt(-9+4*x^2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R atan(----------) +--R 3 +--R (2) ---------------- +--R 3 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R 2atan(---------------) +--R 3 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - atan(----------) + 2atan(---------------) +--R 3 3 +--R (4) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1369 +t0:=1/(x^2*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1369 +r0:=1/9*sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------- +--R 9x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------- +--R +-------+ +--R | 2 2 +--R x\|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1369 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - +--R 9 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1369 +t0:=1/(x^3*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1369 +r0:=2/27*atan(1/3*sqrt(-9+4*x^2))+1/18*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x - 9 | 2 +--R 4x atan(----------) + 3\|4x - 9 +--R 3 +--R (2) --------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-------+ | 2 +--R 3 | 2 4 2 \|4x - 9 - 2x +--R (32x \|4x - 9 - 64x + 72x )atan(---------------) +--R 3 +--R + +--R +-------+ +--R 2 | 2 3 +--R (- 24x + 27)\|4x - 9 + 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 216x \|4x - 9 - 432x + 486x +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1369 +t0:=1/(x^4*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1369 +r0:=1/27*sqrt(-9+4*x^2)/x^3+8/243*sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R 2 | 2 +--R (8x + 9)\|4x - 9 +--R (2) ------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R 2x\|4x - 9 - 4x + 3 +--R (3) ------------------------------------ +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x - 9x )\|4x - 9 - 32x + 54x +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1369 +m0:=a0-r0 +--R +--R +--R 16 +--R (4) --- +--R 243 +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1369 +t0:=1/(x^5*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1369 +r0:=2/81*atan(1/3*sqrt(-9+4*x^2))+1/36*sqrt(-9+4*x^2)/x^4+_ + 1/54*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x - 9 2 | 2 +--R 8x atan(----------) + (6x + 9)\|4x - 9 +--R 3 +--R (2) ----------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x ) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R atan(---------------) +--R 3 +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x + 576x + 2106x - 729)\|4x - 9 + 1536x - 2880x - 3888x +--R + +--R 5832x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (20736x - 23328x )\|4x - 9 - 41472x + 93312x - 26244x +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1369 +t0:=x^5/sqrt(-9-4*x^2) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1369 +r0:=-27/40*sqrt(-9-4*x^2)+3/20*x^2*sqrt(-9-4*x^2)-1/20*x^4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (- 2x + 6x - 27)\|- 4x - 9 +--R (2) ------------------------------ +--R 40 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 8 6 | 2 10 8 6 +---+ +--R (- 15x - 90x )\|- 4x - 9 + (4x + 105x + 270x )\|- 1 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860 +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 4 2 +---+ +--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1 +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1369 +t0:=x^4/sqrt(-9-4*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1369 +r0:=243/256*atan(2*x/sqrt(-9-4*x^2))+27/128*x*sqrt(-9-4*x^2)-_ + 1/16*x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 3 | 2 +--R 243atan(------------) + (- 16x + 54x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 7 5 3 | 2 +--R (- 32x - 468x + 648x + 4374x)\|- 4x - 9 +--R + +--R 7 5 3 +---+ +--R (384x + 1296x - 4860x - 13122x)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 +---+ | 2 4 2 +--R ((- 1458x - 6561)\|- 1 \|- 4x - 9 - 486x - 8748x - 19683) +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1369 +t0:=x^3/sqrt(-9-4*x^2) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1369 +r0:=3/8*sqrt(-9-4*x^2)-1/12*x^2*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2x + 9)\|- 4x - 9 +--R (2) ----------------------- +--R 24 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 2 6 4 +---+ +--R - 9x \|- 4x - 9 + (4x + 27x )\|- 1 +--R (3) -------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (12x + 108)\|- 1 \|- 4x - 9 + 108x + 324 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1 +--R (4) --------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (8x + 72)\|- 1 \|- 4x - 9 + 72x + 216 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1369 +t0:=x^2/sqrt(-9-4*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1369 +r0:=-9/16*atan(2*x/sqrt(-9-4*x^2))-1/8*x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x | 2 +--R - 9atan(------------) - 2x\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (- 4x - 18x)\|- 4x - 9 + (24x + 54x)\|- 1 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 48\|- 1 \|- 4x - 9 + 32x + 144 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 2x +--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 48\|- 1 \|- 4x - 9 + 32x + 144 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1369 +t0:=x/sqrt(-9-4*x^2) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1369 +r0:=-1/4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) - ------------ +--R 4 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +---+ +--R x \|- 1 +--R (3) ---------------------- +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +---+ +--R 3\|- 4x - 9 - 9\|- 1 +--R (4) ------------------------ +--R +---------+ +--R +---+ | 2 +--R 4\|- 1 \|- 4x - 9 + 12 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1369 +t0:=1/sqrt(-9-4*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1369 +r0:=1/2*atan(2*x/sqrt(-9-4*x^2)) +--R +--R +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------------ +--R 2 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R - \|- 1 log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1 +--R \|- 1 log(-------------------------------) +--R x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R - \|- 1 log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1 2x +--R \|- 1 log(-------------------------------) - atan(------------) +--R x +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R 2 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1369 +t0:=1/(x*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 2 +--R x\|- 4x - 9 +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1369 +r0:=1/3*atan(1/3*sqrt(-9-4*x^2)) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R atan(------------) +--R 3 +--R (2) ------------------ +--R 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 - 3\|- 1 +--R \|- 1 log(----------------------) +--R x +--R (3) - --------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 +---+ | 2 +--R +---+ \|- 4x - 9 - 3\|- 1 \|- 4x - 9 +--R - \|- 1 log(----------------------) - atan(------------) +--R x 3 +--R (4) -------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1369 +t0:=1/(x^2*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1369 +r0:=1/9*sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------ +--R 9x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---+ | 2 2 +--R - 3\|- 1 \|- 4x - 9 - 4x - 9 +--R (3) ------------------------------- +--R +---------+ +--R | 2 +---+ +--R 9x\|- 4x - 9 - 27x\|- 1 +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1369 +t0:=1/(x^3*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1369 +r0:=-2/27*atan(1/3*sqrt(-9-4*x^2))+1/18*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x - 9 | 2 +--R - 4x atan(------------) + 3\|- 4x - 9 +--R 3 +--R (2) --------------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +---+ +--R (6x + 27)\|- 4x - 9 + (- 36x - 81)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R 162x \|- 1 \|- 4x - 9 + 108x + 486x +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R +---+ | 2 2 \|- 4x - 9 +--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------) +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 81\|- 1 \|- 4x - 9 + 54x + 243 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1369 +t0:=1/(x^4*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1369 +r0:=1/27*sqrt(-9-4*x^2)/x^3-8/243*sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 8x + 9)\|- 4x - 9 +--R (2) ----------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 +---+ | 2 6 4 2 +--R (72x + 135x - 243)\|- 1 \|- 4x - 9 + 32x + 324x + 243x - 729 +--R (3) ------------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +---+ +--R (243x + 2187x )\|- 4x - 9 + (- 2187x - 6561x )\|- 1 +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1369 +t0:=1/(x^5*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 5 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1369 +r0:=2/81*atan(1/3*sqrt(-9-4*x^2))+1/36*sqrt(-9-4*x^2)/x^4-_ + 1/54*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x - 9 2 | 2 +--R 8x atan(------------) + (- 6x + 9)\|- 4x - 9 +--R 3 +--R (2) ----------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +---+ +--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 +---+ +--R (- 12x - 198x - 162x + 729)\|- 4x - 9 + (144x + 756x - 2187)\|- 1 +--R / +--R +---------+ +--R 6 4 +---+ | 2 8 6 4 +--R (1944x + 8748x )\|- 1 \|- 4x - 9 + 648x + 11664x + 26244x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 +---+ | 2 4 2 \|- 4x - 9 +--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------) +--R 3 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (486x + 2187)\|- 1 \|- 4x - 9 + 162x + 2916x + 6561 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1369 +t0:=1/sqrt(9+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + 9 +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1369 +r0:=asinh(1/3*x*sqrt(b))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asinh(-----) +--R 3 +--R (2) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 2 2 +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x +--R log(--------------------------------------------------) +--R +--------+ +--R | 2 +--R \|b x + 9 - 3 +--R [-------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +--R \|- b \|b x + 9 - 3\|- b +--R 2atan(---------------------------) +--R b x +--R ----------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1302 + +--S 1303 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R +-+ | 2 2 +-+ +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b +--R log(--------------------------------------------------) - asinh(-----) +--R +--------+ 3 +--R | 2 +--R \|b x + 9 - 3 +--R (4) ---------------------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b +--R 2\|b atan(---------------------------) - \|- b asinh(-----) +--R b x 3 +--R (6) ----------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1306 + +)clear all + +--S 1307 of 1369 +t0:=1/sqrt(9-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x + 9 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1369 +r0:=asin(1/3*x*sqrt(b))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asin(-----) +--R 3 +--R (2) ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R [----------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R | 2 +-+ +--R (\|- b x + 9 - 3)\|b +--R 2atan(-----------------------) +--R b x +--R - ------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1309 + +--S 1310 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R \|b log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(-----) +--R 3 +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R (\|- b x + 9 - 3)\|b x\|b +--R - 2atan(-----------------------) - asin(-----) +--R b x 3 +--R (6) ---------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1313 + +)clear all + +--S 1314 of 1369 +t0:=1/sqrt(-9+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x - 9 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(-9+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - 9 +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +---+ | 2 +--R +--------+ \|- b \|b x - 9 +--R +-+ | 2 2 atan(-----------------) +--R log(2x\|b \|b x - 9 + 2b x - 9) b x +--R (3) [----------------------------------,-----------------------] +--R +-+ +---+ +--R 2\|b \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1316 + +--S 1317 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +-+ +--R +-+ | 2 2 x\|b +--R log(2x\|b \|b x - 9 + 2b x - 9) - 2atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - 9 +--R (4) -------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +--R +---+ x\|b +-+ \|- b \|b x - 9 +--R - \|- b atanh(-----------) + \|b atan(-----------------) +--R +--------+ b x +--R | 2 +--R \|b x - 9 +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1369 +t0:=1/sqrt(-9-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1369 +r0:=atan(x*sqrt(b)/sqrt(-9-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R | 2 +-+ +--R +----------+ \|- b x - 9 \|b +--R | 2 +---+ 2 atan(-----------------) +--R log(2x\|- b x - 9 \|- b - 2b x - 9) b x +--R (3) [--------------------------------------,- -----------------------] +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +-+ +--R +-+ | 2 +---+ 2 +---+ x\|b +--R \|b log(2x\|- b x - 9 \|- b - 2b x - 9) - 2\|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R \|- b x - 9 \|b x\|b +--R - atan(-----------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x - 9 +--R (6) ----------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 1369 +t0:=1/sqrt(%pi+b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|b x + %pi +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1369 +r0:=asinh(x*sqrt(b)/sqrt(%pi))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asinh(------) +--R +---+ +--R \|%pi +--R (2) ------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R [---------------------------------------------------------------------, +--R +-+ +--R \|b +--R +----------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x + %pi - \|- b \|%pi +--R 2atan(----------------------------------) +--R b x +--R -----------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R + +--R +-+ +--R x\|b +--R - asinh(------) +--R +---+ +--R \|%pi +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1369 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +----------+ +--R | 2 +--R 2 2 +-+ +---+ 2 3 2 |b x + %pi +--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |---------- +--R \| %pi +--R + +--R 2 4 2 2 +-+ +---+ 2 3 2 +--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R \|b x + %pi +--R + +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R + +--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+ +--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b +--R / +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R |---------- \|b x + %pi +--R \| %pi +--R + +--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3 +--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x +--R + +--R 3 +--R - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +---+ | 2 +---+ +---+ +-+ +--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b +--R 2\|b atan(----------------------------------) - \|- b asinh(------) +--R b x +---+ +--R \|%pi +--R (6) ------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1369 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +----------+ +--R +----------+ | 2 +--R +---+ | 2 |b x + %pi +--R - \|%pi \|b x + %pi + %pi |---------- +--R \| %pi +--R (7) ---------------------------------------- +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R %pi |---------- \|b x + %pi +--R \| %pi +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1369 +t0:=1/sqrt(%pi-b*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|- b x + %pi +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1369 +r0:=asin(x*sqrt(b)/sqrt(%pi))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asin(------) +--R +---+ +--R \|%pi +--R (2) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R / +--R +---+ +--R \|- b +--R , +--R +------------+ +--R +-+ +---+ | 2 +-+ +--R \|b \|%pi - \|- b x + %pi \|b +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(------) +--R +---+ +--R \|%pi +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------+ +--R +------------+ | 2 +--R 2 2 | 2 |- b x + %pi +--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 4 2 2 | 2 +--R (b x - 5b %pi x + 4%pi )\|- b x + %pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R | 2 +--R 2 3 2 |- b x + %pi 3 5 2 3 2 +--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi 2 4 +--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x +--R \| %pi +--R + +--R 2 2 3 +--R 7b %pi x - 4%pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 3 2 | 2 +--R (- 3b %pi x + 4b %pi x)\|- b x + %pi +--R / +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi +---+ +--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 4 2 2 3 | 2 |- b x + %pi +---+ +--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R | 2 +--R 3 5 2 2 3 3 |- b x + %pi +--R (b %pi x - 5b %pi x + 4b %pi x) |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------------+ +--R +-+ +---+ | 2 +-+ +-+ +--R \|b \|%pi - \|- b x + %pi \|b x\|b +--R 2atan(--------------------------------) - asin(------) +--R b x +---+ +--R \|%pi +--R (6) ------------------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1369 +d0b:=D(m0b,x) +--R +--R +--R +------------+ +--R +------------+ | 2 +--R | 2 +---+ |- b x + %pi +--R - \|- b x + %pi \|%pi + %pi |------------ +--R \| %pi +--R (7) -------------------------------------------- +--R +------------+ +--R +------------+ | 2 +--R | 2 |- b x + %pi +--R %pi\|- b x + %pi |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 1369 +t0:=1/sqrt(-%pi+b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|b x - %pi +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(-%pi+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|b x - %pi +--R (2) -------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R +---+ | 2 +--R +----------+ \|- b \|b x - %pi +--R +-+ | 2 2 atan(-------------------) +--R log(2x\|b \|b x - %pi + 2b x - %pi) b x +--R (3) [--------------------------------------,-------------------------] +--R +-+ +---+ +--R 2\|b \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R +-+ | 2 2 x\|b +--R log(2x\|b \|b x - %pi + 2b x - %pi) - 2atanh(-------------) +--R +----------+ +--R | 2 +--R \|b x - %pi +--R (4) -------------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R +---+ x\|b +-+ \|- b \|b x - %pi +--R - \|- b atanh(-------------) + \|b atan(-------------------) +--R +----------+ b x +--R | 2 +--R \|b x - %pi +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 1369 +t0:=1/sqrt(-%pi-b*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1369 +r0:=atan(x*sqrt(b)/sqrt(-%pi-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(---------------) +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R (2) --------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 +-+ +--R +------------+ \|- b x - %pi \|b +--R | 2 +---+ 2 atan(-------------------) +--R log(2x\|- b x - %pi \|- b - 2b x - %pi) b x +--R [------------------------------------------,- -------------------------] +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1351 + +--S 1352 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------+ +-+ +--R +-+ | 2 +---+ 2 +---+ x\|b +--R \|b log(2x\|- b x - %pi \|- b - 2b x - %pi) - 2\|- b atan(---------------) +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R ----------------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------------+ +--R | 2 +-+ +-+ +--R \|- b x - %pi \|b x\|b +--R - atan(-------------------) - atan(---------------) +--R b x +------------+ +--R | 2 +--R \|- b x - %pi +--R (6) --------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1355 + +)clear all + +--S 1356 of 1369 +t0:=1/sqrt(a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R [-------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R 2atan(------------------------------) +--R b x +--R -------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1358 + +--S 1359 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1362 + +)clear all + +--S 1363 of 1369 +t0:=1/sqrt(a-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x + a +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1369 +r0:=atan(x*sqrt(b)/sqrt(a-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x + a +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b + b x\|- b x + a +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- b x + a \|a - a +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R +-+ | 2 +-+ +--R (\|a - \|- b x + a )\|b +--R 2atan(--------------------------) +--R b x +--R ---------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1365 + +--S 1366 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b +--R + +--R +----------+ +--R | 2 +--R b x\|- b x + a +--R / +--R +----------+ +--R | 2 +-+ +--R \|- b x + a \|a - a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x + a +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ | 2 +-+ +-+ +--R (\|a - \|- b x + a )\|b x\|b +--R 2atan(--------------------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x + a +--R (6) ------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1369 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4b.input.pdf b/src/axiom-website/CATS/rich4b.input.pdf new file mode 100644 index 0000000..5c18802 Binary files /dev/null and b/src/axiom-website/CATS/rich4b.input.pdf differ diff --git a/src/axiom-website/CATS/rich4c.input.pamphlet b/src/axiom-website/CATS/rich4c.input.pamphlet new file mode 100644 index 0000000..ea77292 --- /dev/null +++ b/src/axiom-website/CATS/rich4c.input.pamphlet @@ -0,0 +1,16055 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 257 supplied "optimal results". +\item 187 matching answers. +\item 2 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 70 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4c.output +)spool rich4c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1285 +t0:=1/sqrt(-a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x - a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1285 +r0:=atanh(x*sqrt(b)/sqrt(-a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +---+ +-+ | 2 2 +-+ +---+ +--R (\|- a \|b - b x)\|b x - a + (- b x + a)\|b + b x\|- a +--R log(------------------------------------------------------------) +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R [-----------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x - a - \|- b \|- a +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1285 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +---+ +-+ | 2 2 +-+ +---+ +--R (\|- a \|b - b x)\|b x - a + (- b x + a)\|b + b x\|- a +--R log(------------------------------------------------------------) +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1285 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1285 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +---+ +--R +---+ x\|b +-+ \|- b \|b x - a - \|- b \|- a +--R - \|- b atanh(-----------) + 2\|b atan(--------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x - a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1285 +t0:=1/sqrt(-a-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x - a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1285 +r0:=atan(x*sqrt(b)/sqrt(-a-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - a +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +---+ 2 +---+ | 2 +--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b + b x\|- b x - a +--R log(-----------------------------------------------------------------------) +--R +----------+ +--R | 2 +---+ +--R \|- b x - a \|- a + a +--R [---------------------------------------------------------------------------- +--R +---+ +--R \|- b +--R , +--R +----------+ +--R +---+ | 2 +-+ +--R (\|- a - \|- b x - a )\|b +--R 2atan(----------------------------) +--R b x +--R -----------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1285 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b +--R + +--R +----------+ +--R | 2 +--R b x\|- b x - a +--R / +--R +----------+ +--R | 2 +---+ +--R \|- b x - a \|- a + a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - a +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1285 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1285 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +---+ | 2 +-+ +-+ +--R (\|- a - \|- b x - a )\|b x\|b +--R 2atan(----------------------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x - a +--R (6) --------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1285 +t0:=1/sqrt(a^2-x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1285 +r0:=atan(x/sqrt(a^2-x^2)) +--R +--R +--R x +--R (2) atan(------------) +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R (3) - 2atan(----------------) +--R x +--R Type: Union(Expression(Integer),...) +--E 17 + +--S 18 of 1285 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a x +--R (4) - 2atan(----------------) - atan(------------) +--R x +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 19 + +)clear all + +--S 20 of 1285 +t0:=x^(3+m)/sqrt(a+b*x^2) +--R +--R +--R m + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1285 +--r0:=x^(2+m)*sqrt(a+b*x^2)/(b*(3+m))-a*x^(2+m)*_ +--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*sqrt((a+b*x^2)/a)/_ +--(b*(3+m)*sqrt(a+b*x^2)) +--E 21 + +--S 22 of 1285 +--a0:=integrate(t0,x) +--E 22 + +--S 23 of 1285 +--m0:=a0-r0 +--E 23 + +--S 24 of 1285 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 1285 +t0:=x^(2+m)/sqrt(a+b*x^2) +--R +--R +--R m + 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1285 +--r0:=x^(1+m)*sqrt(a+b*x^2)/(b*(2+m))-a*x^(1+m)*_ +--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(b*(2+m)*sqrt(a+b*x^2)) +--E 26 + +--S 27 of 1285 +--a0:=integrate(t0,x) +--E 27 + +--S 28 of 1285 +--m0:=a0-r0 +--E 28 + +--S 29 of 1285 +--d0:=D(m0,x) +--E 29 + +)clear all + +--S 30 of 1285 +t0:=x^(1+m)/sqrt(a+b*x^2) +--R +--R +--R m + 1 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1285 +--r0:=x^(2+m)*hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/((2+m)*sqrt(a+b*x^2)) +--E 31 + +--S 32 of 1285 +--a0:=integrate(t0,x) +--E 32 + +--S 33 of 1285 +--m0:=a0-r0 +--E 33 + +--S 34 of 1285 +--d0:=D(m0,x) +--E 34 + +)clear all + +--S 35 of 1285 +t0:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1285 +--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2)) +--E 36 + +--S 37 of 1285 +--a0:=integrate(t0,x) +--E 37 + +--S 38 of 1285 +--m0:=a0-r0 +--E 38 + +--S 39 of 1285 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 1285 +t0:=x^(-1+m)/sqrt(a+b*x^2) +--R +--R +--R m - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1285 +--r0:=x^m*sqrt(a+b*x^2)/(a*m)-b*(1+m)*x^(2+m)*_ +--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(a*m*(2+m)*sqrt(a+b*x^2)) +--E 41 + +--S 42 of 1285 +--a0:=integrate(t0,x) +--E 42 + +--S 43 of 1285 +--m0:=a0-r0 +--E 43 + +--S 44 of 1285 +--d0:=D(m0,x) +--E 44 + +)clear all + +--S 45 of 1285 +t0:=x^(-2+m)/sqrt(a+b*x^2) +--R +--R +--R m - 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 45 + +--S 46 of 1285 +--r0:=-x^(-1+m)*sqrt(a+b*x^2)/(a*(1-m))+b*m*x^(1+m)*_ +--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(a*(1-m^2)*sqrt(a+b*x^2)) +--E 46 + +--S 47 of 1285 +--a0:=integrate(t0,x) +--E 47 + +--S 48 of 1285 +--m0:=a0-r0 +--E 48 + +--S 49 of 1285 +--d0:=D(m0,x) +--E 49 + +)clear all + +--S 50 of 1285 +t0:=x^(1+m)*(a*(2+m)+b*(3+m)*x^2)/sqrt(a+b*x^2) +--R +--R +--R 2 m + 1 +--R ((b m + 3b)x + a m + 2a)x +--R (1) ------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1285 +r0:=x^(2+m)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (2) x \|b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 52 + +--S 53 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 1285 +t0:=a*(2+m)*x^(1+m)/sqrt(a+b*x^2)+b*(3+m)*x^(3+m)/sqrt(a+b*x^2) +--R +--R +--R m + 3 m + 1 +--R (b m + 3b)x + (a m + 2a)x +--R (1) ----------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1285 +r0:=x^(2+m)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (2) x \|b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 57 + +--S 58 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 59 + +)clear all + +--S 60 of 1285 +t0:=x^(-1+m)*(a*m+b*(-1+m)*x^2)/(a+b*x^2)^(3/2) +--R +--R +--R 2 m - 1 +--R ((b m - b)x + a m)x +--R (1) ------------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1285 +r0:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ (m - 1)log(x) +--R (- x\|b x + a + x\|a )%e +--R (3) --------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R Type: Union(Expression(Integer),...) +--E 62 + +--S 63 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2 +--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a +--R + +--R 2 m +--R (- b x - a)x +--R / +--R +--------+ +--R 2 | 2 2 +-+ +--R (b x + a)\|b x + a + (- b x - a)\|a +--R Type: Expression(Integer) +--E 63 + +--S 64 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 64 + +)clear all + +--S 65 of 1285 +t0:=-b*x^(1+m)/(a+b*x^2)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^2) +--R +--R +--R m + 1 2 m - 1 +--R - b x + (b m x + a m)x +--R (1) --------------------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1285 +r0a:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1285 +r0b:=-b*x^(2+m)/(a*sqrt(a+b*x^2))+x^m*sqrt(a+b*x^2)/a +--R +--R +--R m + 2 2 m +--R - b x + (b x + a)x +--R (3) ------------------------- +--R +--------+ +--R | 2 +--R a\|b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ (m - 1)log(x) +--R (- x\|b x + a + x\|a )%e +--R (4) --------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1285 +m0a:=a0-r0a +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2 +--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a +--R + +--R 2 m +--R (- b x - a)x +--R / +--R +--------+ +--R 2 | 2 2 +-+ +--R (b x + a)\|b x + a + (- b x - a)\|a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1285 +--d0:=normalize m0a +--E 70 + +--S 71 of 1285 +m0b:=a0-r0b +--R +--R +--R (6) +--R +--------+ +--R +-+ | 2 3 2 (m - 1)log(x) +--R (- a x\|a \|b x + a + a b x + a x)%e +--R + +--R +--------+ +--R m + 2 2 m +-+ | 2 2 2 m + 2 +--R (- b x + (b x + a)x )\|a \|b x + a + (b x + a b)x +--R + +--R 2 4 2 2 m +--R (- b x - 2a b x - a )x +--R / +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + a )\|b x + a + (- a b x - a )\|a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1285 +--d0:=normalize m0b +--E 72 + +)clear all + +--S 73 of 1285 +t0:=x*(-1+x^2)^(7/3) +--R +--R +--R +------+ +--R 5 3 3| 2 +--R (1) (x - 2x + x)\|x - 1 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 1285 +r0:=3/20*(-1+x^2)^(10/3) +--R +--R +--R +------+ +--R 6 4 2 3| 2 +--R (3x - 9x + 9x - 3)\|x - 1 +--R (2) ------------------------------ +--R 20 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 6 4 2 3| 2 +--R (3x - 9x + 9x - 3)\|x - 1 +--R (3) ------------------------------ +--R 20 +--R Type: Union(Expression(Integer),...) +--E 75 + +--S 76 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 77 + +)clear all + +--S 78 of 1285 +t0:=x*(1+x^2)^(1/3) +--R +--R +--R +------+ +--R 3| 2 +--R (1) x\|x + 1 +--R Type: Expression(Integer) +--E 78 + +--S 79 of 1285 +r0:=3/8*(1+x^2)^(4/3) +--R +--R +--R +------+ +--R 2 3| 2 +--R (3x + 3)\|x + 1 +--R (2) ------------------ +--R 8 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 2 3| 2 +--R (3x + 3)\|x + 1 +--R (3) ------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 80 + +--S 81 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 82 + +)clear all + +--S 83 of 1285 +t0:=x*(1-x^2)^(1/3) +--R +--R +--R +--------+ +--R 3| 2 +--R (1) x\|- x + 1 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1285 +r0:=-3/8*(1-x^2)^(4/3) +--R +--R +--R +--------+ +--R 2 3| 2 +--R (3x - 3)\|- x + 1 +--R (2) -------------------- +--R 8 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 3| 2 +--R (3x - 3)\|- x + 1 +--R (3) -------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 85 + +--S 86 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 1285 +t0:=x^3*(1+x^2)^(1/3) +--R +--R +--R +------+ +--R 3 3| 2 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 1285 +r0:=-3/8*(1+x^2)^(4/3)+3/14*(1+x^2)^(7/3) +--R +--R +--R +------+ +--R 4 2 3| 2 +--R (12x + 3x - 9)\|x + 1 +--R (2) ------------------------- +--R 56 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 4 2 3| 2 +--R (12x + 3x - 9)\|x + 1 +--R (3) ------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 90 + +--S 91 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 92 + +)clear all + +--S 93 of 1285 +t0:=x/(3+2*x^2)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R 3| 2 +--R \|2x + 3 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1285 +r0:=3/8*(3+2*x^2)^(2/3) +--R +--R +--R +-------+2 +--R 3| 2 +--R 3\|2x + 3 +--R (2) ------------ +--R 8 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +-------+2 +--R 3| 2 +--R 3\|2x + 3 +--R (3) ------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 97 + +)clear all + +--S 98 of 1285 +t0:=x^3/(4+x^2)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 2 +--R \|x + 4 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1285 +r0:=-9/5*(4+x^2)^(2/3)+3/10*x^2*(4+x^2)^(2/3) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (3x - 18)\|x + 4 +--R (2) -------------------- +--R 10 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (3x - 18)\|x + 4 +--R (3) -------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 100 + +--S 101 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 1285 +t0:=x^3/(1+x^2)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1285 +r0:=-9/20*(1+x^2)^(2/3)+3/10*x^2*(1+x^2)^(2/3) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (6x - 9)\|x + 1 +--R (2) ------------------- +--R 20 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (6x - 9)\|x + 1 +--R (3) ------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 107 + +)clear all + +--S 108 of 1285 +t0:=x^3/(-1+x^2)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ----------------- +--R +------+ +--R 2 3| 2 +--R (x - 1)\|x - 1 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1285 +r0:=(-3/2)/(-1+x^2)^(1/3)+3/4*(-1+x^2)^(2/3) +--R +--R +--R 2 +--R 3x - 9 +--R (2) ---------- +--R +------+ +--R 3| 2 +--R 4\|x - 1 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 3x - 9 +--R (3) ---------- +--R +------+ +--R 3| 2 +--R 4\|x - 1 +--R Type: Union(Expression(Integer),...) +--E 110 + +--S 111 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 112 + +)clear all + +--S 113 of 1285 +t0:=x^(7/2)*(a+b*x^2) +--R +--R +--R 5 3 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1285 +r0:=2/9*a*x^(9/2)+2/13*b*x^(13/2) +--R +--R +--R 6 4 +-+ +--R (18b x + 26a x )\|x +--R (2) --------------------- +--R 117 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 6 4 +-+ +--R (18b x + 26a x )\|x +--R (3) --------------------- +--R 117 +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1285 +t0:=x^(5/2)*(a+b*x^2) +--R +--R +--R 4 2 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 118 + +--S 119 of 1285 +r0:=2/7*a*x^(7/2)+2/11*b*x^(11/2) +--R +--R +--R 5 3 +-+ +--R (14b x + 22a x )\|x +--R (2) --------------------- +--R 77 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 3 +-+ +--R (14b x + 22a x )\|x +--R (3) --------------------- +--R 77 +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 1285 +t0:=x^(3/2)*(a+b*x^2) +--R +--R +--R 3 +-+ +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1285 +r0:=2/5*a*x^(5/2)+2/9*b*x^(9/2) +--R +--R +--R 4 2 +-+ +--R (10b x + 18a x )\|x +--R (2) --------------------- +--R 45 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +-+ +--R (10b x + 18a x )\|x +--R (3) --------------------- +--R 45 +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 1285 +t0:=(a+b*x^2)*sqrt(x) +--R +--R +--R 2 +-+ +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1285 +r0:=2/3*a*x^(3/2)+2/7*b*x^(7/2) +--R +--R +--R 3 +-+ +--R (6b x + 14a x)\|x +--R (2) ------------------- +--R 21 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ +--R (6b x + 14a x)\|x +--R (3) ------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1285 +t0:=(a+b*x^2)/sqrt(x) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1285 +r0:=2/5*b*x^(5/2)+2*a*sqrt(x) +--R +--R +--R 2 +-+ +--R (2b x + 10a)\|x +--R (2) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (2b x + 10a)\|x +--R (3) ----------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 135 + +--S 136 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 1285 +t0:=(a+b*x^2)/x^(3/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1285 +r0:=2/3*b*x^(3/2)-2*a/sqrt(x) +--R +--R +--R 2 +--R 2b x - 6a +--R (2) ---------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x - 6a +--R (3) ---------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 140 + +--S 141 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 142 + +)clear all + +--S 143 of 1285 +t0:=(a+b*x^2)/x^(5/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1285 +r0:=-2/3*a/x^(3/2)+2*b*sqrt(x) +--R +--R +--R 2 +--R 6b x - 2a +--R (2) ---------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 6b x - 2a +--R (3) ---------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 1285 +t0:=(a+b*x^2)/x^(7/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1285 +r0:=-2/5*a/x^(5/2)-2*b/sqrt(x) +--R +--R +--R 2 +--R - 10b x - 2a +--R (2) ------------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 10b x - 2a +--R (3) ------------- +--R 2 +-+ +--R 5x \|x +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 152 + +)clear all + +--S 153 of 1285 +t0:=x^(7/2)*(a+b*x^2)^2 +--R +--R +--R 2 7 5 2 3 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1285 +r0:=2/9*a^2*x^(9/2)+4/13*a*b*x^(13/2)+2/17*b^2*x^(17/2) +--R +--R +--R 2 8 6 2 4 +-+ +--R (234b x + 612a b x + 442a x )\|x +--R (2) ----------------------------------- +--R 1989 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 8 6 2 4 +-+ +--R (234b x + 612a b x + 442a x )\|x +--R (3) ----------------------------------- +--R 1989 +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 1285 +t0:=x^(5/2)*(a+b*x^2)^2 +--R +--R +--R 2 6 4 2 2 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1285 +r0:=2/7*a^2*x^(7/2)+4/11*a*b*x^(11/2)+2/15*b^2*x^(15/2) +--R +--R +--R 2 7 5 2 3 +-+ +--R (154b x + 420a b x + 330a x )\|x +--R (2) ----------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 7 5 2 3 +-+ +--R (154b x + 420a b x + 330a x )\|x +--R (3) ----------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 1285 +t0:=x^(3/2)*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +-+ +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1285 +r0:=2/5*a^2*x^(5/2)+4/9*a*b*x^(9/2)+2/13*b^2*x^(13/2) +--R +--R +--R 2 6 4 2 2 +-+ +--R (90b x + 260a b x + 234a x )\|x +--R (2) ---------------------------------- +--R 585 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 4 2 2 +-+ +--R (90b x + 260a b x + 234a x )\|x +--R (3) ---------------------------------- +--R 585 +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 1285 +t0:=(a+b*x^2)^2*sqrt(x) +--R +--R +--R 2 4 2 2 +-+ +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1285 +r0:=2/3*a^2*x^(3/2)+4/7*a*b*x^(7/2)+2/11*b^2*x^(11/2) +--R +--R +--R 2 5 3 2 +-+ +--R (42b x + 132a b x + 154a x)\|x +--R (2) --------------------------------- +--R 231 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 2 +-+ +--R (42b x + 132a b x + 154a x)\|x +--R (3) --------------------------------- +--R 231 +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 1285 +t0:=(a+b*x^2)^2/sqrt(x) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1285 +r0:=4/5*a*b*x^(5/2)+2/9*b^2*x^(9/2)+2*a^2*sqrt(x) +--R +--R +--R 2 4 2 2 +-+ +--R (10b x + 36a b x + 90a )\|x +--R (2) ------------------------------ +--R 45 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +-+ +--R (10b x + 36a b x + 90a )\|x +--R (3) ------------------------------ +--R 45 +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1285 +t0:=(a+b*x^2)^2/x^(3/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1285 +r0:=4/3*a*b*x^(3/2)+2/7*b^2*x^(7/2)-2*a^2/sqrt(x) +--R +--R +--R 2 4 2 2 +--R 6b x + 28a b x - 42a +--R (2) ----------------------- +--R +-+ +--R 21\|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 6b x + 28a b x - 42a +--R (3) ----------------------- +--R +-+ +--R 21\|x +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 1285 +t0:=(a+b*x^2)^2/x^(5/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1285 +r0:=-2/3*a^2/x^(3/2)+2/5*b^2*x^(5/2)+4*a*b*sqrt(x) +--R +--R +--R 2 4 2 2 +--R 6b x + 60a b x - 10a +--R (2) ----------------------- +--R +-+ +--R 15x\|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 6b x + 60a b x - 10a +--R (3) ----------------------- +--R +-+ +--R 15x\|x +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 1285 +t0:=(a+b*x^2)^2/x^(7/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1285 +r0:=-2/5*a^2/x^(5/2)+2/3*b^2*x^(3/2)-4*a*b/sqrt(x) +--R +--R +--R 2 4 2 2 +--R 10b x - 60a b x - 6a +--R (2) ----------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 10b x - 60a b x - 6a +--R (3) ----------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1285 +t0:=x^(7/2)*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1285 +r0:=2/9*a^3*x^(9/2)+6/13*a^2*b*x^(13/2)+6/17*a*b^2*x^(17/2)+2/21*b^3*x^(21/2) +--R +--R +--R 3 10 2 8 2 6 3 4 +-+ +--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x +--R (2) ---------------------------------------------------- +--R 13923 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 10 2 8 2 6 3 4 +-+ +--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x +--R (3) ---------------------------------------------------- +--R 13923 +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 1285 +t0:=x^(5/2)*(a+b*x^2)^3 +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1285 +r0:=2/7*a^3*x^(7/2)+6/11*a^2*b*x^(11/2)+2/5*a*b^2*x^(15/2)+2/19*b^3*x^(19/2) +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x +--R (2) -------------------------------------------------- +--R 7315 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x +--R (3) -------------------------------------------------- +--R 7315 +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 1285 +t0:=x^(3/2)*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1285 +r0:=2/5*a^3*x^(5/2)+2/3*a^2*b*x^(9/2)+6/13*a*b^2*x^(13/2)+2/17*b^3*x^(17/2) +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x +--R (2) -------------------------------------------------- +--R 3315 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x +--R (3) -------------------------------------------------- +--R 3315 +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1285 +t0:=(a+b*x^2)^3*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1285 +r0:=2/3*a^3*x^(3/2)+6/7*a^2*b*x^(7/2)+6/11*a*b^2*x^(11/2)+2/15*b^3*x^(15/2) +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (154b x + 630a b x + 990a b x + 770a x)\|x +--R (2) ---------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (154b x + 630a b x + 990a b x + 770a x)\|x +--R (3) ---------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 1285 +t0:=(a+b*x^2)^3/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1285 +r0:=6/5*a^2*b*x^(5/2)+2/3*a*b^2*x^(9/2)+2/13*b^3*x^(13/2)+2*a^3*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (30b x + 130a b x + 234a b x + 390a )\|x +--R (2) -------------------------------------------- +--R 195 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (30b x + 130a b x + 234a b x + 390a )\|x +--R (3) -------------------------------------------- +--R 195 +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1285 +t0:=(a+b*x^2)^3/x^(3/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1285 +r0:=2*a^2*b*x^(3/2)+6/7*a*b^2*x^(7/2)+2/11*b^3*x^(11/2)-2*a^3/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 14b x + 66a b x + 154a b x - 154a +--R (2) ------------------------------------- +--R +-+ +--R 77\|x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 14b x + 66a b x + 154a b x - 154a +--R (3) ------------------------------------- +--R +-+ +--R 77\|x +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1285 +t0:=(a+b*x^2)^3/x^(5/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1285 +r0:=-2/3*a^3/x^(3/2)+6/5*a*b^2*x^(5/2)+2/9*b^3*x^(9/2)+6*a^2*b*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 54a b x + 270a b x - 30a +--R (2) ------------------------------------ +--R +-+ +--R 45x\|x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 54a b x + 270a b x - 30a +--R (3) ------------------------------------ +--R +-+ +--R 45x\|x +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 1285 +t0:=(a+b*x^2)^3/x^(7/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1285 +r0:=-2/5*a^3/x^(5/2)+2*a*b^2*x^(3/2)+2/7*b^3*x^(7/2)-6*a^2*b/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 70a b x - 210a b x - 14a +--R (2) ------------------------------------ +--R 2 +-+ +--R 35x \|x +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 70a b x - 210a b x - 14a +--R (3) ------------------------------------ +--R 2 +-+ +--R 35x \|x +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 1285 +t0:=x^(7/2)/(a+b*x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1285 +r0:=2/5*x^(5/2)/b-a^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_ + sqrt(2))+a^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_ + sqrt(2))-1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(b^(9/4)*sqrt(2))+1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-2*a*sqrt(x)/b^2 +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5a\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5a\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10a\|a atan(-------------------) + 10a\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 2 +-+4+-+ +-+ +--R (4b x - 20a)\|2 \|b \|x +--R / +--R 2 +-+4+-+ +--R 10b \|2 \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +--R | 5 | 5 +--R 2 | a +-+ 2 | a +--R 5b |- ---- log(a\|x + 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R +------+ +--R | 5 +--R 2 | a +--R +------+ +------+ +------+ 2b |- ---- +--R | 5 | 5 | 5 4| 9 +--R 2 | a +-+ 2 | a 2 | a \| 16b +--R - 5b |- ---- log(a\|x - 2b |- ---- - 10b |- ---- atan(------------) +--R 4| 9 4| 9 4| 9 +-+ +--R \| 16b \| 16b \| 16b a\|x +--R + +--R 2 +-+ +--R (2b x - 10a)\|x +--R / +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - a\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R | 5 | 5 +--R 2 +-+ | a 4+-+ +-+ 2 | a +--R 2b \|2 |- ---- \|b log(a\|x + 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R +------+ +------+ +--R | 5 | 5 +--R 2 +-+ | a 4+-+ +-+ 2 | a +--R - 2b \|2 |- ---- \|b log(a\|x - 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R a\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2a\|a atan(-------------------) - 2a\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | 5 +--R 2 | a +--R +------+ 2b |- ---- +--R | 5 4| 9 +--R 2 +-+ | a 4+-+ \| 16b +--R - 4b \|2 |- ---- \|b atan(------------) +--R 4| 9 +-+ +--R \| 16b a\|x +--R / +--R 2 +-+4+-+ +--R 2b \|2 \|b +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1285 +t0:=x^(5/2)/(a+b*x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1285 +r0:=2/3*x^(3/2)/b+a^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_ + sqrt(2))-a^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_ + sqrt(2))-1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(b^(7/4)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 3\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R - 6\|a atan(-------------------) - 6\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +-+ +--R 4x\|2 \|b \|x +--R / +--R +-+4+-+3 +--R 6b\|2 \|b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | 3 | 3 +--R | a 2 +-+ 5 | a +--R - 3b |- ---- log(a \|x + 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R +------+3 +--R | 3 +--R 5 | a +--R +------+ +------+3 +------+ 8b |- ---- +--R | 3 | 3 | 3 4| 7 +--R | a 2 +-+ 5 | a | a \| 16b +--R 3b |- ---- log(a \|x - 8b |- ---- - 6b |- ---- atan(-------------) +--R 4| 7 4| 7 4| 7 2 +-+ +--R \| 16b \| 16b \| 16b a \|x +--R + +--R +-+ +--R 2x\|x +--R / +--R 3b +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R | 3 | 3 +--R +-+ | a 4+-+3 2 +-+ 5 | a +--R - 2b\|2 |- ---- \|b log(a \|x + 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R +------+ +------+3 +--R | 3 | 3 +--R +-+ | a 4+-+3 2 +-+ 5 | a +--R 2b\|2 |- ---- \|b log(a \|x - 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 2\|a atan(-------------------) + 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R | 3 +--R 5 | a +--R +------+ 8b |- ---- +--R | 3 4| 7 +--R +-+ | a 4+-+3 \| 16b +--R - 4b\|2 |- ---- \|b atan(-------------) +--R 4| 7 2 +-+ +--R \| 16b a \|x +--R / +--R +-+4+-+3 +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1285 +t0:=x^(3/2)/(a+b*x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1285 +r0:=a^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))-_ + a^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))+_ + 1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (b^(5/4)*sqrt(2))-1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(b^(5/4)*sqrt(2))+2*sqrt(x)/b +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2\|a atan(-------------------) - 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +-+ +--R 4\|2 \|b \|x +--R / +--R +-+4+-+ +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +------+ +--R | a +-+ | a | a +-+ | a +--R - b |- ---- log(\|x + 2b |- ---- + b |- ---- log(\|x - 2b |- ----) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 16b \| 16b \| 16b \| 16b +--R + +--R +------+ +--R | a +--R 2b |- ---- +--R +------+ 4| 5 +--R | a \| 16b +-+ +--R 2b |- ---- atan(----------- + 2\|x +--R 4| 5 +-+ +--R \| 16b \|x +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R +-+ | a 4+-+ +-+ | a +--R - 2b\|2 |- ---- \|b log(\|x + 2b |- ----) +--R 4| 5 4| 5 +--R \| 16b \| 16b +--R + +--R +------+ +------+ +--R +-+ | a 4+-+ +-+ | a +--R 2b\|2 |- ---- \|b log(\|x - 2b |- ----) +--R 4| 5 4| 5 +--R \| 16b \| 16b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 2\|a atan(-------------------) + 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | a +--R 2b |- ---- +--R +------+ 4| 5 +--R +-+ | a 4+-+ \| 16b +--R 4b\|2 |- ---- \|b atan(-----------) +--R 4| 5 +-+ +--R \| 16b \|x +--R / +--R +-+4+-+ +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 1285 +t0:=sqrt(x)/(a+b*x^2) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1285 +r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_ + b^(3/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(1/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R 2atan(-------------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R | 1 +-+ 2 | 1 +--R |- ------ log(\|x + 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+ +--------+3 +--R | 1 +-+ 2 | 1 +--R - |- ------ log(\|x - 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+3 +--R 2 | 1 +--R 8a b |- ------ +--R +--------+ 4| 3 +--R | 1 \| 16a b +--R 2 |- ------ atan(-----------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1 +--R 2\|2 |- ------ \|a \|b log(\|x + 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+ +--------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1 +--R - 2\|2 |- ------ \|a \|b log(\|x - 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------+3 +--R 2 | 1 +--R 8a b |- ------ +--R +--------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 16a b +--R 4\|2 |- ------ \|a \|b atan(-----------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R / +--R +-+4+-+4+-+3 +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 1285 +t0:=1/((a+b*x^2)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R 2 +-+ +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1285 +r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_ + atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_ + 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_ + b^(1/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(3/4)*b^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R 2atan(-------------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 4+-+ +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | 1 +-+ | 1 | 1 +-+ | 1 +--R |- ----- log(\|x + 2a |- -----) - |- ----- log(\|x - 2a |- -----) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 16a b \| 16a b \| 16a b \| 16a b +--R + +--R +-------+ +--R | 1 +--R 2a |- ----- +--R +-------+ 4| 3 +--R | 1 \| 16a b +--R - 2 |- ----- atan(------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R 2\|2 |- ----- \|a \|b log(\|x + 2a |- -----) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-------+ +-------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R - 2\|2 |- ----- \|a \|b log(\|x - 2a |- -----) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-------+ +--R | 1 +--R 2a |- ----- +--R +-+4+-+ +-+ 4+-+ +-------+ 4| 3 +--R \|2 \|b \|x - \|a +-+ | 1 4+-+3 4+-+ \| 16a b +--R - 2atan(-------------------) - 4\|2 |- ----- \|a \|b atan(------------) +--R 4+-+ 4| 3 +-+ +--R \|a \| 16a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------------- +--R 3 +-+ +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1285 +r0:=b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_ + b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_ + 1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(5/4)*sqrt(2))+1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(5/4)*sqrt(2))+(-2)/(a*sqrt(x)) +--R +--R +--R (2) +--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ +-+ \|2 \|b \|x + \|a 4+-+ +-+ \|2 \|b \|x - \|a +--R - 2\|b \|x atan(-------------------) - 2\|b \|x atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R +-+4+-+ +-+ +--R 2a\|2 \|a \|x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | b +-+ +-+ 4 | b +--R - a |- ---- \|x log(b\|x + 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | b +-+ +-+ 4 | b +--R a |- ---- \|x log(b\|x - 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+3 +--R 4 | b +--R 8a |- ---- +--R +------+ 4| 5 +--R | b +-+ \| 16a +--R - 2a |- ---- \|x atan(------------- - 2 +--R 4| 5 +-+ +--R \| 16a b\|x +--R / +--R +-+ +--R a\|x +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R +-+ | b 4+-+ +-+ 4 | b +--R - 2a\|2 |- ---- \|a log(b\|x + 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R +-+ | b 4+-+ +-+ 4 | b +--R 2a\|2 |- ---- \|a log(b\|x - 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 2\|b atan(-------------------) + 2\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R 4 | b +--R 8a |- ---- +--R +------+ 4| 5 +--R +-+ | b 4+-+ \| 16a +--R - 4a\|2 |- ---- \|a atan(-------------) +--R 4| 5 +-+ +--R \| 16a b\|x +--R / +--R +-+4+-+ +--R 2a\|2 \|a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 2 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1285 +r0:=(-2/3)/(a*x^(3/2))+b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(7/4)*sqrt(2))-b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(7/4)*sqrt(2))+1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))-1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 3x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 4+-+3 +-+ \|2 \|b \|x + \|a +--R - 6x \|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 4+-+3 +-+ \|2 \|b \|x - \|a +-+4+-+3 +--R - 6x \|b \|x atan(-------------------) - 4\|2 \|a +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+ +--R 6a x\|2 \|a \|x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +--R | 3 | 3 +--R | b +-+ +-+ 2 | b +--R - 3a x |- ---- \|x log(b\|x + 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +------+ +--R | 3 | 3 +--R | b +-+ +-+ 2 | b +--R 3a x |- ---- \|x log(b\|x - 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +--R | 3 +--R 2 | b +--R +------+ 2a |- ---- +--R | 3 4| 7 +--R | b +-+ \| 16a +--R 6a x |- ---- \|x atan(------------ - 2 +--R 4| 7 +-+ +--R \| 16a b\|x +--R / +--R +-+ +--R 3a x\|x +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 +-+ 2 | b +--R - 2a\|2 |- ---- \|a log(b\|x + 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 +-+ 2 | b +--R 2a\|2 |- ---- \|a log(b\|x - 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 2\|b atan(-------------------) + 2\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | 3 +--R 2 | b +--R +------+ 2a |- ---- +--R | 3 4| 7 +--R +-+ | b 4+-+3 \| 16a +--R 4a\|2 |- ---- \|a atan(------------) +--R 4| 7 +-+ +--R \| 16a b\|x +--R / +--R +-+4+-+3 +--R 2a\|2 \|a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 5 3 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1285 +r0:=(-2/5)/(a*x^(5/2))-b^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(9/4)*sqrt(2))+b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(9/4)*sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))-1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+2*b/(a^2*sqrt(x)) +--R +--R +--R (2) +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5b x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5b x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x + \|a +--R 10b x \|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x - \|a 2 +-+4+-+ +--R 10b x \|b \|x atan(------------------- + (20b x - 4a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+ +-+ +--R 10a x \|2 \|a \|x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | 5 | 5 +--R 2 2 | b +-+ 4 +-+ 7 | b +--R 5a x |- ---- \|x log(b \|x + 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 2 | b +-+ 4 +-+ 7 | b +--R - 5a x |- ---- \|x log(b \|x - 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+3 +--R | 5 +--R 7 | b +--R +------+ 8a |- ---- +--R | 5 4| 9 +--R 2 2 | b +-+ \| 16a 2 +--R 10a x |- ---- \|x atan(------------- + 10b x - 2a +--R 4| 9 4 +-+ +--R \| 16a b \|x +--R / +--R 2 2 +-+ +--R 5a x \|x +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 +-+ | b 4+-+ 4 +-+ 7 | b +--R 2a \|2 |- ---- \|a log(b \|x + 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 +-+ | b 4+-+ 4 +-+ 7 | b +--R - 2a \|2 |- ---- \|a log(b \|x - 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2b\|b atan(-------------------) - 2b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R | 5 +--R 7 | b +--R +------+ 8a |- ---- +--R | 5 4| 9 +--R 2 +-+ | b 4+-+ \| 16a +--R 4a \|2 |- ---- \|a atan(-------------) +--R 4| 9 4 +-+ +--R \| 16a b \|x +--R / +--R 2 +-+4+-+ +--R 2a \|2 \|a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 1285 +t0:=x^(7/2)/(a+b*x^2)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1285 +r0:=-1/2*x^(5/2)/(b*(a+b*x^2))+5/4*a^(1/4)*atan(1-b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))-5/4*a^(1/4)*atan(1+b^(1/4)*_ + sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+5/8*a^(1/4)*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-_ + 5/8*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (b^(9/4)*sqrt(2))+5/2*sqrt(x)/b^2 +--R +--R +--R (2) +--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 5a)\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 5a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ \|2 \|b \|x + \|a +--R (- 10b x - 10a)\|a atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ \|2 \|b \|x - \|a 2 +-+4+-+ +-+ +--R (- 10b x - 10a)\|a atan(-------------------) + (16b x + 20a)\|2 \|b \|x +--R 4+-+ +--R \|a +--R / +--R 3 2 2 +-+4+-+ +--R (8b x + 8a b )\|2 \|b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R 3 2 2 | 625a +-+ 2 | 625a +--R (- 2b x - 2a b ) |- ------ log(5\|x + 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R 3 2 2 | 625a +-+ 2 | 625a +--R (2b x + 2a b ) |- ------ log(5\|x - 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--R 2 | 625a +--R 8b |- ------ +--R +--------+ 4| 9 +--R 3 2 2 | 625a \| 4096b 2 +-+ +--R (4b x + 4a b ) |- ------ atan(-------------- + (4b x + 5a)\|x +--R 4| 9 +-+ +--R \| 4096b 5\|x +--R / +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+ +--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a +--R - 8b \|2 |- ------ \|b log(5\|x + 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a +--R 8b \|2 |- ------ \|b log(5\|x - 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10\|a atan(-------------------) + 10\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R 2 | 625a +--R 8b |- ------ +--R +--------+ 4| 9 +--R 2 +-+ | 625a 4+-+ \| 4096b +--R 16b \|2 |- ------ \|b atan(--------------) +--R 4| 9 +-+ +--R \| 4096b 5\|x +--R / +--R 2 +-+4+-+ +--R 8b \|2 \|b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1285 +t0:=x^(5/2)/(a+b*x^2)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1285 +r0:=-1/2*x^(3/2)/(b*(a+b*x^2))-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/4*atan(1+b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/8*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*_ + sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 3a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 3a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (6b x + 6a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+ +--R (6b x + 6a)atan(-------------------) - 4x\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+4+-+3 +--R (8b x + 8a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 5 | 1 +--R (6b x + 6a b) |- -------- log(\|x + 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 5 | 1 +--R (- 6b x - 6a b) |- -------- log(\|x - 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 5 | 1 +--R 512a b |- -------- +--R +----------+ 4| 7 +--R 2 2 | 1 \| 4096a b +-+ +--R (12b x + 12a b) |- -------- atan(--------------------- - x\|x +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1 +--R 24b\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1 +--R - 24b\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 5 | 1 +--R 512a b |- -------- +--R +----------+ 4| 7 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 48b\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+4+-+3 +--R 8b\|2 \|a \|b +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1285 +t0:=x^(3/2)/(a+b*x^2)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1285 +r0:=-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*_ + sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_ + b^(5/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+1/8*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*_ + sqrt(2))-1/2*sqrt(x)/(b*(a+b*x^2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (b x + a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- b x - a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (2b x + 2a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+ +--R (2b x + 2a)atan(-------------------) - 4\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+3 4+-+ +--R (8b x + 8a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R 2 2 | 1 +-+ | 1 +--R (2b x + 2a b) |- -------- log(\|x + 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+ +--R 2 2 | 1 +-+ | 1 +--R (- 2b x - 2a b) |- -------- log(\|x - 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +--R | 1 +--R 8a b |- -------- +--R +----------+ 4| 3 5 +--R 2 2 | 1 \| 4096a b +-+ +--R (- 4b x - 4a b) |- -------- atan(----------------- - \|x +--R 4| 3 5 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R 8b\|2 |- -------- \|a \|b log(\|x + 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R - 8b\|2 |- -------- \|a \|b log(\|x - 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+ +--R | 1 +--R 8a b |- -------- +--R +----------+ 4| 3 5 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 16b\|2 |- -------- \|a \|b atan(-----------------) +--R 4| 3 5 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 8b\|2 \|a \|b +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 1285 +t0:=sqrt(x)/(a+b*x^2)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1285 +r0:=1/2*x^(3/2)/(a*(a+b*x^2))-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(5/4)*b^(3/4)*sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(5/4)*b^(3/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(b)-_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-_ + 1/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(5/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- b x - a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (b x + a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (2b x + 2a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+ +--R (2b x + 2a)atan(-------------------) + 4x\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+4+-+3 +--R (8a b x + 8a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 4 2 | 1 +--R (2a b x + 2a ) |- -------- log(\|x + 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 4 2 | 1 +--R (- 2a b x - 2a ) |- -------- log(\|x - 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 4 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 5 3 +--R 2 2 | 1 \| 4096a b +-+ +--R (4a b x + 4a ) |- -------- atan(--------------------- + x\|x +--R 4| 5 3 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1 +--R 8a\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1 +--R - 8a\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 4 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 5 3 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 16a\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 5 3 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+4+-+3 +--R 8a\|2 \|a \|b +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 1285 +t0:=1/((a+b*x^2)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 4 2 2 +-+ +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1285 +r0:=-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+_ + 3/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*_ + sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+3/8*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+_ + 1/2*sqrt(x)/(a*(a+b*x^2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 3a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 3a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (6b x + 6a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+ +--R (6b x + 6a)atan(-------------------) + 4\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+3 4+-+ +--R (8a b x + 8a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R 2 2 | 1 +-+ 2 | 1 +--R (6a b x + 6a ) |- ------- log(\|x + 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R 2 2 | 1 +-+ 2 | 1 +--R (- 6a b x - 6a ) |- ------- log(\|x - 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +--R 2 | 1 +--R 8a |- ------- +--R +---------+ 4| 7 +--R 2 2 | 1 \| 4096a b +-+ +--R (- 12a b x - 12a ) |- ------- atan(--------------- + \|x +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 24a\|2 |- ------- \|a \|b log(\|x + 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 24a\|2 |- ------- \|a \|b log(\|x - 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +---------+ +--R 2 | 1 +--R 8a |- ------- +--R +---------+ 4| 7 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 48a\|2 |- ------- \|a \|b atan(---------------) +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 8a\|2 \|a \|b +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 5 3 2 +-+ +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1285 +r0:=5/4*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))-_ + 5/4*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_ + sqrt(2))-5/8*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+5/8*b^(1/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+_ + (-5/2)/(a^2*sqrt(x))+1/2/(a*(a+b*x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 5a)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 5a)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (- 10b x - 10a)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (- 10b x - 10a)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ +--R (- 20b x - 16a)\|2 \|a +--R / +--R 2 2 3 +-+4+-+ +-+ +--R (8a b x + 8a )\|2 \|a \|x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R 2 2 3 | 625b +-+ +-+ 7 | 625b +--R (- 2a b x - 2a ) |- ------ \|x log(125b\|x + 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 2 3 | 625b +-+ +-+ 7 | 625b +--R (2a b x + 2a ) |- ------ \|x log(125b\|x - 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+3 +--R 7 | 625b +--R 512a |- ------ +--R +--------+ 4| 9 +--R 2 2 3 | 625b +-+ \| 4096a 2 +--R (- 4a b x - 4a ) |- ------ \|x atan(----------------- - 5b x - 4a +--R 4| 9 +-+ +--R \| 4096a 125b\|x +--R / +--R 2 2 3 +-+ +--R (2a b x + 2a )\|x +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+3 +--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b +--R - 8a \|2 |- ------ \|a log(125b\|x + 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b +--R 8a \|2 |- ------ \|a log(125b\|x - 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10\|b atan(-------------------) + 10\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+3 +--R 7 | 625b +--R 512a |- ------ +--R +--------+ 4| 9 +--R 2 +-+ | 625b 4+-+ \| 4096a +--R - 16a \|2 |- ------ \|a atan(-----------------) +--R 4| 9 +-+ +--R \| 4096a 125b\|x +--R / +--R 2 +-+4+-+ +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 6 4 2 2 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1285 +r0:=(-7/6)/(a^2*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x^2))+7/4*b^(3/4)*_ + atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*sqrt(2))-_ + 7/4*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_ + sqrt(2))+7/8*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))-7/8*b^(3/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 21b x - 21a x)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (21b x + 21a x)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 4+-+3 +-+ \|2 \|b \|x + \|a +--R (- 42b x - 42a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 4+-+3 +-+ \|2 \|b \|x - \|a +--R (- 42b x - 42a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 +--R (- 28b x - 16a)\|2 \|a +--R / +--R 2 3 3 +-+4+-+3 +-+ +--R (24a b x + 24a x)\|2 \|a \|x +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b +--R (- 6a b x - 6a x) |- ------- \|x log(7b\|x + 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b +--R (6a b x + 6a x) |- ------- \|x log(7b\|x - 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +--R | 3 +--R 3 | 2401b +--R +---------+ 8a |- ------- +--R | 3 4| 11 +--R 2 3 3 | 2401b +-+ \| 4096a 2 +--R (12a b x + 12a x) |- ------- \|x atan(--------------- - 7b x - 4a +--R 4| 11 +-+ +--R \| 4096a 7b\|x +--R / +--R 2 3 3 +-+ +--R (6a b x + 6a x)\|x +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 7\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b +--R - 8a \|2 |- ------- \|a log(7b\|x + 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b +--R 8a \|2 |- ------- \|a log(7b\|x - 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 7\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 14\|b atan(-------------------) + 14\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +---------+ +--R | 3 +--R 3 | 2401b +--R +---------+ 8a |- ------- +--R | 3 4| 11 +--R 2 +-+ | 2401b 4+-+3 \| 4096a +--R 16a \|2 |- ------- \|a atan(---------------) +--R 4| 11 +-+ +--R \| 4096a 7b\|x +--R / +--R 2 +-+4+-+3 +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 7 5 2 3 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1285 +r0:=(-9/10)/(a^2*x^(5/2))+1/2/(a*x^(5/2)*(a+b*x^2))-9/4*b^(5/4)*_ + atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+_ + 9/4*b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_ + sqrt(2))+9/8*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-9/8*b^(5/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+_ + 9/2*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 45b x - 45a b x )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (45b x + 45a b x )\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (90b x + 90a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (90b x + 90a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+ +--R (180b x + 144a b x - 16a )\|2 \|a +--R / +--R 3 4 4 2 +-+4+-+ +-+ +--R (40a b x + 40a x )\|2 \|a \|x +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b +--R (10a b x + 10a x ) |- ------- \|x log(729b \|x + 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b +--R (- 10a b x - 10a x ) |- ------- \|x log(729b \|x - 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+3 +--R | 5 +--R 10 | 6561b +--R +---------+ 512a |- ------- +--R | 5 4| 13 +--R 3 4 4 2 | 6561b +-+ \| 4096a 2 4 +--R (20a b x + 20a x ) |- ------- \|x atan(------------------- + 45b x +--R 4| 13 4 +-+ +--R \| 4096a 729b \|x +--R + +--R 2 2 +--R 36a b x - 4a +--R / +--R 3 4 4 2 +-+ +--R (10a b x + 10a x )\|x +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 9b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b +--R 8a \|2 |- ------- \|a log(729b \|x + 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b +--R - 8a \|2 |- ------- \|a log(729b \|x - 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 9b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 18b\|b atan(-------------------) - 18b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +---------+3 +--R | 5 +--R 10 | 6561b +--R +---------+ 512a |- ------- +--R | 5 4| 13 +--R 3 +-+ | 6561b 4+-+ \| 4096a +--R 16a \|2 |- ------- \|a atan(-------------------) +--R 4| 13 4 +-+ +--R \| 4096a 729b \|x +--R / +--R 3 +-+4+-+ +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1285 +t0:=x^(7/2)/(a+b*x^2)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1285 +r0:=-1/4*x^(5/2)/(b*(a+b*x^2)^2)-5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-5/64*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*_ + sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))-5/16*sqrt(x)/(b^2*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 10a b x + 5a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 10a b x - 5a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (- 36b x - 20a)\|2 \|a \|b \|x +--R / +--R 4 4 3 2 2 2 +-+4+-+3 4+-+ +--R (64b x + 128a b x + 64a b )\|2 \|a \|b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (80b x + 160a b x + 80a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x + 64a b |- ------------) +--R 4| 3 9 +--R \| 16777216a b +--R + +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (- 80b x - 160a b x - 80a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x - 64a b |- ------------) +--R 4| 3 9 +--R \| 16777216a b +--R + +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (- 160b x - 320a b x - 160a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R atan(-----------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (- 9b x - 5a)\|x +--R / +--R 4 4 3 2 2 2 +--R 16b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 320b \|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------) +--R 4| 3 9 4| 3 9 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 320b \|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------) +--R 4| 3 9 4| 3 9 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R +--------------+ 4| 3 9 +--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 640b \|2 |- ------------ \|a \|b atan(-----------------------) +--R 4| 3 9 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+3 4+-+ +--R 64b \|2 \|a \|b +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 1285 +t0:=x^(5/2)/(a+b*x^2)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1285 +r0:=-1/4*x^(3/2)/(b*(a+b*x^2)^2)+3/16*x^(3/2)/(a*b*(a+b*x^2))-_ + 3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*_ + sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_ + b^(7/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-3/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 6a b x - 3a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 +-+4+-+4+-+3 +-+ +--R (12b x - 4a x)\|2 \|a \|b \|x +--R / +--R 3 4 2 2 2 3 +-+4+-+4+-+3 +--R (64a b x + 128a b x + 64a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (48a b x + 96a b x + 48a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 48a b x - 96a b x - 48a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (96a b x + 192a b x + 96a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R 4 5 | 1 +--R 262144a b |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R atan(----------------------------) +--R +-+ +--R \|x +--R + +--R 3 +-+ +--R (3b x - a x)\|x +--R / +--R 3 4 2 2 2 3 +--R 16a b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--R +-+ | 1 4+-+4+-+3 +--R 192a b\|2 |- ------------ \|a \|b +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R +-+ | 1 4+-+4+-+3 +--R 192a b\|2 |- ------------ \|a \|b +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 4 5 | 1 +--R 262144a b |- ------------ +--R +--------------+ 4| 5 7 +--R +-+ | 1 4+-+4+-+3 \| 16777216a b +--R 384a b\|2 |- ------------ \|a \|b atan(----------------------------) +--R 4| 5 7 +-+ +--R \| 16777216a b \|x +--R / +--R +-+4+-+4+-+3 +--R 64a b\|2 \|a \|b +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 1285 +t0:=x^(3/2)/(a+b*x^2)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1285 +r0:=-3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*_ + sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*_ + b^(5/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+3/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*_ + sqrt(2))-1/4*sqrt(x)/(b*(a+b*x^2)^2)+1/16*sqrt(x)/(a*b*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 6a b x - 3a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (4b x - 12a)\|2 \|a \|b \|x +--R / +--R 3 4 2 2 2 3 +-+4+-+3 4+-+ +--R (64a b x + 128a b x + 64a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (48a b x + 96a b x + 48a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x + 64a b |- ------------) +--R 4| 7 5 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 48a b x - 96a b x - 48a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x - 64a b |- ------------) +--R 4| 7 5 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 96a b x - 192a b x - 96a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R atan(----------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (b x - 3a)\|x +--R / +--R 3 4 2 2 2 3 +--R 16a b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 192a b\|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------) +--R 4| 7 5 4| 7 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 192a b\|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------) +--R 4| 7 5 4| 7 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R +--------------+ 4| 7 5 +--R +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 384a b\|2 |- ------------ \|a \|b atan(----------------------) +--R 4| 7 5 +-+ +--R \| 16777216a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 64a b\|2 \|a \|b +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1285 +t0:=sqrt(x)/(a+b*x^2)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1285 +r0:=1/4*x^(3/2)/(a*(a+b*x^2)^2)+5/16*x^(3/2)/(a^2*(a+b*x^2))-_ + 5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*_ + sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_ + b^(3/4)*sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))-5/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 10a b x - 5a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 10a b x + 5a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 +-+4+-+4+-+3 +-+ +--R (20b x + 36a x)\|2 \|a \|b \|x +--R / +--R 2 2 4 3 2 4 +-+4+-+4+-+3 +--R (64a b x + 128a b x + 64a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (80a b x + 160a b x + 80a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 80a b x - 160a b x - 80a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (160a b x + 320a b x + 160a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R 7 2 | 1 +--R 262144a b |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R atan(----------------------------) +--R +-+ +--R \|x +--R + +--R 3 +-+ +--R (5b x + 9a x)\|x +--R / +--R 2 2 4 3 2 4 +--R 16a b x + 32a b x + 16a +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 5log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 320a \|2 |- ------------ \|a \|b +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 320a \|2 |- ------------ \|a \|b +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 7 2 | 1 +--R 262144a b |- ------------ +--R +--------------+ 4| 9 3 +--R 2 +-+ | 1 4+-+4+-+3 \| 16777216a b +--R 640a \|2 |- ------------ \|a \|b atan(----------------------------) +--R 4| 9 3 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+4+-+3 +--R 64a \|2 \|a \|b +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 1285 +t0:=1/((a+b*x^2)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 6 2 4 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1285 +r0:=-21/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*_ + sqrt(2))+21/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_ + b^(1/4)*sqrt(2))-21/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))+21/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*_ + sqrt(2))+1/4*sqrt(x)/(a*(a+b*x^2)^2)+7/16*sqrt(x)/(a^2*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (21b x + 42a b x + 21a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 21b x - 42a b x - 21a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (42b x + 84a b x + 42a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (42b x + 84a b x + 42a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (28b x + 44a)\|2 \|a \|b \|x +--R / +--R 2 2 4 3 2 4 +-+4+-+3 4+-+ +--R (64a b x + 128a b x + 64a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (336a b x + 672a b x + 336a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 3 | 1 +--R log(\|x + 64a |- ------------) +--R 4| 11 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 336a b x - 672a b x - 336a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 3 | 1 +--R log(\|x - 64a |- ------------) +--R 4| 11 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 672a b x - 1344a b x - 672a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R 3 | 1 +--R 64a |- ------------ +--R 4| 11 +--R \| 16777216a b +--R atan(---------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (7b x + 11a)\|x +--R / +--R 2 2 4 3 2 4 +--R 16a b x + 32a b x + 16a +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 21log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1 +--R 1344a \|2 |- ------------ \|a \|b log(\|x + 64a |- ------------) +--R 4| 11 4| 11 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1 +--R - 1344a \|2 |- ------------ \|a \|b log(\|x - 64a |- ------------) +--R 4| 11 4| 11 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 21log(- \|2 \|a \|b \|x + x\|b + \|a ) - 42atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 42atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 3 | 1 +--R 64a |- ------------ +--R +--------------+ 4| 11 +--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 2688a \|2 |- ------------ \|a \|b atan(---------------------) +--R 4| 11 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+3 4+-+ +--R 64a \|2 \|a \|b +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 7 2 5 2 3 3 +-+ +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1285 +r0:=45/32*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_ + sqrt(2))-45/32*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(13/4)*sqrt(2))-45/64*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+45/64*b^(1/4)*_ + log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_ + sqrt(2))+(-45/16)/(a^3*sqrt(x))+1/4/(a*(a+b*x^2)^2*sqrt(x))+_ + 9/16/(a^2*(a+b*x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 4 2 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (45b x + 90a b x + 45a )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 4+-+ +-+ +--R (- 45b x - 90a b x - 45a )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+ +--R (- 180b x - 324a b x - 128a )\|2 \|a +--R / +--R 3 2 4 4 2 5 +-+4+-+ +-+ +--R (64a b x + 128a b x + 64a )\|2 \|a \|x +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (- 16a b x - 32a b x - 16a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x + 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (16a b x + 32a b x + 16a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x - 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (- 32a b x - 64a b x - 32a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R 10 | 4100625b +--R 262144a |- ----------- +--R 4| 13 +--R \| 16777216a +--R atan(--------------------------) +--R +-+ +--R 91125b\|x +--R + +--R 2 4 2 2 +--R - 45b x - 81a b x - 32a +--R / +--R 3 2 4 4 2 5 +-+ +--R (16a b x + 32a b x + 16a )\|x +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 45\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R - +--R +-------------+ +--R 3 +-+ | 4100625b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x + 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R 3 +-+ | 4100625b 4+-+ +-+ 10 | 4100625b +--R 64a \|2 |- ----------- \|a log(91125b\|x - 262144a |- ----------- ) +--R 4| 13 4| 13 +--R \| 16777216a \| 16777216a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 45\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 90\|b atan(-------------------) + 90\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+3 +--R 10 | 4100625b +--R 262144a |- ----------- +--R +-------------+ 4| 13 +--R 3 +-+ | 4100625b 4+-+ \| 16777216a +--R - 128a \|2 |- ----------- \|a atan(--------------------------) +--R 4| 13 +-+ +--R \| 16777216a 91125b\|x +--R / +--R 3 +-+4+-+ +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 8 2 6 2 4 3 2 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1285 +r0:=(-77/48)/(a^3*x^(3/2))+1/4/(a*x^(3/2)*(a+b*x^2)^2)+11/16/(a^2*x^(3/2)*_ + (a+b*x^2))+77/32*b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(15/4)*sqrt(2))-77/32*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(15/4)*sqrt(2))+77/64*b^(3/4)*log(sqrt(a)+x*sqrt(b)-_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))-77/64*b^(3/4)*_ + log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 5 3 2 4+-+3 +-+ +--R (- 231b x - 462a b x - 231a x)\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 5 3 2 4+-+3 +-+ +--R (231b x + 462a b x + 231a x)\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x + \|a +--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x - \|a +--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+3 +--R (- 308b x - 484a b x - 128a )\|2 \|a +--R / +--R 3 2 5 4 3 5 +-+4+-+3 +-+ +--R (192a b x + 384a b x + 192a x)\|2 \|a \|x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (- 48a b x - 96a b x - 48a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R +-+ 4 | 35153041b +--R log(77b\|x + 64a |- -----------) +--R 4| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (48a b x + 96a b x + 48a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R +-+ 4 | 35153041b +--R log(77b\|x - 64a |- -----------) +--R 4| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (96a b x + 192a b x + 96a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R 4 | 35153041b +--R 64a |- ----------- +--R 4| 15 +--R \| 16777216a +--R atan(--------------------) +--R +-+ +--R 77b\|x +--R + +--R 2 4 2 2 +--R - 77b x - 121a b x - 32a +--R / +--R 3 2 5 4 3 5 +-+ +--R (48a b x + 96a b x + 48a x)\|x +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 77\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------------+ +-------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b +--R - 64a \|2 |- ----------- \|a log(77b\|x + 64a |- -----------) +--R 4| 15 4| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b +--R 64a \|2 |- ----------- \|a log(77b\|x - 64a |- -----------) +--R 4| 15 4| 15 +--R \| 16777216a \| 16777216a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 77\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 154\|b atan(-------------------) + 154\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+ +--R | 3 +--R 4 | 35153041b +--R +-------------+ 64a |- ----------- +--R | 3 4| 15 +--R 3 +-+ | 35153041b 4+-+3 \| 16777216a +--R 128a \|2 |- ----------- \|a atan(--------------------) +--R 4| 15 +-+ +--R \| 16777216a 77b\|x +--R / +--R 3 +-+4+-+3 +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 9 2 7 2 5 3 3 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1285 +r0:=(-117/80)/(a^3*x^(5/2))+1/4/(a*x^(5/2)*(a+b*x^2)^2)+13/16/(a^2*_ + x^(5/2)*(a+b*x^2))-117/32*b^(5/4)*atan(1-b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/32*b^(5/4)*atan(1+_ + b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/64*_ + b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(17/4)*sqrt(2))-117/64*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))+117/16*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R 3 6 2 4 2 2 4+-+ +-+ +--R (- 585b x - 1170a b x - 585a b x )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 3 6 2 4 2 2 4+-+ +-+ +--R (585b x + 1170a b x + 585a b x )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+4+-+ +--R (2340b x + 4212a b x + 1664a b x - 128a )\|2 \|a +--R / +--R 4 2 6 5 4 6 2 +-+4+-+ +-+ +--R (320a b x + 640a b x + 320a x )\|2 \|a \|x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (80a b x + 160a b x + 80a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x + 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (- 80a b x - 160a b x - 80a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x - 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (160a b x + 320a b x + 160a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 13 | 187388721b +--R 262144a |- ----------- +--R 4| 17 +--R \| 16777216a +--R atan(--------------------------) +--R 4 +-+ +--R 1601613b \|x +--R + +--R 3 6 2 4 2 2 3 +--R 585b x + 1053a b x + 416a b x - 32a +--R / +--R 4 2 6 5 4 6 2 +-+ +--R (80a b x + 160a b x + 80a x )\|x +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 117b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------------+ +--R | 5 +--R 4 +-+ | 187388721b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x + 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R - +--R +-------------+ +--R | 5 +--R 4 +-+ | 187388721b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x - 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 117b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 234b\|b atan(-------------------) - 234b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+3 +--R | 5 +--R 13 | 187388721b +--R +-------------+ 262144a |- ----------- +--R | 5 4| 17 +--R 4 +-+ | 187388721b 4+-+ \| 16777216a +--R 128a \|2 |- ----------- \|a atan(--------------------------) +--R 4| 17 4 +-+ +--R \| 16777216a 1601613b \|x +--R / +--R 4 +-+4+-+ +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1285 +t0:=x^(7/2)/(1+x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1285 +r0:=2/5*x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-2*sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 5log(\|2 \|x + x + 1) - 5log(- \|2 \|x + x + 1) + 10atan(\|2 \|x + 1) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R 10atan(\|2 \|x - 1) + (4x - 20)\|2 \|x +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 5\|2 log(\|2 \|x + x + 1) - 5\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 2 +-+ +--R - 10\|2 atan(------------) - 10\|2 atan(------------) + (8x - 40)\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1285 +t0:=x^(5/2)/(1+x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1285 +r0:=2/3*x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 3log(\|2 \|x + x + 1) - 3log(- \|2 \|x + x + 1) - 6atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ +--R - 6atan(\|2 \|x - 1) + 4x\|2 \|x +--R / +--R +-+ +--R 6\|2 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 3\|2 log(\|2 \|x + x + 1) - 3\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 6\|2 atan(------------) + 6\|2 atan(------------) + 8x\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 1285 +t0:=x^(3/2)/(1+x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1285 +r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_ + 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/_ + sqrt(2)+2*sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) - 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ +--R - 2atan(\|2 \|x - 1) + 4\|2 \|x +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 2\|2 atan(------------) + 2\|2 atan(------------) + 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1285 +t0:=sqrt(x)/(1+x^2) +--R +--R +--R +-+ +--R \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1285 +r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_ + 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +--R 2atan(\|2 \|x - 1) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(------------) - 2\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1285 +t0:=1/((1+x^2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-+ +--R (x + 1)\|x +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1285 +r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R log(\|2 \|x + x + 1) - log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +--R 2atan(\|2 \|x - 1) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R \|2 log(\|2 \|x + x + 1) - \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(------------) - 2\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 1285 +t0:=1/(x^(3/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-+ +--R (x + x)\|x +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1285 +r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/_ + sqrt(2)+(-2)/sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R \|x log(\|2 \|x + x + 1) - \|x log(- \|2 \|x + x + 1) +--R + +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 2\|x atan(\|2 \|x + 1) - 2\|x atan(\|2 \|x - 1) - 4\|2 +--R / +--R +-+ +-+ +--R 2\|2 \|x +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R x\|2 log(\|2 \|x + x + 1) - x\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 2x\|2 atan(------------) + 2x\|2 atan(------------) - 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4x +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 1285 +t0:=1/(x^(5/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R 4 2 +-+ +--R (x + x )\|x +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1285 +r0:=(-2/3)/x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - 3x\|x log(\|2 \|x + x + 1) + 3x\|x log(- \|2 \|x + x + 1) +--R + +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 6x\|x atan(\|2 \|x + 1) - 6x\|x atan(\|2 \|x - 1) - 4\|2 +--R / +--R +-+ +-+ +--R 6x\|2 \|x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R - 3x \|2 log(\|2 \|x + x + 1) + 3x \|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +-+ +--R 6x \|2 atan(------------) + 6x \|2 atan(------------) - 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1285 +t0:=1/(x^(7/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R 5 3 +-+ +--R (x + x )\|x +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1285 +r0:=(-2/5)/x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+2/sqrt(x) +--R +--R +--R (2) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R - 5x \|x log(\|2 \|x + x + 1) + 5x \|x log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ 2 +-+ +--R 10x \|x atan(\|2 \|x + 1) + 10x \|x atan(\|2 \|x - 1) + (20x - 4)\|2 +--R / +--R 2 +-+ +-+ +--R 10x \|2 \|x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R - 5x \|2 log(\|2 \|x + x + 1) + 5x \|2 log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ 1 3 +-+ 1 2 +-+ +--R - 10x \|2 atan(------------) - 10x \|2 atan(------------) + (40x - 8)\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 3 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1285 +t0:=x^(7/2)/(1+x^2)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1285 +r0:=-1/2*x^(5/2)/(1+x^2)+5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)-5/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+5/2*sqrt(x) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 5x - 5)log(\|2 \|x + x + 1) + (5x + 5)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 10x - 10)atan(\|2 \|x + 1) + (- 10x - 10)atan(\|2 \|x - 1) +--R + +--R 2 +-+ +-+ +--R (16x + 20)\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (- 5x - 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ 1 +--R (5x + 5)\|2 log(- \|2 \|x + x + 1) + (10x + 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 2 +-+ 1 2 +-+ +--R (10x + 10)\|2 atan(------------) + (32x + 40)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 1285 +t0:=x^(5/2)/(1+x^2)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1285 +r0:=-1/2*x^(3/2)/(1+x^2)-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+_ + 3/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-3/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 3x - 3)log(\|2 \|x + x + 1) + (3x + 3)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) - 4x\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (- 3x - 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ 1 +--R (3x + 3)\|2 log(- \|2 \|x + x + 1) + (- 6x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 2 +-+ 1 +-+ +--R (- 6x - 6)\|2 atan(------------) - 8x\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1285 +t0:=x^(3/2)/(1+x^2)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1285 +r0:=-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-1/2*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x + 1)log(\|2 \|x + x + 1) + (- x - 1)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) - 4\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (x + 1)\|2 log(\|2 \|x + x + 1) + (- x - 1)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R - 8\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1285 +t0:=sqrt(x)/(1+x^2)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1285 +r0:=1/2*x^(3/2)/(1+x^2)-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)-1/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- x - 1)log(\|2 \|x + x + 1) + (x + 1)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) + 4x\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (- x - 1)\|2 log(\|2 \|x + x + 1) + (x + 1)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R 8x\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1285 +t0:=1/((1+x^2)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 4 2 +-+ +--R (x + 2x + 1)\|x +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1285 +r0:=-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-3/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (3x + 3)log(\|2 \|x + x + 1) + (- 3x - 3)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) + 4\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (3x + 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ +--R (- 3x - 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 6x - 6)\|2 atan(------------) + (- 6x - 6)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R 8\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1285 +t0:=1/(x^(3/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 5 3 +-+ +--R (x + 2x + x)\|x +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1285 +r0:=5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-5/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)+(-5/2)/sqrt(x)+1/2/((1+x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 +-+ +-+ +-+ +--R (5x + 5)\|x log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ +--R (- 5x - 5)\|x log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (- 10x - 10)\|x atan(\|2 \|x + 1) + (- 10x - 10)\|x atan(\|2 \|x - 1) +--R + +--R 2 +-+ +--R (- 20x - 16)\|2 +--R / +--R 2 +-+ +-+ +--R (8x + 8)\|2 \|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ +-+ +-+ +--R (5x + 5x)\|2 log(\|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (- 5x - 5x)\|2 log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ 1 3 +-+ 1 +--R (10x + 10x)\|2 atan(------------) + (10x + 10x)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R 2 +-+ +--R (- 40x - 32)\|x +--R / +--R 3 +--R 16x + 16x +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1285 +t0:=1/(x^(5/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------- +--R 6 4 2 +-+ +--R (x + 2x + x )\|x +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1285 +r0:=(-7/6)/x^(3/2)+1/2/(x^(3/2)*(1+x^2))+7/4*atan(1-sqrt(2)*sqrt(x))/_ + sqrt(2)-7/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+7/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-7/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 3 +-+ +-+ +-+ +--R (- 21x - 21x)\|x log(\|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (21x + 21x)\|x log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (- 42x - 42x)\|x atan(\|2 \|x + 1) +--R + +--R 3 +-+ +-+ +-+ 2 +-+ +--R (- 42x - 42x)\|x atan(\|2 \|x - 1) + (- 28x - 16)\|2 +--R / +--R 3 +-+ +-+ +--R (24x + 24x)\|2 \|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 21x - 21x )\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (21x + 21x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 4 2 +-+ 1 +--R (42x + 42x )\|2 atan(------------) + (42x + 42x )\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R 2 +-+ +--R (- 56x - 32)\|x +--R / +--R 4 2 +--R 48x + 48x +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 7atan(\|2 \|x + 1) + 7atan(\|2 \|x - 1) + 7atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 7atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 1285 +t0:=1/(x^(7/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------- +--R 7 5 3 +-+ +--R (x + 2x + x )\|x +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1285 +r0:=(-9/10)/x^(5/2)+1/2/(x^(5/2)*(1+x^2))-9/4*atan(1-sqrt(2)*sqrt(x))/_ + sqrt(2)+9/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+9/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-9/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+9/2/sqrt(x) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +-+ +--R (- 45x - 45x )\|x log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (45x + 45x )\|x log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ 4 2 +-+ +-+ +-+ +--R (90x + 90x )\|x atan(\|2 \|x + 1) + (90x + 90x )\|x atan(\|2 \|x - 1) +--R + +--R 4 2 +-+ +--R (180x + 144x - 16)\|2 +--R / +--R 4 2 +-+ +-+ +--R (40x + 40x )\|2 \|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 +-+ +-+ +-+ +--R (- 45x - 45x )\|2 log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (45x + 45x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ 1 +--R (- 90x - 90x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 5 3 +-+ 1 4 2 +-+ +--R (- 90x - 90x )\|2 atan(------------) + (360x + 288x - 32)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 5 3 +--R 80x + 80x +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 9atan(\|2 \|x + 1) - 9atan(\|2 \|x - 1) - 9atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 9atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1285 +t0:=x^(7/2)/(1+x^2)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1285 +r0:=-1/4*x^(5/2)/(1+x^2)^2-5/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+5/32*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)+5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-5/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (5x + 10x + 5)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 5x - 10x - 5)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x - 1) + (- 36x - 20)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (5x + 10x + 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 5x - 10x - 5)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 10x - 20x - 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 10x - 20x - 10)\|2 atan(------------) + (- 72x - 40)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 1285 +t0:=x^(5/2)/(1+x^2)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1285 +r0:=-1/4*x^(3/2)/(1+x^2)^2+3/16*x^(3/2)/(1+x^2)-3/32*atan(1-sqrt(2)*_ + sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/64*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-3/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (- 3x - 6x - 3)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (3x + 6x + 3)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ 4 2 +-+ +-+ +--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1) +--R + +--R 3 +-+ +-+ +--R (12x - 4x)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 3x - 6x - 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (3x + 6x + 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 6x - 12x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 3 +-+ +--R (- 6x - 12x - 6)\|2 atan(------------) + (24x - 8x)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1285 +t0:=x^(3/2)/(1+x^2)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1285 +r0:=-3/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-3/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/64*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-1/4*sqrt(x)/(1+x^2)^2+1/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (3x + 6x + 3)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 3x - 6x - 3)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ 4 2 +-+ +-+ +--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1) +--R + +--R 2 +-+ +-+ +--R (4x - 12)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (3x + 6x + 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 3x - 6x - 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 6x - 12x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 6x - 12x - 6)\|2 atan(------------) + (8x - 24)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1285 +t0:=sqrt(x)/(1+x^2)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1285 +r0:=1/4*x^(3/2)/(1+x^2)^2+5/16*x^(3/2)/(1+x^2)-5/32*atan(1-sqrt(2)*_ + sqrt(x))/sqrt(2)+5/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/64*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (- 5x - 10x - 5)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (5x + 10x + 5)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 3 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x - 1) + (20x + 36x)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 5x - 10x - 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (5x + 10x + 5)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 10x - 20x - 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 3 +-+ +--R (- 10x - 20x - 10)\|2 atan(------------) + (40x + 72x)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1285 +t0:=1/((1+x^2)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 6 4 2 +-+ +--R (x + 3x + 3x + 1)\|x +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1285 +r0:=-21/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+21/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-21/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+21/64*log(1+x+_ + sqrt(2)*sqrt(x))/sqrt(2)+1/4*sqrt(x)/(1+x^2)^2+7/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (21x + 42x + 21)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 21x - 42x - 21)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (42x + 84x + 42)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 2 +-+ +-+ +--R (42x + 84x + 42)atan(\|2 \|x - 1) + (28x + 44)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (21x + 42x + 21)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 21x - 42x - 21)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 42x - 84x - 42)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 42x - 84x - 42)\|2 atan(------------) + (56x + 88)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 21atan(\|2 \|x + 1) - 21atan(\|2 \|x - 1) - 21atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 21atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 1285 +t0:=1/(x^(3/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------ +--R 7 5 3 +-+ +--R (x + 3x + 3x + x)\|x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1285 +r0:=45/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-45/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-45/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+45/64*log(1+x+_ + sqrt(2)*sqrt(x))/sqrt(2)+(-45/16)/sqrt(x)+1/4/((1+x^2)^2*sqrt(x))+_ + 9/16/((1+x^2)*sqrt(x)) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +-+ +--R (45x + 90x + 45)\|x log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 45x - 90x - 45)\|x log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 90x - 180x - 90)\|x atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ +-+ 4 2 +-+ +--R (- 90x - 180x - 90)\|x atan(\|2 \|x - 1) + (- 180x - 324x - 128)\|2 +--R / +--R 4 2 +-+ +-+ +--R (64x + 128x + 64)\|2 \|x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 +-+ +-+ +-+ +--R (45x + 90x + 45x)\|2 log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 45x - 90x - 45x)\|2 log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ 1 +--R (90x + 180x + 90x)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 5 3 +-+ 1 4 2 +-+ +--R (90x + 180x + 90x)\|2 atan(------------) + (- 360x - 648x - 256)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 5 3 +--R 128x + 256x + 128x +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 45atan(\|2 \|x + 1) + 45atan(\|2 \|x - 1) + 45atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 45atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1285 +t0:=1/(x^(5/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------- +--R 8 6 4 2 +-+ +--R (x + 3x + 3x + x )\|x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1285 +r0:=(-77/48)/x^(3/2)+1/4/(x^(3/2)*(1+x^2)^2)+11/16/(x^(3/2)*(1+x^2))+_ + 77/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-77/32*atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+77/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-77/64*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 5 3 +-+ +-+ +-+ +--R (- 231x - 462x - 231x)\|x log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (231x + 462x + 231x)\|x log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 462x - 924x - 462x)\|x atan(\|2 \|x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 462x - 924x - 462x)\|x atan(\|2 \|x - 1) +--R + +--R 4 2 +-+ +--R (- 308x - 484x - 128)\|2 +--R / +--R 5 3 +-+ +-+ +--R (192x + 384x + 192x)\|2 \|x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 4 2 +-+ +-+ +-+ +--R (- 231x - 462x - 231x )\|2 log(\|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (231x + 462x + 231x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ 1 +--R (462x + 924x + 462x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 6 4 2 +-+ 1 4 2 +-+ +--R (462x + 924x + 462x )\|2 atan(------------) + (- 616x - 968x - 256)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 6 4 2 +--R 384x + 768x + 384x +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 77atan(\|2 \|x + 1) + 77atan(\|2 \|x - 1) + 77atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 77atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 1285 +t0:=1/(x^(7/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------- +--R 9 7 5 3 +-+ +--R (x + 3x + 3x + x )\|x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1285 +r0:=(-117/80)/x^(5/2)+1/4/(x^(5/2)*(1+x^2)^2)+13/16/(x^(5/2)*(1+x^2))-_ + 117/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+117/32*atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+117/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-117/64*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+117/16/sqrt(x) +--R +--R +--R (2) +--R 6 4 2 +-+ +-+ +-+ +--R (- 585x - 1170x - 585x )\|x log(\|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (585x + 1170x + 585x )\|x log(- \|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x - 1) +--R + +--R 6 4 2 +-+ +--R (2340x + 4212x + 1664x - 128)\|2 +--R / +--R 6 4 2 +-+ +-+ +--R (320x + 640x + 320x )\|2 \|x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 5 3 +-+ +-+ +-+ +--R (- 585x - 1170x - 585x )\|2 log(\|2 \|x + x + 1) +--R + +--R 7 5 3 +-+ +-+ +-+ +--R (585x + 1170x + 585x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 7 5 3 +-+ 1 +--R (- 1170x - 2340x - 1170x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 7 5 3 +-+ 1 +--R (- 1170x - 2340x - 1170x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R + +--R 6 4 2 +-+ +--R (4680x + 8424x + 3328x - 256)\|x +--R / +--R 7 5 3 +--R 640x + 1280x + 640x +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 117atan(\|2 \|x + 1) - 117atan(\|2 \|x - 1) - 117atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 117atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 1285 +t0:=x^(2/3)/(1+x^2) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1285 +r0a:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))-_ + 1/2*atanh(x^(1/3)*sqrt(3)/(1+x^(2/3)))*sqrt(3) +--R +--R +--R (2) +--R +-+3+-+ +--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+ +--R - \|3 atanh(---------) + atan(2\|x + \|3 ) + atan(2\|x - \|3 ) +--R 3+-+2 +--R \|x + 1 +--R + +--R 3+-+ +--R 2atan(\|x ) +--R / +--R 2 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1285 +r0b:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))+_ + 1/4*log(1+x^(2/3)-x^(1/3)*sqrt(3))*sqrt(3)-1/4*log(1+x^(2/3)+_ + x^(1/3)*sqrt(3))*sqrt(3) +--R +--R +--R (3) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R 3+-+ +-+ 3+-+ +-+ 3+-+ +--R 2atan(2\|x + \|3 ) + 2atan(2\|x - \|3 ) + 4atan(\|x ) +--R / +--R 4 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R 3+-+ +--R 2\|x 1 1 +--R - 2atan(---------) - 2atan(------------) - 2atan(------------) +--R 3+-+2 3+-+ +-+ 3+-+ +-+ +--R \|x - 1 2\|x - \|3 2\|x + \|3 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1285 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R +-+3+-+ +--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+ +--R 2\|3 atanh(---------) - 2atan(2\|x + \|3 ) - 2atan(2\|x - \|3 ) +--R 3+-+2 +--R \|x + 1 +--R + +--R 3+-+ +--R 3+-+ 2\|x 1 +--R - 4atan(\|x ) - 2atan(---------) - 2atan(------------) +--R 3+-+2 3+-+ +-+ +--R \|x - 1 2\|x - \|3 +--R + +--R 1 +--R - 2atan(------------) +--R 3+-+ +-+ +--R 2\|x + \|3 +--R / +--R 4 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1285 +d0:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1285 +m0b:=a0-r0b +--R +--R +--R (7) +--R 3+-+ +--R 3+-+ +-+ 3+-+ +-+ 3+-+ 2\|x +--R - atan(2\|x + \|3 ) - atan(2\|x - \|3 ) - 2atan(\|x ) - atan(---------) +--R 3+-+2 +--R \|x - 1 +--R + +--R 1 1 +--R - atan(------------) - atan(------------) +--R 3+-+ +-+ 3+-+ +-+ +--R 2\|x - \|3 2\|x + \|3 +--R / +--R 2 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1285 +t0:=x^(7/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 3 +-+ | 2 +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1285 +--r0:=4/77*a*x^(5/2)*sqrt(a+b*x^2)/b+2/11*x^(9/2)*sqrt(a+b*x^2)-_ +-- 20/231*a^2*sqrt(x)*sqrt(a+b*x^2)/b^2+20/231*a^(13/4)*_ +-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +-- ((-b)^(9/4)*sqrt(a+b*x^2)) +--E 482 + +--S 483 of 1285 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 1285 +--m0:=a0-r0 +--E 484 + +--S 485 of 1285 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 1285 +t0:=x^(5/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 2 +-+ | 2 +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1285 +--r0:=4/45*a*x^(3/2)*sqrt(a+b*x^2)/b+2/9*x^(7/2)*sqrt(a+b*x^2)+4/15*_ +--a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_ +--b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-4/15*a^(11/4)*elliptic_f(_ +--asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2)) +--E 487 + +--S 488 of 1285 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 1285 +--m0:=a0-r0 +--E 489 + +--S 490 of 1285 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 1285 +t0:=x^(3/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R (1) x\|x \|b x + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1285 +--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)+4/21*a*sqrt(x)*sqrt(a+b*x^2)/b+4/21*_ +--a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 492 + +--S 493 of 1285 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 1285 +--m0:=a0-r0 +--E 494 + +--S 495 of 1285 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 1285 +t0:=sqrt(x)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R (1) \|x \|b x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1285 +--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)+4/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-_ +--4/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2)) +--E 497 + +--S 498 of 1285 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 1285 +--m0:=a0-r0 +--E 499 + +--S 500 of 1285 +--d0:=D(m0,x) +--E 500 + +)clear all + +--S 501 of 1285 +t0:=sqrt(a+b*x^2)/sqrt(x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1285 +--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)+4/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 502 + +--S 503 of 1285 +--a0:=integrate(t0,x) +--E 503 + +--S 504 of 1285 +--m0:=a0-r0 +--E 504 + +--S 505 of 1285 +--d0:=D(m0,x) +--E 505 + +)clear all + +--S 506 of 1285 +t0:=sqrt(a+b*x^2)/x^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1285 +--r0:=-2*sqrt(a+b*x^2)/sqrt(x)-4*a^(3/4)*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)+4*a^(3/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 507 + +--S 508 of 1285 +--a0:=integrate(t0,x) +--E 508 + +--S 509 of 1285 +--m0:=a0-r0 +--E 509 + +--S 510 of 1285 +--d0:=D(m0,x) +--E 510 + +)clear all + +--S 511 of 1285 +t0:=sqrt(a+b*x^2)/x^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1285 +--r0:=-2/3*sqrt(a+b*x^2)/x^(3/2)-4/3*a^(1/4)*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 512 + +--S 513 of 1285 +--a0:=integrate(t0,x) +--E 513 + +--S 514 of 1285 +--m0:=a0-r0 +--E 514 + +--S 515 of 1285 +--d0:=D(m0,x) +--E 515 + +)clear all + +--S 516 of 1285 +t0:=sqrt(a+b*x^2)/x^(7/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1285 +--r0:=-2/5*sqrt(a+b*x^2)/x^(5/2)-4/5*b*sqrt(a+b*x^2)/(a*sqrt(x))+4/5*_ +--(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))-4/5*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*sqrt(a+b*x^2)) +--E 517 + +--S 518 of 1285 +--a0:=integrate(t0,x) +--E 518 + +--S 519 of 1285 +--m0:=a0-r0 +--E 519 + +--S 520 of 1285 +--d0:=D(m0,x) +--E 520 + +)clear all + +--S 521 of 1285 +t0:=x^(7/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 5 3 +-+ | 2 +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1285 +--r0:=2/15*x^(9/2)*(a+b*x^2)^(3/2)+8/385*a^2*x^(5/2)*sqrt(a+b*x^2)/b+_ +--4/55*a*x^(9/2)*sqrt(a+b*x^2)-8/231*a^3*sqrt(x)*sqrt(a+b*x^2)/b^2+_ +--8/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 522 + +--S 523 of 1285 +--a0:=integrate(t0,x) +--E 523 + +--S 524 of 1285 +--m0:=a0-r0 +--E 524 + +--S 525 of 1285 +--d0:=D(m0,x) +--E 525 + +)clear all + +--S 526 of 1285 +t0:=x^(5/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 4 2 +-+ | 2 +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1285 +--r0:=2/13*x^(7/2)*(a+b*x^2)^(3/2)+8/195*a^2*x^(3/2)*sqrt(a+b*x^2)/b+_ +--4/39*a*x^(7/2)*sqrt(a+b*x^2)+8/65*a^(15/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-_ +--8/65*a^(15/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 527 + +--S 528 of 1285 +--a0:=integrate(t0,x) +--E 528 + +--S 529 of 1285 +--m0:=a0-r0 +--E 529 + +--S 530 of 1285 +--d0:=D(m0,x) +--E 530 + +)clear all + +--S 531 of 1285 +t0:=x^(3/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 3 +-+ | 2 +--R (1) (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1285 +--r0:=2/11*x^(5/2)*(a+b*x^2)^(3/2)+12/77*a*x^(5/2)*sqrt(a+b*x^2)+_ +--8/77*a^2*sqrt(x)*sqrt(a+b*x^2)/b+8/77*a^(13/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(5/4)*sqrt(a+b*x^2)) +--E 532 + +--S 533 of 1285 +--a0:=integrate(t0,x) +--E 533 + +--S 534 of 1285 +--m0:=a0-r0 +--E 534 + +--S 535 of 1285 +--d0:=D(m0,x) +--E 535 + +)clear all + +--S 536 of 1285 +t0:=(a+b*x^2)^(3/2)*sqrt(x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 +--R (1) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1285 +--r0:=2/9*x^(3/2)*(a+b*x^2)^(3/2)+4/15*a*x^(3/2)*sqrt(a+b*x^2)+_ +--8/15*a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-8/15*a^(11/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 537 + +--S 538 of 1285 +--a0:=integrate(t0,x) +--E 538 + +--S 539 of 1285 +--m0:=a0-r0 +--E 539 + +--S 540 of 1285 +--d0:=D(m0,x) +--E 540 + +)clear all + +--S 541 of 1285 +t0:=(a+b*x^2)^(3/2)/sqrt(x) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1285 +--r0:=2/7*(a+b*x^2)^(3/2)*sqrt(x)+4/7*a*sqrt(x)*sqrt(a+b*x^2)+_ +--8/7*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 542 + +--S 543 of 1285 +--a0:=integrate(t0,x) +--E 543 + +--S 544 of 1285 +--m0:=a0-r0 +--E 544 + +--S 545 of 1285 +--d0:=D(m0,x) +--E 545 + +)clear all + +--S 546 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1285 +--r0:=-2*(a+b*x^2)^(3/2)/sqrt(x)+12/5*b*x^(3/2)*sqrt(a+b*x^2)-_ +--24/5*a^(7/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)+24/5*a^(7/4)*(-b)^(1/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 547 + +--S 548 of 1285 +--a0:=integrate(t0,x) +--E 548 + +--S 549 of 1285 +--m0:=a0-r0 +--E 549 + +--S 550 of 1285 +--d0:=D(m0,x) +--E 550 + +)clear all + +--S 551 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(5/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1285 +--r0:=-2/3*(a+b*x^2)^(3/2)/x^(3/2)+4/3*b*sqrt(x)*sqrt(a+b*x^2)-_ +--8/3*a^(5/4)*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 552 + +--S 553 of 1285 +--a0:=integrate(t0,x) +--E 553 + +--S 554 of 1285 +--m0:=a0-r0 +--E 554 + +--S 555 of 1285 +--d0:=D(m0,x) +--E 555 + +)clear all + +--S 556 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(7/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1285 +--r0:=-2/5*(a+b*x^2)^(3/2)/x^(5/2)-12/5*b*sqrt(a+b*x^2)/sqrt(x)+_ +--24/5*a^(3/4)*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)-24/5*a^(3/4)*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 557 + +--S 558 of 1285 +--a0:=integrate(t0,x) +--E 558 + +--S 559 of 1285 +--m0:=a0-r0 +--E 559 + +--S 560 of 1285 +--d0:=D(m0,x) +--E 560 + +)clear all + +--S 561 of 1285 +t0:=x^(7/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 7 5 2 3 +-+ | 2 +--R (1) (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1285 +--r0:=4/57*a*x^(9/2)*(a+b*x^2)^(3/2)+2/19*x^(9/2)*(a+b*x^2)^(5/2)+_ +--16/1463*a^3*x^(5/2)*sqrt(a+b*x^2)/b+8/209*a^2*x^(9/2)*sqrt(a+b*x^2)-_ +--80/4389*a^4*sqrt(x)*sqrt(a+b*x^2)/b^2+80/4389*a^(21/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(9/4)*sqrt(a+b*x^2)) +--E 562 + +--S 563 of 1285 +--a0:=integrate(t0,x) +--E 563 + +--S 564 of 1285 +--m0:=a0-r0 +--E 564 + +--S 565 of 1285 +--d0:=D(m0,x) +--E 565 + +)clear all + +--S 566 of 1285 +t0:=x^(5/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 +--R (1) (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1285 +--r0:=20/221*a*x^(7/2)*(a+b*x^2)^(3/2)+2/17*x^(7/2)*(a+b*x^2)^(5/2)+_ +--16/663*a^3*x^(3/2)*sqrt(a+b*x^2)/b+40/663*a^2*x^(7/2)*sqrt(a+b*x^2)+_ +--16/221*a^(19/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-16/221*a^(19/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2)) +--E 567 + +--S 568 of 1285 +--a0:=integrate(t0,x) +--E 568 + +--S 569 of 1285 +--m0:=a0-r0 +--E 569 + +--S 570 of 1285 +--d0:=D(m0,x) +--E 570 + +)clear all + +--S 571 of 1285 +t0:=x^(3/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (1) (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1285 +--r0:=4/33*a*x^(5/2)*(a+b*x^2)^(3/2)+2/15*x^(5/2)*(a+b*x^2)^(5/2)+_ +--8/77*a^2*x^(5/2)*sqrt(a+b*x^2)+16/231*a^3*sqrt(x)*sqrt(a+b*x^2)/_ +--b+16/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 572 + +--S 573 of 1285 +--a0:=integrate(t0,x) +--E 573 + +--S 574 of 1285 +--m0:=a0-r0 +--E 574 + +--S 575 of 1285 +--d0:=D(m0,x) +--E 575 + +)clear all + +--S 576 of 1285 +t0:=(a+b*x^2)^(5/2)*sqrt(x) +--R +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 +--R (1) (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1285 +--r0:=20/117*a*x^(3/2)*(a+b*x^2)^(3/2)+2/13*x^(3/2)*(a+b*x^2)^(5/2)+_ +--8/39*a^2*x^(3/2)*sqrt(a+b*x^2)+16/39*a^(15/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2))-16/39*a^(15/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 577 + +--S 578 of 1285 +--a0:=integrate(t0,x) +--E 578 + +--S 579 of 1285 +--m0:=a0-r0 +--E 579 + +--S 580 of 1285 +--d0:=D(m0,x) +--E 580 + +)clear all + +--S 581 of 1285 +t0:=(a+b*x^2)^(5/2)/sqrt(x) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1285 +--r0:=20/77*a*(a+b*x^2)^(3/2)*sqrt(x)+2/11*(a+b*x^2)^(5/2)*sqrt(x)+_ +--40/77*a^2*sqrt(x)*sqrt(a+b*x^2)+80/77*a^(13/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(1/4)*sqrt(a+b*x^2)) +--E 582 + +--S 583 of 1285 +--a0:=integrate(t0,x) +--E 583 + +--S 584 of 1285 +--m0:=a0-r0 +--E 584 + +--S 585 of 1285 +--d0:=D(m0,x) +--E 585 + +)clear all + +--S 586 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(3/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1285 +--r0:=20/9*b*x^(3/2)*(a+b*x^2)^(3/2)-2*(a+b*x^2)^(5/2)/sqrt(x)+_ +--8/3*a*b*x^(3/2)*sqrt(a+b*x^2)-16/3*a^(11/4)*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)+16/3*a^(11/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 587 + +--S 588 of 1285 +--a0:=integrate(t0,x) +--E 588 + +--S 589 of 1285 +--m0:=a0-r0 +--E 589 + +--S 590 of 1285 +--d0:=D(m0,x) +--E 590 + +)clear all + +--S 591 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1285 +--r0:=-2/3*(a+b*x^2)^(5/2)/x^(3/2)+20/21*b*(a+b*x^2)^(3/2)*sqrt(x)+_ +--40/21*a*b*sqrt(x)*sqrt(a+b*x^2)-80/21*a^(9/4)*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 592 + +--S 593 of 1285 +--a0:=integrate(t0,x) +--E 593 + +--S 594 of 1285 +--m0:=a0-r0 +--E 594 + +--S 595 of 1285 +--d0:=D(m0,x) +--E 595 + +)clear all + +--S 596 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(7/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1285 +--r0:=-2/5*(a+b*x^2)^(5/2)/x^(5/2)-4*b*(a+b*x^2)^(3/2)/sqrt(x)+_ +--24/5*b^2*x^(3/2)*sqrt(a+b*x^2)+48/5*a^(7/4)*(-b)^(5/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)-48/5*a^(7/4)*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 597 + +--S 598 of 1285 +--a0:=integrate(t0,x) +--E 598 + +--S 599 of 1285 +--m0:=a0-r0 +--E 599 + +--S 600 of 1285 +--d0:=D(m0,x) +--E 600 + +)clear all + +--S 601 of 1285 +t0:=x^(7/2)/sqrt(a+b*x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1285 +--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)/b-10/21*a*sqrt(x)*sqrt(a+b*x^2)/b^2+_ +--10/21*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 602 + +--S 603 of 1285 +--a0:=integrate(t0,x) +--E 603 + +--S 604 of 1285 +--m0:=a0-r0 +--E 604 + +--S 605 of 1285 +--d0:=D(m0,x) +--E 605 + +)clear all + +--S 606 of 1285 +t0:=x^(5/2)/sqrt(a+b*x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1285 +--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)/b+6/5*a^(7/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2))-6/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 607 + +--S 608 of 1285 +--a0:=integrate(t0,x) +--E 608 + +--S 609 of 1285 +--m0:=a0-r0 +--E 609 + +--S 610 of 1285 +--d0:=D(m0,x) +--E 610 + +)clear all + +--S 611 of 1285 +t0:=x^(3/2)/sqrt(a+b*x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1285 +--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)/b+2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 612 + +--S 613 of 1285 +--a0:=integrate(t0,x) +--E 613 + +--S 614 of 1285 +--m0:=a0-r0 +--E 614 + +--S 615 of 1285 +--d0:=D(m0,x) +--E 615 + +)clear all + +--S 616 of 1285 +t0:=sqrt(x)/sqrt(a+b*x^2) +--R +--R +--R +-+ +--R \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1285 +--r0:=2*a^(3/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-2*a^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 617 + +--S 618 of 1285 +--a0:=integrate(t0,x) +--E 618 + +--S 619 of 1285 +--m0:=a0-r0 +--E 619 + +--S 620 of 1285 +--d0:=D(m0,x) +--E 620 + +)clear all + +--S 621 of 1285 +t0:=1/(sqrt(x)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) --------------- +--R +--------+ +--R +-+ | 2 +--R \|x \|b x + a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1285 +--r0:=2*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 622 + +--S 623 of 1285 +--a0:=integrate(t0,x) +--E 623 + +--S 624 of 1285 +--m0:=a0-r0 +--E 624 + +--S 625 of 1285 +--d0:=D(m0,x) +--E 625 + +)clear all + +--S 626 of 1285 +t0:=1/(x^(3/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +--------+ +--R +-+ | 2 +--R x\|x \|b x + a +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1285 +--r0:=-2*sqrt(a+b*x^2)/(a*sqrt(x))-2*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*sqrt(a+b*x^2))+2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2)) +--E 627 + +--S 628 of 1285 +--a0:=integrate(t0,x) +--E 628 + +--S 629 of 1285 +--m0:=a0-r0 +--E 629 + +--S 630 of 1285 +--d0:=D(m0,x) +--E 630 + +)clear all + +--S 631 of 1285 +t0:=1/(x^(5/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 2 +-+ | 2 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1285 +--r0:=-2/3*sqrt(a+b*x^2)/(a*x^(3/2))+2/3*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(3/4)*sqrt(a+b*x^2)) +--E 632 + +--S 633 of 1285 +--a0:=integrate(t0,x) +--E 633 + +--S 634 of 1285 +--m0:=a0-r0 +--E 634 + +--S 635 of 1285 +--d0:=D(m0,x) +--E 635 + +)clear all + +--S 636 of 1285 +t0:=1/(x^(7/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 3 +-+ | 2 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1285 +--r0:=-2/5*sqrt(a+b*x^2)/(a*x^(5/2))+6/5*b*sqrt(a+b*x^2)/(a^2*sqrt(x))-_ +--6/5*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+6/5*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*sqrt(a+b*x^2)) +--E 637 + +--S 638 of 1285 +--a0:=integrate(t0,x) +--E 638 + +--S 639 of 1285 +--m0:=a0-r0 +--E 639 + +--S 640 of 1285 +--d0:=D(m0,x) +--E 640 + +)clear all + +--S 641 of 1285 +t0:=x^(7/2)/(a+b*x^2)^(3/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1285 +--r0:=-x^(5/2)/(b*sqrt(a+b*x^2))+5/3*sqrt(x)*sqrt(a+b*x^2)/b^2-_ +--5/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 642 + +--S 643 of 1285 +--a0:=integrate(t0,x) +--E 643 + +--S 644 of 1285 +--m0:=a0-r0 +--E 644 + +--S 645 of 1285 +--d0:=D(m0,x) +--E 645 + +)clear all + +--S 646 of 1285 +t0:=x^(5/2)/(a+b*x^2)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1285 +--r0:=-x^(3/2)/(b*sqrt(a+b*x^2))-3*a^(3/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))+_ +--3*a^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 647 + +--S 648 of 1285 +--a0:=integrate(t0,x) +--E 648 + +--S 649 of 1285 +--m0:=a0-r0 +--E 649 + +--S 650 of 1285 +--d0:=D(m0,x) +--E 650 + +)clear all + +--S 651 of 1285 +t0:=x^(3/2)/(a+b*x^2)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1285 +--r0:=-sqrt(x)/(b*sqrt(a+b*x^2))-a^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 652 + +--S 653 of 1285 +--a0:=integrate(t0,x) +--E 653 + +--S 654 of 1285 +--m0:=a0-r0 +--E 654 + +--S 655 of 1285 +--d0:=D(m0,x) +--E 655 + +)clear all + +--S 656 of 1285 +t0:=sqrt(x)/(a+b*x^2)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1285 +--r0:=x^(3/2)/(a*sqrt(a+b*x^2))-elliptic_e(asin((-b)^(1/4)*sqrt(x)/_ +--a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))+_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2)) +--E 657 + +--S 658 of 1285 +--a0:=integrate(t0,x) +--E 658 + +--S 659 of 1285 +--m0:=a0-r0 +--E 659 + +--S 660 of 1285 +--d0:=D(m0,x) +--E 660 + +)clear all + +--S 661 of 1285 +t0:=1/((a+b*x^2)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R 2 +-+ | 2 +--R (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1285 +--r0:=sqrt(x)/(a*sqrt(a+b*x^2))+elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b*x^2)) +--E 662 + +--S 663 of 1285 +--a0:=integrate(t0,x) +--E 663 + +--S 664 of 1285 +--m0:=a0-r0 +--E 664 + +--S 665 of 1285 +--d0:=D(m0,x) +--E 665 + +)clear all + +--S 666 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +--------+ +--R 3 +-+ | 2 +--R (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1285 +--r0:=1/(a*sqrt(x)*sqrt(a+b*x^2))-3*sqrt(a+b*x^2)/(a^2*sqrt(x))-3*_ +--(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+3*(-b)^(1/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*sqrt(a+b*x^2)) +--E 667 + +--S 668 of 1285 +--a0:=integrate(t0,x) +--E 668 + +--S 669 of 1285 +--m0:=a0-r0 +--E 669 + +--S 670 of 1285 +--d0:=D(m0,x) +--E 670 + +)clear all + +--S 671 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +--R 4 2 +-+ | 2 +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1285 +--r0:=1/(a*x^(3/2)*sqrt(a+b*x^2))-5/3*sqrt(a+b*x^2)/(a^2*x^(3/2))+_ +--5/3*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(7/4)*sqrt(a+b*x^2)) +--E 672 + +--S 673 of 1285 +--a0:=integrate(t0,x) +--E 673 + +--S 674 of 1285 +--m0:=a0-r0 +--E 674 + +--S 675 of 1285 +--d0:=D(m0,x) +--E 675 + +)clear all + +--S 676 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +--R 5 3 +-+ | 2 +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1285 +--r0:=1/(a*x^(5/2)*sqrt(a+b*x^2))-7/5*sqrt(a+b*x^2)/(a^2*x^(5/2))+_ +--21/5*b*sqrt(a+b*x^2)/(a^3*sqrt(x))-21/5*(-b)^(5/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(9/4)*sqrt(a+b*x^2))+21/5*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2)) +--E 677 + +--S 678 of 1285 +--a0:=integrate(t0,x) +--E 678 + +--S 679 of 1285 +--m0:=a0-r0 +--E 679 + +--S 680 of 1285 +--d0:=D(m0,x) +--E 680 + +)clear all + +--S 681 of 1285 +t0:=x^(7/2)/(a+b*x^2)^(5/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1285 +--r0:=-1/3*x^(5/2)/(b*(a+b*x^2)^(3/2))-5/6*sqrt(x)/(b^2*sqrt(a+b*x^2))+_ +--5/6*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 682 + +--S 683 of 1285 +--a0:=integrate(t0,x) +--E 683 + +--S 684 of 1285 +--m0:=a0-r0 +--E 684 + +--S 685 of 1285 +--d0:=D(m0,x) +--E 685 + +)clear all + +--S 686 of 1285 +t0:=x^(5/2)/(a+b*x^2)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1285 +--r0:=-1/3*x^(3/2)/(b*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a*b*sqrt(a+b*x^2))+_ +--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))-1/2*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2)) +--E 687 + +--S 688 of 1285 +--a0:=integrate(t0,x) +--E 688 + +--S 689 of 1285 +--m0:=a0-r0 +--E 689 + +--S 690 of 1285 +--d0:=D(m0,x) +--E 690 + +)clear all + +--S 691 of 1285 +t0:=x^(3/2)/(a+b*x^2)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1285 +--r0:=-1/3*sqrt(x)/(b*(a+b*x^2)^(3/2))+1/6*sqrt(x)/(a*b*sqrt(a+b*x^2))-_ +--1/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(3/4)*(-b)^(5/4)*sqrt(a+b*x^2)) +--E 692 + +--S 693 of 1285 +--a0:=integrate(t0,x) +--E 693 + +--S 694 of 1285 +--m0:=a0-r0 +--E 694 + +--S 695 of 1285 +--d0:=D(m0,x) +--E 695 + +)clear all + +--S 696 of 1285 +t0:=sqrt(x)/(a+b*x^2)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1285 +--r0:=1/3*x^(3/2)/(a*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a^2*sqrt(a+b*x^2))-_ +--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2))+1/2*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2)) +--E 697 + +--S 698 of 1285 +--a0:=integrate(t0,x) +--E 698 + +--S 699 of 1285 +--m0:=a0-r0 +--E 699 + +--S 700 of 1285 +--d0:=D(m0,x) +--E 700 + +)clear all + +--S 701 of 1285 +t0:=1/((a+b*x^2)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R +--------+ +--R 2 4 2 2 +-+ | 2 +--R (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1285 +--r0:=1/3*sqrt(x)/(a*(a+b*x^2)^(3/2))+5/6*sqrt(x)/(a^2*sqrt(a+b*x^2))+_ +--5/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^2)) +--E 702 + +--S 703 of 1285 +--a0:=integrate(t0,x) +--E 703 + +--S 704 of 1285 +--m0:=a0-r0 +--E 704 + +--S 705 of 1285 +--d0:=D(m0,x) +--E 705 + +)clear all + +--S 706 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1285 +--r0:=1/3/(a*(a+b*x^2)^(3/2)*sqrt(x))+7/6/(a^2*sqrt(x)*sqrt(a+b*x^2))-_ +--7/2*sqrt(a+b*x^2)/(a^3*sqrt(x))-7/2*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(9/4)*sqrt(a+b*x^2))+7/2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2)) +--E 707 + +--S 708 of 1285 +--a0:=integrate(t0,x) +--E 708 + +--S 709 of 1285 +--m0:=a0-r0 +--E 709 + +--S 710 of 1285 +--d0:=D(m0,x) +--E 710 + +)clear all + +--S 711 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 +--R (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1285 +--r0:=1/3/(a*x^(3/2)*(a+b*x^2)^(3/2))+3/2/(a^2*x^(3/2)*sqrt(a+b*x^2))-_ +--5/2*sqrt(a+b*x^2)/(a^3*x^(3/2))+5/2*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(11/4)*sqrt(a+b*x^2)) +--E 712 + +--S 713 of 1285 +--a0:=integrate(t0,x) +--E 713 + +--S 714 of 1285 +--m0:=a0-r0 +--E 714 + +--S 715 of 1285 +--d0:=D(m0,x) +--E 715 + +)clear all + +--S 716 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +--------+ +--R 2 7 5 2 3 +-+ | 2 +--R (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1285 +--r0:=1/3/(a*x^(5/2)*(a+b*x^2)^(3/2))+11/6/(a^2*x^(5/2)*sqrt(a+b*x^2))-_ +--77/30*sqrt(a+b*x^2)/(a^3*x^(5/2))+77/10*b*sqrt(a+b*x^2)/(a^4*sqrt(x))-_ +--77/10*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(13/4)*sqrt(a+b*x^2))+77/10*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(13/4)*sqrt(a+b*x^2)) +--E 717 + +--S 718 of 1285 +--a0:=integrate(t0,x) +--E 718 + +--S 719 of 1285 +--m0:=a0-r0 +--E 719 + +--S 720 of 1285 +--d0:=D(m0,x) +--E 720 + +)clear all + +--S 721 of 1285 +t0:=x^m*(a+b*x^2)^p +--R +--R +--R m 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1285 +--r0:=x^(1+m)*(a+b*x^2)^p*hypergeometric(1/2*(1+m),-p,1/2*(3+m),-b*x^2/a)/_ +--((1+m)*((a+b*x^2)/a)^p) +--E 722 + +--S 723 of 1285 +--a0:=integrate(t0,x) +--E 723 + +--S 724 of 1285 +--m0:=a0-r0 +--E 724 + +--S 725 of 1285 +--d0:=D(m0,x) +--E 725 + +)clear all + +--S 726 of 1285 +t0:=x^7*(a+b*x^2)^p +--R +--R +--R 7 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1285 +r0:=-1/2*a^3*(a+b*x^2)^(1+p)/(b^4*(1+p))+3/2*a^2*(a+b*x^2)^(2+p)/_ + (b^4*(2+p))-3/2*a*(a+b*x^2)^(3+p)/(b^4*(3+p))+1/2*(a+b*x^2)^(4+p)/_ + (b^4*(4+p)) +--R +--R +--R (2) +--R 3 2 2 p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 2 p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 2 p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 2 p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 8 3 3 3 2 3 6 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 4 3 2 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 2 +--R p log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 8 3 3 3 2 3 6 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 4 3 2 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 2 +--R p log(b x + a) +--R %e +--R + +--R 3 2 2 p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 2 p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 2 p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 2 p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 1285 +t0:=x^5*(a+b*x^2)^p +--R +--R +--R 5 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1285 +r0:=1/2*a^2*(a+b*x^2)^(1+p)/(b^3*(1+p))-a*(a+b*x^2)^(2+p)/(b^3*(2+p))+_ + 1/2*(a+b*x^2)^(3+p)/(b^3*(3+p)) +--R +--R +--R (2) +--R 2 2 p + 3 2 2 p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 2 p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 6 2 2 2 4 2 2 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 2 +--R p log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 6 2 2 2 4 2 2 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 2 +--R p log(b x + a) +--R %e +--R + +--R 2 2 p + 3 2 2 p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 2 p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 1285 +t0:=x^4*(a+b*x^2)^p +--R +--R +--R 4 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1285 +--r0:=-3*a*x*(a+b*x^2)^(1+p)/(b^2*(3+2*p)*(5+2*p))+x^3*(a+b*x^2)^(1+p)/_ +-- (b*(5+2*p))+3*a^2*x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,_ +-- -b*x^2/a)/(b^2*(3+2*p)*(5+2*p)*((a+b*x^2)/a)^p) +--E 737 + +--S 738 of 1285 +--a0:=integrate(t0,x) +--E 738 + +--S 739 of 1285 +--m0:=a0-r0 +--E 739 + +--S 740 of 1285 +--d0:=normalize m0 +--E 740 + +)clear all + +--S 741 of 1285 +t0:=x^3*(a+b*x^2)^p +--R +--R +--R 3 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1285 +r0:=-1/2*a*(a+b*x^2)^(1+p)/(b^2*(1+p))+1/2*(a+b*x^2)^(2+p)/(b^2*(2+p)) +--R +--R +--R 2 p + 2 2 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2 2 4 2 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +--R 2 2 4 2 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 2 p + 2 2 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 1285 +t0:=x^2*(a+b*x^2)^p +--R +--R +--R 2 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1285 +--r0:=x*(a+b*x^2)^(1+p)/(b*(3+2*p))-a*x*(a+b*x^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(b*(3+2*p)*((a+b*x^2)/a)^p) +--E 747 + +--S 748 of 1285 +--a0:=integrate(t0,x) +--E 748 + +--S 749 of 1285 +--m0:=a0-r0 +--E 749 + +--S 750 of 1285 +--d0:=D(m0,x) +--E 750 + +)clear all + +--S 751 of 1285 +t0:=x*(a+b*x^2)^p +--R +--R +--R 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1285 +r0:=1/2*(a+b*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 p + 1 +--R (b x + a) +--R (2) --------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 2b p + 2b +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1285 +m0:=a0-r0 +--R +--R +--R 2 +--R 2 p log(b x + a) 2 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 1285 +t0:=(a+b*x^2)^p +--R +--R +--R 2 p +--R (1) (b x + a) +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1285 +--r0:=x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,-b*x^2/a)/((a+b*x^2)/a)^p +--E 757 + +--S 758 of 1285 +--a0:=integrate(t0,x) +--E 758 + +--S 759 of 1285 +--m0:=a0-r0 +--E 759 + +--S 760 of 1285 +--d0:=D(m0,x) +--E 760 + +)clear all + +--S 761 of 1285 +t0:=(a+b*x^2)^p/x +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1285 +--r0:=1/2*(a+b*x^2)^p*_ +-- hypergeometric(-p,-p,1-p,-a/(b*x^2))/(p*((a+b*x^2)/(b*x^2))^p) +--E 762 + +--S 763 of 1285 +--a0:=integrate(t0,x) +--E 763 + +--S 764 of 1285 +--m0:=a0-r0 +--E 764 + +--S 765 of 1285 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1285 +t0:=(a+b*x^2)^p/x^2 +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1285 +--r0:=-(a+b*x^2)^(1+p)/(a*x)+b*(1+2*p)*x*(a+b*x^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(a*((a+b*x^2)/a)^p) +--E 767 + +--S 768 of 1285 +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1285 +--m0:=a0-r0 +--E 769 + +--S 770 of 1285 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1285 +t0:=(a+b*x^2)^p/x^3 +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1285 +--r0:=-1/2*(a+b*x^2)^(1+p)/(a*x^2)-1/2*b*p*(a+b*x^2)^(1+p)*_ +-- hypergeometric(1,1+p,2+p,(a+b*x^2)/a)/(a^2*(1+p)) +--E 772 + +--S 773 of 1285 +--a0:=integrate(t0,x) +--E 773 + +--S 774 of 1285 +--m0:=a0-r0 +--E 774 + +--S 775 of 1285 +--d0:=D(m0,x) +--E 775 + +)clear all + +--S 776 of 1285 +t0:=x^(9/2)*(a+b*x^2)^p +--R +--R +--R 4 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1285 +--r0:=-14*a*x^(3/2)*(a+b*x^2)^(1+p)/(b^2*(7+4*p)*(11+4*p))+2*x^(7/2)*_ +-- (a+b*x^2)^(1+p)/(b*(11+4*p))+14*a^2*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b^2*(7+4*p)*(11+4*p)*_ +-- ((a+b*x^2)/a)^p) +--E 777 + +--S 778 of 1285 +--a0:=integrate(t0,x) +--E 778 + +--S 779 of 1285 +--m0:=a0-r0 +--E 779 + +--S 780 of 1285 +--d0:=D(m0,x) +--E 780 + +)clear all + +--S 781 of 1285 +t0:=x^(7/2)*(a+b*x^2)^p +--R +--R +--R 3 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1285 +--r0:=2*x^(5/2)*(a+b*x^2)^(1+p)/(b*(9+4*p))-2*a*x^(5/2)*(a+b*x^2)^p*_ +-- hypergeometric(5/4,-p,9/4,-b*x^2/a)/(b*(9+4*p)*((a+b*x^2)/a)^p) +--E 782 + +--S 783 of 1285 +--a0:=integrate(t0,x) +--E 783 + +--S 784 of 1285 +--m0:=a0-r0 +--E 784 + +--S 785 of 1285 +--d0:=D(m0,x) +--E 785 + +)clear all + +--S 786 of 1285 +t0:=x^(5/2)*(a+b*x^2)^p +--R +--R +--R 2 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1285 +--r0:=2*x^(3/2)*(a+b*x^2)^(1+p)/(b*(7+4*p))-2*a*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b*(7+4*p)*((a+b*x^2)/a)^p) +--E 787 + +--S 788 of 1285 +--a0:=integrate(t0,x) +--E 788 + +--S 789 of 1285 +--m0:=a0-r0 +--E 789 + +--S 790 of 1285 +--d0:=D(m0,x) +--E 790 + +)clear all + +--S 791 of 1285 +t0:=x^(3/2)*(a+b*x^2)^p +--R +--R +--R 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1285 +--r0:=2/5*x^(5/2)*(a+b*x^2)^p*hypergeometric(5/4,-p,9/4,-b*x^2/a)/_ +-- ((a+b*x^2)/a)^p +--E 792 + +--S 793 of 1285 +--a0:=integrate(t0,x) +--E 793 + +--S 794 of 1285 +--m0:=a0-r0 +--E 794 + +--S 795 of 1285 +--d0:=D(m0,x) +--E 795 + +)clear all + +--S 796 of 1285 +t0:=x^(1/2)*(a+b*x^2)^p +--R +--R +--R 2 p +-+ +--R (1) (b x + a) \|x +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1285 +--r0:=2/3*x^(3/2)*(a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/_ +-- ((a+b*x^2)/a)^p +--E 797 + +--S 798 of 1285 +--a0:=integrate(t0,x) +--E 798 + +--S 799 of 1285 +--m0:=a0-r0 +--E 799 + +--S 800 of 1285 +--d0:=D(m0,x) +--E 800 + +)clear all + +--S 801 of 1285 +t0:=(a+b*x^2)^p/x^(1/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1285 +--r0:=2*(a+b*x^2)^p*hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/((a+b*x^2)/a)^p +--E 802 + +--S 803 of 1285 +--a0:=integrate(t0,x) +--E 803 + +--S 804 of 1285 +--m0:=a0-r0 +--E 804 + +--S 805 of 1285 +--d0:=D(m0,x) +--E 805 + +)clear all + +--S 806 of 1285 +t0:=(a+b*x^2)^p/x^(3/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1285 +--r0:=2/3*b*(3+4*p)*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a*((a+b*x^2)/a)^p)-_ +-- 2*(a+b*x^2)^(1+p)/(a*sqrt(x)) +--E 807 + +--S 808 of 1285 +--a0:=integrate(t0,x) +--E 808 + +--S 809 of 1285 +--m0:=a0-r0 +--E 809 + +--S 810 of 1285 +--d0:=D(m0,x) +--E 810 + +)clear all + +--S 811 of 1285 +t0:=(a+b*x^2)^p/x^(5/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1285 +--r0:=-2/3*(a+b*x^2)^(1+p)/(a*x^(3/2))+2/3*b*(1+4*p)*(a+b*x^2)^p*_ +-- hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/(a*((a+b*x^2)/a)^p) +--E 812 + +--S 813 of 1285 +--a0:=integrate(t0,x) +--E 813 + +--S 814 of 1285 +--m0:=a0-r0 +--E 814 + +--S 815 of 1285 +--d0:=D(m0,x) +--E 815 + +)clear all + +--S 816 of 1285 +t0:=(a+b*x^2)^p/x^(7/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1285 +--r0:=-2/5*(a+b*x^2)^(1+p)/(a*x^(5/2))-2/15*b^2*(1-4*p)*(3+4*p)*x^(3/2)*_ +-- (a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a^2*((a+b*x^2)/a)^p)+_ +-- 2/5*b*(1-4*p)*(a+b*x^2)^(1+p)/(a^2*sqrt(x)) +--E 817 + +--S 818 of 1285 +--a0:=integrate(t0,x) +--E 818 + +--S 819 of 1285 +--m0:=a0-r0 +--E 819 + +--S 820 of 1285 +--d0:=D(m0,x) +--E 820 + +)clear all + +--S 821 of 1285 +t0:=x^m*(a+b*x^3) +--R +--R +--R 3 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1285 +r0:=a*x^(1+m)/(1+m)+b*x^(4+m)/(4+m) +--R +--R +--R m + 4 m + 1 +--R (b m + b)x + (a m + 4a)x +--R (2) ---------------------------------- +--R 2 +--R m + 5m + 4 +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 m log(x) +--R ((b m + b)x + (a m + 4a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 5m + 4 +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 m log(x) m + 4 +--R ((b m + b)x + (a m + 4a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 4a)x +--R / +--R 2 +--R m + 5m + 4 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1285 +t0:=x^3*(a+b*x^3) +--R +--R +--R 6 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 826 + +--S 827 of 1285 +r0:=1/4*a*x^4+1/7*b*x^7 +--R +--R +--R 1 7 1 4 +--R (2) - b x + - a x +--R 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 827 + +--S 828 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 4 +--R (3) - b x + - a x +--R 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 828 + +--S 829 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 829 + +--S 830 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 830 + +)clear all + +--S 831 of 1285 +t0:=x^2*(a+b*x^3) +--R +--R +--R 5 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 831 + +--S 832 of 1285 +r0:=1/3*a*x^3+1/6*b*x^6 +--R +--R +--R 1 6 1 3 +--R (2) - b x + - a x +--R 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 832 + +--S 833 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 3 +--R (3) - b x + - a x +--R 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 833 + +--S 834 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 834 + +--S 835 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 835 + +)clear all + +--S 836 of 1285 +t0:=x*(a+b*x^3) +--R +--R +--R 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 836 + +--S 837 of 1285 +r0:=1/2*a*x^2+1/5*b*x^5 +--R +--R +--R 1 5 1 2 +--R (2) - b x + - a x +--R 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 837 + +--S 838 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 2 +--R (3) - b x + - a x +--R 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 838 + +--S 839 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 839 + +--S 840 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 840 + +)clear all + +--S 841 of 1285 +t0:=a+b*x^3 +--R +--R +--R 3 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 841 + +--S 842 of 1285 +r0:=a*x+1/4*b*x^4 +--R +--R +--R 1 4 +--R (2) - b x + a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 842 + +--S 843 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 4 +--R (3) - b x + a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 843 + +--S 844 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 844 + +--S 845 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 845 + +)clear all + +--S 846 of 1285 +t0:=(a+b*x^3)/x +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 846 + +--S 847 of 1285 +r0:=1/3*b*x^3+a*log(x) +--R +--R +--R 3 +--R 3a log(x) + b x +--R (2) ---------------- +--R 3 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3a log(x) + b x +--R (3) ---------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1285 +t0:=(a+b*x^3)/x^2 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 851 + +--S 852 of 1285 +r0:=-a/x+1/2*b*x^2 +--R +--R +--R 3 +--R b x - 2a +--R (2) --------- +--R 2x +--R Type: Fraction(Polynomial(Integer)) +--E 852 + +--S 853 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R b x - 2a +--R (3) --------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 1285 +t0:=(a+b*x^3)/x^3 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 856 + +--S 857 of 1285 +r0:=-1/2*a/x^2+b*x +--R +--R +--R 3 1 +--R b x - - a +--R 2 +--R (2) ---------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 857 + +--S 858 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2b x - a +--R (3) --------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1285 +t0:=(a+b*x^3)/x^4 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 861 + +--S 862 of 1285 +r0:=-1/3*a/x^3+b*log(x) +--R +--R +--R 3 +--R 3b x log(x) - a +--R (2) --------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3b x log(x) - a +--R (3) --------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 1285 +t0:=(a+b*x^3)/x^5 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 866 + +--S 867 of 1285 +r0:=-1/4*a/x^4-b/x +--R +--R +--R 3 1 +--R - b x - - a +--R 4 +--R (2) ------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 867 + +--S 868 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 4b x - a +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 868 + +--S 869 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 870 + +)clear all + +--S 871 of 1285 +t0:=(a+b*x^3)/x^6 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 871 + +--S 872 of 1285 +r0:=-1/5*a/x^5-1/2*b/x^2 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 2 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 872 + +--S 873 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 5b x - 2a +--R (3) ------------ +--R 5 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 873 + +--S 874 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 1285 +t0:=(a+b*x^3)/x^7 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 876 + +--S 877 of 1285 +r0:=-1/6*a/x^6-1/3*b/x^3 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 3 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 877 + +--S 878 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 2b x - a +--R (3) ----------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1285 +t0:=(a+b*x^3)/x^8 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 881 + +--S 882 of 1285 +r0:=-1/7*a/x^7-1/4*b/x^4 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 4 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 882 + +--S 883 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 7b x - 4a +--R (3) ------------ +--R 7 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1285 +t0:=x^m*(a+b*x^3)^2 +--R +--R +--R 2 6 3 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1285 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(4+m)/(4+m)+b^2*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 7 2 m + 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 11a m + 28a )x +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 7 2 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 +--R (a m + 11a m + 28a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 7 2 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 +--R (a m + 11a m + 28a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 7 2 m + 4 +--R (- b m - 5b m - 4b )x + (- 2a b m - 16a b m - 14a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 11a m - 28a )x +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1285 +t0:=x^4*(a+b*x^3)^2 +--R +--R +--R 2 10 7 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 891 + +--S 892 of 1285 +r0:=1/5*a^2*x^5+1/4*a*b*x^8+1/11*b^2*x^11 +--R +--R +--R 1 2 11 1 8 1 2 5 +--R (2) -- b x + - a b x + - a x +--R 11 4 5 +--R Type: Polynomial(Fraction(Integer)) +--E 892 + +--S 893 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 11 1 8 1 2 5 +--R (3) -- b x + - a b x + - a x +--R 11 4 5 +--R Type: Polynomial(Fraction(Integer)) +--E 893 + +--S 894 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 894 + +--S 895 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 895 + +)clear all + +--S 896 of 1285 +t0:=x^3*(a+b*x^3)^2 +--R +--R +--R 2 9 6 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 896 + +--S 897 of 1285 +r0:=1/4*a^2*x^4+2/7*a*b*x^7+1/10*b^2*x^10 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R (2) -- b x + - a b x + - a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 897 + +--S 898 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 2 7 1 2 4 +--R (3) -- b x + - a b x + - a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 898 + +--S 899 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 899 + +--S 900 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 900 + +)clear all + +--S 901 of 1285 +t0:=x^2*(a+b*x^3)^2 +--R +--R +--R 2 8 5 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 901 + +--S 902 of 1285 +r0:=1/9*(a+b*x^3)^3/b +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - b x + - a b x + - a b x + - a +--R 9 3 3 9 +--R (2) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 902 + +--S 903 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 1 6 1 2 3 +--R (3) - b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 903 + +--S 904 of 1285 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - a +--R 9 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 904 + +--S 905 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 905 + +)clear all + +--S 906 of 1285 +t0:=x*(a+b*x^3)^2 +--R +--R +--R 2 7 4 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 906 + +--S 907 of 1285 +r0:=1/2*a^2*x^2+2/5*a*b*x^5+1/8*b^2*x^8 +--R +--R +--R 1 2 8 2 5 1 2 2 +--R (2) - b x + - a b x + - a x +--R 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 907 + +--S 908 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 2 5 1 2 2 +--R (3) - b x + - a b x + - a x +--R 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 908 + +--S 909 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 909 + +--S 910 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 910 + +)clear all + +--S 911 of 1285 +t0:=(a+b*x^3)^2 +--R +--R +--R 2 6 3 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 911 + +--S 912 of 1285 +r0:=a^2*x+1/2*a*b*x^4+1/7*b^2*x^7 +--R +--R +--R 1 2 7 1 4 2 +--R (2) - b x + - a b x + a x +--R 7 2 +--R Type: Polynomial(Fraction(Integer)) +--E 912 + +--S 913 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 1 4 2 +--R (3) - b x + - a b x + a x +--R 7 2 +--R Type: Polynomial(Fraction(Integer)) +--E 913 + +--S 914 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 914 + +--S 915 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 915 + +)clear all + +--S 916 of 1285 +t0:=(a+b*x^3)^2/x +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 1285 +r0:=2/3*a*b*x^3+1/6*b^2*x^6+a^2*log(x) +--R +--R +--R 2 2 6 3 +--R 6a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 2 6 3 +--R 6a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 918 + +--S 919 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 1285 +t0:=(a+b*x^3)^2/x^2 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 921 + +--S 922 of 1285 +r0:=-a^2/x+a*b*x^2+1/5*b^2*x^5 +--R +--R +--R 2 6 3 2 +--R b x + 5a b x - 5a +--R (2) -------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 922 + +--S 923 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R b x + 5a b x - 5a +--R (3) -------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 923 + +--S 924 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 1285 +t0:=(a+b*x^3)^2/x^3 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 926 + +--S 927 of 1285 +r0:=-1/2*a^2/x^2+2*a*b*x+1/4*b^2*x^4 +--R +--R +--R 1 2 6 3 1 2 +--R - b x + 2a b x - - a +--R 4 2 +--R (2) ----------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 927 + +--S 928 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R b x + 8a b x - 2a +--R (3) -------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 928 + +--S 929 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 1285 +t0:=(a+b*x^3)^2/x^4 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 1285 +r0:=-1/3*a^2/x^3+1/3*b^2*x^3+2*a*b*log(x) +--R +--R +--R 3 2 6 2 +--R 6a b x log(x) + b x - a +--R (2) ------------------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 2 6 2 +--R 6a b x log(x) + b x - a +--R (3) ------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 933 + +--S 934 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1285 +t0:=(a+b*x^3)^2/x^5 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 936 + +--S 937 of 1285 +r0:=-1/4*a^2/x^4-2*a*b/x+1/2*b^2*x^2 +--R +--R +--R 1 2 6 3 1 2 +--R - b x - 2a b x - - a +--R 2 4 +--R (2) ----------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 937 + +--S 938 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 2b x - 8a b x - a +--R (3) -------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +)clear all + +--S 941 of 1285 +t0:=(a+b*x^3)^2/x^6 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 941 + +--S 942 of 1285 +r0:=-1/5*a^2/x^5-a*b/x^2+b^2*x +--R +--R +--R 2 6 3 1 2 +--R b x - a b x - - a +--R 5 +--R (2) -------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 942 + +--S 943 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 5b x - 5a b x - a +--R (3) -------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 943 + +--S 944 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1285 +t0:=(a+b*x^3)^2/x^7 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 1285 +r0:=-1/6*a^2/x^6-2/3*a*b/x^3+b^2*log(x) +--R +--R +--R 2 6 3 2 +--R 6b x log(x) - 4a b x - a +--R (2) -------------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 6b x log(x) - 4a b x - a +--R (3) -------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 948 + +--S 949 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +)clear all + +--S 951 of 1285 +t0:=(a+b*x^3)^2/x^8 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 951 + +--S 952 of 1285 +r0:=-1/7*a^2/x^7-1/2*a*b/x^4-b^2/x +--R +--R +--R 2 6 1 3 1 2 +--R - b x - - a b x - - a +--R 2 7 +--R (2) ------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 952 + +--S 953 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 14b x - 7a b x - 2a +--R (3) ------------------------ +--R 7 +--R 14x +--R Type: Union(Expression(Integer),...) +--E 953 + +--S 954 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 1285 +t0:=(a+b*x^3)^2/x^9 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 956 + +--S 957 of 1285 +r0:=-1/8*a^2/x^8-2/5*a*b/x^5-1/2*b^2/x^2 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - - a +--R 2 5 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +--S 958 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 20b x - 16a b x - 5a +--R (3) ------------------------- +--R 8 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1285 +t0:=(a+b*x^3)^2/x^10 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1285 +r0:=-1/9*(a+b*x^3)^3/(a*x^9) +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - - a +--R 9 3 3 9 +--R (2) ------------------------------------- +--R 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 962 + +--S 963 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 3b x - 3a b x - a +--R (3) ---------------------- +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1285 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R 9a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1285 +t0:=(a+b*x^3)^2/x^11 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 1285 +r0:=-1/10*a^2/x^10-2/7*a*b/x^7-1/4*b^2/x^4 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - -- a +--R 4 7 10 +--R (2) --------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 967 + +--S 968 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 35b x - 40a b x - 14a +--R (3) -------------------------- +--R 10 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1285 +t0:=(a+b*x^3)^2/x^12 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 971 + +--S 972 of 1285 +r0:=-1/11*a^2/x^11-1/4*a*b/x^8-1/5*b^2/x^5 +--R +--R +--R 1 2 6 1 3 1 2 +--R - - b x - - a b x - -- a +--R 5 4 11 +--R (2) --------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 972 + +--S 973 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 44b x - 55a b x - 20a +--R (3) -------------------------- +--R 11 +--R 220x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1285 +t0:=(a+b*x^3)^2/x^13 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 1285 +r0:=-1/12*a^2/x^12-2/9*a*b/x^9-1/6*b^2/x^6 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - -- a +--R 6 9 12 +--R (2) --------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 977 + +--S 978 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 6b x - 8a b x - 3a +--R (3) ----------------------- +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1285 +t0:=x^m*(a+b*x^3)^3 +--R +--R +--R 3 9 2 6 2 3 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1285 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(4+m)/(4+m)+3*a*b^2*x^(7+m)/(7+m)+_ + b^3*x^(10+m)/(10+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 m + 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 m + 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 21a m + 138a m + 280a )x +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 21a m + 138a m + 280a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 21a m + 138a m + 280a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 10 +--R (- b m - 12b m - 39b m - 28b )x +--R + +--R 2 3 2 2 2 2 m + 7 +--R (- 3a b m - 45a b m - 162a b m - 120a b )x +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- 3a b m - 54a b m - 261a b m - 210a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 21a m - 138a m - 280a )x +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1285 +t0:=x^14*(a+b*x^3)^3 +--R +--R +--R 3 23 2 20 2 17 3 14 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 986 + +--S 987 of 1285 +r0:=1/15*a^3*x^15+1/6*a^2*b*x^18+1/7*a*b^2*x^21+1/24*b^3*x^24 +--R +--R +--R 1 3 24 1 2 21 1 2 18 1 3 15 +--R (2) -- b x + - a b x + - a b x + -- a x +--R 24 7 6 15 +--R Type: Polynomial(Fraction(Integer)) +--E 987 + +--S 988 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 24 1 2 21 1 2 18 1 3 15 +--R (3) -- b x + - a b x + - a b x + -- a x +--R 24 7 6 15 +--R Type: Polynomial(Fraction(Integer)) +--E 988 + +--S 989 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 989 + +--S 990 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 990 + +)clear all + +--S 991 of 1285 +t0:=x^11*(a+b*x^3)^3 +--R +--R +--R 3 20 2 17 2 14 3 11 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 991 + +--S 992 of 1285 +r0:=1/12*a^3*x^12+1/5*a^2*b*x^15+1/6*a*b^2*x^18+1/21*b^3*x^21 +--R +--R +--R 1 3 21 1 2 18 1 2 15 1 3 12 +--R (2) -- b x + - a b x + - a b x + -- a x +--R 21 6 5 12 +--R Type: Polynomial(Fraction(Integer)) +--E 992 + +--S 993 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 21 1 2 18 1 2 15 1 3 12 +--R (3) -- b x + - a b x + - a b x + -- a x +--R 21 6 5 12 +--R Type: Polynomial(Fraction(Integer)) +--E 993 + +--S 994 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 994 + +--S 995 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 995 + +)clear all + +--S 996 of 1285 +t0:=x^8*(a+b*x^3)^3 +--R +--R +--R 3 17 2 14 2 11 3 8 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 996 + +--S 997 of 1285 +r0:=1/9*a^3*x^9+1/4*a^2*b*x^12+1/5*a*b^2*x^15+1/18*b^3*x^18 +--R +--R +--R 1 3 18 1 2 15 1 2 12 1 3 9 +--R (2) -- b x + - a b x + - a b x + - a x +--R 18 5 4 9 +--R Type: Polynomial(Fraction(Integer)) +--E 997 + +--S 998 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 18 1 2 15 1 2 12 1 3 9 +--R (3) -- b x + - a b x + - a b x + - a x +--R 18 5 4 9 +--R Type: Polynomial(Fraction(Integer)) +--E 998 + +--S 999 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 999 + +--S 1000 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1000 + +)clear all + +--S 1001 of 1285 +t0:=x^5*(a+b*x^3)^3 +--R +--R +--R 3 14 2 11 2 8 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1001 + +--S 1002 of 1285 +r0:=-1/12*a*(a+b*x^3)^4/b^2+1/15*(a+b*x^3)^5/b^2 +--R +--R +--R 1 5 15 1 4 12 1 2 3 9 1 3 2 6 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 15 4 3 6 60 +--R (2) -------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1002 + +--S 1003 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 15 1 2 12 1 2 9 1 3 6 +--R (3) -- b x + - a b x + - a b x + - a x +--R 15 4 3 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1003 + +--S 1004 of 1285 +m0:=a0-r0 +--R +--R +--R 1 5 +--R -- a +--R 60 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1004 + +--S 1005 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1005 + +)clear all + +--S 1006 of 1285 +t0:=x^2*(a+b*x^3)^3 +--R +--R +--R 3 11 2 8 2 5 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1006 + +--S 1007 of 1285 +r0:=1/12*(a+b*x^3)^4/b +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 12 3 2 3 12 +--R (2) ------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1007 + +--S 1008 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 12 1 2 9 1 2 6 1 3 3 +--R (3) -- b x + - a b x + - a b x + - a x +--R 12 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1008 + +--S 1009 of 1285 +m0:=a0-r0 +--R +--R +--R 1 4 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1009 + +--S 1010 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1010 + +)clear all + +--S 1011 of 1285 +t0:=(a+b*x^3)^3/x +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1011 + +--S 1012 of 1285 +r0:=a^2*b*x^3+1/2*a*b^2*x^6+1/9*b^3*x^9+a^3*log(x) +--R +--R +--R 3 3 9 2 6 2 3 +--R 18a log(x) + 2b x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 18 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 3 9 2 6 2 3 +--R 18a log(x) + 2b x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 18 +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 1285 +t0:=(a+b*x^3)^3/x^4 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1016 + +--S 1017 of 1285 +r0:=-1/3*a^3/x^3+a*b^2*x^3+1/6*b^3*x^6+3*a^2*b*log(x) +--R +--R +--R 2 3 3 9 2 6 3 +--R 18a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 9 2 6 3 +--R 18a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1285 +t0:=(a+b*x^3)^3/x^7 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 1285 +r0:=-1/6*a^3/x^6-a^2*b/x^3+1/3*b^3*x^3+3*a*b^2*log(x) +--R +--R +--R 2 6 3 9 2 3 3 +--R 18a b x log(x) + 2b x - 6a b x - a +--R (2) ------------------------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 9 2 3 3 +--R 18a b x log(x) + 2b x - 6a b x - a +--R (3) ------------------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1285 +t0:=(a+b*x^3)^3/x^10 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 1285 +r0:=-1/9*a^3/x^9-1/2*a^2*b/x^6-a*b^2/x^3+b^3*log(x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 18b x log(x) - 18a b x - 9a b x - 2a +--R (2) --------------------------------------- +--R 9 +--R 18x +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 18b x log(x) - 18a b x - 9a b x - 2a +--R (3) --------------------------------------- +--R 9 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1285 +t0:=(a+b*x^3)^3/x^13 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1031 + +--S 1032 of 1285 +r0:=-1/12*(a+b*x^3)^4/(a*x^12) +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R - -- b x - - a b x - - a b x - - a b x - -- a +--R 12 3 2 3 12 +--R (2) --------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1032 + +--S 1033 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) -------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 1285 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) --- +--R 12a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1285 +t0:=(a+b*x^3)^3/x^16 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1036 + +--S 1037 of 1285 +r0:=-1/15*a^3/x^15-1/4*a^2*b/x^12-1/3*a*b^2/x^9-1/6*b^3/x^6 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 6 3 4 15 +--R (2) -------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1037 + +--S 1038 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ------------------------------------ +--R 15 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1285 +t0:=(a+b*x^3)^3/x^19 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1041 + +--S 1042 of 1285 +r0:=-1/18*a^3/x^18-1/5*a^2*b/x^15-1/4*a*b^2/x^12-1/9*b^3/x^9 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 9 4 5 18 +--R (2) -------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1042 + +--S 1043 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------- +--R 18 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 1285 +t0:=(a+b*x^3)^3/x^22 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1046 + +--S 1047 of 1285 +r0:=-1/21*a^3/x^21-1/6*a^2*b/x^18-1/5*a*b^2/x^15-1/12*b^3/x^12 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - -- b x - - a b x - - a b x - -- a +--R 12 5 6 21 +--R (2) --------------------------------------- +--R 21 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1047 + +--S 1048 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------- +--R 21 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 1285 +t0:=(a+b*x^3)^3/x^25 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1051 + +--S 1052 of 1285 +r0:=-1/24*a^3/x^24-1/7*a^2*b/x^21-1/6*a*b^2/x^18-1/15*b^3/x^15 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - -- b x - - a b x - - a b x - -- a +--R 15 6 7 24 +--R (2) --------------------------------------- +--R 24 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1052 + +--S 1053 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 56b x - 140a b x - 120a b x - 35a +--R (3) --------------------------------------- +--R 24 +--R 840x +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 1285 +t0:=x^4*(a+b*x^3)^3 +--R +--R +--R 3 13 2 10 2 7 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1056 + +--S 1057 of 1285 +r0:=1/5*a^3*x^5+3/8*a^2*b*x^8+3/11*a*b^2*x^11+1/14*b^3*x^14 +--R +--R +--R 1 3 14 3 2 11 3 2 8 1 3 5 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 14 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1057 + +--S 1058 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 3 2 11 3 2 8 1 3 5 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 14 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1058 + +--S 1059 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1059 + +--S 1060 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1060 + +)clear all + +--S 1061 of 1285 +t0:=x^3*(a+b*x^3)^3 +--R +--R +--R 3 12 2 9 2 6 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1061 + +--S 1062 of 1285 +r0:=1/4*a^3*x^4+3/7*a^2*b*x^7+3/10*a*b^2*x^10+1/13*b^3*x^13 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 13 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1062 + +--S 1063 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 13 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1063 + +--S 1064 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1064 + +--S 1065 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1065 + +)clear all + +--S 1066 of 1285 +t0:=x*(a+b*x^3)^3 +--R +--R +--R 3 10 2 7 2 4 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1066 + +--S 1067 of 1285 +r0:=1/2*a^3*x^2+3/5*a^2*b*x^5+3/8*a*b^2*x^8+1/11*b^3*x^11 +--R +--R +--R 1 3 11 3 2 8 3 2 5 1 3 2 +--R (2) -- b x + - a b x + - a b x + - a x +--R 11 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1067 + +--S 1068 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 11 3 2 8 3 2 5 1 3 2 +--R (3) -- b x + - a b x + - a b x + - a x +--R 11 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1068 + +--S 1069 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1069 + +--S 1070 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1070 + +)clear all + +--S 1071 of 1285 +t0:=(a+b*x^3)^3 +--R +--R +--R 3 9 2 6 2 3 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 1071 + +--S 1072 of 1285 +r0:=a^3*x+3/4*a^2*b*x^4+3/7*a*b^2*x^7+1/10*b^3*x^10 +--R +--R +--R 1 3 10 3 2 7 3 2 4 3 +--R (2) -- b x + - a b x + - a b x + a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1072 + +--S 1073 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 10 3 2 7 3 2 4 3 +--R (3) -- b x + - a b x + - a b x + a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1073 + +--S 1074 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1074 + +--S 1075 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1075 + +)clear all + +--S 1076 of 1285 +t0:=(a+b*x^3)^3/x^2 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 1285 +r0:=-a^3/x+3/2*a^2*b*x^2+3/5*a*b^2*x^5+1/8*b^3*x^8 +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 24a b x + 60a b x - 40a +--R (2) ---------------------------------- +--R 40x +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 24a b x + 60a b x - 40a +--R (3) ---------------------------------- +--R 40x +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1285 +t0:=(a+b*x^3)^3/x^3 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 1285 +r0:=-1/2*a^3/x^2+3*a^2*b*x+3/4*a*b^2*x^4+1/7*b^3*x^7 +--R +--R +--R 1 3 9 3 2 6 2 3 1 3 +--R - b x + - a b x + 3a b x - - a +--R 7 4 2 +--R (2) ---------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1082 + +--S 1083 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 4b x + 21a b x + 84a b x - 14a +--R (3) ---------------------------------- +--R 2 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1285 +t0:=(a+b*x^3)^3/x^5 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 1285 +r0:=-1/4*a^3/x^4-3*a^2*b/x+3/2*a*b^2*x^2+1/5*b^3*x^5 +--R +--R +--R 1 3 9 3 2 6 2 3 1 3 +--R - b x + - a b x - 3a b x - - a +--R 5 2 4 +--R (2) ---------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1087 + +--S 1088 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 4b x + 30a b x - 60a b x - 5a +--R (3) --------------------------------- +--R 4 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1285 +t0:=(a+b*x^3)^3/x^6 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 1285 +r0:=-1/5*a^3/x^5-3/2*a^2*b/x^2+3*a*b^2*x+1/4*b^3*x^4 +--R +--R +--R 1 3 9 2 6 3 2 3 1 3 +--R - b x + 3a b x - - a b x - - a +--R 4 2 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1092 + +--S 1093 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 60a b x - 30a b x - 4a +--R (3) --------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1285 +t0:=(a+b*x^3)^3/x^8 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 1285 +r0:=-1/7*a^3/x^7-3/4*a^2*b/x^4-3*a*b^2/x+1/2*b^3*x^2 +--R +--R +--R 1 3 9 2 6 3 2 3 1 3 +--R - b x - 3a b x - - a b x - - a +--R 2 4 7 +--R (2) ---------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1097 + +--S 1098 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 14b x - 84a b x - 21a b x - 4a +--R (3) ---------------------------------- +--R 7 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1285 +t0:=x^m*(a+b*x^3)^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1285 +r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(4+m)/(4+m)+10*a^3*b^2*x^(7+m)/(7+m)+_ + 10*a^2*b^3*x^(10+m)/(10+m)+5*a*b^4*x^(13+m)/(13+m)+b^5*x^(16+m)/(16+m) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R m + 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R m + 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R m + 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R m + 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R * +--R m log(x) +--R %e +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 3 5 2 5 5 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R * +--R m log(x) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 16 +--R (- b m - 35b m - 445b m - 2485b m - 5714b m - 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 190a b m - 2555a b m - 14810a b m - 34840a b m +--R + +--R 4 +--R - 22400a b +--R * +--R m + 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R - 10a b m - 410a b m - 5950a b m - 36550a b m - 89240a b m +--R + +--R 2 3 +--R - 58240a b +--R * +--R m + 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R - 10a b m - 440a b m - 6970a b m - 47260a b m - 123920a b m +--R + +--R 3 2 +--R - 83200a b +--R * +--R m + 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 235a b m - 4085a b m - 31685a b m - 100630a b m +--R + +--R 4 +--R - 72800a b +--R * +--R m + 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (- a m - 50a m - 955a m - 8650a m - 36824a m - 58240a )x +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1285 +t0:=x^17*(a+b*x^3)^5 +--R +--R +--R 5 32 4 29 2 3 26 3 2 23 4 20 5 17 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1106 + +--S 1107 of 1285 +r0:=1/18*a^5*x^18+5/21*a^4*b*x^21+5/12*a^3*b^2*x^24+10/27*a^2*b^3*x^27+_ + 1/6*a*b^4*x^30+1/33*b^5*x^33 +--R +--R +--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18 +--R (2) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 33 6 27 12 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1107 + +--S 1108 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18 +--R (3) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 33 6 27 12 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1108 + +--S 1109 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1109 + +--S 1110 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1110 + +)clear all + +--S 1111 of 1285 +t0:=x^14*(a+b*x^3)^5 +--R +--R +--R 5 29 4 26 2 3 23 3 2 20 4 17 5 14 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1111 + +--S 1112 of 1285 +r0:=1/15*a^5*x^15+5/18*a^4*b*x^18+10/21*a^3*b^2*x^21+5/12*a^2*b^3*x^24+_ + 5/27*a*b^4*x^27+1/30*b^5*x^30 +--R +--R +--R (2) +--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 30 27 12 21 18 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1112 + +--S 1113 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 30 27 12 21 18 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1113 + +--S 1114 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1114 + +--S 1115 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1115 + +)clear all + +--S 1116 of 1285 +t0:=x^11*(a+b*x^3)^5 +--R +--R +--R 5 26 4 23 2 3 20 3 2 17 4 14 5 11 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1116 + +--S 1117 of 1285 +r0:=1/12*a^5*x^12+1/3*a^4*b*x^15+5/9*a^3*b^2*x^18+10/21*a^2*b^3*x^21+_ + 5/24*a*b^4*x^24+1/27*b^5*x^27 +--R +--R +--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12 +--R (2) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x +--R 27 24 21 9 3 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1117 + +--S 1118 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12 +--R (3) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x +--R 27 24 21 9 3 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1118 + +--S 1119 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1119 + +--S 1120 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1120 + +)clear all + +--S 1121 of 1285 +t0:=x^8*(a+b*x^3)^5 +--R +--R +--R 5 23 4 20 2 3 17 3 2 14 4 11 5 8 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1121 + +--S 1122 of 1285 +r0:=1/18*a^2*(a+b*x^3)^6/b^3-2/21*a*(a+b*x^3)^7/b^3+1/24*(a+b*x^3)^8/b^3 +--R +--R +--R (2) +--R 1 8 24 5 7 21 5 2 6 18 2 3 5 15 5 4 4 12 1 5 3 9 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + - a b x +--R 24 21 9 3 12 9 +--R + +--R 1 8 +--R --- a +--R 504 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1122 + +--S 1123 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 24 5 4 21 5 2 3 18 2 3 2 15 5 4 12 1 5 9 +--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + - a x +--R 24 21 9 3 12 9 +--R Type: Polynomial(Fraction(Integer)) +--E 1123 + +--S 1124 of 1285 +m0:=a0-r0 +--R +--R +--R 1 8 +--R --- a +--R 504 +--R (4) - ------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1124 + +--S 1125 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1125 + +)clear all + +--S 1126 of 1285 +t0:=x^5*(a+b*x^3)^5 +--R +--R +--R 5 20 4 17 2 3 14 3 2 11 4 8 5 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1126 + +--S 1127 of 1285 +r0:=-1/18*a*(a+b*x^3)^6/b^2+1/21*(a+b*x^3)^7/b^2 +--R +--R +--R (2) +--R 1 7 21 5 6 18 2 2 5 15 5 3 4 12 5 4 3 9 1 5 2 6 1 7 +--R -- b x + -- a b x + - a b x + - a b x + - a b x + - a b x - --- a +--R 21 18 3 6 9 6 126 +--R ---------------------------------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1127 + +--S 1128 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 21 5 4 18 2 2 3 15 5 3 2 12 5 4 9 1 5 6 +--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 21 18 3 6 9 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1128 + +--S 1129 of 1285 +m0:=a0-r0 +--R +--R +--R 1 7 +--R --- a +--R 126 +--R (4) ------ +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1129 + +--S 1130 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1130 + +)clear all + +--S 1131 of 1285 +t0:=x^2*(a+b*x^3)^5 +--R +--R +--R 5 17 4 14 2 3 11 3 2 8 4 5 5 2 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1131 + +--S 1132 of 1285 +r0:=1/18*(a+b*x^3)^6/b +--R +--R +--R (2) +--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6 +--R -- b x + - a b x + - a b x + -- a b x + - a b x + - a b x + -- a +--R 18 3 6 9 6 3 18 +--R -------------------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1132 + +--S 1133 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 18 1 4 15 5 2 3 12 10 3 2 9 5 4 6 1 5 3 +--R (3) -- b x + - a b x + - a b x + -- a b x + - a b x + - a x +--R 18 3 6 9 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1133 + +--S 1134 of 1285 +m0:=a0-r0 +--R +--R +--R 1 6 +--R -- a +--R 18 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1134 + +--S 1135 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1135 + +)clear all + +--S 1136 of 1285 +t0:=(a+b*x^3)^5/x +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 1285 +r0:=5/3*a^4*b*x^3+5/3*a^3*b^2*x^6+10/9*a^2*b^3*x^9+5/12*a*b^4*x^12+_ + 1/15*b^5*x^15+a^5*log(x) +--R +--R +--R 5 5 15 4 12 2 3 9 3 2 6 4 3 +--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (2) --------------------------------------------------------------------- +--R 180 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 5 15 4 12 2 3 9 3 2 6 4 3 +--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (3) --------------------------------------------------------------------- +--R 180 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1285 +t0:=(a+b*x^3)^5/x^4 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 1285 +r0:=-1/3*a^5/x^3+10/3*a^3*b^2*x^3+5/3*a^2*b^3*x^6+5/9*a*b^4*x^9+_ + 1/12*b^5*x^12+5*a^4*b*log(x) +--R +--R +--R 4 3 5 15 4 12 2 3 9 3 2 6 5 +--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (2) ------------------------------------------------------------------ +--R 3 +--R 36x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 3 5 15 4 12 2 3 9 3 2 6 5 +--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (3) ------------------------------------------------------------------ +--R 3 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1285 +t0:=(a+b*x^3)^5/x^7 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1146 + +--S 1147 of 1285 +r0:=-1/6*a^5/x^6-5/3*a^4*b/x^3+10/3*a^2*b^3*x^3+5/6*a*b^4*x^6+_ + 1/9*b^5*x^9+10*a^3*b^2*log(x) +--R +--R +--R 3 2 6 5 15 4 12 2 3 9 4 3 5 +--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (2) ---------------------------------------------------------------- +--R 6 +--R 18x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 2 6 5 15 4 12 2 3 9 4 3 5 +--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (3) ---------------------------------------------------------------- +--R 6 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1285 +t0:=(a+b*x^3)^5/x^10 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1151 + +--S 1152 of 1285 +r0:=-1/9*a^5/x^9-5/6*a^4*b/x^6-10/3*a^3*b^2/x^3+5/3*a*b^4*x^3+_ + 1/6*b^5*x^6+10*a^2*b^3*log(x) +--R +--R +--R 2 3 9 5 15 4 12 3 2 6 4 3 5 +--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (2) ---------------------------------------------------------------- +--R 9 +--R 18x +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 3 9 5 15 4 12 3 2 6 4 3 5 +--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (3) ---------------------------------------------------------------- +--R 9 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1285 +t0:=(a+b*x^3)^5/x^13 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1156 + +--S 1157 of 1285 +r0:=-1/12*a^5/x^12-5/9*a^4*b/x^9-5/3*a^3*b^2/x^6-10/3*a^2*b^3/x^3+_ + 1/3*b^5*x^3+5*a*b^4*log(x) +--R +--R +--R 4 12 5 15 2 3 9 3 2 6 4 3 5 +--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (2) ------------------------------------------------------------------ +--R 12 +--R 36x +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 12 5 15 2 3 9 3 2 6 4 3 5 +--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (3) ------------------------------------------------------------------ +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1285 +t0:=(a+b*x^3)^5/x^16 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 1285 +r0:=-1/15*a^5/x^15-5/12*a^4*b/x^12-10/9*a^3*b^2/x^9-5/3*a^2*b^3/x^6-_ + 5/3*a*b^4/x^3+b^5*log(x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (2) --------------------------------------------------------------------- +--R 15 +--R 180x +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (3) --------------------------------------------------------------------- +--R 15 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1285 +t0:=(a+b*x^3)^5/x^19 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 1285 +r0:=-1/18*(a+b*x^3)^6/(a*x^18) +--R +--R +--R (2) +--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6 +--R - -- b x - - a b x - - a b x - -- a b x - - a b x - - a b x - -- a +--R 18 3 6 9 6 3 18 +--R ---------------------------------------------------------------------------- +--R 18 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1167 + +--S 1168 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (3) --------------------------------------------------------- +--R 18 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1285 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) --- +--R 18a +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1285 +t0:=(a+b*x^3)^5/x^22 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 1285 +r0:=-1/21*(a+b*x^3)^6/(a*x^21)+1/126*b*(a+b*x^3)^6/(a^2*x^18) +--R +--R +--R (2) +--R 1 7 21 1 2 5 15 5 3 4 12 5 4 3 9 2 5 2 6 5 6 3 1 7 +--R --- b x - - a b x - - a b x - - a b x - - a b x - -- a b x - -- a +--R 126 6 9 6 3 18 21 +--R --------------------------------------------------------------------------- +--R 2 21 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1172 + +--S 1173 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (3) ------------------------------------------------------------- +--R 21 +--R 126x +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1285 +m0:=a0-r0 +--R +--R +--R 7 +--R b +--R (4) - ----- +--R 2 +--R 126a +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1285 +t0:=(a+b*x^3)^5/x^25 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1176 + +--S 1177 of 1285 +r0:=-1/24*a^5/x^24-5/21*a^4*b/x^21-5/9*a^3*b^2/x^18-2/3*a^2*b^3/x^15-_ + 5/12*a*b^4/x^12-1/9*b^5/x^9 +--R +--R +--R 1 5 15 5 4 12 2 2 3 9 5 3 2 6 5 4 3 1 5 +--R - - b x - -- a b x - - a b x - - a b x - -- a b x - -- a +--R 9 12 3 9 21 24 +--R (2) ---------------------------------------------------------------- +--R 24 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1177 + +--S 1178 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a +--R (3) ----------------------------------------------------------------- +--R 24 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1285 +t0:=(a+b*x^3)^5/x^28 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1181 + +--S 1182 of 1285 +r0:=-1/27*a^5/x^27-5/24*a^4*b/x^24-10/21*a^3*b^2/x^21-5/9*a^2*b^3/x^18-_ + 1/3*a*b^4/x^15-1/12*b^5/x^12 +--R +--R +--R 1 5 15 1 4 12 5 2 3 9 10 3 2 6 5 4 3 1 5 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a +--R 12 3 9 21 24 27 +--R (2) ----------------------------------------------------------------- +--R 27 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1182 + +--S 1183 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) ------------------------------------------------------------------ +--R 27 +--R 1512x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1285 +t0:=(a+b*x^3)^5/x^31 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 1285 +r0:=-1/30*a^5/x^30-5/27*a^4*b/x^27-5/12*a^3*b^2/x^24-10/21*a^2*b^3/x^21-_ + 5/18*a*b^4/x^18-1/15*b^5/x^15 +--R +--R +--R 1 5 15 5 4 12 10 2 3 9 5 3 2 6 5 4 3 1 5 +--R - -- b x - -- a b x - -- a b x - -- a b x - -- a b x - -- a +--R 15 18 21 12 27 30 +--R (2) ------------------------------------------------------------------- +--R 30 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1187 + +--S 1188 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a +--R (3) ---------------------------------------------------------------------- +--R 30 +--R 3780x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1285 +t0:=(a+b*x^3)^5/x^34 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 34 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 1285 +r0:=-1/33*a^5/x^33-1/6*a^4*b/x^30-10/27*a^3*b^2/x^27-5/12*a^2*b^3/x^24-_ + 5/21*a*b^4/x^21-1/18*b^5/x^18 +--R +--R +--R 1 5 15 5 4 12 5 2 3 9 10 3 2 6 1 4 3 1 5 +--R - -- b x - -- a b x - -- a b x - -- a b x - - a b x - -- a +--R 18 21 12 27 6 33 +--R (2) ------------------------------------------------------------------ +--R 33 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1192 + +--S 1193 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 462b x - 1980a b x - 3465a b x - 3080a b x - 1386a b x - 252a +--R ----------------------------------------------------------------------- +--R 33 +--R 8316x +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1285 +t0:=x^4*(a+b*x^3)^5 +--R +--R +--R 5 19 4 16 2 3 13 3 2 10 4 7 5 4 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1196 + +--S 1197 of 1285 +r0:=1/5*a^5*x^5+5/8*a^4*b*x^8+10/11*a^3*b^2*x^11+5/7*a^2*b^3*x^14+_ + 5/17*a*b^4*x^17+1/20*b^5*x^20 +--R +--R +--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5 +--R (2) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x +--R 20 17 7 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1197 + +--S 1198 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5 +--R (3) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x +--R 20 17 7 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1198 + +--S 1199 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1199 + +--S 1200 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1200 + +)clear all + +--S 1201 of 1285 +t0:=x^3*(a+b*x^3)^5 +--R +--R +--R 5 18 4 15 2 3 12 3 2 9 4 6 5 3 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1201 + +--S 1202 of 1285 +r0:=1/4*a^5*x^4+5/7*a^4*b*x^7+a^3*b^2*x^10+10/13*a^2*b^3*x^13+_ + 5/16*a*b^4*x^16+1/19*b^5*x^19 +--R +--R +--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4 +--R (2) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x +--R 19 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1202 + +--S 1203 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4 +--R (3) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x +--R 19 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1203 + +--S 1204 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1204 + +--S 1205 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1205 + +)clear all + +--S 1206 of 1285 +t0:=x*(a+b*x^3)^5 +--R +--R +--R 5 16 4 13 2 3 10 3 2 7 4 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1206 + +--S 1207 of 1285 +r0:=1/2*a^5*x^2+a^4*b*x^5+5/4*a^3*b^2*x^8+10/11*a^2*b^3*x^11+_ + 5/14*a*b^4*x^14+1/17*b^5*x^17 +--R +--R +--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2 +--R (2) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x +--R 17 14 11 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1207 + +--S 1208 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2 +--R (3) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x +--R 17 14 11 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1208 + +--S 1209 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1209 + +--S 1210 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1210 + +)clear all + +--S 1211 of 1285 +t0:=(a+b*x^3)^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 1211 + +--S 1212 of 1285 +r0:=a^5*x+5/4*a^4*b*x^4+10/7*a^3*b^2*x^7+a^2*b^3*x^10+5/13*a*b^4*x^13+_ + 1/16*b^5*x^16 +--R +--R +--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5 +--R (2) -- b x + -- a b x + a b x + -- a b x + - a b x + a x +--R 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1212 + +--S 1213 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5 +--R (3) -- b x + -- a b x + a b x + -- a b x + - a b x + a x +--R 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1213 + +--S 1214 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1214 + +--S 1215 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1215 + +)clear all + +--S 1216 of 1285 +t0:=(a+b*x^3)^5/x^2 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1216 + +--S 1217 of 1285 +r0:=-a^5/x+5/2*a^4*b*x^2+2*a^3*b^2*x^5+5/4*a^2*b^3*x^8+5/11*a*b^4*x^11+_ + 1/14*b^5*x^14 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a +--R (2) ---------------------------------------------------------------- +--R 308x +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a +--R (3) ---------------------------------------------------------------- +--R 308x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1285 +t0:=(a+b*x^3)^5/x^3 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1221 + +--S 1222 of 1285 +r0:=-1/2*a^5/x^2+5*a^4*b*x+5/2*a^3*b^2*x^4+10/7*a^2*b^3*x^7+_ + 1/2*a*b^4*x^10+1/13*b^5*x^13 +--R +--R +--R 1 5 15 1 4 12 10 2 3 9 5 3 2 6 4 3 1 5 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x - - a +--R 13 2 7 2 2 +--R (2) ------------------------------------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1222 + +--S 1223 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 14b x + 91a b x + 260a b x + 455a b x + 910a b x - 91a +--R (3) -------------------------------------------------------------- +--R 2 +--R 182x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1285 +t0:=(a+b*x^3)^5/x^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1226 + +--S 1227 of 1285 +r0:=-1/4*a^5/x^4-5*a^4*b/x+5*a^3*b^2*x^2+2*a^2*b^3*x^5+5/8*a*b^4*x^8+_ + 1/11*b^5*x^11 +--R +--R +--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5 +--R -- b x + - a b x + 2a b x + 5a b x - 5a b x - - a +--R 11 8 4 +--R (2) --------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1227 + +--S 1228 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 8b x + 55a b x + 176a b x + 440a b x - 440a b x - 22a +--R (3) ------------------------------------------------------------- +--R 4 +--R 88x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1285 +t0:=(a+b*x^3)^5/x^6 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 1285 +r0:=-1/5*a^5/x^5-5/2*a^4*b/x^2+10*a^3*b^2*x+5/2*a^2*b^3*x^4+5/7*a*b^4*x^7+_ + 1/10*b^5*x^10 +--R +--R +--R 1 5 15 5 4 12 5 2 3 9 3 2 6 5 4 3 1 5 +--R -- b x + - a b x + - a b x + 10a b x - - a b x - - a +--R 10 7 2 2 5 +--R (2) ------------------------------------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1232 + +--S 1233 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 7b x + 50a b x + 175a b x + 700a b x - 175a b x - 14a +--R (3) ------------------------------------------------------------- +--R 5 +--R 70x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1285 +t0:=(a+b*x^3)^5/x^8 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1236 + +--S 1237 of 1285 +r0:=-1/7*a^5/x^7-5/4*a^4*b/x^4-10*a^3*b^2/x+5*a^2*b^3*x^2+a*b^4*x^5+1/8*b^5*x^8 +--R +--R +--R 1 5 15 4 12 2 3 9 3 2 6 5 4 3 1 5 +--R - b x + a b x + 5a b x - 10a b x - - a b x - - a +--R 8 4 7 +--R (2) -------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1237 + +--S 1238 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 7b x + 56a b x + 280a b x - 560a b x - 70a b x - 8a +--R (3) ----------------------------------------------------------- +--R 7 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1285 +t0:=(a+b*x^3)^5/x^9 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1241 + +--S 1242 of 1285 +r0:=-1/8*a^5/x^8-a^4*b/x^5-5*a^3*b^2/x^2+10*a^2*b^3*x+5/4*a*b^4*x^4+1/7*b^5*x^7 +--R +--R +--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5 +--R - b x + - a b x + 10a b x - 5a b x - a b x - - a +--R 7 4 8 +--R (2) -------------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1242 + +--S 1243 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 8b x + 70a b x + 560a b x - 280a b x - 56a b x - 7a +--R (3) ----------------------------------------------------------- +--R 8 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1285 +t0:=x^m*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1285 +r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(4+m)/(4+m)+28*a^6*b^2*x^(7+m)/(7+m)+_ + 56*a^5*b^3*x^(10+m)/(10+m)+70*a^4*b^4*x^(13+m)/(13+m)+_ + 56*a^3*b^5*x^(16+m)/(16+m)+28*a^2*b^6*x^(19+m)/(19+m)+_ + 8*a*b^7*x^(22+m)/(22+m)+b^8*x^(25+m)/(25+m) +--R +--R +--R (2) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R m + 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R m + 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m + 29390452a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 210422576a b m + 827034544a b m + 1540629440a b m + 896896000a b +--R * +--R m + 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m + 65946104a b m +--R + +--R 3 5 3 3 5 2 3 5 3 5 +--R 482544664a b m + 1929412352a b m + 3637973920a b m + 2130128000a b +--R * +--R m + 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4 +--R 70a b m + 7280a b m + 312340a b m + 7138040a b m + 93585310a b m +--R + +--R 4 4 3 4 4 2 4 4 4 4 +--R 705493880a b m + 2891238280a b m + 5549616800a b m + 3277120000a b +--R * +--R m + 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4 +--R 56a b m + 5992a b m + 265664a b m + 6302128a b m + 86082584a b m +--R + +--R 5 3 3 5 3 2 5 3 5 3 +--R 676856488a b m + 2881562096a b m + 5692950592a b m + 3408204800a b +--R * +--R m + 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4 +--R 28a b m + 3080a b m + 141232a b m + 3490760a b m + 50116612a b m +--R + +--R 6 2 3 6 2 2 6 2 6 2 +--R 418024880a b m + 1898889328a b m + 3962060480a b m + 2434432000a b +--R * +--R m + 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 904a b m + 42896a b m + 1108240a b m + 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b +--R * +--R m + 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m +--R + +--R 8 2 8 8 +--R 147373372a m + 468851120a m + 608608000a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R 29390452a b m + 210422576a b m + 827034544a b m +--R + +--R 2 6 2 6 +--R 1540629440a b m + 896896000a b +--R * +--R 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R 65946104a b m + 482544664a b m + 1929412352a b m +--R + +--R 3 5 3 5 +--R 3637973920a b m + 2130128000a b +--R * +--R 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 7280a b m + 312340a b m + 7138040a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R 93585310a b m + 705493880a b m + 2891238280a b m +--R + +--R 4 4 4 4 +--R 5549616800a b m + 3277120000a b +--R * +--R 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 5992a b m + 265664a b m + 6302128a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R 86082584a b m + 676856488a b m + 2881562096a b m +--R + +--R 5 3 5 3 +--R 5692950592a b m + 3408204800a b +--R * +--R 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 3080a b m + 141232a b m + 3490760a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R 50116612a b m + 418024880a b m + 1898889328a b m +--R + +--R 6 2 6 2 +--R 3962060480a b m + 2434432000a b +--R * +--R 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 904a b m + 42896a b m + 1108240a b m + 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b +--R * +--R 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m +--R + +--R 8 2 8 8 +--R 147373372a m + 468851120a m + 608608000a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R 29390452a b m + 210422576a b m + 827034544a b m +--R + +--R 2 6 2 6 +--R 1540629440a b m + 896896000a b +--R * +--R 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R 65946104a b m + 482544664a b m + 1929412352a b m +--R + +--R 3 5 3 5 +--R 3637973920a b m + 2130128000a b +--R * +--R 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 7280a b m + 312340a b m + 7138040a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R 93585310a b m + 705493880a b m + 2891238280a b m +--R + +--R 4 4 4 4 +--R 5549616800a b m + 3277120000a b +--R * +--R 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 5992a b m + 265664a b m + 6302128a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R 86082584a b m + 676856488a b m + 2881562096a b m +--R + +--R 5 3 5 3 +--R 5692950592a b m + 3408204800a b +--R * +--R 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 3080a b m + 141232a b m + 3490760a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R 50116612a b m + 418024880a b m + 1898889328a b m +--R + +--R 6 2 6 2 +--R 3962060480a b m + 2434432000a b +--R * +--R 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 +--R 8a b m + 904a b m + 42896a b m + 1108240a b m +--R + +--R 7 4 7 3 7 2 +--R 16867592a b m + 152198536a b m + 769795424a b m +--R + +--R 7 7 +--R 1850614240a b m + 1217216000a b +--R * +--R 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m +--R + +--R 8 3 8 2 8 8 +--R 24950324a m + 147373372a m + 468851120a m + 608608000a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - b m - 92b m - 3514b m - 72128b m - 859369b m - 5974388b m +--R + +--R 8 2 8 8 +--R - 22963996b m - 42124592b m - 24344320b +--R * +--R m + 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 760a b m - 29792a b m - 624400a b m - 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R - 53266360a b m - 206729648a b m - 381743680a b m - 221312000a b +--R * +--R m + 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R - 28a b m - 2744a b m - 110656a b m - 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R - 29390452a b m - 210422576a b m - 827034544a b m +--R + +--R 2 6 2 6 +--R - 1540629440a b m - 896896000a b +--R * +--R m + 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R - 56a b m - 5656a b m - 235088a b m - 5197360a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R - 65946104a b m - 482544664a b m - 1929412352a b m +--R + +--R 3 5 3 5 +--R - 3637973920a b m - 2130128000a b +--R * +--R m + 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R - 70a b m - 7280a b m - 312340a b m - 7138040a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R - 93585310a b m - 705493880a b m - 2891238280a b m +--R + +--R 4 4 4 4 +--R - 5549616800a b m - 3277120000a b +--R * +--R m + 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R - 56a b m - 5992a b m - 265664a b m - 6302128a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R - 86082584a b m - 676856488a b m - 2881562096a b m +--R + +--R 5 3 5 3 +--R - 5692950592a b m - 3408204800a b +--R * +--R m + 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R - 28a b m - 3080a b m - 141232a b m - 3490760a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R - 50116612a b m - 418024880a b m - 1898889328a b m +--R + +--R 6 2 6 2 +--R - 3962060480a b m - 2434432000a b +--R * +--R m + 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 904a b m - 42896a b m - 1108240a b m - 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R - 152198536a b m - 769795424a b m - 1850614240a b m - 1217216000a b +--R * +--R m + 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - a m - 116a m - 5698a m - 154280a m - 2508289a m - 24950324a m +--R + +--R 8 2 8 8 +--R - 147373372a m - 468851120a m - 608608000a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1285 +t0:=x^20*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 44 7 41 2 6 38 3 5 35 4 4 32 5 3 29 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 26 7 23 8 20 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1251 + +--S 1252 of 1285 +r0:=1/21*a^8*x^21+1/3*a^7*b*x^24+28/27*a^6*b^2*x^27+28/15*a^5*b^3*x^30+_ + 70/33*a^4*b^4*x^33+14/9*a^3*b^5*x^36+28/39*a^2*b^6*x^39+_ + 4/21*a*b^7*x^42+1/45*b^8*x^45 +--R +--R +--R (2) +--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 45 21 39 9 33 15 +--R + +--R 28 6 2 27 1 7 24 1 8 21 +--R -- a b x + - a b x + -- a x +--R 27 3 21 +--R Type: Polynomial(Fraction(Integer)) +--E 1252 + +--S 1253 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 45 21 39 9 33 15 +--R + +--R 28 6 2 27 1 7 24 1 8 21 +--R -- a b x + - a b x + -- a x +--R 27 3 21 +--R Type: Polynomial(Fraction(Integer)) +--E 1253 + +--S 1254 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1254 + +--S 1255 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1255 + +)clear all + +--S 1256 of 1285 +t0:=x^17*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 41 7 38 2 6 35 3 5 32 4 4 29 5 3 26 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 23 7 20 8 17 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1256 + +--S 1257 of 1285 +r0:=-1/27*a^5*(a+b*x^3)^9/b^6+1/6*a^4*(a+b*x^3)^10/b^6-_ + 10/33*a^3*(a+b*x^3)^11/b^6+5/18*a^2*(a+b*x^3)^12/b^6-_ + 5/39*a*(a+b*x^3)^13/b^6+1/42*(a+b*x^3)^14/b^6 +--R +--R +--R (2) +--R 1 14 42 8 13 39 7 2 12 36 56 3 11 33 7 4 10 30 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x +--R 42 39 9 33 3 +--R + +--R 56 5 9 27 7 6 8 24 8 7 7 21 1 8 6 18 1 14 +--R -- a b x + - a b x + -- a b x + -- a b x - ----- a +--R 27 6 21 18 54054 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1257 + +--S 1258 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 42 8 7 39 7 2 6 36 56 3 5 33 7 4 4 30 56 5 3 27 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x +--R 42 39 9 33 3 27 +--R + +--R 7 6 2 24 8 7 21 1 8 18 +--R - a b x + -- a b x + -- a x +--R 6 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1258 + +--S 1259 of 1285 +m0:=a0-r0 +--R +--R +--R 1 14 +--R ----- a +--R 54054 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1259 + +--S 1260 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1260 + +)clear all + +--S 1261 of 1285 +t0:=x^14*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 38 7 35 2 6 32 3 5 29 4 4 26 5 3 23 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 20 7 17 8 14 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1261 + +--S 1262 of 1285 +r0:=1/27*a^4*(a+b*x^3)^9/b^5-2/15*a^3*(a+b*x^3)^10/b^5+_ + 2/11*a^2*(a+b*x^3)^11/b^5-1/9*a*(a+b*x^3)^12/b^5+_ + 1/39*(a+b*x^3)^13/b^5 +--R +--R +--R (2) +--R 1 13 39 2 12 36 28 2 11 33 28 3 10 30 70 4 9 27 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x +--R 39 9 33 15 27 +--R + +--R 7 5 8 24 4 6 7 21 4 7 6 18 1 8 5 15 1 13 +--R - a b x + - a b x + - a b x + -- a b x + ----- a +--R 3 3 9 15 19305 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1262 + +--S 1263 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 39 2 7 36 28 2 6 33 28 3 5 30 70 4 4 27 7 5 3 24 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 39 9 33 15 27 3 +--R + +--R 4 6 2 21 4 7 18 1 8 15 +--R - a b x + - a b x + -- a x +--R 3 9 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1263 + +--S 1264 of 1285 +m0:=a0-r0 +--R +--R +--R 1 13 +--R ----- a +--R 19305 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1264 + +--S 1265 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1265 + +)clear all + +--S 1266 of 1285 +t0:=x^11*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 35 7 32 2 6 29 3 5 26 4 4 23 5 3 20 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 17 7 14 8 11 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1266 + +--S 1267 of 1285 +r0:=-1/27*a^3*(a+b*x^3)^9/b^4+1/10*a^2*(a+b*x^3)^10/b^4-_ + 1/11*a*(a+b*x^3)^11/b^4+1/36*(a+b*x^3)^12/b^4 +--R +--R +--R (2) +--R 1 12 36 8 11 33 14 2 10 30 56 3 9 27 35 4 8 24 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 36 33 15 27 12 +--R + +--R 8 5 7 21 14 6 6 18 8 7 5 15 1 8 4 12 1 12 +--R - a b x + -- a b x + -- a b x + -- a b x - ---- a +--R 3 9 15 12 5940 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1267 + +--S 1268 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 36 8 7 33 14 2 6 30 56 3 5 27 35 4 4 24 8 5 3 21 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 36 33 15 27 12 3 +--R + +--R 14 6 2 18 8 7 15 1 8 12 +--R -- a b x + -- a b x + -- a x +--R 9 15 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1268 + +--S 1269 of 1285 +m0:=a0-r0 +--R +--R +--R 1 12 +--R ---- a +--R 5940 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1269 + +--S 1270 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1270 + +)clear all + +--S 1271 of 1285 +t0:=x^8*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 32 7 29 2 6 26 3 5 23 4 4 20 5 3 17 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 14 7 11 8 8 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1271 + +--S 1272 of 1285 +r0:=1/27*a^2*(a+b*x^3)^9/b^3-1/15*a*(a+b*x^3)^10/b^3+1/33*(a+b*x^3)^11/b^3 +--R +--R +--R (2) +--R 1 11 33 4 10 30 28 2 9 27 7 3 8 24 10 4 7 21 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x +--R 33 15 27 3 3 +--R + +--R 28 5 6 18 28 6 5 15 2 7 4 12 1 8 3 9 1 11 +--R -- a b x + -- a b x + - a b x + - a b x + ---- a +--R 9 15 3 9 1485 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1272 + +--S 1273 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 33 4 7 30 28 2 6 27 7 3 5 24 10 4 4 21 28 5 3 18 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 33 15 27 3 3 9 +--R + +--R 28 6 2 15 2 7 12 1 8 9 +--R -- a b x + - a b x + - a x +--R 15 3 9 +--R Type: Polynomial(Fraction(Integer)) +--E 1273 + +--S 1274 of 1285 +m0:=a0-r0 +--R +--R +--R 1 11 +--R ---- a +--R 1485 +--R (4) - -------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1274 + +--S 1275 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1275 + +)clear all + +--S 1276 of 1285 +t0:=x^5*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 29 7 26 2 6 23 3 5 20 4 4 17 5 3 14 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 11 7 8 8 5 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1276 + +--S 1277 of 1285 +r0:=-1/27*a*(a+b*x^3)^9/b^2+1/30*(a+b*x^3)^10/b^2 +--R +--R +--R (2) +--R 1 10 30 8 9 27 7 2 8 24 8 3 7 21 35 4 6 18 56 5 5 15 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x +--R 30 27 6 3 9 15 +--R + +--R 7 6 4 12 8 7 3 9 1 8 2 6 1 10 +--R - a b x + - a b x + - a b x - --- a +--R 3 9 6 270 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1277 + +--S 1278 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 30 8 7 27 7 2 6 24 8 3 5 21 35 4 4 18 56 5 3 15 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x +--R 30 27 6 3 9 15 +--R + +--R 7 6 2 12 8 7 9 1 8 6 +--R - a b x + - a b x + - a x +--R 3 9 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1278 + +--S 1279 of 1285 +m0:=a0-r0 +--R +--R +--R 1 10 +--R --- a +--R 270 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1279 + +--S 1280 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1280 + +)clear all + +--S 1281 of 1285 +t0:=x^2*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 26 7 23 2 6 20 3 5 17 4 4 14 5 3 11 6 2 8 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 5 8 2 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 1281 + +--S 1282 of 1285 +r0:=1/27*(a+b*x^3)^9/b +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R -- a b x + - a b x + - a b x + -- a +--R 9 3 3 27 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1282 + +--S 1283 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 27 1 7 24 4 2 6 21 28 3 5 18 14 4 4 15 14 5 3 12 +--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 2 9 4 7 6 1 8 3 +--R -- a b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1283 + +--S 1284 of 1285 +m0:=a0-r0 +--R +--R +--R 1 9 +--R -- a +--R 27 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1284 + +--S 1285 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1285 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4c.input.pdf b/src/axiom-website/CATS/rich4c.input.pdf new file mode 100644 index 0000000..d5d9361 Binary files /dev/null and b/src/axiom-website/CATS/rich4c.input.pdf differ diff --git a/src/axiom-website/CATS/rich4d.input.pamphlet b/src/axiom-website/CATS/rich4d.input.pamphlet new file mode 100644 index 0000000..895334e --- /dev/null +++ b/src/axiom-website/CATS/rich4d.input.pamphlet @@ -0,0 +1,19462 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 232 matching answers. +\item 10 cases where Axiom's result differs from Rubi +\item 17 cases where Axiom supplied 2 results. +\item 2 cases that Axiom failed to integrate. +\item 28 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4d.output +)spool rich4d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1309 +t0:=(a+b*x^3)^8/x +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 1309 +r0:=8/3*a^7*b*x^3+14/3*a^6*b^2*x^6+56/9*a^5*b^3*x^9+35/6*a^4*b^4*x^12+_ + 56/15*a^3*b^5*x^15+14/9*a^2*b^6*x^18+8/21*a*b^7*x^21+_ + 1/24*b^8*x^24+a^8*log(x) +--R +--R +--R (2) +--R 8 8 24 7 21 2 6 18 3 5 15 +--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 2520 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 24 7 21 2 6 18 3 5 15 +--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1309 +t0:=(a+b*x^3)^8/x^4 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 1309 +r0:=-1/3*a^8/x^3+28/3*a^6*b^2*x^3+28/3*a^5*b^3*x^6+70/9*a^4*b^4*x^9+_ + 14/3*a^3*b^5*x^12+28/15*a^2*b^6*x^15+4/9*a*b^7*x^18+1/21*b^8*x^21+_ + 8*a^7*b*log(x) +--R +--R +--R (2) +--R 7 3 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 12 5 3 9 6 2 6 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 3 +--R 315x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 12 5 3 9 6 2 6 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 3 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1309 +t0:=(a+b*x^3)^8/x^7 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 1309 +r0:=-1/6*a^8/x^6-8/3*a^7*b/x^3+56/3*a^5*b^3*x^3+35/3*a^4*b^4*x^6+_ + 56/9*a^3*b^5*x^9+7/3*a^2*b^6*x^12+8/15*a*b^7*x^15+_ + 1/18*b^8*x^18+28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 6 2 6 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 12 5 3 9 7 3 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 6 +--R 90x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 6 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 12 5 3 9 7 3 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 6 +--R 90x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1309 +t0:=(a+b*x^3)^8/x^10 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 1309 +r0:=-1/9*a^8/x^9-4/3*a^7*b/x^6-28/3*a^6*b^2/x^3+70/3*a^4*b^4*x^3+_ + 28/3*a^3*b^5*x^6+28/9*a^2*b^6*x^9+2/3*a*b^7*x^12+_ + 1/15*b^8*x^15+56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 5 3 9 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 12 6 2 6 7 3 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 9 +--R 45x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 9 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 12 6 2 6 7 3 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 9 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1309 +t0:=(a+b*x^3)^8/x^13 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 1309 +r0:=-1/12*a^8/x^12-8/9*a^7*b/x^9-14/3*a^6*b^2/x^6-56/3*a^5*b^3/x^3+_ + 56/3*a^3*b^5*x^3+14/3*a^2*b^6*x^6+8/9*a*b^7*x^9+_ + 1/12*b^8*x^12+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 4 4 12 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 12 +--R 36x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 12 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1309 +t0:=(a+b*x^3)^8/x^16 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 1309 +r0:=-1/15*a^8/x^15-2/3*a^7*b/x^12-28/9*a^6*b^2/x^9-28/3*a^5*b^3/x^6-_ + 70/3*a^4*b^4/x^3+28/3*a^2*b^6*x^3+4/3*a*b^7*x^6+1/9*b^8*x^9+_ + 56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 3 5 15 8 24 7 21 2 6 18 4 4 12 +--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 15 +--R 45x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 15 8 24 7 21 2 6 18 4 4 12 +--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 15 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1309 +t0:=(a+b*x^3)^8/x^19 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1309 +r0:=-1/18*a^8/x^18-8/15*a^7*b/x^15-7/3*a^6*b^2/x^12-56/9*a^5*b^3/x^9-_ + 35/3*a^4*b^4/x^6-56/3*a^3*b^5/x^3+8/3*a*b^7*x^3+_ + 1/6*b^8*x^6+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 2 6 18 8 24 7 21 3 5 15 4 4 12 +--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 18 +--R 90x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 18 8 24 7 21 3 5 15 4 4 12 +--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 18 +--R 90x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1309 +t0:=(a+b*x^3)^8/x^22 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1309 +r0:=-1/21*a^8/x^21-4/9*a^7*b/x^18-28/15*a^6*b^2/x^15-14/3*a^5*b^3/x^12-_ + 70/9*a^4*b^4/x^9-28/3*a^3*b^5/x^6-28/3*a^2*b^6/x^3+_ + 1/3*b^8*x^3+8*a*b^7*log(x) +--R +--R +--R (2) +--R 7 21 8 24 2 6 18 3 5 15 4 4 12 +--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 21 +--R 315x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 21 8 24 2 6 18 3 5 15 4 4 12 +--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 21 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1309 +t0:=(a+b*x^3)^8/x^25 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1309 +r0:=-1/24*a^8/x^24-8/21*a^7*b/x^21-14/9*a^6*b^2/x^18-_ + 56/15*a^5*b^3/x^15-35/6*a^4*b^4/x^12-56/9*a^3*b^5/x^9-_ + 14/3*a^2*b^6/x^6-8/3*a*b^7/x^3+b^8*log(x) +--R +--R +--R (2) +--R 8 24 7 21 2 6 18 3 5 15 +--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 24 +--R 2520x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 +--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 24 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1309 +t0:=(a+b*x^3)^8/x^28 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1309 +r0:=-1/27*(a+b*x^3)^9/(a*x^27) +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R - -- a b x - - a b x - - a b x - -- a +--R 9 3 3 27 +--R / +--R 27 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 6 7 3 8 +--R - 36a b x - 9a b x - a +--R / +--R 27 +--R 27x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1309 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 27a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1309 +t0:=(a+b*x^3)^8/x^31 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1309 +r0:=-1/30*(a+b*x^3)^9/(a*x^30)+1/270*b*(a+b*x^3)^9/(a^2*x^27) +--R +--R +--R (2) +--R 1 10 30 1 2 8 24 8 3 7 21 7 4 6 18 56 5 5 15 35 6 4 12 +--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 270 6 9 3 15 9 +--R + +--R 8 7 3 9 7 8 2 6 8 9 3 1 10 +--R - - a b x - - a b x - -- a b x - -- a +--R 3 6 27 30 +--R / +--R 2 30 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 720a b x - 315a b x - 80a b x - 9a +--R / +--R 30 +--R 270x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1309 +m0:=a0-r0 +--R +--R +--R 10 +--R b +--R (4) - ----- +--R 2 +--R 270a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1309 +t0:=(a+b*x^3)^8/x^34 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 34 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1309 +r0:=-1/33*(a+b*x^3)^9/(a*x^33)+1/165*b*(a+b*x^3)^9/(a^2*x^30)-_ + 1/1485*b^2*(a+b*x^3)^9/(a^3*x^27) +--R +--R +--R (2) +--R 1 11 33 1 3 8 24 2 4 7 21 28 5 6 18 28 6 5 15 +--R - ---- b x - - a b x - - a b x - -- a b x - -- a b x +--R 1485 9 3 15 9 +--R + +--R 10 7 4 12 7 8 3 9 28 9 2 6 4 10 3 1 11 +--R - -- a b x - - a b x - -- a b x - -- a b x - -- a +--R 3 3 27 15 33 +--R / +--R 3 33 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 3465a b x - 1540a b x - 396a b x - 45a +--R / +--R 33 +--R 1485x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1309 +m0:=a0-r0 +--R +--R +--R 11 +--R b +--R (4) ------ +--R 3 +--R 1485a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1309 +t0:=(a+b*x^3)^8/x^37 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 37 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1309 +r0:=-1/36*(a+b*x^3)^9/(a*x^36)+1/132*b*(a+b*x^3)^9/(a^2*x^33)-_ + 1/660*b^2*(a+b*x^3)^9/(a^3*x^30)+1/5940*b^3*(a+b*x^3)^9/(a^4*x^27) +--R +--R +--R (2) +--R 1 12 36 1 4 8 24 8 5 7 21 14 6 6 18 8 7 5 15 +--R ---- b x - -- a b x - -- a b x - -- a b x - - a b x +--R 5940 12 15 9 3 +--R + +--R 35 8 4 12 56 9 3 9 14 10 2 6 8 11 3 1 12 +--R - -- a b x - -- a b x - -- a b x - -- a b x - -- a +--R 12 27 15 33 36 +--R / +--R 4 36 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 12320a b x - 5544a b x - 1440a b x - 165a +--R / +--R 36 +--R 5940x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1309 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ------ +--R 4 +--R 5940a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1309 +t0:=(a+b*x^3)^8/x^40 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 40 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 1309 +r0:=-1/39*a^8/x^39-2/9*a^7*b/x^36-28/33*a^6*b^2/x^33-28/15*a^5*b^3/x^30-_ + 70/27*a^4*b^4/x^27-7/3*a^3*b^5/x^24-4/3*a^2*b^6/x^21-_ + 4/9*a*b^7/x^18-1/15*b^8/x^15 +--R +--R +--R (2) +--R 1 8 24 4 7 21 4 2 6 18 7 3 5 15 70 4 4 12 28 5 3 9 +--R - -- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 15 9 3 3 27 15 +--R + +--R 28 6 2 6 2 7 3 1 8 +--R - -- a b x - - a b x - -- a +--R 33 9 39 +--R / +--R 39 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 67 + +--S 68 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 36036a b x - 16380a b x - 4290a b x - 495a +--R / +--R 39 +--R 19305x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1309 +t0:=(a+b*x^3)^8/x^43 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 43 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 1309 +r0:=-1/42*a^8/x^42-8/39*a^7*b/x^39-7/9*a^6*b^2/x^36-56/33*a^5*b^3/x^33-_ + 7/3*a^4*b^4/x^30-56/27*a^3*b^5/x^27-7/6*a^2*b^6/x^24-_ + 8/21*a*b^7/x^21-1/18*b^8/x^18 +--R +--R +--R (2) +--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 7 4 4 12 56 5 3 9 +--R - -- b x - -- a b x - - a b x - -- a b x - - a b x - -- a b x +--R 18 21 6 27 3 33 +--R + +--R 7 6 2 6 8 7 3 1 8 +--R - - a b x - -- a b x - -- a +--R 9 39 42 +--R / +--R 42 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 91728a b x - 42042a b x - 11088a b x - 1287a +--R / +--R 42 +--R 54054x +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1309 +t0:=(a+b*x^3)^8/x^46 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 46 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 1309 +r0:=-1/45*a^8/x^45-4/21*a^7*b/x^42-28/39*a^6*b^2/x^39-_ + 14/9*a^5*b^3/x^36-70/33*a^4*b^4/x^33-28/15*a^3*b^5/x^30-_ + 28/27*a^2*b^6/x^27-1/3*a*b^7/x^24-1/21*b^8/x^21 +--R +--R +--R (2) +--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 70 4 4 12 14 5 3 9 +--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - -- a b x +--R 21 3 27 15 33 9 +--R + +--R 28 6 2 6 4 7 3 1 8 +--R - -- a b x - -- a b x - -- a +--R 39 21 45 +--R / +--R 45 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 +--R - 6435b x - 45045a b x - 140140a b x - 252252a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 286650a b x - 210210a b x - 97020a b x - 25740a b x - 3003a +--R / +--R 45 +--R 135135x +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1309 +t0:=x^4*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 28 7 25 2 6 22 3 5 19 4 4 16 5 3 13 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 10 7 7 8 4 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1309 +r0:=1/5*a^8*x^5+a^7*b*x^8+28/11*a^6*b^2*x^11+4*a^5*b^3*x^14+_ + 70/17*a^4*b^4*x^17+14/5*a^3*b^5*x^20+28/23*a^2*b^6*x^23+_ + 4/13*a*b^7*x^26+1/29*b^8*x^29 +--R +--R +--R (2) +--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x +--R 29 13 23 5 17 +--R + +--R 28 6 2 11 7 8 1 8 5 +--R -- a b x + a b x + - a x +--R 11 5 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x +--R 29 13 23 5 17 +--R + +--R 28 6 2 11 7 8 1 8 5 +--R -- a b x + a b x + - a x +--R 11 5 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1309 +t0:=x^3*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 27 7 24 2 6 21 3 5 18 4 4 15 5 3 12 6 2 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 6 8 3 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1309 +r0:=1/4*a^8*x^4+8/7*a^7*b*x^7+14/5*a^6*b^2*x^10+56/13*a^5*b^3*x^13+_ + 35/8*a^4*b^4*x^16+56/19*a^3*b^5*x^19+14/11*a^2*b^6*x^22+_ + 8/25*a*b^7*x^25+1/28*b^8*x^28 +--R +--R +--R (2) +--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 28 25 11 19 8 13 +--R + +--R 14 6 2 10 8 7 7 1 8 4 +--R -- a b x + - a b x + - a x +--R 5 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 28 25 11 19 8 13 +--R + +--R 14 6 2 10 8 7 7 1 8 4 +--R -- a b x + - a b x + - a x +--R 5 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1309 +t0:=x*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 25 7 22 2 6 19 3 5 16 4 4 13 5 3 10 6 2 7 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 4 8 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1309 +r0:=1/2*a^8*x^2+8/5*a^7*b*x^5+7/2*a^6*b^2*x^8+56/11*a^5*b^3*x^11+_ + 5*a^4*b^4*x^14+56/17*a^3*b^5*x^17+7/5*a^2*b^6*x^20+_ + 8/23*a*b^7*x^23+1/26*b^8*x^26 +--R +--R +--R (2) +--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x +--R 26 23 5 17 11 +--R + +--R 7 6 2 8 8 7 5 1 8 2 +--R - a b x + - a b x + - a x +--R 2 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x +--R 26 23 5 17 11 +--R + +--R 7 6 2 8 8 7 5 1 8 2 +--R - a b x + - a b x + - a x +--R 2 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 1309 +t0:=(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 6 2 6 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 3 8 +--R 8a b x + a +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1309 +r0:=a^8*x+2*a^7*b*x^4+4*a^6*b^2*x^7+28/5*a^5*b^3*x^10+_ + 70/13*a^4*b^4*x^13+7/2*a^3*b^5*x^16+28/19*a^2*b^6*x^19+_ + 4/11*a*b^7*x^22+1/25*b^8*x^25 +--R +--R +--R (2) +--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 25 11 19 2 13 5 +--R + +--R 6 2 7 7 4 8 +--R 4a b x + 2a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 25 11 19 2 13 5 +--R + +--R 6 2 7 7 4 8 +--R 4a b x + 2a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1309 +t0:=(a+b*x^3)^8/x^2 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1309 +r0:=-a^8/x+4*a^7*b*x^2+28/5*a^6*b^2*x^5+7*a^5*b^3*x^8+_ + 70/11*a^4*b^4*x^11+4*a^3*b^5*x^14+28/17*a^2*b^6*x^17+_ + 2/5*a*b^7*x^20+1/23*b^8*x^23 +--R +--R +--R (2) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 150535a b x + 120428a b x + 86020a b x - 21505a +--R / +--R 21505x +--R Type: Fraction(Polynomial(Integer)) +--E 102 + +--S 103 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 150535a b x + 120428a b x + 86020a b x - 21505a +--R / +--R 21505x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1309 +t0:=(a+b*x^3)^8/x^3 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1309 +r0:=-1/2*a^8/x^2+8*a^7*b*x+7*a^6*b^2*x^4+8*a^5*b^3*x^7+7*a^4*b^4*x^10+_ + 56/13*a^3*b^5*x^13+7/4*a^2*b^6*x^16+8/19*a*b^7*x^19+1/22*b^8*x^22 +--R +--R +--R (2) +--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 4 4 12 5 3 9 +--R -- b x + -- a b x + - a b x + -- a b x + 7a b x + 8a b x +--R 22 19 4 13 +--R + +--R 6 2 6 7 3 1 8 +--R 7a b x + 8a b x - - a +--R 2 +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 494b x + 4576a b x + 19019a b x + 46816a b x + 76076a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 86944a b x + 76076a b x + 86944a b x - 5434a +--R / +--R 2 +--R 10868x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1309 +t0:=(a+b*x^3)^8/x^5 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1309 +r0:=-1/4*a^8/x^4-8*a^7*b/x+14*a^6*b^2*x^2+56/5*a^5*b^3*x^5+_ + 35/4*a^4*b^4*x^8+56/11*a^3*b^5*x^11+2*a^2*b^6*x^14+_ + 8/17*a*b^7*x^17+1/20*b^8*x^20 +--R +--R +--R (2) +--R 1 8 24 8 7 21 2 6 18 56 3 5 15 35 4 4 12 56 5 3 9 +--R -- b x + -- a b x + 2a b x + -- a b x + -- a b x + -- a b x +--R 20 17 11 4 5 +--R + +--R 6 2 6 7 3 1 8 +--R 14a b x - 8a b x - - a +--R 4 +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 187b x + 1760a b x + 7480a b x + 19040a b x + 32725a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 41888a b x + 52360a b x - 29920a b x - 935a +--R / +--R 4 +--R 3740x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1309 +t0:=(a+b*x^3)^8/x^6 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1309 +r0:=-1/5*a^8/x^5-4*a^7*b/x^2+28*a^6*b^2*x+14*a^5*b^3*x^4+10*a^4*b^4*x^7+_ + 28/5*a^3*b^5*x^10+28/13*a^2*b^6*x^13+1/2*a*b^7*x^16+1/19*b^8*x^19 +--R +--R +--R (2) +--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 4 4 12 5 3 9 +--R -- b x + - a b x + -- a b x + -- a b x + 10a b x + 14a b x +--R 19 2 13 5 +--R + +--R 6 2 6 7 3 1 8 +--R 28a b x - 4a b x - - a +--R 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 130b x + 1235a b x + 5320a b x + 13832a b x + 24700a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 34580a b x + 69160a b x - 9880a b x - 494a +--R / +--R 5 +--R 2470x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1309 +t0:=(a+b*x^3)^8/x^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1309 +r0:=-1/7*a^8/x^7-2*a^7*b/x^4-28*a^6*b^2/x+28*a^5*b^3*x^2+_ + 14*a^4*b^4*x^5+7*a^3*b^5*x^8+28/11*a^2*b^6*x^11+4/7*a*b^7*x^14+_ + 1/17*b^8*x^17 +--R +--R +--R (2) +--R 1 8 24 4 7 21 28 2 6 18 3 5 15 4 4 12 5 3 9 +--R -- b x + - a b x + -- a b x + 7a b x + 14a b x + 28a b x +--R 17 7 11 +--R + +--R 6 2 6 7 3 1 8 +--R - 28a b x - 2a b x - - a +--R 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 77b x + 748a b x + 3332a b x + 9163a b x + 18326a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 36652a b x - 36652a b x - 2618a b x - 187a +--R / +--R 7 +--R 1309x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1309 +t0:=(a+b*x^3)^8/x^9 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1309 +r0:=-1/8*a^8/x^8-8/5*a^7*b/x^5-14*a^6*b^2/x^2+56*a^5*b^3*x+_ + 35/2*a^4*b^4*x^4+8*a^3*b^5*x^7+14/5*a^2*b^6*x^10+_ + 8/13*a*b^7*x^13+1/16*b^8*x^16 +--R +--R +--R (2) +--R 1 8 24 8 7 21 14 2 6 18 3 5 15 35 4 4 12 5 3 9 +--R -- b x + -- a b x + -- a b x + 8a b x + -- a b x + 56a b x +--R 16 13 5 2 +--R + +--R 6 2 6 8 7 3 1 8 +--R - 14a b x - - a b x - - a +--R 5 8 +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 65b x + 640a b x + 2912a b x + 8320a b x + 18200a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 58240a b x - 14560a b x - 1664a b x - 130a +--R / +--R 8 +--R 1040x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1309 +t0:=x^5/(a+b*x^3) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 1309 +r0:=1/3*x^3/b-1/3*a*log(a+b*x^3)/b^2 +--R +--R +--R 3 3 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1309 +t0:=x^4/(a+b*x^3) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 1309 +r0:=1/2*x^2/b+1/3*a^(2/3)*log(a^(1/3)+b^(1/3)*x)/b^(5/3)-_ + 1/6*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)+_ + a^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 2x\|b - \|a 2 +-+3+-+2 +--R - 6\|a atan(-------------) + 3x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 +--R - \|3 |-- log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- - 2a x\|3 +--R | 2 3| 2 +--R |a \|b 2 +-+ +--R 6 |-- atan(---------------------- + 3x \|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a 3+-+2 |a |a 2 +--R - \|3 |-- \|b log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- - 2a x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b - \|a |a 3+-+2 \|b +--R 6\|a atan(-------------) + 6 |-- \|b atan(----------------------) +--R +-+3+-+ 3| 2 +--+2 +--R \|3 \|a \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1309 +t0:=x^3/(a+b*x^3) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 1309 +r0:=x/b-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*x)/b^(4/3)+1/6*a^(1/3)*_ + log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+a^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b - \|a +-+3+-+ +--R - 6\|a atan(-------------) + 6x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a | a 2 +-+ | a | a +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(------------------- + 6x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 +--R - \|3 3|- - \|b log(3|- - + x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ 3+-+ 3+-+ +--R +-+ | a 3+-+ | a 3+-+ 2x\|b - \|a +--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(-------------) +--R \| b \| b +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(-------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1309 +t0:=x^2/(a+b*x^3) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1309 +r0:=1/3*log(a+b*x^3)/b +--R +--R +--R 3 +--R log(b x + a) +--R (2) ------------- +--R 3b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(b x + a) +--R (3) ------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1309 +t0:=x/(a+b*x^3) +--R +--R +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1309 +r0:=-1/3*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((a^(1/3)-_ + 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b - x\|a \|b + \|a ) - 2\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b - \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R +-+ 3| 2 2 3| 2 +--R - \|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +------+2 +-+3| 2 +-+ +--R +-+ 3| 2 2x\|3 \|- a b - a b\|3 +--R 2\|3 log(x \|- a b + a b) - 6atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1309 +t0:=1/(a+b*x^3) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1309 +r0:=1/3*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(1/3))-1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))-_ + atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R - \|3 log(x \|b - x\|a \|b + \|a ) + 2\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b - \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +---+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|a b - a x\|a b + a ) + 2\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2x\|3 \|a b - a\|3 +--R 6atan(--------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 6\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 6\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1309 +t0:=1/(x*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1309 +r0:=log(x)/a-1/3*log(a+b*x^3)/a +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1309 +t0:=1/(x^2*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1309 +r0:=(-1)/(a*x)+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x)/a^(4/3)-_ + 1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)+_ + b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - x\|3 \|b log(x \|b - x\|a \|b + \|a ) + 2x\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b - \|a +-+3+-+ +--R - 6x\|b atan(-------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+2 +-+ +--R +-+ |b |b +-+ |b |b |b 2 +--R 2x\|3 3|- log(a 3|- + b x - x\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R |b \|a +-+ +--R 6x 3|- atan(--------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+ +--R 6a x\|3 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|b log(x\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 3+-+ 3+-+ +--R +-+3+-+ |b |b |b 2 3+-+ 2x\|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(-------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(---------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1309 +t0:=1/(x^3*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1309 +r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/a^(5/3)+_ + 1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b - \|a +-+3+-+2 +--R - 2x \|3 \|b log(x\|b + \|a ) - 6x \|b atan(------------- - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+2 +--R 6a x \|3 \|a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | b 2 | b | b 2 2 +--R - x \|3 |- -- log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | b | b +--R 2x \|3 |- -- log(- a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R 2 | b \| a +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 6a x \|3 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|b log(x \|b - x\|a \|b + \|a ) + 2\|3 \|b log(x\|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - \|3 |- -- \|a log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 3+-+ 3+-+ +--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a +--R 2\|3 |- -- \|a log(- a |- -- + b x + 6\|b atan(-------------) +--R 3| 2 3| 2 +-+3+-+ +--R \| a \| a \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1309 +t0:=1/(x^4*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1309 +r0:=(-1/3)/(a*x^3)-b*log(x)/a^2+1/3*b*log(a+b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R b x log(b x + a) - 3b x log(x) - a +--R (2) ----------------------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R b x log(b x + a) - 3b x log(x) - a +--R (3) ----------------------------------- +--R 2 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1309 +t0:=x^4/(a-b*x^3) +--R +--R +--R 4 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1309 +r0:=-1/2*x^2/b-1/3*a^(2/3)*log(a^(1/3)-b^(1/3)*x)/b^(5/3)+_ + 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)-_ + a^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 2x\|b + \|a 2 +-+3+-+2 +--R - 6\|a atan(-------------) - 3x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a | a | a 2 +--R - \|3 |- -- log(b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | a | a +--R 2\|3 |- -- log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 +--R | a \| b 2 +-+ +--R 6 |- -- atan(------------------------ - 3x \|3 +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log(x \|b + x\|a \|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a 3+-+2 | a | a 2 +--R - \|3 |- -- \|b log(b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | a 3+-+2 | a +-+3+-+2 3+-+ 3+-+ +--R 2\|3 |- -- \|b log(- b |- -- + a x + 2\|3 \|a log(- x\|b + \|a ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b + \|a | a 3+-+2 \| b +--R 6\|a atan(-------------) + 6 |- -- \|b atan(------------------------) +--R +-+3+-+ 3| 2 +----+2 +--R \|3 \|a \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1309 +t0:=x^3/(a-b*x^3) +--R +--R +--R 3 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1309 +r0:=-x/b-1/3*a^(1/3)*log(a^(1/3)-b^(1/3)*x)/b^(4/3)+_ + 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+_ + a^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b + \|a +-+3+-+ +--R 6\|a atan(-------------) - 6x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a | a 2 +-+ | a | a +--R - \|3 3|- - log(3|- - - x 3|- - + x + 2\|3 3|- - log(3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - - 2x\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(------------------- - 6x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log(x \|b + x\|a \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 +--R - \|3 3|- - \|b log(3|- - - x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +-+3+-+ 3+-+ 3+-+ +--R 2\|3 3|- - \|b log(3|- - + x + 2\|3 \|a log(- x\|b + \|a ) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R 3+-+ 3+-+ +---+ \|3 3|- - - 2x\|3 +--R 3+-+ 2x\|b + \|a | a 3+-+ \| b +--R - 6\|a atan(-------------) - 6 3|- - \|b atan(-------------------) +--R +-+3+-+ \| b +---+ +--R \|3 \|a | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1309 +t0:=x^2/(a-b*x^3) +--R +--R +--R 2 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1309 +r0:=-1/3*log(a-b*x^3)/b +--R +--R +--R 3 +--R log(- b x + a) +--R (2) - --------------- +--R 3b +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(b x - a) +--R (3) - ------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1309 +t0:=x/(a-b*x^3) +--R +--R +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1309 +r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)+_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-_ + atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b + \|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log(x \|- a b - a b) +--R + +--R +------+2 +------+ +--R +-+ 3| 2 2 3| 2 +--R - \|3 log(- x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b + a b\|3 +--R 6atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x \|- a b - a b) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(- x \|- a b + b x \|- a b - a b) +--R + +--R +------+ +------+ 3+-+ 3+-+ +--R +-+3| 2 3+-+ 3+-+ 3| 2 2x\|b + \|a +--R 2\|3 \|- a b log(- x\|b + \|a ) + 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b + a b\|3 +--R 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1309 +t0:=1/(a-b*x^3) +--R +--R +--R 1 +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1309 +r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(a^(2/3)+_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))+_ + atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b + \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +-----+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|- a b - a x\|- a b + a ) + 2\|3 log(x\|- a b + a) +--R + +--R +-----+ +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b - a\|3 +--R 6atan(----------------------) +--R 3a +--R / +--R +-----+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|- a b - a x\|- a b + a ) +--R + +--R +-----+ +-----+ +--R +-+3+-+2 3+-+ 3| 2 +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|a \|b log(x\|- a b + a + 2\|3 \|- a b log(- x\|b + \|a ) +--R + +--R +-----+ +--R +-----+ 3+-+ 3+-+ +-+3| 2 +-+ +--R 3| 2 2x\|b + \|a 3+-+2 3+-+ 2x\|3 \|- a b - a\|3 +--R - 6\|- a b atan(-------------) + 6\|a \|b atan(----------------------) +--R +-+3+-+ 3a +--R \|3 \|a +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1309 +t0:=1/(x*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ---------- +--R 4 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1309 +r0:=log(x)/a-1/3*log(a-b*x^3)/a +--R +--R +--R 3 +--R 3log(x) - log(- b x + a) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x - a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1309 +t0:=1/(x^2*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 5 2 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1309 +r0:=(-1)/(a*x)-1/3*b^(1/3)*log(a^(1/3)-b^(1/3)*x)/a^(4/3)+_ + 1/6*b^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)-_ + b^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R x\|3 \|b log(x \|b + x\|a \|b + \|a ) - 2x\|3 \|b log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b + \|a +-+3+-+ +--R - 6x\|b atan(-------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R +-+ | b | b | b 2 +--R - x\|3 3|- - log(a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+ +---+2 +--R +-+ | b | b +--R 2x\|3 3|- - log(- a 3|- - + b x) +--R \| a \| a +--R + +--R +---+2 +--R +-+ | b +-+ +--R +---+ a\|3 3|- - + 2b x\|3 +--R | b \| a +-+ +--R 6x 3|- - atan(----------------------- - 6\|3 +--R \| a +---+2 +--R | b +--R 3a 3|- - +--R \| a +--R / +--R +-+ +--R 6a x\|3 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - \|3 3|- - \|a log(a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+ +---+2 +--R +-+ | b 3+-+ | b +-+3+-+ 3+-+ 3+-+ +--R 2\|3 3|- - \|a log(- a 3|- - + b x + 2\|3 \|b log(- x\|b + \|a ) +--R \| a \| a +--R + +--R +---+2 +--R +-+ | b +-+ +--R 3+-+ 3+-+ +---+ a\|3 3|- - + 2b x\|3 +--R 3+-+ 2x\|b + \|a | b 3+-+ \| a +--R 6\|b atan(-------------) + 6 3|- - \|a atan(-----------------------) +--R +-+3+-+ \| a +---+2 +--R \|3 \|a | b +--R 3a 3|- - +--R \| a +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1309 +t0:=1/(x^3*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 6 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1309 +r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)-b^(1/3)*x)/a^(5/3)+_ + 1/6*b^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b + \|a +--R - 2x \|3 \|b log(- x\|b + \|a ) + 6x \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 +--R - 3\|3 \|a +--R / +--R 2 +-+3+-+2 +--R 6a x \|3 \|a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | b 2 | b | b 2 2 +--R - x \|3 |- -- log(a |- -- - a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | b | b +--R 2x \|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R 2 | b \| a +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 6a x \|3 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - \|3 |- -- \|a log(a |- -- - a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +-+3+-+2 3+-+ 3+-+ +--R 2\|3 |- -- \|a log(a |- -- + b x + 2\|3 \|b log(- x\|b + \|a ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b + \|a | b 3+-+2 \| a +--R - 6\|b atan(-------------) - 6 |- -- \|a atan(-----------------------) +--R +-+3+-+ 3| 2 +----+ +--R \|3 \|a \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1309 +t0:=1/(x^4*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 7 4 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1309 +r0:=(-1/3)/(a*x^3)+b*log(x)/a^2-1/3*b*log(a-b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R 3b x log(x) - b x log(- b x + a) - a +--R (2) ------------------------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R - b x log(b x - a) + 3b x log(x) - a +--R (3) ------------------------------------- +--R 2 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1309 +t0:=1/(1+a+b*x^3) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +--R b x + a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1309 +r0:=1/3*log((1+a)^(1/3)+b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))-_ + 1/6*log((1+a)^(2/3)-(1+a)^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))-atan(((1+a)^(1/3)-_ + 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R - \|3 log(x \|b - x\|a + 1 \|b + \|a + 1 ) +--R + +--R 3+-+ 3+-----+ +--R +-+ 3+-+ 3+-----+ 2x\|b - \|a + 1 +--R 2\|3 log(x\|b + \|a + 1 ) + 6atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +-+3+-----+2 3+-+ +--R 6\|3 \|a + 1 \|b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1) +--R + +--R +--------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(a + 2a + 1)b + a + 1) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3 +--R 6atan(---------------------------------------) +--R 3a + 3 +--R / +--R +--------------+ +--R +-+3| 2 +--R 6\|3 \|(a + 2a + 1)b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-----+2 3+-+ +--R \|3 \|a + 1 \|b +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1) +--R + +--R +--------------+ +--R +-+3+-----+2 3+-+ 3| 2 +--R 2\|3 \|a + 1 \|b log(x\|(a + 2a + 1)b + a + 1) +--R + +--R +--------------+ +--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R \|3 \|(a + 2a + 1)b log(x \|b - x\|a + 1 \|b + \|a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 3+-+ 3+-----+ +--R - 2\|3 \|(a + 2a + 1)b log(x\|b + \|a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 3+-----+2 3+-+ 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3 +--R 6\|a + 1 \|b atan(---------------------------------------) +--R 3a + 3 +--R + +--R +--------------+ 3+-+ 3+-----+ +--R 3| 2 2x\|b - \|a + 1 +--R - 6\|(a + 2a + 1)b atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +--------------+ +--R +-+3+-----+2 3+-+3| 2 +--R 6\|3 \|a + 1 \|b \|(a + 2a + 1)b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1309 +t0:=1/(1+a-b*x^3) +--R +--R +--R 1 +--R (1) - ------------ +--R 3 +--R b x - a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1309 +r0:=-1/3*log((1+a)^(1/3)-b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))+_ + 1/6*log((1+a)^(2/3)+(1+a)^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))+atan(((1+a)^(1/3)+_ + 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R \|3 log(x \|b + x\|a + 1 \|b + \|a + 1 ) +--R + +--R 3+-+ 3+-----+ +--R +-+ 3+-+ 3+-----+ 2x\|b + \|a + 1 +--R - 2\|3 log(- x\|b + \|a + 1 ) + 6atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +-+3+-----+2 3+-+ +--R 6\|3 \|a + 1 \|b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a +--R + +--R 2a + 1 +--R + +--R +----------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(- a - 2a - 1)b + a + 1) +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3 +--R 6atan(-----------------------------------------) +--R 3a + 3 +--R / +--R +----------------+ +--R +-+3| 2 +--R 6\|3 \|(- a - 2a - 1)b +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R - \|3 \|(- a - 2a - 1)b log(x \|b + x\|a + 1 \|b + \|a + 1 ) +--R + +--R - +--R +-+3+-----+2 3+-+ +--R \|3 \|a + 1 \|b +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a +--R + +--R 2a + 1 +--R + +--R +----------------+ +--R +-+3+-----+2 3+-+ 3| 2 +--R 2\|3 \|a + 1 \|b log(x\|(- a - 2a - 1)b + a + 1) +--R + +--R +----------------+ +--R +-+3| 2 3+-+ 3+-----+ +--R 2\|3 \|(- a - 2a - 1)b log(- x\|b + \|a + 1 ) +--R + +--R +----------------+ 3+-+ 3+-----+ +--R 3| 2 2x\|b + \|a + 1 +--R - 6\|(- a - 2a - 1)b atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 3+-----+2 3+-+ 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3 +--R 6\|a + 1 \|b atan(-----------------------------------------) +--R 3a + 3 +--R / +--R +----------------+ +--R +-+3| 2 3+-----+2 3+-+ +--R 6\|3 \|(- a - 2a - 1)b \|a + 1 \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1309 +t0:=1/(-1+a+b*x^3) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +--R b x + a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1309 +r0:=1/3*log((1-a)^(1/3)-b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))-_ + 1/6*log((1-a)^(2/3)+(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_ + b^(1/3))-atan(((1-a)^(1/3)+2*b^(1/3)*x)/((1-a)^(1/3)*_ + sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R - \|3 log(x \|b + x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R 3+-+ 3+-------+ +--R +-+ 3+-+ 3+-------+ 2x\|b + \|- a + 1 +--R 2\|3 log(- x\|b + \|- a + 1 ) - 6atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +-+3+-------+2 3+-+ +--R 6\|3 \|- a + 1 \|b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1) +--R + +--R +--------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(a - 2a + 1)b + a - 1) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3 +--R 6atan(---------------------------------------) +--R 3a - 3 +--R / +--R +--------------+ +--R +-+3| 2 +--R 6\|3 \|(a - 2a + 1)b +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-------+2 3+-+ +--R \|3 \|- a + 1 \|b +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1) +--R + +--R +--------------+ +--R +-+3+-------+2 3+-+ 3| 2 +--R 2\|3 \|- a + 1 \|b log(x\|(a - 2a + 1)b + a - 1) +--R + +--R +--------------+ +--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R \|3 \|(a - 2a + 1)b log(x \|b + x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 3+-+ 3+-------+ +--R - 2\|3 \|(a - 2a + 1)b log(- x\|b + \|- a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 3+-------+2 3+-+ 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3 +--R 6\|- a + 1 \|b atan(---------------------------------------) +--R 3a - 3 +--R + +--R +--------------+ 3+-+ 3+-------+ +--R 3| 2 2x\|b + \|- a + 1 +--R 6\|(a - 2a + 1)b atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +--------------+ +--R +-+3+-------+2 3+-+3| 2 +--R 6\|3 \|- a + 1 \|b \|(a - 2a + 1)b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1309 +t0:=1/(-1+a-b*x^3) +--R +--R +--R 1 +--R (1) - ------------ +--R 3 +--R b x - a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1309 +r0:=-1/3*log((1-a)^(1/3)+b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))+_ + 1/6*log((1-a)^(2/3)-(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_ + b^(1/3))+atan(((1-a)^(1/3)-2*b^(1/3)*x)/((1-a)^(1/3)*_ + sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R \|3 log(x \|b - x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R 3+-+ 3+-------+ +--R +-+ 3+-+ 3+-------+ 2x\|b - \|- a + 1 +--R - 2\|3 log(x\|b + \|- a + 1 ) - 6atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +-+3+-------+2 3+-+ +--R 6\|3 \|- a + 1 \|b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a +--R + +--R - 2a + 1 +--R + +--R +----------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(- a + 2a - 1)b + a - 1) +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3 +--R 6atan(-----------------------------------------) +--R 3a - 3 +--R / +--R +----------------+ +--R +-+3| 2 +--R 6\|3 \|(- a + 2a - 1)b +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R - \|3 \|(- a + 2a - 1)b log(x \|b - x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R +----------------+ +--R +-+3| 2 3+-+ 3+-------+ +--R 2\|3 \|(- a + 2a - 1)b log(x\|b + \|- a + 1 ) +--R + +--R - +--R +-+3+-------+2 3+-+ +--R \|3 \|- a + 1 \|b +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a +--R + +--R - 2a + 1 +--R + +--R +----------------+ +--R +-+3+-------+2 3+-+ 3| 2 +--R 2\|3 \|- a + 1 \|b log(x\|(- a + 2a - 1)b + a - 1) +--R + +--R +----------------+ 3+-+ 3+-------+ +--R 3| 2 2x\|b - \|- a + 1 +--R 6\|(- a + 2a - 1)b atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 3+-------+2 3+-+ 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3 +--R 6\|- a + 1 \|b atan(-----------------------------------------) +--R 3a - 3 +--R / +--R +----------------+ +--R +-+3| 2 3+-------+2 3+-+ +--R 6\|3 \|(- a + 2a - 1)b \|- a + 1 \|b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1309 +t0:=x^5/(a+b*x^3)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1309 +r0:=1/3*a/(b^2*(a+b*x^3))+1/3*log(a+b*x^3)/b^2 +--R +--R +--R 3 3 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 3 2 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 3 2 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1309 +t0:=x^4/(a+b*x^3)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1309 +r0:=-1/3*x^2/(b*(a+b*x^3))-2/9*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(5/3))+_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+3+-+2 +--R - 3x \|3 \|a \|b +--R / +--R 2 3 +-+3+-+3+-+2 +--R (9b x + 9a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 3 +-+ 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +------+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6b x - 6a)atan(--------------------------) - 3x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 2 3 +-+3| 2 +--R (9b x + 9a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1309 +t0:=x^3/(a+b*x^3)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1309 +r0:=-1/3*x/(b*(a+b*x^3))+1/9*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R - 6x\|3 \|a \|b +--R / +--R 2 3 +-+3+-+2 3+-+ +--R (18b x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3 +--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R - 6x\|3 \|a b +--R / +--R +---+ +--R 2 3 +-+3| 2 +--R (18b x + 18a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1309 +t0:=x^2/(a+b*x^3)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1309 +r0:=(-1/3)/(b*(a+b*x^3)) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - ---------- +--R 2 3 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 3 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1309 +t0:=x/(a+b*x^3)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1309 +r0:=1/3*x^2/(a*(a+b*x^3))-1/9*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(2/3))+_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+3+-+2 +--R 6x \|3 \|a \|b +--R / +--R 3 2 +-+3+-+3+-+2 +--R (18a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 3 +-+ 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +------+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6b x - 6a)atan(--------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 3 2 +-+3| 2 +--R (18a b x + 18a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1309 +t0:=1/(a+b*x^3)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1309 +r0:=1/3*x/(a*(a+b*x^3))+2/9*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(1/3))-_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R 3x\|3 \|a \|b +--R / +--R 3 2 +-+3+-+2 3+-+ +--R (9a b x + 9a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3 +--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R 3x\|3 \|a b +--R / +--R +---+ +--R 3 2 +-+3| 2 +--R (9a b x + 9a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1309 +t0:=1/(x*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 7 4 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1309 +r0:=1/3/(a*(a+b*x^3))+log(x)/a^2-1/3*log(a+b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3a +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1309 +t0:=1/(x^2*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 5 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1309 +r0:=(-4/3)/(a^2*x)+1/3/(a*x*(a+b*x^3))+4/9*b^(1/3)*log(a^(1/3)+_ + b^(1/3)*x)/a^(7/3)-2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 4 +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 2b x - 2a x)\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 4 +-+3+-+ 3+-+ 3+-+ +--R (4b x + 4a x)\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 4 3+-+ 2x\|b - \|a 3 +-+3+-+ +--R (- 12b x - 12a x)\|b atan(-------------) + (- 12b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 4 3 +-+3+-+ +--R (9a b x + 9a x)\|3 \|a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 4 +-+ |b |b +--R (4b x + 4a x)\|3 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 4 +-+ |b |b |b 2 +--R (- 2b x - 2a x)\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R 4 |b \|a 3 +-+ +--R (12b x + 12a x) 3|- atan(--------------------- + (- 12b x - 9a)\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 4 3 +-+ +--R (9a b x + 9a x)\|3 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R 2\|3 \|b log(x \|b - x\|a \|b + \|a ) - 4\|3 \|b log(x\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R +-+3+-+ |b |b |b 2 +--R - 2\|3 \|a 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R 3+-+ 3+-+ +-+ a\|3 3|- - 2b x\|3 +--R 3+-+ 2x\|b - \|a 3+-+ |b \|a +--R 12\|b atan(-------------) + 12\|a 3|- atan(---------------------) +--R +-+3+-+ \|a +-+2 +--R \|3 \|a |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1309 +t0:=1/(x^3*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 6 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1309 +r0:=(-5/6)/(a^2*x^2)+1/3/(a*x^2*(a+b*x^3))-5/9*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*x)/a^(8/3)+5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 5 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (5b x + 5a x )\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 5 2 +-+3+-+2 3+-+ 3+-+ +--R (- 10b x - 10a x )\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 5 2 3+-+2 2x\|b - \|a 3 +-+3+-+2 +--R (- 30b x - 30a x )\|b atan(-------------) + (- 15b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 5 3 2 +-+3+-+2 +--R (18a b x + 18a x )\|3 \|a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 5 2 +-+ | b 2 | b | b 2 2 +--R (- 5b x - 5a x )\|3 |- -- log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 5 2 +-+ | b | b +--R (10b x + 10a x )\|3 |- -- log(- a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R 5 2 | b \| a +--R (- 30b x - 30a x ) |- -- atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 +-+ +--R (- 15b x - 9a)\|3 +--R / +--R 2 5 3 2 +-+ +--R (18a b x + 18a x )\|3 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log(x\|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - 5\|3 |- -- \|a log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 3+-+ 3+-+ +--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a +--R 10\|3 |- -- \|a log(- a |- -- + b x + 30\|b atan(-------------) +--R 3| 2 3| 2 +-+3+-+ +--R \| a \| a \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1309 +t0:=1/(x^4*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 7 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1309 +r0:=(-2/3)/(a^2*x^3)+1/3/(a*x^3*(a+b*x^3))-2*b*log(x)/a^3+_ + 2/3*b*log(a+b*x^3)/a^3 +--R +--R +--R (2) +--R 2 6 3 3 2 6 3 3 2 +--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 6 4 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 3 2 6 3 3 2 +--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 6 4 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1309 +t0:=x^8/(a+b*x^3)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1309 +r0:=-1/6*a^2/(b^3*(a+b*x^3)^2)+2/3*a/(b^3*(a+b*x^3))+1/3*log(a+b*x^3)/b^3 +--R +--R +--R 2 6 3 2 3 3 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ---------------------------------------------------- +--R 5 6 4 3 2 3 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 3 3 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ---------------------------------------------------- +--R 5 6 4 3 2 3 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1309 +t0:=x^7/(a+b*x^3)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1309 +r0:=-1/6*x^5/(b*(a+b*x^3)^2)-5/18*x^2/(b^2*(a+b*x^3))-5/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(1/3)*b^(8/3))+5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(1/3)*b^(8/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (5b x + 10a b x + 5a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 10b x - 20a b x - 10a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (30b x + 60a b x + 30a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 2 +-+3+-+3+-+2 +--R (- 24b x - 15a x )\|3 \|a \|b +--R / +--R 4 6 3 3 2 2 +-+3+-+3+-+2 +--R (54b x + 108a b x + 54a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (10b x + 20a b x + 10a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 30b x - 60a b x - 30a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (- 24b x - 15a x )\|3 \|- a b +--R / +--R +------+ +--R 4 6 3 3 2 2 +-+3| 2 +--R (54b x + 108a b x + 54a b )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 10\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - 5\|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 10\|3 \|a \|b log(x \|- a b + a b) - 30\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 30\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 54b \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1309 +t0:=x^6/(a+b*x^3)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1309 +r0:=-1/6*x^4/(b*(a+b*x^3)^2)-2/9*x/(b^2*(a+b*x^3))+2/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-2/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (4b x + 8a b x + 4a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (12b x + 24a b x + 12a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+2 3+-+ +--R (- 21b x - 12a x)\|3 \|a \|b +--R / +--R 4 6 3 3 2 2 +-+3+-+2 3+-+ +--R (54b x + 108a b x + 54a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (4b x + 8a b x + 4a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (12b x + 24a b x + 12a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (- 21b x - 12a x)\|3 \|a b +--R / +--R +---+ +--R 4 6 3 3 2 2 +-+3| 2 +--R (54b x + 108a b x + 54a b )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 27b \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1309 +t0:=x^5/(a+b*x^3)^3 +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1309 +r0:=1/6*x^6/(a*(a+b*x^3)^2) +--R +--R +--R 1 6 +--R - x +--R 6 +--R (2) --------------------- +--R 2 6 2 3 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 312 + +--S 313 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 2b x - a +--R (3) ------------------------ +--R 4 6 3 3 2 2 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1309 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 6a b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1309 +t0:=x^4/(a+b*x^3)^3 +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1309 +r0:=-1/6*x^2/(b*(a+b*x^3)^2)+1/9*x^2/(a*b*(a+b*x^3))-1/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(4/3)*b^(5/3))+1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(4/3)*b^(5/3))-1/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + 2a b x + a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 2b x - 4a b x - 2a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a 5 2 +-+3+-+3+-+2 +--R (6b x + 12a b x + 6a )atan(-------------) + (6b x - 3a x )\|3 \|a \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 6 2 2 3 3 +-+3+-+3+-+2 +--R (54a b x + 108a b x + 54a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- b x - 2a b x - a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (2b x + 4a b x + 2a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 6b x - 12a b x - 6a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (6b x - 3a x )\|3 \|- a b +--R / +--R +------+ +--R 3 6 2 2 3 3 +-+3| 2 +--R (54a b x + 108a b x + 54a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1309 +t0:=x^3/(a+b*x^3)^3 +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1309 +r0:=-1/6*x/(b*(a+b*x^3)^2)+1/18*x/(a*b*(a+b*x^3))+1/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - 2a b x - a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (2b x + 4a b x + 2a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a 4 +-+3+-+2 3+-+ +--R (6b x + 12a b x + 6a )atan(-------------) + (3b x - 6a x)\|3 \|a \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 6 2 2 3 3 +-+3+-+2 3+-+ +--R (54a b x + 108a b x + 54a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- b x - 2a b x - a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (2b x + 4a b x + 2a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (6b x + 12a b x + 6a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (3b x - 6a x)\|3 \|a b +--R / +--R +---+ +--R 3 6 2 2 3 3 +-+3| 2 +--R (54a b x + 108a b x + 54a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1309 +t0:=x^2/(a+b*x^3)^3 +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1309 +r0:=(-1/6)/(b*(a+b*x^3)^2) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - -------------------- +--R 3 6 2 3 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 6 2 3 2 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1309 +t0:=x/(a+b*x^3)^3 +--R +--R +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1309 +r0:=1/6*x^2/(a*(a+b*x^3)^2)+2/9*x^2/(a^2*(a+b*x^3))-2/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(7/3)*b^(2/3))+1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(7/3)*b^(2/3))-2/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (2b x + 4a b x + 2a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 4b x - 8a b x - 4a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (12b x + 24a b x + 12a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 2 +-+3+-+3+-+2 +--R (12b x + 21a x )\|3 \|a \|b +--R / +--R 2 2 6 3 3 4 +-+3+-+3+-+2 +--R (54a b x + 108a b x + 54a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (4b x + 8a b x + 4a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 12b x - 24a b x - 12a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (12b x + 21a x )\|3 \|- a b +--R / +--R +------+ +--R 2 2 6 3 3 4 +-+3| 2 +--R (54a b x + 108a b x + 54a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1309 +t0:=1/(a+b*x^3)^3 +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1309 +r0:=1/6*x/(a*(a+b*x^3)^2)+5/18*x/(a^2*(a+b*x^3))+5/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(8/3)*b^(1/3))-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(8/3)*b^(1/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (10b x + 20a b x + 10a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (30b x + 60a b x + 30a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+2 3+-+ +--R (15b x + 24a x)\|3 \|a \|b +--R / +--R 2 2 6 3 3 4 +-+3+-+2 3+-+ +--R (54a b x + 108a b x + 54a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (10b x + 20a b x + 10a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (30b x + 60a b x + 30a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (15b x + 24a x)\|3 \|a b +--R / +--R +---+ +--R 2 2 6 3 3 4 +-+3| 2 +--R (54a b x + 108a b x + 54a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - 5\|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+2 3+-+ 2x\|3 \|a b - a\|3 +--R - 10\|3 \|a b log(x\|b + \|a ) + 30\|a \|b atan(--------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 2x\|b - \|a +--R - 30\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1309 +t0:=1/(x*(a+b*x^3)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 10 2 7 2 4 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1309 +r0:=1/6/(a*(a+b*x^3)^2)+1/3/(a^2*(a+b*x^3))+log(x)/a^3-1/3*log(a+b*x^3)/a^3 +--R +--R +--R (2) +--R 2 6 3 2 3 2 6 3 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x) +--R + +--R 3 2 +--R 2a b x + 3a +--R / +--R 3 2 6 4 3 5 +--R 6a b x + 12a b x + 6a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 2 3 2 6 3 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x) +--R + +--R 3 2 +--R 2a b x + 3a +--R / +--R 3 2 6 4 3 5 +--R 6a b x + 12a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1309 +t0:=x^8*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 8 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1309 +r0:=2/9*a^2*(a+b*x^3)^(3/2)/b^3-4/15*a*(a+b*x^3)^(5/2)/b^3+_ + 2/21*(a+b*x^3)^(7/2)/b^3 +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 | 3 +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) ---------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 | 3 +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) ---------------------------------------------- +--R 3 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1309 +t0:=x^5*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 5 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1309 +r0:=-2/9*a*(a+b*x^3)^(3/2)/b^2+2/15*(a+b*x^3)^(5/2)/b^2 +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x + 2a b x - 4a )\|b x + a +--R (2) ---------------------------------- +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x + 2a b x - 4a )\|b x + a +--R (3) ---------------------------------- +--R 2 +--R 45b +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1309 +t0:=x^2*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 2 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1309 +r0:=2/9*(a+b*x^3)^(3/2)/b +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x + 2a)\|b x + a +--R (2) ----------------------- +--R 9b +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x + 2a)\|b x + a +--R (3) ----------------------- +--R 9b +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1309 +t0:=sqrt(a+b*x^3)/x +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1309 +r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))*sqrt(a)+2/3*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R +-+ \|b x + a | 3 +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 3 3 +--------+ +--R +-+ - 2\|a \|b x + a + b x + 2a | 3 +--R \|a log(------------------------------) + 2\|b x + a +--R 3 +--R x +--R [------------------------------------------------------, +--R 3 +--R +--------+ +--R | 3 +--------+ +--R +---+ \|b x + a | 3 +--R - 2\|- a atan(-----------) + 2\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 363 + +--S 364 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 3 3 | 3 +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R \|a log(------------------------------) + 2\|a atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ \|b x + a +---+ \|b x + a +--R 2\|a atanh(-----------) - 2\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1309 +t0:=sqrt(a+b*x^3)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1309 +r0:=-1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)-1/3*sqrt(a+b*x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 3 \|b x + a +-+ | 3 +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 3 +-+ +--R 3x \|a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a +-+ | 3 +--R b x log(---------------------------------) - 2\|a \|b x + a +--R 3 +--R x +--R [-------------------------------------------------------------, +--R 3 +-+ +--R 6x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 3 \|- a \|b x + a +---+ | 3 +--R - b x atan(-----------------) - \|- a \|b x + a +--R a +--R -------------------------------------------------] +--R 3 +---+ +--R 3x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 370 + +--S 371 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(---------------------------------) + 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 6\|a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R b\|- a atanh(-----------) - b\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 3\|- a \|a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 374 + +)clear all + +--S 375 of 1309 +t0:=sqrt(a+b*x^3)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1309 +r0:=1/12*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/6*sqrt(a+b*x^3)/x^6-_ + 1/12*b*sqrt(a+b*x^3)/(a*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 2 6 \|b x + a 3 +-+ | 3 +--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 6 +-+ +--R 12a x \|a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 2 6 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3 +--R b x log(-------------------------------) + (- 2b x - 4a)\|a \|b x + a +--R 3 +--R x +--R [------------------------------------------------------------------------, +--R 6 +-+ +--R 24a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 2 6 \|- a \|b x + a 3 +---+ | 3 +--R b x atan(-----------------) + (- b x - 2a)\|- a \|b x + a +--R a +--R ------------------------------------------------------------] +--R 6 +---+ +--R 12a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 377 + +--S 378 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(-------------------------------) - 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 24a\|a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R - b \|- a atanh(-----------) + b \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 12a\|- a \|a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 1309 +t0:=x^3*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R 3 | 3 +--R (1) x \|27x + 8 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1309 +--r0:=16/495*x*sqrt(8+27*x^3)+2/11*x^4*sqrt(8+27*x^3)-256/1485*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 383 + +--S 384 of 1309 +--a0:=integrate(t0,x) +--E 384 + +--S 385 of 1309 +--m0:=a0-r0 +--E 385 + +--S 386 of 1309 +--d0:=D(m0,x) +--E 386 + +)clear all + +--S 387 of 1309 +t0:=sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R | 3 +--R (1) \|27x + 8 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1309 +--r0:=2/5*x*sqrt(8+27*x^3)+16/5*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 388 + +--S 389 of 1309 +--a0:=integrate(t0,x) +--E 389 + +--S 390 of 1309 +--m0:=a0-r0 +--E 390 + +--S 391 of 1309 +--d0:=D(m0,x) +--E 391 + +)clear all + +--S 392 of 1309 +t0:=sqrt(8+27*x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--R \|27x + 8 +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1309 +--r0:=-1/2*sqrt(8+27*x^3)/x^2+27/2*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 393 + +--S 394 of 1309 +--a0:=integrate(t0,x) +--E 394 + +--S 395 of 1309 +--m0:=a0-r0 +--E 395 + +--S 396 of 1309 +--d0:=D(m0,x) +--E 396 + +)clear all + +--S 397 of 1309 +t0:=x^4*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R 4 | 3 +--R (1) x \|27x + 8 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1309 +--r0:=16/819*x^2*sqrt(8+27*x^3)+2/13*x^5*sqrt(8+27*x^3)-_ +-- 512/7371*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))+1024/7371*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 398 + +--S 399 of 1309 +--a0:=integrate(t0,x) +--E 399 + +--S 400 of 1309 +--m0:=a0-r0 +--E 400 + +--S 401 of 1309 +--d0:=D(m0,x) +--E 401 + +)clear all + +--S 402 of 1309 +t0:=x*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R | 3 +--R (1) x\|27x + 8 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1309 +--r0:=2/7*x^2*sqrt(8+27*x^3)+16/21*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-32/21*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 403 + +--S 404 of 1309 +--a0:=integrate(t0,x) +--E 404 + +--S 405 of 1309 +--m0:=a0-r0 +--E 405 + +--S 406 of 1309 +--d0:=D(m0,x) +--E 406 + +)clear all + +--R +--S 407 of 1309 +t0:=sqrt(8+27*x^3)/x^2 +--R +--R +--R +--------+ +--R | 3 +--R \|27x + 8 +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1309 +--r0:=-sqrt(8+27*x^3)/x+9*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-18*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 408 + +--S 409 of 1309 +--a0:=integrate(t0,x) +--E 409 + +--S 410 of 1309 +--m0:=a0-r0 +--E 410 + +--S 411 of 1309 +--d0:=D(m0,x) +--E 411 + +)clear all + +--S 412 of 1309 +t0:=x^8/sqrt(a+b*x^3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1309 +r0:=16/45*a^2*sqrt(a+b*x^3)/b^3-8/45*a*x^3*sqrt(a+b*x^3)/b^2+_ + 2/15*x^6*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x - 8a b x + 16a )\|b x + a +--R (2) ----------------------------------- +--R 3 +--R 45b +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x - 8a b x + 16a )\|b x + a +--R (3) ----------------------------------- +--R 3 +--R 45b +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 416 + +)clear all + +--S 417 of 1309 +t0:=x^5/sqrt(a+b*x^3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1309 +r0:=-4/9*a*sqrt(a+b*x^3)/b^2+2/9*x^3*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x - 4a)\|b x + a +--R (2) ----------------------- +--R 2 +--R 9b +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x - 4a)\|b x + a +--R (3) ----------------------- +--R 2 +--R 9b +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 421 + +)clear all + +--S 422 of 1309 +t0:=x^2/sqrt(a+b*x^3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1309 +r0:=2/3*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R | 3 +--R 2\|b x + a +--R (2) ------------ +--R 3b +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2\|b x + a +--R (3) ------------ +--R 3b +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 1309 +t0:=1/(x*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 3 +--R x\|b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1309 +r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 3 +-+ +--------+ +--R - 2a\|b x + a + (b x + 2a)\|a +---+ | 3 +--R log(---------------------------------) \|- a \|b x + a +--R 3 2atan(-----------------) +--R x a +--R (3) [--------------------------------------,- ------------------------] +--R +-+ +---+ +--R 3\|a 3\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 429 + +--S 430 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(-----------) - 2\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 3\|- a \|a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1309 +t0:=1/(x^4*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1309 +r0:=1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/3*sqrt(a+b*x^3)/(a*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 3 \|b x + a +-+ | 3 +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 3 2a\|b x + a + (b x + 2a)\|a +-+ | 3 +--R b x log(-------------------------------) - 2\|a \|b x + a +--R 3 +--R x +--R [-----------------------------------------------------------, +--R 3 +-+ +--R 6a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 3 \|- a \|b x + a +---+ | 3 +--R b x atan(-----------------) - \|- a \|b x + a +--R a +--R -----------------------------------------------] +--R 3 +---+ +--R 3a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 436 + +--S 437 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-------------------------------) - 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - b\|- a atanh(-----------) + b\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 3a\|- a \|a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1309 +t0:=1/(x^7*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 7 | 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1309 +r0:=-1/4*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)-_ + 1/6*sqrt(a+b*x^3)/(a*x^6)+1/4*b*sqrt(a+b*x^3)/(a^2*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 2 6 \|b x + a 3 +-+ | 3 +--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 6 +-+ +--R 12a x \|a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 2 6 - 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3 +--R 3b x log(---------------------------------) + (6b x - 4a)\|a \|b x + a +--R 3 +--R x +--R [-------------------------------------------------------------------------, +--R 2 6 +-+ +--R 24a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 2 6 \|- a \|b x + a 3 +---+ | 3 +--R - 3b x atan(-----------------) + (3b x - 2a)\|- a \|b x + a +--R a +--R --------------------------------------------------------------] +--R 2 6 +---+ +--R 12a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 443 + +--S 444 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(---------------------------------) + 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R b \|- a atanh(-----------) - b \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1309 +t0:=x^3/sqrt(8+27*x^3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1309 +--r0:=2/135*x*sqrt(8+27*x^3)-32/405*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 449 + +--S 450 of 1309 +--a0:=integrate(t0,x) +--E 450 + +--S 451 of 1309 +--m0:=a0-r0 +--E 451 + +--S 452 of 1309 +--d0:=D(m0,x) +--E 452 + +)clear all + +--S 453 of 1309 +t0:=1/sqrt(8+27*x^3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1309 +--r0:=2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1-3*x-%i*sqrt(3)))*sqrt((2+3*x)/(3+%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 454 + +--S 455 of 1309 +--a0:=integrate(t0,x) +--E 455 + +--S 456 of 1309 +--m0:=a0-r0 +--E 456 + +--S 457 of 1309 +--d0:=D(m0,x) +--E 457 + +)clear all + +--S 458 of 1309 +t0:=1/(x^3*sqrt(8+27*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 3 +--R x \|27x + 8 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1309 +--r0:=-1/16*sqrt(8+27*x^3)/x^2-9/16*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 459 + +--S 460 of 1309 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 1309 +--m0:=a0-r0 +--E 461 + +--S 462 of 1309 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 1309 +t0:=x^4/sqrt(8+27*x^3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1309 +--r0:=2/189*x^2*sqrt(8+27*x^3)-64/1701*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))+128/1701*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 464 + +--S 465 of 1309 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 1309 +--m0:=a0-r0 +--E 466 + +--S 467 of 1309 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 1309 +t0:=x/sqrt(8+27*x^3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1309 +--r0:=2/9*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-4/9*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 469 + +--S 470 of 1309 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 1309 +--m0:=a0-r0 +--E 471 + +--S 472 of 1309 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 1309 +t0:=1/(x^2*sqrt(8+27*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 3 +--R x \|27x + 8 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1309 +--r0:=-1/8*sqrt(8+27*x^3)/x+3/8*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-3/4*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 474 + +--S 475 of 1309 +--a0:=integrate(t0,x) +--E 475 + +--S 476 of 1309 +--m0:=a0-r0 +--E 476 + +--S 477 of 1309 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 of 1309 +t0:=x^5/(1+x^3)^(3/2) +--R +--R +--R 5 +--R x +--R (1) ----------------- +--R +------+ +--R 3 | 3 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1309 +r0:=2/3/sqrt(1+x^3)+2/3*sqrt(1+x^3) +--R +--R +--R 3 +--R 2x + 4 +--R (2) ---------- +--R +------+ +--R | 3 +--R 3\|x + 1 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2x + 4 +--R (3) ---------- +--R +------+ +--R | 3 +--R 3\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1309 +t0:=x^8*(1-x^3)^(1/3) +--R +--R +--R +--------+ +--R 8 3| 3 +--R (1) x \|- x + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1309 +r0:=-1/4*(1-x^3)^(4/3)+2/7*(1-x^3)^(7/3)-1/10*(1-x^3)^(10/3) +--R +--R +--R +--------+ +--R 9 6 3 3| 3 +--R (14x - 2x - 3x - 9)\|- x + 1 +--R (2) --------------------------------- +--R 140 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 9 6 3 3| 3 +--R (14x - 2x - 3x - 9)\|- x + 1 +--R (3) --------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1309 +t0:=x^5*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 5 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1309 +r0:=-1/4*a*(a+b*x^3)^(4/3)/b^2+1/7*(a+b*x^3)^(7/3)/b^2 +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (4b x + a b x - 3a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (4b x + a b x - 3a )\|b x + a +--R (3) --------------------------------- +--R 2 +--R 28b +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1309 +t0:=x^4*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 4 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1309 +r0:=1/18*a*x^2*(a+b*x^3)^(1/3)/b+1/6*x^5*(a+b*x^3)^(1/3)+_ + 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(5/3)-_ + 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(5/3)+1/9*a^2*_ + atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b +--R 2a \|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 5 2 +-+3+-+2 3| 3 +--R (9b x + 3a x )\|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R 2 +-+ \|b \|b x + a + b x\|b \|b x + a + b x +--R - a \|3 log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a atan(-------------------------------) +--R 3b x +--R + +--R +--+ +--------+ +--R 5 2 +-+3| 2 3| 3 +--R (9b x + 3a x )\|3 \|b \|b x + a +--R / +--R +--+ +--R +-+3| 2 +--R 54b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R 2 +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x +--R - a \|3 \|b log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R 2 +-+3+-+2 \|b \|b x + a - b x +--R 2a \|3 \|b log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +--+ 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R a \|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 2 +-+3| 2 \|b x + a - x\|b +--R - 2a \|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2 3+-+2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a \|b atan(-------------------------------) +--R 3b x +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 2 3| 2 \|b x + a + 2x\|b +--R - 6a \|b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 54b\|3 \|b \|b +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1309 +t0:=x^3*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1309 +--r0:=1/10*a*x*(a+b*x^3)^(1/3)/b+1/5*x^4*(a+b*x^3)^(1/3)-_ +-- 1/10*a^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3)) +--E 499 + +--S 500 of 1309 +--a0:=integrate(t0,x) +--E 500 + +--S 501 of 1309 +--m0:=a0-r0 +--E 501 + +--S 502 of 1309 +--d0:=D(m0,x) +--E 502 + +)clear all + +--S 503 of 1309 +t0:=x^2*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 2 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1309 +r0:=1/4*(a+b*x^3)^(4/3)/b +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (2) --------------------- +--R 4b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (3) --------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1309 +t0:=x*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1309 +r0:=1/3*x^2*(a+b*x^3)^(1/3)-1/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(2/3)+1/18*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)-_ + 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2a\|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 2 +-+3+-+2 3| 3 +--R 6x \|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 18\|3 \|b +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - a\|3 log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|- b \|b x + a + b x +--R 2a\|3 log(------------------------) +--R x +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +----+ +--------+ +--R 2\|3 \|- b \|b x + a - b x\|3 2 +-+3| 2 3| 3 +--R 6a atan(---------------------------------) + 6x \|3 \|- b \|b x + a +--R 3b x +--R / +--R +----+ +--R +-+3| 2 +--R 18\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - a\|3 \|b log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|- b \|b x + a + b x +--R 2a\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +----+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R 2a\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3 +--R 6a \|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R 6a\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 18\|3 \|- b \|b +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1309 +t0:=(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1309 +--r0:=1/2*x*(a+b*x^3)^(1/3)+1/2*a*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 514 + +--S 515 of 1309 +--a0:=integrate(t0,x) +--E 515 + +--S 516 of 1309 +--m0:=a0-r0 +--E 516 + +--S 517 of 1309 +--d0:=D(m0,x) +--E 517 + +)clear all + +--S 518 of 1309 +t0:=(a+b*x^3)^(1/3)/x +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1309 +r0:=(a+b*x^3)^(1/3)+1/3*a^(1/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_ + 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|b x + a + \|a +--R 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3| 3 +--R 6\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ +-+3| 3 +-+3+-+ +--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|3 \|b x + a + \|3 \|a +--R 2\|3 \|a log(\|b x + a - \|a ) - 6\|a atan(---------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--------+ +--R +-+3| 3 +--R 6\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+3+-+ 3| 3 3+-+ +-+3+-+ 3| 3 3+-+ +--R \|3 \|a log(\|b x + a - \|a ) - \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+3+-+ 3| 3 3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a 3+-+ 2\|b x + a + \|a +--R - 3\|a atan(---------------------------) + 3\|a atan(-------------------) +--R 3+-+ +-+3+-+ +--R 3\|a \|3 \|a +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1309 +t0:=(a+b*x^3)^(1/3)/x^2 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1309 +r0:=-(a+b*x^3)^(1/3)/x-1/3*b^(1/3)*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))+_ + 1/6*b^(1/3)*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_ + b^(1/3)*x/(a+b*x^3)^(1/3))-b^(1/3)*_ + atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+-+ \|b x + a + x\|b \|b x + a + x \|b +--R x\|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+3+-+ \|b x + a - x\|b 3+-+ \|b x + a + 2x\|b +--R - 2x\|3 \|b log(-------------------) - 6x\|b atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R +-+3| 3 +--R - 6\|3 \|b x + a +--R / +--R +-+ +--R 6x\|3 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1309 +--a0:=integrate(t0,x) +--E 525 + +--S 526 of 1309 +--m0:=a0-r0 +--E 526 + +--S 527 of 1309 +--d0:=D(m0,x) +--E 527 + +)clear all + +--S 528 of 1309 +t0:=(a+b*x^3)^(1/3)/x^3 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1309 +--r0:=-1/2*(a+b*x^3)^(1/3)/x^2+1/2*b*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 529 + +--S 530 of 1309 +--a0:=integrate(t0,x) +--E 530 + +--S 531 of 1309 +--m0:=a0-r0 +--E 531 + +--S 532 of 1309 +--d0:=D(m0,x) +--E 532 + +)clear all + +--S 533 of 1309 +t0:=(a+b*x^3)^(1/3)/x^4 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1309 +r0:=-1/3*(a+b*x^3)^(1/3)/x^3+1/9*b*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-_ + 1/18*b*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_ + (a+b*x^3)^(2/3))/a^(2/3)-1/3*b*atan((a^(1/3)+_ + 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +--R - 6\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+2 +--R 18x \|3 \|a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+ +--R 3 +-+ 3| 2 3| 3 +--R 2b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--+ +--------+ +--R 3 2\|3 \|a \|b x + a + a\|3 +-+3| 2 3| 3 +--R - 6b x atan(-----------------------------) - 6\|3 \|a \|b x + a +--R 3a +--R / +--R +--+ +--R 3 +-+3| 2 +--R 18x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - b\|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R b\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +--R 2b\|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 3+-+ +--R - 2b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(-----------------------------) +--R 3a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6b\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 18\|3 \|a \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1309 +t0:=x^5*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 5 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1309 +r0:=-1/5*a*(a+b*x^3)^(5/3)/b^2+1/8*(a+b*x^3)^(8/3)/b^2 +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x + 2a b x - 3a )\|b x + a +--R (2) ----------------------------------- +--R 2 +--R 40b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x + 2a b x - 3a )\|b x + a +--R (3) ----------------------------------- +--R 2 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1309 +t0:=x^4*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 4 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1309 +--r0:=1/14*a*x^2*(a+b*x^3)^(2/3)/b+1/7*x^5*(a+b*x^3)^(2/3)-_ +-- 1/14*a^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3)) +--E 544 + +--S 545 of 1309 +--a0:=integrate(t0,x) +--E 545 + +--S 546 of 1309 +--m0:=a0-r0 +--E 546 + +--S 547 of 1309 +--d0:=D(m0,x) +--E 547 + +)clear all + +--S 548 of 1309 +t0:=x^3*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1309 +r0:=1/9*a*x*(a+b*x^3)^(2/3)/b+1/6*x^4*(a+b*x^3)^(2/3)+_ + 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_ + b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/9*a^2*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b +--R 2a \|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R 4 +-+3+-+3| 3 +--R (9b x + 6a x)\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a \|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 +--R 6a atan(-------------------------------) +--R 3b x +--R + +--R +--------+2 +--R 4 +-+3+-+3| 3 +--R (9b x + 6a x)\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a \|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b +--R - 2a \|3 log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 2 \|b x + a + 2x\|b +--R 6a atan(-------------------------------) + 6a atan(--------------------) +--R 3b x +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1309 +t0:=x^2*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 2 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1309 +r0:=1/5*(a+b*x^3)^(5/3)/b +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (2) ---------------------- +--R 5b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (3) ---------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1309 +t0:=x*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1309 +--r0:=1/4*x^2*(a+b*x^3)^(2/3)+1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 559 + +--S 560 of 1309 +--a0:=integrate(t0,x) +--E 560 + +--S 561 of 1309 +--m0:=a0-r0 +--E 561 + +--S 562 of 1309 +--d0:=D(m0,x) +--E 562 + +)clear all + +--S 563 of 1309 +t0:=(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3| 3 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1309 +r0:=1/3*x*(a+b*x^3)^(2/3)-2/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(1/3)+1/9*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_ + 2/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2a\|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R 3x\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 9\|3 \|b +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - a\|3 log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+ \|- b \|b x + a - b x +--R 2a\|3 log(------------------------) +--R x +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--------+2 +--R 2\|3 \|- b \|b x + a + b x\|3 +-+3+---+3| 3 +--R 6a atan(---------------------------------) + 3x\|3 \|- b \|b x + a +--R 3b x +--R / +--R +-+3+---+ +--R 9\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - a\|3 \|b log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+3+-+ \|- b \|b x + a - b x +--R 2a\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+3+---+ \|b x + a - x\|b +--R 2a\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3 +--R 6a\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ \|b x + a + 2x\|b +--R - 6a\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+---+3+-+ +--R 9\|3 \|- b \|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1309 +t0:=(a+b*x^3)^(2/3)/x +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1309 +r0:=1/2*(a+b*x^3)^(2/3)+1/3*a^(2/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_ + 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_ + (a+b*x^3)^(2/3))+a^(2/3)*atan((a^(1/3)+_ + 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a +--R 2\|3 \|a log(- \|b x + a + \|a ) + 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3| 3 +--R 3\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+2 +--+2 +--------+ +--+ +--R +-+3| 2 3| 3 3| 2 3| 3 3| 2 +--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--+ +--------+ +--+2 +--R +-+3| 2 3| 3 3| 2 +--R 2\|3 \|a log(a\|b x + a - \|a ) +--R + +--R +--------+ +--+2 +--R +--+ +-+3| 3 +-+3| 2 +--------+2 +--R 3| 2 2a\|3 \|b x + a + \|3 \|a +-+3| 3 +--R 6\|a atan(------------------------------) + 3\|3 \|b x + a +--R +--+2 +--R 3| 2 +--R 3\|a +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+2 +--+2 +--------+ +--+ +--R +-+3| 2 3| 3 3| 2 3| 3 3| 2 +--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--------+2 +--------+ +--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2 +--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--+2 +--R +-+3| 2 3| 3 3| 2 +--R 2\|3 \|a log(a\|b x + a - \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a +--R - 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--+2 +--R +--+ +-+3| 3 +-+3| 2 +--R 3| 2 2a\|3 \|b x + a + \|3 \|a +--R 6\|a atan(------------------------------) +--R +--+2 +--R 3| 2 +--R 3\|a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1309 +t0:=(a+b*x^3)^(2/3)/x^2 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1309 +--r0:=-(a+b*x^3)^(2/3)/x+b*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 574 + +--S 575 of 1309 +--a0:=integrate(t0,x) +--E 575 + +--S 576 of 1309 +--m0:=a0-r0 +--E 576 + +--S 577 of 1309 +--d0:=D(m0,x) +--E 577 + +)clear all + +--S 578 of 1309 +t0:=(a+b*x^3)^(2/3)/x^3 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1309 +r0:=-1/2*(a+b*x^3)^(2/3)/x^2-1/3*b^(2/3)*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))+1/6*b^(2/3)*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))+_ + b^(2/3)*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+3+-+2 \|b x + a + x\|b \|b x + a + x \|b +--R x \|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 2 +-+3+-+2 \|b x + a - x\|b +--R - 2x \|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--------+2 +--R 2 3+-+2 \|b x + a + 2x\|b +-+3| 3 +--R 6x \|b atan(-------------------- - 3\|3 \|b x + a +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R 2 +-+ +--R 6x \|3 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1309 +--a0:=integrate(t0,x) +--E 580 + +--S 581 of 1309 +--m0:=a0-r0 +--E 581 + +--S 582 of 1309 +--d0:=D(m0,x) +--E 582 + +)clear all + +--S 583 of 1309 +t0:=(a+b*x^3)^(2/3)/x^4 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1309 +r0:=-1/3*(a+b*x^3)^(2/3)/x^3+2/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(1/3)-1/9*b*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_ + 2/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R - 3\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+ +--R 9x \|3 \|a +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3 +-+ 3+-+3| 3 3+-+2 3| 3 +--R - b x \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+ +--R 3 +-+ 3+-+2 3| 3 +--R 2b x \|3 log(\|a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--------+2 +--R 3 2\|3 \|a \|b x + a + a\|3 +-+3+-+3| 3 +--R 6b x atan(-----------------------------) - 3\|3 \|a \|b x + a +--R 3a +--R / +--R 3 +-+3+-+ +--R 9x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - b\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R b\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2b\|3 log(\|a \|b x + a - a) - 2b\|3 log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6b atan(-----------------------------) - 6b atan(-------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 9\|3 \|a +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1309 +t0:=x^8*(1-x^3)^(6/5) +--R +--R +--R +--------+ +--R 11 8 5| 3 +--R (1) (- x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1309 +r0:=-5/33*(1-x^3)^(11/5)+5/24*(1-x^3)^(16/5)-5/63*(1-x^3)^(21/5) +--R +--R +--R +--------+ +--R 12 9 6 3 5| 3 +--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1 +--R (2) ------------------------------------------------- +--R 5544 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 12 9 6 3 5| 3 +--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1 +--R (3) ------------------------------------------------- +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1309 +t0:=x^11/(a+b*x^3)^(1/3) +--R +--R +--R 11 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1309 +r0:=-81/440*a^3*(a+b*x^3)^(2/3)/b^4+27/220*a^2*x^3*_ + (a+b*x^3)^(2/3)/b^3-9/88*a*x^6*(a+b*x^3)^(2/3)/b^2+_ + 1/11*x^9*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (40b x - 45a b x + 54a b x - 81a )\|b x + a +--R (2) ------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (40b x - 45a b x + 54a b x - 81a )\|b x + a +--R (3) ------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1309 +t0:=x^8/(a+b*x^3)^(1/3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1309 +r0:=9/40*a^2*(a+b*x^3)^(2/3)/b^3-3/20*a*x^3*(a+b*x^3)^(2/3)/b^2+_ + 1/8*x^6*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x - 6a b x + 9a )\|b x + a +--R (2) ----------------------------------- +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x - 6a b x + 9a )\|b x + a +--R (3) ----------------------------------- +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1309 +t0:=x^5/(a+b*x^3)^(1/3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1309 +r0:=-3/10*a*(a+b*x^3)^(2/3)/b^2+1/5*x^3*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (2b x - 3a)\|b x + a +--R (2) ------------------------ +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (2b x - 3a)\|b x + a +--R (3) ------------------------ +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1309 +t0:=x^2/(a+b*x^3)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1309 +r0:=1/2*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1309 +t0:=1/(x*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R 3| 3 +--R x\|b x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1309 +r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(1/3)-1/6*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_ + 1/3*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 3+-+2 +--R - log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3| 3 3+-+ +-+ 2\|b x + a + \|a +--R 2log(- \|b x + a + \|a ) + 2\|3 atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 6\|a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+ +--R +--------+ +-+3+-+2 3| 3 +-+ +--R +-+ 3+-+2 3| 3 2\|3 \|a \|b x + a + a\|3 +--R 2\|3 log(\|a \|b x + a - a) + 6atan(-----------------------------) +--R 3a +--R / +--R +-+3+-+ +--R 6\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 615 + +--S 616 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 log(\|a \|b x + a - a) - 2\|3 log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6atan(-----------------------------) - 6atan(-------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6\|3 \|a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +)clear all + +--S 618 of 1309 +t0:=1/(x^4*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1309 +r0:=-1/3*(a+b*x^3)^(2/3)/(a*x^3)-1/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(4/3)+1/18*b*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(4/3)-_ + 1/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R - 6\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3 +-+ 3+---+3| 3 3+---+2 3| 3 +--R - b x \|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +--------+ +--R 3 +-+ 3+---+2 3| 3 +--R 2b x \|3 log(\|- a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--------+2 +--R 3 2\|3 \|- a \|b x + a + a\|3 +-+3+---+3| 3 +--R 6b x atan(-------------------------------) - 6\|3 \|- a \|b x + a +--R 3a +--R / +--R 3 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 620 + +--S 621 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+3+-+ 3+---+3| 3 3+---+2 3| 3 +--R - b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +--------+2 +--------+ +--R +-+3+---+ 3| 3 3+-+3| 3 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +-+3+-+ 3+---+2 3| 3 +--R 2b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+---+ 3| 3 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b\|a atan(-------------------------------) +--R 3a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 6b\|- a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1309 +t0:=x^7/(a+b*x^3)^(1/3) +--R +--R +--R 7 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1309 +--r0:=-5/28*a*x^2*(a+b*x^3)^(2/3)/b^2+1/7*x^5*(a+b*x^3)^(2/3)/b+_ +-- 5/28*a^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b^2*(a+b*x^3)^(1/3)) +--E 624 + +--S 625 of 1309 +--a0:=integrate(t0,x) +--E 625 + +--S 626 of 1309 +--m0:=a0-r0 +--E 626 + +--S 627 of 1309 +--d0:=D(m0,x) +--E 627 + +)clear all + +--S 628 of 1309 +t0:=x^4/(a+b*x^3)^(1/3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1309 +--r0:=1/4*x^2*(a+b*x^3)^(2/3)/b-1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3)) +--E 629 + +--S 630 of 1309 +--a0:=integrate(t0,x) +--E 630 + +--S 631 of 1309 +--m0:=a0-r0 +--E 631 + +--S 632 of 1309 +--d0:=D(m0,x) +--E 632 + +)clear all + +--S 633 of 1309 +t0:=x/(a+b*x^3)^(1/3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1309 +--r0:=1/2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 634 + +--S 635 of 1309 +--a0:=integrate(t0,x) +--E 635 + +--S 636 of 1309 +--m0:=a0-r0 +--E 636 + +--S 637 of 1309 +--d0:=D(m0,x) +--E 637 + +)clear all + +--S 638 of 1309 +t0:=1/(x^2*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1309 +--r0:=-(a+b*x^3)^(2/3)/(a*x)+1/2*b*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a*(a+b*x^3)^(1/3)) +--E 639 + +--S 640 of 1309 +--a0:=integrate(t0,x) +--E 640 + +--S 641 of 1309 +--m0:=a0-r0 +--E 641 + +--S 642 of 1309 +--d0:=D(m0,x) +--E 642 + +)clear all + +--S 643 of 1309 +t0:=1/(x^5*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1309 +--r0:=-1/4*(a+b*x^3)^(2/3)/(a*x^4)+1/2*b*(a+b*x^3)^(2/3)/(a^2*x)-_ +-- 1/4*b^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a^2*(a+b*x^3)^(1/3)) +--E 644 + +--S 645 of 1309 +--a0:=integrate(t0,x) +--E 645 + +--S 646 of 1309 +--m0:=a0-r0 +--E 646 + +--S 647 of 1309 +--d0:=D(m0,x) +--E 647 + +)clear all + +--S 648 of 1309 +t0:=x^3/(a+b*x^3)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1309 +r0:=1/3*x*(a+b*x^3)^(2/3)/b+1/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(4/3)-1/18*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R 2a\|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R 6x\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a\|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--------+2 +--R 2\|3 \|b \|b x + a + b x\|3 +-+3+-+3| 3 +--R 6a atan(-------------------------------) + 6x\|3 \|b \|b x + a +--R 3b x +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a\|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+ \|b x + a - x\|b +--R - 2a\|3 log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|b \|b x + a + b x\|3 \|b x + a + 2x\|b +--R 6a atan(-------------------------------) + 6a atan(--------------------) +--R 3b x +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1309 +t0:=1/(a+b*x^3)^(1/3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1309 +r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_ + 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(1/3)+atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2\|3 log(-------------------) + 6atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R / +--R +-+3+-+ +--R 6\|3 \|b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - \|3 log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+ \|- b \|b x + a - b x +--R 2\|3 log(------------------------) +--R x +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 2\|3 \|- b \|b x + a + b x\|3 +--R 6atan(---------------------------------) +--R 3b x +--R / +--R +-+3+---+ +--R 6\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - \|3 \|b log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+3+-+ \|- b \|b x + a - b x +--R 2\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b +--R - \|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+3+---+ \|b x + a - x\|b +--R 2\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3 +--R 6\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ \|b x + a + 2x\|b +--R - 6\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+---+3+-+ +--R 6\|3 \|- b \|b +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1309 +t0:=1/(x^3*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1309 +r0:=-1/2*(a+b*x^3)^(2/3)/(a*x^2) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (2) - ------------ +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (3) - ------------ +--R 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1309 +t0:=1/(x^6*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 6 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1309 +r0:=-1/5*(a+b*x^3)^(2/3)/(a*x^5)+3/10*b*(a+b*x^3)^(2/3)/(a^2*x^2) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (3b x - 2a)\|b x + a +--R (2) ------------------------ +--R 2 5 +--R 10a x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (3b x - 2a)\|b x + a +--R (3) ------------------------ +--R 2 5 +--R 10a x +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1309 +t0:=1/(x^9*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 9 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1309 +r0:=-1/8*(a+b*x^3)^(2/3)/(a*x^8)+3/20*b*(a+b*x^3)^(2/3)/(a^2*x^5)-_ + 9/40*b^2*(a+b*x^3)^(2/3)/(a^3*x^2) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (- 9b x + 6a b x - 5a )\|b x + a +--R (2) ------------------------------------- +--R 3 8 +--R 40a x +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (- 9b x + 6a b x - 5a )\|b x + a +--R (3) ------------------------------------- +--R 3 8 +--R 40a x +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1309 +t0:=1/(x^12*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R 12 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1309 +r0:=-1/11*(a+b*x^3)^(2/3)/(a*x^11)+9/88*b*(a+b*x^3)^(2/3)/(a^2*x^8)-_ + 27/220*b^2*(a+b*x^3)^(2/3)/(a^3*x^5)+81/440*b^3*(a+b*x^3)^(2/3)/(a^4*x^2) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 54a b x + 45a b x - 40a )\|b x + a +--R (2) ------------------------------------------------- +--R 4 11 +--R 440a x +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 54a b x + 45a b x - 40a )\|b x + a +--R (3) ------------------------------------------------- +--R 4 11 +--R 440a x +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1309 +t0:=x^11/(a+b*x^3)^(2/3) +--R +--R +--R 11 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1309 +r0:=-81/140*a^3*(a+b*x^3)^(1/3)/b^4+27/140*a^2*x^3*(a+b*x^3)^(1/3)/b^3-_ + 9/70*a*x^6*(a+b*x^3)^(1/3)/b^2+1/10*x^9*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (14b x - 18a b x + 27a b x - 81a )\|b x + a +--R (2) ------------------------------------------------ +--R 4 +--R 140b +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (14b x - 18a b x + 27a b x - 81a )\|b x + a +--R (3) ------------------------------------------------ +--R 4 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1309 +t0:=x^8/(a+b*x^3)^(2/3) +--R +--R +--R 8 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1309 +r0:=9/14*a^2*(a+b*x^3)^(1/3)/b^3-3/14*a*x^3*(a+b*x^3)^(1/3)/b^2+_ + 1/7*x^6*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (2b x - 3a b x + 9a )\|b x + a +--R (2) ---------------------------------- +--R 3 +--R 14b +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (2b x - 3a b x + 9a )\|b x + a +--R (3) ---------------------------------- +--R 3 +--R 14b +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1309 +t0:=x^5/(a+b*x^3)^(2/3) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1309 +r0:=-3/4*a*(a+b*x^3)^(1/3)/b^2+1/4*x^3*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x - 3a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x - 3a)\|b x + a +--R (3) ---------------------- +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1309 +t0:=x^2/(a+b*x^3)^(2/3) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1309 +r0:=(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1309 +t0:=1/(x*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1309 +r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-1/6*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(2/3)-_ + atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+ 3| 3 3+-+ 2\|b x + a + \|a +--R 2\|3 log(- \|b x + a + \|a ) - 6atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6\|3 \|a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+ +--R +--+ +--------+ +-+3| 2 3| 3 +-+ +--R +-+ 3| 2 3| 3 2\|3 \|a \|b x + a + a\|3 +--R 2\|3 log(\|a \|b x + a - a) - 6atan(-----------------------------) +--R 3a +--R / +--R +--+ +--R +-+3| 2 +--R 6\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +-+3| 2 3| 3 3+-+ +--R 2\|3 \|a log(\|a \|b x + a - a) - 2\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6\|a atan(-----------------------------) +--R 3a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 6\|3 \|a \|a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1309 +t0:=1/(x^4*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 4 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1309 +r0:=-1/3*(a+b*x^3)^(1/3)/(a*x^3)-2/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(5/3)+1/9*b*log(a^(2/3)+a^(1/3)*_ + (a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(5/3)+2/3*b*_ + atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +--R - 3\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+2 +--R 9a x \|3 \|a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - b x \|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--------+ +--R 3 +-+ 3| 2 3| 3 +--R 2b x \|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +----+ +--------+ +--R 3 2\|3 \|- a \|b x + a - a\|3 +-+3| 2 3| 3 +--R 6b x atan(-------------------------------) - 3\|3 \|- a \|b x + a +--R 3a +--R / +--R +----+ +--R 3 +-+3| 2 +--R 9a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - b\|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +--R 2b\|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(-------------------------------) +--R 3a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R - 6b\|- a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 9a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1309 +t0:=x^4/(a+b*x^3)^(2/3) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1309 +r0:=1/3*x^2*(a+b*x^3)^(1/3)/b+2/9*a*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/_ + b^(5/3)-1/9*a*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(5/3)+2/3*a*atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R 2a\|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 2 +-+3+-+2 3| 3 +--R 3x \|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 9b\|3 \|b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|b \|b x + a + b x\|b \|b x + a + b x +--R - a\|3 log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--+ +--------+ +--R 2\|3 \|b \|b x + a + b x\|3 2 +-+3| 2 3| 3 +--R - 6a atan(-------------------------------) + 3x \|3 \|b \|b x + a +--R 3b x +--R / +--R +--+ +--R +-+3| 2 +--R 9b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x +--R - a\|3 \|b log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|b \|b x + a - b x +--R 2a\|3 \|b log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +--+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R - 2a\|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a \|b atan(-------------------------------) +--R 3b x +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R - 6a\|b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 9b\|3 \|b \|b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1309 +t0:=x/(a+b*x^3)^(2/3) +--R +--R +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1309 +r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)+_ + 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(2/3)-atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2\|3 log(-------------------) - 6atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R / +--R +-+3+-+2 +--R 6\|3 \|b +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - \|3 log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|- b \|b x + a + b x +--R 2\|3 log(------------------------) +--R x +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2\|3 \|- b \|b x + a - b x\|3 +--R 6atan(---------------------------------) +--R 3b x +--R / +--R +----+ +--R +-+3| 2 +--R 6\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - \|3 \|b log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|- b \|b x + a + b x +--R 2\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +----+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R - \|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R 2\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3 +--R 6\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R 6\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 6\|3 \|- b \|b +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1309 +t0:=1/(x^2*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 2 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1309 +r0:=-(a+b*x^3)^(1/3)/(a*x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (2) - ----------- +--R a x +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (3) - ----------- +--R a x +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1309 +t0:=1/(x^5*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 5 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1309 +r0:=-1/4*(a+b*x^3)^(1/3)/(a*x^4)+3/4*b*(a+b*x^3)^(1/3)/(a^2*x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (3b x - a)\|b x + a +--R (2) ---------------------- +--R 2 4 +--R 4a x +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (3b x - a)\|b x + a +--R (3) ---------------------- +--R 2 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1309 +t0:=1/(x^8*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 8 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1309 +r0:=-1/7*(a+b*x^3)^(1/3)/(a*x^7)+3/14*b*(a+b*x^3)^(1/3)/(a^2*x^4)-_ + 9/14*b^2*(a+b*x^3)^(1/3)/(a^3*x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (- 9b x + 3a b x - 2a )\|b x + a +--R (2) ------------------------------------ +--R 3 7 +--R 14a x +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (- 9b x + 3a b x - 2a )\|b x + a +--R (3) ------------------------------------ +--R 3 7 +--R 14a x +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1309 +t0:=1/(x^11*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) --------------- +--R +--------+2 +--R 11 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1309 +r0:=-1/10*(a+b*x^3)^(1/3)/(a*x^10)+9/70*b*(a+b*x^3)^(1/3)/(a^2*x^7)-_ + 27/140*b^2*(a+b*x^3)^(1/3)/(a^3*x^4)+81/140*b^3*(a+b*x^3)^(1/3)/(a^4*x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 27a b x + 18a b x - 14a )\|b x + a +--R (2) ------------------------------------------------ +--R 4 10 +--R 140a x +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 27a b x + 18a b x - 14a )\|b x + a +--R (3) ------------------------------------------------ +--R 4 10 +--R 140a x +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1309 +t0:=x^6/(a+b*x^3)^(2/3) +--R +--R +--R 6 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1309 +--r0:=-2/5*a*x*(a+b*x^3)^(1/3)/b^2+1/5*x^4*(a+b*x^3)^(1/3)/b+_ +-- 2/5*a^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b^2*(a+b*x^3)^(2/3)) +--E 739 + +--S 740 of 1309 +--a0:=integrate(t0,x) +--E 740 + +--S 741 of 1309 +--m0:=a0-r0 +--E 741 + +--S 742 of 1309 +--d0:=D(m0,x) +--E 742 + +)clear all + +--S 743 of 1309 +t0:=x^3/(a+b*x^3)^(2/3) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1309 +--r0:=1/2*x*(a+b*x^3)^(1/3)/b-1/2*a*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3)) +--E 744 + +--S 745 of 1309 +--a0:=integrate(t0,x) +--E 745 + +--S 746 of 1309 +--m0:=a0-r0 +--E 746 + +--S 747 of 1309 +--d0:=D(m0,x) +--E 747 + +)clear all + +--S 748 of 1309 +t0:=1/(a+b*x^3)^(2/3) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1309 +--r0:=x*((a+b*x^3)/a)^(2/3)*_ +--hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 749 + +--S 750 of 1309 +--a0:=integrate(t0,x) +--E 750 + +--S 751 of 1309 +--m0:=a0-r0 +--E 751 + +--S 752 of 1309 +--d0:=D(m0,x) +--E 752 + +)clear all + +--S 753 of 1309 +t0:=1/(x^3*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 3 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1309 +--r0:=-1/2*(a+b*x^3)^(1/3)/(a*x^2)-1/2*b*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a*(a+b*x^3)^(2/3)) +--E 754 + +--S 755 of 1309 +--a0:=integrate(t0,x) +--E 755 + +--S 756 of 1309 +--m0:=a0-r0 +--E 756 + +--S 757 of 1309 +--d0:=D(m0,x) +--E 757 + +)clear all + +--S 758 of 1309 +t0:=1/(x^6*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 6 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1309 +--r0:=-1/5*(a+b*x^3)^(1/3)/(a*x^5)+2/5*b*(a+b*x^3)^(1/3)/(a^2*x^2)+_ +-- 2/5*b^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a^2*(a+b*x^3)^(2/3)) +--E 759 + +--S 760 of 1309 +--a0:=integrate(t0,x) +--E 760 + +--S 761 of 1309 +--m0:=a0-r0 +--E 761 + +--S 762 of 1309 +--d0:=D(m0,x) +--E 762 + +)clear all + +--S 763 of 1309 +t0:=x^2/(2+x^3)^(1/4) +--R +--R +--R 2 +--R x +--R (1) --------- +--R +------+ +--R 4| 3 +--R \|x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1309 +r0:=4/9*(2+x^3)^(3/4) +--R +--R +--R +------+3 +--R 4| 3 +--R 4\|x + 2 +--R (2) ----------- +--R 9 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +------+3 +--R 4| 3 +--R 4\|x + 2 +--R (3) ----------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1309 +t0:=sqrt(x)/(1+x^3) +--R +--R +--R +-+ +--R \|x +--R (1) ------ +--R 3 +--R x + 1 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1309 +r0:=2/3*atan(x^(3/2)) +--R +--R +--R +-+ +--R 2atan(x\|x ) +--R (2) ------------ +--R 3 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2atan(x\|x ) +--R (3) ------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1309 +t0:=x^2*(a+b*x^3)^p +--R +--R +--R 2 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1309 +r0:=1/3*(a+b*x^3)^(1+p)/(b*(1+p)) +--R +--R +--R 3 p + 1 +--R (b x + a) +--R (2) --------------- +--R 3b p + 3b +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 3b p + 3b +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1309 +m0:=a0-r0 +--R +--R +--R 3 +--R 3 p log(b x + a) 3 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 3b p + 3b +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1309 +t0:=x^5*(a+b*x^3)^p +--R +--R +--R 5 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1309 +r0:=-1/3*a*(a+b*x^3)^(1+p)/(b^2*(1+p))+1/3*(a+b*x^3)^(2+p)/(b^2*(2+p)) +--R +--R +--R 3 p + 2 3 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2 2 6 3 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R 2 2 6 3 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 3 p + 2 3 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1309 +t0:=x^8*(a+b*x^3)^p +--R +--R +--R 8 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1309 +r0:=1/3*a^2*(a+b*x^3)^(1+p)/(b^3*(1+p))-_ + 2/3*a*(a+b*x^3)^(2+p)/(b^3*(2+p))+1/3*(a+b*x^3)^(3+p)/(b^3*(3+p)) +--R +--R +--R (2) +--R 2 3 p + 3 2 3 p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 3 p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 9 2 2 2 6 2 3 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 3 +--R p log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 9 2 2 2 6 2 3 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 3 +--R p log(b x + a) +--R %e +--R + +--R 2 3 p + 3 2 3 p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 3 p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1309 +t0:=x^11*(a+b*x^3)^p +--R +--R +--R 11 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1309 +r0:=-1/3*a^3*(a+b*x^3)^(1+p)/(b^4*(1+p))+a^2*(a+b*x^3)^(2+p)/(b^4*(2+p))-_ + a*(a+b*x^3)^(3+p)/(b^4*(3+p))+1/3*(a+b*x^3)^(4+p)/(b^4*(4+p)) +--R +--R +--R (2) +--R 3 2 3 p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 3 p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 3 p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 3 p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 12 3 3 3 2 3 9 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 6 3 3 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 3 +--R p log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 12 3 3 3 2 3 9 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 6 3 3 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 3 +--R p log(b x + a) +--R %e +--R + +--R 3 2 3 p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 3 p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 3 p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 3 p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1309 +t0:=x^m*(a+b*x^4) +--R +--R +--R 4 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1309 +r0:=a*x^(1+m)/(1+m)+b*x^(5+m)/(5+m) +--R +--R +--R m + 5 m + 1 +--R (b m + b)x + (a m + 5a)x +--R (2) ---------------------------------- +--R 2 +--R m + 6m + 5 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 5 m log(x) +--R ((b m + b)x + (a m + 5a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 6m + 5 +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 m log(x) m + 5 +--R ((b m + b)x + (a m + 5a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 5a)x +--R / +--R 2 +--R m + 6m + 5 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1309 +t0:=x^5*(a+b*x^4) +--R +--R +--R 9 5 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 798 + +--S 799 of 1309 +r0:=1/6*a*x^6+1/10*b*x^10 +--R +--R +--R 1 10 1 6 +--R (2) -- b x + - a x +--R 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 799 + +--S 800 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 10 1 6 +--R (3) -- b x + - a x +--R 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 800 + +--S 801 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 801 + +--S 802 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 802 + +)clear all + +--S 803 of 1309 +t0:=x^4*(a+b*x^4) +--R +--R +--R 8 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 803 + +--S 804 of 1309 +r0:=1/5*a*x^5+1/9*b*x^9 +--R +--R +--R 1 9 1 5 +--R (2) - b x + - a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 804 + +--S 805 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 9 1 5 +--R (3) - b x + - a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 805 + +--S 806 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 806 + +--S 807 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 807 + +)clear all + +--S 808 of 1309 +t0:=x^3*(a+b*x^4) +--R +--R +--R 7 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 808 + +--S 809 of 1309 +r0:=1/4*a*x^4+1/8*b*x^8 +--R +--R +--R 1 8 1 4 +--R (2) - b x + - a x +--R 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 809 + +--S 810 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 8 1 4 +--R (3) - b x + - a x +--R 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 810 + +--S 811 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 811 + +--S 812 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 812 + +)clear all + +--S 813 of 1309 +t0:=x^2*(a+b*x^4) +--R +--R +--R 6 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 813 + +--S 814 of 1309 +r0:=1/3*a*x^3+1/7*b*x^7 +--R +--R +--R 1 7 1 3 +--R (2) - b x + - a x +--R 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 814 + +--S 815 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 3 +--R (3) - b x + - a x +--R 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 815 + +--S 816 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 816 + +--S 817 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 817 + +)clear all + +--S 818 of 1309 +t0:=x*(a+b*x^4) +--R +--R +--R 5 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 818 + +--S 819 of 1309 +r0:=1/2*a*x^2+1/6*b*x^6 +--R +--R +--R 1 6 1 2 +--R (2) - b x + - a x +--R 6 2 +--R Type: Polynomial(Fraction(Integer)) +--E 819 + +--S 820 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 2 +--R (3) - b x + - a x +--R 6 2 +--R Type: Polynomial(Fraction(Integer)) +--E 820 + +--S 821 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 821 + +--S 822 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 822 + +)clear all + +--S 823 of 1309 +t0:=a+b*x^4 +--R +--R +--R 4 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 823 + +--S 824 of 1309 +r0:=a*x+1/5*b*x^5 +--R +--R +--R 1 5 +--R (2) - b x + a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 824 + +--S 825 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 5 +--R (3) - b x + a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 825 + +--S 826 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 826 + +--S 827 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 827 + +)clear all + +--S 828 of 1309 +t0:=(a+b*x^4)/x +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 828 + +--S 829 of 1309 +r0:=1/4*b*x^4+a*log(x) +--R +--R +--R 4 +--R 4a log(x) + b x +--R (2) ---------------- +--R 4 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4a log(x) + b x +--R (3) ---------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1309 +t0:=(a+b*x^4)/x^2 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 833 + +--S 834 of 1309 +r0:=-a/x+1/3*b*x^3 +--R +--R +--R 4 +--R b x - 3a +--R (2) --------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 834 + +--S 835 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R b x - 3a +--R (3) --------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1309 +t0:=(a+b*x^4)/x^3 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 838 + +--S 839 of 1309 +r0:=-1/2*a/x^2+1/2*b*x^2 +--R +--R +--R 1 4 1 +--R - b x - - a +--R 2 2 +--R (2) ------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 839 + +--S 840 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R b x - a +--R (3) -------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1309 +t0:=(a+b*x^4)/x^4 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1309 +r0:=-1/3*a/x^3+b*x +--R +--R +--R 4 1 +--R b x - - a +--R 3 +--R (2) ---------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 844 + +--S 845 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 3b x - a +--R (3) --------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1309 +t0:=(a+b*x^4)/x^5 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1309 +r0:=-1/4*a/x^4+b*log(x) +--R +--R +--R 4 +--R 4b x log(x) - a +--R (2) --------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4b x log(x) - a +--R (3) --------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1309 +t0:=(a+b*x^4)/x^6 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 853 + +--S 854 of 1309 +r0:=-1/5*a/x^5-b/x +--R +--R +--R 4 1 +--R - b x - - a +--R 5 +--R (2) ------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 854 + +--S 855 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 5b x - a +--R (3) ----------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1309 +t0:=(a+b*x^4)/x^7 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 858 + +--S 859 of 1309 +r0:=-1/6*a/x^6-1/2*b/x^2 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 2 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 859 + +--S 860 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 3b x - a +--R (3) ----------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1309 +t0:=(a+b*x^4)/x^8 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 863 + +--S 864 of 1309 +r0:=-1/7*a/x^7-1/3*b/x^3 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 3 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 864 + +--S 865 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 7b x - 3a +--R (3) ------------ +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1309 +t0:=(a+b*x^4)/x^9 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 868 + +--S 869 of 1309 +r0:=-1/8*a/x^8-1/4*b/x^4 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 4 8 +--R (2) -------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 869 + +--S 870 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 2b x - a +--R (3) ----------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1309 +t0:=(a+b*x^4)/x^10 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 873 + +--S 874 of 1309 +r0:=-1/9*a/x^9-1/5*b/x^5 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 5 9 +--R (2) -------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 874 + +--S 875 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 9b x - 5a +--R (3) ------------ +--R 9 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1309 +t0:=x^m*(a+b*x^4)^2 +--R +--R +--R 2 8 4 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1309 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(5+m)/(5+m)+b^2*x^(9+m)/(9+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 9 2 m + 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 14a m + 45a )x +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 9 2 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 +--R (a m + 14a m + 45a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 9 2 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 +--R (a m + 14a m + 45a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 9 2 m + 5 +--R (- b m - 6b m - 5b )x + (- 2a b m - 20a b m - 18a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 14a m - 45a )x +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1309 +t0:=x^5*(a+b*x^4)^2 +--R +--R +--R 2 13 9 2 5 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 883 + +--S 884 of 1309 +r0:=1/6*a^2*x^6+1/5*a*b*x^10+1/14*b^2*x^14 +--R +--R +--R 1 2 14 1 10 1 2 6 +--R (2) -- b x + - a b x + - a x +--R 14 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 884 + +--S 885 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 14 1 10 1 2 6 +--R (3) -- b x + - a b x + - a x +--R 14 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 885 + +--S 886 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 886 + +--S 887 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 887 + +)clear all + +--S 888 of 1309 +t0:=x^4*(a+b*x^4)^2 +--R +--R +--R 2 12 8 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 888 + +--S 889 of 1309 +r0:=1/5*a^2*x^5+2/9*a*b*x^9+1/13*b^2*x^13 +--R +--R +--R 1 2 13 2 9 1 2 5 +--R (2) -- b x + - a b x + - a x +--R 13 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 889 + +--S 890 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 13 2 9 1 2 5 +--R (3) -- b x + - a b x + - a x +--R 13 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 890 + +--S 891 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 891 + +--S 892 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 892 + +)clear all + +--S 893 of 1309 +t0:=x^3*(a+b*x^4)^2 +--R +--R +--R 2 11 7 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 893 + +--S 894 of 1309 +r0:=1/12*(a+b*x^4)^3/b +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R -- b x + - a b x + - a b x + -- a +--R 12 4 4 12 +--R (2) -------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 894 + +--S 895 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 12 1 8 1 2 4 +--R (3) -- b x + - a b x + - a x +--R 12 4 4 +--R Type: Polynomial(Fraction(Integer)) +--E 895 + +--S 896 of 1309 +m0:=a0-r0 +--R +--R +--R 1 3 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 896 + +--S 897 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 897 + +)clear all + +--S 898 of 1309 +t0:=x^2*(a+b*x^4)^2 +--R +--R +--R 2 10 6 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 898 + +--S 899 of 1309 +r0:=1/3*a^2*x^3+2/7*a*b*x^7+1/11*b^2*x^11 +--R +--R +--R 1 2 11 2 7 1 2 3 +--R (2) -- b x + - a b x + - a x +--R 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 899 + +--S 900 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 11 2 7 1 2 3 +--R (3) -- b x + - a b x + - a x +--R 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 900 + +--S 901 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 901 + +--S 902 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 902 + +)clear all + +--S 903 of 1309 +t0:=x*(a+b*x^4)^2 +--R +--R +--R 2 9 5 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 903 + +--S 904 of 1309 +r0:=1/2*a^2*x^2+1/3*a*b*x^6+1/10*b^2*x^10 +--R +--R +--R 1 2 10 1 6 1 2 2 +--R (2) -- b x + - a b x + - a x +--R 10 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 904 + +--S 905 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 1 6 1 2 2 +--R (3) -- b x + - a b x + - a x +--R 10 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 905 + +--S 906 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 906 + +--S 907 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 907 + +)clear all + +--S 908 of 1309 +t0:=(a+b*x^4)^2 +--R +--R +--R 2 8 4 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 908 + +--S 909 of 1309 +r0:=a^2*x+2/5*a*b*x^5+1/9*b^2*x^9 +--R +--R +--R 1 2 9 2 5 2 +--R (2) - b x + - a b x + a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 909 + +--S 910 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 2 5 2 +--R (3) - b x + - a b x + a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 910 + +--S 911 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 911 + +--S 912 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 912 + +)clear all + +--S 913 of 1309 +t0:=(a+b*x^4)^2/x +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1309 +r0:=1/2*a*b*x^4+1/8*b^2*x^8+a^2*log(x) +--R +--R +--R 2 2 8 4 +--R 8a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 8 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 2 8 4 +--R 8a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1309 +t0:=(a+b*x^4)^2/x^2 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1309 +r0:=-a^2/x+2/3*a*b*x^3+1/7*b^2*x^7 +--R +--R +--R 2 8 4 2 +--R 3b x + 14a b x - 21a +--R (2) ----------------------- +--R 21x +--R Type: Fraction(Polynomial(Integer)) +--E 919 + +--S 920 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3b x + 14a b x - 21a +--R (3) ----------------------- +--R 21x +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1309 +t0:=(a+b*x^4)^2/x^3 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 923 + +--S 924 of 1309 +r0:=-1/2*a^2/x^2+a*b*x^2+1/6*b^2*x^6 +--R +--R +--R 1 2 8 4 1 2 +--R - b x + a b x - - a +--R 6 2 +--R (2) ---------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 924 + +--S 925 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R b x + 6a b x - 3a +--R (3) -------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 925 + +--S 926 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1309 +t0:=(a+b*x^4)^2/x^4 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1309 +r0:=-1/3*a^2/x^3+2*a*b*x+1/5*b^2*x^5 +--R +--R +--R 1 2 8 4 1 2 +--R - b x + 2a b x - - a +--R 5 3 +--R (2) ----------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 929 + +--S 930 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3b x + 30a b x - 5a +--R (3) ---------------------- +--R 3 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 930 + +--S 931 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1309 +t0:=(a+b*x^4)^2/x^5 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 933 + +--S 934 of 1309 +r0:=-1/4*a^2/x^4+1/4*b^2*x^4+2*a*b*log(x) +--R +--R +--R 4 2 8 2 +--R 8a b x log(x) + b x - a +--R (2) ------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 2 8 2 +--R 8a b x log(x) + b x - a +--R (3) ------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 935 + +--S 936 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 937 + +)clear all + +--S 938 of 1309 +t0:=x^m*(a+b*x^4)^3 +--R +--R +--R 3 12 2 8 2 4 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1309 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(5+m)/(5+m)+3*a*b^2*x^(9+m)/(9+m)+_ + b^3*x^(13+m)/(13+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 m + 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 27a m + 227a m + 585a )x +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 27a m + 227a m + 585a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Union(Expression(Integer),...) +--E 940 + +--S 941 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 27a m + 227a m + 585a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 13 +--R (- b m - 15b m - 59b m - 45b )x +--R + +--R 2 3 2 2 2 2 m + 9 +--R (- 3a b m - 57a b m - 249a b m - 195a b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (- 3a b m - 69a b m - 417a b m - 351a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 27a m - 227a m - 585a )x +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1309 +t0:=x^5*(a+b*x^4)^3 +--R +--R +--R 3 17 2 13 2 9 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 943 + +--S 944 of 1309 +r0:=1/6*a^3*x^6+3/10*a^2*b*x^10+3/14*a*b^2*x^14+1/18*b^3*x^18 +--R +--R +--R 1 3 18 3 2 14 3 2 10 1 3 6 +--R (2) -- b x + -- a b x + -- a b x + - a x +--R 18 14 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 944 + +--S 945 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 18 3 2 14 3 2 10 1 3 6 +--R (3) -- b x + -- a b x + -- a b x + - a x +--R 18 14 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 945 + +--S 946 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 946 + +--S 947 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 947 + +)clear all + +--S 948 of 1309 +t0:=x^4*(a+b*x^4)^3 +--R +--R +--R 3 16 2 12 2 8 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 948 + +--S 949 of 1309 +r0:=1/5*a^3*x^5+1/3*a^2*b*x^9+3/13*a*b^2*x^13+1/17*b^3*x^17 +--R +--R +--R 1 3 17 3 2 13 1 2 9 1 3 5 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 17 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 949 + +--S 950 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 17 3 2 13 1 2 9 1 3 5 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 17 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 950 + +--S 951 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 951 + +--S 952 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 952 + +)clear all + +--S 953 of 1309 +t0:=x^3*(a+b*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 953 + +--S 954 of 1309 +r0:=1/16*(a+b*x^4)^4/b +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 16 4 8 4 16 +--R (2) -------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 954 + +--S 955 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 16 1 2 12 3 2 8 1 3 4 +--R (3) -- b x + - a b x + - a b x + - a x +--R 16 4 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 955 + +--S 956 of 1309 +m0:=a0-r0 +--R +--R +--R 1 4 +--R -- a +--R 16 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 956 + +--S 957 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +)clear all + +--S 958 of 1309 +t0:=x^2*(a+b*x^4)^3 +--R +--R +--R 3 14 2 10 2 6 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 958 + +--S 959 of 1309 +r0:=1/3*a^3*x^3+3/7*a^2*b*x^7+3/11*a*b^2*x^11+1/15*b^3*x^15 +--R +--R +--R 1 3 15 3 2 11 3 2 7 1 3 3 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 15 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 959 + +--S 960 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 15 3 2 11 3 2 7 1 3 3 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 15 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 960 + +--S 961 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 961 + +--S 962 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 962 + +)clear all + +--S 963 of 1309 +t0:=x*(a+b*x^4)^3 +--R +--R +--R 3 13 2 9 2 5 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 963 + +--S 964 of 1309 +r0:=1/2*a^3*x^2+1/2*a^2*b*x^6+3/10*a*b^2*x^10+1/14*b^3*x^14 +--R +--R +--R 1 3 14 3 2 10 1 2 6 1 3 2 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 14 10 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 964 + +--S 965 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 3 2 10 1 2 6 1 3 2 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 14 10 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 965 + +--S 966 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 966 + +--S 967 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 967 + +)clear all + +--S 968 of 1309 +t0:=(a+b*x^4)^3 +--R +--R +--R 3 12 2 8 2 4 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 968 + +--S 969 of 1309 +r0:=a^3*x+3/5*a^2*b*x^5+1/3*a*b^2*x^9+1/13*b^3*x^13 +--R +--R +--R 1 3 13 1 2 9 3 2 5 3 +--R (2) -- b x + - a b x + - a b x + a x +--R 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 969 + +--S 970 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 1 2 9 3 2 5 3 +--R (3) -- b x + - a b x + - a b x + a x +--R 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 970 + +--S 971 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 971 + +--S 972 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 972 + +)clear all + +--S 973 of 1309 +t0:=(a+b*x^4)^3/x +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1309 +r0:=3/4*a^2*b*x^4+3/8*a*b^2*x^8+1/12*b^3*x^12+a^3*log(x) +--R +--R +--R 3 3 12 2 8 2 4 +--R 24a log(x) + 2b x + 9a b x + 18a b x +--R (2) ---------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 12 2 8 2 4 +--R 24a log(x) + 2b x + 9a b x + 18a b x +--R (3) ---------------------------------------- +--R 24 +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1309 +t0:=(a+b*x^4)^3/x^2 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 978 + +--S 979 of 1309 +r0:=-a^3/x+a^2*b*x^3+3/7*a*b^2*x^7+1/11*b^3*x^11 +--R +--R +--R 3 12 2 8 2 4 3 +--R 7b x + 33a b x + 77a b x - 77a +--R (2) ----------------------------------- +--R 77x +--R Type: Fraction(Polynomial(Integer)) +--E 979 + +--S 980 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 7b x + 33a b x + 77a b x - 77a +--R (3) ----------------------------------- +--R 77x +--R Type: Union(Expression(Integer),...) +--E 980 + +--S 981 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +)clear all + +--S 983 of 1309 +t0:=(a+b*x^4)^3/x^3 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 983 + +--S 984 of 1309 +r0:=-1/2*a^3/x^2+3/2*a^2*b*x^2+1/2*a*b^2*x^6+1/10*b^3*x^10 +--R +--R +--R 1 3 12 1 2 8 3 2 4 1 3 +--R -- b x + - a b x + - a b x - - a +--R 10 2 2 2 +--R (2) ------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 984 + +--S 985 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 5a b x + 15a b x - 5a +--R (3) -------------------------------- +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 985 + +--S 986 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 987 + +)clear all + +--S 988 of 1309 +t0:=(a+b*x^4)^3/x^4 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 988 + +--S 989 of 1309 +r0:=-1/3*a^3/x^3+3*a^2*b*x+3/5*a*b^2*x^5+1/9*b^3*x^9 +--R +--R +--R 1 3 12 3 2 8 2 4 1 3 +--R - b x + - a b x + 3a b x - - a +--R 9 5 3 +--R (2) ----------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 989 + +--S 990 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 5b x + 27a b x + 135a b x - 15a +--R (3) ------------------------------------ +--R 3 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 990 + +--S 991 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 992 + +)clear all + +--S 993 of 1309 +t0:=(a+b*x^4)^3/x^5 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 993 + +--S 994 of 1309 +r0:=-1/4*a^3/x^4+3/4*a*b^2*x^4+1/8*b^3*x^8+3*a^2*b*log(x) +--R +--R +--R 2 4 3 12 2 8 3 +--R 24a b x log(x) + b x + 6a b x - 2a +--R (2) -------------------------------------- +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 12 2 8 3 +--R 24a b x log(x) + b x + 6a b x - 2a +--R (3) -------------------------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 995 + +--S 996 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 997 + +)clear all + +--S 998 of 1309 +t0:=x^5/(a+c*x^4) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 998 + +--S 999 of 1309 +r0:=1/2*x^2/c-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(a)/c^(3/2) +--R +--R +--R 2 +-+ +--R +-+ x \|c 2 +-+ +--R - \|a atan(------) + x \|c +--R +-+ +--R \|a +--R (2) --------------------------- +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 2 | a 4 |a +--R +---+ - 2c x |- - + c x - a +-+ |- +--R | a \| c 2 |a \|c 2 +--R |- - log(------------------------) + 2x |- atan(----) + x +--R \| c 4 \|c 2 +--R c x + a x +--R (3) [-----------------------------------------,-------------------] +--R 4c 2c +--R Type: Union(List(Expression(Integer)),...) +--E 1000 + +--S 1001 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | a 4 +--R +---+ - 2c x |- - + c x - a 2 +-+ +--R | a +-+ \| c +-+ x \|c +--R |- - \|c log(------------------------) + 2\|a atan(------) +--R \| c 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R 2 +-+ +-+ |- +--R +-+ x \|c |a +-+ \|c +--R \|a atan(------) + |- \|c atan(----) +--R +-+ \|c 2 +--R \|a x +--R (6) ------------------------------------- +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1004 + +)clear all + +--S 1005 of 1309 +t0:=x^4/(a+c*x^4) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1005 + +--S 1006 of 1309 +r0:=x/c+1/2*a^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))-_ + 1/2*a^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))+_ + 1/4*a^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(c^(5/4)*sqrt(2))-1/4*a^(1/4)*log(a^(1/4)*c^(1/4)*_ + x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - \|a log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R \|a log(- x\|2 \|a \|c + x \|c + \|a ) - 2\|a atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +-+4+-+ +--R - 2\|a atan(----------------) + 4x\|2 \|c +--R 4+-+ +--R \|a +--R / +--R +-+4+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | a | a | a | a +--R - c |- ----- log(4c |- ----- + x + c |- ----- log(- 4c |- ----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 256c \| 256c \| 256c \| 256c +--R + +--R +-------+ +--R | a +--R 4c |- ----- +--R +-------+ 4| 5 +--R | a \| 256c +--R 2c |- ----- atan(------------ + x +--R 4| 5 x +--R \| 256c +--R / +--R c +--R Type: Union(Expression(Integer),...) +--E 1007 + +--S 1008 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R \|a log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | a 4+-+ | a +--R - 4c\|2 |- ----- \|c log(4c |- ----- + x) +--R 4| 5 4| 5 +--R \| 256c \| 256c +--R + +--R +-------+ +-------+ +--R +-+ | a 4+-+ | a +--R 4c\|2 |- ----- \|c log(- 4c |- ----- + x) +--R 4| 5 4| 5 +--R \| 256c \| 256c +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R - \|a log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|a atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-------+ +--R | a +--R 4c |- ----- +--R +-+4+-+ 4+-+ +-------+ 4| 5 +--R 4+-+ x\|2 \|c - \|a +-+ | a 4+-+ \| 256c +--R 2\|a atan(----------------) + 8c\|2 |- ----- \|c atan(------------) +--R 4+-+ 4| 5 x +--R \|a \| 256c +--R / +--R +-+4+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1009 + +)clear all + +--S 1010 of 1309 +t0:=x^3/(a+c*x^4) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1010 + +--S 1011 of 1309 +r0:=1/4*log(a+c*x^4)/c +--R +--R +--R 4 +--R log(c x + a) +--R (2) ------------- +--R 4c +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R log(c x + a) +--R (3) ------------- +--R 4c +--R Type: Union(Expression(Integer),...) +--E 1012 + +--S 1013 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1309 +t0:=x^2/(a+c*x^4) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1015 + +--S 1016 of 1309 +r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_ + 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_ + 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2))-_ + 1/4*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) + 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R 2atan(----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R | 1 2 | 1 +--R |- ------- log(64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+ +---------+3 +--R | 1 2 | 1 +--R - |- ------- log(- 64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+3 +--R 2 | 1 +--R 64a c |- ------- +--R +---------+ 4| 3 +--R | 1 \| 256a c +--R 2 |- ------- atan(-------------------) +--R 4| 3 x +--R \| 256a c +--R Type: Union(Expression(Integer),...) +--E 1017 + +--S 1018 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------+ +---------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 +--R 4\|2 |- ------- \|a \|c log(64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+ +---------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 +--R - 4\|2 |- ------- \|a \|c log(- 64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+3 +--R 2 | 1 +--R 64a c |- ------- +--R +---------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 256a c +--R 8\|2 |- ------- \|a \|c atan(-------------------) +--R 4| 3 x +--R \| 256a c +--R / +--R +-+4+-+4+-+3 +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1309 +t0:=x/(a+c*x^4) +--R +--R +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1020 + +--S 1021 of 1309 +r0:=1/2*atan(x^2*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R 2 +-+ +--R x \|c +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 2\|a \|c +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +-----+ 2 +--R (c x - a)\|- a c + 2a c x 2 +---+ +--R log(----------------------------) x \|a c +--R 4 atan(--------) +--R c x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 4\|- a c 2\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1022 + +--S 1023 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 2\|a \|c \|a c +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1309 +t0:=1/(a+c*x^4) +--R +--R +--R 1 +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1027 + +--S 1028 of 1309 +r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))+_ + 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))-_ + 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2))+1/4*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ 2 +-+ +-+ +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) - log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R x\|2 \|c + \|a x\|2 \|c - \|a +--R 2atan(----------------) + 2atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R +-+4+-+3 4+-+ +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R |- ------ log(4a |- ------ + x) - |- ------ log(- 4a |- ------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 256a c \| 256a c \| 256a c \| 256a c +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 +--R | 1 \| 256a c +--R - 2 |- ------ atan(-------------) +--R 4| 3 x +--R \| 256a c +--R Type: Union(Expression(Integer),...) +--E 1029 + +--S 1030 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R 4\|2 |- ------ \|a \|c log(4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +--------+ +--------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R - 4\|2 |- ------ \|a \|c log(- 4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +-+4+-+ 4+-+ +--------+ 4| 3 +--R x\|2 \|c - \|a +-+ | 1 4+-+3 4+-+ \| 256a c +--R - 2atan(----------------) - 8\|2 |- ------ \|a \|c atan(-------------) +--R 4+-+ 4| 3 x +--R \|a \| 256a c +--R / +--R +-+4+-+3 4+-+ +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1309 +t0:=1/(x*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ---------- +--R 5 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1032 + +--S 1033 of 1309 +r0:=log(x)/a-1/4*log(a+c*x^4)/a +--R +--R +--R 4 +--R - log(c x + a) + 4log(x) +--R (2) ------------------------- +--R 4a +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - log(c x + a) + 4log(x) +--R (3) ------------------------- +--R 4a +--R Type: Union(Expression(Integer),...) +--E 1034 + +--S 1035 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1036 + +)clear all + +--S 1037 of 1309 +t0:=1/(x^2*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 2 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1037 + +--S 1038 of 1309 +r0:=(-1)/(a*x)+1/2*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_ + sqrt(2))-1/2*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_ + sqrt(2))-1/4*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2))+1/4*c^(1/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R x\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - x\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c + \|a 4+-+ x\|2 \|c - \|a +-+4+-+ +--R - 2x\|c atan(----------------) - 2x\|c atan(----------------) - 4\|2 \|a +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R +-+4+-+ +--R 4a x\|2 \|a +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+3 +--R | c 4 | c +--R - a x |- ----- log(64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+3 +--R | c 4 | c +--R a x |- ----- log(- 64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+3 +--R 4 | c +--R 64a |- ----- +--R +-------+ 4| 5 +--R | c \| 256a +--R - 2a x |- ----- atan(--------------- - 1 +--R 4| 5 c x +--R \| 256a +--R / +--R a x +--R Type: Union(Expression(Integer),...) +--E 1039 + +--S 1040 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+3 +--R +-+ | c 4+-+ 4 | c +--R - 4a\|2 |- ----- \|a log(64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+3 +--R +-+ | c 4+-+ 4 | c +--R 4a\|2 |- ----- \|a log(- 64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R \|c log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-------+3 +--R 4 | c +--R 64a |- ----- +--R +-+4+-+ 4+-+ +-------+ 4| 5 +--R 4+-+ x\|2 \|c - \|a +-+ | c 4+-+ \| 256a +--R 2\|c atan(----------------) - 8a\|2 |- ----- \|a atan(---------------) +--R 4+-+ 4| 5 c x +--R \|a \| 256a +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1041 + +)clear all + +--S 1042 of 1309 +t0:=1/(x^3*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 3 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1042 + +--S 1043 of 1309 +r0:=(-1/2)/(a*x^2)-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(3/2) +--R +--R +--R 2 +-+ +--R 2 +-+ x \|c +-+ +--R - x \|c atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 2 +-+ +--R 2a x \|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 2 | c 4 |c +--R +---+ - 2a x |- - + c x - a +-+ a |- +--R 2 | c \| a 2 |c \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 4 \|a 2 +--R c x + a c x +--R (3) [-----------------------------------------,---------------------] +--R 2 2 +--R 4a x 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 1044 + +--S 1045 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R |- - \|a log(------------------------) + 2\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R \|c atan(------) + \|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) -------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1048 + +)clear all + +--S 1049 of 1309 +t0:=1/(x^4*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 4 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1049 + +--S 1050 of 1309 +r0:=(-1/3)/(a*x^3)+1/2*c^(3/4)*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))-1/2*c^(3/4)*atan(1+c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))+1/4*c^(3/4)*_ + log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*_ + sqrt(c))/(a^(7/4)*sqrt(2))-1/4*c^(3/4)*log(a^(1/4)*c^(1/4)*x*_ + sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 3x \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 3x \|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 3 4+-+3 x\|2 \|c + \|a 3 4+-+3 x\|2 \|c - \|a +--R - 6x \|c atan(---------------- - 6x \|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 3 +-+4+-+3 +--R 12a x \|2 \|a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 3 | 3 +--R 3 | c 2 | c +--R - 3a x |- ----- log(4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R 3 | c 2 | c +--R 3a x |- ----- log(- 4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +--R | 3 +--R 2 | c +--R +-------+ 4a |- ----- +--R | 3 4| 7 +--R 3 | c \| 256a +--R 6a x |- ----- atan(------------- - 1 +--R 4| 7 c x +--R \| 256a +--R / +--R 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 1051 + +--S 1052 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R +-+ | c 4+-+3 2 | c +--R - 4a\|2 |- ----- \|a log(4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R +-+ | c 4+-+3 2 | c +--R 4a\|2 |- ----- \|a log(- 4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - \|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 2\|c atan(----------------) + 2\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------+ +--R | 3 +--R 2 | c +--R +-------+ 4a |- ----- +--R | 3 4| 7 +--R +-+ | c 4+-+3 \| 256a +--R 8a\|2 |- ----- \|a atan(-------------) +--R 4| 7 c x +--R \| 256a +--R / +--R +-+4+-+3 +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1053 + +)clear all + +--S 1054 of 1309 +t0:=1/(x^5*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 5 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1054 + +--S 1055 of 1309 +r0:=(-1/4)/(a*x^4)-c*log(x)/a^2+1/4*c*log(a+c*x^4)/a^2 +--R +--R +--R 4 4 4 +--R c x log(c x + a) - 4c x log(x) - a +--R (2) ----------------------------------- +--R 2 4 +--R 4a x +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R c x log(c x + a) - 4c x log(x) - a +--R (3) ----------------------------------- +--R 2 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 1056 + +--S 1057 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1309 +t0:=x^7/(a+c*x^4)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1059 + +--S 1060 of 1309 +r0:=1/4*a/(c^2*(a+c*x^4))+1/4*log(a+c*x^4)/c^2 +--R +--R +--R 4 4 +--R (c x + a)log(c x + a) + a +--R (2) --------------------------- +--R 3 4 2 +--R 4c x + 4a c +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R (c x + a)log(c x + a) + a +--R (3) --------------------------- +--R 3 4 2 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1061 + +--S 1062 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1309 +t0:=x^6/(a+c*x^4)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1064 + +--S 1065 of 1309 +r0:=-1/4*x^3/(c*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_ + 3/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_ + 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2))-_ + 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 3a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 3a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 3 +-+4+-+4+-+3 +--R - 4x \|2 \|a \|c +--R / +--R 2 4 +-+4+-+4+-+3 +--R (16c x + 16a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+3 +--R 2 4 | 1 5 | 1 +--R (12c x + 12a c) |- --------- log(4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R 2 4 | 1 5 | 1 +--R (- 12c x - 12a c) |- --------- log(- 4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 5 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 7 +--R 2 4 | 1 \| 65536a c 3 +--R (24c x + 24a c) |- --------- atan(----------------------- - x +--R 4| 7 x +--R \| 65536a c +--R / +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1066 + +--S 1067 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 5 | 1 +--R 48c\|2 |- --------- \|a \|c log(4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 5 | 1 +--R - 48c\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+3 +--R 5 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 7 +--R +-+ | 1 4+-+4+-+3 \| 65536a c +--R 96c\|2 |- --------- \|a \|c atan(-----------------------) +--R 4| 7 x +--R \| 65536a c +--R / +--R +-+4+-+4+-+3 +--R 16c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1309 +t0:=x^5/(a+c*x^4)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1069 + +--S 1070 of 1309 +r0:=-1/4*x^2/(c*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R 2 +-+ +--R 4 x \|c 2 +-+ +-+ +--R (c x + a)atan(------) - x \|a \|c +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 2 4 +-+ +-+ +--R (4c x + 4a c)\|a \|c +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-----+ 2 +--R 4 (c x - a)\|- a c + 2a c x 2 +-----+ +--R (c x + a)log(----------------------------) - 2x \|- a c +--R 4 +--R c x + a +--R [---------------------------------------------------------, +--R 2 4 +-----+ +--R (8c x + 8a c)\|- a c +--R 2 +---+ +--R 4 x \|a c 2 +---+ +--R (c x + a)atan(--------) - x \|a c +--R a +--R -----------------------------------] +--R 2 4 +---+ +--R (4c x + 4a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1071 + +--S 1072 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1309 +t0:=x^4/(a+c*x^4)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 1309 +r0:=-1/4*x/(c*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(3/4)*c^(5/4)*sqrt(2))+_ + 1/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*_ + c^(5/4)*sqrt(2))-1/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2))+_ + 1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (c x + a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- c x - a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 4+-+ +--R - 4x\|2 \|a \|c +--R / +--R 2 4 +-+4+-+3 4+-+ +--R (16c x + 16a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+ +--R 2 4 | 1 | 1 +--R (4c x + 4a c) |- --------- log(16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+ +--R 2 4 | 1 | 1 +--R (- 4c x - 4a c) |- --------- log(- 16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +--R | 1 +--R 16a c |- --------- +--R +-----------+ 4| 3 5 +--R 2 4 | 1 \| 65536a c +--R (- 8c x - 8a c) |- --------- atan(------------------- - x +--R 4| 3 5 x +--R \| 65536a c +--R / +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R 16c\|2 |- --------- \|a \|c log(16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R - 16c\|2 |- --------- \|a \|c log(- 16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R | 1 +--R 16a c |- --------- +--R +-----------+ 4| 3 5 +--R +-+ | 1 4+-+3 4+-+ \| 65536a c +--R - 32c\|2 |- --------- \|a \|c atan(-------------------) +--R 4| 3 5 x +--R \| 65536a c +--R / +--R +-+4+-+3 4+-+ +--R 16c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1309 +t0:=x^3/(a+c*x^4)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 1309 +r0:=(-1/4)/(c*(a+c*x^4)) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - ---------- +--R 2 4 +--R c x + a c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1082 + +--S 1083 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1309 +t0:=x^2/(a+c*x^4)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 1309 +r0:=1/4*x^3/(a*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_ + (a^(5/4)*c^(3/4)*sqrt(2))+1/8*atan(1+c^(1/4)*x*sqrt(2)/_ + a^(1/4))/(a^(5/4)*c^(3/4)*sqrt(2))+1/16*log(-a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(3/4)*_ + sqrt(2))-1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(5/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- c x - a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (c x + a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 3 +-+4+-+4+-+3 +--R 4x \|2 \|a \|c +--R / +--R 4 2 +-+4+-+4+-+3 +--R (16a c x + 16a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+3 +--R 4 2 | 1 4 2 | 1 +--R (4a c x + 4a ) |- --------- log(4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R 4 2 | 1 4 2 | 1 +--R (- 4a c x - 4a ) |- --------- log(- 4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 4 2 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 5 3 +--R 4 2 | 1 \| 65536a c 3 +--R (8a c x + 8a ) |- --------- atan(----------------------- + x +--R 4| 5 3 x +--R \| 65536a c +--R / +--R 4 2 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 4 2 | 1 +--R 16a\|2 |- --------- \|a \|c log(4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 4 2 | 1 +--R - 16a\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+3 +--R 4 2 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 5 3 +--R +-+ | 1 4+-+4+-+3 \| 65536a c +--R 32a\|2 |- --------- \|a \|c atan(-----------------------) +--R 4| 5 3 x +--R \| 65536a c +--R / +--R +-+4+-+4+-+3 +--R 16a\|2 \|a \|c +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1309 +t0:=x/(a+c*x^4)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 1309 +r0:=1/4*x^2/(a*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c)) +--R +--R +--R 2 +-+ +--R 4 x \|c 2 +-+ +-+ +--R (c x + a)atan(------) + x \|a \|c +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 4 2 +-+ +-+ +--R (4a c x + 4a )\|a \|c +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-----+ 2 +--R 4 (c x - a)\|- a c + 2a c x 2 +-----+ +--R (c x + a)log(----------------------------) + 2x \|- a c +--R 4 +--R c x + a +--R [---------------------------------------------------------, +--R 4 2 +-----+ +--R (8a c x + 8a )\|- a c +--R 2 +---+ +--R 4 x \|a c 2 +---+ +--R (c x + a)atan(--------) + x \|a c +--R a +--R -----------------------------------] +--R 4 2 +---+ +--R (4a c x + 4a )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1093 + +--S 1094 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4a\|a \|c \|a c +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1097 + +)clear all + +--S 1098 of 1309 +t0:=1/(a+c*x^4)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1098 + +--S 1099 of 1309 +r0:=1/4*x/(a*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_ + (a^(7/4)*c^(1/4)*sqrt(2))+3/8*atan(1+c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*c^(1/4)*sqrt(2))-_ + 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(7/4)*c^(1/4)*sqrt(2))+_ + 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/_ + (a^(7/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 3a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 3a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 4+-+ +--R 4x\|2 \|a \|c +--R / +--R 4 2 +-+4+-+3 4+-+ +--R (16a c x + 16a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R 4 2 | 1 2 | 1 +--R (12a c x + 12a ) |- -------- log(16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R 4 2 | 1 2 | 1 +--R (- 12a c x - 12a ) |- -------- log(- 16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +--R 2 | 1 +--R 16a |- -------- +--R +----------+ 4| 7 +--R 4 2 | 1 \| 65536a c +--R (- 24a c x - 24a ) |- -------- atan(----------------- + x +--R 4| 7 x +--R \| 65536a c +--R / +--R 4 2 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1100 + +--S 1101 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 48a\|2 |- -------- \|a \|c log(16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R - 48a\|2 |- -------- \|a \|c log(- 16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +----------+ +--R 2 | 1 +--R 16a |- -------- +--R +----------+ 4| 7 +--R +-+ | 1 4+-+3 4+-+ \| 65536a c +--R - 96a\|2 |- -------- \|a \|c atan(-----------------) +--R 4| 7 x +--R \| 65536a c +--R / +--R +-+4+-+3 4+-+ +--R 16a\|2 \|a \|c +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1102 + +)clear all + +--S 1103 of 1309 +t0:=1/(x*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 9 5 2 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1103 + +--S 1104 of 1309 +r0:=1/4/(a*(a+c*x^4))+log(x)/a^2-1/4*log(a+c*x^4)/a^2 +--R +--R +--R 4 4 4 +--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 4 3 +--R 4a c x + 4a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 4 3 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1105 + +--S 1106 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1107 + +)clear all + +--S 1108 of 1309 +t0:=1/(x^2*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 6 2 2 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1108 + +--S 1109 of 1309 +r0:=(-5/4)/(a^2*x)+1/4/(a*x*(a+c*x^4))+5/8*c^(1/4)*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-5/8*c^(1/4)*_ + atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-_ + 5/16*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2))+5/16*c^(1/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2)) +--R +--R +--R (2) +--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 5a x)\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 5a x)\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 5 4+-+ x\|2 \|c + \|a +--R (- 10c x - 10a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 5 4+-+ x\|2 \|c - \|a 4 +-+4+-+ +--R (- 10c x - 10a x)\|c atan(----------------) + (- 20c x - 16a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 5 3 +-+4+-+ +--R (16a c x + 16a x)\|2 \|a +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R 2 5 3 | 625c 7 | 625c +--R (- 4a c x - 4a x) |- ------- log(4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+3 +--R 2 5 3 | 625c 7 | 625c +--R (4a c x + 4a x) |- ------- log(- 4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+3 +--R 7 | 625c +--R 4096a |- ------- +--R +---------+ 4| 9 +--R 2 5 3 | 625c \| 65536a 4 +--R (- 8a c x - 8a x) |- ------- atan(------------------- - 5c x - 4a +--R 4| 9 125c x +--R \| 65536a +--R / +--R 2 5 3 +--R 4a c x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1110 + +--S 1111 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - 5\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------+ +---------+3 +--R 2 +-+ | 625c 4+-+ 7 | 625c +--R - 16a \|2 |- ------- \|a log(4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+3 +--R 2 +-+ | 625c 4+-+ 7 | 625c +--R 16a \|2 |- ------- \|a log(- 4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R 5\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 10\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +--R 10\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+3 +--R 7 | 625c +--R 4096a |- ------- +--R +---------+ 4| 9 +--R 2 +-+ | 625c 4+-+ \| 65536a +--R - 32a \|2 |- ------- \|a atan(-------------------) +--R 4| 9 125c x +--R \| 65536a +--R / +--R 2 +-+4+-+ +--R 16a \|2 \|a +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1112 + +)clear all + +--S 1113 of 1309 +t0:=1/(x^3*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 11 7 2 3 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1113 + +--S 1114 of 1309 +r0:=(-3/4)/(a^2*x^2)+1/4/(a*x^2*(a+c*x^4))-_ + 3/4*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(5/2) +--R +--R +--R 2 +-+ +--R 6 2 +-+ x \|c 4 +-+ +--R (- 3c x - 3a x )\|c atan(------) + (- 3c x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 6 3 2 +-+ +--R (4a c x + 4a x )\|a +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a +--R 6 2 | c \| a 4 +--R (3c x + 3a x ) |- - log(------------------------) - 6c x - 4a +--R \| a 4 +--R c x + a +--R [---------------------------------------------------------------, +--R 2 6 3 2 +--R 8a c x + 8a x +--R +-+ +--R |c +--R +-+ a |- +--R 6 2 |c \|a 4 +--R (3c x + 3a x ) |- atan(-----) - 3c x - 2a +--R \|a 2 +--R c x +--R -------------------------------------------] +--R 2 6 3 2 +--R 4a c x + 4a x +--R Type: Union(List(Expression(Integer)),...) +--E 1115 + +--S 1116 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R 3 |- - \|a log(------------------------ + 6\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R 3\|c atan(------) + 3\|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) ---------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1309 +t0:=1/(x^4*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 12 8 2 4 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1120 + +--S 1121 of 1309 +r0:=(-7/12)/(a^2*x^3)+1/4/(a*x^3*(a+c*x^4))+7/8*c^(3/4)*_ + atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*sqrt(2))-_ + 7/8*c^(3/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*_ + sqrt(2))+7/16*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2))-7/16*c^(3/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 21a x )\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 21a x )\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 7 3 4+-+3 x\|2 \|c + \|a +--R (- 42c x - 42a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 7 3 4+-+3 x\|2 \|c - \|a 4 +-+4+-+3 +--R (- 42c x - 42a x )\|c atan(----------------) + (- 28c x - 16a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 7 3 3 +-+4+-+3 +--R (48a c x + 48a x )\|2 \|a +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 7 3 3 | 2401c 3 | 2401c +--R (- 12a c x - 12a x ) |- -------- log(16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 7 3 3 | 2401c 3 | 2401c +--R (12a c x + 12a x ) |- -------- log(- 16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R 3 | 2401c +--R +----------+ 16a |- -------- +--R | 3 4| 11 +--R 2 7 3 3 | 2401c \| 65536a 4 +--R (24a c x + 24a x ) |- -------- atan(----------------- - 7c x - 4a +--R 4| 11 7c x +--R \| 65536a +--R / +--R 2 7 3 3 +--R 12a c x + 12a x +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 7\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 +-+ | 2401c 4+-+3 3 | 2401c +--R - 16a \|2 |- -------- \|a log(16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 +-+ | 2401c 4+-+3 3 | 2401c +--R 16a \|2 |- -------- \|a log(- 16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 7\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 14\|c atan(----------------) + 14\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +----------+ +--R | 3 +--R 3 | 2401c +--R +----------+ 16a |- -------- +--R | 3 4| 11 +--R 2 +-+ | 2401c 4+-+3 \| 65536a +--R 32a \|2 |- -------- \|a atan(-----------------) +--R 4| 11 7c x +--R \| 65536a +--R / +--R 2 +-+4+-+3 +--R 16a \|2 \|a +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1309 +t0:=x^11/(a+c*x^4)^3 +--R +--R +--R 11 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1125 + +--S 1126 of 1309 +r0:=-1/8*a^2/(c^3*(a+c*x^4)^2)+1/2*a/(c^3*(a+c*x^4))+1/4*log(a+c*x^4)/c^3 +--R +--R +--R 2 8 4 2 4 4 2 +--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a +--R (2) ---------------------------------------------------- +--R 5 8 4 4 2 3 +--R 8c x + 16a c x + 8a c +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 4 4 2 +--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a +--R (3) ---------------------------------------------------- +--R 5 8 4 4 2 3 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1309 +t0:=x^10/(a+c*x^4)^3 +--R +--R +--R 10 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1130 + +--S 1131 of 1309 +r0:=-1/8*x^7/(c*(a+c*x^4)^2)-7/32*x^3/(c^2*(a+c*x^4))-_ + 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(11/4)*_ + sqrt(2))+21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*_ + c^(11/4)*sqrt(2))+21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2))-21/128*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 42a c x - 21a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 42a c x + 21a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (- 44c x - 28a x )\|2 \|a \|c +--R / +--R 4 8 3 4 2 2 +-+4+-+4+-+3 +--R (128c x + 256a c x + 128a c )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (672c x + 1344a c x + 672a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 672c x - 1344a c x - 672a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(- 2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (1344c x + 2688a c x + 1344a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R 2097152a c |- -------------- +--R 4| 11 +--R \| 268435456a c +--R atan(-------------------------------) +--R x +--R + +--R 7 3 +--R - 11c x - 7a x +--R / +--R 4 8 3 4 2 2 +--R 32c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 21log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 2688c \|2 |- -------------- \|a \|c +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R - +--R +----------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 2688c \|2 |- -------------- \|a \|c +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(- 2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +----------------+3 +--R 8 | 1 +--R 2097152a c |- -------------- +--R +----------------+ 4| 11 +--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 5376c \|2 |- -------------- \|a \|c atan(-------------------------------) +--R 4| 11 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+4+-+3 +--R 128c \|2 \|a \|c +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1309 +t0:=x^9/(a+c*x^4)^3 +--R +--R +--R 9 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1135 + +--S 1136 of 1309 +r0:=-1/8*x^6/(c*(a+c*x^4)^2)-3/16*x^2/(c^2*(a+c*x^4))+_ + 3/16*atan(x^2*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (3c x + 6a c x + 3a )atan(------) + (- 5c x - 3a x )\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 4 8 3 4 2 2 +-+ +-+ +--R (16c x + 32a c x + 16a c )\|a \|c +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (3c x + 6a c x + 3a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (- 10c x - 6a x )\|- a c +--R / +--R 4 8 3 4 2 2 +-----+ +--R (32c x + 64a c x + 32a c )\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (3c x + 6a c x + 3a )atan(--------) + (- 5c x - 3a x )\|a c +--R a +--R ---------------------------------------------------------------] +--R 4 8 3 4 2 2 +---+ +--R (16c x + 32a c x + 16a c )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1137 + +--S 1138 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 32c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R 3\|a \|c atan(--------) - 3\|a c atan(------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1309 +t0:=x^8/(a+c*x^4)^3 +--R +--R +--R 8 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1309 +r0:=-1/8*x^5/(c*(a+c*x^4)^2)-5/32*x/(c^2*(a+c*x^4))-_ + 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))+_ + 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))-_ + 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2))+_ + 5/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 10a c x + 5a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 10a c x - 5a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (- 36c x - 20a x)\|2 \|a \|c +--R / +--R 4 8 3 4 2 2 +-+4+-+3 4+-+ +--R (128c x + 256a c x + 128a c )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (160c x + 320a c x + 160a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 160c x - 320a c x - 160a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 320c x - 640a c x - 320a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R atan(-------------------------) +--R x +--R + +--R 5 +--R - 9c x - 5a x +--R / +--R 4 8 3 4 2 2 +--R 32c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 5log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 640c \|2 |- ------------- \|a \|c log(128a c |- ------------- + x) +--R 4| 3 9 4| 3 9 +--R \| 268435456a c \| 268435456a c +--R + +--R - +--R +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +--R 640c \|2 |- ------------- \|a \|c +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R +---------------+ 4| 3 9 +--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 1280c \|2 |- ------------- \|a \|c atan(-------------------------) +--R 4| 3 9 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+3 4+-+ +--R 128c \|2 \|a \|c +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1309 +t0:=x^7/(a+c*x^4)^3 +--R +--R +--R 7 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1309 +r0:=1/8*x^8/(a*(a+c*x^4)^2) +--R +--R +--R 1 8 +--R - x +--R 8 +--R (2) --------------------- +--R 2 8 2 4 3 +--R a c x + 2a c x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1148 + +--S 1149 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 2c x - a +--R (3) ------------------------ +--R 4 8 3 4 2 2 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1149 + +--S 1150 of 1309 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 8a c +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +)clear all + +--S 1152 of 1309 +t0:=x^6/(a+c*x^4)^3 +--R +--R +--R 6 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1152 + +--S 1153 of 1309 +r0:=-1/8*x^3/(c*(a+c*x^4)^2)+3/32*x^3/(a*c*(a+c*x^4))-_ + 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_ + 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_ + 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2))-3/128*log(a^(1/4)*c^(1/4)*_ + x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 6a c x - 3a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 6a c x + 3a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (12c x - 4a x )\|2 \|a \|c +--R / +--R 3 8 2 2 4 3 +-+4+-+4+-+3 +--R (128a c x + 256a c x + 128a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (96a c x + 192a c x + 96a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 96a c x - 192a c x - 96a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (192a c x + 384a c x + 192a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R 2097152a c |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R atan(------------------------------) +--R x +--R + +--R 7 3 +--R 3c x - a x +--R / +--R 3 8 2 2 4 3 +--R 32a c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1154 + +--S 1155 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +--R +-+ | 1 4+-+4+-+3 +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R - +--R +---------------+ +--R +-+ | 1 4+-+4+-+3 +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+3 +--R 4 5 | 1 +--R 2097152a c |- ------------- +--R +---------------+ 4| 5 7 +--R +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 768a c\|2 |- ------------- \|a \|c atan(------------------------------) +--R 4| 5 7 x +--R \| 268435456a c +--R / +--R +-+4+-+4+-+3 +--R 128a c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1156 + +)clear all + +--S 1157 of 1309 +t0:=x^5/(a+c*x^4)^3 +--R +--R +--R 5 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1157 + +--S 1158 of 1309 +r0:=-1/8*x^2/(c*(a+c*x^4)^2)+1/16*x^2/(a*c*(a+c*x^4))+_ + 1/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (c x + 2a c x + a )atan(------) + (c x - a x )\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 3 8 2 2 4 3 +-+ +-+ +--R (16a c x + 32a c x + 16a c)\|a \|c +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (c x + 2a c x + a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (2c x - 2a x )\|- a c +--R / +--R 3 8 2 2 4 3 +-----+ +--R (32a c x + 64a c x + 32a c)\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (c x + 2a c x + a )atan(--------) + (c x - a x )\|a c +--R a +--R ---------------------------------------------------------] +--R 3 8 2 2 4 3 +---+ +--R (16a c x + 32a c x + 16a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1159 + +--S 1160 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 32a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 16a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1163 + +)clear all + +--S 1164 of 1309 +t0:=x^4/(a+c*x^4)^3 +--R +--R +--R 4 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1164 + +--S 1165 of 1309 +r0:=-1/8*x/(c*(a+c*x^4)^2)+1/32*x/(a*c*(a+c*x^4))-_ + 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))+_ + 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))-_ + 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2))+3/128*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 6a c x + 3a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 6a c x - 3a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (4c x - 12a x)\|2 \|a \|c +--R / +--R 3 8 2 2 4 3 +-+4+-+3 4+-+ +--R (128a c x + 256a c x + 128a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (96a c x + 192a c x + 96a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 96a c x - 192a c x - 96a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 192a c x - 384a c x - 192a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R atan(------------------------) +--R x +--R + +--R 5 +--R c x - 3a x +--R / +--R 3 8 2 2 4 3 +--R 32a c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1166 + +--S 1167 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 384a c\|2 |- ------------- \|a \|c log(128a c |- ------------- + x) +--R 4| 7 5 4| 7 5 +--R \| 268435456a c \| 268435456a c +--R + +--R - +--R +---------------+ +--R +-+ | 1 4+-+3 4+-+ +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R +---------------+ 4| 7 5 +--R +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 768a c\|2 |- ------------- \|a \|c atan(------------------------) +--R 4| 7 5 x +--R \| 268435456a c +--R / +--R +-+4+-+3 4+-+ +--R 128a c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1168 + +)clear all + +--S 1169 of 1309 +t0:=x^3/(a+c*x^4)^3 +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1169 + +--S 1170 of 1309 +r0:=(-1/8)/(c*(a+c*x^4)^2) +--R +--R +--R 1 +--R - +--R 8 +--R (2) - -------------------- +--R 3 8 2 4 2 +--R c x + 2a c x + a c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1170 + +--S 1171 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 8 2 4 2 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1171 + +--S 1172 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1173 + +)clear all + +--S 1174 of 1309 +t0:=x^2/(a+c*x^4)^3 +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1174 + +--S 1175 of 1309 +r0:=1/8*x^3/(a*(a+c*x^4)^2)+5/32*x^3/(a^2*(a+c*x^4))-_ + 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_ + 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_ + 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2))-5/128*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 10a c x - 5a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 10a c x + 5a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (20c x + 36a x )\|2 \|a \|c +--R / +--R 2 2 8 3 4 4 +-+4+-+4+-+3 +--R (128a c x + 256a c x + 128a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (160a c x + 320a c x + 160a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 160a c x - 320a c x - 160a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (320a c x + 640a c x + 320a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R 2097152a c |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R atan(------------------------------) +--R x +--R + +--R 7 3 +--R 5c x + 9a x +--R / +--R 2 2 8 3 4 4 +--R 32a c x + 64a c x + 32a +--R Type: Union(Expression(Integer),...) +--E 1176 + +--S 1177 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 5log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 640a \|2 |- ------------- \|a \|c +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R - +--R +---------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 640a \|2 |- ------------- \|a \|c +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+3 +--R 7 2 | 1 +--R 2097152a c |- ------------- +--R +---------------+ 4| 9 3 +--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 1280a \|2 |- ------------- \|a \|c atan(------------------------------) +--R 4| 9 3 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+4+-+3 +--R 128a \|2 \|a \|c +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1178 + +)clear all + +--S 1179 of 1309 +t0:=x/(a+c*x^4)^3 +--R +--R +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1179 + +--S 1180 of 1309 +r0:=1/8*x^2/(a*(a+c*x^4)^2)+3/16*x^2/(a^2*(a+c*x^4))+_ + 3/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (3c x + 6a c x + 3a )atan(------) + (3c x + 5a x )\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 2 2 8 3 4 4 +-+ +-+ +--R (16a c x + 32a c x + 16a )\|a \|c +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (3c x + 6a c x + 3a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (6c x + 10a x )\|- a c +--R / +--R 2 2 8 3 4 4 +-----+ +--R (32a c x + 64a c x + 32a )\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (3c x + 6a c x + 3a )atan(--------) + (3c x + 5a x )\|a c +--R a +--R -------------------------------------------------------------] +--R 2 2 8 3 4 4 +---+ +--R (16a c x + 32a c x + 16a )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1181 + +--S 1182 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 32a \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R 3\|a \|c atan(--------) - 3\|a c atan(------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16a \|a \|c \|a c +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1309 +t0:=1/(a+c*x^4)^3 +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 1309 +r0:=1/8*x/(a*(a+c*x^4)^2)+7/32*x/(a^2*(a+c*x^4))-_ + 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))+_ + 21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))-_ + 21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2))+_ + 21/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 42a c x + 21a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 42a c x - 21a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (28c x + 44a x)\|2 \|a \|c +--R / +--R 2 2 8 3 4 4 +-+4+-+3 4+-+ +--R (128a c x + 256a c x + 128a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (672a c x + 1344a c x + 672a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R log(128a |- ------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 672a c x - 1344a c x - 672a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R log(- 128a |- ------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 1344a c x - 2688a c x - 1344a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R 128a |- ------------- +--R 4| 11 +--R \| 268435456a c +--R atan(-----------------------) +--R x +--R + +--R 5 +--R 7c x + 11a x +--R / +--R 2 2 8 3 4 4 +--R 32a c x + 64a c x + 32a +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 21log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1 +--R 2688a \|2 |- ------------- \|a \|c log(128a |- ------------- + x) +--R 4| 11 4| 11 +--R \| 268435456a c \| 268435456a c +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1 +--R - 2688a \|2 |- ------------- \|a \|c log(- 128a |- ------------- + x) +--R 4| 11 4| 11 +--R \| 268435456a c \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 3 | 1 +--R 128a |- ------------- +--R +---------------+ 4| 11 +--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 5376a \|2 |- ------------- \|a \|c atan(-----------------------) +--R 4| 11 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+3 4+-+ +--R 128a \|2 \|a \|c +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1309 +t0:=1/(x*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 13 2 9 2 5 3 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 1309 +r0:=1/8/(a*(a+c*x^4)^2)+1/4/(a^2*(a+c*x^4))+log(x)/a^3-1/4*log(a+c*x^4)/a^3 +--R +--R +--R (2) +--R 2 8 4 2 4 2 8 4 2 +--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x) +--R + +--R 4 2 +--R 2a c x + 3a +--R / +--R 3 2 8 4 4 5 +--R 8a c x + 16a c x + 8a +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 4 2 4 2 8 4 2 +--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x) +--R + +--R 4 2 +--R 2a c x + 3a +--R / +--R 3 2 8 4 4 5 +--R 8a c x + 16a c x + 8a +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1309 +t0:=1/(x^2*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 14 2 10 2 6 3 2 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 1309 +r0:=(-45/32)/(a^3*x)+1/8/(a*x*(a+c*x^4)^2)+9/32/(a^2*x*(a+c*x^4))+_ + 45/64*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_ + 45/64*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_ + 45/128*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(13/4)*sqrt(2))+_ + 45/128*c^(1/4)*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(13/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (45c x + 90a c x + 45a x)\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (- 45c x - 90a c x - 45a x)\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 9 5 2 4+-+ x\|2 \|c + \|a +--R (- 90c x - 180a c x - 90a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 9 5 2 4+-+ x\|2 \|c - \|a +--R (- 90c x - 180a c x - 90a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 8 4 2 +-+4+-+ +--R (- 180c x - 324a c x - 128a )\|2 \|a +--R / +--R 3 2 9 4 5 5 +-+4+-+ +--R (128a c x + 256a c x + 128a x)\|2 \|a +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (- 32a c x - 64a c x - 32a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (32a c x + 64a c x + 32a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(- 2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (- 64a c x - 128a c x - 64a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R 2097152a |- ------------ +--R 4| 13 +--R \| 268435456a +--R atan(----------------------------) +--R 91125c x +--R + +--R 2 8 4 2 +--R - 45c x - 81a c x - 32a +--R / +--R 3 2 9 4 5 5 +--R 32a c x + 64a c x + 32a x +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - 45\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R - +--R +--------------+ +--R 3 +-+ | 4100625c 4+-+ +--R 128a \|2 |- ------------ \|a +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 +-+ | 4100625c 4+-+ +--R 128a \|2 |- ------------ \|a +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(- 2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R 45\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 90\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +--R 90\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 10 | 4100625c +--R 2097152a |- ------------ +--R +--------------+ 4| 13 +--R 3 +-+ | 4100625c 4+-+ \| 268435456a +--R - 256a \|2 |- ------------ \|a atan(----------------------------) +--R 4| 13 91125c x +--R \| 268435456a +--R / +--R 3 +-+4+-+ +--R 128a \|2 \|a +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1309 +t0:=1/(x^3*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 15 2 11 2 7 3 3 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1201 + +--S 1202 of 1309 +r0:=(-15/16)/(a^3*x^2)+1/8/(a*x^2*(a+c*x^4)^2)+_ + 5/16/(a^2*x^2*(a+c*x^4))-15/16*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(7/2) +--R +--R +--R (2) +--R 2 +-+ +--R 2 10 6 2 2 +-+ x \|c +--R (- 15c x - 30a c x - 15a x )\|c atan(------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (- 15c x - 25a c x - 8a )\|a +--R / +--R 3 2 10 4 6 5 2 +-+ +--R (16a c x + 32a c x + 16a x )\|a +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a +--R 2 10 6 2 2 | c \| a +--R (15c x + 30a c x + 15a x ) |- - log(------------------------) +--R \| a 4 +--R c x + a +--R + +--R 2 8 4 2 +--R - 30c x - 50a c x - 16a +--R / +--R 3 2 10 4 6 5 2 +--R 32a c x + 64a c x + 32a x +--R , +--R +-+ +--R |c +--R +-+ a |- +--R 2 10 6 2 2 |c \|a 2 8 4 2 +--R (15c x + 30a c x + 15a x ) |- atan(-----) - 15c x - 25a c x - 8a +--R \|a 2 +--R c x +--R ----------------------------------------------------------------------] +--R 3 2 10 4 6 5 2 +--R 16a c x + 32a c x + 16a x +--R Type: Union(List(Expression(Integer)),...) +--E 1203 + +--S 1204 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R 15 |- - \|a log(------------------------ + 30\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R 32a \|a +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R 15\|c atan(------) + 15\|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) ------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1207 + +)clear all + +--S 1208 of 1309 +t0:=1/(x^4*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 16 2 12 2 8 3 4 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1208 + +--S 1209 of 1309 +r0:=(-77/96)/(a^3*x^3)+1/8/(a*x^3*(a+c*x^4)^2)+_ + 11/32/(a^2*x^3*(a+c*x^4))+77/64*c^(3/4)*atan(1-c^(1/4)*_ + x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))-77/64*c^(3/4)*_ + atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))+_ + 77/128*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(15/4)*sqrt(2))-77/128*c^(3/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(15/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 231c x - 462a c x - 231a x )\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (231c x + 462a c x + 231a x )\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 11 7 2 3 4+-+3 x\|2 \|c + \|a +--R (- 462c x - 924a c x - 462a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 11 7 2 3 4+-+3 x\|2 \|c - \|a +--R (- 462c x - 924a c x - 462a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 8 4 2 +-+4+-+3 +--R (- 308c x - 484a c x - 128a )\|2 \|a +--R / +--R 3 2 11 4 7 5 3 +-+4+-+3 +--R (384a c x + 768a c x + 384a x )\|2 \|a +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (- 96a c x - 192a c x - 96a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R log(128a |- ------------ + 77c x) +--R 4| 15 +--R \| 268435456a +--R + +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (96a c x + 192a c x + 96a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R log(- 128a |- ------------ + 77c x) +--R 4| 15 +--R \| 268435456a +--R + +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (192a c x + 384a c x + 192a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R 128a |- ------------ +--R 4| 15 +--R \| 268435456a +--R atan(----------------------) +--R 77c x +--R + +--R 2 8 4 2 +--R - 77c x - 121a c x - 32a +--R / +--R 3 2 11 4 7 5 3 +--R 96a c x + 192a c x + 96a x +--R Type: Union(Expression(Integer),...) +--E 1210 + +--S 1211 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 77\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +--------------+ +--------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c +--R - 128a \|2 |- ------------ \|a log(128a |- ------------ + 77c x) +--R 4| 15 4| 15 +--R \| 268435456a \| 268435456a +--R + +--R +--------------+ +--------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c +--R 128a \|2 |- ------------ \|a log(- 128a |- ------------ + 77c x) +--R 4| 15 4| 15 +--R \| 268435456a \| 268435456a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 77\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 154\|c atan(----------------) + 154\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R +--------------+ 128a |- ------------ +--R | 3 4| 15 +--R 3 +-+ | 35153041c 4+-+3 \| 268435456a +--R 256a \|2 |- ------------ \|a atan(----------------------) +--R 4| 15 77c x +--R \| 268435456a +--R / +--R 3 +-+4+-+3 +--R 128a \|2 \|a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1212 + +)clear all + +--S 1213 of 1309 +t0:=x^4/(2+3*x^4) +--R +--R +--R 4 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1213 + +--S 1214 of 1309 +r0:=1/3*x+1/6*atan(1-6^(1/4)*x)/6^(1/4)-1/6*atan(1+6^(1/4)*x)/6^(1/4)+_ + 1/12*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)-_ + 1/12*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ +--R - 2atan(x\|6 + 1) - 2atan(x\|6 - 1) + 4x\|6 +--R / +--R 4+-+ +--R 12\|6 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 4+--+2 +-+4+--+ +--R - \|2 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+ 2 4+--+2 +-+4+--+ +-+ 2 +--R \|2 log(x \|24 - 2x\|2 \|24 + 4) + 2\|2 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+ 2 4+--+ +--R 2\|2 atan(--------------) + 4x\|24 +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+--+ +--R 12\|24 +--R Type: Union(Expression(Integer),...) +--E 1215 + +--S 1216 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R - \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R \|24 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+ +--R - \|24 log(- x \|2 \|3 + x \|3 + \|2 ) + 2\|24 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+ 2 +--R 2\|24 atan(x\|6 - 1) + 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+4+-+ 2 +--R 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+-+4+--+ +--R 12\|6 \|24 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2 +--R (- 4x \|2 \|3 + 4x \|2 \|3 + 6x + 4)\|6 +--R + +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2 +--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6 + 12x \|2 \|3 +--R + +--R 4 +-+ +-+ 6 2 +--R - 12x \|2 \|3 - 18x - 12x +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2 +--R ((36x + 24x )\|2 \|3 + (- 36x - 24x )\|2 \|3 - 54x - 72x - 24)\|6 +--R Type: Expression(Integer) +--E 1217 + +)clear all + +--S 1218 of 1309 +t0:=x^3/(2+3*x^4) +--R +--R +--R 3 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1218 + +--S 1219 of 1309 +r0:=1/12*log(2+3*x^4) +--R +--R +--R 4 +--R log(3x + 2) +--R (2) ------------ +--R 12 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R log(3x + 2) +--R (3) ------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 1220 + +--S 1221 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1222 + +)clear all + +--S 1223 of 1309 +t0:=x^2/(2+3*x^4) +--R +--R +--R 2 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1223 + +--S 1224 of 1309 +r0:=-1/2*atan(1-6^(1/4)*x)/6^(3/4)+1/2*atan(1+6^(1/4)*x)/6^(3/4)+_ + 1/4*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_ + 1/4*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ +--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1) +--R / +--R 4+-+3 +--R 4\|6 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+4+--+3 2 4+--+2 +--R - \|2 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R +-+ +-+4+--+3 2 4+--+2 +-+ 18 +--R \|2 log(- x\|2 \|54 + 3x \|54 + 18) - 2\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+ 18 +--R - 2\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+--+ +--R 8\|54 +--R Type: Union(Expression(Integer),...) +--E 1225 + +--S 1226 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+3 +-+4+--+3 2 4+--+2 +--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+ +--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+3 18 +--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+4+-+3 18 +--R - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+-+3 4+--+ +--R 8\|6 \|54 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R 2 4+-+3 4+-+3 4+-+4+-+ 4+-+3 2 4+-+2 +--R (- x \|2 \|3 + 2\|2 \|3 )\|6 + 6x \|6 - 12 +--R (5) ------------------------------------------------- +--R 4 4+-+2 +--R (36x + 24)\|6 +--R Type: Expression(Integer) +--E 1227 + +)clear all + +--S 1228 of 1309 +t0:=x/(2+3*x^4) +--R +--R +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1228 + +--S 1229 of 1309 +r0:=1/2*atan(x^2*sqrt(3/2))/sqrt(6) +--R +--R +--R 2 +-+ +--R x \|3 +--R atan(------) +--R +-+ +--R \|2 +--R (2) ------------ +--R +-+ +--R 2\|6 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|6 +--R atan(------) +--R 2 +--R (3) ------------ +--R +-+ +--R 2\|6 +--R Type: Union(Expression(Integer),...) +--E 1230 + +--S 1231 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +-+ +--R x \|6 x \|3 +--R atan(------) - atan(------) +--R 2 +-+ +--R \|2 +--R (4) --------------------------- +--R +-+ +--R 2\|6 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1309 +d0:=D(m0,x) +--R +--R +--R +-+ +-+ +-+ +--R - x\|2 \|3 \|6 + 6x +--R (5) -------------------- +--R 4 +--R 18x + 12 +--R Type: Expression(Integer) +--E 1232 + +)clear all + +--S 1233 of 1309 +t0:=1/(2+3*x^4) +--R +--R +--R 1 +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1233 + +--S 1234 of 1309 +r0:=-1/4*atan(1-6^(1/4)*x)/6^(1/4)+1/4*atan(1+6^(1/4)*x)/6^(1/4)-_ + 1/8*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)+_ + 1/8*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R log(x \|2 \|3 + x \|3 + \|2 ) - log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ +--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1) +--R / +--R 4+-+ +--R 8\|6 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 4+--+2 +-+4+--+ +-+ 2 4+--+2 +-+4+--+ +--R \|2 log(x \|24 + 2x\|2 \|24 + 4) - \|2 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R +-+ 2 +-+ 2 +--R - 2\|2 atan(--------------) - 2\|2 atan(--------------) +--R +-+4+--+ +-+4+--+ +--R x\|2 \|24 - 2 x\|2 \|24 + 2 +--R / +--R 4+--+ +--R 8\|24 +--R Type: Union(Expression(Integer),...) +--E 1235 + +--S 1236 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R - \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - \|24 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+ +--R \|24 log(- x \|2 \|3 + x \|3 + \|2 ) - 2\|24 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+ 2 +--R - 2\|24 atan(x\|6 - 1) - 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+4+-+ 2 +--R - 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+-+4+--+ +--R 8\|6 \|24 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2 +--R (4x \|2 \|3 - 4x \|2 \|3 - 6x - 4)\|6 +--R + +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2 +--R ((- 3x - 2x )\|2 \|3 + (3x + 2)\|2 \|2 )\|3 \|6 - 12x \|2 \|3 +--R + +--R 4 +-+ +-+ 6 2 +--R 12x \|2 \|3 + 18x + 12x +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2 +--R ((24x + 16x )\|2 \|3 + (- 24x - 16x )\|2 \|3 - 36x - 48x - 16)\|6 +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1309 +t0:=1/(x*(2+3*x^4)) +--R +--R +--R 1 +--R (1) -------- +--R 5 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1238 + +--S 1239 of 1309 +r0:=-1/4*atanh(1+3*x^4) +--R +--R +--R 4 +--R atanh(3x + 1) +--R (2) - -------------- +--R 4 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - log(3x + 2) + 4log(x) +--R (3) ------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 1240 + +--S 1241 of 1309 +m0:=a0-r0 +--R +--R +--R 4 4 +--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1) +--R (4) ------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1242 + +)clear all + +--S 1243 of 1309 +t0:=1/(x^2*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 6 2 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1243 + +--S 1244 of 1309 +r0:=(-1/2)/x+1/4*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_ + 1/4*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-1/8*3^(1/4)*_ + log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_ + 1/8*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4) +--R +--R +--R (2) +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R x\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+ 4+-+ +--R - x\|3 log(- x \|2 \|3 + x \|3 + \|2 ) - 2x\|3 atan(x\|6 + 1) +--R + +--R 4+-+ 4+-+ 4+-+3 +--R - 2x\|3 atan(x\|6 - 1) - 4\|2 +--R / +--R 4+-+3 +--R 8x \|2 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R x\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - x\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+3 +--R +-+4+-+ 2\|3 +--R - 2x\|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+ 2\|3 4+-+ +--R 2x\|2 \|3 atan(--------------------) - 8\|2 +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+ +--R 16x\|2 +--R Type: Union(Expression(Integer),...) +--E 1245 + +--S 1246 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R \|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - \|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ 4+-+ +--R 4\|3 atan(x\|6 + 1) + 4\|3 atan(x\|6 - 1) +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R - 2\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R 2\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+3 +--R 16\|2 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3 +--R (4x \|2 \|3 + (- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 )\|6 +--R + +--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+ +--R (8x \|2 \|3 + (- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 )\|6 +--R + +--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2 +--R ((- 6x - 4x )\|2 \|3 + (6x + 4)\|2 \|2 - 48x )\|3 +--R + +--R 4 +-+4+-+2 +-+ 6 2 4+-+2 +--R 24x \|2 \|2 \|3 + (36x + 24x )\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 72x - 96x - 32)\|2 +--R Type: Expression(Integer) +--E 1247 + +)clear all + +--S 1248 of 1309 +t0:=1/(x^3*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 7 3 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1248 + +--S 1249 of 1309 +r0:=(-1/4)/x^2-1/4*atan(x^2*sqrt(3/2))*sqrt(3/2) +--R +--R +--R 2 +-+ +--R 2 +-+ x \|3 +-+ +--R - x \|3 atan(------) - \|2 +--R +-+ +--R \|2 +--R (2) --------------------------- +--R 2 +-+ +--R 4x \|2 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2 +-+ 2\|3 +-+ +--R x \|3 atan(-------) - \|2 +--R 2 +-+ +--R 3x \|2 +--R (3) -------------------------- +--R 2 +-+ +--R 4x \|2 +--R Type: Union(Expression(Integer),...) +--E 1250 + +--S 1251 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ +-+ +--R +-+ x \|3 +-+ 2\|3 +--R \|3 atan(------) + \|3 atan(-------) +--R +-+ 2 +-+ +--R \|2 3x \|2 +--R (4) ------------------------------------ +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1252 + +)clear all + +--S 1253 of 1309 +t0:=1/(x^4*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 8 4 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1253 + +--S 1254 of 1309 +r0:=(-1/6)/x^3+1/8*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)-_ + 1/8*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)+1/16*3^(3/4)*_ + log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)-_ + 1/16*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4) +--R +--R +--R (2) +--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R - 3x \|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+ 3 4+-+3 4+-+ +--R 3x \|3 log(- x \|2 \|3 + x \|3 + \|2 - 6x \|3 atan(x\|6 + 1) +--R + +--R 3 4+-+3 4+-+ 4+-+ +--R - 6x \|3 atan(x\|6 - 1 - 8\|2 +--R / +--R 3 4+-+ +--R 48x \|2 +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - 3x \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R 3x \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+--+ +--R 3 +-+4+--+ 2\|27 +--R - 6x \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R 3 +-+4+--+ 2\|27 4+-+ +--R 6x \|2 \|27 atan(-------------------) - 8\|8 +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 3 4+-+ +--R 48x \|8 +--R Type: Union(Expression(Integer),...) +--E 1255 + +--S 1256 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+ +--R - \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 + 2\|3 \|8 atan(x\|6 + 1) +--R + +--R 4+--+ +--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27 +--R 2\|3 \|8 atan(x\|6 - 1 - 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R +-+4+-+4+--+ 2\|27 +--R 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4+-+4+-+ +--R 16\|2 \|8 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 +-+4+-+ +-+ 6 2 4+-+ 4+-+3 4 4+-+3 4+-4+-+3 +--R ((- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 + 6x \|2 \|)\|6 +--R + +--R 2 +-+4+-+ +-+ 4 4+-+ 4+-+3 2 4+-+3 4+-4+-+ +--R ((- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 + 12x \|2 \|)\|6 +--R + +--R 2 4+-+2 2 +-+4+-+2 6 2 +-+ 4 4+-+2 +--R - 48x \|3 + (24x \|2 \|2 + 18x + 12x )\|3 + (36x + 24)\|2 +--R + +--R 4 +-+ +--R (- 18x - 12)\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 72x - 96x - 32)\|2 +--R Type: Expression(Integer) +--E 1257 + +)clear all + +--S 1258 of 1309 +t0:=x^3/(2+3*x^4)^2 +--R +--R +--R 3 +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1258 + +--S 1259 of 1309 +r0:=(-1/12)/(2+3*x^4) +--R +--R +--R 1 +--R -- +--R 36 +--R (2) - ------ +--R 4 2 +--R x + - +--R 3 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1259 + +--S 1260 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 4 +--R 36x + 24 +--R Type: Union(Expression(Integer),...) +--E 1260 + +--S 1261 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1262 + +)clear all + +--S 1263 of 1309 +t0:=x^2/(2+3*x^4)^2 +--R +--R +--R 2 +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1263 + +--S 1264 of 1309 +r0:=1/8*x^3/(2+3*x^4)-1/16*atan(1-6^(1/4)*x)/6^(3/4)+_ + 1/16*atan(1+6^(1/4)*x)/6^(3/4)+_ + 1/32*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_ + 1/32*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4) +--R +--R +--R (2) +--R 4 4+-+3 4+-+ 2 +-+ +-+ +--R (- 3x - 2)log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+ 2 +-+ +-+ 4 4+-+ +--R (3x + 2)log(- x \|2 \|3 + x \|3 + \|2 ) + (6x + 4)atan(x\|6 + 1) +--R + +--R 4 4+-+ 3 4+-+3 +--R (6x + 4)atan(x\|6 - 1) + 4x \|6 +--R / +--R 4 4+-+3 +--R (96x + 64)\|6 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ +-+4+--+3 2 4+--+2 +--R (- 3x - 2)\|2 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4 +-+ +-+4+--+3 2 4+--+2 +--R (3x + 2)\|2 log(- x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4 +-+ 18 +--R (- 6x - 4)\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R 4 +-+ 18 3 4+--+ +--R (- 6x - 4)\|2 atan(----------------) + 8x \|54 +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4 4+--+ +--R (192x + 128)\|54 +--R Type: Union(Expression(Integer),...) +--E 1265 + +--S 1266 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+3 +-+4+--+3 2 4+--+2 +--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+ +--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+3 18 +--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+4+-+3 18 +--R - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+-+3 4+--+ +--R 64\|6 \|54 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+3 +--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6 +--R + +--R 4 4+-+2 4+-+2 4 +-+ +-+ 6 2 4+-+2 2 4+-+2 4+-+2 +--R (12x \|2 \|3 - 12x \|2 \|3 - 18x - 12x )\|6 - 24x \|2 \|3 +--R + +--R 2 +-+ +-+ 4 +--R 24x \|2 \|3 + 36x + 24 +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 +--R (576x + 384x )\|2 \|3 + (- 576x - 384x )\|2 \|3 - 864x - 1152x +--R + +--R - 384 +--R * +--R 4+-+2 +--R \|6 +--R Type: Expression(Integer) +--E 1267 + +)clear all + +--S 1268 of 1309 +t0:=x/(2+3*x^4)^2 +--R +--R +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1268 + +--S 1269 of 1309 +r0:=1/8*x^2/(2+3*x^4)+1/8*atan(x^2*sqrt(3/2))/sqrt(6) +--R +--R +--R 2 +-+ +--R 4 x \|3 2 +-+ +--R (3x + 2)atan(------) + x \|6 +--R +-+ +--R \|2 +--R (2) ------------------------------ +--R 4 +-+ +--R (24x + 16)\|6 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R 4 x \|6 2 +-+ +--R (3x + 2)atan(------) + x \|6 +--R 2 +--R (3) ------------------------------ +--R 4 +-+ +--R (24x + 16)\|6 +--R Type: Union(Expression(Integer),...) +--E 1270 + +--S 1271 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +-+ +--R x \|6 x \|3 +--R atan(------) - atan(------) +--R 2 +-+ +--R \|2 +--R (4) --------------------------- +--R +-+ +--R 8\|6 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1309 +d0:=D(m0,x) +--R +--R +--R +-+ +-+ +-+ +--R - x\|2 \|3 \|6 + 6x +--R (5) -------------------- +--R 4 +--R 72x + 48 +--R Type: Expression(Integer) +--E 1272 + +)clear all + +--S 1273 of 1309 +t0:=1/(2+3*x^4)^2 +--R +--R +--R 1 +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1273 + +--S 1274 of 1309 +r0:=1/8*x/(2+3*x^4)-1/32*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)+_ + 1/32*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)-_ + 1/64*3^(3/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)+_ + 1/64*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4) +--R +--R +--R (2) +--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R (3x + 2)\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R (- 3x - 2)\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+ 4 4+-+3 4+-+ 4+-+ +--R (6x + 4)\|3 atan(x\|6 + 1) + (6x + 4)\|3 atan(x\|6 - 1) + 8x\|2 +--R / +--R 4 4+-+ +--R (192x + 128)\|2 +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R (3x + 2)\|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R (- 3x - 2)\|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+--+ +--R 4 +-+4+--+ 2\|27 +--R (6x + 4)\|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R 4 +-+4+--+ 2\|27 4+-+ +--R (- 6x - 4)\|2 \|27 atan(-------------------) + 8x\|8 +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4 4+-+ +--R (192x + 128)\|8 +--R Type: Union(Expression(Integer),...) +--E 1275 + +--S 1276 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+ +--R \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 - 2\|3 \|8 atan(x\|6 + 1) +--R + +--R 4+--+ +--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27 +--R - 2\|3 \|8 atan(x\|6 - 1 + 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R +-+4+-+4+--+ 2\|27 +--R - 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4+-+4+-+ +--R 64\|2 \|8 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1309 +d0:=normalize(D(m0,x)) +--R +--R +--R 2 4+-+4+-+3 4+-+3 4+-+4+-+3 4+-+ 2 4+-+2 4+-+2 +--R - x \|2 \|3 \|6 - 2\|2 \|3 \|6 + 6x \|3 + 6\|2 +--R (5) ------------------------------------------------------- +--R 4 4+-+2 +--R (96x + 64)\|2 +--R Type: Expression(Integer) +--E 1277 + +)clear all + +--S 1278 of 1309 +t0:=1/(x*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) --------------- +--R 9 5 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1278 + +--S 1279 of 1309 +r0:=1/8/(2+3*x^4)-1/8*atanh(1+3*x^4) +--R +--R +--R 4 4 +--R (- 3x - 2)atanh(3x + 1) + 1 +--R (2) ----------------------------- +--R 4 +--R 24x + 16 +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R (- 3x - 2)log(3x + 2) + (12x + 8)log(x) + 2 +--R (3) ---------------------------------------------- +--R 4 +--R 48x + 32 +--R Type: Union(Expression(Integer),...) +--E 1280 + +--S 1281 of 1309 +m0:=a0-r0 +--R +--R +--R 4 4 +--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1) +--R (4) ------------------------------------------ +--R 16 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1282 + +)clear all + +--S 1283 of 1309 +t0:=1/(x^2*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 10 6 2 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1283 + +--S 1284 of 1309 +r0:=(-5/16)/x+1/8/(x*(2+3*x^4))+5/32*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_ + 5/32*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-_ + 5/64*3^(1/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_ + 5/64*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4) +--R +--R +--R (2) +--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R (15x + 10x)\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R (- 15x - 10x)\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 5 4+-+ 4+-+ 5 4+-+ 4+-+ +--R (- 30x - 20x)\|3 atan(x\|6 + 1) + (- 30x - 20x)\|3 atan(x\|6 - 1) +--R + +--R 4 4+-+3 +--R (- 60x - 32)\|2 +--R / +--R 5 4+-+3 +--R (192x + 128x)\|2 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R (15x + 10x)\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R (- 15x - 10x)\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+3 +--R 5 +-+4+-+ 2\|3 +--R (- 30x - 20x)\|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R 5 +-+4+-+ 2\|3 4 4+-+ +--R (30x + 20x)\|2 \|3 atan(--------------------) + (- 120x - 64)\|2 +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 5 4+-+ +--R (384x + 256x)\|2 +--R Type: Union(Expression(Integer),...) +--E 1285 + +--S 1286 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R 5\|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 10\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R 10\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - 5\|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ 4+-+ +--R 20\|3 atan(x\|6 + 1) + 20\|3 atan(x\|6 - 1) +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R - 10\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R 10\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+3 +--R 128\|2 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3 +--R (20x \|2 \|3 + (- 10x \|2 \|2 \|3 + (- 15x - 10x )\|2 )\|3 )\|6 +--R + +--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+ +--R (40x \|2 \|3 + (- 20x \|2 \|2 \|3 + (- 30x - 20)\|2 )\|3 )\|6 +--R + +--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2 +--R ((- 30x - 20x )\|2 \|3 + (30x + 20)\|2 \|2 - 240x )\|3 +--R + +--R 4 +-+4+-+2 +-+ 6 2 4+-+2 +--R 120x \|2 \|2 \|3 + (180x + 120x )\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (768x + 512x )\|3 + (- 384x - 256x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 576x - 768x - 256)\|2 +--R Type: Expression(Integer) +--E 1287 + +)clear all + +--S 1288 of 1309 +t0:=1/(x^3*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 11 7 3 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1288 + +--S 1289 of 1309 +r0:=(-3/16)/x^2+1/8/(x^2*(2+3*x^4))-3/16*atan(x^2*sqrt(3/2))*sqrt(3/2) +--R +--R +--R 2 +-+ +--R 6 2 +-+ x \|3 4 +-+ +--R (- 9x - 6x )\|3 atan(------) + (- 9x - 4)\|2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------------- +--R 6 2 +-+ +--R (48x + 32x )\|2 +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 6 2 +-+ 2\|3 4 +-+ +--R (9x + 6x )\|3 atan(-------) + (- 9x - 4)\|2 +--R 2 +-+ +--R 3x \|2 +--R (3) ---------------------------------------------- +--R 6 2 +-+ +--R (48x + 32x )\|2 +--R Type: Union(Expression(Integer),...) +--E 1290 + +--S 1291 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ +-+ +--R +-+ x \|3 +-+ 2\|3 +--R 3\|3 atan(------) + 3\|3 atan(-------) +--R +-+ 2 +-+ +--R \|2 3x \|2 +--R (4) -------------------------------------- +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1292 + +)clear all + +--S 1293 of 1309 +t0:=1/(1+a+(-1+a)*x^4) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 +--R (a - 1)x + a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1293 + +--S 1294 of 1309 +r0:=-1/2*atan((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4))-_ + 1/2*atanh((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4)) +--R +--R +--R 4+-----+ 4+-----+ +--R x\|a - 1 x\|a - 1 +--R - atanh(----------) - atan(----------) +--R 4+-------+ 4+-------+ +--R \|- a - 1 \|- a - 1 +--R (2) -------------------------------------- +--R 4+-------+3 4+-----+ +--R 2\|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((4a + 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((- 4a - 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R | 1 +--R 2 |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R (4a + 4) |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R atan(---------------------------------------) +--R x +--R Type: Union(Expression(Integer),...) +--E 1295 + +--S 1296 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 2\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((4a + 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 2\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((- 4a - 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R 4+-----+ 4+-----+ +--R x\|a - 1 x\|a - 1 +--R atanh(----------) + atan(----------) +--R 4+-------+ 4+-------+ +--R \|- a - 1 \|- a - 1 +--R + +--R - +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 4\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R (4a + 4) |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R atan(---------------------------------------) +--R x +--R / +--R 4+-------+3 4+-----+ +--R 2\|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1297 + +)clear all + +--S 1298 of 1309 +t0:=x^7*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 7 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1309 +r0:=-1/6*a*(a+c*x^4)^(3/2)/c^2+1/10*(a+c*x^4)^(5/2)/c^2 +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (3c x + a c x - 2a )\|c x + a +--R (2) --------------------------------- +--R 2 +--R 30c +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (3c x + a c x - 2a )\|c x + a +--R (3) --------------------------------- +--R 2 +--R 30c +--R Type: Union(Expression(Integer),...) +--E 1300 + +--S 1301 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1302 + +)clear all + +--S 1303 of 1309 +t0:=x^5*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 5 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1309 +r0:=-1/16*a^2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+_ + 1/16*a*x^2*sqrt(a+c*x^4)/c+1/8*x^6*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 x \|c 6 2 +-+ | 4 +--R - a atanh(-----------) + (2c x + a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R 16c\|c +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((4a c x + 8a )\|a \|c x + a - a c x - 8a c x - 8a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +-+ | 4 +--R (- 2c x - 17a c x - 24a c x - 8a x )\|c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +-+ +-+ +--R (8c x + 28a c x + 28a c x + 8a x )\|a \|c +--R / +--R +--------+ +--R 2 4 +-+ +-+ | 4 +--R (64c x + 128a c)\|a \|c \|c x + a +--R + +--R 3 8 2 4 2 +-+ +--R (- 16c x - 128a c x - 128a c)\|c +--R , +--R +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((- 8a c x - 16a )\|a \|c x + a + 2a c x + 16a c x + 16a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +---+ | 4 +--R (- 2c x - 17a c x - 24a c x - 8a x )\|- c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +---+ +-+ +--R (8c x + 28a c x + 28a c x + 8a x )\|- c \|a +--R / +--R +--------+ +--R 2 4 +---+ +-+ | 4 +--R (64c x + 128a c)\|- c \|a \|c x + a +--R + +--R 3 8 2 4 2 +---+ +--R (- 16c x - 128a c x - 128a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1305 + +--S 1306 of 1309 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 2 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 2 x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 16c\|c +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1309 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a +--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 16c\|- c \|c +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1309 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4d.input.pdf b/src/axiom-website/CATS/rich4d.input.pdf new file mode 100644 index 0000000..2b154f1 Binary files /dev/null and b/src/axiom-website/CATS/rich4d.input.pdf differ diff --git a/src/axiom-website/CATS/rich4e.input.pamphlet b/src/axiom-website/CATS/rich4e.input.pamphlet new file mode 100644 index 0000000..3df315e --- /dev/null +++ b/src/axiom-website/CATS/rich4e.input.pamphlet @@ -0,0 +1,28917 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 261 supplied "optimal results". +\item 193 matching answers. +\item 39 cases where Axiom differs from Rubi +\item 27 cases where Axiom supplied 2 results. +\item 3 cases that Axiom failed to integrate. +\item 40 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4e.output +)spool rich4e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1347 +t0:=x^3*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 3 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1347 +r0:=1/6*(a+c*x^4)^(3/2)/c +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (2) --------------------- +--R 6c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (3) --------------------- +--R 6c +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1347 +t0:=x*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--R (1) x\|c x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1347 +r0:=1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c)+1/4*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R x \|c 2 +-+ | 4 +--R a atanh(-----------) + x \|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ---------------------------------------- +--R +-+ +--R 4\|c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2a\|a \|c x + a - a c x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|c \|c x + a + (- 4c x - 8a)\|c +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 2 \|- c \|c x + a - \|- c \|a +--R (4a\|a \|c x + a - 2a c x - 4a )atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 4 +---+ +--R 8\|- c \|a \|c x + a + (- 4c x - 8a)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 8 + +--S 9 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 4\|c +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - a\|- c atanh(-----------) + 2a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 4\|- c \|c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1347 +t0:=sqrt(a+c*x^4)/x +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))*sqrt(a)+1/2*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R +-+ \|c x + a | 4 +--R - \|a atanh(-----------) + \|c x + a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|a \|c x + a + c x + 2a | 4 +--R \|a log(------------------------------) + 2\|c x + a +--R 4 +--R x +--R [------------------------------------------------------, +--R 4 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|c x + a | 4 +--R - \|- a atan(-----------) + \|c x + a +--R +---+ +--R \|- a +--R ---------------------------------------] +--R 2 +--R Type: Union(List(Expression(Integer)),...) +--E 15 + +--S 16 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R \|a log(------------------------------) + 2\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R \|a atanh(-----------) - \|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 19 + +)clear all + +--S 20 of 1347 +t0:=sqrt(a+c*x^4)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*sqrt(c)-1/2*sqrt(a+c*x^4)/x^2 +--R +--R +--R 2 +-+ +--------+ +--R 2 +-+ x \|c | 4 +--R x \|c atanh(-----------) - \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|c \|c x + a - x \|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|c x + a - 2x \|a +--R , +--R +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|c x + a - \|a +--R (2x \|- c \|c x + a - 2x \|- c \|a )atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|c x + a - 2x \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 22 + +--S 23 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R \|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - \|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - \|c atanh(-----------) + 2\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 26 + +)clear all + +--S 27 of 1347 +t0:=sqrt(a+c*x^4)/x^5 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1347 +r0:=-1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a)-1/4*sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 \|c x + a +-+ | 4 +--R - c x atanh(-----------) - \|a \|c x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 4 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 - 2a\|c x + a + (c x + 2a)\|a +-+ | 4 +--R c x log(---------------------------------) - 2\|a \|c x + a +--R 4 +--R x +--R [-------------------------------------------------------------, +--R 4 +-+ +--R 8x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- a \|c x + a +---+ | 4 +--R - c x atan(-----------------) - \|- a \|c x + a +--R a +--R -------------------------------------------------] +--R 4 +---+ +--R 4x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 29 + +--S 30 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R c log(---------------------------------) + 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R c\|- a atanh(-----------) - c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1347 +t0:=sqrt(a+c*x^4)/x^7 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1347 +r0:=-1/6*(a+c*x^4)^(3/2)/(a*x^6) +--R +--R +--R +--------+ +--R 4 | 4 +--R (- c x - a)\|c x + a +--R (2) ----------------------- +--R 6 +--R 6a x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3 +--R (3c x + 7a c x + 4a )\|a \|c x + a - c x - 6a c x - 9a c x - 4a +--R ------------------------------------------------------------------------ +--R +--------+ +--R 10 2 6 | 4 10 2 6 +-+ +--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 36 + +--S 37 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 38 + +)clear all + +--S 39 of 1347 +t0:=sqrt(a+c*x^4)/x^9 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1347 +r0:=1/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-_ + 1/8*sqrt(a+c*x^4)/x^8-1/16*c*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 8 \|c x + a 4 +-+ | 4 +--R c x atanh(-----------) + (- c x - 2a)\|a \|c x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 8 +-+ +--R 16a x \|a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4 +--R c x log(-------------------------------) + (- 2c x - 4a)\|a \|c x + a +--R 4 +--R x +--R [------------------------------------------------------------------------, +--R 8 +-+ +--R 32a x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- a \|c x + a 4 +---+ | 4 +--R c x atan(-----------------) + (- c x - 2a)\|- a \|c x + a +--R a +--R ------------------------------------------------------------] +--R 8 +---+ +--R 16a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 41 + +--S 42 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 32a\|a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a +--R - c \|- a atanh(-----------) + c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 16a\|- a \|a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1347 +t0:=sqrt(a+c*x^4)/x^11 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1347 +r0:=-1/10*(a+c*x^4)^(3/2)/(a*x^10)+1/15*c*(a+c*x^4)^(3/2)/(a^2*x^6) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (2c x - a c x - 3a )\|c x + a +--R (2) --------------------------------- +--R 2 10 +--R 30a x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 10c x - 35a c x + 3a c x + 76a c x + 48a )\|a \|c x + a +--R + +--R 5 20 4 16 2 3 12 3 2 8 4 4 5 +--R 2c x + 25a c x + 40a c x - 35a c x - 100a c x - 48a +--R / +--R +--------+ +--R 2 2 18 3 14 4 10 | 4 +--R (30a c x + 360a c x + 480a x )\|c x + a +--R + +--R 2 2 18 3 14 4 10 +-+ +--R (- 150a c x - 600a c x - 480a x )\|a +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1347 +t0:=x^4*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1347 +--r0:=2/21*a*x*sqrt(a+c*x^4)/c+1/7*x^5*sqrt(a+c*x^4)+2/21*a^(9/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 52 + +--S 53 of 1347 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 1347 +--m0:=a0-r0 +--E 54 + +--S 55 of 1347 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 1347 +t0:=x^2*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 2 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1347 +--r0:=1/5*x^3*sqrt(a+c*x^4)+2/5*a^(7/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(3/4)*sqrt(a+c*x^4))-2/5*a^(7/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 57 + +--S 58 of 1347 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 1347 +--m0:=a0-r0 +--E 59 + +--S 60 of 1347 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 1347 +t0:=sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--R (1) \|c x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1347 +--r0:=1/3*x*sqrt(a+c*x^4)+2/3*a^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 62 + +--S 63 of 1347 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 1347 +--m0:=a0-r0 +--E 64 + +--S 65 of 1347 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 1347 +t0:=sqrt(a+c*x^4)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1347 +--r0:=-sqrt(a+c*x^4)/x-2*a^(3/4)*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)+2*a^(3/4)*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 67 + +--S 68 of 1347 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 1347 +--m0:=a0-r0 +--E 69 + +--S 70 of 1347 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 1347 +t0:=sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1347 +--r0:=-1/3*sqrt(a+c*x^4)/x^3-2/3*a^(1/4)*(-c)^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 72 + +--S 73 of 1347 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 1347 +--m0:=a0-r0 +--E 74 + +--S 75 of 1347 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 1347 +t0:=sqrt(a+c*x^4)/x^6 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1347 +--r0:=-1/5*sqrt(a+c*x^4)/x^5-2/5*c*sqrt(a+c*x^4)/(a*x)+_ +-- 2/5*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4))-2/5*(-c)^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4)) +--E 77 + +--S 78 of 1347 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 1347 +--m0:=a0-r0 +--E 79 + +--S 80 of 1347 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 1347 +t0:=x^7*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 11 7 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1347 +r0:=-1/10*a*(a+c*x^4)^(5/2)/c^2+1/14*(a+c*x^4)^(7/2)/c^2 +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (5c x + 8a c x + a c x - 2a )\|c x + a +--R (2) -------------------------------------------- +--R 2 +--R 70c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (5c x + 8a c x + a c x - 2a )\|c x + a +--R (3) -------------------------------------------- +--R 2 +--R 70c +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1347 +t0:=x^5*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 9 5 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1347 +r0:=1/12*x^6*(a+c*x^4)^(3/2)-1/32*a^3*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))/c^(3/2)+1/32*a^2*x^2*sqrt(a+c*x^4)/c+_ + 1/16*a*x^6*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 3 x \|c 2 10 6 2 2 +-+ | 4 +--R - 3a atanh(-----------) + (8c x + 14a c x + 3a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 96c\|c +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 8 4 4 5 +-+ | 4 3 3 12 4 2 8 +--R (18a c x + 96a c x + 96a )\|a \|c x + a - 3a c x - 54a c x +--R + +--R 5 4 6 +--R - 144a c x - 96a +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x +--R + +--R 5 2 +--R - 96a x +--R * +--R +--------+ +--R +-+ | 4 +--R \|c \|c x + a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x +--R + +--R 5 2 +--R 96a x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------+ +--R 3 8 2 4 2 +-+ +-+ | 4 +--R (576c x + 3072a c x + 3072a c)\|a \|c \|c x + a +--R + +--R 4 12 3 8 2 2 4 3 +-+ +--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|c +--R , +--R +--R +--------+ +--R 3 2 8 4 4 5 +-+ | 4 3 3 12 +--R (- 36a c x - 192a c x - 192a )\|a \|c x + a + 6a c x +--R + +--R 4 2 8 5 4 6 +--R 108a c x + 288a c x + 192a +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x +--R + +--R 5 2 +--R - 96a x +--R * +--R +--------+ +--R +---+ | 4 +--R \|- c \|c x + a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x +--R + +--R 5 2 +--R 96a x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------+ +--R 3 8 2 4 2 +---+ +-+ | 4 +--R (576c x + 3072a c x + 3072a c)\|- c \|a \|c x + a +--R + +--R 4 12 3 8 2 2 4 3 +---+ +--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 88 + +--S 89 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 3 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 3 x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 32c\|c +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 3 +---+ x \|c 3 +-+ \|- c \|c x + a - \|- c \|a +--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 32c\|- c \|c +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 92 + +)clear all + +--S 93 of 1347 +t0:=x^3*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 7 3 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1347 +r0:=1/10*(a+c*x^4)^(5/2)/c +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (c x + 2a c x + a )\|c x + a +--R (2) -------------------------------- +--R 10c +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (c x + 2a c x + a )\|c x + a +--R (3) -------------------------------- +--R 10c +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 97 + +)clear all + +--S 98 of 1347 +t0:=x*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 5 | 4 +--R (1) (c x + a x)\|c x + a +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1347 +r0:=1/8*x^2*(a+c*x^4)^(3/2)+3/16*a^2*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))/sqrt(c)+3/16*a*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 x \|c 6 2 +-+ | 4 +--R 3a atanh(-----------) + (2c x + 5a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R 16\|c +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((12a c x + 24a )\|a \|c x + a - 3a c x - 24a c x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +-+ | 4 +--R (- 2c x - 21a c x - 56a c x - 40a x )\|c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +-+ +-+ +--R (8c x + 44a c x + 76a c x + 40a x )\|a \|c +--R / +--R +--------+ +--R 4 +-+ +-+ | 4 2 8 4 2 +-+ +--R (64c x + 128a)\|a \|c \|c x + a + (- 16c x - 128a c x - 128a )\|c +--R , +--R +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((24a c x + 48a )\|a \|c x + a - 6a c x - 48a c x - 48a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +---+ | 4 +--R (- 2c x - 21a c x - 56a c x - 40a x )\|- c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +---+ +-+ +--R (8c x + 44a c x + 76a c x + 40a x )\|- c \|a +--R / +--R +--------+ +--R 4 +---+ +-+ | 4 +--R (64c x + 128a)\|- c \|a \|c x + a +--R + +--R 2 8 4 2 +---+ +--R (- 16c x - 128a c x - 128a )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 100 + +--S 101 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 2 (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R 3a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 2 x \|c +--R - 3a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 16\|c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a +--R - 3a \|- c atanh(-----------) + 6a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 16\|- c \|c +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 104 + +)clear all + +--S 105 of 1347 +t0:=(a+c*x^4)^(3/2)/x +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1347 +r0:=1/6*(a+c*x^4)^(3/2)-1/2*a^(3/2)*atanh(sqrt(a+c*x^4)/sqrt(a))+_ + 1/2*a*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R +-+ \|c x + a 4 | 4 +--R - 3a\|a atanh(-----------) + (c x + 4a)\|c x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|a \|c x + a + c x + 2a 4 | 4 +--R 3a\|a log(------------------------------) + (2c x + 8a)\|c x + a +--R 4 +--R x +--R [-------------------------------------------------------------------, +--R 12 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|c x + a 4 | 4 +--R - 3a\|- a atan(-----------) + (c x + 4a)\|c x + a +--R +---+ +--R \|- a +--R ----------------------------------------------------] +--R 6 +--R Type: Union(List(Expression(Integer)),...) +--E 107 + +--S 108 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R a\|a log(------------------------------) + 2a\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R a\|a atanh(-----------) - a\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 1347 +t0:=(a+c*x^4)^(3/2)/x^3 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1347 +r0:=-1/2*(a+c*x^4)^(3/2)/x^2+3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*_ + sqrt(c)+3/4*c*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 +-+ x \|c 4 | 4 +--R 3a x \|c atanh(-----------) + (c x - 2a)\|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ---------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a c x + 12a x )\|c \|c x + a + (- 9a c x - 12a x )\|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x +--R + +--R 3 +--R - 8a +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a +--R , +--R +--R +--------+ +--R 6 2 2 +---+ | 4 +--R (6a c x + 24a x )\|- c \|c x + a +--R + +--R 6 2 2 +---+ +-+ +--R (- 18a c x - 24a x )\|- c \|a +--R * +--R +--------+ +--R | 4 +-+ +--R \|c x + a - \|a +--R atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x +--R + +--R 3 +--R - 8a +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 114 + +--S 115 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R 3a\|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - 3a\|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 4 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - 3a\|c atanh(-----------) + 6a\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1347 +t0:=(a+c*x^4)^(3/2)/x^5 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1347 +r0:=-1/4*(a+c*x^4)^(3/2)/x^4-3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))*_ + sqrt(a)+3/4*c*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ \|c x + a 4 | 4 +--R - 3c x \|a atanh(-----------) + (2c x - a)\|c x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R 4 +-+ - 2\|a \|c x + a + c x + 2a 4 | 4 +--R 3c x \|a log(------------------------------) + (4c x - 2a)\|c x + a +--R 4 +--R x +--R [----------------------------------------------------------------------, +--R 4 +--R 8x +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ \|c x + a 4 | 4 +--R - 3c x \|- a atan(-----------) + (2c x - a)\|c x + a +--R +---+ +--R \|- a +--R -------------------------------------------------------] +--R 4 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 121 + +--S 122 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R 3c\|a log(------------------------------) + 6c\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R 3c\|a atanh(-----------) - 3c\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ---------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1347 +t0:=(a+c*x^4)^(3/2)/x^7 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1347 +r0:=-1/6*(a+c*x^4)^(3/2)/x^6+1/2*c^(3/2)*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))-1/2*c*sqrt(a+c*x^4)/x^2 +--R +--R +--R 2 +-+ +--------+ +--R 6 +-+ x \|c 4 | 4 +--R 3c x \|c atanh(-----------) + (- 4c x - a)\|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3c x + 12a c x )\|c \|c x + a + (- 9c x - 12a c x )\|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a +--R , +--R +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6c x + 24a c x )\|- c \|c x + a +--R + +--R 2 10 6 +---+ +-+ +--R (- 18c x - 24a c x )\|- c \|a +--R * +--R +--------+ +--R | 4 +-+ +--R \|c x + a - \|a +--R atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 128 + +--S 129 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R c\|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - c\|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - c\|c atanh(-----------) + 2c\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1347 +t0:=(a+c*x^4)^(3/2)/x^9 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1347 +r0:=-1/8*(a+c*x^4)^(3/2)/x^8-3/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/_ + sqrt(a)-3/16*c*sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 8 \|c x + a 4 +-+ | 4 +--R - 3c x atanh(-----------) + (- 5c x - 2a)\|a \|c x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 8 +-+ +--R 16x \|a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 - 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4 +--R 3c x log(---------------------------------) + (- 10c x - 4a)\|a \|c x + a +--R 4 +--R x +--R [---------------------------------------------------------------------------- +--R 8 +-+ +--R 32x \|a +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- a \|c x + a 4 +---+ | 4 +--R - 3c x atan(-----------------) + (- 5c x - 2a)\|- a \|c x + a +--R a +--R ----------------------------------------------------------------] +--R 8 +---+ +--R 16x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 135 + +--S 136 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2 - 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a +--R 3c log(---------------------------------) + 6c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 32\|a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a +--R 3c \|- a atanh(-----------) - 3c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 16\|- a \|a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 139 + +)clear all + +--S 140 of 1347 +t0:=(a+c*x^4)^(3/2)/x^11 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1347 +r0:=-1/10*(a+c*x^4)^(5/2)/(a*x^10) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (- c x - 2a c x - a )\|c x + a +--R (2) ---------------------------------- +--R 10 +--R 10a x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 5 20 +--R (5c x + 30a c x + 61a c x + 52a c x + 16a )\|a \|c x + a - c x +--R + +--R 4 16 2 3 12 3 2 8 4 4 5 +--R - 15a c x - 55a c x - 85a c x - 60a c x - 16a +--R / +--R +--------+ +--R 2 18 2 14 3 10 | 4 +--R (10a c x + 120a c x + 160a x )\|c x + a +--R + +--R 2 18 2 14 3 10 +-+ +--R (- 50a c x - 200a c x - 160a x )\|a +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1347 +t0:=(a+c*x^4)^(3/2)/x^13 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1347 +r0:=-1/12*(a+c*x^4)^(3/2)/x^12+1/32*c^3*atanh(sqrt(a+c*x^4)/sqrt(a))/_ + a^(3/2)-1/16*c*sqrt(a+c*x^4)/x^8-1/32*c^2*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 3 12 \|c x + a 2 8 4 2 +-+ | 4 +--R 3c x atanh(-----------) + (- 3c x - 14a c x - 8a )\|a \|c x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------------- +--R 12 +-+ +--R 96a x \|a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R | 4 4 +-+ +--R 3 12 2a\|c x + a + (c x + 2a)\|a +--R 3c x log(-------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 +--R (- 6c x - 28a c x - 16a )\|a \|c x + a +--R / +--R 12 +-+ +--R 192a x \|a +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 3 12 \|- a \|c x + a 2 8 4 2 +---+ | 4 +--R 3c x atan(-----------------) + (- 3c x - 14a c x - 8a )\|- a \|c x + a +--R a +--R ---------------------------------------------------------------------------] +--R 12 +---+ +--R 96a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 147 + +--S 148 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 3 2a\|c x + a + (c x + 2a)\|a 3 \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 64a\|a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 3 +---+ \|c x + a 3 +-+ \|- a \|c x + a +--R - c \|- a atanh(-----------) + c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 32a\|- a \|a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 151 + +)clear all + +--S 152 of 1347 +t0:=(a+c*x^4)^(3/2)/x^15 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 15 +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1347 +r0:=-1/14*(a+c*x^4)^(5/2)/(a*x^14)+1/35*c*(a+c*x^4)^(5/2)/(a^2*x^10) +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (2c x - a c x - 8a c x - 5a )\|c x + a +--R (2) -------------------------------------------- +--R 2 14 +--R 70a x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 24 5 20 2 4 16 3 3 12 4 2 8 +--R - 14c x - 105a c x - 112a c x + 467a c x + 1240a c x +--R + +--R 5 4 6 +--R 1072a c x + 320a +--R * +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a +--R + +--R 7 28 6 24 2 5 20 3 4 16 4 3 12 5 2 8 +--R 2c x + 49a c x + 175a c x - 21a c x - 973a c x - 1736a c x +--R + +--R 6 4 7 +--R - 1232a c x - 320a +--R / +--R +--------+ +--R 2 3 26 3 2 22 4 18 5 14 | 4 +--R (70a c x + 1680a c x + 5600a c x + 4480a x )\|c x + a +--R + +--R 2 3 26 3 2 22 4 18 5 14 +-+ +--R (- 490a c x - 3920a c x - 7840a c x - 4480a x )\|a +--R Type: Union(Expression(Integer),...) +--E 154 + +--S 155 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1347 +t0:=x^4*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 8 4 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1347 +--r0:=1/11*x^5*(a+c*x^4)^(3/2)+4/77*a^2*x*sqrt(a+c*x^4)/c+_ +-- 6/77*a*x^5*sqrt(a+c*x^4)+4/77*a^(13/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 158 + +--S 159 of 1347 +--a0:=integrate(t0,x) +--E 159 + +--S 160 of 1347 +--m0:=a0-r0 +--E 160 + +--S 161 of 1347 +--d0:=D(m0,x) +--E 161 + +)clear all + +--S 162 of 1347 +t0:=x^2*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 6 2 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1347 +--r0:=1/9*x^3*(a+c*x^4)^(3/2)+2/15*a*x^3*sqrt(a+c*x^4)+_ +-- 4/15*a^(11/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-4/15*a^(11/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 163 + +--S 164 of 1347 +--a0:=integrate(t0,x) +--E 164 + +--S 165 of 1347 +--m0:=a0-r0 +--E 165 + +--S 166 of 1347 +--d0:=D(m0,x) +--E 166 + +)clear all + +--S 167 of 1347 +t0:=(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1347 +--r0:=1/7*x*(a+c*x^4)^(3/2)+2/7*a*x*sqrt(a+c*x^4)+4/7*a^(9/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 168 + +--S 169 of 1347 +--a0:=integrate(t0,x) +--E 169 + +--S 170 of 1347 +--m0:=a0-r0 +--E 170 + +--S 171 of 1347 +--d0:=D(m0,x) +--E 171 + +)clear all + +--S 172 of 1347 +t0:=(a+c*x^4)^(3/2)/x^2 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1347 +--r0:=-(a+c*x^4)^(3/2)/x+6/5*c*x^3*sqrt(a+c*x^4)-12/5*a^(7/4)*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- sqrt(a+c*x^4)+12/5*a^(7/4)*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 173 + +--S 174 of 1347 +--a0:=integrate(t0,x) +--E 174 + +--S 175 of 1347 +--m0:=a0-r0 +--E 175 + +--S 176 of 1347 +--d0:=D(m0,x) +--E 176 + +)clear all + +--S 177 of 1347 +t0:=(a+c*x^4)^(3/2)/x^4 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1347 +--r0:=-1/3*(a+c*x^4)^(3/2)/x^3+2/3*c*x*sqrt(a+c*x^4)-_ +-- 4/3*a^(5/4)*(-c)^(3/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 178 + +--S 179 of 1347 +--a0:=integrate(t0,x) +--E 179 + +--S 180 of 1347 +--m0:=a0-r0 +--E 180 + +--S 181 of 1347 +--d0:=D(m0,x) +--E 181 + +)clear all + +--S 182 of 1347 +t0:=(a+c*x^4)^(3/2)/x^6 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1347 +--r0:=-1/5*(a+c*x^4)^(3/2)/x^5-6/5*c*sqrt(a+c*x^4)/x+_ +-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)-_ +-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_f(asin((-c)^(1/4)*x/_ +-- a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 183 + +--S 184 of 1347 +--a0:=integrate(t0,x) +--E 184 + +--S 185 of 1347 +--m0:=a0-r0 +--E 185 + +--S 186 of 1347 +--d0:=D(m0,x) +--E 186 + +)clear all + +--S 187 of 1347 +t0:=(a+c*x^4)^(3/2)/x^8 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1347 +--r0:=-1/7*(a+c*x^4)^(3/2)/x^7-2/7*c*sqrt(a+c*x^4)/x^3+_ +-- 4/7*a^(1/4)*(-c)^(7/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 188 + +--S 189 of 1347 +--a0:=integrate(t0,x) +--E 189 + +--S 190 of 1347 +--m0:=a0-r0 +--E 190 + +--S 191 of 1347 +--d0:=D(m0,x) +--E 191 + +)clear all + +--S 192 of 1347 +t0:=(1+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (1) (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1347 +--r0:=1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+_ +-- 2/7*x*sqrt(1+x^4) +--E 193 + +--S 194 of 1347 +--a0:=integrate(t0,x) +--E 194 + +--S 195 of 1347 +--m0:=a0-r0 +--E 195 + +--S 196 of 1347 +--d0:=D(m0,x) +--E 196 + +)clear all + +--S 197 of 1347 +t0:=(1-x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) (- x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1347 +--r0:=1/7*x*(1-x^4)^(3/2)+4/7*elliptic_f(asin(x),-1)+2/7*x*sqrt(1-x^4) +--E 198 + +--S 199 of 1347 +--a0:=integrate(t0,x) +--E 199 + +--S 200 of 1347 +--m0:=a0-r0 +--E 200 + +--S 201 of 1347 +--d0:=D(m0,x) +--E 201 + +)clear all + +--S 202 of 1347 +t0:=x^7*sqrt(5+3*x^4) +--R +--R +--R +-------+ +--R 7 | 4 +--R (1) x \|3x + 5 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1347 +r0:=-5/54*(5+3*x^4)^(3/2)+1/90*(5+3*x^4)^(5/2) +--R +--R +--R +-------+ +--R 8 4 | 4 +--R (27x + 15x - 50)\|3x + 5 +--R (2) ---------------------------- +--R 270 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 8 4 | 4 +--R (27x + 15x - 50)\|3x + 5 +--R (3) ---------------------------- +--R 270 +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 206 + +)clear all + +--S 207 of 1347 +t0:=x^3*sqrt(5+x^4) +--R +--R +--R +------+ +--R 3 | 4 +--R (1) x \|x + 5 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1347 +r0:=1/6*(5+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (x + 5)\|x + 5 +--R (2) ----------------- +--R 6 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 4 | 4 +--R (x + 5)\|x + 5 +--R (3) ----------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 211 + +)clear all + +--S 212 of 1347 +t0:=x*sqrt(3+2*x^4) +--R +--R +--R +-------+ +--R | 4 +--R (1) x\|2x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1347 +r0:=3/4*asinh(x^2*sqrt(2/3))/sqrt(2)+1/4*x^2*sqrt(3+2*x^4) +--R +--R +--R +-------+ 2 +-+ +--R 2 +-+ | 4 x \|2 +--R x \|2 \|2x + 3 + 3asinh(------) +--R +-+ +--R \|3 +--R (2) --------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 4 4 +--R (3\|3 \|2x + 3 - 3x - 9) +--R * +--R +-------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R +-+ | 4 +--R \|3 \|2x + 3 - 3 +--R + +--R +-------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- x - 3x )\|2 \|2x + 3 + (2x + 3x )\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 4 4 +-+ +--R 4\|2 \|3 \|2x + 3 + (- 4x - 12)\|2 +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ 2 +-+ +--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2 x \|2 +--R 3log(------------------------------------------------------) - 3asinh(------) +--R +-------+ +-+ +--R +-+ | 4 \|3 +--R \|3 \|2x + 3 - 3 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1347 +t0:=x*sqrt(-2+x^4) +--R +--R +--R +------+ +--R | 4 +--R (1) x\|x - 2 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1347 +r0:=-1/2*atanh(x^2/sqrt(-2+x^4))+1/4*x^2*sqrt(-2+x^4) +--R +--R +--R 2 +------+ +--R x 2 | 4 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 4 +--R \|x - 2 +--R (2) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 2 | 4 4 | 4 2 6 2 | 4 8 4 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x - 2x +--R ----------------------------------------------------------------------------- +--R +------+ +--R 2 | 4 4 +--R 4x \|x - 2 - 4x + 4 +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 4 +--R \|x - 2 +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 221 + +)clear all + +--S 222 of 1347 +t0:=(1+x^4)^(1/2) +--R +--R +--R +------+ +--R | 4 +--R (1) \|x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1347 +--r0:=-2/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/3*x*sqrt(1+x^4) +--E 223 + +--S 224 of 1347 +--a0:=integrate(t0,x) +--E 224 + +--S 225 of 1347 +--m0:=a0-r0 +--E 225 + +--S 226 of 1347 +--d0:=D(m0,x) +--E 226 + +)clear all + +--S 227 of 1347 +t0:=(1-x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (1) \|- x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1347 +--r0:=2/3*elliptic_f(asin(x),-1)+1/3*x*sqrt(1-x^4) +--E 228 + +--S 229 of 1347 +--a0:=integrate(t0,x) +--E 229 + +--S 230 of 1347 +--m0:=a0-r0 +--E 230 + +--S 231 of 1347 +--d0:=D(m0,x) +--E 231 + +)clear all + +--S 232 of 1347 +t0:=x^7/sqrt(a+c*x^4) +--R +--R +--R 7 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1347 +r0:=-1/3*a*sqrt(a+c*x^4)/c^2+1/6*x^4*sqrt(a+c*x^4)/c +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x - 2a)\|c x + a +--R (2) ---------------------- +--R 2 +--R 6c +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x - 2a)\|c x + a +--R (3) ---------------------- +--R 2 +--R 6c +--R Type: Union(Expression(Integer),...) +--E 234 + +--S 235 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 236 + +)clear all + +--S 237 of 1347 +t0:=x^5/sqrt(a+c*x^4) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1347 +r0:=-1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+1/4*x^2*sqrt(a+c*x^4)/c +--R +--R +--R 2 +-+ +--------+ +--R x \|c 2 +-+ | 4 +--R - a atanh(-----------) + x \|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------ +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2a\|a \|c x + a - a c x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8c\|a \|c \|c x + a + (- 4c x - 8a c)\|c +--R , +--R +--R +--------+ +--R +-+ | 4 4 2 +--R (- 4a\|a \|c x + a + 2a c x + 4a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 8c\|- c \|a \|c x + a + (- 4c x - 8a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 239 + +--S 240 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R a\|- c atanh(-----------) - 2a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 4c\|- c \|c +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1347 +t0:=x^3/sqrt(a+c*x^4) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1347 +r0:=1/2*sqrt(a+c*x^4)/c +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ----------- +--R 2c +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (3) ----------- +--R 2c +--R Type: Union(Expression(Integer),...) +--E 246 + +--S 247 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 248 + +)clear all + +--S 249 of 1347 +t0:=x/sqrt(a+c*x^4) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c) +--R +--R +--R 2 +-+ +--R x \|c +--R atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------ +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|c +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R ------------------------------------] +--R +---+ +--R \|- c +--R Type: Union(List(Expression(Integer)),...) +--E 251 + +--S 252 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - \|- c atanh(-----------) + 2\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- c \|c +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1347 +t0:=1/(x*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 4 +--R x\|c x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2a\|c x + a + (c x + 2a)\|a +---+ | 4 +--R log(---------------------------------) \|- a \|c x + a +--R 4 atan(-----------------) +--R x a +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|a 2\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 258 + +--S 259 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R \|- a atanh(-----------) - \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1347 +t0:=1/(x^3*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1347 +r0:=-1/2*sqrt(a+c*x^4)/(a*x^2) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) - ----------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R (3) ---------------------------- +--R +--------+ +--R 2 | 4 2 +-+ +--R 2a x \|c x + a - 2a x \|a +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1347 +t0:=1/(x^5*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1347 +r0:=1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-1/4*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 \|c x + a +-+ | 4 +--R c x atanh(-----------) - \|a \|c x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 4 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 2a\|c x + a + (c x + 2a)\|a +-+ | 4 +--R c x log(-------------------------------) - 2\|a \|c x + a +--R 4 +--R x +--R [-----------------------------------------------------------, +--R 4 +-+ +--R 8a x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- a \|c x + a +---+ | 4 +--R c x atan(-----------------) - \|- a \|c x + a +--R a +--R -----------------------------------------------] +--R 4 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R - c\|- a atanh(-----------) + c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 1347 +t0:=1/(x^7*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 7 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1347 +r0:=-1/6*sqrt(a+c*x^4)/(a*x^6)+1/3*c*sqrt(a+c*x^4)/(a^2*x^2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (2c x - a)\|c x + a +--R (2) ---------------------- +--R 2 6 +--R 6a x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3 +--R (- 6c x - 5a c x + 4a )\|a \|c x + a + 2c x + 9a c x + 3a c x - 4a +--R --------------------------------------------------------------------------- +--R +--------+ +--R 2 10 3 6 | 4 2 10 3 6 +-+ +--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1347 +t0:=x^6/sqrt(a+b*x^4) +--R +--R +--R 6 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1347 +--r0:=1/5*x^3*sqrt(a+b*x^4)/b+3/5*a^(7/4)*_ +-- elliptic_e(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4))-_ +-- 3/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4)) +--E 281 + +--S 282 of 1347 +--a0:=integrate(t0,x) +--E 282 + +--S 283 of 1347 +--m0:=a0-r0 +--E 283 + +--S 284 of 1347 +--d0:=D(m0,x) +--E 284 + +)clear all + +--S 285 of 1347 +t0:=x^4/sqrt(a+c*x^4) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1347 +--r0:=1/3*x*sqrt(a+c*x^4)/c+1/3*a^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 286 + +--S 287 of 1347 +--a0:=integrate(t0,x) +--E 287 + +--S 288 of 1347 +--m0:=a0-r0 +--E 288 + +--S 289 of 1347 +--d0:=D(m0,x) +--E 289 + +)clear all + +--S 290 of 1347 +t0:=x^2/sqrt(a+c*x^4) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1347 +--r0:=a^(3/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-a^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 291 + +--S 292 of 1347 +--a0:=integrate(t0,x) +--E 292 + +--S 293 of 1347 +--m0:=a0-r0 +--E 293 + +--S 294 of 1347 +--d0:=D(m0,x) +--E 294 + +)clear all + +--S 295 of 1347 +t0:=1/sqrt(a+c*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1347 +--r0:=a^(1/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 296 + +--S 297 of 1347 +--a0:=integrate(t0,x) +--E 297 + +--S 298 of 1347 +--m0:=a0-r0 +--E 298 + +--S 299 of 1347 +--d0:=D(m0,x) +--E 299 + +)clear all + +--S 300 of 1347 +t0:=1/(x^2*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1347 +--r0:=-sqrt(a+c*x^4)/(a*x)-(-c)^(1/4)*elliptic_e(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*_ +-- sqrt(a+c*x^4))+(-c)^(1/4)*elliptic_f(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4)) +--E 301 + +--S 302 of 1347 +--a0:=integrate(t0,x) +--E 302 + +--S 303 of 1347 +--m0:=a0-r0 +--E 303 + +--S 304 of 1347 +--d0:=D(m0,x) +--E 304 + +)clear all + +--S 305 of 1347 +t0:=1/(x^4*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1347 +--r0:=-1/3*sqrt(a+c*x^4)/(a*x^3)+1/3*(-c)^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(3/4)*sqrt(a+c*x^4)) +--E 306 + +--S 307 of 1347 +--a0:=integrate(t0,x) +--E 307 + +--S 308 of 1347 +--m0:=a0-r0 +--E 308 + +--S 309 of 1347 +--d0:=D(m0,x) +--E 309 + +)clear all + +--S 310 of 1347 +t0:=x^9/(a+c*x^4)^(3/2) +--R +--R +--R 9 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1347 +r0:=-3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(5/2)-_ + 1/2*x^6/(c*sqrt(a+c*x^4))+3/4*x^2*sqrt(a+c*x^4)/c^2 +--R +--R +--R +--------+ 2 +-+ +--R | 4 x \|c 6 2 +-+ +--R - 3a\|c x + a atanh(-----------) + (c x + 3a x )\|c +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 +-+ | 4 +--R 4c \|c \|c x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((9a c x + 12a )\|a \|c x + a - 3a c x - 15a c x - 12a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (- c x - 7a c x - 12a x )\|c \|c x + a +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (3c x + 13a c x + 12a x )\|a \|c +--R / +--R +--------+ +--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+ +--R (12c x + 16a c )\|a \|c \|c x + a + (- 4c x - 20a c x - 16a c )\|c +--R , +--R +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((- 18a c x - 24a )\|a \|c x + a + 6a c x + 30a c x + 24a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (- c x - 7a c x - 12a x )\|- c \|c x + a +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (3c x + 13a c x + 12a x )\|- c \|a +--R / +--R +--------+ +--R 3 4 2 +---+ +-+ | 4 +--R (12c x + 16a c )\|- c \|a \|c x + a +--R + +--R 4 8 3 4 2 2 +---+ +--R (- 4c x - 20a c x - 16a c )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 312 + +--S 313 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R 3a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R 3a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R 3a\|- c atanh(-----------) - 6a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1347 +t0:=x^7/(a+c*x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1347 +r0:=1/2*a/(c^2*sqrt(a+c*x^4))+1/2*sqrt(a+c*x^4)/c^2 +--R +--R +--R 4 +--R c x + 2a +--R (2) -------------- +--R +--------+ +--R 2 | 4 +--R 2c \|c x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R c x + 2a +--R (3) -------------- +--R +--------+ +--R 2 | 4 +--R 2c \|c x + a +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1347 +t0:=x^5/(a+c*x^4)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)-1/2*x^2/(c*sqrt(a+c*x^4)) +--R +--R +--R +--------+ 2 +-+ +--R | 4 x \|c 2 +-+ +--R \|c x + a atanh(-----------) - x \|c +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 4 +--R 2c\|c \|c x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R (\|a \|c x + a - c x - a) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R x \|c \|c x + a - x \|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 2c\|a \|c \|c x + a + (- 2c x - 2a c)\|c +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 \|- c \|c x + a - \|- c \|a +--R (2\|a \|c x + a - 2c x - 2a)atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 2 +---+ | 4 2 +---+ +-+ +--R x \|- c \|c x + a - x \|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 2c\|- c \|a \|c x + a + (- 2c x - 2a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 324 + +--S 325 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - \|- c atanh(-----------) + 2\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2c\|- c \|c +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 1347 +t0:=x^3/(a+c*x^4)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1347 +r0:=(-1/2)/(c*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (2) - ------------- +--R +--------+ +--R | 4 +--R 2c\|c x + a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +--------+ +--R | 4 +--R 2c\|c x + a +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1347 +t0:=x/(a+c*x^4)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1347 +r0:=1/2*x^2/(a*sqrt(a+c*x^4)) +--R +--R +--R 2 +--R x +--R (2) ------------- +--R +--------+ +--R | 4 +--R 2a\|c x + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 | 4 2 +-+ +--R - x \|c x + a + x \|a +--R (3) --------------------------------- +--R +--------+ +--R +-+ | 4 4 2 +--R 2a\|a \|c x + a - 2a c x - 2a +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1347 +t0:=1/(x*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R 5 | 4 +--R (c x + a x)\|c x + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)+1/2/(a*sqrt(a+c*x^4)) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 \|c x + a +-+ +--R - \|c x + a atanh(-----------) + \|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 4 +--R 2a\|a \|c x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 4 4 +-+ +--R | 4 - 2a\|c x + a + (c x + 2a)\|a +-+ +--R \|c x + a log(---------------------------------) + 2\|a +--R 4 +--R x +--R [---------------------------------------------------------, +--R +--------+ +--R +-+ | 4 +--R 4a\|a \|c x + a +--R +--------+ +--R +--------+ +---+ | 4 +--R | 4 \|- a \|c x + a +---+ +--R - \|c x + a atan(-----------------) + \|- a +--R a +--R ---------------------------------------------] +--R +--------+ +--R +---+ | 4 +--R 2a\|- a \|c x + a +--R Type: Union(List(Expression(Integer)),...) +--E 341 + +--S 342 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R \|- a atanh(-----------) - \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1347 +t0:=1/(x^3*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 7 3 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1347 +r0:=1/2/(a*x^2*sqrt(a+c*x^4))-sqrt(a+c*x^4)/(a^2*x^2) +--R +--R +--R 4 +--R - 2c x - a +--R (2) ---------------- +--R +--------+ +--R 2 2 | 4 +--R 2a x \|c x + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 +-+ | 4 2 8 4 2 +--R (4c x + 2a)\|a \|c x + a - 2c x - 5a c x - 2a +--R (3) ------------------------------------------------------ +--R +--------+ +--R 2 6 3 2 | 4 2 6 3 2 +-+ +--R (2a c x + 4a x )\|c x + a + (- 4a c x - 4a x )\|a +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1347 +t0:=1/(x^5*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 9 5 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1347 +r0:=3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(5/2)+1/2/(a*x^4*sqrt(a+c*x^4))-_ + 3/4*sqrt(a+c*x^4)/(a^2*x^4) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 \|c x + a 4 +-+ +--R 3c x \|c x + a atanh(-----------) + (- 3c x - a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 4 +-+ | 4 +--R 4a x \|a \|c x + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 4 4 +-+ +--R 4 | 4 2a\|c x + a + (c x + 2a)\|a 4 +-+ +--R 3c x \|c x + a log(-------------------------------) + (- 6c x - 2a)\|a +--R 4 +--R x +--R [-------------------------------------------------------------------------, +--R +--------+ +--R 2 4 +-+ | 4 +--R 8a x \|a \|c x + a +--R +--------+ +--R +--------+ +---+ | 4 +--R 4 | 4 \|- a \|c x + a 4 +---+ +--R 3c x \|c x + a atan(-----------------) + (- 3c x - a)\|- a +--R a +--R -------------------------------------------------------------] +--R +--------+ +--R 2 4 +---+ | 4 +--R 4a x \|- a \|c x + a +--R Type: Union(List(Expression(Integer)),...) +--E 353 + +--S 354 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R 3c log(-------------------------------) - 6c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) --------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R - 3c\|- a atanh(-----------) + 3c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1347 +t0:=x^6/(a+c*x^4)^(3/2) +--R +--R +--R 6 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1347 +--r0:=-1/2*x^3/(c*sqrt(a+c*x^4))-3/2*a^(3/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(7/4)*sqrt(a+c*x^4))+3/2*a^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(7/4)*sqrt(a+c*x^4)) +--E 359 + +--S 360 of 1347 +--a0:=integrate(t0,x) +--E 360 + +--S 361 of 1347 +--m0:=a0-r0 +--E 361 + +--S 362 of 1347 +--d0:=D(m0,x) +--E 362 + +)clear all + +--S 363 of 1347 +t0:=x^4/(a+c*x^4)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1347 +--r0:=-1/2*x/(c*sqrt(a+c*x^4))-1/2*a^(1/4)*elliptic_f(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 364 + +--S 365 of 1347 +--a0:=integrate(t0,x) +--E 365 + +--S 366 of 1347 +--m0:=a0-r0 +--E 366 + +--S 367 of 1347 +--d0:=D(m0,x) +--E 367 + +)clear all + +--S 368 of 1347 +t0:=x^2/(a+c*x^4)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1347 +--r0:=1/2*x^3/(a*sqrt(a+c*x^4))-1/2*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- (a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4))+1/2*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4)) +--E 369 + +--S 370 of 1347 +--a0:=integrate(t0,x) +--E 370 + +--S 371 of 1347 +--m0:=a0-r0 +--E 371 + +--S 372 of 1347 +--d0:=D(m0,x) +--E 372 + +)clear all + +--S 373 of 1347 +t0:=1/(a+c*x^4)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1347 +--r0:=1/2*x/(a*sqrt(a+c*x^4))+1/2*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(3/4)*(-c)^(1/4)*sqrt(a+c*x^4)) +--E 374 + +--S 375 of 1347 +--a0:=integrate(t0,x) +--E 375 + +--S 376 of 1347 +--m0:=a0-r0 +--E 376 + +--S 377 of 1347 +--d0:=D(m0,x) +--E 377 + +)clear all + +--S 378 of 1347 +t0:=1/(x^2*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 6 2 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1347 +--r0:=1/2/(a*x*sqrt(a+c*x^4))-3/2*sqrt(a+c*x^4)/(a^2*x)-3/2*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- (a^(5/4)*sqrt(a+c*x^4))+3/2*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(5/4)*sqrt(a+c*x^4)) +--E 379 + +--S 380 of 1347 +--a0:=integrate(t0,x) +--E 380 + +--S 381 of 1347 +--m0:=a0-r0 +--E 381 + +--S 382 of 1347 +--d0:=D(m0,x) +--E 382 + +)clear all + +--S 383 of 1347 +t0:=1/(a+b*x^4)^(5/2) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R 2 8 4 2 | 4 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1347 +--r0:=1/6*x/(a*(a+b*x^4)^(3/2))+5/12*x/(a^2*sqrt(a+b*x^4))+_ +-- 5/12*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^4)) +--E 384 + +--S 385 of 1347 +--a0:=integrate(t0,x) +--E 385 + +--S 386 of 1347 +--m0:=a0-r0 +--E 386 + +--S 387 of 1347 +--d0:=D(m0,x) +--E 387 + +)clear all + +--S 388 of 1347 +t0:=x^7/sqrt(16-x^4) +--R +--R +--R 7 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1347 +r0:=-16/3*sqrt(16-x^4)-1/6*x^4*sqrt(16-x^4) +--R +--R +--R +---------+ +--R 4 | 4 +--R (- x - 32)\|- x + 16 +--R (2) ----------------------- +--R 6 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 4 +--R (- x - 32)\|- x + 16 +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1347 +t0:=x^6/sqrt(16-x^4) +--R +--R +--R 6 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1347 +--r0:=96/5*elliptic_e(asin(1/2*x),-1)-96/5*elliptic_f(asin(1/2*x),-1)-_ +-- 1/5*x^3*sqrt(16-x^4) +--E 394 + +--S 395 of 1347 +--a0:=integrate(t0,x) +--E 395 + +--S 396 of 1347 +--m0:=a0-r0 +--E 396 + +--S 397 of 1347 +--d0:=D(m0,x) +--E 397 + +)clear all + +--S 398 of 1347 +t0:=x^5/sqrt(16-x^4) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1347 +r0:=4*asin(1/4*x^2)-1/4*x^2*sqrt(16-x^4) +--R +--R +--R +---------+ 2 +--R 2 | 4 x +--R - x \|- x + 16 + 16asin(--) +--R 4 +--R (2) ----------------------------- +--R 4 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 4 +--R | 4 4 \|- x + 16 - 4 +--R (- 256\|- x + 16 - 32x + 1024)atan(----------------) +--R 2 +--R x +--R + +--R +---------+ +--R 6 2 | 4 6 2 +--R (- x + 32x )\|- x + 16 + 8x - 128x +--R / +--R +---------+ +--R | 4 4 +--R 32\|- x + 16 + 4x - 128 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 4 2 +--R \|- x + 16 - 4 x +--R (4) - 8atan(----------------) - 4asin(--) +--R 2 4 +--R x +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1347 +t0:=x^4/sqrt(16-x^4) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1347 +--r0:=8/3*elliptic_f(asin(1/2*x),-1)-1/3*x*sqrt(16-x^4) +--E 404 + +--S 405 of 1347 +--a0:=integrate(t0,x) +--E 405 + +--S 406 of 1347 +--m0:=a0-r0 +--E 406 + +--S 407 of 1347 +--d0:=D(m0,x) +--E 407 + +)clear all + +--S 408 of 1347 +t0:=x^3/sqrt(16-x^4) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1347 +r0:=-1/2*sqrt(16-x^4) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (2) - ------------ +--R 2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (3) - ------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1347 +t0:=x^2/sqrt(16-x^4) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1347 +--r0:=2*elliptic_e(asin(1/2*x),-1)-2*elliptic_f(asin(1/2*x),-1) +--E 414 + +--S 415 of 1347 +--a0:=integrate(t0,x) +--E 415 + +--S 416 of 1347 +--m0:=a0-r0 +--E 416 + +--S 417 of 1347 +--d0:=D(m0,x) +--E 417 + +)clear all + +--S 418 of 1347 +t0:=x/sqrt(16-x^4) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1347 +r0:=1/2*asin(1/4*x^2) +--R +--R +--R 2 +--R x +--R asin(--) +--R 4 +--R (2) -------- +--R 2 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 - 4 +--R (3) - atan(----------------) +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 4 2 +--R \|- x + 16 - 4 x +--R - 2atan(----------------) - asin(--) +--R 2 4 +--R x +--R (4) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1347 +t0:=1/sqrt(16-x^4) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1347 +--r0:=1/2*elliptic_f(asin(1/2*x),-1) +--E 424 + +--S 425 of 1347 +--a0:=integrate(t0,x) +--E 425 + +--S 426 of 1347 +--m0:=a0-r0 +--E 426 + +--S 427 of 1347 +--d0:=D(m0,x) +--E 427 + +)clear all + +--S 428 of 1347 +t0:=1/(x*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 4 +--R x\|- x + 16 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1347 +r0:=-1/8*atanh(1/4*sqrt(16-x^4)) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R atanh(------------) +--R 4 +--R (2) - ------------------- +--R 8 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +---------+ +--R | 4 | 4 +--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4) +--R (3) ----------------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R +---------+ +---------+ | 4 +--R | 4 | 4 \|- x + 16 +--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4) + 2atanh(------------) +--R 4 +--R (4) ---------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1347 +t0:=1/(x^2*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1347 +--r0:=-1/8*elliptic_e(asin(1/2*x),-1)+1/8*elliptic_f(asin(1/2*x),-1)-_ +-- 1/16*sqrt(16-x^4)/x +--E 434 + +--S 435 of 1347 +--a0:=integrate(t0,x) +--E 435 + +--S 436 of 1347 +--m0:=a0-r0 +--E 436 + +--S 437 of 1347 +--d0:=D(m0,x) +--E 437 + +)clear all + +--S 438 of 1347 +t0:=1/(x^3*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1347 +r0:=-1/32*sqrt(16-x^4)/x^2 +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (2) - ------------ +--R 2 +--R 32x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 4 +--R 4\|- x + 16 + x - 16 +--R (3) ------------------------ +--R +---------+ +--R 2 | 4 2 +--R 32x \|- x + 16 - 128x +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1347 +t0:=1/(x^4*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1347 +--r0:=1/96*elliptic_f(asin(1/2*x),-1)-1/48*sqrt(16-x^4)/x^3 +--E 444 + +--S 445 of 1347 +--a0:=integrate(t0,x) +--E 445 + +--S 446 of 1347 +--m0:=a0-r0 +--E 446 + +--S 447 of 1347 +--d0:=D(m0,x) +--E 447 + +)clear all + +--S 448 of 1347 +t0:=x^7/(1+x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1347 +r0:=1/2/sqrt(1+x^4)+1/2*sqrt(1+x^4) +--R +--R +--R 4 +--R x + 2 +--R (2) ---------- +--R +------+ +--R | 4 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R x + 2 +--R (3) ---------- +--R +------+ +--R | 4 +--R 2\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1347 +t0:=1/(1+x^4)^(3/2) +--R +--R +--R 1 +--R (1) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1347 +--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/2*x/sqrt(1+x^4) +--E 454 + +--S 455 of 1347 +--a0:=integrate(t0,x) +--E 455 + +--S 456 of 1347 +--m0:=a0-r0 +--E 456 + +--S 457 of 1347 +--d0:=D(m0,x) +--E 457 + +)clear all + +--S 458 of 1347 +t0:=1/(1+x^4)^(5/2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +------+ +--R 8 4 | 4 +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1347 +--r0:=1/6*x/(1+x^4)^(3/2)-5/12*(-1)^(3/4)*_ +-- elliptic_f(asin((-1)^(1/4)*x),-1)+5/12*x/sqrt(1+x^4) +--E 459 + +--S 460 of 1347 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 1347 +--m0:=a0-r0 +--E 461 + +--S 462 of 1347 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 1347 +t0:=1/(1-x^4)^(3/2) +--R +--R +--R 1 +--R (1) - ------------------- +--R +--------+ +--R 4 | 4 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1347 +--r0:=1/2*elliptic_f(asin(x),-1)+1/2*x/sqrt(1-x^4) +--E 464 + +--S 465 of 1347 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 1347 +--m0:=a0-r0 +--E 466 + +--S 467 of 1347 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 1347 +t0:=1/(1-x^4)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R 8 4 | 4 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1347 +--r0:=1/6*x/(1-x^4)^(3/2)+5/12*elliptic_f(asin(x),-1)+5/12*x/sqrt(1-x^4) +--E 469 + +--S 470 of 1347 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 1347 +--m0:=a0-r0 +--E 471 + +--S 472 of 1347 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 1347 +t0:=x/sqrt(-4+x^4) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 4 +--R \|x - 4 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1347 +r0:=1/2*atanh(x^2/sqrt(-4+x^4)) +--R +--R +--R 2 +--R x +--R atanh(---------) +--R +------+ +--R | 4 +--R \|x - 4 +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 2 +--R log(\|x - 4 - x ) +--R (3) - ------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R - log(\|x - 4 - x ) - atanh(---------) +--R +------+ +--R | 4 +--R \|x - 4 +--R (4) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1347 +t0:=x/sqrt(4+x^4) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 4 +--R \|x + 4 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1347 +r0:=1/2*asinh(1/2*x^2) +--R +--R +--R 2 +--R x +--R asinh(--) +--R 2 +--R (2) --------- +--R 2 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 2 +--R log(\|x + 4 - x ) +--R (3) - ------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R - log(\|x + 4 - x ) - asinh(--) +--R 2 +--R (4) --------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1347 +t0:=1/(x*sqrt(-1+x^4)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 4 +--R x\|x - 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1347 +r0:=1/2*atan(sqrt(-1+x^4)) +--R +--R +--R +------+ +--R | 4 +--R atan(\|x - 1 ) +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 +--R atan(\|x - 1 ) +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1347 +t0:=x^(7/2)*(a+c*x^4) +--R +--R +--R 7 3 +-+ +--R (1) (c x + a x )\|x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1347 +r0:=2/9*a*x^(9/2)+2/17*c*x^(17/2) +--R +--R +--R 8 4 +-+ +--R (18c x + 34a x )\|x +--R (2) --------------------- +--R 153 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 8 4 +-+ +--R (18c x + 34a x )\|x +--R (3) --------------------- +--R 153 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1347 +t0:=x^(5/2)*(a+c*x^4) +--R +--R +--R 6 2 +-+ +--R (1) (c x + a x )\|x +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1347 +r0:=2/7*a*x^(7/2)+2/15*c*x^(15/2) +--R +--R +--R 7 3 +-+ +--R (14c x + 30a x )\|x +--R (2) --------------------- +--R 105 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 7 3 +-+ +--R (14c x + 30a x )\|x +--R (3) --------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1347 +t0:=x^(3/2)*(a+c*x^4) +--R +--R +--R 5 +-+ +--R (1) (c x + a x)\|x +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1347 +r0:=2/5*a*x^(5/2)+2/13*c*x^(13/2) +--R +--R +--R 6 2 +-+ +--R (10c x + 26a x )\|x +--R (2) --------------------- +--R 65 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 2 +-+ +--R (10c x + 26a x )\|x +--R (3) --------------------- +--R 65 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1347 +t0:=(a+c*x^4)*sqrt(x) +--R +--R +--R 4 +-+ +--R (1) (c x + a)\|x +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1347 +r0:=2/3*a*x^(3/2)+2/11*c*x^(11/2) +--R +--R +--R 5 +-+ +--R (6c x + 22a x)\|x +--R (2) ------------------- +--R 33 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ +--R (6c x + 22a x)\|x +--R (3) ------------------- +--R 33 +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1347 +t0:=(a+c*x^4)/sqrt(x) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1347 +r0:=2/9*c*x^(9/2)+2*a*sqrt(x) +--R +--R +--R 4 +-+ +--R (2c x + 18a)\|x +--R (2) ----------------- +--R 9 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R (2c x + 18a)\|x +--R (3) ----------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1347 +t0:=(a+c*x^4)/x^(3/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1347 +r0:=2/7*c*x^(7/2)-2*a/sqrt(x) +--R +--R +--R 4 +--R 2c x - 14a +--R (2) ----------- +--R +-+ +--R 7\|x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 2c x - 14a +--R (3) ----------- +--R +-+ +--R 7\|x +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1347 +t0:=(a+c*x^4)/x^(5/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1347 +r0:=-2/3*a/x^(3/2)+2/5*c*x^(5/2) +--R +--R +--R 4 +--R 6c x - 10a +--R (2) ----------- +--R +-+ +--R 15x\|x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 6c x - 10a +--R (3) ----------- +--R +-+ +--R 15x\|x +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1347 +t0:=(a+c*x^4)/x^(7/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1347 +r0:=-2/5*a/x^(5/2)+2/3*c*x^(3/2) +--R +--R +--R 4 +--R 10c x - 6a +--R (2) ----------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 10c x - 6a +--R (3) ----------- +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 527 + +)clear all + +--S 528 of 1347 +t0:=x^(7/2)*(a+c*x^4)^2 +--R +--R +--R 2 11 7 2 3 +-+ +--R (1) (c x + 2a c x + a x )\|x +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1347 +r0:=2/9*a^2*x^(9/2)+4/17*a*c*x^(17/2)+2/25*c^2*x^(25/2) +--R +--R +--R 2 12 8 2 4 +-+ +--R (306c x + 900a c x + 850a x )\|x +--R (2) ------------------------------------ +--R 3825 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 12 8 2 4 +-+ +--R (306c x + 900a c x + 850a x )\|x +--R (3) ------------------------------------ +--R 3825 +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 532 + +)clear all + +--S 533 of 1347 +t0:=x^(5/2)*(a+c*x^4)^2 +--R +--R +--R 2 10 6 2 2 +-+ +--R (1) (c x + 2a c x + a x )\|x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1347 +r0:=2/7*a^2*x^(7/2)+4/15*a*c*x^(15/2)+2/23*c^2*x^(23/2) +--R +--R +--R 2 11 7 2 3 +-+ +--R (210c x + 644a c x + 690a x )\|x +--R (2) ------------------------------------ +--R 2415 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 11 7 2 3 +-+ +--R (210c x + 644a c x + 690a x )\|x +--R (3) ------------------------------------ +--R 2415 +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1347 +t0:=x^(3/2)*(a+c*x^4)^2 +--R +--R +--R 2 9 5 2 +-+ +--R (1) (c x + 2a c x + a x)\|x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1347 +r0:=2/5*a^2*x^(5/2)+4/13*a*c*x^(13/2)+2/21*c^2*x^(21/2) +--R +--R +--R 2 10 6 2 2 +-+ +--R (130c x + 420a c x + 546a x )\|x +--R (2) ------------------------------------ +--R 1365 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 10 6 2 2 +-+ +--R (130c x + 420a c x + 546a x )\|x +--R (3) ------------------------------------ +--R 1365 +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1347 +t0:=(a+c*x^4)^2*sqrt(x) +--R +--R +--R 2 8 4 2 +-+ +--R (1) (c x + 2a c x + a )\|x +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1347 +r0:=2/3*a^2*x^(3/2)+4/11*a*c*x^(11/2)+2/19*c^2*x^(19/2) +--R +--R +--R 2 9 5 2 +-+ +--R (66c x + 228a c x + 418a x)\|x +--R (2) --------------------------------- +--R 627 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 9 5 2 +-+ +--R (66c x + 228a c x + 418a x)\|x +--R (3) --------------------------------- +--R 627 +--R Type: Union(Expression(Integer),...) +--E 545 + +--S 546 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 547 + +)clear all + +--S 548 of 1347 +t0:=(a+c*x^4)^2/sqrt(x) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1347 +r0:=4/9*a*c*x^(9/2)+2/17*c^2*x^(17/2)+2*a^2*sqrt(x) +--R +--R +--R 2 8 4 2 +-+ +--R (18c x + 68a c x + 306a )\|x +--R (2) ------------------------------- +--R 153 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +-+ +--R (18c x + 68a c x + 306a )\|x +--R (3) ------------------------------- +--R 153 +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1347 +t0:=(a+c*x^4)^2/x^(3/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1347 +r0:=4/7*a*c*x^(7/2)+2/15*c^2*x^(15/2)-2*a^2/sqrt(x) +--R +--R +--R 2 8 4 2 +--R 14c x + 60a c x - 210a +--R (2) ------------------------- +--R +-+ +--R 105\|x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 14c x + 60a c x - 210a +--R (3) ------------------------- +--R +-+ +--R 105\|x +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1347 +t0:=(a+c*x^4)^2/x^(5/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1347 +r0:=-2/3*a^2/x^(3/2)+4/5*a*c*x^(5/2)+2/13*c^2*x^(13/2) +--R +--R +--R 2 8 4 2 +--R 30c x + 156a c x - 130a +--R (2) -------------------------- +--R +-+ +--R 195x\|x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 30c x + 156a c x - 130a +--R (3) -------------------------- +--R +-+ +--R 195x\|x +--R Type: Union(Expression(Integer),...) +--E 560 + +--S 561 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 562 + +)clear all + +--S 563 of 1347 +t0:=(a+c*x^4)^2/x^(7/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1347 +r0:=-2/5*a^2/x^(5/2)+4/3*a*c*x^(3/2)+2/11*c^2*x^(11/2) +--R +--R +--R 2 8 4 2 +--R 30c x + 220a c x - 66a +--R (2) ------------------------- +--R 2 +-+ +--R 165x \|x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 30c x + 220a c x - 66a +--R (3) ------------------------- +--R 2 +-+ +--R 165x \|x +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1347 +t0:=x^(7/2)*(a+c*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a x )\|x +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1347 +r0:=2/9*a^3*x^(9/2)+6/17*a^2*c*x^(17/2)+6/25*a*c^2*x^(25/2)+2/33*c^3*x^(33/2) +--R +--R +--R 3 16 2 12 2 8 3 4 +-+ +--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x +--R (2) ------------------------------------------------------- +--R 42075 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 16 2 12 2 8 3 4 +-+ +--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x +--R (3) ------------------------------------------------------- +--R 42075 +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1347 +t0:=x^(5/2)*(a+c*x^4)^3 +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (1) (c x + 3a c x + 3a c x + a x )\|x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1347 +r0:=2/7*a^3*x^(7/2)+2/5*a^2*c*x^(15/2)+6/23*a*c^2*x^(23/2)+2/31*c^3*x^(31/2) +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x +--R (2) ----------------------------------------------------- +--R 24955 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x +--R (3) ----------------------------------------------------- +--R 24955 +--R Type: Union(Expression(Integer),...) +--E 575 + +--S 576 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 577 + +)clear all + +--S 578 of 1347 +t0:=x^(3/2)*(a+c*x^4)^3 +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a x)\|x +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1347 +r0:=2/5*a^3*x^(5/2)+6/13*a^2*c*x^(13/2)+2/7*a*c^2*x^(21/2)+2/29*c^3*x^(29/2) +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x +--R (2) ---------------------------------------------------- +--R 13195 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x +--R (3) ---------------------------------------------------- +--R 13195 +--R Type: Union(Expression(Integer),...) +--E 580 + +--S 581 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1347 +t0:=(a+c*x^4)^3*sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a )\|x +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1347 +r0:=2/3*a^3*x^(3/2)+6/11*a^2*c*x^(11/2)+6/19*a*c^2*x^(19/2)+2/27*c^3*x^(27/2) +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x +--R (2) -------------------------------------------------- +--R 5643 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x +--R (3) -------------------------------------------------- +--R 5643 +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1347 +t0:=(a+c*x^4)^3/sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1347 +r0:=2/3*a^2*c*x^(9/2)+6/17*a*c^2*x^(17/2)+2/25*c^3*x^(25/2)+2*a^3*sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (102c x + 450a c x + 850a c x + 2550a )\|x +--R (2) ----------------------------------------------- +--R 1275 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (102c x + 450a c x + 850a c x + 2550a )\|x +--R (3) ----------------------------------------------- +--R 1275 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1347 +t0:=(a+c*x^4)^3/x^(3/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1347 +r0:=6/7*a^2*c*x^(7/2)+2/5*a*c^2*x^(15/2)+2/23*c^3*x^(23/2)-2*a^3/sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 70c x + 322a c x + 690a c x - 1610a +--R (2) ---------------------------------------- +--R +-+ +--R 805\|x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 70c x + 322a c x + 690a c x - 1610a +--R (3) ---------------------------------------- +--R +-+ +--R 805\|x +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1347 +t0:=(a+c*x^4)^3/x^(5/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1347 +r0:=-2/3*a^3/x^(3/2)+6/5*a^2*c*x^(5/2)+6/13*a*c^2*x^(13/2)+2/21*c^3*x^(21/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R 130c x + 630a c x + 1638a c x - 910a +--R (2) ----------------------------------------- +--R +-+ +--R 1365x\|x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 130c x + 630a c x + 1638a c x - 910a +--R (3) ----------------------------------------- +--R +-+ +--R 1365x\|x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1347 +t0:=(a+c*x^4)^3/x^(7/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1347 +r0:=-2/5*a^3/x^(5/2)+2*a^2*c*x^(3/2)+6/11*a*c^2*x^(11/2)+2/19*c^3*x^(19/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R 110c x + 570a c x + 2090a c x - 418a +--R (2) ----------------------------------------- +--R 2 +-+ +--R 1045x \|x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 110c x + 570a c x + 2090a c x - 418a +--R (3) ----------------------------------------- +--R 2 +-+ +--R 1045x \|x +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1347 +t0:=x^(9/2)/(a+c*x^4) +--R +--R +--R 4 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1347 +r0:=2/3*x^(3/2)/c+1/2*(-a)^(3/8)*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/c^(11/8)-1/2*(-a)^(3/8)*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/c^(11/8)+1/2*(-a)^(3/8)*_ + atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/(c^(11/8)*_ + sqrt(2))-1/2*(-a)^(3/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/(c^(11/8)*sqrt(2))-1/4*(-a)^(3/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(11/8)*sqrt(2))+1/4*(-a)^(3/8)*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 3\|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3\|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a +--R - 6\|2 \|- a atanh(--------) - 6\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x +--R - 6\|- a atan(---------------------) + 6\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+3 +-+ +--R 8x\|2 \|c \|x +--R / +--R +-+8+-+3 +--R 12c\|2 \|c +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 3 +--R | a +--R 3c |- -------- +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a +-+ 4 | a +--R 3c\|2 |- -------- log(a\|x + 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a +-+ 4 | a +--R - 3c\|2 |- -------- log(a\|x - 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +--R | 3 +--R | a +--R 3c |- -------- +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R +-+ | a \| 65536c +--R 6c\|2 |- -------- atan(------------------) +--R 8| 11 +-+ +--R \| 65536c a\|x +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a \| 65536c +--R - 6c |- -------- atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x - 64c |- -------- +--R 8| 11 +--R \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a \| 65536c +-+ +-+ +--R - 6c |- -------- atan(------------------------------ + 2x\|2 \|x +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x + 64c |- -------- +--R 8| 11 +--R \| 65536c +--R / +--R +-+ +--R 3c\|2 +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 3 +--R | a 8+-+3 +--R 4c |- -------- \|c +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a 8+-+3 +-+ 4 | a +--R 4c\|2 |- -------- \|c log(a\|x + 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a 8+-+3 +-+ 4 | a +--R - 4c\|2 |- -------- \|c log(a\|x - 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +--R | 3 +--R | a 8+-+3 +--R 4c |- -------- \|c +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a +--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x +--R 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R +-+ | a 8+-+3 \| 65536c +--R 8c\|2 |- -------- \|c atan(------------------) +--R 8| 11 +-+ +--R \| 65536c a\|x +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a 8+-+3 \| 65536c +--R - 8c |- -------- \|c atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x - 64c |- -------- +--R 8| 11 +--R \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a 8+-+3 \| 65536c +--R - 8c |- -------- \|c atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x + 64c |- -------- +--R 8| 11 +--R \| 65536c +--R / +--R +-+8+-+3 +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1347 +t0:=x^(7/2)/(a+c*x^4) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1347 +r0:=-1/2*(-a)^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)-_ + 1/2*(-a)^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)+_ + 1/2*(-a)^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + (c^(9/8)*sqrt(2))-1/2*(-a)^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/(c^(9/8)*sqrt(2))+1/4*(-a)^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/(c^(9/8)*_ + sqrt(2))+2*sqrt(x)/c +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a +--R - 2\|2 \|- a atanh(--------) - 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x +--R - 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ +--R 8\|2 \|c \|x +--R / +--R +-+8+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +---------+2 +--R | a +-+ | a +-+ 2 | a +--R - c |- ------- log(4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a +-+ | a +--R - c\|2 |- ------- log(\|x + 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a +-+ | a +--R c\|2 |- ------- log(\|x - 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +---------+2 +--R | a +-+ | a +-+ 2 | a +--R c |- ------- log(- 4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R +-+ | a \| 65536c +--R 2c\|2 |- ------- atan(--------------) +--R 8| 9 +-+ +--R \| 65536c \|x +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a \| 65536c +--R 2c |- ------- atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x - 4c |- ------- +--R 8| 9 +--R \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a \| 65536c +-+ +-+ +--R 2c |- ------- atan(------------------------- + 2\|2 \|x +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x + 4c |- ------- +--R 8| 9 +--R \| 65536c +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression(Integer),...) +--E 615 + +--S 616 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +---------+ +---------+ +---------+2 +--R | a 8+-+ +-+ | a +-+ 2 | a +--R - 4c |- ------- \|c log(4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a 8+-+ +-+ | a +--R - 4c\|2 |- ------- \|c log(\|x + 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a 8+-+ +-+ | a +--R 4c\|2 |- ------- \|c log(\|x - 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +---------+2 +--R | a 8+-+ +-+ | a +-+ 2 | a +--R 4c |- ------- \|c log(- 4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a +--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x +--R 2\|- a atan(---------------------) + 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R +-+ | a 8+-+ \| 65536c +--R 8c\|2 |- ------- \|c atan(--------------) +--R 8| 9 +-+ +--R \| 65536c \|x +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a 8+-+ \| 65536c +--R 8c |- ------- \|c atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x - 4c |- ------- +--R 8| 9 +--R \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a 8+-+ \| 65536c +--R 8c |- ------- \|c atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x + 4c |- ------- +--R 8| 9 +--R \| 65536c +--R / +--R +-+8+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +)clear all + +--S 618 of 1347 +t0:=x^(5/2)/(a+c*x^4) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1347 +r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*_ + c^(7/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(1/8)*c^(7/8)*sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*_ + sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+8+-+7 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+ | 1 +-+ 6 | 1 +--R \|2 |- --------- log(\|x + 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+ | 1 +-+ 6 | 1 +--R - \|2 |- --------- log(\|x - 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R | 1 \| 65536a c +--R 2 |- --------- atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x - 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R | 1 \| 65536a c +--R 2 |- --------- atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x + 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 620 + +--S 621 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+ | 1 8+-+7 +--R 4\|- a |- --------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x + 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x - 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+ | 1 8+-+7 +--R 4\|- a |- --------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 65536a c +--R 8\|- a |- --------- \|c atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x - 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 65536a c +--R 8\|- a |- --------- \|c atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x + 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+8+---+8+-+7 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 7 9 2 6 5 3 5 | 1 +--R (- 12288a c x + 55296a c x - 6144a c x) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+4 +--R 5 8 2 4 4 3 3 | 1 +--R (1600a c x - 2944a c x + 64a c ) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 7 2 2 3 | 1 2 10 6 2 2 +--R (- 168a c x + 120a c x ) |- --------- - c x + 13a c x - 4a x +--R 8| 7 +--R \| 65536a c +--R / +--R +-----------+6 +--R 8 10 2 7 6 3 6 2 | 1 +--R (32768a c x - 8192a c x - 40960a c x ) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+4 +--R 6 9 2 5 5 3 4 | 1 +--R (- 3328a c x - 2048a c x + 1280a c x) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+2 +--R 4 8 2 3 4 3 2 | 1 3 11 2 7 +--R (272a c x + 256a c x - 16a c ) |- --------- + 4c x - 10a c x +--R 8| 7 +--R \| 65536a c +--R + +--R 2 3 +--R - 14a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1347 +t0:=x^(3/2)/(a+c*x^4) +--R +--R +--R +-+ +--R x\|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1347 +r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_ + c^(5/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(5/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*_ + sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+3 8+-+5 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+ | 1 +-+ 2 3 | 1 +--R - \|2 |- --------- log(\|x + 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+ | 1 +-+ 2 3 | 1 +--R \|2 |- --------- log(\|x - 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R | 1 \| 65536a c +--R - 2 |- --------- atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x - 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R | 1 \| 65536a c +--R - 2 |- --------- atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x + 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 625 + +--S 626 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+3 | 1 8+-+5 +--R 4\|- a |- --------- \|c +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x + 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x - 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+3 | 1 8+-+5 +--R 4\|- a |- --------- \|c +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 65536a c +--R - 8\|- a |- --------- \|c atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x - 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 65536a c +--R - 8\|- a |- --------- \|c atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x + 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-+8+---+3 8+-+5 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 2 6 10 3 5 6 4 4 2 | 1 +--R (8192a c x - 106496a c x + 32768a c x ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 4 7 3 3 3 | 1 +--R (- 5376a c x + 3840a c x ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 8 2 2 4 3 | 1 2 9 5 2 +--R (- 200a c x + 368a c x - 8a c) |- --------- - 6c x + 27a c x - 3a x +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-----------+6 +--R 3 6 8 4 5 4 5 4 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 5 9 3 4 5 4 3 | 1 +--R (6656a c x + 4096a c x - 2560a c x) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+2 +--R 4 10 2 3 6 3 2 2 | 1 3 11 2 7 +--R (256a c x - 64a c x - 320a c x ) |- --------- + 8c x - 20a c x +--R 8| 3 5 +--R \| 65536a c +--R + +--R 2 3 +--R - 28a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1347 +t0:=sqrt(x)/(a+c*x^4) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1347 +r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))+_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8)*_ + sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_ + c^(3/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(3/8)*sqrt(2))+1/4*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(5/8)*c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+5 8+-+3 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 +-+ 2 | 1 +--R - \|2 |- --------- log(\|x + 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 +-+ 2 | 1 +--R \|2 |- --------- log(\|x - 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R | 1 \| 65536a c +--R 2 |- --------- atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x - 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R | 1 \| 65536a c +--R 2 |- --------- atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x + 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 630 + +--S 631 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+5 | 1 8+-+3 +--R 4\|- a |- --------- \|c +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x + 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x - 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+5 | 1 8+-+3 +--R 4\|- a |- --------- \|c +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 65536a c +--R 8\|- a |- --------- \|c atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x - 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 65536a c +--R 8\|- a |- --------- \|c atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x + 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-+8+---+5 8+-+3 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 4 4 7 5 3 3 | 1 +--R (- 172032a c x + 122880a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 4 10 3 3 6 4 2 2 | 1 +--R (1024a c x - 13312a c x + 4096a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 9 2 2 5 3 | 1 2 8 4 2 +--R (192a c x - 864a c x + 96a c x) |- --------- + 25c x - 46a c x + a +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-----------+6 +--R 4 5 10 5 4 6 6 3 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+4 +--R 3 4 9 4 3 5 5 2 | 1 +--R (13312a c x + 8192a c x - 5120a c x) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+2 +--R 2 3 8 3 2 4 4 | 1 3 11 2 7 +--R (1088a c x + 1024a c x - 64a c) |- --------- - 16c x + 40a c x +--R 8| 5 3 +--R \| 65536a c +--R + +--R 2 3 +--R 56a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 632 + +)clear all + +--S 633 of 1347 +t0:=1/((a+c*x^4)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R 4 +-+ +--R (c x + a)\|x +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1347 +r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))+_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(1/8)*sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(7/8)*c^(1/8)*sqrt(2))+1/4*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*_ + c^(1/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+7 8+-+ +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +----------+2 +--R | 1 +-+ | 1 +-+ 2 | 1 +--R |- -------- log(4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 8| 7 +--R \| 65536a c \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 +-+ | 1 +--R \|2 |- -------- log(\|x + 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 +-+ | 1 +--R - \|2 |- -------- log(\|x - 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +----------+2 +--R | 1 +-+ | 1 +-+ 2 | 1 +--R - |- -------- log(- 4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 8| 7 +--R \| 65536a c \| 65536a c \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R | 1 \| 65536a c +--R - 2 |- -------- atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x - 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R | 1 \| 65536a c +--R - 2 |- -------- atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x + 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 635 + +--S 636 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +----------+ +--R 8+---+7 | 1 8+-+ +--R 4\|- a |- -------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +----------+ +----------+2 +--R +-+ | 1 +-+ 2 | 1 +--R log(4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+8+---+7 | 1 8+-+ +-+ | 1 +--R 4\|2 \|- a |- -------- \|c log(\|x + 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+8+---+7 | 1 8+-+ +-+ | 1 +--R - 4\|2 \|- a |- -------- \|c log(\|x - 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +----------+ +--R 8+---+7 | 1 8+-+ +--R 4\|- a |- -------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +----------+ +----------+2 +--R +-+ | 1 +-+ 2 | 1 +--R log(- 4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 65536a c +--R - 8\|- a |- -------- \|c atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x - 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 65536a c +--R - 8\|- a |- -------- \|c atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x + 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+8+---+7 8+-+ +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1347 sometimes Axiom computes a zero +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+6 +--R 6 8 7 4 8+---+2 | 1 +--R (- 34816a c x + 2048a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 9 5 5 8+---+2 | 1 +--R (1664a c x - 640a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 10 3 6 8+---+2 | 1 +--R (- 64a c x + 80a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 11 7 8+---+2 +--R (2c x - 7a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 7 7 3 4+---+8+---+2 | 1 +--R (- 69632a c x + 4096a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 8 5 4 4+---+8+---+2 | 1 +--R (3328a c x - 1280a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 9 3 5 4+---+8+---+2 | 1 +--R (- 128a c x + 160a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 10 6 4+---+8+---+2 +--R (4c x - 14a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 6 7 2 8+---+6 +--R (69632a c x - 4096a x )\|- a +--R + +--R 6 6 7 2 4+---+2 8+---+2 +--R (- 34816a c x + 2048a x )\|- a \|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 7 5 3 8+---+6 +--R (- 3328a c x + 1280a x )\|- a +--R + +--R 4 7 5 3 4+---+2 8+---+2 +--R (1664a c x - 640a x )\|- a \|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 8 3 4 8+---+6 +--R (128a c x - 160a x )\|- a +--R + +--R 2 8 3 4 4+---+2 8+---+2 +--R (- 64a c x + 80a x )\|- a \|- a +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 8+---+6 9 5 4+---+2 8+---+2 +--R (- 4c x + 14a x )\|- a + (2c x - 7a x )\|- a \|- a +--R * +--R 8+-+6 +--R \|c +--R + +--R +----------+6 +--R 6 7 7 3 8+---+4 | 1 +--R (- 34816a c x + 2048a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 8 5 4 8+---+4 | 1 +--R (1664a c x - 640a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 9 3 5 8+---+4 | 1 +--R (- 64a c x + 80a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 10 6 8+---+4 +--R (2c x - 7a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 6 7 2 4+---+8+---+4 | 1 +--R (- 69632a c x + 4096a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 7 5 3 4+---+8+---+4 | 1 +--R (3328a c x - 1280a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 8 3 4 4+---+8+---+4 | 1 +--R (- 128a c x + 160a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 4+---+8+---+4 +--R (4c x - 14a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 5 7 4+---+2 8+---+4 6 2 9 +--R (- 34816a c x + 2048a x)\|- a \|- a + 102400a c x +--R + +--R 7 5 +--R - 118784a c x +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 6 5 2 4+---+2 8+---+4 4 2 10 5 6 +--R (1664a c x - 640a x )\|- a \|- a - 3072a c x + 10496a c x +--R + +--R 6 2 +--R - 256a x +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 7 3 3 4+---+2 8+---+4 2 2 11 3 7 +--R (- 64a c x + 80a x )\|- a \|- a + 64a c x - 704a c x +--R + +--R 4 3 +--R 96a x +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 8 4 4+---+2 8+---+4 8 2 4 +--R (2c x - 7a x )\|- a \|- a + 38a c x - 16a x +--R * +--R 8+-+4 +--R \|c +--R + +--R +----------+6 +--R 5 2 10 6 6 8+---+6 | 1 +--R (51200a c x - 59392a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 3 2 11 4 7 5 3 8+---+6 | 1 +--R (- 1536a c x + 5248a c x - 128a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 12 2 8 3 4 8+---+6 | 1 +--R (32a c x - 352a c x + 48a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 8+---+6 +--R (19c x - 8a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R 5 2 9 6 5 4+---+8+---+6 6 2 9 +--R (102400a c x - 118784a c x )\|- a \|- a - 34816a c x +--R + +--R 7 5 8 +--R - 32768a c x + 2048a x +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 3 2 10 4 6 5 2 4+---+8+---+6 +--R (- 3072a c x + 10496a c x - 256a x )\|- a \|- a +--R + +--R 4 2 10 5 6 6 2 +--R 1664a c x + 1024a c x - 640a x +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 2 7 3 3 4+---+8+---+6 2 2 11 +--R (64a c x - 704a c x + 96a x )\|- a \|- a - 64a c x +--R + +--R 3 7 4 3 +--R 16a c x + 80a x +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 8 4 4+---+8+---+6 2 12 8 2 4 +--R (38c x - 16a x )\|- a \|- a + 2c x - 5a c x - 7a x +--R * +--R 4+-+ +--R \|c +--R + +--R 5 2 8 6 4 4+---+2 8+---+6 +--R (51200a c x - 59392a c x )\|- a \|- a +--R + +--R 6 2 8 7 4 8+---+2 +--R (- 69632a c x + 4096a c x )\|- a +--R + +--R 6 2 8 7 4 8 4+---+ +--R (34816a c x + 32768a c x - 2048a )\|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 3 2 9 4 5 5 4+---+2 8+---+6 +--R (- 1536a c x + 5248a c x - 128a x)\|- a \|- a +--R + +--R 4 2 9 5 5 8+---+2 +--R (3328a c x - 1280a c x )\|- a +--R + +--R 4 2 9 5 5 6 4+---+ +--R (- 1664a c x - 1024a c x + 640a x)\|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 10 2 6 3 2 4+---+2 8+---+6 +--R (32a c x - 352a c x + 48a x )\|- a \|- a +--R + +--R 2 2 10 3 6 8+---+2 +--R (- 128a c x + 160a c x )\|- a +--R + +--R 2 2 10 3 6 4 2 4+---+ +--R (64a c x - 16a c x - 80a x )\|- a +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 7 3 4+---+2 8+---+6 2 11 7 8+---+2 +--R (19c x - 8a x )\|- a \|- a + (4c x - 14a c x )\|- a +--R + +--R 2 11 7 2 3 4+---+ +--R (- 2c x + 5a c x + 7a x )\|- a +--R * +--R 8+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 2 9 7 5 | 1 +--R (34816a c x - 2048a c x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 10 5 6 | 1 +--R (- 1664a c x + 640a c x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 11 3 7 | 1 2 12 8 +--R (64a c x - 80a c x ) |- -------- - 2c x + 7a c x +--R 8| 7 +--R \| 65536a c +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 2 8 7 4 4+---+ | 1 +--R (69632a c x - 4096a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 9 5 5 4+---+ | 1 +--R (- 3328a c x + 1280a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 10 3 6 4+---+ | 1 +--R (128a c x - 160a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 7 4+---+ +--R (- 4c x + 14a c x )\|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 2 7 7 3 8+---+4 6 2 7 7 3 4+---+2 +--R ((69632a c x - 4096a c x )\|- a + (34816a c x - 2048a c x )\|- a ) +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 2 8 5 4 8+---+4 +--R (- 3328a c x + 1280a c x )\|- a +--R + +--R 4 2 8 5 4 4+---+2 +--R (- 1664a c x + 640a c x )\|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 2 9 3 5 8+---+4 2 2 9 3 5 4+---+2 +--R ((128a c x - 160a c x )\|- a + (64a c x - 80a c x )\|- a ) +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 10 6 8+---+4 2 10 6 4+---+2 +--R (- 4c x + 14a c x )\|- a + (- 2c x + 7a c x )\|- a +--R / +--R +----------+6 +--R 7 2 9 8 5 9 | 1 +--R (278528a c x + 262144a c x - 16384a x) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 5 2 10 6 6 7 2 | 1 +--R (- 13312a c x - 8192a c x + 5120a x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 3 2 11 4 7 5 3 | 1 2 12 +--R (512a c x - 128a c x - 640a x ) |- -------- - 16a c x +--R 8| 7 +--R \| 65536a c +--R + +--R 2 8 3 4 +--R 40a c x + 56a x +--R * +--R 8+-+4 +--R \|c +--R + +--R +----------+6 +--R 6 2 10 7 6 8 2 8+---+6 | 1 +--R (139264a c x + 131072a c x - 8192a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 11 5 7 6 3 8+---+6 | 1 +--R (- 6656a c x - 4096a c x + 2560a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 12 3 8 4 4 8+---+6 | 1 +--R (256a c x - 64a c x - 320a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 13 9 2 5 8+---+6 +--R (- 8c x + 20a c x + 28a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R 6 2 9 7 5 8 4+---+8+---+6 +--R (278528a c x + 262144a c x - 16384a x)\|- a \|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 2 10 5 6 6 2 4+---+8+---+6 +--R (- 13312a c x - 8192a c x + 5120a x )\|- a \|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 11 3 7 4 3 4+---+8+---+6 | 1 +--R (512a c x - 128a c x - 640a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 12 8 2 4 4+---+8+---+6 +--R (- 16c x + 40a c x + 56a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R +----------+6 +--R 6 2 8 7 4 8 4+---+2 8+---+6 | 1 +--R (139264a c x + 131072a c x - 8192a )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 9 5 5 6 4+---+2 8+---+6 | 1 +--R (- 6656a c x - 4096a c x + 2560a x)\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 10 3 6 4 2 4+---+2 8+---+6 | 1 +--R (256a c x - 64a c x - 320a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 7 2 3 4+---+2 8+---+6 +--R (- 8c x + 20a c x + 28a x )\|- a \|- a +--R * +--R 8+-+2 +--R \|c +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 637 + +)clear all + +--S 638 of 1347 +t0:=1/(x^(3/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ---------------- +--R 5 +-+ +--R (c x + a x)\|x +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1347 +r0:=1/2*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_ + 1/2*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_ + 1/2*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*sqrt(2))+1/2*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+1/4*c^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(9/8)*sqrt(2))-1/4*c^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_ + sqrt(2))+(-2)/(a*sqrt(x)) +--R +--R +--R (2) +--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+ +-+ \|c \|x 8+-+ +-+ \|2 \|c \|x + \|- a +--R 2\|2 \|c \|x atanh(--------) - 2\|c \|x atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+ +-+ \|2 \|c \|x - \|- a +-+8+-+ +-+ \|c \|x +--R - 2\|c \|x atan(---------------------) - 2\|2 \|c \|x atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+ +--R - 8\|2 \|- a +--R / +--R +-+8+---+ +-+ +--R 4a\|2 \|- a \|x +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +---------+ +--R | c +-+ +--R a |- ------- \|x +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c +-+ +-+ 8 | c +--R - a\|2 |- ------- \|x log(c\|x + 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c +-+ +-+ 8 | c +--R a\|2 |- ------- \|x log(c\|x - 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +--R | c +-+ +--R a |- ------- \|x +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c +-+ \| 65536a +--R - 2a |- ------- \|x atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x - 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c +-+ \| 65536a +-+ +--R - 2a |- ------- \|x atan(-------------------------------- - 2\|2 +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x + 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R / +--R +-+ +-+ +--R a\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 640 + +--S 641 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +---------+ +--R | c 8+---+ +--R 4a |- ------- \|- a +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c 8+---+ +-+ 8 | c +--R - 4a\|2 |- ------- \|- a log(c\|x + 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c 8+---+ +-+ 8 | c +--R 4a\|2 |- ------- \|- a log(c\|x - 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +--R | c 8+---+ +--R 4a |- ------- \|- a +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R 8+-+ +-+ +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+8+-+ \|c \|x +--R \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 \|c atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R 8+-+ \|2 \|c \|x + \|- a 8+-+ \|2 \|c \|x - \|- a +--R 2\|c atan(---------------------) + 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+8+-+ \|c \|x +--R 2\|2 \|c atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c 8+---+ \| 65536a +--R - 8a |- ------- \|- a atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x - 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c 8+---+ \| 65536a +--R - 8a |- ------- \|- a atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x + 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R / +--R +-+8+---+ +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +---------+6 +--R 7 2 9 8 5 9 | c +--R (12288a c x - 55296a c x + 6144a x) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+4 +--R 5 2 8 6 4 7 | c +--R (- 1600a c x + 2944a c x - 64a ) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+2 +--R 3 2 7 4 3 | c 3 10 2 6 2 2 +--R (168a c x - 120a c x ) |- ------- + c x - 13a c x + 4a c x +--R 8| 9 +--R \| 65536a +--R / +--R +---------+6 +--R 8 2 10 9 6 10 2 | c +--R (32768a c x - 8192a c x - 40960a x ) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+4 +--R 6 2 9 7 5 8 | c +--R (- 3328a c x - 2048a c x + 1280a x) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+2 +--R 4 2 8 5 4 6 | c 3 11 2 2 7 +--R (272a c x + 256a c x - 16a ) |- ------- + 4a c x - 10a c x +--R 8| 9 +--R \| 65536a +--R + +--R 3 3 +--R - 14a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1347 +t0:=1/(x^(5/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------------- +--R 6 2 +-+ +--R (c x + a x )\|x +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1347 +r0:=(-2/3)/(a*x^(3/2))-1/2*c^(3/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(11/8)-1/2*c^(3/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(11/8)-1/2*c^(3/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*sqrt(2))+1/2*c^(3/8)*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(11/8)*sqrt(2))-1/4*c^(3/8)*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_ + sqrt(2))+1/4*c^(3/8)*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 3x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+3 +-+ \|c \|x 8+-+3 +-+ \|2 \|c \|x + \|- a +--R 6x\|2 \|c \|x atanh(--------) - 6x \|c \|x atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+3 +-+ \|2 \|c \|x - \|- a +-+8+-+3 +-+ \|c \|x +--R - 6x \|c \|x atan(---------------------) + 6x\|2 \|c \|x atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+3 +--R - 8\|2 \|- a +--R / +--R +-+8+---+3 +-+ +--R 12a x\|2 \|- a \|x +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 3 +--R | c +-+ +--R 3a x |- -------- \|x +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c +-+ 2 +-+ 7 | c +--R 3a x\|2 |- -------- \|x log(c \|x + 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c +-+ 2 +-+ 7 | c +--R - 3a x\|2 |- -------- \|x log(c \|x - 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R | c +-+ +--R 3a x |- -------- \|x +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c +-+ \| 65536a +--R 6a x |- -------- \|x atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x - 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c +-+ \| 65536a +-+ +--R 6a x |- -------- \|x atan(--------------------------------- - 2\|2 +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x + 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R / +--R +-+ +-+ +--R 3a x\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 645 + +--S 646 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 3 +--R | c 8+---+3 +--R 4a |- -------- \|- a +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c 8+---+3 2 +-+ 7 | c +--R 4a\|2 |- -------- \|- a log(c \|x + 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c 8+---+3 2 +-+ 7 | c +--R - 4a\|2 |- -------- \|- a log(c \|x - 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R | c 8+---+3 +--R 4a |- -------- \|- a +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+3 \|c \|x 8+-+3 \|2 \|c \|x + \|- a +--R - 2\|2 \|c atanh(--------) + 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+3 \|2 \|c \|x - \|- a +-+8+-+3 \|c \|x +--R 2\|c atan(---------------------) - 2\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c 8+---+3 \| 65536a +--R 8a |- -------- \|- a atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x - 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c 8+---+3 \| 65536a +--R 8a |- -------- \|- a atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x + 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R / +--R +-+8+---+3 +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +----------+6 +--R | 3 +--R 8 3 10 9 2 6 10 2 | c +--R (- 8192a c x + 106496a c x - 32768a c x ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+4 +--R | 3 +--R 6 3 7 7 2 3 | c +--R (5376a c x - 3840a c x ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+2 +--R | 3 +--R 3 4 8 4 3 4 5 2 | c 5 9 4 5 2 3 +--R (200a c x - 368a c x + 8a c ) |- -------- + 6c x - 27a c x + 3a c x +--R 8| 11 +--R \| 65536a +--R / +--R +----------+6 +--R | 3 +--R 10 2 8 11 4 12 | c +--R (139264a c x + 131072a c x - 8192a ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+4 +--R | 3 +--R 7 3 9 8 2 5 9 | c +--R (6656a c x + 4096a c x - 2560a c x) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+2 +--R | 3 +--R 4 4 10 5 3 6 6 2 2 | c 5 11 2 4 7 +--R (256a c x - 64a c x - 320a c x ) |- -------- + 8a c x - 20a c x +--R 8| 11 +--R \| 65536a +--R + +--R 3 3 3 +--R - 28a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 647 + +)clear all + +--S 648 of 1347 +t0:=1/(x^(7/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------------- +--R 7 3 +-+ +--R (c x + a x )\|x +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1347 +r0:=(-2/5)/(a*x^(5/2))+1/2*c^(5/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(13/8)-1/2*c^(5/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(13/8)+1/2*c^(5/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*sqrt(2))-1/2*c^(5/8)*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_ + 1/4*c^(5/8)*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2))+1/4*c^(5/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 5x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 +-+8+-+5 +-+ \|c \|x +--R 10x \|2 \|c \|x atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8+-+5 +-+ \|2 \|c \|x + \|- a +--R 10x \|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8+-+5 +-+ \|2 \|c \|x - \|- a +--R 10x \|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 +-+8+-+5 +-+ \|c \|x +-+8+---+5 +--R - 10x \|2 \|c \|x atan(--------) - 8\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R 2 +-+8+---+5 +-+ +--R 20a x \|2 \|- a \|x +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 5 +--R 2 | c +-+ +--R 5a x |- -------- \|x +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R 2 +-+ | c +-+ 2 +-+ 5 | c +--R 5a x \|2 |- -------- \|x log(c \|x + 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R 2 +-+ | c +-+ 2 +-+ 5 | c +--R - 5a x \|2 |- -------- \|x log(c \|x - 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 5 +--R 2 | c +-+ +--R 5a x |- -------- \|x +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R 2 | c +-+ \| 65536a +--R - 10a x |- -------- \|x atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x - 64a |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R 2 | c +-+ \| 65536a +-+ +--R - 10a x |- -------- \|x atan(------------------------------- - 2\|2 +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x + 64a |- -------- +--R 8| 13 +--R \| 65536a +--R / +--R 2 +-+ +-+ +--R 5a x \|2 \|x +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 5 +--R | c 8+---+5 +--R 4a |- -------- \|- a +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R +-+ | c 8+---+5 2 +-+ 5 | c +--R 4a\|2 |- -------- \|- a log(c \|x + 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R +-+ | c 8+---+5 2 +-+ 5 | c +--R - 4a\|2 |- -------- \|- a log(c \|x - 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 5 +--R | c 8+---+5 +--R 4a |- -------- \|- a +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+5 \|c \|x 8+-+5 \|2 \|c \|x + \|- a +--R - 2\|2 \|c atanh(--------) - 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+5 \|2 \|c \|x - \|- a +-+8+-+5 \|c \|x +--R - 2\|c atan(---------------------) + 2\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R | c 8+---+5 \| 65536a +--R - 8a |- -------- \|- a atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x - 64a |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R | c 8+---+5 \| 65536a +--R - 8a |- -------- \|- a atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x + 64a |- -------- +--R 8| 13 +--R \| 65536a +--R / +--R +-+8+---+5 +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +----------+6 +--R | 5 +--R 10 2 7 11 3 | c +--R (172032a c x - 122880a c x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+4 +--R | 5 +--R 6 4 10 7 3 6 8 2 2 | c +--R (- 1024a c x + 13312a c x - 4096a c x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+2 +--R | 5 +--R 3 5 9 4 4 5 5 3 | c 6 8 5 4 +--R (- 192a c x + 864a c x - 96a c x) |- -------- - 25c x + 46a c x +--R 8| 13 +--R \| 65536a +--R + +--R 2 4 +--R - a c +--R / +--R +----------+6 +--R | 5 +--R 11 2 10 12 6 13 2 | c +--R (131072a c x - 32768a c x - 163840a x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+4 +--R | 5 +--R 8 3 9 9 2 5 10 | c +--R (13312a c x + 8192a c x - 5120a c x) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+2 +--R | 5 +--R 5 4 8 6 3 4 7 2 | c 6 11 2 5 7 +--R (1088a c x + 1024a c x - 64a c ) |- -------- - 16a c x + 40a c x +--R 8| 13 +--R \| 65536a +--R + +--R 3 4 3 +--R 56a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1347 +t0:=x^(13/2)/(a+c*x^4)^2 +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1347 +r0:=-1/4*x^(7/2)/(c*(a+c*x^4))+7/16*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atan(1-c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8)*sqrt(2))+_ + 7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(1/8)*c^(15/8)*sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*_ + c^(15/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 14c x - 14a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (14c x + 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (14c x + 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 3 +-+8+---+8+-+7 +-+ +--R (14c x + 14a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+8+-+7 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (28c x + 28a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (28c x + 28a c)\|2 |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x + 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 28c x - 28a c)\|2 |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x - 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 28c x - 28a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (56c x + 56a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x - 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (56c x + 56a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x + 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 3 +-+ +-+ +--R - x \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 224c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 224c\|2 \|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x + 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 224c\|2 \|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x - 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 224c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 14atan(---------------------) - 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 448c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x - 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 448c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x + 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R / +--R +-+8+---+8+-+7 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 9 2 12 5 3 11 +--R (- 22548578304a c x + 101468602368a c x - 11274289152a c x) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 9 8 2 8 4 3 7 | 1 +--R (45875200a c x - 84410368a c x + 1835008a c ) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 7 2 4 3 | 1 2 10 6 +--R (- 75264a c x + 53760a c x ) |- ------------------ - 7c x + 91a c x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 2 2 +--R - 28a x +--R / +--R 15 10 2 14 6 3 13 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 11 9 2 10 5 3 9 +--R (- 109051904a c x - 67108864a c x + 41943040a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 7 8 2 6 4 3 5 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R 32c x - 80a c x - 112a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1347 +t0:=x^(11/2)/(a+c*x^4)^2 +--R +--R +--R 5 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1347 +r0:=-1/4*x^(5/2)/(c*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(13/8))-5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(13/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(3/8)*c^(13/8)*sqrt(2))+5/16*_ + atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_ + c^(13/8)*sqrt(2))-5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2))+_ + 5/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 10c x - 10a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (10c x + 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (10c x + 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+ +--R (- 10c x - 10a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+3 8+-+5 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (20c x + 20a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 20c x - 20a c)\|2 |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (20c x + 20a c)\|2 |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 20c x - 20a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 40c x - 40a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 40c x - 40a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 +-+ +-+ +--R - x \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 160c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 160c\|2 \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 160c\|2 \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 160c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 10atan(---------------------) - 10atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 10\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 320c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 320c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R / +--R +-+8+---+3 8+-+5 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 12 10 3 11 6 4 10 2 +--R (10737418240a c x - 139586437120a c x + 42949672960a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 2 8 7 3 7 3 | 1 +--R (- 110100480a c x + 78643200a c x ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 8 2 4 4 3 3 | 1 +--R (- 64000a c x + 117760a c x - 2560a c ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 9 5 2 +--R - 30c x + 135a c x - 15a x +--R / +--R 3 13 8 4 12 4 5 11 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 10 9 3 9 5 4 8 +--R (218103808a c x + 134217728a c x - 83886080a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 7 10 2 6 6 3 5 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R 64c x - 160a c x - 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1347 +t0:=x^(9/2)/(a+c*x^4)^2 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1347 +r0:=-1/4*x^(3/2)/(c*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(5/8)*c^(11/8))-3/16*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8))+3/16*atan(1-c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8)*sqrt(2))-3/16*_ + atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_ + c^(11/8)*sqrt(2))-3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2))+_ + 3/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 6c x - 6a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 6c x - 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 6c x - 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+ +--R (6c x + 6a)\|2 atan(--------) - 8x\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+5 8+-+3 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (12c x + 12a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 12c x - 12a c)\|2 |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (12c x + 12a c)\|2 |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 12c x - 12a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R - 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (24c x + 24a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (24c x + 24a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R - x\|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 96c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 96c\|2 \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 96c\|2 \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 96c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R - 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 6atan(---------------------) + 6atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 6\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 192c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 192c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R / +--R +-+8+---+5 8+-+3 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--------------------+6 +--R 4 10 7 5 9 3 | 1 +--R (- 135291469824a c x + 96636764160a c x ) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 2 8 10 3 7 6 4 6 2 +--R (12582912a c x - 163577856a c x + 50331648a c x ) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 9 2 4 5 3 3 | 1 +--R (36864a c x - 165888a c x + 18432a c x) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 2 8 4 2 +--R 75c x - 138a c x + 3a +--R / +--R 4 12 10 5 11 6 6 10 2 +--R (274877906944a c x - 68719476736a c x - 343597383680a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 3 9 9 4 8 5 5 7 +--R (436207616a c x + 268435456a c x - 167772160a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 2 6 8 3 5 4 4 4 | 1 +--R (557056a c x + 524288a c x - 32768a c ) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R - 128c x + 320a c x + 448a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1347 +t0:=x^(7/2)/(a+c*x^4)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1347 +r0:=-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))-_ + 1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))+_ + 1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8)*_ + sqrt(2))-1/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(9/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*sqrt(2))-1/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*_ + sqrt(2))-1/4*sqrt(x)/(c*(a+c*x^4)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 2c x - 2a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 2c x - 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 2c x - 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+ +--R (- 2c x - 2a)\|2 atan(--------) - 8\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+7 8+-+ +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 2 4 | 1 +--R (4c x + 4a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 +-+ | 1 +--R (4c x + 4a c)\|2 |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x + 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 +-+ | 1 +--R (- 4c x - 4a c)\|2 |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x - 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 4c x - 4a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R - 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 8c x - 8a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x - 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 8c x - 8a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x + 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R - \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 32c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 32c\|2 \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x + 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 32c\|2 \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x - 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 32c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R - 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 64c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x - 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 64c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x + 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R / +--R +-+8+---+7 8+-+ +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 8 8 6 7 4 7 6 +--R (13421772800a c x - 24696061952a c x + 536870912a c ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 3 6 9 4 5 5 5 4 | 1 +--R (- 6291456a c x + 28311552a c x - 3145728a c x) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 10 2 3 6 3 2 2 | 1 7 +--R (2048a c x - 26624a c x + 8192a c x ) |- ----------------- + 21c x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 3 +--R - 15a x +--R / +--R 6 9 8 7 8 4 8 7 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 4 7 9 5 6 5 6 5 +--R (- 218103808a c x - 134217728a c x + 83886080a c x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 5 10 3 4 6 4 3 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 3 11 2 7 2 3 +--R - 64c x + 160a c x + 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1347 +t0:=x^(5/2)/(a+c*x^4)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1347 +r0:=1/4*x^(7/2)/(a*(a+c*x^4))-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*c^(7/8))+1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*c^(7/8))+1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-1/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-_ + 1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(9/8)*c^(7/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x+_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 2c x - 2a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (2c x + 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 4 \|2 \|c \|x - \|- a 4 +-+ \|c \|x +--R (2c x + 2a)atan(---------------------) + (2c x + 2a)\|2 atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 3 +-+8+---+8+-+7 +-+ +--R 8x \|2 \|- a \|c \|x +--R / +--R 4 2 +-+8+---+8+-+7 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 4 2 | 1 +--R (4a c x + 4a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (4a c x + 4a )\|2 |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x + 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (- 4a c x - 4a )\|2 |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x - 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 4a c x - 4a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (8a c x + 8a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x - 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (8a c x + 8a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x + 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 3 +-+ +-+ +--R x \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 32a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 32a\|2 \|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x + 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 32a\|2 \|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x - 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 32a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 64a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x - 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 64a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x + 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R / +--R +-+8+---+8+-+7 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 7 7 9 8 6 5 9 5 +--R (- 3221225472a c x + 14495514624a c x - 1610612736a c x) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 5 5 8 6 4 4 7 3 | 1 +--R (6553600a c x - 12058624a c x + 262144a c ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 3 3 7 4 2 3 | 1 2 10 6 +--R (- 10752a c x + 7680a c x ) |- ----------------- - c x + 13a c x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 2 2 +--R - 4a x +--R / +--R 8 8 10 9 7 6 10 6 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a c x ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 6 6 9 7 5 5 8 4 +--R (- 109051904a c x - 67108864a c x + 41943040a c x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 4 8 5 3 4 6 2 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R 32a c x - 80a c x - 112a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1347 +t0:=x^(3/2)/(a+c*x^4)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1347 +r0:=1/4*x^(5/2)/(a*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(5/8))+3/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(5/8))+3/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))+_ + 3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_ + c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 6c x - 6a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (6c x + 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (6c x + 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+ +--R (- 6c x - 6a)\|2 atan(--------) + 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+3 8+-+5 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 4 2 | 1 +--R (12a c x + 12a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (- 12a c x - 12a )\|2 |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (12a c x + 12a )\|2 |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 12a c x - 12a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 24a c x - 24a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 24a c x - 24a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 2 +-+ +-+ +--R x \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 96a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 96a\|2 \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 96a\|2 \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 96a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 6atan(---------------------) - 6atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 6\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 192a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 192a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R / +--R +-+8+---+3 8+-+5 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 8 6 10 9 5 6 10 4 2 +--R (6442450944a c x - 83751862272a c x + 25769803776a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 6 4 7 7 3 3 | 1 +--R (- 66060288a c x + 47185920a c x ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 3 8 4 2 4 5 | 1 2 9 +--R (- 38400a c x + 70656a c x - 1536a c) |- ------------------ - 18c x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 5 2 +--R 81a c x - 9a x +--R / +--R 10 6 8 11 5 4 12 4 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 7 5 9 8 4 5 9 3 +--R (218103808a c x + 134217728a c x - 83886080a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 4 4 10 5 3 6 6 2 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R 64a c x - 160a c x - 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1347 +t0:=sqrt(x)/(a+c*x^4)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1347 +r0:=1/4*x^(3/2)/(a*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(13/8)*c^(3/8))+5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(13/8)*c^(3/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+5/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+_ + 5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(3/8)*sqrt(2))-5/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*_ + c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 10c x - 10a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 10c x - 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 10c x - 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+ +--R (10c x + 10a)\|2 atan(--------) + 8x\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+5 8+-+3 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 4 2 | 1 +--R (20a c x + 20a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (- 20a c x - 20a )\|2 |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (20a c x + 20a )\|2 |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 20a c x - 20a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R - 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (40a c x + 40a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (40a c x + 40a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R x\|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 160a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 160a\|2 \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 160a\|2 \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 160a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R - 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 10atan(---------------------) + 10atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 10\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 320a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 320a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R / +--R +-+8+---+5 8+-+3 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--------------------+6 +--R 10 4 7 11 3 3 | 1 +--R (- 225485783040a c x + 161061273600a c x ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 6 4 10 7 3 6 8 2 2 +--R (20971520a c x - 272629760a c x + 83886080a c x ) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 3 9 4 2 5 5 | 1 +--R (61440a c x - 276480a c x + 30720a c x) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 2 8 4 2 +--R 125c x - 230a c x + 5a +--R / +--R 11 5 10 12 4 6 13 3 2 +--R (274877906944a c x - 68719476736a c x - 343597383680a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 8 4 9 9 3 5 10 2 +--R (436207616a c x + 268435456a c x - 167772160a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 3 8 6 2 4 7 | 1 +--R (557056a c x + 524288a c x - 32768a c) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R - 128a c x + 320a c x + 448a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1347 +t0:=1/((a+c*x^4)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 8 4 2 +-+ +--R (c x + 2a c x + a )\|x +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1347 +r0:=7/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))+_ + 7/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))-_ + 7/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_ + c^(1/8)*sqrt(2))+7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(15/8)*c^(1/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*_ + sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*sqrt(2))+1/4*_ + sqrt(x)/(a*(a+c*x^4)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 14c x - 14a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 14c x - 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 14c x - 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+ +--R (- 14c x - 14a)\|2 atan(--------) + 8\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+7 8+-+ +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 4 2 | 1 +--R (28a c x + 28a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +-------------------+2 +--R 2 +-+ | 1 +-+ 4 | 1 +--R 32a \|2 |- ----------------- \|x + 1024a |- ----------------- +--R 8| 15 8| 15 +--R \| 1099511627776a c \| 1099511627776a c +--R + +--R x +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (28a c x + 28a )\|2 |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x + 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (- 28a c x - 28a )\|2 |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x - 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 28a c x - 28a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 1 +-+ +--R - 32a \|2 |- ----------------- \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 | 1 +--R 1024a |- ----------------- + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 56a c x - 56a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 56a c x - 56a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 224a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +-------------------+2 +--R 2 +-+ | 1 +-+ 4 | 1 +--R 32a \|2 |- ----------------- \|x + 1024a |- ----------------- +--R 8| 15 8| 15 +--R \| 1099511627776a c \| 1099511627776a c +--R + +--R x +--R + +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 224a\|2 \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x + 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 224a\|2 \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x - 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 224a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 1 +-+ +--R - 32a \|2 |- ----------------- \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 | 1 +--R 1024a |- ----------------- + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 14atan(---------------------) + 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 448a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 448a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R / +--R +-+8+---+7 8+-+ +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 11 2 8 12 4 13 +--R (93952409600a c x - 172872433664a c x + 3758096384a ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 7 2 9 8 5 9 | 1 +--R (- 44040192a c x + 198180864a c x - 22020096a x) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 3 2 10 4 6 5 2 | 1 +--R (14336a c x - 186368a c x + 57344a x ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 7 3 +--R 147c x - 105a x +--R / +--R 13 2 8 14 4 15 +--R (292057776128a c x + 274877906944a c x - 17179869184a ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 9 2 9 10 5 11 +--R (- 218103808a c x - 134217728a c x + 83886080a x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 5 2 10 6 6 7 2 | 1 +--R (131072a c x - 32768a c x - 163840a x ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 2 11 2 7 3 3 +--R - 64a c x + 160a c x + 224a x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1347 +t0:=1/(x^(3/2)*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 9 5 2 +-+ +--R (c x + 2a c x + a x)\|x +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1347 +r0:=-9/16*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_ + 9/16*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_ + 9/16*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(17/8)*sqrt(2))-9/16*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*sqrt(2))-9/32*c^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(17/8)*sqrt(2))+9/32*c^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(17/8)*_ + sqrt(2))+(-9/4)/(a^2*sqrt(x))+1/4/(a*(a+c*x^4)*sqrt(x)) +--R +--R +--R (2) +--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 9a)\|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 9a)\|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+8+-+ +-+ \|c \|x +--R (18c x + 18a)\|2 \|c \|x atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 8+-+ +-+ \|2 \|c \|x + \|- a +--R (- 18c x - 18a)\|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 8+-+ +-+ \|2 \|c \|x - \|- a +--R (- 18c x - 18a)\|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+8+-+ +-+ \|c \|x 4 +-+8+---+ +--R (- 18c x - 18a)\|2 \|c \|x atan(--------) + (- 72c x - 64a)\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R 2 4 3 +-+8+---+ +-+ +--R (32a c x + 32a )\|2 \|- a \|x +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 4a c x - 4a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 +-+ | 43046721c +-+ +--R (- 4a c x - 4a )\|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x + 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 +-+ | 43046721c +-+ +--R (4a c x + 4a )\|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x - 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (4a c x + 4a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R - 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 8a c x - 8a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x - 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 8a c x - 8a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x + 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 4 +-+ +--R (- 9c x - 8a)\|2 +--R / +--R 2 4 3 +-+ +-+ +--R (4a c x + 4a )\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 9\|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 32a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R - +--R +------------------+ +--R 2 +-+ | 43046721c 8+---+ +--R 32a \|2 |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x + 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 +-+ | 43046721c 8+---+ +--R 32a \|2 |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x - 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 32a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R - 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9\|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+ \|c \|x 8+-+ \|2 \|c \|x + \|- a +--R - 18\|2 \|c atanh(--------) + 18\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+ \|2 \|c \|x - \|- a +-+8+-+ \|c \|x +--R 18\|c atan(---------------------) + 18\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 64a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x - 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 64a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x + 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R / +--R 2 +-+8+---+ +--R 32a \|2 \|- a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 2 9 14 5 15 +--R (28991029248a c x - 130459631616a c x + 14495514624a x) +--R * +--R +------------------+6 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 9 2 8 10 4 11 +--R (- 4777574400a c x + 8790736896a c x - 191102976a ) +--R * +--R +------------------+4 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+2 +--R 5 2 7 6 3 | 43046721c 3 10 +--R (634894848a c x - 453496320a c x ) |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R 2 6 2 2 +--R - 62178597a c x + 19131876a c x +--R / +--R 15 2 10 16 6 17 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a x ) +--R * +--R +------------------+6 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 11 2 9 12 5 13 +--R (- 8833204224a c x - 5435817984a c x + 3397386240a x) +--R * +--R +------------------+4 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+2 +--R 7 2 8 8 4 9 | 43046721c +--R (913711104a c x + 859963392a c x - 53747712a ) |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 2 3 11 3 2 7 4 3 +--R 17006112a c x - 42515280a c x - 59521392a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1347 +t0:=x^(15/2)/(a+c*x^4)^3 +--R +--R +--R 7 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1347 +r0:=-1/8*x^(9/2)/(c*(a+c*x^4)^2)-9/256*atan(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))-9/256*_ + atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))+_ + 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(17/8)*sqrt(2))-9/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8)*sqrt(2))+_ + 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_ + 9/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_ + 9/64*sqrt(x)/(c^2*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 18c x - 36a c x - 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 18c x - 36a c x - 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (- 136c x - 72a)\|2 \|- a \|c \|x +--R / +--R 4 8 3 4 2 2 +-+8+---+7 8+-+ +--R (512c x + 1024a c x + 512a c )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (576c x + 1152a c x + 576a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 +-+ | 1 +--R (576c x + 1152a c x + 576a c )\|2 |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 +-+ | 1 +--R (- 576c x - 1152a c x - 576a c )\|2 |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 576c x - 1152a c x - 576a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 1152c x - 2304a c x - 1152a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 1152c x - 2304a c x - 1152a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (- 17c x - 9a)\|2 \|x +--R / +--R 4 8 3 4 2 2 +-+ +--R (64c x + 128a c x + 64a c )\|2 +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 4608c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 4608c \|2 \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 4608c \|2 \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 4608c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 18atan(---------------------) + 18atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 18\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 9216c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 9216c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+7 8+-+ +--R 512c \|2 \|- a \|c +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 14 8 6 13 4 +--R 2026619832316723200a c x - 3728980491462770688a c x +--R + +--R 7 12 +--R 81064793292668928a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 3 10 9 4 9 5 5 8 +--R (- 3710851743744a c x + 16698832846848a c x - 1855425871872a c x) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 6 10 2 5 6 3 4 2 +--R (4718592a c x - 61341696a c x + 18874368a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 189c x - 135a x +--R / +--R 6 16 8 7 15 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 8 14 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 12 9 5 11 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 6 10 +--R 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 2 8 10 3 7 6 4 6 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 11 3 7 2 2 3 +--R - 1024c x + 2560a c x + 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1347 +t0:=x^(13/2)/(a+c*x^4)^3 +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1347 +r0:=-1/8*x^(7/2)/(c*(a+c*x^4)^2)+7/64*x^(7/2)/(a*c*(a+c*x^4))-_ + 7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_ + 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_ + 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*_ + c^(15/8)*sqrt(2))-7/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8)*sqrt(2))-_ + 7/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(9/8)*c^(15/8)*sqrt(2))+7/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_ + c^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (14c x + 28a c x + 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (14c x + 28a c x + 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (14c x + 28a c x + 14a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 7 3 +-+8+---+8+-+7 +-+ +--R (56c x - 8a x )\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+8+-+7 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (448a c x + 896a c x + 448a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (448a c x + 896a c x + 448a c)\|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (- 448a c x - 896a c x - 448a c)\|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 448a c x - 896a c x - 448a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +--R 9223372036854775808a c \|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-+ +--R \|x +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (896a c x + 1792a c x + 896a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (896a c x + 1792a c x + 896a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +-+ +-+ +--R (7c x - a x )\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 3584a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 3584a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R 8 13 +-+ +--R 9223372036854775808a c \|2 +--R * +--R +-----------------------------+7 +--R | 1 +-+ +--R |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 14atan(---------------------) - 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 7168a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 7168a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+8+-+7 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 7 13 9 8 12 5 +--R - 378302368699121664a c x + 1702360659146047488a c x +--R + +--R 9 11 +--R - 189151184349560832a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 5 9 8 6 8 4 7 7 +--R (3006477107200a c x - 5531917877248a c x + 120259084288a c ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 3 5 7 4 4 3 | 1 +--R (- 19267584a c x + 13762560a c x ) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 2 10 6 2 2 +--R - 7c x + 91a c x - 28a x +--R / +--R 8 15 10 9 14 6 +--R 18446744073709551616a c x - 4611686018427387904a c x +--R + +--R 10 13 2 +--R - 23058430092136939520a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 6 11 9 7 10 5 +--R - 114349209288704a c x - 70368744177664a c x +--R + +--R 8 9 +--R 43980465111040a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 4 7 8 5 6 4 6 5 +--R (570425344a c x + 536870912a c x - 33554432a c ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R 512a c x - 1280a c x - 1792a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1347 +t0:=x^(11/2)/(a+c*x^4)^3 +--R +--R +--R 5 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1347 +r0:=-1/8*x^(5/2)/(c*(a+c*x^4)^2)+5/64*x^(5/2)/(a*c*(a+c*x^4))+_ + 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8))+_ + 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*_ + c^(13/8))+15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(13/8)*sqrt(2))-15/256*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8)*sqrt(2))+_ + 15/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2))-_ + 15/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (30c x + 60a c x + 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (30c x + 60a c x + 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 6 2 +-+8+---+3 8+-+5 +-+ +--R (40c x - 24a x )\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+3 8+-+5 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (960a c x + 1920a c x + 960a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 3 8 2 2 4 3 +-+ +--R (- 960a c x - 1920a c x - 960a c)\|2 +--R * +--R +------------------------------+ +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x + 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (960a c x + 1920a c x + 960a c)\|2 |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x - 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 960a c x - 1920a c x - 960a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 1920a c x - 3840a c x - 1920a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x - 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 1920a c x - 3840a c x - 1920a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x + 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 6 2 +-+ +-+ +--R (5c x - 3a x )\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x + 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x - 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 30atan(---------------------) - 30atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 30\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x - 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x + 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+3 8+-+5 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 8 12 10 9 11 6 +--R 540431955284459520a c x - 7025615418697973760a c x +--R + +--R 10 10 2 +--R 2161727821137838080a c x +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 6 8 7 7 7 3 +--R (- 21646635171840a c x + 15461882265600a c x ) +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 3 5 8 4 4 4 5 3 +--R (- 49152000a c x + 90439680a c x - 1966080a c ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 2 9 5 2 +--R - 90c x + 405a c x - 45a x +--R / +--R 10 13 8 11 12 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 12 11 +--R - 4611686018427387904a c +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 7 10 9 8 9 5 +--R 228698418577408a c x + 140737488355328a c x +--R + +--R 9 8 +--R - 87960930222080a c x +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 4 7 10 5 6 6 6 5 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R 1024a c x - 2560a c x - 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1347 +t0:=x^(9/2)/(a+c*x^4)^3 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1347 +r0:=-1/8*x^(3/2)/(c*(a+c*x^4)^2)+3/64*x^(3/2)/(a*c*(a+c*x^4))-_ + 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))+_ + 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))-_ + 15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*_ + c^(11/8)*sqrt(2))+15/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*c^(11/8)*sqrt(2))+15/512*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2))-15/512*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 30c x - 60a c x - 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 30c x - 60a c x - 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (30c x + 60a c x + 30a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 5 +-+8+---+5 8+-+3 +-+ +--R (24c x - 40a x)\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+5 8+-+3 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (960a c x + 1920a c x + 960a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 3 8 2 2 4 3 +-+ +--R (- 960a c x - 1920a c x - 960a c)\|2 +--R * +--R +------------------------------+ +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x + 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (960a c x + 1920a c x + 960a c)\|2 |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x - 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 960a c x - 1920a c x - 960a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R - 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (1920a c x + 3840a c x + 1920a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x - 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (1920a c x + 3840a c x + 1920a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x + 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 5 +-+ +-+ +--R (3c x - 5a x)\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x + 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x - 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R - 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 30atan(---------------------) + 30atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 30\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x - 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x + 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+5 8+-+3 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 10 10 7 11 9 3 +--R (- 11349071060973649920a c x + 8106479329266892800a c x ) +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 6 8 10 7 7 6 8 6 2 +--R (4123168604160a c x - 53601191854080a c x + 16492674416640a c x ) +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 3 5 9 4 4 5 5 3 +--R (47185920a c x - 212336640a c x + 23592960a c x) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 2 8 4 2 +--R 375c x - 690a c x + 15a +--R / +--R 11 12 10 12 11 6 +--R 73786976294838206464a c x - 18446744073709551616a c x +--R + +--R 13 10 2 +--R - 92233720368547758080a c x +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 8 9 9 9 8 5 +--R 457396837154816a c x + 281474976710656a c x +--R + +--R 10 7 +--R - 175921860444160a c x +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 5 6 8 6 5 4 7 4 +--R (2281701376a c x + 2147483648a c x - 134217728a c ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R - 2048a c x + 5120a c x + 7168a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1347 +t0:=x^(7/2)/(a+c*x^4)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1347 +r0:=7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))+_ + 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))-_ + 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_ + c^(9/8)*sqrt(2))+7/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(15/8)*c^(9/8)*sqrt(2))-7/512*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(15/8)*c^(9/8)*sqrt(2))+7/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*_ + c^(9/8)*sqrt(2))-1/8*sqrt(x)/(c*(a+c*x^4)^2)+1/64*_ + sqrt(x)/(a*c*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 14c x - 28a c x - 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 14c x - 28a c x - 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (8c x - 56a)\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+7 8+-+ +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (448a c x + 896a c x + 448a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (448a c x + 896a c x + 448a c)\|2 |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (- 448a c x - 896a c x - 448a c)\|2 |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 448a c x - 896a c x - 448a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 896a c x - 1792a c x - 896a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 896a c x - 1792a c x - 896a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (c x - 7a)\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 3584a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 3584a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 14atan(---------------------) + 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 7168a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 7168a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+7 8+-+ +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 11 8 8 12 7 4 +--R 1576259869579673600a c x - 2900318160026599424a c x +--R + +--R 13 6 +--R 63050394783186944a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 7 6 9 8 5 5 9 4 +--R (- 2886218022912a c x + 12987981103104a c x - 1443109011456a c x) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 3 4 10 4 3 6 5 2 2 +--R (3670016a c x - 47710208a c x + 14680064a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 147c x - 105a x +--R / +--R 13 9 8 14 8 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 15 7 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 9 7 9 10 6 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 11 5 +--R 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 5 5 10 6 4 6 7 3 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 3 11 2 2 7 3 3 +--R - 1024a c x + 2560a c x + 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1347 +t0:=x^(5/2)/(a+c*x^4)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1347 +r0:=1/8*x^(7/2)/(a*(a+c*x^4)^2)+9/64*x^(7/2)/(a^2*(a+c*x^4))+_ + 9/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_ + 9/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_ + 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(17/8)*c^(7/8)*sqrt(2))+9/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8)*sqrt(2))+_ + 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(17/8)*c^(7/8)*sqrt(2))-9/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(17/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (18c x + 36a c x + 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (18c x + 36a c x + 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (18c x + 36a c x + 18a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 7 3 +-+8+---+8+-+7 +-+ +--R (72c x + 136a x )\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+8+-+7 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (576a c x + 1152a c x + 576a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (576a c x + 1152a c x + 576a )\|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (- 576a c x - 1152a c x - 576a )\|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 576a c x - 1152a c x - 576a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +--R 9223372036854775808a c \|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-+ +--R \|x +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (1152a c x + 2304a c x + 1152a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (1152a c x + 2304a c x + 1152a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +-+ +-+ +--R (9c x + 17a x )\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 4608a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+ | 1 8+-+7 +--R 4608a \|2 \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+ | 1 8+-+7 +--R 4608a \|2 \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 4608a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R 15 6 +-+ +--R 9223372036854775808a c \|2 +--R * +--R +-----------------------------+7 +--R | 1 +-+ +--R |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 18atan(---------------------) - 18atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 18\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 9216a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 9216a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+8+-+7 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 7 9 14 6 5 +--R - 486388759756013568a c x + 2188749418902061056a c x +--R + +--R 15 5 +--R - 243194379878006784a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 9 5 8 10 4 4 11 3 +--R (3865470566400a c x - 7112465842176a c x + 154618822656a c ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 3 7 6 2 3 | 1 +--R (- 24772608a c x + 17694720a c x ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 2 10 6 2 2 +--R - 9c x + 117a c x - 36a x +--R / +--R 15 8 10 16 7 6 +--R 18446744073709551616a c x - 4611686018427387904a c x +--R + +--R 17 6 2 +--R - 23058430092136939520a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 11 6 9 12 5 5 +--R - 114349209288704a c x - 70368744177664a c x +--R + +--R 13 4 +--R 43980465111040a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 7 4 8 8 3 4 9 2 +--R (570425344a c x + 536870912a c x - 33554432a c ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R 512a c x - 1280a c x - 1792a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1347 +t0:=x^(3/2)/(a+c*x^4)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1347 +r0:=1/8*x^(5/2)/(a*(a+c*x^4)^2)+11/64*x^(5/2)/(a^2*(a+c*x^4))-_ + 33/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_ + 33/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_ + 33/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*_ + c^(5/8)*sqrt(2))+33/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8)*sqrt(2))-_ + 33/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2))+_ + 33/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (33c x + 66a c x + 33a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 33c x - 66a c x - 33a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 66c x - 132a c x - 66a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (66c x + 132a c x + 66a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (66c x + 132a c x + 66a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 66c x - 132a c x - 66a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 6 2 +-+8+---+3 8+-+5 +-+ +--R (88c x + 152a x )\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+3 8+-+5 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (2112a c x + 4224a c x + 2112a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 2112a c x - 4224a c x - 2112a )\|2 +--R * +--R +-----------------------------+ +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x + 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (2112a c x + 4224a c x + 2112a )\|2 |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x - 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 2112a c x - 4224a c x - 2112a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4224a c x - 8448a c x - 4224a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x - 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4224a c x - 8448a c x - 4224a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x + 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 6 2 +-+ +-+ +--R (11c x + 19a x )\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 33log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 16896a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+3 | 1 8+-+5 +--R 16896a \|2 \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x + 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+3 | 1 8+-+5 +--R 16896a \|2 \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x - 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 16896a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 33log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 66\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 66atan(---------------------) - 66atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 66\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 33792a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x - 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 33792a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x + 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+3 8+-+5 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 14 6 10 15 5 6 +--R 1188950301625810944a c x - 15456353921135542272a c x +--R + +--R 16 4 2 +--R 4755801206503243776a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 10 4 7 11 3 3 +--R (- 47622597378048a c x + 34016140984320a c x ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 5 3 8 6 2 4 7 +--R (- 108134400a c x + 198967296a c x - 4325376a c) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 9 5 2 +--R - 198c x + 891a c x - 99a x +--R / +--R 17 6 8 18 5 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 19 4 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 12 5 9 13 4 5 +--R 228698418577408a c x + 140737488355328a c x +--R + +--R 14 3 +--R - 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 7 4 10 8 3 6 9 2 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R 1024a c x - 2560a c x - 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1347 +t0:=sqrt(x)/(a+c*x^4)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1347 +r0:=1/8*x^(3/2)/(a*(a+c*x^4)^2)+13/64*x^(3/2)/(a^2*(a+c*x^4))+_ + 65/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))-_ + 65/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))+_ + 65/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*_ + c^(3/8)*sqrt(2))-65/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8)*sqrt(2))-_ + 65/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2))+65/512*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (65c x + 130a c x + 65a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 65c x - 130a c x - 65a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 130c x - 260a c x - 130a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 130c x - 260a c x - 130a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 130c x - 260a c x - 130a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (130c x + 260a c x + 130a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 5 +-+8+---+5 8+-+3 +-+ +--R (104c x + 168a x)\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+5 8+-+3 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (4160a c x + 8320a c x + 4160a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 4160a c x - 8320a c x - 4160a )\|2 +--R * +--R +-----------------------------+ +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x + 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (4160a c x + 8320a c x + 4160a )\|2 |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x - 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4160a c x - 8320a c x - 4160a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R - 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (8320a c x + 16640a c x + 8320a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x - 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (8320a c x + 16640a c x + 8320a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x + 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 5 +-+ +-+ +--R (13c x + 21a x)\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 65log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 33280a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+5 | 1 8+-+3 +--R 33280a \|2 \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x + 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+5 | 1 8+-+3 +--R 33280a \|2 \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x - 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 33280a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R - 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 65log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 130\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 130atan(---------------------) + 130atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 130\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 66560a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x - 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 66560a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x + 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+5 8+-+3 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 16 4 7 17 3 3 +--R (- 49179307930885816320a c x + 35128077093489868800a c x ) +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 10 4 10 11 3 6 +--R 17867063951360a c x - 232271831367680a c x +--R + +--R 12 2 2 +--R 71468255805440a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 5 3 9 6 2 5 7 +--R (204472320a c x - 920125440a c x + 102236160a c x) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 8 4 2 +--R 1625c x - 2990a c x + 65a +--R / +--R 18 5 10 19 4 6 +--R 73786976294838206464a c x - 18446744073709551616a c x +--R + +--R 20 3 2 +--R - 92233720368547758080a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 13 4 9 14 3 5 +--R 457396837154816a c x + 281474976710656a c x +--R + +--R 15 2 +--R - 175921860444160a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 8 3 8 9 2 4 10 +--R (2281701376a c x + 2147483648a c x - 134217728a c) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R - 2048a c x + 5120a c x + 7168a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1347 +t0:=1/((a+c*x^4)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 12 2 8 2 4 3 +-+ +--R (c x + 3a c x + 3a c x + a )\|x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1347 +r0:=-105/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))-_ + 105/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))+_ + 105/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*_ + c^(1/8)*sqrt(2))-105/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(23/8)*c^(1/8)*sqrt(2))+105/512*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*_ + c^(1/8)*sqrt(2))-105/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*c^(1/8)*sqrt(2))+_ + 1/8*sqrt(x)/(a*(a+c*x^4)^2)+15/64*sqrt(x)/(a^2*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 105c x - 210a c x - 105a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (105c x + 210a c x + 105a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 210c x - 420a c x - 210a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 210c x - 420a c x - 210a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 210c x - 420a c x - 210a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 210c x - 420a c x - 210a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (120c x + 184a)\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+7 8+-+ +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (6720a c x + 13440a c x + 6720a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (6720a c x + 13440a c x + 6720a )\|2 |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x + 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 6720a c x - 13440a c x - 6720a )\|2 +--R * +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x - 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 6720a c x - 13440a c x - 6720a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R - 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 13440a c x - 26880a c x - 13440a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x - 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 13440a c x - 26880a c x - 13440a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x + 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (15c x + 23a)\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 740 + +--S 741 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 105log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 53760a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 53760a \|2 \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x + 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 53760a \|2 \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x - 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 53760a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R - 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 105log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 210\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 210atan(---------------------) + 210atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 210\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 107520a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x - 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 107520a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x + 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+7 8+-+ +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 17 2 8 18 4 +--R 23643898043695104000a c x - 43504772400398991360a c x +--R + +--R 19 +--R 945755921747804160a +--R * +--R +----------------------------+6 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 11 2 9 12 5 13 +--R (- 43293270343680a c x + 194819716546560a c x - 21646635171840a x) +--R * +--R +----------------------------+4 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 5 2 10 6 6 7 2 +--R (55050240a c x - 715653120a c x + 220200960a x ) +--R * +--R +----------------------------+2 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 2205c x - 1575a x +--R / +--R 20 2 8 21 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 22 +--R - 4611686018427387904a +--R * +--R +----------------------------+6 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 14 2 9 15 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 16 +--R 87960930222080a x +--R * +--R +----------------------------+4 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 8 2 10 9 6 10 2 +--R (536870912a c x - 134217728a c x - 671088640a x ) +--R * +--R +----------------------------+2 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 2 2 11 3 7 4 3 +--R - 1024a c x + 2560a c x + 3584a x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 742 + +)clear all + +--S 743 of 1347 +t0:=x^7*(a+b*x^4)^p +--R +--R +--R 7 4 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1347 +r0:=-1/4*a*(a+b*x^4)^(1+p)/(b^2*(1+p))+1/4*(a+b*x^4)^(2+p)/(b^2*(2+p)) +--R +--R +--R 4 p + 2 4 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 2 2 8 4 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Union(Expression(Integer),...) +--E 745 + +--S 746 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 +--R 2 2 8 4 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 4 p + 2 4 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 1347 +t0:=x^3*(a+b*x^4)^p +--R +--R +--R 3 4 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1347 +r0:=1/4*(a+b*x^4)^(1+p)/(b*(1+p)) +--R +--R +--R 4 p + 1 +--R (b x + a) +--R (2) --------------- +--R 4b p + 4b +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 4b p + 4b +--R Type: Union(Expression(Integer),...) +--E 750 + +--S 751 of 1347 +m0:=a0-r0 +--R +--R +--R 4 +--R 4 p log(b x + a) 4 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 4b p + 4b +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 1347 +t0:=(a+b*x^4)^p/x +--R +--R +--R 4 p +--R (b x + a) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1347 +--r0:=1/4*(a+b*x^4)^p*hypergeometric(-p,-p,1-p,-a/(b*x^4))/_ +-- (p*((a+b*x^4)/(b*x^4))^p) +--E 754 + +--S 755 of 1347 +--a0:=integrate(t0,x) +--E 755 + +--S 756 of 1347 +--m0:=a0-r0 +--E 756 + +--S 757 of 1347 +--d0:=D(m0,x) +--E 757 + +)clear all + +--S 758 of 1347 +t0:=x^7*(1+x^4)^(1/3) +--R +--R +--R +------+ +--R 7 3| 4 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1347 +r0:=-3/16*(1+x^4)^(4/3)+3/28*(1+x^4)^(7/3) +--R +--R +--R +------+ +--R 8 4 3| 4 +--R (12x + 3x - 9)\|x + 1 +--R (2) ------------------------- +--R 112 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 8 4 3| 4 +--R (12x + 3x - 9)\|x + 1 +--R (3) ------------------------- +--R 112 +--R Type: Union(Expression(Integer),...) +--E 760 + +--S 761 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 1347 +t0:=x^3/(1+x^4)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ----------------- +--R +------+ +--R 4 3| 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1347 +r0:=(-3/4)/(1+x^4)^(1/3) +--R +--R +--R 3 +--R (2) - ---------- +--R +------+ +--R 3| 4 +--R 4\|x + 1 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R (3) - ---------- +--R +------+ +--R 3| 4 +--R 4\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1347 +t0:=x^3/(1+x^4)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1347 +r0:=3/8*(1+x^4)^(2/3) +--R +--R +--R +------+2 +--R 3| 4 +--R 3\|x + 1 +--R (2) ----------- +--R 8 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 3| 4 +--R 3\|x + 1 +--R (3) ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1347 +t0:=x^3/(1+x^4)^(1/4) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 4| 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1347 +r0:=1/3*(1+x^4)^(3/4) +--R +--R +--R +------+3 +--R 4| 4 +--R \|x + 1 +--R (2) ---------- +--R 3 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+3 +--R 4| 4 +--R \|x + 1 +--R (3) ---------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1347 +t0:=x^24/(a+b*x^5) +--R +--R +--R 24 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 778 + +--S 779 of 1347 +r0:=-1/5*a^3*x^5/b^4+1/10*a^2*x^10/b^3-1/15*a*x^15/b^2+1/20*x^20/b+_ + 1/5*a^4*log(a+b*x^5)/b^5 +--R +--R +--R 4 5 4 20 3 15 2 2 10 3 5 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) ----------------------------------------------------------- +--R 5 +--R 60b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 5 4 20 3 15 2 2 10 3 5 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) ----------------------------------------------------------- +--R 5 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1347 +t0:=x^19/(a+b*x^5) +--R +--R +--R 19 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1347 +r0:=1/5*a^2*x^5/b^3-1/10*a*x^10/b^2+1/15*x^15/b-1/5*a^3*log(a+b*x^5)/b^4 +--R +--R +--R 3 5 3 15 2 10 2 5 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 30b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 5 3 15 2 10 2 5 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) ------------------------------------------------ +--R 4 +--R 30b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1347 +t0:=x^14/(a+b*x^5) +--R +--R +--R 14 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 788 + +--S 789 of 1347 +r0:=-1/5*a*x^5/b^2+1/10*x^10/b+1/5*a^2*log(a+b*x^5)/b^3 +--R +--R +--R 2 5 2 10 5 +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 10b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 5 2 10 5 +--R 2a log(b x + a) + b x - 2a b x +--R (3) ---------------------------------- +--R 3 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1347 +t0:=x^9/(a+b*x^5) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 793 + +--S 794 of 1347 +r0:=1/5*x^5/b-1/5*a*log(a+b*x^5)/b^2 +--R +--R +--R 5 5 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 5b +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1347 +t0:=x^4/(a+b*x^5) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 798 + +--S 799 of 1347 +r0:=1/5*log(a+b*x^5)/b +--R +--R +--R 5 +--R log(b x + a) +--R (2) ------------- +--R 5b +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(b x + a) +--R (3) ------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 800 + +--S 801 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 802 + +)clear all + +--S 803 of 1347 +t0:=1/(x*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ---------- +--R 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 803 + +--S 804 of 1347 +r0:=log(x)/a-1/5*log(a+b*x^5)/a +--R +--R +--R 5 +--R - log(b x + a) + 5log(x) +--R (2) ------------------------- +--R 5a +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(b x + a) + 5log(x) +--R (3) ------------------------- +--R 5a +--R Type: Union(Expression(Integer),...) +--E 805 + +--S 806 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 807 + +)clear all + +--S 808 of 1347 +t0:=1/(x^6*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 808 + +--S 809 of 1347 +r0:=(-1/5)/(a*x^5)-b*log(x)/a^2+1/5*b*log(a+b*x^5)/a^2 +--R +--R +--R 5 5 5 +--R b x log(b x + a) - 5b x log(x) - a +--R (2) ----------------------------------- +--R 2 5 +--R 5a x +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R b x log(b x + a) - 5b x log(x) - a +--R (3) ----------------------------------- +--R 2 5 +--R 5a x +--R Type: Union(Expression(Integer),...) +--E 810 + +--S 811 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 812 + +)clear all + +--S 813 of 1347 +t0:=1/(x^11*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ------------- +--R 16 11 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 813 + +--S 814 of 1347 +r0:=(-1/10)/(a*x^10)+1/5*b/(a^2*x^5)+b^2*log(x)/a^3-1/5*b^2*log(a+b*x^5)/a^3 +--R +--R +--R 2 10 5 2 10 5 2 +--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a +--R (2) ---------------------------------------------------- +--R 3 10 +--R 10a x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 10 5 2 10 5 2 +--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a +--R (3) ---------------------------------------------------- +--R 3 10 +--R 10a x +--R Type: Union(Expression(Integer),...) +--E 815 + +--S 816 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 817 + +)clear all + +--S 818 of 1347 +t0:=x^24/(a+b*x^5)^2 +--R +--R +--R 24 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 818 + +--S 819 of 1347 +r0:=3/5*a^2*x^5/b^4-1/5*a*x^10/b^3+1/15*x^15/b^2-_ + 1/5*a^4/(b^5*(a+b*x^5))-4/5*a^3*log(a+b*x^5)/b^5 +--R +--R +--R (2) +--R 3 5 4 5 4 20 3 15 2 2 10 3 5 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x +--R + +--R 4 +--R - 3a +--R / +--R 6 5 5 +--R 15b x + 15a b +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 4 5 4 20 3 15 2 2 10 3 5 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x +--R + +--R 4 +--R - 3a +--R / +--R 6 5 5 +--R 15b x + 15a b +--R Type: Union(Expression(Integer),...) +--E 820 + +--S 821 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1347 +t0:=x^19/(a+b*x^5)^2 +--R +--R +--R 19 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 823 + +--S 824 of 1347 +r0:=-2/5*a*x^5/b^3+1/10*x^10/b^2+1/5*a^3/(b^4*(a+b*x^5))+_ + 3/5*a^2*log(a+b*x^5)/b^4 +--R +--R +--R 2 5 3 5 3 15 2 10 2 5 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) --------------------------------------------------------------- +--R 5 5 4 +--R 10b x + 10a b +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 5 3 15 2 10 2 5 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) --------------------------------------------------------------- +--R 5 5 4 +--R 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 825 + +--S 826 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1347 +t0:=x^14/(a+b*x^5)^2 +--R +--R +--R 14 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 828 + +--S 829 of 1347 +r0:=1/5*x^5/b^2-1/5*a^2/(b^3*(a+b*x^5))-2/5*a*log(a+b*x^5)/b^3 +--R +--R +--R 5 2 5 2 10 5 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) ---------------------------------------------------- +--R 4 5 3 +--R 5b x + 5a b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 2 5 2 10 5 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) ---------------------------------------------------- +--R 4 5 3 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1347 +t0:=x^9/(a+b*x^5)^2 +--R +--R +--R 9 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 833 + +--S 834 of 1347 +r0:=1/5*a/(b^2*(a+b*x^5))+1/5*log(a+b*x^5)/b^2 +--R +--R +--R 5 5 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 5 2 +--R 5b x + 5a b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 5 2 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1347 +t0:=x^4/(a+b*x^5)^2 +--R +--R +--R 4 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 838 + +--S 839 of 1347 +r0:=(-1/5)/(b*(a+b*x^5)) +--R +--R +--R 1 +--R - +--R 5 +--R (2) - ---------- +--R 2 5 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 839 + +--S 840 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 5 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1347 +t0:=1/(x*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 11 6 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1347 +r0:=1/5/(a*(a+b*x^5))+log(x)/a^2-1/5*log(a+b*x^5)/a^2 +--R +--R +--R 5 5 5 +--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 5 3 +--R 5a b x + 5a +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 5 3 +--R 5a b x + 5a +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1347 +t0:=1/(x^6*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 16 11 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1347 +r0:=(-2/5)/(a^2*x^5)+1/5/(a*x^5*(a+b*x^5))-_ + 2*b*log(x)/a^3+2/5*b*log(a+b*x^5)/a^3 +--R +--R +--R (2) +--R 2 10 5 5 2 10 5 5 2 +--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a +--R ----------------------------------------------------------------------------- +--R 3 10 4 5 +--R 5a b x + 5a x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 5 5 2 10 5 5 2 +--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a +--R ----------------------------------------------------------------------------- +--R 3 10 4 5 +--R 5a b x + 5a x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1347 +t0:=1/(x^11*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 21 16 2 11 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 853 + +--S 854 of 1347 +r0:=(-3/10)/(a^2*x^10)+3/5*b/(a^3*x^5)+1/5/(a*x^10*(a+b*x^5))+_ + 3*b^2*log(x)/a^4-3/5*b^2*log(a+b*x^5)/a^4 +--R +--R +--R (2) +--R 3 15 2 10 5 3 15 2 10 +--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x) +--R + +--R 2 10 2 5 3 +--R 6a b x + 3a b x - a +--R / +--R 4 15 5 10 +--R 10a b x + 10a x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 15 2 10 5 3 15 2 10 +--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x) +--R + +--R 2 10 2 5 3 +--R 6a b x + 3a b x - a +--R / +--R 4 15 5 10 +--R 10a b x + 10a x +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1347 +t0:=x^9/(2*b+b*x^5) +--R +--R +--R 9 +--R x +--R (1) --------- +--R 5 +--R b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 858 + +--S 859 of 1347 +r0:=1/5*x^5/b-2/5*log(2+x^5)/b +--R +--R +--R 5 5 +--R - 2log(x + 2) + x +--R (2) ------------------- +--R 5b +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - 2log(x + 2) + x +--R (3) ------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1347 +t0:=x^4/(2*b+b*x^5) +--R +--R +--R 4 +--R x +--R (1) --------- +--R 5 +--R b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 863 + +--S 864 of 1347 +r0:=1/5*log(2+x^5)/b +--R +--R +--R 5 +--R log(x + 2) +--R (2) ----------- +--R 5b +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(x + 2) +--R (3) ----------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1347 +t0:=1/(x*(2*b+b*x^5)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 +--R b x + 2b x +--R Type: Fraction(Polynomial(Integer)) +--E 868 + +--S 869 of 1347 +r0:=-1/5*atanh(1+x^5)/b +--R +--R +--R 5 +--R atanh(x + 1) +--R (2) - ------------- +--R 5b +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(x + 2) + 5log(x) +--R (3) ----------------------- +--R 10b +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R - log(x + 2) + 5log(x) + 2atanh(x + 1) +--R (4) ---------------------------------------- +--R 10b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1347 +t0:=1/(x^6*(2*b+b*x^5)) +--R +--R +--R 1 +--R (1) ------------- +--R 11 6 +--R b x + 2b x +--R Type: Fraction(Polynomial(Integer)) +--E 873 + +--S 874 of 1347 +r0:=(-1/10)/(b*x^5)+1/10*atanh(1+x^5)/b +--R +--R +--R 5 5 +--R x atanh(x + 1) - 1 +--R (2) ------------------- +--R 5 +--R 10b x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R x log(x + 2) - 5x log(x) - 2 +--R (3) ----------------------------- +--R 5 +--R 20b x +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R log(x + 2) - 5log(x) - 2atanh(x + 1) +--R (4) -------------------------------------- +--R 20b +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1347 +t0:=x^9/(3+b*x^5) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 5 +--R b x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 878 + +--S 879 of 1347 +r0:=1/5*x^5/b-3/5*log(3+b*x^5)/b^2 +--R +--R +--R 5 5 +--R - 3log(b x + 3) + b x +--R (2) ----------------------- +--R 2 +--R 5b +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - 3log(b x + 3) + b x +--R (3) ----------------------- +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1347 +t0:=x^4/(3+b*x^5) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 5 +--R b x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 883 + +--S 884 of 1347 +r0:=1/5*log(3+b*x^5)/b +--R +--R +--R 5 +--R log(b x + 3) +--R (2) ------------- +--R 5b +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(b x + 3) +--R (3) ------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 885 + +--S 886 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1347 +t0:=1/(x*(3+b*x^5)) +--R +--R +--R 1 +--R (1) --------- +--R 6 +--R b x + 3x +--R Type: Fraction(Polynomial(Integer)) +--E 888 + +--S 889 of 1347 +r0:=-2/15*atanh(1+2/3*b*x^5) +--R +--R +--R 5 +--R 2b x + 3 +--R 2atanh(---------) +--R 3 +--R (2) - ----------------- +--R 15 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(b x + 3) + 5log(x) +--R (3) ------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 890 + +--S 891 of 1347 +m0:=a0-r0 +--R +--R +--R 5 +--R 5 2b x + 3 +--R - log(b x + 3) + 5log(x) + 2atanh(---------) +--R 3 +--R (4) --------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1347 +t0:=1/(x^6*(3+b*x^5)) +--R +--R +--R 1 +--R (1) ----------- +--R 11 6 +--R b x + 3x +--R Type: Fraction(Polynomial(Integer)) +--E 893 + +--S 894 of 1347 +r0:=(-1/15)/x^5+2/45*b*atanh(1+2/3*b*x^5) +--R +--R +--R 5 +--R 5 2b x + 3 +--R 2b x atanh(---------) - 3 +--R 3 +--R (2) ------------------------- +--R 5 +--R 45x +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R b x log(b x + 3) - 5b x log(x) - 3 +--R (3) ----------------------------------- +--R 5 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 895 + +--S 896 of 1347 +m0:=a0-r0 +--R +--R +--R 5 +--R 5 2b x + 3 +--R b log(b x + 3) - 5b log(x) - 2b atanh(---------) +--R 3 +--R (4) ------------------------------------------------- +--R 45 +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1347 +t0:=x^5/(1+x^5) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 898 + +--S 899 of 1347 +r0:=x-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*_ + (1-sqrt(5))+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) + 20x\|2 +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I - 5%%ID1 - 5%%ID0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I - 5%%ID1 - 5%%ID0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--I 10%%ID1 log(- 5%%ID1 + x) + 10%%ID0 log(- 5%%ID0 + x) - 2log(x + 1) + 10x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 900 + +--S 901 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-+ +-+ +--I 20\|2 %%ID1 log(- 5%%ID1 + x) + 20\|2 %%ID0 log(- 5%%ID0 + x) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R - 200x + 200x - 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1347 +t0:=x^4/(1+x^5) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 903 + +--S 904 of 1347 +r0:=1/5*log(1+x^5) +--R +--R +--R 5 +--R log(x + 1) +--R (2) ----------- +--R 5 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(x + 1) +--R (3) ----------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 905 + +--S 906 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1347 +t0:=x^3/(1+x^5) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 908 + +--S 909 of 1347 +r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))+_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/sqrt(2*_ + (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--I - 5%%IE1 - 5%%IE0 + 1 +--R * +--R log +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--I - 5%%IE1 - 5%%IE0 + 1 +--R * +--R log +--R - +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--I 10%%IE1 +--R * +--R log +--R 2 2 3 +--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0 +--R + +--R 2 +--I 25%%IE0 - 5%%IE0 + x +--R + +--R 3 2 +--I 10%%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1) - 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 910 + +--S 911 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2 +--R * +--R log +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2 +--R * +--R log +--R - +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-+ +--I 20\|2 %%IE1 +--R * +--R log +--R 2 2 3 +--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0 +--R + +--R 2 +--I 25%%IE0 - 5%%IE0 + x +--R + +--R +-+ 3 2 +--I 20\|2 %%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R 200x - 200x + 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 912 + +)clear all + +--S 913 of 1347 +t0:=x^2/(1+x^5) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1347 +r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--I - 5%%IF1 - 5%%IF0 - 1 +--R * +--R log +--I (5%%IF1 + 5%%IF0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--I - 5%%IF1 - 5%%IF0 - 1 +--R * +--R log +--I (- 5%%IF1 - 5%%IF0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R 2 2 +--I 10%%IF1 log(25%%IF1 + x) + 10%%IF0 log(25%%IF0 + x) + 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2 +--R * +--R log +--I (5%%IF1 + 5%%IF0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2 +--R * +--R log +--I (- 5%%IF1 - 5%%IF0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-+ 2 +-+ 2 +--I 20\|2 %%IF1 log(25%%IF1 + x) + 20\|2 %%IF0 log(25%%IF0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1347 +t0:=x/(1+x^5) +--R +--R +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1347 +r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))+_ + 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--I - 5%%IG1 - 5%%IG0 + 1 +--R * +--R log +--I ((25%%IG0 - 5)%%IG1 - 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--I - 5%%IG1 - 5%%IG0 + 1 +--R * +--R log +--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--I 10%%IG1 +--R * +--R log +--R 2 2 3 +--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0 +--R + +--R 2 +--I - 25%%IG0 + 5%%IG0 + x - 1 +--R + +--R 3 +--I 10%%IG0 log(- 125%%IG0 + x) - 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2 +--R * +--R log +--I ((25%%IG0 - 5)%%IG1 - 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2 +--R * +--R log +--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-+ +--I 20\|2 %%IG1 +--R * +--R log +--R 2 2 3 +--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0 +--R + +--R 2 +--I - 25%%IG0 + 5%%IG0 + x - 1 +--R + +--R +-+ 3 +--I 20\|2 %%IG0 log(- 125%%IG0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1347 +t0:=1/(1+x^5) +--R +--R +--R 1 +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 923 + +--S 924 of 1347 +r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 - 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 - 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--I 10%%IH1 log(5%%IH1 + x) + 10%%IH0 log(5%%IH0 + x) + 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 925 + +--S 926 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-+ +-+ +--I 20\|2 %%IH1 log(5%%IH1 + x) + 20\|2 %%IH0 log(5%%IH0 + x) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R 200x - 200x + 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1347 +t0:=1/(x*(1+x^5)) +--R +--R +--R 1 +--R (1) ------ +--R 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1347 +r0:=-2/5*atanh(1+2*x^5) +--R +--R +--R 5 +--R 2atanh(2x + 1) +--R (2) - --------------- +--R 5 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(x + 1) + 5log(x) +--R (3) ----------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 930 + +--S 931 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R - log(x + 1) + 5log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1347 +t0:=1/(x^2*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 7 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 933 + +--S 934 of 1347 +r0:=(-1)/x+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4x\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4x\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (x\|2 \|5 - x\|2 )log(x\|5 + 2x - x + 2) + 4x\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- x\|2 \|5 - x\|2 )log(- x\|5 + 2x - x + 2) - 20\|2 +--R / +--R +-+ +--R 20x\|2 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--I - 5x %%II1 - 5x %%II0 - x +--R * +--R log +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--I - 5x %%II1 - 5x %%II0 - x +--R * +--R log +--R - +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--I 10x %%II1 +--R * +--R log +--R 2 2 3 +--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0 +--R + +--R 2 +--I 25%%II0 + 5%%II0 + x +--R + +--R 3 2 +--I 10x %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1) + 2x log(x + 1) - 10 +--R / +--R 10x +--R Type: Union(Expression(Integer),...) +--E 935 + +--S 936 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2 +--R * +--R log +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2 +--R * +--R log +--R - +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-+ +--I 20\|2 %%II1 +--R * +--R log +--R 2 2 3 +--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0 +--R + +--R 2 +--I 25%%II0 + 5%%II0 + x +--R + +--R +-+ 3 2 +--I 20\|2 %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R - 200x + 200x - 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 937 + +)clear all + +--S 938 of 1347 +t0:=1/(x^3*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 8 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 938 + +--S 939 of 1347 +r0:=(-1/2)/x^2-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*_ + (1-sqrt(5))+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_ + (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*_ + (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R 2 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4x \|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R 2 | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4x \|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R 2 +-+ +-+ 2 +-+ +-+ 2 2 +-+ +--R (x \|2 \|5 + x \|2 )log(x\|5 + 2x - x + 2) - 4x \|2 log(x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ 2 +-+ +--R (- x \|2 \|5 + x \|2 )log(- x\|5 + 2x - x + 2) - 10\|2 +--R / +--R 2 +-+ +--R 20x \|2 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R 2 | 2 2 +--I - x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 2 +--I - 5x %%IJ1 - 5x %%IJ0 + x +--R * +--R log +--I (5%%IJ1 + 5%%IJ0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R 2 | 2 2 +--I x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 2 +--I - 5x %%IJ1 - 5x %%IJ0 + x +--R * +--R log +--I (- 5%%IJ1 - 5%%IJ0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R 2 2 2 2 2 +--I 10x %%IJ1 log(25%%IJ1 + x) + 10x %%IJ0 log(25%%IJ0 + x) - 2x log(x + 1) +--R + +--R - 5 +--R / +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 940 + +--S 941 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2 +--R * +--R log +--I (5%%IJ1 + 5%%IJ0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2 +--R * +--R log +--I (- 5%%IJ1 - 5%%IJ0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-+ 2 +-+ 2 +--I 20\|2 %%IJ1 log(25%%IJ1 + x) + 20\|2 %%IJ0 log(25%%IJ0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1347 +t0:=1/(x^4*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 9 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 943 + +--S 944 of 1347 +r0:=(-1/3)/x^3+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*_ + (1-sqrt(5))-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_ + (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*_ + sqrt(1/10*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R 3 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 12x \|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R 3 | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 12x \|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R 3 +-+ +-+ 3 +-+ +-+ 2 3 +-+ +--R (- 3x \|2 \|5 - 3x \|2 )log(x\|5 + 2x - x + 2) + 12x \|2 log(x + 1) +--R + +--R 3 +-+ +-+ 3 +-+ +-+ 2 +-+ +--R (3x \|2 \|5 - 3x \|2 )log(- x\|5 + 2x - x + 2) - 20\|2 +--R / +--R 3 +-+ +--R 60x \|2 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R 3 | 2 2 +--I 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 3 3 3 +--I - 15x %%IK1 - 15x %%IK0 - 3x +--R * +--R log +--I ((25%%IK0 + 5)%%IK1 + 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R 3 | 2 2 +--I - 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 3 3 3 +--I - 15x %%IK1 - 15x %%IK0 - 3x +--R * +--R log +--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R 3 +--I 30x %%IK1 +--R * +--R log +--R 2 2 +--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1 +--R + +--R 3 2 +--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1 +--R + +--R 3 3 3 +--I 30x %%IK0 log(125%%IK0 + x) + 6x log(x + 1) - 10 +--R / +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 945 + +--S 946 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2 +--R * +--R log +--I ((25%%IK0 + 5)%%IK1 + 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2 +--R * +--R log +--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-+ +--I 20\|2 %%IK1 +--R * +--R log +--R 2 2 +--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1 +--R + +--R 3 2 +--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1 +--R + +--R +-+ 3 +--I 20\|2 %%IK0 log(125%%IK0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 947 + +)clear all + +--S 948 of 1347 +t0:=1/(a+b*x^5) +--R +--R +--R 1 +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 948 + +--S 949 of 1347 +r0a:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_ + 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_ + (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_ + b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5-sqrt(5)))))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5)) +--R +--R +--R (2) +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +----------+ 5+-+ +-+ 5+-+ +--R +-+ 5+-+ 5+-+ | +-+ 4x\|b + (- \|5 - 1)\|a +--R 4\|2 log(x\|b + \|a ) + 4\|- \|5 + 5 atan(-------------------------) +--R +------------+ +--R | +-+ 5+-+ +--R \|- 2\|5 + 10 \|a +--R + +--R +--------+ 5+-+ +-+ 5+-+ +--R | +-+ 4x\|b + (\|5 - 1)\|a +--R 4\|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +-+5+-+4 5+-+ +--R 20\|2 \|a \|b +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1347 +r0b:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_ + 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_ + (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_ + b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_ + 1/5*atan(1/2*(-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_ + (a^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5)) +--R +--R +--R (3) +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ 5+-+ 5+-+ +--R 4\|2 log(x\|b + \|a ) +--R + +--R +--------+ +--R +----------+ 5+-+ +-+ 5+-+ | +-+ +--R | +-+ (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------------------) +--R +--+5+-+ +--R 2\|10 \|a +--R + +--R +--------+ 5+-+ +-+ 5+-+ +--R | +-+ 4x\|b + (\|5 - 1)\|a +--R 4\|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +-+5+-+4 5+-+ +--R 20\|2 \|a \|b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1 +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1 +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I 10\|a b %%IM1 log(5a %%IM1 + x) + 10\|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R 5| 4 +--R 2log(x\|a b + a) +--R / +--R +---+ +--R 5| 4 +--R 10\|a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+ 5| 4 +--R 4\|2 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+5| 4 5+-+ 5+-+ +--R - 4\|2 \|a b log(x\|b + \|a ) +--R + +--R +----------+ +---+ 5+-+ +-+ 5+-+ +--R | +-+ 5| 4 4x\|b + (- \|5 - 1)\|a +--R - 4\|- \|5 + 5 \|a b atan(-------------------------) +--R +------------+ +--R | +-+ 5+-+ +--R \|- 2\|5 + 10 \|a +--R + +--R +---+ +--------+ 5+-+ +-+ 5+-+ +--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a +--R - 4\|a b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 20\|2 \|a \|b \|a b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R +--------+ +--R 2 +-+5+-+2 +-+ +-+ +-+ 5+-+5+-+ +-+5+-+2 | +-+ +--R (- 2x \|2 \|b + (x\|2 \|5 + x\|2 )\|a \|b - 2\|2 \|a )\|\|5 + 5 +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 2 +-+ | +-+ | +-+ 2 5+-+2 +--R (- 2x \|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40x )\|b +--R + +--R +------------+ +----------+ +--R +-+ +-+ +-+ | +-+ | +-+ 5+-+5+-+ +--R ((- x\|2 \|5 + x\|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40x)\|a \|b +--R + +--R +------------+ +----------+ +--R +-+ | +-+ | +-+ 5+-+2 +--R (- 2\|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40)\|a +--R / +--R 4 5+-+3 5+-+4 3 5+-+4 5+-+3 2 5+-+2 5+-+5+-+ 5+-+2 +--R 80x \|a \|b - 80x \|a \|b + 80a x \|b - 80a x\|a \|b + 80a \|a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1347 +m0a:=a0-r0b +--R +--R +--R (7) +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+ 5| 4 +--R 4\|2 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+5| 4 5+-+ 5+-+ +--R - 4\|2 \|a b log(x\|b + \|a ) +--R + +--R +--------+ +--R +----------+ +---+ 5+-+ +-+ 5+-+ | +-+ +--R | +-+ 5| 4 (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5 +--R - 4\|- \|5 + 5 \|a b atan(--------------------------------------) +--R +--+5+-+ +--R 2\|10 \|a +--R + +--R +---+ +--------+ 5+-+ +-+ 5+-+ +--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a +--R - 4\|a b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 20\|2 \|a \|b \|a b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Polynomial(Integer) +--E 955 + +)clear all + +--S 956 of 1347 +t0:=x^(23/2)/sqrt(a+b*x^5) +--R +--R +--R 11 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1347 +r0:=3/20*a^2*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(5/2)-_ + 3/20*a*x^(5/2)*sqrt(a+b*x^5)/b^2+1/10*x^(15/2)*sqrt(a+b*x^5)/b +--R +--R +--R 2 +-+ +-+ +--------+ +--R 2 x \|b \|x 7 2 +-+ +-+ | 5 +--R 3a atanh(-----------) + (2b x - 3a x )\|b \|x \|b x + a +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ---------------------------------------------------------- +--R 2 +-+ +--R 20b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1347 +--a0:=integrate(t0,x) +--E 958 + +--S 959 of 1347 +--m0:=a0-r0 +--E 959 + +--S 960 of 1347 +--d0:=D(m0,x) +--E 960 + +)clear all + +--S 961 of 1347 +t0:=x^(13/2)/sqrt(a+b*x^5) +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1347 +r0:=-1/5*a*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(3/2)+_ + 1/5*x^(5/2)*sqrt(a+b*x^5)/b +--R +--R +--R 2 +-+ +-+ +--------+ +--R x \|b \|x 2 +-+ +-+ | 5 +--R - a atanh(-----------) + x \|b \|x \|b x + a +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ---------------------------------------------- +--R +-+ +--R 5b\|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1347 +--a0:=integrate(t0,x) +--E 963 + +--S 964 of 1347 +--m0:=a0-r0 +--E 964 + +--S 965 of 1347 +--d0:=D(m0,x) +--E 965 + +)clear all + +--S 966 of 1347 +t0:=x^(3/2)/sqrt(a+b*x^5) +--R +--R +--R +-+ +--R x\|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1347 +r0:=2/5*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/sqrt(b) +--R +--R +--R 2 +-+ +-+ +--R x \|b \|x +--R 2atanh(-----------) +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1347 +--a0:=integrate(t0,x) +--E 968 + +--S 969 of 1347 +--m0:=a0-r0 +--E 969 + +--S 970 of 1347 +--d0:=D(m0,x) +--E 970 + +)clear all + +--S 971 of 1347 +t0:=1/(x^(7/2)*sqrt(a+b*x^5)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 3 +-+ | 5 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1347 +r0:=-2/5*sqrt(a+b*x^5)/(a*x^(5/2)) +--R +--R +--R +--------+ +--R | 5 +--R 2\|b x + a +--R (2) - ------------ +--R 2 +-+ +--R 5a x \|x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 5 3 +--R - 2\|x \|b x + a + (- b - a - 1)x +--R (3) ------------------------------------ +--R 3 +--R 5a x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R - b - a - 1 +--R (4) ----------- +--R 5a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1347 +t0:=1/(x^(17/2)*sqrt(a+b*x^5)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 8 +-+ | 5 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1347 +r0:=-2/15*sqrt(a+b*x^5)/(a*x^(15/2))+4/15*b*sqrt(a+b*x^5)/(a^2*x^(5/2)) +--R +--R +--R +--------+ +--R 5 | 5 +--R (4b x - 2a)\|b x + a +--R (2) ----------------------- +--R 2 7 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 5 +-+ | 5 2 2 8 +--R (12b x - 6a)\|x \|b x + a + (- 2b + (- a - 18)b + a + 9a)x +--R (3) ---------------------------------------------------------------- +--R 2 8 +--R 45a x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 2b + (- a - 18)b + a + 9a +--R (4) ----------------------------- +--R 2 +--R 45a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1347 +t0:=x^(23/2)/sqrt(1+x^5) +--R +--R +--R 11 +-+ +--R x \|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1347 +r0:=3/20*asinh(x^(5/2))-3/20*x^(5/2)*sqrt(1+x^5)+1/10*x^(15/2)*sqrt(1+x^5) +--R +--R +--R +------+ +--R 2 +-+ 7 2 +-+ | 5 +--R 3asinh(x \|x ) + (2x - 3x )\|x \|x + 1 +--R (2) ----------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R 2 +-+ | 5 5 7 2 +-+ | 5 +--R - 3log(- 2x \|x \|x + 1 + 2x + 1) + (4x - 6x )\|x \|x + 1 +--R (3) --------------------------------------------------------------- +--R 40 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ +--R 2 +-+ | 5 5 2 +-+ +--R - 3log(- 2x \|x \|x + 1 + 2x + 1) - 6asinh(x \|x ) +--R (4) ----------------------------------------------------- +--R 40 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1347 +t0:=x^(13/2)/sqrt(1+x^5) +--R +--R +--R 6 +-+ +--R x \|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1347 +r0:=-1/5*asinh(x^(5/2))+1/5*x^(5/2)*sqrt(1+x^5) +--R +--R +--R +------+ +--R 2 +-+ 2 +-+ | 5 +--R - asinh(x \|x ) + x \|x \|x + 1 +--R (2) --------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 987 + +-- (1 . failed) cannot be coerced to mode +-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3)))) +--S 988 of 1347 +--a0:=integrate(t0,x) +--E 988 + +--S 989 of 1347 +--m0:=a0-r0 +--E 989 + +--S 990 of 1347 +--d0:=normalize(D(m0,x)) +--E 990 + +)clear all + +--S 991 of 1347 +t0:=x^(3/2)/sqrt(1+x^5) +--R +--R +--R +-+ +--R x\|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1347 +r0:=2/5*asinh(x^(5/2)) +--R +--R +--R 2 +-+ +--R 2asinh(x \|x ) +--R (2) -------------- +--R 5 +--R Type: Expression(Integer) +--E 992 + +-- (1 . failed) cannot be coerced to mode +-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3)))) +--S 993 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 2 +-+ | 5 5 +--R log(- 2x \|x \|x + 1 + 2x + 1) +--R (3) - --------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ +--R 2 +-+ | 5 5 2 +-+ +--R - log(- 2x \|x \|x + 1 + 2x + 1) - 2asinh(x \|x ) +--R (4) ---------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1347 +t0:=1/(x^(7/2)*sqrt(1+x^5)) +--R +--R +--R 1 +--R (1) --------------- +--R +------+ +--R 3 +-+ | 5 +--R x \|x \|x + 1 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1347 +r0:=-2/5*sqrt(1+x^5)/x^(5/2) +--R +--R +--R +------+ +--R | 5 +--R 2\|x + 1 +--R (2) - ---------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R +-+ | 5 3 +--R - 2\|x \|x + 1 + 3x +--R (3) ---------------------- +--R 3 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 3 +--R (4) - +--R 5 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1347 +t0:=1/(x^(17/2)*sqrt(1+x^5)) +--R +--R +--R 1 +--R (1) --------------- +--R +------+ +--R 8 +-+ | 5 +--R x \|x \|x + 1 +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1347 +r0:=-2/15*sqrt(1+x^5)/x^(15/2)+4/15*sqrt(1+x^5)/x^(5/2) +--R +--R +--R +------+ +--R 5 | 5 +--R (4x - 2)\|x + 1 +--R (2) ------------------ +--R 7 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 5 +-+ | 5 8 +--R (8x - 4)\|x \|x + 1 + 9x +--R (3) ---------------------------- +--R 8 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 3 +--R (4) -- +--R 10 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1347 +t0:=x^8/(a+b*x^6) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1006 + +--S 1007 of 1347 +r0:=1/3*x^3/b-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R 3 +-+ +--R +-+ x \|b 3 +-+ +--R - \|a atan(------) + x \|b +--R +-+ +--R \|a +--R (2) --------------------------- +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 3 | a 6 |a +--R +---+ - 2b x |- - + b x - a +-+ |- +--R | a \| b 3 |a \|b 3 +--R |- - log(------------------------) + 2x |- atan(----) + x +--R \| b 6 \|b 3 +--R b x + a x +--R (3) [-----------------------------------------,-------------------] +--R 6b 3b +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | a 6 +--R +---+ - 2b x |- - + b x - a 3 +-+ +--R | a +-+ \| b +-+ x \|b +--R |- - \|b log(------------------------) + 2\|a atan(------) +--R \| b 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 6b\|b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R 3 +-+ +-+ |- +--R +-+ x \|b |a +-+ \|b +--R \|a atan(------) + |- \|b atan(----) +--R +-+ \|b 3 +--R \|a x +--R (6) ------------------------------------- +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1347 +t0:=x^7/(a+b*x^6) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1013 + +--S 1014 of 1347 +r0:=1/2*x^2/b-1/6*a^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/b^(4/3)+_ + 1/12*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/b^(4/3)+_ + 1/2*a^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_ + sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x \|a \|b + \|a ) - 2\|3 \|a log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 3+-+ 2x \|b - \|a 2 +-+3+-+ +--R - 6\|a atan(--------------) + 6x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 12b\|3 \|b +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a 2 | a 4 +-+ | a | a 2 +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x ) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a 2 +-+ +--R +---+ \|3 3|- - + 2x \|3 +--R | a \| b 2 +-+ +--R - 6 3|- - atan(-------------------- + 6x \|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 12b\|3 +--R Type: Union(Expression(Integer),...) +--E 1015 + +--S 1016 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x \|a \|b + \|a ) + 2\|3 \|a log(x \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a 2 | a 4 +--R - \|3 3|- - \|b log(3|- - + x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ 2 3+-+ 3+-+ +--R +-+ | a 3+-+ | a 2 3+-+ 2x \|b - \|a +--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(--------------) +--R \| b \| b +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a 2 +-+ +--R +---+ \|3 3|- - + 2x \|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(--------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 12b\|3 \|b +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1347 +t0:=x^6/(a+b*x^6) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1018 + +--S 1019 of 1347 +r0:=x/b-1/3*a^(1/6)*atan(b^(1/6)*x/a^(1/6))/b^(7/6)-_ + 1/3*a^(1/6)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2))-1/3*a^(1/6)*_ + atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|a \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+6+-+3+-+ x\|b +-+3+-+6+-+ +--R - \|2 \|a \|b atan(-----) + 3x\|2 \|b \|b +--R 6+-+ +--R \|a +--R / +--R +-+3+-+6+-+ +--R 3b\|2 \|b \|b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+2 +---------+ +--R | a 2 | a | a 2 +--R - b |- ------- log(36b |- ------- + 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+2 +---------+ +--R | a 2 | a | a 2 +--R b |- ------- log(36b |- ------- - 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R | a | a +--R - 2b |- ------- log(6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R | a | a +--R 2b |- ------- log(- 6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | a \| 46656b +--R - 2b\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- - x +--R 6| 7 +--R \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | a \| 46656b +--R 2b\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- + x +--R 6| 7 +--R \| 46656b +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1020 + +--S 1021 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|a \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------+ +--R +-+ | a 3+-+6+-+ +--R 3b\|2 |- ------- \|b \|b +--R 6| 7 +--R \| 46656b +--R * +--R +---------+2 +---------+ +--R 2 | a | a 2 +--R log(36b |- ------- + 6b x |- ------- + x ) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | a 3+-+6+-+ 2 | a | a 2 +--R 3b\|2 |- ------- \|b \|b log(36b |- ------- - 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R +-+ | a 3+-+6+-+ | a +--R - 6b\|2 |- ------- \|b \|b log(6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R +-+ | a 3+-+6+-+ | a +--R 6b\|2 |- ------- \|b \|b log(- 6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R 6+-+ +--R +-+6+-+3+-+ x\|b +--R 2\|2 \|a \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | a 3+-+6+-+ \| 46656b +--R - 6b\|2 \|3 |- ------- \|b \|b atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- - x +--R 6| 7 +--R \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | a 3+-+6+-+ \| 46656b +--R 6b\|2 \|3 |- ------- \|b \|b atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- + x +--R 6| 7 +--R \| 46656b +--R / +--R +-+3+-+6+-+ +--R 6b\|2 \|b \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1022 + +)clear all + +--S 1023 of 1347 +t0:=x^5/(a+b*x^6) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1023 + +--S 1024 of 1347 +r0:=1/6*log(a+b*x^6)/b +--R +--R +--R 6 +--R log(b x + a) +--R (2) ------------- +--R 6b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(b x + a) +--R (3) ------------- +--R 6b +--R Type: Union(Expression(Integer),...) +--E 1025 + +--S 1026 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1027 + +)clear all + +--S 1028 of 1347 +t0:=x^4/(a+b*x^6) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1028 + +--S 1029 of 1347 +r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(1/6)*b^(5/6))+_ + 1/3*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3))))-1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +---------------------+ +---------------------+ +--R 6+-+ | +-------+ | +-------+ +--R 3+-+2 x\|b | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|b atan(-----)\|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R 6+-+ +--R \|a +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 3\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 4 | 1 +--R 2 |- --------- log(7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 4 | 1 +--R - 2 |- --------- log(- 7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(- 7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- --------- atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- --------- atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1030 + +--S 1031 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +-----------+ +--R | 1 6+-+3+-+2 6+-+5 +--R 3 |- --------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 6+-+3+-+2 6+-+5 4 | 1 +--R 6 |- --------- \|a \|b \|b log(7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 6+-+3+-+2 6+-+5 4 | 1 +--R - 6 |- --------- \|a \|b \|b log(- 7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +-----------+ +--R | 1 6+-+3+-+2 6+-+5 +--R 3 |- --------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(- 7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R 6+-+ +--R 3+-+2 x\|b +--R - 2\|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b +--R - 6\|3 |- --------- \|a \|b \|b atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b +--R 6\|3 |- --------- \|a \|b \|b atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- + x +--R 6| 5 +--R \| 46656a b +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 6\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1032 + +)clear all + +--S 1033 of 1347 +t0:=x^3/(a+b*x^6) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1033 + +--S 1034 of 1347 +r0:=-1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(1/3)*b^(2/3))+1/12*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(1/3)*b^(2/3))-_ + 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+ +--R \|3 log(x \|b - x \|a \|b + \|a ) - 2\|3 log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2x \|b - \|a +--R 6atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 12\|3 \|a \|b +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R +-+ 2 3| 2 4 3| 2 +--R - \|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +------+2 2 +-+3| 2 +-+ +--R +-+ 2 3| 2 2x \|3 \|- a b - a b\|3 +--R 2\|3 log(x \|- a b + a b) - 6atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 12\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1035 + +--S 1036 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x \|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 4 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 2 3+-+ 3+-+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 12\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1347 +t0:=x^2/(a+b*x^6) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1038 + +--S 1039 of 1347 +r0:=1/3*atan(x^3*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R 3 +-+ +--R x \|b +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 3\|a \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +-----+ 3 +--R (b x - a)\|- a b + 2a b x 3 +---+ +--R log(----------------------------) x \|a b +--R 6 atan(--------) +--R b x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 6\|- a b 3\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 6\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 3\|a \|b \|a b +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1347 +t0:=x/(a+b*x^6) +--R +--R +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1045 + +--S 1046 of 1347 +r0:=1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(2/3)*b^(1/3))-1/12*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(2/3)*b^(1/3))-_ + 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+ +--R - \|3 log(x \|b - x \|a \|b + \|a ) + 2\|3 log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2x \|b - \|a +--R 6atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 12\|3 \|a \|b +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +---+ +--R +-+ 4 3| 2 2 3| 2 2 +-+ 2 3| 2 +--R - \|3 log(x \|a b - a x \|a b + a ) + 2\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +--R 2x \|3 \|a b - a\|3 +--R 6atan(---------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 12\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 12\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1347 +t0:=1/(a+b*x^6) +--R +--R +--R 1 +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1050 + +--S 1051 of 1347 +r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*b^(1/6))+1/3*atan(b^(1/3)*_ + x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*_ + sqrt(2))+1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R / +--R +-+6+-+5 3+-+6+-+ +--R 3\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R |- -------- log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R - |- -------- log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R 2 |- -------- log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R - 2 |- -------- log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 3\|2 |- -------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +----------+2 +----------+ +--R 2 | 1 | 1 2 +--R log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 3\|2 |- -------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +----------+2 +----------+ +--R 2 | 1 | 1 2 +--R log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R 6\|2 |- -------- \|a \|b \|b log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R - 6\|2 |- -------- \|a \|b \|b log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - 2\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b +--R 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b +--R - 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 6\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1347 +t0:=1/(x*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ---------- +--R 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1055 + +--S 1056 of 1347 +r0:=log(x)/a-1/6*log(a+b*x^6)/a +--R +--R +--R 6 +--R - log(b x + a) + 6log(x) +--R (2) ------------------------- +--R 6a +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(b x + a) + 6log(x) +--R (3) ------------------------- +--R 6a +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1347 +t0:=1/(x^2*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1060 + +--S 1061 of 1347 +r0:=(-1)/(a*x)-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/3*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(7/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3))))+1/3*b^(1/3)*atanh(b^(1/3)*x*_ + sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(2)/(a^(7/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R x\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - x\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +---------------------+ +--R 6+-+ | +-------+ +--R 6+-+ x\|b 6+-+ | +-+ | 3+-+2 3+-+ +--R (- x\|b atan(-----) - 3\|a )\|\|3 \|- \|b - \|b +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 3a x\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R - 2a x |- ------- log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R 2a x |- ------- log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R a x |- ------- log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a x\|3 |- ------- atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a x\|3 |- ------- atan(------------------------- - 2 +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------+ +--R | b 6+-+ +--R 3a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R - 6a |- ------- \|a log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R 6a |- ------- \|a log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R | b 6+-+ +--R 3a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 6+-+ +--R 6+-+ x\|b +--R 2\|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R 6a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 6a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 6a\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1347 +t0:=1/(x^3*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1065 + +--S 1066 of 1347 +r0:=(-1/2)/(a*x^2)+1/6*b^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/a^(4/3)-_ + 1/12*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(4/3)+_ + 1/2*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_ + sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - x \|3 \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2 +-+3+-+ 2 3+-+ 3+-+ 2 3+-+ 2x \|b - \|a +-+3+-+ +--R 2x \|3 \|b log(x \|b + \|a ) - 6x \|b atan(-------------- - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R 12a x \|3 \|a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 2 +-+ |b |b 2 +--R 2x \|3 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 2 +-+ |b 2 |b |b 4 +--R - x \|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 2 |b \|a +-+ +--R 6x 3|- atan(---------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R 12a x \|3 +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b 2 +--R 2\|3 \|a 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 2 3+-+ 3+-+ +--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 12a\|3 \|a +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1347 +t0:=1/(x^4*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1070 + +--S 1071 of 1347 +r0:=(-1/3)/(a*x^3)-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R 3 +-+ +--R 3 +-+ x \|b +-+ +--R - x \|b atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 3 | b 6 |b +--R +---+ - 2a x |- - + b x - a +-+ a |- +--R 3 | b \| a 3 |b \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 6 \|a 3 +--R b x + a b x +--R (3) [-----------------------------------------,---------------------] +--R 3 3 +--R 6a x 3a x +--R Type: Union(List(Expression(Integer)),...) +--E 1072 + +--S 1073 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a 3 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 3 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 3 +--R \|a b x +--R (6) -------------------------------------- +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1347 +t0:=x^8/(a+b*x^6)^2 +--R +--R +--R 8 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1347 +r0:=-1/6*x^3/(b*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R 3 +-+ +--R 6 x \|b 3 +-+ +-+ +--R (b x + a)atan(------) - x \|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 2 6 +-+ +-+ +--R (6b x + 6a b)\|a \|b +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-----+ 3 +--R 6 (b x - a)\|- a b + 2a b x 3 +-----+ +--R (b x + a)log(----------------------------) - 2x \|- a b +--R 6 +--R b x + a +--R [---------------------------------------------------------, +--R 2 6 +-----+ +--R (12b x + 12a b)\|- a b +--R 3 +---+ +--R 6 x \|a b 3 +---+ +--R (b x + a)atan(--------) - x \|a b +--R a +--R -----------------------------------] +--R 2 6 +---+ +--R (6b x + 6a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1079 + +--S 1080 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 12b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 6b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1083 + +)clear all + +--S 1084 of 1347 +t0:=x^7/(a+b*x^6)^2 +--R +--R +--R 7 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1084 + +--S 1085 of 1347 +r0:=-1/6*x^2/(b*(a+b*x^6))+1/18*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(2/3)*b^(4/3))-1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_ + b^(2/3)*x^4)/(a^(2/3)*b^(4/3))-1/6*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+2 3+-+ +--R - 6x \|3 \|a \|b +--R / +--R 2 6 +-+3+-+2 3+-+ +--R (36b x + 36a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 6 +-+ 4 3| 2 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +---+ +--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2 +--R (6b x + 6a)atan(---------------------) - 6x \|3 \|a b +--R 3a +--R / +--R +---+ +--R 2 6 +-+3| 2 +--R (36b x + 36a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 36b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1088 + +)clear all + +--S 1089 of 1347 +t0:=x^6/(a+b*x^6)^2 +--R +--R +--R 6 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1089 + +--S 1090 of 1347 +r0:=-1/6*x/(b*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*_ + b^(7/6))+1/18*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/_ + (a^(5/6)*b^(4/3)*sqrt(2))+1/18*atanh(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(4/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R (b x + a)\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R (b x + a)\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+ +--R (b x + a)\|2 \|b atan(-----) - 3x\|2 \|a \|b \|b +--R 6+-+ +--R \|a +--R / +--R 2 6 +-+6+-+5 3+-+6+-+ +--R (18b x + 18a b)\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 2 6 | 1 +--R (3b x + 3a b) |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- + 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 2 6 | 1 +--R (- 3b x - 3a b) |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- - 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 2 6 | 1 | 1 +--R (6b x + 6a b) |- -------------- log(36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 2 6 | 1 | 1 +--R (- 6b x - 6a b) |- -------------- log(- 36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R +----------------+ 6| 5 7 +--R 2 6 +-+ | 1 \| 2176782336a b +--R (6b x + 6a b)\|3 |- -------------- atan(----------------------------) +--R 6| 5 7 +----------------+ +--R \| 2176782336a b | 1 +--R 18a b |- -------------- - x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R +----------------+ 6| 5 7 +--R 2 6 +-+ | 1 \| 2176782336a b +--R (- 6b x - 6a b)\|3 |- -------------- atan(----------------------------) +--R 6| 5 7 +----------------+ +--R \| 2176782336a b | 1 +--R 18a b |- -------------- + x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R - x +--R / +--R 2 6 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1091 + +--S 1092 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 9b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- + 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 9b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- - 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R 18b\|2 |- -------------- \|a \|b \|b log(36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R | 1 +--R log(- 36a b |- -------------- + x) +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R atan(----------------------------) +--R +----------------+ +--R | 1 +--R 18a b |- -------------- - x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R atan(----------------------------) +--R +----------------+ +--R | 1 +--R 18a b |- -------------- + x +--R 6| 5 7 +--R \| 2176782336a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 18b\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1093 + +)clear all + +--S 1094 of 1347 +t0:=x^5/(a+b*x^6)^2 +--R +--R +--R 5 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1094 + +--S 1095 of 1347 +r0:=(-1/6)/(b*(a+b*x^6)) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - ---------- +--R 2 6 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1095 + +--S 1096 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 6 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1096 + +--S 1097 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1098 + +)clear all + +--S 1099 of 1347 +t0:=x^4/(a+b*x^6)^2 +--R +--R +--R 4 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1099 + +--S 1100 of 1347 +r0:=1/6*x^5/(a*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/_ + (a^(7/6)*b^(5/6))+1/9*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*_ + sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))-1/9*_ + atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*sqrt(2)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 6 6+-+5 | +-+ | 3+-+2 3+-+ +--R (- 2b x - 2a)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 6 6+-+5 | +-+ | 3+-+2 3+-+ +--R (2b x + 2a)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+2 x\|b 5 +-+6+-+3+-+2 6+-+5 +--R ((b x + a)\|2 \|b atan(-----) + 3x \|2 \|a \|b \|b ) +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +--R | +-------+ +--R 6 2 +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ +--R (18a b x + 18a )\|2 \|a \|b \|b \|\|3 \|- \|b - \|b +--R * +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 6 2 | 1 +--R (3a b x + 3a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (6a b x + 6a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 6a b x - 6a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(- 60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 3a b x - 3a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R - 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (- 6a b x - 6a )\|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- - x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (6a b x + 6a )\|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R 5 +--R x +--R / +--R 6 2 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1101 + +--S 1102 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 9a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(- 60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 9a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R - 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+2 x\|b +--R - \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- - x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 18a\|2 \|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1103 + +)clear all + +--S 1104 of 1347 +t0:=x^3/(a+b*x^6)^2 +--R +--R +--R 3 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1104 + +--S 1105 of 1347 +r0:=1/6*x^4/(a*(a+b*x^6))-1/18*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(4/3)*b^(2/3))+1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + x^2+b^(2/3)*x^4)/(a^(4/3)*b^(2/3))-1/6*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (- 2b x - 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+3+-+2 +--R 6x \|3 \|a \|b +--R / +--R 6 2 +-+3+-+3+-+2 +--R (36a b x + 36a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 6 +-+ 2 3| 2 4 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +------+ +--R 6 2x \|3 \|- a b - a b\|3 4 +-+3| 2 +--R (- 6b x - 6a)atan(---------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 6 2 +-+3| 2 +--R (36a b x + 36a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1106 + +--S 1107 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x \|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 4 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 2 3+-+ 3+-+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 36a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1108 + +)clear all + +--S 1109 of 1347 +t0:=x^2/(a+b*x^6)^2 +--R +--R +--R 2 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1109 + +--S 1110 of 1347 +r0:=1/6*x^3/(a*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R 3 +-+ +--R 6 x \|b 3 +-+ +-+ +--R (b x + a)atan(------) + x \|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 6 2 +-+ +-+ +--R (6a b x + 6a )\|a \|b +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-----+ 3 +--R 6 (b x - a)\|- a b + 2a b x 3 +-----+ +--R (b x + a)log(----------------------------) + 2x \|- a b +--R 6 +--R b x + a +--R [---------------------------------------------------------, +--R 6 2 +-----+ +--R (12a b x + 12a )\|- a b +--R 3 +---+ +--R 6 x \|a b 3 +---+ +--R (b x + a)atan(--------) + x \|a b +--R a +--R -----------------------------------] +--R 6 2 +---+ +--R (6a b x + 6a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1111 + +--S 1112 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 12a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 6a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1347 +t0:=x/(a+b*x^6)^2 +--R +--R +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1116 + +--S 1117 of 1347 +r0:=1/6*x^2/(a*(a+b*x^6))+1/9*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(5/3)*b^(1/3))-1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_ + b^(2/3)*x^4)/(a^(5/3)*b^(1/3))-1/3*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+2 3+-+ +--R 3x \|3 \|a \|b +--R / +--R 6 2 +-+3+-+2 3+-+ +--R (18a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 6 +-+ 4 3| 2 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +---+ +--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2 +--R (6b x + 6a)atan(---------------------) + 3x \|3 \|a b +--R 3a +--R / +--R +---+ +--R 6 2 +-+3| 2 +--R (18a b x + 18a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1347 +t0:=1/(a+b*x^6)^2 +--R +--R +--R 1 +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1121 + +--S 1122 of 1347 +r0:=1/6*x/(a*(a+b*x^6))+5/18*atan(b^(1/6)*x/a^(1/6))/_ + (a^(11/6)*b^(1/6))+5/18*atan(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*_ + b^(1/3)*sqrt(2))+5/18*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*b^(1/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ +--R (5b x + 5a)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ +--R (5b x + 5a)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+ +--R (5b x + 5a)\|2 \|b atan(-----) + 3x\|2 \|a \|b \|b +--R 6+-+ +--R \|a +--R / +--R 6 2 +-+6+-+5 3+-+6+-+ +--R (18a b x + 18a )\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 6 2 | 1 +--R (15a b x + 15a ) |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- + 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 15a b x - 15a ) |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- - 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 6 2 | 1 2 | 1 +--R (30a b x + 30a ) |- -------------- log(36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 6 2 | 1 2 | 1 +--R (- 30a b x - 30a ) |- -------------- log(- 36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R +----------------+ 6| 11 +--R 6 2 +-+ | 1 \| 2176782336a b +--R (30a b x + 30a )\|3 |- -------------- atan(---------------------------) +--R 6| 11 +----------------+ +--R \| 2176782336a b 2 | 1 +--R 18a |- -------------- - x +--R 6| 11 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (- 30a b x - 30a )\|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- + x +--R 6| 11 +--R \| 2176782336a b +--R + +--R x +--R / +--R 6 2 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 5\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 5\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 45a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- + 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 45a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- - 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ 2 | 1 +--R 90a\|2 |- -------------- \|a \|b \|b log(36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 | 1 +--R log(- 36a |- -------------- + x) +--R 6| 11 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - 5\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- - x +--R 6| 11 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- + x +--R 6| 11 +--R \| 2176782336a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 18a\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1347 +t0:=1/(x*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 13 7 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1126 + +--S 1127 of 1347 +r0:=1/6/(a*(a+b*x^6))+log(x)/a^2-1/6*log(a+b*x^6)/a^2 +--R +--R +--R 6 6 6 +--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 6 3 +--R 6a b x + 6a +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 6 3 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1347 +t0:=1/(x^2*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 14 8 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1131 + +--S 1132 of 1347 +r0:=(-7/6)/(a^2*x)+1/6/(a*x*(a+b*x^6))-7/18*b^(1/6)*atan(b^(1/6)*_ + x/a^(1/6))/a^(13/6)-7/9*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*_ + sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))+7/9*_ + b^(1/3)*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*sqrt(2)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 7 3+-+ | +-+ | 3+-+2 3+-+ +--R (14b x + 14a x)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 7 3+-+ | +-+ | 3+-+2 3+-+ +--R (- 14b x - 14a x)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 7 +-+6+-+ x\|b 6 +-+6+-+ +--R ((- 7b x - 7a x)\|2 \|b atan(-----) + (- 21b x - 18a)\|2 \|a ) +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 2 7 3 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R (18a b x + 18a x)\|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 7 3 | 117649b +--R (- 3a b x - 3a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +---------------+4 +--R 11 | 117649b 9 | 117649b +--R 60466176a x |- ------------- - 11757312a |- ------------- +--R 6| 13 6| 13 +--R \| 2176782336a \| 2176782336a +--R + +--R 2 +--R 16807b x +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (- 6a b x - 6a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (6a b x + 6a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(- 60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (3a b x + 3a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +---------------+4 +--R 11 | 117649b 9 | 117649b +--R - 60466176a x |- ------------- - 11757312a |- ------------- +--R 6| 13 6| 13 +--R \| 2176782336a \| 2176782336a +--R + +--R 2 +--R 16807b x +--R + +--R +---------------+ +--R 2 7 3 +-+ | 117649b +--R (6a b x + 6a x)\|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- - 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 +-+ | 117649b +--R (- 6a b x - 6a x)\|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R 6 +--R - 7b x - 6a +--R / +--R 2 7 3 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 14\|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 14\|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 9a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +--R 11 | 117649b +--R 60466176a x |- ------------- +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+4 +--R 9 | 117649b 2 +--R - 11757312a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R - +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 18a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 18a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(- 60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 9a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +--R 11 | 117649b +--R - 60466176a x |- ------------- +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+4 +--R 9 | 117649b 2 +--R - 11757312a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R 6+-+ +--R +-+6+-+ x\|b +--R 7\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------------+ +--R 2 +-+ +-+ | 117649b 6+-+ +--R 18a \|2 \|3 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- - 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R - +--R +---------------+ +--R 2 +-+ +-+ | 117649b 6+-+ +--R 18a \|2 \|3 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 2 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 18a \|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1347 +t0:=1/(x^3*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 15 9 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 1347 +r0:=(-2/3)/(a^2*x^2)+1/6/(a*x^2*(a+b*x^6))+2/9*b^(1/3)*_ + log(a^(1/3)+b^(1/3)*x^2)/a^(7/3)-1/9*b^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(7/3)+2/3*b^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 8 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- 2b x - 2a x )\|3 \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R 8 2 +-+3+-+ 2 3+-+ 3+-+ +--R (4b x + 4a x )\|3 \|b log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 8 2 3+-+ 2x \|b - \|a 6 +-+3+-+ +--R (- 12b x - 12a x )\|b atan(--------------) + (- 12b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 8 3 2 +-+3+-+ +--R (18a b x + 18a x )\|3 \|a +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 8 2 +-+ |b |b 2 +--R (4b x + 4a x )\|3 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 8 2 +-+ |b 2 |b |b 4 +--R (- 2b x - 2a x )\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 8 2 |b \|a 6 +-+ +--R (12b x + 12a x ) 3|- atan(---------------------- + (- 12b x - 9a)\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 8 3 2 +-+ +--R (18a b x + 18a x )\|3 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b 2 +--R 2\|3 \|a 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 2 3+-+ 3+-+ +--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1347 +t0:=1/(x^4*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 16 10 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 1347 +r0:=(-1/2)/(a^2*x^3)+1/6/(a*x^3*(a+b*x^6))-1/2*atan(x^3*_ + sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R 3 +-+ +--R 9 3 +-+ x \|b 6 +-+ +--R (- 3b x - 3a x )\|b atan(------) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 9 3 3 +-+ +--R (6a b x + 6a x )\|a +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a +--R 9 3 | b \| a 6 +--R (3b x + 3a x ) |- - log(------------------------) - 6b x - 4a +--R \| a 6 +--R b x + a +--R [---------------------------------------------------------------, +--R 2 9 3 3 +--R 12a b x + 12a x +--R +-+ +--R |b +--R +-+ a |- +--R 9 3 |b \|a 6 +--R (3b x + 3a x ) |- atan(-----) - 3b x - 2a +--R \|a 3 +--R b x +--R -------------------------------------------] +--R 2 9 3 3 +--R 6a b x + 6a x +--R Type: Union(List(Expression(Integer)),...) +--E 1143 + +--S 1144 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a 3 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 3 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 3 +--R \|a b x +--R (6) -------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1147 + +)clear all + +--S 1148 of 1347 +t0:=x^8/(1-x^6) +--R +--R +--R 8 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1148 + +--S 1149 of 1347 +r0:=-1/3*x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R atanh(x ) - x +--R (2) -------------- +--R 3 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2x +--R (3) ------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1150 + +--S 1151 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1152 + +)clear all + +--S 1153 of 1347 +t0:=x^7/(1-x^6) +--R +--R +--R 7 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1153 + +--S 1154 of 1347 +r0:=-1/2*x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/_ + sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R -------------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1155 + +--S 1156 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1157 + +)clear all + +--S 1158 of 1347 +t0:=x^6/(1-x^6) +--R +--R +--R 6 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1158 + +--S 1159 of 1347 +r0a:=-x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +-+ +--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------) - 6x\|3 +--R 2 2 +--R x + 1 x - 1 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1347 +r0b:=-x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +-+ +--R 6atan(------------) + 6atan(------------) - 12x\|3 +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------) - 12x\|3 +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1161 + +--S 1162 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R 6atan(------------) + 6atan(------------) + 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1347 +t0:=x^5/(1-x^6) +--R +--R +--R 5 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 1347 +r0:=-1/6*log(1-x^6) +--R +--R +--R 6 +--R log(- x + 1) +--R (2) - ------------- +--R 6 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(x - 1) +--R (3) - ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1347 +t0:=x^4/(1-x^6) +--R +--R +--R 4 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 1347 +r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +--R 2\|3 atanh(x) + \|3 atanh(------) + 3atan(------) +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1347 +r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)+_ + 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +--R - 6atan(------------) - 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +--R - 2\|3 log(x - 1) - 6atan(------------) - 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R - 6atan(------------) - 6atan(------------) - 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1178 + +)clear all + +--S 1179 of 1347 +t0:=x^3/(1-x^6) +--R +--R +--R 3 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1179 + +--S 1180 of 1347 +r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) - 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1181 + +--S 1182 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1183 + +)clear all + +--S 1184 of 1347 +t0:=x^2/(1-x^6) +--R +--R +--R 2 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1184 + +--S 1185 of 1347 +r0:=1/3*atanh(x^3) +--R +--R +--R 3 +--R atanh(x ) +--R (2) --------- +--R 3 +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R log(x + 1) - log(x - 1) +--R (3) ------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1186 + +--S 1187 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1188 + +)clear all + +--S 1189 of 1347 +t0:=x/(1-x^6) +--R +--R +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1189 + +--S 1190 of 1347 +r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1191 + +--S 1192 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1193 + +)clear all + +--S 1194 of 1347 +t0:=1/(1-x^6) +--R +--R +--R 1 +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1194 + +--S 1195 of 1347 +r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------) +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1347 +r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)-_ + 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +--R 6atan(------------) + 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R 6atan(------------) + 6atan(------------) + 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1201 + +)clear all + +--S 1202 of 1347 +t0:=1/(x*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------ +--R 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1202 + +--S 1203 of 1347 +r0:=-1/3*atanh(1-2*x^6) +--R +--R +--R 6 +--R atanh(2x - 1) +--R (2) -------------- +--R 3 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(x - 1) + 6log(x) +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1204 + +--S 1205 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + 6log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1206 + +)clear all + +--S 1207 of 1347 +t0:=1/(x^2*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------- +--R 8 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1207 + +--S 1208 of 1347 +r0a:=(-1)/x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/_ + (1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +-+ +--R 2x\|3 atanh(x) + x\|3 atanh(------) + 3x atan(------) - 6\|3 +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------------------- +--R +-+ +--R 6x\|3 +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1347 +r0b:=(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 4x\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 6x atan(------------) - 6x atan(------------) - 12\|3 +--R 3 3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 2x\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 2x\|3 log(x - 1) - 6x atan(------------) - 6x atan(------------) - 12\|3 +--R 3 3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Union(Expression(Integer),...) +--E 1210 + +--S 1211 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R - 6atan(------------) - 6atan(------------) - 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1347 +t0:=1/(x^3*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------- +--R 9 3 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1347 +r0:=(-1/2)/x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-_ + 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1347 +t0:=1/(x^4*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 10 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1347 +r0:=(-1/3)/x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R x atanh(x ) - 1 +--R (2) --------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 3 +--R x log(x + 1) - x log(x - 1) - 2 +--R (3) --------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1347 +t0:=1/(x^5*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 11 5 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1347 +r0:=(-1/4)/x^4-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+_ + 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) + 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 3\|3 +--R / +--R 4 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1347 +t0:=1/(x^6*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 12 6 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1347 +r0:=(-1/5)/x^5+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 20x \|3 atanh(x) +--R + +--R +-+ +-+ +--R 5 (2x + 1)\|3 5 (2x - 1)\|3 +-+ +--R 30x atan(------------) + 30x atan(------------) - 12\|3 +--R 3 3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 10x \|3 log(x + 1) +--R + +--R +-+ +-+ +--R 5 +-+ 5 (2x + 1)\|3 5 (2x - 1)\|3 +--R - 10x \|3 log(x - 1) + 30x atan(------------) + 30x atan(------------) +--R 3 3 +--R + +--R +-+ +--R - 12\|3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1347 +m0:=a0-r0 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (4) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1347 +t0:=1/(x^7*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 13 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1347 +r0:=(-1/6)/x^6-1/3*atanh(1-2*x^6) +--R +--R +--R 6 6 +--R 2x atanh(2x - 1) - 1 +--R (2) --------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R - x log(x - 1) + 6x log(x) - 1 +--R (3) ------------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + 6log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1347 +t0:=1/(x^8*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 14 8 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1347 +r0:=(-1/7)/x^7+(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 28x \|3 atanh(x) +--R + +--R +-+ +-+ +--R 7 (2x + 1)\|3 7 (2x - 1)\|3 6 +-+ +--R - 42x atan(------------) - 42x atan(------------) + (- 84x - 12)\|3 +--R 3 3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 14x \|3 log(x + 1) +--R + +--R +-+ +-+ +--R 7 +-+ 7 (2x + 1)\|3 7 (2x - 1)\|3 +--R - 14x \|3 log(x - 1) - 42x atan(------------) - 42x atan(------------) +--R 3 3 +--R + +--R 6 +-+ +--R (- 84x - 12)\|3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1347 +m0:=a0-r0 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (4) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1347 +t0:=x^8/(1+x^6) +--R +--R +--R 8 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1347 +r0:=1/3*x^3-1/3*atan(x^3) +--R +--R +--R 3 3 +--R - atan(x ) + x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - atan(x ) + x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1347 +t0:=x^7/(1+x^6) +--R +--R +--R 7 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1347 +r0:=1/2*x^2-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_ + 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+ +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+ +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1347 +t0:=x^6/(1+x^6) +--R +--R +--R 6 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1347 +r0:=x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) + 12x\|3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 2x +--R 2sin(----------)atan(-------------------) + atan(------) + 6x +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R - 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- 2x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1347 +t0:=x^5/(1+x^6) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1347 +r0:=1/6*log(1+x^6) +--R +--R +--R 6 +--R log(x + 1) +--R (2) ----------- +--R 6 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(x + 1) +--R (3) ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1347 +t0:=x^4/(1+x^6) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1347 +r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))+_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R - 2sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R 2sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 2x +--R - atan(------) +--R 2 +--R x - 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (4x + 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x +--R 2 2 +--R + +--R 4 +--R 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (2x + 6x - 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x +--R 2 2 +--R + +--R 8 +--R x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1347 +t0:=x^3/(1+x^6) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1347 +r0:=-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1347 +t0:=x^2/(1+x^6) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1347 +r0:=1/3*atan(x^3) +--R +--R +--R 3 +--R atan(x ) +--R (2) -------- +--R 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R atan(x ) +--R (3) -------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1347 +t0:=x/(1+x^6) +--R +--R +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1347 +r0:=1/6*log(1+x^2)-1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (3) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1347 +t0:=1/(1+x^6) +--R +--R +--R 1 +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1347 +r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))-_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R 2sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 2x +--R - 2sin(----------)atan(-------------------) - atan(------) +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R - 4\|3 sin(----------)atan(-------------------) - 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) + 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (2x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((4x - 2x )cos(----------) + 2x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (2x - x )cos(----------) + (- 2x + 2x )cos(----------) + x - 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1347 +t0:=1/(x*(1+x^6)) +--R +--R +--R 1 +--R (1) ------ +--R 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1347 +r0:=-1/3*atanh(1+2*x^6) +--R +--R +--R 6 +--R atanh(2x + 1) +--R (2) - -------------- +--R 3 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(x + 1) + 6log(x) +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x + 1) + 6log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1347 +t0:=1/(x^2*(1+x^6)) +--R +--R +--R 1 +--R (1) ------- +--R 8 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1347 +r0:=(-1)/x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-1/6*atan(2*x+sqrt(3))-_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3x log(x\|3 + x + 1) - 3x log(- x\|3 + x + 1) - 2x\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2x\|3 atan(\|3 - 2x) - 4x\|3 atan(x) - 12\|3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R 2x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R - 2x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 2x +--R x atan(------) - 6 +--R 2 +--R x - 1 +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((4x + 4x )cos(----------) - 4x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (- 4x - 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (6x + 6x )cos(----------) + (- 4x + 2x )cos(----------) + 6x +--R 2 2 +--R + +--R 4 +--R - 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((- 8x - 8x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (4x + 4x )cos(----------) + (4x - 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (16x + 12x + 2x )cos(----------) + x - 5x + 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (- 4x - 4x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 2x - 6x + 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (x + x )cos(----------) + (4x - 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (6x - 3x )cos(----------) + (- x + 5x - 3x )cos(----------) + 2x +--R 2 2 +--R + +--R 8 +--R - x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1347 +t0:=1/(x^3*(1+x^6)) +--R +--R +--R 1 +--R (1) ------- +--R 9 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1347 +r0:=(-1/2)/x^2+1/6*log(1+x^2)-1/12*log(1-x^2+x^4)+1/2*_ + atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3 +--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3 +--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1347 +t0:=1/(x^4*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 10 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1347 +r0:=(-1/3)/x^3-1/3*atan(x^3) +--R +--R +--R 3 3 +--R - x atan(x ) - 1 +--R (2) ---------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - x atan(x ) - 1 +--R (3) ---------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1347 +t0:=1/(x^5*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 11 5 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1347 +r0:=(-1/4)/x^4-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_ + 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+ +--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+ +--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1347 +t0:=1/(x^6*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 12 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1315 + +--S 1316 of 1347 +r0:=(-1/5)/x^5-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 +--R - 15x log(x\|3 + x + 1) + 15x log(- x\|3 + x + 1) +--R + +--R 5 +-+ +-+ 5 +-+ +-+ 5 +-+ +--R - 10x \|3 atan(\|3 + 2x) + 10x \|3 atan(\|3 - 2x) - 20x \|3 atan(x) +--R + +--R +-+ +--R - 12\|3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R 5 \|3 +--R 5x cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 5 \|3 +--R 5x cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R 5 \|3 2 +--R - 10x sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R 5 \|3 2 5 2x +--R 10x sin(----------)atan(-------------------) + 5x atan(------) - 6 +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R - 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- 2x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1347 +t0:=1/(x^7*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 13 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1320 + +--S 1321 of 1347 +r0:=(-1/6)/x^6+1/3*atanh(1+2*x^6) +--R +--R +--R 6 6 +--R 2x atanh(2x + 1) - 1 +--R (2) --------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R x log(x + 1) - 6x log(x) - 1 +--R (3) ----------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R log(x + 1) - 6log(x) - 2atanh(2x + 1) +--R (4) --------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1347 +t0:=1/(x^8*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 14 8 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1325 + +--S 1326 of 1347 +r0:=(-1/7)/x^7+1/x+1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 +--R - 21x log(x\|3 + x + 1) + 21x log(- x\|3 + x + 1) +--R + +--R 7 +-+ +-+ 7 +-+ +-+ 7 +-+ +--R 14x \|3 atan(\|3 + 2x) - 14x \|3 atan(\|3 - 2x) + 28x \|3 atan(x) +--R + +--R 6 +-+ +--R (84x - 12)\|3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R 7 \|3 +--R 7x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 7 \|3 +--R 7x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R 7 \|3 2 2 +--R - 14x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R 7 \|3 2 2 +--R 14x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 7 2x 6 +--R - 7x atan(------) + 42x - 6 +--R 2 +--R x - 1 +--R / +--R 7 +--R 42x +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (4x + 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x +--R 2 2 +--R + +--R 4 +--R 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (2x + 6x - 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x +--R 2 2 +--R + +--R 8 +--R x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1347 +t0:=1/(2-3*x^6) +--R +--R +--R 1 +--R (1) - ------- +--R 6 +--R 3x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1330 + +--S 1331 of 1347 +r0a:=1/2*atan(3*2^(1/6)*3^(1/3)*x/(2^(1/3)*3^(2/3)-3*x^2))/(2^(5/6)*_ + 3^(2/3))+1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))+_ + 1/6*atanh(2^(1/6)*3^(5/6)*x/(2^(1/3)*3^(2/3)+3*x^2))/_ + (2^(5/6)*3^(1/6)) +--R +--R +--R (2) +--R 6+-+6+-+5 6+-+ 6+-+3+-+ +--R 3+-+2 x\|2 \|3 3+-+2 x\|3 6+-+ 3x\|2 \|3 +--R \|3 atanh(---------------) + 2\|3 atanh(-----) + 3\|3 atan(---------------) +--R 3+-+3+-+2 2 6+-+ 3+-+3+-+2 2 +--R \|2 \|3 + 3x \|2 \|2 \|3 - 3x +--R ----------------------------------------------------------------------------- +--R 6+-+5 3+-+2 6+-+ +--R 6\|2 \|3 \|3 +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1347 +r0b:=-1/2*atan(1/3*(2^(1/6)*3^(5/6)-6*x)/_ + (2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+1/2*atan(1/3*_ + (2^(1/6)*3^(5/6)+6*x)/(2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+_ + 1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))-_ + 1/12*log(2^(1/3)-6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6))+_ + 1/12*log(2^(1/3)+6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6)) +--R +--R +--R (3) +--R 3+-+2 6+-+ 2 3+-+ 3+-+ 3+-+2 6+-+ 2 3+-+ 3+-+ +--R \|3 log(x\|6 + x \|3 + \|2 ) - \|3 log(- x\|6 + x \|3 + \|2 ) +--R + +--R 6+-+ 3+-+2 6+-+5 6+-+5 3+-+2 +--R 3+-+2 x\|3 6+-+ \|3 \|3 + 3x \|2 \|3 +--R 4\|3 atanh(-----) + 6\|3 atan(--------------------------) +--R 6+-+ 9 +--R \|2 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+ \|3 \|3 - 3x \|2 \|3 +--R - 6\|3 atan(--------------------------) +--R 9 +--R / +--R 6+-+5 3+-+2 6+-+ +--R 12\|2 \|3 \|3 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R 2 6+--+2 6+--+ 2 6+--+2 6+--+ +--R log(x \|96 + 2x\|96 + 4) - log(x \|96 - 2x\|96 + 4) +--R + +--R +-+ +--R 6+--+ 6+--+ +-+ \|3 +--R 2log(x\|96 + 2) - 2log(x\|96 - 2) - 2\|3 atan(----------) +--R 6+--+ +--R x\|96 - 1 +--R + +--R +-+ +--R +-+ \|3 +--R - 2\|3 atan(----------) +--R 6+--+ +--R x\|96 + 1 +--R / +--R 6+--+ +--R 12\|96 +--R Type: Union(Expression(Integer),...) +--E 1333 + +--S 1334 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+ +--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2) +--R + +--R 6+-+6+-+5 6+-+ +--R 3+-+2 6+--+ x\|2 \|3 3+-+2 6+--+ x\|3 +--R - 2\|3 \|96 atanh(--------------- - 4\|3 \|96 atanh(-----) +--R 3+-+3+-+2 2 6+-+ +--R \|2 \|3 + 3x \|2 +--R + +--R 6+-+3+-+ +-+ +--R 6+-+6+--+ 3x\|2 \|3 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 6\|3 \|96 atan(---------------) - 2\|2 \|3 \|3 \|3 atan(----------) +--R 3+-+3+-+2 2 6+--+ +--R \|2 \|3 - 3x x\|96 - 1 +--R + +--R +-+ +--R 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 2\|2 \|3 \|3 \|3 atan(----------) +--R 6+--+ +--R x\|96 + 1 +--R / +--R 6+-+5 3+-+2 6+-+6+--+ +--R 12\|2 \|3 \|3 \|96 +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2 +--R (- 12x \|2 \|2 + (27x + 54x )\|2 )\|3 +--R + +--R 10 6+-+4 10 4 3+-+2 3+-+ 2 3+-+6+-+4 14 +--R (18x \|2 + (27x + 18x )\|2 )\|3 + 12x \|2 \|2 + 27x +--R + +--R 8 2 +--R 108x - 12x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2 +--R ((- 63x - 30x )\|2 \|2 + (3x + 10x )\|2 )\|3 +--R + +--R 8 2 3+-+2 6+-+2 14 8 2 3+-+ +--R ((- 45x - 6x )\|2 \|2 - 27x - 48x - 4x )\|3 +--R + +--R 12 6 6+-+2 12 6 3+-+ +--R (- 135x - 144x + 12)\|2 + (27x + 42x - 16)\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+ +--R (15x + 2x )\|2 \|2 \|3 + (27x + 12x + 4)\|2 \|3 +--R + +--R 10 4 6+-+4 10 4 3+-+6+-+2 +--R (108x + 36x )\|2 + (- 63x - 30x )\|2 \|2 +--R / +--R 12 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2 +--R ((36x - 24x )\|2 \|2 + (- 216x + 144x )\|2 )\|3 +--R + +--R 16 10 6+-+4 10 4 3+-+2 3+-+ +--R ((- 54x + 36x )\|2 + (- 108x + 72x )\|2 )\|3 +--R + +--R 8 2 3+-+6+-+4 14 8 +--R (- 36x + 24x )\|2 \|2 - 324x + 216x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2 +--R ((216x - 144x )\|2 \|2 + (- 36x + 24x )\|2 )\|3 +--R + +--R 8 2 3+-+2 6+-+2 14 8 3+-+ +--R ((108x - 72x )\|2 \|2 + 216x - 144x )\|3 +--R + +--R 12 6 6+-+2 12 6 3+-+ +--R (648x - 432x )\|2 + (- 216x + 216x - 48)\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+ +--R (- 36x + 24x )\|2 \|2 \|3 + (- 108x + 72x )\|2 \|3 +--R + +--R 10 4 6+-+4 10 4 3+-+6+-+2 +--R (- 324x + 216x )\|2 + (216x - 144x )\|2 \|2 +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1347 +m0b:=a0-r0b +--R +--R +--R (7) +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+ +--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2) +--R + +--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+ +--R - \|3 \|96 log(x\|6 + x \|3 + \|2 ) +--R + +--R 6+-+ +--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+ 3+-+2 6+--+ x\|3 +--R \|3 \|96 log(- x\|6 + x \|3 + \|2 - 4\|3 \|96 atanh(-----) +--R 6+-+ +--R \|2 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+6+--+ \|3 \|3 + 3x \|2 \|3 +--R - 6\|3 \|96 atan(--------------------------) +--R 9 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+6+--+ \|3 \|3 - 3x \|2 \|3 +--R 6\|3 \|96 atan(--------------------------) +--R 9 +--R + +--R +-+ +-+ +--R 6+-+5 +-+3+-+2 6+-+ \|3 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 2\|2 \|3 \|3 \|3 atan(---------- - 2\|2 \|3 \|3 \|3 atan(----------) +--R 6+--+ 6+--+ +--R x\|96 - 1 x\|96 + 1 +--R / +--R 6+-+5 3+-+2 6+-+6+--+ +--R 12\|2 \|3 \|3 \|96 +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) +--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 8 +--R (- 144x - 192x )\|2 \|3 + (- 108x - 36x )\|2 \|3 - 564x +--R + +--R 2 +--R 16x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 6+-+4 3+-+2 8 3+-+ 12 6 6+-+2 6+-+2 +--R ((252x + 48x )\|2 \|3 + 324x \|3 + (288x + 672x )\|2 )\|3 +--R + +--R 8 2 3+-+2 10 4 6+-+4 +--R (144x + 48x )\|3 + (- 144x - 228x )\|2 +--R * +--R 6+-+2 +--R \|6 +--R + +--R 6 3+-+6+-+3+-+2 10 4 6+-+5 3+-+ +--R (- 12x + 8)\|2 \|2 \|3 + (- 27x + 18x )\|2 \|3 +--R + +--R 8 2 3+-+6+-+5 8 2 6+-+ +--R (27x - 18x )\|2 \|2 + (36x - 24x )\|2 +--R * +--R 6+-+5 +--R \|3 +--R + +--R 10 4 6+-+5 10 4 3+-+6+-+3 3+-+2 +--R ((- 27x + 18x )\|2 + (72x - 48x )\|2 \|2 )\|3 +--R + +--R 8 2 3+-+6+-+5 14 8 2 6+-+ 3+-+ +--R ((27x - 18x )\|2 \|2 + (- 144x + 102x - 4x )\|2 )\|3 +--R + +--R 12 6 6+-+3 12 6 3+-+6+-+ +--R (- 216x + 144x )\|2 + (144x - 102x + 4)\|2 \|2 +--R * +--R 6+-+3 +--R \|3 +--R + +--R 8 2 3+-+6+-+5 8 2 6+-+ 3+-+2 +--R ((- 54x + 36x )\|2 \|2 + (54x - 36x )\|2 )\|3 +--R + +--R 12 6 6+-+3 6 3+-+6+-+ 3+-+ +--R ((216x - 144x )\|2 + (- 54x + 36)\|2 \|2 )\|3 +--R + +--R 10 4 6+-+5 10 4 3+-+6+-+3 +--R (162x - 108x )\|2 + (- 216x + 144x )\|2 \|2 +--R * +--R 6+-+ +--R \|3 +--R * +--R 6+-+ +--R \|6 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (216x + 72x )\|2 \|2 + (144x + 192x )\|2 \|2 + 564x +--R + +--R 4 +--R - 16x +--R * +--R 3+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (108x + 36x )\|2 \|2 + (432x + 576x )\|2 +--R + +--R 8 2 3+-+ +--R (1128x - 32x )\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 6 3+-+2 +--R (324x + 108x )\|2 + (864x + 1152x )\|2 \|2 + (564x - 16)\|2 +--R * +--R 6+-+4 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 8 3+-+ +--R ((- 252x - 48x )\|2 \|2 + (- 288x - 672x )\|2 - 648x \|2) +--R * +--R 3+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (- 756x - 144x )\|2 + (- 576x - 1344x )\|2 \|2 +--R + +--R 6 3+-+2 +--R - 324x \|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (- 1512x - 288x )\|2 \|2 + (- 288x - 672x )\|2 \|2 - 972x +--R * +--R 6+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 6 3+-+2 3+-+2 +--R ((144x + 228x )\|2 + (- 144x - 48)\|2 )\|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+ +--R ((288x + 456x )\|2 \|2 - 432x - 144x )\|3 +--R + +--R 8 2 3+-+2 6+-+4 8 2 3+-+ +--R (144x + 228x )\|2 \|2 + (- 864x - 288x )\|2 +--R / +--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 14 +--R (864x - 576x )\|2 \|3 + (324x - 216x )\|2 \|3 + 1728x +--R + +--R 8 2 +--R - 1224x + 48x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 6+-+4 3+-+2 8 2 3+-+ +--R (- 648x + 432x )\|2 \|3 + (- 648x + 432x )\|3 +--R + +--R 12 6 6+-+2 +--R (- 2592x + 1728x )\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 10 4 6+-+4 +--R (- 432x + 288x )\|3 + (972x - 648x )\|2 +--R * +--R 6+-+2 +--R \|6 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 +--R (- 648x + 432x )\|2 \|2 + (- 864x + 576x )\|2 \|2 +--R + +--R 16 10 4 +--R - 1728x + 1224x - 48x +--R * +--R 3+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (- 324x + 216x )\|2 \|2 + (- 2592x + 1728x )\|2 +--R + +--R 14 8 2 3+-+ +--R (- 3456x + 2448x - 96x )\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (- 972x + 648x )\|2 + (- 5184x + 3456x )\|2 \|2 +--R + +--R 12 6 3+-+2 +--R (- 1728x + 1224x - 48)\|2 +--R * +--R 6+-+4 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (648x - 432x )\|2 \|2 + (2592x - 1728x )\|2 +--R + +--R 8 2 3+-+ +--R (1296x - 864x )\|2 +--R * +--R 3+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (1944x - 1296x )\|2 + (5184x - 3456x )\|2 \|2 +--R + +--R 6 3+-+2 +--R (648x - 432)\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (3888x - 2592x )\|2 \|2 + (2592x - 1728x )\|2 \|2 + 1944x +--R + +--R 4 +--R - 1296x +--R * +--R 6+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 6 3+-+2 3+-+2 +--R ((- 972x + 648x )\|2 + (432x - 288)\|2 )\|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+ +--R ((- 1944x + 1296x )\|2 \|2 + 1296x - 864x )\|3 +--R + +--R 8 2 3+-+2 6+-+4 8 2 3+-+ +--R (- 972x + 648x )\|2 \|2 + (2592x - 1728x )\|2 +--R Type: Expression(Integer) +--E 1337 + +)clear all + +--S 1338 of 1347 +t0:=x^8*sqrt(-1+4*x^6) +--R +--R +--R +-------+ +--R 8 | 6 +--R (1) x \|4x - 1 +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1347 +r0:=-1/192*atanh(2*x^3/sqrt(-1+4*x^6))-1/96*x^3*sqrt(-1+4*x^6)+_ + 1/12*x^9*sqrt(-1+4*x^6) +--R +--R +--R 3 +-------+ +--R 2x 9 3 | 6 +--R - atanh(----------) + (16x - 2x )\|4x - 1 +--R +-------+ +--R | 6 +--R \|4x - 1 +--R (2) -------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 9 3 | 6 12 6 | 6 3 +--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x ) +--R + +--R +-------+ +--R 21 15 9 3 | 6 24 18 12 +--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x +--R + +--R 6 +--R - 16x +--R / +--R +-------+ +--R 9 3 | 6 12 6 +--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192 +--R Type: Union(Expression(Integer),...) +--E 1340 + +--S 1341 of 1347 +m0:=a0-r0 +--R +--R +--R +-------+ 3 +--R | 6 3 2x +--R log(\|4x - 1 - 2x ) + atanh(----------) +--R +-------+ +--R | 6 +--R \|4x - 1 +--R (4) ----------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1342 + +)clear all + +--S 1343 of 1347 +t0:=x^5*sqrt(a^6-x^6) +--R +--R +--R +---------+ +--R 5 | 6 6 +--R (1) x \|- x + a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1347 +r0:=-1/9*(a^6-x^6)^(3/2) +--R +--R +--R +---------+ +--R 6 6 | 6 6 +--R (x - a )\|- x + a +--R (2) --------------------- +--R 9 +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 6 6 | 6 6 +--R (x - a )\|- x + a +--R (3) --------------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 1345 + +--S 1346 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1347 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4e.input.pdf b/src/axiom-website/CATS/rich4e.input.pdf new file mode 100644 index 0000000..2b54cad Binary files /dev/null and b/src/axiom-website/CATS/rich4e.input.pdf differ diff --git a/src/axiom-website/CATS/rich4f.input.pamphlet b/src/axiom-website/CATS/rich4f.input.pamphlet new file mode 100644 index 0000000..e70485a --- /dev/null +++ b/src/axiom-website/CATS/rich4f.input.pamphlet @@ -0,0 +1,21558 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 311 matching answers. +\item 59 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4f.output +)spool rich4f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1369 +t0:=x^2*sqrt(-2+x^6) +--R +--R +--R +------+ +--R 2 | 6 +--R (1) x \|x - 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1369 +r0:=-1/3*atanh(x^3/sqrt(-2+x^6))+1/6*x^3*sqrt(-2+x^6) +--R +--R +--R 3 +------+ +--R x 3 | 6 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 6 +--R \|x - 2 +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 3 | 6 6 | 6 3 9 3 | 6 12 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 6 +--R - 2x +--R / +--R +------+ +--R 3 | 6 6 +--R 6x \|x - 2 - 6x + 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ 3 +--R | 6 3 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 6 +--R \|x - 2 +--R (4) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1369 +t0:=x^2/sqrt(1-x^6) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 6 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1369 +r0:=1/3*asin(x^3) +--R +--R +--R 3 +--R asin(x ) +--R (2) -------- +--R 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 6 +--R \|- x + 1 - 1 +--R 2atan(---------------) +--R 3 +--R x +--R (3) - ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 6 +--R \|- x + 1 - 1 3 +--R - 2atan(---------------) - asin(x ) +--R 3 +--R x +--R (4) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1369 +t0:=x^2/sqrt(1+x^6) +--R +--R +--R 2 +--R x +--R (1) --------- +--R +------+ +--R | 6 +--R \|x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1369 +r0:=1/3*asinh(x^3) +--R +--R +--R 3 +--R asinh(x ) +--R (2) --------- +--R 3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 6 3 +--R log(\|x + 1 - x ) +--R (3) - ------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 6 3 3 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1369 +t0:=1/(x*sqrt(1+x^6)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 6 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1369 +r0:=-1/3*atanh(sqrt(1+x^6)) +--R +--R +--R +------+ +--R | 6 +--R atanh(\|x + 1 ) +--R (2) - ---------------- +--R 3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (3) ----------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 6 | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1369 +t0:=1/(x*sqrt(-25+x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 6 +--R x\|x - 25 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1369 +r0:=1/15*atan(1/5*sqrt(-25+x^6)) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (2) ---------------- +--R 15 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (3) ---------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1369 +t0:=x^(1/3)/(1-x^6) +--R +--R +--R 3+-+ +--R \|x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1369 +r0:=-1/6*log(1-x^(2/3))+1/12*log(1+x^(2/3)+x^(4/3))-1/6*cos(2/9*%pi)*_ + log(1+x^(4/3)+2*x^(2/3)*cos(1/9*%pi))+1/6*cos(1/9*%pi)*log(1+_ + x^(4/3)-2*x^(2/3)*sin(1/18*%pi))-1/6*log(1+x^(4/3)-2*x^(2/3)*_ + cos(2/9*%pi))*sin(1/18*%pi)-1/2*atan((1+2*x^(2/3))/sqrt(3))/_ + sqrt(3)-1/3*atan((x^(2/3)+cos(1/9*%pi))/sqrt(1-cos(1/9*%pi)^2))*_ + cos(1/9*%pi)*(1-cos(2/9*%pi))/sqrt(1-cos(1/9*%pi)^2)+1/3*_ + atan((x^(2/3)-cos(2/9*%pi))/sqrt(1-cos(2/9*%pi)^2))*cos(2/9*%pi)*_ + (1-sin(1/18*%pi))/sqrt(1-cos(2/9*%pi)^2)+1/3*atan((x^(2/3)-_ + sin(1/18*%pi))/sqrt(1-sin(1/18*%pi)^2))*(1+cos(1/9*%pi))*_ + sin(1/18*%pi)/sqrt(1-sin(1/18*%pi)^2) +--R +--R +--R (2) +--R +----------------+ +---------------+ +--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2 +--R (4\|3 cos(---) + 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1 +--R 9 18 \| 9 \| 9 +--R * +--R 3+-+2 %pi +--R \|x - sin(---) +--R 18 +--R atan(------------------) +--R +---------------+ +--R | %pi 2 +--R |- sin(---) + 1 +--R \| 18 +--R + +--R +---------------+ +--R +-+ 2%pi %pi +-+ 2%pi | %pi 2 +--R (- 4\|3 cos(----)sin(---) + 4\|3 cos(----)) |- sin(---) + 1 +--R 9 18 9 \| 18 +--R * +--R 3+-+2 2%pi +--R +---------------+ \|x - cos(----) +--R | %pi 2 9 +--R |- cos(---) + 1 atan(-------------------) +--R \| 9 +----------------+ +--R | 2%pi 2 +--R |- cos(----) + 1 +--R \| 9 +--R + +--R +---------------+ +--R +-+ %pi 2%pi +-+ %pi | %pi 2 +--R (4\|3 cos(---)cos(----) - 4\|3 cos(---)) |- sin(---) + 1 +--R 9 9 9 \| 18 +--R * +--R 3+-+2 %pi +--R +----------------+ \|x + cos(---) +--R | 2%pi 2 9 +--R |- cos(----) + 1 atan(------------------) +--R \| 9 +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +--R - 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) +--R 9 9 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(- \|x + 1) +--R + +--R +-+ %pi 2%pi 3+-+2 3+-+ +--R - 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R 3+-+2 +--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1 +--R 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) - 6atan(----------) +--R 9 18 +-+ +--R \|3 +--R * +--R +---------------+ +----------------+ +---------------+ +--R | %pi 2 | 2%pi 2 | %pi 2 +--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R / +--R +---------------+ +----------------+ +---------------+ +--R +-+ | %pi 2 | 2%pi 2 | %pi 2 +--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R \|3 +-+ \|3 | %pi 2 +--R (3sin(----------) - \|3 cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R \|3 +-+ \|3 | %pi 2 +--R (- 3sin(----------) - \|3 cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +---------------+ +----------------+ +--R +-+ \|3 | %pi 2 | 2%pi 2 +--R 2\|3 cos(----------) |- sin(---) + 1 |- cos(----) + 1 +--R 3 \| 18 \| 9 +--R * +--R +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R +-+ \|3 \|3 | %pi 2 +--R (- 2\|3 sin(----------) + 6cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +---------------+ +----------------+ +--R +-+ \|3 | %pi 2 | 2%pi 2 +--R 4\|3 sin(----------) |- sin(---) + 1 |- cos(----) + 1 +--R 3 \| 18 \| 9 +--R * +--R +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R +-+ \|3 \|3 | %pi 2 +--R (- 2\|3 sin(----------) - 6cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +----------------+ +---------------+ +--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2 +--R (- 4\|3 cos(---) - 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1 +--R 9 18 \| 9 \| 9 +--R * +--R 3+-+2 %pi +--R \|x - sin(---) +--R 18 +--R atan(------------------) +--R +---------------+ +--R | %pi 2 +--R |- sin(---) + 1 +--R \| 18 +--R + +--R +---------------+ +--R +-+ 2%pi %pi +-+ 2%pi | %pi 2 +--R (4\|3 cos(----)sin(---) - 4\|3 cos(----)) |- sin(---) + 1 +--R 9 18 9 \| 18 +--R * +--R 3+-+2 2%pi +--R +---------------+ \|x - cos(----) +--R | %pi 2 9 +--R |- cos(---) + 1 atan(-------------------) +--R \| 9 +----------------+ +--R | 2%pi 2 +--R |- cos(----) + 1 +--R \| 9 +--R + +--R +---------------+ +--R +-+ %pi 2%pi +-+ %pi | %pi 2 +--R (- 4\|3 cos(---)cos(----) + 4\|3 cos(---)) |- sin(---) + 1 +--R 9 9 9 \| 18 +--R * +--R 3+-+2 %pi +--R +----------------+ \|x + cos(---) +--R | 2%pi 2 9 +--R |- cos(----) + 1 atan(------------------) +--R \| 9 +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +-+ 3+-+2 +--R 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R 9 9 +--R + +--R +-+ 3+-+2 +--R 2\|3 log(- \|x + 1) +--R + +--R +-+ %pi 2%pi 3+-+2 3+-+ +--R 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R 3+-+2 +--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1 +--R - 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) + 6atan(----------) +--R 9 18 +-+ +--R \|3 +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R * +--R +---------------+ +----------------+ +---------------+ +--R | %pi 2 | 2%pi 2 | %pi 2 +--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R / +--R +---------------+ +----------------+ +---------------+ +--R +-+ | %pi 2 | 2%pi 2 | %pi 2 +--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1369 Value stack overflow +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1369 +t0:=x^8*(a+b*x^7) +--R +--R +--R 15 8 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1369 +r0:=1/9*a*x^9+1/16*b*x^16 +--R +--R +--R 1 16 1 9 +--R (2) -- b x + - a x +--R 16 9 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 16 1 9 +--R (3) -- b x + - a x +--R 16 9 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 1369 +t0:=x^9/(a+b*x^8) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1369 +r0:=1/2*x^2/b+1/4*a^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_ + sqrt(2))-1/4*a^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_ + sqrt(2))+1/8*a^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+_ + x^4*sqrt(b))/(b^(5/4)*sqrt(2))-1/8*a^(1/4)*log(a^(1/4)*b^(1/4)*_ + x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(b^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|a log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a +--R \|a log(- x \|2 \|a \|b + x \|b + \|a ) - 2\|a atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b - \|a 2 +-+4+-+ +--R - 2\|a atan(-----------------) + 4x \|2 \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | a | a 2 +--R - 2b |- ------ log(8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--R | a +--R 8b |- ------ +--R +--------+ +--------+ +--------+ 4| 5 +--R | a | a 2 | a \| 4096b +--R 2b |- ------ log(- 8b |- ------ + x + 4b |- ------ atan(-------------) +--R 4| 5 4| 5 4| 5 2 +--R \| 4096b \| 4096b \| 4096b x +--R + +--R 2 +--R x +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R \|a log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ | a 4+-+ | a 2 +--R - 8b\|2 |- ------ \|b log(8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R +-+ | a 4+-+ | a 2 +--R 8b\|2 |- ------ \|b log(- 8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|a log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b + \|a 4+-+ x \|2 \|b - \|a +--R 2\|a atan(-----------------) + 2\|a atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R | a +--R 8b |- ------ +--R +--------+ 4| 5 +--R +-+ | a 4+-+ \| 4096b +--R 16b\|2 |- ------ \|b atan(-------------) +--R 4| 5 2 +--R \| 4096b x +--R / +--R +-+4+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1369 +t0:=x^7/(a+b*x^8) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1369 +r0:=1/8*log(a+b*x^8)/b +--R +--R +--R 8 +--R log(b x + a) +--R (2) ------------- +--R 8b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(b x + a) +--R (3) ------------- +--R 8b +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1369 +t0:=x^5/(a+b*x^8) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1369 +r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_ + (a^(1/4)*b^(3/4)*sqrt(2))-1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(1/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R 2atan(-----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R | 1 2 | 1 2 +--R |- -------- log(512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R | 1 2 | 1 2 +--R - |- -------- log(- 512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 3 +--R | 1 \| 4096a b +--R 2 |- -------- atan(---------------------) +--R 4| 3 2 +--R \| 4096a b x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 2 +--R 8\|2 |- -------- \|a \|b log(512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 2 +--R - 8\|2 |- -------- \|a \|b log(- 512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R - log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 16\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 3 2 +--R \| 4096a b x +--R / +--R +-+4+-+4+-+3 +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1369 +t0:=x^3/(a+b*x^8) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1369 +r0:=1/4*atan(x^4*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R 4 +-+ +--R x \|b +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 4\|a \|b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +-----+ 4 +--R (b x - a)\|- a b + 2a b x 4 +---+ +--R log(----------------------------) x \|a b +--R 8 atan(--------) +--R b x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 8\|- a b 4\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 53 + +--S 54 of 1369 +m0a:=a0.1-r0 +--R +--R +--R 8 +-----+ 4 4 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 8 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8\|- a b \|a \|b +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1369 +m0b:=a0.2-r0 +--R +--R +--R 4 +---+ 4 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4\|a \|b \|a b +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1369 +t0:=x/(a+b*x^8) +--R +--R +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 58 + +--S 59 of 1369 +r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_ + 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_ + 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_ + (a^(3/4)*b^(1/4)*sqrt(2))+1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(3/4)*b^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R - log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R 2atan(-----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 4+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R | 1 | 1 2 +--R |- ------- log(8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +--R | 1 +--R 8a |- ------- +--R +---------+ +---------+ +---------+ 4| 3 +--R | 1 | 1 2 | 1 \| 4096a b +--R - |- ------- log(- 8a |- ------- + x ) - 2 |- ------- atan(--------------) +--R 4| 3 4| 3 4| 3 2 +--R \| 4096a b \| 4096a b \| 4096a b x +--R Type: Union(Expression(Integer),...) +--E 60 + +--S 61 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ | 1 2 +--R 8\|2 |- ------- \|a \|b log(8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ | 1 2 +--R - 8\|2 |- ------- \|a \|b log(- 8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+ +--R | 1 +--R 8a |- ------- +--R +---------+ 4| 3 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 16\|2 |- ------- \|a \|b atan(--------------) +--R 4| 3 2 +--R \| 4096a b x +--R / +--R +-+4+-+3 4+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 62 + +)clear all + +--S 63 of 1369 +t0:=1/(x*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ---------- +--R 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 63 + +--S 64 of 1369 +r0:=log(x)/a-1/8*log(a+b*x^8)/a +--R +--R +--R 8 +--R - log(b x + a) + 8log(x) +--R (2) ------------------------- +--R 8a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(b x + a) + 8log(x) +--R (3) ------------------------- +--R 8a +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 67 + +)clear all + +--S 68 of 1369 +t0:=1/(x^3*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 68 + +--S 69 of 1369 +r0:=(-1/2)/(a*x^2)+1/4*b^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(5/4)*sqrt(2))-1/4*b^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(5/4)*sqrt(2))-1/8*b^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2))+1/8*b^(1/4)*log(a^(1/4)*_ + b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R x \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - x \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 2 4+-+ x \|2 \|b + \|a 2 4+-+ x \|2 \|b - \|a +--R - 2x \|b atan(----------------- - 2x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R 2 +-+4+-+ +--R 8a x \|2 \|a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R 2 | b 4 | b 2 +--R - 2a x |- ------ log(512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 | b 4 | b 2 +--R 2a x |- ------ log(- 512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+3 +--R 4 | b +--R 512a |- ------ +--R +--------+ 4| 5 +--R 2 | b \| 4096a +--R - 4a x |- ------ atan(----------------- - 1 +--R 4| 5 2 +--R \| 4096a b x +--R / +--R 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 70 + +--S 71 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+3 +--R +-+ | b 4+-+ 4 | b 2 +--R - 8a\|2 |- ------ \|a log(512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R +-+ | b 4+-+ 4 | b 2 +--R 8a\|2 |- ------ \|a log(- 512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a +--R \|b log(- x \|2 \|a \|b + x \|b + \|a ) + 2\|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b - \|a +--R 2\|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +--------+3 +--R 4 | b +--R 512a |- ------ +--R +--------+ 4| 5 +--R +-+ | b 4+-+ \| 4096a +--R - 16a\|2 |- ------ \|a atan(-----------------) +--R 4| 5 2 +--R \| 4096a b x +--R / +--R +-+4+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 1369 +t0:=1/(x^5*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 13 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 73 + +--S 74 of 1369 +r0:=(-1/4)/(a*x^4)-1/4*atan(x^4*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R 4 +-+ +--R 4 +-+ x \|b +-+ +--R - x \|b atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 4 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 4 | b 8 |b +--R +---+ - 2a x |- - + b x - a +-+ a |- +--R 4 | b \| a 4 |b \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 8 \|a 4 +--R b x + a b x +--R (3) [-----------------------------------------,---------------------] +--R 4 4 +--R 8a x 4a x +--R Type: Union(List(Expression(Integer)),...) +--E 75 + +--S 76 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 4 | b 8 +--R +---+ - 2a x |- - + b x - a 4 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 8 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 4 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 4 +--R \|a b x +--R (6) -------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 79 + +)clear all + +--S 80 of 1369 +t0:=1/(x^7*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 15 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 80 + +--S 81 of 1369 +r0:=(-1/6)/(a*x^6)+1/4*b^(3/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(7/4)*sqrt(2))-1/4*b^(3/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(7/4)*sqrt(2))+1/8*b^(3/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2))-1/8*b^(3/4)*log(a^(1/4)*_ + b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - 3x \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R 3x \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 6 4+-+3 x \|2 \|b + \|a 6 4+-+3 x \|2 \|b - \|a +--R - 6x \|b atan(----------------- - 6x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 6 +-+4+-+3 +--R 24a x \|2 \|a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 3 | 3 +--R 6 | b 2 | b 2 +--R - 6a x |- ------ log(8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 6 | b 2 | b 2 +--R 6a x |- ------ log(- 8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--R | 3 +--R 2 | b +--R +--------+ 8a |- ------ +--R | 3 4| 7 +--R 6 | b \| 4096a +--R 12a x |- ------ atan(-------------- - 1 +--R 4| 7 2 +--R \| 4096a b x +--R / +--R 6 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 82 + +--S 83 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 2 | b 2 +--R - 8a\|2 |- ------ \|a log(8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 2 | b 2 +--R 8a\|2 |- ------ \|a log(- 8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 4+-+3 x \|2 \|b + \|a 4+-+3 x \|2 \|b - \|a +--R 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R 2 | b +--R +--------+ 8a |- ------ +--R | 3 4| 7 +--R +-+ | b 4+-+3 \| 4096a +--R 16a\|2 |- ------ \|a atan(--------------) +--R 4| 7 2 +--R \| 4096a b x +--R / +--R +-+4+-+3 +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 1369 +t0:=1/(x^9*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 17 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 1369 +r0:=(-1/8)/(a*x^8)-b*log(x)/a^2+1/8*b*log(a+b*x^8)/a^2 +--R +--R +--R 8 8 8 +--R b x log(b x + a) - 8b x log(x) - a +--R (2) ----------------------------------- +--R 2 8 +--R 8a x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R b x log(b x + a) - 8b x log(x) - a +--R (3) ----------------------------------- +--R 2 8 +--R 8a x +--R Type: Union(Expression(Integer),...) +--E 87 + +--S 88 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 89 + +)clear all + +--S 90 of 1369 +t0:=x^8/(a+b*x^8) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 90 + +--S 91 of 1369 +r0:=x/b-1/4*(-a)^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/b^(9/8)-1/4*(-a)^(1/8)*_ + atanh(b^(1/8)*x/(-a)^(1/8))/b^(9/8)+1/4*(-a)^(1/8)*atan(1-b^(1/8)*_ + x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*_ + atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))+1/8*_ + (-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/(b^(9/8)*sqrt(2))-1/8*(-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*_ + x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/(b^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- a log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|b +--R \|- a log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|- a atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+---+ x\|2 \|b + \|- a 8+---+ x\|2 \|b - \|- a +--R - 2\|- a atan(------------------) - 2\|- a atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+---+ x\|b +-+8+-+ +--R - 2\|2 \|- a atan(------) + 8x\|2 \|b +--R 8+---+ +--R \|- a +--R / +--R +-+8+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | a +--R b |- ---------- +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- + 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+2 +------------+ +--R | a 2 | a +-+ | a 2 +--R b |- ---------- log(64b |- ---------- - 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 8| 9 +--R \| 16777216b \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a | a +--R - b\|2 |- ---------- log(8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a | a +--R b\|2 |- ---------- log(- 8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R +-+ | a \| 16777216b +--R 2b\|2 |- ---------- atan(-----------------) +--R 8| 9 x +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a \| 16777216b +--R - 2b |- ---------- atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a \| 16777216b +-+ +--R 2b |- ---------- atan(------------------------- + x\|2 +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216b +--R / +--R +-+ +--R b\|2 +--R Type: Union(Expression(Integer),...) +--E 92 + +--S 93 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|- a log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +------------+ +--R | a 8+-+ +--R 8b |- ---------- \|b +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- + 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +--R | a 8+-+ +--R 8b |- ---------- \|b +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- - 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a 8+-+ | a +--R - 8b\|2 |- ---------- \|b log(8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a 8+-+ | a +--R 8b\|2 |- ---------- \|b log(- 8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- a log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R +-+8+---+ x\|b 8+---+ x\|2 \|b + \|- a +--R 2\|2 \|- a atanh(------) + 2\|- a atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 8+---+ x\|2 \|b - \|- a +-+8+---+ x\|b +--R 2\|- a atan(------------------) + 2\|2 \|- a atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R +-+ | a 8+-+ \| 16777216b +--R 16b\|2 |- ---------- \|b atan(-----------------) +--R 8| 9 x +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a 8+-+ \| 16777216b +--R - 16b |- ---------- \|b atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a 8+-+ \| 16777216b +--R 16b |- ---------- \|b atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216b +--R / +--R +-+8+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 94 + +)clear all + +--S 95 of 1369 +t0:=x^6/(a+b*x^8) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 95 + +--S 96 of 1369 +r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(1/8)*b^(7/8)*_ + sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(1/8)*b^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+8+-+7 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--------------+6 +--R 6 +-+ | 1 5 | 1 +--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------ +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+7 +--R +-+ | 1 6 | 1 +--R \|2 |- ------------ log(2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+7 +--R +-+ | 1 6 | 1 +--R - \|2 |- ------------ log(- 2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--R 6 +-+ | 1 +--R - 2097152a b x\|2 |- ------------ +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+6 +--R 5 | 1 2 +--R - 262144a b |- ------------ + x +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R +-+ | 1 \| 16777216a b +--R 2\|2 |- ------------ atan(-----------------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 97 + +--S 98 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 8\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--------------+6 +--R 6 +-+ | 1 5 | 1 +--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------ +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+7 +--R +-+8+---+ | 1 8+-+7 6 | 1 +--R 8\|2 \|- a |- ------------ \|b log(2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R +-+8+---+ | 1 8+-+7 +--R 8\|2 \|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +--------------+7 +--R 6 | 1 +--R log(- 2097152a b |- ------------ + x) +--R 8| 7 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 8\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--R 6 +-+ | 1 +--R - 2097152a b x\|2 |- ------------ +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+6 +--R 5 | 1 2 +--R - 262144a b |- ------------ + x +--R 8| 7 +--R \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +--R - 2atan(------------------) - 2atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+ x\|b +--R - 2\|2 atan(------) +--R 8+---+ +--R \|- a +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R +-+8+---+ | 1 8+-+7 \| 16777216a b +--R 16\|2 \|- a |- ------------ \|b atan(-----------------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 16\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R 8| 7 +--R \| 16777216a b +--R atan(-------------------------------------) +--R +--------------+7 +--R 6 | 1 +-+ +--R 2097152a b |- ------------ - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+8+---+8+-+7 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 1369 +t0:=x^4/(a+b*x^8) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 1369 +r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))-1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(3/8)*b^(5/8)*_ + sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/((-a)^(3/8)*b^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+3 8+-+5 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 3 5 +--R \| 16777216a b +--R * +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 2 +--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x ) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+ | 1 2 3 | 1 +--R - \|2 |- ------------ log(32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+ | 1 2 3 | 1 +--R \|2 |- ------------ log(- 32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 3 5 +--R \| 16777216a b +--R * +--R log +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 +--R - 32768a b x\|2 |- ------------ - 64a b |- ------------ +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R +-+ | 1 \| 16777216a b +--R 2\|2 |- ------------ atan(---------------------------) +--R 8| 3 5 x +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ - x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ + x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 102 + +--S 103 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+3 | 1 8+-+5 +--R 8\|- a |- ------------ \|b +--R 8| 3 5 +--R \| 16777216a b +--R * +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 2 +--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x ) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+8+---+3 | 1 8+-+5 2 3 | 1 +--R - 8\|2 \|- a |- ------------ \|b log(32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+8+---+3 | 1 8+-+5 2 3 | 1 +--R 8\|2 \|- a |- ------------ \|b log(- 32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+3 | 1 8+-+5 +--R 8\|- a |- ------------ \|b +--R 8| 3 5 +--R \| 16777216a b +--R * +--R log +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 +--R - 32768a b x\|2 |- ------------ - 64a b |- ------------ +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +--R - 2atan(------------------) - 2atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+ x\|b +--R 2\|2 atan(------) +--R 8+---+ +--R \|- a +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R +-+8+---+3 | 1 8+-+5 \| 16777216a b +--R 16\|2 \|- a |- ------------ \|b atan(---------------------------) +--R 8| 3 5 x +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ - x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 16777216a b +--R - 16\|- a |- ------------ \|b atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ + x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R / +--R +-+8+---+3 8+-+5 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 104 + +)clear all + +--S 105 of 1369 +t0:=x^2/(a+b*x^8) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 105 + +--S 106 of 1369 +r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-_ + 1/8*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_ + ((-a)^(5/8)*b^(3/8)*sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+_ + (-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(5/8)*b^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R - 2atan(------------------) - 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+5 8+-+3 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 5 3 +--R \| 16777216a b +--R * +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 2 +--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x ) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 5 3 +--R \| 16777216a b +--R * +--R log +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 +--R 262144a b |- ------------ - 512a b x\|2 |- ------------ +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+3 +--R +-+ | 1 2 | 1 +--R - \|2 |- ------------ log(512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+3 +--R +-+ | 1 2 | 1 +--R \|2 |- ------------ log(- 512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R +-+ | 1 \| 16777216a b +--R - 2\|2 |- ------------ atan(-------------------------) +--R 8| 5 3 x +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ - x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ + x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 107 + +--S 108 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+5 | 1 8+-+3 +--R 8\|- a |- ------------ \|b +--R 8| 5 3 +--R \| 16777216a b +--R * +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 2 +--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x ) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+5 | 1 8+-+3 +--R 8\|- a |- ------------ \|b +--R 8| 5 3 +--R \| 16777216a b +--R * +--R log +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 +--R 262144a b |- ------------ - 512a b x\|2 |- ------------ +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+3 +--R +-+8+---+5 | 1 8+-+3 2 | 1 +--R - 8\|2 \|- a |- ------------ \|b log(512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+3 +--R +-+8+---+5 | 1 8+-+3 2 | 1 +--R 8\|2 \|- a |- ------------ \|b log(- 512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R +-+8+---+5 | 1 8+-+3 \| 16777216a b +--R - 16\|2 \|- a |- ------------ \|b atan(-------------------------) +--R 8| 5 3 x +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 16777216a b +--R - 16\|- a |- ------------ \|b atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ - x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ + x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R / +--R +-+8+---+5 8+-+3 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 109 + +)clear all + +--S 110 of 1369 +t0:=1/(a+b*x^8) +--R +--R +--R 1 +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 110 + +--S 111 of 1369 +r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))+1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(7/8)*b^(1/8)*_ + sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/((-a)^(7/8)*b^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R - 2atan(------------------) - 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+7 8+-+ +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 1 +--R |- ----------- +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- + 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +-------------+ +--R | 1 +--R |- ----------- +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- - 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+ | 1 | 1 +--R \|2 |- ----------- log(8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+ | 1 | 1 +--R - \|2 |- ----------- log(- 8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R +-+ | 1 \| 16777216a b +--R - 2\|2 |- ----------- atan(------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R | 1 \| 16777216a b +--R 2 |- ----------- atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R | 1 \| 16777216a b +--R - 2 |- ----------- atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 112 + +--S 113 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +-------------+ +--R 8+---+7 | 1 8+-+ +--R 8\|- a |- ----------- \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- + 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +-------------+ +--R 8+---+7 | 1 8+-+ +--R 8\|- a |- ----------- \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- - 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+8+---+7 | 1 8+-+ | 1 +--R 8\|2 \|- a |- ----------- \|b log(8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+8+---+7 | 1 8+-+ | 1 +--R - 8\|2 \|- a |- ----------- \|b log(- 8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R +-+8+---+7 | 1 8+-+ \| 16777216a b +--R - 16\|2 \|- a |- ----------- \|b atan(------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 16777216a b +--R 16\|- a |- ----------- \|b atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 16777216a b +--R - 16\|- a |- ----------- \|b atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+8+---+7 8+-+ +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 1369 +t0:=1/(x^2*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 1369 +r0:=(-1)/(a*x)+1/4*b^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-_ + 1/4*b^(1/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-1/4*b^(1/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+_ + 1/4*b^(1/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*_ + sqrt(2))+1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(9/8)*sqrt(2))-1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*_ + x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R x\|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b +--R - x\|b log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2x\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a +--R - 2x\|b atan(------------------) - 2x\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+ x\|b +-+8+---+ +--R - 2x\|2 \|b atan(------) - 8\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+ +--R 8a x\|2 \|- a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | b +--R a x |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8 | b +--R - a x\|2 |- ---------- log(2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8 | b +--R a x\|2 |- ---------- log(- 2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b +--R a x |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b \| 16777216a +--R - 2a x\|2 |- ---------- atan(-------------------------) +--R 8| 9 b x +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +--R 2a x |- ---------- atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- - b x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +-+ +--R - 2a x |- ---------- atan(----------------------------------- - \|2 +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- + b x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+ +--R a x\|2 +--R Type: Union(Expression(Integer),...) +--E 117 + +--S 118 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +------------+ +--R | b 8+---+ +--R 8a |- ---------- \|- a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8+---+ 8 | b +--R - 8a\|2 |- ---------- \|- a log(2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8+---+ 8 | b +--R 8a\|2 |- ---------- \|- a log(- 2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b 8+---+ +--R 8a |- ---------- \|- a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b +--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a +--R 2\|b atan(------------------) + 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+ x\|b +--R 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b 8+---+ \| 16777216a +--R - 16a\|2 |- ---------- \|- a atan(-------------------------) +--R 8| 9 b x +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b 8+---+ \| 16777216a +--R 16a |- ---------- \|- a atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- - b x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b 8+---+ \| 16777216a +--R - 16a |- ---------- \|- a atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- + b x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+8+---+ +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 119 + +)clear all + +--S 120 of 1369 +t0:=1/(x^4*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 12 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 120 + +--S 121 of 1369 +r0:=(-1/3)/(a*x^3)-1/4*b^(3/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-_ + 1/4*b^(3/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-1/4*b^(3/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*sqrt(2))+_ + 1/4*b^(3/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*_ + sqrt(2))-1/8*b^(3/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(11/8)*sqrt(2))+1/8*b^(3/8)*log((-a)^(1/4)+_ + b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 3x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 3x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 3 +-+8+-+3 x\|b 3 8+-+3 x\|2 \|b + \|- a +--R 6x \|2 \|b atanh(------) - 6x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 3 8+-+3 x\|2 \|b - \|- a 3 +-+8+-+3 x\|b +--R - 6x \|b atan(------------------ + 6x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+3 +--R - 8\|2 \|- a +--R / +--R 3 +-+8+---+3 +--R 24a x \|2 \|- a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 3 +--R 3 | b +--R 3a x |- ----------- +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R 3 +-+ | b 7 | b 2 +--R 3a x \|2 |- ----------- log(32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R 3 +-+ | b 7 | b 2 +--R - 3a x \|2 |- ----------- log(- 32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 | b +--R 3a x |- ----------- +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 +-+ | b \| 16777216a +--R - 6a x \|2 |- ----------- atan(------------------------) +--R 8| 11 2 +--R \| 16777216a b x +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 | b \| 16777216a +--R - 6a x |- ----------- atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- - b x\|2 +--R 8| 11 +--R \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 | b \| 16777216a +-+ +--R 6a x |- ----------- atan(---------------------------------- - \|2 +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- + b x\|2 +--R 8| 11 +--R \| 16777216a +--R / +--R 3 +-+ +--R 3a x \|2 +--R Type: Union(Expression(Integer),...) +--E 122 + +--S 123 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 3 +--R | b 8+---+3 +--R 8a |- ----------- \|- a +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R +-+ | b 8+---+3 7 | b 2 +--R 8a\|2 |- ----------- \|- a log(32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R +-+ | b 8+---+3 7 | b 2 +--R - 8a\|2 |- ----------- \|- a log(- 32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R | b 8+---+3 +--R 8a |- ----------- \|- a +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+3 x\|b +--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+3 x\|2 \|b + \|- a 8+-+3 x\|2 \|b - \|- a +--R 2\|b atan(------------------) + 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+3 x\|b +--R - 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R +-+ | b 8+---+3 \| 16777216a +--R - 16a\|2 |- ----------- \|- a atan(------------------------) +--R 8| 11 2 +--R \| 16777216a b x +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R | b 8+---+3 \| 16777216a +--R - 16a |- ----------- \|- a atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- - b x\|2 +--R 8| 11 +--R \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R | b 8+---+3 \| 16777216a +--R 16a |- ----------- \|- a atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- + b x\|2 +--R 8| 11 +--R \| 16777216a +--R / +--R +-+8+---+3 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 124 + +)clear all + +--S 125 of 1369 +t0:=1/(x^6*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 14 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 125 + +--S 126 of 1369 +r0:=(-1/5)/(a*x^5)+1/4*b^(5/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)-_ + 1/4*b^(5/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)+1/4*b^(5/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_ + 1/4*b^(5/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*_ + sqrt(2))-1/8*b^(5/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(13/8)*sqrt(2))+1/8*b^(5/8)*log((-a)^(1/4)+_ + b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 5x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 5x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 5 +-+8+-+5 x\|b 5 8+-+5 x\|2 \|b + \|- a +--R 10x \|2 \|b atanh(------) + 10x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 5 8+-+5 x\|2 \|b - \|- a 5 +-+8+-+5 x\|b +--R 10x \|b atan(------------------ - 10x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+5 +--R - 8\|2 \|- a +--R / +--R 5 +-+8+---+5 +--R 40a x \|2 \|- a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 5 +--R 5 | b +--R 5a x |- ----------- +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 5 | b +--R 5a x |- ----------- +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R 5 +-+ | b 5 | b 2 +--R 5a x \|2 |- ----------- log(512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R 5 +-+ | b 5 | b 2 +--R - 5a x \|2 |- ----------- log(- 512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 +-+ | b \| 16777216a +--R 10a x \|2 |- ----------- atan(----------------------) +--R 8| 13 2 +--R \| 16777216a b x +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 | b \| 16777216a +--R 10a x |- ----------- atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- - b x\|2 +--R 8| 13 +--R \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 | b \| 16777216a +-+ +--R - 10a x |- ----------- atan(-------------------------------- - \|2 +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- + b x\|2 +--R 8| 13 +--R \| 16777216a +--R / +--R 5 +-+ +--R 5a x \|2 +--R Type: Union(Expression(Integer),...) +--E 127 + +--S 128 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 5 +--R | b 8+---+5 +--R 8a |- ----------- \|- a +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R | b 8+---+5 +--R 8a |- ----------- \|- a +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R +-+ | b 8+---+5 5 | b 2 +--R 8a\|2 |- ----------- \|- a log(512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R +-+ | b 8+---+5 5 | b 2 +--R - 8a\|2 |- ----------- \|- a log(- 512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+5 x\|b +--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+5 x\|2 \|b + \|- a 8+-+5 x\|2 \|b - \|- a +--R - 2\|b atan(------------------) - 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+5 x\|b +--R 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R +-+ | b 8+---+5 \| 16777216a +--R 16a\|2 |- ----------- \|- a atan(----------------------) +--R 8| 13 2 +--R \| 16777216a b x +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R | b 8+---+5 \| 16777216a +--R 16a |- ----------- \|- a atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- - b x\|2 +--R 8| 13 +--R \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R | b 8+---+5 \| 16777216a +--R - 16a |- ----------- \|- a atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- + b x\|2 +--R 8| 13 +--R \| 16777216a +--R / +--R +-+8+---+5 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 1369 +t0:=1/(x^8*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 16 8 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 1369 +r0:=(-1/7)/(a*x^7)-1/4*b^(7/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)-_ + 1/4*b^(7/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)+1/4*b^(7/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*sqrt(2))-_ + 1/4*b^(7/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*_ + sqrt(2))+1/8*b^(7/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*_ + b^(1/8)*x*sqrt(2))/((-a)^(15/8)*sqrt(2))-1/8*b^(7/8)*_ + log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_ + ((-a)^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 7x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 7x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 7 +-+8+-+7 x\|b 7 8+-+7 x\|2 \|b + \|- a +--R 14x \|2 \|b atanh(------) + 14x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 7 8+-+7 x\|2 \|b - \|- a 7 +-+8+-+7 x\|b +--R 14x \|b atan(------------------ + 14x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+7 +--R - 8\|2 \|- a +--R / +--R 7 +-+8+---+7 +--R 56a x \|2 \|- a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 7 +--R 7 | b +--R 7a x |- ----------- +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 7 | b +--R 7a x |- ----------- +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R 7 +-+ | b 2 | b +--R - 7a x \|2 |- ----------- log(8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R 7 +-+ | b 2 | b +--R 7a x \|2 |- ----------- log(- 8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 +-+ | b \| 16777216a +--R 14a x \|2 |- ----------- atan(-------------------) +--R 8| 15 b x +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 | b \| 16777216a +--R - 14a x |- ----------- atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- - b x\|2 +--R 8| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 | b \| 16777216a +-+ +--R 14a x |- ----------- atan(----------------------------- - \|2 +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- + b x\|2 +--R 8| 15 +--R \| 16777216a +--R / +--R 7 +-+ +--R 7a x \|2 +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 7 +--R | b 8+---+7 +--R 8a |- ----------- \|- a +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R | b 8+---+7 +--R 8a |- ----------- \|- a +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R +-+ | b 8+---+7 2 | b +--R - 8a\|2 |- ----------- \|- a log(8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R +-+ | b 8+---+7 2 | b +--R 8a\|2 |- ----------- \|- a log(- 8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+7 x\|b +--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+7 x\|2 \|b + \|- a 8+-+7 x\|2 \|b - \|- a +--R - 2\|b atan(------------------) - 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+7 x\|b +--R - 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R +-+ | b 8+---+7 \| 16777216a +--R 16a\|2 |- ----------- \|- a atan(-------------------) +--R 8| 15 b x +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R | b 8+---+7 \| 16777216a +--R - 16a |- ----------- \|- a atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- - b x\|2 +--R 8| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R | b 8+---+7 \| 16777216a +--R 16a |- ----------- \|- a atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- + b x\|2 +--R 8| 15 +--R \| 16777216a +--R / +--R +-+8+---+7 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R 10 4+-+2 8 4+---+4+-+ 6 8+---+4 6 4+---+28+-+6 +--R (- b x \|b - 2b x \|- a \|b - 2b x \|- a - b x \|- a )\|b +--R + +--R 8 8+---+2 4+-+2 6 4+---+8+---+2 4+-+ 4 8+---+6 +--R b x \|- a \|b + 2b x \|- a \|- a \| - 2b x \|- a +--R + +--R 4 4+---+2 8+---+2 +--R b x \|- a \|- a +--R * +--R 8+-+4 +--R \|b +--R + +--R 6 8+---+4 4+-+2 4 4+---+8+---+4 4+-+ 2 4+---+2 8+---+4 +--R b x \|- a \|b + 2b x \|- a \|- a \| + b x \|- a \|- a +--R + +--R 2 +--R - 2a b x +--R * +--R 8+-+2 +--R \|b +--R + +--R 4 8+---+6 4+-+2 2 4+---+8+---+6 2 10 2 4+-+ +--R - b x \|- a \|b + (- 2b x \|- a \|- a + b x + a b x )\|b +--R + +--R 4+---+2 8+---+6 2 8 8+---+2 2 8 4+---+ +--R - b \|- a \|- a + 2b x \|- a + (- b x - a b)\|- a +--R / +--R 2 10 3 2 8+-+2 12 2 4 8+---+6 4+-+2 +--R (8a b x + 8a x )\|b + (4a b x + 4a x )\|- a \|b +--R + +--R 10 2 2 4+---+8+---+6 4+-+ 8 2 4+---+2 8+---+6 +--R (8a b x + 8a x )\|- a \|- a \|b + (4a b x + 4a )\|- a \|- a +--R Type: Expression(Integer) +--E 134 + +)clear all + +--S 135 of 1369 +t0:=1/(a-b*x^8) +--R +--R +--R 1 +--R (1) - -------- +--R 8 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 135 + +--S 136 of 1369 +r0:=1/4*atan(b^(1/8)*x/a^(1/8))/(a^(7/8)*b^(1/8))+1/4*atanh(b^(1/8)*_ + x/a^(1/8))/(a^(7/8)*b^(1/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))-1/8*log(a^(1/4)+_ + b^(1/4)*x^2-a^(1/8)*b^(1/8)*x*sqrt(2))/(a^(7/8)*b^(1/8)*sqrt(2))+_ + 1/8*log(a^(1/4)+b^(1/4)*x^2+a^(1/8)*b^(1/8)*x*sqrt(2))/_ + (a^(7/8)*b^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+8+-+8+-+ 2 4+-+ 4+-+ +--R log(x\|2 \|a \|b + x \|b + \|a ) - log(- x\|2 \|a \|b + x \|b + \|a ) +--R + +--R 8+-+ +-+8+-+ 8+-+ +-+8+-+ 8+-+ +--R +-+ x\|b x\|2 \|b + \|a x\|2 \|b - \|a +--R 2\|2 atanh(-----) + 2atan(----------------) + 2atan(----------------) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R 8+-+ +--R +-+ x\|b +--R 2\|2 atan(-----) +--R 8+-+ +--R \|a +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R |----------- log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R - |----------- log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R \|2 |----------- log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R - \|2 |----------- log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 \|16777216a b +--R - 2\|2 |----------- atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R - 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R - log(x\|2 \|a \|b + x \|b + \|a ) +--R + +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R - +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R 8\|2 |----------- \|a \|b log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R - 8\|2 |----------- \|a \|b log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R 8+-+ +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+ x\|b +--R log(- x\|2 \|a \|b + x \|b + \|a ) - 2\|2 atanh(-----) +--R 8+-+ +--R \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R x\|2 \|b + \|a x\|2 \|b - \|a +-+ x\|b +--R - 2atan(----------------) - 2atan(----------------) - 2\|2 atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 8+-+7 8+-+ \|16777216a b +--R - 16\|2 |----------- \|a \|b atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R - 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 8+-+2 4+-+2 6 4+-+8+-+2 4+-+ 4 8+-+6 4 4+-+2 8+-+8+-+6 +--R (- x \|a \|b - 2x \|a \|a \| + 2x \|a - x \|a \|a)\|b +--R + +--R 6 8+-+4 4+-+2 4 4+-+8+-+4 4+-+ 2 4+-+2 8+-+4 2 8+-+4 +--R (- x \|a \|b - 2x \|a \|a \| - x \|a \|a - 2a x )\|b +--R + +--R 4 8+-+6 4+-+2 2 4+-+8+-+6 10 2 4+-+ 4+-+2 8+-+6 +--R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a +--R + +--R 8 8+-+2 8 4+-+ +--R - 2b x \|a + (b x - a)\|a +--R * +--R 8+-+2 +--R \|b +--R + +--R 10 4+-+2 8 4+-+4+-+ 6 8+-+4 6 4+-+2 +--R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a +--R / +--R 10 2 2 8+-+4 +--R (8a b x - 8a x )\|b +--R + +--R 12 4 8+-+6 4+-+2 10 2 4+-+8+-+6 4+-+ +--R (- 4b x + 4a x )\|a \|b + (- 8b x + 8a x )\|a \|a \|b +--R + +--R 8 4+-+2 8+-+6 +--R (- 4b x + 4a)\|a \|a +--R * +--R 8+-+2 +--R \|b +--R Type: Expression(Integer) +--E 139 + +)clear all + +--S 140 of 1369 +t0:=x^9/(1-x^8) +--R +--R +--R 9 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 140 + +--S 141 of 1369 +r0:=-1/2*x^2+1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 2 +--R atanh(x ) + atan(x ) - 2x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R log(x + 1) - log(x - 1) + 2atan(x ) - 4x +--R (3) ------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1369 +t0:=x^7/(1-x^8) +--R +--R +--R 7 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 1369 +r0:=-1/8*log(1-x^8) +--R +--R +--R 8 +--R log(- x + 1) +--R (2) - ------------- +--R 8 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(x - 1) +--R (3) - ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 8 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +)clear all + +--S 150 of 1369 +t0:=x^5/(1-x^8) +--R +--R +--R 5 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 150 + +--S 151 of 1369 +r0:=-1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 +--R atanh(x ) - atan(x ) +--R (2) -------------------- +--R 4 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atan(x ) +--R (3) ------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 154 + +)clear all + +--S 155 of 1369 +t0:=x^3/(1-x^8) +--R +--R +--R 3 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 155 + +--S 156 of 1369 +r0:=1/4*atanh(x^4) +--R +--R +--R 4 +--R atanh(x ) +--R (2) --------- +--R 4 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R log(x + 1) - log(x - 1) +--R (3) ------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 1369 +m0:=a0-r0 +--R +--R +--R 4 4 4 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 1369 +t0:=x/(1-x^8) +--R +--R +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 1369 +r0:=1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 +--R atanh(x ) + atan(x ) +--R (2) -------------------- +--R 4 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) + 2atan(x ) +--R (3) ------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 164 + +)clear all + +--S 165 of 1369 +t0:=1/(x*(1-x^8)) +--R +--R +--R 1 +--R (1) - ------ +--R 9 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 165 + +--S 166 of 1369 +r0:=-1/4*atanh(1-2*x^8) +--R +--R +--R 8 +--R atanh(2x - 1) +--R (2) -------------- +--R 4 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(x - 1) + 8log(x) +--R (3) ----------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + 8log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 169 + +)clear all + +--S 170 of 1369 +t0:=1/(x^3*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 11 3 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 170 + +--S 171 of 1369 +r0:=(-1/2)/x^2-1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 2 2 +--R x atanh(x ) - x atan(x ) - 2 +--R (2) ---------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 +--R x log(x + 1) - x log(x - 1) - 2x atan(x ) - 4 +--R (3) ----------------------------------------------- +--R 2 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 1369 +t0:=1/(x^5*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 13 5 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 1369 +r0:=(-1/4)/x^4+1/4*atanh(x^4) +--R +--R +--R 4 4 +--R x atanh(x ) - 1 +--R (2) --------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 4 +--R x log(x + 1) - x log(x - 1) - 2 +--R (3) --------------------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 1369 +m0:=a0-r0 +--R +--R +--R 4 4 4 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 179 + +)clear all + +--S 180 of 1369 +t0:=1/(x^7*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 15 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 180 + +--S 181 of 1369 +r0:=(-1/6)/x^6+1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 6 2 6 2 +--R 3x atanh(x ) + 3x atan(x ) - 2 +--R (2) ------------------------------ +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 2 6 2 6 2 +--R 3x log(x + 1) - 3x log(x - 1) + 6x atan(x ) - 4 +--R (3) ------------------------------------------------- +--R 6 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 184 + +)clear all + +--S 185 of 1369 +t0:=1/(x^9*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 17 9 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 185 + +--S 186 of 1369 +r0:=(-1/8)/x^8-1/4*atanh(1-2*x^8) +--R +--R +--R 8 8 +--R 2x atanh(2x - 1) - 1 +--R (2) --------------------- +--R 8 +--R 8x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R - x log(x - 1) + 8x log(x) - 1 +--R (3) ------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + 8log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 1369 +t0:=x^8/(1-x^8) +--R +--R +--R 8 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 1369 +r0:=-x+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x) - 8x\|2 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +-+ +--R - 2atan(---------) - 8x\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 194 + +)clear all + +--S 195 of 1369 +t0:=x^6/(1-x^8) +--R +--R +--R 6 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 195 + +--S 196 of 1369 +r0:=-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) - 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 199 + +)clear all + +--S 200 of 1369 +t0:=x^4/(1-x^8) +--R +--R +--R 4 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 200 + +--S 201 of 1369 +r0:=1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) + 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R log(- x\|2 + x + 1) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 1369 +t0:=x^2/(1-x^8) +--R +--R +--R 2 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 1369 +r0:=-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) - 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R log(- x\|2 + x + 1) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 209 + +)clear all + +--S 210 of 1369 +t0:=1/(1-x^8) +--R +--R +--R 1 +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 210 + +--S 211 of 1369 +r0:=1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 214 + +)clear all + +--S 215 of 1369 +t0:=1/(x^2*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 10 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 215 + +--S 216 of 1369 +r0:=(-1)/x-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R x log(x\|2 + x + 1) - x log(- x\|2 + x + 1) + 2x\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +-+ +--R - 2x atan(x\|2 + 1) - 2x atan(x\|2 - 1) - 2x\|2 atan(x) - 8\|2 +--R / +--R +-+ +--R 8x\|2 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R x log(x\|2 + x + 1) + x\|2 log(x + 1) - x\|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - x log(- x\|2 + x + 1) + x\|2 atan(------) + 2x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +-+ +--R 2x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8x\|2 +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 1369 +t0:=1/(x^4*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 12 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 1369 +r0:=(-1/3)/x^3+1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 3 +-+ 2 3 +-+ 2 3 +-+ +--R - 3x log(x\|2 + x + 1) + 3x log(- x\|2 + x + 1) + 6x \|2 atanh(x) +--R + +--R 3 +-+ 3 +-+ 3 +-+ +-+ +--R - 6x atan(x\|2 + 1) - 6x atan(x\|2 - 1) + 6x \|2 atan(x) - 8\|2 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 2 3 +-+ 3 +-+ +--R - 3x log(x\|2 + x + 1) + 3x \|2 log(x + 1) - 3x \|2 log(x - 1) +--R + +--R 3 +-+ 2 3 +-+ 2x 3 1 +--R 3x log(- x\|2 + x + 1) - 3x \|2 atan(------) + 6x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 3 1 +-+ +--R 6x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 224 + +)clear all + +--S 225 of 1369 +t0:=1/(x^6*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 14 6 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 225 + +--S 226 of 1369 +r0:=(-1/5)/x^5-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R - 5x log(x\|2 + x + 1) + 5x log(- x\|2 + x + 1) + 10x \|2 atanh(x) +--R + +--R 5 +-+ 5 +-+ 5 +-+ +-+ +--R 10x atan(x\|2 + 1) + 10x atan(x\|2 - 1) - 10x \|2 atan(x) - 8\|2 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 2 5 +-+ 5 +-+ +--R - 5x log(x\|2 + x + 1) + 5x \|2 log(x + 1) - 5x \|2 log(x - 1) +--R + +--R 5 +-+ 2 5 +-+ 2x 5 1 +--R 5x log(- x\|2 + x + 1) + 5x \|2 atan(------) - 10x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 5 1 +-+ +--R - 10x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 229 + +)clear all + +--S 230 of 1369 +t0:=1/(x^8*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 16 8 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 230 + +--S 231 of 1369 +r0:=(-1/7)/x^7+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x log(x\|2 + x + 1) - 7x log(- x\|2 + x + 1) + 14x \|2 atanh(x) +--R + +--R 7 +-+ 7 +-+ 7 +-+ +-+ +--R 14x atan(x\|2 + 1) + 14x atan(x\|2 - 1) + 14x \|2 atan(x) - 8\|2 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +-+ 2 7 +-+ 7 +-+ +--R 7x log(x\|2 + x + 1) + 7x \|2 log(x + 1) - 7x \|2 log(x - 1) +--R + +--R 7 +-+ 2 7 +-+ 2x 7 1 +--R - 7x log(- x\|2 + x + 1) - 7x \|2 atan(------) - 14x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 7 1 +-+ +--R - 14x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 1369 +t0:=x^9/(1+x^8) +--R +--R +--R 9 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 235 + +--S 236 of 1369 +r0:=1/2*x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_ + x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) - 2atan(x \|2 + 1) +--R + +--R 2 +-+ 2 +-+ +--R - 2atan(x \|2 - 1) + 4x \|2 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 2 +--R 2\|2 atan(----------) + 2\|2 atan(----------) + 8x +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 239 + +)clear all + +--S 240 of 1369 +t0:=x^7/(1+x^8) +--R +--R +--R 7 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 240 + +--S 241 of 1369 +r0:=1/8*log(1+x^8) +--R +--R +--R 8 +--R log(x + 1) +--R (2) ----------- +--R 8 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(x + 1) +--R (3) ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 244 + +)clear all + +--S 245 of 1369 +t0:=x^5/(1+x^8) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 245 + +--S 246 of 1369 +r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) + 2atan(x \|2 + 1) +--R + +--R 2 +-+ +--R 2atan(x \|2 - 1) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------) - 2\|2 atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1369 +t0:=x^3/(1+x^8) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 250 + +--S 251 of 1369 +r0:=1/4*atan(x^4) +--R +--R +--R 4 +--R atan(x ) +--R (2) -------- +--R 4 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R atan(x ) +--R (3) -------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 254 + +)clear all + +--S 255 of 1369 +t0:=x/(1+x^8) +--R +--R +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 255 + +--S 256 of 1369 +r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R log(x \|2 + x + 1) - log(- x \|2 + x + 1) + 2atan(x \|2 + 1) +--R + +--R 2 +-+ +--R 2atan(x \|2 - 1) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R \|2 log(x \|2 + x + 1) - \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------) - 2\|2 atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 259 + +)clear all + +--S 260 of 1369 +t0:=1/(x*(1+x^8)) +--R +--R +--R 1 +--R (1) ------ +--R 9 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 260 + +--S 261 of 1369 +r0:=-1/4*atanh(1+2*x^8) +--R +--R +--R 8 +--R atanh(2x + 1) +--R (2) - -------------- +--R 4 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(x + 1) + 8log(x) +--R (3) ----------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x + 1) + 8log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 1369 +t0:=1/(x^3*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 11 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 265 + +--S 266 of 1369 +r0:=(-1/2)/x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*_ + sqrt(2))/sqrt(2)-1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 2 +-+ 4 2 2 +-+ 4 2 2 +-+ +--R x log(x \|2 + x + 1) - x log(- x \|2 + x + 1) - 2x atan(x \|2 + 1) +--R + +--R 2 2 +-+ +-+ +--R - 2x atan(x \|2 - 1) - 4\|2 +--R / +--R 2 +-+ +--R 8x \|2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 +-+ 4 2 +-+ 2 +-+ 4 +--R x \|2 log(x \|2 + x + 1) - x \|2 log(- x \|2 + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(----------) + 2x \|2 atan(----------) - 8 +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 269 + +)clear all + +--S 270 of 1369 +t0:=1/(x^5*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 13 5 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 270 + +--S 271 of 1369 +r0:=(-1/4)/x^4-1/4*atan(x^4) +--R +--R +--R 4 4 +--R - x atan(x ) - 1 +--R (2) ---------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R - x atan(x ) - 1 +--R (3) ---------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 1369 +t0:=1/(x^7*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 15 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 275 + +--S 276 of 1369 +r0:=(-1/6)/x^6+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_ + x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 6 2 +-+ 4 6 2 +-+ 4 +--R - 3x log(x \|2 + x + 1) + 3x log(- x \|2 + x + 1) +--R + +--R 6 2 +-+ 6 2 +-+ +-+ +--R - 6x atan(x \|2 + 1) - 6x atan(x \|2 - 1) - 4\|2 +--R / +--R 6 +-+ +--R 24x \|2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 2 +-+ 4 6 +-+ 2 +-+ 4 +--R - 3x \|2 log(x \|2 + x + 1) + 3x \|2 log(- x \|2 + x + 1) +--R + +--R 6 +-+ 1 6 +-+ 1 +--R 6x \|2 atan(----------) + 6x \|2 atan(----------) - 8 +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 6 +--R 48x +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1369 +t0:=1/(x^9*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 17 9 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 280 + +--S 281 of 1369 +r0:=(-1/8)/x^8+1/4*atanh(1+2*x^8) +--R +--R +--R 8 8 +--R 2x atanh(2x + 1) - 1 +--R (2) --------------------- +--R 8 +--R 8x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R x log(x + 1) - 8x log(x) - 1 +--R (3) ----------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R log(x + 1) - 8log(x) - 2atanh(2x + 1) +--R (4) --------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 284 + +)clear all + +--S 285 of 1369 +t0:=x^8/(1+x^8) +--R +--R +--R 8 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 285 + +--S 286 of 1369 +r0:=x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 16x +--R / +--R 16 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R \|- 1 \|2 log(- \|- 1 + x) + \|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(------) + 2\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +-+ +--R 2\|- 1 atan(--------------) + 8x\|2 +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 289 + +)clear all + +--S 290 of 1369 +t0:=x^6/(1+x^8) +--R +--R +--R 6 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 290 + +--S 291 of 1369 +r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R / +--R 16 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R - 2\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R - 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 4\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 atan(---------------) + 4\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 1369 +t0:=x^4/(1+x^8) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 295 + +--S 296 of 1369 +r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+_ + x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/4*atan((-2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+_ + sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R / +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R 8\|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+5 8+---+ 8+---+5 +-+ 8+---+2 2 +--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+5 8+---+5 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------) +--R x +-+ 8+---+5 +--R x\|2 - \|- 1 +--R + +--R 8+---+5 +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+5 +--R \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+5 8+---+5 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------) +--R x +-+ 8+---+5 +--R x\|2 - \|- 1 +--R + +--R 8+---+5 +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +--R x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 4 +-+ 4 | +-+ | +-+ +--R ((- 3x - 1)\|2 + 4x + 2)\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 4 +-+ 4 | +-+ | +-+ 4 +--R ((- 3x - 1)\|2 - 4x - 2)\|- 2\|2 + 4 \|- \|2 + 2 + 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 299 + +)clear all + +--S 300 of 1369 +t0:=x^2/(1+x^8) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 300 + +--S 301 of 1369 +r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_ + 1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R / +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R 8\|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3 +--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+3 8+---+ 8+---+3 +-+ 8+---+6 2 +--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3 +--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+3 +--R \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ +--R ((- x - 3x )\|2 + 2x + 4x )\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ 2 +--R ((- x - 3x )\|2 - 2x - 4x )\|- 2\|2 + 4 \|- \|2 + 2 + 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 304 + +)clear all + +--S 305 of 1369 +t0:=1/(1+x^8) +--R +--R +--R 1 +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 305 + +--S 306 of 1369 +r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R / +--R 16 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R - \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(------) - 2\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R - 2\|- 1 \|2 log(- \|- 1 + x) - 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 4\|- 1 \|2 atan(------) - 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1369 +t0:=1/(x^2*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 10 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 310 + +--S 311 of 1369 +r0:=(-1)/x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R x\|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R x\|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - x\|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - x\|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R | +-+ +--R 2x\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R | +-+ +--R 2x\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2x\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2x\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - 16 +--R / +--R 16x +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R - x\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - x\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R x\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R x\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2x\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +-+ +--R - 2x\|- 1 atan(---------------) - 2x\|- 1 atan(---------------) - 8\|2 +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 8x\|2 +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R - 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R 2\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 4\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R - 4\|- 1 atan(---------------) - 4\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +)clear all + +--S 315 of 1369 +t0:=1/(x^4*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 12 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 315 + +--S 316 of 1369 +r0:=(-1/3)/x^3+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-_ + sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+sqrt(2-sqrt(2)))/_ + sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+1/4*atan((2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R 3 | +-+ | +-+ 2 +--R 3x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 3 | +-+ | +-+ 2 +--R - 3x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 3 | +-+ | +-+ 2 +--R 3x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R 3 | +-+ | +-+ 2 +--R - 3x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R 3 | +-+ +--R 6x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R 3 | +-+ +--R 6x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R 3 | +-+ +--R 6x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R 3 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 6x \|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R - 8\|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R 3 | +-+ | +-+ +--R 24x \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - 3x \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 3 8+---+ +-+ 8+---+5 3 8+---+ +-+ 8+---+5 +--R 3x \|- 1 \|2 log(\|- 1 + x - 3x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+5 +--R 3 8+---+ 8+---+5 +-+ 8+---+2 2 3 8+---+ +-+ \|- 1 +--R 3x \|- 1 log(- x \|- 1 \|2 - \|- 1 + x - 6x \|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+5 8+---+5 +--R 3 8+---+ \|- 1 3 8+---+ \|- 1 +-+ +--R 6x \|- 1 atan(--------------- + 6x \|- 1 atan(--------------- - 8\|2 +--R +-+ 8+---+5 +-+ 8+---+5 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+ +-+ 8+---+5 8+---+ +-+ 8+---+5 +--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+5 +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ \|- 1 +--R \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+5 8+---+5 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +-+ 8+---+5 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 4 +-+ 4 | +-+ | +-+ +--R ((3x + 1)\|2 - 4x - 2)\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 4 +-+ 4 | +-+ | +-+ 4 +--R ((3x + 1)\|2 + 4x + 2)\|- 2\|2 + 4 \|- \|2 + 2 - 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 319 + +)clear all + +--S 320 of 1369 +t0:=1/(x^6*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 14 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 320 + +--S 321 of 1369 +r0:=(-1/5)/x^5+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2-x*_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2+x*_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2)))-1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R 5 | +-+ | +-+ 2 +--R - 5x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 5 | +-+ | +-+ 2 +--R 5x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 5 | +-+ | +-+ 2 +--R - 5x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R 5 | +-+ | +-+ 2 +--R 5x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R 5 | +-+ +--R 10x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R 5 | +-+ +--R 10x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R 5 | +-+ +--R 10x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R 5 | +-+ +--R 10x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R - 8\|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R 5 | +-+ | +-+ +--R 40x \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - 5x \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 5 8+---+ +-+ 8+---+3 5 8+---+ +-+ 8+---+3 +--R 5x \|- 1 \|2 log(\|- 1 + x - 5x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 5 8+---+ 8+---+3 +-+ 8+---+6 2 +--R 5x \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 5 8+---+ +-+ \|- 1 5 8+---+ \|- 1 +--R 10x \|- 1 \|2 atan(------- - 10x \|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 5 8+---+ \|- 1 +-+ +--R - 10x \|- 1 atan(--------------- - 8\|2 +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ +-+ 8+---+3 8+---+ +-+ 8+---+3 +--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+3 +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+3 8+---+3 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) - 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +-+ 8+---+3 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ +--R ((x + 3x )\|2 - 2x - 4x )\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ 2 +--R ((x + 3x )\|2 + 2x + 4x )\|- 2\|2 + 4 \|- \|2 + 2 - 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 1369 +t0:=1/(x^8*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 16 8 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 325 + +--S 326 of 1369 +r0:=(-1/7)/x^7+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R 7 | +-+ | +-+ 2 +--R - 7x \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R 7 | +-+ | +-+ 2 +--R - 7x \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R 7 | +-+ | +-+ 2 +--R 7x \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R 7 | +-+ | +-+ 2 +--R 7x \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R 7 | +-+ +--R 14x \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R 7 | +-+ +--R 14x \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 14x \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 14x \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - 16 +--R / +--R 7 +--R 112x +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ 8+---+ +--R - 7x \|- 1 log(x\|- 1 \|2 + \|- 1 + x - 7x \|- 1 \|2 log(\|- 1 + x) +--R + +--R 7 8+---+ +-+ 8+---+ +--R 7x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ +--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ \|- 1 +--R 7x \|- 1 log(- x\|- 1 \|2 + \|- 1 + x + 14x \|- 1 \|2 atan(------) +--R x +--R + +--R 8+---+ 8+---+ +--R 7 8+---+ \|- 1 7 8+---+ \|- 1 +-+ +--R 14x \|- 1 atan(-------------- + 14x \|- 1 atan(-------------- - 8\|2 +--R +-+ 8+---+ +-+ 8+---+ +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 329 + +)clear all + +--S 330 of 1369 +t0:=x^3*sqrt(1+x^8) +--R +--R +--R +------+ +--R 3 | 8 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1369 +r0:=1/8*asinh(x^4)+1/8*x^4*sqrt(1+x^8) +--R +--R +--R +------+ +--R 4 | 8 4 +--R x \|x + 1 + asinh(x ) +--R (2) ----------------------- +--R 8 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 +--R (- 2x \|x + 1 + 2x + 1)log(\|x + 1 - x ) + (- 2x - x )\|x + 1 +--R + +--R 16 8 +--R 2x + 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 16x \|x + 1 - 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 332 + +--S 333 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 8 4 4 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 334 + +)clear all + +--S 335 of 1369 +t0:=x*sqrt(1+x^8) +--R +--R +--R +------+ +--R | 8 +--R (1) x\|x + 1 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1369 +--r0:=-1/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)+1/6*x^2*sqrt(1+x^8) +--E 336 + +--S 337 of 1369 +--a0:=integrate(t0,x) +--E 337 + +--S 338 of 1369 +--m0:=a0-r0 +--E 338 + +--S 339 of 1369 +--d0:=D(m0,x) +--E 339 + +)clear all + +--S 340 of 1369 +t0:=sqrt(1+x^8)/x +--R +--R +--R +------+ +--R | 8 +--R \|x + 1 +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1369 +r0:=-1/4*atanh(sqrt(1+x^8))+1/4*sqrt(1+x^8) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - atanh(\|x + 1 ) + \|x + 1 +--R (2) ------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1 +--R (3) ------------------------------------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 342 + +--S 343 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 344 + +)clear all + +--S 345 of 1369 +t0:=sqrt(1+x^8)/x^3 +--R +--R +--R +------+ +--R | 8 +--R \|x + 1 +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1369 +--r0:=-(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+(-1)^(1/4)*_ +-- elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2 +--E 346 + +--S 347 of 1369 +--a0:=integrate(t0,x) +--E 347 + +--S 348 of 1369 +--m0:=a0-r0 +--E 348 + +--S 349 of 1369 +--d0:=D(m0,x) +--E 349 + +)clear all + +--S 350 of 1369 +t0:=x^3*sqrt(-2+x^8) +--R +--R +--R +------+ +--R 3 | 8 +--R (1) x \|x - 2 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1369 +r0:=-1/4*atanh(x^4/sqrt(-2+x^8))+1/8*x^4*sqrt(-2+x^8) +--R +--R +--R 4 +------+ +--R x 4 | 8 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 8 +--R \|x - 2 +--R (2) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 16 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 8 +--R - 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 8x \|x - 2 - 8x + 8 +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ 4 +--R | 8 4 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 8 +--R \|x - 2 +--R (4) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 1369 +t0:=x^3/sqrt(1+x^8) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R | 8 +--R \|x + 1 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1369 +r0:=1/4*asinh(x^4) +--R +--R +--R 4 +--R asinh(x ) +--R (2) --------- +--R 4 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 8 4 +--R log(\|x + 1 - x ) +--R (3) - ------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 8 4 4 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 359 + +)clear all + +--S 360 of 1369 +t0:=x/sqrt(1+x^8) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 8 +--R \|x + 1 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1369 +--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1) +--E 361 + +--S 362 of 1369 +--a0:=integrate(t0,x) +--E 362 + +--S 363 of 1369 +--m0:=a0-r0 +--E 363 + +--S 364 of 1369 +--d0:=D(m0,x) +--E 364 + +)clear all + +--S 365 of 1369 +t0:=1/(x*sqrt(1+x^8)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 8 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1369 +r0:=-1/4*atanh(sqrt(1+x^8)) +--R +--R +--R +------+ +--R | 8 +--R atanh(\|x + 1 ) +--R (2) - ---------------- +--R 4 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (3) ----------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1369 +t0:=1/(x^3*sqrt(1+x^8)) +--R +--R +--R 1 +--R (1) ----------- +--R +------+ +--R 3 | 8 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1369 +--r0:=-1/2*(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+_ +-- 1/2*(-1)^(1/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2 +--E 371 + +--S 372 of 1369 +--a0:=integrate(t0,x) +--E 372 + +--S 373 of 1369 +--m0:=a0-r0 +--E 373 + +--S 374 of 1369 +--d0:=D(m0,x) +--E 374 + +)clear all + +--S 375 of 1369 +t0:=1/(1-x^10) +--R +--R +--R 1 +--R (1) - ------- +--R 10 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 375 + +--S 376 of 1369 +r0:=1/5*atanh(x)+1/20*atanh(1/2*x*(1-sqrt(5))/(1+x^2))*_ + (1-sqrt(5))+1/20*atanh(1/2*x*(1+sqrt(5))/(1+x^2))*_ + (1+sqrt(5))+1/20*atan(1/2*x*sqrt(10-2*sqrt(5))/(1-x^2))*_ + sqrt(10-2*sqrt(5))+1/20*atan(1/2*x*sqrt(10+2*sqrt(5))/_ + (1-x^2))*sqrt(10+2*sqrt(5)),1/5*atanh(x)-1/20*log(1+x^2-_ + x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))+1/20*_ + log(1+x^2+x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))-_ + 1/10*atan((-2*x+sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*_ + (5+sqrt(5))))*sqrt(1/2*(5-sqrt(5)))+1/10*atan((2*x+_ + sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/20*log(1+x^2-x*sqrt(1/2*(3+sqrt(5))))*_ + sqrt(1/2*(3+sqrt(5)))+1/20*log(1+x^2+x*sqrt(1/2*(3+sqrt(5))))*_ + sqrt(1/2*(3+sqrt(5)))-1/10*atan((-2*x+sqrt(1/2*(3-sqrt(5))))*_ + sqrt(2/(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))+1/10*_ + atan((2*x+sqrt(1/2*(3-sqrt(5))))*sqrt(2/(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R [ +--R +----------+ +--R +----------+ | +-+ +--R | +-+ x\|2\|5 + 10 +--R - \|2\|5 + 10 atan(--------------) +--R 2 +--R 2x - 2 +--R + +--R +------------+ +--R +------------+ | +-+ +-+ +--R | +-+ x\|- 2\|5 + 10 +-+ x\|5 + x +--R - \|- 2\|5 + 10 atan(----------------) + (\|5 + 1)atanh(---------) +--R 2 2 +--R 2x - 2 2x + 2 +--R + +--R +-+ +--R +-+ x\|5 - x +--R (\|5 - 1)atanh(---------) + 4atanh(x) +--R 2 +--R 2x + 2 +--R / +--R 20 +--R , +--R +--R +--------+ +--R +--------+ | +-+ 2 +-+ +--R | +-+ x\|\|5 + 3 + (x + 1)\|2 +--R \|\|5 + 3 log(---------------------------) +--R +-+ +--R \|2 +--R + +--R +----------+ +--R +----------+ | +-+ 2 +-+ +--R | +-+ x\|- \|5 + 3 + (x + 1)\|2 +--R \|- \|5 + 3 log(-----------------------------) +--R +-+ +--R \|2 +--R + +--R +----------+ +--R +----------+ | +-+ 2 +-+ +--R | +-+ - x\|- \|5 + 3 + (x + 1)\|2 +--R - \|- \|5 + 3 log(-------------------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--R +--------+ | +-+ 2 +-+ +--R | +-+ - x\|\|5 + 3 + (x + 1)\|2 +--R - \|\|5 + 3 log(-----------------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +----------+ | +-+ +-+ | +-+ +--R | +-+ (\|\|5 + 3 + 2x\|2 )\|\|5 + 5 +--R 2\|- \|5 + 5 atan(---------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +--------+ +--------+ +--R +----------+ | +-+ +-+ | +-+ +--R | +-+ (\|\|5 + 3 - 2x\|2 )\|\|5 + 5 +--R - 2\|- \|5 + 5 atan(---------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +----------+ +----------+ +--R +--------+ | +-+ +-+ | +-+ +--R | +-+ (\|- \|5 + 3 + 2x\|2 )\|- \|5 + 5 +--R 2\|\|5 + 5 atan(-------------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +----------+ +----------+ +--R +--------+ | +-+ +-+ | +-+ +--R | +-+ (\|- \|5 + 3 - 2x\|2 )\|- \|5 + 5 +-+ +--R - 2\|\|5 + 5 atan(-------------------------------------) + 4\|2 atanh(x) +--R +-+ +--+ +--R \|2 \|10 +--R / +--R +-+ +--R 20\|2 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 376 + +--S 377 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 +--R + +--R - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 +--R + +--R - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x) +--R + +--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x) + 2log(x + 1) +--R + +--R - 2log(x - 1) +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 +--R + +--R - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 +--R + +--R - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x) +--R + +--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x) +--R + +--R +----------+ +------------+ +--R +----------+ | +-+ +------------+ | +-+ +--R | +-+ x\|2\|5 + 10 | +-+ x\|- 2\|5 + 10 +--R \|2\|5 + 10 atan(--------------) + \|- 2\|5 + 10 atan(----------------) +--R 2 2 +--R 2x - 2 2x - 2 +--R + +--R +-+ +--R +-+ x\|5 + x +--R 2log(x + 1) - 2log(x - 1) + (- \|5 - 1)atanh(---------) +--R 2 +--R 2x + 2 +--R + +--R +-+ +--R +-+ x\|5 - x +--R (- \|5 + 1)atanh(---------) - 4atanh(x) +--R 2 +--R 2x + 2 +--R / +--R 20 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1369 +t0:=x^4/sqrt(1-x^10) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 10 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1369 +r0:=1/5*asin(x^5) +--R +--R +--R 5 +--R asin(x ) +--R (2) -------- +--R 5 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 10 +--R \|- x + 1 - 1 +--R 2atan(----------------) +--R 5 +--R x +--R (3) - ----------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 382 + +--S 383 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 10 +--R \|- x + 1 - 1 5 +--R - 2atan(----------------) - asin(x ) +--R 5 +--R x +--R (4) ------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 1369 +t0:=x^4/sqrt(-2+x^10) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 10 +--R \|x - 2 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1369 +r0:=1/5*atanh(x^5/sqrt(-2+x^10)) +--R +--R +--R 5 +--R x +--R atanh(----------) +--R +-------+ +--R | 10 +--R \|x - 2 +--R (2) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 10 5 +--R log(\|x - 2 - x ) +--R (3) - -------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ 5 +--R | 10 5 x +--R - log(\|x - 2 - x ) - atanh(----------) +--R +-------+ +--R | 10 +--R \|x - 2 +--R (4) ------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 389 + +)clear all + +--S 390 of 1369 +t0:=x^5/(9+x^12) +--R +--R +--R 5 +--R x +--R (1) ------- +--R 12 +--R x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 390 + +--S 391 of 1369 +r0:=1/18*atan(1/3*x^6) +--R +--R +--R 6 +--R x +--R atan(--) +--R 3 +--R (2) -------- +--R 18 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R x +--R atan(--) +--R 3 +--R (3) -------- +--R 18 +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 394 + +)clear all + +--S 395 of 1369 +t0:=x^5/(9-x^12) +--R +--R +--R 5 +--R x +--R (1) - ------- +--R 12 +--R x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 395 + +--S 396 of 1369 +r0:=1/18*atanh(1/3*x^6) +--R +--R +--R 6 +--R x +--R atanh(--) +--R 3 +--R (2) --------- +--R 18 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 6 +--R log(x + 3) - log(x - 3) +--R (3) ------------------------- +--R 36 +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 1369 +m0:=a0-r0 +--R +--R +--R 6 +--R 6 6 x +--R log(x + 3) - log(x - 3) - 2atanh(--) +--R 3 +--R (4) -------------------------------------- +--R 36 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 1369 +t0:=x^5*sqrt(9+x^12) +--R +--R +--R +-------+ +--R 5 | 12 +--R (1) x \|x + 9 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1369 +r0:=3/4*asinh(1/3*x^6)+1/12*x^6*sqrt(9+x^12) +--R +--R +--R +-------+ 6 +--R 6 | 12 x +--R x \|x + 9 + 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 12 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 6 | 12 12 | 12 6 +--R (- 18x \|x + 9 + 18x + 81)log(\|x + 9 - x ) +--R + +--R +-------+ +--R 18 6 | 12 24 12 +--R (- 2x - 9x )\|x + 9 + 2x + 18x +--R / +--R +-------+ +--R 6 | 12 12 +--R 24x \|x + 9 - 24x - 108 +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ 6 +--R | 12 6 x +--R - 3log(\|x + 9 - x ) - 3asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 404 + +)clear all + +--S 405 of 1369 +t0:=(a+b/x)*x^6 +--R +--R +--R 6 5 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 405 + +--S 406 of 1369 +r0:=1/6*b*x^6+1/7*a*x^7 +--R +--R +--R 1 7 1 6 +--R (2) - a x + - b x +--R 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 406 + +--S 407 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 7 6 +--R 6a x + 7b x +--R (3) ------------- +--R 42 +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 409 + +)clear all + +--S 410 of 1369 +t0:=(a+b/x)*x^5 +--R +--R +--R 5 4 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 410 + +--S 411 of 1369 +r0:=1/5*b*x^5+1/6*a*x^6 +--R +--R +--R 1 6 1 5 +--R (2) - a x + - b x +--R 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 411 + +--S 412 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 5 +--R 5a x + 6b x +--R (3) ------------- +--R 30 +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1369 +t0:=(a+b/x)*x^4 +--R +--R +--R 4 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 415 + +--S 416 of 1369 +r0:=1/4*b*x^4+1/5*a*x^5 +--R +--R +--R 1 5 1 4 +--R (2) - a x + - b x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 416 + +--S 417 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 4 +--R 4a x + 5b x +--R (3) ------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 419 + +)clear all + +--S 420 of 1369 +t0:=(a+b/x)*x^3 +--R +--R +--R 3 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 420 + +--S 421 of 1369 +r0:=1/3*b*x^3+1/4*a*x^4 +--R +--R +--R 1 4 1 3 +--R (2) - a x + - b x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 421 + +--S 422 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 3 +--R 3a x + 4b x +--R (3) ------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 424 + +)clear all + +--S 425 of 1369 +t0:=(a+b/x)*x^2 +--R +--R +--R 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 425 + +--S 426 of 1369 +r0:=1/2*b*x^2+1/3*a*x^3 +--R +--R +--R 1 3 1 2 +--R (2) - a x + - b x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 426 + +--S 427 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2a x + 3b x +--R (3) ------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 1369 +t0:=(a+b/x)*x +--R +--R +--R (1) a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 430 + +--S 431 of 1369 +r0:=b*x+1/2*a*x^2 +--R +--R +--R 1 2 +--R (2) - a x + b x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 431 + +--S 432 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R a x + 2b x +--R (3) ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 434 + +)clear all + +--S 435 of 1369 +t0:=a+b/x +--R +--R +--R a x + b +--R (1) ------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 435 + +--S 436 of 1369 +r0:=a*x+b*log(x) +--R +--R +--R (2) b log(x) + a x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) b log(x) + a x +--R Type: Union(Expression(Integer),...) +--E 437 + +--S 438 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 439 + +)clear all + +--S 440 of 1369 +t0:=(a+b/x)/x +--R +--R +--R a x + b +--R (1) ------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 440 + +--S 441 of 1369 +r0:=-b/x+a*log(x) +--R +--R +--R a x log(x) - b +--R (2) -------------- +--R x +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1369 +a0:=integrate(t0,x) +--R +--R +--R a x log(x) - b +--R (3) -------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 1369 +t0:=(a+b/x)/x^2 +--R +--R +--R a x + b +--R (1) ------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 445 + +--S 446 of 1369 +r0:=-1/2*b/x^2-a/x +--R +--R +--R 1 +--R - a x - - b +--R 2 +--R (2) ----------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 446 + +--S 447 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 2a x - b +--R (3) ---------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 449 + +)clear all + +--S 450 of 1369 +t0:=(a+b/x)/x^3 +--R +--R +--R a x + b +--R (1) ------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 450 + +--S 451 of 1369 +r0:=-1/3*b/x^3-1/2*a/x^2 +--R +--R +--R 1 1 +--R - - a x - - b +--R 2 3 +--R (2) ------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 451 + +--S 452 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 3a x - 2b +--R (3) ----------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1369 +t0:=(a+b/x)/x^4 +--R +--R +--R a x + b +--R (1) ------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 455 + +--S 456 of 1369 +r0:=-1/4*b/x^4-1/3*a/x^3 +--R +--R +--R 1 1 +--R - - a x - - b +--R 3 4 +--R (2) ------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 456 + +--S 457 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 4a x - 3b +--R (3) ----------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 1369 +t0:=(a+b/x)/x^5 +--R +--R +--R a x + b +--R (1) ------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 460 + +--S 461 of 1369 +r0:=-1/5*b/x^5-1/4*a/x^4 +--R +--R +--R 1 1 +--R - - a x - - b +--R 4 5 +--R (2) ------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 461 + +--S 462 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 5a x - 4b +--R (3) ----------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 462 + +--S 463 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 464 + +)clear all + +--S 465 of 1369 +t0:=(a+b/x)/x^6 +--R +--R +--R a x + b +--R (1) ------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 465 + +--S 466 of 1369 +r0:=-1/6*b/x^6-1/5*a/x^5 +--R +--R +--R 1 1 +--R - - a x - - b +--R 5 6 +--R (2) ------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 466 + +--S 467 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 6a x - 5b +--R (3) ----------- +--R 6 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 467 + +--S 468 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 469 + +)clear all + +--S 470 of 1369 +t0:=(a+b/x)^2*x^6 +--R +--R +--R 2 6 5 2 4 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 470 + +--S 471 of 1369 +r0:=1/5*b^2*x^5+1/3*a*b*x^6+1/7*a^2*x^7 +--R +--R +--R 1 2 7 1 6 1 2 5 +--R (2) - a x + - a b x + - b x +--R 7 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 471 + +--S 472 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 7 6 2 5 +--R 15a x + 35a b x + 21b x +--R (3) -------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 472 + +--S 473 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 1369 +t0:=(a+b/x)^2*x^5 +--R +--R +--R 2 5 4 2 3 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 475 + +--S 476 of 1369 +r0:=1/4*b^2*x^4+2/5*a*b*x^5+1/6*a^2*x^6 +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (2) - a x + - a b x + - b x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 476 + +--S 477 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 6 5 2 4 +--R 10a x + 24a b x + 15b x +--R (3) -------------------------- +--R 60 +--R Type: Union(Expression(Integer),...) +--E 477 + +--S 478 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 479 + +)clear all + +--S 480 of 1369 +t0:=(a+b/x)^2*x^4 +--R +--R +--R 2 4 3 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 480 + +--S 481 of 1369 +r0:=1/3*b^2*x^3+1/2*a*b*x^4+1/5*a^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (2) - a x + - a b x + - b x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 481 + +--S 482 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 5 4 2 3 +--R 6a x + 15a b x + 10b x +--R (3) ------------------------- +--R 30 +--R Type: Union(Expression(Integer),...) +--E 482 + +--S 483 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 484 + +)clear all + +--S 485 of 1369 +t0:=(a+b/x)^2*x^3 +--R +--R +--R 2 3 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 485 + +--S 486 of 1369 +r0:=1/2*b^2*x^2+2/3*a*b*x^3+1/4*a^2*x^4 +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (2) - a x + - a b x + - b x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 486 + +--S 487 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 2 2 +--R 3a x + 8a b x + 6b x +--R (3) ----------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 487 + +--S 488 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1369 +t0:=(a+b/x)^2*x^2 +--R +--R +--R 2 2 2 +--R (1) a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 490 + +--S 491 of 1369 +r0:=1/3*(a+b/x)^3*x^3/a +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (2) ---------------------------- +--R 3a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R a x + 3a b x + 3b x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 492 + +--S 493 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R 3a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 494 + +)clear all + +--S 495 of 1369 +t0:=(a+b/x)^2*x +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 495 + +--S 496 of 1369 +r0:=2*a*b*x+1/2*a^2*x^2+b^2*log(x) +--R +--R +--R 2 2 2 +--R 2b log(x) + a x + 4a b x +--R (2) ------------------------- +--R 2 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b log(x) + a x + 4a b x +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 497 + +--S 498 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 499 + +)clear all + +--S 500 of 1369 +t0:=(a+b/x)^2 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 500 + +--S 501 of 1369 +r0:=-b^2/x+a^2*x+2*a*b*log(x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + a x - b +--R (2) ------------------------- +--R x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + a x - b +--R (3) ------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 502 + +--S 503 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 1369 +t0:=(a+b/x)^2/x +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 505 + +--S 506 of 1369 +r0:=-1/2*b^2/x^2-2*a*b/x+a^2*log(x) +--R +--R +--R 2 2 2 +--R 2a x log(x) - 4a b x - b +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a x log(x) - 4a b x - b +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 507 + +--S 508 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 509 + +)clear all + +--S 510 of 1369 +t0:=(a+b/x)^2/x^2 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 510 + +--S 511 of 1369 +r0:=-1/3*(a+b/x)^3/b +--R +--R +--R 3 3 2 2 2 3 +--R - a x - 3a b x - 3a b x - b +--R (2) ------------------------------ +--R 3 +--R 3b x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 3a x - 3a b x - b +--R (3) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 512 + +--S 513 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R a +--R (4) -- +--R 3b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 514 + +)clear all + +--S 515 of 1369 +t0:=(a+b/x)^2/x^3 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 515 + +--S 516 of 1369 +r0:=-1/4*b^2/x^4-2/3*a*b/x^3-1/2*a^2/x^2 +--R +--R +--R 1 2 2 2 1 2 +--R - - a x - - a b x - - b +--R 2 3 4 +--R (2) ------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 516 + +--S 517 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 6a x - 8a b x - 3b +--R (3) ---------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 517 + +--S 518 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1369 +t0:=(a+b/x)^2/x^4 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 520 + +--S 521 of 1369 +r0:=-1/5*b^2/x^5-1/2*a*b/x^4-1/3*a^2/x^3 +--R +--R +--R 1 2 2 1 1 2 +--R - - a x - - a b x - - b +--R 3 2 5 +--R (2) ------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 521 + +--S 522 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 10a x - 15a b x - 6b +--R (3) ------------------------ +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 522 + +--S 523 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1369 +t0:=(a+b/x)^2/x^5 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 525 + +--S 526 of 1369 +r0:=-1/6*b^2/x^6-2/5*a*b/x^5-1/4*a^2/x^4 +--R +--R +--R 1 2 2 2 1 2 +--R - - a x - - a b x - - b +--R 4 5 6 +--R (2) ------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 526 + +--S 527 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 15a x - 24a b x - 10b +--R (3) ------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 527 + +--S 528 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 529 + +)clear all + +--S 530 of 1369 +t0:=(a+b/x)^2/x^6 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 530 + +--S 531 of 1369 +r0:=-1/7*b^2/x^7-1/3*a*b/x^6-1/5*a^2/x^5 +--R +--R +--R 1 2 2 1 1 2 +--R - - a x - - a b x - - b +--R 5 3 7 +--R (2) ------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 531 + +--S 532 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 21a x - 35a b x - 15b +--R (3) ------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 532 + +--S 533 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 1369 +t0:=(a+b/x)^3*x^6 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 535 + +--S 536 of 1369 +r0:=1/4*b^3*x^4+3/5*a*b^2*x^5+1/2*a^2*b*x^6+1/7*a^3*x^7 +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (2) - a x + - a b x + - a b x + - b x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 536 + +--S 537 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 6 2 5 3 4 +--R 20a x + 70a b x + 84a b x + 35b x +--R (3) ------------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 537 + +--S 538 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 539 + +)clear all + +--S 540 of 1369 +t0:=(a+b/x)^3*x^5 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 540 + +--S 541 of 1369 +r0:=1/3*b^3*x^3+3/4*a*b^2*x^4+3/5*a^2*b*x^5+1/6*a^3*x^6 +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (2) - a x + - a b x + - a b x + - b x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 541 + +--S 542 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R 10a x + 36a b x + 45a b x + 20b x +--R (3) ------------------------------------- +--R 60 +--R Type: Union(Expression(Integer),...) +--E 542 + +--S 543 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1369 +t0:=(a+b/x)^3*x^4 +--R +--R +--R 3 4 2 3 2 2 3 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 545 + +--S 546 of 1369 +r0:=-1/4*b*(b+a*x)^4/a^2+1/5*(b+a*x)^5/a^2 +--R +--R +--R 1 5 5 3 4 4 3 2 3 1 2 3 2 1 5 +--R - a x + - a b x + a b x + - a b x - -- b +--R 5 4 2 20 +--R (2) --------------------------------------------- +--R 2 +--R a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 546 + +--S 547 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 5 2 4 2 3 3 2 +--R 4a x + 15a b x + 20a b x + 10b x +--R (3) ------------------------------------ +--R 20 +--R Type: Union(Expression(Integer),...) +--E 547 + +--S 548 of 1369 +m0:=a0-r0 +--R +--R +--R 5 +--R b +--R (4) ---- +--R 2 +--R 20a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1369 +t0:=(a+b/x)^3*x^3 +--R +--R +--R 3 3 2 2 2 3 +--R (1) a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 550 + +--S 551 of 1369 +r0:=1/4*(a+b/x)^4*x^4/a +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R a x + 4a b x + 6a b x + 4a b x + b +--R (2) -------------------------------------- +--R 4a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R a x + 4a b x + 6a b x + 4b x +--R (3) ------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1369 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) - -- +--R 4a +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1369 +t0:=(a+b/x)^3*x^2 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 555 + +--S 556 of 1369 +r0:=3*a*b^2*x+3/2*a^2*b*x^2+1/3*a^3*x^3+b^3*log(x) +--R +--R +--R 3 3 3 2 2 2 +--R 6b log(x) + 2a x + 9a b x + 18a b x +--R (2) ------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 2 2 2 +--R 6b log(x) + 2a x + 9a b x + 18a b x +--R (3) ------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 557 + +--S 558 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +)clear all + +--S 560 of 1369 +t0:=(a+b/x)^3*x +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 560 + +--S 561 of 1369 +r0:=-b^3/x+3*a^2*b*x+1/2*a^3*x^2+3*a*b^2*log(x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + a x + 6a b x - 2b +--R (2) ------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + a x + 6a b x - 2b +--R (3) ------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 562 + +--S 563 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1369 +t0:=(a+b/x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 565 + +--S 566 of 1369 +r0:=-1/2*b^3/x^2-3*a*b^2/x+a^3*x+3*a^2*b*log(x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2a x - 6a b x - b +--R (2) ----------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2a x - 6a b x - b +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 567 + +--S 568 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 569 + +)clear all + +--S 570 of 1369 +t0:=(a+b/x)^3/x +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 570 + +--S 571 of 1369 +r0:=-1/3*b^3/x^3-3/2*a*b^2/x^2-3*a^2*b/x+a^3*log(x) +--R +--R +--R 3 3 2 2 2 3 +--R 6a x log(x) - 18a b x - 9a b x - 2b +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 6a x log(x) - 18a b x - 9a b x - 2b +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 572 + +--S 573 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 574 + +)clear all + +--S 575 of 1369 +t0:=(a+b/x)^3/x^2 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 575 + +--S 576 of 1369 +r0:=-1/4*(a+b/x)^4/b +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (2) ---------------------------------------- +--R 4 +--R 4b x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (3) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 577 + +--S 578 of 1369 +m0:=a0-r0 +--R +--R +--R 4 +--R a +--R (4) -- +--R 4b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 1369 +t0:=(a+b/x)^3/x^3 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 580 + +--S 581 of 1369 +r0:=-1/5*b^3/x^5-3/4*a*b^2/x^4-a^2*b/x^3-1/2*a^3/x^2 +--R +--R +--R 1 3 3 2 2 3 2 1 3 +--R - - a x - a b x - - a b x - - b +--R 2 4 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 581 + +--S 582 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 10a x - 20a b x - 15a b x - 4b +--R (3) ----------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 582 + +--S 583 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 584 + +)clear all + +--S 585 of 1369 +t0:=(a+b/x)^3/x^4 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 585 + +--S 586 of 1369 +r0:=-1/6*b^3/x^6-3/5*a*b^2/x^5-3/4*a^2*b/x^4-1/3*a^3/x^3 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 3 4 5 6 +--R (2) ------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 586 + +--S 587 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 20a x - 45a b x - 36a b x - 10b +--R (3) ------------------------------------ +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 587 + +--S 588 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 589 + +)clear all + +--S 590 of 1369 +t0:=(a+b/x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 590 + +--S 591 of 1369 +r0:=-1/7*b^3/x^7-1/2*a*b^2/x^6-3/5*a^2*b/x^5-1/4*a^3/x^4 +--R +--R +--R 1 3 3 3 2 2 1 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 4 5 2 7 +--R (2) ------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 591 + +--S 592 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 35a x - 84a b x - 70a b x - 20b +--R (3) ------------------------------------ +--R 7 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 592 + +--S 593 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1369 +t0:=(a+b/x)^3/x^6 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 595 + +--S 596 of 1369 +r0:=-1/8*b^3/x^8-3/7*a*b^2/x^7-1/2*a^2*b/x^6-1/5*a^3/x^5 +--R +--R +--R 1 3 3 1 2 2 3 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 5 2 7 8 +--R (2) ------------------------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 596 + +--S 597 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 56a x - 140a b x - 120a b x - 35b +--R (3) -------------------------------------- +--R 8 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 597 + +--S 598 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 599 + +)clear all + +--S 600 of 1369 +t0:=x^4/(a+b/x) +--R +--R +--R 5 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 600 + +--S 601 of 1369 +r0:=b^4*x/a^5-1/2*b^3*x^2/a^4+1/3*b^2*x^3/a^3-1/4*b*x^4/a^2+_ + 1/5*x^5/a-b^5*log(b+a*x)/a^6 +--R +--R +--R 5 5 5 4 4 3 2 3 2 3 2 4 +--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x +--R (2) ---------------------------------------------------------------------- +--R 6 +--R 60a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 4 4 3 2 3 2 3 2 4 +--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x +--R (3) ---------------------------------------------------------------------- +--R 6 +--R 60a +--R Type: Union(Expression(Integer),...) +--E 602 + +--S 603 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 604 + +)clear all + +--S 605 of 1369 +t0:=x^3/(a+b/x) +--R +--R +--R 4 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 605 + +--S 606 of 1369 +r0:=-b^3*x/a^4+1/2*b^2*x^2/a^3-1/3*b*x^3/a^2+1/4*x^4/a+b^4*log(b+a*x)/a^5 +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x +--R (2) ------------------------------------------------------ +--R 5 +--R 12a +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x +--R (3) ------------------------------------------------------ +--R 5 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 607 + +--S 608 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1369 +t0:=x^2/(a+b/x) +--R +--R +--R 3 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 of 1369 +r0:=b^2*x/a^3-1/2*b*x^2/a^2+1/3*x^3/a-b^3*log(b+a*x)/a^4 +--R +--R +--R 3 3 3 2 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (2) -------------------------------------------- +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 2 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (3) -------------------------------------------- +--R 4 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 612 + +--S 613 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1369 +t0:=x/(a+b/x) +--R +--R +--R 2 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 615 + +--S 616 of 1369 +r0:=-b*x/a^2+1/2*x^2/a+b^2*log(b+a*x)/a^3 +--R +--R +--R 2 2 2 +--R 2b log(a x + b) + a x - 2a b x +--R (2) ------------------------------- +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b log(a x + b) + a x - 2a b x +--R (3) ------------------------------- +--R 3 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 617 + +--S 618 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +)clear all + +--S 620 of 1369 +t0:=1/(a+b/x) +--R +--R +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 620 + +--S 621 of 1369 +r0:=x/a-b*log(b+a*x)/a^2 +--R +--R +--R - b log(a x + b) + a x +--R (2) ---------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - b log(a x + b) + a x +--R (3) ---------------------- +--R 2 +--R a +--R Type: Union(Expression(Integer),...) +--E 622 + +--S 623 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 1369 +t0:=1/((a+b/x)*x) +--R +--R +--R 1 +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 625 + +--S 626 of 1369 +r0:=log(b+a*x)/a +--R +--R +--R log(a x + b) +--R (2) ------------ +--R a +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1369 +a0:=integrate(t0,x) +--R +--R +--R log(a x + b) +--R (3) ------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 627 + +--S 628 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 629 + +)clear all + +--S 630 of 1369 +t0:=1/((a+b/x)*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 630 + +--S 631 of 1369 +r0:=-log(a+b/x)/b +--R +--R +--R a x + b +--R log(-------) +--R x +--R (2) - ------------ +--R b +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - log(a x + b) + log(x) +--R (3) ----------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 632 + +--S 633 of 1369 +m0:=a0-r0 +--R +--R +--R a x + b +--R - log(a x + b) + log(x) + log(-------) +--R x +--R (4) -------------------------------------- +--R b +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 634 + +)clear all + +--S 635 of 1369 +t0:=1/((a+b/x)*x^3) +--R +--R +--R 1 +--R (1) ----------- +--R 3 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 635 + +--S 636 of 1369 +r0:=(-1)/(b*x)-a*log(x)/b^2+a*log(b+a*x)/b^2 +--R +--R +--R a x log(a x + b) - a x log(x) - b +--R (2) --------------------------------- +--R 2 +--R b x +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1369 +a0:=integrate(t0,x) +--R +--R +--R a x log(a x + b) - a x log(x) - b +--R (3) --------------------------------- +--R 2 +--R b x +--R Type: Union(Expression(Integer),...) +--E 637 + +--S 638 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 1369 +t0:=1/((a+b/x)*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R 4 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 640 + +--S 641 of 1369 +r0:=(-1/2)/(b*x^2)+a/(b^2*x)+a^2*log(x)/b^3-a^2*log(b+a*x)/b^3 +--R +--R +--R 2 2 2 2 2 +--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b +--R (2) ----------------------------------------------- +--R 3 2 +--R 2b x +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b +--R (3) ----------------------------------------------- +--R 3 2 +--R 2b x +--R Type: Union(Expression(Integer),...) +--E 642 + +--S 643 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 644 + +)clear all + +--S 645 of 1369 +t0:=1/((a+b/x)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 645 + +--S 646 of 1369 +r0:=(-1/3)/(b*x^3)+1/2*a/(b^2*x^2)-a^2/(b^3*x)-a^3*log(x)/b^4+_ + a^3*log(b+a*x)/b^4 +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b +--R (2) -------------------------------------------------------- +--R 4 3 +--R 6b x +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b +--R (3) -------------------------------------------------------- +--R 4 3 +--R 6b x +--R Type: Union(Expression(Integer),...) +--E 647 + +--S 648 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 649 + +)clear all + +--S 650 of 1369 +t0:=1/((a+b/x)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 5 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 650 + +--S 651 of 1369 +r0:=(-1/4)/(b*x^4)+1/3*a/(b^2*x^3)-1/2*a^2/(b^3*x^2)+a^3/(b^4*x)+_ + a^4*log(x)/b^5-a^4*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12b x +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12b x +--R Type: Union(Expression(Integer),...) +--E 652 + +--S 653 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1369 +t0:=1/((a+b/x)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 6 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 655 + +--S 656 of 1369 +r0:=(-1/5)/(b*x^5)+1/4*a/(b^2*x^4)-1/3*a^2/(b^3*x^3)+_ + 1/2*a^3/(b^4*x^2)-a^4/(b^5*x)-a^5*log(x)/b^6+a^5*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 5 5 4 4 3 2 3 2 3 2 +--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x +--R + +--R 4 5 +--R 15a b x - 12b +--R / +--R 6 5 +--R 60b x +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 4 3 2 3 2 3 2 +--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x +--R + +--R 4 5 +--R 15a b x - 12b +--R / +--R 6 5 +--R 60b x +--R Type: Union(Expression(Integer),...) +--E 657 + +--S 658 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 659 + +)clear all + +--S 660 of 1369 +t0:=x^5/(a+b/x)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 660 + +--S 661 of 1369 +r0:=-6*b^5*x/a^7+5/2*b^4*x^2/a^6-4/3*b^3*x^3/a^5+3/4*b^2*x^4/a^4-_ + 2/5*b*x^5/a^3+1/6*x^6/a^2+b^7/(a^8*(b+a*x))+7*b^6*log(b+a*x)/a^8 +--R +--R +--R (2) +--R 6 7 7 7 6 6 5 2 5 4 3 4 +--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x +--R + +--R 3 4 3 2 5 2 6 7 +--R 70a b x - 210a b x - 360a b x + 60b +--R / +--R 9 8 +--R 60a x + 60a b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 7 6 6 5 2 5 4 3 4 +--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x +--R + +--R 3 4 3 2 5 2 6 7 +--R 70a b x - 210a b x - 360a b x + 60b +--R / +--R 9 8 +--R 60a x + 60a b +--R Type: Union(Expression(Integer),...) +--E 662 + +--S 663 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1369 +t0:=x^4/(a+b/x)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1369 +r0:=5*b^4*x/a^6-2*b^3*x^2/a^5+b^2*x^3/a^4-1/2*b*x^4/a^3+1/5*x^5/a^2-_ + b^6/(a^7*(b+a*x))-6*b^5*log(b+a*x)/a^7 +--R +--R +--R (2) +--R 5 6 6 6 5 5 4 2 4 3 3 3 +--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x +--R + +--R 2 4 2 5 6 +--R 30a b x + 50a b x - 10b +--R / +--R 8 7 +--R 10a x + 10a b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 6 5 5 4 2 4 3 3 3 +--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x +--R + +--R 2 4 2 5 6 +--R 30a b x + 50a b x - 10b +--R / +--R 8 7 +--R 10a x + 10a b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1369 +t0:=x^3/(a+b/x)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1369 +r0:=-4*b^3*x/a^5+3/2*b^2*x^2/a^4-2/3*b*x^3/a^3+1/4*x^4/a^2+_ + b^5/(a^6*(b+a*x))+5*b^4*log(b+a*x)/a^6 +--R +--R +--R (2) +--R 4 5 5 5 4 4 3 2 3 2 3 2 +--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12b +--R / +--R 7 6 +--R 12a x + 12a b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 5 4 4 3 2 3 2 3 2 +--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12b +--R / +--R 7 6 +--R 12a x + 12a b +--R Type: Union(Expression(Integer),...) +--E 672 + +--S 673 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +)clear all + +--S 675 of 1369 +t0:=x^2/(a+b/x)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 675 + +--S 676 of 1369 +r0:=3*b^2*x/a^4-b*x^2/a^3+1/3*x^3/a^2-b^4/(a^5*(b+a*x))-4*b^3*log(b+a*x)/a^5 +--R +--R +--R (2) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 677 + +--S 678 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 679 + +)clear all + +--S 680 of 1369 +t0:=x/(a+b/x)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 680 + +--S 681 of 1369 +r0:=-2*b*x/a^3+1/2*x^2/a^2+b^3/(a^4*(b+a*x))+3*b^2*log(b+a*x)/a^4 +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 682 + +--S 683 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1369 +t0:=1/(a+b/x)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 685 + +--S 686 of 1369 +r0:=x/a^2-b^2/(a^3*(b+a*x))-2*b*log(b+a*x)/a^3 +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) ------------------------------------------------ +--R 4 3 +--R a x + a b +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) ------------------------------------------------ +--R 4 3 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 687 + +--S 688 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 689 + +)clear all + +--S 690 of 1369 +t0:=1/((a+b/x)^2*x) +--R +--R +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 690 + +--S 691 of 1369 +r0:=b/(a^2*(b+a*x))+log(b+a*x)/a^2 +--R +--R +--R (a x + b)log(a x + b) + b +--R (2) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (a x + b)log(a x + b) + b +--R (3) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 692 + +--S 693 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 694 + +)clear all + +--S 695 of 1369 +t0:=1/((a+b/x)^2*x^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 695 + +--S 696 of 1369 +r0:=1/(b*(a+b/x)) +--R +--R +--R x +--R (2) ---------- +--R 2 +--R a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 696 + +--S 697 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 697 + +--S 698 of 1369 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - --- +--R a b +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1369 +t0:=1/((a+b/x)^2*x^3) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 3 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 700 + +--S 701 of 1369 +r0:=1/(b*(b+a*x))+log(x)/b^2-log(b+a*x)/b^2 +--R +--R +--R (- a x - b)log(a x + b) + (a x + b)log(x) + b +--R (2) --------------------------------------------- +--R 2 3 +--R a b x + b +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (- a x - b)log(a x + b) + (a x + b)log(x) + b +--R (3) --------------------------------------------- +--R 2 3 +--R a b x + b +--R Type: Union(Expression(Integer),...) +--E 702 + +--S 703 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 704 + +)clear all + +--S 705 of 1369 +t0:=1/((a+b/x)^2*x^4) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 4 3 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 705 + +--S 706 of 1369 +r0:=(-1)/(b^2*x)-a/(b^2*(b+a*x))-2*a*log(x)/b^3+2*a*log(b+a*x)/b^3 +--R +--R +--R 2 2 2 2 2 +--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b +--R (2) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + b x +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b +--R (3) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + b x +--R Type: Union(Expression(Integer),...) +--E 707 + +--S 708 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 709 + +)clear all + +--S 710 of 1369 +t0:=1/((a+b/x)^2*x^5) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 5 4 2 3 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 710 + +--S 711 of 1369 +r0:=(-1/2)/(b^2*x^2)+2*a/(b^3*x)+a^2/(b^3*(b+a*x))+3*a^2*log(x)/b^4-_ + 3*a^2*log(b+a*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - b +--R / +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - b +--R / +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 712 + +--S 713 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1369 +t0:=1/((a+b/x)^2*x^6) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 5 2 4 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 715 + +--S 716 of 1369 +r0:=(-1/3)/(b^2*x^3)+a/(b^3*x^2)-3*a^2/(b^4*x)-a^3/(b^4*(b+a*x))-_ + 4*a^3*log(x)/b^5+4*a^3*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - b +--R / +--R 5 4 6 3 +--R 3a b x + 3b x +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - b +--R / +--R 5 4 6 3 +--R 3a b x + 3b x +--R Type: Union(Expression(Integer),...) +--E 717 + +--S 718 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 719 + +)clear all + +--S 720 of 1369 +t0:=1/((a+b/x)^2*x^7) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 6 2 5 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 720 + +--S 721 of 1369 +r0:=(-1/4)/(b^2*x^4)+2/3*a/(b^3*x^3)-3/2*a^2/(b^4*x^2)+4*a^3/(b^5*x)+_ + a^4/(b^5*(b+a*x))+5*a^4*log(x)/b^6-5*a^4*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x +--R + +--R 3 2 3 2 3 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3b +--R / +--R 6 5 7 4 +--R 12a b x + 12b x +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x +--R + +--R 3 2 3 2 3 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3b +--R / +--R 6 5 7 4 +--R 12a b x + 12b x +--R Type: Union(Expression(Integer),...) +--E 722 + +--S 723 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1369 +t0:=1/((a+b/x)^2*x^8) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 7 2 6 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 725 + +--S 726 of 1369 +r0:=(-1/5)/(b^2*x^5)+1/2*a/(b^3*x^4)-a^2/(b^4*x^3)+2*a^3/(b^5*x^2)-_ + 5*a^4/(b^6*x)-a^5/(b^6*(b+a*x))-6*a^5*log(x)/b^7+6*a^5*log(b+a*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 6 6 5 5 5 5 +--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x +--R + +--R 4 2 4 3 3 3 2 4 2 5 6 +--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b +--R / +--R 7 6 8 5 +--R 10a b x + 10b x +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 6 6 5 5 5 5 +--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x +--R + +--R 4 2 4 3 3 3 2 4 2 5 6 +--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b +--R / +--R 7 6 8 5 +--R 10a b x + 10b x +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1369 +t0:=x^4/(a+b/x)^3 +--R +--R +--R 7 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1369 +r0:=15*b^4*x/a^7-5*b^3*x^2/a^6+2*b^2*x^3/a^5-3/4*b*x^4/a^4+1/5*x^5/a^3+_ + 1/2*b^7/(a^8*(b+a*x)^2)-7*b^6/(a^8*(b+a*x))-21*b^5*log(b+a*x)/a^8 +--R +--R +--R (2) +--R 2 5 2 6 7 7 7 6 6 5 2 5 +--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b +--R / +--R 10 2 9 8 2 +--R 20a x + 40a b x + 20a b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 7 7 6 6 5 2 5 +--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b +--R / +--R 10 2 9 8 2 +--R 20a x + 40a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 732 + +--S 733 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 1369 +t0:=x^3/(a+b/x)^3 +--R +--R +--R 6 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 735 + +--S 736 of 1369 +r0:=-10*b^3*x/a^6+3*b^2*x^2/a^5-b*x^3/a^4+1/4*x^4/a^3-_ + 1/2*b^6/(a^7*(b+a*x)^2)+6*b^5/(a^7*(b+a*x))+15*b^4*log(b+a*x)/a^7 +--R +--R +--R (2) +--R 2 4 2 5 6 6 6 5 5 4 2 4 +--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x +--R + +--R 3 3 3 2 4 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22b +--R / +--R 9 2 8 7 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 6 6 6 5 5 4 2 4 +--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x +--R + +--R 3 3 3 2 4 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22b +--R / +--R 9 2 8 7 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 737 + +--S 738 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 739 + +)clear all + +--S 740 of 1369 +t0:=x^2/(a+b/x)^3 +--R +--R +--R 5 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 740 + +--S 741 of 1369 +r0:=6*b^2*x/a^5-3/2*b*x^2/a^4+1/3*x^3/a^3+1/2*b^5/(a^6*(b+a*x)^2)-_ + 5*b^4/(a^6*(b+a*x))-10*b^3*log(b+a*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 5 5 4 4 3 2 3 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x +--R + +--R 2 3 2 4 5 +--R 63a b x + 6a b x - 27b +--R / +--R 8 2 7 6 2 +--R 6a x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 5 5 4 4 3 2 3 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x +--R + +--R 2 3 2 4 5 +--R 63a b x + 6a b x - 27b +--R / +--R 8 2 7 6 2 +--R 6a x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 742 + +--S 743 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 of 1369 +t0:=x/(a+b/x)^3 +--R +--R +--R 4 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 745 + +--S 746 of 1369 +r0:=-3*b*x/a^4+1/2*x^2/a^3-1/2*b^4/(a^5*(b+a*x)^2)+4*b^3/(a^5*(b+a*x))+_ + 6*b^2*log(b+a*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7b +--R / +--R 7 2 6 5 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7b +--R / +--R 7 2 6 5 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 747 + +--S 748 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 749 + +)clear all + +--S 750 of 1369 +t0:=1/(a+b/x)^3 +--R +--R +--R 3 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 750 + +--S 751 of 1369 +r0:=x/a^3+1/2*b^3/(a^4*(b+a*x)^2)-3*b^2/(a^4*(b+a*x))-3*b*log(b+a*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 752 + +--S 753 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 754 + +)clear all + +--S 755 of 1369 +t0:=1/((a+b/x)^3*x) +--R +--R +--R 2 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 755 + +--S 756 of 1369 +r0:=-1/2*b^2/(a^3*(b+a*x)^2)+2*b/(a^3*(b+a*x))+log(b+a*x)/a^3 +--R +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (2) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (3) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 757 + +--S 758 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 759 + +)clear all + +--S 760 of 1369 +t0:=1/((a+b/x)^3*x^2) +--R +--R +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 760 + +--S 761 of 1369 +r0:=1/2/(b*(a+b/x)^2) +--R +--R +--R 2 +--R x +--R (2) ---------------------- +--R 2 2 2 3 +--R 2a b x + 4a b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 2a x - b +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 762 + +--S 763 of 1369 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R 2a b +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 764 + +)clear all + +--S 765 of 1369 +t0:=1/((a+b/x)^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 765 + +--S 766 of 1369 +r0:=(-1/2)/(a*(a+b/x)^2*x^2) +--R +--R +--R 1 +--R (2) - ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 767 + +--S 768 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 769 + +)clear all + +--S 770 of 1369 +t0:=1/((a+b/x)^3*x^4) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 770 + +--S 771 of 1369 +r0:=1/2/(b*(b+a*x)^2)+1/(b^2*(b+a*x))+log(x)/b^3-log(b+a*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x) +--R + +--R 2 +--R 2a b x + 3b +--R / +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x) +--R + +--R 2 +--R 2a b x + 3b +--R / +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Union(Expression(Integer),...) +--E 772 + +--S 773 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 774 + +)clear all + +--S 775 of 1369 +t0:=1/((a+b/x)^3*x^5) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 775 + +--S 776 of 1369 +r0:=(-1)/(b^3*x)-1/2*a/(b^2*(b+a*x)^2)-2*a/(b^3*(b+a*x))-3*a*log(x)/b^4+_ + 3*a*log(b+a*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 +--R (6a x + 12a b x + 6a b x)log(a x + b) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 +--R (6a x + 12a b x + 6a b x)log(a x + b) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 777 + +--S 778 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 779 + +)clear all + +--S 780 of 1369 +t0:=1/((a+b/x)^3*x^6) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 780 + +--S 781 of 1369 +r0:=(-1/2)/(b^3*x^2)+3*a/(b^4*x)+1/2*a^2/(b^3*(b+a*x)^2)+_ + 3*a^2/(b^4*(b+a*x))+6*a^2*log(x)/b^5-6*a^2*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 782 + +--S 783 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 784 + +)clear all + +--S 785 of 1369 +t0:=1/((a+b/x)^3*x^7) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 785 + +--S 786 of 1369 +r0:=(-1/3)/(b^3*x^3)+3/2*a/(b^4*x^2)-6*a^2/(b^5*x)-_ + 1/2*a^3/(b^4*(b+a*x)^2)-4*a^3/(b^5*(b+a*x))-10*a^3*log(x)/b^6+_ + 10*a^3*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 3 +--R (60a x + 120a b x + 60a b x )log(a x + b) +--R + +--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2 +--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2b +--R / +--R 2 6 5 7 4 8 3 +--R 6a b x + 12a b x + 6b x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 3 2 3 +--R (60a x + 120a b x + 60a b x )log(a x + b) +--R + +--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2 +--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2b +--R / +--R 2 6 5 7 4 8 3 +--R 6a b x + 12a b x + 6b x +--R Type: Union(Expression(Integer),...) +--E 787 + +--S 788 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 789 + +)clear all + +--S 790 of 1369 +t0:=1/((a+b/x)^3*x^8) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 7 2 6 3 5 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 790 + +--S 791 of 1369 +r0:=(-1/4)/(b^3*x^4)+a/(b^4*x^3)-3*a^2/(b^5*x^2)+10*a^3/(b^6*x)+_ + 1/2*a^4/(b^5*(b+a*x)^2)+5*a^4/(b^6*(b+a*x))+15*a^4*log(x)/b^7-_ + 15*a^4*log(b+a*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 +--R (- 60a x - 120a b x - 60a b x )log(a x + b) +--R + +--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3 +--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 2 4 2 5 6 +--R - 5a b x + 2a b x - b +--R / +--R 2 7 6 8 5 9 4 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 +--R (- 60a x - 120a b x - 60a b x )log(a x + b) +--R + +--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3 +--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 2 4 2 5 6 +--R - 5a b x + 2a b x - b +--R / +--R 2 7 6 8 5 9 4 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 792 + +--S 793 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1369 +t0:=1/((a+b/x)^3*x^9) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 8 2 7 3 6 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1369 +r0:=(-1/5)/(b^3*x^5)+3/4*a/(b^4*x^4)-2*a^2/(b^5*x^3)+5*a^3/(b^6*x^2)-_ + 15*a^4/(b^7*x)-1/2*a^5/(b^6*(b+a*x)^2)-6*a^5/(b^7*(b+a*x))-_ + 21*a^5*log(x)/b^8+21*a^5*log(b+a*x)/b^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 +--R (420a x + 840a b x + 420a b x )log(a x + b) +--R + +--R 7 7 6 6 5 2 5 6 6 5 2 5 +--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b +--R / +--R 2 8 7 9 6 10 5 +--R 20a b x + 40a b x + 20b x +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 +--R (420a x + 840a b x + 420a b x )log(a x + b) +--R + +--R 7 7 6 6 5 2 5 6 6 5 2 5 +--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b +--R / +--R 2 8 7 9 6 10 5 +--R 20a b x + 40a b x + 20b x +--R Type: Union(Expression(Integer),...) +--E 797 + +--S 798 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1369 +t0:=x^3*sqrt(a+b/x) +--R +--R +--R +-------+ +--R 3 |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1369 +r0:=-5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/64*b^3*x*_ + sqrt(a+b/x)/a^3-5/96*b^2*x^2*sqrt(a+b/x)/a^2+1/24*b*x^3*_ + sqrt(a+b/x)/a+1/4*x^4*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 16a b x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 8a b x - 10a b x + 15b x)\|- a |------- +--R \| x +--R / +--R 3 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1369 +t0:=x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R 2 |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1369 +r0:=1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-1/8*b^2*x*_ + sqrt(a+b/x)/a^2+1/12*b*x^2*sqrt(a+b/x)/a+1/3*x^3*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------- +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |------- +--R a \| x +--R --------------------------------------------------------------------] +--R 2 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1369 +t0:=x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1369 +r0:=-1/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+1/4*b*x*sqrt(a+b/x)/a+_ + 1/2*x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R - b atanh(----------) + (2a x + b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R - b atan(----------------) + (2a x + b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 816 + +--S 817 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1369 +t0:=sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R (1) |------- +--R \| x +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1369 +r0:=b*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [---------------------------------------------------------, +--R +-+ +--R 2\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R b atan(----------------) + x\|- a |------- +--R a \| x +--R --------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 823 + +--S 824 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1369 +t0:=sqrt(a+b/x)/x +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (2) 2\|a atanh(----------) - 2 |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------, +--R \| x \| x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 2\|- a atan(----------) - 2 |-------] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 830 + +--S 831 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (4) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 2\|a atanh(----------) + 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 834 + +)clear all + +--S 835 of 1369 +t0:=sqrt(a+b/x)/x^2 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b +--R +--R +--R +-------+ +--R |a x + b +--R (- 2a x - 2b) |------- +--R \| x +--R (2) ----------------------- +--R 3b x +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R (- 2a x - 2b) |------- +--R \| x +--R (3) ----------------------- +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 837 + +--S 838 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 839 + +)clear all + +--S 840 of 1369 +t0:=sqrt(a+b/x)/x^3 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1369 +r0:=2/3*a*(a+b/x)^(3/2)/b^2-2/5*(a+b/x)^(5/2)/b^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x - 2a b x - 6b ) |------- +--R \| x +--R (2) -------------------------------- +--R 2 2 +--R 15b x +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x - 2a b x - 6b ) |------- +--R \| x +--R (3) -------------------------------- +--R 2 2 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 842 + +--S 843 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 844 + +)clear all + +--S 845 of 1369 +t0:=sqrt(a+b/x)/x^4 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1369 +r0:=-2/3*a^2*(a+b/x)^(3/2)/b^3+4/5*a*(a+b/x)^(5/2)/b^3-2/7*(a+b/x)^(7/2)/b^3 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |------- +--R \| x +--R (2) ---------------------------------------------- +--R 3 3 +--R 105b x +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |------- +--R \| x +--R (3) ---------------------------------------------- +--R 3 3 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 847 + +--S 848 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 849 + +)clear all + +--S 850 of 1369 +t0:=sqrt(a+b/x)/x^5 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1369 +r0:=2/3*a^3*(a+b/x)^(3/2)/b^4-6/5*a^2*(a+b/x)^(5/2)/b^4+6/7*_ + a*(a+b/x)^(7/2)/b^4-2/9*(a+b/x)^(9/2)/b^4 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |------- +--R \| x +--R (2) --------------------------------------------------------- +--R 4 4 +--R 315b x +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |------- +--R \| x +--R (3) --------------------------------------------------------- +--R 4 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 852 + +--S 853 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1369 +t0:=sqrt(a+b/x)/x^6 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1369 +r0:=-2/3*a^4*(a+b/x)^(3/2)/b^5+8/5*a^3*(a+b/x)^(5/2)/b^5-_ + 12/7*a^2*(a+b/x)^(7/2)/b^5+8/9*a*(a+b/x)^(9/2)/b^5-2/11*_ + (a+b/x)^(11/2)/b^5 +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |------- +--R \| x +--R ------------------------------------------------------------------------- +--R 5 5 +--R 3465b x +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |------- +--R \| x +--R ------------------------------------------------------------------------- +--R 5 5 +--R 3465b x +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1369 +t0:=(a+b/x)^(3/2)*x^3 +--R +--R +--R +-------+ +--R 3 2 |a x + b +--R (1) (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1369 +r0:=1/4*(a+b/x)^(3/2)*x^4+3/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-_ + 3/64*b^3*x*sqrt(a+b/x)/a^2+1/32*b^2*x^2*sqrt(a+b/x)/a+_ + 1/8*b*x^3*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R 3b atanh(----------) + (16a x + 24a b x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R ------------------------------------------------------------------------- +--R 2 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (32a x + 48a b x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 128a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 3b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (16a x + 24a b x + 2a b x - 3b x)\|- a |------- +--R \| x +--R / +--R 2 +---+ +--R 64a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 862 + +--S 863 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 866 + +)clear all + +--S 867 of 1369 +t0:=(a+b/x)^(3/2)*x^2 +--R +--R +--R +-------+ +--R 2 |a x + b +--R (1) (a x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 867 + +--S 868 of 1369 +r0:=1/3*(a+b/x)^(3/2)*x^3-1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+_ + 1/8*b^2*x*sqrt(a+b/x)/a+1/4*b*x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 3b atanh(----------) + (8a x + 14a b x + 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 24a\|a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 28a b x + 6b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 48a\|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 3b atan(----------------) + (8a x + 14a b x + 3b x)\|- a |------- +--R a \| x +--R -----------------------------------------------------------------------] +--R +---+ +--R 24a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 869 + +--S 870 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 873 + +)clear all + +--S 874 of 1369 +t0:=(a+b/x)^(3/2)*x +--R +--R +--R +-------+ +--R |a x + b +--R (1) (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1369 +r0:=1/2*(a+b/x)^(3/2)*x^2+3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+_ + 3/4*b*x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x + 5b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x + 10b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x + 5b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 876 + +--S 877 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1369 +t0:=(a+b/x)^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1369 +r0:=(a+b/x)^(3/2)*x+3*b*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-3*b*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (2) 3b\|a atanh(----------) + (a x - 2b) |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R 3b\|a log(2x\|a |------- + 2a x + b) + (2a x - 4b) |------- +--R \| x \| x +--R [--------------------------------------------------------------, +--R 2 +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 3b\|- a atan(----------) + (a x - 2b) |------- ] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 883 + +--S 884 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R 3b\|a log(2x\|a |------- + 2a x + b) - 6b\|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 3b\|a atanh(----------) + 3b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1369 +t0:=(a+b/x)^(3/2)/x +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1369 +r0:=-2/3*(a+b/x)^(3/2)+2*a^(3/2)*atanh(sqrt(a+b/x)/sqrt(a))-2*a*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R 6a x\|a atanh(----------) + (- 8a x - 2b) |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R 3a x\|a log(2x\|a |------- + 2a x + b) + (- 8a x - 2b) |------- +--R \| x \| x +--R [------------------------------------------------------------------, +--R 3x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 6a x\|- a atan(----------) + (- 8a x - 2b) |------- +--R +---+ \| x +--R \|- a +--R ----------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 890 + +--S 891 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (4) a\|a log(2x\|a |------- + 2a x + b) - 2a\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 2a\|a atanh(----------) + 2a\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1369 +t0:=(a+b/x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1369 +r0:=-2/5*(a+b/x)^(5/2)/b +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |------- +--R \| x +--R (2) ---------------------------------- +--R 2 +--R 5b x +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |------- +--R \| x +--R (3) ---------------------------------- +--R 2 +--R 5b x +--R Type: Union(Expression(Integer),...) +--E 897 + +--S 898 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1369 +t0:=(a+b/x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1369 +r0:=2/5*a*(a+b/x)^(5/2)/b^2-2/7*(a+b/x)^(7/2)/b^2 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |------- +--R \| x +--R (2) -------------------------------------------- +--R 2 3 +--R 35b x +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |------- +--R \| x +--R (3) -------------------------------------------- +--R 2 3 +--R 35b x +--R Type: Union(Expression(Integer),...) +--E 902 + +--S 903 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1369 +t0:=(a+b/x)^(3/2)/x^4 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1369 +r0:=-2/5*a^2*(a+b/x)^(5/2)/b^3+4/7*a*(a+b/x)^(7/2)/b^3-2/9*(a+b/x)^(9/2)/b^3 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |------- +--R \| x +--R (2) ---------------------------------------------------------- +--R 3 4 +--R 315b x +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |------- +--R \| x +--R (3) ---------------------------------------------------------- +--R 3 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 907 + +--S 908 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1369 +t0:=(a+b/x)^(3/2)/x^5 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1369 +r0:=2/5*a^3*(a+b/x)^(5/2)/b^4-6/7*a^2*(a+b/x)^(7/2)/b^4+2/3*a*_ + (a+b/x)^(9/2)/b^4-2/11*(a+b/x)^(11/2)/b^4 +--R +--R +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |------- +--R \| x +--R (2) ---------------------------------------------------------------------- +--R 4 5 +--R 1155b x +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |------- +--R \| x +--R (3) ---------------------------------------------------------------------- +--R 4 5 +--R 1155b x +--R Type: Union(Expression(Integer),...) +--E 912 + +--S 913 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1369 +t0:=(a+b/x)^(3/2)/x^6 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1369 +r0:=-2/5*a^4*(a+b/x)^(5/2)/b^5+8/7*a^3*(a+b/x)^(7/2)/b^5-_ + 4/3*a^2*(a+b/x)^(9/2)/b^5+8/11*a*(a+b/x)^(11/2)/b^5-_ + 2/13*(a+b/x)^(13/2)/b^5 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x +--R + +--R 6 +--R - 2310b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 6 +--R 15015b x +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x +--R + +--R 6 +--R - 2310b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 6 +--R 15015b x +--R Type: Union(Expression(Integer),...) +--E 917 + +--S 918 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +)clear all + +--S 920 of 1369 +t0:=(a+b/x)^(3/2)/x^7 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1369 +r0:=2/5*a^5*(a+b/x)^(5/2)/b^6-10/7*a^4*(a+b/x)^(7/2)/b^6+_ + 20/9*a^3*(a+b/x)^(9/2)/b^6-20/11*a^2*(a+b/x)^(11/2)/b^6+_ + 10/13*a*(a+b/x)^(13/2)/b^6-2/15*(a+b/x)^(15/2)/b^6 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x +--R + +--R 6 7 +--R - 7392a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 6 7 +--R 45045b x +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x +--R + +--R 6 7 +--R - 7392a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 6 7 +--R 45045b x +--R Type: Union(Expression(Integer),...) +--E 922 + +--S 923 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1369 +t0:=(a+b/x)^(5/2)*x^3 +--R +--R +--R +-------+ +--R 2 3 2 2 |a x + b +--R (1) (a x + 2a b x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1369 +r0:=5/24*b*(a+b/x)^(3/2)*x^3+1/4*(a+b/x)^(5/2)*x^4-_ + 5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+5/64*b^3*x*_ + sqrt(a+b/x)/a+5/32*b^2*x^2*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R - 15b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x + 136a b x + 118a b x + 15b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 192a\|a +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 272a b x + 236a b x + 30b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 384a\|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 136a b x + 118a b x + 15b x)\|- a |------- +--R \| x +--R / +--R +---+ +--R 192a\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 927 + +--S 928 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 64a\|- a \|a +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 931 + +)clear all + +--S 932 of 1369 +t0:=(a+b/x)^(5/2)*x^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (1) (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1369 +r0:=5/12*b*(a+b/x)^(3/2)*x^2+1/3*(a+b/x)^(5/2)*x^3+5/8*b^3*_ + atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+5/8*b^2*x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 15b atanh(----------) + (8a x + 26a b x + 33b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 24\|a +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 52a b x + 66b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 48\|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 15b atan(----------------) + (8a x + 26a b x + 33b x)\|- a |------- +--R a \| x +--R -----------------------------------------------------------------------] +--R +---+ +--R 24\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 934 + +--S 935 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(2a x |------- + (2a x + b)\|a ) - 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 938 + +)clear all + +--S 939 of 1369 +t0:=(a+b/x)^(5/2)*x +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1369 +r0:=5/4*b*(a+b/x)^(3/2)*x+1/2*(a+b/x)^(5/2)*x^2+15/4*b^2*_ + atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-15/4*b^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 +-+ \| x 2 2 2 |a x + b +--R 15b \|a atanh(----------) + (2a x + 9a b x - 8b ) |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 2 +-+ +-+ |a x + b +--R 15b \|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x + 18a b x - 16b ) |------- +--R \| x +--R / +--R 8 +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 +---+ \| x 2 2 2 |a x + b +--R 15b \|- a atan(----------) + (2a x + 9a b x - 8b ) |------- +--R +---+ \| x +--R \|- a +--R -------------------------------------------------------------] +--R 4 +--R Type: Union(List(Expression(Integer)),...) +--E 941 + +--S 942 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 +-+ +-+ |a x + b 2 +-+ \| x +--R 15b \|a log(2x\|a |------- + 2a x + b) - 30b \|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R 2 +-+ \| x 2 +---+ \| x +--R - 15b \|a atanh(----------) + 15b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1369 +t0:=(a+b/x)^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1369 +r0:=-5/3*b*(a+b/x)^(3/2)+(a+b/x)^(5/2)*x+5*a^(3/2)*b*_ + atanh(sqrt(a+b/x)/sqrt(a))-5*a*b*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x 2 2 2 |a x + b +--R 15a b x\|a atanh(----------) + (3a x - 14a b x - 2b ) |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R +-+ +-+ |a x + b +--R 15a b x\|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (6a x - 28a b x - 4b ) |------- +--R \| x +--R / +--R 6x +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x 2 2 2 |a x + b +--R 15a b x\|- a atan(----------) + (3a x - 14a b x - 2b ) |------- +--R +---+ \| x +--R \|- a +--R -----------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 948 + +--S 949 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R 5a b\|a log(2x\|a |------- + 2a x + b) - 10a b\|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 5a b\|a atanh(----------) + 5a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 952 + +)clear all + +--S 953 of 1369 +t0:=(a+b/x)^(5/2)/x +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1369 +r0:=-2/3*a*(a+b/x)^(3/2)-2/5*(a+b/x)^(5/2)+2*a^(5/2)*_ + atanh(sqrt(a+b/x)/sqrt(a))-2*a^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 2 +-+ \| x 2 2 2 |a x + b +--R 30a x \|a atanh(----------) + (- 46a x - 22a b x - 6b ) |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------------ +--R 2 +--R 15x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 2 2 +-+ +-+ |a x + b +--R 15a x \|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (- 46a x - 22a b x - 6b ) |------- +--R \| x +--R / +--R 2 +--R 15x +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 2 +---+ \| x 2 2 2 |a x + b +--R 30a x \|- a atan(----------) + (- 46a x - 22a b x - 6b ) |------- +--R +---+ \| x +--R \|- a +--R -------------------------------------------------------------------] +--R 2 +--R 15x +--R Type: Union(List(Expression(Integer)),...) +--E 955 + +--S 956 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 +-+ +-+ |a x + b 2 +-+ \| x +--R (4) a \|a log(2x\|a |------- + 2a x + b) - 2a \|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R 2 +-+ \| x 2 +---+ \| x +--R (6) - 2a \|a atanh(----------) + 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 959 + +)clear all + +--S 960 of 1369 +t0:=(a+b/x)^(5/2)/x^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1369 +r0:=-2/7*(a+b/x)^(7/2)/b +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 2a x - 6a b x - 6a b x - 2b ) |------- +--R \| x +--R (2) -------------------------------------------- +--R 3 +--R 7b x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 2a x - 6a b x - 6a b x - 2b ) |------- +--R \| x +--R (3) -------------------------------------------- +--R 3 +--R 7b x +--R Type: Union(Expression(Integer),...) +--E 962 + +--S 963 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 964 + +)clear all + +--S 965 of 1369 +t0:=(a+b/x)^(5/2)/x^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1369 +r0:=2/7*a*(a+b/x)^(7/2)/b^2-2/9*(a+b/x)^(9/2)/b^2 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |------- +--R \| x +--R (2) ------------------------------------------------------- +--R 2 4 +--R 63b x +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |------- +--R \| x +--R (3) ------------------------------------------------------- +--R 2 4 +--R 63b x +--R Type: Union(Expression(Integer),...) +--E 967 + +--S 968 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 969 + +)clear all + +--S 970 of 1369 +t0:=(a+b/x)^(5/2)/x^4 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 6 +--R x +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1369 +r0:=-2/7*a^2*(a+b/x)^(7/2)/b^3+4/9*a*(a+b/x)^(9/2)/b^3-2/11*(a+b/x)^(11/2)/b^3 +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |------- +--R \| x +--R ----------------------------------------------------------------------- +--R 3 5 +--R 693b x +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |------- +--R \| x +--R ----------------------------------------------------------------------- +--R 3 5 +--R 693b x +--R Type: Union(Expression(Integer),...) +--E 972 + +--S 973 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 974 + +)clear all + +--S 975 of 1369 +t0:=(a+b/x)^(5/2)/x^5 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 7 +--R x +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1369 +r0:=2/7*a^3*(a+b/x)^(7/2)/b^4-2/3*a^2*(a+b/x)^(9/2)/b^4+_ + 6/11*a*(a+b/x)^(11/2)/b^4-2/13*(a+b/x)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b ) +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 4 6 +--R 3003b x +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b ) +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 4 6 +--R 3003b x +--R Type: Union(Expression(Integer),...) +--E 977 + +--S 978 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 979 + +)clear all + +--S 980 of 1369 +t0:=(a+b/x)^(5/2)/x^6 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 8 +--R x +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1369 +r0:=-2/7*a^4*(a+b/x)^(7/2)/b^5+8/9*a^3*(a+b/x)^(9/2)/b^5-_ + 12/11*a^2*(a+b/x)^(11/2)/b^5+8/13*a*(a+b/x)^(13/2)/b^5-_ + 2/15*(a+b/x)^(15/2)/b^5 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x +--R + +--R 6 7 +--R - 14322a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 7 +--R 45045b x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x +--R + +--R 6 7 +--R - 14322a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 7 +--R 45045b x +--R Type: Union(Expression(Integer),...) +--E 982 + +--S 983 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1369 +t0:=x^3/sqrt(a+b/x) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1369 +r0:=35/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-35/64*b^3*x*_ + sqrt(a+b/x)/a^4+35/96*b^2*x^2*sqrt(a+b/x)/a^3-7/24*b*x^3*_ + sqrt(a+b/x)/a^2+1/4*x^4*sqrt(a+b/x)/a +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R 105b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 105b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x - 112a b x + 140a b x - 210b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 105b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|- a |------- +--R \| x +--R / +--R 4 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 987 + +--S 988 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 991 + +)clear all + +--S 992 of 1369 +t0:=x^2/sqrt(a+b/x) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1369 +r0:=-5/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/8*b^2*x*_ + sqrt(a+b/x)/a^3-5/12*b*x^2*sqrt(a+b/x)/a^2+1/3*x^3*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |------- +--R a \| x +--R -------------------------------------------------------------------------] +--R 3 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 994 + +--S 995 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1369 +t0:=x/sqrt(a+b/x) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1369 +r0:=3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-3/4*b*x*_ + sqrt(a+b/x)/a^2+1/2*x^2*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |------- +--R \| x \| x +--R [----------------------------------------------------------------------, +--R 2 +-+ +--R 8a \|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x - 3b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R 2 +---+ +--R 4a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1001 + +--S 1002 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1369 +t0:=1/sqrt(a+b/x) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1369 +r0:=-b*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+x*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R - b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------, +--R +-+ +--R 2a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R - b atan(----------------) + x\|- a |------- +--R a \| x +--R ----------------------------------------------] +--R +---+ +--R a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1369 +t0:=1/(x*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------) +--R \| x a +--R (3) [------------------------------------,-----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1369 +t0:=1/(x^2*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1369 +r0:=-2*sqrt(a+b/x)/b +--R +--R +--R +-------+ +--R |a x + b +--R 2 |------- +--R \| x +--R (2) - ----------- +--R b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R 2 |------- +--R \| x +--R (3) - ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1022 + +--S 1023 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +)clear all + +--S 1025 of 1369 +t0:=1/(x^3*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b^2+2*a*sqrt(a+b/x)/b^2 +--R +--R +--R +-------+ +--R |a x + b +--R (4a x - 2b) |------- +--R \| x +--R (2) --------------------- +--R 2 +--R 3b x +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R (4a x - 2b) |------- +--R \| x +--R (3) --------------------- +--R 2 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 1027 + +--S 1028 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +)clear all + +--S 1030 of 1369 +t0:=1/(x^4*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1369 +r0:=4/3*a*(a+b/x)^(3/2)/b^3-2/5*(a+b/x)^(5/2)/b^3-2*a^2*sqrt(a+b/x)/b^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |------- +--R \| x +--R (2) ----------------------------------- +--R 3 2 +--R 15b x +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |------- +--R \| x +--R (3) ----------------------------------- +--R 3 2 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1369 +t0:=1/(x^5*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1369 +r0:=-2*a^2*(a+b/x)^(3/2)/b^4+6/5*a*(a+b/x)^(5/2)/b^4-_ + 2/7*(a+b/x)^(7/2)/b^4+2*a^3*sqrt(a+b/x)/b^4 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |------- +--R \| x +--R (2) ---------------------------------------------- +--R 4 3 +--R 35b x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |------- +--R \| x +--R (3) ---------------------------------------------- +--R 4 3 +--R 35b x +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1369 +t0:=1/(x^6*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 6 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1369 +r0:=8/3*a^3*(a+b/x)^(3/2)/b^5-12/5*a^2*(a+b/x)^(5/2)/b^5+_ + 8/7*a*(a+b/x)^(7/2)/b^5-2/9*(a+b/x)^(9/2)/b^5-2*a^4*sqrt(a+b/x)/b^5 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |------- +--R \| x +--R (2) ------------------------------------------------------------- +--R 5 4 +--R 315b x +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |------- +--R \| x +--R (3) ------------------------------------------------------------- +--R 5 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1369 +t0:=x^2/(a+b/x)^(3/2) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1369 +r0:=-35/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-2*x^3/(a*sqrt(a+b/x))+_ + 35/8*b^2*x*sqrt(a+b/x)/a^4-35/12*b*x^2*sqrt(a+b/x)/a^3+_ + 7/3*x^3*sqrt(a+b/x)/a^2 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b \| x 3 3 2 2 2 3 +-+ +--R - 105b |------- atanh(----------) + (8a x - 14a b x + 35a b x + 105b )\|a +--R \| x +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R +-------+ +--R 4 +-+ |a x + b +--R 24a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 3 |a x + b |a x + b +-+ +--R 105b |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (16a x - 28a b x + 70a b x + 210b )\|a +--R / +--R +-------+ +--R 4 +-+ |a x + b +--R 48a \|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 3 |a x + b \| x +--R - 105b |------- atan(----------------) +--R \| x a +--R + +--R 3 3 2 2 2 3 +---+ +--R (8a x - 14a b x + 35a b x + 105b )\|- a +--R / +--R +-------+ +--R 4 +---+ |a x + b +--R 24a \|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1047 + +--S 1048 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 35b log(- 2a x |------- + (2a x + b)\|a ) + 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 35b \|- a atanh(----------) - 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 4 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1051 + +)clear all + +--S 1052 of 1369 +t0:=x/(a+b/x)^(3/2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1369 +r0:=15/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-2*x^2/(a*sqrt(a+b/x))-_ + 15/4*b*x*sqrt(a+b/x)/a^3+5/2*x^2*sqrt(a+b/x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b \| x 2 2 2 +-+ +--R 15b |------- atanh(----------) + (2a x - 5a b x - 15b )\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R +-------+ +--R 3 +-+ |a x + b +--R 4a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 |a x + b |a x + b +-+ +--R 15b |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 2 2 2 +-+ +--R (4a x - 10a b x - 30b )\|a +--R / +--R +-------+ +--R 3 +-+ |a x + b +--R 8a \|a |------- +--R \| x +--R , +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 |a x + b \| x 2 2 2 +---+ +--R 15b |------- atan(----------------) + (2a x - 5a b x - 15b )\|- a +--R \| x a +--R --------------------------------------------------------------------] +--R +-------+ +--R 3 +---+ |a x + b +--R 4a \|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1054 + +--S 1055 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 15b log(2a x |------- + (2a x + b)\|a ) - 30b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 15b \|- a atanh(----------) + 15b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 3 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1369 +t0:=1/(a+b/x)^(3/2) +--R +--R +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1369 +r0:=-3*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-2*x/(a*sqrt(a+b/x))+_ + 3*x*sqrt(a+b/x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R - 3b |------- atanh(----------) + (a x + 3b)\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------------------ +--R +-------+ +--R 2 +-+ |a x + b +--R a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +-+ +--R 3b |------- log(- 2a x |------- + (2a x + b)\|a ) + (2a x + 6b)\|a +--R \| x \| x +--R [--------------------------------------------------------------------, +--R +-------+ +--R 2 +-+ |a x + b +--R 2a \|a |------- +--R \| x +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R - 3b |------- atan(----------------) + (a x + 3b)\|- a +--R \| x a +--R -------------------------------------------------------] +--R +-------+ +--R 2 +---+ |a x + b +--R a \|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1061 + +--S 1062 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R 3b log(- 2a x |------- + (2a x + b)\|a ) + 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R 3b\|- a atanh(----------) - 3b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1369 +t0:=1/((a+b/x)^(3/2)*x) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(a+b/x)) +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R 2 |------- atanh(---------- - 2\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------ +--R +-------+ +--R +-+ |a x + b +--R a\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +-+ +--R |------- log(2a x |------- + (2a x + b)\|a ) - 2\|a +--R \| x \| x +--R [------------------------------------------------------, +--R +-------+ +--R +-+ |a x + b +--R a\|a |------- +--R \| x +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R 2 |------- atan(---------------- - 2\|- a +--R \| x a +--R -------------------------------------------] +--R +-------+ +--R +---+ |a x + b +--R a\|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1068 + +--S 1069 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1072 + +)clear all + +--S 1073 of 1369 +t0:=1/((a+b/x)^(3/2)*x^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R +-------+ +--R 2 |a x + b +--R (a x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1369 +r0:=2/(b*sqrt(a+b/x)) +--R +--R +--R 2 +--R (2) ----------- +--R +-------+ +--R |a x + b +--R b |------- +--R \| x +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) ----------- +--R +-------+ +--R |a x + b +--R b |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1075 + +--S 1076 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1077 + +)clear all + +--S 1078 of 1369 +t0:=1/((a+b/x)^(3/2)*x^3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 3 2 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1369 +r0:=-2*a/(b^2*sqrt(a+b/x))-2*sqrt(a+b/x)/b^2 +--R +--R +--R - 4a x - 2b +--R (2) ------------- +--R +-------+ +--R 2 |a x + b +--R b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 4a x - 2b +--R (3) ------------- +--R +-------+ +--R 2 |a x + b +--R b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1080 + +--S 1081 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1082 + +)clear all + +--S 1083 of 1369 +t0:=1/((a+b/x)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 4 3 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b^3+2*a^2/(b^3*sqrt(a+b/x))+4*a*sqrt(a+b/x)/b^3 +--R +--R +--R 2 2 2 +--R 16a x + 8a b x - 2b +--R (2) --------------------- +--R +-------+ +--R 3 2 |a x + b +--R 3b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 16a x + 8a b x - 2b +--R (3) --------------------- +--R +-------+ +--R 3 2 |a x + b +--R 3b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1085 + +--S 1086 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1087 + +)clear all + +--S 1088 of 1369 +t0:=1/((a+b/x)^(3/2)*x^5) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 5 4 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1369 +r0:=2*a*(a+b/x)^(3/2)/b^4-2/5*(a+b/x)^(5/2)/b^4-2*a^3/(b^4*sqrt(a+b/x))-_ + 6*a^2*sqrt(a+b/x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (2) ---------------------------------- +--R +-------+ +--R 4 3 |a x + b +--R 5b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (3) ---------------------------------- +--R +-------+ +--R 4 3 |a x + b +--R 5b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1090 + +--S 1091 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1092 + +)clear all + +--S 1093 of 1369 +t0:=1/((a+b/x)^(3/2)*x^6) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 6 5 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1369 +r0:=-4*a^2*(a+b/x)^(3/2)/b^5+8/5*a*(a+b/x)^(5/2)/b^5-_ + 2/7*(a+b/x)^(7/2)/b^5+2*a^4/(b^5*sqrt(a+b/x))+8*a^3*sqrt(a+b/x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 256a x + 128a b x - 32a b x + 16a b x - 10b +--R (2) ----------------------------------------------- +--R +-------+ +--R 5 4 |a x + b +--R 35b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 256a x + 128a b x - 32a b x + 16a b x - 10b +--R (3) ----------------------------------------------- +--R +-------+ +--R 5 4 |a x + b +--R 35b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1095 + +--S 1096 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1097 + +)clear all + +--S 1098 of 1369 +t0:=1/((a+b/x)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 7 6 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1369 +r0:=20/3*a^3*(a+b/x)^(3/2)/b^6-4*a^2*(a+b/x)^(5/2)/b^6+_ + 10/7*a*(a+b/x)^(7/2)/b^6-2/9*(a+b/x)^(9/2)/b^6-_ + 2*a^5/(b^6*sqrt(a+b/x))-10*a^4*sqrt(a+b/x)/b^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b +--R (2) ------------------------------------------------------------ +--R +-------+ +--R 6 5 |a x + b +--R 63b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b +--R (3) ------------------------------------------------------------ +--R +-------+ +--R 6 5 |a x + b +--R 63b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1100 + +--S 1101 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1102 + +)clear all + +--S 1103 of 1369 +t0:=x^2/(a+b/x)^(5/2) +--R +--R +--R 4 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1369 +r0:=-2/3*x^3/(a*(a+b/x)^(3/2))-105/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/_ + a^(11/2)-6*x^3/(a^2*sqrt(a+b/x))+105/8*b^2*x*sqrt(a+b/x)/a^5-_ + 35/4*b*x^2*sqrt(a+b/x)/a^4+7*x^3*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 4 |a x + b \| x +--R (- 315a b x - 315b ) |------- atanh(----------) +--R \| x +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|a +--R / +--R +-------+ +--R 6 5 +-+ |a x + b +--R (24a x + 24a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 3 4 |a x + b |a x + b +-+ +--R (315a b x + 315b ) |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (16a x - 36a b x + 126a b x + 840a b x + 630b )\|a +--R / +--R +-------+ +--R 6 5 +-+ |a x + b +--R (48a x + 48a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 3 4 |a x + b \| x +--R (- 315a b x - 315b ) |------- atan(----------------) +--R \| x a +--R + +--R 4 4 3 3 2 2 2 3 4 +---+ +--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|- a +--R / +--R +-------+ +--R 6 5 +---+ |a x + b +--R (24a x + 24a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1105 + +--S 1106 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 105b log(- 2a x |------- + (2a x + b)\|a ) + 210b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 105b \|- a atanh(----------) - 105b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 5 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1369 +t0:=x/(a+b/x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1369 +r0:=-2/3*x^2/(a*(a+b/x)^(3/2))+35/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/_ + a^(9/2)-14/3*x^2/(a^2*sqrt(a+b/x))-35/4*b*x*sqrt(a+b/x)/a^4+_ + 35/6*x^2*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 3 |a x + b \| x +--R (105a b x + 105b ) |------- atanh(----------) +--R \| x +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (6a x - 21a b x - 140a b x - 105b )\|a +--R / +--R +-------+ +--R 5 4 +-+ |a x + b +--R (12a x + 12a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 3 |a x + b |a x + b +-+ +--R (105a b x + 105b ) |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (12a x - 42a b x - 280a b x - 210b )\|a +--R / +--R +-------+ +--R 5 4 +-+ |a x + b +--R (24a x + 24a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 3 |a x + b \| x +--R (105a b x + 105b ) |------- atan(----------------) +--R \| x a +--R + +--R 3 3 2 2 2 3 +---+ +--R (6a x - 21a b x - 140a b x - 105b )\|- a +--R / +--R +-------+ +--R 5 4 +---+ |a x + b +--R (12a x + 12a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1112 + +--S 1113 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1116 + +)clear all + +--S 1117 of 1369 +t0:=1/(a+b/x)^(5/2) +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1369 +r0:=-2/3*x/(a*(a+b/x)^(3/2))-5*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-_ + 10/3*x/(a^2*sqrt(a+b/x))+5*x*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b \| x 2 2 2 +-+ +--R (- 15a b x - 15b ) |------- atanh(----------) + (3a x + 20a b x + 15b )\|a +--R \| x +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R 4 3 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 |a x + b |a x + b +-+ +--R (15a b x + 15b ) |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 2 2 2 +-+ +--R (6a x + 40a b x + 30b )\|a +--R / +--R +-------+ +--R 4 3 +-+ |a x + b +--R (6a x + 6a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 |a x + b \| x +--R (- 15a b x - 15b ) |------- atan(----------------) +--R \| x a +--R + +--R 2 2 2 +---+ +--R (3a x + 20a b x + 15b )\|- a +--R / +--R +-------+ +--R 4 3 +---+ |a x + b +--R (3a x + 3a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1119 + +--S 1120 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R 5b\|- a atanh(----------) - 5b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 3 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1123 + +)clear all + +--S 1124 of 1369 +t0:=1/((a+b/x)^(5/2)*x) +--R +--R +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1369 +r0:=(-2/3)/(a*(a+b/x)^(3/2))+2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)+_ + (-2)/(a^2*sqrt(a+b/x)) +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R (6a x + 6b) |------- atanh(----------) + (- 8a x - 6b)\|a +--R \| x +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 3 2 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +--R (3a x + 3b) |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R +-+ +--R (- 8a x - 6b)\|a +--R / +--R +-------+ +--R 3 2 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R , +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R (6a x + 6b) |------- atan(----------------) + (- 8a x - 6b)\|- a +--R \| x a +--R -----------------------------------------------------------------] +--R +-------+ +--R 3 2 +---+ |a x + b +--R (3a x + 3a b)\|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1126 + +--S 1127 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1369 +t0:=1/((a+b/x)^(5/2)*x^2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1369 +r0:=2/3/(b*(a+b/x)^(3/2)) +--R +--R +--R 2x +--R (2) ------------------------ +--R +-------+ +--R 2 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2x +--R (3) ------------------------ +--R +-------+ +--R 2 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1369 +t0:=1/((a+b/x)^(5/2)*x^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +-------+ +--R 2 3 2 2 |a x + b +--R (a x + 2a b x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1369 +r0:=-2/3*a/(b^2*(a+b/x)^(3/2))+2/(b^2*sqrt(a+b/x)) +--R +--R +--R 4a x + 6b +--R (2) ------------------------ +--R +-------+ +--R 2 3 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4a x + 6b +--R (3) ------------------------ +--R +-------+ +--R 2 3 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1369 +t0:=1/((a+b/x)^(5/2)*x^4) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 4 3 2 2 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1369 +r0:=2/3*a^2/(b^3*(a+b/x)^(3/2))-4*a/(b^3*sqrt(a+b/x))-2*sqrt(a+b/x)/b^3 +--R +--R +--R 2 2 2 +--R - 16a x - 24a b x - 6b +--R (2) -------------------------- +--R +-------+ +--R 3 2 4 |a x + b +--R (3a b x + 3b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 16a x - 24a b x - 6b +--R (3) -------------------------- +--R +-------+ +--R 3 2 4 |a x + b +--R (3a b x + 3b x) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1369 +t0:=1/((a+b/x)^(5/2)*x^5) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 5 4 2 3 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1369 +r0:=-2/3*a^3/(b^4*(a+b/x)^(3/2))-2/3*(a+b/x)^(3/2)/b^4+_ + 6*a^2/(b^4*sqrt(a+b/x))+6*a*sqrt(a+b/x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 32a x + 48a b x + 12a b x - 2b +--R (2) --------------------------------- +--R +-------+ +--R 4 3 5 2 |a x + b +--R (3a b x + 3b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 32a x + 48a b x + 12a b x - 2b +--R (3) --------------------------------- +--R +-------+ +--R 4 3 5 2 |a x + b +--R (3a b x + 3b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1369 +t0:=1/((a+b/x)^(5/2)*x^6) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 6 5 2 4 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1369 +r0:=2/3*a^4/(b^5*(a+b/x)^(3/2))+8/3*a*(a+b/x)^(3/2)/b^5-_ + 2/5*(a+b/x)^(5/2)/b^5-8*a^3/(b^5*sqrt(a+b/x))-12*a^2*sqrt(a+b/x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 256a x - 384a b x - 96a b x + 16a b x - 6b +--R (2) ------------------------------------------------ +--R +-------+ +--R 5 4 6 3 |a x + b +--R (15a b x + 15b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 256a x - 384a b x - 96a b x + 16a b x - 6b +--R (3) ------------------------------------------------ +--R +-------+ +--R 5 4 6 3 |a x + b +--R (15a b x + 15b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1369 +t0:=1/((a+b/x)^(5/2)*x^7) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 7 6 2 5 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1369 +r0:=-2/3*a^5/(b^6*(a+b/x)^(3/2))-20/3*a^2*(a+b/x)^(3/2)/b^6+_ + 2*a*(a+b/x)^(5/2)/b^6-2/7*(a+b/x)^(7/2)/b^6+_ + 10*a^4/(b^6*sqrt(a+b/x))+20*a^3*sqrt(a+b/x)/b^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 6 5 7 4 |a x + b +--R (21a b x + 21b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b +--R (3) ---------------------------------------------------------- +--R +-------+ +--R 6 5 7 4 |a x + b +--R (21a b x + 21b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1369 +t0:=(a+b/x)*x^(5/2) +--R +--R +--R 2 +-+ +--R (1) (a x + b x)\|x +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1369 +r0:=2/5*b*x^(5/2)+2/7*a*x^(7/2) +--R +--R +--R 3 2 +-+ +--R (10a x + 14b x )\|x +--R (2) --------------------- +--R 35 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ +--R (10a x + 14b x )\|x +--R (3) --------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1369 +t0:=(a+b/x)*x^(3/2) +--R +--R +--R +-+ +--R (1) (a x + b)\|x +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1369 +r0:=2/3*b*x^(3/2)+2/5*a*x^(5/2) +--R +--R +--R 2 +-+ +--R (6a x + 10b x)\|x +--R (2) ------------------- +--R 15 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (6a x + 10b x)\|x +--R (3) ------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1369 +t0:=(a+b/x)*x^(1/2) +--R +--R +--R +-+ +--R (a x + b)\|x +--R (1) ------------- +--R x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1369 +r0:=2/3*a*x^(3/2)+2*b*sqrt(x) +--R +--R +--R +-+ +--R (2a x + 6b)\|x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (2a x + 6b)\|x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1369 +t0:=(a+b/x)/x^(1/2) +--R +--R +--R a x + b +--R (1) ------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1369 +r0:=-2*b/sqrt(x)+2*a*sqrt(x) +--R +--R +--R 2a x - 2b +--R (2) --------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2a x - 2b +--R (3) --------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1369 +t0:=(a+b/x)/x^(3/2) +--R +--R +--R a x + b +--R (1) ------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1369 +r0:=-2/3*b/x^(3/2)-2*a/sqrt(x) +--R +--R +--R - 6a x - 2b +--R (2) ----------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 6a x - 2b +--R (3) ----------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1369 +t0:=(a+b/x)/x^(5/2) +--R +--R +--R a x + b +--R (1) ------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1369 +r0:=-2/5*b/x^(5/2)-2/3*a/x^(3/2) +--R +--R +--R - 10a x - 6b +--R (2) ------------ +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 10a x - 6b +--R (3) ------------ +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1369 +t0:=(a+b/x)^2*x^(5/2) +--R +--R +--R 2 2 2 +-+ +--R (1) (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1369 +r0:=2/3*b^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*a^2*x^(7/2) +--R +--R +--R 2 3 2 2 +-+ +--R (30a x + 84a b x + 70b x)\|x +--R (2) ------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +-+ +--R (30a x + 84a b x + 70b x)\|x +--R (3) ------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1369 +t0:=(a+b/x)^2*x^(3/2) +--R +--R +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1369 +r0:=4/3*a*b*x^(3/2)+2/5*a^2*x^(5/2)+2*b^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (6a x + 20a b x + 30b )\|x +--R (2) ---------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-+ +--R (6a x + 20a b x + 30b )\|x +--R (3) ---------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1369 +t0:=(a+b/x)^2*x^(1/2) +--R +--R +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R (1) ------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1369 +r0:=2/3*a^2*x^(3/2)-2*b^2/sqrt(x)+4*a*b*sqrt(x) +--R +--R +--R 2 2 2 +--R 2a x + 12a b x - 6b +--R (2) --------------------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a x + 12a b x - 6b +--R (3) --------------------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1369 +t0:=(a+b/x)^2/x^(1/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1369 +r0:=-2/3*b^2/x^(3/2)-4*a*b/sqrt(x)+2*a^2*sqrt(x) +--R +--R +--R 2 2 2 +--R 6a x - 12a b x - 2b +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 6a x - 12a b x - 2b +--R (3) --------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1369 +t0:=(a+b/x)^2/x^(3/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1369 +r0:=-2/5*b^2/x^(5/2)-4/3*a*b/x^(3/2)-2*a^2/sqrt(x) +--R +--R +--R 2 2 2 +--R - 30a x - 20a b x - 6b +--R (2) ------------------------ +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 30a x - 20a b x - 6b +--R (3) ------------------------ +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 1369 +t0:=(a+b/x)^2/x^(5/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1369 +r0:=-2/7*b^2/x^(7/2)-4/5*a*b/x^(5/2)-2/3*a^2/x^(3/2) +--R +--R +--R 2 2 2 +--R - 70a x - 84a b x - 30b +--R (2) ------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 70a x - 84a b x - 30b +--R (3) ------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1369 +t0:=(a+b/x)^3*x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1369 +r0:=2*a*b^2*x^(3/2)+6/5*a^2*b*x^(5/2)+2/7*a^3*x^(7/2)+2*b^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10a x + 42a b x + 70a b x + 70b )\|x +--R (2) ---------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10a x + 42a b x + 70a b x + 70b )\|x +--R (3) ---------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1369 +t0:=(a+b/x)^3*x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1369 +r0:=2*a^2*b*x^(3/2)+2/5*a^3*x^(5/2)-2*b^3/sqrt(x)+6*a*b^2*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 10a b x + 30a b x - 10b +--R (2) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 10a b x + 30a b x - 10b +--R (3) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1369 +t0:=(a+b/x)^3*x^(1/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1369 +r0:=-2/3*b^3/x^(3/2)+2/3*a^3*x^(3/2)-6*a*b^2/sqrt(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 18a b x - 18a b x - 2b +--R (2) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 18a b x - 18a b x - 2b +--R (3) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1369 +t0:=(a+b/x)^3/x^(1/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1369 +r0:=-2/5*b^3/x^(5/2)-2*a*b^2/x^(3/2)-6*a^2*b/sqrt(x)+2*a^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 10a x - 30a b x - 10a b x - 2b +--R (2) --------------------------------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 10a x - 30a b x - 10a b x - 2b +--R (3) --------------------------------- +--R 2 +-+ +--R 5x \|x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1369 +t0:=(a+b/x)^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1369 +r0:=-2/7*b^3/x^(7/2)-6/5*a*b^2/x^(5/2)-2*a^2*b/x^(3/2)-2*a^3/sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R - 70a x - 70a b x - 42a b x - 10b +--R (2) ------------------------------------ +--R 3 +-+ +--R 35x \|x +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 70a x - 70a b x - 42a b x - 10b +--R (3) ------------------------------------ +--R 3 +-+ +--R 35x \|x +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1369 +t0:=(a+b/x)^3/x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 5 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1369 +r0:=-2/9*b^3/x^(9/2)-6/7*a*b^2/x^(7/2)-6/5*a^2*b/x^(5/2)-2/3*a^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R - 210a x - 378a b x - 270a b x - 70b +--R (2) --------------------------------------- +--R 4 +-+ +--R 315x \|x +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 210a x - 378a b x - 270a b x - 70b +--R (3) --------------------------------------- +--R 4 +-+ +--R 315x \|x +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1369 +t0:=x^(5/2)/(a+b/x) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1369 +r0:=2/3*b^2*x^(3/2)/a^3-2/5*b*x^(5/2)/a^2+2/7*x^(7/2)/a+2*b^(7/2)*_ + atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-2*b^3*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 3 +-+ \|a \|x 3 3 2 2 2 3 +-+ +-+ +--R 210b \|b atan(--------) + (30a x - 42a b x + 70a b x - 210b )\|a \|x +--R +-+ +--R \|b +--R ----------------------------------------------------------------------- +--R 4 +-+ +--R 105a \|a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 3 | b \| a +--R 105b |- - log(----------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (30a x - 42a b x + 70a b x - 210b )\|x +--R / +--R 4 +--R 105a +--R , +--R +-+ +-+ +--R 3 |b \|x 3 3 2 2 2 3 +-+ +--R 210b |- atan(----) + (30a x - 42a b x + 70a b x - 210b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------------------------] +--R 4 +--R 105a +--R Type: Union(List(Expression(Integer)),...) +--E 1253 + +--S 1254 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R 3 | b +-+ \| a 3 +-+ \|a \|x +--R b |- - \|a log(----------------------) - 2b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 3 +-+ |b \|x 3 +-+ \|a \|x +--R 2b \|a |- atan(----) - 2b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1257 + +)clear all + +--S 1258 of 1369 +t0:=x^(3/2)/(a+b/x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1369 +r0:=-2/3*b*x^(3/2)/a^2+2/5*x^(5/2)/a-2*b^(5/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/a^(7/2)+2*b^2*sqrt(x)/a^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|a \|x 2 2 2 +-+ +-+ +--R - 30b \|b atan(--------) + (6a x - 10a b x + 30b )\|a \|x +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------- +--R 3 +-+ +--R 15a \|a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 | b \| a 2 2 2 +-+ +--R 15b |- - log(------------------------) + (6a x - 10a b x + 30b )\|x +--R \| a a x + b +--R [----------------------------------------------------------------------, +--R 3 +--R 15a +--R +-+ +-+ +--R 2 |b \|x 2 2 2 +-+ +--R - 30b |- atan(----) + (6a x - 10a b x + 30b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------------] +--R 3 +--R 15a +--R Type: Union(List(Expression(Integer)),...) +--E 1260 + +--S 1261 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R b |- - \|a log(------------------------) + 2b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 2b \|a |- atan(----) + 2b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ----------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1369 +t0:=x^(1/2)/(a+b/x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1369 +r0:=2/3*x^(3/2)/a+2*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(5/2)-_ + 2*b*sqrt(x)/a^2 +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R 6b\|b atan(--------) + (2a x - 6b)\|a \|x +--R +-+ +--R \|b +--R (2) ------------------------------------------ +--R 2 +-+ +--R 3a \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R | b \| a +-+ +--R 3b |- - log(----------------------) + (2a x - 6b)\|x +--R \| a a x + b +--R [-----------------------------------------------------, +--R 2 +--R 3a +--R +-+ +-+ +--R |b \|x +-+ +--R 6b |- atan(----) + (2a x - 6b)\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ----------------------------------] +--R 2 +--R 3a +--R Type: Union(List(Expression(Integer)),...) +--E 1267 + +--S 1268 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R b |- - \|a log(----------------------) - 2b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 2b\|a |- atan(----) - 2b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1271 + +)clear all + +--S 1272 of 1369 +t0:=1/((a+b/x)*x^(1/2)) +--R +--R +--R x +--R (1) ------------- +--R +-+ +--R (a x + b)\|x +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1369 +r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(3/2)+2*sqrt(x)/a +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R - 2\|b atan(--------) + 2\|a \|x +--R +-+ +--R \|b +--R (2) --------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |b \|x +-+ +--R | b +-+ - 2 |- atan(---- + 2\|x +--R +---+ - 2a |- - \|x + a x - b \|a +-+ +--R | b \| a +-+ |b +--R |- - log(------------------------) + 2\|x |- +--R \| a a x + b \|a +--R [-------------------------------------------,-------------------------] +--R a a +--R Type: Union(List(Expression(Integer)),...) +--E 1274 + +--S 1275 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R |- - \|a log(------------------------) + 2\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 2\|a |- atan(----) + 2\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1278 + +)clear all + +--S 1279 of 1369 +t0:=1/((a+b/x)*x^(3/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (a x + b)\|x +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1369 +r0:=2*atan(sqrt(a)*sqrt(x)/sqrt(b))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|a \|x +--R 2atan(--------) +--R +-+ +--R \|b +--R (2) --------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-----+ +---+ +-+ +--R 2a b\|x + (a x - b)\|- a b \|a b \|x +--R log(----------------------------) 2atan(----------) +--R a x + b b +--R (3) [---------------------------------,-----------------] +--R +-----+ +---+ +--R \|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1281 + +--S 1282 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 2\|a \|b atan(----------) - 2\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 1369 +t0:=1/((a+b/x)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (a x + b x)\|x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1369 +r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(3/2)+(-2)/(b*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R - 2\|a \|x atan(--------) - 2\|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R +-+ +-+ +--R b\|b \|x +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |a +-+ a\|x +--R | a +-+ - 2 |- \|x atan(----- - 2 +--R +---+ - 2b |- - \|x + a x - b \|b +-+ +--R | a +-+ \| b |a +--R |- - \|x log(------------------------) - 2 b |- +--R \| b a x + b \|b +--R [-------------------------------------------,--------------------------] +--R +-+ +-+ +--R b\|x b\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1288 + +--S 1289 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R |- - \|b log(------------------------) + 2\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 2 |- \|b atan(----- + 2\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1292 + +)clear all + +--S 1293 of 1369 +t0:=1/((a+b/x)*x^(7/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (a x + b x )\|x +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1369 +r0:=(-2/3)/(b*x^(3/2))+2*a^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(5/2)+_ + 2*a/(b^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R 6a x\|a \|x atan(--------) + (6a x - 2b)\|b +--R +-+ +--R \|b +--R (2) -------------------------------------------- +--R 2 +-+ +-+ +--R 3b x\|b \|x +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R | a +-+ \| b +--R 3a x |- - \|x log(----------------------) + 6a x - 2b +--R \| b a x + b +--R [-----------------------------------------------------, +--R 2 +-+ +--R 3b x\|x +--R +-+ +-+ +--R |a +-+ a\|x +--R 6a x |- \|x atan(-----) + 6a x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R -----------------------------------] +--R 2 +-+ +--R 3b x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1295 + +--S 1296 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R a |- - \|b log(----------------------) - 2a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 2a |- \|b atan(-----) - 2a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1369 +t0:=1/((a+b/x)*x^(9/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (a x + b x )\|x +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1369 +r0:=(-2/5)/(b*x^(5/2))+2/3*a/(b^2*x^(3/2))-2*a^(5/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(7/2)-2*a^2/(b^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+ +--R - 30a x \|a \|x atan(--------) + (- 30a x + 10a b x - 6b )\|b +--R +-+ +--R \|b +--R (2) --------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15b x \|b \|x +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 2 2 | a +-+ \| b 2 2 2 +--R 15a x |- - \|x log(------------------------) - 30a x + 10a b x - 6b +--R \| b a x + b +--R [----------------------------------------------------------------------, +--R 3 2 +-+ +--R 15b x \|x +--R +-+ +-+ +--R 2 2 |a +-+ a\|x 2 2 2 +--R - 30a x |- \|x atan(-----) - 30a x + 10a b x - 6b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R ----------------------------------------------------] +--R 3 2 +-+ +--R 15b x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 1302 + +--S 1303 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R a |- - \|b log(------------------------) + 2a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 2a |- \|b atan(-----) + 2a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1306 + +)clear all + +--S 1307 of 1369 +t0:=x^(5/2)/(a+b/x)^2 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1369 +r0:=3*b^2*x^(3/2)/a^4-9/5*b*x^(5/2)/a^3+9/7*x^(7/2)/a^2-x^(9/2)/_ + (a*(b+a*x))+9*b^(7/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(11/2)-_ + 9*b^3*sqrt(x)/a^5 +--R +--R +--R (2) +--R +-+ +-+ +--R 3 4 +-+ \|a \|x +--R (315a b x + 315b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|a \|x +--R / +--R 6 5 +-+ +--R (35a x + 35a b)\|a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 3 4 | b \| a +--R (315a b x + 315b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (20a x - 36a b x + 84a b x - 420a b x - 630b )\|x +--R / +--R 6 5 +--R 70a x + 70a b +--R , +--R +--R +-+ +-+ +--R 3 4 |b \|x +--R (315a b x + 315b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|x +--R / +--R 6 5 +--R 35a x + 35a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1309 + +--S 1310 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R 3 | b +-+ \| a 3 +-+ \|a \|x +--R 9b |- - \|a log(----------------------) - 18b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 3 +-+ |b \|x 3 +-+ \|a \|x +--R 9b \|a |- atan(----) - 9b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1313 + +)clear all + +--S 1314 of 1369 +t0:=x^(3/2)/(a+b/x)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1369 +r0:=-7/3*b*x^(3/2)/a^3+7/5*x^(5/2)/a^2-x^(7/2)/(a*(b+a*x))-_ + 7*b^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)+7*b^2*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 3 +-+ \|a \|x +--R (- 105a b x - 105b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (6a x - 14a b x + 70a b x + 105b )\|a \|x +--R / +--R 5 4 +-+ +--R (15a x + 15a b)\|a +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 3 | b \| a +--R (105a b x + 105b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (12a x - 28a b x + 140a b x + 210b )\|x +--R / +--R 5 4 +--R 30a x + 30a b +--R , +--R +--R +-+ +-+ +--R 2 3 |b \|x +--R (- 105a b x - 105b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (6a x - 14a b x + 70a b x + 105b )\|x +--R / +--R 5 4 +--R 15a x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1316 + +--S 1317 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R 7b |- - \|a log(------------------------) + 14b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 7b \|a |- atan(----) + 7b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ----------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1369 +t0:=x^(1/2)/(a+b/x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1369 +r0:=5/3*x^(3/2)/a^2-x^(5/2)/(a*(b+a*x))+5*b^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/a^(7/2)-5*b*sqrt(x)/a^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|a \|x 2 2 2 +-+ +-+ +--R (15a b x + 15b )\|b atan(--------) + (2a x - 10a b x - 15b )\|a \|x +--R +-+ +--R \|b +--R (2) --------------------------------------------------------------------- +--R 4 3 +-+ +--R (3a x + 3a b)\|a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 2 | b \| a +--R (15a b x + 15b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 2 2 2 +-+ +--R (4a x - 20a b x - 30b )\|x +--R / +--R 4 3 +--R 6a x + 6a b +--R , +--R +-+ +-+ +--R 2 |b \|x 2 2 2 +-+ +--R (15a b x + 15b ) |- atan(----) + (2a x - 10a b x - 15b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -------------------------------------------------------------] +--R 4 3 +--R 3a x + 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 5b |- - \|a log(----------------------) - 10b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 5b\|a |- atan(----) - 5b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 1369 +t0:=1/((a+b/x)^2*x^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1369 +r0:=-x^(3/2)/(a*(b+a*x))-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*_ + sqrt(b)/a^(5/2)+3*sqrt(x)/a^2 +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R (- 3a x - 3b)\|b atan(--------) + (2a x + 3b)\|a \|x +--R +-+ +--R \|b +--R (2) ----------------------------------------------------- +--R 3 2 +-+ +--R (a x + a b)\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R | b \| a +-+ +--R (3a x + 3b) |- - log(------------------------) + (4a x + 6b)\|x +--R \| a a x + b +--R [----------------------------------------------------------------, +--R 3 2 +--R 2a x + 2a b +--R +-+ +-+ +--R |b \|x +-+ +--R (- 3a x - 3b) |- atan(----) + (2a x + 3b)\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------] +--R 3 2 +--R a x + a b +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 3 |- - \|a log(------------------------ + 6\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 3\|a |- atan(----) + 3\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1369 +t0:=1/((a+b/x)^2*x^(3/2)) +--R +--R +--R x +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1369 +r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*sqrt(b))-sqrt(x)/(a*(b+a*x)) +--R +--R +--R +-+ +-+ +--R \|a \|x +-+ +-+ +-+ +--R (a x + b)atan(--------) - \|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a x + a b)\|a \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (a x - b)\|- a b +-----+ +-+ +--R (a x + b)log(----------------------------) - 2\|- a b \|x +--R a x + b +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a x + 2a b)\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (a x + b)atan(----------) - \|a b \|x +--R b +--R --------------------------------------] +--R 2 +---+ +--R (a x + a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 1369 +t0:=1/((a+b/x)^2*x^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1369 +r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(b+a*x)) +--R +--R +--R +-+ +-+ +--R \|a \|x +-+ +-+ +-+ +--R (a x + b)atan(--------) + \|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a b x + b )\|a \|b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (a x - b)\|- a b +-----+ +-+ +--R (a x + b)log(----------------------------) + 2\|- a b \|x +--R a x + b +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a b x + 2b )\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (a x + b)atan(----------) + \|a b \|x +--R b +--R --------------------------------------] +--R 2 +---+ +--R (a b x + b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 1369 +t0:=1/((a+b/x)^2*x^(7/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (a x + 2a b x + b x)\|x +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1369 +r0:=-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(5/2)+(-3)/_ + (b^2*sqrt(x))+1/(b*(b+a*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R (- 3a x - 3b)\|a \|x atan(--------) + (- 3a x - 2b)\|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-+ +--R (a b x + b )\|b \|x +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R | a +-+ \| b +--R (3a x + 3b) |- - \|x log(------------------------) - 6a x - 4b +--R \| b a x + b +--R [--------------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x + 2b )\|x +--R +-+ +-+ +--R |a +-+ a\|x +--R (- 3a x - 3b) |- \|x atan(-----) - 3a x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R --------------------------------------------] +--R 2 3 +-+ +--R (a b x + b )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1351 + +--S 1352 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 3 |- - \|b log(------------------------ + 6\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 3 |- \|b atan(----- + 3\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1355 + +)clear all + +--S 1356 of 1369 +t0:=1/((a+b/x)^2*x^(9/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (a x + 2a b x + b x )\|x +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1369 +r0:=(-5/3)/(b^2*x^(3/2))+1/(b*x^(3/2)*(b+a*x))+5*a^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(7/2)+5*a/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+ +--R (15a x + 15a b x)\|a \|x atan(--------) + (15a x + 10a b x - 2b )\|b +--R +-+ +--R \|b +--R ----------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x + 3b x)\|b \|x +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R 2 2 | a +-+ \| b 2 2 +--R (15a x + 15a b x) |- - \|x log(----------------------) + 30a x +--R \| b a x + b +--R + +--R 2 +--R 20a b x - 4b +--R / +--R 3 2 4 +-+ +--R (6a b x + 6b x)\|x +--R , +--R +-+ +-+ +--R 2 2 |a +-+ a\|x 2 2 2 +--R (15a x + 15a b x) |- \|x atan(-----) + 15a x + 10a b x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R --------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x + 3b x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1358 + +--S 1359 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 5a |- - \|b log(----------------------) - 10a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 5a |- \|b atan(-----) - 5a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1362 + +)clear all + +--S 1363 of 1369 +t0:=1/((a+b/x)^2*x^(11/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 5 4 2 3 +-+ +--R (a x + 2a b x + b x )\|x +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1369 +r0:=(-7/5)/(b^2*x^(5/2))+7/3*a/(b^3*x^(3/2))+1/(b*x^(5/2)*(b+a*x))-_ + 7*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(9/2)-7*a^2/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 +-+ +-+ \|a \|x +--R (- 105a x - 105a b x )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 105a x - 70a b x + 14a b x - 6b )\|b +--R / +--R 4 3 5 2 +-+ +-+ +--R (15a b x + 15b x )\|b \|x +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 3 3 2 2 | a +-+ \| b 3 3 +--R (105a x + 105a b x ) |- - \|x log(------------------------) - 210a x +--R \| b a x + b +--R + +--R 2 2 2 3 +--R - 140a b x + 28a b x - 12b +--R / +--R 4 3 5 2 +-+ +--R (30a b x + 30b x )\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 |a +-+ a\|x 3 3 2 2 +--R (- 105a x - 105a b x ) |- \|x atan(-----) - 105a x - 70a b x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 2 3 +--R 14a b x - 6b +--R / +--R 4 3 5 2 +-+ +--R (15a b x + 15b x )\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1365 + +--S 1366 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R 7a |- - \|b log(------------------------) + 14a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 7a |- \|b atan(-----) + 7a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ------------------------------------------------ +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1369 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4f.input.pdf b/src/axiom-website/CATS/rich4f.input.pdf new file mode 100644 index 0000000..2c09231 Binary files /dev/null and b/src/axiom-website/CATS/rich4f.input.pdf differ diff --git a/src/axiom-website/CATS/rich4g.input.pamphlet b/src/axiom-website/CATS/rich4g.input.pamphlet new file mode 100644 index 0000000..845cb44 --- /dev/null +++ b/src/axiom-website/CATS/rich4g.input.pamphlet @@ -0,0 +1,29082 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4g.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 188 matching answers. +\item 98 cases where Axiom differs from Rubi +\item 52 cases where Axiom supplied 2 results. +\item 24 cases that Axiom failed to integrate. +\item 2 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4g.output +)spool rich4g.output +)set message test on +)set message auto off +)clear all + + +--S 1 of 1379 +t0:=x^(3/2)/(a+b/x)^3 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1379 +r0:=-21/4*b*x^(3/2)/a^4+63/20*x^(5/2)/a^3-1/2*x^(9/2)/(a*(b+a*x)^2)-_ + 9/4*x^(7/2)/(a^2*(b+a*x))-63/4*b^(5/2)*atan(sqrt(a)*sqrt(x)/_ + sqrt(b))/a^(11/2)+63/4*b^2*sqrt(x)/a^5 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 4 +-+ \|a \|x +--R (- 315a b x - 630a b x - 315b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|a \|x +--R / +--R 7 2 6 5 2 +-+ +--R (20a x + 40a b x + 20a b )\|a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 2 2 3 4 | b \| a +--R (315a b x + 630a b x + 315b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (16a x - 48a b x + 336a b x + 1050a b x + 630b )\|x +--R / +--R 7 2 6 5 2 +--R 40a x + 80a b x + 40a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 4 |b \|x +--R (- 315a b x - 630a b x - 315b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|x +--R / +--R 7 2 6 5 2 +--R 20a x + 40a b x + 20a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R 63b |- - \|a log(------------------------) + 126b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 63b \|a |- atan(----) + 63b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1379 +t0:=x^(1/2)/(a+b/x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1379 +r0:=35/12*x^(3/2)/a^3-1/2*x^(7/2)/(a*(b+a*x)^2)-7/4*x^(5/2)/(a^2*(b+a*x))+_ + 35/4*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-35/4*b*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|a \|x +--R (105a b x + 210a b x + 105b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8a x - 56a b x - 175a b x - 105b )\|a \|x +--R / +--R 6 2 5 4 2 +-+ +--R (12a x + 24a b x + 12a b )\|a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 2 2 2 3 | b \| a +--R (105a b x + 210a b x + 105b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (16a x - 112a b x - 350a b x - 210b )\|x +--R / +--R 6 2 5 4 2 +--R 24a x + 48a b x + 24a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 |b \|x +--R (105a b x + 210a b x + 105b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (8a x - 56a b x - 175a b x - 105b )\|x +--R / +--R 6 2 5 4 2 +--R 12a x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 35b |- - \|a log(----------------------) - 70b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 35b\|a |- atan(----) - 35b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1379 +t0:=1/((a+b/x)^3*x^(1/2)) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1379 +r0:=-1/2*x^(5/2)/(a*(b+a*x)^2)-5/4*x^(3/2)/(a^2*(b+a*x))-_ + 15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(7/2)+15/4*sqrt(x)/a^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|a \|x +--R (- 15a x - 30a b x - 15b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 2 2 2 +-+ +-+ +--R (8a x + 25a b x + 15b )\|a \|x +--R / +--R 5 2 4 3 2 +-+ +--R (4a x + 8a b x + 4a b )\|a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 2 2 | b \| a +--R (15a x + 30a b x + 15b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 2 2 2 +-+ +--R (16a x + 50a b x + 30b )\|x +--R / +--R 5 2 4 3 2 +--R 8a x + 16a b x + 8a b +--R , +--R +-+ +-+ +--R 2 2 2 |b \|x 2 2 2 +-+ +--R (- 15a x - 30a b x - 15b ) |- atan(----) + (8a x + 25a b x + 15b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ------------------------------------------------------------------------] +--R 5 2 4 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 15 |- - \|a log(------------------------ + 30\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 15\|a |- atan(----) + 15\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1379 +t0:=1/((a+b/x)^3*x^(3/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1379 +r0:=-1/2*x^(3/2)/(a*(b+a*x)^2)+3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/_ + (a^(5/2)*sqrt(b))-3/4*sqrt(x)/(a^2*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (3a x + 6a b x + 3b )atan(--------) + (- 5a x - 3b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) ---------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4a x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (3a x + 6a b x + 3b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (- 10a x - 6b)\|- a b \|x +--R / +--R 4 2 3 2 2 +-----+ +--R (8a x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3a x + 6a b x + 3b )atan(----------) + (- 5a x - 3b)\|a b \|x +--R b +--R ----------------------------------------------------------------] +--R 4 2 3 2 2 +---+ +--R (4a x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 24 + +--S 25 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4a \|a \|b \|a b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 28 + +)clear all + +--S 29 of 1379 +t0:=1/((a+b/x)^3*x^(5/2)) +--R +--R +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1379 +r0:=1/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(a*(b+a*x)^2)+1/4*sqrt(x)/(a*b*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (a x + 2a b x + b )atan(--------) + (a x - b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) ---------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (a x + 2a b x + b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (2a x - 2b)\|- a b \|x +--R / +--R 3 2 2 2 3 +-----+ +--R (8a b x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (a x + 2a b x + b )atan(----------) + (a x - b)\|a b \|x +--R b +--R ----------------------------------------------------------] +--R 3 2 2 2 3 +---+ +--R (4a b x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 31 + +--S 32 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R 4a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1379 +t0:=1/((a+b/x)^3*x^(7/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1379 +r0:=3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(5/2)*sqrt(a))+_ + 1/2*sqrt(x)/(b*(b+a*x)^2)+3/4*sqrt(x)/(b^2*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (3a x + 6a b x + 3b )atan(--------) + (3a x + 5b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x + 8a b x + 4b )\|a \|b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (3a x + 6a b x + 3b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (6a x + 10b)\|- a b \|x +--R / +--R 2 2 2 3 4 +-----+ +--R (8a b x + 16a b x + 8b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3a x + 6a b x + 3b )atan(----------) + (3a x + 5b)\|a b \|x +--R b +--R --------------------------------------------------------------] +--R 2 2 2 3 4 +---+ +--R (4a b x + 8a b x + 4b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 38 + +--S 39 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4b \|a \|b \|a b +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 1379 +t0:=1/((a+b/x)^3*x^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b x)\|x +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1379 +r0:=-15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(7/2)+_ + (-15/4)/(b^3*sqrt(x))+1/2/(b*(b+a*x)^2*sqrt(x))+5/4/(b^2*(b+a*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|a \|x +--R (- 15a x - 30a b x - 15b )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 2 2 2 +-+ +--R (- 15a x - 25a b x - 8b )\|b +--R / +--R 2 3 2 4 5 +-+ +-+ +--R (4a b x + 8a b x + 4b )\|b \|x +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 2 2 2 | a +-+ \| b +--R (15a x + 30a b x + 15b ) |- - \|x log(------------------------) +--R \| b a x + b +--R + +--R 2 2 2 +--R - 30a x - 50a b x - 16b +--R / +--R 2 3 2 4 5 +-+ +--R (8a b x + 16a b x + 8b )\|x +--R , +--R +-+ +-+ +--R 2 2 2 |a +-+ a\|x 2 2 2 +--R (- 15a x - 30a b x - 15b ) |- \|x atan(-----) - 15a x - 25a b x - 8b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R -----------------------------------------------------------------------] +--R 2 3 2 4 5 +-+ +--R (4a b x + 8a b x + 4b )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 45 + +--S 46 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 15 |- - \|b log(------------------------ + 30\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 15 |- \|b atan(----- + 15\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ---------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 48 + +--S 49 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 49 + +)clear all + +--S 50 of 1379 +t0:=1/((a+b/x)^3*x^(11/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (a x + 3a b x + 3a b x + b x )\|x +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1379 +r0:=(-35/12)/(b^3*x^(3/2))+1/2/(b*x^(3/2)*(b+a*x)^2)+_ + 7/4/(b^2*x^(3/2)*(b+a*x))+35/4*a^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(9/2)+35/4*a/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|a \|x +--R (105a x + 210a b x + 105a b x)\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (105a x + 175a b x + 56a b x - 8b )\|b +--R / +--R 2 4 3 5 2 6 +-+ +-+ +--R (12a b x + 24a b x + 12b x)\|b \|x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R 3 3 2 2 2 | a +-+ \| b +--R (105a x + 210a b x + 105a b x) |- - \|x log(----------------------) +--R \| b a x + b +--R + +--R 3 3 2 2 2 3 +--R 210a x + 350a b x + 112a b x - 16b +--R / +--R 2 4 3 5 2 6 +-+ +--R (24a b x + 48a b x + 24b x)\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 2 |a +-+ a\|x 3 3 +--R (105a x + 210a b x + 105a b x) |- \|x atan(-----) + 105a x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 2 2 2 3 +--R 175a b x + 56a b x - 8b +--R / +--R 2 4 3 5 2 6 +-+ +--R (12a b x + 24a b x + 12b x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 52 + +--S 53 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 35a |- - \|b log(----------------------) - 70a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 35a |- \|b atan(-----) - 35a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ---------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 56 + +)clear all + +--S 57 of 1379 +t0:=1/((a+b/x)^3*x^(13/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 6 2 5 2 4 3 3 +-+ +--R (a x + 3a b x + 3a b x + b x )\|x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1379 +r0:=(-63/20)/(b^3*x^(5/2))+21/4*a/(b^4*x^(3/2))+_ + 1/2/(b*x^(5/2)*(b+a*x)^2)+9/4/(b^2*x^(5/2)*(b+a*x))-_ + 63/4*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(11/2)-_ + 63/4*a^2/(b^5*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 4 4 3 3 2 2 2 +-+ +-+ \|a \|x +--R (- 315a x - 630a b x - 315a b x )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (- 315a x - 525a b x - 168a b x + 24a b x - 8b )\|b +--R / +--R 2 5 4 6 3 7 2 +-+ +-+ +--R (20a b x + 40a b x + 20b x )\|b \|x +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R 4 4 3 3 2 2 2 | a +-+ +--R (315a x + 630a b x + 315a b x ) |- - \|x +--R \| b +--R * +--R +---+ +--R | a +-+ +--R - 2b |- - \|x + a x - b +--R \| b +--R log(------------------------) +--R a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 630a x - 1050a b x - 336a b x + 48a b x - 16b +--R / +--R 2 5 4 6 3 7 2 +-+ +--R (40a b x + 80a b x + 40b x )\|x +--R , +--R +--R +-+ +-+ +--R 4 4 3 3 2 2 2 |a +-+ a\|x 4 4 +--R (- 315a x - 630a b x - 315a b x ) |- \|x atan(-----) - 315a x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 3 3 2 2 2 3 4 +--R - 525a b x - 168a b x + 24a b x - 8b +--R / +--R 2 5 4 6 3 7 2 +-+ +--R (20a b x + 40a b x + 20b x )\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R 63a |- - \|b log(------------------------) + 126a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------------- +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 63a |- \|b atan(-----) + 63a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------------- +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1379 +t0:=(a+b/x)^(1/2)*x^(7/2) +--R +--R +--R +-------+ +--R 3 |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1379 +r0:=-32/315*b^3*(a+b/x)^(3/2)*x^(3/2)/a^4+16/105*b^2*(a+b/x)^(3/2)*_ + x^(5/2)/a^3-4/21*b*(a+b/x)^(3/2)*x^(7/2)/a^2+2/9*(a+b/x)^(3/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------------------- +--R 4 +--R 315a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------------------- +--R 4 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1379 +t0:=(a+b/x)^(1/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1379 +r0:=16/105*b^2*(a+b/x)^(3/2)*x^(3/2)/a^3-8/35*b*(a+b/x)^(3/2)*x^(5/2)/_ + a^2+2/7*(a+b/x)^(3/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------ +--R 3 +--R 105a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------ +--R 3 +--R 105a +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1379 +t0:=(a+b/x)^(1/2)*x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1379 +r0:=-4/15*b*(a+b/x)^(3/2)*x^(3/2)/a^2+2/5*(a+b/x)^(3/2)*x^(5/2)/a +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ------------------------------------ +--R 2 +--R 15a +--R Type: Expression(Integer) +--E 75 + +--S 76 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ------------------------------------ +--R 2 +--R 15a +--R Type: Union(Expression(Integer),...) +--E 76 + +--S 77 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1379 +t0:=(a+b/x)^(1/2)*x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1379 +r0:=2/3*(a+b/x)^(3/2)*x^(3/2)/a +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x + 2b) |------- \|x +--R \| x +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x + 2b) |------- \|x +--R \| x +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 81 + +--S 82 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 83 + +)clear all + +--S 84 of 1379 +t0:=(a+b/x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)+2*sqrt(a+b/x)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R (2) - 2\|b atanh(--------------) + 2 |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1379 +--a0:=integrate(t0,x) +--E 86 + +--S 87 of 1379 +--m0:=a0-r0 +--E 87 + +--S 88 of 1379 +--d0:=D(m0,x) +--E 88 + +)clear all + +--S 89 of 1379 +t0:=(a+b/x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1379 +r0:=-a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-sqrt(a+b/x)/sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R - a\|x atanh(--------------) - |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------- +--R +-+ +-+ +--R \|b \|x +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1379 +--a0:=integrate(t0,x) +--E 91 + +--S 92 of 1379 +--m0:=a0-r0 +--E 92 + +--S 93 of 1379 +--d0:=D(m0,x) +--E 93 + +)clear all + +--S 94 of 1379 +t0:=(a+b/x)^(1/2)/x^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1379 +r0:=1/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_ + 1/2*sqrt(a+b/x)/x^(3/2)-1/4*a*sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R a x\|x atanh(--------------) + (- a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------------------- +--R +-+ +-+ +--R 4b x\|b \|x +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1379 +--a0:=integrate(t0,x) +--E 96 + +--S 97 of 1379 +--m0:=a0-r0 +--E 97 + +--S 98 of 1379 +--d0:=D(m0,x) +--E 98 + +)clear all + +--S 99 of 1379 +t0:=(a+b/x)^(1/2)/x^(7/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1379 +r0:=-1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_ + 1/3*sqrt(a+b/x)/x^(5/2)-1/12*a*sqrt(a+b/x)/(b*x^(3/2))+_ + 1/8*a^2*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 3a x \|x atanh(--------------) + (3a x - 2a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ----------------------------------------------------------------------- +--R 2 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1379 +--a0:=integrate(t0,x) +--E 101 + +--S 102 of 1379 +--m0:=a0-r0 +--E 102 + +--S 103 of 1379 +--d0:=D(m0,x) +--E 103 + +)clear all + +--S 104 of 1379 +t0:=(a+b/x)^(3/2)*x^(9/2) +--R +--R +--R +-------+ +--R 4 3 |a x + b +-+ +--R (1) (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1379 +r0:=-32/1155*b^3*(a+b/x)^(5/2)*x^(5/2)/a^4+16/231*b^2*(a+b/x)^(5/2)*_ + x^(7/2)/a^3-4/33*b*(a+b/x)^(5/2)*x^(9/2)/a^2+_ + 2/11*(a+b/x)^(5/2)*x^(11/2)/a +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 4 +--R 1155a +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 4 +--R 1155a +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1379 +t0:=(a+b/x)^(3/2)*x^(7/2) +--R +--R +--R +-------+ +--R 3 2 |a x + b +-+ +--R (1) (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1379 +r0:=16/315*b^2*(a+b/x)^(5/2)*x^(5/2)/a^3-8/63*b*(a+b/x)^(5/2)*_ + x^(7/2)/a^2+2/9*(a+b/x)^(5/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------------------ +--R 3 +--R 315a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------------------ +--R 3 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 111 + +--S 112 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 113 + +)clear all + +--S 114 of 1379 +t0:=(a+b/x)^(3/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 |a x + b +-+ +--R (1) (a x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1379 +r0:=-4/35*b*(a+b/x)^(5/2)*x^(5/2)/a^2+2/7*(a+b/x)^(5/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------ +--R 2 +--R 35a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------ +--R 2 +--R 35a +--R Type: Union(Expression(Integer),...) +--E 116 + +--S 117 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1379 +t0:=(a+b/x)^(3/2)*x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1379 +r0:=2/5*(a+b/x)^(5/2)*x^(5/2)/a +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (2a x + 4a b x + 2b ) |------- \|x +--R \| x +--R (2) ------------------------------------ +--R 5a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (2a x + 4a b x + 2b ) |------- \|x +--R \| x +--R (3) ------------------------------------ +--R 5a +--R Type: Union(Expression(Integer),...) +--E 121 + +--S 122 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1379 +t0:=(a+b/x)^(3/2)*x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1379 +r0:=2/3*(a+b/x)^(3/2)*x^(3/2)-2*b^(3/2)*atanh(sqrt(b)/_ + (sqrt(a+b/x)*sqrt(x)))+2*b*sqrt(a+b/x)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R - 6b\|b atanh(--------------) + (2a x + 8b) |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1379 +--a0:=integrate(t0,x) +--E 126 + +--S 127 of 1379 +--m0:=a0-r0 +--E 127 + +--S 128 of 1379 +--d0:=D(m0,x) +--E 128 + +)clear all + +--S 129 of 1379 +t0:=(a+b/x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1379 +r0:=-3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_ + 3*b*sqrt(a+b/x)/sqrt(x)+2*(a+b/x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ +-+ \|b |a x + b +--R - 3a\|b \|x atanh(--------------) + (2a x - b) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) -------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1379 +--a0:=integrate(t0,x) +--E 131 + +--S 132 of 1379 +--m0:=a0-r0 +--E 132 + +--S 133 of 1379 +--d0:=D(m0,x) +--E 133 + +)clear all + +--S 134 of 1379 +t0:=(a+b/x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1379 +r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_ + 1/2*(a+b/x)^(3/2)/sqrt(x)-3/4*a*sqrt(a+b/x)/sqrt(x) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R - 3a x\|x atanh(--------------) + (- 5a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------------------------- +--R +-+ +-+ +--R 4x\|b \|x +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1379 +--a0:=integrate(t0,x) +--E 136 + +--S 137 of 1379 +--m0:=a0-r0 +--E 137 + +--S 138 of 1379 +--d0:=D(m0,x) +--E 138 + +)clear all + +--S 139 of 1379 +t0:=(a+b/x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1379 +r0:=-1/3*(a+b/x)^(3/2)/x^(3/2)+1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(3/2)-1/4*a*sqrt(a+b/x)/x^(3/2)-1/8*a^2*_ + sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R 3a x \|x atanh(--------------) + (- 3a x - 14a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1379 +--a0:=integrate(t0,x) +--E 141 + +--S 142 of 1379 +--m0:=a0-r0 +--E 142 + +--S 143 of 1379 +--d0:=D(m0,x) +--E 143 + +)clear all + +--S 144 of 1379 +t0:=(a+b/x)^(5/2)*x^(11/2) +--R +--R +--R +-------+ +--R 2 5 4 2 3 |a x + b +-+ +--R (1) (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1379 +r0:=-32/3003*b^3*(a+b/x)^(7/2)*x^(7/2)/a^4+16/429*b^2*(a+b/x)^(7/2)*_ + x^(9/2)/a^3-12/143*b*(a+b/x)^(7/2)*x^(11/2)/a^2+_ + 2/13*(a+b/x)^(7/2)*x^(13/2)/a +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b ) +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R / +--R 4 +--R 3003a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b ) +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R / +--R 4 +--R 3003a +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 148 + +)clear all + +--S 149 of 1379 +t0:=(a+b/x)^(5/2)*x^(9/2) +--R +--R +--R +-------+ +--R 2 4 3 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1379 +r0:=16/693*b^2*(a+b/x)^(7/2)*x^(7/2)/a^3-8/99*b*(a+b/x)^(7/2)*_ + x^(9/2)/a^2+2/11*(a+b/x)^(7/2)*x^(11/2)/a +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R 3 +--R 693a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R 3 +--R 693a +--R Type: Union(Expression(Integer),...) +--E 151 + +--S 152 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1379 +t0:=(a+b/x)^(5/2)*x^(7/2) +--R +--R +--R +-------+ +--R 2 3 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1379 +r0:=-4/63*b*(a+b/x)^(7/2)*x^(7/2)/a^2+2/9*(a+b/x)^(7/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ----------------------------------------------------------- +--R 2 +--R 63a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ----------------------------------------------------------- +--R 2 +--R 63a +--R Type: Union(Expression(Integer),...) +--E 156 + +--S 157 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 158 + +)clear all + +--S 159 of 1379 +t0:=(a+b/x)^(5/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1379 +r0:=2/7*(a+b/x)^(7/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x +--R \| x +--R (2) ---------------------------------------------- +--R 7a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x +--R \| x +--R (3) ---------------------------------------------- +--R 7a +--R Type: Union(Expression(Integer),...) +--E 161 + +--S 162 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 163 + +)clear all + +--S 164 of 1379 +t0:=(a+b/x)^(5/2)*x^(3/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R (1) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1379 +r0:=2/3*b*(a+b/x)^(3/2)*x^(3/2)+2/5*(a+b/x)^(5/2)*x^(5/2)-2*b^(5/2)*_ + atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))+2*b^2*sqrt(a+b/x)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 30b \|b atanh(--------------) + (6a x + 22a b x + 46b ) |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R 15 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1379 +--a0:=integrate(t0,x) +--E 166 + +--S 167 of 1379 +--m0:=a0-r0 +--E 167 + +--S 168 of 1379 +--d0:=D(m0,x) +--E 168 + +)clear all + +--S 169 of 1379 +t0:=(a+b/x)^(5/2)*x^(1/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R (1) ---------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1379 +r0:=2/3*(a+b/x)^(5/2)*x^(3/2)-5*a*b^(3/2)*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))-5*b^2*sqrt(a+b/x)/sqrt(x)+10/3*b*(a+b/x)^(3/2)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ \|b 2 2 2 |a x + b +--R - 15a b\|b \|x atanh(--------------) + (2a x + 14a b x - 3b ) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1379 +--a0:=integrate(t0,x) +--E 171 + +--S 172 of 1379 +--m0:=a0-r0 +--E 172 + +--S 173 of 1379 +--d0:=D(m0,x) +--E 173 + +)clear all + +--S 174 of 1379 +t0:=(a+b/x)^(5/2)/x^(1/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1379 +r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_ + 5/2*b*(a+b/x)^(3/2)/sqrt(x)-15/4*a*b*sqrt(a+b/x)/sqrt(x)+_ + 2*(a+b/x)^(5/2)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ +-+ \|b 2 2 2 |a x + b +--R - 15a x\|b \|x atanh(--------------) + (8a x - 9a b x - 2b ) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ----------------------------------------------------------------------- +--R +-+ +--R 4x\|x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1379 +--a0:=integrate(t0,x) +--E 176 + +--S 177 of 1379 +--m0:=a0-r0 +--E 177 + +--S 178 of 1379 +--d0:=D(m0,x) +--E 178 + +)clear all + +--S 179 of 1379 +t0:=(a+b/x)^(5/2)/x^(3/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1379 +r0:=-5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_ + 5/12*a*(a+b/x)^(3/2)/sqrt(x)-1/3*(a+b/x)^(5/2)/sqrt(x)-_ + 5/8*a^2*sqrt(a+b/x)/sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 15a x \|x atanh(--------------) + (- 33a x - 26a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ---------------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 24x \|b \|x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1379 +--a0:=integrate(t0,x) +--E 181 + +--S 182 of 1379 +--m0:=a0-r0 +--E 182 + +--S 183 of 1379 +--d0:=D(m0,x) +--E 183 + +)clear all + +--S 184 of 1379 +t0:=(a+b/x)^(5/2)/x^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1379 +r0:=-5/24*a*(a+b/x)^(3/2)/x^(3/2)-1/4*(a+b/x)^(5/2)/x^(3/2)+_ + 5/64*a^4*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_ + 5/32*a^2*sqrt(a+b/x)/x^(3/2)-5/64*a^3*sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R (2) +--R +-+ +--R 4 3 +-+ \|b +--R 15a x \|x atanh(--------------) +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (- 15a x - 118a b x - 136a b x - 48b ) |------- \|b +--R \| x +--R / +--R 3 +-+ +-+ +--R 192b x \|b \|x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1379 +--a0:=integrate(t0,x) +--E 186 + +--S 187 of 1379 +--m0:=a0-r0 +--E 187 + +--S 188 of 1379 +--d0:=D(m0,x) +--E 188 + +)clear all + +--S 189 of 1379 +t0:=x^(7/2)/(a+b/x)^(1/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1379 +r0:=-128/315*b^3*x^(3/2)*sqrt(a+b/x)/a^4+32/105*b^2*x^(5/2)*_ + sqrt(a+b/x)/a^3-16/63*b*x^(7/2)*sqrt(a+b/x)/a^2+2/9*x^(9/2)*_ + sqrt(a+b/x)/a+256/315*b^4*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x +--R \| x +--R (2) --------------------------------------------------------------- +--R 5 +--R 315a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x +--R \| x +--R (3) --------------------------------------------------------------- +--R 5 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 191 + +--S 192 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 193 + +)clear all + +--S 194 of 1379 +t0:=x^(5/2)/(a+b/x)^(1/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1379 +r0:=16/35*b^2*x^(3/2)*sqrt(a+b/x)/a^3-12/35*b*x^(5/2)*sqrt(a+b/x)/a^2+_ + 2/7*x^(7/2)*sqrt(a+b/x)/a-32/35*b^3*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (2) -------------------------------------------------- +--R 4 +--R 35a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (3) -------------------------------------------------- +--R 4 +--R 35a +--R Type: Union(Expression(Integer),...) +--E 196 + +--S 197 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 1379 +t0:=x^(3/2)/(a+b/x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1379 +r0:=-8/15*b*x^(3/2)*sqrt(a+b/x)/a^2+2/5*x^(5/2)*sqrt(a+b/x)/a+_ + 16/15*b^2*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------- +--R 3 +--R 15a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------- +--R 3 +--R 15a +--R Type: Union(Expression(Integer),...) +--E 201 + +--S 202 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 203 + +)clear all + +--S 204 of 1379 +t0:=x^(1/2)/(a+b/x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1379 +r0:=2/3*x^(3/2)*sqrt(a+b/x)/a-4/3*b*sqrt(a+b/x)*sqrt(x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x - 4b) |------- \|x +--R \| x +--R (2) ------------------------- +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x - 4b) |------- \|x +--R \| x +--R (3) ------------------------- +--R 2 +--R 3a +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 208 + +)clear all + +--S 209 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(1/2)) +--R +--R +--R 1 +--R (1) -------------- +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1379 +r0:=2*sqrt(a+b/x)*sqrt(x)/a +--R +--R +--R +-------+ +--R |a x + b +-+ +--R 2 |------- \|x +--R \| x +--R (2) --------------- +--R a +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R 2 |------- \|x +--R \| x +--R (3) --------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(3/2)) +--R +--R +--R 1 +--R (1) --------------- +--R +-------+ +--R |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R 2atanh(--------------) +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) - ---------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1379 +--a0:=integrate(t0,x) +--E 216 + +--S 217 of 1379 +--m0:=a0-r0 +--E 217 + +--S 218 of 1379 +--d0:=D(m0,x) +--E 218 + +)clear all + +--S 219 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 2 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1379 +r0:=a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R a\|x atanh(--------------) - |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------- +--R +-+ +-+ +--R b\|b \|x +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1379 +--a0:=integrate(t0,x) +--E 221 + +--S 222 of 1379 +--m0:=a0-r0 +--E 222 + +--S 223 of 1379 +--d0:=D(m0,x) +--E 223 + +)clear all + +--S 224 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 3 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1379 +r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_ + 1/2*sqrt(a+b/x)/(b*x^(3/2))+3/4*a*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R - 3a x\|x atanh(--------------) + (3a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ----------------------------------------------------------- +--R 2 +-+ +-+ +--R 4b x\|b \|x +--R Type: Expression(Integer) +--E 225 + +--S 226 of 1379 +--a0:=integrate(t0,x) +--E 226 + +--S 227 of 1379 +--m0:=a0-r0 +--E 227 + +--S 228 of 1379 +--d0:=D(m0,x) +--E 228 + +)clear all + +--S 229 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 4 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1379 +r0:=5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)-_ + 1/3*sqrt(a+b/x)/(b*x^(5/2))+5/12*a*sqrt(a+b/x)/(b^2*x^(3/2))-_ + 5/8*a^2*sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R 15a x \|x atanh(--------------) + (- 15a x + 10a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1379 +--a0:=integrate(t0,x) +--E 231 + +--S 232 of 1379 +--m0:=a0-r0 +--E 232 + +--S 233 of 1379 +--d0:=D(m0,x) +--E 233 + +)clear all + +--S 234 of 1379 +t0:=x^(5/2)/(a+b/x)^(3/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1379 +r0:=-2*x^(7/2)/(a*sqrt(a+b/x))+128/35*b^2*x^(3/2)*sqrt(a+b/x)/a^4-_ + 96/35*b*x^(5/2)*sqrt(a+b/x)/a^3+16/7*x^(7/2)*sqrt(a+b/x)/a^2-_ + 256/35*b^3*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (10a x - 16a b x + 32a b x - 128a b x - 256b )\|x +--R (2) ----------------------------------------------------- +--R +-------+ +--R 5 |a x + b +--R 35a x |------- +--R \| x +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 3 2 4 3 2 3 3 2 2 +--R (30a b + 30a )x + (- 48a b - 48a b)x + (96a b + 96a b )x +--R + +--R 4 2 3 5 4 +--R (- 384a b - 384a b )x - 768b - 768a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 5 2 4 3 2 3 4 3 2 +--R 1152a b + (1728a + 128a)b + (432a + 64a )b + (- 72a - 16a )b +--R + +--R 5 4 6 5 +--R (27a + 8a )b - 45a - 5a +--R * +--R x +--R + +--R 6 5 2 4 3 2 3 +--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b +--R + +--R 4 3 2 5 4 +--R (27a + 8a )b + (- 45a - 5a )b +--R / +--R 6 7 5 2 6 +--R (105a b + 105a )x + 105a b + 105a b +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 2 3 3 2 2 +--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b +--R + +--R 4 3 5 4 +--R (27a + 8a )b - 45a - 5a +--R / +--R 5 6 +--R 105a b + 105a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 238 + +)clear all + +--S 239 of 1379 +t0:=x^(3/2)/(a+b/x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1379 +r0:=-2*x^(5/2)/(a*sqrt(a+b/x))-16/5*b*x^(3/2)*sqrt(a+b/x)/a^3+_ + 12/5*x^(5/2)*sqrt(a+b/x)/a^2+32/5*b^2*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (2a x - 4a b x + 16a b x + 32b )\|x +--R (2) -------------------------------------- +--R +-------+ +--R 4 |a x + b +--R 5a x |------- +--R \| x +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 3 2 2 4 +--R (8a b + 8a )x + (- 16a b - 16a b)x + (64a b + 64a b )x + 128b +--R + +--R 3 +--R 128a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 4 2 3 3 2 2 4 3 5 +--R 256a b + (384a + 16a)b + (96a + 8a )b + (- 16a - 2a )b + 16a +--R + +--R 4 +--R a +--R * +--R x +--R + +--R 5 4 2 3 3 2 2 4 3 +--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + (16a + a )b +--R / +--R 5 6 4 2 5 +--R (20a b + 20a )x + 20a b + 20a b +--R Type: Union(Expression(Integer),...) +--E 241 + +--S 242 of 1379 +m0:=a0-r0 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + 16a + a +--R (4) ------------------------------------------------------------------- +--R 4 5 +--R 20a b + 20a +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1379 +t0:=x^(1/2)/(a+b/x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1379 +r0:=-2*x^(3/2)/(a*sqrt(a+b/x))+8/3*x^(3/2)*sqrt(a+b/x)/a^2-_ + 16/3*b*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R 2 2 2 +-+ +--R (2a x - 8a b x - 16b )\|x +--R (2) --------------------------- +--R +-------+ +--R 3 |a x + b +--R 3a x |------- +--R \| x +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 3 2 2 2 3 2 |a x + b +-+ +--R ((6a b + 6a )x + (- 24a b - 24a b)x - 48b - 48a b ) |------- \|x +--R \| x +--R + +--R 3 2 2 3 2 4 3 4 +--R (72a b + (108a + 8a)b + (27a + 4a )b - 9a - a )x + 72b +--R + +--R 3 2 2 3 2 +--R (108a + 8)b + (27a + 4a)b + (- 9a - a )b +--R / +--R 4 5 3 2 4 +--R (9a b + 9a )x + 9a b + 9a b +--R Type: Union(Expression(Integer),...) +--E 246 + +--S 247 of 1379 +m0:=a0-r0 +--R +--R +--R 3 2 2 3 2 +--R 72b + (108a + 8)b + (27a + 4a)b - 9a - a +--R (4) --------------------------------------------- +--R 3 4 +--R 9a b + 9a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 248 + +)clear all + +--S 249 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(1/2)) +--R +--R +--R x +--R (1) ----------------------- +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1379 +r0:=-2*sqrt(x)/(a*sqrt(a+b/x))+4*sqrt(a+b/x)*sqrt(x)/a^2 +--R +--R +--R +-+ +--R (2a x + 4b)\|x +--R (2) --------------- +--R +-------+ +--R 2 |a x + b +--R a x |------- +--R \| x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 |a x + b +-+ +--R ((10a b + 10a )x + 20b + 20a b) |------- \|x +--R \| x +--R + +--R 2 2 3 2 3 2 2 +--R (50a b + (75a + 2a)b + 25a + a )x + 50b + (75a + 2)b + (25a + a)b +--R / +--R 3 4 2 2 3 +--R (5a b + 5a )x + 5a b + 5a b +--R Type: Union(Expression(Integer),...) +--E 251 + +--S 252 of 1379 +m0:=a0-r0 +--R +--R +--R 2 2 +--R 50b + (75a + 2)b + 25a + a +--R (4) ---------------------------- +--R 2 3 +--R 5a b + 5a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 253 + +)clear all + +--S 254 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1379 +r0:=(-2)/(a*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R 2 +--R (2) - --------------- +--R +-------+ +--R |a x + b +-+ +--R a |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ 2 2 +--R (- 4b - 4a) |------- \|x + (- 4a b - 4a - a)x - 4b + (- 4a - 1)b +--R \| x +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 +--R (2a b + 2a )x + 2a b + 2a b +--R Type: Union(Expression(Integer),...) +--E 256 + +--S 257 of 1379 +m0:=a0-r0 +--R +--R +--R - 4b - 4a - 1 +--R (4) ------------- +--R 2 +--R 2a b + 2a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +-------+ +--R 2 |a x + b +-+ +--R (a x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)+2/(b*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R - 2 |------- \|x atanh(-------------- + 2\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ---------------------------------------------- +--R +-------+ +--R |a x + b +-+ +-+ +--R b |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1379 +--a0:=integrate(t0,x) +--E 261 + +--S 262 of 1379 +--m0:=a0-r0 +--E 262 + +--S 263 of 1379 +--d0:=D(m0,x) +--E 263 + +)clear all + +--S 264 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1379 +r0:=3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)+2/(b*x^(3/2)*_ + sqrt(a+b/x))-3*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R 3a x |------- \|x atanh(--------------) + (- 3a x - b)\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 2 |a x + b +-+ +-+ +--R b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1379 +--a0:=integrate(t0,x) +--E 266 + +--S 267 of 1379 +--m0:=a0-r0 +--E 267 + +--S 268 of 1379 +--d0:=D(m0,x) +--E 268 + +)clear all + +--S 269 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 4 3 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1379 +r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)+2/(b*x^(5/2)*_ + sqrt(a+b/x))-5/2*sqrt(a+b/x)/(b^2*x^(3/2))+15/4*a*_ + sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 2 2 |a x + b +-+ \|b 2 2 2 +-+ +--R - 15a x |------- \|x atanh(--------------) + (15a x + 5a b x - 2b )\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +-+ +--R 4b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1379 +--a0:=integrate(t0,x) +--E 271 + +--S 272 of 1379 +--m0:=a0-r0 +--E 272 + +--S 273 of 1379 +--d0:=D(m0,x) +--E 273 + +)clear all + +--S 274 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(11/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 5 4 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1379 +r0:=35/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(9/2)+_ + 2/(b*x^(7/2)*sqrt(a+b/x))-7/3*sqrt(a+b/x)/(b^2*x^(5/2))+_ + 35/12*a*sqrt(a+b/x)/(b^3*x^(3/2))-35/8*a^2*sqrt(a+b/x)/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 3 3 |a x + b +-+ \|b +--R 105a x |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 105a x - 35a b x + 14a b x - 8b )\|b +--R / +--R +-------+ +--R 4 3 |a x + b +-+ +-+ +--R 24b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1379 +--a0:=integrate(t0,x) +--E 276 + +--S 277 of 1379 +--m0:=a0-r0 +--E 277 + +--S 278 of 1379 +--d0:=D(m0,x) +--E 278 + +)clear all + +--S 279 of 1379 +t0:=x^(5/2)/(a+b/x)^(5/2) +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1379 +r0:=-2/3*x^(7/2)/(a*(a+b/x)^(3/2))-20/3*x^(7/2)/(a^2*sqrt(a+b/x))+_ + 256/21*b^2*x^(3/2)*sqrt(a+b/x)/a^5-64/7*b*x^(5/2)*sqrt(a+b/x)/_ + a^4+160/21*x^(7/2)*sqrt(a+b/x)/a^3-512/21*b^3*sqrt(a+b/x)*sqrt(x)/a^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +-+ +--R (6a x - 12a b x + 32a b x - 192a b x - 768a b x - 512b )\|x +--R (2) ---------------------------------------------------------------- +--R +-------+ +--R 7 2 6 |a x + b +--R (21a x + 21a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 7 5 4 3 5 2 6 4 +--R (12a b + 24a b + 12a )x + (- 24a b - 48a b - 24a b)x +--R + +--R 3 4 4 3 5 2 3 2 5 3 4 4 3 2 +--R (64a b + 128a b + 64a b )x + (- 384a b - 768a b - 384a b )x +--R + +--R 6 2 5 3 4 7 6 2 5 +--R (- 1536a b - 3072a b - 1536a b )x - 1024b - 2048a b - 1024a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 6 3 2 5 4 3 4 5 4 3 +--R 1024a b + (2560a + 256a )b + (1920a + 384a )b + (320a + 96a )b +--R + +--R 6 5 2 7 6 8 7 +--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a +--R * +--R 2 +--R x +--R + +--R 7 2 6 3 2 5 4 3 4 +--R 2048a b + (5120a + 512a)b + (3840a + 768a )b + (640a + 192a )b +--R + +--R 5 4 3 6 5 2 7 6 +--R (- 80a - 32a )b + (24a + 12a )b + (- 24a - 6a )b +--R * +--R x +--R + +--R 8 7 2 6 3 2 5 +--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b +--R + +--R 4 3 4 5 4 3 6 5 2 +--R (- 40a - 16a )b + (12a + 6a )b + (- 12a - 3a )b +--R / +--R 8 2 9 10 2 7 3 8 2 9 6 4 +--R (42a b + 84a b + 42a )x + (84a b + 168a b + 84a b)x + 42a b +--R + +--R 7 3 8 2 +--R 84a b + 42a b +--R Type: Union(Expression(Integer),...) +--E 281 + +--S 282 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 2 4 3 2 3 +--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b +--R + +--R 4 3 2 5 4 6 5 +--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a +--R / +--R 6 2 7 8 +--R 42a b + 84a b + 42a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 283 + +)clear all + +--S 284 of 1379 +t0:=x^(3/2)/(a+b/x)^(5/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1379 +r0:=-2/3*x^(5/2)/(a*(a+b/x)^(3/2))-16/3*x^(5/2)/(a^2*sqrt(a+b/x))-_ + 128/15*b*x^(3/2)*sqrt(a+b/x)/a^4+32/5*x^(5/2)*sqrt(a+b/x)/_ + a^3+256/15*b^2*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (6a x - 16a b x + 96a b x + 384a b x + 256b )\|x +--R (2) ---------------------------------------------------- +--R +-------+ +--R 6 2 5 |a x + b +--R (15a x + 15a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 6 4 3 3 4 2 5 3 +--R (24a b + 48a b + 24a )x + (- 64a b - 128a b - 64a b)x +--R + +--R 2 4 3 3 4 2 2 5 2 4 3 3 +--R (384a b + 768a b + 384a b )x + (1536a b + 3072a b + 1536a b )x +--R + +--R 6 5 2 4 +--R 1024b + 2048a b + 1024a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 5 3 2 4 4 3 3 5 4 2 +--R 2048a b + (5120a + 128a )b + (3840a + 192a )b + (640a + 48a )b +--R + +--R 6 5 7 6 +--R (- 80a - 8a )b + 48a + 3a +--R * +--R 2 +--R x +--R + +--R 6 2 5 3 2 4 +--R 4096a b + (10240a + 256a)b + (7680a + 384a )b +--R + +--R 4 3 3 5 4 2 6 5 +--R (1280a + 96a )b + (- 160a - 16a )b + (96a + 6a )b +--R * +--R x +--R + +--R 7 6 2 5 3 2 4 +--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b +--R + +--R 4 3 3 5 4 2 +--R (- 80a - 8a )b + (48a + 3a )b +--R / +--R 7 2 8 9 2 6 3 7 2 8 5 4 +--R (60a b + 120a b + 60a )x + (120a b + 240a b + 120a b)x + 60a b +--R + +--R 6 3 7 2 +--R 120a b + 60a b +--R Type: Union(Expression(Integer),...) +--E 286 + +--S 287 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 2 3 3 2 2 +--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b +--R + +--R 4 3 5 4 +--R (- 80a - 8a )b + 48a + 3a +--R / +--R 5 2 6 7 +--R 60a b + 120a b + 60a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1379 +t0:=x^(1/2)/(a+b/x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1379 +r0:=-2/3*x^(3/2)/(a*(a+b/x)^(3/2))-4*x^(3/2)/(a^2*sqrt(a+b/x))+_ + 16/3*x^(3/2)*sqrt(a+b/x)/a^3-32/3*b*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (2a x - 12a b x - 48a b x - 32b )\|x +--R (2) --------------------------------------- +--R +-------+ +--R 5 2 4 |a x + b +--R (3a x + 3a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 5 3 2 3 3 2 4 2 +--R (6a b + 12a b + 6a )x + (- 36a b - 72a b - 36a b)x +--R + +--R 4 2 3 3 2 5 4 2 3 +--R (- 144a b - 288a b - 144a b )x - 96b - 192a b - 96a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 4 3 2 3 4 3 2 5 4 6 +--R 144a b + (360a + 16a )b + (270a + 24a )b + (45a + 6a )b - 9a +--R + +--R 5 +--R - a +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 2 3 4 3 2 +--R 288a b + (720a + 32a)b + (540a + 48a )b + (90a + 12a )b +--R + +--R 5 4 +--R (- 18a - 2a )b +--R * +--R x +--R + +--R 6 5 2 4 3 2 3 4 3 2 +--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b + (- 9a - a )b +--R / +--R 6 2 7 8 2 5 3 6 2 7 4 4 5 3 +--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b +--R + +--R 6 2 +--R 9a b +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 1379 +m0:=a0-r0 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b - 9a - a +--R (4) ------------------------------------------------------------------ +--R 4 2 5 6 +--R 9a b + 18a b + 9a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1379 +r0:=-2/3*sqrt(x)/(a*(a+b/x)^(3/2))-8/3*sqrt(x)/(a^2*sqrt(a+b/x))+_ + 16/3*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R 2 2 2 +-+ +--R (6a x + 24a b x + 16b )\|x +--R (2) ---------------------------- +--R +-------+ +--R 4 2 3 |a x + b +--R (3a x + 3a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 4 2 3 2 2 3 4 +--R (30a b + 60a b + 30a )x + (120a b + 240a b + 120a b)x + 80b +--R + +--R 3 2 2 +--R 160a b + 80a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 3 3 2 2 4 3 5 4 2 +--R (200a b + (500a + 8a )b + (375a + 12a )b + 75a + 3a )x +--R + +--R 4 2 3 3 2 2 4 3 5 +--R (400a b + (1000a + 16a)b + (750a + 24a )b + (150a + 6a )b)x + 200b +--R + +--R 4 2 3 3 2 2 +--R (500a + 8)b + (375a + 12a)b + (75a + 3a )b +--R / +--R 5 2 6 7 2 4 3 5 2 6 3 4 4 3 +--R (15a b + 30a b + 15a )x + (30a b + 60a b + 30a b)x + 15a b + 30a b +--R + +--R 5 2 +--R 15a b +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 1379 +m0:=a0-r0 +--R +--R +--R 3 2 2 3 2 +--R 200b + (500a + 8)b + (375a + 12a)b + 75a + 3a +--R (4) -------------------------------------------------- +--R 3 2 4 5 +--R 15a b + 30a b + 15a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +)clear all + +--S 299 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(3/2)) +--R +--R +--R x +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1379 +r0:=(-2/3)/(a*(a+b/x)^(3/2)*sqrt(x))+(-4/3)/(a^2*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R - 6a x - 4b +--R (2) --------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +--R (3a x + 3a b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 3 3 2 2 |a x + b +-+ +--R ((- 18a b - 36a b - 18a )x - 12b - 24a b - 12a b) |------- \|x +--R \| x +--R + +--R 2 2 3 2 4 3 2 +--R (18a b + (45a + 2a )b + 27a + 3a )x +--R + +--R 3 2 2 3 2 4 3 +--R (36a b + (90a + 4a)b + (54a + 6a )b)x + 18b + (45a + 2)b +--R + +--R 2 2 +--R (27a + 3a)b +--R / +--R 4 2 5 6 2 3 3 4 2 5 2 4 3 3 +--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b +--R + +--R 4 2 +--R 9a b +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 1379 +m0:=a0-r0 +--R +--R +--R 2 2 +--R 18b + (45a + 2)b + 27a + 3a +--R (4) ----------------------------- +--R 2 2 3 4 +--R 9a b + 18a b + 9a +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1379 +r0:=(-2/3)/(a*(a+b/x)^(3/2)*x^(3/2)) +--R +--R +--R 2 +--R (2) - --------------------------- +--R +-------+ +--R 2 |a x + b +-+ +--R (3a x + 3a b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 |a x + b +-+ 2 3 2 2 +--R (- 4b - 8a b - 4a ) |------- \|x + (4a b + 4a + a )x +--R \| x +--R + +--R 2 2 3 2 +--R (8a b + (8a + 2a)b)x + 4b + (4a + 1)b +--R / +--R 3 2 4 5 2 2 3 3 2 4 4 2 3 +--R (6a b + 12a b + 6a )x + (12a b + 24a b + 12a b)x + 6a b + 12a b +--R + +--R 3 2 +--R 6a b +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 1379 +m0:=a0-r0 +--R +--R +--R 4b + 4a + 1 +--R (4) ------------------- +--R 2 2 3 +--R 6a b + 12a b + 6a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 308 + +)clear all + +--S 309 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R +-------+ +--R 2 3 2 2 |a x + b +-+ +--R (a x + 2a b x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(3/2))-2*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(5/2)+2/(b^2*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R (- 6a x - 6b) |------- \|x atanh(--------------) + (6a x + 8b)\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------------------------------ +--R +-------+ +--R 2 3 |a x + b +-+ +-+ +--R (3a b x + 3b ) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1379 +--a0:=integrate(t0,x) +--E 311 + +--S 312 of 1379 +--m0:=a0-r0 +--E 312 + +--S 313 of 1379 +--d0:=D(m0,x) +--E 313 + +)clear all + +--S 314 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +-------+ +--R 2 4 3 2 2 |a x + b +-+ +--R (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(5/2))+5*a*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(7/2)+10/3/(b^2*x^(3/2)*sqrt(a+b/x))-_ + 5*sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 2 2 |a x + b +-+ \|b +--R (15a x + 15a b x) |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 2 2 +-+ +--R (- 15a x - 20a b x - 3b )\|b +--R / +--R +-------+ +--R 3 2 4 |a x + b +-+ +-+ +--R (3a b x + 3b x) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1379 +--a0:=integrate(t0,x) +--E 316 + +--S 317 of 1379 +--m0:=a0-r0 +--E 317 + +--S 318 of 1379 +--d0:=D(m0,x) +--E 318 + +)clear all + +--S 319 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(11/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +-------+ +--R 2 5 4 2 3 |a x + b +-+ +--R (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(7/2))-35/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(9/2)+14/3/(b^2*x^(5/2)*sqrt(a+b/x))-_ + 35/6*sqrt(a+b/x)/(b^3*x^(3/2))+35/4*a*sqrt(a+b/x)/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 3 3 2 2 |a x + b +-+ \|b +--R (- 105a x - 105a b x ) |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (105a x + 140a b x + 21a b x - 6b )\|b +--R / +--R +-------+ +--R 4 3 5 2 |a x + b +-+ +-+ +--R (12a b x + 12b x ) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1379 +--a0:=integrate(t0,x) +--E 321 + +--S 322 of 1379 +--m0:=a0-r0 +--E 322 + +--S 323 of 1379 +--d0:=D(m0,x) +--E 323 + +)clear all + +--S 324 of 1379 +t0:=(a+b/x^2)*x^6 +--R +--R +--R 6 4 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 324 + +--S 325 of 1379 +r0:=1/5*b*x^5+1/7*a*x^7 +--R +--R +--R 1 7 1 5 +--R (2) - a x + - b x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 325 + +--S 326 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 7 5 +--R 5a x + 7b x +--R (3) ------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 326 + +--S 327 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 1379 +t0:=(a+b/x^2)*x^5 +--R +--R +--R 5 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 329 + +--S 330 of 1379 +r0:=1/4*b*x^4+1/6*a*x^6 +--R +--R +--R 1 6 1 4 +--R (2) - a x + - b x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 330 + +--S 331 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 6 4 +--R 2a x + 3b x +--R (3) ------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1379 +t0:=(a+b/x^2)*x^4 +--R +--R +--R 4 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 334 + +--S 335 of 1379 +r0:=1/3*b*x^3+1/5*a*x^5 +--R +--R +--R 1 5 1 3 +--R (2) - a x + - b x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 335 + +--S 336 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 5 3 +--R 3a x + 5b x +--R (3) ------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1379 +t0:=(a+b/x^2)*x^3 +--R +--R +--R 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 339 + +--S 340 of 1379 +r0:=1/2*b*x^2+1/4*a*x^4 +--R +--R +--R 1 4 1 2 +--R (2) - a x + - b x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 340 + +--S 341 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +--R a x + 2b x +--R (3) ------------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +)clear all + +--S 344 of 1379 +t0:=(a+b/x^2)*x^2 +--R +--R +--R 2 +--R (1) a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 344 + +--S 345 of 1379 +r0:=b*x+1/3*a*x^3 +--R +--R +--R 1 3 +--R (2) - a x + b x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 345 + +--S 346 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R a x + 3b x +--R (3) ----------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 1379 +t0:=(a+b/x^2)*x +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1379 +r0:=1/2*a*x^2+b*log(x) +--R +--R +--R 2 +--R 2b log(x) + a x +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b log(x) + a x +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 353 + +)clear all + +--S 354 of 1379 +t0:=a+b/x^2 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 354 + +--S 355 of 1379 +r0:=-b/x+a*x +--R +--R +--R 2 +--R a x - b +--R (2) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R a x - b +--R (3) -------- +--R x +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1379 +t0:=(a+b/x^2)/x +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 359 + +--S 360 of 1379 +r0:=-1/2*b/x^2+a*log(x) +--R +--R +--R 2 +--R 2a x log(x) - b +--R (2) --------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2a x log(x) - b +--R (3) --------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1379 +t0:=(a+b/x^2)/x^2 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 364 + +--S 365 of 1379 +r0:=-1/3*b/x^3-a/x +--R +--R +--R 2 1 +--R - a x - - b +--R 3 +--R (2) ------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 365 + +--S 366 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3a x - b +--R (3) ----------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 1379 +t0:=(a+b/x^2)/x^3 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 1379 +r0:=-1/4*b/x^4-1/2*a/x^2 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 2 4 +--R (2) -------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 370 + +--S 371 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2a x - b +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1379 +t0:=(a+b/x^2)/x^4 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 374 + +--S 375 of 1379 +r0:=-1/5*b/x^5-1/3*a/x^3 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 3 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 375 + +--S 376 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5a x - 3b +--R (3) ------------ +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1379 +t0:=(a+b/x^2)/x^5 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 379 + +--S 380 of 1379 +r0:=-1/6*b/x^6-1/4*a/x^4 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 4 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 380 + +--S 381 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3a x - 2b +--R (3) ------------ +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1379 +t0:=(a+b/x^2)/x^6 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 384 + +--S 385 of 1379 +r0:=-1/7*b/x^7-1/5*a/x^5 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 5 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 385 + +--S 386 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 7a x - 5b +--R (3) ------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1379 +t0:=(a+b/x^2)^2*x^6 +--R +--R +--R 2 6 4 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 389 + +--S 390 of 1379 +r0:=1/3*b^2*x^3+2/5*a*b*x^5+1/7*a^2*x^7 +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (2) - a x + - a b x + - b x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 390 + +--S 391 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 7 5 2 3 +--R 15a x + 42a b x + 35b x +--R (3) -------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1379 +t0:=(a+b/x^2)^2*x^5 +--R +--R +--R 2 5 3 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 394 + +--S 395 of 1379 +r0:=1/6*(a+b/x^2)^3*x^6/a +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (2) ----------------------------- +--R 6a +--R Type: Fraction(Polynomial(Integer)) +--E 395 + +--S 396 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 6 4 2 2 +--R a x + 3a b x + 3b x +--R (3) ---------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R 6a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1379 +t0:=(a+b/x^2)^2*x^4 +--R +--R +--R 2 4 2 2 +--R (1) a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 399 + +--S 400 of 1379 +r0:=b^2*x+2/3*a*b*x^3+1/5*a^2*x^5 +--R +--R +--R 1 2 5 2 3 2 +--R (2) - a x + - a b x + b x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 400 + +--S 401 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 2 +--R 3a x + 10a b x + 15b x +--R (3) ------------------------ +--R 15 +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1379 +t0:=(a+b/x^2)^2*x^3 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 404 + +--S 405 of 1379 +r0:=a*b*x^2+1/4*a^2*x^4+b^2*log(x) +--R +--R +--R 2 2 4 2 +--R 4b log(x) + a x + 4a b x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4b log(x) + a x + 4a b x +--R (3) -------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1379 +t0:=(a+b/x^2)^2*x^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 409 + +--S 410 of 1379 +r0:=-b^2/x+2*a*b*x+1/3*a^2*x^3 +--R +--R +--R 2 4 2 2 +--R a x + 6a b x - 3b +--R (2) -------------------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 410 + +--S 411 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R a x + 6a b x - 3b +--R (3) -------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1379 +t0:=(a+b/x^2)^2*x +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 414 + +--S 415 of 1379 +r0:=-1/2*b^2/x^2+1/2*a^2*x^2+2*a*b*log(x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + a x - b +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + a x - b +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1379 +t0:=(a+b/x^2)^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 419 + +--S 420 of 1379 +r0:=-1/3*b^2/x^3-2*a*b/x+a^2*x +--R +--R +--R 2 4 2 1 2 +--R a x - 2a b x - - b +--R 3 +--R (2) --------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 420 + +--S 421 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 3a x - 6a b x - b +--R (3) -------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1379 +t0:=(a+b/x^2)^2/x +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 424 + +--S 425 of 1379 +r0:=-1/4*b^2/x^4-a*b/x^2+a^2*log(x) +--R +--R +--R 2 4 2 2 +--R 4a x log(x) - 4a b x - b +--R (2) -------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 4a x log(x) - 4a b x - b +--R (3) -------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1379 +t0:=(a+b/x^2)^2/x^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 429 + +--S 430 of 1379 +r0:=-1/5*b^2/x^5-2/3*a*b/x^3-a^2/x +--R +--R +--R 2 4 2 2 1 2 +--R - a x - - a b x - - b +--R 3 5 +--R (2) ------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 430 + +--S 431 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 15a x - 10a b x - 3b +--R (3) ------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1379 +t0:=(a+b/x^2)^2/x^3 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 434 + +--S 435 of 1379 +r0:=-1/6*(a+b/x^2)^3/b +--R +--R +--R 3 6 2 4 2 2 3 +--R - a x - 3a b x - 3a b x - b +--R (2) ------------------------------- +--R 6 +--R 6b x +--R Type: Fraction(Polynomial(Integer)) +--E 435 + +--S 436 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 3a x - 3a b x - b +--R (3) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R a +--R (4) -- +--R 6b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1379 +t0:=(a+b/x^2)^2/x^4 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 439 + +--S 440 of 1379 +r0:=-1/7*b^2/x^7-2/5*a*b/x^5-1/3*a^2/x^3 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - a x - - a b x - - b +--R 3 5 7 +--R (2) -------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 440 + +--S 441 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 35a x - 42a b x - 15b +--R (3) -------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1379 +t0:=(a+b/x^2)^2/x^5 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 444 + +--S 445 of 1379 +r0:=-1/8*b^2/x^8-1/3*a*b/x^6-1/4*a^2/x^4 +--R +--R +--R 1 2 4 1 2 1 2 +--R - - a x - - a b x - - b +--R 4 3 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 445 + +--S 446 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 6a x - 8a b x - 3b +--R (3) ----------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1379 +t0:=(a+b/x^2)^2/x^6 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 449 + +--S 450 of 1379 +r0:=-1/9*b^2/x^9-2/7*a*b/x^7-1/5*a^2/x^5 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - a x - - a b x - - b +--R 5 7 9 +--R (2) -------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 450 + +--S 451 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 63a x - 90a b x - 35b +--R (3) -------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1379 +t0:=(a+b/x^2)^3*x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R (1) a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 454 + +--S 455 of 1379 +r0:=b^3*x+a*b^2*x^3+3/5*a^2*b*x^5+1/7*a^3*x^7 +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (2) - a x + - a b x + a b x + b x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 455 + +--S 456 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 5 2 3 3 +--R 5a x + 21a b x + 35a b x + 35b x +--R (3) ----------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1379 +t0:=(a+b/x^2)^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 459 + +--S 460 of 1379 +r0:=3/2*a*b^2*x^2+3/4*a^2*b*x^4+1/6*a^3*x^6+b^3*log(x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12b log(x) + 2a x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12b log(x) + 2a x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1379 +t0:=(a+b/x^2)^3*x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 464 + +--S 465 of 1379 +r0:=-b^3/x+3*a*b^2*x+a^2*b*x^3+1/5*a^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 5a b x + 15a b x - 5b +--R (2) ------------------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 465 + +--S 466 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 5a b x + 15a b x - 5b +--R (3) ------------------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1379 +t0:=(a+b/x^2)^3*x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 469 + +--S 470 of 1379 +r0:=-1/2*b^3/x^2+3/2*a^2*b*x^2+1/4*a^3*x^4+3*a*b^2*log(x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + a x + 6a b x - 2b +--R (2) ------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + a x + 6a b x - 2b +--R (3) ------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1379 +t0:=(a+b/x^2)^3*x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 474 + +--S 475 of 1379 +r0:=-1/3*b^3/x^3-3*a*b^2/x+3*a^2*b*x+1/3*a^3*x^3 +--R +--R +--R 1 3 6 2 4 2 2 1 3 +--R - a x + 3a b x - 3a b x - - b +--R 3 3 +--R (2) --------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 475 + +--S 476 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 9a b x - 9a b x - b +--R (3) ----------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1379 +t0:=(a+b/x^2)^3*x +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 479 + +--S 480 of 1379 +r0:=-1/4*b^3/x^4-3/2*a*b^2/x^2+1/2*a^3*x^2+3*a^2*b*log(x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2a x - 6a b x - b +--R (2) ------------------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2a x - 6a b x - b +--R (3) ------------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1379 +t0:=(a+b/x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 484 + +--S 485 of 1379 +r0:=-1/5*b^3/x^5-a*b^2/x^3-3*a^2*b/x+a^3*x +--R +--R +--R 3 6 2 4 2 2 1 3 +--R a x - 3a b x - a b x - - b +--R 5 +--R (2) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 485 + +--S 486 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 5a x - 15a b x - 5a b x - b +--R (3) ------------------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1379 +t0:=(a+b/x^2)^3/x +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 489 + +--S 490 of 1379 +r0:=-1/6*b^3/x^6-3/4*a*b^2/x^4-3/2*a^2*b/x^2+a^3*log(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12a x log(x) - 18a b x - 9a b x - 2b +--R (2) --------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12a x log(x) - 18a b x - 9a b x - 2b +--R (3) --------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1379 +t0:=(a+b/x^2)^3/x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 494 + +--S 495 of 1379 +r0:=-1/7*b^3/x^7-3/5*a*b^2/x^5-a^2*b/x^3-a^3/x +--R +--R +--R 3 6 2 4 3 2 2 1 3 +--R - a x - a b x - - a b x - - b +--R 5 7 +--R (2) --------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 495 + +--S 496 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35a x - 35a b x - 21a b x - 5b +--R (3) ------------------------------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1379 +t0:=(a+b/x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 499 + +--S 500 of 1379 +r0:=-1/8*(a+b/x^2)^4/b +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (2) ----------------------------------------- +--R 8 +--R 8b x +--R Type: Fraction(Polynomial(Integer)) +--E 500 + +--S 501 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (3) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1379 +m0:=a0-r0 +--R +--R +--R 4 +--R a +--R (4) -- +--R 8b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1379 +t0:=(a+b/x^2)^3/x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 504 + +--S 505 of 1379 +r0:=-1/9*b^3/x^9-3/7*a*b^2/x^7-3/5*a^2*b/x^5-1/3*a^3/x^3 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 3 5 7 9 +--R (2) ------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 505 + +--S 506 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 105a x - 189a b x - 135a b x - 35b +--R (3) ---------------------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1379 +t0:=(a+b/x^2)^3/x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 509 + +--S 510 of 1379 +r0:=-1/10*b^3/x^10-3/8*a*b^2/x^8-1/2*a^2*b/x^6-1/4*a^3/x^4 +--R +--R +--R 1 3 6 1 2 4 3 2 2 1 3 +--R - - a x - - a b x - - a b x - -- b +--R 4 2 8 10 +--R (2) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 510 + +--S 511 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 10a x - 20a b x - 15a b x - 4b +--R (3) ------------------------------------ +--R 10 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1379 +t0:=(a+b/x^2)^3/x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 514 + +--S 515 of 1379 +r0:=-1/11*b^3/x^11-1/3*a*b^2/x^9-3/7*a^2*b/x^7-1/5*a^3/x^5 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - a x - - a b x - - a b x - -- b +--R 5 7 3 11 +--R (2) -------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 515 + +--S 516 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 231a x - 495a b x - 385a b x - 105b +--R (3) ----------------------------------------- +--R 11 +--R 1155x +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1379 +t0:=x^6/(a+b/x^2) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 519 + +--S 520 of 1379 +r0:=-b^3*x/a^4+1/3*b^2*x^3/a^3-1/5*b*x^5/a^2+1/7*x^7/a+_ + b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 3 7 2 5 2 3 3 +-+ +--R 105b \|b atan(-----) + (15a x - 21a b x + 35a b x - 105b x)\|a +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------------ +--R 4 +-+ +--R 105a \|a +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 3 | b \| a 3 7 2 5 2 3 +--R 105b |- - log(---------------------) + 30a x - 42a b x + 70a b x +--R \| a 2 +--R a x + b +--R + +--R 3 +--R - 210b x +--R / +--R 4 +--R 210a +--R , +--R +-+ +--R |b +--R +-+ |- +--R 3 |b \|a 3 7 2 5 2 3 3 +--R - 105b |- atan(----) + 15a x - 21a b x + 35a b x - 105b x +--R \|a x +--R -------------------------------------------------------------] +--R 4 +--R 105a +--R Type: Union(List(Expression(Integer)),...) +--E 521 + +--S 522 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R 3 | b +-+ \| a 3 +-+ x\|a +--R b |- - \|a log(---------------------) - 2b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 3 +-+ |b \|a 3 +-+ x\|a +--R - b \|a |- atan(----) - b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1379 +t0:=x^5/(a+b/x^2) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1379 +r0:=1/2*b^2*x^2/a^3-1/4*b*x^4/a^2+1/6*x^6/a-1/2*b^3*log(b+a*x^2)/a^4 +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (2) ---------------------------------------------- +--R 4 +--R 12a +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (3) ---------------------------------------------- +--R 4 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1379 +t0:=x^4/(a+b/x^2) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1379 +r0:=b^2*x/a^3-1/3*b*x^3/a^2+1/5*x^5/a-b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(7/2) +--R +--R +--R +-+ +--R 2 +-+ x\|a 2 5 3 2 +-+ +--R - 15b \|b atan(-----) + (3a x - 5a b x + 15b x)\|a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------- +--R 3 +-+ +--R 15a \|a +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 | b \| a 2 5 3 2 +--R 15b |- - log(-----------------------) + 6a x - 10a b x + 30b x +--R \| a 2 +--R a x + b +--R [-----------------------------------------------------------------, +--R 3 +--R 30a +--R +-+ +--R |b +--R +-+ |- +--R 2 |b \|a 2 5 3 2 +--R 15b |- atan(----) + 3a x - 5a b x + 15b x +--R \|a x +--R --------------------------------------------] +--R 3 +--R 15a +--R Type: Union(List(Expression(Integer)),...) +--E 533 + +--S 534 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R b |- - \|a log(-----------------------) + 2b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R b \|a |- atan(----) + b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1379 +t0:=x^3/(a+b/x^2) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 538 + +--S 539 of 1379 +r0:=-1/2*b*x^2/a^2+1/4*x^4/a+1/2*b^2*log(b+a*x^2)/a^3 +--R +--R +--R 2 2 2 4 2 +--R 2b log(a x + b) + a x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 4a +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 4 2 +--R 2b log(a x + b) + a x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 4a +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1379 +t0:=x^2/(a+b/x^2) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 543 + +--S 544 of 1379 +r0:=-b*x/a^2+1/3*x^3/a+b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(5/2) +--R +--R +--R +-+ +--R +-+ x\|a 3 +-+ +--R 3b\|b atan(-----) + (a x - 3b x)\|a +--R +-+ +--R \|b +--R (2) ------------------------------------- +--R 2 +-+ +--R 3a \|a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R | b \| a 3 +--R 3b |- - log(---------------------) + 2a x - 6b x +--R \| a 2 +--R a x + b +--R [-------------------------------------------------, +--R 2 +--R 6a +--R +-+ +--R |b +--R +-+ |- +--R |b \|a 3 +--R - 3b |- atan(----) + a x - 3b x +--R \|a x +--R --------------------------------] +--R 2 +--R 3a +--R Type: Union(List(Expression(Integer)),...) +--E 545 + +--S 546 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R b |- - \|a log(---------------------) - 2b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - b\|a |- atan(----) - b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1379 +t0:=x/(a+b/x^2) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 550 + +--S 551 of 1379 +r0:=1/2*x^2/a-1/2*b*log(b+a*x^2)/a^2 +--R +--R +--R 2 2 +--R - b log(a x + b) + a x +--R (2) ------------------------ +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - b log(a x + b) + a x +--R (3) ------------------------ +--R 2 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1379 +t0:=1/(a+b/x^2) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 555 + +--S 556 of 1379 +r0:=x/a-atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|a +-+ +--R - \|b atan(-----) + x\|a +--R +-+ +--R \|b +--R (2) ------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | b 2 +-+ +--R +---+ - 2a x |- - + a x - b |b +--R | b \| a +-+ |- +--R |- - log(-----------------------) + 2x |b \|a +--R \| a 2 |- atan(----) + x +--R a x + b \|a x +--R (3) [---------------------------------------,------------------] +--R 2a a +--R Type: Union(List(Expression(Integer)),...) +--E 557 + +--S 558 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R |- - \|a log(-----------------------) + 2\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R \|a |- atan(----) + \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 1379 +t0:=1/((a+b/x^2)*x) +--R +--R +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 562 + +--S 563 of 1379 +r0:=1/2*log(b+a*x^2)/a +--R +--R +--R 2 +--R log(a x + b) +--R (2) ------------- +--R 2a +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(a x + b) +--R (3) ------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 564 + +--S 565 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 566 + +)clear all + +--S 567 of 1379 +t0:=1/((a+b/x^2)*x^2) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 567 + +--S 568 of 1379 +r0:=atan(x*sqrt(a)/sqrt(b))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|a +--R atan(-----) +--R +-+ +--R \|b +--R (2) ----------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +--R (a x - b)\|- a b + 2a b x +---+ +--R log(---------------------------) x\|a b +--R 2 atan(-------) +--R a x + b b +--R (3) [--------------------------------,-------------] +--R +-----+ +---+ +--R 2\|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 569 + +--S 570 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a b \|a \|b +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1379 +t0:=1/((a+b/x^2)*x^3) +--R +--R +--R 1 +--R (1) ---------- +--R 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 574 + +--S 575 of 1379 +r0:=-1/2*log(a+b/x^2)/b +--R +--R +--R 2 +--R a x + b +--R log(--------) +--R 2 +--R x +--R (2) - ------------- +--R 2b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(a x + b) + 2log(x) +--R (3) ------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1379 +m0:=a0-r0 +--R +--R +--R 2 +--R 2 a x + b +--R - log(a x + b) + 2log(x) + log(--------) +--R 2 +--R x +--R (4) ----------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1379 +t0:=1/((a+b/x^2)*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R 4 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 579 + +--S 580 of 1379 +r0:=(-1)/(b*x)-atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|a +-+ +--R - x\|a atan(-----) - \|b +--R +-+ +--R \|b +--R (2) ------------------------- +--R +-+ +--R b x\|b +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | a 2 +-+ +--R +---+ - 2b x |- - + a x - b |a +--R | a \| b +-+ b |- +--R x |- - log(-----------------------) - 2 |a \|b +--R \| b 2 x |- atan(-----) - 1 +--R a x + b \|b a x +--R (3) [---------------------------------------,--------------------] +--R 2b x b x +--R Type: Union(List(Expression(Integer)),...) +--E 581 + +--S 582 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R |- - \|b log(-----------------------) + 2\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R |- \|b atan(-----) + \|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1379 +t0:=1/((a+b/x^2)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1379 +r0:=(-1/2)/(b*x^2)-a*log(x)/b^2+1/2*a*log(b+a*x^2)/b^2 +--R +--R +--R 2 2 2 +--R a x log(a x + b) - 2a x log(x) - b +--R (2) ----------------------------------- +--R 2 2 +--R 2b x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R a x log(a x + b) - 2a x log(x) - b +--R (3) ----------------------------------- +--R 2 2 +--R 2b x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1379 +t0:=1/((a+b/x^2)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1379 +r0:=(-1/3)/(b*x^3)+a/(b^2*x)+a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 2 +-+ +--R 3a x \|a atan(-----) + (3a x - b)\|b +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 3 +-+ +--R 3b x \|b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 3 | a \| b 2 +--R 3a x |- - log(---------------------) + 6a x - 2b +--R \| b 2 +--R a x + b +--R [--------------------------------------------------, +--R 2 3 +--R 6b x +--R +-+ +--R |a +--R +-+ b |- +--R 3 |a \|b 2 +--R - 3a x |- atan(-----) + 3a x - b +--R \|b a x +--R ----------------------------------] +--R 2 3 +--R 3b x +--R Type: Union(List(Expression(Integer)),...) +--E 593 + +--S 594 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R a |- - \|b log(---------------------) - 2a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - a |- \|b atan(-----) - a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1379 +t0:=1/((a+b/x^2)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 5 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 598 + +--S 599 of 1379 +r0:=(-1/4)/(b*x^4)+1/2*a/(b^2*x^2)+a^2*log(x)/b^3-1/2*a^2*log(b+a*x^2)/b^3 +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b +--R (2) ------------------------------------------------- +--R 3 4 +--R 4b x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b +--R (3) ------------------------------------------------- +--R 3 4 +--R 4b x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1379 +t0:=1/((a+b/x^2)*x^8) +--R +--R +--R 1 +--R (1) ----------- +--R 8 6 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 603 + +--S 604 of 1379 +r0:=(-1/5)/(b*x^5)+1/3*a/(b^2*x^3)-a^2/(b^3*x)-_ + a^(5/2)*atan(x*sqrt(a)/sqrt(b))/b^(7/2) +--R +--R +--R +-+ +--R 2 5 +-+ x\|a 2 4 2 2 +-+ +--R - 15a x \|a atan(-----) + (- 15a x + 5a b x - 3b )\|b +--R +-+ +--R \|b +--R (2) -------------------------------------------------------- +--R 3 5 +-+ +--R 15b x \|b +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 2 5 | a \| b 2 4 2 2 +--R 15a x |- - log(-----------------------) - 30a x + 10a b x - 6b +--R \| b 2 +--R a x + b +--R [------------------------------------------------------------------, +--R 3 5 +--R 30b x +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 |a \|b 2 4 2 2 +--R 15a x |- atan(-----) - 15a x + 5a b x - 3b +--R \|b a x +--R ----------------------------------------------] +--R 3 5 +--R 15b x +--R Type: Union(List(Expression(Integer)),...) +--E 605 + +--S 606 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R 2 | a +-+ \| b 2 +-+ x\|a +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R 2 |a +-+ \|b 2 +-+ x\|a +--R a |- \|b atan(-----) + a \|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1379 +t0:=x^6/(a+b/x^2)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 of 1379 +r0:=-9/2*b^3*x/a^5+3/2*b^2*x^3/a^4-9/10*b*x^5/a^3+9/14*x^7/a^2-_ + 1/2*x^9/(a*(b+a*x^2))+9/2*b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 +-+ x\|a +--R (315a b x + 315b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b x)\|a +--R / +--R 6 2 5 +-+ +--R (70a x + 70a b)\|a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 3 2 4 | b \| a 4 9 3 7 +--R (315a b x + 315b ) |- - log(---------------------) + 20a x - 36a b x +--R \| a 2 +--R a x + b +--R + +--R 2 2 5 3 3 4 +--R 84a b x - 420a b x - 630b x +--R / +--R 6 2 5 +--R 140a x + 140a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 3 2 4 |b \|a 4 9 3 7 2 2 5 +--R (- 315a b x - 315b ) |- atan(----) + 10a x - 18a b x + 42a b x +--R \|a x +--R + +--R 3 3 4 +--R - 210a b x - 315b x +--R / +--R 6 2 5 +--R 70a x + 70a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 612 + +--S 613 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R 3 | b +-+ \| a 3 +-+ x\|a +--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 3 +-+ |b \|a 3 +-+ x\|a +--R - 9b \|a |- atan(----) - 9b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 616 + +)clear all + +--S 617 of 1379 +t0:=x^5/(a+b/x^2)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 617 + +--S 618 of 1379 +r0:=3/2*b^2*x^2/a^4-1/2*b*x^4/a^3+1/6*x^6/a^2-1/2*b^4/(a^5*(b+a*x^2))-_ + 2*b^3*log(b+a*x^2)/a^5 +--R +--R +--R (2) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6a x + 6a b +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 619 + +--S 620 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1379 +t0:=x^4/(a+b/x^2)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 622 + +--S 623 of 1379 +r0:=7/2*b^2*x/a^4-7/6*b*x^3/a^3+7/10*x^5/a^2-1/2*x^7/(a*(b+a*x^2))-_ + 7/2*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 3 +-+ x\|a +--R (- 105a b x - 105b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6a x - 14a b x + 70a b x + 105b x)\|a +--R / +--R 5 2 4 +-+ +--R (30a x + 30a b)\|a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 2 3 | b \| a 3 7 +--R (105a b x + 105b ) |- - log(-----------------------) + 12a x +--R \| a 2 +--R a x + b +--R + +--R 2 5 2 3 3 +--R - 28a b x + 140a b x + 210b x +--R / +--R 5 2 4 +--R 60a x + 60a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 2 3 |b \|a 3 7 2 5 2 3 3 +--R (105a b x + 105b ) |- atan(----) + 6a x - 14a b x + 70a b x + 105b x +--R \|a x +--R ------------------------------------------------------------------------] +--R 5 2 4 +--R 30a x + 30a b +--R Type: Union(List(Expression(Integer)),...) +--E 624 + +--S 625 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R 7b \|a |- atan(----) + 7b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1379 +t0:=x^3/(a+b/x^2)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 629 + +--S 630 of 1379 +r0:=-b*x^2/a^3+1/4*x^4/a^2+1/2*b^3/(a^4*(b+a*x^2))+3/2*b^2*log(b+a*x^2)/a^4 +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ------------------------------------------------------------- +--R 5 2 4 +--R 4a x + 4a b +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ------------------------------------------------------------- +--R 5 2 4 +--R 4a x + 4a b +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1379 +t0:=x^2/(a+b/x^2)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 634 + +--S 635 of 1379 +r0:=-5/2*b*x/a^3+5/6*x^3/a^2-1/2*x^5/(a*(b+a*x^2))+5/2*b^(3/2)*_ + atan(x*sqrt(a)/sqrt(b))/a^(7/2) +--R +--R +--R +-+ +--R 2 2 +-+ x\|a 2 5 3 2 +-+ +--R (15a b x + 15b )\|b atan(-----) + (2a x - 10a b x - 15b x)\|a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------------- +--R 4 2 3 +-+ +--R (6a x + 6a b)\|a +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 2 | b \| a 2 5 3 2 +--R (15a b x + 15b ) |- - log(---------------------) + 4a x - 20a b x - 30b x +--R \| a 2 +--R a x + b +--R [---------------------------------------------------------------------------- +--R 4 2 3 +--R 12a x + 12a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 2 |b \|a 2 5 3 2 +--R (- 15a b x - 15b ) |- atan(----) + 2a x - 10a b x - 15b x +--R \|a x +--R ------------------------------------------------------------] +--R 4 2 3 +--R 6a x + 6a b +--R Type: Union(List(Expression(Integer)),...) +--E 636 + +--S 637 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - 5b\|a |- atan(----) - 5b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1379 +t0:=x/(a+b/x^2)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 1379 +r0:=1/2*x^2/a^2-1/2*b^2/(a^3*(b+a*x^2))-b*log(b+a*x^2)/a^3 +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) --------------------------------------------------- +--R 4 2 3 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) --------------------------------------------------- +--R 4 2 3 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1379 +t0:=1/(a+b/x^2)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 646 + +--S 647 of 1379 +r0:=3/2*x/a^2-1/2*x^3/(a*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 2 +-+ x\|a 3 +-+ +--R (- 3a x - 3b)\|b atan(-----) + (2a x + 3b x)\|a +--R +-+ +--R \|b +--R (2) -------------------------------------------------- +--R 3 2 2 +-+ +--R (2a x + 2a b)\|a +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 | b \| a 3 +--R (3a x + 3b) |- - log(-----------------------) + 4a x + 6b x +--R \| a 2 +--R a x + b +--R [-------------------------------------------------------------, +--R 3 2 2 +--R 4a x + 4a b +--R +-+ +--R |b +--R +-+ |- +--R 2 |b \|a 3 +--R (3a x + 3b) |- atan(----) + 2a x + 3b x +--R \|a x +--R -----------------------------------------] +--R 3 2 2 +--R 2a x + 2a b +--R Type: Union(List(Expression(Integer)),...) +--E 648 + +--S 649 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 3 |- - \|a log(----------------------- + 6\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R 3\|a |- atan(----) + 3\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1379 +t0:=1/((a+b/x^2)^2*x) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 653 + +--S 654 of 1379 +r0:=1/2*b/(a^2*(b+a*x^2))+1/2*log(b+a*x^2)/a^2 +--R +--R +--R 2 2 +--R (a x + b)log(a x + b) + b +--R (2) --------------------------- +--R 3 2 2 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (a x + b)log(a x + b) + b +--R (3) --------------------------- +--R 3 2 2 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1379 +t0:=1/((a+b/x^2)^2*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 of 1379 +r0:=-1/2*x/(a*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|a +-+ +-+ +--R (a x + b)atan(-----) - x\|a \|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a x + 2a b)\|a \|b +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (a x - b)\|- a b + 2a b x +-----+ +--R (a x + b)log(---------------------------) - 2x\|- a b +--R 2 +--R a x + b +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a x + 4a b)\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (a x + b)atan(-------) - x\|a b +--R b +--R ---------------------------------] +--R 2 2 +---+ +--R (2a x + 2a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 660 + +--S 661 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1379 +t0:=1/((a+b/x^2)^2*x^3) +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1379 +r0:=1/2/(b*(a+b/x^2)) +--R +--R +--R 2 +--R x +--R (2) ------------- +--R 2 2 +--R 2a b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 666 + +--S 667 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2a b +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1379 +t0:=1/((a+b/x^2)^2*x^4) +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1379 +r0:=1/2*x/(b*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|a +-+ +-+ +--R (a x + b)atan(-----) + x\|a \|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x + 2b )\|a \|b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (a x - b)\|- a b + 2a b x +-----+ +--R (a x + b)log(---------------------------) + 2x\|- a b +--R 2 +--R a x + b +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a b x + 4b )\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (a x + b)atan(-------) + x\|a b +--R b +--R ---------------------------------] +--R 2 2 +---+ +--R (2a b x + 2b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 672 + +--S 673 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1379 +t0:=1/((a+b/x^2)^2*x^5) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 677 + +--S 678 of 1379 +r0:=1/2/(b*(b+a*x^2))+log(x)/b^2-1/2*log(b+a*x^2)/b^2 +--R +--R +--R 2 2 2 +--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b +--R (2) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2b +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2b +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1379 +t0:=1/((a+b/x^2)^2*x^6) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 682 + +--S 683 of 1379 +r0:=(-3/2)/(b^2*x)+1/2/(b*x*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*_ + sqrt(a)/b^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 2 +-+ +--R (- 3a x - 3b x)\|a atan(-----) + (- 3a x - 2b)\|b +--R +-+ +--R \|b +--R (2) ---------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x + 2b x)\|b +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 3 | a \| b 2 +--R (3a x + 3b x) |- - log(-----------------------) - 6a x - 4b +--R \| b 2 +--R a x + b +--R [-------------------------------------------------------------, +--R 2 3 3 +--R 4a b x + 4b x +--R +-+ +--R |a +--R +-+ b |- +--R 3 |a \|b 2 +--R (3a x + 3b x) |- atan(-----) - 3a x - 2b +--R \|b a x +--R ------------------------------------------] +--R 2 3 3 +--R 2a b x + 2b x +--R Type: Union(List(Expression(Integer)),...) +--E 684 + +--S 685 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 3 |- - \|b log(----------------------- + 6\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R 3 |- \|b atan(----- + 3\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) --------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1379 +t0:=1/((a+b/x^2)^2*x^7) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1379 +r0:=(-1)/(b^2*x^2)+1/2/(b*x^2*(b+a*x^2))-2*a*log(x)/b^3+a*log(b+a*x^2)/b^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2b x +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1379 +t0:=1/((a+b/x^2)^2*x^8) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 6 2 4 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1379 +r0:=(-5/6)/(b^2*x^3)+5/2*a/(b^3*x)+1/2/(b*x^3*(b+a*x^2))+5/2*a^(3/2)*_ + atan(x*sqrt(a)/sqrt(b))/b^(7/2) +--R +--R +--R +-+ +--R 2 5 3 +-+ x\|a 2 4 2 2 +-+ +--R (15a x + 15a b x )\|a atan(-----) + (15a x + 10a b x - 2b )\|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------------ +--R 3 5 4 3 +-+ +--R (6a b x + 6b x )\|b +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 2 5 3 | a \| b 2 4 2 +--R (15a x + 15a b x ) |- - log(---------------------) + 30a x + 20a b x +--R \| b 2 +--R a x + b +--R + +--R 2 +--R - 4b +--R / +--R 3 5 4 3 +--R 12a b x + 12b x +--R , +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 3 |a \|b 2 4 2 2 +--R (- 15a x - 15a b x ) |- atan(-----) + 15a x + 10a b x - 2b +--R \|b a x +--R --------------------------------------------------------------] +--R 3 5 4 3 +--R 6a b x + 6b x +--R Type: Union(List(Expression(Integer)),...) +--E 696 + +--S 697 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - 5a |- \|b atan(-----) - 5a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1379 +t0:=1/((a+b/x^2)^2*x^9) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 7 2 5 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 1379 +r0:=(-3/4)/(b^2*x^4)+3/2*a/(b^3*x^2)+1/2/(b*x^4*(b+a*x^2))+3*a^2*_ + log(x)/b^4-3/2*a^2*log(b+a*x^2)/b^4 +--R +--R +--R (2) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - b +--R / +--R 4 6 5 4 +--R 4a b x + 4b x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - b +--R / +--R 4 6 5 4 +--R 4a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1379 +t0:=x^5/(a+b/x^2)^3 +--R +--R +--R 11 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 of 1379 +r0:=3*b^2*x^2/a^5-3/4*b*x^4/a^4+1/6*x^6/a^3+1/4*b^5/(a^6*(b+a*x^2)^2)-_ + 5/2*b^4/(a^6*(b+a*x^2))-5*b^3*log(b+a*x^2)/a^6 +--R +--R +--R (2) +--R 2 3 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x +--R + +--R 3 2 6 2 3 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27b +--R / +--R 8 4 7 2 6 2 +--R 12a x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x +--R + +--R 3 2 6 2 3 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27b +--R / +--R 8 4 7 2 6 2 +--R 12a x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1379 +t0:=x^4/(a+b/x^2)^3 +--R +--R +--R 10 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 711 + +--S 712 of 1379 +r0:=63/8*b^2*x/a^5-21/8*b*x^3/a^4+63/40*x^5/a^3-1/4*x^9/(a*(b+a*x^2)^2)-_ + 9/8*x^7/(a^2*(b+a*x^2))-63/8*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 4 3 2 4 +-+ x\|a +--R (- 315a b x - 630a b x - 315b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b x)\|a +--R / +--R 7 4 6 2 5 2 +-+ +--R (40a x + 80a b x + 40a b )\|a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 2 4 3 2 4 | b \| a +--R (315a b x + 630a b x + 315b ) |- - log(-----------------------) +--R \| a 2 +--R a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +--R 16a x - 48a b x + 336a b x + 1050a b x + 630b x +--R / +--R 7 4 6 2 5 2 +--R 80a x + 160a b x + 80a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 2 2 4 3 2 4 |b \|a 4 9 3 7 +--R (315a b x + 630a b x + 315b ) |- atan(----) + 8a x - 24a b x +--R \|a x +--R + +--R 2 2 5 3 3 4 +--R 168a b x + 525a b x + 315b x +--R / +--R 7 4 6 2 5 2 +--R 40a x + 80a b x + 40a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 713 + +--S 714 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R 63b \|a |- atan(----) + 63b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1379 +t0:=x^3/(a+b/x^2)^3 +--R +--R +--R 9 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 of 1379 +r0:=-3/2*b*x^2/a^4+1/4*x^4/a^3-1/4*b^4/(a^5*(b+a*x^2)^2)+2*b^3/_ + (a^5*(b+a*x^2))+3*b^2*log(b+a*x^2)/a^5 +--R +--R +--R (2) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7b +--R / +--R 7 4 6 2 5 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7b +--R / +--R 7 4 6 2 5 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1379 +t0:=x^2/(a+b/x^2)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 723 + +--S 724 of 1379 +r0:=-35/8*b*x/a^4+35/24*x^3/a^3-1/4*x^7/(a*(b+a*x^2)^2)-7/8*x^5/_ + (a^2*(b+a*x^2))+35/8*b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 3 +-+ x\|a +--R (105a b x + 210a b x + 105b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (8a x - 56a b x - 175a b x - 105b x)\|a +--R / +--R 6 4 5 2 4 2 +-+ +--R (24a x + 48a b x + 24a b )\|a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 4 2 2 3 | b \| a +--R (105a b x + 210a b x + 105b ) |- - log(---------------------) +--R \| a 2 +--R a x + b +--R + +--R 3 7 2 5 2 3 3 +--R 16a x - 112a b x - 350a b x - 210b x +--R / +--R 6 4 5 2 4 2 +--R 48a x + 96a b x + 48a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 2 4 2 2 3 |b \|a 3 7 2 5 +--R (- 105a b x - 210a b x - 105b ) |- atan(----) + 8a x - 56a b x +--R \|a x +--R + +--R 2 3 3 +--R - 175a b x - 105b x +--R / +--R 6 4 5 2 4 2 +--R 24a x + 48a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 725 + +--S 726 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - 35b\|a |- atan(----) - 35b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1379 +t0:=x/(a+b/x^2)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1379 +r0:=1/2*x^2/a^3+1/4*b^3/(a^4*(b+a*x^2)^2)-3/2*b^2/(a^4*(b+a*x^2))-_ + 3/2*b*log(b+a*x^2)/a^4 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R --------------------------------------------------------------------------- +--R 6 4 5 2 4 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R --------------------------------------------------------------------------- +--R 6 4 5 2 4 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 732 + +--S 733 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 1379 +t0:=1/(a+b/x^2)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 735 + +--S 736 of 1379 +r0:=15/8*x/a^3-1/4*x^5/(a*(b+a*x^2)^2)-5/8*x^3/(a^2*(b+a*x^2))-_ + 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 +-+ x\|a 2 5 3 2 +-+ +--R (- 15a x - 30a b x - 15b )\|b atan(-----) + (8a x + 25a b x + 15b x)\|a +--R +-+ +--R \|b +--R ---------------------------------------------------------------------------- +--R 5 4 4 2 3 2 +-+ +--R (8a x + 16a b x + 8a b )\|a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 4 2 2 | b \| a 2 5 +--R (15a x + 30a b x + 15b ) |- - log(-----------------------) + 16a x +--R \| a 2 +--R a x + b +--R + +--R 3 2 +--R 50a b x + 30b x +--R / +--R 5 4 4 2 3 2 +--R 16a x + 32a b x + 16a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 4 2 2 |b \|a 2 5 3 2 +--R (15a x + 30a b x + 15b ) |- atan(----) + 8a x + 25a b x + 15b x +--R \|a x +--R -------------------------------------------------------------------] +--R 5 4 4 2 3 2 +--R 8a x + 16a b x + 8a b +--R Type: Union(List(Expression(Integer)),...) +--E 737 + +--S 738 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 15 |- - \|a log(----------------------- + 30\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R 15\|a |- atan(----) + 15\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1379 +t0:=1/((a+b/x^2)^3*x) +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 1379 +r0:=-1/4*b^2/(a^3*(b+a*x^2)^2)+b/(a^3*(b+a*x^2))+1/2*log(b+a*x^2)/a^3 +--R +--R +--R 2 4 2 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (2) ---------------------------------------------------- +--R 5 4 4 2 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (3) ---------------------------------------------------- +--R 5 4 4 2 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 744 + +--S 745 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 1379 +t0:=1/((a+b/x^2)^3*x^2) +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 747 + +--S 748 of 1379 +r0:=-1/4*x^3/(a*(b+a*x^2)^2)-3/8*x/(a^2*(b+a*x^2))+_ + 3/8*atan(x*sqrt(a)/sqrt(b))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (3a x + 6a b x + 3b )atan(-----) + (- 5a x - 3b x)\|a \|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------- +--R 4 4 3 2 2 2 +-+ +-+ +--R (8a x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (3a x + 6a b x + 3b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (- 10a x - 6b x)\|- a b +--R / +--R 4 4 3 2 2 2 +-----+ +--R (16a x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3a x + 6a b x + 3b )atan(-------) + (- 5a x - 3b x)\|a b +--R b +--R -------------------------------------------------------------] +--R 4 4 3 2 2 2 +---+ +--R (8a x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 749 + +--S 750 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1379 +t0:=1/((a+b/x^2)^3*x^3) +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1379 +r0:=1/4/(b*(a+b/x^2)^2) +--R +--R +--R 4 +--R x +--R (2) ----------------------- +--R 2 4 2 2 3 +--R 4a b x + 8a b x + 4b +--R Type: Fraction(Polynomial(Integer)) +--E 755 + +--S 756 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2a x - b +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1379 +t0:=1/((a+b/x^2)^3*x^4) +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 759 + +--S 760 of 1379 +r0:=-1/4*x/(a*(b+a*x^2)^2)+1/8*x/(a*b*(b+a*x^2))+_ + 1/8*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (a x + 2a b x + b )atan(-----) + (a x - b x)\|a \|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (a x + 2a b x + b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (2a x - 2b x)\|- a b +--R / +--R 3 4 2 2 2 3 +-----+ +--R (16a b x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (a x + 2a b x + b )atan(-------) + (a x - b x)\|a b +--R b +--R -------------------------------------------------------] +--R 3 4 2 2 2 3 +---+ +--R (8a b x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 761 + +--S 762 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1379 +t0:=1/((a+b/x^2)^3*x^5) +--R +--R +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 1379 +r0:=(-1/4)/(a*(a+b/x^2)^2*x^4) +--R +--R +--R 1 +--R (2) - ----------------------- +--R 3 4 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Fraction(Polynomial(Integer)) +--E 767 + +--S 768 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 4 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 1379 +t0:=1/((a+b/x^2)^3*x^6) +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 771 + +--S 772 of 1379 +r0:=1/4*x/(b*(b+a*x^2)^2)+3/8*x/(b^2*(b+a*x^2))+_ + 3/8*atan(x*sqrt(a)/sqrt(b))/(b^(5/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (3a x + 6a b x + 3b )atan(-----) + (3a x + 5b x)\|a \|b +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x + 16a b x + 8b )\|a \|b +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (3a x + 6a b x + 3b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (6a x + 10b x)\|- a b +--R / +--R 2 2 4 3 2 4 +-----+ +--R (16a b x + 32a b x + 16b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3a x + 6a b x + 3b )atan(-------) + (3a x + 5b x)\|a b +--R b +--R -----------------------------------------------------------] +--R 2 2 4 3 2 4 +---+ +--R (8a b x + 16a b x + 8b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 773 + +--S 774 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1379 +t0:=1/((a+b/x^2)^3*x^7) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 7 2 5 2 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 778 + +--S 779 of 1379 +r0:=1/4/(b*(b+a*x^2)^2)+1/2/(b^2*(b+a*x^2))+log(x)/b^3-1/2*log(b+a*x^2)/b^3 +--R +--R +--R (2) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x) +--R + +--R 2 2 +--R 2a b x + 3b +--R / +--R 2 3 4 4 2 5 +--R 4a b x + 8a b x + 4b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x) +--R + +--R 2 2 +--R 2a b x + 3b +--R / +--R 2 3 4 4 2 5 +--R 4a b x + 8a b x + 4b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1379 +t0:=1/((a+b/x^2)^3*x^8) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1379 +r0:=(-15/8)/(b^3*x)+1/4/(b*x*(b+a*x^2)^2)+5/8/(b^2*x*(b+a*x^2))-_ + 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|a +--R (- 15a x - 30a b x - 15b x)\|a atan(-----) +--R +-+ +--R \|b +--R + +--R 2 4 2 2 +-+ +--R (- 15a x - 25a b x - 8b )\|b +--R / +--R 2 3 5 4 3 5 +-+ +--R (8a b x + 16a b x + 8b x)\|b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 2 5 3 2 | a \| b 2 4 +--R (15a x + 30a b x + 15b x) |- - log(-----------------------) - 30a x +--R \| b 2 +--R a x + b +--R + +--R 2 2 +--R - 50a b x - 16b +--R / +--R 2 3 5 4 3 5 +--R 16a b x + 32a b x + 16b x +--R , +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 3 2 |a \|b 2 4 2 2 +--R (15a x + 30a b x + 15b x) |- atan(-----) - 15a x - 25a b x - 8b +--R \|b a x +--R --------------------------------------------------------------------] +--R 2 3 5 4 3 5 +--R 8a b x + 16a b x + 8b x +--R Type: Union(List(Expression(Integer)),...) +--E 785 + +--S 786 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 15 |- - \|b log(----------------------- + 30\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R 15 |- \|b atan(----- + 15\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 789 + +)clear all + +--S 790 of 1379 +t0:=1/((a+b/x^2)^3*x^9) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 790 + +--S 791 of 1379 +r0:=(-3/2)/(b^3*x^2)+1/4/(b*x^2*(b+a*x^2)^2)+3/4/(b^2*x^2*(b+a*x^2))-_ + 3*a*log(x)/b^4+3/2*a*log(b+a*x^2)/b^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 2 +--R (6a x + 12a b x + 6a b x )log(a x + b) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 6 5 4 6 2 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (6a x + 12a b x + 6a b x )log(a x + b) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 6 5 4 6 2 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 792 + +--S 793 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1379 +t0:=1/((a+b/x^2)^3*x^10) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 10 2 8 2 6 3 4 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1379 +r0:=(-35/24)/(b^3*x^3)+35/8*a/(b^4*x)+1/4/(b*x^3*(b+a*x^2)^2)+_ + 7/8/(b^2*x^3*(b+a*x^2))+35/8*a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 2 3 +-+ x\|a +--R (105a x + 210a b x + 105a b x )\|a atan(-----) +--R +-+ +--R \|b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105a x + 175a b x + 56a b x - 8b )\|b +--R / +--R 2 4 7 5 5 6 3 +-+ +--R (24a b x + 48a b x + 24b x )\|b +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 3 7 2 5 2 3 | a \| b +--R (105a x + 210a b x + 105a b x ) |- - log(---------------------) +--R \| b 2 +--R a x + b +--R + +--R 3 6 2 4 2 2 3 +--R 210a x + 350a b x + 112a b x - 16b +--R / +--R 2 4 7 5 5 6 3 +--R 48a b x + 96a b x + 48b x +--R , +--R +--R +-+ +--R |a +--R +-+ b |- +--R 3 7 2 5 2 3 |a \|b 3 6 +--R (- 105a x - 210a b x - 105a b x ) |- atan(-----) + 105a x +--R \|b a x +--R + +--R 2 4 2 2 3 +--R 175a b x + 56a b x - 8b +--R / +--R 2 4 7 5 5 6 3 +--R 24a b x + 48a b x + 24b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 797 + +--S 798 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - 35a |- \|b atan(-----) - 35a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) --------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 801 + +)clear all + +--S 802 of 1379 +t0:=1/((a+b/x^2)^3*x^11) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 11 2 9 2 7 3 5 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 802 + +--S 803 of 1379 +r0:=(-3/2)/(b^3*x^4)+3*a/(b^4*x^2)+1/4/(b*x^4*(b+a*x^2)^2)+_ + 1/(b^2*x^4*(b+a*x^2))+6*a^2*log(x)/b^5-3*a^2*log(b+a*x^2)/b^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 8 6 6 7 4 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 8 6 6 7 4 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 804 + +--S 805 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1379 +t0:=(a+b/x^2)^(1/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1379 +r0:=-1/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/8*b*x^2*_ + sqrt(a+b/x^2)/a+1/4*x^4*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 14 5 12 4 2 10 3 3 8 +--R - 11a x - 231a b x - 1452a b x - 4048a b x +--R + +--R 2 4 6 5 4 6 2 +--R - 5632a b x - 3840a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 2 5 4 6 2 +--R - 3840a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 5 6 3 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 5 6 3 7 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 2 5 5 6 3 +--R 3840a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x +--R + +--R 2 5 6 6 4 7 2 +--R 7424a b x + 4352a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x +--R + +--R 2 6 4 7 2 +--R 4352a b x + 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 2 6 +--R 3328a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 2 6 +--R - 3840a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (4a b x + 8b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (- a b x - 8a b x - 8b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (- 8a b x - 16b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (2a b x + 16a b x + 16b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1379 +t0:=(a+b/x^2)^(1/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1379 +r0:=1/3*(a+b/x^2)^(3/2)*x^3/a +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + b x) |-------- +--R | 2 +--R \| x +--R (2) ----------------------- +--R 3a +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b +--R (3) ------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 | 2 +--R ((- a x - 5a b x - 4b x) |-------- \|b - 3a b x - 6a b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b +--R (a x + 6a b x + 6a b x )\|b + (3a b x + 7a b x + 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 2 2 +--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 19a b x - 66a b x - 80a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1379 +t0:=(a+b/x^2)^(1/2)*x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1379 +r0:=1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a)+1/2*x^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- a \|b \|a x + b + (- 2a x - 4b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 821 + +--S 822 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 9 4 7 3 2 5 2 3 3 4 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 5 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 4\|- a \|a \|b \|a x + b + (- 2a x - 4b)\|- a \|a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 4a x - 12a b x - 8b x) |-------- \|b - a x - 9a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 16a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1379 +t0:=(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (1) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b |a x + b +--R (2) - \|b atanh(------------) + x |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b - b\|b )log(------------------) + a x \|b +--R x +--R (3) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b +--R (b\|a x + b - b\|b )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ +-+ | 2 +--------+ +--R | 2 +-+ \|b |a x + b +-+ | 2 +--R (b\|a x + b - b\|b )atanh(------------) - x |-------- \|b \|a x + b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R a x \|b + b x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x - 7a b x - 4b )\|b + (- a x - 5a b x - 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b x) |-------- \|b + a x + 6a b x + 9a b x + 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ | 2 +--R (3a x + 4b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (- a x - 5a b x - 4b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1379 +t0:=(a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (2) \|a atanh(-----------) - |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 833 + +--S 834 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x)\|a +--R / +--R +--------+ +--R | 2 +--R 2 8 6 2 4 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 2a x - 2b x) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1379 +t0:=(a+b/x^2)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1379 +r0:=-1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-1/2*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|b |a x + b +-+ +--R - a x atanh(------------) - |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------- +--R +-+ +--R 2x\|b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (2a b x \|a x + b + (- a x - 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (2a x \|b \|a x + b - a x - 2a b x )log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 +-+ | 2 2 4 2 \|b +--R (2a x \|b \|a x + b - a x - 2a b x )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 | 2 4 2 +-+ +--R 4b x \|a x + b + (- 2a x - 4b x )\|b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (5a x + 25a b x + 36a b x + 16b x) |-------- \|b + a x + 14a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 41a b x + 44a b x + 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1379 +t0:=(a+b/x^2)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (- a x - b) |-------- +--R | 2 +--R \| x +--R (2) ----------------------- +--R 2 +--R 3b x +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b )\|b \|a x + b - a x - 6a b x - 9a b x - 4b +--R ----------------------------------------------------------------------- +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((3a x + 7a b x + 4b )\|b + (a x + 5a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (- 3a x - 7a b x - 4b x) |-------- \|b - a x - 6a b x - 9a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 19a b x - 66a b x - 80a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1379 +t0:=(a+b/x^2)^(1/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1379 +r0:=1/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-_ + 1/4*sqrt(a+b/x^2)/x^3-1/8*a*sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 \|b 2 |a x + b +-+ +--R a x atanh(------------) + (- a x - 2b) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 3 +-+ +--R 8b x \|b +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+ +--R ((- 4a b x - 8a b x )\|a x + b + (a x + 8a b x + 8a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (a b x + 10a b x + 24a b x + 16b )\|a x + b +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 4a b x - 20a b x - 32a b x - 16b )\|b +--R / +--R +--------+ +--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4 +--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (a x + 10a b x + 24a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (4a b x + 16a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6 +--R (- a x - 10a b x - 24a b x - 16b x) |-------- \|b - 4a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R - 20a b x - 32a b x - 16b +--R / +--R +--------+ +--R 2 6 3 4 | 2 2 8 2 6 3 4 +-+ +--R (32a b x + 64b x )\|a x + b + (- 8a b x - 64a b x - 64b x )\|b +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 9a x - 129a b x - 552a b x - 1008a b x - 832a b x - 256b ) +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x + 960a b x + 256b +--R / +--R +--------+ +--R | 2 +--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1379 +t0:=(a+b/x^2)^(3/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (1) (a x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1379 +r0:=1/4*(a+b/x^2)^(3/2)*x^4+3/8*b^2*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/sqrt(a)+3/8*b*x^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 21a b x - 56a b x - 40b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|b +--R / +--R +--------+ +--R 2 +---+ +-+ | 2 2 4 2 2 +---+ +--R (32a x + 64b)\|- a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 855 + +--S 856 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 36a b x - 40b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 21a b x - 56a b x - 40b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 21a b x + 56a b x + 40b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R - 11a x - 242a b x - 1683a b x - 5500a b x - 9680a b x +--R + +--R 3 5 5 2 6 3 7 +--R - 9472a b x - 4864a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 3 5 6 2 6 4 7 2 +--R - 7424a b x - 4352a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 13872a b x + 11776a b x + 5376a b x + 1024b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 3 5 6 2 6 4 7 2 +--R 9472a b x + 4864a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 4 5 7 +--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x + 13872a b x +--R + +--R 3 6 5 2 7 3 8 +--R 11776a b x + 5376a b x + 1024a b x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 2 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 3 6 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 3 6 +--R 3840a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 4 6 2 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 36a b x - 40b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 21a b x + 56a b x + 40b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +---+ +-+ +-+ | 2 +--R (32a x + 64b)\|- a \|a \|b \|a x + b +--R + +--R 2 4 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64b )\|- a \|a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - a x - 34a b x - 225a b x - 608a b x - 800a b x - 512a b x +--R + +--R 6 +--R - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 8a x + 104a b x + 456a b x + 952a b x + 1040a b x + 576a b x +--R + +--R 6 +--R 128b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 +--R 128b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 3 3 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1379 +t0:=(a+b/x^2)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (1) (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1379 +r0:=1/3*(a+b/x^2)^(3/2)*x^3-b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))+_ + b*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 3 |a x + b +--R - 3b\|b atanh(------------) + (a x + 4b x) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (- 3a b x - 12a b x )\|a x + b + (a x + 9a b x + 12a b x )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 862 + +--S 863 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 2 3 | 2 2 2 3 +-+ \|b +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 +--R ((- a x - 8a b x - 16b x) |-------- \|b - 3a b x - 12a b x ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 12a b x )\|b + (3a b x + 16a b x + 16b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 8 2 6 2 4 3 2 |a x + b +-+ | 2 +--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1379 +t0:=(a+b/x^2)^(3/2)*x +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1379 +r0:=1/2*(a+b/x^2)^(3/2)*x^2+3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-_ + 3/2*b*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x 2 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R , +--R +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 867 + +--S 868 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 3 6 +--R - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 4 6 2 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 4 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 4 6 2 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 5 6 3 7 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 3 7 +--R 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 9 2 7 2 5 3 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1379 +t0:=(a+b/x^2)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1379 +r0:=-1/2*(a+b/x^2)^(3/2)*x-3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*_ + sqrt(b)+3/2*a*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 2 |a x + b +--R - 3a x\|b atanh(------------) + (2a x - b) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 4a b x + 3a b x + 4b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + 3a b x - 5a b x - 4b )\|b +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x +--R Type: Union(Expression(Integer),...) +--E 874 + +--S 875 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3 +--R ((- 2a x - 7a b x + 4b x) |-------- \|b - 4a b x + 3a b x + 4b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + 3a b x - 5a b x - 4b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (6a b x + 5a b x - 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 10 2 8 2 6 3 4 |a x + b +-+ | 2 +--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 876 + +)clear all + +--S 877 of 1379 +t0:=(a+b/x^2)^(3/2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)+a^(3/2)*atanh(sqrt(a+b/x^2)/sqrt(a))-a*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 |a x + b +--R 3a x \|a atanh(-----------) + (- 4a x - b) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +--R 3x +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R , +--R +--R +--------+ +--R 2 5 3 +---+ | 2 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 5 3 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 879 + +--S 880 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x +--R | 2 +--R \| x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 3 6 +--R - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 4 6 2 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 4 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 4 6 2 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 5 6 3 7 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 3 7 +--R 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 5 +--R - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 5 3 +---+ | 2 2 5 3 +---+ +-+ +--R ((6a x + 24a b x )\|- a \|a x + b + (- 18a x - 24a b x )\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x +--R | 2 +--R \| x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 883 + +)clear all + +--S 884 of 1379 +t0:=(a+b/x^2)^(3/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1379 +r0:=-1/4*(a+b/x^2)^(3/2)/x-3/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_ + sqrt(b)-3/8*a*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 \|b 2 |a x + b +-+ +--R - 3a x atanh(------------) + (- 5a x - 2b) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------------------------- +--R 3 +-+ +--R 8x \|b +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|a x + b +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3a x - 24a b x - 24a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (5a b x + 42a b x + 56a b x + 16b )\|a x + b +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 20a b x - 68a b x - 64a b x - 16b )\|b +--R / +--R +--------+ +--R 6 2 4 +-+ | 2 2 8 2 6 3 4 +--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x +--R Type: Union(Expression(Integer),...) +--E 886 + +--S 887 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (5a x + 42a b x + 56a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (20a b x + 48a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6 +--R (- 5a x - 42a b x - 56a b x - 16b x) |-------- \|b - 20a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R - 68a b x - 64a b x - 16b +--R / +--R +--------+ +--R 6 2 4 | 2 2 8 6 2 4 +-+ +--R (32a b x + 64b x )\|a x + b + (- 8a x - 64a b x - 64b x )\|b +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 2 6 +--R - 1088a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 3 6 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R / +--R +--------+ +--R | 2 +--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1379 +t0:=(a+b/x^2)^(3/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1379 +r0:=-1/5*(a+b/x^2)^(5/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (- a x - 2a b x - b ) |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------- +--R 4 +--R 5b x +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b \|a x + b - a x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80b x )\|a x + b +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80b x )\|b +--R Type: Union(Expression(Integer),...) +--E 891 + +--S 892 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 14a b x + 41a b x + 44a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ 5 10 +--R (- 5a x - 30a b x - 61a b x - 52a b x - 16b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80b x )\|a x + b +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80b x )\|b +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x +--R + +--R 5 3 6 +--R - 2048a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 52a b x - 501a b x - 1970a b x - 3920a b x +--R + +--R 2 5 4 6 2 7 +--R - 4192a b x - 2304a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 10a x + 190a b x + 1182a b x + 3530a b x + 5760a b x +--R + +--R 2 5 4 6 2 7 +--R 5280a b x + 2560a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x +--R + +--R 6 3 7 +--R 2304a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 893 + +)clear all + +--S 894 of 1379 +t0:=(a+b/x^2)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1379 +r0:=-1/6*(a+b/x^2)^(3/2)/x^3+1/16*a^3*atanh(sqrt(b)/_ + (x*sqrt(a+b/x^2)))/b^(3/2)-1/8*a*sqrt(a+b/x^2)/x^3-1/16*a^2*_ + sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 3 5 \|b 2 4 2 2 |a x + b +-+ +--R 3a x atanh(------------) + (- 3a x - 14a b x - 8b ) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------------------------------- +--R 5 +-+ +--R 48b x \|b +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 4 2 8 3 3 6 | 2 +--R (- 18a b x - 96a b x - 96a b x )\|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 +-+ +--R (3a x + 54a b x + 144a b x + 96a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256b ) +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +-+ +--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b )\|b +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 +-+ | 2 3 2 12 +--R (288a b x + 1536a b x + 1536b x )\|b \|a x + b - 48a b x +--R + +--R 2 3 10 4 8 5 6 +--R - 864a b x - 2304a b x - 1536b x +--R Type: Union(Expression(Integer),...) +--E 896 + +--S 897 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10 +--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x +--R + +--R 4 2 8 3 3 6 +--R 144a b x + 96a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10 +--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x +--R + +--R 4 2 8 3 3 6 +--R 144a b x + 96a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (3a x + 68a b x + 404a b x + 912a b x + 832a b x + 256b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (18a b x + 180a b x + 592a b x + 704a b x + 256b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 3a x - 68a b x - 404a b x - 912a b x - 832a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R - 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 | 2 +--R (288a b x + 1536a b x + 1536b x )\|a x + b +--R + +--R 3 12 2 2 10 3 8 4 6 +-+ +--R (- 48a b x - 864a b x - 2304a b x - 1536b x )\|b +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 13a x - 390a b x - 3653a b x - 16172a b x - 39520a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 56576a b x - 47360a b x - 21504a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 898 + +)clear all + +--S 899 of 1379 +t0:=(a+b/x^2)^(5/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1379 +r0:=5/8*b*(a+b/x^2)^(3/2)*x^2+1/4*(a+b/x^2)^(5/2)*x^4+_ + 15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-15/8*b^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 4 2 2 |a x + b +--R 15b \|a atanh(-----------) + (2a x + 9a b x - 8b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) --------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240b x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R , +--R +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480b x)\|- a \|a x + b +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480b x)\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 901 + +--S 902 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240b x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (75a b x + 300a b x + 240b x)\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 6 6 4 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 17 6 15 5 2 13 4 3 11 3 4 9 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 7 6 5 7 3 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 17 6 15 5 2 13 4 3 11 3 4 9 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 7 6 5 7 3 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 8 6 6 7 4 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (75a b x + 300a b x + 240b x)\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480b x)\|- a \|a x + b +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480b x)\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 3 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 905 + +)clear all + +--S 906 of 1379 +t0:=(a+b/x^2)^(5/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1379 +r0:=5/3*b*(a+b/x^2)^(3/2)*x+1/3*(a+b/x^2)^(5/2)*x^3-_ + 5/2*a*b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))-5/2*b^2*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 2 4 2 2 |a x + b +--R - 15a b x\|b atanh(------------) + (2a x + 14a b x - 3b ) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------------------------------------- +--R 6x +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x +--R Type: Union(Expression(Integer),...) +--E 908 + +--S 909 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 2a x - 38a b x - 197a b x - 188a b x + 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 10a b x - 96a b x - 129a b x + 60a b x + 48b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (10a b x + 110a b x + 297a b x + 164a b x - 48b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 19152a b x + 14336a b x + 5888a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8 +--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x +--R + +--R 3 6 6 2 7 4 8 2 9 +--R 25648a b x + 17152a b x + 6400a b x + 1024b +--R / +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 910 + +)clear all + +--S 911 of 1379 +t0:=(a+b/x^2)^(5/2)*x +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1379 +r0:=-5/6*b*(a+b/x^2)^(3/2)+1/2*(a+b/x^2)^(5/2)*x^2+5/2*a^(3/2)*b*_ + atanh(sqrt(a+b/x^2)/sqrt(a))-5/2*a*b*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 4 2 2 |a x + b +--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) -------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R , +--R +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 913 + +--S 914 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 8 6 6 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 9 6 7 7 5 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 5 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1379 +t0:=(a+b/x^2)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1379 +r0:=-5/8*a*(a+b/x^2)^(3/2)*x-1/4*(a+b/x^2)^(5/2)*x-15/8*a^2*_ + atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+15/8*a^2*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 +-+ \|b 2 4 2 2 |a x + b +--R - 15a x \|b atanh(------------) + (8a x - 9a b x - 2b ) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------------------------------- +--R 3 +--R 8x +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128b x +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 8a x - 87a b x - 18a b x + 168a b x + 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 32a b x - 19a b x + 190a b x + 184a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (40a b x + 115a b x - 62a b x - 184a b x - 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128b x +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 19152a b x + 14336a b x + 5888a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8 +--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x +--R + +--R 3 6 6 2 7 4 8 2 9 +--R 25648a b x + 17152a b x + 6400a b x + 1024b +--R / +--R 5 16 4 14 3 2 12 2 3 10 4 8 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 6 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 8 6 6 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1379 +t0:=(a+b/x^2)^(5/2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1379 +r0:=-1/3*a*(a+b/x^2)^(3/2)-1/5*(a+b/x^2)^(5/2)+a^(5/2)*_ + atanh(sqrt(a+b/x^2)/sqrt(a))-a^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 4 +-+ \| x 2 4 2 2 |a x + b +--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 4 +--R 15x +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R , +--R +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 925 + +--S 926 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 11 6 9 7 7 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1379 +t0:=(a+b/x^2)^(5/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1379 +r0:=-5/24*a*(a+b/x^2)^(3/2)/x-1/6*(a+b/x^2)^(5/2)/x-_ + 5/16*a^3*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-5/16*a^2*_ + sqrt(a+b/x^2)/x +--R +--R +--R (2) +--R +--------+ +--R +-+ | 2 +--R 3 5 \|b 2 4 2 2 |a x + b +-+ +--R - 15a x atanh(------------) + (- 33a x - 26a b x - 8b ) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R ------------------------------------------------------------------------ +--R 5 +-+ +--R 48x \|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 4 2 8 3 3 6 | 2 +--R (90a b x + 480a b x + 480a b x )\|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 +-+ +--R (- 15a x - 270a b x - 720a b x - 480a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R (33a b x + 620a b x + 2060a b x + 2448a b x + 1216a b x + 256b ) +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x +--R + +--R 6 +--R - 256b +--R * +--R +-+ +--R \|b +--R / +--R +--------+ +--R 2 10 2 8 3 6 +-+ | 2 3 12 +--R (288a b x + 1536a b x + 1536b x )\|b \|a x + b - 48a b x +--R + +--R 2 2 10 3 8 4 6 +--R - 864a b x - 2304a b x - 1536b x +--R Type: Union(Expression(Integer),...) +--E 932 + +--S 933 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 +--R (90a x + 480a b x + 480a b x )\|b \|a x + b - 15a x +--R + +--R 5 10 4 2 8 3 3 6 +--R - 270a b x - 720a b x - 480a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 +--R (90a x + 480a b x + 480a b x )\|b \|a x + b - 15a x +--R + +--R 5 10 4 2 8 3 3 6 +--R - 270a b x - 720a b x - 480a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R 33a x + 620a b x + 2060a b x + 2448a b x + 1216a b x +--R + +--R 5 +--R 256b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (198a b x + 1212a b x + 1936a b x + 1088a b x + 256b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 33a x - 620a b x - 2060a b x - 2448a b x - 1216a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x - 256b +--R / +--R +--------+ +--R 2 10 2 8 3 6 | 2 +--R (288a b x + 1536a b x + 1536b x )\|a x + b +--R + +--R 3 12 2 10 2 8 3 6 +-+ +--R (- 48a x - 864a b x - 2304a b x - 1536b x )\|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 9 18 8 16 7 2 14 6 3 12 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 10 4 5 8 3 6 6 2 7 4 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 2 9 +--R - 25600a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 9 19 8 17 7 2 15 6 3 13 5 4 11 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 9 3 6 7 2 7 5 8 3 9 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 19 8 17 7 2 15 6 3 13 5 4 11 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 9 3 6 7 2 7 5 8 3 9 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 9 2 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x + 27648a b x +--R + +--R 10 +--R 4096b +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1379 +t0:=(a+b/x^2)^(5/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1379 +r0:=-1/7*(a+b/x^2)^(7/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (- a x - 3a b x - 3a b x - b ) |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------- +--R 6 +--R 7b x +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 7a x + 77a b x + 301a b x + 575a b x + 584a b x + 304a b x +--R + +--R 6 +--R 64b +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R - a x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64b +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448b x )\|a x + b +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b +--R Type: Union(Expression(Integer),...) +--E 937 + +--S 938 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 7a x + 77a b x + 301a b x + 575a b x + 584a b x +--R + +--R 5 2 6 +--R 304a b x + 64b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x +--R + +--R 6 +--R 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R - 7a x - 77a b x - 301a b x - 575a b x - 584a b x - 304a b x +--R + +--R 6 +--R - 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R - a x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64b +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448b x )\|a x + b +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R - 14a x - 490a b x - 5418a b x - 28814a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 86784a b x - 159168a b x - 181760a b x - 126464a b x +--R + +--R 8 3 9 +--R - 49152a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - a x - 101a b x - 1865a b x - 14407a b x - 59906a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 149856a b x - 236992a b x - 239360a b x - 150016a b x +--R + +--R 9 2 10 +--R - 53248a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R 14a x + 504a b x + 5908a b x + 34232a b x + 115598a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 245952a b x + 340928a b x + 308224a b x + 175616a b x +--R + +--R 9 2 10 +--R 57344a b x + 8192b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 101a b x + 1865a b x + 14407a b x + 59906a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 149856a b x + 236992a b x + 239360a b x + 150016a b x +--R + +--R 9 3 10 +--R 53248a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 13 6 11 7 9 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x +--R + +--R 2 5 13 6 11 7 9 +--R - 52736a b x - 32768a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1379 +t0:=(a+b/x^2)^(5/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1379 +r0:=-5/48*a*(a+b/x^2)^(3/2)/x^3-1/8*(a+b/x^2)^(5/2)/x^3+5/128*a^4*_ + atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-5/64*a^2*_ + sqrt(a+b/x^2)/x^3-5/128*a^3*sqrt(a+b/x^2)/(b*x) +--R +--R +--R (2) +--R +-+ +--R 4 7 \|b +--R 15a x atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 15a x - 118a b x - 136a b x - 48b ) |-------- \|b +--R | 2 +--R \| x +--R / +--R 7 +-+ +--R 384b x \|b +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 6 2 12 5 3 10 4 4 8 | 2 +--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +-+ +--R (15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 2 6 4 7 2 8 +--R 57600a b x + 29696a b x + 6144b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 2 6 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144b +--R * +--R +-+ +--R \|b +--R / +--R +--------+ +--R 3 2 14 2 3 12 4 10 5 8 +-+ | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152b x )\|b \|a x + b +--R + +--R 4 2 16 3 3 14 2 4 12 5 10 6 8 +--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x +--R Type: Union(Expression(Integer),...) +--E 942 + +--S 943 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 7 14 6 12 5 2 10 4 3 8 +-+ | 2 +--R (- 120a x - 1200a b x - 2880a b x - 1920a b x )\|b \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 7 14 6 12 5 2 10 4 3 8 +-+ | 2 +--R (- 120a x - 1200a b x - 2880a b x - 1920a b x )\|b \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 15a x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 2 5 4 6 2 7 +--R 57600a b x + 29696a b x + 6144b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 2 11 4 3 9 3 4 7 +--R 120a b x + 2144a b x + 13408a b x + 35840a b x +--R + +--R 2 5 5 6 3 7 +--R 45056a b x + 26624a b x + 6144b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 15a x - 598a b x - 6312a b x - 27120a b x - 55424a b x +--R + +--R 2 5 5 6 3 7 +--R - 57600a b x - 29696a b x - 6144b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 2 6 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144b +--R / +--R +--------+ +--R 3 2 14 2 3 12 4 10 5 8 | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152b x )\|a x + b +--R + +--R 4 16 3 2 14 2 3 12 4 10 5 8 +-+ +--R (- 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x )\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 11 22 10 20 9 2 18 8 3 16 +--R - 17a x - 867a b x - 13923a b x - 108545a b x +--R + +--R 7 4 14 6 5 12 5 6 10 4 7 8 +--R - 489872a b x - 1397536a b x - 2635136a b x - 3337984a b x +--R + +--R 3 8 6 2 9 4 10 2 11 +--R - 2816000a b x - 1519616a b x - 475136a b x - 65536b +--R * +--R +-+ +--R \|b +--R + +--R 11 23 10 21 9 2 19 8 3 17 +--R - a x - 147a b x - 3795a b x - 40081a b x +--R + +--R 7 4 15 6 5 13 5 6 11 4 7 9 +--R - 225648a b x - 765088a b x - 1661056a b x - 2369280a b x +--R + +--R 3 8 7 2 9 5 10 3 11 +--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 11 23 10 21 9 2 19 8 3 17 7 4 15 +--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x +--R + +--R 6 5 13 5 6 11 4 7 9 3 8 7 +--R 1397536a b x + 2635136a b x + 3337984a b x + 2816000a b x +--R + +--R 2 9 5 10 3 11 +--R 1519616a b x + 475136a b x + 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 12 24 11 22 10 2 20 9 3 18 8 4 16 +--R a x + 148a b x + 3942a b x + 43876a b x + 265729a b x +--R + +--R 7 5 14 6 6 12 5 7 10 4 8 8 +--R 990736a b x + 2426144a b x + 4030336a b x + 4583168a b x +--R + +--R 3 9 6 2 10 4 11 2 12 +--R 3520512a b x + 1748992a b x + 507904a b x + 65536b +--R / +--R 8 26 7 24 6 2 22 5 3 20 4 4 18 +--R 17a x + 816a b x + 11424a b x + 71808a b x + 239360a b x +--R + +--R 3 5 16 2 6 14 7 12 8 10 +--R 452608a b x + 487424a b x + 278528a b x + 65536b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 28 8 26 7 2 24 6 3 22 5 4 20 +--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x +--R + +--R 4 5 18 3 6 16 2 7 14 8 12 +--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x +--R + +--R 9 10 +--R - 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 944 + +)clear all + +--S 945 of 1379 +t0:=x^3/(a+b/x^2)^(1/2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1379 +r0:=3/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-3/8*b*x^2*_ + sqrt(a+b/x^2)/a^2+1/4*x^4*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 947 + +--S 948 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 4 +--R - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 5 +--R - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 5 6 3 +--R 3328a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 5 6 3 +--R - 3840a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 4 +--R 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 2 6 +--R - 3328a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 2 6 +--R 3840a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 9 2 2 7 3 5 4 3 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 951 + +)clear all + +--S 952 of 1379 +t0:=x/(a+b/x^2)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1379 +r0:=-1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/2*x^2*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 954 + +--S 955 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 +--R - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 2 +---+ +-+ +--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ 2 5 3 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b +--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 958 + +)clear all + +--S 959 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R [-------------------------------------------------------------, +--R +-+ +--R \|a +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R 2atan(------------------------------) +--R a x +--R -------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 961 + +--S 962 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b 2 3 +-+ +--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2 +--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 +---+ | 2 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ a x +--R \|a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1379 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 |a x + b +--R - \|a x + b + x |-------- +--R | 2 +--R \| x +--R (7) ---------------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R x |-------- \|a x + b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^3) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1379 +r0:=-sqrt(a+b/x^2)/b +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (2) - ----------- +--R b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R (3) -------------------------- +--R +--------+ +--R | 2 +-+ +--R b x\|a x + b - b x\|b +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R (4) -------------------------------------------------------------- +--R +--------+ +--R | 2 +-+ +--R b x\|a x + b - b x\|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^5) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 5 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b^2+a*sqrt(a+b/x^2)/b^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (2a x - b) |-------- +--R | 2 +--R \| x +--R (2) ---------------------- +--R 2 2 +--R 3b x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 6a x - 5a b x + 4b )\|b \|a x + b + 2a x + 9a b x + 3a b x - 4b +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 6a x - 5a b x + 4b )\|b + (- 2a x - 7a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (6a x + 5a b x - 4b x) |-------- \|b + 2a x + 9a b x + 3a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^7) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 7 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1379 +r0:=2/3*a*(a+b/x^2)^(3/2)/b^3-1/5*(a+b/x^2)^(5/2)/b^3-a^2*sqrt(a+b/x^2)/b^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (- 8a x + 4a b x - 3b ) |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------ +--R 3 4 +--R 15b x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b \|a x + b - 8a x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 100a b x - 175a b x - 55a b x - 20a b x - 48b +--R / +--R +--------+ +--R 2 3 9 4 7 5 5 | 2 +--R (15a b x + 180a b x + 240b x )\|a x + b +--R + +--R 2 3 9 4 7 5 5 +-+ +--R (- 75a b x - 300a b x - 240b x )\|b +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (8a x + 92a b x + 83a b x - 28a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 40a x - 140a b x - 63a b x + 4a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 8a x - 100a b x - 175a b x - 55a b x - 20a b x - 48b +--R / +--R +--------+ +--R 2 3 9 4 7 5 5 | 2 +--R (15a b x + 180a b x + 240b x )\|a x + b +--R + +--R 2 3 9 4 7 5 5 +-+ +--R (- 75a b x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^9) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 9 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1379 +r0:=-a^2*(a+b/x^2)^(3/2)/b^4+3/5*a*(a+b/x^2)^(5/2)/b^4-_ + 1/7*(a+b/x^2)^(7/2)/b^4+a^3*sqrt(a+b/x^2)/b^4 +--R +--R +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (16a x - 8a b x + 6a b x - 5b ) |-------- +--R | 2 +--R \| x +--R (2) --------------------------------------------- +--R 4 6 +--R 35b x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x +--R + +--R 5 2 6 +--R 176a b x + 320b +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x +--R + +--R 6 2 7 +--R - 336a b x - 320b +--R / +--R +--------+ +--R 3 4 13 2 5 11 6 9 7 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b +--R + +--R 3 4 13 2 5 11 6 9 7 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x +--R + +--R 5 2 6 +--R 176a b x + 320b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 16a x - 376a b x - 1094a b x - 523a b x + 152a b x +--R + +--R 5 3 6 +--R 16a b x + 320b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 112a x + 840a b x + 1386a b x + 429a b x - 120a b x +--R + +--R 5 3 6 +--R - 176a b x - 320b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x +--R + +--R 6 2 7 +--R - 336a b x - 320b +--R / +--R +--------+ +--R 3 4 13 2 5 11 6 9 7 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b +--R + +--R 3 4 13 2 5 11 6 9 7 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 14a x - 448a b x - 4032a b x - 15360a b x - 28160a b x +--R + +--R 5 3 6 +--R - 24576a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x +--R + +--R 2 5 4 6 2 7 +--R - 39424a b x - 28672a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x +--R + +--R 2 5 4 6 2 7 +--R 52736a b x + 32768a b x + 8192b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 5 6 3 7 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 13 6 11 7 9 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x +--R + +--R 2 5 13 6 11 7 9 +--R - 52736a b x - 32768a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1379 +t0:=x^4/(a+b/x^2)^(1/2) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1379 +r0:=8/15*b^2*x*sqrt(a+b/x^2)/a^3-4/15*b*x^3*sqrt(a+b/x^2)/a^2+_ + 1/5*x^5*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (3a x - 4a b x + 8b x) |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------- +--R 3 +--R 15a +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 8 2 6 | 2 2 10 8 2 6 +-+ +--R (- 15a b x - 40b x )\|a x + b + (3a x + 35a b x + 40b x )\|b +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15a x + 180a b x + 240b )\|b \|a x + b - 75a b x - 300a b x - 240b +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 3a x - 32a b x - 8a b x - 32a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 +--R - 15a b x - 40a b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 +-+ +--R (3a x + 35a b x + 40a b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (15a b x + 40a b x + 8a b x + 96a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 5 4 4 2 3 2 +-+ | 2 5 4 4 2 2 +--R (15a x + 180a b x + 240a b )\|b \|a x + b - 75a b x - 300a b x +--R + +--R 3 3 +--R - 240a b +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x - 512b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1379 +t0:=x^2/(a+b/x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1379 +r0:=-2/3*b*x*sqrt(a+b/x^2)/a^2+1/3*x^3*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x - 2b x) |-------- +--R | 2 +--R \| x +--R (2) ------------------------ +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3b x \|a x + b + (a x + 3b x )\|b +--R (3) --------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ 2 4 | 2 +--R ((- a x - 2a b x + 8b x) |-------- \|b - 3a b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 +-+ 2 5 2 3 3 |a x + b +--R (a x + 3a b x )\|b + (3a b x - 2a b x - 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ | 2 3 2 2 2 +--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 4 3 2 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 8 2 6 2 4 3 2 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1379 +t0:=1/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1379 +r0:=x*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------ +--R a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|b +--R (3) ------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 +-+ |a x + b +--R - x |-------- \|b \|a x + b + a x \|b + b x |-------- +--R | 2 | 2 +--R \| x \| x +--R (4) --------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R a\|b \|a x + b - a b +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b | 2 2 |a x + b +-+ +--R (a x + 2b) |-------- \|a x + b + (- 2a x - 2b) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) - ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|a x + b - \|b +--R \|b log(------------------) +--R x +--R (3) --------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 2 +-+ +-+ +--R \|a x + b - \|b \|b +--R log(------------------) + atanh(------------) +--R x +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (4) --------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1379 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (5) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b +-+ | 2 4 2 |a x + b +--R x |-------- \|b \|a x + b + (- a x - b x ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^4) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 4 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1379 +r0:=1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-1/2*sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|b |a x + b +-+ +--R a x atanh(------------) - |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------------- +--R +-+ +--R 2b x\|b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (- 2a b x \|a x + b + (a x + 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 4 3 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (- 2a x \|b \|a x + b + a x + 2a b x )log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 +-+ | 2 2 4 2 \|b +--R (- 2a x \|b \|a x + b + a x + 2a b x )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 | 2 4 2 2 +-+ +--R 4b x \|a x + b + (- 2a b x - 4b x )\|b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4 2 2 +-+ +--R (- 5a x - 20a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (- a x - 12a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (5a x + 20a b x + 16b x) |-------- \|b + a x + 13a b x + 28a b x +--R | 2 +--R \| x +--R + +--R 3 +--R 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 1379 +t0:=1/(x*sqrt(-a+b/x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +----------+ +--R | 2 +--R |- a x + b +--R x |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1379 +r0:=-atan(sqrt(-a+b/x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R atan(-------------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- a +--R +----------+ +--R +-+ +-+ | 2 +-+ +--R \|a \|b - \|- a x + b \|a +--R 2atan(----------------------------) +--R a x +--R -----------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1013 + +--S 1014 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|a +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a +--R + +--R +----------+ +--R | 2 +--R a x\|- a x + b +--R / +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R + +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R +---+ \| x +--R \|- a atan(-------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +----------+ +--R +----------+ | 2 +--R 3 | 2 +---+ 2 4 2 |- a x + b +--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 +---+ 2 3 | 2 +--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b +--R * +--R +-+ +--R \|b +--R + +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 | 2 +---+ 3 5 2 3 2 +--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x +--R / +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +-+ +--R |---------- \|b +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 5 3 2 | 2 +---+ 3 6 2 4 +--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x +--R + +--R 2 2 +--R 4a b x +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R +----------+ |---------- +--R +-+ +-+ | 2 +-+ | 2 +--R \|a \|b - \|- a x + b \|a \| x +--R 2atan(----------------------------) + atan(-------------) +--R a x +-+ +--R \|a +--R (6) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1379 +d0b:=D(m0b,x) +--R +--R +--R +----------+ +--R | 2 +----------+ +--R |- a x + b | 2 +--R x |---------- - \|- a x + b +--R | 2 +--R \| x +--R (7) ------------------------------ +--R +----------+ +--R +----------+ | 2 +--R | 2 |- a x + b +--R x\|- a x + b |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1379 +t0:=1/(x^2*sqrt(2+b/x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R | 2 +--R 2 |2x + b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1379 +r0:=-asinh(sqrt(b)/(x*sqrt(2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R asinh(-----) +--R +-+ +--R x\|2 +--R (2) - ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (3) -------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1020 + +--S 1021 of 1379 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +--R \|2x + b - \|b \|b +--R log(-----------------) + asinh(-----) +--R x +-+ +--R x\|2 +--R (4) ------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 1022 + +)clear all + +--S 1023 of 1379 +t0:=1/(x^2*sqrt(2-b/x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R | 2 +--R 2 |2x - b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1379 +r0:=-asin(sqrt(b)/(x*sqrt(2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R asin(-----) +--R +-+ +--R x\|2 +--R (2) - ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (3) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 1025 + +--S 1026 of 1379 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|b +--R - \|- b \|b log(-------------------) + b asin(-----) +--R x +-+ +--R x\|2 +--R (4) ---------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 1027 + +)clear all + +--S 1028 of 1379 +t0:=x^3/(a+b/x^2)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1379 +r0:=15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(7/2)-x^4/(a*sqrt(a+b/x^2))-_ + 15/8*b*x^2*sqrt(a+b/x^2)/a^3+5/4*x^4*sqrt(a+b/x^2)/a^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 |a x + b \| x 2 4 2 2 +-+ +--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a +--R | 2 +-+ +--R \| x \|a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b +--R 8a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 +--R (75a b x + 300a b x + 240b )\|b \|a x + b - 15a b x +--R + +--R 2 3 4 4 2 5 +--R - 195a b x - 420a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a \|b +--R / +--R +--------+ +--R 5 4 4 2 3 2 +-+ +-+ | 2 +--R (40a x + 160a b x + 128a b )\|a \|b \|a x + b +--R + +--R 6 6 5 4 4 2 2 3 3 +-+ +--R (- 8a x - 104a b x - 224a b x - 128a b )\|a +--R , +--R +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 +--R (150a b x + 600a b x + 480b )\|b \|a x + b - 30a b x +--R + +--R 2 3 4 4 2 5 +--R - 390a b x - 840a b x - 480b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|b +--R / +--R +--------+ +--R 5 4 4 2 3 2 +---+ +-+ | 2 +--R (40a x + 160a b x + 128a b )\|- a \|b \|a x + b +--R + +--R 6 6 5 4 4 2 2 3 3 +---+ +--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1030 + +--S 1031 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 300a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 195a b x - 420a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (- 75a b x - 300a b x - 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (15a b x + 195a b x + 420a b x + 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+ +--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 4 4 2 3 2 +-+ |a x + b +-+ | 2 +--R (40a x + 160a b x + 128a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b +--R (- 8a x - 104a b x - 224a b x - 128a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 18 5 16 4 2 14 3 3 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x +--R + +--R 2 4 10 5 8 6 6 +--R 16640a b x + 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 8 6 6 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 9 6 7 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 9 6 7 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 +--R - 13a x - 377a b x - 3276a b x - 12896a b x +--R + +--R 3 4 11 2 5 9 6 7 7 5 +--R - 26624a b x - 29952a b x - 17408a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 10 2 6 8 7 6 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 3 5 5 2 6 3 7 +--R 29952a b x + 17408a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 4 5 7 3 6 5 2 7 3 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 +---+ |a x + b +-+ | 2 +--R (- 75a b x - 300a b x - 240b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 +---+ |a x + b +--R (15a b x + 195a b x + 420a b x + 240b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 +-+ |a x + b +-+ | 2 +--R (150a b x + 600a b x + 480b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 +-+ |a x + b +--R (- 30a b x - 390a b x - 840a b x - 480b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+ +--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|- a \|a \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+ +--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 4 4 2 3 2 +---+ +-+ |a x + b +-+ | 2 +--R (40a x + 160a b x + 128a b )\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b +--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 14 3 12 2 2 10 3 8 4 6 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 51a b x + 450a b x + 1520a b x + 2400a b x + 1792a b x +--R + +--R 6 +--R 512b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x +--R + +--R 5 2 6 +--R - 2048a b x - 512b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1379 +t0:=x/(a+b/x^2)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1379 +r0:=-3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-x^2/(a*sqrt(a+b/x^2))+_ + 3/2*x^2*sqrt(a+b/x^2)/a^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R |a x + b \| x 2 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 2 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R 2a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (- a x - 7a b x - 12b x)\|a \|a x + b +--R + +--R 2 5 3 2 +-+ +-+ +--R (3a x + 13a b x + 12b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (6a x + 8a b)\|a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|a +--R , +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (- a x - 7a b x - 12b x)\|- a \|a x + b +--R + +--R 2 5 3 2 +---+ +-+ +--R (3a x + 13a b x + 12b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+ +--R (6a x + 8a b)\|- a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1037 + +--S 1038 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 |a x + b +-+ | 2 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 |a x + b +-+ | 2 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 7a b x - 12b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (a x + 8a b x + 19a b x + 12b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 2 +-+ |a x + b +-+ | 2 +--R (6a x + 8a b)\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 4 3 2 2 2 +-+ |a x + b +--R (- 2a x - 10a b x - 8a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+ +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 3 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +-+ +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 +--R 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x +--R + +--R 5 2 6 +--R 960a b x + 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 2 6 +--R - 1088a b x - 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 2 5 3 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x - 960a b x +--R + +--R 6 +--R - 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 2 +---+ |a x + b +-+ | 2 +--R (9a b x + 12b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 +---+ |a x + b +--R (- 3a b x - 15a b x - 12b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 +-+ |a x + b +-+ | 2 +--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 +-+ |a x + b +--R (6a b x + 30a b x + 24b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 2 4 2 2 +---+ +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +--R (- a x - 7a b x - 12b x)\|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x)\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +---+ +-+ +--R (a x + 8a b x + 19a b x + 12b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 2 +---+ +-+ |a x + b +-+ | 2 +--R (6a x + 8a b)\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 4 3 2 2 2 +---+ +-+ |a x + b +--R (- 2a x - 10a b x - 8a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 5 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 9 2 7 2 5 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1041 + +)clear all + +--S 1042 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+(-1)/(a*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R |a x + b \| x +-+ +--R |-------- atanh(-----------) - \|a +--R | 2 +-+ +--R \| x \|a +--R (2) ------------------------------------ +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R a\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|b \|a x + b - a x - b) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R x\|a \|a x + b - x\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R a\|a \|b \|a x + b + (- a x - a b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 \|- a \|a x + b - \|- a \|b +--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------) +--R a x +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R x\|- a \|a x + b - x\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R a\|- a \|b \|a x + b + (- a x - a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1044 + +--S 1045 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 |a x + b +--R ( |-------- \|b \|a x + b + (- a x - b) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ +--------+ |-------- +--R | 2 +--------+ | 2 | 2 +--R |a x + b +-+ | 2 2 |a x + b \| x +--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------) +--R | 2 | 2 +-+ +--R \| x \| x \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ +-+ +-+ |a x + b | 2 +-+ |a x + b +-+ +--R (\|a \|b + x\|a |-------- )\|a x + b - x\|a |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R + +--R 2 +-+ +--R (- a x - b)\|a +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b +-+ | 2 2 2 +-+ |a x + b +--R a\|a |-------- \|b \|a x + b + (- a x - a b)\|a |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b 3 6 2 4 +--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x +--R | 2 +--R \| x +--R + +--R 2 2 +--R - 16a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (- a x - 12a b x - 16a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (a x + 13a b x + 28a b x + 16b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (5a x + 20a b x + 16a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 3 6 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x + 13a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 +--R 28a b x + 16a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ |a x + b +-+ | 2 2 +---+ |a x + b +--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b +-+ | 2 2 +-+ |a x + b +--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R +---+ +-+ +-+ +---+ +-+ |a x + b | 2 +--R (\|- a \|a \|b + x\|- a \|a |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +-+ 2 +---+ +-+ +--R - x\|- a \|a |-------- \|b + (- a x - b)\|- a \|a +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ +-+ |a x + b +-+ | 2 2 2 +---+ +-+ |a x + b +--R a\|- a \|a |-------- \|b \|a x + b + (- a x - a b)\|- a \|a |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 2 |a x + b +-+ 3 | 2 3 +-+ +--R (- 2x |-------- \|b - a x - 2b x)\|a x + b + (2a x + 2b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 2 |a x + b +--R (a x + 2b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1048 + +)clear all + +--S 1049 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1379 +r0:=1/(b*sqrt(a+b/x^2)) +--R +--R +--R 1 +--R (2) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R b |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R - x\|a x + b + x\|b +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R b\|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1051 + +--S 1052 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (4) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 2 |a x + b +--R b |-------- \|b \|a x + b + (- a b x - b ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 3a b x + 2b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1053 + +)clear all + +--S 1054 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^5) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 5 3 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1379 +r0:=-a/(b^2*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^2 +--R +--R +--R 2 +--R - 2a x - b +--R (2) --------------- +--R +--------+ +--R | 2 +--R 2 2 |a x + b +--R b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 4 2 2 +--R (4a x + 2b)\|b \|a x + b - 2a x - 5a b x - 2b +--R (3) --------------------------------------------------- +--R +--------+ +--R 2 3 3 | 2 2 3 3 +-+ +--R (a b x + 2b x)\|a x + b + (- 2a b x - 2b x)\|b +--R Type: Union(Expression(Integer),...) +--E 1056 + +--S 1057 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((4a x + 2b x) |-------- \|b + 2a x + 5a b x + 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (- 4a x - 6a b x - 2b )\|b + (- 2a x - 5a b x - 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 4 3 2 |a x + b | 2 2 4 3 2 |a x + b +-+ +--R (a b x + 2b x ) |-------- \|a x + b + (- 2a b x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 4a x - 8b x) |-------- \|b - a x - 8a b x - 8b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (4a x + 12a b x + 8b )\|b + (a x + 8a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 9 2 7 2 5 3 3 |a x + b | 2 +--R (a x + 9a b x + 16a b x + 8b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (- 4a x - 16a b x - 20a b x - 8b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 7 5 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b^3+a^2/(b^3*sqrt(a+b/x^2))+2*a*sqrt(a+b/x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R 8a x + 4a b x - b +--R (2) -------------------- +--R +--------+ +--R | 2 +--R 3 4 |a x + b +--R 3b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (- 32a x - 80a b x - 28a b x + 8b )\|b \|a x + b + 8a x + 68a b x +--R + +--R 2 2 4 3 2 4 +--R 95a b x + 24a b x - 8b +--R / +--R +--------+ +--R 2 3 7 4 5 5 3 | 2 +--R (3a b x + 24a b x + 24b x )\|a x + b +--R + +--R 2 3 7 4 5 5 3 +-+ +--R (- 12a b x - 36a b x - 24b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1061 + +--S 1062 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 32a x - 80a b x - 28a b x + 8b x) |-------- \|b - 8a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 68a b x - 95a b x - 24a b x + 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (32a x + 112a b x + 108a b x + 20a b x - 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (8a x + 68a b x + 95a b x + 24a b x - 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 3 8 4 6 5 4 |a x + b | 2 +--R (3a b x + 24a b x + 24b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 3 8 4 6 5 4 |a x + b +-+ +--R (- 12a b x - 36a b x - 24b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 32a b x - 160a b x - 256a b x - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^9) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 9 7 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1379 +r0:=a*(a+b/x^2)^(3/2)/b^4-1/5*(a+b/x^2)^(5/2)/b^4-a^3/(b^4*_ + sqrt(a+b/x^2))-3*a^2*sqrt(a+b/x^2)/b^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R - 16a x - 8a b x + 2a b x - b +--R (2) --------------------------------- +--R +--------+ +--R | 2 +--R 4 6 |a x + b +--R 5b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x +--R + +--R 6 +--R - 32b +--R / +--R +--------+ +--R 3 4 11 2 5 9 6 7 7 5 | 2 +--R (5a b x + 90a b x + 240a b x + 160b x )\|a x + b +--R + +--R 3 4 11 2 5 9 6 7 7 5 +-+ +--R (- 30a b x - 190a b x - 320a b x - 160b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1066 + +--S 1067 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 16a x + 296a b x + 910a b x + 861a b x + 178a b x - 16a b x +--R + +--R 6 +--R 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 6 +-+ +--R (- 96a x - 656a b x - 1316a b x - 954a b x - 166a b x - 32b )\|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x +--R + +--R 6 +--R - 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 4 12 2 5 10 6 8 7 6 |a x + b | 2 +--R (5a b x + 90a b x + 240a b x + 160b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 4 12 2 5 10 6 8 7 6 |a x + b +-+ +--R (- 30a b x - 190a b x - 320a b x - 160b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 2 6 +--R - 6144a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 2 6 +--R 7168a b x + 2048b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x +--R + +--R 6 +--R 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R a x + 73a b x + 912a b x + 4424a b x + 10496a b x +--R + +--R 2 5 11 6 9 7 7 +--R 13056a b x + 8192a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - 12a x - 304a b x - 2364a b x - 8472a b x - 16128a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 16896a b x - 9216a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1379 +t0:=x^2/(a+b/x^2)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1379 +r0:=-x^3/(a*sqrt(a+b/x^2))-8/3*b*x*sqrt(a+b/x^2)/a^3+4/3*x^3*sqrt(a+b/x^2)/a^2 +--R +--R +--R 2 4 2 2 +--R a x - 4a b x - 8b +--R (2) -------------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R 3a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4b x \|a x + b + (a x + 4b x )\|b +--R (3) --------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (3a x + 24a b x + 24b )\|b \|a x + b - 12a b x - 36a b x - 24b +--R Type: Union(Expression(Integer),...) +--E 1071 + +--S 1072 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- a x - 4a b x + 32a b x + 96a b x + 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 |a x + b +--R - 4a b x |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4 +--R (a x + 4a b x ) |-------- \|b + 4a b x - 4a b x - 72a b x +--R | 2 +--R \| x +--R + +--R 4 2 5 +--R - 128a b x - 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 5 4 3 3 2 |a x + b +-+ | 2 +--R (3a x + 24a b x + 24a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 5 4 2 3 3 3 |a x + b +--R (- 12a b x - 36a b x - 24a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 10 2 2 8 3 6 4 4 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1073 + +)clear all + +--S 1074 of 1379 +t0:=1/(a+b/x^2)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1379 +r0:=-x/(a*sqrt(a+b/x^2))+2*x*sqrt(a+b/x^2)/a^2 +--R +--R +--R 2 +--R a x + 2b +--R (2) -------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R x \|b +--R (3) ------------------------------------------ +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (a x + 2b)\|b \|a x + b - 2a b x - 2b +--R Type: Union(Expression(Integer),...) +--E 1076 + +--S 1077 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +--R 2 4 2 2 +-+ | 2 2 5 |a x + b +-+ 2 4 +--R (- a x - 4a b x - 4b )\|b \|a x + b + a x |-------- \|b + 2a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R 6a b x + 4b +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 3 3 2 |a x + b +-+ | 2 3 3 2 2 |a x + b +--R (a x + 2a b x) |-------- \|b \|a x + b + (- 2a b x - 2a b x) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R 5 3 |a x + b +-+ 2 6 4 2 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ 2 7 5 2 3 |a x + b +--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 9a b x + 16a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 4a x - 16a b x - 20a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1078 + +)clear all + +--S 1079 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1379 +r0:=(-1)/(a*x*sqrt(a+b/x^2)) +--R +--R +--R 1 +--R (2) - -------------- +--R +--------+ +--R | 2 +--R |a x + b +--R a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|b +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R b\|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1081 + +--S 1082 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 2 +--R +-+ | 2 3 |a x + b +-+ 2 2 +--R b\|b \|a x + b + a x |-------- \|b - a b x - b +--R | 2 +--R \| x +--R (4) --------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 3 2 |a x + b +--R a b x |-------- \|b \|a x + b + (- a b x - a b x) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1083 + +)clear all + +--S 1084 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 4 2 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)+1/(b*x*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +-+ +--R |a x + b \|b +-+ +--R - x |-------- atanh(------------) + \|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------- +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b + (- a x - b)\|b )log(------------------) - a x \|b +--R x +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 3 +--R b \|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 3 |a x + b +--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 3 |a x + b +--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R +--------+ | 2 +--R | 2 2 +-+ 3 |a x + b +--R - b\|a x + b + (a x + b)\|b - a x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b | 2 3 2 |a x + b +-+ +--R b x |-------- \|a x + b + (- a b x - b x) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 6 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1088 + +)clear all + +--S 1089 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^6) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 6 4 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1379 +r0:=3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(5/2)+_ + 1/(b*x^3*sqrt(a+b/x^2))-3/2*sqrt(a+b/x^2)/(b^2*x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 3 |a x + b \|b 2 +-+ +--R 3a x |-------- atanh(------------) + (- 3a x - b)\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 3 |a x + b +-+ +--R 2b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R ((- 9a b x - 12a b x )\|a x + b + (3a x + 15a b x + 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 3a b x + 5a b x + 4b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + a b x - 7a b x - 4b )\|b +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 2 3 6 4 4 5 2 +--R (6a b x + 8b x )\|b \|a x + b - 2a b x - 10a b x - 8b x +--R Type: Union(Expression(Integer),...) +--E 1091 + +--S 1092 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 |a x + b +-+ | 2 +--R (- 9a x - 12a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (3a x + 15a b x + 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 |a x + b +-+ | 2 +--R (- 9a x - 12a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (3a x + 15a b x + 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3 +--R ((- 3a x + 5a b x + 4b x) |-------- \|b + 9a b x + 15a b x + 4b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3a x - 16a b x - 17a b x - 4b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (2a x + a b x - 7a b x - 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 5 4 3 |a x + b | 2 +--R (6a b x + 8b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 2 7 3 5 4 3 |a x + b +-+ +--R (- 2a b x - 10a b x - 8b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 7a x - 56a b x - 112a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 104a b x + 144a b x + 64b +--R / +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1093 + +)clear all + +--S 1094 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^8) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 8 6 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1379 +r0:=-15/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(7/2)+_ + 1/(b*x^5*sqrt(a+b/x^2))-5/4*sqrt(a+b/x^2)/(b^2*x^3)+_ + 15/8*a*sqrt(a+b/x^2)/(b^3*x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 2 5 |a x + b \|b 2 4 2 2 +-+ +--R - 15a x |-------- atanh(------------) + (15a x + 5a b x - 2b )\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) --------------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 5 |a x + b +-+ +--R 8b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (75a b x + 300a b x + 240a b x )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 +-+ +--R (- 15a x - 195a b x - 420a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (25a b x - 25a b x - 170a b x - 56a b x + 32b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b )\|b +--R / +--R +--------+ +--R 2 4 8 5 6 6 4 +-+ | 2 3 4 10 2 5 8 +--R (40a b x + 160a b x + 128b x )\|b \|a x + b - 8a b x - 104a b x +--R + +--R 6 6 7 4 +--R - 224a b x - 128b x +--R Type: Union(Expression(Integer),...) +--E 1096 + +--S 1097 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 |a x + b +-+ | 2 +--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 |a x + b +--R (- 15a x - 195a b x - 420a b x - 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 |a x + b +-+ | 2 +--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 |a x + b +--R (- 15a x - 195a b x - 420a b x - 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (25a x - 25a b x - 170a b x - 56a b x + 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 75a b x - 325a b x - 330a b x - 40a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (15a x + 200a b x + 483a b x + 354a b x + 24a b x - 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 9 5 7 6 5 |a x + b | 2 +--R (40a b x + 160a b x + 128b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 3 11 2 4 9 5 7 6 5 |a x + b +-+ +--R (- 8a b x - 104a b x - 224a b x - 128b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 +--R - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 +--R - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 +--R 1024b +--R / +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 8 6 6 +--R 3840a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1098 + +)clear all + +--S 1099 of 1379 +t0:=x^3/(a+b/x^2)^(5/2) +--R +--R +--R 7 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1379 +r0:=-1/3*x^4/(a*(a+b/x^2)^(3/2))+35/8*b^2*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/a^(9/2)-7/3*x^4/(a^2*sqrt(a+b/x^2))-35/8*b*x^2*_ + sqrt(a+b/x^2)/a^4+35/12*x^4*sqrt(a+b/x^2)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 2 3 |a x + b \| x +--R (105a b x + 105b ) |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x - 21a b x - 140a b x - 105b )\|a +--R / +--R +--------+ +--R | 2 +--R 5 2 4 +-+ |a x + b +--R (24a x + 24a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 8 3 3 6 2 4 4 5 2 6 +-+ +--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R - 105a b x - 2730a b x - 13545a b x - 26040a b x - 21840a b x +--R + +--R 7 +--R - 6720b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +-+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a \|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +-+ +--R \|a +--R , +--R +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b ) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R - 210a b x - 5460a b x - 27090a b x - 52080a b x - 43680a b x +--R + +--R 7 +--R - 13440b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- a \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +---+ +-+ +--R \|- a \|b +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +---+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +---+ +--R \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1101 + +--S 1102 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 +--R - 105a b x - 2730a b x - 13545a b x - 26040a b x +--R + +--R 6 2 7 +--R - 21840a b x - 6720b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x +--R + +--R 7 +--R 6720b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x +--R + +--R 5 2 6 +--R 20720a b x + 6720b +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x +--R + +--R 2 5 4 6 2 7 +--R - 32424a b x - 24080a b x - 6720b +--R * +--R +-+ +--R \|a +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 8 24 7 22 6 2 20 5 3 18 +--R 17a x + 816a b x + 11424a b x + 71808a b x +--R + +--R 4 4 16 3 5 14 2 6 12 7 10 +--R 239360a b x + 452608a b x + 487424a b x + 278528a b x +--R + +--R 8 8 +--R 65536b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 9 24 8 22 7 2 20 6 3 18 +--R - 17a x - 816a b x - 11424a b x - 71808a b x +--R + +--R 5 4 16 4 5 14 3 6 12 2 7 10 +--R - 239360a b x - 452608a b x - 487424a b x - 278528a b x +--R + +--R 8 8 +--R - 65536a b x +--R * +--R +-+ +--R \|b +--R + +--R 9 25 8 23 7 2 21 6 3 19 5 4 17 +--R - a x - 144a b x - 3360a b x - 29568a b x - 126720a b x +--R + +--R 4 5 15 3 6 13 2 7 11 8 9 +--R - 292864a b x - 372736a b x - 245760a b x - 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 25 8 23 7 2 21 6 3 19 5 4 17 +--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x +--R + +--R 4 5 15 3 6 13 2 7 11 8 9 +--R 419584a b x + 665600a b x + 618496a b x + 311296a b x +--R + +--R 9 7 +--R 65536b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 25 8 23 7 2 21 6 3 19 +--R 17a x + 816a b x + 11424a b x + 71808a b x +--R + +--R 5 4 17 4 5 15 3 6 13 2 7 11 +--R 239360a b x + 452608a b x + 487424a b x + 278528a b x +--R + +--R 8 9 +--R 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 25 8 23 7 2 21 6 3 19 +--R - 17a x - 833a b x - 12240a b x - 83232a b x +--R + +--R 5 4 17 4 5 15 3 6 13 2 7 11 +--R - 311168a b x - 691968a b x - 940032a b x - 765952a b x +--R + +--R 8 9 9 7 +--R - 344064a b x - 65536b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 26 8 24 7 2 22 6 3 20 5 4 18 +--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x +--R + +--R 4 5 16 3 6 14 2 7 12 8 10 +--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x +--R + +--R 9 8 +--R - 65536b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 26 9 24 8 2 22 7 3 20 6 4 18 +--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x +--R + +--R 5 5 16 4 6 14 3 7 12 2 8 10 9 8 +--R 419584a b x + 665600a b x + 618496a b x + 311296a b x + 65536a b x +--R / +--R 11 21 10 19 9 2 17 8 3 15 +--R 17a x + 850a b x + 13073a b x + 95472a b x +--R + +--R 7 4 13 6 5 11 5 6 9 4 7 7 +--R 394400a b x + 1003136a b x + 1632000a b x + 1705984a b x +--R + +--R 3 8 5 2 9 3 10 +--R 1110016a b x + 409600a b x + 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 11 22 10 20 9 2 18 8 3 16 +--R - a x - 147a b x - 3795a b x - 40081a b x +--R + +--R 7 4 14 6 5 12 5 6 10 4 7 8 +--R - 225648a b x - 765088a b x - 1661056a b x - 2369280a b x +--R + +--R 3 8 6 2 9 4 10 2 11 +--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 11 22 10 20 9 2 18 8 3 16 7 4 14 +--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x +--R + +--R 6 5 12 5 6 10 4 7 8 3 8 6 +--R 1397536a b x + 2635136a b x + 3337984a b x + 2816000a b x +--R + +--R 2 9 4 10 2 11 +--R 1519616a b x + 475136a b x + 65536b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 12 23 11 21 10 2 19 9 3 17 8 4 15 +--R - a x - 147a b x - 3795a b x - 40081a b x - 225648a b x +--R + +--R 7 5 13 6 6 11 5 7 9 4 8 7 +--R - 765088a b x - 1661056a b x - 2369280a b x - 2213888a b x +--R + +--R 3 9 5 2 10 3 11 +--R - 1306624a b x - 442368a b x - 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R +---+ |a x + b +-+ | 2 +--R \|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x +--R + +--R 7 +--R 6720b +--R * +--R +--------+ +--R | 2 +--R +---+ |a x + b +--R \|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R +-+ |a x + b +-+ | 2 +--R \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 +--R - 210a b x - 5460a b x - 27090a b x - 52080a b x +--R + +--R 6 2 7 +--R - 43680a b x - 13440b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x +--R + +--R 5 2 6 +--R 20720a b x + 6720b +--R * +--R +---+ +-+ +-+ +--R \|- a \|a \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +--R \|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +-+ +--R \|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x +--R + +--R 2 5 4 6 2 7 +--R - 32424a b x - 24080a b x - 6720b +--R * +--R +---+ +-+ +--R \|- a \|a +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +---+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|a +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +--R \|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 6 20 5 18 4 2 16 3 3 14 +--R - 14a x - 448a b x - 4032a b x - 15360a b x +--R + +--R 2 4 12 5 10 6 8 +--R - 28160a b x - 24576a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 39424a b x - 28672a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x +--R + +--R 2 5 11 6 9 7 7 +--R 52736a b x + 32768a b x + 8192b x +--R * +--R +-+ +--R \|b +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 12 6 10 7 8 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 100a b x + 1765a b x + 12642a b x + 47264a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 102592a b x + 134400a b x + 104960a b x + 45056a b x + 8192b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R - 14a x - 490a b x - 5418a b x - 28814a b x - 86784a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R - 159168a b x - 181760a b x - 126464a b x - 49152a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1379 +t0:=x/(a+b/x^2)^(5/2) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1379 +r0:=-1/3*x^2/(a*(a+b/x^2)^(3/2))-5/2*b*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/a^(7/2)-5/3*x^2/(a^2*sqrt(a+b/x^2))+5/2*x^2*sqrt(a+b/x^2)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 2 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R 2 4 2 2 +-+ +--R (3a x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 2 +--R 4 2 3 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a \|b +--R / +--R +--------+ +--R 6 6 5 4 4 2 2 3 3 +-+ +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|a \|b \|a x + b +--R + +--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+ +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a +--R , +--R +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|b +--R / +--R +--------+ +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|b \|a x + b +--R + +--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+ +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1108 + +--S 1109 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+ |a x + b +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 18 5 16 4 2 14 3 3 12 +--R - 13a x - 364a b x - 2912a b x - 9984a b x +--R + +--R 2 4 10 5 8 6 6 +--R - 16640a b x - 13312a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 8 6 6 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 9 6 7 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 9 6 7 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 9 6 7 7 5 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 10 2 6 8 7 6 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 4 5 7 3 6 5 2 7 3 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 19 9 17 8 2 15 7 3 13 6 4 11 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 5 5 9 4 6 7 3 7 5 2 8 3 9 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 +---+ |a x + b +-+ +--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +---+ +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 +-+ |a x + b +--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b +-+ +--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+ +-+ |a x + b +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 14 3 12 2 2 10 3 8 4 6 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x +--R + +--R 6 2 7 +--R 2304a b x + 512b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 4 6 2 7 +--R - 5280a b x - 2560a b x - 512b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1112 + +)clear all + +--S 1113 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x) +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2))+atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)+_ + (-1)/(a^2*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 |a x + b \| x 2 +-+ +--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a +--R | 2 +-+ +--R \| x \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 2 2 +-+ |a x + b +--R (3a x + 3a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x +--R + +--R 2 2 3 +--R - 27a b x - 12b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (4a x + 19a b x + 12b x)\|a \|a x + b +--R + +--R 2 5 3 2 +-+ +-+ +--R (- 12a x - 25a b x - 12b x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (9a x + 21a b x + 12a b )\|a \|b \|a x + b +--R + +--R 5 6 4 4 3 2 2 2 3 +-+ +--R (- 3a x - 18a b x - 27a b x - 12a b )\|a +--R , +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x +--R + +--R 2 2 3 +--R - 54a b x - 24b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (4a x + 19a b x + 12b x)\|- a \|a x + b +--R + +--R 2 5 3 2 +---+ +-+ +--R (- 12a x - 25a b x - 12b x)\|- a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (9a x + 21a b x + 12a b )\|- a \|b \|a x + b +--R + +--R 5 6 4 4 3 2 2 2 3 +---+ +--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1115 + +--S 1116 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b +-+ | 2 +--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (3a x + 18a b x + 27a b x + 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +-+ +--R (12a x + 25a b x + 12b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (4a x + 19a b x + 12b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 4 3 2 2 2 +-+ |a x + b +-+ | 2 +--R (9a x + 21a b x + 12a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 6 4 4 3 2 2 2 3 +-+ |a x + b +--R (- 3a x - 18a b x - 27a b x - 12a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+ +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x +--R + +--R 5 3 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 2 5 3 6 +--R 1088a b x + 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 4 6 2 7 +--R - 2352a b x - 1216a b x - 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x +--R + +--R 2 5 4 6 2 7 +--R 2928a b x + 1344a b x + 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 3 5 5 2 6 3 7 +--R - 2352a b x - 1216a b x - 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 +---+ |a x + b +-+ | 2 +--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 +---+ |a x + b +--R (3a x + 18a b x + 27a b x + 12b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 +-+ |a x + b +-+ | 2 +--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 2 4 2 2 +---+ +-+ +-+ +--R (12a x + 25a b x + 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +--R (4a x + 19a b x + 12b x)\|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x)\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +---+ +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 4 3 2 2 2 +---+ +-+ |a x + b +-+ | 2 +--R (9a x + 21a b x + 12a b )\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 6 4 4 3 2 2 2 3 +---+ +-+ |a x + b +--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 5 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 9 2 7 2 5 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^3) +--R +--R +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)) +--R +--R +--R 2 +--R x +--R (2) -------------------------- +--R +--------+ +--R | 2 +--R 2 2 |a x + b +--R (3a b x + 3b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (- a x - 4b x )\|a x + b + (3a x + 4b x )\|b +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 4 2 +-+ 5 3 |a x + b | 2 +--R ((- 3a x - 4b x )\|b + (- a x - 4b x ) |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 3 |a x + b +-+ 2 6 4 2 2 +--R (3a x + 4b x ) |-------- \|b + a x + 5a b x + 4b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 3 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +-+ 3 7 2 5 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x)\|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^5) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (a x + 2a b x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1379 +r0:=-1/3*a/(b^2*(a+b/x^2)^(3/2))+1/(b^2*sqrt(a+b/x^2)) +--R +--R +--R 2 +--R 2a x + 3b +--R (2) -------------------------- +--R +--------+ +--R | 2 +--R 2 2 3 |a x + b +--R (3a b x + 3b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 5 3 2 | 2 2 5 3 2 +-+ +--R (- 2a x - 11a b x - 12b x)\|a x + b + (6a x + 17a b x + 12b x)\|b +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 2 +-+ +--R (- 6a x - 17a b x - 12b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (- 2a x - 11a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (6a x + 17a b x + 12b x) |-------- \|b + 2a x + 13a b x + 23a b x +--R | 2 +--R \| x +--R + +--R 3 +--R 12b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^7) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1379 +r0:=1/3*a^2/(b^3*(a+b/x^2)^(3/2))-2*a/(b^3*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R - 8a x - 12a b x - 3b +--R (2) ---------------------------- +--R +--------+ +--R | 2 +--R 3 4 4 2 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (32a x + 112a b x + 108a b x + 24b )\|b \|a x + b - 8a x - 76a b x +--R + +--R 2 2 4 3 2 4 +--R - 163a b x - 120a b x - 24b +--R / +--R +--------+ +--R 3 3 7 2 4 5 5 3 6 | 2 +--R (3a b x + 27a b x + 48a b x + 24b x)\|a x + b +--R + +--R 3 3 7 2 4 5 5 3 6 +-+ +--R (- 12a b x - 48a b x - 60a b x - 24b x)\|b +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (32a x + 112a b x + 108a b x + 24b x) |-------- \|b + 8a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 76a b x + 163a b x + 120a b x + 24b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 32a x - 144a b x - 220a b x - 132a b x - 24b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 8a x - 76a b x - 163a b x - 120a b x - 24b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 3 8 2 4 6 5 4 6 2 |a x + b | 2 +--R (3a b x + 27a b x + 48a b x + 24b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 3 8 2 4 6 5 4 6 2 |a x + b +-+ +--R (- 12a b x - 48a b x - 60a b x - 24b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 32a b x - 160a b x - 256a b x - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 5 5 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 3 +--R 128b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x +--R + +--R 5 5 6 3 +--R - 576a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^9) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 9 7 2 5 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1379 +r0:=-1/3*a^3/(b^4*(a+b/x^2)^(3/2))-1/3*(a+b/x^2)^(3/2)/b^4+_ + 3*a^2/(b^4*sqrt(a+b/x^2))+3*a*sqrt(a+b/x^2)/b^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R 16a x + 24a b x + 6a b x - b +--R (2) -------------------------------- +--R +--------+ +--R | 2 +--R 4 6 5 4 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 96a x - 656a b x - 1316a b x - 954a b x - 160a b x + 32b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x +--R + +--R 6 +--R - 32b +--R / +--R +--------+ +--R 4 4 11 3 5 9 2 6 7 7 5 8 3 | 2 +--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x )\|a x + b +--R + +--R 4 4 11 3 5 9 2 6 7 7 5 8 3 +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 96a x - 656a b x - 1316a b x - 954a b x - 160a b x +--R + +--R 5 +--R 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 16a x - 312a b x - 1206a b x - 1771a b x - 1038a b x +--R + +--R 5 2 6 +--R - 144a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 96a x + 752a b x + 1972a b x + 2270a b x + 1114a b x +--R + +--R 5 2 6 +--R 128a b x - 32b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x +--R + +--R 5 3 6 +--R 144a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b +--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 2 6 +--R - 6144a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 2 6 +--R 7168a b x + 2048b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x +--R + +--R 6 +--R 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 8 21 7 19 6 2 17 5 3 15 4 4 13 +--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x +--R + +--R 3 5 11 2 6 9 7 7 8 5 +--R 23552a b x + 21248a b x + 10240a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 8 21 7 19 6 2 17 5 3 15 4 4 13 +--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x +--R + +--R 3 5 11 2 6 9 7 7 8 5 +--R - 33024a b x - 26112a b x - 11264a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1379 +t0:=x^2/(a+b/x^2)^(5/2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1379 +r0:=-1/3*x^3/(a*(a+b/x^2)^(3/2))-2*x^3/(a^2*sqrt(a+b/x^2))-_ + 16/3*b*x*sqrt(a+b/x^2)/a^4+8/3*x^3*sqrt(a+b/x^2)/a^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x - 6a b x - 24a b x - 16b +--R (2) -------------------------------- +--R +--------+ +--R | 2 +--R 5 3 4 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 10 2 8 | 2 2 12 10 2 8 +-+ +--R (- 6a b x - 12b x )\|a x + b + (a x + 12a b x + 12b x )\|b +--R / +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (3a x + 57a b x + 198a b x + 240a b x + 96b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 18a b x - 132a b x - 306a b x - 288a b x - 96b +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 12a b x + 84a b x + 704a b x + 1632a b x +--R + +--R 5 2 6 +--R 1536a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 2 9 |a x + b +--R (- 6a b x - 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 6 13 5 11 4 2 9 |a x + b +-+ 6 12 5 2 10 +--R (a x + 12a b x + 12a b x ) |-------- \|b + 6a b x + 2a b x +--R | 2 +--R \| x +--R + +--R 4 3 8 3 4 6 2 5 4 6 2 7 +--R - 308a b x - 1360a b x - 2336a b x - 1792a b x - 512b +--R / +--R +--------+ +--R | 2 +--R 8 9 7 7 6 2 5 5 3 3 4 4 |a x + b +-+ +--R (3a x + 57a b x + 198a b x + 240a b x + 96a b x) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 8 9 7 2 7 6 3 5 5 4 3 4 5 |a x + b +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 7 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 8 6 6 +--R - 6144a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 8 6 6 +--R 7168a b x + 2048b x +--R * +--R +-+ +--R \|b +--R + +--R 6 19 5 17 4 2 15 3 3 13 2 4 11 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x +--R + +--R 5 9 6 7 +--R 6144a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 23552a b x + 21248a b x + 10240a b x + 2048b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 33024a b x - 26112a b x - 11264a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1379 +t0:=1/(a+b/x^2)^(5/2) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1379 +r0:=-1/3*x/(a*(a+b/x^2)^(3/2))-4/3*x/(a^2*sqrt(a+b/x^2))+_ + 8/3*x*sqrt(a+b/x^2)/a^3 +--R +--R +--R 2 4 2 2 +--R 3a x + 12a b x + 8b +--R (2) --------------------------- +--R +--------+ +--R | 2 +--R 4 3 3 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4b x \|a x + b + (3a x + 4b x )\|b +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (3a x + 27a b x + 48a b x + 24b )\|b \|a x + b - 12a b x - 48a b x +--R + +--R 3 2 4 +--R - 60a b x - 24b +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 3a x - 36a b x - 128a b x - 160a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 |a x + b +--R - 4a b x |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4 +--R (3a x + 4a b x ) |-------- \|b + 12a b x + 84a b x + 200a b x +--R | 2 +--R \| x +--R + +--R 4 2 5 +--R 192a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 6 7 5 5 4 2 3 3 3 |a x + b +-+ | 2 +--R (3a x + 27a b x + 48a b x + 24a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 7 5 2 5 4 3 3 3 4 |a x + b +--R (- 12a b x - 48a b x - 60a b x - 24a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 10 2 2 8 3 6 4 4 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 +--R 128b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x +--R + +--R 5 2 6 +--R - 576a b x - 128b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^2) +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x)+(-2/3)/(a^2*x*sqrt(a+b/x^2)) +--R +--R +--R 2 +--R - 3a x - 2b +--R (2) --------------------------- +--R +--------+ +--R | 2 +--R 3 3 2 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3b x \|a x + b + (2a x + 3b x )\|b +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 3 +-+ 2 5 |a x + b | 2 +--R ((9a b x + 18a b x + 8b )\|b - 3a b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 |a x + b +-+ 3 6 2 2 4 3 2 4 +--R (2a x + 3a b x ) |-------- \|b - 3a b x - 17a b x - 22a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 5 3 2 3 2 3 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 7 4 2 5 3 3 3 2 4 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 4 3 2 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 8 2 6 2 4 3 2 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^4) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x^3) +--R +--R +--R 1 +--R (2) - --------------------------- +--R +--------+ +--R | 2 +--R 2 3 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 3 +-+ 2 5 2 3 |a x + b | 2 +--R ((3a b x + 4b )\|b + (- 3a b x - 6a b x ) |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +-+ 2 2 4 3 2 4 +--R (a x + 6a b x + 6a b x ) |-------- \|b - a b x - 5a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 5 2 3 3 4 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 2 7 3 3 5 2 4 3 5 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^6) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)*x^3)-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_ + b^(5/2)+1/(b^2*x*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 3 |a x + b \|b 2 +-+ +--R (- 3a x - 3b x) |-------- atanh(------------) + (3a x + 4b)\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 3 3 |a x + b +-+ +--R (3a b x + 3b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (9a b x + 21a b x + 12b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3a x - 18a b x - 27a b x - 12b )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (9a b x + 12a b x )\|a x + b + (- 4a x - 15a b x - 12a b x )\|b +--R / +--R +--------+ +--R 2 3 4 4 2 5 +-+ | 2 3 3 6 2 4 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 5 2 6 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 |a x + b +-+ 2 4 2 2 3 +--R ((9a x + 12a b x ) |-------- \|b - 9a b x - 24a b x - 16b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (3a x + 19a b x + 32a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (- 4a x - 15a b x - 12a b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 3 5 4 3 5 |a x + b | 2 +--R (9a b x + 21a b x + 12b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 7 2 3 5 4 3 5 |a x + b +-+ +--R (- 3a b x - 18a b x - 27a b x - 12b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 7a x - 56a b x - 112a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 104a b x + 144a b x + 64b +--R / +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R - a x - 27a b x - 155a b x - 377a b x - 456a b x - 272a b x +--R + +--R 6 2 +--R - 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^8) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)*x^5)+5/2*a*atanh(sqrt(b)/(x*_ + sqrt(a+b/x^2)))/b^(7/2)+5/3/(b^2*x^3*sqrt(a+b/x^2))-_ + 5/2*sqrt(a+b/x^2)/(b^3*x) +--R +--R +--R (2) +--R +--------+ +--R | 2 +-+ +--R 2 5 3 |a x + b \|b +--R (15a x + 15a b x ) |-------- atanh(------------) +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 2 4 2 2 +-+ +--R (- 15a x - 20a b x - 3b )\|b +--R / +--R +--------+ +--R | 2 +--R 3 5 4 3 |a x + b +-+ +--R (6a b x + 6b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 | 2 +--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +-+ +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b )\|b +--R / +--R +--------+ +--R 3 4 8 2 5 6 6 4 7 2 +-+ | 2 4 4 10 +--R (30a b x + 150a b x + 216a b x + 96b x )\|b \|a x + b - 6a b x +--R + +--R 3 5 8 2 6 6 7 4 8 2 +--R - 84a b x - 246a b x - 264a b x - 96b x +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +-+ +--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +-+ +--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 55a x - 150a b x - 21a b x + 132a b x + 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R 75a b x + 400a b x + 655a b x + 380a b x + 48b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 15a x - 215a b x - 683a b x - 839a b x - 404a b x - 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 4 9 2 5 7 6 5 7 3 |a x + b | 2 +--R (30a b x + 150a b x + 216a b x + 96b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 3 11 3 4 9 2 5 7 6 5 7 3 |a x + b +-+ +--R (- 6a b x - 84a b x - 246a b x - 264a b x - 96b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 +--R - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 +--R - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 +--R 1024b +--R / +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 8 6 6 7 4 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 10 2 6 8 7 6 8 4 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1379 +t0:=(1+1/x^2)^(1/3)/x^3 +--R +--R +--R +------+ +--R | 2 +--R |x + 1 +--R |------ +--R 3| 2 +--R \| x +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1379 +r0:=-3/8*(1+1/x^2)^(4/3) +--R +--R +--R +------+ +--R | 2 +--R 2 |x + 1 +--R (- 3x - 3) |------ +--R 3| 2 +--R \| x +--R (2) -------------------- +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 2 +--R 2 |x + 1 +--R (- 3x - 3) |------ +--R 3| 2 +--R \| x +--R (3) -------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1379 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 2 +--R 4 |x + 1 +--R (3x - 3) |------ +--R 3| 2 +--R \| x +--R (4) ------------------ +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1379 +d0:=D(m0,x) +--R +--R +--R 4 2 +--R - x + 6x + 7 +--R (5) -------------- +--R +------+2 +--R | 2 +--R 7 |x + 1 +--R 4x |------ +--R 3| 2 +--R \| x +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1379 +t0:=(1+1/x^2)^(5/3)/x^3 +--R +--R +--R +------+2 +--R | 2 +--R 2 |x + 1 +--R (x + 1) |------ +--R 3| 2 +--R \| x +--R (1) ------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1379 +r0:=-3/16*(1+1/x^2)^(8/3) +--R +--R +--R +------+2 +--R | 2 +--R 4 2 |x + 1 +--R (- 3x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (2) --------------------------- +--R 4 +--R 16x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R | 2 +--R 4 2 |x + 1 +--R (- 3x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (3) --------------------------- +--R 8 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1379 +m0:=a0-r0 +--R +--R +--R +------+2 +--R | 2 +--R 8 6 2 |x + 1 +--R (3x + 6x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (4) ------------------------------- +--R 8 +--R 16x +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1379 +d0:=D(m0,x) +--R +--R +--R 8 6 4 2 +--R - 4x - 5x + 9x + 17x + 7 +--R (5) ---------------------------- +--R +------+ +--R | 2 +--R 11 |x + 1 +--R 4x |------ +--R 3| 2 +--R \| x +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1379 +t0:=x^5/(a+b/x^3) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1180 + +--S 1181 of 1379 +r0:=-1/3*b*x^3/a^2+1/6*x^6/a+1/3*b^2*log(b+a*x^3)/a^3 +--R +--R +--R 2 3 2 6 3 +--R 2b log(a x + b) + a x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 6 3 +--R 2b log(a x + b) + a x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1379 +t0:=x^4/(a+b/x^3) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1185 + +--S 1186 of 1379 +r0:=-1/2*b*x^2/a^2+1/5*x^5/a-1/3*b^(5/3)*log(b^(1/3)+a^(1/3)*x)/_ + a^(8/3)+1/6*b^(5/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/_ + a^(8/3)-b^(5/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/_ + (a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R 5b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 3+-+ 3+-+ 3+-+2 \|b - 2x\|a +--R - 10b\|3 \|b log(\|b + x\|a ) - 30b \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 5 2 +-+3+-+2 +--R (6a x - 15b x )\|3 \|a +--R / +--R 2 +-+3+-+2 +--R 30a \|3 \|a +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | b | b +--R 10b\|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b | b | b 2 +--R - 5b\|3 |- -- log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R | b \| a 5 2 +-+ +--R 30b |- -- atan(------------------------ + (6a x - 15b x )\|3 +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 30a \|3 +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b +--R 2b\|3 \|b log(\|b + x\|a ) + 2b\|3 |- -- \|a log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 | b | b 2 +--R - b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R | b 3+-+2 \| a 3+-+2 \|b - 2x\|a +--R 6b |- -- \|a atan(------------------------ + 6b \|b atan(-------------) +--R 3| 2 +----+2 +-+3+-+ +--R \| a | 2 \|3 \|b +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 6a \|3 \|a +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1379 +t0:=x^3/(a+b/x^3) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1190 + +--S 1191 of 1379 +r0:=-b*x/a^2+1/4*x^4/a+1/3*b^(4/3)*log(b^(1/3)+a^(1/3)*x)/a^(7/3)-_ + 1/6*b^(4/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(7/3)-_ + b^(4/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R - 2b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ 3+-+ 3+-+ 3+-+ \|b - 2x\|a +--R 4b\|3 \|b log(\|b + x\|a ) - 12b\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 4 +-+3+-+ +--R (3a x - 12b x)\|3 \|a +--R / +--R 2 +-+3+-+ +--R 12a \|3 \|a +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+ |b |b |b 2 +-+ |b |b +--R - 2b\|3 3|- log(3|- - x 3|- + x + 4b\|3 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 +--R |b \|a 4 +-+ +--R - 12b 3|- atan(----------------- + (3a x - 12b x)\|3 +--R \|a +-+ +--R |b +--R 3 3|- +--R \|a +--R / +--R 2 +-+ +--R 12a \|3 +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 2b\|3 \|b log(\|b + x\|a ) +--R + +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b +--R - b\|3 \|a 3|- log(3|- - x 3|- + x + 2b\|3 \|a 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+ +--R 3+-+ |b \|a 3+-+ \|b - 2x\|a +--R - 6b\|a 3|- atan(----------------- + 6b\|b atan(-------------) +--R \|a +-+ +-+3+-+ +--R |b \|3 \|b +--R 3 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 6a \|3 \|a +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1379 +t0:=x^2/(a+b/x^3) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1195 + +--S 1196 of 1379 +r0:=1/3*x^3/a-1/3*b*log(b+a*x^3)/a^2 +--R +--R +--R 3 3 +--R - b log(a x + b) + a x +--R (2) ------------------------ +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - b log(a x + b) + a x +--R (3) ------------------------ +--R 2 +--R 3a +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1379 +t0:=x/(a+b/x^3) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1200 + +--S 1201 of 1379 +r0:=1/2*x^2/a+1/3*b^(2/3)*log(b^(1/3)+a^(1/3)*x)/a^(5/3)-_ + 1/6*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 \|b - 2x\|a 2 +-+3+-+2 +--R 6\|b atan(-------------) + 3x \|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |b |b +--R 2\|3 |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |b |b |b 2 +--R - \|3 |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 +--R |b \|a 2 +-+ +--R 6 |-- atan(---------------------- + 3x \|3 +--R 3| 2 +--+2 +--R \|a | 2 +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R +-+ +--R 6a\|3 +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+3+-+2 |b |b +--R 2\|3 \|a |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+3+-+2 |b |b |b 2 +--R - \|3 \|a |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a +--R 6\|a |-- atan(---------------------- - 6\|b atan(-------------) +--R 3| 2 +--+2 +-+3+-+ +--R \|a | 2 \|3 \|b +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1379 +t0:=1/(a+b/x^3) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1205 + +--S 1206 of 1379 +r0:=x/a-1/3*b^(1/3)*log(b^(1/3)+a^(1/3)*x)/a^(4/3)+1/6*b^(1/3)*_ + log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(4/3)+b^(1/3)*_ + atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +-+3+-+ +--R 6\|b atan(-------------) + 6x\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | b | b | b 2 +-+ | b | b +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x) +--R \| a \| a \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | b \| a +-+ +--R - 6 3|- - atan(------------------- + 6x\|3 +--R \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R / +--R +-+ +--R 6a\|3 +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - \|3 3|- - \|a log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ +---+ +---+ \|3 3|- - + 2x\|3 +--R +-+ | b 3+-+ | b | b 3+-+ \| a +--R 2\|3 3|- - \|a log(- 3|- - + x - 6 3|- - \|a atan(-------------------) +--R \| a \| a \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +--R - 6\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1379 +t0:=1/((a+b/x^3)*x) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1379 +r0:=1/3*log(b+a*x^3)/a +--R +--R +--R 3 +--R log(a x + b) +--R (2) ------------- +--R 3a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(a x + b) +--R (3) ------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1379 +t0:=1/((a+b/x^3)*x^2) +--R +--R +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1379 +r0:=-1/3*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(b^(2/3)-_ + a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(1/3))-atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(\|b - x\|a \|b + x \|a ) - 2\|3 log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R \|b - 2x\|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +-----+2 +--R +-+ 3| 2 2 3| 2 +-+ 3| 2 +--R - \|3 log(x \|- a b + a x \|- a b - a b) + 2\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b - a b\|3 +--R - 6atan(-------------------------) +--R 3a b +--R / +--R +-----+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1379 +t0:=1/((a+b/x^3)*x^3) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1379 +r0:=1/3*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(2/3))-1/6*log(b^(2/3)-_ + a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+ +--R - \|3 log(\|b - x\|a \|b + x \|a ) + 2\|3 log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R \|b - 2x\|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +----+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|a b - b x\|a b + b ) + 2\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +--R 2x\|3 \|a b - b\|3 +--R 6atan(---------------------) +--R 3b +--R / +--R +----+ +--R +-+3| 2 +--R 6\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 6\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1379 +t0:=1/((a+b/x^3)*x^4) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1379 +r0:=-1/3*log(a+b/x^3)/b +--R +--R +--R 3 +--R a x + b +--R log(--------) +--R 3 +--R x +--R (2) - ------------- +--R 3b +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(a x + b) + 3log(x) +--R (3) ------------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R 3 a x + b +--R - log(a x + b) + 3log(x) + log(--------) +--R 3 +--R x +--R (4) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1379 +t0:=1/((a+b/x^3)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1379 +r0:=(-1)/(b*x)+1/3*a^(1/3)*log(b^(1/3)+a^(1/3)*x)/b^(4/3)-1/6*a^(1/3)*_ + log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(4/3)+a^(1/3)*_ + atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - x\|3 \|a log(\|b - x\|a \|b + x \|a ) + 2x\|3 \|a log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +-+3+-+ +--R 6x\|a atan(-------------) - 6\|3 \|b +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6b x\|3 \|b +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+2 +-+ +--R +-+ |a |a +-+ |a |a |a 2 +--R 2x\|3 3|- log(b 3|- + a x - x\|3 3|- log(- b x 3|- + b 3|- + a x ) +--R \|b \|b \|b \|b \|b +--R + +--R +-+2 +--R +-+ |a +-+ +--R +-+ b\|3 3|- - 2a x\|3 +--R |a \|b +-+ +--R 6x 3|- atan(--------------------- - 6\|3 +--R \|b +-+2 +--R |a +--R 3b 3|- +--R \|b +--R / +--R +-+ +--R 6b x\|3 +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(\|b - x\|a \|b + x \|a ) - 2\|3 \|a log(\|b + x\|a ) +--R + +--R +-+ +-+2 +--R +-+ |a 3+-+ |a +--R 2\|3 3|- \|b log(b 3|- + a x) +--R \|b \|b +--R + +--R +-+ +-+2 +-+ +--R +-+ |a 3+-+ |a |a 2 +--R - \|3 3|- \|b log(- b x 3|- + b 3|- + a x ) +--R \|b \|b \|b +--R + +--R +-+2 +--R +-+ |a +-+ +--R +-+ b\|3 3|- - 2a x\|3 3+-+ 3+-+ +--R |a 3+-+ \|b 3+-+ \|b - 2x\|a +--R 6 3|- \|b atan(--------------------- - 6\|a atan(-------------) +--R \|b +-+2 +-+3+-+ +--R |a \|3 \|b +--R 3b 3|- +--R \|b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1379 +t0:=1/((a+b/x^3)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1379 +r0:=(-1/2)/(b*x^2)-1/3*a^(2/3)*log(b^(1/3)+a^(1/3)*x)/b^(5/3)+_ + 1/6*a^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(5/3)+_ + a^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R x \|3 \|a log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 \|b - 2x\|a +-+3+-+2 +--R - 2x \|3 \|a log(\|b + x\|a ) + 6x \|a atan(------------- - 3\|3 \|b +--R +-+3+-+ +--R \|3 \|b +--R / +--R 2 +-+3+-+2 +--R 6b x \|3 \|b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | a 2 | a | a 2 2 +--R - x \|3 |- -- log(b |- -- + a b x |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | a | a +--R 2x \|3 |- -- log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 +--R 2 | a \| b +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R 2 +-+ +--R 6b x \|3 +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|a log(\|b - x\|a \|b + x \|a ) + 2\|3 \|a log(\|b + x\|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a 3+-+2 2 | a | a 2 2 +--R - \|3 |- -- \|b log(b |- -- + a b x |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | a 3+-+2 | a +--R 2\|3 |- -- \|b log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R | a 3+-+2 \| b 3+-+2 \|b - 2x\|a +--R - 6 |- -- \|b atan(----------------------- - 6\|a atan(-------------) +--R 3| 2 +----+ +-+3+-+ +--R \| b | 2 \|3 \|b +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1379 +t0:=1/((a+b/x^3)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1379 +r0:=(-1/3)/(b*x^3)-a*log(x)/b^2+1/3*a*log(b+a*x^3)/b^2 +--R +--R +--R 3 3 3 +--R a x log(a x + b) - 3a x log(x) - b +--R (2) ----------------------------------- +--R 2 3 +--R 3b x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R a x log(a x + b) - 3a x log(x) - b +--R (3) ----------------------------------- +--R 2 3 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1379 +t0:=x^5/(a+b/x^3)^2 +--R +--R +--R 11 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1379 +r0:=-2/3*b*x^3/a^3+1/6*x^6/a^2+1/3*b^3/(a^4*(b+a*x^3))+b^2*log(b+a*x^3)/a^4 +--R +--R +--R 2 3 3 3 3 9 2 6 2 3 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ------------------------------------------------------------- +--R 5 3 4 +--R 6a x + 6a b +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 3 3 9 2 6 2 3 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ------------------------------------------------------------- +--R 5 3 4 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1379 +t0:=x^4/(a+b/x^3)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1379 +r0:=-4/3*b*x^2/a^3+8/15*x^5/a^2-1/3*x^8/(a*(b+a*x^3))-8/9*b^(5/3)*_ + log(b^(1/3)+a^(1/3)*x)/a^(11/3)+4/9*b^(5/3)*log(b^(2/3)-a^(1/3)*_ + b^(1/3)*x+a^(2/3)*x^2)/a^(11/3)-8/3*b^(5/3)*atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R (20a b x + 20b )\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 2 +-+3+-+2 3+-+ 3+-+ +--R (- 40a b x - 40b )\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 2 3+-+2 \|b - 2x\|a +--R (- 120a b x - 120b )\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 8 5 2 2 +-+3+-+2 +--R (9a x - 36a b x - 60b x )\|3 \|a +--R / +--R 4 3 3 +-+3+-+2 +--R (45a x + 45a b)\|3 \|a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +--R | 2 | 2 +--R 3 2 +-+ | b | b +--R (40a b x + 40b )\|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 3 2 +-+ | b | b | b 2 +--R (- 20a b x - 20b )\|3 |- -- log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R 3 2 | b \| a +--R (120a b x + 120b ) |- -- atan(------------------------) +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 8 5 2 2 +-+ +--R (9a x - 36a b x - 60b x )\|3 +--R / +--R 4 3 3 +-+ +--R (45a x + 45a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - 4b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b +--R 8b\|3 \|b log(\|b + x\|a ) + 8b\|3 |- -- \|a log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 | b | b 2 +--R - 4b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R 24b |- -- \|a atan(------------------------) +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 \|b - 2x\|a +--R 24b \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 +-+3+-+2 +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1379 +t0:=x^3/(a+b/x^3)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1379 +r0:=-7/3*b*x/a^3+7/12*x^4/a^2-1/3*x^7/(a*(b+a*x^3))+7/9*b^(4/3)*_ + log(b^(1/3)+a^(1/3)*x)/a^(10/3)-7/18*b^(4/3)*log(b^(2/3)-a^(1/3)*_ + b^(1/3)*x+a^(2/3)*x^2)/a^(10/3)-7/3*b^(4/3)*atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 2 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- 14a b x - 14b )\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 2 +-+3+-+ 3+-+ 3+-+ +--R (28a b x + 28b )\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 2 3+-+ \|b - 2x\|a +--R (- 84a b x - 84b )\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 7 4 2 +-+3+-+ +--R (9a x - 63a b x - 84b x)\|3 \|a +--R / +--R 4 3 3 +-+3+-+ +--R (36a x + 36a b)\|3 \|a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +--R 3 2 +-+ |b |b |b 2 +--R (- 14a b x - 14b )\|3 3|- log(3|- - x 3|- + x ) +--R \|a \|a \|a +--R + +--R +-+ +-+ +--R 3 2 +-+ |b |b +--R (28a b x + 28b )\|3 3|- log(3|- + x) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 +--R 3 2 |b \|a +--R (- 84a b x - 84b ) 3|- atan(-----------------) +--R \|a +-+ +--R |b +--R 3 3|- +--R \|a +--R + +--R 2 7 4 2 +-+ +--R (9a x - 63a b x - 84b x)\|3 +--R / +--R 4 3 3 +-+ +--R (36a x + 36a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R 7b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 14b\|3 \|b log(\|b + x\|a ) +--R + +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b +--R - 7b\|3 \|a 3|- log(3|- - x 3|- + x + 14b\|3 \|a 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+ +--R 3+-+ |b \|a 3+-+ \|b - 2x\|a +--R - 42b\|a 3|- atan(----------------- + 42b\|b atan(-------------) +--R \|a +-+ +-+3+-+ +--R |b \|3 \|b +--R 3 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1379 +t0:=x^2/(a+b/x^3)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1379 +r0:=1/3*x^3/a^2-1/3*b^2/(a^3*(b+a*x^3))-2/3*b*log(b+a*x^3)/a^3 +--R +--R +--R 3 2 3 2 6 3 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) --------------------------------------------------- +--R 4 3 3 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 2 6 3 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) --------------------------------------------------- +--R 4 3 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1379 +t0:=x/(a+b/x^3)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1379 +r0:=5/6*x^2/a^2-1/3*x^5/(a*(b+a*x^3))+5/9*b^(2/3)*log(b^(1/3)+_ + a^(1/3)*x)/a^(8/3)-5/18*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_ + x+a^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/_ + (b^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- 5a x - 5b)\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 +-+3+-+2 3+-+ 3+-+ +--R (10a x + 10b)\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+2 \|b - 2x\|a 5 2 +-+3+-+2 +--R (30a x + 30b)\|b atan(-------------) + (9a x + 15b x )\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 3 2 +-+3+-+2 +--R (18a x + 18a b)\|3 \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R 3 +-+ |b |b +--R (10a x + 10b)\|3 |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 3 +-+ |b |b |b 2 +--R (- 5a x - 5b)\|3 |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 +--R 3 |b \|a 5 2 +-+ +--R (30a x + 30b) |-- atan(---------------------- + (9a x + 15b x )\|3 +--R 3| 2 +--+2 +--R \|a | 2 +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R 3 3 2 +-+ +--R (18a x + 18a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+3+-+2 |b |b +--R 10\|3 \|a |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R 5\|3 \|b log(\|b - x\|a \|b + x \|a ) - 10\|3 \|b log(\|b + x\|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+3+-+2 |b |b |b 2 +--R - 5\|3 \|a |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a +--R 30\|a |-- atan(---------------------- - 30\|b atan(-------------) +--R 3| 2 +--+2 +-+3+-+ +--R \|a | 2 \|3 \|b +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R 2 +-+3+-+2 +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1379 +t0:=1/(a+b/x^3)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1379 +r0:=4/3*x/a^2-1/3*x^4/(a*(b+a*x^3))-4/9*b^(1/3)*log(b^(1/3)+_ + a^(1/3)*x)/a^(7/3)+2/9*b^(1/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_ + x+a^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((b^(1/3)-2*a^(1/3)*x)/_ + (b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (2a x + 2b)\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R (- 4a x - 4b)\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ \|b - 2x\|a 4 +-+3+-+ +--R (12a x + 12b)\|b atan(-------------) + (9a x + 12b x)\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 3 2 +-+3+-+ +--R (9a x + 9a b)\|3 \|a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R 3 +-+ | b | b | b 2 +--R (- 2a x - 2b)\|3 3|- - log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +---+ +--R 3 +-+ | b | b +--R (4a x + 4b)\|3 3|- - log(- 3|- - + x) +--R \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R 3 | b \| a 4 +-+ +--R (- 12a x - 12b) 3|- - atan(------------------- + (9a x + 12b x)\|3 +--R \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R / +--R 3 3 2 +-+ +--R (9a x + 9a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log(\|b - x\|a \|b + x \|a ) + 4\|3 \|b log(\|b + x\|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - 2\|3 3|- - \|a log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ +---+ +---+ \|3 3|- - + 2x\|3 +--R +-+ | b 3+-+ | b | b 3+-+ \| a +--R 4\|3 3|- - \|a log(- 3|- - + x - 12 3|- - \|a atan(-------------------) +--R \| a \| a \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +--R - 12\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1379 +t0:=1/((a+b/x^3)^2*x) +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1379 +r0:=1/3*b/(a^2*(b+a*x^3))+1/3*log(b+a*x^3)/a^2 +--R +--R +--R 3 3 +--R (a x + b)log(a x + b) + b +--R (2) --------------------------- +--R 3 3 2 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R (a x + b)log(a x + b) + b +--R (3) --------------------------- +--R 3 3 2 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1379 +t0:=1/((a+b/x^3)^2*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1379 +r0:=-1/3*x^2/(a*(b+a*x^3))-2/9*log(b^(1/3)+a^(1/3)*x)/(a^(5/3)*b^(1/3))+_ + 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_ + 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*_ + b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 +-+3+-+2 3+-+ +--R - 3x \|3 \|a \|b +--R / +--R 2 3 +-+3+-+2 3+-+ +--R (9a x + 9a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6a x - 6b)atan(-------------------------) - 3x \|3 \|- a b +--R 3a b +--R / +--R +-----+ +--R 2 3 +-+3| 2 +--R (9a x + 9a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 9a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1379 +t0:=1/((a+b/x^3)^2*x^3) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1379 +r0:=-1/3*x/(a*(b+a*x^3))+1/9*log(b^(1/3)+a^(1/3)*x)/(a^(4/3)*b^(2/3))-_ + 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_ + 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*_ + b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R +-+3+-+3+-+2 +--R - 6x\|3 \|a \|b +--R / +--R 2 3 +-+3+-+3+-+2 +--R (18a x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- a x - b)\|3 log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +----+ +--R 3 2x\|3 \|a b - b\|3 +-+3| 2 +--R (6a x + 6b)atan(---------------------) - 6x\|3 \|a b +--R 3b +--R / +--R +----+ +--R 2 3 +-+3| 2 +--R (18a x + 18a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 18a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1379 +t0:=1/((a+b/x^3)^2*x^4) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1379 +r0:=1/3/(b*(a+b/x^3)) +--R +--R +--R 3 +--R x +--R (2) ------------- +--R 3 2 +--R 3a b x + 3b +--R Type: Fraction(Polynomial(Integer)) +--E 1291 + +--S 1292 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 3a b +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1379 +t0:=1/((a+b/x^3)^2*x^5) +--R +--R +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1379 +r0:=1/3*x^2/(b*(b+a*x^3))-1/9*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(4/3))+_ + 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_ + 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*_ + b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 +-+3+-+2 3+-+ +--R 6x \|3 \|a \|b +--R / +--R 3 2 +-+3+-+2 3+-+ +--R (18a b x + 18b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6a x - 6b)atan(-------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +-----+ +--R 3 2 +-+3| 2 +--R (18a b x + 18b )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 18b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1379 +t0:=1/((a+b/x^3)^2*x^6) +--R +--R +--R 1 +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1379 +r0:=1/3*x/(b*(b+a*x^3))+2/9*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(5/3))-_ + 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_ + 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*_ + b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R +-+3+-+3+-+2 +--R 3x\|3 \|a \|b +--R / +--R 3 2 +-+3+-+3+-+2 +--R (9a b x + 9b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- a x - b)\|3 log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +----+ +--R 3 2x\|3 \|a b - b\|3 +-+3| 2 +--R (6a x + 6b)atan(---------------------) + 3x\|3 \|a b +--R 3b +--R / +--R +----+ +--R 3 2 +-+3| 2 +--R (9a b x + 9b )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 9b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1379 +t0:=1/((a+b/x^3)^2*x^7) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 7 4 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1379 +r0:=1/3/(b*(b+a*x^3))+log(x)/b^2-1/3*log(b+a*x^3)/b^2 +--R +--R +--R 3 3 3 +--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b +--R (2) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3b +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b +--R (3) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3b +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1379 +t0:=x^5*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 5 |a x + b +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1379 +r0:=-1/12*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/12*b*x^3*_ + sqrt(a+b/x^3)/a+1/6*x^6*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R | b 2 2 | b |a x + b 2 3 3 +--R - 2a |---- log(8a x |---- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + b x ) |-------- +--R \| x +--R / +--R 12a +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R +-+ | b 2 2 | b |a x + b 2 3 3 +--R - 2a\|a |---- log(8a x |---- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x - b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R +-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--------+ +--R | 4 | 3 | 3 +--R 3 7 2 4 | b 2 7 3 4 |a x + b |a x + b +--R ((- 8a x - 8a b x ) |---- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|16a \| x +--R + +--R +--------+ +----+ +--R | 3 | 4 +--R 3 8 2 5 |a x + b | b 2 2 8 3 5 4 2 +--R (8a x + 8a b x ) |-------- |---- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|16a +--R / +--R +--------+ +----+ +--------+ +--------+ +--R | 3 | 4 | 3 | 3 +--R 2 2 |a x + b | b |a x + b 2 3 3 |a x + b +--R 8a x |-------- |---- |-------- + (2a b x + b ) |-------- +--R | 3 | 3 \| x | 3 +--R \| x \|16a \| x +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1379 +t0:=x^2*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 2 |a x + b +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1379 +r0:=1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a)+1/3*x^3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 |b |a x + b 3 2 2 |a x + b +--R - |-- log(2a x |-- |-------- - 2a b x - b ) + 2x |-------- +--R \| a \| a \| x \| x +--R (3) ----------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 |b |a x + b 3 2 +--R - \|a |-- log(2a x |-- |-------- - 2a b x - b ) +--R \| a \| a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R - 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6\|a +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 4 |a x + b |b 4 2 |a x + b +--R (- 2a x |-------- |-- - 2a b x - b x) |-------- +--R | 3 \| a \| x +--R \| x +--R + +--R +--+ +--------+ +--R | 2 | 3 +--R 2 5 2 |b 5 2 2 |a x + b +--R (2a x + 2a b x ) |-- + (2a b x + b x ) |-------- +--R \| a | 3 +--R \| x +--R / +--R +--+ +--------+ +--R | 2 | 3 +--R 2 |b |a x + b 3 2 +--R 2a x |-- |-------- - 2a b x - b +--R \| a \| x +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1379 +t0:=sqrt(a+b/x^3)/x +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1379 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-2/3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x |a x + b +--R 2\|a atanh(-----------) - 2 |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 |a x + b +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4 |-------- +--R \| x \| x +--R (3) ---------------------------------------------------------- +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 +-+ \| x +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4x\|a atanh(-----------) +--R \| x +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b +--R - 4 |-------- + 4x |-------- +--R \| x | 3 +--R \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +--+ 5 2 |a x + b |a x + b +--R ((- a x - b x )\|4a + (- 2a x - b x ) |-------- ) |-------- +--R | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +--R 6 3 |a x + b +--+ 2 6 3 2 +--R (a x + b x ) |-------- \|4a + 2a x + 3a b x + b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 | 3 +--R 6 |a x + b +--+ |a x + b 7 4 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1379 +t0:=sqrt(a+b/x^3)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1379 +r0:=-2/9*(a+b/x^3)^(3/2)/b +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 2a x - 2b) |-------- +--R | 3 +--R \| x +--R (2) ------------------------- +--R 3 +--R 9b x +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 2a x - 2b) |-------- +--R \| x +--R (3) ------------------------- +--R 6 +--R 9b x +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 6 3 |a x + b +--R (- 2a x - 2b) |-------- + (2a x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------------------------------ +--R 6 +--R 9b x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1379 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 2 |a x + b 2 6 3 2 |a x + b +--R (- 9a b x - 9b x) |-------- + (4a x + 17a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 8 |a x + b |a x + b +--R 9b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1379 +t0:=sqrt(a+b/x^3)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1379 +r0:=2/9*a*(a+b/x^3)^(3/2)/b^2-2/15*(a+b/x^3)^(5/2)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (4a x - 2a b x - 6b ) |-------- +--R | 3 +--R \| x +--R (2) ---------------------------------- +--R 2 6 +--R 45b x +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (4a x - 2a b x - 6b ) |-------- +--R \| x +--R (3) ---------------------------------- +--R 2 9 +--R 45b x +--R Type: Union(Expression(Integer),...) +--E 1332 + +--S 1333 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (4a x - 2a b x - 6b ) |-------- + (- 4a x + 2a b x + 6b x ) |-------- +--R \| x | 3 +--R \| x +--R --------------------------------------------------------------------------- +--R 2 9 +--R 45b x +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 4 3 |a x + b +--R (- 45a b x - 45b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 8a x - 4a b x + 61a b x + 57b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 11 |a x + b |a x + b +--R 45b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1379 +t0:=sqrt(a+b/x^3)/x^10 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1379 +r0:=-2/9*a^2*(a+b/x^3)^(3/2)/b^3+4/15*a*(a+b/x^3)^(5/2)/b^3-_ + 2/21*(a+b/x^3)^(7/2)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------ +--R 3 9 +--R 315b x +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 3 12 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 1337 + +--S 1338 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (16a x - 8a b x + 6a b x + 30b x ) |-------- +--R | 3 +--R \| x +--R / +--R 3 12 +--R 315b x +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 3 4 4 |a x + b +--R (- 315a b x - 315b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (32a x + 16a b x - 4a b x + 387a b x + 375b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 14 |a x + b |a x + b +--R 315b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1379 +t0:=(a+b/x^3)^(3/2)*x^5 +--R +--R +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (1) (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1379 +r0:=1/6*(a+b/x^3)^(3/2)*x^6+1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/_ + sqrt(a)+1/4*b*x^3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 12\|a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+ +--------+ +--R | 4 | 4 | 3 +--R |9b 2 |9b |a x + b 2 3 3 +--R - 2 |--- log(8a x |--- |-------- - 6a b x - 3b ) +--R \|16a \|16a \| x +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + 5b x ) |-------- +--R \| x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 1342 + +--S 1343 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+ +---+ +--------+ +--R | 4 | 4 | 3 +--R +-+ |9b 2 |9b |a x + b 2 3 3 +--R - 2\|a |--- log(8a x |--- |-------- - 6a b x - 3b ) +--R \|16a \|16a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R - 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x - 5b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R +-+ +--R 12\|a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--R | 4 +--R 3 8 2 5 2 2 |9b +--R (- 8a x - 16a b x - 8a b x ) |--- +--R \|16a +--R + +--R +--------+ +--R | 3 +--R 2 2 8 3 5 4 2 |a x + b +--R (- 6a b x - 9a b x - 3b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +---+ +--R | 3 | 4 +--R 3 9 2 6 2 3 |a x + b |9b 3 2 9 2 3 6 +--R (8a x + 16a b x + 8a b x ) |-------- |--- + 6a b x + 15a b x +--R | 3 \|16a +--R \| x +--R + +--R 4 3 5 +--R 12a b x + 3b +--R / +--R +--------+ +---+ +--------+ +--------+ +--R | 3 | 4 | 3 | 3 +--R 3 |a x + b |9b |a x + b 2 4 3 |a x + b +--R 8a x |-------- |--- |-------- + (- 6a b x - 3b x) |-------- +--R | 3 \|16a \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1379 +t0:=(a+b/x^3)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1379 +r0:=1/3*(a+b/x^3)^(3/2)*x^3+b*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-_ + b*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x 3 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-----+ +-----+ | 3 +--R | 2 2 | 2 |a x + b 3 2 +--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b ) +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (2a x - 4b) |-------- +--R \| x +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1347 + +--S 1348 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +-----+ +-----+ | 3 +--R | 2 2 | 2 |a x + b 3 2 +--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b ) +--R \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x 3 |a x + b +--R - 6b x\|a atanh(-----------) + (2a x - 4b) |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (- 2a x + 4b x) |-------- +--R | 3 +--R \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----+ +--R 2 8 5 2 2 | 2 +--R (- 2a x - 4a b x - 2b x )\|9a b +--R + +--R +--------+ +--R | 3 +--R 2 8 2 5 3 2 |a x + b +--R (- 6a b x - 9a b x - 3b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +-----+ +--R 2 9 6 2 3 |a x + b | 2 3 9 2 2 6 +--R (2a x + 4a b x + 2b x ) |-------- \|9a b + 6a b x + 15a b x +--R | 3 +--R \| x +--R + +--R 3 3 4 +--R 12a b x + 3b +--R / +--R +--------+ +--------+ +--------+ +--R | 3 +-----+ | 3 | 3 +--R 6 |a x + b | 2 |a x + b 7 2 4 |a x + b +--R 2x |-------- \|9a b |-------- + (- 6a b x - 3b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1349 + +)clear all + +--S 1350 of 1379 +t0:=(a+b/x^3)^(3/2)/x +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1379 +r0:=-2/9*(a+b/x^3)^(3/2)+2/3*a^(3/2)*atanh(sqrt(a+b/x^3)/sqrt(a))-_ + 2/3*a*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 +-+ \| x 3 |a x + b +--R 6a x \|a atanh(-----------) + (- 8a x - 2b) |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------- +--R 3 +--R 9x +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +---+ +---+ | 3 +--R 4 | 3 2 | 3 |a x + b 2 3 +--R - 3x \|4a log(x \|4a |-------- - 2a x - a b) +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 16a x - 4b) |-------- +--R \| x +--R / +--R 4 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1352 + +--S 1353 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +---+ +---+ | 3 +--R 4 | 3 2 | 3 |a x + b 2 3 +--R - 3x \|4a log(x \|4a |-------- - 2a x - a b) +--R \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 4 +-+ \| x 3 |a x + b +--R - 12a x \|a atanh(-----------) + (- 16a x - 4b) |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (16a x + 4b x) |-------- +--R | 3 +--R \| x +--R / +--R 4 +--R 18x +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--R 2 8 5 2 2 | 3 +--R (- a x - 2a b x - b x )\|4a +--R + +--R +--------+ +--R | 3 +--R 3 8 2 5 2 2 |a x + b +--R (- 2a x - 3a b x - a b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +---+ +--R 2 9 6 2 3 |a x + b | 3 4 9 3 6 2 2 3 3 +--R (a x + 2a b x + b x ) |-------- \|4a + 2a x + 5a b x + 4a b x + a b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 +---+ | 3 | 3 +--R 9 |a x + b | 3 |a x + b 2 10 7 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - a b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1354 + +)clear all + +--S 1355 of 1379 +t0:=(a+b/x^3)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1379 +r0:=-2/15*(a+b/x^3)^(5/2)/b +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------ +--R 6 +--R 15b x +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- +--R \| x +--R (3) ------------------------------------ +--R 9 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 1357 + +--S 1358 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- + (2a x + 4a b x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R --------------------------------------------------------------------------- +--R 9 +--R 15b x +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 7 2 4 3 |a x + b +--R (- 15a b x - 30a b x - 15b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x + 27a b x + 42a b x + 19b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 11 |a x + b |a x + b +--R 15b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1359 + +)clear all + +--S 1360 of 1379 +t0:=(a+b/x^3)^(3/2)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1379 +r0:=2/15*a*(a+b/x^3)^(5/2)/b^2-2/21*(a+b/x^3)^(7/2)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R | 3 +--R \| x +--R (2) ---------------------------------------------- +--R 2 9 +--R 105b x +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R \| x +--R (3) ---------------------------------------------- +--R 2 12 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 1362 + +--S 1363 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (- 4a x + 2a b x + 16a b x + 10b x ) |-------- +--R | 3 +--R \| x +--R / +--R 2 12 +--R 105b x +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 2 7 3 4 4 |a x + b +--R (- 105a b x - 210a b x - 105b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 8a x - 4a b x + 141a b x + 262a b x + 125b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 14 |a x + b |a x + b +--R 105b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1379 +t0:=(a+b/x^3)^(3/2)/x^10 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 1379 +r0:=-2/15*a^2*(a+b/x^3)^(5/2)/b^3+4/21*a*(a+b/x^3)^(7/2)/b^3-_ + 2/27*(a+b/x^3)^(9/2)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------------------- +--R 3 12 +--R 945b x +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R \| x +--R (3) ------------------------------------------------------------- +--R 3 15 +--R 945b x +--R Type: Union(Expression(Integer),...) +--E 1367 + +--S 1368 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 15 3 12 2 2 9 3 6 4 3 |a x + b +--R (16a x - 8a b x + 6a b x + 100a b x + 70b x ) |-------- +--R | 3 +--R \| x +--R / +--R 3 15 +--R 945b x +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 3 7 4 4 5 |a x + b +--R (- 945a b x - 1890a b x - 945b x) |-------- +--R \| x +--R + +--R 5 15 4 12 3 2 9 2 3 6 4 3 5 +--R (32a x + 16a b x - 4a b x + 1157a b x + 2230a b x + 1085b ) +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 17 |a x + b |a x + b +--R 945b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1369 + +)clear all + +--S 1370 of 1379 +t0:=x^4*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 4 |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1379 +--r0:=81/160*x^2*sqrt(8+27/x^3)+1/5*x^5*sqrt(8+27/x^3)+_ +-- 729/160*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 1371 + +--S 1372 of 1379 +--a0:=integrate(t0,x) +--E 1372 + +--S 1373 of 1379 +--m0:=a0-r0 +--E 1373 + +--S 1374 of 1379 +--d0:=D(m0,x) +--E 1374 + +)clear all + +--S 1375 of 1379 +t0:=x*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1379 +--r0:=1/2*x^2*sqrt(8+27/x^3)-27/2*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 1376 + +--S 1377 of 1379 +--a0:=integrate(t0,x) +--E 1377 + +--S 1378 of 1379 +--m0:=a0-r0 +--E 1378 + +--S 1379 of 1379 +--d0:=D(m0,x) +--E 1379 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4g.input.pdf b/src/axiom-website/CATS/rich4g.input.pdf new file mode 100644 index 0000000..1580459 Binary files /dev/null and b/src/axiom-website/CATS/rich4g.input.pdf differ diff --git a/src/axiom-website/CATS/rich4h.input.pamphlet b/src/axiom-website/CATS/rich4h.input.pamphlet new file mode 100644 index 0000000..4f31122 --- /dev/null +++ b/src/axiom-website/CATS/rich4h.input.pamphlet @@ -0,0 +1,24104 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4h.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 173 matching answers. +\item 60 cases where Axiom's results differs from Rubi +\item 25 cases where Axiom supplied 2 results. +\item 4 cases that Axiom failed to integrate. +\item 42 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4h.output +)spool rich4h.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1325 +t0:=sqrt(8+27/x^3)/x^2 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1325 +--r0:=-2/5*sqrt(8+27/x^3)/x-16/5*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+_ +-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_ +-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/_ +-- (3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 2 + +--S 3 of 1325 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 1325 +--m0:=a0-r0 +--E 4 + +--S 5 of 1325 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 1325 +t0:=sqrt(8+27/x^3)/x^5 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1325 +--r0:=-2/11*sqrt(8+27/x^3)/x^4-16/495*sqrt(8+27/x^3)/x+256/1485*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 7 + +--S 8 of 1325 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 1325 +--m0:=a0-r0 +--E 9 + +--S 10 of 1325 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 1325 +t0:=x^3*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 3 |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1325 +--r0:=81/64*x*sqrt(8+27/x^3)+1/4*x^4*sqrt(8+27/x^3)-243/64*(-1)^(1/4)*_ +-- (2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3))))+243/32*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_ +-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 12 + +--S 13 of 1325 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 1325 +--m0:=a0-r0 +--E 14 + +--S 15 of 1325 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 1325 +t0:=sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R (1) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1325 +--r0:=x*sqrt(8+27/x^3)-9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+_ +-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_ +-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+18*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 17 + +--S 18 of 1325 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1325 +--m0:=a0-r0 +--E 19 + +--S 20 of 1325 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1325 +t0:=sqrt(8+27/x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1325 +--r0:=-2/7*sqrt(8+27/x^3)/x^2-16/21*(-1)^(1/4)*(2+3/x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3))))+32/21*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 22 + +--S 23 of 1325 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 1325 +--m0:=a0-r0 +--E 24 + +--S 25 of 1325 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 1325 +t0:=sqrt(8+27/x^3)/x^6 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1325 +--r0:=-2/13*sqrt(8+27/x^3)/x^5-16/819*sqrt(8+27/x^3)/x^2+_ +-- 512/7371*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-1024/7371*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 27 + +--S 28 of 1325 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 1325 +--m0:=a0-r0 +--E 29 + +--S 30 of 1325 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1325 +t0:=x^8/sqrt(a+b/x^3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1325 +r0:=-5/24*b^3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)+5/24*b^2*x^3*_ + sqrt(a+b/x^3)/a^3-5/36*b*x^6*sqrt(a+b/x^3)/a^2+1/9*x^9*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 \| x 2 9 6 2 3 +-+ |a x + b +--R - 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 3 +-+ +--R 72a \|a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 6 | 6 | 3 +--R 3 |25b 4 2 |25b |a x + b 3 3 4 +--R - 12a |---- log(16a x |---- |-------- + 10a b x + 5b ) +--R | 7 | 7 \| x +--R \|64a \|64a +--R + +--R +--------+ +--R | 3 +--R 2 8 5 2 2 |a x + b +--R (8a x - 10a b x + 15b x ) |-------- +--R \| x +--R / +--R 3 +--R 72a +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 6 | 6 | 3 +--R 3 +-+ |25b 4 2 |25b |a x + b 3 3 4 +--R - 12a \|a |---- log(16a x |---- |-------- + 10a b x + 5b ) +--R | 7 | 7 \| x +--R \|64a \|64a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 \| x 2 8 5 2 2 +-+ |a x + b +--R 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 2 9 6 2 3 +-+ |a x + b +--R (- 8a x + 10a b x - 15b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R 3 +-+ +--R 72a \|a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--R | 6 | 3 +--R 5 13 4 10 |25b 3 13 4 10 |a x + b +--R ((- 16a x - 16a b x ) |---- + (10a b x + 5b x ) |-------- ) +--R | 7 | 3 +--R \|64a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +----+ +--R | 3 | 6 +--R 5 14 4 11 |a x + b |25b 2 3 14 4 11 5 8 +--R (16a x + 16a b x ) |-------- |---- - 10a b x - 15a b x - 5b x +--R | 3 | 7 +--R \| x \|64a +--R / +--R +--------+ +----+ +--------+ +--R | 3 | 6 | 3 +--R 5 5 4 2 |a x + b |25b |a x + b +--R (16a x + 16a b x ) |-------- |---- |-------- +--R | 3 | 7 \| x +--R \| x \|64a +--R + +--R +--------+ +--R | 3 +--R 2 3 6 4 3 5 |a x + b +--R (10a b x + 15a b x + 5b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1325 +t0:=x^5/sqrt(a+b/x^3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1325 +r0:=1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-1/4*b*x^3*_ + sqrt(a+b/x^3)/a^2+1/6*x^6*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 12a \|a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R 2 | 9b 3 2 | 9b |a x + b 2 3 3 +--R - 2a |---- log(8a x |---- |-------- - 6a b x - 3b ) +--R | 5 | 5 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x - 3b x ) |-------- +--R \| x +--R / +--R 2 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R 2 +-+ | 9b 3 2 | 9b |a x + b 2 3 3 +--R - 2a \|a |---- log(8a x |---- |-------- - 6a b x - 3b ) +--R | 5 | 5 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R - 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x + 3b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R 2 +-+ +--R 12a \|a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--R | 4 | 3 +--R 4 10 3 7 | 9b 2 10 3 7 |a x + b +--R ((- 8a x - 8a b x ) |---- + (- 6a b x - 3b x ) |-------- ) +--R | 5 | 3 +--R \|16a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +----+ +--R | 3 | 4 +--R 4 11 3 8 |a x + b | 9b 2 2 11 3 8 4 5 +--R (8a x + 8a b x ) |-------- |---- + 6a b x + 9a b x + 3b x +--R | 3 | 5 +--R \| x \|16a +--R / +--R +--------+ +----+ +--------+ +--R | 3 | 4 | 3 +--R 4 5 3 2 |a x + b | 9b |a x + b +--R (8a x + 8a b x ) |-------- |---- |-------- +--R | 3 | 5 \| x +--R \| x \|16a +--R + +--R +--------+ +--R | 3 +--R 2 2 6 3 3 4 |a x + b +--R (- 6a b x - 9a b x - 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1325 +t0:=x^2/sqrt(a+b/x^3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1325 +r0:=-1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/3*x^3*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 2 |b |a x + b 3 2 2 |a x + b +--R - a |-- log(2a x |-- |-------- + 2a b x + b ) + 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R (3) ------------------------------------------------------------------ +--R 6a +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 2 |b |a x + b 3 2 +--R - a\|a |-- log(2a x |-- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 3 7 2 4 |b 7 2 4 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |-- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--+ +--R | 3 | 2 +--R 3 8 2 5 |a x + b |b 2 8 2 5 3 2 +--R (2a x + 2a b x ) |-------- |-- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|a +--R / +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 3 5 2 2 |a x + b |b |a x + b +--R (2a x + 2a b x ) |-------- |-- |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R | 3 +--R 2 6 2 3 3 |a x + b +--R (2a b x + 3a b x + b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1325 +t0:=1/(x*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 3 +--R |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1325 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |a x + b 3 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (3) - ----------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 3 | 3 +--R |1 +-+ 2 |1 |a x + b 3 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 3 | 3 +--R 3 |1 |a x + b 3 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +-+ +--R 4 |a x + b 2 4 |1 +--R (2a x + b x) |-------- + (2a x + 2a b x) |- +--R | 3 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 +-+ | 3 +--R 4 |a x + b |a x + b 2 5 2 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 3 \| x \|a | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1325 +t0:=1/(x^4*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 4 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1325 +r0:=-2/3*sqrt(a+b/x^3)/b +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R | 3 +--R \| x +--R (2) - ------------ +--R 3b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R \| x +--R (3) - ------------ +--R 3 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 2 |-------- + 2x |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------- +--R 3 +--R 3b x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 3b x |-------- + (4a x + 7b) |-------- +--R \| x | 3 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 |a x + b |a x + b +--R 3b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1325 +t0:=1/(x^7*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 7 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1325 +r0:=-2/9*(a+b/x^3)^(3/2)/b^2+2/3*a*sqrt(a+b/x^3)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (4a x - 2b) |-------- +--R | 3 +--R \| x +--R (2) ----------------------- +--R 2 3 +--R 9b x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (4a x - 2b) |-------- +--R \| x +--R (3) ----------------------- +--R 2 6 +--R 9b x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 6 3 |a x + b +--R (4a x - 2b) |-------- + (- 4a x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------------------------------ +--R 2 6 +--R 9b x +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 |a x + b 2 6 3 2 |a x + b +--R - 9b x |-------- + (- 8a x - 4a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) --------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 |a x + b |a x + b +--R 9b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1325 +t0:=1/(x^10*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R | 3 +--R 10 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1325 +r0:=4/9*a*(a+b/x^3)^(3/2)/b^3-2/15*(a+b/x^3)^(5/2)/b^3-2/3*a^2*_ + sqrt(a+b/x^3)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------- +--R 3 6 +--R 45b x +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- +--R \| x +--R (3) ------------------------------------- +--R 3 9 +--R 45b x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- + (16a x - 8a b x + 6b x ) |-------- +--R \| x | 3 +--R \| x +--R ----------------------------------------------------------------------------- +--R 3 9 +--R 45b x +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b +--R - 45b x |-------- + (32a x + 16a b x - 4a b x + 57b ) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 11 |a x + b |a x + b +--R 45b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1325 +t0:=1/(x^13*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R | 3 +--R 13 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1325 +r0:=-2/3*a^2*(a+b/x^3)^(3/2)/b^4+2/5*a*(a+b/x^3)^(5/2)/b^4-_ + 2/21*(a+b/x^3)^(7/2)/b^4+2/3*a^3*sqrt(a+b/x^3)/b^4 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------ +--R 4 9 +--R 105b x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 4 12 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (- 32a x + 16a b x - 12a b x + 10b x ) |-------- +--R | 3 +--R \| x +--R / +--R 4 12 +--R 105b x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 4 |a x + b +--R - 105b x |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 64a x - 32a b x + 8a b x - 4a b x + 125b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 14 |a x + b |a x + b +--R 105b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1325 +t0:=x^5/(a+b/x^3)^(3/2) +--R +--R +--R 8 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1325 +r0:=5/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)-2/3*x^6/_ + (a*sqrt(a+b/x^3))-5/4*b*x^3*sqrt(a+b/x^3)/a^3+5/6*x^6*sqrt(a+b/x^3)/a^2 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 2 |a x + b \| x 2 6 3 2 +-+ +--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a +--R | 3 +-+ +--R \| x \|a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R | 3 +--R 3 +-+ |a x + b +--R 12a \|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ +--------+ +--R | 4 | 4 | 3 +--R 4 3 3 |225b 4 2 |225b |a x + b 2 3 3 +--R (- 2a x - 2a b) |----- log(8a x |----- |-------- - 30a b x - 15b ) +--R | 7 | 7 \| x +--R \| 16a \| 16a +--R + +--R +--------+ +--R | 3 +--R 2 8 5 2 2 |a x + b +--R (2a x - 5a b x - 15b x ) |-------- +--R \| x +--R / +--R 4 3 3 +--R 12a x + 12a b +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +-----+ +--R | 3 | 4 +--R 4 3 3 +-+ |a x + b |225b +--R (- 2a x - 2a b)\|a |-------- |----- +--R | 3 | 7 +--R \| x \| 16a +--R * +--R +-----+ +--------+ +--R | 4 | 3 +--R 4 2 |225b |a x + b 2 3 3 +--R log(8a x |----- |-------- - 30a b x - 15b ) +--R | 7 \| x +--R \| 16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 2 3 3 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 5 2 2 +-+ |a x + b |a x + b +--R (2a x - 5a b x - 15b x )\|a |-------- |-------- +--R | 3 \| x +--R \| x +--R + +--R 3 9 2 6 2 3 3 +-+ +--R (- 2a x + 3a b x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 3 +--R 4 3 3 +-+ |a x + b +--R (12a x + 12a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----+ +--------+ +--R | 4 | 3 +--R 5 13 4 10 |225b 2 13 3 10 |a x + b +--R ((- 8a x - 8a b x ) |----- + (- 30a b x - 15b x ) |-------- ) +--R | 7 | 3 +--R \| 16a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +-----+ +--R | 3 | 4 +--R 5 14 4 11 |a x + b |225b 2 2 14 3 11 4 8 +--R (8a x + 8a b x ) |-------- |----- + 30a b x + 45a b x + 15b x +--R | 3 | 7 +--R \| x \| 16a +--R / +--R +--------+ +-----+ +--------+ +--R | 3 | 4 | 3 +--R 6 8 5 5 4 2 2 |a x + b |225b |a x + b +--R (8a x + 16a b x + 8a b x ) |-------- |----- |-------- +--R | 3 | 7 \| x +--R \| x \| 16a +--R + +--R +--------+ +--R | 3 +--R 3 2 9 2 3 6 4 3 5 |a x + b +--R (- 30a b x - 75a b x - 60a b x - 15b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1325 +t0:=x^2/(a+b/x^3)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1325 +r0:=-b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-2/3*x^3/(a*sqrt(a+b/x^3))+_ + x^3*sqrt(a+b/x^3)/a^2 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R |a x + b \| x 3 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 3 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 3 +--R 2 +-+ |a x + b +--R 3a \|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+ +--------+ +--R | 2 | 2 | 3 +--R 3 3 2 |9b 3 2 |9b |a x + b 3 2 +--R (- a x - a b) |--- log(2a x |--- |-------- + 6a b x + 3b ) +--R | 5 | 5 \| x +--R \| a \| a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + 6b x ) |-------- +--R \| x +--R / +--R 3 3 2 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +---+ +--R | 3 | 2 +--R 3 3 2 +-+ |a x + b |9b +--R (- a x - a b)\|a |-------- |--- +--R | 3 | 5 +--R \| x \| a +--R * +--R +---+ +--------+ +--R | 2 | 3 +--R 3 2 |9b |a x + b 3 2 +--R log(2a x |--- |-------- + 6a b x + 3b ) +--R | 5 \| x +--R \| a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 3 2 |a x + b \| x +--R (6a b x + 6b ) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +-+ |a x + b |a x + b 2 6 3 2 +-+ +--R (2a x + 6b x )\|a |-------- |-------- + (- 2a x - 8a b x - 6b )\|a +--R | 3 \| x +--R \| x +--R / +--R +--------+ +--R | 3 +--R 3 3 2 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 4 10 3 7 |9b 10 2 7 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |--- + (6a b x + 3b x ) |-------- ) |-------- +--R | 5 | 3 \| x +--R \| a \| x +--R + +--R +--------+ +---+ +--R | 3 | 2 +--R 4 11 3 8 |a x + b |9b 2 11 2 8 3 5 +--R (2a x + 2a b x ) |-------- |--- - 6a b x - 9a b x - 3b x +--R | 3 | 5 +--R \| x \| a +--R / +--R +--------+ +---+ +--------+ +--R | 3 | 2 | 3 +--R 5 8 4 5 3 2 2 |a x + b |9b |a x + b +--R (2a x + 4a b x + 2a b x ) |-------- |--- |-------- +--R | 3 | 5 \| x +--R \| x \| a +--R + +--R +--------+ +--R | 3 +--R 3 9 2 2 6 3 3 4 |a x + b +--R (6a b x + 15a b x + 12a b x + 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1325 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+(-2/3)/(a*sqrt(a+b/x^3)) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R |a x + b \| x +-+ +--R 2 |-------- atanh(-----------) - 2\|a +--R | 3 +-+ +--R \| x \|a +--R (2) -------------------------------------- +--R +--------+ +--R | 3 +--R +-+ |a x + b +--R 3a\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R +--+ +--+ | 3 | 3 +--R 2 3 | 1 2 2 | 1 |a x + b 3 2 |a x + b +--R (- a x - a b) |-- log(2a x |-- |-------- - 2a x - b) - 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R -------------------------------------------------------------------------- +--R 2 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +--+ | 3 +--+ | 3 +--R 2 3 | 1 +-+ |a x + b 2 2 | 1 |a x + b 3 +--R (- a x - a b) |-- \|a |-------- log(2a x |-- |-------- - 2a x - b) +--R | 3 | 3 | 3 \| x +--R \|a \| x \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 3 |a x + b \| x +--R (- 2a x - 2b) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 +-+ |a x + b |a x + b 3 +-+ +--R - 2x \|a |-------- |-------- + (2a x + 2b)\|a +--R | 3 \| x +--R \| x +--R / +--R +--------+ +--R | 3 +--R 2 3 +-+ |a x + b +--R (3a x + 3a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 3 +--+ | 3 +--R 7 4 |a x + b 3 7 2 4 | 1 |a x + b +--R ((- 2a x - b x ) |-------- + (- 2a x - 2a b x ) |-- ) |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R +--+ | 3 +--R 3 8 2 5 | 1 |a x + b 2 8 5 2 2 +--R (2a x + 2a b x ) |-- |-------- + 2a x + 3a b x + b x +--R | 3 | 3 +--R \|a \| x +--R / +--R +--------+ +--------+ +--R +--+ | 3 | 3 +--R 4 8 3 5 2 2 2 | 1 |a x + b |a x + b +--R (2a x + 4a b x + 2a b x ) |-- |-------- |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 2a x - 5a b x - 4a b x - b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (a x + b x) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1325 +r0:=2/3/(b*sqrt(a+b/x^3)) +--R +--R +--R 2 +--R (2) ------------- +--R +--------+ +--R | 3 +--R |a x + b +--R 3b |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R \| x +--R (3) ------------- +--R 3 2 +--R 3a b x + 3b +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b 3 +--R 2 |-------- |-------- - 2a x - 2b +--R | 3 \| x +--R \| x +--R (4) ------------------------------------ +--R +--------+ +--R | 3 +--R 3 2 |a x + b +--R (3a b x + 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 3b x |-------- + (- 4a x - b) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 2 |a x + b |a x + b +--R (3a b x + 3b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 3 +--R 7 4 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1325 +r0:=-2/3*a/(b^2*sqrt(a+b/x^3))-2/3*sqrt(a+b/x^3)/b^2 +--R +--R +--R 3 +--R - 4a x - 2b +--R (2) ---------------- +--R +--------+ +--R | 3 +--R 2 3 |a x + b +--R 3b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 4a x - 2b) |-------- +--R \| x +--R (3) ------------------------- +--R 2 6 3 3 +--R 3a b x + 3b x +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b |a x + b 2 6 3 2 +--R (- 4a x - 2b) |-------- |-------- + 4a x + 6a b x + 2b +--R | 3 \| x +--R \| x +--R (4) ------------------------------------------------------------ +--R +--------+ +--R | 3 +--R 2 6 3 3 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 |a x + b 2 6 3 2 |a x + b +--R - 3b x |-------- + (8a x + 12a b x + 7b ) |-------- +--R \| x | 3 +--R \| x +--R (5) ------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 3 5 |a x + b |a x + b +--R (3a b x + 3b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^10) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R | 3 +--R 10 7 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1325 +r0:=-2/9*(a+b/x^3)^(3/2)/b^3+2/3*a^2/(b^3*sqrt(a+b/x^3))+_ + 4/3*a*sqrt(a+b/x^3)/b^3 +--R +--R +--R 2 6 3 2 +--R 16a x + 8a b x - 2b +--R (2) ---------------------- +--R +--------+ +--R | 3 +--R 3 6 |a x + b +--R 9b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (16a x + 8a b x - 2b ) |-------- +--R \| x +--R (3) ----------------------------------- +--R 3 9 4 6 +--R 9a b x + 9b x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b |a x + b 3 9 2 6 +--R (16a x + 8a b x - 2b ) |-------- |-------- - 16a x - 24a b x +--R | 3 \| x +--R \| x +--R + +--R 2 3 3 +--R - 6a b x + 2b +--R / +--R +--------+ +--R | 3 +--R 3 9 4 6 |a x + b +--R (9a b x + 9b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b +--R - 9b x |-------- + (- 32a x - 48a b x - 12a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) ---------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 11 4 8 |a x + b |a x + b +--R (9a b x + 9b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^13) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R | 3 +--R 13 10 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1325 +r0:=2/3*a*(a+b/x^3)^(3/2)/b^4-2/15*(a+b/x^3)^(5/2)/b^4-_ + 2/3*a^3/(b^4*sqrt(a+b/x^3))-2*a^2*sqrt(a+b/x^3)/b^4 +--R +--R +--R 3 9 2 6 2 3 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (2) ----------------------------------- +--R +--------+ +--R | 3 +--R 4 9 |a x + b +--R 15b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 32a x - 16a b x + 4a b x - 2b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 4 12 5 9 +--R 15a b x + 15b x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 9 2 6 2 3 3 |a x + b |a x + b 4 12 +--R (- 32a x - 16a b x + 4a b x - 2b ) |-------- |-------- + 32a x +--R | 3 \| x +--R \| x +--R + +--R 3 9 2 2 6 3 3 4 +--R 48a b x + 12a b x - 2a b x + 2b +--R / +--R +--------+ +--R | 3 +--R 4 12 5 9 |a x + b +--R (15a b x + 15b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 4 |a x + b +--R - 15b x |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (64a x + 96a b x + 24a b x - 4a b x + 19b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 14 5 11 |a x + b |a x + b +--R (15a b x + 15b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1325 +t0:=x^4/sqrt(8+27/x^3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1325 +--r0:=-189/1280*x^2*sqrt(8+27/x^3)+1/40*x^5*sqrt(8+27/x^3)-_ +-- 1701/1280*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 107 + +--S 108 of 1325 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 1325 +--m0:=a0-r0 +--E 109 + +--S 110 of 1325 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 1325 +t0:=x/sqrt(8+27/x^3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1325 +--r0:=1/16*x^2*sqrt(8+27/x^3)+9/16*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 112 + +--S 113 of 1325 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 1325 +--m0:=a0-r0 +--E 114 + +--S 115 of 1325 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 1325 +t0:=1/(x^2*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 2 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1325 +--r0:=-2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 117 + +--S 118 of 1325 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 1325 +--m0:=a0-r0 +--E 119 + +--S 120 of 1325 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 1325 +t0:=1/(x^5*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 5 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1325 +--r0:=-2/135*sqrt(8+27/x^3)/x+32/405*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 122 + +--S 123 of 1325 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 1325 +--m0:=a0-r0 +--E 124 + +--S 125 of 1325 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 1325 +t0:=x^3/sqrt(8+27/x^3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1325 +--r0:=-135/512*x*sqrt(8+27/x^3)+1/32*x^4*sqrt(8+27/x^3)+_ +-- 405/512*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-405/256*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 127 + +--S 128 of 1325 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 1325 +--m0:=a0-r0 +--E 129 + +--S 130 of 1325 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 1325 +t0:=1/sqrt(8+27/x^3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1325 +--r0:=1/8*x*sqrt(8+27/x^3)-3/8*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*_ +-- sqrt(3))))+3/4*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 132 + +--S 133 of 1325 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 1325 +--m0:=a0-r0 +--E 134 + +--S 135 of 1325 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 1325 +t0:=1/(x^3*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 3 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1325 +--r0:=-2/9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+4/9*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 137 + +--S 138 of 1325 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 1325 +--m0:=a0-r0 +--E 139 + +--S 140 of 1325 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 1325 +t0:=1/(x^6*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 6 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1325 +--r0:=-2/189*sqrt(8+27/x^3)/x^2+64/1701*(-1)^(1/4)*(2+3/x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+_ +-- 3/x)/(3+%i*sqrt(3))))-128/1701*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_ +-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 142 + +--S 143 of 1325 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 1325 +--m0:=a0-r0 +--E 144 + +--S 145 of 1325 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 1325 +t0:=1/(a+b/x^4) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 4 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1325 +r0:=x/a+1/2*b^(1/4)*atan(1-a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))-_ + 1/2*b^(1/4)*atan(1+a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))+_ + 1/4*b^(1/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+x^2*sqrt(a)+sqrt(b))/_ + (a^(5/4)*sqrt(2))-1/4*b^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+_ + x^2*sqrt(a)+sqrt(b))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R - \|b log(x\|2 \|a \|b + \|b + x \|a ) +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ 4+-+ \|b + x\|2 \|a +--R \|b log(- x\|2 \|a \|b + \|b + x \|a ) - 2\|b atan(----------------) +--R 4+-+ +--R \|b +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ \|b - x\|2 \|a +-+4+-+ +--R 2\|b atan(----------------) + 4x\|2 \|a +--R 4+-+ +--R \|b +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | b | b | b | b +--R - a |- ----- log(4a |- ----- + x + a |- ----- log(- 4a |- ----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 256a \| 256a \| 256a \| 256a +--R + +--R +-------+ +--R | b +--R 4a |- ----- +--R +-------+ 4| 5 +--R | b \| 256a +--R 2a |- ----- atan(------------ + x +--R 4| 5 x +--R \| 256a +--R / +--R a +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R \|b log(x\|2 \|a \|b + \|b + x \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | b 4+-+ | b +--R - 4a\|2 |- ----- \|a log(4a |- ----- + x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R +-+ | b 4+-+ | b +--R 4a\|2 |- ----- \|a log(- 4a |- ----- + x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R - \|b log(- x\|2 \|a \|b + \|b + x \|a ) +--R + +--R +-------+ +--R | b +--R 4a |- ----- +--R +-------+ 4| 5 4+-+ +-+4+-+ +--R +-+ | b 4+-+ \| 256a 4+-+ \|b + x\|2 \|a +--R 8a\|2 |- ----- \|a atan(------------ + 2\|b atan(----------------) +--R 4| 5 x 4+-+ +--R \| 256a \|b +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ \|b - x\|2 \|a +--R - 2\|b atan(----------------) +--R 4+-+ +--R \|b +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1325 +t0:=(a+b/x^4)^(1/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 3 |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1325 +r0:=1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a)+1/4*x^4*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R \| x 4 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 4 +---+ +--R 8\|- a \|b \|a x + b + (- 4a x - 8b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 153 + +--S 154 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +-+ | 4 4 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4 +--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +-+ +-+ 8 4 +-+ |a x + b +--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 18 4 14 3 2 10 2 3 6 4 2 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 22 5 18 4 2 14 3 3 10 2 4 6 5 2 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 4 +--R 4 15 3 11 2 2 7 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 19 4 15 3 2 11 2 3 7 4 3 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +---+ +-+ | 4 4 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 4 4 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b +--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 4 4 +---+ +-+ +--R 8\|- a \|a \|b \|a x + b + (- 4a x - 8b)\|- a \|a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 4a x - 12a b x - 8b x ) |-------- \|b - a x - 9a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 9a b x + 16a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 9 5 2 |a x + b | 4 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 1325 +t0:=(a+b/x^4)^(1/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1325 +--r0:=1/3*x^3*sqrt(a+b/x^4)+2/3*a^(1/4)*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 159 + +--S 160 of 1325 +--a0:=integrate(t0,x) +--E 160 + +--S 161 of 1325 +--m0:=a0-r0 +--E 161 + +--S 162 of 1325 +--d0:=D(m0,x) +--E 162 + +)clear all + +--S 163 of 1325 +t0:=(a+b/x^4)^(1/2)*x +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1325 +r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)+1/2*x^2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R +-+ | 4 +--R +-+ \|b 2 |a x + b +--R - \|b atanh(-------------) + x |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|b \|a x + b + a x + 2b | 4 +--R \|b log(------------------------------) + 2\|a x + b +--R 4 +--R x +--R [------------------------------------------------------, +--R 4 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|a x + b | 4 +--R - \|- b atan(-----------) + \|a x + b +--R +---+ +--R \|- b +--R ---------------------------------------] +--R 2 +--R Type: Union(List(Expression(Integer)),...) +--E 165 + +--S 166 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +-+ +--R +-+ - 2\|b \|a x + b + a x + 2b +-+ \|b +--R \|b log(------------------------------) + 2\|b atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R 2\|a x + b - 2x |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b +-+ 4 | 4 4 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +--R (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ | 4 5 +--R 2x\|b \|a x + b - a x - 2b x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--------+ +--R +-+ \|b +---+ \|a x + b | 4 +--R \|b atanh(-------------) - \|- b atan(-----------) + \|a x + b +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 |a x + b +--R - x |-------- +--R | 4 +--R \| x +--R / +--R 2 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b | 4 4 +--R - x |-------- \|a x + b + a x + b +--R | 4 +--R \| x +--R (7) ------------------------------------- +--R +--------+ +--R | 4 +--R x\|a x + b +--R Type: Expression(Integer) +--E 169 + +)clear all + +--S 170 of 1325 +t0:=(a+b/x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R (1) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1325 +--r0:=x*sqrt(a+b/x^4)+2*a^(3/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-2*a^(3/4)*_ +-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 171 + +--S 172 of 1325 +--a0:=integrate(t0,x) +--E 172 + +--S 173 of 1325 +--m0:=a0-r0 +--E 173 + +--S 174 of 1325 +--d0:=D(m0,x) +--E 174 + +)clear all + +--S 175 of 1325 +t0:=(a+b/x^4)^(1/2)/x +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))*sqrt(a)-1/2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R +-+ \| x |a x + b +--R \|a atanh(-----------) - |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|a \|a x + b - x \|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R , +--R +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b +--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 177 + +--S 178 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|a \|a x + b - x \|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R 2 +-+ | 4 2 +-+ +-+ \| x +--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 4 | 4 +--R \| x \| x +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 14 2 10 2 6 3 2 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 4 +--R \| x +--R + +--R 3 12 2 2 8 3 4 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 4 +--R \| x +--R + +--R 3 12 2 2 8 3 4 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x )\|a +--R / +--R +--------+ +--R | 4 +--R 2 15 11 2 7 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 19 2 15 2 11 3 7 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R 2 +-+ | 4 2 +-+ +-+ \| x +--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b +--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 4 | 4 +--R \| x \| x +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 6 2 |a x + b +-+ 2 8 4 2 | 4 +--R ((- 2a x - 2b x ) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ 2 10 6 2 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 9 5 |a x + b | 4 9 5 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 181 + +)clear all + +--S 182 of 1325 +t0:=(a+b/x^4)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1325 +--r0:=-1/3*sqrt(a+b/x^4)/x-2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 183 + +--S 184 of 1325 +--a0:=integrate(t0,x) +--E 184 + +--S 185 of 1325 +--m0:=a0-r0 +--E 185 + +--S 186 of 1325 +--d0:=D(m0,x) +--E 186 + +)clear all + +--S 187 of 1325 +t0:=(a+b/x^4)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1325 +r0:=-1/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-1/4*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 \|b |a x + b +-+ +--R - a x atanh(-------------) - |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) -------------------------------------------- +--R 2 +-+ +--R 4x \|b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 - 2b\|a x + b + (a x + 2b)\|b +-+ | 4 +--R a x log(---------------------------------) - 2\|b \|a x + b +--R 4 +--R x +--R [-------------------------------------------------------------, +--R 4 +-+ +--R 8x \|b +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- b \|a x + b +---+ | 4 +--R - a x atan(-----------------) - \|- b \|a x + b +--R b +--R -------------------------------------------------] +--R 4 +---+ +--R 4x \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 189 + +--S 190 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +-+ +--R 4 - 2b\|a x + b + (a x + 2b)\|b 4 \|b +--R a x log(---------------------------------) + 2a x atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R +-+ | 4 2 |a x + b +-+ +--R - 2\|b \|a x + b + 2x |-------- \|b +--R | 4 +--R \| x +--R / +--R 4 +-+ +--R 8x \|b +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1325 +d0a:=D(m0a,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (5) --------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 4 +---+ \|b 4 +-+ \|- b \|a x + b +--R a x \|- b atanh(-------------) - a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R +---+ +-+ | 4 2 +---+ |a x + b +-+ +--R - \|- b \|b \|a x + b + x \|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 4 +---+ +-+ +--R 4x \|- b \|b +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (7) --------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 193 + +)clear all + +--S 194 of 1325 +t0:=(a+b/x^4)^(1/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1325 +--r0:=-1/5*sqrt(a+b/x^4)/x^3-2/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+_ +-- 2/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 195 + +--S 196 of 1325 +--a0:=integrate(t0,x) +--E 196 + +--S 197 of 1325 +--m0:=a0-r0 +--E 197 + +--S 198 of 1325 +--d0:=D(m0,x) +--E 198 + +)clear all + +--S 199 of 1325 +t0:=(a+b/x^4)^(3/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1325 +r0:=1/4*(a+b/x^4)^(3/2)*x^4+3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))*_ + sqrt(a)-3/4*b*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R +-+ \| x 4 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x +--R + +--R 3 +--R - 8b +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R , +--R +--R +--------+ +--R 6 2 2 +---+ | 4 +--R (6a b x + 24b x )\|- a \|a x + b +--R + +--R 6 2 2 +---+ +-+ +--R (- 18a b x - 24b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x +--R + +--R 3 +--R - 8b +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 201 + +--S 202 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (- 3a x + 2a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 2a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 4 +--R \| x +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 26 5 22 4 2 18 3 3 14 2 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 6 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 6 26 5 22 4 2 18 3 3 14 +--R - 9a x - 138a b x - 681a b x - 1560a b x +--R + +--R 2 4 10 5 6 6 2 +--R - 1840a b x - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 8 6 4 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 8 6 4 7 +--R 2352a b x + 1216a b x + 256b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 8 6 4 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 8 6 4 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R 2352a b x + 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 23 3 19 2 2 15 3 11 4 7 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 5 +--R - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 5 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 5 7 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 6 2 2 +---+ | 4 6 2 2 +---+ +-+ +--R ((6a b x + 24b x )\|- a \|a x + b + (- 18a b x - 24b x )\|- a \|b ) +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 2 8 4 2 +-+ +--R (- 3a x + 2a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 2a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 4 +--R \| x +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 17 2 13 2 9 3 5 |a x + b | 4 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1325 +t0:=(a+b/x^4)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1325 +--r0:=1/3*(a+b/x^4)^(3/2)*x^3-2/3*b*sqrt(a+b/x^4)/x+4/3*a^(5/4)*_ +-- (-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 207 + +--S 208 of 1325 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 1325 +--m0:=a0-r0 +--E 209 + +--S 210 of 1325 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 1325 +t0:=(a+b/x^4)^(3/2)*x +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1325 +r0:=1/2*(a+b/x^4)^(3/2)*x^2-3/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*_ + sqrt(b)-3/4*b*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 +-+ \|b 4 |a x + b +--R - 3a x \|b atanh(-------------) + (2a x - b) |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) -------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R 4 +-+ - 2\|b \|a x + b + a x + 2b 4 | 4 +--R 3a x \|b log(------------------------------) + (4a x - 2b)\|a x + b +--R 4 +--R x +--R [----------------------------------------------------------------------, +--R 4 +--R 8x +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ \|a x + b 4 | 4 +--R - 3a x \|- b atan(-----------) + (2a x - b)\|a x + b +--R +---+ +--R \|- b +--R -------------------------------------------------------] +--R 4 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 213 + +--S 214 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +--R 4 +-+ - 2\|b \|a x + b + a x + 2b +--R 3a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 4 +-+ \|b 4 | 4 +--R 6a x \|b atanh(-------------) + (4a x - 2b)\|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +--R (- 4a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 2 8 4 2 +-+ +--R (- 2a x - 4a b x - 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 3a b x - 2b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (2a x + 4a b x + 2b x ) |-------- \|b + a x + 4a b x + 5a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 |a x + b +-+ | 4 11 7 |a x + b +--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--R 4 +-+ \|b 4 +---+ \|a x + b +--R 3a x \|b atanh(-------------) - 3a x \|- b atan(-----------) +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (2a x - b)\|a x + b + (- 2a x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R +--------+ | 4 +--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b +--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |-------- +--R | 4 +--R \| x +--R ------------------------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 7 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1325 +t0:=(a+b/x^4)^(3/2) +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1325 +--r0:=-1/5*(a+b/x^4)^(3/2)*x+6/5*a*x*sqrt(a+b/x^4)+12/5*a^(7/4)*_ +-- (-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-12/5*a^(7/4)*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 219 + +--S 220 of 1325 +--a0:=integrate(t0,x) +--E 220 + +--S 221 of 1325 +--m0:=a0-r0 +--E 221 + +--S 222 of 1325 +--d0:=D(m0,x) +--E 222 + +)clear all + +--S 223 of 1325 +t0:=(a+b/x^4)^(3/2)/x +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1325 +r0:=-1/6*(a+b/x^4)^(3/2)+1/2*a^(3/2)*atanh(sqrt(a+b/x^4)/sqrt(a))-_ + 1/2*a*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 4 +-+ \| x 4 |a x + b +--R 3a x \|a atanh(-----------) + (- 4a x - b) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 4 +--R 6x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R , +--R +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 10 6 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 225 + +--S 226 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (12a x + 19a b x + 4b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (4a x + 17a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 21a b x - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 26 5 22 4 2 18 3 3 14 2 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 6 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 6 26 5 22 4 2 18 3 3 14 +--R - 9a x - 138a b x - 681a b x - 1560a b x +--R + +--R 2 4 10 5 6 6 2 +--R - 1840a b x - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 8 6 4 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 8 6 4 7 +--R 2352a b x + 1216a b x + 256b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 8 6 4 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 8 6 4 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R 2352a b x + 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 27 3 23 2 2 19 3 15 4 11 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 9 +--R - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 10 6 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 2 8 4 2 +-+ +--R (12a x + 19a b x + 4b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (4a x + 17a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 21a b x - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 21 2 17 2 13 3 9 |a x + b | 4 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 229 + +)clear all + +--S 230 of 1325 +t0:=(a+b/x^4)^(3/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1325 +--r0:=-1/7*(a+b/x^4)^(3/2)/x-2/7*a*sqrt(a+b/x^4)/x-4/7*a^(9/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- ((-b)^(1/4)*sqrt(a+b/x^4)) +--E 231 + +--S 232 of 1325 +--a0:=integrate(t0,x) +--E 232 + +--S 233 of 1325 +--m0:=a0-r0 +--E 233 + +--S 234 of 1325 +--d0:=D(m0,x) +--E 234 + +)clear all + +--S 235 of 1325 +t0:=(a+b/x^4)^(3/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1325 +r0:=-1/8*(a+b/x^4)^(3/2)/x^2-3/16*a^2*atanh(sqrt(b)/(x^2*_ + sqrt(a+b/x^4)))/sqrt(b)-3/16*a*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 6 \|b 4 |a x + b +-+ +--R - 3a x atanh(-------------) + (- 5a x - 2b) |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ----------------------------------------------------------- +--R 6 +-+ +--R 16x \|b +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 4 +-+ | 4 +--R 3a x log(---------------------------------) + (- 10a x - 4b)\|b \|a x + b +--R 4 +--R x +--R [---------------------------------------------------------------------------- +--R 8 +-+ +--R 32x \|b +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- b \|a x + b 4 +---+ | 4 +--R - 3a x atan(-----------------) + (- 5a x - 2b)\|- b \|a x + b +--R b +--R ----------------------------------------------------------------] +--R 8 +---+ +--R 16x \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 237 + +--S 238 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +-+ +--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 2 8 \|b +--R 3a x log(---------------------------------) + 6a x atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 +-+ | 4 6 2 |a x + b +-+ +--R (- 10a x - 4b)\|b \|a x + b + (10a x + 4b x ) |-------- \|b +--R | 4 +--R \| x +--R / +--R 8 +-+ +--R 32x \|b +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 2 8 2 4 3 +--R ((- a x - 3a b x - 2b x ) |-------- \|b - 2a b x - 4a b x - 2b ) +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (a x + 4a b x + 5a b x + 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 2 6 3 2 |a x + b +--R (2a b x + 4a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 11 |a x + b | 4 15 11 |a x + b +-+ +--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 2 8 +---+ \|b 2 8 +-+ \|- b \|a x + b +--R 3a x \|- b atanh(-------------) - 3a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 +---+ +-+ | 4 6 2 +---+ |a x + b +-+ +--R (- 5a x - 2b)\|- b \|b \|a x + b + (5a x + 2b x )\|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 8 +---+ +-+ +--R 16x \|- b \|b +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R +--------+ | 4 +--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b +--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |-------- +--R | 4 +--R \| x +--R ------------------------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 11 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 241 + +)clear all + +--S 242 of 1325 +t0:=(a+b/x^4)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1325 +--r0:=-1/9*(a+b/x^4)^(3/2)/x^3-2/15*a*sqrt(a+b/x^4)/x^3-4/15*a^(11/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- ((-b)^(3/4)*sqrt(a+b/x^4))+4/15*a^(11/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_ +-- sqrt(a+b/x^4)) +--E 243 + +--S 244 of 1325 +--a0:=integrate(t0,x) +--E 244 + +--S 245 of 1325 +--m0:=a0-r0 +--E 245 + +--S 246 of 1325 +--d0:=D(m0,x) +--E 246 + +)clear all + +--S 247 of 1325 +t0:=(a+b/x^4)^(5/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1325 +r0:=-5/12*b*(a+b/x^4)^(3/2)+1/4*(a+b/x^4)^(5/2)*x^4+5/4*a^(3/2)*b*_ + atanh(sqrt(a+b/x^4)/sqrt(a))-5/4*a*b*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 4 +-+ \| x 2 8 4 2 |a x + b +--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) -------------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R , +--R +--R +--------+ +--R 3 14 2 2 10 3 6 +---+ | 4 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 249 + +--S 250 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 38 8 34 7 2 30 6 3 26 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 6 9 2 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 9 38 8 34 7 2 30 6 3 26 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 6 9 2 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x +--R + +--R 9 4 +--R - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 4 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x +--R + +--R 9 4 +--R 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 4 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 6 10 2 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 6 10 2 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 35 5 31 4 2 27 3 3 23 2 4 19 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 15 6 11 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 17 6 13 7 9 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 17 6 13 7 9 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 19 6 15 7 11 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 14 2 2 10 3 6 +---+ | 4 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 34 7 30 6 2 26 5 3 22 4 4 18 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 14 2 6 10 7 6 8 2 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 9 +--R - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 253 + +)clear all + +--S 254 of 1325 +t0:=(a+b/x^4)^(5/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1325 +--r0:=-10/21*b*(a+b/x^4)^(3/2)/x+1/3*(a+b/x^4)^(5/2)*x^3-20/21*a*b*_ +-- sqrt(a+b/x^4)/x+40/21*a^(9/4)*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 255 + +--S 256 of 1325 +--a0:=integrate(t0,x) +--E 256 + +--S 257 of 1325 +--m0:=a0-r0 +--E 257 + +--S 258 of 1325 +--d0:=D(m0,x) +--E 258 + +)clear all + +--S 259 of 1325 +t0:=(a+b/x^4)^(5/2)*x +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1325 +r0:=-5/8*b*(a+b/x^4)^(3/2)/x^2+1/2*(a+b/x^4)^(5/2)*x^2-15/16*a^2*_ + atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)-15/16*a*b*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 6 +-+ \|b 2 8 4 2 |a x + b +--R - 15a x \|b atanh(-------------) + (8a x - 9a b x - 2b ) |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) --------------------------------------------------------------------- +--R 6 +--R 16x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b +--R 15a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 | 4 +--R (16a x - 18a b x - 4b )\|a x + b +--R / +--R 8 +--R 32x +--R , +--R +--------+ +--R | 4 +--------+ +--R 2 8 +---+ \|a x + b 2 8 4 2 | 4 +--R - 15a x \|- b atan(-----------) + (8a x - 9a b x - 2b )\|a x + b +--R +---+ +--R \|- b +--R --------------------------------------------------------------------] +--R 8 +--R 16x +--R Type: Union(List(Expression(Integer)),...) +--E 261 + +--S 262 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b +--R 15a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 2 8 +-+ \|b 2 8 4 2 | 4 +--R 30a x \|b atanh(-------------) + (16a x - 18a b x - 4b )\|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- 16a x + 18a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R / +--R 8 +--R 32x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 3 12 2 8 2 4 3 +-+ +--R (- 2a x - 6a b x - 6a b x - 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (- a x - 4a b x - 5a b x - 2b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +-+ 4 16 3 12 +--R (2a x + 6a b x + 6a b x + 2b x ) |-------- \|b + a x + 5a b x +--R | 4 +--R \| x +--R + +--R 2 2 8 3 4 4 +--R 9a b x + 7a b x + 2b +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 11 |a x + b +-+ | 4 15 11 |a x + b +--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--R 2 8 +-+ \|b 2 8 +---+ \|a x + b +--R 15a x \|b atanh(-------------) - 15a x \|- b atan(-----------) +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R 2 8 4 2 | 4 +--R (8a x - 9a b x - 2b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- 8a x + 9a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R 8 +--R 16x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (- a x - 3a b x - 3a b x - b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 3a b x + 3a b x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 11 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1325 +t0:=(a+b/x^4)^(5/2) +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1325 +--r0:=-2/9*a*(a+b/x^4)^(3/2)*x-1/9*(a+b/x^4)^(5/2)*x+4/3*a^2*x*_ +-- sqrt(a+b/x^4)+8/3*a^(11/4)*(-b)^(1/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4)-8/3*a^(11/4)*(-b)^(1/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 267 + +--S 268 of 1325 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 1325 +--m0:=a0-r0 +--E 269 + +--S 270 of 1325 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 1325 +t0:=(a+b/x^4)^(5/2)/x +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1325 +r0:=-1/6*a*(a+b/x^4)^(3/2)-1/10*(a+b/x^4)^(5/2)+1/2*a^(5/2)*_ + atanh(sqrt(a+b/x^4)/sqrt(a))-1/2*a^2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 2 8 +-+ \| x 2 8 4 2 |a x + b +--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 8 +--R 30x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R , +--R +--R +--------+ +--R 4 18 3 14 2 2 10 +---+ | 4 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 273 + +--S 274 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 38 8 34 7 2 30 6 3 26 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 6 9 2 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 9 38 8 34 7 2 30 6 3 26 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 6 9 2 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x +--R + +--R 9 4 +--R - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 4 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x +--R + +--R 9 4 +--R 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 4 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 6 10 2 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 6 10 2 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 39 5 35 4 2 31 3 3 27 2 4 23 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 19 6 15 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 21 6 17 7 13 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 21 6 17 7 13 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 43 6 39 5 2 35 4 3 31 3 4 27 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 23 6 19 7 15 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 18 3 14 2 2 10 +---+ | 4 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 34 7 30 6 2 26 5 3 22 4 4 18 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 14 2 6 10 7 6 8 2 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 33 4 29 3 2 25 2 3 21 4 17 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 13 +--R - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1325 +t0:=(a+b/x^4)^(5/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1325 +--r0:=-10/77*a*(a+b/x^4)^(3/2)/x-1/11*(a+b/x^4)^(5/2)/x-20/77*a^2*_ +-- sqrt(a+b/x^4)/x-40/77*a^(13/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 279 + +--S 280 of 1325 +--a0:=integrate(t0,x) +--E 280 + +--S 281 of 1325 +--m0:=a0-r0 +--E 281 + +--S 282 of 1325 +--d0:=D(m0,x) +--E 282 + +)clear all + +--S 283 of 1325 +t0:=(a+b/x^4)^(5/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1325 +r0:=-5/48*a*(a+b/x^4)^(3/2)/x^2-1/12*(a+b/x^4)^(5/2)/x^2-5/32*a^3*_ + atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-5/32*a^2*sqrt(a+b/x^4)/x^2 +--R +--R +--R (2) +--R +--------+ +--R +-+ | 4 +--R 3 10 \|b 2 8 4 2 |a x + b +-+ +--R - 15a x atanh(-------------) + (- 33a x - 26a b x - 8b ) |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R -------------------------------------------------------------------------- +--R 10 +-+ +--R 96x \|b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R | 4 4 +-+ +--R 3 12 - 2b\|a x + b + (a x + 2b)\|b +--R 15a x log(---------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 +--R (- 66a x - 52a b x - 16b )\|b \|a x + b +--R / +--R 12 +-+ +--R 192x \|b +--R , +--R +--R +--------+ +--R +---+ | 4 +--R 3 12 \|- b \|a x + b +--R - 15a x atan(-----------------) +--R b +--R + +--R +--------+ +--R 2 8 4 2 +---+ | 4 +--R (- 33a x - 26a b x - 8b )\|- b \|a x + b +--R / +--R 12 +---+ +--R 96x \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 285 + +--S 286 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +--R 3 12 - 2b\|a x + b + (a x + 2b)\|b +--R 15a x log(---------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 3 12 \|b 2 8 4 2 +-+ | 4 +--R 30a x atanh(-------------) + (- 66a x - 52a b x - 16b )\|b \|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ +--R (66a x + 52a b x + 16b x ) |-------- \|b +--R | 4 +--R \| x +--R / +--R 12 +-+ +--R 192x \|b +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +-+ 3 12 +--R (- a x - 4a b x - 5a b x - 2b x ) |-------- \|b - 2a b x +--R | 4 +--R \| x +--R + +--R 2 2 8 3 4 4 +--R - 6a b x - 6a b x - 2b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (a x + 5a b x + 9a b x + 7a b x + 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 2 10 3 6 4 2 |a x + b +--R (2a b x + 6a b x + 6a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 15 |a x + b | 4 19 15 |a x + b +-+ +--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 3 12 +---+ \|b 3 12 +-+ \|- b \|a x + b +--R 15a x \|- b atanh(-------------) - 15a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R 2 8 4 2 +---+ +-+ | 4 +--R (- 33a x - 26a b x - 8b )\|- b \|b \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ |a x + b +-+ +--R (33a x + 26a b x + 8b x )\|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 12 +---+ +-+ +--R 96x \|- b \|b +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (- a x - 3a b x - 3a b x - b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 3a b x + 3a b x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 15 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 289 + +)clear all + +--S 290 of 1325 +t0:=(a+b/x^4)^(5/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1325 +--r0:=-10/117*a*(a+b/x^4)^(3/2)/x^3-1/13*(a+b/x^4)^(5/2)/x^3-_ +-- 4/39*a^2*sqrt(a+b/x^4)/x^3-8/39*a^(15/4)*elliptic_e(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_ +-- sqrt(a+b/x^4))+8/39*a^(15/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 291 + +--S 292 of 1325 +--a0:=integrate(t0,x) +--E 292 + +--S 293 of 1325 +--m0:=a0-r0 +--E 293 + +--S 294 of 1325 +--d0:=D(m0,x) +--E 294 + +)clear all + +--S 295 of 1325 +t0:=x^3/(a+b/x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1325 +r0:=-1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+1/4*x^4*sqrt(a+b/x^4)/a +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R \| x 4 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 4 4 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 8a\|- a \|b \|a x + b + (- 4a x - 8a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 297 + +--S 298 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +-+ | 4 4 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4 +--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +-+ +-+ 8 4 +-+ |a x + b +--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 +-+ |a x + b +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- +--R | 4 +--R \| x +--R + +--R 4 17 3 13 2 2 9 3 5 +--R - 7a x - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 19 3 15 2 2 11 3 7 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 19 3 15 2 2 11 3 7 4 3 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 19 3 15 2 2 11 3 7 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 19 3 15 2 2 11 3 7 4 3 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 21 3 17 2 2 13 3 9 4 5 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 4 +--R \| x +--R + +--R 5 21 4 17 3 2 13 2 3 9 4 5 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 4 +--R 4 14 3 10 2 2 6 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +---+ +-+ | 4 4 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 4 4 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b +--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 4 2 4 +---+ +-+ +--R 8a\|- a \|a \|b \|a x + b + (- 4a x - 8a b)\|- a \|a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 9 5 |a x + b +-+ 2 11 7 2 3 | 4 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 11 7 2 3 +-+ 2 13 9 2 5 |a x + b +--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 301 + +)clear all + +--S 302 of 1325 +t0:=x^2/(a+b/x^4)^(1/2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1325 +--r0:=1/3*x^3*sqrt(a+b/x^4)/a-1/3*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(3/4)*sqrt(a+b/x^4)) +--E 303 + +--S 304 of 1325 +--a0:=integrate(t0,x) +--E 304 + +--S 305 of 1325 +--m0:=a0-r0 +--E 305 + +--S 306 of 1325 +--d0:=D(m0,x) +--E 306 + +)clear all + +--S 307 of 1325 +t0:=x/(a+b/x^4)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1325 +r0:=1/2*x^2*sqrt(a+b/x^4)/a +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ------------- +--R 2a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 +--R \|a x + b +--R (3) ----------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (4) --------------------------- +--R 2a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 3 |a x + b +--R - x\|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------ +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 311 + +)clear all + +--S 312 of 1325 +t0:=1/(a+b/x^4)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1325 +--r0:=x*sqrt(a+b/x^4)/a+(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4))-_ +-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4)) +--E 313 + +--S 314 of 1325 +--a0:=integrate(t0,x) +--E 314 + +--S 315 of 1325 +--m0:=a0-r0 +--E 315 + +--S 316 of 1325 +--d0:=D(m0,x) +--E 316 + +)clear all + +--S 317 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 4 +--R |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|a +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R ------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 319 + +--S 320 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 6 2 +-+ |a x + b 2 6 2 +-+ +--R ((3a x + 4b x )\|a |-------- - 3a x - 4a b x )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 |a x + b 2 8 4 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 8 4 |a x + b 2 8 4 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b 3 10 2 6 2 2 +--R (- a x - 5a b x - 4b x )\|a |-------- + a x + 5a b x + 4a b x +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--R 2 7 3 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 11 2 7 2 3 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 +---+ | 4 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ 2 +--R \|a a x +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 323 + +)clear all + +--S 324 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1325 +--r0:=-a^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 325 + +--S 326 of 1325 +--a0:=integrate(t0,x) +--E 326 + +--S 327 of 1325 +--m0:=a0-r0 +--E 327 + +--S 328 of 1325 +--d0:=D(m0,x) +--E 328 + +)clear all + +--S 329 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^3) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 3 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1325 +r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R atanh(-------------) +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) - -------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2b\|a x + b + (a x + 2b)\|b +---+ | 4 +--R log(---------------------------------) \|- b \|a x + b +--R 4 atan(-----------------) +--R x b +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|b 2\|- b +--R Type: Union(List(Expression(Integer)),...) +--E 331 + +--S 332 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R | 4 4 +-+ +-+ +--R - 2b\|a x + b + (a x + 2b)\|b \|b +--R log(---------------------------------) + 2atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (4) -------------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ 2 |a x + b | 4 +--R ((- a x - 2b)\|b - 2b x |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +-+ 4 2 +--R (a x + 2b x ) |-------- \|b + 2a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 3 |a x + b +-+ | 4 7 2 3 |a x + b +--R (a x + 2b x ) |-------- \|b \|a x + b + (- 2a b x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 4 +--R +---+ \|b +-+ \|- b \|a x + b +--R \|- b atanh(-------------) - \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R 3 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^4) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1325 +--r0:=-a^(3/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+a^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 337 + +--S 338 of 1325 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 1325 +--m0:=a0-r0 +--E 339 + +--S 340 of 1325 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 1325 +t0:=x^3/(a+b/x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1325 +r0:=-3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(5/2)-_ + 1/2*x^4/(a*sqrt(a+b/x^4))+3/4*x^4*sqrt(a+b/x^4)/a^2 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R |a x + b \| x 4 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 4 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 4 +--R 2 +-+ |a x + b +--R 4a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (- a x - 7a b x - 12b x )\|a \|a x + b +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (3a x + 13a b x + 12b x )\|a \|b +--R / +--R +--------+ +--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+ +--R (12a x + 16a b)\|a \|b \|a x + b + (- 4a x - 20a b x - 16a b )\|a +--R , +--R +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (- a x - 7a b x - 12b x )\|- a \|a x + b +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (3a x + 13a b x + 12b x )\|- a \|b +--R / +--R +--------+ +--R 3 4 2 +---+ +-+ | 4 +--R (12a x + 16a b)\|- a \|b \|a x + b +--R + +--R 4 8 3 4 2 2 +---+ +--R (- 4a x - 20a b x - 16a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 343 + +--S 344 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 4 2 |a x + b +-+ | 4 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 2 |a x + b +-+ | 4 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +--R (- a x - 7a b x - 12b x )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (a x + 8a b x + 19a b x + 12b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 4 2 +-+ |a x + b +-+ | 4 +--R (12a x + 16a b)\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 8 3 4 2 2 +-+ |a x + b +--R (- 4a x - 20a b x - 16a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 25 3 21 2 2 17 3 13 4 9 +-+ +--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 7 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 7 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 6 22 5 18 4 2 14 3 3 10 2 4 6 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 2 +--R 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 6 24 5 20 4 2 16 3 3 12 2 4 8 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x +--R + +--R 5 4 6 +--R 960a b x + 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 24 5 20 4 2 16 3 3 12 2 4 8 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 4 6 +--R - 1088a b x - 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 26 6 22 5 2 18 4 3 14 3 4 10 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 2 5 6 6 2 +--R - 960a b x - 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--------+ +--R 4 2 +---+ |a x + b +-+ | 4 +--R (9a b x + 12b )\|- a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 +---+ |a x + b +--R (- 3a b x - 15a b x - 12b )\|- a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 2 +-+ |a x + b +-+ | 4 +--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 +-+ |a x + b +--R (6a b x + 30a b x + 24b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 2 8 4 2 +---+ +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +--R (- a x - 7a b x - 12b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +---+ +-+ +--R (a x + 8a b x + 19a b x + 12b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 4 2 +---+ +-+ |a x + b +-+ | 4 +--R (12a x + 16a b)\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 8 3 4 2 2 +---+ +-+ |a x + b +--R (- 4a x - 20a b x - 16a b )\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 4 +--R \| x +--R + +--R 2 11 3 7 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 19 2 15 2 11 3 7 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 16 3 12 2 2 8 3 4 4 |a x + b | 4 +--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1325 +t0:=x^2/(a+b/x^4)^(3/2) +--R +--R +--R 6 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1325 +--r0:=-1/2*x^3/(a*sqrt(a+b/x^4))+5/6*x^3*sqrt(a+b/x^4)/a^2-_ +-- 5/6*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(7/4)*sqrt(a+b/x^4)) +--E 349 + +--S 350 of 1325 +--a0:=integrate(t0,x) +--E 350 + +--S 351 of 1325 +--m0:=a0-r0 +--E 351 + +--S 352 of 1325 +--d0:=D(m0,x) +--E 352 + +)clear all + +--S 353 of 1325 +t0:=x/(a+b/x^4)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1325 +r0:=-1/2*x^2/(a*sqrt(a+b/x^4))+x^2*sqrt(a+b/x^4)/a^2 +--R +--R +--R 4 +--R a x + 2b +--R (2) ---------------- +--R +--------+ +--R | 4 +--R 2 2 |a x + b +--R 2a x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R a x + 2b +--R (3) -------------- +--R +--------+ +--R 2 | 4 +--R 2a \|a x + b +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (- a x - 2b)\|a x + b + (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R (4) ---------------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 2 |a x + b | 4 +--R 2a x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 5 | 4 7 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) -------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 4 |a x + b | 4 +--R (a x + b) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1325 +t0:=1/(a+b/x^4)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1325 +--r0:=-1/2*x/(a*sqrt(a+b/x^4))+3/2*x*sqrt(a+b/x^4)/a^2+_ +-- 3/2*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4))-3/2*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4)) +--E 359 + +--S 360 of 1325 +--a0:=integrate(t0,x) +--E 360 + +--S 361 of 1325 +--m0:=a0-r0 +--E 361 + +--S 362 of 1325 +--d0:=D(m0,x) +--E 362 + +)clear all + +--S 363 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+(-1/2)/(a*sqrt(a+b/x^4)) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R |a x + b \| x +-+ +--R |-------- atanh(-----------) - \|a +--R | 4 +-+ +--R \| x \|a +--R (2) ------------------------------------ +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R 2a\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R (\|b \|a x + b - a x - b) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R x \|a \|a x + b - x \|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 2a\|a \|b \|a x + b + (- 2a x - 2a b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 \|- a \|a x + b - \|- a \|b +--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 +---+ | 4 2 +---+ +-+ +--R x \|- a \|a x + b - x \|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 2a\|- a \|b \|a x + b + (- 2a x - 2a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 365 + +--S 366 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R |a x + b +-+ | 4 4 |a x + b +--R ( |-------- \|b \|a x + b + (- a x - b) |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ +--------+ |-------- +--R | 4 +--------+ | 4 | 4 +--R |a x + b +-+ | 4 4 |a x + b \| x +--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------) +--R | 4 | 4 +-+ +--R \| x \| x \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ +-+ 2 +-+ |a x + b | 4 2 +-+ |a x + b +-+ +--R (\|a \|b + x \|a |-------- )\|a x + b - x \|a |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R + +--R 4 +-+ +--R (- a x - b)\|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ |a x + b +-+ | 4 2 4 +-+ |a x + b +--R 2a\|a |-------- \|b \|a x + b + (- 2a x - 2a b)\|a |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 2 13 9 2 5 +-+ |a x + b 3 13 2 9 +--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x +--R | 4 +--R \| x +--R + +--R 2 5 +--R - 16a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 15 2 11 2 7 |a x + b +--R (- a x - 12a b x - 16a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 15 2 11 2 7 3 3 +-+ +--R (a x + 13a b x + 28a b x + 16b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 15 2 11 2 7 |a x + b +--R (5a x + 20a b x + 16a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 15 2 11 2 7 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 +-+ |a x + b 4 17 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 4 +--R \| x +--R + +--R 3 13 2 2 9 3 5 +--R 13a b x + 28a b x + 16a b x +--R / +--R +--------+ +--R | 4 +--R 4 14 3 10 2 2 6 3 2 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +---+ |a x + b +-+ | 4 4 +---+ |a x + b +--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ |a x + b +-+ | 4 4 +-+ |a x + b +--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R +---+ +-+ +-+ 2 +---+ +-+ |a x + b | 4 +--R (\|- a \|a \|b + x \|- a \|a |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 +---+ +-+ |a x + b +-+ 4 +---+ +-+ +--R - x \|- a \|a |-------- \|b + (- a x - b)\|- a \|a +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R +---+ +-+ |a x + b +-+ | 4 +--R 2a\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 4 +---+ +-+ |a x + b +--R (- 2a x - 2a b)\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 5 |a x + b +-+ 7 3 | 4 7 3 +-+ +--R (- 2x |-------- \|b - a x - 2b x )\|a x + b + (2a x + 2b x )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 9 5 |a x + b +--R (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1325 +--r0:=(-1/2)/(a*x*sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b/x^4)) +--E 371 + +--S 372 of 1325 +--a0:=integrate(t0,x) +--E 372 + +--S 373 of 1325 +--m0:=a0-r0 +--E 373 + +--S 374 of 1325 +--d0:=D(m0,x) +--E 374 + +)clear all + +--S 375 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^3) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1325 +r0:=(-1/2)/(a*x^2*sqrt(a+b/x^4)) +--R +--R +--R 1 +--R (2) - ---------------- +--R +--------+ +--R | 4 +--R 2 |a x + b +--R 2a x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +--------+ +--R | 4 +--R 2a\|a x + b +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (4) --------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b | 4 +--R 2a x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 3 |a x + b +--R - x\|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) -------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 4 |a x + b | 4 +--R (a x + b) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1325 +--r0:=(-1/2)/(a*x^3*sqrt(a+b/x^4))+1/2*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*_ +-- sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b/x^4)) +--E 381 + +--S 382 of 1325 +--a0:=integrate(t0,x) +--E 382 + +--S 383 of 1325 +--m0:=a0-r0 +--E 383 + +--S 384 of 1325 +--d0:=D(m0,x) +--E 384 + +)clear all + +--S 385 of 1325 +t0:=x^3/(a+b/x^4)^(5/2) +--R +--R +--R 11 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1325 +r0:=-1/6*x^4/(a*(a+b/x^4)^(3/2))-5/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/_ + a^(7/2)-5/6*x^4/(a^2*sqrt(a+b/x^4))+5/4*x^4*sqrt(a+b/x^4)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R 4 2 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 4 +-+ +--R \| x \|a +--R + +--R 2 8 4 2 +-+ +--R (3a x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 4 +--R 4 4 3 +-+ |a x + b +--R (12a x + 12a b)\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 12 2 2 8 3 4 4 +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a \|b +--R / +--R +--------+ +--R 6 12 5 8 4 2 4 3 3 +-+ +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|a \|b \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a +--R , +--R +--R +--------+ +--R 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|b +--R / +--R +--------+ +--R 6 12 5 8 4 2 4 3 3 +---+ +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|b \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 387 + +--S 388 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 6 12 5 8 4 2 4 3 3 +-+ |a x + b +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+ |a x + b +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 37 5 33 4 2 29 3 3 25 +--R - 13a x - 364a b x - 2912a b x - 9984a b x +--R + +--R 2 4 21 5 17 6 13 +--R - 16640a b x - 13312a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 17 6 13 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 19 6 15 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 19 6 15 7 11 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 19 6 15 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 19 6 15 7 11 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 21 6 17 7 13 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 8 41 7 37 6 2 33 5 3 29 4 4 25 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 21 2 6 17 7 13 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 9 34 8 30 7 2 26 6 3 22 5 4 18 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 4 5 14 3 6 10 2 7 6 8 2 +--R 56576a b x + 47360a b x + 21504a b x + 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 9 36 8 32 7 2 28 6 3 24 5 4 20 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 16 3 6 12 2 7 8 8 4 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 36 8 32 7 2 28 6 3 24 5 4 20 +--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x +--R + +--R 4 5 16 3 6 12 2 7 8 8 4 9 +--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 10 38 9 34 8 2 30 7 3 26 6 4 22 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 5 5 18 4 6 14 3 7 10 2 8 6 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R 3 12 2 2 8 3 4 4 +---+ |a x + b +-+ +--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +---+ +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--R 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 4 16 3 12 2 2 8 3 4 4 +---+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a +--R * +--R +-+ +--R \|b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +---+ +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--R 6 12 5 8 4 2 4 3 3 +---+ +-+ |a x + b +-+ +--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+ +-+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 29 3 25 2 2 21 3 17 4 13 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 +--R 10a x + 170a b x + 832a b x + 1696a b x + 1536a b x +--R + +--R 5 11 +--R 512b x +--R * +--R +-+ +--R \|b +--R + +--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x +--R + +--R 2 5 8 6 4 7 +--R 4192a b x + 2304a b x + 512b +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 8 6 4 7 +--R - 5280a b x - 2560a b x - 512b +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 391 + +)clear all + +--S 392 of 1325 +t0:=x^2/(a+b/x^4)^(5/2) +--R +--R +--R 10 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1325 +--r0:=-1/6*x^3/(a*(a+b/x^4)^(3/2))-3/4*x^3/(a^2*sqrt(a+b/x^4))+_ +-- 5/4*x^3*sqrt(a+b/x^4)/a^3-5/4*(-b)^(3/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(11/4)*_ +-- sqrt(a+b/x^4)) +--E 393 + +--S 394 of 1325 +--a0:=integrate(t0,x) +--E 394 + +--S 395 of 1325 +--m0:=a0-r0 +--E 395 + +--S 396 of 1325 +--d0:=D(m0,x) +--E 396 + +)clear all + +--S 397 of 1325 +t0:=x/(a+b/x^4)^(5/2) +--R +--R +--R 9 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1325 +r0:=-1/6*x^2/(a*(a+b/x^4)^(3/2))-2/3*x^2/(a^2*sqrt(a+b/x^4))+_ + 4/3*x^2*sqrt(a+b/x^4)/a^3 +--R +--R +--R 2 8 4 2 +--R 3a x + 12a b x + 8b +--R (2) ---------------------------- +--R +--------+ +--R | 4 +--R 4 6 3 2 |a x + b +--R (6a x + 6a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3a x + 12a b x + 8b +--R (3) ------------------------- +--R +--------+ +--R 4 4 3 | 4 +--R (6a x + 6a b)\|a x + b +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 8 4 2 | 4 +--R (- 3a x - 12a b x - 8b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (3a x + 12a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 6 3 2 |a x + b | 4 +--R (6a x + 6a b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 9 | 4 11 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 2a b x + b ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 401 + +)clear all + +--S 402 of 1325 +t0:=1/(a+b/x^4)^(5/2) +--R +--R +--R 8 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1325 +--r0:=-1/6*x/(a*(a+b/x^4)^(3/2))-7/12*x/(a^2*sqrt(a+b/x^4))+_ +-- 7/4*x*sqrt(a+b/x^4)/a^3+7/4*(-b)^(1/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4))-7/4*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4)) +--E 403 + +--S 404 of 1325 +--a0:=integrate(t0,x) +--E 404 + +--S 405 of 1325 +--m0:=a0-r0 +--E 405 + +--S 406 of 1325 +--d0:=D(m0,x) +--E 406 + +)clear all + +--S 407 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x) +--R +--R +--R 7 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1325 +r0:=(-1/6)/(a*(a+b/x^4)^(3/2))+1/2*atanh(sqrt(a+b/x^4)/_ + sqrt(a))/a^(5/2)+(-1/2)/(a^2*sqrt(a+b/x^4)) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R 4 |a x + b \| x 4 +-+ +--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a +--R | 4 +-+ +--R \| x \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R | 4 +--R 3 4 2 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 +--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x +--R + +--R 2 4 3 +--R - 27a b x - 12b +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (4a x + 19a b x + 12b x )\|a \|a x + b +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (- 12a x - 25a b x - 12b x )\|a \|b +--R / +--R +--------+ +--R 4 8 3 4 2 2 +-+ +-+ | 4 +--R (18a x + 42a b x + 24a b )\|a \|b \|a x + b +--R + +--R 5 12 4 8 3 2 4 2 3 +-+ +--R (- 6a x - 36a b x - 54a b x - 24a b )\|a +--R , +--R +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 +--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x +--R + +--R 2 4 3 +--R - 54a b x - 24b +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (4a x + 19a b x + 12b x )\|- a \|a x + b +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (- 12a x - 25a b x - 12b x )\|- a \|b +--R / +--R +--------+ +--R 4 8 3 4 2 2 +---+ +-+ | 4 +--R (18a x + 42a b x + 24a b )\|- a \|b \|a x + b +--R + +--R 5 12 4 8 3 2 4 2 3 +---+ +--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 409 + +--S 410 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b +-+ | 4 +--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b +-+ | 4 +--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 |a x + b +--R (3a x + 18a b x + 27a b x + 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +-+ +--R (12a x + 25a b x + 12b )\|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +--R (4a x + 19a b x + 12b x )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 8 3 4 2 2 +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24a b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 12 4 8 3 2 4 2 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 25 3 21 2 2 17 3 13 4 9 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x +--R + +--R 5 7 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x +--R + +--R 5 7 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 7 26 6 22 5 2 18 4 3 14 3 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 2 5 6 6 2 +--R 1088a b x + 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 8 6 4 7 +--R - 2352a b x - 1216a b x - 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x +--R + +--R 2 5 8 6 4 7 +--R 2928a b x + 1344a b x + 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 30 7 26 6 2 22 5 3 18 4 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 3 5 10 2 6 6 7 2 +--R - 2352a b x - 1216a b x - 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 +---+ |a x + b +-+ | 4 +--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 +---+ |a x + b +--R (3a x + 18a b x + 27a b x + 12b )\|- a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 2 8 4 2 +---+ +-+ +-+ +--R (12a x + 25a b x + 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +--R (4a x + 19a b x + 12b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +---+ +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 8 3 4 2 2 +---+ +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24a b )\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 12 4 8 3 2 4 2 3 +---+ +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 4 +--R \| x +--R + +--R 2 11 3 7 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 19 2 15 2 11 3 7 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R / +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1325 +--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x)+(-5/12)/(a^2*x*sqrt(a+b/x^4))-_ +-- 5/12*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b/x^4)) +--E 415 + +--S 416 of 1325 +--a0:=integrate(t0,x) +--E 416 + +--S 417 of 1325 +--m0:=a0-r0 +--E 417 + +--S 418 of 1325 +--d0:=D(m0,x) +--E 418 + +)clear all + +--S 419 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^3) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1325 +r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^2)+(-1/3)/(a^2*x^2*sqrt(a+b/x^4)) +--R +--R +--R 4 +--R - 3a x - 2b +--R (2) ---------------------------- +--R +--------+ +--R | 4 +--R 3 6 2 2 |a x + b +--R (6a x + 6a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 3a x - 2b +--R (3) ------------------------- +--R +--------+ +--R 3 4 2 | 4 +--R (6a x + 6a b)\|a x + b +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (3a x + 2b)\|a x + b + (- 3a x - 2b x ) |-------- +--R | 4 +--R \| x +--R (4) ------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 3 6 2 2 |a x + b | 4 +--R (6a x + 6a b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 5 | 4 7 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 2a b x + b ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^4) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1325 +--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^3)+(-1/4)/(a^2*x^3*sqrt(a+b/x^4))+_ +-- 1/4*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4))-_ +-- 1/4*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4)) +--E 425 + +--S 426 of 1325 +--a0:=integrate(t0,x) +--E 426 + +--S 427 of 1325 +--m0:=a0-r0 +--E 427 + +--S 428 of 1325 +--d0:=D(m0,x) +--E 428 + +)clear all + +--S 429 of 1325 +t0:=1/(a+b/x^5) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 5 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 429 + +--S 430 of 1325 +r0:=x/a-1/5*b^(1/5)*log(b^(1/5)+a^(1/5)*x)/a^(6/5)+1/20*b^(1/5)*_ + log(2*b^(2/5)+2*a^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*_ + (1-sqrt(5))/a^(6/5)+1/20*b^(1/5)*log(2*b^(2/5)+2*a^(2/5)*x^2-_ + a^(1/5)*b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/a^(6/5)+1/5*b^(1/5)*_ + atan(1/2*(-4*a^(1/5)*x+b^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_ + (b^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/a^(6/5)+1/5*b^(1/5)*_ + atan((-4*a^(1/5)*x+b^(1/5)*(1-sqrt(5)))/(b^(1/5)*sqrt(2*_ + (5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/a^(6/5) +--R +--R +--R (2) +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (- \|2 \|5 + \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (\|2 \|5 + \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+5+-+ 5+-+ 5+-+ +--R - 4\|2 \|b log(\|b + x\|a ) +--R + +--R +--------+ +--R +----------+ +-+ 5+-+ 5+-+ | +-+ +--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5 +--R 4\|- \|5 + 5 \|b atan(------------------------------------) +--R +--+5+-+ +--R 2\|10 \|b +--R + +--R +--------+ +-+ 5+-+ 5+-+ +--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a +-+5+-+ +--R - 4\|b \|\|5 + 5 atan(-----------------------) + 20x\|2 \|a +--R +----------+ +--R 5+-+ | +-+ +--R \|b \|2\|5 + 10 +--R / +--R +-+5+-+ +--R 20a\|2 \|a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CZ1 - 5a %%CZ0 - 5|- - +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CZ1 - 5a %%CZ0 - 5|- - +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R 10a %%CZ1 log(- 5a %%CZ1 + x) + 10a %%CZ0 log(- 5a %%CZ0 + x) +--R + +--R +---+ +---+ +--R | b | b +--R 2 5|- - log(- 5|- - + x + 10x +--R \| a \| a +--R / +--R 10a +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+5+-+ +--R 10a\|2 \|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R +-+5+-+ +-+5+-+ +-+ | b 5+-+ +--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R +-+5+-+ +--R 10a\|2 \|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R +-+5+-+ +-+5+-+ +-+ | b 5+-+ +--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R +-+5+-+ +--R 20a\|2 \|a %%CZ1 log(- 5a %%CZ1 + x) +--R + +--R +-+5+-+ +--R 20a\|2 \|a %%CZ0 log(- 5a %%CZ0 + x) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (\|2 \|5 - \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (- \|2 \|5 - \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +---+ +---+ +--R +-+5+-+ 5+-+ 5+-+ +-+ | b 5+-+ | b +--R 4\|2 \|b log(\|b + x\|a ) + 4\|2 5|- - \|a log(- 5|- - + x) +--R \| a \| a +--R + +--R +--------+ +--R +----------+ +-+ 5+-+ 5+-+ | +-+ +--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5 +--R - 4\|- \|5 + 5 \|b atan(------------------------------------) +--R +--+5+-+ +--R 2\|10 \|b +--R + +--R +--------+ +-+ 5+-+ 5+-+ +--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a +--R 4\|b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|b \|2\|5 + 10 +--R / +--R +-+5+-+ +--R 20a\|2 \|a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +-+ 5+-+4 +-+ +-+ +-+ 5+-+5+-+3 +--R (\|2 \|5 + 5\|2 )\|b + (- 3x\|2 \|5 - 5x\|2 )\|a \|b +--R + +--R 2 +-+ +-+ 2 +-+ 5+-+2 5+-+2 +--R (x \|2 \|5 + 5x \|2 )\|a \|b +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R +-+ +--+ | +-+ 5+-+4 +--R 2\|2 \|10 \|- \|5 + 5 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ +--+ | +-+ 5+-+5+-+3 +--R (x\|2 \|5 - x\|2 )\|10 \|- \|5 + 5 \|a \|b +--R + +--R +----------+ +--R 2 +-+ +--+ | +-+ 5+-+2 5+-+2 +--R 2x \|2 \|10 \|- \|5 + 5 \|a \|b +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R +-+ 5+-+4 +-+ 5+-+5+-+3 +--R (- 20\|5 - 100)\|b + (20x\|5 + 100x)\|a \|b +--R + +--R 2 +-+ 2 5+-+2 5+-+2 +--R (- 20x \|5 - 100x )\|a \|b +--R / +--R +-+ 5+-+4 +-+ 5+-+5+-+3 +--R (40a\|5 + 200a)\|b + (- 40a x\|5 - 200a x)\|a \|b +--R + +--R 2 +-+ 2 5+-+2 5+-+2 3 +-+ 3 5+-+3 5+-+ +--R (40a x \|5 + 200a x )\|a \|b + (- 40a x \|5 - 200a x )\|a \|b +--R + +--R 4 +-+ 4 5+-+4 +--R (40a x \|5 + 200a x )\|a +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1325 +t0:=1/(x*sqrt(a+b/x^5)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 5 +--R |a x + b +--R x |-------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1325 +r0:=2/5*atanh(sqrt(a+b/x^5)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R |-------- +--R | 5 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |a x + b 5 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (3) - ----------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 5 | 5 +--R |1 +-+ 3 |1 |a x + b 5 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 5 |1 |a x + b 5 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 5 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 7 2 |a x + b 2 7 2 |1 +--R (2a x + b x ) |-------- + (2a x + 2a b x ) |- +--R | 5 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 6 |a x + b |a x + b 2 8 3 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 5 \| x \|a | 5 +--R \| x \| x +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1325 +t0:=1/(x*sqrt(-a+b/x^5)) +--R +--R +--R 1 +--R (1) -------------- +--R +----------+ +--R | 5 +--R |- a x + b +--R x |---------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1325 +r0:=-2/5*atan(sqrt(-a+b/x^5)/sqrt(a))/sqrt(a) +--R +--R +--R +----------+ +--R | 5 +--R |- a x + b +--R |---------- +--R | 5 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (2) - -------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- a x + b | 1 5 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (3) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------+ +--R | 5 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 5 +---+ | 5 +--R | 1 +-+ 3 |- a x + b | 1 5 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 5 |- a x + b |- a x + b 2 7 2 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x ) |- - +--R \| x | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 7 2 |- a x + b 5 |- a x + b +--R (2a x - b x ) |---------- + (- 2a x + b) |---------- +--R | 5 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 8 3 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 5 +--R \| x +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1325 +t0:=1/(a+b/x^6) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 6 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 444 + +--S 445 of 1325 +r0:=x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/3*atan(a^(1/6)*x*_ + sqrt(2)/sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2))-1/3*atanh(a^(1/6)*x*_ + sqrt(2)/sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R - \|\|3 \|- \|b + \|b atanh(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R - \|\|3 \|- \|b - \|b atan(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+6+-+ x\|a +-+6+-+ +--R - \|2 \|b atan(-----) + 3x\|2 \|a +--R 6+-+ +--R \|b +--R / +--R +-+6+-+ +--R 3a\|2 \|a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R - a |- ------- log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R a |- ------- log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R - 2a |- ------- log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R 2a |- ------- log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 2a +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R 2\|\|3 \|- \|b + \|b atanh(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R 2\|\|3 \|- \|b - \|b atan(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | b 6+-+ 2 | b | b 2 +--R - 3a\|2 |- ------- \|a log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | b 6+-+ 2 | b | b 2 +--R 3a\|2 |- ------- \|a log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R +-+ | b 6+-+ | b +--R - 6a\|2 |- ------- \|a log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R +-+ | b 6+-+ | b +--R 6a\|2 |- ------- \|a log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | b 6+-+ \| 46656a +--R - 6a\|2 \|3 |- ------- \|a atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 6+-+ +--R +-+ +-+ | b 6+-+ \| 46656a +-+6+-+ x\|a +--R 6a\|2 \|3 |- ------- \|a atan(------------------ + 2\|2 \|b atan(-----) +--R 6| 7 +---------+ 6+-+ +--R \| 46656a | b \|b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R +-+6+-+ +--R 6a\|2 \|a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1325 +t0:=1/(a+b/x^8) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 8 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 449 + +--S 450 of 1325 +r0:=x/a-1/4*(-b)^(1/8)*atan(a^(1/8)*x/(-b)^(1/8))/a^(9/8)-1/4*(-b)^(1/8)*_ + atanh(a^(1/8)*x/(-b)^(1/8))/a^(9/8)+1/4*(-b)^(1/8)*atan(1-a^(1/8)*_ + x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))-1/4*(-b)^(1/8)*atan(1+_ + a^(1/8)*x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))+1/8*(-b)^(1/8)*_ + log((-b)^(1/4)+a^(1/4)*x^2-a^(1/8)*(-b)^(1/8)*x*sqrt(2))/(a^(9/8)*_ + sqrt(2))-1/8*(-b)^(1/8)*log((-b)^(1/4)+a^(1/4)*x^2+a^(1/8)*_ + (-b)^(1/8)*x*sqrt(2))/(a^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- b log(x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R 8+-+ +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|a +--R \|- b log(- x\|2 \|- b \|a + x \|a + \|- b ) - 2\|2 \|- b atanh(------) +--R 8+---+ +--R \|- b +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+---+ x\|2 \|a + \|- b 8+---+ x\|2 \|a - \|- b +--R - 2\|- b atan(------------------) - 2\|- b atan(------------------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R 8+-+ +--R +-+8+---+ x\|a +-+8+-+ +--R - 2\|2 \|- b atan(------) + 8x\|2 \|a +--R 8+---+ +--R \|- b +--R / +--R +-+8+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | b +--R a |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- + 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+2 +------------+ +--R | b 2 | b +-+ | b 2 +--R a |- ---------- log(64a |- ---------- - 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 8| 9 +--R \| 16777216a \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b | b +--R - a\|2 |- ---------- log(8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b | b +--R a\|2 |- ---------- log(- 8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b \| 16777216a +--R 2a\|2 |- ---------- atan(-----------------) +--R 8| 9 x +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +--R - 2a |- ---------- atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +-+ +--R 2a |- ---------- atan(------------------------- + x\|2 +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+ +--R a\|2 +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|- b log(x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R - +--R +------------+ +--R | b 8+-+ +--R 8a |- ---------- \|a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- + 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b 8+-+ +--R 8a |- ---------- \|a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- - 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b 8+-+ | b +--R - 8a\|2 |- ---------- \|a log(8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b 8+-+ | b +--R 8a\|2 |- ---------- \|a log(- 8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- b log(- x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R +-+8+---+ x\|a 8+---+ x\|2 \|a + \|- b +--R 2\|2 \|- b atanh(------) + 2\|- b atan(------------------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 8+---+ x\|2 \|a - \|- b +-+8+---+ x\|a +--R 2\|- b atan(------------------) + 2\|2 \|- b atan(------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b 8+-+ \| 16777216a +--R 16a\|2 |- ---------- \|a atan(-----------------) +--R 8| 9 x +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b 8+-+ \| 16777216a +--R - 16a |- ---------- \|a atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b 8+-+ \| 16777216a +--R 16a |- ---------- \|a atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+8+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1325 +t0:=x^m*(a+b*sqrt(x))^p +--R +--R +--R m +-+ p +--R (1) x (b\|x + a) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1325 +--r0:=2*x^(1/2*(1+2*m))*(a+b*sqrt(x))^(1+p)/(b*(2+2*m+p))-_ +-- 2*a*(1+2*m)*x^m*hypergeometric(-2*m,1+p,2+p,(a+b*sqrt(x))/a)*_ +-- (a+b*sqrt(x))^(1+p)/(b^2*(1+p)*(2+2*m+p)*(-b*sqrt(x)/a)^(2*m)) +--E 455 + +--S 456 of 1325 +--a0:=integrate(t0,x) +--E 456 + +--S 457 of 1325 +--m0:=a0-r0 +--E 457 + +--S 458 of 1325 +--d0:=D(m0,x) +--E 458 + +)clear all + +--S 459 of 1325 +t0:=x^m*(a+b*sqrt(x)) +--R +--R +--R m +-+ m +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1325 +r0:=a*x^(1+m)/(1+m)+2*b*x^(3/2+m)/(3+2*m) +--R +--R +--R 2m + 3 +--R ------ +--R 2 m + 1 +--R (2b m + 2b)x + (2a m + 3a)x +--R (2) -------------------------------------- +--R 2 +--R 2m + 5m + 3 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ m log(x) +--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e +--R (3) ------------------------------------------- +--R 2 +--R 2m + 5m + 3 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 2m + 3 +--R ------ +--R +-+ m log(x) 2 +--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e + (- 2b m - 2b)x +--R + +--R m + 1 +--R (- 2a m - 3a)x +--R / +--R 2 +--R 2m + 5m + 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1325 +t0:=x^4*(a+b*sqrt(x)) +--R +--R +--R 4 +-+ 4 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1325 +r0:=1/5*a*x^5+2/11*b*x^(11/2) +--R +--R +--R 5 +-+ 5 +--R 10b x \|x + 11a x +--R (2) ------------------- +--R 55 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ 5 +--R 10b x \|x + 11a x +--R (3) ------------------- +--R 55 +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1325 +t0:=x^3*(a+b*sqrt(x)) +--R +--R +--R 3 +-+ 3 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1325 +r0:=1/4*a*x^4+2/9*b*x^(9/2) +--R +--R +--R 4 +-+ 4 +--R 8b x \|x + 9a x +--R (2) ----------------- +--R 36 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ 4 +--R 8b x \|x + 9a x +--R (3) ----------------- +--R 36 +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1325 +t0:=x^2*(a+b*sqrt(x)) +--R +--R +--R 2 +-+ 2 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1325 +r0:=1/3*a*x^3+2/7*b*x^(7/2) +--R +--R +--R 3 +-+ 3 +--R 6b x \|x + 7a x +--R (2) ----------------- +--R 21 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 +--R 6b x \|x + 7a x +--R (3) ----------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1325 +t0:=x*(a+b*sqrt(x)) +--R +--R +--R +-+ +--R (1) b x\|x + a x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1325 +r0:=1/2*a*x^2+2/5*b*x^(5/2) +--R +--R +--R 2 +-+ 2 +--R 4b x \|x + 5a x +--R (2) ----------------- +--R 10 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 +--R 4b x \|x + 5a x +--R (3) ----------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1325 +t0:=a+b*sqrt(x) +--R +--R +--R +-+ +--R (1) b\|x + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1325 +r0:=a*x+2/3*b*x^(3/2) +--R +--R +--R +-+ +--R 2b x\|x + 3a x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2b x\|x + 3a x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1325 +t0:=(a+b*sqrt(x))/x +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1325 +r0:=a*log(x)+2*b*sqrt(x) +--R +--R +--R +-+ +--R (2) 2b\|x + a log(x) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) 2a log(\|x ) + 2b\|x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1325 +t0:=(a+b*sqrt(x))/x^2 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1325 +r0:=-a/x-2*b/sqrt(x) +--R +--R +--R +-+ +--R - a\|x - 2b x +--R (2) -------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 2b\|x - a +--R (3) ------------ +--R x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1325 +t0:=(a+b*sqrt(x))/x^3 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1325 +r0:=-1/2*a/x^2-2/3*b/x^(3/2) +--R +--R +--R +-+ +--R - 3a\|x - 4b x +--R (2) --------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 4b\|x - 3a +--R (3) ------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1325 +t0:=(a+b*sqrt(x))/x^4 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1325 +r0:=-1/3*a/x^3-2/5*b/x^(5/2) +--R +--R +--R +-+ +--R - 5a\|x - 6b x +--R (2) --------------- +--R 3 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 6b\|x - 5a +--R (3) ------------- +--R 3 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1325 +t0:=x^m*(a+b*sqrt(x))^2 +--R +--R +--R m +-+ 2 2 m +--R (1) 2a b x \|x + (b x + a )x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1325 +r0:=a^2*x^(1+m)/(1+m)+4*a*b*x^(3/2+m)/(3+2*m)+b^2*x^(2+m)/(2+m) +--R +--R +--R (2) +--R 2m + 3 +--R ------ +--R 2 2 2 2 m + 2 2 2 +--R (2b m + 5b m + 3b )x + (4a b m + 12a b m + 8a b)x +--R + +--R 2 2 2 2 m + 1 +--R (2a m + 7a m + 6a )x +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 2 2 2 2 +--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x +--R + +--R 2 2 2 2 +--R (2a m + 7a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 2 2 2 2 +--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x +--R + +--R 2 2 2 2 +--R (2a m + 7a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2m + 3 +--R ------ +--R 2 2 2 2 m + 2 2 2 +--R (- 2b m - 5b m - 3b )x + (- 4a b m - 12a b m - 8a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- 2a m - 7a m - 6a )x +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1325 +t0:=x^4*(a+b*sqrt(x))^2 +--R +--R +--R 4 +-+ 2 5 2 4 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1325 +r0:=1/5*a^2*x^5+4/11*a*b*x^(11/2)+1/6*b^2*x^6 +--R +--R +--R 5 +-+ 2 6 2 5 +--R 120a b x \|x + 55b x + 66a x +--R (2) ------------------------------- +--R 330 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ 2 6 2 5 +--R 120a b x \|x + 55b x + 66a x +--R (3) ------------------------------- +--R 330 +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1325 +t0:=x^3*(a+b*sqrt(x))^2 +--R +--R +--R 3 +-+ 2 4 2 3 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1325 +r0:=1/4*a^2*x^4+4/9*a*b*x^(9/2)+1/5*b^2*x^5 +--R +--R +--R 4 +-+ 2 5 2 4 +--R 80a b x \|x + 36b x + 45a x +--R (2) ------------------------------ +--R 180 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ 2 5 2 4 +--R 80a b x \|x + 36b x + 45a x +--R (3) ------------------------------ +--R 180 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1325 +t0:=x^2*(a+b*sqrt(x))^2 +--R +--R +--R 2 +-+ 2 3 2 2 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1325 +r0:=1/3*a^2*x^3+4/7*a*b*x^(7/2)+1/4*b^2*x^4 +--R +--R +--R 3 +-+ 2 4 2 3 +--R 48a b x \|x + 21b x + 28a x +--R (2) ------------------------------ +--R 84 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 2 4 2 3 +--R 48a b x \|x + 21b x + 28a x +--R (3) ------------------------------ +--R 84 +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1325 +t0:=x*(a+b*sqrt(x))^2 +--R +--R +--R +-+ 2 2 2 +--R (1) 2a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1325 +r0:=1/2*a^2*x^2+4/5*a*b*x^(5/2)+1/3*b^2*x^3 +--R +--R +--R 2 +-+ 2 3 2 2 +--R 24a b x \|x + 10b x + 15a x +--R (2) ------------------------------ +--R 30 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 3 2 2 +--R 24a b x \|x + 10b x + 15a x +--R (3) ------------------------------ +--R 30 +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 533 + +)clear all + +--S 534 of 1325 +t0:=(a+b*sqrt(x))^2 +--R +--R +--R +-+ 2 2 +--R (1) 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1325 +r0:=a^2*x+4/3*a*b*x^(3/2)+1/2*b^2*x^2 +--R +--R +--R +-+ 2 2 2 +--R 8a b x\|x + 3b x + 6a x +--R (2) ------------------------- +--R 6 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 2 +--R 8a b x\|x + 3b x + 6a x +--R (3) ------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1325 +t0:=(a+b*sqrt(x))^2/x +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1325 +r0:=b^2*x+a^2*log(x)+4*a*b*sqrt(x) +--R +--R +--R +-+ 2 2 +--R (2) 4a b\|x + a log(x) + b x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +-+ 2 +--R (3) 2a log(\|x ) + 4a b\|x + b x +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1325 +t0:=(a+b*sqrt(x))^2/x^2 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1325 +r0:=-a^2/x+b^2*log(x)-4*a*b/sqrt(x) +--R +--R +--R 2 2 +-+ +--R (b x log(x) - a )\|x - 4a b x +--R (2) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +-+ 2 +--R 2b x log(\|x ) - 4a b\|x - a +--R (3) ------------------------------ +--R x +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 2b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 548 + +)clear all + +--S 549 of 1325 +t0:=(a+b*sqrt(x))^2/x^3 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1325 +r0:=-1/2*a^2/x^2-4/3*a*b/x^(3/2)-b^2/x +--R +--R +--R 2 2 +-+ +--R (- 6b x - 3a )\|x - 8a b x +--R (2) --------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 8a b\|x - 6b x - 3a +--R (3) ----------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 551 + +--S 552 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 1325 +t0:=(a+b*sqrt(x))^2/x^4 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1325 +r0:=-1/3*a^2/x^3-4/5*a*b/x^(5/2)-1/2*b^2/x^2 +--R +--R +--R 2 2 +-+ +--R (- 15b x - 10a )\|x - 24a b x +--R (2) ------------------------------ +--R 3 +-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 24a b\|x - 15b x - 10a +--R (3) -------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 556 + +--S 557 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1325 +t0:=(a+b*sqrt(x))^2/x^5 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1325 +r0:=-1/4*a^2/x^4-4/7*a*b/x^(7/2)-1/3*b^2/x^3 +--R +--R +--R 2 2 +-+ +--R (- 28b x - 21a )\|x - 48a b x +--R (2) ------------------------------ +--R 4 +-+ +--R 84x \|x +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 48a b\|x - 28b x - 21a +--R (3) -------------------------- +--R 4 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 561 + +--S 562 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 563 + +)clear all + +--S 564 of 1325 +t0:=x^m*(a+b*sqrt(x))^3 +--R +--R +--R 3 2 m +-+ 2 3 m +--R (1) (b x + 3a b)x \|x + (3a b x + a )x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1325 +r0:=a^3*x^(1+m)/(1+m)+6*a^2*b*x^(3/2+m)/(3+2*m)+3*a*b^2*x^(2+m)/(2+m)+_ + 2*b^3*x^(5/2+m)/(5+2*m) +--R +--R +--R (2) +--R 2m + 5 +--R ------ +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 2m + 3 +--R ------ +--R 2 3 2 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (4a m + 24a m + 47a m + 30a )x +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R * +--R +-+ +--R \|x +--R + +--R 2 3 2 2 2 2 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 3 3 3 2 3 3 +--R (4a m + 24a m + 47a m + 30a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Union(Expression(Integer),...) +--E 566 + +--S 567 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R * +--R +-+ +--R \|x +--R + +--R 2 3 2 2 2 2 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 3 3 3 2 3 3 +--R (4a m + 24a m + 47a m + 30a )x +--R * +--R m log(x) +--R %e +--R + +--R 2m + 5 +--R ------ +--R 3 3 3 2 3 3 2 +--R (- 4b m - 18b m - 26b m - 12b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 12a b m - 60a b m - 93a b m - 45a b )x +--R + +--R 2m + 3 +--R ------ +--R 2 3 2 2 2 2 2 +--R (- 12a b m - 66a b m - 114a b m - 60a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- 4a m - 24a m - 47a m - 30a )x +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 568 + +)clear all + +--S 569 of 1325 +t0:=x^4*(a+b*sqrt(x))^3 +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1325 +r0:=1/5*a^3*x^5+6/11*a^2*b*x^(11/2)+1/2*a*b^2*x^6+2/13*b^3*x^(13/2) +--R +--R +--R 3 6 2 5 +-+ 2 6 3 5 +--R (220b x + 780a b x )\|x + 715a b x + 286a x +--R (2) ----------------------------------------------- +--R 1430 +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 5 +-+ 2 6 3 5 +--R (220b x + 780a b x )\|x + 715a b x + 286a x +--R (3) ----------------------------------------------- +--R 1430 +--R Type: Union(Expression(Integer),...) +--E 571 + +--S 572 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1325 +t0:=x^3*(a+b*sqrt(x))^3 +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1325 +r0:=1/4*a^3*x^4+2/3*a^2*b*x^(9/2)+3/5*a*b^2*x^5+2/11*b^3*x^(11/2) +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (120b x + 440a b x )\|x + 396a b x + 165a x +--R (2) ----------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (120b x + 440a b x )\|x + 396a b x + 165a x +--R (3) ----------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1325 +t0:=x^2*(a+b*sqrt(x))^3 +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1325 +r0:=1/3*a^3*x^3+6/7*a^2*b*x^(7/2)+3/4*a*b^2*x^4+2/9*b^3*x^(9/2) +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (56b x + 216a b x )\|x + 189a b x + 84a x +--R (2) --------------------------------------------- +--R 252 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (56b x + 216a b x )\|x + 189a b x + 84a x +--R (3) --------------------------------------------- +--R 252 +--R Type: Union(Expression(Integer),...) +--E 581 + +--S 582 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +)clear all + +--S 584 of 1325 +t0:=x*(a+b*sqrt(x))^3 +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (1) (b x + 3a b x)\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1325 +r0:=1/2*a^3*x^2+6/5*a^2*b*x^(5/2)+a*b^2*x^3+2/7*b^3*x^(7/2) +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (20b x + 84a b x )\|x + 70a b x + 35a x +--R (2) ------------------------------------------- +--R 70 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (20b x + 84a b x )\|x + 70a b x + 35a x +--R (3) ------------------------------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 586 + +--S 587 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1325 +t0:=(a+b*sqrt(x))^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (1) (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1325 +r0:=-1/2*a*(a+b*sqrt(x))^4/b^2+2/5*(a+b*sqrt(x))^5/b^2 +--R +--R +--R 5 2 2 3 +-+ 4 2 3 2 5 +--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a +--R (2) ----------------------------------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (4b x + 20a b x)\|x + 15a b x + 10a x +--R (3) ---------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 591 + +--S 592 of 1325 +m0:=a0-r0 +--R +--R +--R 5 +--R a +--R (4) ---- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 1325 +t0:=(a+b*sqrt(x))^3/x +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1325 +r0:=3*a*b^2*x+2/3*b^3*x^(3/2)+a^3*log(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 2 +-+ 3 2 +--R (2b x + 18a b)\|x + 3a log(x) + 9a b x +--R (2) --------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R 6a log(\|x ) + (2b x + 18a b)\|x + 9a b x +--R (3) ------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 596 + +--S 597 of 1325 +m0:=a0-r0 +--R +--R +--R 3 +-+ 3 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1325 +t0:=(a+b*sqrt(x))^3/x^2 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1325 +r0:=-a^3/x+3*a*b^2*log(x)-6*a^2*b/sqrt(x)+2*b^3*sqrt(x) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (3a b x log(x) - a )\|x + 2b x - 6a b x +--R (2) ----------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 3 2 +-+ 3 +--R 6a b x log(\|x ) + (2b x - 6a b)\|x - a +--R (3) ----------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 6a b log(\|x ) - 3a b log(x) +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1325 +t0:=(a+b*sqrt(x))^3/x^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1325 +r0:=-1/2*(a+b*sqrt(x))^4/(a*x^2) +--R +--R +--R 3 3 +-+ 4 2 2 2 4 +--R (- 4a b x - 4a b)\|x - b x - 6a b x - a +--R (2) ------------------------------------------ +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 4b x - 4a b)\|x - 6a b x - a +--R (3) --------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) -- +--R 2a +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1325 +t0:=(a+b*sqrt(x))^3/x^4 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1325 +r0:=-1/3*a^3/x^3-6/5*a^2*b/x^(5/2)-3/2*a*b^2/x^2-2/3*b^3/x^(3/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 45a b x - 10a )\|x - 20b x - 36a b x +--R (2) ----------------------------------------- +--R 3 +-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 20b x - 36a b)\|x - 45a b x - 10a +--R (3) -------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1325 +t0:=(a+b*sqrt(x))^3/x^5 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1325 +r0:=-1/4*a^3/x^4-6/7*a^2*b/x^(7/2)-a*b^2/x^3-2/5*b^3/x^(5/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 140a b x - 35a )\|x - 56b x - 120a b x +--R (2) ------------------------------------------- +--R 4 +-+ +--R 140x \|x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 56b x - 120a b)\|x - 140a b x - 35a +--R (3) ---------------------------------------- +--R 4 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1325 +t0:=(a+b*sqrt(x))^3/x^6 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 6 +--R x +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1325 +r0:=-1/5*a^3/x^5-2/3*a^2*b/x^(9/2)-3/4*a*b^2/x^4-2/7*b^3/x^(7/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 315a b x - 84a )\|x - 120b x - 280a b x +--R (2) -------------------------------------------- +--R 5 +-+ +--R 420x \|x +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 120b x - 280a b)\|x - 315a b x - 84a +--R (3) ----------------------------------------- +--R 5 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1325 +t0:=x^m*(a+b*sqrt(x))^5 +--R +--R +--R 5 2 2 3 4 m +-+ 4 2 3 2 5 m +--R (1) (b x + 10a b x + 5a b)x \|x + (5a b x + 10a b x + a )x +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1325 +r0:=a^5*x^(1+m)/(1+m)+10*a^4*b*x^(3/2+m)/(3+2*m)+10*a^3*_ + b^2*x^(2+m)/(2+m)+20*a^2*b^3*x^(5/2+m)/(5+2*m)+5*a*_ + b^4*x^(3+m)/(3+m)+2*b^5*x^(7/2+m)/(7+2*m) +--R +--R +--R (2) +--R 2m + 7 +--R ------ +--R 5 5 5 4 5 3 5 2 5 5 2 +--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m + 1050a b ) +--R * +--R m + 3 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 +--R (80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m + 2520a b ) +--R * +--R 2m + 5 +--R ------ +--R 2 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 3 2 +--R (80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m + 3150a b ) +--R * +--R m + 2 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m + 2100a b) +--R * +--R 2m + 3 +--R ------ +--R 2 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x +--R / +--R 6 5 4 3 2 +--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 3 +--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m +--R + +--R 2 3 +--R 2520a b +--R * +--R 2 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m +--R + +--R 4 +--R 2100a b +--R * +--R x +--R * +--R +-+ +--R \|x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m +--R + +--R 4 +--R 1050a b +--R * +--R 3 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m +--R + +--R 3 2 +--R 3150a b +--R * +--R 2 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x +--R * +--R m log(x) +--R %e +--R / +--R 6 5 4 3 2 +--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630 +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 3 5 2 5 5 3 +--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m +--R + +--R 2 3 +--R 2520a b +--R * +--R 2 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m +--R + +--R 4 +--R 2100a b +--R * +--R x +--R * +--R +-+ +--R \|x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m +--R + +--R 4 +--R 1050a b +--R * +--R 3 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m +--R + +--R 3 2 +--R 3150a b +--R * +--R 2 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x +--R * +--R m log(x) +--R %e +--R + +--R 2m + 7 +--R ------ +--R 5 5 5 4 5 3 5 2 5 5 2 +--R (- 8b m - 80b m - 310b m - 580b m - 522b m - 180b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 40a b m - 420a b m - 1690a b m - 3255a b m - 2995a b m +--R + +--R 4 +--R - 1050a b +--R * +--R m + 3 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R - 80a b m - 880a b m - 3700a b m - 7400a b m - 7020a b m +--R + +--R 2 3 +--R - 2520a b +--R * +--R 2m + 5 +--R ------ 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+--R 5 6 2 3 5 4 4 +-+ 4 6 3 2 5 5 4 +--R (792b x + 9360a b x + 5720a b x )\|x + 4290a b x + 10296a b x + 1287a x +--R ----------------------------------------------------------------------------- +--R 5148 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 2 3 5 4 4 +-+ 4 6 3 2 5 5 4 +--R (792b x + 9360a b x + 5720a b x )\|x + 4290a b x + 10296a b x + 1287a x +--R ----------------------------------------------------------------------------- +--R 5148 +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 1325 +t0:=x^2*(a+b*sqrt(x))^5 +--R +--R +--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2 +--R (1) (b x + 10a b x + 5a b x )\|x + 5a b x + 10a b x + a x +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1325 +r0:=1/3*a^5*x^3+10/7*a^4*b*x^(7/2)+5/2*a^3*b^2*x^4+20/9*a^2*_ + b^3*x^(9/2)+a*b^4*x^5+2/11*b^5*x^(11/2) +--R +--R +--R (2) +--R 5 5 2 3 4 4 3 +-+ 4 5 3 2 4 5 3 +--R (252b x + 3080a b x + 1980a b x )\|x + 1386a b x + 3465a b x + 462a x +--R --------------------------------------------------------------------------- +--R 1386 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 2 3 4 4 3 +-+ 4 5 3 2 4 5 3 +--R (252b x + 3080a b x + 1980a b x )\|x + 1386a b x + 3465a b x + 462a x +--R --------------------------------------------------------------------------- +--R 1386 +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +)clear all + +--S 644 of 1325 +t0:=x*(a+b*sqrt(x))^5 +--R +--R +--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5 +--R (1) (b x + 10a b x + 5a b x)\|x + 5a b x + 10a b x + a x +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1325 +r0:=1/2*a^5*x^2+2*a^4*b*x^(5/2)+10/3*a^3*b^2*x^3+20/7*a^2*_ + b^3*x^(7/2)+5/4*a*b^4*x^4+2/9*b^5*x^(9/2) +--R +--R +--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2 +--R (56b x + 720a b x + 504a b x )\|x + 315a b x + 840a b x + 126a x +--R (2) ---------------------------------------------------------------------- +--R 252 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 4 2 3 3 4 2 +-+ 4 4 3 2 3 5 2 +--R (56b x + 720a b x + 504a b x )\|x + 315a b x + 840a b x + 126a x +--R (3) ---------------------------------------------------------------------- +--R 252 +--R Type: Union(Expression(Integer),...) +--E 646 + +--S 647 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1325 +t0:=(a+b*sqrt(x))^5 +--R +--R +--R 5 2 2 3 4 +-+ 4 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+--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1325 +r0:=10*a^3*b^2*x+20/3*a^2*b^3*x^(3/2)+5/2*a*b^4*x^2+2/5*b^5*x^(5/2)+_ + a^5*log(x)+10*a^4*b*sqrt(x) +--R +--R +--R 5 2 2 3 4 +-+ 5 4 2 3 2 +--R (12b x + 200a b x + 300a b)\|x + 30a log(x) + 75a b x + 300a b x +--R (2) ------------------------------------------------------------------- +--R 30 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2 +--R 60a log(\|x ) + (12b x + 200a b x + 300a b)\|x + 75a b x + 300a b x +--R (3) ---------------------------------------------------------------------- +--R 30 +--R Type: Union(Expression(Integer),...) +--E 656 + +--S 657 of 1325 +m0:=a0-r0 +--R +--R +--R 5 +-+ 5 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 658 + +)clear all + +--S 659 of 1325 +t0:=(a+b*sqrt(x))^5/x^2 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1325 +r0:=-a^5/x+5*a*b^4*x+2/3*b^5*x^(3/2)+10*a^3*b^2*log(x)-_ + 10*a^4*b/sqrt(x)+20*a^2*b^3*sqrt(x) +--R +--R +--R 3 2 4 2 5 +-+ 5 3 2 3 2 4 +--R (30a b x log(x) + 15a b x - 3a )\|x + 2b x + 60a b x - 30a b x +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 5 2 2 3 4 +-+ 4 2 5 +--R 60a b x log(\|x ) + (2b x + 60a b x - 30a b)\|x + 15a b x - 3a +--R (3) ------------------------------------------------------------------ +--R 3x +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1325 +m0:=a0-r0 +--R +--R +--R 3 2 +-+ 3 2 +--R (4) 20a b log(\|x ) - 10a b log(x) +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1325 +t0:=(a+b*sqrt(x))^5/x^3 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1325 +r0:=-1/2*a^5/x^2-10/3*a^4*b/x^(3/2)-10*a^3*b^2/x+5*a*b^4*log(x)-_ + 20*a^2*b^3/sqrt(x)+2*b^5*sqrt(x) +--R +--R +--R 4 2 3 2 5 +-+ 5 3 2 3 2 4 +--R (30a b x log(x) - 60a b x - 3a )\|x + 12b x - 120a b x - 20a b x +--R (2) ------------------------------------------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +-+ 5 2 2 3 4 +-+ 3 2 5 +--R 60a b x log(\|x ) + (12b x - 120a b x - 20a b)\|x - 60a b x - 3a +--R (3) ------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R (4) 10a b log(\|x ) - 5a b log(x) +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 668 + +)clear all + +--S 669 of 1325 +t0:=(a+b*sqrt(x))^5/x^4 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1325 +r0:=-1/3*(a+b*sqrt(x))^6/(a*x^3) +--R +--R +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (- 6a b x - 20a b x - 6a b)\|x - b x - 15a b x - 15a b x - a +--R (2) ----------------------------------------------------------------- +--R 3 +--R 3a x +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (- 6b x - 20a b x - 6a b)\|x - 15a b x - 15a b x - a +--R (3) -------------------------------------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) -- +--R 3a +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 673 + +)clear all + +--S 674 of 1325 +t0:=(a+b*sqrt(x))^5/x^5 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1325 +r0:=-1/4*a^5/x^4-10/7*a^4*b/x^(7/2)-10/3*a^3*b^2/x^3-_ + 4*a^2*b^3/x^(5/2)-5/2*a*b^4/x^2-2/3*b^5/x^(3/2) +--R +--R +--R 4 2 3 2 5 +-+ 5 3 2 3 2 4 +--R (- 210a b x - 280a b x - 21a )\|x - 56b x - 336a b x - 120a b x +--R (2) ------------------------------------------------------------------- +--R 4 +-+ 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126a )\|x - 252b x - 1800a b x - 700a b x +--R ------------------------------------------------------------------------ +--R 5 +-+ +--R 630x \|x +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (- 252b x - 1800a b x - 700a b)\|x - 1050a b x - 1575a b x - 126a +--R (3) --------------------------------------------------------------------- +--R 5 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 681 + +--S 682 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 683 + +)clear all + +--S 684 of 1325 +t0:=(a+b*sqrt(x))^5/x^7 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1325 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+r0:=1/5*a^10*x^5+20/11*a^9*b*x^(11/2)+15/2*a^8*b^2*x^6+240/13*a^7*_ + b^3*x^(13/2)+30*a^6*b^4*x^7+168/5*a^5*b^5*x^(15/2)+105/4*a^4*_ + b^6*x^8+240/17*a^3*b^7*x^(17/2)+5*a^2*b^8*x^9+20/19*a*_ + b^9*x^(19/2)+1/10*b^10*x^10 +--R +--R +--R (2) +--R 9 9 3 7 8 5 5 7 7 3 6 +--R 972400a b x + 13041600a b x + 31039008a b x + 17054400a b x +--R + +--R 9 5 +--R 1679600a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 10 2 8 9 4 6 8 6 4 7 +--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x +--R + +--R 8 2 6 10 5 +--R 6928350a b x + 184756a x +--R / +--R 923780 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 9 3 7 8 5 5 7 7 3 6 +--R 972400a b x + 13041600a b x + 31039008a b x + 17054400a b x +--R + +--R 9 5 +--R 1679600a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 10 2 8 9 4 6 8 6 4 7 +--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x +--R + +--R 8 2 6 10 5 +--R 6928350a b x + 184756a x +--R / +--R 923780 +--R Type: Union(Expression(Integer),...) +--E 696 + +--S 697 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +)clear all + +--S 699 of 1325 +t0:=x^3*(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 7 3 7 6 5 5 5 7 3 4 9 3 +-+ 10 8 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x +--R + +--R 2 8 7 4 6 6 6 4 5 8 2 4 10 3 +--R 45a b x + 210a b x + 210a b x + 45a b x + a x +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1325 +r0:=1/4*a^10*x^4+20/9*a^9*b*x^(9/2)+9*a^8*b^2*x^5+240/11*a^7*b^3*_ + x^(11/2)+35*a^6*b^4*x^6+504/13*a^5*b^5*x^(13/2)+30*a^4*b^6*_ + x^7+16*a^3*b^7*x^(15/2)+45/8*a^2*b^8*x^8+20/17*a*b^9*x^(17/2)+_ + 1/9*b^10*x^9 +--R +--R +--R (2) +--R 9 8 3 7 7 5 5 6 7 3 5 +--R 205920a b x + 2800512a b x + 6785856a b x + 3818880a b x +--R + +--R 9 4 +--R 388960a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 9 2 8 8 4 6 7 6 4 6 8 2 5 +--R 19448b x + 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x + 210a b x + 45a b x + a x +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1325 +r0:=-2/11*a^5*(a+b*sqrt(x))^11/b^6+5/6*a^4*(a+b*sqrt(x))^12/b^6-_ + 20/13*a^3*(a+b*sqrt(x))^13/b^6+10/7*a^2*(a+b*sqrt(x))^14/b^6-_ + 2/3*a*(a+b*sqrt(x))^15/b^6+1/8*(a+b*sqrt(x))^16/b^6 +--R +--R +--R (2) +--R 15 7 3 13 6 5 11 5 7 9 4 +--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x +--R + +--R 9 7 3 +--R 68640a b x +--R * +--R +-+ +--R \|x +--R + +--R 16 8 2 14 7 4 12 6 6 10 5 8 8 4 +--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x +--R + +--R 10 6 3 16 +--R 8008a b x - a +--R / +--R 6 +--R 24024b +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 7 3 7 6 5 5 5 7 3 4 +--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x +--R + +--R 9 3 +--R 68640a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 8 2 8 7 4 6 6 6 4 5 8 2 4 +--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x +--R + +--R 10 3 +--R 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30030a b x +--R + +--R 10 4 2 14 +--R 1001a b x - a +--R / +--R 4 +--R 2002b +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 6 3 7 5 5 5 4 7 3 3 9 2 +-+ +--R (3080a b x + 43680a b x + 112112a b x + 68640a b x + 8008a b x )\|x +--R + +--R 10 7 2 8 6 4 6 5 6 4 4 8 2 3 +--R 286b x + 15015a b x + 84084a b x + 105105a b x + 30030a b x +--R + +--R 10 2 +--R 1001a x +--R / +--R 2002 +--R Type: Union(Expression(Integer),...) +--E 711 + +--S 712 of 1325 +m0:=a0-r0 +--R +--R +--R 14 +--R a +--R (4) ------ +--R 4 +--R 2002b +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +)clear all + +--S 714 of 1325 +t0:=(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1325 +r0:=-2/11*a*(a+b*sqrt(x))^11/b^2+1/6*(a+b*sqrt(x))^12/b^2 +--R +--R +--R (2) +--R 11 5 3 9 4 5 7 3 7 5 2 9 3 +-+ +--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x +--R + +--R 12 6 2 10 5 4 8 4 6 6 3 8 4 2 10 2 +--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a b x +--R + +--R 12 +--R - a +--R / +--R 2 +--R 66b +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 5 3 7 4 5 5 3 7 3 2 9 +-+ +--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x +--R + +--R 10 6 2 8 5 4 6 4 6 4 3 8 2 2 10 +--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a x +--R / +--R 66 +--R Type: Union(Expression(Integer),...) +--E 716 + +--S 717 of 1325 +m0:=a0-r0 +--R +--R +--R 12 +--R a +--R (4) ---- +--R 2 +--R 66b +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 718 + +)clear all + 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127008a b x + 100800a b x + 25200a b)\|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 8 2 +--R 252b x + 14175a b x + 88200a b x + 132300a b x + 56700a b x +--R / +--R 1260 +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1325 +m0:=a0-r0 +--R +--R +--R 10 +-+ 10 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1325 +t0:=(a+b*sqrt(x))^10/x^2 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1325 +r0:=-a^10/x+210*a^6*b^4*x+168*a^5*b^5*x^(3/2)+105*a^4*b^6*x^2+_ + 48*a^3*b^7*x^(5/2)+15*a^2*b^8*x^3+20/7*a*b^9*x^(7/2)+_ + 1/4*b^10*x^4+45*a^8*b^2*log(x)-20*a^9*b/sqrt(x)+240*a^7*b^3*sqrt(x) +--R +--R +--R (2) +--R 8 2 10 5 2 8 4 4 6 3 6 4 2 +--R 1260a b x log(x) + 7b x + 420a b x + 2940a b x + 5880a b x +--R + +--R 10 +--R - 28a +--R * +--R +-+ +--R \|x +--R + +--R 9 5 3 7 4 5 5 3 7 3 2 9 +--R 80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b x +--R / +--R +-+ +--R 28x\|x +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 +-+ +--R 2520a b x log(\|x ) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b)\|x + 7b x +--R + +--R 2 8 4 4 6 3 6 4 2 10 +--R 420a b x + 2940a b x + 5880a b x - 28a +--R / +--R 28x +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1325 +m0:=a0-r0 +--R +--R +--R 8 2 +-+ 8 2 +--R (4) 90a b log(\|x ) - 45a b log(x) +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1325 +t0:=(a+b*sqrt(x))^10/x^3 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 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all + +--S 889 of 1325 +t0:=x^3/(a+b*sqrt(x)) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1325 +r0:=-a^5*x/b^6+2/3*a^4*x^(3/2)/b^5-1/2*a^3*x^2/b^4+2/5*a^2*x^(5/2)/b^3-_ + 1/3*a*x^3/b^2+2/7*x^(7/2)/b-2*a^7*log(a+b*sqrt(x))/b^8+2*a^6*sqrt(x)/b^7 +--R +--R +--R (2) +--R 7 +-+ 7 3 2 5 2 4 3 6 +-+ +--R - 420a log(b\|x + a) + (60b x + 84a b x + 140a b x + 420a b)\|x +--R + +--R 6 3 3 4 2 5 2 +--R - 70a b x - 105a b x - 210a b x +--R / +--R 8 +--R 210b +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +-+ 7 3 2 5 2 4 3 6 +-+ +--R - 420a log(b\|x + a) + (60b x + 84a b x + 140a b x + 420a b)\|x +--R + +--R 6 3 3 4 2 5 2 +--R - 70a b x - 105a b x - 210a b x +--R / +--R 8 +--R 210b +--R Type: Union(Expression(Integer),...) +--E 891 + +--S 892 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 893 + +)clear all + +--S 894 of 1325 +t0:=x^2/(a+b*sqrt(x)) +--R +--R +--R 2 +--R x +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1325 +r0:=-a^3*x/b^4+2/3*a^2*x^(3/2)/b^3-1/2*a*x^2/b^2+2/5*x^(5/2)/b-_ + 2*a^5*log(a+b*sqrt(x))/b^6+2*a^4*sqrt(x)/b^5 +--R +--R +--R (2) +--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2 +--R - 60a log(b\|x + a) + (12b x + 20a b x + 60a b)\|x - 15a b x - 30a b x +--R -------------------------------------------------------------------------- +--R 6 +--R 30b +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2 +--R - 60a log(b\|x + a) + (12b x + 20a b x + 60a b)\|x - 15a b x - 30a b x +--R -------------------------------------------------------------------------- +--R 6 +--R 30b +--R Type: Union(Expression(Integer),...) +--E 896 + +--S 897 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 898 + +)clear all + +--S 899 of 1325 +t0:=x/(a+b*sqrt(x)) +--R +--R +--R x +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1325 +r0:=-a*x/b^2+2/3*x^(3/2)/b-2*a^3*log(a+b*sqrt(x))/b^4+2*a^2*sqrt(x)/b^3 +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x +--R (2) ------------------------------------------------ +--R 4 +--R 3b +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x +--R (3) ------------------------------------------------ +--R 4 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 901 + +--S 902 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1325 +t0:=1/(a+b*sqrt(x)) +--R +--R +--R 1 +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1325 +r0:=-2*a*log(a+b*sqrt(x))/b^2+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R - 2a log(b\|x + a) + 2b\|x +--R (2) ---------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R - 2a log(b\|x + a) + 2b\|x +--R (3) ---------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 906 + +--S 907 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 908 + +)clear all + +--S 909 of 1325 +t0:=1/(x*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R b x\|x + a x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1325 +r0:=log(x)/a-2*log(a+b*sqrt(x))/a +--R +--R +--R +-+ +--R - 2log(b\|x + a) + log(x) +--R (2) -------------------------- +--R a +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R - 2log(b\|x + a) + 2log(\|x ) +--R (3) ------------------------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 911 + +--S 912 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 913 + +)clear all + +--S 914 of 1325 +t0:=1/(x*(2+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------ +--R +-+ +--R b x\|x + 2x +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1325 +r0:=-2*atanh(1+b*sqrt(x)) +--R +--R +--R +-+ +--R (2) - 2atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) - log(b\|x + 2) + log(\|x ) +--R Type: Union(Expression(Integer),...) +--E 916 + +--S 917 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +-+ +-+ +--R (4) - log(b\|x + 2) + log(\|x ) + 2atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 2 +-+ 2 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1325 +r0:=(-1)/(a*x)+b^2*log(x)/a^3-2*b^2*log(a+b*sqrt(x))/a^3+2*b/(a^2*sqrt(x)) +--R +--R +--R 2 +-+ +-+ 2 2 +-+ +--R - 2b x\|x log(b\|x + a) + (b x log(x) - a )\|x + 2a b x +--R (2) --------------------------------------------------------- +--R 3 +-+ +--R a x\|x +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 +-+ +-+ 2 +--R - 2b x log(b\|x + a) + 2b x log(\|x ) + 2a b\|x - a +--R (3) ------------------------------------------------------ +--R 3 +--R a x +--R Type: Union(Expression(Integer),...) +--E 921 + +--S 922 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 923 + +)clear all + +--S 924 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 3 +-+ 3 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1325 +r0:=(-1/2)/(a*x^2)+2/3*b/(a^2*x^(3/2))-b^2/(a^3*x)+b^4*log(x)/a^5-_ + 2*b^4*log(a+b*sqrt(x))/a^5+2*b^3/(a^4*sqrt(x)) +--R +--R +--R (2) +--R 4 2 +-+ +-+ 4 2 2 2 4 +-+ 3 2 +--R - 12b x \|x log(b\|x + a) + (6b x log(x) - 6a b x - 3a )\|x + 12a b x +--R + +--R 3 +--R 4a b x +--R / +--R 5 2 +-+ +--R 6a x \|x +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ 4 2 +-+ 3 3 +-+ 2 2 +--R - 12b x log(b\|x + a) + 12b x log(\|x ) + (12a b x + 4a b)\|x - 6a b x +--R + +--R 4 +--R - 3a +--R / +--R 5 2 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 926 + +--S 927 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 928 + +)clear all + +--S 929 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 4 +-+ 4 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1325 +r0:=(-1/3)/(a*x^3)+2/5*b/(a^2*x^(5/2))-1/2*b^2/(a^3*x^2)+2/3*_ + b^3/(a^4*x^(3/2))-b^4/(a^5*x)+b^6*log(x)/a^7-2*b^6*log(a+b*_ + sqrt(x))/a^7+2*b^5/(a^6*sqrt(x)) +--R +--R +--R (2) +--R 6 3 +-+ +-+ +--R - 60b x \|x log(b\|x + a) +--R + +--R 6 3 2 4 2 4 2 6 +-+ 5 3 3 3 2 +--R (30b x log(x) - 30a b x - 15a b x - 10a )\|x + 60a b x + 20a b x +--R + +--R 5 +--R 12a b x +--R / +--R 7 3 +-+ +--R 30a x \|x +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 +-+ 6 3 +-+ +--R - 60b x log(b\|x + a) + 60b x log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 2 4 2 4 2 6 +--R (60a b x + 20a b x + 12a b)\|x - 30a b x - 15a b x - 10a +--R / +--R 7 3 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 931 + +--S 932 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +)clear all + +--S 934 of 1325 +t0:=x^3/(a+b*sqrt(x))^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1325 +r0:=5*a^4*x/b^6-8/3*a^3*x^(3/2)/b^5+3/2*a^2*x^2/b^4-4/5*a*x^(5/2)/b^3+_ + 1/3*x^3/b^2+14*a^6*log(a+b*sqrt(x))/b^8-12*a^5*sqrt(x)/b^7+_ + 2*a^7/(b^8*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 +-+ 7 +-+ +--R (420a b\|x + 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x +--R + +--R 5 2 7 +--R - 210a b x + 60a +--R / +--R 9 +-+ 8 +--R 30b \|x + 30a b +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 7 +-+ +--R (420a b\|x + 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x +--R + +--R 5 2 7 +--R - 210a b x + 60a +--R / +--R 9 +-+ 8 +--R 30b \|x + 30a b +--R Type: Union(Expression(Integer),...) +--E 936 + +--S 937 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 938 + +)clear all + +--S 939 of 1325 +t0:=x^2/(a+b*sqrt(x))^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1325 +r0:=3*a^2*x/b^4-4/3*a*x^(3/2)/b^3+1/2*x^2/b^2+10*a^4*log(a+b*sqrt(x))/b^6-_ + 8*a^3*sqrt(x)/b^5+2*a^5/(b^6*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+ +--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x +--R + +--R 4 2 3 2 5 +--R - 5a b x - 30a b x + 12a +--R / +--R 7 +-+ 6 +--R 6b \|x + 6a b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+ +--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x +--R + +--R 4 2 3 2 5 +--R - 5a b x - 30a b x + 12a +--R / +--R 7 +-+ 6 +--R 6b \|x + 6a b +--R Type: Union(Expression(Integer),...) +--E 941 + +--S 942 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 943 + +)clear all + +--S 944 of 1325 +t0:=x/(a+b*sqrt(x))^2 +--R +--R +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1325 +r0:=x/b^2+6*a^2*log(a+b*sqrt(x))/b^4-4*a*sqrt(x)/b^3+2*a^3/(b^4*(a+b*sqrt(x))) +--R +--R +--R 2 +-+ 3 +-+ 3 2 +-+ 2 3 +--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a +--R (2) ---------------------------------------------------------------- +--R 5 +-+ 4 +--R b \|x + a b +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 3 +-+ 3 2 +-+ 2 3 +--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a +--R (3) ---------------------------------------------------------------- +--R 5 +-+ 4 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 946 + +--S 947 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1325 +t0:=1/(a+b*sqrt(x))^2 +--R +--R +--R 1 +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1325 +r0:=2*log(a+b*sqrt(x))/b^2+2*a/(b^2*(a+b*sqrt(x))) +--R +--R +--R +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) + 2a +--R (2) -------------------------------- +--R 3 +-+ 2 +--R b \|x + a b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) + 2a +--R (3) -------------------------------- +--R 3 +-+ 2 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1325 +t0:=1/(x*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-+ 2 2 2 +--R 2a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1325 +r0:=log(x)/a^2-2*log(a+b*sqrt(x))/a^2+2/(a*(a+b*sqrt(x))) +--R +--R +--R +-+ +-+ +-+ +--R (- 2b\|x - 2a)log(b\|x + a) + b log(x)\|x + a log(x) + 2a +--R (2) ------------------------------------------------------------ +--R 2 +-+ 3 +--R a b\|x + a +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +-+ +-+ +--R (- 2b\|x - 2a)log(b\|x + a) + (2b\|x + 2a)log(\|x ) + 2a +--R (3) ----------------------------------------------------------- +--R 2 +-+ 3 +--R a b\|x + a +--R Type: Union(Expression(Integer),...) +--E 956 + +--S 957 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +)clear all + +--S 959 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 +-+ 2 3 2 2 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1325 +r0:=(-3)/(a^2*x)+3*b^2*log(x)/a^4-6*b^2*log(a+b*sqrt(x))/a^4+_ + 6*b/(a^3*sqrt(x))+2/(a*x*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 2 +-+ 3 2 +-+ 2 2 3 +-+ +--R (- 6a b x\|x - 6b x )log(b\|x + a) + (3a b x log(x) + 6a b x - a )\|x +--R + +--R 3 2 2 +--R 3b x log(x) + 3a b x +--R / +--R 5 +-+ 4 2 +--R a x\|x + a b x +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 2 +-+ 3 +-+ 2 +-+ +--R (- 6b x\|x - 6a b x)log(b\|x + a) + (6b x\|x + 6a b x)log(\|x ) +--R + +--R 2 +-+ 2 3 +--R 3a b\|x + 6a b x - a +--R / +--R 4 +-+ 5 +--R a b x\|x + a x +--R Type: Union(Expression(Integer),...) +--E 961 + +--S 962 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 6b log(\|x ) - 3b log(x) +--R (4) ------------------------ +--R 4 +--R a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 3 +-+ 2 4 2 3 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1325 +r0:=(-5/2)/(a^2*x^2)+10/3*b/(a^3*x^(3/2))-5*b^2/(a^4*x)+_ + 5*b^4*log(x)/a^6-10*b^4*log(a+b*sqrt(x))/a^6+10*b^3/(a^5*_ + sqrt(x))+2/(a*x^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 2 +-+ 5 3 +-+ +--R (- 60a b x \|x - 60b x )log(b\|x + a) +--R + +--R 4 2 4 2 3 2 5 +-+ 5 3 2 3 2 +--R (30a b x log(x) + 60a b x - 10a b x - 3a )\|x + 30b x log(x) + 30a b x +--R + +--R 4 +--R 5a b x +--R / +--R 7 2 +-+ 6 3 +--R 6a x \|x + 6a b x +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 +-+ 4 2 +-+ +--R (- 60b x \|x - 60a b x )log(b\|x + a) +--R + +--R 5 2 +-+ 4 2 +-+ 2 3 4 +-+ 4 2 +--R (60b x \|x + 60a b x )log(\|x ) + (30a b x + 5a b)\|x + 60a b x +--R + +--R 3 2 5 +--R - 10a b x - 3a +--R / +--R 6 2 +-+ 7 2 +--R 6a b x \|x + 6a x +--R Type: Union(Expression(Integer),...) +--E 966 + +--S 967 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 10b log(\|x ) - 5b log(x) +--R (4) ------------------------- +--R 6 +--R a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 968 + +)clear all + +--S 969 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 4 +-+ 2 5 2 4 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1325 +r0:=(-7/3)/(a^2*x^3)+14/5*b/(a^3*x^(5/2))-7/2*b^2/(a^4*x^2)+_ + 14/3*b^3/(a^5*x^(3/2))-7*b^4/(a^6*x)+7*b^6*log(x)/a^8-_ + 14*b^6*log(a+b*sqrt(x))/a^8+14*b^5/(a^7*sqrt(x))+2/(a*x^3*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 3 +-+ 7 4 +-+ +--R (- 420a b x \|x - 420b x )log(b\|x + a) +--R + +--R 6 3 6 3 3 4 2 5 2 7 +-+ +--R (210a b x log(x) + 420a b x - 70a b x - 21a b x - 10a )\|x +--R + +--R 7 4 2 5 3 4 3 2 6 +--R 210b x log(x) + 210a b x + 35a b x + 14a b x +--R / +--R 9 3 +-+ 8 4 +--R 30a x \|x + 30a b x +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 +-+ 6 3 +-+ +--R (- 420b x \|x - 420a b x )log(b\|x + a) +--R + +--R 7 3 +-+ 6 3 +-+ 2 5 2 4 3 6 +-+ +--R (420b x \|x + 420a b x )log(\|x ) + (210a b x + 35a b x + 14a b)\|x +--R + +--R 6 3 3 4 2 5 2 7 +--R 420a b x - 70a b x - 21a b x - 10a +--R / +--R 8 3 +-+ 9 3 +--R 30a b x \|x + 30a x +--R Type: Union(Expression(Integer),...) +--E 971 + +--S 972 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 14b log(\|x ) - 7b log(x) +--R (4) ------------------------- +--R 8 +--R a +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 973 + +)clear all + +--S 974 of 1325 +t0:=x^3/(a+b*sqrt(x))^3 +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1325 +r0:=-10*a^3*x/b^6+4*a^2*x^(3/2)/b^5-3/2*a*x^2/b^4+2/5*x^(5/2)/b^3-_ + 42*a^5*log(a+b*sqrt(x))/b^8+30*a^4*sqrt(x)/b^7+_ + a^7/(b^8*(a+b*sqrt(x))^2)-14*a^6/(b^8*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 5 3 7 +-+ 6 2 8 +-+ +--R ((- 420a b x - 1260a b)\|x - 1260a b x - 420a )log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3 +--R (- 3a b x - 21a b x + 640a b x + 30a b)\|x + 4b x + 7a b x +--R + +--R 4 4 2 6 2 8 +--R 105a b x + 660a b x - 130a +--R / +--R 11 2 9 +-+ 10 3 8 +--R (10b x + 30a b )\|x + 30a b x + 10a b +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 5 2 7 +-+ +--R (- 840a b\|x - 420a b x - 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (4b x + 14a b x + 140a b x + 160a b)\|x - 7a b x - 35a b x +--R + +--R 5 2 7 +--R 500a b x - 130a +--R / +--R 9 +-+ 10 2 8 +--R 20a b \|x + 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 976 + +--S 977 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 978 + +)clear all + +--S 979 of 1325 +t0:=x^2/(a+b*sqrt(x))^3 +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1325 +r0:=-3*a*x/b^4+2/3*x^(3/2)/b^3-20*a^3*log(a+b*sqrt(x))/b^6+_ + 12*a^2*sqrt(x)/b^5+a^5/(b^6*(a+b*sqrt(x))^2)-10*a^4/(b^6*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 3 5 +-+ 4 2 6 +-+ +--R ((- 60a b x - 180a b)\|x - 180a b x - 60a )log(b\|x + a) +--R + +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (- 3a b x + 83a b x - 21a b)\|x + 2b x + 15a b x + 69a b x - 27a +--R / +--R 9 2 7 +-+ 8 3 6 +--R (3b x + 9a b )\|x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ 3 2 5 +-+ +--R (- 120a b\|x - 60a b x - 60a )log(b\|x + a) +--R + +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (2b x + 20a b x + 6a b)\|x - 5a b x + 63a b x - 27a +--R / +--R 7 +-+ 8 2 6 +--R 6a b \|x + 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 981 + +--S 982 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 983 + +)clear all + +--S 984 of 1325 +t0:=x/(a+b*sqrt(x))^3 +--R +--R +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1325 +r0:=-6*a*log(a+b*sqrt(x))/b^4+2*sqrt(x)/b^3+a^3/(b^4*(a+b*sqrt(x))^2)-_ + 6*a^2/(b^4*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 3 +-+ 2 2 4 +-+ +--R ((- 6a b x - 18a b)\|x - 18a b x - 6a )log(b\|x + a) +--R + +--R 3 3 +-+ 4 2 4 +--R (6a b x - 9a b)\|x + 2b x - 5a +--R / +--R 7 2 5 +-+ 6 3 4 +--R (b x + 3a b )\|x + 3a b x + a b +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 3 +-+ 3 2 +-+ 2 3 +--R (- 12a b\|x - 6a b x - 6a )log(b\|x + a) + (2b x - 4a b)\|x + 4a b x - 5a +--R ----------------------------------------------------------------------------- +--R 5 +-+ 6 2 4 +--R 2a b \|x + b x + a b +--R Type: Union(Expression(Integer),...) +--E 986 + +--S 987 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 988 + +)clear all + +--S 989 of 1325 +t0:=1/(a+b*sqrt(x))^3 +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1325 +r0:=x/(a*(a+b*sqrt(x))^2) +--R +--R +--R x +--R (2) --------------------- +--R 2 +-+ 2 3 +--R 2a b\|x + a b x + a +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 2b\|x - a +--R (3) ---------------------- +--R 3 +-+ 4 2 2 +--R 2a b \|x + b x + a b +--R Type: Union(Expression(Integer),...) +--E 991 + +--S 992 of 1325 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 993 + +)clear all + +--S 994 of 1325 +t0:=1/(x*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 2 2 +-+ 2 2 3 +--R (b x + 3a b x)\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1325 +r0:=log(x)/a^3-2*log(a+b*sqrt(x))/a^3+1/(a*(a+b*sqrt(x))^2)+_ + 2/(a^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 2 +-+ 2 3 +-+ +--R ((- 2b x - 6a b)\|x - 6a b x - 2a )log(b\|x + a) +--R + +--R 3 2 2 +-+ 2 3 2 3 +--R ((b x + 3a b)log(x) + 5a b)\|x + (3a b x + a )log(x) + 2a b x + 3a +--R / +--R 3 3 5 +-+ 4 2 6 +--R (a b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 2 +-+ +--R (- 4a b\|x - 2b x - 2a )log(b\|x + a) +--R + +--R +-+ 2 2 +-+ +-+ 2 +--R (4a b\|x + 2b x + 2a )log(\|x ) + 2a b\|x + 3a +--R / +--R 4 +-+ 3 2 5 +--R 2a b\|x + a b x + a +--R Type: Union(Expression(Integer),...) +--E 996 + +--S 997 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 3 2 2 +-+ 2 3 3 2 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1325 +r0:=(-6)/(a^3*x)+6*b^2*log(x)/a^5-12*b^2*log(a+b*sqrt(x))/a^5+_ + 12*b/(a^4*sqrt(x))+1/(a*x*(a+b*sqrt(x))^2)+4/(a^2*x*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 2 3 2 +-+ 5 3 2 3 2 +-+ +--R ((- 36a b x - 12a b x)\|x - 12b x - 36a b x )log(b\|x + a) +--R + +--R 4 2 3 2 4 2 3 2 5 +-+ +--R ((18a b x + 6a b x)log(x) + 12a b x + 22a b x - a )\|x +--R + +--R 5 3 2 3 2 2 3 2 4 +--R (6b x + 18a b x )log(x) + 30a b x + 3a b x +--R / +--R 6 2 2 8 +-+ 5 3 3 7 2 +--R (3a b x + a x)\|x + a b x + 3a b x +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 4 2 2 2 +-+ +--R (- 24a b x\|x - 12b x - 12a b x)log(b\|x + a) +--R + +--R 3 +-+ 4 2 2 2 +-+ 3 3 +-+ +--R (24a b x\|x + 12b x + 12a b x)log(\|x ) + (12a b x + 4a b)\|x +--R + +--R 2 2 4 +--R 18a b x - a +--R / +--R 6 +-+ 5 2 2 7 +--R 2a b x\|x + a b x + a x +--R Type: Union(Expression(Integer),...) +--E 1001 + +--S 1002 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 12b log(\|x ) - 6b log(x) +--R (4) ------------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +)clear all + +--S 1004 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 4 2 3 +-+ 2 4 3 3 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1325 +r0:=(-15/2)/(a^3*x^2)+10*b/(a^4*x^(3/2))-15*b^2/(a^5*x)+15*b^4*_ + log(x)/a^7-30*b^4*log(a+b*sqrt(x))/a^7+30*b^3/(a^6*sqrt(x))+_ + 1/(a*x^2*(a+b*sqrt(x))^2)+6/(a^2*x^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 3 3 4 2 +-+ 7 4 2 5 3 +-+ +--R ((- 180a b x - 60a b x )\|x - 60b x - 180a b x )log(b\|x + a) +--R + +--R 6 3 3 4 2 6 3 3 4 2 5 2 7 +-+ +--R ((90a b x + 30a b x )log(x) + 60a b x + 110a b x - 3a b x - a )\|x +--R + +--R 7 4 2 5 3 2 5 3 4 3 2 6 +--R (30b x + 90a b x )log(x) + 150a b x + 15a b x + a b x +--R / +--R 8 2 3 10 2 +-+ 7 3 4 9 3 +--R (6a b x + 2a x )\|x + 2a b x + 6a b x +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 +-+ 6 3 2 4 2 +-+ +--R (- 120a b x \|x - 60b x - 60a b x )log(b\|x + a) +--R + +--R 5 2 +-+ 6 3 2 4 2 +-+ +--R (120a b x \|x + 60b x + 60a b x )log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 2 4 2 4 2 6 +--R (60a b x + 20a b x + 2a b)\|x + 90a b x - 5a b x - a +--R / +--R 8 2 +-+ 7 2 3 9 2 +--R 4a b x \|x + 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 1006 + +--S 1007 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 30b log(\|x ) - 15b log(x) +--R (4) -------------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 +-+ 2 5 3 4 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1325 +r0:=(-28/3)/(a^3*x^3)+56/5*b/(a^4*x^(5/2))-14*b^2/(a^5*x^2)+_ + 56/3*b^3/(a^6*x^(3/2))-28*b^4/(a^7*x)+28*b^6*log(x)/a^9-_ + 56*b^6*log(a+b*sqrt(x))/a^9+56*b^5/(a^8*sqrt(x))+_ + 1/(a*x^3*(a+b*sqrt(x))^2)+8/(a^2*x^3*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 8 4 3 6 3 +-+ 9 5 2 7 4 +-+ +--R ((- 2520a b x - 840a b x )\|x - 840b x - 2520a b x )log(b\|x + a) +--R + +--R 8 4 3 6 3 8 4 3 6 3 5 4 2 +--R (1260a b x + 420a b x )log(x) + 840a b x + 1540a b x - 42a b x +--R + +--R 7 2 9 +--R - 6a b x - 5a +--R * +--R +-+ +--R \|x +--R + +--R 9 5 2 7 4 2 7 4 4 5 3 6 3 2 8 +--R (420b x + 1260a b x )log(x) + 2100a b x + 210a b x + 14a b x + 3a b x +--R / +--R 10 2 4 12 3 +-+ 9 3 5 11 4 +--R (45a b x + 15a x )\|x + 15a b x + 45a b x +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 +-+ 8 4 2 6 3 +-+ +--R (- 1680a b x \|x - 840b x - 840a b x )log(b\|x + a) +--R + +--R 7 3 +-+ 8 4 2 6 3 +-+ +--R (1680a b x \|x + 840b x + 840a b x )log(\|x ) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 2 6 3 4 4 2 +--R (840a b x + 280a b x + 28a b x + 8a b)\|x + 1260a b x - 70a b x +--R + +--R 6 2 8 +--R - 14a b x - 5a +--R / +--R 10 3 +-+ 9 2 4 11 3 +--R 30a b x \|x + 15a b x + 15a x +--R Type: Union(Expression(Integer),...) +--E 1011 + +--S 1012 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 56b log(\|x ) - 28b log(x) +--R (4) -------------------------- +--R 9 +--R a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1013 + +)clear all + +--S 1014 of 1325 +t0:=x^2*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R 2 | +-+ +--R (1) x \|b\|x + a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1325 +r0:=-4/3*a^5*(a+b*sqrt(x))^(3/2)/b^6+4*a^4*(a+b*sqrt(x))^(5/2)/b^6-_ + 40/7*a^3*(a+b*sqrt(x))^(7/2)/b^6+40/9*a^2*(a+_ + b*sqrt(x))^(9/2)/b^6-20/11*a*(a+b*sqrt(x))^(11/2)/b^6+_ + 4/13*(a+b*sqrt(x))^(13/2)/b^6 +--R +--R +--R (2) +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (252a b x + 320a b x + 512a b)\|x + 2772b x - 280a b x - 384a b x +--R + +--R 6 +--R - 1024a +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 9009b +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (252a b x + 320a b x + 512a b)\|x + 2772b x - 280a b x - 384a b x +--R + +--R 6 +--R - 1024a +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 9009b +--R Type: Union(Expression(Integer),...) +--E 1016 + +--S 1017 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1018 + +)clear all + +--S 1019 of 1325 +t0:=x*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R (1) x\|b\|x + a +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1325 +r0:=-4/3*a^3*(a+b*sqrt(x))^(3/2)/b^4+12/5*a^2*(a+b*sqrt(x))^(5/2)/b^4-_ + 12/7*a*(a+b*sqrt(x))^(7/2)/b^4+4/9*(a+b*sqrt(x))^(9/2)/b^4 +--R +--R +--R +---------+ +--R 3 3 +-+ 4 2 2 2 4 | +-+ +--R ((20a b x + 32a b)\|x + 140b x - 24a b x - 64a )\|b\|x + a +--R (2) -------------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3 3 +-+ 4 2 2 2 4 | +-+ +--R ((20a b x + 32a b)\|x + 140b x - 24a b x - 64a )\|b\|x + a +--R (3) -------------------------------------------------------------- +--R 4 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1021 + +--S 1022 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1325 +t0:=sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R (1) \|b\|x + a +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1325 +r0:=-4/3*a*(a+b*sqrt(x))^(3/2)/b^2+4/5*(a+b*sqrt(x))^(5/2)/b^2 +--R +--R +--R +---------+ +--R +-+ 2 2 | +-+ +--R (4a b\|x + 12b x - 8a )\|b\|x + a +--R (2) ------------------------------------ +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +-+ 2 2 | +-+ +--R (4a b\|x + 12b x - 8a )\|b\|x + a +--R (3) ------------------------------------ +--R 2 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1026 + +--S 1027 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1028 + +)clear all + +--S 1029 of 1325 +t0:=sqrt(a+b*sqrt(x))/x +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1325 +r0:=-4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))*sqrt(a)+4*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R +-+ \|b\|x + a | +-+ +--R (2) - 4\|a atanh(------------) + 4\|b\|x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +-+ | +-+ +-+ +---------+ +--R +-+ - 2\|a \|b\|x + a + b\|x + 2a | +-+ +--R [2\|a log(--------------------------------) + 4\|b\|x + a , +--R +-+ +--R \|x +--R +---------+ +--R | +-+ +---------+ +--R +---+ \|b\|x + a | +-+ +--R - 4\|- a atan(------------) + 4\|b\|x + a ] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1031 + +--S 1032 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R +-+ - 2\|a \|b\|x + a + b\|x + 2a +-+ \|b\|x + a +--R (4) 2\|a log(--------------------------------) + 4\|a atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ \|b\|x + a +---+ \|b\|x + a +--R (6) 4\|a atanh(------------) - 4\|- a atan(------------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1325 +t0:=sqrt(a+b*sqrt(x))/x^2 +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1325 +r0:=1/2*b^2*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(3/2)-sqrt(a+b*sqrt(x))/x-_ + 1/2*b*sqrt(a+b*sqrt(x))/(a*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R 2 +-+ \|b\|x + a +-+ +-+ +-+ | +-+ +--R b x\|x atanh(------------) + (- 2a\|a \|x - b x\|a )\|b\|x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R +-+ +-+ +--R 2a x\|a \|x +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 2 2a\|b\|x + a + b\|a \|x + 2a\|a +--R b x log(-----------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R +-+ +-+ +-+ | +-+ +--R (- 2b\|a \|x - 4a\|a )\|b\|x + a +--R / +--R +-+ +--R 4a x\|a +--R , +--R +---------+ +--R +---+ | +-+ +---------+ +--R 2 \|- a \|b\|x + a +---+ +-+ +---+ | +-+ +--R b x atan(------------------) + (- b\|- a \|x - 2a\|- a )\|b\|x + a +--R a +--R ---------------------------------------------------------------------] +--R +---+ +--R 2a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1038 + +--S 1039 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 2 2a\|b\|x + a + b\|a \|x + 2a\|a 2 \|b\|x + a +--R b log(-----------------------------------) - 2b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ------------------------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 2 +---+ \|b\|x + a 2 +-+ \|- a \|b\|x + a +--R - b \|- a atanh(------------) + b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1042 + +)clear all + +--S 1043 of 1325 +t0:=sqrt(a+b*sqrt(x))/x^3 +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1325 +r0:=5/32*b^4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(7/2)-_ + 1/2*sqrt(a+b*sqrt(x))/x^2-1/12*b*sqrt(a+b*sqrt(x))/(a*x^(3/2))+_ + 5/48*b^2*sqrt(a+b*sqrt(x))/(a^2*x)-5/32*b^3*_ + sqrt(a+b*sqrt(x))/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +---------+ +--R | +-+ +--R 4 2 +-+ \|b\|x + a +--R 15b x \|x atanh(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 2 3 +-+ +-+ 3 2 2 +-+ | +-+ +--R ((10a b x - 48a )\|a \|x + (- 15b x - 8a b x)\|a )\|b\|x + a +--R / +--R 3 2 +-+ +-+ +--R 96a x \|a \|x +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 4 2 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 15b x log(-----------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R 3 2 +-+ +-+ 2 3 +-+ | +-+ +--R ((- 30b x - 16a b)\|a \|x + (20a b x - 96a )\|a )\|b\|x + a +--R / +--R 3 2 +-+ +--R 192a x \|a +--R , +--R +--R +---------+ +--R +---+ | +-+ +--R 4 2 \|- a \|b\|x + a +--R 15b x atan(------------------) +--R a +--R + +--R +---------+ +--R 3 2 +---+ +-+ 2 3 +---+ | +-+ +--R ((- 15b x - 8a b)\|- a \|x + (10a b x - 48a )\|- a )\|b\|x + a +--R / +--R 3 2 +---+ +--R 96a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1045 + +--S 1046 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 4 2a\|b\|x + a + b\|a \|x + 2a\|a 4 \|b\|x + a +--R 5b log(-----------------------------------) - 10b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) --------------------------------------------------------------------- +--R 3 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 4 +---+ \|b\|x + a 4 +-+ \|- a \|b\|x + a +--R - 5b \|- a atanh(------------) + 5b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------------- +--R 3 +---+ +-+ +--R 32a \|- a \|a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1325 +t0:=x^2/sqrt(a+b*sqrt(x)) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1325 +r0:=512/693*a^4*(a+b*sqrt(x))^(3/2)/b^6-512/231*a^5*sqrt(a+b*sqrt(x))/_ + b^6-128/231*a^3*x*sqrt(a+b*sqrt(x))/b^4+320/693*a^2*x^(3/2)*_ + sqrt(a+b*sqrt(x))/b^3-40/99*a*x^2*sqrt(a+b*sqrt(x))/b^2+_ + 4/11*x^(5/2)*sqrt(a+b*sqrt(x))/b +--R +--R +--R (2) +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R ((252b x + 320a b x + 512a b)\|x - 280a b x - 384a b x - 1024a ) +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 693b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R ((252b x + 320a b x + 512a b)\|x - 280a b x - 384a b x - 1024a ) +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 693b +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1325 +t0:=x/sqrt(a+b*sqrt(x)) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1325 +r0:=32/35*a^2*(a+b*sqrt(x))^(3/2)/b^4-96/35*a^3*sqrt(a+b*sqrt(x))/b^4-_ + 24/35*a*x*sqrt(a+b*sqrt(x))/b^2+4/7*x^(3/2)*sqrt(a+b*sqrt(x))/b +--R +--R +--R +---------+ +--R 3 2 +-+ 2 3 | +-+ +--R ((20b x + 32a b)\|x - 24a b x - 64a )\|b\|x + a +--R (2) -------------------------------------------------- +--R 4 +--R 35b +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3 2 +-+ 2 3 | +-+ +--R ((20b x + 32a b)\|x - 24a b x - 64a )\|b\|x + a +--R (3) -------------------------------------------------- +--R 4 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1325 +t0:=1/sqrt(a+b*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1325 +r0:=4/3*(a+b*sqrt(x))^(3/2)/b^2-4*a*sqrt(a+b*sqrt(x))/b^2 +--R +--R +--R +---------+ +--R +-+ | +-+ +--R (4b\|x - 8a)\|b\|x + a +--R (2) ------------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +-+ | +-+ +--R (4b\|x - 8a)\|b\|x + a +--R (3) ------------------------- +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1325 +t0:=1/(x*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | +-+ +--R x\|b\|x + a +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1325 +r0:=-4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/sqrt(a) +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R 4atanh(------------) +--R +-+ +--R \|a +--R (2) - -------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +-+ +-+ +-+ +---------+ +--R - 2a\|b\|x + a + b\|a \|x + 2a\|a +---+ | +-+ +--R 2log(-------------------------------------) \|- a \|b\|x + a +--R +-+ 4atan(------------------) +--R \|x a +--R [-------------------------------------------,- -------------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1067 + +--S 1068 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R - 2a\|b\|x + a + b\|a \|x + 2a\|a \|b\|x + a +--R 2log(-------------------------------------) + 4atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R +---+ \|b\|x + a +-+ \|- a \|b\|x + a +--R 4\|- a atanh(------------) - 4\|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1325 +t0:=1/(x^2*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | +-+ +--R x \|b\|x + a +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1325 +r0:=-3/2*b^2*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(5/2)-_ + sqrt(a+b*sqrt(x))/(a*x)+3/2*b*sqrt(a+b*sqrt(x))/(a^2*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R 2 +-+ \|b\|x + a +-+ +-+ +-+ | +-+ +--R - 3b x\|x atanh(------------) + (- 2a\|a \|x + 3b x\|a )\|b\|x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 2a x\|a \|x +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 3b x log(-------------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R +-+ +-+ +-+ | +-+ +--R (6b\|a \|x - 4a\|a )\|b\|x + a +--R / +--R 2 +-+ +--R 4a x\|a +--R , +--R +---------+ +--R +---+ | +-+ +---------+ +--R 2 \|- a \|b\|x + a +---+ +-+ +---+ | +-+ +--R - 3b x atan(------------------) + (3b\|- a \|x - 2a\|- a )\|b\|x + a +--R a +--R -----------------------------------------------------------------------] +--R 2 +---+ +--R 2a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1074 + +--S 1075 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a 2 \|b\|x + a +--R 3b log(-------------------------------------) + 6b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 2 +---+ \|b\|x + a 2 +-+ \|- a \|b\|x + a +--R 3b \|- a atanh(------------) - 3b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1078 + +)clear all + +--S 1079 of 1325 +t0:=1/(x^3*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | +-+ +--R x \|b\|x + a +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1325 +r0:=-35/32*b^4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(9/2)-_ + 1/2*sqrt(a+b*sqrt(x))/(a*x^2)+7/12*b*sqrt(a+b*sqrt(x))/_ + (a^2*x^(3/2))-35/48*b^2*sqrt(a+b*sqrt(x))/(a^3*x)+35/32*b^3*_ + sqrt(a+b*sqrt(x))/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +---------+ +--R | +-+ +--R 4 2 +-+ \|b\|x + a +--R - 105b x \|x atanh(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 2 3 +-+ +-+ 3 2 2 +-+ | +-+ +--R ((- 70a b x - 48a )\|a \|x + (105b x + 56a b x)\|a )\|b\|x + a +--R / +--R 4 2 +-+ +-+ +--R 96a x \|a \|x +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 4 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 105b x log(-------------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R 3 2 +-+ +-+ 2 3 +-+ | +-+ +--R ((210b x + 112a b)\|a \|x + (- 140a b x - 96a )\|a )\|b\|x + a +--R / +--R 4 2 +-+ +--R 192a x \|a +--R , +--R +--R +---------+ +--R +---+ | +-+ +--R 4 2 \|- a \|b\|x + a +--R - 105b x atan(------------------) +--R a +--R + +--R +---------+ +--R 3 2 +---+ +-+ 2 3 +---+ | +-+ +--R ((105b x + 56a b)\|- a \|x + (- 70a b x - 48a )\|- a )\|b\|x + a +--R / +--R 4 2 +---+ +--R 96a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1081 + +--S 1082 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 4 - 2a\|b\|x + a + b\|a \|x + 2a\|a 4 \|b\|x + a +--R 35b log(-------------------------------------) + 70b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R ------------------------------------------------------------------------ +--R 4 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 4 +---+ \|b\|x + a 4 +-+ \|- a \|b\|x + a +--R 35b \|- a atanh(------------) - 35b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------------- +--R 4 +---+ +-+ +--R 32a \|- a \|a +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1325 +t0:=sqrt(x)*(a+b*sqrt(x))^n +--R +--R +--R +-+ +-+ n +--R (1) \|x (b\|x + a) +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1325 +r0:=2*a^2*(a+b*sqrt(x))^(1+n)/(b^3*(1+n))-4*a*(a+b*sqrt(x))^(2+n)/_ + (b^3*(2+n))+2*(a+b*sqrt(x))^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 +-+ n + 3 2 +-+ n + 2 +--R (2n + 6n + 4)(b\|x + a) + (- 4a n - 16a n - 12a)(b\|x + a) +--R + +--R 2 2 2 2 +-+ n + 1 +--R (2a n + 10a n + 12a )(b\|x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 +-+ 2 2 2 3 +--R (((2b n + 6b n + 4b )x - 4a b n)\|x + (2a b n + 2a b n)x + 4a ) +--R * +--R +-+ +--R n log(b\|x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 +-+ 2 2 2 3 +--R (((2b n + 6b n + 4b )x - 4a b n)\|x + (2a b n + 2a b n)x + 4a ) +--R * +--R +-+ +--R n log(b\|x + a) +--R %e +--R + +--R 2 +-+ n + 3 2 +-+ n + 2 +--R (- 2n - 6n - 4)(b\|x + a) + (4a n + 16a n + 12a)(b\|x + a) +--R + +--R 2 2 2 2 +-+ n + 1 +--R (- 2a n - 10a n - 12a )(b\|x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1325 +t0:=(a+b*sqrt(x))^n/sqrt(x) +--R +--R +--R +-+ n +--R (b\|x + a) +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1325 +r0:=2*(a+b*sqrt(x))^(1+n)/(b*(1+n)) +--R +--R +--R +-+ n + 1 +--R 2(b\|x + a) +--R (2) ----------------- +--R b n + b +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R +-+ n log(b\|x + a) +--R (2b\|x + 2a)%e +--R (3) ------------------------------- +--R b n + b +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R +-+ n log(b\|x + a) +-+ n + 1 +--R (2b\|x + 2a)%e - 2(b\|x + a) +--R (4) --------------------------------------------------- +--R b n + b +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1325 +t0:=(1+sqrt(x))/sqrt(x) +--R +--R +--R +-+ +--R \|x + 1 +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1325 +r0:=x+2*sqrt(x) +--R +--R +--R +-+ +--R (2) 2\|x + x +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (3) 2\|x + x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1325 +t0:=(1+sqrt(x))^2/sqrt(x) +--R +--R +--R +-+ +--R 2\|x + x + 1 +--R (1) ------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1325 +r0:=2/3*(1+sqrt(x))^3 +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x + 2 +--R (2) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x +--R (3) ----------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - - +--R 3 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1325 +t0:=(1+sqrt(x))^3/sqrt(x) +--R +--R +--R +-+ +--R (x + 3)\|x + 3x + 1 +--R (1) -------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1325 +r0:=1/2*(1+sqrt(x))^4 +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x + 1 +--R (2) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x +--R (3) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 1325 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - - +--R 2 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 1325 +t0:=sqrt(x)/(1+sqrt(x)) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1325 +r0:=x+2*log(1+sqrt(x))-2*sqrt(x) +--R +--R +--R +-+ +-+ +--R (2) 2log(\|x + 1) - 2\|x + x +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) 2log(\|x + 1) - 2\|x + x +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))) +--R +--R +--R 1 +--R (1) -------- +--R +-+ +--R \|x + x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1325 +r0:=2*log(1+sqrt(x)) +--R +--R +--R +-+ +--R (2) 2log(\|x + 1) +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (3) 2log(\|x + 1) +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))^2) +--R +--R +--R 1 +--R (1) ---------------- +--R +-+ +--R (x + 1)\|x + 2x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1325 +r0:=(-2)/(1+sqrt(x)) +--R +--R +--R 2 +--R (2) - -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - -------- +--R +-+ +--R \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))^3) +--R +--R +--R 1 +--R (1) ---------------------- +--R +-+ 2 +--R (3x + 1)\|x + x + 3x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1325 +r0:=(-1)/(1+sqrt(x))^2 +--R +--R +--R 1 +--R (2) - ------------- +--R +-+ +--R 2\|x + x + 1 +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +-+ +--R 2\|x + x + 1 +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1325 +t0:=sqrt(x)*sqrt(1+sqrt(x)) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (1) \|x \|\|x + 1 +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1325 +r0:=4/3*(1+sqrt(x))^(3/2)-8/5*(1+sqrt(x))^(5/2)+4/7*(1+sqrt(x))^(7/2) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R ((60x - 16)\|x + 12x + 32)\|\|x + 1 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R ((60x - 16)\|x + 12x + 32)\|\|x + 1 +--R (3) -------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1325 +t0:=sqrt(1+sqrt(x))/sqrt(x) +--R +--R +--R +--------+ +--R | +-+ +--R \|\|x + 1 +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1325 +r0:=4/3*(1+sqrt(x))^(3/2) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (4\|x + 4)\|\|x + 1 +--R (2) ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (4\|x + 4)\|\|x + 1 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1325 +t0:=x^(1/3)/(1+sqrt(x)) +--R +--R +--R 3+-+ +--R \|x +--R (1) -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1325 +r0:=-3*x^(1/3)+6/5*x^(5/6)-2*log(1+x^(1/6))+log(1-x^(1/6)+x^(1/3))-_ + 2*atan((1-2*x^(1/6))/sqrt(3))*sqrt(3) +--R +--R +--R (2) +--R 6+-+ +--R 6+-+ 6+-+ 3+-+ +-+ 2\|x - 1 +--R - 10log(\|x + 1) + 5log(- \|x + \|x + 1) + 10\|3 atan(---------) +--R +-+ +--R \|3 +--R + +--R 6+-+5 3+-+ +--R 6\|x - 15\|x +--R / +--R 5 +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6+-+ +--R 6+-+2 6+-+ 6+-+ +-+ 2\|x - 1 6+-+5 +--R 5log(\|x - \|x + 1) - 10log(\|x + 1) + 10\|3 atan(---------) + 6\|x +--R +-+ +--R \|3 +--R + +--R 6+-+2 +--R - 15\|x +--R / +--R 5 +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1325 +m0:=a0-r0 +--R +--R +--R 6+-+2 6+-+ 6+-+ 3+-+ 6+-+2 3+-+ +--R (4) log(\|x - \|x + 1) - log(- \|x + \|x + 1) - 3\|x + 3\|x +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1325 +t0:=x^4/(a+b*x^(3/2))^(2/3) +--R +--R +--R 4 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1325 +--r0:=-7/20*a*x^2*(a+b*x^(3/2))^(1/3)/b^2+1/4*x^(7/2)*(a+b*x^(3/2))^(1/3)/_ +-- b+7/10*a^2*(a+b*x^(3/2))^(1/3)*sqrt(x)/b^3-7/10*a^3*((a+b*_ +-- x^(3/2))/a)^(2/3)*hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*_ +-- sqrt(x)/(b^3*(a+b*x^(3/2))^(2/3)) +--E 1147 + +--S 1148 of 1325 +--a0:=integrate(t0,x) +--E 1148 + +--S 1149 of 1325 +--m0:=a0-r0 +--E 1149 + +--S 1150 of 1325 +--d0:=D(m0,x) +--E 1150 + +)clear all + +--S 1151 of 1325 +t0:=x^3/(a+b*x^(3/2))^(2/3) +--R +--R +--R 3 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1325 +r0:=-5/9*a*x*(a+b*x^(3/2))^(1/3)/b^2+1/3*x^(5/2)*(a+b*x^(3/2))^(1/3)/b-_ + 10/27*a^2*log(1-b^(1/3)*sqrt(x)/(a+b*x^(3/2))^(1/3))/b^(8/3)+_ + 5/27*a^2*log(1+b^(2/3)*x/(a+b*x^(3/2))^(2/3)+b^(1/3)*sqrt(x)/_ + (a+b*x^(3/2))^(1/3))/b^(8/3)-10/9*a^2*atan((1+2*b^(1/3)*sqrt(x)/_ + (a+b*x^(3/2))^(1/3))/sqrt(3))/(b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 3| +-+ 3+-+ +-+3| +-+ 3+-+2 +--R 2 +-+ \|b x\|x + a + \|b \|x \|b x\|x + a + x \|b +--R 5a \|3 log(--------------------------------------------------) +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +-+ +--R 2 +-+ \|b x\|x + a - \|b \|x +--R - 10a \|3 log(-------------------------) +--R +-----------+ +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +-+ +--R 2 \|b x\|x + a + 2\|b \|x +--R - 30a atan(--------------------------) +--R +-----------+ +--R +-+3| +-+ +--R \|3 \|b x\|x + a +--R + +--R +-----------+ +--R 2 +-+3+-+2 +-+ +-+3+-+2 3| +-+ +--R (9b x \|3 \|b \|x - 15a x\|3 \|b )\|b x\|x + a +--R / +--R 2 +-+3+-+2 +--R 27b \|3 \|b +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1325 +--a0:=integrate(t0,x) +--E 1153 + +--S 1154 of 1325 +--m0:=a0-r0 +--E 1154 + +--S 1155 of 1325 +--d0:=D(m0,x) +--E 1155 + +)clear all + +--S 1156 of 1325 +t0:=x^2/(a+b*x^(3/2))^(2/3) +--R +--R +--R 2 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1325 +r0:=-3/2*a*(a+b*x^(3/2))^(1/3)/b^2+1/2*x^(3/2)*(a+b*x^(3/2))^(1/3)/b +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (b x\|x - 3a)\|b x\|x + a +--R (2) ---------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (b x\|x - 3a)\|b x\|x + a +--R (3) ---------------------------- +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1325 +t0:=x/(a+b*x^(3/2))^(2/3) +--R +--R +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1325 +--r0:=(a+b*x^(3/2))^(1/3)*sqrt(x)/b-a*((a+b*x^(3/2))/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*sqrt(x)/(b*(a+b*x^(3/2))^(2/3)) +--E 1162 + +--S 1163 of 1325 +--a0:=integrate(t0,x) +--E 1163 + +--S 1164 of 1325 +--m0:=a0-r0 +--E 1164 + +--S 1165 of 1325 +--d0:=D(m0,x) +--E 1165 + +)clear all + +--S 1166 of 1325 +t0:=1/(a+b*x^(3/2))^(2/3) +--R +--R +--R 1 +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1325 +r0:=-2/3*log(1-b^(1/3)*sqrt(x)/(a+b*x^(3/2))^(1/3))/b^(2/3)+1/3*_ + log(1+b^(2/3)*x/(a+b*x^(3/2))^(2/3)+b^(1/3)*sqrt(x)/(a+_ + b*x^(3/2))^(1/3))/b^(2/3)-2*atan((1+2*b^(1/3)*sqrt(x)/(a+_ + b*x^(3/2))^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 3| +-+ 3+-+ +-+3| +-+ 3+-+2 +--R +-+ \|b x\|x + a + \|b \|x \|b x\|x + a + x \|b +--R \|3 log(--------------------------------------------------) +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +-----------+ +--R 3| +-+ 3+-+ +-+ 3| +-+ 3+-+ +-+ +--R +-+ \|b x\|x + a - \|b \|x \|b x\|x + a + 2\|b \|x +--R - 2\|3 log(-------------------------) - 6atan(--------------------------) +--R +-----------+ +-----------+ +--R 3| +-+ +-+3| +-+ +--R \|b x\|x + a \|3 \|b x\|x + a +--R / +--R +-+3+-+2 +--R 3\|3 \|b +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1325 +--a0:=integrate(t0,x) +--E 1168 + +--S 1169 of 1325 +--m0:=a0-r0 +--E 1169 + +--S 1170 of 1325 +--d0:=D(m0,x) +--E 1170 + +)clear all + +--S 1171 of 1325 +t0:=1/(x*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1325 +r0:=2/3*log(a^(1/3)-(a+b*x^(3/2))^(1/3))/a^(2/3)-1/3*log(a^(2/3)+_ + a^(1/3)*(a+b*x^(3/2))^(1/3)+(a+b*x^(3/2))^(2/3))/a^(2/3)-_ + 2*atan((a^(1/3)+2*(a+b*x^(3/2))^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R +-+ 3| +-+ 3+-+3| +-+ 3+-+2 +--R - \|3 log(\|b x\|x + a + \|a \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R +-----------+ 3| +-+ 3+-+ +--R +-+ 3| +-+ 3+-+ 2\|b x\|x + a + \|a +--R 2\|3 log(- \|b x\|x + a + \|a ) - 6atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 3\|3 \|a +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1325 +--a0:=integrate(t0,x) +--E 1173 + +--S 1174 of 1325 +--m0:=a0-r0 +--E 1174 + +--S 1175 of 1325 +--d0:=D(m0,x) +--E 1175 + +)clear all + +--S 1176 of 1325 +t0:=1/(x^2*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 2 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1325 +--r0:=-(a+b*x^(3/2))^(1/3)/(a*x)-b*((a+b*x^(3/2))/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*sqrt(x)/(a*(a+b*x^(3/2))^(2/3)) +--E 1177 + +--S 1178 of 1325 +--a0:=integrate(t0,x) +--E 1178 + +--S 1179 of 1325 +--m0:=a0-r0 +--E 1179 + +--S 1180 of 1325 +--d0:=D(m0,x) +--E 1180 + +)clear all + +--S 1181 of 1325 +t0:=1/(x^3*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 3 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1325 +r0:=-1/2*(a+b*x^(3/2))^(1/3)/(a*x^2)+3/2*b*(a+b*x^(3/2))^(1/3)/(a^2*sqrt(x)) +--R +--R +--R +-----------+ +--R +-+ 2 3| +-+ +--R (- a\|x + 3b x )\|b x\|x + a +--R (2) ------------------------------- +--R 2 2 +-+ +--R 2a x \|x +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (3b x\|x - a)\|b x\|x + a +--R (3) ---------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1325 +t0:=1/(x^4*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 4 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1325 +r0:=-1/3*(a+b*x^(3/2))^(1/3)/(a*x^3)+5/9*b*(a+b*x^(3/2))^(1/3)/_ + (a^2*x^(3/2))+10/27*b^2*log(a^(1/3)-(a+b*x^(3/2))^(1/3))/a^(8/3)-_ + 5/27*b^2*log(a^(2/3)+a^(1/3)*(a+b*x^(3/2))^(1/3)+(a+b*_ + x^(3/2))^(2/3))/a^(8/3)-10/9*b^2*atan((a^(1/3)+2*(a+b*_ + x^(3/2))^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 2 3 +-+ +-+ 3| +-+ 3+-+3| +-+ 3+-+2 +--R - 5b x \|3 \|x log(\|b x\|x + a + \|a \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R 2 3 +-+ +-+ 3| +-+ 3+-+ +--R 10b x \|3 \|x log(- \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +--R 2 3 +-+ 2\|b x\|x + a + \|a +--R - 30b x \|x atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-----------+ +--R +-+3+-+2 +-+ 2 +-+3+-+2 3| +-+ +--R (- 9a\|3 \|a \|x + 15b x \|3 \|a )\|b x\|x + a +--R / +--R 2 3 +-+3+-+2 +-+ +--R 27a x \|3 \|a \|x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1325 +--a0:=integrate(t0,x) +--E 1188 + +--S 1189 of 1325 +--m0:=a0-r0 +--E 1189 + +--S 1190 of 1325 +--d0:=D(m0,x) +--E 1190 + +)clear all + +--S 1191 of 1325 +t0:=sqrt(x)/(1+x^(3/2)) +--R +--R +--R +-+ +--R \|x +--R (1) --------- +--R +-+ +--R x\|x + 1 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1325 +r0:=2/3*log(1+x^(3/2)) +--R +--R +--R +-+ +--R 2log(x\|x + 1) +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2log(x\|x + 1) +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1325 +t0:=(a+b*x^(1/3))*x^4 +--R +--R +--R 4 3+-+ 4 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1325 +r0:=1/5*a*x^5+3/16*b*x^(16/3) +--R +--R +--R 5 3+-+ 5 +--R 15b x \|x + 16a x +--R (2) ------------------- +--R 80 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 3+-+ 5 +--R 15b x \|x + 16a x +--R (3) ------------------- +--R 80 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1325 +t0:=(a+b*x^(1/3))*x^3 +--R +--R +--R 3 3+-+ 3 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1325 +r0:=1/4*a*x^4+3/13*b*x^(13/3) +--R +--R +--R 4 3+-+ 4 +--R 12b x \|x + 13a x +--R (2) ------------------- +--R 52 +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+ 4 +--R 12b x \|x + 13a x +--R (3) ------------------- +--R 52 +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1325 +t0:=(a+b*x^(1/3))*x^2 +--R +--R +--R 2 3+-+ 2 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1325 +r0:=1/3*a*x^3+3/10*b*x^(10/3) +--R +--R +--R 3 3+-+ 3 +--R 9b x \|x + 10a x +--R (2) ------------------ +--R 30 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3 +--R 9b x \|x + 10a x +--R (3) ------------------ +--R 30 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1325 +t0:=(a+b*x^(1/3))*x +--R +--R +--R 3+-+ +--R (1) b x\|x + a x +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1325 +r0:=1/2*a*x^2+3/7*b*x^(7/3) +--R +--R +--R 2 3+-+ 2 +--R 6b x \|x + 7a x +--R (2) ----------------- +--R 14 +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 +--R 6b x \|x + 7a x +--R (3) ----------------- +--R 14 +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 1325 +t0:=a+b*x^(1/3) +--R +--R +--R 3+-+ +--R (1) b\|x + a +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1325 +r0:=a*x+3/4*b*x^(4/3) +--R +--R +--R 3+-+ +--R 3b x\|x + 4a x +--R (2) --------------- +--R 4 +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R 3b x\|x + 4a x +--R (3) --------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1325 +t0:=(a+b*x^(1/3))/x +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1325 +r0:=3*b*x^(1/3)+a*log(x) +--R +--R +--R 3+-+ +--R (2) 3b\|x + a log(x) +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3) 3a log(\|x ) + 3b\|x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1325 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1325 +t0:=(a+b*x^(1/3))/x^2 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1325 +r0:=-a/x-3/2*b/x^(2/3) +--R +--R +--R 3+-+2 +--R - 2a \|x - 3b x +--R (2) ----------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 3b\|x - 2a +--R (3) ------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1325 +t0:=(a+b*x^(1/3))/x^3 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1325 +r0:=-1/2*a/x^2-3/5*b/x^(5/3) +--R +--R +--R 3+-+2 +--R - 5a \|x - 6b x +--R (2) ----------------- +--R 2 3+-+2 +--R 10x \|x +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 6b\|x - 5a +--R (3) ------------- +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1325 +t0:=(a+b*x^(1/3))/x^4 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1325 +r0:=-1/3*a/x^3-3/8*b/x^(8/3) +--R +--R +--R 3+-+2 +--R - 8a \|x - 9b x +--R (2) ----------------- +--R 3 3+-+2 +--R 24x \|x +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 9b\|x - 8a +--R (3) ------------- +--R 3 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1325 +t0:=(a+b*x^(1/3))^2*x^4 +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1325 +r0:=1/5*a^2*x^5+3/8*a*b*x^(16/3)+3/17*b^2*x^(17/3) +--R +--R +--R 2 5 3+-+2 5 3+-+ 2 5 +--R 120b x \|x + 255a b x \|x + 136a x +--R (2) -------------------------------------- +--R 680 +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3+-+2 5 3+-+ 2 5 +--R 120b x \|x + 255a b x \|x + 136a x +--R (3) -------------------------------------- +--R 680 +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1325 +t0:=(a+b*x^(1/3))^2*x^3 +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1325 +r0:=1/4*a^2*x^4+6/13*a*b*x^(13/3)+3/14*b^2*x^(14/3) +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R 78b x \|x + 168a b x \|x + 91a x +--R (2) ------------------------------------ +--R 364 +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R 78b x \|x + 168a b x \|x + 91a x +--R (3) ------------------------------------ +--R 364 +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1325 +t0:=(a+b*x^(1/3))^2*x^2 +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1325 +r0:=1/3*a^2*x^3+3/5*a*b*x^(10/3)+3/11*b^2*x^(11/3) +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R 45b x \|x + 99a b x \|x + 55a x +--R (2) ----------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R 45b x \|x + 99a b x \|x + 55a x +--R (3) ----------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 1253 + +--S 1254 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +)clear all + +--S 1256 of 1325 +t0:=(a+b*x^(1/3))^2*x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R (1) b x \|x + 2a b x\|x + a x +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1325 +r0:=1/2*a^2*x^2+6/7*a*b*x^(7/3)+3/8*b^2*x^(8/3) +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R 21b x \|x + 48a b x \|x + 28a x +--R (2) ----------------------------------- +--R 56 +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R 21b x \|x + 48a b x \|x + 28a x +--R (3) ----------------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 1258 + +--S 1259 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1260 + +)clear all + +--S 1261 of 1325 +t0:=(a+b*x^(1/3))^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R (1) b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1325 +r0:=a^2*x+3/2*a*b*x^(4/3)+3/5*b^2*x^(5/3) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 6b x \|x + 15a b x\|x + 10a x +--R (2) -------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 6b x \|x + 15a b x\|x + 10a x +--R (3) -------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 1263 + +--S 1264 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 1325 +t0:=(a+b*x^(1/3))^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1325 +r0:=6*a*b*x^(1/3)+3/2*b^2*x^(2/3)+a^2*log(x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 3b \|x + 12a b\|x + 2a log(x) +--R (2) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(\|x ) + 3b \|x + 12a b\|x +--R (3) ----------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1268 + +--S 1269 of 1325 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 1325 +t0:=(a+b*x^(1/3))^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1325 +r0:=-(a+b*x^(1/3))^3/(a*x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 3a b \|x - 3a b\|x - b x - a +--R (2) ---------------------------------- +--R a x +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 3b \|x - 3a b\|x - a +--R (3) -------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 1325 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 1325 +t0:=(a+b*x^(1/3))^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1325 +r0:=-1/2*a^2/x^2-6/5*a*b/x^(5/3)-3/4*b^2/x^(4/3) +--R +--R +--R 2 3+-+2 2 3+-+ +--R - 10a \|x - 15b x\|x - 24a b x +--R (2) --------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 15b \|x - 24a b\|x - 10a +--R (3) ------------------------------ +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1278 + +--S 1279 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +)clear all + +--S 1281 of 1325 +t0:=(a+b*x^(1/3))^2/x^4 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1325 +r0:=-1/3*a^2/x^3-3/4*a*b/x^(8/3)-3/7*b^2/x^(7/3) +--R +--R +--R 2 3+-+2 2 3+-+ +--R - 28a \|x - 36b x\|x - 63a b x +--R (2) --------------------------------- +--R 3 3+-+2 +--R 84x \|x +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 36b \|x - 63a b\|x - 28a +--R (3) ------------------------------ +--R 3 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 1283 + +--S 1284 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 1325 +t0:=(a+b*x^(1/3))^3*x^4 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1325 +r0:=1/5*a^3*x^5+9/16*a^2*b*x^(16/3)+9/17*a*b^2*x^(17/3)+1/6*b^3*x^6 +--R +--R +--R 2 5 3+-+2 2 5 3+-+ 3 6 3 5 +--R 2160a b x \|x + 2295a b x \|x + 680b x + 816a x +--R (2) ---------------------------------------------------- +--R 4080 +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3+-+2 2 5 3+-+ 3 6 3 5 +--R 2160a b x \|x + 2295a b x \|x + 680b x + 816a x +--R (3) ---------------------------------------------------- +--R 4080 +--R Type: Union(Expression(Integer),...) +--E 1288 + +--S 1289 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 1325 +t0:=(a+b*x^(1/3))^3*x^3 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1325 +r0:=1/4*a^3*x^4+9/13*a^2*b*x^(13/3)+9/14*a*b^2*x^(14/3)+1/5*b^3*x^5 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364b x + 455a x +--R (2) ---------------------------------------------------- +--R 1820 +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364b x + 455a x +--R (3) ---------------------------------------------------- +--R 1820 +--R Type: Union(Expression(Integer),...) +--E 1293 + +--S 1294 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 1325 +t0:=(a+b*x^(1/3))^3*x^2 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1325 +r0:=1/3*a^3*x^3+9/10*a^2*b*x^(10/3)+9/11*a*b^2*x^(11/3)+1/4*b^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165b x + 220a x +--R (2) -------------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165b x + 220a x +--R (3) -------------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 1298 + +--S 1299 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1300 + +)clear all + +--S 1301 of 1325 +t0:=(a+b*x^(1/3))^3*x +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R (1) 3a b x \|x + 3a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1325 +r0:=1/2*a^3*x^2+9/7*a^2*b*x^(7/3)+9/8*a*b^2*x^(8/3)+1/3*b^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56b x + 84a x +--R (2) ------------------------------------------------ +--R 168 +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56b x + 84a x +--R (3) ------------------------------------------------ +--R 168 +--R Type: Union(Expression(Integer),...) +--E 1303 + +--S 1304 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1305 + +)clear all + +--S 1306 of 1325 +t0:=(a+b*x^(1/3))^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R (1) 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1325 +r0:=a^3*x+9/4*a^2*b*x^(4/3)+9/5*a*b^2*x^(5/3)+1/2*b^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10b x + 20a x +--R (2) -------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10b x + 20a x +--R (3) -------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 1308 + +--S 1309 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1310 + +)clear all + +--S 1311 of 1325 +t0:=(a+b*x^(1/3))^3/x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1325 +r0:=9*a^2*b*x^(1/3)+9/2*a*b^2*x^(2/3)+b^3*x+a^3*log(x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 9a b \|x + 18a b\|x + 2a log(x) + 2b x +--R (2) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6a log(\|x ) + 9a b \|x + 18a b\|x + 2b x +--R (3) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1313 + +--S 1314 of 1325 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 1325 +t0:=(a+b*x^(1/3))^3/x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1325 +r0:=-a^3/x-9/2*a^2*b/x^(2/3)-9*a*b^2/x^(1/3)+b^3*log(x) +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (2b x log(x) - 2a )\|x - 18a b x\|x - 9a b x +--R (2) ----------------------------------------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b x log(\|x ) - 18a b \|x - 9a b\|x - 2a +--R (3) --------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1318 + +--S 1319 of 1325 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1325 +t0:=(a+b*x^(1/3))^3/x^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1325 +r0:=-1/2*a^3/x^2-9/5*a^2*b/x^(5/3)-9/4*a*b^2/x^(4/3)-b^3/x +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 20b x - 10a )\|x - 45a b x\|x - 36a b x +--R (2) --------------------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 45a b \|x - 36a b\|x - 20b x - 10a +--R (3) ---------------------------------------- +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1323 + +--S 1324 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4h.input.pdf b/src/axiom-website/CATS/rich4h.input.pdf new file mode 100644 index 0000000..e3f3b98 Binary files /dev/null and b/src/axiom-website/CATS/rich4h.input.pdf differ diff --git a/src/axiom-website/CATS/rich4i.input.pamphlet b/src/axiom-website/CATS/rich4i.input.pamphlet new file mode 100644 index 0000000..1160c52 --- /dev/null +++ b/src/axiom-website/CATS/rich4i.input.pamphlet @@ -0,0 +1,16239 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4i.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 259 supplied "optimal results". +\item 197 matching answers. +\item 6 cases where Axiom supplied 2 results. +\item 8 cases that Axiom failed to integrate. +\item 55 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +f)set break resume +)sys rm -f rich4i.output +)spool rich4i.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1299 +t0:=(a+b*x^(1/3))^3/x^4 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1299 +r0:=-1/3*a^3/x^3-9/8*a^2*b/x^(8/3)-9/7*a*b^2/x^(7/3)-1/2*b^3/x^2 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 84b x - 56a )\|x - 216a b x\|x - 189a b x +--R (2) ----------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 216a b \|x - 189a b\|x - 84b x - 56a +--R (3) ------------------------------------------ +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1299 +t0:=(a+b*x^(1/3))^5*x^4 +--R +--R +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ 2 3 5 5 4 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1299 +r0:=1/5*a^5*x^5+15/16*a^4*b*x^(16/3)+30/17*a^3*b^2*x^(17/3)+_ + 5/3*a^2*b^3*x^6+15/19*a*b^4*x^(19/3)+3/20*b^5*x^(20/3) +--R +--R +--R (2) +--R 5 6 3 2 5 3+-+2 4 6 4 5 3+-+ +--R (11628b x + 136800a b x )\|x + (61200a b x + 72675a b x )\|x +--R + +--R 2 3 6 5 5 +--R 129200a b x + 15504a x +--R / +--R 77520 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 3 2 5 3+-+2 4 6 4 5 3+-+ +--R (11628b x + 136800a b x )\|x + (61200a b x + 72675a b x )\|x +--R + +--R 2 3 6 5 5 +--R 129200a b x + 15504a x +--R / +--R 77520 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1299 +t0:=(a+b*x^(1/3))^5*x^3 +--R +--R +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ 2 3 4 5 3 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1299 +r0:=1/4*a^5*x^4+15/13*a^4*b*x^(13/3)+15/7*a^3*b^2*x^(14/3)+2*a^2*b^3*x^5+_ + 15/16*a*b^4*x^(16/3)+3/17*b^5*x^(17/3) +--R +--R +--R (2) +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ +--R (4368b x + 53040a b x )\|x + (23205a b x + 28560a b x )\|x +--R + +--R 2 3 5 5 4 +--R 49504a b x + 6188a x +--R / +--R 24752 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ +--R (4368b x + 53040a b x )\|x + (23205a b x + 28560a b x )\|x +--R + +--R 2 3 5 5 4 +--R 49504a b x + 6188a x +--R / +--R 24752 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1299 +t0:=(a+b*x^(1/3))^5*x^2 +--R +--R +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 5 2 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1299 +r0:=1/3*a^5*x^3+3/2*a^4*b*x^(10/3)+30/11*a^3*b^2*x^(11/3)+_ + 5/2*a^2*b^3*x^4+15/13*a*b^4*x^(13/3)+3/14*b^5*x^(14/3) +--R +--R +--R (2) +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ +--R (1287b x + 16380a b x )\|x + (6930a b x + 9009a b x )\|x +--R + +--R 2 3 4 5 3 +--R 15015a b x + 2002a x +--R / +--R 6006 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ +--R (1287b x + 16380a b x )\|x + (6930a b x + 9009a b x )\|x +--R + +--R 2 3 4 5 3 +--R 15015a b x + 2002a x +--R / +--R 6006 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1299 +t0:=(a+b*x^(1/3))^5*x +--R +--R +--R 5 2 3 2 3+-+2 4 2 4 3+-+ 2 3 2 5 +--R (1) (b x + 10a b x)\|x + (5a b x + 5a b x)\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1299 +r0:=1/2*a^5*x^2+15/7*a^4*b*x^(7/3)+15/4*a^3*b^2*x^(8/3)+10/3*a^2*b^3*_ + x^3+3/2*a*b^4*x^(10/3)+3/11*b^5*x^(11/3) +--R +--R +--R (2) +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 +--R (252b x + 3465a b x )\|x + (1386a b x + 1980a b x )\|x + 3080a b x +--R + +--R 5 2 +--R 462a x +--R / +--R 924 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 +--R (252b x + 3465a b x )\|x + (1386a b x + 1980a b x )\|x + 3080a b x +--R + +--R 5 2 +--R 462a x +--R / +--R 924 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1299 +t0:=(a+b*x^(1/3))^5 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (1) (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1299 +r0:=1/2*a^2*(a+b*x^(1/3))^6/b^3-6/7*a*(a+b*x^(1/3))^7/b^3+_ + 3/8*(a+b*x^(1/3))^8/b^3 +--R +--R +--R (2) +--R 8 2 3 5 3+-+2 7 2 4 4 3+-+ 2 6 2 +--R (21b x + 336a b x)\|x + (120a b x + 210a b x)\|x + 280a b x +--R + +--R 5 3 8 +--R 56a b x + a +--R / +--R 3 +--R 56b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 3 2 3+-+2 4 2 4 3+-+ 2 3 2 5 +--R (21b x + 336a b x)\|x + (120a b x + 210a b x)\|x + 280a b x + 56a x +--R ------------------------------------------------------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1299 +m0:=a0-r0 +--R +--R +--R 8 +--R a +--R (4) - ---- +--R 3 +--R 56b +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1299 +t0:=(a+b*x^(1/3))^5/x +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1299 +r0:=15*a^4*b*x^(1/3)+15*a^3*b^2*x^(2/3)+10*a^2*b^3*x+15/4*a*_ + b^4*x^(4/3)+3/5*b^5*x^(5/3)+a^5*log(x) +--R +--R +--R (2) +--R 5 3 2 3+-+2 4 4 3+-+ 5 2 3 +--R (12b x + 300a b )\|x + (75a b x + 300a b)\|x + 20a log(x) + 200a b x +--R ----------------------------------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R 60a log(\|x ) + (12b x + 300a b )\|x + (75a b x + 300a b)\|x + 200a b x +--R -------------------------------------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1299 +m0:=a0-r0 +--R +--R +--R 5 3+-+ 5 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1299 +t0:=(a+b*x^(1/3))^5/x^2 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1299 +r0:=-a^5/x-15/2*a^4*b/x^(2/3)-30*a^3*b^2/x^(1/3)+15*a*b^4*x^(1/3)+_ + 3/2*b^5*x^(2/3)+10*a^2*b^3*log(x) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 4 +--R (20a b x log(x) - 2a )\|x + (3b x - 60a b x)\|x + 30a b x - 15a b x +--R ------------------------------------------------------------------------ +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+ 5 3 2 3+-+2 4 4 3+-+ 5 +--R 60a b x log(\|x ) + (3b x - 60a b )\|x + (30a b x - 15a b)\|x - 2a +--R (3) ---------------------------------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3 3+-+ 2 3 +--R (4) 30a b log(\|x ) - 10a b log(x) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1299 +t0:=(a+b*x^(1/3))^5/x^3 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1299 +r0:=-1/2*(a+b*x^(1/3))^6/(a*x^2) +--R +--R +--R (2) +--R 5 4 2 3+-+2 2 4 5 3+-+ 6 2 3 3 6 +--R (- 6a b x - 15a b )\|x + (- 15a b x - 6a b)\|x - b x - 20a b x - a +--R ----------------------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 6b x - 15a b )\|x + (- 15a b x - 6a b)\|x - 20a b x - a +--R (3) -------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1299 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) -- +--R 2a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1299 +t0:=(a+b*x^(1/3))^5/x^4 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1299 +r0:=-1/3*a^5/x^3-15/8*a^4*b/x^(8/3)-30/7*a^3*b^2/x^(7/3)-5*a^2*b^3/x^2-_ + 3*a*b^4/x^(5/3)-3/4*b^5/x^(4/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 4 +--R (- 840a b x - 56a )\|x + (- 126b x - 720a b x)\|x - 504a b x - 315a b x +--R ---------------------------------------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 126b x - 720a b )\|x + (- 504a b x - 315a b)\|x - 840a b x - 56a +--R ----------------------------------------------------------------------- +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1299 +t0:=(a+b*x^(1/3))^5/x^5 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1299 +r0:=-1/4*a^5/x^4-15/11*a^4*b/x^(11/3)-3*a^3*b^2/x^(10/3)-_ + 10/3*a^2*b^3/x^3-15/8*a*b^4/x^(8/3)-3/7*b^5/x^(7/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 +--R (- 6160a b x - 462a )\|x + (- 792b x - 5544a b x)\|x - 3465a b x +--R + +--R 4 +--R - 2520a b x +--R / +--R 4 3+-+2 +--R 1848x \|x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 792b x - 5544a b )\|x + (- 3465a b x - 2520a b)\|x - 6160a b x - 462a +--R ---------------------------------------------------------------------------- +--R 4 +--R 1848x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1299 +t0:=(a+b*x^(1/3))^5/x^6 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1299 +r0:=-1/5*a^5/x^5-15/14*a^4*b/x^(14/3)-30/13*a^3*b^2/x^(13/3)-_ + 5/2*a^2*b^3/x^4-15/11*a*b^4/x^(11/3)-3/10*b^5/x^(10/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ +--R (- 25025a b x - 2002a )\|x + (- 3003b x - 23100a b x)\|x +--R + +--R 4 2 4 +--R - 13650a b x - 10725a b x +--R / +--R 5 3+-+2 +--R 10010x \|x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R (- 3003b x - 23100a b )\|x + (- 13650a b x - 10725a b)\|x - 25025a b x +--R + +--R 5 +--R - 2002a +--R / +--R 5 +--R 10010x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1299 +t0:=(a+b*x^(1/3))^5/x^7 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1299 +r0:=-1/6*a^5/x^6-15/17*a^4*b/x^(17/3)-15/8*a^3*b^2/x^(16/3)-_ + 2*a^2*b^3/x^5-15/14*a*b^4/x^(14/3)-3/13*b^5/x^(13/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ +--R (- 74256a b x - 6188a )\|x + (- 8568b x - 69615a b x)\|x +--R + +--R 4 2 4 +--R - 39780a b x - 32760a b x +--R / +--R 6 3+-+2 +--R 37128x \|x +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R (- 8568b x - 69615a b )\|x + (- 39780a b x - 32760a b)\|x - 74256a b x +--R + +--R 5 +--R - 6188a +--R / +--R 6 +--R 37128x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1299 +t0:=(a+b*x^(1/3))^10*x^4 +--R +--R +--R (1) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ 9 7 4 6 6 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 5 10 4 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1299 +r0:=1/5*a^10*x^5+15/8*a^9*b*x^(16/3)+135/17*a^8*b^2*x^(17/3)+_ + 20*a^7*b^3*x^6+630/19*a^6*b^4*x^(19/3)+189/5*a^5*b^5*x^(20/3)+_ + 30*a^4*b^6*x^7+180/11*a^3*b^7*x^(22/3)+135/23*a^2*b^8*x^(23/3)+_ + 5/4*a*b^9*x^8+3/25*b^10*x^(25/3) +--R +--R +--R (2) +--R 2 8 7 5 5 6 8 2 5 3+-+2 +--R (95931000a b x + 617795640a b x + 129789000a b x )\|x +--R + +--R 10 8 3 7 7 6 4 6 9 5 3+-+ +--R (1961256b x + 267444000a b x + 541926000a b x + 30644625a b x )\|x +--R + +--R 9 8 4 6 7 7 3 6 10 5 +--R 20429750a b x + 490314000a b x + 326876000a b x + 3268760a x +--R / +--R 16343800 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 5 5 6 8 2 5 3+-+2 +--R (95931000a b x + 617795640a b x + 129789000a b x )\|x +--R + +--R 10 8 3 7 7 6 4 6 9 5 3+-+ +--R (1961256b x + 267444000a b x + 541926000a b x + 30644625a b x )\|x +--R + +--R 9 8 4 6 7 7 3 6 10 5 +--R 20429750a b x + 490314000a b x + 326876000a b x + 3268760a x +--R / +--R 16343800 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1299 +t0:=(a+b*x^(1/3))^10*x^3 +--R +--R +--R (1) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ 9 6 4 6 5 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 4 10 3 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1299 +r0:=1/4*a^10*x^4+30/13*a^9*b*x^(13/3)+135/14*a^8*b^2*x^(14/3)+_ + 24*a^7*b^3*x^5+315/8*a^6*b^4*x^(16/3)+756/17*a^5*b^5*x^(17/3)+_ + 35*a^4*b^6*x^6+360/19*a^3*b^7*x^(19/3)+27/4*a^2*b^8*x^(20/3)+_ + 10/7*a*b^9*x^7+3/22*b^10*x^(22/3) +--R +--R +--R (2) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (17459442a b x + 115026912a b x + 24942060a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ +--R (352716b x + 49008960a b x + 101846745a b x + 5969040a b x )\|x +--R + +--R 9 7 4 6 6 7 3 5 10 4 +--R 3695120a b x + 90530440a b x + 62078016a b x + 646646a x +--R / +--R 2586584 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (17459442a b x + 115026912a b x + 24942060a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ +--R (352716b x + 49008960a b x + 101846745a b x + 5969040a b x )\|x +--R + +--R 9 7 4 6 6 7 3 5 10 4 +--R 3695120a b x + 90530440a b x + 62078016a b x + 646646a x +--R / +--R 2586584 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1299 +t0:=(a+b*x^(1/3))^10*x^2 +--R +--R +--R (1) +--R 2 8 4 5 5 3 8 2 2 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 5 3 7 4 6 4 3 9 2 3+-+ 9 5 4 6 4 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 3 10 2 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1299 +r0:=1/3*a^10*x^3+3*a^9*b*x^(10/3)+135/11*a^8*b^2*x^(11/3)+_ + 30*a^7*b^3*x^4+630/13*a^6*b^4*x^(13/3)+54*a^5*b^5*x^(14/3)+_ + 42*a^4*b^6*x^5+45/2*a^3*b^7*x^(16/3)+135/17*a^2*b^8*x^(17/3)+_ + 5/3*a*b^9*x^6+3/19*b^10*x^(19/3) +--R +--R +--R (2) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (2200770a b x + 14965236a b x + 3401190a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ +--R (43758b x + 6235515a b x + 13430340a b x + 831402a b x )\|x +--R + +--R 9 6 4 6 5 7 3 4 10 3 +--R 461890a b x + 11639628a b x + 8314020a b x + 92378a x +--R / +--R 277134 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (2200770a b x + 14965236a b x + 3401190a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ +--R (43758b x + 6235515a b x + 13430340a b x + 831402a b x )\|x +--R + +--R 9 6 4 6 5 7 3 4 10 3 +--R 461890a b x + 11639628a b x + 8314020a b x + 92378a x +--R / +--R 277134 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1299 +t0:=(a+b*x^(1/3))^10*x +--R +--R +--R (1) +--R 2 8 3 5 5 2 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 3+-+ 9 4 4 6 3 +--R (b x + 120a b x + 210a b x + 10a b x)\|x + 10a b x + 210a b x +--R + +--R 7 3 2 10 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1299 +r0:=-3/11*a^5*(a+b*x^(1/3))^11/b^6+5/4*a^4*(a+b*x^(1/3))^12/b^6-_ + 30/13*a^3*(a+b*x^(1/3))^13/b^6+15/7*a^2*(a+b*x^(1/3))^14/b^6-_ + a*(a+b*x^(1/3))^15/b^6+3/16*(a+b*x^(1/3))^16/b^6 +--R +--R +--R (2) +--R 2 14 4 5 11 3 8 8 2 3+-+2 +--R (154440a b x + 1100736a b x + 270270a b x )\|x +--R + +--R 16 5 3 13 4 6 10 3 9 7 2 3+-+ +--R (3003b x + 443520a b x + 1009008a b x + 68640a b x )\|x +--R + +--R 15 5 4 12 4 7 9 3 10 6 2 16 +--R 32032a b x + 840840a b x + 640640a b x + 8008a b x - a +--R / +--R 6 +--R 16016b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 4 5 5 3 8 2 2 3+-+2 +--R (154440a b x + 1100736a b x + 270270a b x )\|x +--R + +--R 10 5 3 7 4 6 4 3 9 2 3+-+ +--R (3003b x + 443520a b x + 1009008a b x + 68640a b x )\|x +--R + +--R 9 5 4 6 4 7 3 3 10 2 +--R 32032a b x + 840840a b x + 640640a b x + 8008a x +--R / +--R 16016 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1299 +m0:=a0-r0 +--R +--R +--R 16 +--R a +--R (4) ------- +--R 6 +--R 16016b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1299 +t0:=(a+b*x^(1/3))^10 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1299 +r0:=3/11*a^2*(a+b*x^(1/3))^11/b^3-1/2*a*(a+b*x^(1/3))^12/b^3+_ + 3/13*(a+b*x^(1/3))^13/b^3 +--R +--R +--R (2) +--R 2 11 3 5 8 2 8 5 3+-+2 +--R (3510a b x + 27027a b x + 7722a b x)\|x +--R + +--R 13 4 3 10 3 6 7 2 9 4 3+-+ 12 4 +--R (66b x + 10296a b x + 25740a b x + 2145a b x)\|x + 715a b x +--R + +--R 4 9 3 7 6 2 10 3 13 +--R 20020a b x + 17160a b x + 286a b x + a +--R / +--R 3 +--R 286b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 3 5 5 2 8 2 3+-+2 +--R (3510a b x + 27027a b x + 7722a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 3+-+ 9 4 +--R (66b x + 10296a b x + 25740a b x + 2145a b x)\|x + 715a b x +--R + +--R 4 6 3 7 3 2 10 +--R 20020a b x + 17160a b x + 286a x +--R / +--R 286 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1299 +m0:=a0-r0 +--R +--R +--R 13 +--R a +--R (4) - ----- +--R 3 +--R 286b +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1299 +t0:=(a+b*x^(1/3))^10/x +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1299 +r0:=30*a^9*b*x^(1/3)+135/2*a^8*b^2*x^(2/3)+120*a^7*b^3*x+_ + 315/2*a^6*b^4*x^(4/3)+756/5*a^5*b^5*x^(5/3)+105*a^4*b^6*x^2+_ + 360/7*a^3*b^7*x^(7/3)+135/8*a^2*b^8*x^(8/3)+10/3*a*b^9*x^3+_ + 3/10*b^10*x^(10/3)+a^10*log(x) +--R +--R +--R (2) +--R 2 8 2 5 5 8 2 3+-+2 +--R (14175a b x + 127008a b x + 56700a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 10 +--R (252b x + 43200a b x + 132300a b x + 25200a b)\|x + 840a log(x) +--R + +--R 9 3 4 6 2 7 3 +--R 2800a b x + 88200a b x + 100800a b x +--R / +--R 840 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a log(\|x ) + (14175a b x + 127008a b x + 56700a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (252b x + 43200a b x + 132300a b x + 25200a b)\|x + 2800a b x +--R + +--R 4 6 2 7 3 +--R 88200a b x + 100800a b x +--R / +--R 840 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1299 +m0:=a0-r0 +--R +--R +--R 10 3+-+ 10 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1299 +t0:=(a+b*x^(1/3))^10/x^2 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1299 +r0:=-a^10/x-15*a^9*b/x^(2/3)-135*a^8*b^2/x^(1/3)+630*a^6*b^4*x^(1/3)+_ + 378*a^5*b^5*x^(2/3)+210*a^4*b^6*x+90*a^3*b^7*x^(4/3)+_ + 27*a^2*b^8*x^(5/3)+5*a*b^9*x^2+3/7*b^10*x^(7/3)+120*a^7*b^3*log(x) +--R +--R +--R (2) +--R 7 3 9 3 4 6 2 10 3+-+2 +--R (840a b x log(x) + 35a b x + 1470a b x - 7a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 6 4 2 +--R (189a b x + 2646a b x - 945a b x)\|x + 3b x + 630a b x + 4410a b x +--R + +--R 9 +--R - 105a b x +--R / +--R 3+-+2 +--R 7x \|x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (189a b x + 2646a b x - 945a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (3b x + 630a b x + 4410a b x - 105a b)\|x + 35a b x + 1470a b x +--R + +--R 10 +--R - 7a +--R / +--R 7x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1299 +m0:=a0-r0 +--R +--R +--R 7 3 3+-+ 7 3 +--R (4) 360a b log(\|x ) - 120a b log(x) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1299 +t0:=(a+b*x^(1/3))^10/x^3 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 3 +--R x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1299 +r0:=-1/2*a^10/x^2-6*a^9*b/x^(5/3)-135/4*a^8*b^2/x^(4/3)-120*a^7*b^3/x-_ + 315*a^6*b^4/x^(2/3)-756*a^5*b^5/x^(1/3)+360*a^3*b^7*x^(1/3)+_ + 135/2*a^2*b^8*x^(2/3)+10*a*b^9*x+3/4*b^10*x^(4/3)+210*a^4*b^6*log(x) +--R +--R +--R (2) +--R 4 6 2 9 3 7 3 10 3+-+2 +--R (840a b x log(x) + 40a b x - 480a b x - 2a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 +--R (270a b x - 3024a b x - 135a b x)\|x + 3b x + 1440a b x +--R + +--R 6 4 2 9 +--R - 1260a b x - 24a b x +--R / +--R 2 3+-+2 +--R 4x \|x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 2 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (270a b x - 3024a b x - 135a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 7 3 10 +--R (3b x + 1440a b x - 1260a b x - 24a b)\|x + 40a b x - 480a b x - 2a +--R / +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1299 +m0:=a0-r0 +--R +--R +--R 4 6 3+-+ 4 6 +--R (4) 630a b log(\|x ) - 210a b log(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1299 +t0:=(a+b*x^(1/3))^10/x^4 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 4 +--R x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1299 +r0:=-1/3*a^10/x^3-15/4*a^9*b/x^(8/3)-135/7*a^8*b^2/x^(7/3)-_ + 60*a^7*b^3/x^2-126*a^6*b^4/x^(5/3)-189*a^5*b^5/x^(4/3)-_ + 210*a^4*b^6/x-180*a^3*b^7/x^(2/3)-135*a^2*b^8/x^(1/3)+_ + 3*b^10*x^(1/3)+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (840a b x log(x) - 17640a b x - 5040a b x - 28a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 +--R (- 11340a b x - 15876a b x - 1620a b x)\|x + 252b x - 15120a b x +--R + +--R 6 4 2 9 +--R - 10584a b x - 315a b x +--R / +--R 3 3+-+2 +--R 84x \|x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (- 11340a b x - 15876a b x - 1620a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 4 6 2 +--R (252b x - 15120a b x - 10584a b x - 315a b)\|x - 17640a b x +--R + +--R 7 3 10 +--R - 5040a b x - 28a +--R / +--R 3 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R (4) 30a b log(\|x ) - 10a b log(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1299 +t0:=(a+b*x^(1/3))^10/x^5 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 5 +--R x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1299 +r0:=-1/4*(a+b*x^(1/3))^11/(a*x^4)+1/44*b*(a+b*x^(1/3))^11/(a^2*x^(11/3)) +--R +--R +--R (2) +--R 12 4 3 9 3 6 6 2 9 3 12 3+-+2 +--R (b x - 440a b x - 4620a b x - 1760a b x - 11a )\|x +--R + +--R 4 8 3 7 5 2 10 2 3+-+ 2 10 4 5 7 3 +--R (- 1485a b x - 4752a b x - 594a b x)\|x - 66a b x - 3168a b x +--R + +--R 8 4 2 11 +--R - 3465a b x - 120a b x +--R / +--R 2 4 3+-+2 +--R 44a x \|x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1485a b x - 4752a b x - 594a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 66b x - 3168a b x - 3465a b x - 120a b)\|x - 440a b x +--R + +--R 4 6 2 7 3 10 +--R - 4620a b x - 1760a b x - 11a +--R / +--R 4 +--R 44x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1299 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ---- +--R 2 +--R 44a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1299 +t0:=(a+b*x^(1/3))^10/x^6 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 6 +--R x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1299 +r0:=-1/5*(a+b*x^(1/3))^11/(a*x^5)+2/35*b*(a+b*x^(1/3))^11/(a^2*x^(14/3))-_ + 6/455*b^2*(a+b*x^(1/3))^11/(a^3*x^(13/3))+_ + 1/455*b^3*(a+b*x^(1/3))^11/(a^4*x^4)-_ + 1/5005*b^4*(a+b*x^(1/3))^11/(a^5*x^(11/3)) +--R +--R +--R (2) +--R 15 5 6 9 3 9 6 2 12 3 15 3+-+2 +--R (- b x - 25025a b x - 350350a b x - 150150a b x - 1001a )\|x +--R + +--R 7 8 3 10 5 2 13 2 3+-+ 5 10 4 +--R (- 96525a b x - 378378a b x - 51975a b x)\|x - 3003a b x +--R + +--R 8 7 3 11 4 2 14 +--R - 225225a b x - 286650a b x - 10725a b x +--R / +--R 5 5 3+-+2 +--R 5005a x \|x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 96525a b x - 378378a b x - 51975a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 3003b x - 225225a b x - 286650a b x - 10725a b)\|x - 25025a b x +--R + +--R 4 6 2 7 3 10 +--R - 350350a b x - 150150a b x - 1001a +--R / +--R 5 +--R 5005x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1299 +m0:=a0-r0 +--R +--R +--R 15 +--R b +--R (4) ------ +--R 5 +--R 5005a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1299 +t0:=(a+b*x^(1/3))^10/x^7 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 7 +--R x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1299 +r0:=-1/6*a^10/x^6-30/17*a^9*b/x^(17/3)-135/16*a^8*b^2/x^(16/3)-_ + 24*a^7*b^3/x^5-45*a^6*b^4/x^(14/3)-756/13*a^5*b^5/x^(13/3)-_ + 105/2*a^4*b^6/x^4-360/11*a^3*b^7/x^(11/3)-27/2*a^2*b^8/x^(10/3)-_ + 10/3*a*b^9/x^3-3/8*b^10/x^(8/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 388960a b x - 6126120a b x - 2800512a b x - 19448a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 1575288a b x - 6785856a b x - 984555a b x)\|x - 43758b x +--R + +--R 3 7 3 6 4 2 9 +--R - 3818880a b x - 5250960a b x - 205920a b x +--R / +--R 6 3+-+2 +--R 116688x \|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1575288a b x - 6785856a b x - 984555a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 43758b x - 3818880a b x - 5250960a b x - 205920a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 388960a b x - 6126120a b x - 2800512a b x - 19448a +--R / +--R 6 +--R 116688x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1299 +t0:=(a+b*x^(1/3))^10/x^8 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 8 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1299 +r0:=-1/7*a^10/x^7-3/2*a^9*b/x^(20/3)-135/19*a^8*b^2/x^(19/3)-_ + 20*a^7*b^3/x^6-630/17*a^6*b^4/x^(17/3)-189/4*a^5*b^5/x^(16/3)-_ + 42*a^4*b^6/x^5-180/7*a^3*b^7/x^(14/3)-135/13*a^2*b^8/x^(13/3)-_ + 5/2*a*b^9/x^4-3/11*b^10/x^(11/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 3233230a b x - 54318264a b x - 25865840a b x - 184756a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 13430340a b x - 61108047a b x - 9189180a b x)\|x - 352716b x +--R + +--R 3 7 3 6 4 2 9 +--R - 33256080a b x - 47927880a b x - 1939938a b x +--R / +--R 7 3+-+2 +--R 1293292x \|x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 13430340a b x - 61108047a b x - 9189180a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 352716b x - 33256080a b x - 47927880a b x - 1939938a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 3233230a b x - 54318264a b x - 25865840a b x - 184756a +--R / +--R 7 +--R 1293292x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1299 +t0:=(a+b*x^(1/3))^10/x^9 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 9 +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1299 +r0:=-1/8*a^10/x^8-30/23*a^9*b/x^(23/3)-135/22*a^8*b^2/x^(22/3)-_ + 120/7*a^7*b^3/x^7-63/2*a^6*b^4/x^(20/3)-756/19*a^5*b^5/x^(19/3)-_ + 35*a^4*b^6/x^6-360/17*a^3*b^7/x^(17/3)-135/16*a^2*b^8/x^(16/3)-_ + 2*a*b^9/x^5-3/14*b^10/x^(14/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 18305056a b x - 320338480a b x - 156900480a b x - 1144066a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 77224455a b x - 364174272a b x - 56163240a b x)\|x - 1961256b x +--R + +--R 3 7 3 6 4 2 9 +--R - 193818240a b x - 288304632a b x - 11938080a b x +--R / +--R 8 3+-+2 +--R 9152528x \|x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 77224455a b x - 364174272a b x - 56163240a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 1961256b x - 193818240a b x - 288304632a b x - 11938080a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 18305056a b x - 320338480a b x - 156900480a b x - 1144066a +--R / +--R 8 +--R 9152528x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1299 +t0:=(a+b*x^(1/3))^10/x^10 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 10 +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1299 +r0:=-1/9*a^10/x^9-15/13*a^9*b/x^(26/3)-27/5*a^8*b^2/x^(25/3)-_ + 15*a^7*b^3/x^8-630/23*a^6*b^4/x^(23/3)-378/11*a^5*b^5/x^(22/3)-_ + 30*a^4*b^6/x^7-18*a^3*b^7/x^(20/3)-135/19*a^2*b^8/x^(19/3)-_ + 5/3*a*b^9/x^6-3/17*b^10/x^(17/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 79676025a b x - 1434168450a b x - 717084225a b x - 5311735a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ +--R (- 339671475a b x - 1642774770a b x - 258150321a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 +--R - 8436285b x - 860501070a b x - 1309458150a b x - 55160325a b x +--R / +--R 9 3+-+2 +--R 47805615x \|x +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 339671475a b x - 1642774770a b x - 258150321a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 8436285b x - 860501070a b x - 1309458150a b x - 55160325a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 79676025a b x - 1434168450a b x - 717084225a b x - 5311735a +--R / +--R 9 +--R 47805615x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1299 +t0:=(a+b*x^(1/3))^15*x^5 +--R +--R +--R (1) +--R 14 9 4 11 8 7 8 7 10 5 6 13 2 5 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 9 5 10 8 8 7 7 11 4 6 14 5 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 10 3 12 9 6 9 8 9 6 7 12 3 6 15 5 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1299 +r0:=1/6*a^15*x^6+45/19*a^14*b*x^(19/3)+63/4*a^13*b^2*x^(20/3)+_ + 65*a^12*b^3*x^7+4095/22*a^11*b^4*x^(22/3)+9009/23*a^10*_ + b^5*x^(23/3)+5005/8*a^9*b^6*x^8+3861/5*a^8*b^7*x^(25/3)+_ + 1485/2*a^7*b^8*x^(26/3)+5005/9*a^6*b^9*x^9+1287/4*a^5*_ + b^10*x^(28/3)+4095/29*a^4*b^11*x^(29/3)+91/2*a^3*b^12*x^10+_ + 315/31*a^2*b^13*x^(31/3)+45/32*a*b^14*x^(32/3)+1/11*b^15*x^11 +--R +--R +--R (2) +--R 14 10 4 11 9 7 8 8 +--R 8751023325a b x + 878723445600a b x + 4620540315600a b x +--R + +--R 10 5 7 13 2 6 +--R 2437502427360a b x + 98011461240a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 10 5 10 9 8 7 8 +--R 63233200800a b x + 2002234136760a b x + 4805361928224a b x +--R + +--R 11 4 7 14 6 +--R 1158317269200a b x + 14738565600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 11 3 12 10 6 9 9 +--R 565722720b x + 283144221360a b x + 3460651594400a b x +--R + +--R 9 6 8 12 3 7 15 6 +--R 3893233043700a b x + 404491744800a b x + 1037158320a x +--R / +--R 6222949920 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 10 4 11 9 7 8 8 +--R 8751023325a b x + 878723445600a b x + 4620540315600a b x +--R + +--R 10 5 7 13 2 6 +--R 2437502427360a b x + 98011461240a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 10 5 10 9 8 7 8 +--R 63233200800a b x + 2002234136760a b x + 4805361928224a b x +--R + +--R 11 4 7 14 6 +--R 1158317269200a b x + 14738565600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 11 3 12 10 6 9 9 +--R 565722720b x + 283144221360a b x + 3460651594400a b x +--R + +--R 9 6 8 12 3 7 15 6 +--R 3893233043700a b x + 404491744800a b x + 1037158320a x +--R / +--R 6222949920 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1299 +t0:=(a+b*x^(1/3))^15*x^4 +--R +--R +--R (1) +--R 14 8 4 11 7 7 8 6 10 5 5 13 2 4 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 8 5 10 7 8 7 6 11 4 5 14 4 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 12 3 5 15 4 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1299 +r0:=1/5*a^15*x^5+45/16*a^14*b*x^(16/3)+315/17*a^13*b^2*x^(17/3)+_ + 455/6*a^12*b^3*x^6+4095/19*a^11*b^4*x^(19/3)+9009/20*a^10*_ + b^5*x^(20/3)+715*a^9*b^6*x^7+1755/2*a^8*b^7*x^(22/3)+_ + 19305/23*a^7*b^8*x^(23/3)+5005/8*a^6*b^9*x^8+9009/25*a^5*_ + b^10*x^(25/3)+315/2*a^4*b^11*x^(26/3)+455/9*a^3*b^12*x^9+_ + 45/4*a^2*b^13*x^(28/3)+45/29*a*b^14*x^(29/3)+1/10*b^15*x^10 +--R +--R +--R (2) +--R 14 9 4 11 8 7 8 7 +--R 1203498000a b x + 122155047000a b x + 650987766000a b x +--R + +--R 10 5 6 13 2 5 +--R 349363434420a b x + 14371182000a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 9 5 10 8 8 7 7 +--R 8725360500a b x + 279490747536a b x + 680578119000a b x +--R + +--R 11 4 6 14 5 +--R 167159538000a b x + 2181340125a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 10 3 12 9 6 9 8 +--R 77558760b x + 39210262000a b x + 485226992250a b x +--R + +--R 9 6 7 12 3 6 15 5 +--R 554545134000a b x + 58815393000a b x + 155117520a x +--R / +--R 775587600 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 9 4 11 8 7 8 7 +--R 1203498000a b x + 122155047000a b x + 650987766000a b x +--R + +--R 10 5 6 13 2 5 +--R 349363434420a b x + 14371182000a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 9 5 10 8 8 7 7 +--R 8725360500a b x + 279490747536a b x + 680578119000a b x +--R + +--R 11 4 6 14 5 +--R 167159538000a b x + 2181340125a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 10 3 12 9 6 9 8 +--R 77558760b x + 39210262000a b x + 485226992250a b x +--R + +--R 9 6 7 12 3 6 15 5 +--R 554545134000a b x + 58815393000a b x + 155117520a x +--R / +--R 775587600 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1299 +t0:=(a+b*x^(1/3))^15*x^3 +--R +--R +--R (1) +--R 14 7 4 11 6 7 8 5 10 5 4 13 2 3 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 7 5 10 6 8 7 5 11 4 4 14 3 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 8 3 12 7 6 9 6 9 6 5 12 3 4 15 3 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1299 +r0:=1/4*a^15*x^4+45/13*a^14*b*x^(13/3)+45/2*a^13*b^2*x^(14/3)+_ + 91*a^12*b^3*x^5+4095/16*a^11*b^4*x^(16/3)+9009/17*a^10*b^5*_ + x^(17/3)+5005/6*a^9*b^6*x^6+19305/19*a^8*b^7*x^(19/3)+_ + 3861/4*a^7*b^8*x^(20/3)+715*a^6*b^9*x^7+819/2*a^5*b^10*_ + x^(22/3)+4095/23*a^4*b^11*x^(23/3)+455/8*a^3*b^12*x^8+_ + 63/5*a^2*b^13*x^(25/3)+45/26*a*b^14*x^(26/3)+1/9*b^15*x^9 +--R +--R +--R (2) +--R 14 8 4 11 7 7 8 6 +--R 120349800a b x + 12380331600a b x + 67119083460a b x +--R + +--R 10 5 5 13 2 4 +--R 36849692880a b x + 1564547400a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 8 5 10 7 8 7 6 +--R 876146544a b x + 28474762680a b x + 70651666800a b x +--R + +--R 11 4 5 14 4 +--R 17796726675a b x + 240699600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 +--R 7726160b x + 3954828150a b x + 49717839600a b x + 58004146200a b x +--R + +--R 12 3 5 15 4 +--R 6327725040a b x + 17383860a x +--R / +--R 69535440 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 8 4 11 7 7 8 6 +--R 120349800a b x + 12380331600a b x + 67119083460a b x +--R + +--R 10 5 5 13 2 4 +--R 36849692880a b x + 1564547400a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 8 5 10 7 8 7 6 +--R 876146544a b x + 28474762680a b x + 70651666800a b x +--R + +--R 11 4 5 14 4 +--R 17796726675a b x + 240699600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 +--R 7726160b x + 3954828150a b x + 49717839600a b x + 58004146200a b x +--R + +--R 12 3 5 15 4 +--R 6327725040a b x + 17383860a x +--R / +--R 69535440 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1299 +t0:=(a+b*x^(1/3))^15*x^2 +--R +--R +--R (1) +--R 14 6 4 11 5 7 8 4 10 5 3 13 2 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 6 5 10 5 8 7 4 11 4 3 14 2 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 7 3 12 6 6 9 5 9 6 4 12 3 3 15 2 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1299 +r0:=3/16*a^8*(a+b*x^(1/3))^16/b^9-24/17*a^7*(a+b*x^(1/3))^17/b^9+_ + 14/3*a^6*(a+b*x^(1/3))^18/b^9-168/19*a^5*(a+b*x^(1/3))^19/b^9+_ + 21/2*a^4*(a+b*x^(1/3))^20/b^9-8*a^3*(a+b*x^(1/3))^21/b^9+_ + 42/11*a^2*(a+b*x^(1/3))^22/b^9-24/23*a*(a+b*x^(1/3))^23/b^9+_ + 1/8*(a+b*x^(1/3))^24/b^9 +--R +--R +--R (2) +--R 23 7 4 20 6 7 17 5 +--R 7674480a b x + 803134332a b x + 4454358480a b x +--R + +--R 10 14 4 13 11 3 +--R 2524136472a b x + 112326480a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 22 7 5 19 6 8 16 5 +--R 56163240a b x + 1859890032a b x + 4732755885a b x +--R + +--R 11 13 4 14 10 3 +--R 1235591280a b x + 17651304a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 24 8 3 21 7 6 18 6 9 15 5 +--R 490314b x + 254963280a b x + 3272028760a b x + 3926434512a b x +--R + +--R 12 12 4 15 9 3 24 +--R 446185740a b x + 1307504a b x + a +--R / +--R 9 +--R 3922512b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 7 4 11 6 7 8 5 +--R 7674480a b x + 803134332a b x + 4454358480a b x +--R + +--R 10 5 4 13 2 3 +--R 2524136472a b x + 112326480a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 7 5 10 6 8 7 5 +--R 56163240a b x + 1859890032a b x + 4732755885a b x +--R + +--R 11 4 4 14 3 +--R 1235591280a b x + 17651304a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 8 3 12 7 6 9 6 9 6 5 +--R 490314b x + 254963280a b x + 3272028760a b x + 3926434512a b x +--R + +--R 12 3 4 15 3 +--R 446185740a b x + 1307504a x +--R / +--R 3922512 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1299 +m0:=a0-r0 +--R +--R +--R 24 +--R a +--R (4) - --------- +--R 9 +--R 3922512b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1299 +t0:=(a+b*x^(1/3))^15*x +--R +--R +--R (1) +--R 14 5 4 11 4 7 8 3 10 5 2 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x)\|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 14 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x)\|x +--R + +--R 15 6 3 12 5 6 9 4 9 6 3 12 3 2 15 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1299 +r0:=-3/16*a^5*(a+b*x^(1/3))^16/b^6+15/17*a^4*(a+b*x^(1/3))^17/b^6-_ + 5/3*a^3*(a+b*x^(1/3))^18/b^6+30/19*a^2*(a+b*x^(1/3))^19/b^6-_ + 3/4*a*(a+b*x^(1/3))^20/b^6+1/7*(a+b*x^(1/3))^21/b^6 +--R +--R +--R (2) +--R 20 6 4 17 5 7 14 4 10 11 3 +--R 244188a b x + 26142480a b x + 149652360a b x + 88884432a b x +--R + +--R 13 8 2 +--R 4273290a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 19 6 5 16 5 8 13 4 +--R 1799280a b x + 61108047a b x + 161164080a b x +--R + +--R 11 10 3 14 7 2 +--R 44442216a b x + 697680a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 21 7 3 18 6 6 15 5 9 12 4 +--R 15504b x + 8230040a b x + 108636528a b x + 135795660a b x +--R + +--R 12 9 3 15 6 2 21 +--R 16460080a b x + 54264a b x - a +--R / +--R 6 +--R 108528b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 6 4 11 5 7 8 4 10 5 3 +--R 244188a b x + 26142480a b x + 149652360a b x + 88884432a b x +--R + +--R 13 2 2 +--R 4273290a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 6 5 10 5 8 7 4 11 4 3 +--R 1799280a b x + 61108047a b x + 161164080a b x + 44442216a b x +--R + +--R 14 2 +--R 697680a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 7 3 12 6 6 9 5 9 6 4 +--R 15504b x + 8230040a b x + 108636528a b x + 135795660a b x +--R + +--R 12 3 3 15 2 +--R 16460080a b x + 54264a x +--R / +--R 108528 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1299 +m0:=a0-r0 +--R +--R +--R 21 +--R a +--R (4) -------- +--R 6 +--R 108528b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1299 +t0:=(a+b*x^(1/3))^15 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1299 +r0:=3/16*a^2*(a+b*x^(1/3))^16/b^3-6/17*a*(a+b*x^(1/3))^17/b^3+_ + 1/6*(a+b*x^(1/3))^18/b^3 +--R +--R +--R (2) +--R 17 5 4 14 4 7 11 3 10 8 2 +--R 2160a b x + 238680a b x + 1432080a b x + 918918a b x +--R + +--R 13 5 +--R 51408a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 16 5 5 13 4 8 10 3 11 7 2 +--R 16065a b x + 565488a b x + 1575288a b x + 477360a b x +--R + +--R 14 4 +--R 9180a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 18 6 3 15 5 6 12 4 9 9 3 12 6 2 +--R 136b x + 74256a b x + 1021020a b x + 1361360a b x + 185640a b x +--R + +--R 15 3 18 +--R 816a b x + a +--R / +--R 3 +--R 816b +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 5 4 11 4 7 8 3 10 5 2 +--R 2160a b x + 238680a b x + 1432080a b x + 918918a b x +--R + +--R 13 2 +--R 51408a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 +--R 16065a b x + 565488a b x + 1575288a b x + 477360a b x +--R + +--R 14 +--R 9180a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 6 3 12 5 6 9 4 9 6 3 12 3 2 +--R 136b x + 74256a b x + 1021020a b x + 1361360a b x + 185640a b x +--R + +--R 15 +--R 816a x +--R / +--R 816 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1299 +m0:=a0-r0 +--R +--R +--R 18 +--R a +--R (4) - ----- +--R 3 +--R 816b +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1299 +t0:=(a+b*x^(1/3))^15/x +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1299 +r0:=45*a^14*b*x^(1/3)+315/2*a^13*b^2*x^(2/3)+455*a^12*b^3*x+_ + 4095/4*a^11*b^4*x^(4/3)+9009/5*a^10*b^5*x^(5/3)+5005/2*a^9*_ + b^6*x^2+19305/7*a^8*b^7*x^(7/3)+19305/8*a^7*b^8*x^(8/3)+_ + 5005/3*a^6*b^9*x^3+9009/10*a^5*b^10*x^(10/3)+4095/11*a^4*_ + b^11*x^(11/3)+455/4*a^3*b^12*x^4+315/13*a^2*b^13*x^(13/3)+_ + 45/14*a*b^14*x^(14/3)+1/5*b^15*x^5+a^15*log(x) +--R +--R +--R (2) +--R 14 4 4 11 3 7 8 2 10 5 +--R 386100a b x + 44717400a b x + 289864575a b x + 216432216a b x +--R + +--R 13 2 +--R 18918900a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R 2910600a b x + 108216108a b x + 331273800a b x + 122972850a b x +--R + +--R 14 +--R 5405400a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 15 5 3 12 4 6 9 3 +--R 120120a log(x) + 24024b x + 13663650a b x + 200400200a b x +--R + +--R 9 6 2 12 3 +--R 300600300a b x + 54654600a b x +--R / +--R 120120 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 3+-+ +--R 360360a log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 10 5 +--R 386100a b x + 44717400a b x + 289864575a b x + 216432216a b x +--R + +--R 13 2 +--R 18918900a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R 2910600a b x + 108216108a b x + 331273800a b x + 122972850a b x +--R + +--R 14 +--R 5405400a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 +--R 24024b x + 13663650a b x + 200400200a b x + 300600300a b x +--R + +--R 12 3 +--R 54654600a b x +--R / +--R 120120 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1299 +m0:=a0-r0 +--R +--R +--R 15 3+-+ 15 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1299 +t0:=(a+b*x^(1/3))^15/x^2 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1299 +r0:=-a^15/x-45/2*a^14*b/x^(2/3)-315*a^13*b^2/x^(1/3)+4095*a^11*_ + b^4*x^(1/3)+9009/2*a^10*b^5*x^(2/3)+5005*a^9*b^6*x+_ + 19305/4*a^8*b^7*x^(4/3)+3861*a^7*b^8*x^(5/3)+5005/2*a^6*_ + b^9*x^2+1287*a^5*b^10*x^(7/3)+4095/8*a^4*b^11*x^(8/3)+_ + 455/3*a^3*b^12*x^3+63/2*a^2*b^13*x^(10/3)+45/11*a*b^14*_ + x^(11/3)+1/4*b^15*x^4+455*a^12*b^3*log(x) +--R +--R +--R (2) +--R 12 3 15 5 3 12 4 6 9 3 +--R 120120a b x log(x) + 66b x + 40040a b x + 660660a b x +--R + +--R 9 6 2 15 +--R 1321320a b x - 264a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 10 5 2 +--R 1080a b x + 135135a b x + 1019304a b x + 1189188a b x +--R + +--R 13 2 +--R - 83160a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 14 +--R 8316a b x + 339768a b x + 1274130a b x + 1081080a b x - 5940a b x +--R / +--R 3+-+2 +--R 264x \|x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 3 3+-+ +--R 360360a b x log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 10 5 +--R 1080a b x + 135135a b x + 1019304a b x + 1189188a b x +--R + +--R 13 2 +--R - 83160a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R 8316a b x + 339768a b x + 1274130a b x + 1081080a b x +--R + +--R 14 +--R - 5940a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 15 +--R 66b x + 40040a b x + 660660a b x + 1321320a b x - 264a +--R / +--R 264x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1299 +m0:=a0-r0 +--R +--R +--R 12 3 3+-+ 12 3 +--R (4) 1365a b log(\|x ) - 455a b log(x) +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1299 +t0:=(a+b*x^(1/3))^15/x^3 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 3 +--R x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1299 +r0:=-1/2*a^15/x^2-9*a^14*b/x^(5/3)-315/4*a^13*b^2/x^(4/3)-455*a^12*_ + b^3/x-4095/2*a^11*b^4/x^(2/3)-9009*a^10*b^5/x^(1/3)+19305*a^8*_ + b^7*x^(1/3)+19305/2*a^7*b^8*x^(2/3)+5005*a^6*b^9*x+9009/4*_ + a^5*b^10*x^(4/3)+819*a^4*b^11*x^(5/3)+455/2*a^3*b^12*x^2+_ + 45*a^2*b^13*x^(7/3)+45/8*a*b^14*x^(8/3)+1/3*b^15*x^3+5005*a^9*b^6*log(x) +--R +--R +--R (2) +--R 9 6 2 15 5 3 12 4 6 9 3 +--R 120120a b x log(x) + 8b x + 5460a b x + 120120a b x +--R + +--R 12 3 15 +--R - 10920a b x - 12a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 10 5 2 13 2 +--R (135a b x + 19656a b x + 231660a b x - 216216a b x - 1890a b x) +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 14 +--R 1080a b x + 54054a b x + 463320a b x - 49140a b x - 216a b x +--R / +--R 2 3+-+2 +--R 24x \|x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 6 2 3+-+ +--R 360360a b x log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 10 5 13 2 +--R (135a b x + 19656a b x + 231660a b x - 216216a b x - 1890a b ) +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ +--R (1080a b x + 54054a b x + 463320a b x - 49140a b x - 216a b)\|x +--R + +--R 15 5 3 12 4 6 9 3 12 3 15 +--R 8b x + 5460a b x + 120120a b x - 10920a b x - 12a +--R / +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1299 +m0:=a0-r0 +--R +--R +--R 9 6 3+-+ 9 6 +--R (4) 15015a b log(\|x ) - 5005a b log(x) +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1299 +t0:=(a+b*x^(1/3))^15/x^4 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 4 +--R x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1299 +r0:=-1/3*a^15/x^3-45/8*a^14*b/x^(8/3)-45*a^13*b^2/x^(7/3)-455/2*a^12*_ + b^3/x^2-819*a^11*b^4/x^(5/3)-9009/4*a^10*b^5/x^(4/3)-5005*a^9*_ + b^6/x-19305/2*a^8*b^7/x^(2/3)-19305*a^7*b^8/x^(1/3)+9009*a^5*_ + b^10*x^(1/3)+4095/2*a^4*b^11*x^(2/3)+455*a^3*b^12*x+_ + 315/4*a^2*b^13*x^(4/3)+9*a*b^14*x^(5/3)+1/2*b^15*x^2+5005*a^6*b^9*log(x) +--R +--R +--R (2) +--R 6 9 3 15 5 3 12 4 9 6 2 +--R 120120a b x log(x) + 12b x + 10920a b x - 120120a b x +--R + +--R 12 3 15 +--R - 5460a b x - 8a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 10 5 2 13 2 +--R (216a b x + 49140a b x - 463320a b x - 54054a b x - 1080a b x) +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 14 +--R 1890a b x + 216216a b x - 231660a b x - 19656a b x - 135a b x +--R / +--R 3 3+-+2 +--R 24x \|x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 9 3 3+-+ +--R 360360a b x log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (216a b x + 49140a b x - 463320a b x - 54054a b x - 1080a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ +--R (1890a b x + 216216a b x - 231660a b x - 19656a b x - 135a b)\|x +--R + +--R 15 5 3 12 4 9 6 2 12 3 15 +--R 12b x + 10920a b x - 120120a b x - 5460a b x - 8a +--R / +--R 3 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1299 +m0:=a0-r0 +--R +--R +--R 6 9 3+-+ 6 9 +--R (4) 15015a b log(\|x ) - 5005a b log(x) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1299 +t0:=(a+b*x^(1/3))^15/x^6 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 6 +--R x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1299 +r0:=-1/5*a^15/x^5-45/14*a^14*b/x^(14/3)-315/13*a^13*b^2/x^(13/3)-_ + 455/4*a^12*b^3/x^4-4095/11*a^11*b^4/x^(11/3)-9009/10*a^10*_ + b^5/x^(10/3)-5005/3*a^9*b^6/x^3-19305/8*a^8*b^7/x^(8/3)-_ + 19305/7*a^7*b^8/x^(7/3)-5005/2*a^6*b^9/x^2-9009/5*a^5*_ + b^10/x^(5/3)-4095/4*a^4*b^11/x^(4/3)-455*a^3*b^12/x-_ + 315/2*a^2*b^13/x^(2/3)-45*a*b^14/x^(1/3)+b^15*log(x) +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R 120120b x log(x) - 54654600a b x - 300600300a b x +--R + +--R 9 6 2 12 3 15 +--R - 200400200a b x - 13663650a b x - 24024a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 5405400a b x - 122972850a b x - 331273800a b x +--R + +--R 10 5 2 13 2 +--R - 108216108a b x - 2910600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 +--R - 18918900a b x - 216432216a b x - 289864575a b x - 44717400a b x +--R + +--R 14 +--R - 386100a b x +--R / +--R 5 3+-+2 +--R 120120x \|x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 5 3+-+ +--R 360360b x log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 +--R - 5405400a b x - 122972850a b x - 331273800a b x +--R + +--R 10 5 13 2 +--R - 108216108a b x - 2910600a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 18918900a b x - 216432216a b x - 289864575a b x +--R + +--R 11 4 14 +--R - 44717400a b x - 386100a b +--R * +--R 3+-+ +--R \|x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 +--R - 54654600a b x - 300600300a b x - 200400200a b x - 13663650a b x +--R + +--R 15 +--R - 24024a +--R / +--R 5 +--R 120120x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1299 +m0:=a0-r0 +--R +--R +--R 15 3+-+ 15 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1299 +t0:=(a+b*x^(1/3))^15/x^7 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 7 +--R x +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1299 +r0:=-1/6*(a+b*x^(1/3))^16/(a*x^6)+1/51*b*(a+b*x^(1/3))^16/(a^2*x^(17/3))-_ + 1/816*b^2*(a+b*x^(1/3))^16/(a^3*x^(16/3)) +--R +--R +--R (2) +--R 18 6 3 15 5 6 12 4 9 9 3 12 6 2 +--R - b x - 816a b x - 185640a b x - 1361360a b x - 1021020a b x +--R + +--R 15 3 18 +--R - 74256a b x - 136a +--R * +--R 3+-+2 +--R \|x +--R + +--R 4 14 5 7 11 4 10 8 3 13 5 2 +--R - 9180a b x - 477360a b x - 1575288a b x - 565488a b x +--R + +--R 16 2 +--R - 16065a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 5 13 5 8 10 4 11 7 3 14 4 2 +--R - 51408a b x - 918918a b x - 1432080a b x - 238680a b x +--R + +--R 17 +--R - 2160a b x +--R / +--R 3 6 3+-+2 +--R 816a x \|x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 10 5 +--R - 9180a b x - 477360a b x - 1575288a b x - 565488a b x +--R + +--R 13 2 +--R - 16065a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R - 51408a b x - 918918a b x - 1432080a b x - 238680a b x +--R + +--R 14 +--R - 2160a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 12 3 +--R - 816b x - 185640a b x - 1361360a b x - 1021020a b x - 74256a b x +--R + +--R 15 +--R - 136a +--R / +--R 6 +--R 816x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1299 +m0:=a0-r0 +--R +--R +--R 18 +--R b +--R (4) ----- +--R 3 +--R 816a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1299 +t0:=(a+b*x^(1/3))^15/x^8 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 8 +--R x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1299 +r0:=-1/7*(a+b*x^(1/3))^16/(a*x^7)+1/28*b*(a+b*x^(1/3))^16/(a^2*x^(20/3))-_ + 1/133*b^2*(a+b*x^(1/3))^16/(a^3*x^(19/3))+1/798*b^3*_ + (a+b*x^(1/3))^16/(a^4*x^6)-1/6783*b^4*(a+b*x^(1/3))^16/_ + (a^5*x^(17/3))+1/108528*b^5*(a+b*x^(1/3))^16/(a^6*x^(16/3)) +--R +--R +--R (2) +--R 21 7 6 15 5 9 12 4 12 9 3 +--R b x - 54264a b x - 16460080a b x - 135795660a b x +--R + +--R 15 6 2 18 3 21 +--R - 108636528a b x - 8230040a b x - 15504a +--R * +--R 3+-+2 +--R \|x +--R + +--R 7 14 5 10 11 4 13 8 3 +--R - 697680a b x - 44442216a b x - 161164080a b x +--R + +--R 16 5 2 19 2 +--R - 61108047a b x - 1799280a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 8 13 5 11 10 4 14 7 3 17 4 2 +--R - 4273290a b x - 88884432a b x - 149652360a b x - 26142480a b x +--R + +--R 20 +--R - 244188a b x +--R / +--R 6 7 3+-+2 +--R 108528a x \|x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 10 5 +--R - 697680a b x - 44442216a b x - 161164080a b x - 61108047a b x +--R + +--R 13 2 +--R - 1799280a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R - 4273290a b x - 88884432a b x - 149652360a b x - 26142480a b x +--R + +--R 14 +--R - 244188a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 +--R - 54264b x - 16460080a b x - 135795660a b x - 108636528a b x +--R + +--R 12 3 15 +--R - 8230040a b x - 15504a +--R / +--R 7 +--R 108528x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1299 +m0:=a0-r0 +--R +--R +--R 21 +--R b +--R (4) - -------- +--R 6 +--R 108528a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1299 +t0:=(a+b*x^(1/3))^15/x^9 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 9 +--R x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1299 +r0:=-1/8*(a+b*x^(1/3))^16/(a*x^8)+1/23*b*(a+b*x^(1/3))^16/(a^2*x^(23/3))-_ + 7/506*b^2*(a+b*x^(1/3))^16/(a^3*x^(22/3))+1/253*b^3*_ + (a+b*x^(1/3))^16/(a^4*x^7)-1/1012*b^4*(a+b*x^(1/3))^16/_ + (a^5*x^(20/3))+1/4807*b^5*(a+b*x^(1/3))^16/(a^6*x^(19/3))-_ + 1/28842*b^6*(a+b*x^(1/3))^16/(a^7*x^6)+1/245157*b^7*_ + (a+b*x^(1/3))^16/(a^8*x^(17/3))-1/3922512*b^8*_ + (a+b*x^(1/3))^16/(a^9*x^(16/3)) +--R +--R +--R (2) +--R 24 8 9 15 5 12 12 4 15 9 3 +--R - b x - 1307504a b x - 446185740a b x - 3926434512a b x +--R + +--R 18 6 2 21 3 24 +--R - 3272028760a b x - 254963280a b x - 490314a +--R * +--R 3+-+2 +--R \|x +--R + +--R 10 14 5 13 11 4 16 8 3 +--R - 17651304a b x - 1235591280a b x - 4732755885a b x +--R + +--R 19 5 2 22 2 +--R - 1859890032a b x - 56163240a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 11 13 5 14 10 4 17 7 3 +--R - 112326480a b x - 2524136472a b x - 4454358480a b x +--R + +--R 20 4 2 23 +--R - 803134332a b x - 7674480a b x +--R / +--R 9 8 3+-+2 +--R 3922512a x \|x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 17651304a b x - 1235591280a b x - 4732755885a b x +--R + +--R 10 5 13 2 +--R - 1859890032a b x - 56163240a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 112326480a b x - 2524136472a b x - 4454358480a b x +--R + +--R 11 4 14 +--R - 803134332a b x - 7674480a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 +--R - 1307504b x - 446185740a b x - 3926434512a b x - 3272028760a b x +--R + +--R 12 3 15 +--R - 254963280a b x - 490314a +--R / +--R 8 +--R 3922512x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1299 +m0:=a0-r0 +--R +--R +--R 24 +--R b +--R (4) --------- +--R 9 +--R 3922512a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1299 +t0:=(a+b*x^(1/3))^15/x^10 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 10 +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1299 +r0:=-1/9*a^15/x^9-45/26*a^14*b/x^(26/3)-63/5*a^13*b^2/x^(25/3)-_ + 455/8*a^12*b^3/x^8-4095/23*a^11*b^4/x^(23/3)-819/2*a^10*_ + b^5/x^(22/3)-715*a^9*b^6/x^7-3861/4*a^8*b^7/x^(20/3)-_ + 19305/19*a^7*b^8/x^(19/3)-5005/6*a^6*b^9/x^6-9009/17*a^5*_ + b^10/x^(17/3)-4095/16*a^4*b^11/x^(16/3)-91*a^3*b^12/x^5-_ + 45/2*a^2*b^13/x^(14/3)-45/13*a*b^14/x^(13/3)-1/4*b^15/x^4 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 17383860b x - 6327725040a b x - 58004146200a b x +--R + +--R 9 6 2 12 3 15 +--R - 49717839600a b x - 3954828150a b x - 7726160a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 240699600a b x - 17796726675a b x - 70651666800a b x +--R + +--R 10 5 2 13 2 +--R - 28474762680a b x - 876146544a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 1564547400a b x - 36849692880a b x - 67119083460a b x +--R + +--R 11 4 2 14 +--R - 12380331600a b x - 120349800a b x +--R / +--R 9 3+-+2 +--R 69535440x \|x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 240699600a b x - 17796726675a b x - 70651666800a b x +--R + +--R 10 5 13 2 +--R - 28474762680a b x - 876146544a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 1564547400a b x - 36849692880a b x - 67119083460a b x +--R + +--R 11 4 14 +--R - 12380331600a b x - 120349800a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 17383860b x - 6327725040a b x - 58004146200a b x +--R + +--R 9 6 2 12 3 15 +--R - 49717839600a b x - 3954828150a b x - 7726160a +--R / +--R 9 +--R 69535440x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1299 +t0:=(a+b*x^(1/3))^15/x^11 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 11 +--R x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1299 +r0:=-1/10*a^15/x^10-45/29*a^14*b/x^(29/3)-45/4*a^13*b^2/x^(28/3)-_ + 455/9*a^12*b^3/x^9-315/2*a^11*b^4/x^(26/3)-9009/25*a^10*_ + b^5/x^(25/3)-5005/8*a^9*b^6/x^8-19305/23*a^8*b^7/x^(23/3)-_ + 1755/2*a^7*b^8/x^(22/3)-715*a^6*b^9/x^7-9009/20*a^5*b^10/_ + x^(20/3)-4095/19*a^4*b^11/x^(19/3)-455/6*a^3*b^12/x^6-_ + 315/17*a^2*b^13/x^(17/3)-45/16*a*b^14/x^(16/3)-1/5*b^15/x^5 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 155117520b x - 58815393000a b x - 554545134000a b x +--R + +--R 9 6 2 12 3 15 +--R - 485226992250a b x - 39210262000a b x - 77558760a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 2181340125a b x - 167159538000a b x - 680578119000a b x +--R + +--R 10 5 2 13 2 +--R - 279490747536a b x - 8725360500a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 14371182000a b x - 349363434420a b x - 650987766000a b x +--R + +--R 11 4 2 14 +--R - 122155047000a b x - 1203498000a b x +--R / +--R 10 3+-+2 +--R 775587600x \|x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 2181340125a b x - 167159538000a b x - 680578119000a b x +--R + +--R 10 5 13 2 +--R - 279490747536a b x - 8725360500a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 14371182000a b x - 349363434420a b x - 650987766000a b x +--R + +--R 11 4 14 +--R - 122155047000a b x - 1203498000a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 155117520b x - 58815393000a b x - 554545134000a b x +--R + +--R 9 6 2 12 3 15 +--R - 485226992250a b x - 39210262000a b x - 77558760a +--R / +--R 10 +--R 775587600x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1299 +t0:=(a+b*x^(1/3))^15/x^12 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 12 +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1299 +r0:=-1/11*a^15/x^11-45/32*a^14*b/x^(32/3)-315/31*a^13*b^2/x^(31/3)-_ + 91/2*a^12*b^3/x^10-4095/29*a^11*b^4/x^(29/3)-1287/4*_ + a^10*b^5/x^(28/3)-5005/9*a^9*b^6/x^9-1485/2*a^8*b^7/x^(26/3)-_ + 3861/5*a^7*b^8/x^(25/3)-5005/8*a^6*b^9/x^8-9009/23*a^5*b^10/_ + x^(23/3)-4095/22*a^4*b^11/x^(22/3)-65*a^3*b^12/x^7-_ + 63/4*a^2*b^13/x^(20/3)-45/19*a*b^14/x^(19/3)-1/6*b^15/x^6 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 1037158320b x - 404491744800a b x - 3893233043700a b x +--R + +--R 9 6 2 12 3 15 +--R - 3460651594400a b x - 283144221360a b x - 565722720a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 14738565600a b x - 1158317269200a b x - 4805361928224a b x +--R + +--R 10 5 2 13 2 +--R - 2002234136760a b x - 63233200800a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 98011461240a b x - 2437502427360a b x - 4620540315600a b x +--R + +--R 11 4 2 14 +--R - 878723445600a b x - 8751023325a b x +--R / +--R 11 3+-+2 +--R 6222949920x \|x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 14738565600a b x - 1158317269200a b x - 4805361928224a b x +--R + +--R 10 5 13 2 +--R - 2002234136760a b x - 63233200800a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 98011461240a b x - 2437502427360a b x - 4620540315600a b x +--R + +--R 11 4 14 +--R - 878723445600a b x - 8751023325a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 1037158320b x - 404491744800a b x - 3893233043700a b x +--R + +--R 9 6 2 12 3 15 +--R - 3460651594400a b x - 283144221360a b x - 565722720a +--R / +--R 11 +--R 6222949920x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1299 +t0:=x^3/(a+b*x^(1/3)) +--R +--R +--R 3 +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1299 +r0:=3*a^10*x^(1/3)/b^11-3/2*a^9*x^(2/3)/b^10+a^8*x/b^9-3/4*a^7*_ + x^(4/3)/b^8+3/5*a^6*x^(5/3)/b^7-1/2*a^5*x^2/b^6+3/7*a^4*_ + x^(7/3)/b^5-3/8*a^3*x^(8/3)/b^4+1/3*a^2*x^3/b^3-3/10*a*_ + x^(10/3)/b^2+3/11*x^(11/3)/b-3*a^11*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 11 3+-+ +--R - 27720a log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (2520b x - 3465a b x + 5544a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 2772a b x + 3960a b x - 6930a b x + 27720a b)\|x + 3080a b x +--R + +--R 5 6 2 8 3 +--R - 4620a b x + 9240a b x +--R / +--R 12 +--R 9240b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3+-+ +--R - 27720a log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (2520b x - 3465a b x + 5544a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 2772a b x + 3960a b x - 6930a b x + 27720a b)\|x + 3080a b x +--R + +--R 5 6 2 8 3 +--R - 4620a b x + 9240a b x +--R / +--R 12 +--R 9240b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1299 +t0:=x^2/(a+b*x^(1/3)) +--R +--R +--R 2 +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1299 +r0:=-3*a^7*x^(1/3)/b^8+3/2*a^6*x^(2/3)/b^7-a^5*x/b^6+3/4*a^4*_ + x^(4/3)/b^5-3/5*a^3*x^(5/3)/b^4+1/2*a^2*x^2/b^3-3/7*_ + a*x^(7/3)/b^2+3/8*x^(8/3)/b+3*a^8*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R 840a log(b\|x + a) + (105b x - 168a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 +--R (- 120a b x + 210a b x - 840a b)\|x + 140a b x - 280a b x +--R / +--R 9 +--R 280b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R 840a log(b\|x + a) + (105b x - 168a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 +--R (- 120a b x + 210a b x - 840a b)\|x + 140a b x - 280a b x +--R / +--R 9 +--R 280b +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1299 +t0:=x/(a+b*x^(1/3)) +--R +--R +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1299 +r0:=3*a^4*x^(1/3)/b^5-3/2*a^3*x^(2/3)/b^4+a^2*x/b^3-3/4*a*_ + x^(4/3)/b^2+3/5*x^(5/3)/b-3*a^5*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ +--R - 60a log(b\|x + a) + (12b x - 30a b )\|x + (- 15a b x + 60a b)\|x +--R + +--R 2 3 +--R 20a b x +--R / +--R 6 +--R 20b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ +--R - 60a log(b\|x + a) + (12b x - 30a b )\|x + (- 15a b x + 60a b)\|x +--R + +--R 2 3 +--R 20a b x +--R / +--R 6 +--R 20b +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1299 +t0:=1/(a+b*x^(1/3)) +--R +--R +--R 1 +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1299 +r0:=-3*a*x^(1/3)/b^2+3/2*x^(2/3)/b+3*a^2*log(a+b*x^(1/3))/b^3 +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(b\|x + a) + 3b \|x - 6a b\|x +--R (2) --------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(b\|x + a) + 3b \|x - 6a b\|x +--R (3) --------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1299 +t0:=1/((a+b*x^(1/3))*x) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-+ +--R b x\|x + a x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1299 +r0:=-3*log(a+b*x^(1/3))/a+log(x)/a +--R +--R +--R 3+-+ +--R - 3log(b\|x + a) + log(x) +--R (2) -------------------------- +--R a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R - 3log(b\|x + a) + 3log(\|x ) +--R (3) ------------------------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1299 +t0:=1/((2+b*x^(1/3))*x) +--R +--R +--R 1 +--R (1) ------------ +--R 3+-+ +--R b x\|x + 2x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1299 +r0:=-3*atanh(1+b*x^(1/3)) +--R +--R +--R 3+-+ +--R (2) - 3atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R - 3log(b\|x + 2) + 3log(\|x ) +--R (3) ------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R - 3log(b\|x + 2) + 3log(\|x ) + 6atanh(b\|x + 1) +--R (4) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1299 +t0:=1/((a+b*x^(1/3))*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R 2 3+-+ 2 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1299 +r0:=(-1)/(a*x)+3/2*b/(a^2*x^(2/3))-3*b^2/(a^3*x^(1/3))+3*b^3*_ + log(a+b*x^(1/3))/a^4-b^3*log(x)/a^4 +--R +--R +--R (2) +--R 3 3+-+2 3+-+ 3 3 3+-+2 2 3+-+ 2 +--R 6b x \|x log(b\|x + a) + (- 2b x log(x) - 2a )\|x - 6a b x\|x + 3a b x +--R --------------------------------------------------------------------------- +--R 4 3+-+2 +--R 2a x \|x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b x log(b\|x + a) - 6b x log(\|x ) - 6a b \|x + 3a b\|x - 2a +--R (3) ------------------------------------------------------------------ +--R 4 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 3b log(\|x ) + b log(x) +--R (4) ------------------------- +--R 4 +--R a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1299 +t0:=1/((a+b*x^(1/3))*x^3) +--R +--R +--R 1 +--R (1) --------------- +--R 3 3+-+ 3 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1299 +r0:=(-1/2)/(a*x^2)+3/5*b/(a^2*x^(5/3))-3/4*b^2/(a^3*x^(4/3))+_ + b^3/(a^4*x)-3/2*b^4/(a^5*x^(2/3))+3*b^5/(a^6*x^(1/3))-_ + 3*b^6*log(a+b*x^(1/3))/a^7+b^6*log(x)/a^7 +--R +--R +--R (2) +--R 6 2 3+-+2 3+-+ 6 2 3 3 6 3+-+2 +--R - 60b x \|x log(b\|x + a + (20b x log(x) + 20a b x - 10a )\|x +--R + +--R 5 2 4 2 3+-+ 2 4 2 5 +--R (60a b x - 15a b x)\|x - 30a b x + 12a b x +--R / +--R 7 2 3+-+2 +--R 20a x \|x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 3+-+ 6 2 3+-+ 5 4 2 3+-+2 +--R - 60b x log(b\|x + a) + 60b x log(\|x ) + (60a b x - 15a b )\|x +--R + +--R 2 4 5 3+-+ 3 3 6 +--R (- 30a b x + 12a b)\|x + 20a b x - 10a +--R / +--R 7 2 +--R 20a x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 3b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1299 +t0:=1/((a+b*x^(1/3))*x^4) +--R +--R +--R 1 +--R (1) --------------- +--R 4 3+-+ 4 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1299 +r0:=(-1/3)/(a*x^3)+3/8*b/(a^2*x^(8/3))-3/7*b^2/(a^3*x^(7/3))+_ + 1/2*b^3/(a^4*x^2)-3/5*b^4/(a^5*x^(5/3))+3/4*b^5/(a^6*x^(4/3))-_ + b^6/(a^7*x)+3/2*b^7/(a^8*x^(2/3))-3*b^8/(a^9*x^(1/3))+_ + 3*b^9*log(a+b*x^(1/3))/a^10-b^9*log(x)/a^10 +--R +--R +--R (2) +--R 9 3 3+-+2 3+-+ +--R 2520b x \|x log(b\|x + a) +--R + +--R 9 3 3 6 2 6 3 9 3+-+2 +--R (- 840b x log(x) - 840a b x + 420a b x - 280a )\|x +--R + +--R 8 3 4 5 2 7 2 3+-+ 2 7 3 5 4 2 +--R (- 2520a b x + 630a b x - 360a b x)\|x + 1260a b x - 504a b x +--R + +--R 8 +--R 315a b x +--R / +--R 10 3 3+-+2 +--R 840a x \|x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3 3+-+ 9 3 3+-+ +--R 2520b x log(b\|x + a) - 2520b x log(\|x ) +--R + +--R 8 2 4 5 7 2 3+-+2 +--R (- 2520a b x + 630a b x - 360a b )\|x +--R + +--R 2 7 2 5 4 8 3+-+ 3 6 2 6 3 9 +--R (1260a b x - 504a b x + 315a b)\|x - 840a b x + 420a b x - 280a +--R / +--R 10 3 +--R 840a x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 3b log(\|x ) + b log(x) +--R (4) ------------------------- +--R 10 +--R a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1299 +t0:=x^3/(a+b*x^(1/3))^2 +--R +--R +--R 3 +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1299 +r0:=3*a^11/(b^12*(a+b*x^(1/3)))-30*a^9*x^(1/3)/b^11+27/2*a^8*_ + x^(2/3)/b^10-8*a^7*x/b^9+21/4*a^6*x^(4/3)/b^8-18/5*a^5*_ + x^(5/3)/b^7+5/2*a^4*x^2/b^6-12/7*a^3*x^(7/3)/b^5+9/8*a^2*_ + x^(8/3)/b^4-2/3*a*x^3/b^3+3/10*x^(10/3)/b^2+33*a^10*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 10 3+-+ 11 3+-+ +--R (27720a b\|x + 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (252b x - 495a b x + 1386a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 308a b x + 660a b x - 2310a b x - 25200a b)\|x + 385a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 4620a b x + 2520a +--R / +--R 13 3+-+ 12 +--R 840b \|x + 840a b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3+-+ 11 3+-+ +--R (27720a b\|x + 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (252b x - 495a b x + 1386a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 308a b x + 660a b x - 2310a b x - 25200a b)\|x + 385a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 4620a b x + 2520a +--R / +--R 13 3+-+ 12 +--R 840b \|x + 840a b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1299 +t0:=x^2/(a+b*x^(1/3))^2 +--R +--R +--R 2 +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1299 +r0:=-3*a^8/(b^9*(a+b*x^(1/3)))+21*a^6*x^(1/3)/b^8-9*a^5*x^(2/3)/b^7+_ + 5*a^4*x/b^6-3*a^3*x^(4/3)/b^5+9/5*a^2*x^(5/3)/b^4-a*x^2/b^3+_ + 3/7*x^(7/3)/b^2-24*a^7*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 7 3+-+ 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R (- 840a b\|x - 840a )log(b\|x + a) + (15b x - 42a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 8 +--R (- 20a b x + 70a b x + 735a b)\|x + 28a b x - 140a b x - 105a +--R / +--R 10 3+-+ 9 +--R 35b \|x + 35a b +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3+-+ 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R (- 840a b\|x - 840a )log(b\|x + a) + (15b x - 42a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 8 +--R (- 20a b x + 70a b x + 735a b)\|x + 28a b x - 140a b x - 105a +--R / +--R 10 3+-+ 9 +--R 35b \|x + 35a b +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1299 +t0:=x/(a+b*x^(1/3))^2 +--R +--R +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1299 +r0:=3*a^5/(b^6*(a+b*x^(1/3)))-12*a^3*x^(1/3)/b^5+9/2*a^2*x^(2/3)/b^4-_ + 2*a*x/b^3+3/4*x^(4/3)/b^2+15*a^4*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (60a b\|x + 60a )log(b\|x + a) + (3b x - 30a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x - 48a b)\|x + 10a b x + 12a +--R / +--R 7 3+-+ 6 +--R 4b \|x + 4a b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (60a b\|x + 60a )log(b\|x + a) + (3b x - 30a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x - 48a b)\|x + 10a b x + 12a +--R / +--R 7 3+-+ 6 +--R 4b \|x + 4a b +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1299 +t0:=1/(a+b*x^(1/3))^2 +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1299 +r0:=-3*a^2/(b^3*(a+b*x^(1/3)))+3*x^(1/3)/b^2-6*a*log(a+b*x^(1/3))/b^3 +--R +--R +--R 3+-+ 2 3+-+ 2 3+-+2 3+-+ 2 +--R (- 6a b\|x - 6a )log(b\|x + a) + 3b \|x + 3a b\|x - 3a +--R (2) ------------------------------------------------------------ +--R 4 3+-+ 3 +--R b \|x + a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 2 3+-+ 2 3+-+2 3+-+ 2 +--R (- 6a b\|x - 6a )log(b\|x + a) + 3b \|x + 3a b\|x - 3a +--R (3) ------------------------------------------------------------ +--R 4 3+-+ 3 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1299 +t0:=1/((a+b*x^(1/3))^2*x) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 3+-+2 3+-+ 2 +--R b x \|x + 2a b x\|x + a x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1299 +r0:=3/(a*(a+b*x^(1/3)))-3*log(a+b*x^(1/3))/a^2+log(x)/a^2 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (- 3b\|x - 3a)log(b\|x + a) + b log(x)\|x + a log(x) + 3a +--R (2) ------------------------------------------------------------ +--R 2 3+-+ 3 +--R a b\|x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ 3+-+ 3+-+ +--R (- 3b\|x - 3a)log(b\|x + a) + (3b\|x + 3a)log(\|x ) + 3a +--R (3) ----------------------------------------------------------- +--R 2 3+-+ 3 +--R a b\|x + a +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 3+-+2 2 3+-+ 2 2 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1299 +r0:=(-4)/(a^2*x)+3/(a*(a+b*x^(1/3))*x)+6*b/(a^3*x^(2/3))-_ + 12*b^2/(a^4*x^(1/3))+12*b^3*log(a+b*x^(1/3))/a^5-4*b^3*log(x)/a^5 +--R +--R +--R (2) +--R 4 3+-+ 3 3+-+ 2 2 3+-+2 +--R (12b x\|x + 12a b x)log(b\|x + a) - 6a b \|x +--R + +--R 4 3 3+-+ 3 3 4 +--R (- 4b x log(x) + 2a b)\|x - 4a b x log(x) - 12a b x - a +--R / +--R 5 3+-+ 6 +--R a b x\|x + a x +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3+-+ 3 3+-+ 4 3+-+ 3 3+-+ +--R (12b x\|x + 12a b x)log(b\|x + a) + (- 12b x\|x - 12a b x)log(\|x ) +--R + +--R 2 2 3+-+2 3 3+-+ 3 4 +--R - 6a b \|x + 2a b\|x - 12a b x - a +--R / +--R 5 3+-+ 6 +--R a b x\|x + a x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 12b log(\|x ) + 4b log(x) +--R (4) --------------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 3 3+-+2 3 3+-+ 2 3 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1299 +r0:=(-7/2)/(a^2*x^2)+3/(a*(a+b*x^(1/3))*x^2)+21/5*b/(a^3*x^(5/3))-_ + 21/4*b^2/(a^4*x^(4/3))+7*b^3/(a^5*x)-21/2*b^4/(a^6*x^(2/3))+_ + 21*b^5/(a^7*x^(1/3))-21*b^6*log(a+b*x^(1/3))/a^8+7*b^6*log(x)/a^8 +--R +--R +--R (2) +--R 7 2 3+-+ 6 2 3+-+ 2 5 5 2 3+-+2 +--R (- 420b x \|x - 420a b x )log(b\|x + a) + (210a b x - 21a b )\|x +--R + +--R 7 2 3 4 6 3+-+ 6 2 6 2 +--R (140b x log(x) - 70a b x + 14a b)\|x + 140a b x log(x) + 420a b x +--R + +--R 4 3 7 +--R 35a b x - 10a +--R / +--R 8 2 3+-+ 9 2 +--R 20a b x \|x + 20a x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 2 3+-+ 6 2 3+-+ +--R (- 420b x \|x - 420a b x )log(b\|x + a) +--R + +--R 7 2 3+-+ 6 2 3+-+ 2 5 5 2 3+-+2 +--R (420b x \|x + 420a b x )log(\|x ) + (210a b x - 21a b )\|x +--R + +--R 3 4 6 3+-+ 6 2 4 3 7 +--R (- 70a b x + 14a b)\|x + 420a b x + 35a b x - 10a +--R / +--R 8 2 3+-+ 9 2 +--R 20a b x \|x + 20a x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 21b log(\|x ) - 7b log(x) +--R (4) ------------------------- +--R 8 +--R a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^4) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 4 3+-+2 4 3+-+ 2 4 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1299 +r0:=(-10/3)/(a^2*x^3)+3/(a*(a+b*x^(1/3))*x^3)+15/4*b/(a^3*x^(8/3))-_ + 30/7*b^2/(a^4*x^(7/3))+5*b^3/(a^5*x^2)-6*b^4/(a^6*x^(5/3))+_ + 15/2*b^5/(a^7*x^(4/3))-10*b^6/(a^8*x)+15*b^7/(a^9*x^(2/3))-_ + 30*b^8/(a^10*x^(1/3))+30*b^9*log(a+b*x^(1/3))/a^11-10*b^9*log(x)/a^11 +--R +--R +--R (2) +--R 10 3 3+-+ 9 3 3+-+ +--R (2520b x \|x + 2520a b x )log(b\|x + a) +--R + +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1260a b x + 126a b x - 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 840b x log(x) + 420a b x - 84a b x + 35a b)\|x - 840a b x log(x) +--R + +--R 9 3 4 6 2 7 3 10 +--R - 2520a b x - 210a b x + 60a b x - 28a +--R / +--R 11 3 3+-+ 12 3 +--R 84a b x \|x + 84a x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3 3+-+ 9 3 3+-+ +--R (2520b x \|x + 2520a b x )log(b\|x + a) +--R + +--R 10 3 3+-+ 9 3 3+-+ +--R (- 2520b x \|x - 2520a b x )log(\|x ) +--R + +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1260a b x + 126a b x - 45a b )\|x +--R + +--R 3 7 2 6 4 9 3+-+ 9 3 4 6 2 7 3 +--R (420a b x - 84a b x + 35a b)\|x - 2520a b x - 210a b x + 60a b x +--R + +--R 10 +--R - 28a +--R / +--R 11 3 3+-+ 12 3 +--R 84a b x \|x + 84a x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 30b log(\|x ) + 10b log(x) +--R (4) ---------------------------- +--R 11 +--R a +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1299 +t0:=x^3/(a+b*x^(1/3))^3 +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1299 +r0:=3/2*a^11/(b^12*(a+b*x^(1/3))^2)-33*a^10/(b^12*(a+b*x^(1/3)))+_ + 135*a^8*x^(1/3)/b^11-54*a^7*x^(2/3)/b^10+28*a^6*x/b^9-_ + 63/4*a^5*x^(4/3)/b^8+9*a^4*x^(5/3)/b^7-5*a^3*x^2/b^6+_ + 18/7*a^2*x^(7/3)/b^5-9/8*a*x^(8/3)/b^4+1/3*x^3/b^3-_ + 165*a^9*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 9 2 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b\|x - 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (56b x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b)\|x + 110a b x +--R + +--R 5 6 2 8 3 11 +--R - 462a b x + 9240a b x - 5292a +--R / +--R 14 3+-+2 13 3+-+ 2 12 +--R 168b \|x + 336a b \|x + 168a b +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 2 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b\|x - 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (56b x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b)\|x + 110a b x +--R + +--R 5 6 2 8 3 11 +--R - 462a b x + 9240a b x - 5292a +--R / +--R 14 3+-+2 13 3+-+ 2 12 +--R 168b \|x + 336a b \|x + 168a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1299 +t0:=x^2/(a+b*x^(1/3))^3 +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1299 +r0:=-3/2*a^8/(b^9*(a+b*x^(1/3))^2)+24*a^7/(b^9*(a+b*x^(1/3)))-_ + 63*a^5*x^(1/3)/b^8+45/2*a^4*x^(2/3)/b^7-10*a^3*x/b^6+_ + 9/2*a^2*x^(4/3)/b^5-9/5*a*x^(5/3)/b^4+1/2*x^2/b^3+_ + 84*a^6*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 6 2 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b\|x + 840a )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ +--R (5b x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b)\|x +--R + +--R 2 6 2 5 3 8 +--R 14a b x - 280a b x + 225a +--R / +--R 11 3+-+2 10 3+-+ 2 9 +--R 10b \|x + 20a b \|x + 10a b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b\|x + 840a )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ +--R (5b x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b)\|x +--R + +--R 2 6 2 5 3 8 +--R 14a b x - 280a b x + 225a +--R / +--R 11 3+-+2 10 3+-+ 2 9 +--R 10b \|x + 20a b \|x + 10a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1299 +t0:=x/(a+b*x^(1/3))^3 +--R +--R +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1299 +r0:=3/2*a^5/(b^6*(a+b*x^(1/3))^2)-15*a^4/(b^6*(a+b*x^(1/3)))+_ + 18*a^2*x^(1/3)/b^5-9/2*a*x^(2/3)/b^4+x/b^3-30*a^3*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 3 2 3+-+2 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (- 60a b \|x - 120a b\|x - 60a )log(b\|x + a) + (2b x + 63a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x + 6a b)\|x + 20a b x - 27a +--R / +--R 8 3+-+2 7 3+-+ 2 6 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3+-+2 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (- 60a b \|x - 120a b\|x - 60a )log(b\|x + a) + (2b x + 63a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x + 6a b)\|x + 20a b x - 27a +--R / +--R 8 3+-+2 7 3+-+ 2 6 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1299 +t0:=1/(a+b*x^(1/3))^3 +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1299 +r0:=-3/2*a^2/(b^3*(a+b*x^(1/3))^2)+6*a/(b^3*(a+b*x^(1/3)))+_ + 3*log(a+b*x^(1/3))/b^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(b\|x + a) + 12a b\|x + 9a +--R (2) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 2 3 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(b\|x + a) + 12a b\|x + 9a +--R (3) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 2 3 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1299 +t0:=1/((a+b*x^(1/3))^3*x) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 3a b x \|x + 3a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1299 +r0:=3/2/(a*(a+b*x^(1/3))^2)+3/(a^2*(a+b*x^(1/3)))-_ + 3*log(a+b*x^(1/3))/a^3+log(x)/a^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 2 3+-+ 2 3+-+2 +--R (- 6b \|x - 12a b\|x - 6a )log(b\|x + a) + 2b log(x)\|x +--R + +--R 3+-+ 2 2 +--R (4a b log(x) + 6a b)\|x + 2a log(x) + 9a +--R / +--R 3 2 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b\|x + 2a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 2 3+-+ +--R (- 6b \|x - 12a b\|x - 6a )log(b\|x + a) +--R + +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(\|x ) + 6a b\|x + 9a +--R / +--R 3 2 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b\|x + 2a +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^2) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1299 +r0:=(-10)/(a^3*x)+3/2/(a*(a+b*x^(1/3))^2*x)+15/2/(a^2*(a+b*x^(1/3))*x)+_ + 15*b/(a^4*x^(2/3))-30*b^2/(a^5*x^(1/3))+30*b^3*log(a+b*x^(1/3))/a^6-_ + 10*b^3*log(x)/a^6 +--R +--R +--R (2) +--R 5 3+-+2 4 3+-+ 2 3 3+-+ +--R (60b x \|x + 120a b x\|x + 60a b x)log(b\|x + a) +--R + +--R 5 3 2 3+-+2 4 4 4 3+-+ +--R (- 20b x log(x) - 20a b )\|x + (- 40a b x log(x) - 60a b x + 5a b)\|x +--R + +--R 2 3 2 3 5 +--R - 20a b x log(x) - 90a b x - 2a +--R / +--R 6 2 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2a x +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 2 3 3+-+ +--R (60b x \|x + 120a b x\|x + 60a b x)log(b\|x + a) +--R + +--R 5 3+-+2 4 3+-+ 2 3 3+-+ 3 2 3+-+2 +--R (- 60b x \|x - 120a b x\|x - 60a b x)log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 60a b x + 5a b)\|x - 90a b x - 2a +--R / +--R 6 2 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2a x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 30b log(\|x ) + 10b log(x) +--R (4) ---------------------------- +--R 6 +--R a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1299 +r0:=(-14)/(a^3*x^2)+3/2/(a*(a+b*x^(1/3))^2*x^2)+12/(a^2*(a+b*x^(1/3))*x^2)+_ + 84/5*b/(a^4*x^(5/3))-21*b^2/(a^5*x^(4/3))+28*b^3/(a^6*x)-_ + 42*b^4/(a^7*x^(2/3))+84*b^5/(a^8*x^(1/3))-_ + 84*b^6*log(a+b*x^(1/3))/a^9+28*b^6*log(x)/a^9 +--R +--R +--R (2) +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (- 840b x \|x - 1680a b x \|x - 840a b x )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 +--R (280b x log(x) + 280a b x - 14a b )\|x +--R + +--R 7 2 7 2 4 4 7 3+-+ 2 6 2 +--R (560a b x log(x) + 840a b x - 70a b x + 8a b)\|x + 280a b x log(x) +--R + +--R 2 6 2 5 3 8 +--R 1260a b x + 28a b x - 5a +--R / +--R 9 2 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10a x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (- 840b x \|x - 1680a b x \|x - 840a b x )log(b\|x + a) +--R + +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (840b x \|x + 1680a b x \|x + 840a b x )log(\|x ) +--R + +--R 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ 2 6 2 +--R (280a b x - 14a b )\|x + (840a b x - 70a b x + 8a b)\|x + 1260a b x +--R + +--R 5 3 8 +--R 28a b x - 5a +--R / +--R 9 2 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10a x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 84b log(\|x ) - 28b log(x) +--R (4) -------------------------- +--R 9 +--R a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1299 +r0:=(-55/3)/(a^3*x^3)+3/2/(a*(a+b*x^(1/3))^2*x^3)+33/2/(a^2*_ + (a+b*x^(1/3))*x^3)+165/8*b/(a^4*x^(8/3))-165/7*b^2/_ + (a^5*x^(7/3))+55/2*b^3/(a^6*x^2)-33*b^4/(a^7*x^(5/3))+_ + 165/4*b^5/(a^8*x^(4/3))-55*b^6/(a^9*x)+165/2*b^7/(a^10*x^(2/3))-_ + 165*b^8/(a^11*x^(1/3))+165*b^9*log(a+b*x^(1/3))/a^12-55*b^9*log(x)/a^12 +--R +--R +--R (2) +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (27720b x \|x + 55440a b x \|x + 27720a b x )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (- 9240b x log(x) - 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 10 3 4 7 2 7 4 10 +--R (- 18480a b x log(x) - 27720a b x + 2310a b x - 264a b x + 77a b) +--R * +--R 3+-+ +--R \|x +--R + +--R 2 9 3 2 9 3 5 6 2 8 3 11 +--R - 9240a b x log(x) - 41580a b x - 924a b x + 165a b x - 56a +--R / +--R 12 2 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168a x +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (27720b x \|x + 55440a b x \|x + 27720a b x )log(b\|x + a) +--R + +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (- 27720b x \|x - 55440a b x \|x - 27720a b x )log(\|x ) +--R + +--R 3 8 2 6 5 9 2 3+-+2 +--R (- 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 27720a b x + 2310a b x - 264a b x + 77a b)\|x - 41580a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 165a b x - 56a +--R / +--R 12 2 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168a x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 165b log(\|x ) + 55b log(x) +--R (4) ----------------------------- +--R 12 +--R a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1299 +t0:=1/sqrt(1+x^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R |3+-+ +--R \|\|x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1299 +r0:=-4*(1+x^(1/3))^(3/2)+6/5*(1+x^(1/3))^(5/2)+6*sqrt(1+x^(1/3)) +--R +--R +--R +--------+ +--R 3+-+2 3+-+ |3+-+ +--R (6\|x - 8\|x + 16)\|\|x + 1 +--R (2) -------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3+-+2 3+-+ |3+-+ +--R (6\|x - 8\|x + 16)\|\|x + 1 +--R (3) -------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1299 +t0:=1/((1+x^(1/3))*x^(3/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-+3+-+ +-+ +--R x\|x \|x + x\|x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1299 +r0:=6/x^(1/6)+6*atan(x^(1/6))+(-2)/sqrt(x) +--R +--R +--R +-+6+-+ 6+-+ 6+-+ +-+ +--R 6\|x \|x atan(\|x ) - 2\|x + 6\|x +--R (2) ----------------------------------- +--R +-+6+-+ +--R \|x \|x +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 6+-+3 6+-+ 6+-+2 +--R 6\|x atan(\|x ) + 6\|x - 2 +--R (3) ----------------------------- +--R 6+-+3 +--R \|x +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1299 +m0:=a0-r0 +--R +--R +--R 6+-+3 +-+ +--R 2\|x - 2\|x +--R (4) -------------- +--R +-+6+-+3 +--R \|x \|x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1299 +t0:=x^(2/3)/(1+x^(1/3)) +--R +--R +--R 3+-+2 +--R \|x +--R (1) -------- +--R 3+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1299 +r0:=-3*x^(1/3)+3/2*x^(2/3)-x+3/4*x^(4/3)+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 12log(\|x + 1) + 6\|x + (3x - 12)\|x - 4x +--R (2) --------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 12log(\|x + 1) + 6\|x + (3x - 12)\|x - 4x +--R (3) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1299 +t0:=1/(1+x^(2/3)) +--R +--R +--R 1 +--R (1) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1299 +r0:=3*x^(1/3)-3*atan(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (2) - 3atan(\|x ) + 3\|x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3) - 3atan(\|x ) + 3\|x +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1299 +t0:=1/((1+x^(2/3))*x^(1/3)) +--R +--R +--R 1 +--R (1) -------- +--R 3+-+ +--R \|x + x +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1299 +r0:=3/2*log(1+x^(2/3)) +--R +--R +--R 3+-+2 +--R 3log(\|x + 1) +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 +--R 3log(\|x + 1) +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1299 +t0:=1/((1+x^(2/3))*x^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-+2 3+-+ +--R \|x + x\|x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1299 +r0:=3*atan(x^(1/3)) +--R +--R +--R 3+-+ +--R (2) 3atan(\|x ) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R (3) 3atan(\|x ) +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1299 +t0:=sqrt(-1+x^(2/3))/x^(1/3) +--R +--R +--R +---------+ +--R |3+-+2 +--R \|\|x - 1 +--R (1) ------------ +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1299 +r0:=(-1+x^(2/3))^(3/2) +--R +--R +--R +---------+ +--R 3+-+2 |3+-+2 +--R (2) (\|x - 1)\|\|x - 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 3+-+2 3+-+ 2 +--R (4x \|x + 3\|x - 7x)\|\|x - 1 + 6\|x - 9x\|x + 4x - 1 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 3+-+2 |3+-+2 3+-+ +--R (4\|x - 1)\|\|x - 1 - 3\|x + 4x +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1299 +t0:=(1+x^(2/3))^(3/2)/x^(1/3) +--R +--R +--R +---------+ +--R 3+-+2 |3+-+2 +--R (\|x + 1)\|\|x + 1 +--R (1) ----------------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1299 +r0:=3/5*(1+x^(2/3))^(5/2) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 +--R (6\|x + 3x\|x + 3)\|\|x + 1 +--R (2) --------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 +--R (6\|x + 3x\|x + 3)\|\|x + 1 +--R (3) --------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1299 +t0:=sqrt(x)/(1+x^(2/3)) +--R +--R +--R +-+ +--R \|x +--R (1) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1299 +r0:=-6*x^(1/6)+6/5*x^(5/6)-3*atan(1-x^(1/6)*sqrt(2))/sqrt(2)+_ + 3*atan(1+x^(1/6)*sqrt(2))/sqrt(2)-3/2*log(1+x^(1/3)-_ + x^(1/6)*sqrt(2))/sqrt(2)+3/2*log(1+x^(1/3)+x^(1/6)*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+6+-+ 3+-+ +-+6+-+ 3+-+ +--R 15log(\|2 \|x + \|x + 1) - 15log(- \|2 \|x + \|x + 1) +--R + +--R +-+6+-+ +-+6+-+ +-+6+-+5 +-+6+-+ +--R 30atan(\|2 \|x + 1) + 30atan(\|2 \|x - 1) + 12\|2 \|x - 60\|2 \|x +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 6+-+2 +-+6+-+ +-+ 6+-+2 +-+6+-+ +--R 15\|2 log(\|x + \|2 \|x + 1) - 15\|2 log(\|x - \|2 \|x + 1) +--R + +--R +-+ 1 +-+ 1 6+-+5 6+-+ +--R - 30\|2 atan(------------) - 30\|2 atan(------------) + 24\|x - 120\|x +--R +-+6+-+ +-+6+-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 6+-+2 +-+6+-+ 6+-+2 +-+6+-+ +--R 3log(\|x + \|2 \|x + 1) - 3log(\|x - \|2 \|x + 1) +--R + +--R +-+6+-+ 3+-+ +-+6+-+ 3+-+ +--R - 3log(\|2 \|x + \|x + 1) + 3log(- \|2 \|x + \|x + 1) +--R + +--R +-+6+-+ +-+6+-+ 1 +--R - 6atan(\|2 \|x + 1) - 6atan(\|2 \|x - 1) - 6atan(------------) +--R +-+6+-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 6atan(------------) +--R +-+6+-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1299 +t0:=x^(1/3)/(-1+x^(5/6)) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------- +--R 6+-+5 +--R \|x - 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1299 +r0a:=6/5*log(1-x^(1/6))-3/10*log(2+2*x^(1/3)+x^(1/6)*(1+sqrt(5)))*_ + (1-sqrt(5))-3/10*log(2+2*x^(1/3)+x^(1/6)*(1-sqrt(5)))*(1+sqrt(5))+_ + 2*sqrt(x)+3/5*atan((1+4*x^(1/6)-sqrt(5))/sqrt(10+2*sqrt(5)))*_ + sqrt(10-2*sqrt(5))-3/5*atan((1+4*x^(1/6)+sqrt(5))/sqrt(10-2*_ + sqrt(5)))*sqrt(10+2*sqrt(5)) +--R +--R +--R (2) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (3\|5 - 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 3\|5 - 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x + \|5 + 1 +--R - 6\|2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+ +--R 6\|- 2\|5 + 10 atan(----------------) + 20\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1299 +r0b:=6/5*log(1-x^(1/6))-3/10*log(2+2*_ + x^(1/3)+x^(1/6)*(1+sqrt(5)))*(1-sqrt(5))-3/10*log(2+2*x^(1/3)+_ + x^(1/6)*(1-sqrt(5)))*(1+sqrt(5))+2*sqrt(x)+6*atan((1+4*x^(1/6)-_ + sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-3/5*_ + atan(1/2*(1+4*x^(1/6)+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*sqrt(2*(5+sqrt(5))) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (3\|2 \|5 - 3\|2 )log((\|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 6+-+ +--R 12\|2 log(- \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (- 3\|2 \|5 - 3\|2 )log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +--------+ +--R +----------+ 6+-+ +-+ | +-+ +--R +-+ | +-+ (4\|x + \|5 + 1)\|\|5 + 5 +--R - 6\|2 \|2\|5 + 10 atan(-----------------------------) +--R +--+ +--R 2\|10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+ +-+ +--R 12\|- \|5 + 5 atan(----------------) + 20\|2 \|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--R 10%%BJ1 log(- 25%%BJ1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--R 10%%BJ0 log(- 25%%BJ0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 1299 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R 2 6+-+ +--R 10%%BJ1 log(- 25%%BJ1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 3\|5 + 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 12log(- \|x + 1) + (3\|5 + 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +----------+ 6+-+ +-+ +--R 2 6+-+ | +-+ 4\|x + \|5 + 1 +--R 10%%BJ0 log(- 25%%BJ0 + 36\|x ) + 6\|2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 6+-+3 +-+ +--R - 6\|- 2\|5 + 10 atan(----------------) + 20\|x - 20\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1299 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R +------------+ +--R +-+ | +-+ +-+3+-+6+-+4 +--R x\|5 \|- 2\|5 + 10 \|x \|x \|x +--R + +--R +------------+ +--R +-+ | +-+ +-+3+-+2 +--R - x\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+ +--R (- x - 2x)\|5 \|- 2\|5 + 10 \|x \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+2 +--R (x - x)\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ | +-+ +-+3+-+ 2 +-+ | +-+ +-+ +--R 2x \|5 \|- 2\|5 + 10 \|x \|x - x \|5 \|- 2\|5 + 10 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+2 +--R (x + 2x)\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +------------+ +--R +-+ | +-+ +-+3+-+ 3 2 +-+ | +-+ +-+ +--R x\|5 \|- 2\|5 + 10 \|x \|x + (x + x )\|5 \|- 2\|5 + 10 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ | +-+ +-+3+-+2 2 +-+ | +-+ +-+3+-+ +--R - 2x \|5 \|- 2\|5 + 10 \|x \|x - x \|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +--R 3 +-+ | +-+ +-+ +--R - x \|5 \|- 2\|5 + 10 \|x +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ 2 3+-+2 +--R ((40x - 8)\|x - 80x + 80x)\|x +--R + +--R 2 +-+ 3 2 3+-+ 2 +-+ 2 +--R ((- 4x - 8x)\|x - 40x - 80x + 40x)\|x + (8x - 8x)\|x + 40x +--R * +--R 6+-+5 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+2 +--R ((- 8x - 8x)\|x + 40x - 160x )\|x +--R + +--R 2 +-+ 3 2 3+-+ 2 +-+ 3 +--R ((8x - 8x)\|x + 40x - 80x )\|x + 8x \|x - 80x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ 3 3+-+2 2 +-+ 3 3+-+ +--R ((16x - 24x)\|x + 80x )\|x + ((- 32x - 8x)\|x + 40x )\|x +--R + +--R 2 +-+ 4 +--R - 8x \|x + 40x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ 3 2 +-+ +--R ((64x - 24x)\|x \|x + (40x + 48x - 8x)\|x \|x + (8x - 8x )\|x ) +--R * +--R 6+-+2 +--R \|x +--R + +--R 3 2 +-+3+-+2 +--R (- 40x + 104x - 24x)\|x \|x +--R + +--R 3 2 +-+ 2 3+-+ 3 2 +-+ +--R ((- 40x + 48x - 12x)\|x - 40x )\|x + (48x - 8x )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 3 2 +-+ 2 3+-+2 +--R ((- 80x + 24x - 32x)\|x + 40x )\|x +--R + +--R 3 2 +-+ 3 2 3+-+ 4 3 2 +-+ +--R ((- 40x + 16x )\|x + 80x + 40x )\|x + (- 40x + 8x - 8x )\|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ 6+-+5 +--R ((80x - 80x)\|x \|x + (40x + 80x - 40x)\|x \|x - 40x \|x )\|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ 6+-+4 +--R ((- 40x + 160x )\|x \|x + (- 40x + 80x )\|x \|x + 80x \|x )\|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 80x \|x \|x - 40x \|x \|x - 40x \|x )\|x + 40x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 40x \|x \|x + (- 80x - 40x )\|x \|x +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1299 +m0b:=a0-r0b +--R +--R +--R (7) +--R +-------------------------------------------------------------+ +--R +-+ | 2 2 +--R \|2 \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R +-+ +-+ +-+ +--R - 5\|2 %%BJ1 - 5\|2 %%BJ0 - 6\|2 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R +-+ +-+ +-+ +--R - 5\|2 %%BJ1 - 5\|2 %%BJ0 - 6\|2 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-+ 2 6+-+ +--R 10\|2 %%BJ1 log(- 25%%BJ1 + 36\|x ) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (- 3\|2 \|5 + 3\|2 )log((\|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 6+-+ +-+ 6+-+ +--R 12\|2 log(\|x - 1) - 12\|2 log(- \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (3\|2 \|5 + 3\|2 )log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 2 6+-+ +--R 10\|2 %%BJ0 log(- 25%%BJ0 + 36\|x ) +--R + +--R +--------+ +--R +----------+ 6+-+ +-+ | +-+ +--R +-+ | +-+ (4\|x + \|5 + 1)\|\|5 + 5 +--R 6\|2 \|2\|5 + 10 atan(-----------------------------) +--R +--+ +--R 2\|10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+6+-+3 +-+ +-+ +--R - 12\|- \|5 + 5 atan(----------------) + 20\|2 \|x - 20\|2 \|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1299 +d0b:=D(m0b,x) +--R +--R +--R (8) +--R +--+ +-+3+-+2 2 +--+ +-+ 6+-+5 +--R (4x\|10 \|x \|x + 2x \|10 \|x )\|x +--R + +--R +--+ +-+3+-+2 +-+ 2 +--+ +-+3+-+ 6+-+4 +--R (2x\|10 \|x \|x + (x\|5 + 2x + 3x)\|10 \|x \|x )\|x +--R + +--R +-+ 2 +--+ +-+3+-+2 +--R (- x\|5 - 2x + 3x)\|10 \|x \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+ 2 +--+ +-+ +--R ((- x - 2x)\|5 - 3x )\|10 \|x \|x + 2x \|10 \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+2 +--R ((x - x)\|5 - 3x - x)\|10 \|x \|x +--R + +--R 2 +-+ +--+ +-+3+-+ 2 +-+ 3 2 +--+ +-+ +--R (2x \|5 + 2x)\|10 \|x \|x + (- x \|5 - 2x - x )\|10 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+2 +--R ((x + 2x)\|5 + x )\|10 \|x \|x +--R + +--R +-+ 2 +--+ +-+3+-+ +--R (x\|5 - 2x - x)\|10 \|x \|x +--R + +--R 3 2 +-+ 3 2 +--+ +-+ +--R ((x + x )\|5 + x + x )\|10 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +--+ +-+3+-+2 +--R (- 2x \|5 - 4x)\|10 \|x \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+ 3 +-+ 3 2 +--+ +-+ +--R (- x \|5 + x - 2x)\|10 \|x \|x + (- x \|5 - x - 2x )\|10 \|x +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ +-+3+-+2 +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R (- x \|2 \|5 - 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+5 +--R \|x +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ +-+3+-+2 +--R (- x\|2 \|5 - 5x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((x - 4x)\|2 \|5 + (5x - 10x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- x - 5x)\|2 \|5 + (5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R (- x \|2 \|5 - 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((4x - 2x)\|2 \|5 + 10x \|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((5x - x)\|2 \|5 + (5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ 3 +-+ | +-+ +-+ +--R ((x - 2x )\|2 \|5 + 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ +-+ | +-+ +-+3+-+2 +--R ((2x + 5x)\|2 \|5 + 5x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((x + 3x)\|2 \|5 + (5x + 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ | +-+ +-+ +--R (2x + 2x )\|2 \|5 \|- \|5 + 5 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((- 5x + 2x)\|2 \|5 + (- 5x + 10x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- 3x + x)\|2 \|5 + (- 5x + 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R ((- 2x + x )\|2 \|5 + 5x \|2 )\|- \|5 + 5 \|x +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ 2 +--R ((40x - 8)\|5 + 200x - 40)\|x + (- 80x + 80x)\|5 - 400x +--R + +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ +--R ((- 4x - 8x)\|5 - 20x - 40x)\|x + (- 40x - 80x + 40x)\|5 +--R + +--R 3 2 +--R - 200x - 400x + 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((8x - 8x)\|5 + 40x - 40x)\|x + 40x \|5 + 200x +--R * +--R 6+-+5 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ 3 +--R ((- 8x - 8x)\|5 - 40x - 40x)\|x + (40x - 160x )\|5 + 200x +--R + +--R 2 +--R - 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ 3 +--R ((8x - 8x)\|5 + 40x - 40x)\|x + (40x - 80x )\|5 + 200x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 +--R (8x \|5 + 40x )\|x - 80x \|5 - 400x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 3+-+2 +--R (((16x - 24x)\|5 + 80x - 120x)\|x + 80x \|5 + 400x )\|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 3+-+ +--R (((- 32x - 8x)\|5 - 160x - 40x)\|x + 40x \|5 + 200x )\|x +--R + +--R 2 +-+ 2 +-+ 4 +-+ 4 +--R (- 8x \|5 - 40x )\|x + 40x \|5 + 200x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +-+3+-+2 +--R ((64x - 24x)\|5 + 320x - 120x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((40x + 48x - 8x)\|5 + 200x + 240x - 40x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((8x - 8x )\|5 + 40x - 40x )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+2 +--R ((- 40x + 104x - 24x)\|5 - 200x + 520x - 120x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+ 2 +-+ +--R ((- 40x + 48x - 12x)\|5 - 200x + 240x - 60x)\|x - 40x \|5 +--R + +--R 2 +--R - 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((48x - 8x )\|5 + 240x - 40x )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ 2 +-+ +--R ((- 80x + 24x - 32x)\|5 - 400x + 120x - 160x)\|x + 40x \|5 +--R + +--R 2 +--R 200x +--R * +--R 3+-+2 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ 3 2 +-+ 3 +--R ((- 40x + 16x )\|5 - 200x + 80x )\|x + (80x + 40x )\|5 + 400x +--R + +--R 2 +--R 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 4 3 2 +-+ 4 3 2 +-+ +--R ((- 40x + 8x - 8x )\|5 - 200x + 40x - 40x )\|x +--R / +--R 2 +-+ 2 +-+3+-+2 +--R ((80x - 80x)\|5 + 400x - 400x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((40x + 80x - 40x)\|5 + 200x + 400x - 200x)\|x \|x +--R + +--R 2 +-+ 2 +-+ +--R (- 40x \|5 - 200x )\|x +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+2 +--R ((- 40x + 160x )\|5 - 200x + 800x )\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ 3 +-+ 3 +-+ +--R ((- 40x + 80x )\|5 - 200x + 400x )\|x \|x + (80x \|5 + 400x )\|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+ 3 +-+3+-+2 3 +-+ 3 +-+3+-+ +--R (- 80x \|5 - 400x )\|x \|x + (- 40x \|5 - 200x )\|x \|x +--R + +--R 4 +-+ 4 +-+ +--R (- 40x \|5 - 200x )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +-+3+-+6+-+ 2 +-+ 2 +-+3+-+2 +--R (40x \|5 + 200x )\|x \|x \|x + (- 40x \|5 - 200x )\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((- 80x - 40x )\|5 - 400x - 200x )\|x \|x +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1299 +t0:=sqrt(3+(-1)/sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R (1) |--------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1299 +r0:=-1/6*atanh(sqrt(3+(-1)/sqrt(x))/sqrt(3))/sqrt(3)+_ + x*sqrt(3+(-1)/sqrt(x))-1/6*sqrt(x)*sqrt(3+(-1)/sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R |--------- +---------+ +--R | +-+ | +-+ +--R \| \|x +-+ +-+ +-+ |3\|x - 1 +--R - atanh(------------) + (- \|3 \|x + 6x\|3 ) |--------- +--R +-+ | +-+ +--R \|3 \| \|x +--R (2) --------------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +--R +-+ +-+ |3\|x - 1 +-+ +-+ +-+ +--R \|x log(6\|x |--------- - 6\|3 \|x + \|3 ) +--R | +-+ +--R \| \|x +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ +-+ |3\|x - 1 +--R (12x\|3 \|x - 2x\|3 ) |--------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +-+ +--R 12\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1299 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R +---------+ |--------- +--R | +-+ | +-+ +--R +-+ |3\|x - 1 +-+ +-+ +-+ \| \|x +--R log(6\|x |--------- - 6\|3 \|x + \|3 ) + 2atanh(------------) +--R | +-+ +-+ +--R \| \|x \|3 +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1299 +t0:=1/sqrt(1+1/sqrt(x)) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | +-+ +--R |\|x + 1 +--R |-------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1299 +r0:=3/2*atanh(sqrt(1+1/sqrt(x)))+x*sqrt(1+1/sqrt(x))-_ + 3/2*sqrt(x)*sqrt(1+1/sqrt(x)) +--R +--R +--R +--------+ +--------+ +--R | +-+ | +-+ +--R |\|x + 1 +-+ |\|x + 1 +--R 3atanh( |-------- ) + (- 3\|x + 2x) |-------- +--R | +-+ | +-+ +--R \| \|x \| \|x +--R (2) ----------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | +-+ | +-+ +--R +-+ |\|x + 1 +-+ |\|x + 1 +--R 3\|x log( |-------- + 1) - 3\|x log( |-------- - 1) +--R | +-+ | +-+ +--R \| \|x \| \|x +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|x + 1 +--R (4x\|x - 6x) |-------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +--R 4\|x +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1299 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R |\|x + 1 |\|x + 1 |\|x + 1 +--R 3log( |-------- + 1) - 3log( |-------- - 1) - 6atanh( |-------- ) +--R | +-+ | +-+ | +-+ +--R \| \|x \| \|x \| \|x +--R (4) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1299 +t0:=(a+b/x^(1/3))*x^4 +--R +--R +--R 4 3+-+ 4 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1299 +r0:=3/14*b*x^(14/3)+1/5*a*x^5 +--R +--R +--R 4 3+-+2 5 +--R 15b x \|x + 14a x +--R (2) -------------------- +--R 70 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+2 5 +--R 15b x \|x + 14a x +--R (3) -------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1299 +t0:=(a+b/x^(1/3))*x^3 +--R +--R +--R 3 3+-+ 3 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1299 +r0:=3/11*b*x^(11/3)+1/4*a*x^4 +--R +--R +--R 3 3+-+2 4 +--R 12b x \|x + 11a x +--R (2) -------------------- +--R 44 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+2 4 +--R 12b x \|x + 11a x +--R (3) -------------------- +--R 44 +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1299 +t0:=(a+b/x^(1/3))*x^2 +--R +--R +--R 2 3+-+ 2 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1299 +r0:=3/8*b*x^(8/3)+1/3*a*x^3 +--R +--R +--R 2 3+-+2 3 +--R 9b x \|x + 8a x +--R (2) ------------------ +--R 24 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3 +--R 9b x \|x + 8a x +--R (3) ------------------ +--R 24 +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1299 +t0:=(a+b/x^(1/3))*x +--R +--R +--R 3+-+ +--R a x\|x + b x +--R (1) ------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1299 +r0:=3/5*b*x^(5/3)+1/2*a*x^2 +--R +--R +--R 3+-+2 2 +--R 6b x \|x + 5a x +--R (2) ------------------ +--R 10 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 +--R 6b x \|x + 5a x +--R (3) ------------------ +--R 10 +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1299 +t0:=a+b/x^(1/3) +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1299 +r0:=3/2*b*x^(2/3)+a*x +--R +--R +--R 3+-+2 +--R 3b \|x + 2a x +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 +--R 3b \|x + 2a x +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1299 +t0:=(a+b/x^(1/3))/x +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1299 +r0:=-3*b/x^(1/3)+a*log(x) +--R +--R +--R 3+-+ +--R a log(x)\|x - 3b +--R (2) ----------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R 3a\|x log(\|x ) - 3b +--R (3) -------------------- +--R 3+-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1299 +t0:=(a+b/x^(1/3))/x^2 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 2 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1299 +r0:=-3/4*b/x^(4/3)-a/x +--R +--R +--R 3+-+ +--R - 4a\|x - 3b +--R (2) ------------- +--R 3+-+ +--R 4x\|x +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 4a\|x - 3b +--R (3) ------------- +--R 3+-+ +--R 4x\|x +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1299 +t0:=(a+b/x^(1/3))/x^3 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1299 +r0:=-3/7*b/x^(7/3)-1/2*a/x^2 +--R +--R +--R 3+-+ +--R - 7a\|x - 6b +--R (2) ------------- +--R 2 3+-+ +--R 14x \|x +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 7a\|x - 6b +--R (3) ------------- +--R 2 3+-+ +--R 14x \|x +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1299 +t0:=(a+b/x^(1/3))/x^4 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 4 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1299 +r0:=-3/10*b/x^(10/3)-1/3*a/x^3 +--R +--R +--R 3+-+ +--R - 10a\|x - 9b +--R (2) -------------- +--R 3 3+-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 10a\|x - 9b +--R (3) -------------- +--R 3 3+-+ +--R 30x \|x +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1299 +t0:=(a+b/x^(1/3))^2*x^4 +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1299 +r0:=3/13*b^2*x^(13/3)+3/7*a*b*x^(14/3)+1/5*a^2*x^5 +--R +--R +--R 4 3+-+2 2 4 3+-+ 2 5 +--R 195a b x \|x + 105b x \|x + 91a x +--R (2) ------------------------------------- +--R 455 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+2 2 4 3+-+ 2 5 +--R 195a b x \|x + 105b x \|x + 91a x +--R (3) ------------------------------------- +--R 455 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1299 +t0:=(a+b/x^(1/3))^2*x^3 +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1299 +r0:=3/10*b^2*x^(10/3)+6/11*a*b*x^(11/3)+1/4*a^2*x^4 +--R +--R +--R 3 3+-+2 2 3 3+-+ 2 4 +--R 120a b x \|x + 66b x \|x + 55a x +--R (2) ------------------------------------ +--R 220 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+2 2 3 3+-+ 2 4 +--R 120a b x \|x + 66b x \|x + 55a x +--R (3) ------------------------------------ +--R 220 +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1299 +t0:=(a+b/x^(1/3))^2*x^2 +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1299 +r0:=3/7*b^2*x^(7/3)+3/4*a*b*x^(8/3)+1/3*a^2*x^3 +--R +--R +--R 2 3+-+2 2 2 3+-+ 2 3 +--R 63a b x \|x + 36b x \|x + 28a x +--R (2) ----------------------------------- +--R 84 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 2 3+-+ 2 3 +--R 63a b x \|x + 36b x \|x + 28a x +--R (3) ----------------------------------- +--R 84 +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1299 +t0:=(a+b/x^(1/3))^2*x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a x \|x + 2a b x\|x + b x +--R (1) ---------------------------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1299 +r0:=3/4*b^2*x^(4/3)+6/5*a*b*x^(5/3)+1/2*a^2*x^2 +--R +--R +--R 3+-+2 2 3+-+ 2 2 +--R 24a b x \|x + 15b x\|x + 10a x +--R (2) ---------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 3+-+ 2 2 +--R 24a b x \|x + 15b x\|x + 10a x +--R (3) ---------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1299 +t0:=(a+b/x^(1/3))^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1299 +r0:=(b+a*x^(1/3))^3/a +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (2) --------------------------------- +--R a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 3+-+ 2 +--R (3) 3a b \|x + 3b \|x + a x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1299 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1299 +t0:=(a+b/x^(1/3))^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1299 +r0:=-3/2*b^2/x^(2/3)-6*a*b/x^(1/3)+a^2*log(x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 2a log(x)\|x - 12a b\|x - 3b +--R (2) -------------------------------- +--R 3+-+2 +--R 2\|x +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 3+-+ 2 +--R 6a \|x log(\|x - 12a b\|x - 3b +--R (3) ----------------------------------- +--R 3+-+2 +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1299 +t0:=(a+b/x^(1/3))^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 2 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1299 +r0:=-3/5*b^2/x^(5/3)-3/2*a*b/x^(4/3)-a^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 10a \|x - 15a b\|x - 6b +--R (2) ----------------------------- +--R 3+-+2 +--R 10x \|x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 10a \|x - 15a b\|x - 6b +--R (3) ----------------------------- +--R 3+-+2 +--R 10x \|x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1299 +t0:=(a+b/x^(1/3))^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1299 +r0:=-3/8*b^2/x^(8/3)-6/7*a*b/x^(7/3)-1/2*a^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 28a \|x - 48a b\|x - 21b +--R (2) ------------------------------ +--R 2 3+-+2 +--R 56x \|x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 28a \|x - 48a b\|x - 21b +--R (3) ------------------------------ +--R 2 3+-+2 +--R 56x \|x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1299 +t0:=(a+b/x^(1/3))^2/x^4 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 4 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1299 +r0:=-3/11*b^2/x^(11/3)-3/5*a*b/x^(10/3)-1/3*a^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 55a \|x - 99a b\|x - 45b +--R (2) ------------------------------ +--R 3 3+-+2 +--R 165x \|x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 55a \|x - 99a b\|x - 45b +--R (3) ------------------------------ +--R 3 3+-+2 +--R 165x \|x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1299 +t0:=(a+b/x^(1/3))^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R (1) 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1299 +r0:=1/4*b^3*x^4+9/13*a*b^2*x^(13/3)+9/14*a^2*b*x^(14/3)+1/5*a^3*x^5 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364a x + 455b x +--R (2) ---------------------------------------------------- +--R 1820 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364a x + 455b x +--R (3) ---------------------------------------------------- +--R 1820 +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1299 +t0:=(a+b/x^(1/3))^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R (1) 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1299 +r0:=1/3*b^3*x^3+9/10*a*b^2*x^(10/3)+9/11*a^2*b*x^(11/3)+1/4*a^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165a x + 220b x +--R (2) -------------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165a x + 220b x +--R (3) -------------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1299 +t0:=(a+b/x^(1/3))^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R (1) 3a b x \|x + 3a b x\|x + a x + b x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1299 +r0:=1/2*b^3*x^2+9/7*a*b^2*x^(7/3)+9/8*a^2*b*x^(8/3)+1/3*a^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56a x + 84b x +--R (2) ------------------------------------------------ +--R 168 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56a x + 84b x +--R (3) ------------------------------------------------ +--R 168 +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1299 +t0:=(a+b/x^(1/3))^3*x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R (1) 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1299 +r0:=b^3*x+9/4*a*b^2*x^(4/3)+9/5*a^2*b*x^(5/3)+1/2*a^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10a x + 20b x +--R (2) -------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10a x + 20b x +--R (3) -------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1299 +t0:=(a+b/x^(1/3))^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1299 +r0:=9*a*b^2*x^(1/3)+9/2*a^2*b*x^(2/3)+a^3*x+b^3*log(x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 9a b \|x + 18a b \|x + 2b log(x) + 2a x +--R (2) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b log(\|x ) + 9a b \|x + 18a b \|x + 2a x +--R (3) --------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1299 +t0:=(a+b/x^(1/3))^3/x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1299 +r0:=-b^3/x-9/2*a*b^2/x^(2/3)-9*a^2*b/x^(1/3)+a^3*log(x) +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (2a x log(x) - 2b )\|x - 18a b x\|x - 9a b x +--R (2) ----------------------------------------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6a x log(\|x ) - 18a b \|x - 9a b \|x - 2b +--R (3) ---------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 533 + +)clear all + +--S 534 of 1299 +t0:=(a+b/x^(1/3))^3/x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1299 +r0:=-1/2*b^3/x^2-9/5*a*b^2/x^(5/3)-9/4*a^2*b/x^(4/3)-a^3/x +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 20a x - 10b )\|x - 45a b x\|x - 36a b x +--R (2) --------------------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 45a b \|x - 36a b \|x - 20a x - 10b +--R (3) ----------------------------------------- +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1299 +t0:=(a+b/x^(1/3))^3/x^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1299 +r0:=-1/3*b^3/x^3-9/8*a*b^2/x^(8/3)-9/7*a^2*b/x^(7/3)-1/2*a^3/x^2 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 84a x - 56b )\|x - 216a b x\|x - 189a b x +--R (2) ----------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 216a b \|x - 189a b \|x - 84a x - 56b +--R (3) ------------------------------------------- +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1299 +t0:=(a+b/x^(1/3))^3/x^4 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1299 +r0:=-1/4*b^3/x^4-9/11*a*b^2/x^(11/3)-9/10*a^2*b/x^(10/3)-1/3*a^3/x^3 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 220a x - 165b )\|x - 594a b x\|x - 540a b x +--R (2) ------------------------------------------------- +--R 4 3+-+2 +--R 660x \|x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 594a b \|x - 540a b \|x - 220a x - 165b +--R (3) --------------------------------------------- +--R 4 +--R 660x +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 548 + +)clear all + +--S 549 of 1299 +t0:=x^2/(a+b/x^(1/3)) +--R +--R +--R 2 3+-+ +--R x \|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1299 +r0:=3*b^8*x^(1/3)/a^9-3/2*b^7*x^(2/3)/a^8+b^6*x/a^7-3/4*b^5*x^(4/3)/_ + a^6+3/5*b^4*x^(5/3)/a^5-1/2*b^3*x^2/a^4+3/7*b^2*x^(7/3)/a^3-_ + 3/8*b*x^(8/3)/a^2+1/3*x^3/a-3*b^9*log(b+a*x^(1/3))/a^10 +--R +--R +--R (2) +--R 9 3+-+ 8 2 5 4 2 7 3+-+2 +--R - 2520b log(a\|x + b) + (- 315a b x + 504a b x - 1260a b )\|x +--R + +--R 7 2 2 4 5 8 3+-+ 9 3 6 3 2 3 6 +--R (360a b x - 630a b x + 2520a b )\|x + 280a x - 420a b x + 840a b x +--R / +--R 10 +--R 840a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3+-+ 8 2 5 4 2 7 3+-+2 +--R - 2520b log(a\|x + b) + (- 315a b x + 504a b x - 1260a b )\|x +--R + +--R 7 2 2 4 5 8 3+-+ 9 3 6 3 2 3 6 +--R (360a b x - 630a b x + 2520a b )\|x + 280a x - 420a b x + 840a b x +--R / +--R 10 +--R 840a +--R Type: Union(Expression(Integer),...) +--E 551 + +--S 552 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 1299 +t0:=x/(a+b/x^(1/3)) +--R +--R +--R 3+-+ +--R x\|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1299 +r0:=-3*b^5*x^(1/3)/a^6+3/2*b^4*x^(2/3)/a^5-b^3*x/a^4+_ + 3/4*b^2*x^(4/3)/a^3-3/5*b*x^(5/3)/a^2+1/2*x^2/a+3*b^6*_ + log(b+a*x^(1/3))/a^7 +--R +--R +--R (2) +--R 6 3+-+ 5 2 4 3+-+2 4 2 5 3+-+ +--R 60b log(a\|x + b) + (- 12a b x + 30a b )\|x + (15a b x - 60a b )\|x +--R + +--R 6 2 3 3 +--R 10a x - 20a b x +--R / +--R 7 +--R 20a +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3+-+ 5 2 4 3+-+2 4 2 5 3+-+ +--R 60b log(a\|x + b) + (- 12a b x + 30a b )\|x + (15a b x - 60a b )\|x +--R + +--R 6 2 3 3 +--R 10a x - 20a b x +--R / +--R 7 +--R 20a +--R Type: Union(Expression(Integer),...) +--E 556 + +--S 557 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1299 +t0:=1/(a+b/x^(1/3)) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1299 +r0:=3*b^2*x^(1/3)/a^3-3/2*b*x^(2/3)/a^2+x/a-3*b^3*log(b+a*x^(1/3))/a^4 +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R - 6b log(a\|x + b) - 3a b \|x + 6a b \|x + 2a x +--R (2) --------------------------------------------------- +--R 4 +--R 2a +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R - 6b log(a\|x + b) - 3a b \|x + 6a b \|x + 2a x +--R (3) --------------------------------------------------- +--R 4 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 561 + +--S 562 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 563 + +)clear all + +--S 564 of 1299 +t0:=1/((a+b/x^(1/3))*x) +--R +--R +--R 3+-+ +--R \|x +--R (1) ------------- +--R 3+-+ +--R a x\|x + b x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1299 +r0:=3*log(b+a*x^(1/3))/a +--R +--R +--R 3+-+ +--R 3log(a\|x + b) +--R (2) --------------- +--R a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R 3log(a\|x + b) +--R (3) --------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 566 + +--S 567 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 568 + +)clear all + +--S 569 of 1299 +t0:=1/((a+b/x^(1/3))*x^2) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 2 3+-+ 2 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1299 +r0:=(-3/2)/(b*x^(2/3))+3*a/(b^2*x^(1/3))-3*a^2*log(b+a*x^(1/3))/b^3+_ + a^2*log(x)/b^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+2 3+-+ 2 +--R - 6a \|x log(a\|x + b + 2a log(x)\|x + 6a b\|x - 3b +--R (2) ---------------------------------------------------------- +--R 3 3+-+2 +--R 2b \|x +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+2 3+-+ 3+-+ 2 +--R - 6a \|x log(a\|x + b + 6a \|x log(\|x + 6a b\|x - 3b +--R (3) ------------------------------------------------------------- +--R 3 3+-+2 +--R 2b \|x +--R Type: Union(Expression(Integer),...) +--E 571 + +--S 572 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R 3a log(\|x ) - a log(x) +--R (4) ----------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1299 +t0:=1/((a+b/x^(1/3))*x^3) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 3 3+-+ 3 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1299 +r0:=(-3/5)/(b*x^(5/3))+3/4*a/(b^2*x^(4/3))-a^2/(b^3*x)+_ + 3/2*a^3/(b^4*x^(2/3))-3*a^4/(b^5*x^(1/3))+_ + 3*a^5*log(b+a*x^(1/3))/b^6-a^5*log(x)/b^6 +--R +--R +--R (2) +--R 5 3+-+2 3+-+ 5 2 3 3+-+2 +--R 60a x \|x log(a\|x + b) + (- 20a x log(x) - 20a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 15a b )\|x + 30a b x - 12b +--R / +--R 6 3+-+2 +--R 20b x \|x +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 3+-+ 5 3+-+2 3+-+ 2 3 3+-+2 +--R 60a x \|x log(a\|x + b) - 60a x \|x log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 15a b )\|x + 30a b x - 12b +--R / +--R 6 3+-+2 +--R 20b x \|x +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1299 +m0:=a0-r0 +--R +--R +--R 5 3+-+ 5 +--R - 3a log(\|x ) + a log(x) +--R (4) ------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1299 +t0:=1/((a+b/x^(1/3))*x^4) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 4 3+-+ 4 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1299 +r0:=(-3/8)/(b*x^(8/3))+3/7*a/(b^2*x^(7/3))-1/2*a^2/(b^3*x^2)+_ + 3/5*a^3/(b^4*x^(5/3))-3/4*a^4/(b^5*x^(4/3))+a^5/(b^6*x)-_ + 3/2*a^6/(b^7*x^(2/3))+3*a^7/(b^8*x^(1/3))-_ + 3*a^8*log(b+a*x^(1/3))/b^9+a^8*log(x)/b^9 +--R +--R +--R (2) +--R 8 2 3+-+2 3+-+ 8 2 5 3 2 6 3+-+2 +--R - 840a x \|x log(a\|x + b + (280a x log(x) + 280a b x - 140a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 6 2 2 3 5 8 +--R (840a b x - 210a b x + 120a b )\|x - 420a b x + 168a b x - 105b +--R / +--R 9 2 3+-+2 +--R 280b x \|x +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 3+-+ 8 2 3+-+2 3+-+ +--R - 840a x \|x log(a\|x + b + 840a x \|x log(\|x ) +--R + +--R 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (280a b x - 140a b )\|x + (840a b x - 210a b x + 120a b )\|x +--R + +--R 6 2 2 3 5 8 +--R - 420a b x + 168a b x - 105b +--R / +--R 9 2 3+-+2 +--R 280b x \|x +--R Type: Union(Expression(Integer),...) +--E 581 + +--S 582 of 1299 +m0:=a0-r0 +--R +--R +--R 8 3+-+ 8 +--R 3a log(\|x ) - a log(x) +--R (4) ----------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +)clear all + +--S 584 of 1299 +t0:=1/((a+b/x^(1/3))*x^5) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 5 3+-+ 5 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1299 +r0:=(-3/11)/(b*x^(11/3))+3/10*a/(b^2*x^(10/3))-1/3*a^2/(b^3*x^3)+_ + 3/8*a^3/(b^4*x^(8/3))-3/7*a^4/(b^5*x^(7/3))+1/2*a^5/(b^6*x^2)-_ + 3/5*a^6/(b^7*x^(5/3))+3/4*a^7/(b^8*x^(4/3))-a^8/(b^9*x)+_ + 3/2*a^9/(b^10*x^(2/3))-3*a^10/(b^11*x^(1/3))+_ + 3*a^11*log(b+a*x^(1/3))/b^12-a^11*log(x)/b^12 +--R +--R +--R (2) +--R 11 3 3+-+2 3+-+ +--R 27720a x \|x log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a x log(x) - 9240a b x + 4620a b x - 3080a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 6930a b x - 3960a b x + 2772a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 5544a b x + 3465a b x - 2520b +--R / +--R 12 3 3+-+2 +--R 9240b x \|x +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 3+-+ 11 3 3+-+2 3+-+ +--R 27720a x \|x log(a\|x + b - 27720a x \|x log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a b x + 4620a b x - 3080a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 6930a b x - 3960a b x + 2772a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 5544a b x + 3465a b x - 2520b +--R / +--R 12 3 3+-+2 +--R 9240b x \|x +--R Type: Union(Expression(Integer),...) +--E 586 + +--S 587 of 1299 +m0:=a0-r0 +--R +--R +--R 11 3+-+ 11 +--R - 3a log(\|x ) + a log(x) +--R (4) --------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1299 +t0:=x^2/(a+b/x^(1/3))^2 +--R +--R +--R 2 3+-+2 +--R x \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1299 +r0:=-3*b^10/(a^11*(b+a*x^(1/3)))+27*b^8*x^(1/3)/a^10-12*b^7*x^(2/3)/a^9+_ + 7*b^6*x/a^8-9/2*b^5*x^(4/3)/a^7+3*b^4*x^(5/3)/a^6-2*b^3*x^2/a^5+_ + 9/7*b^2*x^(7/3)/a^4-3/4*b*x^(8/3)/a^3+1/3*x^3/a^2-_ + 30*b^9*log(b+a*x^(1/3))/a^11 +--R +--R +--R (2) +--R 9 3+-+ 10 3+-+ +--R (- 2520a b \|x - 2520b )log(a\|x + b) +--R + +--R 8 2 2 5 5 2 8 3+-+2 +--R (45a b x - 126a b x + 1260a b )\|x +--R + +--R 10 3 7 3 2 4 6 9 3+-+ 9 3 6 4 2 +--R (28a x - 60a b x + 210a b x + 2268a b )\|x - 35a b x + 84a b x +--R + +--R 3 7 10 +--R - 420a b x - 252b +--R / +--R 12 3+-+ 11 +--R 84a \|x + 84a b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3+-+ 10 3+-+ +--R (- 2520a b \|x - 2520b )log(a\|x + b) +--R + +--R 8 2 2 5 5 2 8 3+-+2 +--R (45a b x - 126a b x + 1260a b )\|x +--R + +--R 10 3 7 3 2 4 6 9 3+-+ 9 3 6 4 2 +--R (28a x - 60a b x + 210a b x + 2268a b )\|x - 35a b x + 84a b x +--R + +--R 3 7 10 +--R - 420a b x - 252b +--R / +--R 12 3+-+ 11 +--R 84a \|x + 84a b +--R Type: Union(Expression(Integer),...) +--E 591 + +--S 592 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 1299 +t0:=x/(a+b/x^(1/3))^2 +--R +--R +--R 3+-+2 +--R x \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1299 +r0:=3*b^7/(a^8*(b+a*x^(1/3)))-18*b^5*x^(1/3)/a^7+15/2*b^4*x^(2/3)/a^6-_ + 4*b^3*x/a^5+9/4*b^2*x^(4/3)/a^4-6/5*b*x^(5/3)/a^3+1/2*x^2/a^2+_ + 21*b^6*log(b+a*x^(1/3))/a^8 +--R +--R +--R (2) +--R 6 3+-+ 7 3+-+ 5 2 2 5 3+-+2 +--R (420a b \|x + 420b )log(a\|x + b) + (21a b x - 210a b )\|x +--R + +--R 7 2 4 3 6 3+-+ 6 2 3 4 7 +--R (10a x - 35a b x - 360a b )\|x - 14a b x + 70a b x + 60b +--R / +--R 9 3+-+ 8 +--R 20a \|x + 20a b +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3+-+ 7 3+-+ 5 2 2 5 3+-+2 +--R (420a b \|x + 420b )log(a\|x + b) + (21a b x - 210a b )\|x +--R + +--R 7 2 4 3 6 3+-+ 6 2 3 4 7 +--R (10a x - 35a b x - 360a b )\|x - 14a b x + 70a b x + 60b +--R / +--R 9 3+-+ 8 +--R 20a \|x + 20a b +--R Type: Union(Expression(Integer),...) +--E 596 + +--S 597 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1299 +t0:=1/(a+b/x^(1/3))^2 +--R +--R +--R 3+-+2 +--R \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1299 +r0:=-3*b^4/(a^5*(b+a*x^(1/3)))+9*b^2*x^(1/3)/a^4-3*b*x^(2/3)/a^3+_ + x/a^2-12*b^3*log(b+a*x^(1/3))/a^5 +--R +--R +--R (2) +--R 3 3+-+ 4 3+-+ 2 2 3+-+2 4 3 3+-+ +--R (- 12a b \|x - 12b )log(a\|x + b) + 6a b \|x + (a x + 9a b )\|x +--R + +--R 3 4 +--R - 2a b x - 3b +--R / +--R 6 3+-+ 5 +--R a \|x + a b +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3+-+ 4 3+-+ 2 2 3+-+2 4 3 3+-+ +--R (- 12a b \|x - 12b )log(a\|x + b) + 6a b \|x + (a x + 9a b )\|x +--R + +--R 3 4 +--R - 2a b x - 3b +--R / +--R 6 3+-+ 5 +--R a \|x + a b +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1299 +t0:=1/((a+b/x^(1/3))^2*x) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ---------------------------- +--R 2 3+-+2 3+-+ 2 +--R a x \|x + 2a b x\|x + b x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1299 +r0:=3*b/(a^2*(b+a*x^(1/3)))+3*log(b+a*x^(1/3))/a^2 +--R +--R +--R 3+-+ 3+-+ +--R (3a\|x + 3b)log(a\|x + b) + 3b +--R (2) -------------------------------- +--R 3 3+-+ 2 +--R a \|x + a b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3a\|x + 3b)log(a\|x + b) + 3b +--R (3) -------------------------------- +--R 3 3+-+ 2 +--R a \|x + a b +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^2) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 2 3+-+2 2 3+-+ 2 2 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1299 +r0:=(-6)/(b^2*x^(1/3))+3/(b*(b+a*x^(1/3))*x^(1/3))+_ + 6*a*log(b+a*x^(1/3))/b^3-2*a*log(x)/b^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 3+-+ 2 3+-+2 +--R (6a \|x + 6a b\|x )log(a\|x + b) - 2a log(x)\|x +--R + +--R 3+-+ 2 +--R (- 2a b log(x) - 6a b)\|x - 3b +--R / +--R 3 3+-+2 4 3+-+ +--R a b \|x + b \|x +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 3+-+ 2 3+-+2 3+-+ 3+-+ +--R (6a \|x + 6a b\|x )log(a\|x + b) + (- 6a \|x - 6a b\|x )log(\|x ) +--R + +--R 3+-+ 2 +--R - 6a b\|x - 3b +--R / +--R 3 3+-+2 4 3+-+ +--R a b \|x + b \|x +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R - 6a log(\|x ) + 2a log(x) +--R (4) -------------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^3) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 3 3+-+2 3 3+-+ 2 3 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1299 +r0:=(-15/4)/(b^2*x^(4/3))+3/(b*(b+a*x^(1/3))*x^(4/3))+_ + 5*a/(b^3*x)-15/2*a^2/(b^4*x^(2/3))+15*a^3/(b^5*x^(1/3))-_ + 15*a^4*log(b+a*x^(1/3))/b^6+5*a^4*log(x)/b^6 +--R +--R +--R (2) +--R 5 2 3+-+ 4 2 3+-+ 3 2 5 3+-+2 +--R (- 60a x \|x - 60a b x )log(a\|x + b) + (30a b x - 3b )\|x +--R + +--R 5 2 2 3 3+-+ 4 2 4 2 4 +--R (20a x log(x) - 10a b x)\|x + 20a b x log(x) + 60a b x + 5a b x +--R / +--R 6 2 3+-+ 7 2 +--R 4a b x \|x + 4b x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 3+-+ +--R (- 60a x \|x - 60a b x\|x )log(a\|x + b) +--R + +--R 5 3+-+2 4 3+-+ 3+-+ 2 3 3+-+2 +--R (60a x \|x + 60a b x\|x )log(\|x ) - 10a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (60a b x + 5a b )\|x + 30a b x - 3b +--R / +--R 6 3+-+2 7 3+-+ +--R 4a b x \|x + 4b x\|x +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1299 +m0:=a0-r0 +--R +--R +--R 4 3+-+ 4 +--R 15a log(\|x ) - 5a log(x) +--R (4) ------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^4) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 4 3+-+2 4 3+-+ 2 4 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1299 +r0:=(-24/7)/(b^2*x^(7/3))+3/(b*(b+a*x^(1/3))*x^(7/3))+4*a/(b^3*x^2)-_ + 24/5*a^2/(b^4*x^(5/3))+6*a^3/(b^5*x^(4/3))-8*a^4/(b^6*x)+_ + 12*a^5/(b^7*x^(2/3))-24*a^6/(b^8*x^(1/3))+_ + 24*a^7*log(b+a*x^(1/3))/b^9-8*a^7*log(x)/b^9 +--R +--R +--R (2) +--R 8 3 3+-+ 7 3 3+-+ +--R (840a x \|x + 840a b x )log(a\|x + b) +--R + +--R 6 2 2 3 5 8 3+-+2 +--R (- 420a b x + 42a b x - 15b )\|x +--R + +--R 8 3 5 3 2 2 6 3+-+ 7 3 7 3 +--R (- 280a x log(x) + 140a b x - 28a b x)\|x - 280a b x log(x) - 840a b x +--R + +--R 4 4 2 7 +--R - 70a b x + 20a b x +--R / +--R 9 3 3+-+ 10 3 +--R 35a b x \|x + 35b x +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 3+-+ +--R (840a x \|x + 840a b x \|x)log(a\|x + b) +--R + +--R 8 2 3+-+2 7 2 3+-+ 3+-+ 5 3 2 6 3+-+2 +--R (- 840a x \|x - 840a b x \|x)log(\|x ) + (140a b x - 28a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 6 2 2 3 5 8 +--R (- 840a b x - 70a b x + 20a b )\|x - 420a b x + 42a b x - 15b +--R / +--R 9 2 3+-+2 10 2 3+-+ +--R 35a b x \|x + 35b x \|x +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1299 +m0:=a0-r0 +--R +--R +--R 7 3+-+ 7 +--R - 24a log(\|x ) + 8a log(x) +--R (4) --------------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^5) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 5 3+-+2 5 3+-+ 2 5 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1299 +r0:=(-33/10)/(b^2*x^(10/3))+3/(b*(b+a*x^(1/3))*x^(10/3))+_ + 11/3*a/(b^3*x^3)-33/8*a^2/(b^4*x^(8/3))+33/7*a^3/(b^5*x^(7/3))-_ + 11/2*a^4/(b^6*x^2)+33/5*a^5/(b^7*x^(5/3))-33/4*a^6/(b^8*x^(4/3))+_ + 11*a^7/(b^9*x)-33/2*a^8/(b^10*x^(2/3))+_ + 33*a^9/(b^11*x^(1/3))-33*a^10*log(b+a*x^(1/3))/b^12+11*a^10*log(x)/b^12 +--R +--R +--R (2) +--R 11 4 3+-+ 10 4 3+-+ +--R (- 27720a x \|x - 27720a b x )log(a\|x + b) +--R + +--R 9 2 3 6 5 2 3 8 11 3+-+2 +--R (13860a b x - 1386a b x + 495a b x - 252b )\|x +--R + +--R 11 4 8 3 3 5 6 2 2 9 3+-+ +--R (9240a x log(x) - 4620a b x + 924a b x - 385a b x)\|x +--R + +--R 10 4 10 4 7 4 3 4 7 2 10 +--R 9240a b x log(x) + 27720a b x + 2310a b x - 660a b x + 308a b x +--R / +--R 12 4 3+-+ 13 4 +--R 840a b x \|x + 840b x +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 3+-+ +--R (- 27720a x \|x - 27720a b x \|x)log(a\|x + b) +--R + +--R 11 3 3+-+2 10 3 3+-+ 3+-+ +--R (27720a x \|x + 27720a b x \|x)log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 4620a b x + 924a b x - 385a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (27720a b x + 2310a b x - 660a b x + 308a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 1386a b x + 495a b x - 252b +--R / +--R 12 3 3+-+2 13 3 3+-+ +--R 840a b x \|x + 840b x \|x +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1299 +m0:=a0-r0 +--R +--R +--R 10 3+-+ 10 +--R 33a log(\|x ) - 11a log(x) +--R (4) ---------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1299 +t0:=x^2/(a+b/x^(1/3))^3 +--R +--R +--R 3 +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1299 +r0:=3/2*b^11/(a^12*(b+a*x^(1/3))^2)-33*b^10/(a^12*(b+a*x^(1/3)))+_ + 135*b^8*x^(1/3)/a^11-54*b^7*x^(2/3)/a^10+28*b^6*x/a^9-_ + 63/4*b^5*x^(4/3)/a^8+9*b^4*x^(5/3)/a^7-5*b^3*x^2/a^6+_ + 18/7*b^2*x^(7/3)/a^5-9/8*b*x^(8/3)/a^4+1/3*x^3/a^3-_ + 165*b^9*log(b+a*x^(1/3))/a^12 +--R +--R +--R (2) +--R 2 9 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b \|x - 27720b )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (56a x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b )\|x + 110a b x +--R + +--R 6 5 2 3 8 11 +--R - 462a b x + 9240a b x - 5292b +--R / +--R 14 3+-+2 13 3+-+ 12 2 +--R 168a \|x + 336a b\|x + 168a b +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b \|x - 27720b )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (56a x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b )\|x + 110a b x +--R + +--R 6 5 2 3 8 11 +--R - 462a b x + 9240a b x - 5292b +--R / +--R 14 3+-+2 13 3+-+ 12 2 +--R 168a \|x + 336a b\|x + 168a b +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1299 +t0:=x/(a+b/x^(1/3))^3 +--R +--R +--R 2 +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1299 +r0:=-3/2*b^8/(a^9*(b+a*x^(1/3))^2)+24*b^7/(a^9*(b+a*x^(1/3)))-_ + 63*b^5*x^(1/3)/a^8+45/2*b^4*x^(2/3)/a^7-10*b^3*x/a^6+_ + 9/2*b^2*x^(4/3)/a^5-9/5*b*x^(5/3)/a^4+1/2*x^2/a^3+_ + 84*b^6*log(b+a*x^(1/3))/a^9 +--R +--R +--R (2) +--R 2 6 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b \|x + 840b )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (5a x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b )\|x +--R + +--R 6 2 2 3 5 8 +--R 14a b x - 280a b x + 225b +--R / +--R 11 3+-+2 10 3+-+ 9 2 +--R 10a \|x + 20a b\|x + 10a b +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b \|x + 840b )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (5a x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b )\|x +--R + +--R 6 2 2 3 5 8 +--R 14a b x - 280a b x + 225b +--R / +--R 11 3+-+2 10 3+-+ 9 2 +--R 10a \|x + 20a b\|x + 10a b +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 1299 +t0:=1/(a+b/x^(1/3))^3 +--R +--R +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1299 +r0:=3/2*b^5/(a^6*(b+a*x^(1/3))^2)-15*b^4/(a^6*(b+a*x^(1/3)))+_ + 18*b^2*x^(1/3)/a^5-9/2*b*x^(2/3)/a^4+x/a^3-30*b^3*log(b+a*x^(1/3))/a^6 +--R +--R +--R (2) +--R 2 3 3+-+2 4 3+-+ 5 3+-+ 5 2 3 3+-+2 +--R (- 60a b \|x - 120a b \|x - 60b )log(a\|x + b) + (2a x + 63a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 5a b x + 6a b )\|x + 20a b x - 27b +--R / +--R 8 3+-+2 7 3+-+ 6 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3+-+2 4 3+-+ 5 3+-+ 5 2 3 3+-+2 +--R (- 60a b \|x - 120a b \|x - 60b )log(a\|x + b) + (2a x + 63a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 5a b x + 6a b )\|x + 20a b x - 27b +--R / +--R 8 3+-+2 7 3+-+ 6 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +)clear all + +--S 644 of 1299 +t0:=1/((a+b/x^(1/3))^3*x) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1299 +r0:=-3/2*b^2/(a^3*(b+a*x^(1/3))^2)+6*b/(a^3*(b+a*x^(1/3)))+_ + 3*log(b+a*x^(1/3))/a^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(a\|x + b) + 12a b\|x + 9b +--R (2) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 3 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(a\|x + b) + 12a b\|x + 9b +--R (3) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 3 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 646 + +--S 647 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^2) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 3a b x \|x + 3a b x\|x + a x + b x +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1299 +r0:=3/2/(b*(b+a*x^(1/3))^2)+3/(b^2*(b+a*x^(1/3)))-_ + 3*log(b+a*x^(1/3))/b^3+log(x)/b^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 2 3+-+ 2 3+-+2 +--R (- 6a \|x - 12a b\|x - 6b )log(a\|x + b) + 2a log(x)\|x +--R + +--R 3+-+ 2 2 +--R (4a b log(x) + 6a b)\|x + 2b log(x) + 9b +--R / +--R 2 3 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b \|x + 2b +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 2 3+-+ +--R (- 6a \|x - 12a b\|x - 6b )log(a\|x + b) +--R + +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(\|x ) + 6a b\|x + 9b +--R / +--R 2 3 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b \|x + 2b +--R Type: Union(Expression(Integer),...) +--E 651 + +--S 652 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 653 + +)clear all + +--S 654 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1299 +r0:=(-10)/(b^3*x)+3/2/(b*(b+a*x^(1/3))^2*x)+15/2/(b^2*(b+a*x^(1/3))*x)+_ + 15*a/(b^4*x^(2/3))-30*a^2/(b^5*x^(1/3))+30*a^3*_ + log(b+a*x^(1/3))/b^6-10*a^3*log(x)/b^6 +--R +--R +--R (2) +--R 5 3+-+2 4 3+-+ 3 2 3+-+ +--R (60a x \|x + 120a b x\|x + 60a b x)log(a\|x + b) +--R + +--R 5 2 3 3+-+2 4 4 4 3+-+ +--R (- 20a x log(x) - 20a b )\|x + (- 40a b x log(x) - 60a b x + 5a b )\|x +--R + +--R 3 2 3 2 5 +--R - 20a b x log(x) - 90a b x - 2b +--R / +--R 2 6 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2b x +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 3 2 3+-+ +--R (60a x \|x + 120a b x\|x + 60a b x)log(a\|x + b) +--R + +--R 5 3+-+2 4 3+-+ 3 2 3+-+ 2 3 3+-+2 +--R (- 60a x \|x - 120a b x\|x - 60a b x)log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 5a b )\|x - 90a b x - 2b +--R / +--R 2 6 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2b x +--R Type: Union(Expression(Integer),...) +--E 656 + +--S 657 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 30a log(\|x ) + 10a log(x) +--R (4) ---------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 658 + +)clear all + +--S 659 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1299 +r0:=(-14)/(b^3*x^2)+3/2/(b*(b+a*x^(1/3))^2*x^2)+12/(b^2*_ + (b+a*x^(1/3))*x^2)+84/5*a/(b^4*x^(5/3))-21*a^2/(b^5*x^(4/3))+_ + 28*a^3/(b^6*x)-42*a^4/(b^7*x^(2/3))+84*a^5/(b^8*x^(1/3))-_ + 84*a^6*log(b+a*x^(1/3))/b^9+28*a^6*log(x)/b^9 +--R +--R +--R (2) +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (- 840a x \|x - 1680a b x \|x - 840a b x )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 +--R (280a x log(x) + 280a b x - 14a b )\|x +--R + +--R 7 2 7 2 4 4 7 3+-+ 6 2 2 +--R (560a b x log(x) + 840a b x - 70a b x + 8a b )\|x + 280a b x log(x) +--R + +--R 6 2 2 3 5 8 +--R 1260a b x + 28a b x - 5b +--R / +--R 2 9 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10b x +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (- 840a x \|x - 1680a b x \|x - 840a b x )log(a\|x + b) +--R + +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (840a x \|x + 1680a b x \|x + 840a b x )log(\|x ) +--R + +--R 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ 6 2 2 +--R (280a b x - 14a b )\|x + (840a b x - 70a b x + 8a b )\|x + 1260a b x +--R + +--R 3 5 8 +--R 28a b x - 5b +--R / +--R 2 9 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10b x +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 84a log(\|x ) - 28a log(x) +--R (4) -------------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^5) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1299 +r0:=(-55/3)/(b^3*x^3)+3/2/(b*(b+a*x^(1/3))^2*x^3)+33/2/(b^2*(b+_ + a*x^(1/3))*x^3)+165/8*a/(b^4*x^(8/3))-165/7*a^2/(b^5*x^(7/3))+_ + 55/2*a^3/(b^6*x^2)-33*a^4/(b^7*x^(5/3))+165/4*a^5/(b^8*x^(4/3))-_ + 55*a^6/(b^9*x)+165/2*a^7/(b^10*x^(2/3))-165*a^8/(b^11*x^(1/3))+_ + 165*a^9*log(b+a*x^(1/3))/b^12-55*a^9*log(x)/b^12 +--R +--R +--R (2) +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (27720a x \|x + 55440a b x \|x + 27720a b x )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a x log(x) - 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 10 3 7 4 2 4 7 10 +--R (- 18480a b x log(x) - 27720a b x + 2310a b x - 264a b x + 77a b ) +--R * +--R 3+-+ +--R \|x +--R + +--R 9 2 3 9 2 3 6 5 2 3 8 11 +--R - 9240a b x log(x) - 41580a b x - 924a b x + 165a b x - 56b +--R / +--R 2 12 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168b x +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (27720a x \|x + 55440a b x \|x + 27720a b x )log(a\|x + b) +--R + +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (- 27720a x \|x - 55440a b x \|x - 27720a b x )log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 2310a b x - 264a b x + 77a b )\|x - 41580a b x +--R + +--R 6 5 2 3 8 11 +--R - 924a b x + 165a b x - 56b +--R / +--R 2 12 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168b x +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 165a log(\|x ) + 55a log(x) +--R (4) ----------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 668 + +)clear all + +--S 669 of 1299 +t0:=1/(1+b/x^(1/3)) +--R +--R +--R 3+-+ +--R \|x +--R (1) -------- +--R 3+-+ +--R \|x + b +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1299 +r0:=3*b^2*x^(1/3)-3/2*b*x^(2/3)+x-3*b^3*log(b+x^(1/3)) +--R +--R +--R 3 3+-+ 3+-+2 2 3+-+ +--R - 6b log(\|x + b) - 3b \|x + 6b \|x + 2x +--R (2) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3+-+2 2 3+-+ +--R - 6b log(\|x + b) - 3b \|x + 6b \|x + 2x +--R (3) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 673 + +)clear all + +--S 674 of 1299 +t0:=x^(2/3)*(1+x^(5/3))^(2/3) +--R +--R +--R +-----------+2 +--R 3+-+2 3| 3+-+2 +--R (1) \|x \|x \|x + 1 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1299 +r0:=9/25*(1+x^(5/3))^(5/3) +--R +--R +--R +-----------+2 +--R 3+-+2 3| 3+-+2 +--R (9x \|x + 9)\|x \|x + 1 +--R (2) ----------------------------- +--R 25 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1299 +--a0:=integrate(t0,x) +--E 676 + +--S 677 of 1299 +--m0:=a0-r0 +--E 677 + +--S 678 of 1299 +--d0:=D(m0,x) +--E 678 + +)clear all + +--S 679 of 1299 +t0:=x^(7/3)*(a^(10/3)-x^(10/3))^(19/7) +--R +--R +--R +-----------------+5 +--R 3 5 3+-+3+-+2 6 2 3+-+2 3+-+ 9 7| 3 3+-+ 3 3+-+ +--R (1) (- 2a x \|a \|x + a x \|a \| + x )\|- x \|x + a \|a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1299 +r0:=-21/260*(a^(10/3)-x^(10/3))^(26/7) +--R +--R +--R (2) +--R +-----------------+5 +--R 3 6 3+-+3+-+2 6 3 3+-+2 3+-+ 10 10 7| 3 3+-+ 3 3+-+ +--R (- 63a x \|a \|x + 63a x \|a \| + 21x - 21a )\|- x \|x + a \|a +--R -------------------------------------------------------------------------- +--R 260 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1299 +--a0:=integrate(t0,x) +--E 681 + +--S 682 of 1299 +--m0:=a0-r0 +--E 682 + +--S 683 of 1299 +--d0:=D(m0,x) +--E 683 + +)clear all + +--S 684 of 1299 +t0:=1/(1+x^(1/5)) +--R +--R +--R 1 +--R (1) -------- +--R 5+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1299 +r0:=-5*x^(1/5)+5/2*x^(2/5)-5/3*x^(3/5)+5/4*x^(4/5)+5*log(1+x^(1/5)) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (2) ------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (3) ------------------------------------------------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 686 + +--S 687 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1299 +t0:=1/(x^(1/5)*sqrt(1+x^(4/5))) +--R +--R +--R 1 +--R (1) ---------------- +--R +---------+ +--R 5+-+ |5+-+4 +--R \|x \|\|x + 1 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1299 +r0:=5/2*sqrt(1+x^(4/5)) +--R +--R +--R +---------+ +--R |5+-+4 +--R 5\|\|x + 1 +--R (2) ------------- +--R 2 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1299 +--a0:=integrate(t0,x) +--E 691 + +--S 692 of 1299 +--m0:=a0-r0 +--E 692 + +--S 693 of 1299 +--d0:=D(m0,x) +--E 693 + +)clear all + +--S 694 of 1299 +t0:=(a+b/x^(3/5))^(2/3) +--R +--R +--R +-----------+2 +--R | 5+-+3 +--R |a \|x + b +--R (1) |----------- +--R 3| 5+-+3 +--R \| \|x +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1299 +r0:=(a+b/x^(3/5))^(5/3)*x/a +--R +--R +--R +-----------+2 +--R | 5+-+3 +--R 5+-+3 |a \|x + b +--R (a x \|x + b x) |----------- +--R 3| 5+-+3 +--R \| \|x +--R (2) -------------------------------- +--R 5+-+3 +--R a \|x +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1299 +--a0:=integrate(t0,x) +--E 696 + +--S 697 of 1299 +--m0:=a0-r0 +--E 697 + +--S 698 of 1299 +--d0:=D(m0,x) +--E 698 + +)clear all + +--S 699 of 1299 +t0:=(a+b/x^(3/2))^(2/3) +--R +--R +--R +-----------+2 +--R | +-+ +--R |a x\|x + b +--R (1) |----------- +--R 3| +-+ +--R \| x\|x +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1299 +r0:=(a+b/x^(3/2))^(2/3)*x+2/3*b^(2/3)*log(1-b^(1/3)/((a+_ + b/x^(3/2))^(1/3)*sqrt(x)))-1/3*b^(2/3)*log(1+b^(2/3)/_ + ((a+b/x^(3/2))^(2/3)*x)+b^(1/3)/((a+b/x^(3/2))^(1/3)*sqrt(x)))-_ + 2*b^(2/3)*atan((1+2*b^(1/3)/((a+b/x^(3/2))^(1/3)*sqrt(x)))/_ + sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R | +-+ | +-+ +--R +-+ |a x\|x + b 3+-+ |a x\|x + b 3+-+2 +-+ +--R x\|x |----------- + x\|b |----------- + \|b \|x +--R 3| +-+ 3| +-+ +--R +-+3+-+2 \| x\|x \| x\|x +--R - \|3 \|b log(------------------------------------------------------) +--R +-----------+2 +--R | +-+ +--R +-+ |a x\|x + b +--R x\|x |----------- +--R 3| +-+ +--R \| x\|x +--R + +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b 3+-+ +--R \|x |----------- - \|b +--R 3| +-+ +--R +-+3+-+2 \| x\|x +--R 2\|3 \|b log(-------------------------) +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b +--R \|x |----------- +--R 3| +-+ +--R \| x\|x +--R + +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b 3+-+ +--R \|x |----------- + 2\|b +-----------+2 +--R 3| +-+ | +-+ +--R 3+-+2 \| x\|x +-+ |a x\|x + b +--R - 6\|b atan(--------------------------) + 3x\|3 |----------- +--R +-----------+ 3| +-+ +--R | +-+ \| x\|x +--R +-+ +-+ |a x\|x + b +--R \|3 \|x |----------- +--R 3| +-+ +--R \| x\|x +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1299 +--a0:=integrate(t0,x) +--E 701 + +--S 702 of 1299 +--m0:=a0-r0 +--E 702 + +--S 703 of 1299 +--d0:=D(m0,x) +--E 703 + +)clear all + +--S 704 of 1299 +t0:=x^m*(a+b*x^n) +--R +--R +--R m n m +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1299 +r0:=a*x^(1+m)/(1+m)+b*x^(1+m+n)/(1+m+n) +--R +--R +--R n + m + 1 m + 1 +--R (b m + b)x + (a n + a m + a)x +--R (2) ------------------------------------------- +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1299 +a0:=integrate(t0,x) +--R +--R +--R m log(x) n log(x) m log(x) +--R (b m + b)x %e %e + (a n + a m + a)x %e +--R (3) ------------------------------------------------------------- +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(x) n log(x) m log(x) +--R (b m + b)x %e %e + (a n + a m + a)x %e +--R + +--R n + m + 1 m + 1 +--R (- b m - b)x + (- a n - a m - a)x +--R / +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1299 +t0:=x^3*(a+b*x^n) +--R +--R +--R 3 n 3 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1299 +r0:=1/4*a*x^4+b*x^(4+n)/(4+n) +--R +--R +--R n + 4 4 +--R 4b x + (a n + 4a)x +--R (2) ------------------------ +--R 4n + 16 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 n log(x) 4 +--R 4b x %e + (a n + 4a)x +--R (3) ------------------------------ +--R 4n + 16 +--R Type: Union(Expression(Integer),...) +--E 711 + +--S 712 of 1299 +m0:=a0-r0 +--R +--R +--R 4 n log(x) n + 4 +--R b x %e - b x +--R (4) ------------------------- +--R n + 4 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +)clear all + +--S 714 of 1299 +t0:=x^2*(a+b*x^n) +--R +--R +--R 2 n 2 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1299 +r0:=1/3*a*x^3+b*x^(3+n)/(3+n) +--R +--R +--R n + 3 3 +--R 3b x + (a n + 3a)x +--R (2) ------------------------ +--R 3n + 9 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 +--R 3b x %e + (a n + 3a)x +--R (3) ------------------------------ +--R 3n + 9 +--R Type: Union(Expression(Integer),...) +--E 716 + +--S 717 of 1299 +m0:=a0-r0 +--R +--R +--R 3 n log(x) n + 3 +--R b x %e - b x +--R (4) ------------------------- +--R n + 3 +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 718 + +)clear all + +--S 719 of 1299 +t0:=x*(a+b*x^n) +--R +--R +--R n +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1299 +r0:=1/2*a*x^2+b*x^(2+n)/(2+n) +--R +--R +--R n + 2 2 +--R 2b x + (a n + 2a)x +--R (2) ------------------------ +--R 2n + 4 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 +--R 2b x %e + (a n + 2a)x +--R (3) ------------------------------ +--R 2n + 4 +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) n + 2 +--R b x %e - b x +--R (4) ------------------------- +--R n + 2 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1299 +t0:=a+b*x^n +--R +--R +--R n +--R (1) b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1299 +r0:=a*x+b*x^(1+n)/(1+n) +--R +--R +--R n + 1 +--R b x + (a n + a)x +--R (2) --------------------- +--R n + 1 +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b x %e + (a n + a)x +--R (3) --------------------------- +--R n + 1 +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n + 1 +--R b x %e - b x +--R (4) ------------------------- +--R n + 1 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1299 +t0:=(a+b*x^n)/x +--R +--R +--R n +--R b x + a +--R (1) -------- +--R x +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1299 +r0:=b*x^n/n+a*log(x) +--R +--R +--R n +--R b x + a n log(x) +--R (2) ----------------- +--R n +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e + a n log(x) +--R (3) ------------------------- +--R n +--R Type: Union(Expression(Integer),...) +--E 731 + +--S 732 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R b %e - b x +--R (4) ------------------- +--R n +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 733 + +)clear all + +--S 734 of 1299 +t0:=(a+b*x^n)/x^2 +--R +--R +--R n +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1299 +r0:=-a/x-b*x^(-1+n)/(1-n) +--R +--R +--R n - 1 +--R b x x - a n + a +--R (2) -------------------- +--R (n - 1)x +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e - a n + a +--R (3) ---------------------- +--R (n - 1)x +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n - 1 +--R b %e - b x x +--R (4) ------------------------- +--R (n - 1)x +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 1299 +t0:=(a+b*x^n)/x^3 +--R +--R +--R n +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1299 +r0:=-1/2*a/x^2-b*x^(-2+n)/(2-n) +--R +--R +--R 2 n - 2 +--R 2b x x - a n + 2a +--R (2) ---------------------- +--R 2 +--R (2n - 4)x +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R 2b %e - a n + 2a +--R (3) ------------------------ +--R 2 +--R (2n - 4)x +--R Type: Union(Expression(Integer),...) +--E 741 + +--S 742 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 2 n - 2 +--R b %e - b x x +--R (4) ------------------------- +--R 2 +--R (n - 2)x +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1299 +t0:=x^m*(a+b*x^n)^2 +--R +--R +--R 2 m n 2 m n 2 m +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1299 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(1+m+n)/(1+m+n)+b^2*x^(1+m+2*n)/(1+m+2*n) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2n + m + 1 +--R ((b m + b )n + b m + 2b m + b )x +--R + +--R 2 n + m + 1 +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x +--R + +--R 2 2 2 2 2 2 2 2 m + 1 +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 m log(x) n log(x) 2 +--R ((b m + b )n + b m + 2b m + b )x %e (%e ) +--R + +--R 2 m log(x) n log(x) +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x %e %e +--R + +--R 2 2 2 2 2 2 2 2 m log(x) +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x %e +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 m log(x) n log(x) 2 +--R ((b m + b )n + b m + 2b m + b )x %e (%e ) +--R + +--R 2 m log(x) n log(x) +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x %e %e +--R + +--R 2 2 2 2 2 2 2 2 m log(x) +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x %e +--R + +--R 2 2 2 2 2 2 2n + m + 1 +--R ((- b m - b )n - b m - 2b m - b )x +--R + +--R 2 n + m + 1 +--R ((- 4a b m - 4a b)n - 2a b m - 4a b m - 2a b)x +--R + +--R 2 2 2 2 2 2 2 2 m + 1 +--R (- 2a n + (- 3a m - 3a )n - a m - 2a m - a )x +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1299 +t0:=x^3*(a+b*x^n)^2 +--R +--R +--R 2 3 n 2 3 n 2 3 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1299 +r0:=1/4*a^2*x^4+1/2*b^2*x^(2*(2+n))/(2+n)+2*a*b*x^(4+n)/(4+n) +--R +--R +--R 2 2 2n + 4 n + 4 2 2 2 2 4 +--R (2b n + 8b )x + (8a b n + 16a b)x + (a n + 6a n + 8a )x +--R (2) -------------------------------------------------------------------- +--R 2 +--R 4n + 24n + 32 +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 n log(x) 2 4 n log(x) +--R (2b n + 8b )x (%e ) + (8a b n + 16a b)x %e +--R + +--R 2 2 2 2 4 +--R (a n + 6a n + 8a )x +--R / +--R 2 +--R 4n + 24n + 32 +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 n log(x) 2 4 n log(x) +--R (b n + 4b )x (%e ) + (4a b n + 8a b)x %e +--R + +--R 2 2 2n + 4 n + 4 +--R (- b n - 4b )x + (- 4a b n - 8a b)x +--R / +--R 2 +--R 2n + 12n + 16 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1299 +t0:=x^2*(a+b*x^n)^2 +--R +--R +--R 2 2 n 2 2 n 2 2 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1299 +r0:=1/3*a^2*x^3+2*a*b*x^(3+n)/(3+n)+b^2*x^(3+2*n)/(3+2*n) +--R +--R +--R 2 2 2n + 3 n + 3 2 2 2 2 3 +--R (3b n + 9b )x + (12a b n + 18a b)x + (2a n + 9a n + 9a )x +--R (2) ---------------------------------------------------------------------- +--R 2 +--R 6n + 27n + 27 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 n log(x) 2 3 n log(x) +--R (3b n + 9b )x (%e ) + (12a b n + 18a b)x %e +--R + +--R 2 2 2 2 3 +--R (2a n + 9a n + 9a )x +--R / +--R 2 +--R 6n + 27n + 27 +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 n log(x) 2 3 n log(x) +--R (b n + 3b )x (%e ) + (4a b n + 6a b)x %e +--R + +--R 2 2 2n + 3 n + 3 +--R (- b n - 3b )x + (- 4a b n - 6a b)x +--R / +--R 2 +--R 2n + 9n + 9 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1299 +t0:=x*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1299 +r0:=1/2*a^2*x^2+1/2*b^2*x^(2*(1+n))/(1+n)+2*a*b*x^(2+n)/(2+n) +--R +--R +--R 2 2 2n + 2 n + 2 2 2 2 2 2 +--R (b n + 2b )x + (4a b n + 4a b)x + (a n + 3a n + 2a )x +--R (2) ------------------------------------------------------------------ +--R 2 +--R 2n + 6n + 4 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 n log(x) 2 2 n log(x) +--R (b n + 2b )x (%e ) + (4a b n + 4a b)x %e +--R + +--R 2 2 2 2 2 +--R (a n + 3a n + 2a )x +--R / +--R 2 +--R 2n + 6n + 4 +--R Type: Union(Expression(Integer),...) +--E 761 + +--S 762 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 n log(x) 2 2 n log(x) +--R (b n + 2b )x (%e ) + (4a b n + 4a b)x %e +--R + +--R 2 2 2n + 2 n + 2 +--R (- b n - 2b )x + (- 4a b n - 4a b)x +--R / +--R 2 +--R 2n + 6n + 4 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +)clear all + +--S 764 of 1299 +t0:=(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 +--R (1) b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1299 +r0:=a^2*x+2*a*b*x^(1+n)/(1+n)+b^2*x^(1+2*n)/(1+2*n) +--R +--R +--R 2 2 2n + 1 n + 1 2 2 2 2 +--R (b n + b )x + (4a b n + 2a b)x + (2a n + 3a n + a )x +--R (2) ---------------------------------------------------------------- +--R 2 +--R 2n + 3n + 1 +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) +--R (b n + b )x (%e ) + (4a b n + 2a b)x %e +--R + +--R 2 2 2 2 +--R (2a n + 3a n + a )x +--R / +--R 2 +--R 2n + 3n + 1 +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) +--R (b n + b )x (%e ) + (4a b n + 2a b)x %e +--R + +--R 2 2 2n + 1 n + 1 +--R (- b n - b )x + (- 4a b n - 2a b)x +--R / +--R 2 +--R 2n + 3n + 1 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 768 + +)clear all + +--S 769 of 1299 +t0:=(a+b*x^n)^2/x +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1299 +r0:=2*a*b*x^n/n+1/2*b^2*x^(2*n)/n+a^2*log(x) +--R +--R +--R 2 2n n 2 +--R b x + 4a b x + 2a n log(x) +--R (2) ----------------------------- +--R 2n +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 4a b %e + 2a n log(x) +--R (3) ----------------------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 771 + +--S 772 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) 2 n log(x) 2 2n n +--R b (%e ) + 4a b %e - b x - 4a b x +--R (4) --------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 773 + +)clear all + +--S 774 of 1299 +t0:=(a+b*x^n)^2/x^2 +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1299 +r0:=-a^2/x-2*a*b*x^(-1+n)/(1-n)-b^2*x^(-1+2*n)/(1-2*n) +--R +--R +--R 2 2 2n - 1 n - 1 2 2 2 2 +--R (b n - b )x x + (4a b n - 2a b)x x - 2a n + 3a n - a +--R (2) ----------------------------------------------------------------- +--R 2 +--R (2n - 3n + 1)x +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) 2 2 2 2 +--R (b n - b )(%e ) + (4a b n - 2a b)%e - 2a n + 3a n - a +--R ----------------------------------------------------------------------- +--R 2 +--R (2n - 3n + 1)x +--R Type: Union(Expression(Integer),...) +--E 776 + +--S 777 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) +--R (b n - b )(%e ) + (4a b n - 2a b)%e +--R + +--R 2 2 2n - 1 n - 1 +--R (- b n + b )x x + (- 4a b n + 2a b)x x +--R / +--R 2 +--R (2n - 3n + 1)x +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1299 +t0:=(a+b*x^n)^2/x^3 +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1299 +r0:=-1/2*a^2/x^2-1/2*b^2/((1-n)*x^(2*(1-n)))-2*a*b*x^(-2+n)/(2-n) +--R +--R +--R (2) +--R 2 - 2n + 2 n - 2 2 2 2 2 - 2n + 2 +--R (4a b n - 4a b)x x x + (- a n + 3a n - 2a )x +--R + +--R 2 2 2 +--R (b n - 2b )x +--R / +--R 2 2 - 2n + 2 +--R (2n - 6n + 4)x x +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) 2 2 2 2 +--R (b n - 2b )(%e ) + (4a b n - 4a b)%e - a n + 3a n - 2a +--R ------------------------------------------------------------------------ +--R 2 2 +--R (2n - 6n + 4)x +--R Type: Union(Expression(Integer),...) +--E 781 + +--S 782 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 - 2n + 2 n log(x) 2 - 2n + 2 n log(x) +--R (b n - 2b )x (%e ) + (4a b n - 4a b)x %e +--R + +--R 2 - 2n + 2 n - 2 2 2 2 +--R (- 4a b n + 4a b)x x x + (- b n + 2b )x +--R / +--R 2 2 - 2n + 2 +--R (2n - 6n + 4)x x +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +)clear all + +--S 784 of 1299 +t0:=x^m*(a+b*x^n)^3 +--R +--R +--R 3 m n 3 2 m n 2 2 m n 3 m +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1299 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(1+m+n)/(1+m+n)+_ + 3*a*b^2*x^(1+m+2*n)/(1+m+2*n)+b^3*x^(1+m+3*n)/(1+m+3*n) +--R +--R +--R (2) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b ) +--R * +--R 3n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R 2n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R n + m + 1 +--R x +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m + 1 +--R x +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b )x +--R * +--R m log(x) n log(x) 3 +--R %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) 2 +--R x %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) +--R x %e %e +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m log(x) +--R x %e +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 786 + +--S 787 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b )x +--R * +--R m log(x) n log(x) 3 +--R %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) 2 +--R x %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) +--R x %e %e +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m log(x) +--R x %e +--R + +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((- 2b m - 2b )n + (- 3b m - 6b m - 3b )n - b m - 3b m - 3b m - b ) +--R * +--R 3n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (- 9a b m - 9a b )n + (- 12a b m - 24a b m - 12a b )n - 3a b m +--R + +--R 2 2 2 2 +--R - 9a b m - 9a b m - 3a b +--R * +--R 2n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (- 18a b m - 18a b)n + (- 15a b m - 30a b m - 15a b)n - 3a b m +--R + +--R 2 2 2 2 +--R - 9a b m - 9a b m - 3a b +--R * +--R n + m + 1 +--R x +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 +--R - 6a n + (- 11a m - 11a )n + (- 6a m - 12a m - 6a )n - a m +--R + +--R 3 2 3 3 +--R - 3a m - 3a m - a +--R * +--R m + 1 +--R x +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 788 + +)clear all + +--S 789 of 1299 +t0:=x^3*(a+b*x^n)^3 +--R +--R +--R 3 3 n 3 2 3 n 2 2 3 n 3 3 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1299 +r0:=1/4*a^3*x^4+3/2*a*b^2*x^(2*(2+n))/(2+n)+3*a^2*b*x^(4+n)/(4+n)+_ + b^3*x^(4+3*n)/(4+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 4 2 2 2 2 2n + 4 +--R (4b n + 24b n + 32b )x + (18a b n + 96a b n + 96a b )x +--R + +--R 2 2 2 2 n + 4 3 3 3 2 3 3 4 +--R (36a b n + 120a b n + 96a b)x + (3a n + 22a n + 48a n + 32a )x +--R / +--R 3 2 +--R 12n + 88n + 192n + 128 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 4 n log(x) 3 +--R (4b n + 24b n + 32b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) 2 +--R (18a b n + 96a b n + 96a b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) +--R (36a b n + 120a b n + 96a b)x %e +--R + +--R 3 3 3 2 3 3 4 +--R (3a n + 22a n + 48a n + 32a )x +--R / +--R 3 2 +--R 12n + 88n + 192n + 128 +--R Type: Union(Expression(Integer),...) +--E 791 + +--S 792 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 4 n log(x) 3 +--R (2b n + 12b n + 16b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) 2 +--R (9a b n + 48a b n + 48a b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) +--R (18a b n + 60a b n + 48a b)x %e +--R + +--R 3 2 3 3 3n + 4 2 2 2 2 2n + 4 +--R (- 2b n - 12b n - 16b )x + (- 9a b n - 48a b n - 48a b )x +--R + +--R 2 2 2 2 n + 4 +--R (- 18a b n - 60a b n - 48a b)x +--R / +--R 3 2 +--R 6n + 44n + 96n + 64 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 793 + +)clear all + +--S 794 of 1299 +t0:=x^2*(a+b*x^n)^3 +--R +--R +--R 3 2 n 3 2 2 n 2 2 2 n 3 2 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1299 +r0:=1/3*a^3*x^3+1/3*b^3*x^(3*(1+n))/(1+n)+3*a^2*b*x^(3+n)/(3+n)+_ + 3*a*b^2*x^(3+2*n)/(3+2*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 3 2 2 2 2 2n + 3 +--R (2b n + 9b n + 9b )x + (9a b n + 36a b n + 27a b )x +--R + +--R 2 2 2 2 n + 3 3 3 3 2 3 3 3 +--R (18a b n + 45a b n + 27a b)x + (2a n + 11a n + 18a n + 9a )x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 n log(x) 3 +--R (2b n + 9b n + 9b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 2 +--R (9a b n + 36a b n + 27a b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 3 3 3 2 3 3 3 +--R (18a b n + 45a b n + 27a b)x %e + (2a n + 11a n + 18a n + 9a )x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Union(Expression(Integer),...) +--E 796 + +--S 797 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 n log(x) 3 +--R (2b n + 9b n + 9b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 2 +--R (9a b n + 36a b n + 27a b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 3 2 3 3 3n + 3 +--R (18a b n + 45a b n + 27a b)x %e + (- 2b n - 9b n - 9b )x +--R + +--R 2 2 2 2 2n + 3 +--R (- 9a b n - 36a b n - 27a b )x +--R + +--R 2 2 2 2 n + 3 +--R (- 18a b n - 45a b n - 27a b)x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 798 + +)clear all + +--S 799 of 1299 +t0:=x*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1299 +r0:=1/2*a^3*x^2+3/2*a*b^2*x^(2*(1+n))/(1+n)+3*a^2*b*x^(2+n)/(2+n)+_ + b^3*x^(2+3*n)/(2+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 2 2 2 2 2 2n + 2 +--R (2b n + 6b n + 4b )x + (9a b n + 24a b n + 12a b )x +--R + +--R 2 2 2 2 n + 2 3 3 3 2 3 3 2 +--R (18a b n + 30a b n + 12a b)x + (3a n + 11a n + 12a n + 4a )x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 n log(x) 3 +--R (2b n + 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 +--R (9a b n + 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 3 3 3 2 3 3 2 +--R (18a b n + 30a b n + 12a b)x %e + (3a n + 11a n + 12a n + 4a )x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Union(Expression(Integer),...) +--E 801 + +--S 802 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 n log(x) 3 +--R (2b n + 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 +--R (9a b n + 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 3 2 3 3 3n + 2 +--R (18a b n + 30a b n + 12a b)x %e + (- 2b n - 6b n - 4b )x +--R + +--R 2 2 2 2 2n + 2 +--R (- 9a b n - 24a b n - 12a b )x +--R + +--R 2 2 2 2 n + 2 +--R (- 18a b n - 30a b n - 12a b)x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 803 + +)clear all + +--S 804 of 1299 +t0:=(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (1) b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1299 +r0:=a^3*x+3*a^2*b*x^(1+n)/(1+n)+3*a*b^2*x^(1+2*n)/(1+2*n)+b^3*x^(1+3*n)/(1+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 1 2 2 2 2 2n + 1 +--R (2b n + 3b n + b )x + (9a b n + 12a b n + 3a b )x +--R + +--R 2 2 2 2 n + 1 3 3 3 2 3 3 +--R (18a b n + 15a b n + 3a b)x + (6a n + 11a n + 6a n + a )x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n + 3b n + b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n + 12a b n + 3a b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n + 15a b n + 3a b)x %e + (6a n + 11a n + 6a n + a )x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Union(Expression(Integer),...) +--E 806 + +--S 807 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 +--R (2b n + 3b n + b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n + 12a b n + 3a b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 3 2 3 3 3n + 1 +--R (18a b n + 15a b n + 3a b)x %e + (- 2b n - 3b n - b )x +--R + +--R 2 2 2 2 2n + 1 2 2 2 2 n + 1 +--R (- 9a b n - 12a b n - 3a b )x + (- 18a b n - 15a b n - 3a b)x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 808 + +)clear all + +--S 809 of 1299 +t0:=(a+b*x^n)^3/x +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1299 +r0:=3*a^2*b*x^n/n+3/2*a*b^2*x^(2*n)/n+1/3*b^3*x^(3*n)/n+a^3*log(x) +--R +--R +--R 3 3n 2 2n 2 n 3 +--R 2b x + 9a b x + 18a b x + 6a n log(x) +--R (2) ------------------------------------------ +--R 6n +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 9a b (%e ) + 18a b %e + 6a n log(x) +--R (3) ---------------------------------------------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 811 + +--S 812 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 3n +--R 2b (%e ) + 9a b (%e ) + 18a b %e - 2b x +--R + +--R 2 2n 2 n +--R - 9a b x - 18a b x +--R / +--R 6n +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1299 +t0:=(a+b*x^n)^3/x^2 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1299 +r0:=-a^3/x-3*a^2*b*x^(-1+n)/(1-n)-3*a*b^2*x^(-1+2*n)/(1-2*n)-_ + b^3*x^(-1+3*n)/(1-3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n - 1 2 2 2 2 2n - 1 +--R (2b n - 3b n + b )x x + (9a b n - 12a b n + 3a b )x x +--R + +--R 2 2 2 2 n - 1 3 3 3 2 3 3 +--R (18a b n - 15a b n + 3a b)x x - 6a n + 11a n - 6a n + a +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 3b n + b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 12a b n + 3a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n - 15a b n + 3a b)%e - 6a n + 11a n - 6a n + a +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 3b n + b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 12a b n + 3a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 2 3 3 3n - 1 +--R (18a b n - 15a b n + 3a b)%e + (- 2b n + 3b n - b )x x +--R + +--R 2 2 2 2 2n - 1 +--R (- 9a b n + 12a b n - 3a b )x x +--R + +--R 2 2 2 2 n - 1 +--R (- 18a b n + 15a b n - 3a b)x x +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1299 +t0:=(a+b*x^n)^3/x^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1299 +r0:=-1/2*a^3/x^2-3/2*a*b^2/((1-n)*x^(2*(1-n)))-_ + 3*a^2*b*x^(-2+n)/(2-n)-b^3*x^(-2+3*n)/(2-3*n) +--R +--R +--R (2) +--R 3 2 3 3 2 - 2n + 2 3n - 2 +--R (2b n - 6b n + 4b )x x x +--R + +--R 2 2 2 2 2 - 2n + 2 n - 2 +--R (18a b n - 30a b n + 12a b)x x x +--R + +--R 3 3 3 2 3 3 - 2n + 2 2 2 2 2 2 +--R (- 3a n + 11a n - 12a n + 4a )x + (9a b n - 24a b n + 12a b )x +--R / +--R 3 2 2 - 2n + 2 +--R (6n - 22n + 24n - 8)x x +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 6b n + 4b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 24a b n + 12a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n - 30a b n + 12a b)%e - 3a n + 11a n - 12a n + 4a +--R / +--R 3 2 2 +--R (6n - 22n + 24n - 8)x +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 - 2n + 2 n log(x) 3 +--R (2b n - 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 - 2n + 2 n log(x) 2 +--R (9a b n - 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 - 2n + 2 n log(x) +--R (18a b n - 30a b n + 12a b)x %e +--R + +--R 3 2 3 3 2 - 2n + 2 3n - 2 +--R (- 2b n + 6b n - 4b )x x x +--R + +--R 2 2 2 2 2 - 2n + 2 n - 2 +--R (- 18a b n + 30a b n - 12a b)x x x +--R + +--R 2 2 2 2 2 +--R (- 9a b n + 24a b n - 12a b )x +--R / +--R 3 2 2 - 2n + 2 +--R (6n - 22n + 24n - 8)x x +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1299 +t0:=x^m/(a+b*x^n) +--R +--R +--R m +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1299 +--r0:=x^(1+m)*hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a*(1+m)) +--E 825 + +--S 826 of 1299 +--a0:=integrate(t0,x) +--E 826 + +--S 827 of 1299 +--m0:=a0-r0 +--E 827 + +--S 828 of 1299 +--d0:=D(m0,x) +--E 828 + +)clear all + +--S 829 of 1299 +t0:=x/(a+b*x^n) +--R +--R +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1299 +--r0:=1/2*x^2*hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/a +--E 830 + +--S 831 of 1299 +--a0:=integrate(t0,x) +--E 831 + +--S 832 of 1299 +--m0:=a0-r0 +--E 832 + +--S 833 of 1299 +--d0:=D(m0,x) +--E 833 + +)clear all + +--S 834 of 1299 +t0:=1/(a+b*x^n) +--R +--R +--R 1 +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1299 +--r0:=x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/a +--E 835 + +--S 836 of 1299 +--a0:=integrate(t0,x) +--E 836 + +--S 837 of 1299 +--m0:=a0-r0 +--E 837 + +--S 838 of 1299 +--d0:=D(m0,x) +--E 838 + +)clear all + +--S 839 of 1299 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1299 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 841 + +--S 842 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 843 + +)clear all + +--S 844 of 1299 +t0:=1/(x^2*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------- +--R 2 n 2 +--R b x x + a x +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1299 +--r0:=-hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a*x) +--E 845 + +--S 846 of 1299 +--a0:=integrate(t0,x) +--E 846 + +--S 847 of 1299 +--m0:=a0-r0 +--E 847 + +--S 848 of 1299 +--d0:=D(m0,x) +--E 848 + +)clear all + +--S 849 of 1299 +t0:=1/(x^3*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------- +--R 3 n 3 +--R b x x + a x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1299 +--r0:=-1/2*hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a*x^2) +--E 850 + +--S 851 of 1299 +--a0:=integrate(t0,x) +--E 851 + +--S 852 of 1299 +--m0:=a0-r0 +--E 852 + +--S 853 of 1299 +--d0:=D(m0,x) +--E 853 + +)clear all + +--S 854 of 1299 +t0:=x^m/(a+b*x^n)^2 +--R +--R +--R m +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1299 +--r0:=x^(1+m)/(a*n*(a+b*x^n))-(1+m-n)*x^(1+m)*_ +-- hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a^2*(1+m)*n) +--E 855 + +--S 856 of 1299 +--a0:=integrate(t0,x) +--E 856 + +--S 857 of 1299 +--m0:=a0-r0 +--E 857 + +--S 858 of 1299 +--d0:=D(m0,x) +--E 858 + +)clear all + +--S 859 of 1299 +t0:=x/(a+b*x^n)^2 +--R +--R +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1299 +--r0:=x^2/(a*n*(a+b*x^n))-1/2*(2-n)*x^2*_ +-- hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/(a^2*n) +--E 860 + +--S 861 of 1299 +--a0:=integrate(t0,x) +--E 861 + +--S 862 of 1299 +--m0:=a0-r0 +--E 862 + +--S 863 of 1299 +--d0:=D(m0,x) +--E 863 + +)clear all + +--S 864 of 1299 +t0:=1/(a+b*x^n)^2 +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1299 +--r0:=x/(a*n*(a+b*x^n))-(1-n)*x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/(a^2*n) +--E 865 + +--S 866 of 1299 +--a0:=integrate(t0,x) +--E 866 + +--S 867 of 1299 +--m0:=a0-r0 +--E 867 + +--S 868 of 1299 +--d0:=D(m0,x) +--E 868 + +)clear all + +--S 869 of 1299 +t0:=1/(x*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 n 2 n 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1299 +r0:=1/(a*n*(a+b*x^n))+log(x)/a^2-log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R (- b x - a)log(b x + a) + b n log(x)x + a n log(x) + a +--R (2) --------------------------------------------------------- +--R 2 n 3 +--R a b n x + a n +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) n log(x) n log(x) +--R (- b %e - a)log(b %e + a) + b n log(x)%e +--R + +--R a n log(x) + a +--R / +--R 2 n log(x) 3 +--R a b n %e + a n +--R Type: Union(Expression(Integer),...) +--E 871 + +--S 872 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((- b x - a b)%e - a b x - a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((b x + a b)%e + a b x + a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 2 2 n 3 n log(x) 3 n 4 +--R (a b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 873 + +)clear all + +--S 874 of 1299 +t0:=1/(x^2*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 2 n 2 2 n 2 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1299 +--r0:=1/(a*n*x*(a+b*x^n))-(1+n)*_ +-- hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a^2*n*x) +--E 875 + +--S 876 of 1299 +--a0:=integrate(t0,x) +--E 876 + +--S 877 of 1299 +--m0:=a0-r0 +--E 877 + +--S 878 of 1299 +--d0:=D(m0,x) +--E 878 + +)clear all + +--S 879 of 1299 +t0:=1/(x^3*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 3 n 2 3 n 2 3 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1299 +--r0:=1/(a*n*x^2*(a+b*x^n))-1/2*(2+n)*_ +-- hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a^2*n*x^2) +--E 880 + +--S 881 of 1299 +--a0:=integrate(t0,x) +--E 881 + +--S 882 of 1299 +--m0:=a0-r0 +--E 882 + +--S 883 of 1299 +--d0:=D(m0,x) +--E 883 + +)clear all + +--S 884 of 1299 +t0:=x^m/(a+b*x^n)^3 +--R +--R +--R m +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1299 +--r0:=1/2*x^(1+m)/(a*n*(a+b*x^n)^2)-1/2*(1+m-2*n)*x^(1+m)/_ +-- (a^2*n^2*(a+b*x^n))+1/2*(1+m-2*n)*(1+m-n)*x^(1+m)*_ +-- hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a^3*(1+m)*n^2) +--E 885 + +--S 886 of 1299 +--a0:=integrate(t0,x) +--E 886 + +--S 887 of 1299 +--m0:=a0-r0 +--E 887 + +--S 888 of 1299 +--d0:=D(m0,x) +--E 888 + +)clear all + +--S 889 of 1299 +t0:=x/(a+b*x^n)^3 +--R +--R +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1299 +--r0:=1/2*x^2/(a*n*(a+b*x^n)^2)-(1-n)*x^2/(a^2*n^2*(a+b*x^n))+_ +-- 1/2*(1-n)*(2-n)*x^2*hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/(a^3*n^2) +--E 890 + +--S 891 of 1299 +--a0:=integrate(t0,x) +--E 891 + +--S 892 of 1299 +--m0:=a0-r0 +--E 892 + +--S 893 of 1299 +--d0:=D(m0,x) +--E 893 + +)clear all + +--S 894 of 1299 +t0:=1/(a+b*x^n)^3 +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1299 +--r0:=1/2*x/(a*n*(a+b*x^n)^2)-1/2*(1-2*n)*x/(a^2*n^2*(a+b*x^n))+_ +-- 1/2*(1-2*n)*(1-n)*x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/(a^3*n^2) +--E 895 + +--S 896 of 1299 +--a0:=integrate(t0,x) +--E 896 + +--S 897 of 1299 +--m0:=a0-r0 +--E 897 + +--S 898 of 1299 +--d0:=D(m0,x) +--E 898 + +)clear all + +--S 899 of 1299 +t0:=1/(x*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------ +--R 3 n 3 2 n 2 2 n 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1299 +r0:=1/2/(a*n*(a+b*x^n)^2)+1/(a^2*n*(a+b*x^n))+log(x)/a^3-log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n 2 n 2 n 2 +--R (- 2b (x ) - 4a b x - 2a )log(b x + a) + 2b n log(x)(x ) +--R + +--R n 2 2 +--R (4a b n log(x) + 2a b)x + 2a n log(x) + 3a +--R / +--R 3 2 n 2 4 n 5 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (- 2b (%e ) - 4a b %e - 2a )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) + (4a b n log(x) + 2a b)%e + 2a n log(x) +--R + +--R 2 +--R 3a +--R / +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 2a b n (%e ) + 4a b n %e + 2a n +--R Type: Union(Expression(Integer),...) +--E 901 + +--S 902 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 2a b x - 3a b )(%e ) + (2a b (x ) - 4a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 4a b x +--R / +--R 3 4 n 2 4 3 n 5 2 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 4 3 n 2 5 2 n 6 n log(x) 5 2 n 2 6 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 7 +--R 2a n +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1299 +t0:=1/(x^2*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 2 n 3 2 2 n 2 2 2 n 3 2 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1299 +--r0:=1/2/(a*n*x*(a+b*x^n)^2)+1/2*(1+2*n)/(a^2*n^2*x*(a+b*x^n))-_ +-- 1/2*(1+n)*(1+2*n)*hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a^3*n^2*x) +--E 905 + +--S 906 of 1299 +--a0:=integrate(t0,x) +--E 906 + +--S 907 of 1299 +--m0:=a0-r0 +--E 907 + +--S 908 of 1299 +--d0:=D(m0,x) +--E 908 + +)clear all + +--S 909 of 1299 +t0:=1/(x^3*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 3 n 3 2 3 n 2 2 3 n 3 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1299 +--r0:=1/2/(a*n*x^2*(a+b*x^n)^2)+(1+n)/(a^2*n^2*x^2*(a+b*x^n))-_ +-- 1/2*(1+n)*(2+n)*hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a^3*n^2*x^2) +--E 910 + +--S 911 of 1299 +--a0:=integrate(t0,x) +--E 911 + +--S 912 of 1299 +--m0:=a0-r0 +--E 912 + +--S 913 of 1299 +--d0:=D(m0,x) +--E 913 + +)clear all + +--S 914 of 1299 +t0:=x^m*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R m | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1299 +--r0:=2*x^(1+m)*sqrt(a+b*x^n)/(2+2*m+n)+a*n*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*sqrt(a+b*x^n)) +--E 915 + +--S 916 of 1299 +--a0:=integrate(t0,x) +--E 916 + +--S 917 of 1299 +--m0:=a0-r0 +--E 917 + +--S 918 of 1299 +--d0:=D(m0,x) +--E 918 + +)clear all + +--S 919 of 1299 +t0:=x*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R | n +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1299 +--r0:=2*x^2*sqrt(a+b*x^n)/(4+n)+1/2*a*n*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((4+n)*sqrt(a+b*x^n)) +--E 920 + +--S 921 of 1299 +--a0:=integrate(t0,x) +--E 921 + +--S 922 of 1299 +--m0:=a0-r0 +--E 922 + +--S 923 of 1299 +--d0:=D(m0,x) +--E 923 + +)clear all + +--S 924 of 1299 +t0:=(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R | n +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1299 +--r0:=2*x*sqrt(a+b*x^n)/(2+n)+a*n*x*_ +-- hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((2+n)*sqrt(a+b*x^n)) +--E 925 + +--S 926 of 1299 +--a0:=integrate(t0,x) +--E 926 + +--S 927 of 1299 +--m0:=a0-r0 +--E 927 + +--S 928 of 1299 +--d0:=D(m0,x) +--E 928 + +)clear all + +--S 929 of 1299 +t0:=(a+b*x^n)^(1/2)/x +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))*sqrt(a)/n+2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 931 + +--S 932 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--------+ +--R | n log(x) +-+ \|b x + a | n +--R 2\|b %e + a + 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R + +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1299 +t0:=(a+b*x^n)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1299 +--r0:=-2*sqrt(a+b*x^n)/((2-n)*x)+a*n*_ +-- hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((2-n)*x*sqrt(a+b*x^n)) +--E 937 + +--S 938 of 1299 +--a0:=integrate(t0,x) +--E 938 + +--S 939 of 1299 +--m0:=a0-r0 +--E 939 + +--S 940 of 1299 +--d0:=D(m0,x) +--E 940 + +)clear all + +--S 941 of 1299 +t0:=(a+b*x^n)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1299 +--r0:=-2*sqrt(a+b*x^n)/((4-n)*x^2)+1/2*a*n*_ +-- hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4-n)*x^2*sqrt(a+b*x^n)) +--E 942 + +--S 943 of 1299 +--a0:=integrate(t0,x) +--E 943 + +--S 944 of 1299 +--m0:=a0-r0 +--E 944 + +--S 945 of 1299 +--d0:=D(m0,x) +--E 945 + +)clear all + +--S 946 of 1299 +t0:=x^m*(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R m n m | n +--R (1) (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1299 +--r0:=2*x^(1+m)*(a+b*x^n)^(3/2)/(2+2*m+3*n)+6*a*n*x^(1+m)*_ +-- sqrt(a+b*x^n)/((2+2*m+n)*(2+2*m+3*n))+3*a^2*n^2*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*(2+2*m+3*n)*sqrt(a+b*x^n)) +--E 947 + +--S 948 of 1299 +--a0:=integrate(t0,x) +--E 948 + +--S 949 of 1299 +--m0:=a0-r0 +--E 949 + +--S 950 of 1299 +--d0:=D(m0,x) +--E 950 + +)clear all + +--S 951 of 1299 +t0:=x*(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R n | n +--R (1) (b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1299 +--r0:=2*x^2*(a+b*x^n)^(3/2)/(4+3*n)+6*a*n*x^2*sqrt(a+b*x^n)/_ +-- ((4+n)*(4+3*n))+3/2*a^2*n^2*x^2*hypergeometric(1/2,2/n,_ +-- (2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((4+n)*(4+3*n)*sqrt(a+b*x^n)) +--E 952 + +--S 953 of 1299 +--a0:=integrate(t0,x) +--E 953 + +--S 954 of 1299 +--m0:=a0-r0 +--E 954 + +--S 955 of 1299 +--d0:=D(m0,x) +--E 955 + +)clear all + +--S 956 of 1299 +t0:=(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R n | n +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1299 +--r0:=2*x*(a+b*x^n)^(3/2)/(2+3*n)+6*a*n*x*sqrt(a+b*x^n)/(4+8*n+3*n^2)+_ +-- 3*a^2*n^2*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4+8*n+3*n^2)*sqrt(a+b*x^n)) +--E 957 + +--S 958 of 1299 +--a0:=integrate(t0,x) +--E 958 + +--S 959 of 1299 +--m0:=a0-r0 +--E 959 + +--S 960 of 1299 +--d0:=D(m0,x) +--E 960 + +)clear all + +--S 961 of 1299 +t0:=(a+b*x^n)^(3/2)/x +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1299 +r0:=2/3*(a+b*x^n)^(3/2)/n-2*a^(3/2)*atanh(sqrt(a+b*x^n)/sqrt(a))/n+2*a*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a n | n +--R - 6a\|a atanh(-----------) + (2b x + 8a)\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 3n +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R 3a\|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 8a)\|b %e + a +--R / +--R 3n +--R , +--R +--R +----------------+ +--R | n log(x) +--R +---+ \|b %e + a +--R - 6a\|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 8a)\|b %e + a +--R / +--R 3n +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R 3a\|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n log(x) | n log(x) +-+ \|b x + a +--R (2b %e + 8a)\|b %e + a + 6a\|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R n | n +--R (- 2b x - 8a)\|b x + a +--R / +--R 3n +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +--R +---+ \|b %e + a +--R - 6a\|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +--------+ +--R +----------------+ | n +--R n log(x) | n log(x) +-+ \|b x + a +--R (2b %e + 8a)\|b %e + a + 6a\|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R n | n +--R (- 2b x - 8a)\|b x + a +--R / +--R 3n +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1299 +t0:=(a+b*x^n)^(3/2)/x^2 +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1299 +--r0:=-2*(a+b*x^n)^(3/2)/((2-3*n)*x)+6*a*n*sqrt(a+b*x^n)/_ +-- ((4-8*n+3*n^2)*x)-3*a^2*n^2*hypergeometric(1/2,(-1)/n,_ +-- (-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((4-8*n+3*n^2)*x*sqrt(a+b*x^n)) +--E 969 + +--S 970 of 1299 +--a0:=integrate(t0,x) +--E 970 + +--S 971 of 1299 +--m0:=a0-r0 +--E 971 + +--S 972 of 1299 +--d0:=D(m0,x) +--E 972 + +)clear all + +--S 973 of 1299 +t0:=(a+b*x^n)^(3/2)/x^3 +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1299 +--r0:=-2*(a+b*x^n)^(3/2)/((4-3*n)*x^2)+6*a*n*sqrt(a+b*x^n)/_ +-- ((16-16*n+3*n^2)*x^2)-3/2*a^2*n^2*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((16-16*n+3*n^2)*x^2*sqrt(a+b*x^n)) +--E 974 + +--S 975 of 1299 +--a0:=integrate(t0,x) +--E 975 + +--S 976 of 1299 +--m0:=a0-r0 +--E 976 + +--S 977 of 1299 +--d0:=D(m0,x) +--E 977 + +)clear all + +--S 978 of 1299 +t0:=x^m*(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 m n 2 m n 2 m | n +--R (1) (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1299 +--r0:=10*a*n*x^(1+m)*(a+b*x^n)^(3/2)/((2+2*m+3*n)*(2+2*m+5*n))+_ +-- 2*x^(1+m)*(a+b*x^n)^(5/2)/(2+2*m+5*n)+30*a^2*n^2*x^(1+m)*_ +-- sqrt(a+b*x^n)/((2+2*m+n)*(2+2*m+3*n)*(2+2*m+5*n))+15*a^3*n^3*_ +-- x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*(2+2*m+3*n)*_ +-- (2+2*m+5*n)*sqrt(a+b*x^n)) +--E 979 + +--S 980 of 1299 +--a0:=integrate(t0,x) +--E 980 + +--S 981 of 1299 +--m0:=a0-r0 +--E 981 + +--S 982 of 1299 +--d0:=D(m0,x) +--E 982 + +)clear all + +--S 983 of 1299 +t0:=x*(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (1) (b x (x ) + 2a b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1299 +--r0:=10*a*n*x^2*(a+b*x^n)^(3/2)/(16+32*n+15*n^2)+2*x^2*(a+_ +-- b*x^n)^(5/2)/(4+5*n)+30*a^2*n^2*x^2*sqrt(a+b*x^n)/((4+n)*_ +-- (4+3*n)*(4+5*n))+15/2*a^3*n^3*x^2*hypergeometric(1/2,2/n,(2+n)/n,_ +-- -b*x^n/a)*sqrt((a+b*x^n)/a)/((4+n)*(4+3*n)*(4+5*n)*sqrt(a+b*x^n)) +--E 984 + +--S 985 of 1299 +--a0:=integrate(t0,x) +--E 985 + +--S 986 of 1299 +--m0:=a0-r0 +--E 986 + +--S 987 of 1299 +--d0:=D(m0,x) +--E 987 + +)clear all + +--S 988 of 1299 +t0:=(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (1) (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1299 +--r0:=10*a*n*x*(a+b*x^n)^(3/2)/(4+16*n+15*n^2)+2*x*(a+b*x^n)^(5/2)/_ +-- (2+5*n)+30*a^2*n^2*x*sqrt(a+b*x^n)/(8+36*n+46*n^2+15*n^3)+_ +-- 15*a^3*n^3*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((8+36*n+46*n^2+15*n^3)*sqrt(a+b*x^n)) +--E 989 + +--S 990 of 1299 +--a0:=integrate(t0,x) +--E 990 + +--S 991 of 1299 +--m0:=a0-r0 +--E 991 + +--S 992 of 1299 +--d0:=D(m0,x) +--E 992 + +)clear all + +--S 993 of 1299 +t0:=(a+b*x^n)^(5/2)/x +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1299 +r0:=2/3*a*(a+b*x^n)^(3/2)/n+2/5*(a+b*x^n)^(5/2)/n-2*a^(5/2)*atanh(sqrt(a+b*x^n)/sqrt(a))/n+2*a^2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R - 30a \|a atanh(-----------) + (6b (x ) + 22a b x + 46a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------------- +--R 15n +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R 2 +-+ - 2\|a \|b %e + a + b %e + 2a +--R 15a \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R / +--R 15n +--R , +--R +--R +----------------+ +--R | n log(x) +--R 2 +---+ \|b %e + a +--R - 30a \|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R / +--R 15n +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 995 + +--S 996 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R 2 +-+ - 2\|a \|b %e + a + b %e + 2a +--R 15a \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R 30a \|a atanh(-----------) + (- 6b (x ) - 22a b x - 46a )\|b x + a +--R +-+ +--R \|a +--R / +--R 15n +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +--R 2 +---+ \|b %e + a +--R - 30a \|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R 30a \|a atanh(-----------) + (- 6b (x ) - 22a b x - 46a )\|b x + a +--R +-+ +--R \|a +--R / +--R 15n +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 999 + +)clear all + +--S 1000 of 1299 +t0:=(a+b*x^n)^(5/2)/x^2 +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1299 +--r0:=10*a*n*(a+b*x^n)^(3/2)/((4-16*n+15*n^2)*x)-2*(a+b*x^n)^(5/2)/_ +-- ((2-5*n)*x)-30*a^2*n^2*sqrt(a+b*x^n)/((2-5*n)*(4-8*n+3*n^2)*x)+_ +-- 15*a^3*n^3*hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((2-5*n)*(4-8*n+3*n^2)*x*sqrt(a+b*x^n)) +--E 1001 + +--S 1002 of 1299 +--a0:=integrate(t0,x) +--E 1002 + +--S 1003 of 1299 +--m0:=a0-r0 +--E 1003 + +--S 1004 of 1299 +--d0:=D(m0,x) +--E 1004 + +)clear all + +--S 1005 of 1299 +t0:=(a+b*x^n)^(5/2)/x^3 +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1299 +--r0:=10*a*n*(a+b*x^n)^(3/2)/((16-32*n+15*n^2)*x^2)-2*(a+b*x^n)^(5/2)/_ +-- ((4-5*n)*x^2)-30*a^2*n^2*sqrt(a+b*x^n)/((4-5*n)*(16-16*n+3*n^2)*_ +-- x^2)+15/2*a^3*n^3*hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4-5*n)*(16-16*n+3*n^2)*x^2*sqrt(a+b*x^n)) +--E 1006 + +--S 1007 of 1299 +--a0:=integrate(t0,x) +--E 1007 + +--S 1008 of 1299 +--m0:=a0-r0 +--E 1008 + +--S 1009 of 1299 +--d0:=D(m0,x) +--E 1009 + +)clear all + +--S 1010 of 1299 +t0:=x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1299 +--r0:=x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*sqrt(a+b*x^n)) +--E 1011 + +--S 1012 of 1299 +--a0:=integrate(t0,x) +--E 1012 + +--S 1013 of 1299 +--m0:=a0-r0 +--E 1013 + +--S 1014 of 1299 +--d0:=D(m0,x) +--E 1014 + +)clear all + +--S 1015 of 1299 +t0:=x/(a+b*x^n)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1299 +--r0:=1/2*x^2*hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/sqrt(a+b*x^n) +--E 1016 + +--S 1017 of 1299 +--a0:=integrate(t0,x) +--E 1017 + +--S 1018 of 1299 +--m0:=a0-r0 +--E 1018 + +--S 1019 of 1299 +--d0:=D(m0,x) +--E 1019 + +)clear all + +--S 1020 of 1299 +t0:=1/(a+b*x^n)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1299 +--r0:=x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/sqrt(a+b*x^n) +--E 1021 + +--S 1022 of 1299 +--a0:=integrate(t0,x) +--E 1022 + +--S 1023 of 1299 +--m0:=a0-r0 +--E 1023 + +--S 1024 of 1299 +--d0:=D(m0,x) +--E 1024 + +)clear all + +--S 1025 of 1299 +t0:=1/(x*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | n +--R x\|b x + a +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a)) +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R [-------------------------------------------------------, +--R +-+ +--R n\|a +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R 2atan(-------------------------) +--R a +--R - --------------------------------] +--R +---+ +--R n\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1027 + +--S 1028 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--------+ +--R | n log(x) +-+ n log(x) +-+ | n +--R - 2a\|b %e + a + b\|a %e + 2a\|a \|b x + a +--R log(--------------------------------------------------) + 2atanh(-----------) +--R n log(x) +-+ +--R %e \|a +--R ----------------------------------------------------------------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1299 +m0b:=a0.2-r0 +--R +--R +--R +----------------+ +--------+ +--R +---+ | n log(x) | n +--R +-+ \|- a \|b %e + a +---+ \|b x + a +--R - 2\|a atan(-------------------------) + 2\|- a atanh(-----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------------------------ +--R +---+ +-+ +--R n\|- a \|a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1299 +t0:=1/(x^2*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | n +--R x \|b x + a +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1299 +--r0:=-hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(x*sqrt(a+b*x^n)) +--E 1033 + +--S 1034 of 1299 +--a0:=integrate(t0,x) +--E 1034 + +--S 1035 of 1299 +--m0:=a0-r0 +--E 1035 + +--S 1036 of 1299 +--d0:=D(m0,x) +--E 1036 + +)clear all + +--S 1037 of 1299 +t0:=1/(x^3*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | n +--R x \|b x + a +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1299 +--r0:=-1/2*hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(x^2*sqrt(a+b*x^n)) +--E 1038 + +--S 1039 of 1299 +--a0:=integrate(t0,x) +--E 1039 + +--S 1040 of 1299 +--m0:=a0-r0 +--E 1040 + +--S 1041 of 1299 +--d0:=D(m0,x) +--E 1041 + +)clear all + +--S 1042 of 1299 +t0:=x^m/(a+b*x^n)^(3/2) +--R +--R +--R m +--R x +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1299 +--r0:=2*x^(1+m)/(a*n*sqrt(a+b*x^n))-(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a*(1+m)*n*sqrt(a+b*x^n)) +--E 1043 + +--S 1044 of 1299 +--a0:=integrate(t0,x) +--E 1044 + +--S 1045 of 1299 +--m0:=a0-r0 +--E 1045 + +--S 1046 of 1299 +--d0:=D(m0,x) +--E 1046 + +)clear all + +--S 1047 of 1299 +t0:=x/(a+b*x^n)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1299 +--r0:=2*x^2/(a*n*sqrt(a+b*x^n))-1/2*(4-n)*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*n*sqrt(a+b*x^n)) +--E 1048 + +--S 1049 of 1299 +--a0:=integrate(t0,x) +--E 1049 + +--S 1050 of 1299 +--m0:=a0-r0 +--E 1050 + +--S 1051 of 1299 +--d0:=D(m0,x) +--E 1051 + +)clear all + +--S 1052 of 1299 +t0:=1/(a+b*x^n)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1299 +--r0:=2*x/(a*n*sqrt(a+b*x^n))-(2-n)*x*_ +-- hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*n*sqrt(a+b*x^n)) +--E 1053 + +--S 1054 of 1299 +--a0:=integrate(t0,x) +--E 1054 + +--S 1055 of 1299 +--m0:=a0-r0 +--E 1055 + +--S 1056 of 1299 +--d0:=D(m0,x) +--E 1056 + +)clear all + +--S 1057 of 1299 +t0:=1/(x*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R n | n +--R (b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)+2/(a*n*sqrt(a+b*x^n)) +--R +--R +--R +--------+ +--R +--------+ | n +--R | n \|b x + a +-+ +--R - 2\|b x + a atanh(-----------) + 2\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R +--------+ +--R +-+ | n +--R a n\|a \|b x + a +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +-+ +--R 2\|a +--R / +--R +----------------+ +--R +-+ | n log(x) +--R a n\|a \|b %e + a +--R , +--R +----------------+ +--R +----------------+ +---+ | n log(x) +--R | n log(x) \|- a \|b %e + a +---+ +--R - 2\|b %e + a atan(-------------------------) + 2\|- a +--R a +--R ---------------------------------------------------------------] +--R +----------------+ +--R +---+ | n log(x) +--R a n\|- a \|b %e + a +--R Type: Union(List(Expression(Integer)),...) +--E 1059 + +--S 1060 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +----------------+ +--R | n | n log(x) +--R \|b x + a \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +--------+ | n +----------------+ +--R | n \|b x + a +-+ | n log(x) +--R (2\|b x + a atanh(-----------) - 2\|a )\|b %e + a +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ | n +--R 2\|a \|b x + a +--R / +--R +--------+ +----------------+ +--R +-+ | n | n log(x) +--R a n\|a \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +--------+ +----------------+ +---+ | n log(x) +--R +-+ | n | n log(x) \|- a \|b %e + a +--R - 2\|a \|b x + a \|b %e + a atan(-------------------------) +--R a +--R + +--R +--------+ +--R +--------+ | n +----------------+ +--R +---+ | n \|b x + a +---+ +-+ | n log(x) +--R (2\|- a \|b x + a atanh(-----------) - 2\|- a \|a )\|b %e + a +--R +-+ +--R \|a +--R + +--R +--------+ +--R +---+ +-+ | n +--R 2\|- a \|a \|b x + a +--R / +--R +--------+ +----------------+ +--R +---+ +-+ | n | n log(x) +--R a n\|- a \|a \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1299 +t0:=1/(x^2*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R 2 n 2 | n +--R (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1299 +--r0:=2/(a*n*x*sqrt(a+b*x^n))-(2+n)*hypergeometric(1/2,(-1)/n,_ +-- (-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a*n*x*sqrt(a+b*x^n)) +--E 1065 + +--S 1066 of 1299 +--a0:=integrate(t0,x) +--E 1066 + +--S 1067 of 1299 +--m0:=a0-r0 +--E 1067 + +--S 1068 of 1299 +--d0:=D(m0,x) +--E 1068 + +)clear all + +--S 1069 of 1299 +t0:=1/(x^3*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R 3 n 3 | n +--R (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1299 +--r0:=2/(a*n*x^2*sqrt(a+b*x^n))-1/2*(4+n)*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a*n*x^2*sqrt(a+b*x^n)) +--E 1070 + +--S 1071 of 1299 +--a0:=integrate(t0,x) +--E 1071 + +--S 1072 of 1299 +--m0:=a0-r0 +--E 1072 + +--S 1073 of 1299 +--d0:=D(m0,x) +--E 1073 + +)clear all + +--S 1074 of 1299 +t0:=x^m/(a+b*x^n)^(5/2) +--R +--R +--R m +--R x +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1299 +--r0:=2/3*x^(1+m)/(a*n*(a+b*x^n)^(3/2))-2/3*(2+2*m-3*n)*x^(1+m)/_ +-- (a^2*n^2*sqrt(a+b*x^n))+1/3*(2+2*m-3*n)*(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*(1+m)*n^2*sqrt(a+b*x^n)) +--E 1075 + +--S 1076 of 1299 +--a0:=integrate(t0,x) +--E 1076 + +--S 1077 of 1299 +--m0:=a0-r0 +--E 1077 + +--S 1078 of 1299 +--d0:=D(m0,x) +--E 1078 + +)clear all + +--S 1079 of 1299 +t0:=x/(a+b*x^n)^(5/2) +--R +--R +--R x +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1299 +--r0:=2/3*x^2/(a*n*(a+b*x^n)^(3/2))-2/3*(4-3*n)*x^2/(a^2*n^2*_ +-- sqrt(a+b*x^n))+1/6*(4-3*n)*(4-n)*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a^2*n^2*sqrt(a+b*x^n)) +--E 1080 + +--S 1081 of 1299 +--a0:=integrate(t0,x) +--E 1081 + +--S 1082 of 1299 +--m0:=a0-r0 +--E 1082 + +--S 1083 of 1299 +--d0:=D(m0,x) +--E 1083 + +)clear all + +--S 1084 of 1299 +t0:=1/(a+b*x^n)^(5/2) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1299 +--r0:=2/3*x/(a*n*(a+b*x^n)^(3/2))-2/3*(2-3*n)*x/(a^2*n^2*sqrt(a+b*x^n))+_ +-- 1/3*(2-3*n)*(2-n)*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*n^2*sqrt(a+b*x^n)) +--E 1085 + +--S 1086 of 1299 +--a0:=integrate(t0,x) +--E 1086 + +--S 1087 of 1299 +--m0:=a0-r0 +--E 1087 + +--S 1088 of 1299 +--d0:=D(m0,x) +--E 1088 + +)clear all + +--S 1089 of 1299 +t0:=1/(x*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b x (x ) + 2a b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1299 +r0:=2/3/(a*n*(a+b*x^n)^(3/2))-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)+2/(a^2*n*sqrt(a+b*x^n)) +--R +--R +--R +--------+ +--R +--------+ | n +--R n | n \|b x + a n +-+ +--R (- 6b x - 6a)\|b x + a atanh(-----------) + (6b x + 8a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 2 n 3 +-+ | n +--R (3a b n x + 3a n)\|a \|b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R n log(x) | n log(x) +--R (3b %e + 3a)\|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +-+ n log(x) +-+ +--R 6b\|a %e + 8a\|a +--R / +--R +----------------+ +--R 2 +-+ n log(x) 3 +-+ | n log(x) +--R (3a b n\|a %e + 3a n\|a )\|b %e + a +--R , +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (- 6b %e - 6a)\|b %e + a +--R * +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R atan(-------------------------) +--R a +--R + +--R +---+ n log(x) +---+ +--R 6b\|- a %e + 8a\|- a +--R / +--R +----------------+ +--R 2 +---+ n log(x) 3 +---+ | n log(x) +--R (3a b n\|- a %e + 3a n\|- a )\|b %e + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1091 + +--S 1092 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((3b x + 3a b)%e + 3a b x + 3a )\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((6b x + 6a b)%e + 6a b x + 6a )\|b x + a +--R * +--R +--------+ +--R | n +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 n +-+ n log(x) n 2 +-+ +--R (- 6b x - 8a b)\|a %e + (- 6a b x - 8a )\|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 2 n +-+ n log(x) n 2 +-+ | n +--R ((6b x + 6a b)\|a %e + (8a b x + 8a )\|a )\|b x + a +--R / +--R +--------+ +--R 2 2 n 3 +-+ n log(x) 3 n 4 +-+ | n +--R ((3a b n x + 3a b n)\|a %e + (3a b n x + 3a n)\|a )\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 n +-+ n log(x) n 2 +-+ | n +--R ((- 6b x - 6a b)\|a %e + (- 6a b x - 6a )\|a )\|b x + a +--R * +--R +----------------+ +--R +----------------+ +---+ | n log(x) +--R | n log(x) \|- a \|b %e + a +--R \|b %e + a atan(-------------------------) +--R a +--R + +--R +--------+ +--R 2 n +---+ n log(x) n 2 +---+ | n +--R ((6b x + 6a b)\|- a %e + (6a b x + 6a )\|- a )\|b x + a +--R * +--R +--------+ +--R | n +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 n +---+ +-+ n log(x) n 2 +---+ +-+ +--R (- 6b x - 8a b)\|- a \|a %e + (- 6a b x - 8a )\|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 2 n +---+ +-+ n log(x) n 2 +---+ +-+ | n +--R ((6b x + 6a b)\|- a \|a %e + (8a b x + 8a )\|- a \|a )\|b x + a +--R / +--R 2 2 n 3 +---+ +-+ n log(x) 3 n 4 +---+ +-+ +--R ((3a b n x + 3a b n)\|- a \|a %e + (3a b n x + 3a n)\|- a \|a ) +--R * +--R +--------+ +----------------+ +--R | n | n log(x) +--R \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1299 +t0:=1/(x^2*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R +--------+ +--R 2 2 n 2 2 n 2 2 | n +--R (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1299 +--r0:=2/3/(a*n*x*(a+b*x^n)^(3/2))+2/3*(2+3*n)/(a^2*n^2*x*sqrt(a+b*x^n))-_ +-- 1/3*(2+n)*(2+3*n)*hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*n^2*x*sqrt(a+b*x^n)) +--E 1097 + +--S 1098 of 1299 +--a0:=integrate(t0,x) +--E 1098 + +--S 1099 of 1299 +--m0:=a0-r0 +--E 1099 + +--S 1100 of 1299 +--d0:=D(m0,x) +--E 1100 + +)clear all + +--S 1101 of 1299 +t0:=1/(x^3*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R +--------+ +--R 2 3 n 2 3 n 2 3 | n +--R (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1299 +--r0:=2/3/(a*n*x^2*(a+b*x^n)^(3/2))+2/3*(4+3*n)/(a^2*n^2*x^2*_ +-- sqrt(a+b*x^n))-1/6*(4+n)*(4+3*n)*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a^2*n^2*x^2*sqrt(a+b*x^n)) +--E 1102 + +--S 1103 of 1299 +--a0:=integrate(t0,x) +--E 1103 + +--S 1104 of 1299 +--m0:=a0-r0 +--E 1104 + +--S 1105 of 1299 +--d0:=D(m0,x) +--E 1105 + +)clear all + +--S 1106 of 1299 +t0:=x^(3+2*n)/sqrt(a+b*x^n) +--R +--R +--R 2n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1299 +--r0:=-4*a*(4+n)*x^4*sqrt(a+b*x^n)/(b^2*(8+n)*(8+3*n))+2*x^(4+n)*_ +-- sqrt(a+b*x^n)/(b*(8+3*n))+4*a^2*(4+n)*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (b^2*(8+n)*(8+3*n)*sqrt(a+b*x^n)) +--E 1107 + +--S 1108 of 1299 +--a0:=integrate(t0,x) +--E 1108 + +--S 1109 of 1299 +--m0:=a0-r0 +--E 1109 + +--S 1110 of 1299 +--d0:=D(m0,x) +--E 1110 + +)clear all + +--S 1111 of 1299 +t0:=x^(3+n)/sqrt(a+b*x^n) +--R +--R +--R n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1299 +--r0:=2*x^4*sqrt(a+b*x^n)/(b*(8+n))-2*a*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b*(8+n)*sqrt(a+b*x^n)) +--E 1112 + +--S 1113 of 1299 +--a0:=integrate(t0,x) +--E 1113 + +--S 1114 of 1299 +--m0:=a0-r0 +--E 1114 + +--S 1115 of 1299 +--d0:=D(m0,x) +--E 1115 + +)clear all + +--S 1116 of 1299 +t0:=x^(3-n)/sqrt(a+b*x^n) +--R +--R +--R - n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1299 +--r0:=x^(4-n)*sqrt(a+b*x^n)/(a*(4-n))-1/8*b*(8-n)*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*(4-n)*sqrt(a+b*x^n)) +--E 1117 + +--S 1118 of 1299 +--a0:=integrate(t0,x) +--E 1118 + +--S 1119 of 1299 +--m0:=a0-r0 +--E 1119 + +--S 1120 of 1299 +--d0:=D(m0,x) +--E 1120 + +)clear all + +--S 1121 of 1299 +t0:=x^(3-2*n)/sqrt(a+b*x^n) +--R +--R +--R - 2n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1299 +--r0:=1/2*x^(4-2*n)*sqrt(a+b*x^n)/(a*(2-n))-1/4*b*(8-3*n)*x^(4-n)*_ +-- sqrt(a+b*x^n)/(a^2*(2-n)*(4-n))+1/32*b^2*(8-3*n)*(8-n)*_ +-- x^4*hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a^2*(2-n)*(4-n)*sqrt(a+b*x^n)) +--E 1122 + +--S 1123 of 1299 +--a0:=integrate(t0,x) +--E 1123 + +--S 1124 of 1299 +--m0:=a0-r0 +--E 1124 + +--S 1125 of 1299 +--d0:=D(m0,x) +--E 1125 + +)clear all + +--S 1126 of 1299 +t0:=x^(m+2*n)/sqrt(a+b*x^n) +--R +--R +--R 2n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1299 +--r0:=-4*a*(1+m+n)*x^(1+m)*sqrt(a+b*x^n)/(b^2*(2+2*m+n)*(2+2*m+3*n))+_ +-- 2*x^(1+m+n)*sqrt(a+b*x^n)/(b*(2+2*m+3*n))+4*a^2*(1+m+n)*_ +-- x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b^2*(2+2*m+n)*(2+2*m+3*n)*sqrt(a+b*x^n)) +--E 1127 + +--S 1128 of 1299 +--a0:=integrate(t0,x) +--E 1128 + +--S 1129 of 1299 +--m0:=a0-r0 +--E 1129 + +--S 1130 of 1299 +--d0:=D(m0,x) +--E 1130 + +)clear all + +--S 1131 of 1299 +t0:=x^(m+n)/sqrt(a+b*x^n) +--R +--R +--R n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1299 +--r0:=2*x^(1+m)*sqrt(a+b*x^n)/(b*(2+2*m+n))-2*a*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b*(2+2*m+n)*sqrt(a+b*x^n)) +--E 1132 + +--S 1133 of 1299 +--a0:=integrate(t0,x) +--E 1133 + +--S 1134 of 1299 +--m0:=a0-r0 +--E 1134 + +--S 1135 of 1299 +--d0:=D(m0,x) +--E 1135 + +)clear all + +--S 1136 of 1299 +t0:=x^(m-n)/sqrt(a+b*x^n) +--R +--R +--R - n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1299 +--r0:=x^(1+m-n)*sqrt(a+b*x^n)/(a*(1+m-n))-1/2*b*(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a*(1+m)*(1+m-n)*sqrt(a+b*x^n)) +--E 1137 + +--S 1138 of 1299 +--a0:=integrate(t0,x) +--E 1138 + +--S 1139 of 1299 +--m0:=a0-r0 +--E 1139 + +--S 1140 of 1299 +--d0:=D(m0,x) +--E 1140 + +)clear all + +--S 1141 of 1299 +t0:=x^(m-2*n)/sqrt(a+b*x^n) +--R +--R +--R - 2n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1299 +--r0:=x^(1+m-2*n)*sqrt(a+b*x^n)/(a*(1+m-2*n))-1/2*b*(2+2*m-3*n)*_ +-- x^(1+m-n)*sqrt(a+b*x^n)/(a^2*(1+m-2*n)*(1+m-n))+1/4*b^2*_ +-- (2+2*m-3*n)*(2+2*m-n)*x^(1+m)*hypergeometric(1/2,(1+m)/n,_ +-- (1+m+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a^2*(1+m)*(1+m-2*n)*_ +-- (1+m-n)*sqrt(a+b*x^n)) +--E 1142 + +--S 1143 of 1299 +--a0:=integrate(t0,x) +--E 1143 + +--S 1144 of 1299 +--m0:=a0-r0 +--E 1144 + +--S 1145 of 1299 +--d0:=D(m0,x) +--E 1145 + +)clear all + +--S 1146 of 1299 +t0:=-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^n) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (1) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1299 +r0a:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1299 +r0b:=-b*x^(m+n)/(a*sqrt(a+b*x^n))+x^m*sqrt(a+b*x^n)/a +--R +--R +--R n + m m n m +--R - b x + b x x + a x +--R (3) -------------------------- +--R +--------+ +--R | n +--R a\|b x + a +--R Type: Expression(Integer) +--E 1148 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1149 of 1299 +--a0:=integrate(t0,x) +--E 1149 + +--S 1150 of 1299 +--m0a:=a0-r0a +--E 1150 + +--S 1151 of 1299 +--d0a:=D(m0a,x) +--E 1151 + +--S 1152 of 1299 +--m0b:=a0-r0b +--E 1152 + +--S 1153 of 1299 +--d0b:=D(m0b,x) +--E 1153 + +)clear all + +--S 1154 of 1299 +t0:=x^m/sqrt(a+b*x^(-2+m)) +--R +--R +--R m +--R x +--R (1) --------------- +--R +------------+ +--R | m - 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1299 +--r0:=2*x^(1+m)*hypergeometric(1/2,1/2*(4+m)/(2-m),1/2*(8-m)/(2-m),_ +-- -a*x^(2-m)/b)*sqrt((b+a*x^(2-m))/b)/((4+m)*sqrt(a+b*x^(-2+m))) +--E 1155 + +--S 1156 of 1299 +--a0:=integrate(t0,x) +--E 1156 + +--S 1157 of 1299 +--m0:=a0-r0 +--E 1157 + +--S 1158 of 1299 +--d0:=D(m0,x) +--E 1158 + +)clear all + +--S 1159 of 1299 +t0:=x^m/sqrt(a+b*x^(2-m)) +--R +--R +--R m +--R x +--R (1) ----------------- +--R +--------------+ +--R | - m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1299 +--r0:=x^(1+m)*sqrt(a+b*x^(2-m))/(a*(1+m))-1/6*b*(4+m)*x^3*_ +-- hypergeometric(1/2,3/(2-m),(5-m)/(2-m),-b*x^(2-m)/a)*_ +-- sqrt((a+b*x^(2-m))/a)/(a*(1+m)*sqrt(a+b*x^(2-m))) +--E 1160 + +--S 1161 of 1299 +--a0:=integrate(t0,x) +--E 1161 + +--S 1162 of 1299 +--m0:=a0-r0 +--E 1162 + +--S 1163 of 1299 +--d0:=D(m0,x) +--E 1163 + +)clear all + +--S 1164 of 1299 +t0:=6*a*x^2/(b*(4+m)*sqrt(a+b*x^(-2+m)))+x^m/sqrt(a+b*x^(-2+m)) +--R +--R +--R m 2 +--R (b m + 4b)x + 6a x +--R (1) ------------------------- +--R +------------+ +--R | m - 2 +--R (b m + 4b)\|b x + a +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1299 +r0a:=2*x^3*sqrt(a+b*x^(-2+m))/(b*(4+m)) +--R +--R +--R +------------+ +--R 3 | m - 2 +--R 2x \|b x + a +--R (2) ------------------ +--R b m + 4b +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1299 +r0b:=2*x^(1+m)*(b+a*x^(2-m))/(b*(4+m)*sqrt(a+b*x^(-2+m))) +--R +--R +--R - m + 2 m + 1 +--R (2a x + 2b)x +--R (3) ------------------------- +--R +------------+ +--R | m - 2 +--R (b m + 4b)\|b x + a +--R Type: Expression(Integer) +--E 1166 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1167 of 1299 +--a0:=integrate(t0,x) +--E 1167 + +--S 1168 of 1299 +--m0a:=a0-r0a +--E 1168 + +--S 1169 of 1299 +--d0a:=D(m0a,x) +--E 1169 + +--S 1170 of 1299 +--m0b:=a0-r0b +--E 1170 + +--S 1171 of 1299 +--d0b:=D(m0b,x) +--E 1171 + +)clear all + +--S 1172 of 1299 +t0:=1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2) +--R +--R +--R m - 1 n m - 1 +--R (- b n + 2b m)x x + 2a m x +--R (1) ------------------------------------ +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1299 +r0:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R (m - 1)log(x) | n log(x) +--R x %e \|b %e + a +--R (3) ------------------------------------ +--R n log(x) +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +----------------+ +--R (m - 1)log(x) | n | n log(x) m n log(x) m +--R x %e \|b x + a \|b %e + a - b x %e - a x +--R ----------------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1176 + +)clear all + +--S 1177 of 1299 +t0:=-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^n) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (1) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1299 +r0a:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1299 +r0b:=-b*x^(m+n)/(a*sqrt(a+b*x^n))+x^m*sqrt(a+b*x^n)/a +--R +--R +--R n + m m n m +--R - b x + b x x + a x +--R (3) -------------------------- +--R +--------+ +--R | n +--R a\|b x + a +--R Type: Expression(Integer) +--E 1179 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1180 of 1299 +--a0:=integrate(t0,x) +--E 1180 + +--S 1181 of 1299 +--m0a:=a0-r0a +--E 1181 + +--S 1182 of 1299 +--d0a:=D(m0a,x) +--E 1182 + +--S 1183 of 1299 +--m0b:=a0-r0b +--E 1183 + +--S 1184 of 1299 +--d0b:=D(m0b,x) +--E 1184 + +)clear all + +--S 1185 of 1299 +t0:=(a+b*x^n)^(1/3)/x +--R +--R +--R +--------+ +--R 3| n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1299 +r0:=3*(a+b*x^n)^(1/3)/n+a^(1/3)*log(a^(1/3)-(a+b*x^n)^(1/3))/n-_ + 1/2*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x^n)^(1/3)+(a+b*x^n)^(2/3))/n-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x^n)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/n +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3+-+ 3| n 3+-+3| n 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| n 3+-+ +--R 3+-+ 3| n 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) - 2\|3 \|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R 3| n +--R 6\|b x + a +--R / +--R 2n +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+2 +----------------+ +--R 3+-+ 3| n log(x) 3+-+3| n log(x) 3+-+2 +--R - \|a log(\|b %e + a + \|a \|b %e + a + \|a ) +--R + +--R +----------------+ +--R 3+-+ 3| n log(x) 3+-+ +--R 2\|a log(\|b %e + a - \|a ) +--R + +--R +----------------+ +--R 3| n log(x) 3+-+ +----------------+ +--R +-+3+-+ 2\|b %e + a + \|a 3| n log(x) +--R - 2\|3 \|a atan(---------------------------) + 6\|b %e + a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+2 +----------------+ +--R 3+-+ 3| n log(x) 3+-+3| n log(x) 3+-+2 +--R - \|a log(\|b %e + a + \|a \|b %e + a + \|a ) +--R + +--R +----------------+ +--R 3+-+ 3| n log(x) 3+-+ +--R 2\|a log(\|b %e + a - \|a ) +--R + +--R +----------------+ +--R 3| n log(x) 3+-+ +----------------+ +--R +-+3+-+ 2\|b %e + a + \|a 3| n log(x) +--R - 2\|3 \|a atan(---------------------------) + 6\|b %e + a +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--------+ +--R 3+-+ 3| n 3+-+3| n 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| n 3+-+ +--R 3+-+ 3| n 3+-+ +-+3+-+ 2\|b x + a + \|a +--R - 2\|a log(- \|b x + a + \|a ) + 2\|3 \|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R 3| n +--R - 6\|b x + a +--R / +--R 2n +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n) +--R +--R +--R n 4n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1299 +r0:=1/4*a*x^(4*n)/n+1/5*b*x^(5*n)/n +--R +--R +--R 5n 4n +--R 4b x + 5a x +--R (2) --------------- +--R 20n +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 5 n log(x) 4 +--R 4b (%e ) + 5a (%e ) +--R (3) ----------------------------------- +--R 20n +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 5 n log(x) 4 5n 4n +--R 4b (%e ) + 5a (%e ) - 4b x - 5a x +--R (4) ----------------------------------------------------- +--R 20n +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1299 +t0:=x^(-1+3*n)*(a+b*x^n) +--R +--R +--R n 3n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1299 +r0:=1/3*a*x^(3*n)/n+1/4*b*x^(4*n)/n +--R +--R +--R 4n 3n +--R 3b x + 4a x +--R (2) --------------- +--R 12n +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 4 n log(x) 3 +--R 3b (%e ) + 4a (%e ) +--R (3) ----------------------------------- +--R 12n +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 4 n log(x) 3 4n 3n +--R 3b (%e ) + 4a (%e ) - 3b x - 4a x +--R (4) ----------------------------------------------------- +--R 12n +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1299 +t0:=x^(-1+2*n)*(a+b*x^n) +--R +--R +--R n 2n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1299 +r0:=1/2*a*x^(2*n)/n+1/3*b*x^(3*n)/n +--R +--R +--R 3n 2n +--R 2b x + 3a x +--R (2) --------------- +--R 6n +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 3 n log(x) 2 +--R 2b (%e ) + 3a (%e ) +--R (3) ----------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 3 n log(x) 2 3n 2n +--R 2b (%e ) + 3a (%e ) - 2b x - 3a x +--R (4) ----------------------------------------------------- +--R 6n +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1299 +t0:=x^(-1+n)*(a+b*x^n) +--R +--R +--R n - 1 n n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1299 +r0:=a*x^n/n+1/2*b*x^(2*n)/n +--R +--R +--R 2n n +--R b x + 2a x +--R (2) ------------- +--R 2n +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 2 n log(x) +--R b (%e ) + 2a %e +--R (3) ------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 2 n log(x) 2n n +--R b (%e ) + 2a %e - b x - 2a x +--R (4) ----------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1299 +t0:=(a+b*x^n)/x +--R +--R +--R n +--R b x + a +--R (1) -------- +--R x +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1299 +r0:=b*x^n/n+a*log(x) +--R +--R +--R n +--R b x + a n log(x) +--R (2) ----------------- +--R n +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e + a n log(x) +--R (3) ------------------------- +--R n +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R b %e - b x +--R (4) ------------------- +--R n +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1299 +t0:=x^(-1-n)*(a+b*x^n) +--R +--R +--R - n - 1 n - n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1299 +r0:=-a/(n*x^n)+b*log(x) +--R +--R +--R n +--R b n log(x)x - a +--R (2) ---------------- +--R n +--R n x +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b n log(x)%e - a +--R (3) ------------------------ +--R n log(x) +--R n %e +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R a %e - a x +--R (4) ------------------- +--R n n log(x) +--R n x %e +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1299 +t0:=x^(-1-2*n)*(a+b*x^n) +--R +--R +--R - 2n - 1 n - 2n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1299 +r0:=-1/2*a/(n*x^(2*n))-b/(n*x^n) +--R +--R +--R 2n n +--R - 2b x - a x +--R (2) --------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 2b %e - a +--R (3) ------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1299 +m0:=a0-r0 +--R +--R +--R 2n n n log(x) 2 n 2n n log(x) n 2n +--R (2b x + a x )(%e ) - 2b x x %e - a x x +--R (4) ----------------------------------------------------------- +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1299 +t0:=x^(-1-3*n)*(a+b*x^n) +--R +--R +--R - 3n - 1 n - 3n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1299 +r0:=-1/3*a/(n*x^(3*n))-1/2*b/(n*x^(2*n)) +--R +--R +--R 3n 2n +--R - 3b x - 2a x +--R (2) ----------------- +--R 2n 3n +--R 6n x x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 3b %e - 2a +--R (3) -------------------- +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1299 +m0:=a0-r0 +--R +--R +--R 3n 2n n log(x) 3 2n 3n n log(x) 2n 3n +--R (3b x + 2a x )(%e ) - 3b x x %e - 2a x x +--R (4) ---------------------------------------------------------------- +--R 2n 3n n log(x) 3 +--R 6n x x (%e ) +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1299 +t0:=x^(-1-4*n)*(a+b*x^n) +--R +--R +--R - 4n - 1 n - 4n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1299 +r0:=-1/4*a/(n*x^(4*n))-1/3*b/(n*x^(3*n)) +--R +--R +--R 4n 3n +--R - 4b x - 3a x +--R (2) ----------------- +--R 3n 4n +--R 12n x x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 4b %e - 3a +--R (3) -------------------- +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1299 +m0:=a0-r0 +--R +--R +--R 4n 3n n log(x) 4 3n 4n n log(x) 3n 4n +--R (4b x + 3a x )(%e ) - 4b x x %e - 3a x x +--R (4) ---------------------------------------------------------------- +--R 3n 4n n log(x) 4 +--R 12n x x (%e ) +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1299 +t0:=x^(-1-5*n)*(a+b*x^n) +--R +--R +--R - 5n - 1 n - 5n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1299 +r0:=-1/5*a/(n*x^(5*n))-1/4*b/(n*x^(4*n)) +--R +--R +--R 5n 4n +--R - 5b x - 4a x +--R (2) ----------------- +--R 4n 5n +--R 20n x x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 5b %e - 4a +--R (3) -------------------- +--R n log(x) 5 +--R 20n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1299 +m0:=a0-r0 +--R +--R +--R 5n 4n n log(x) 5 4n 5n n log(x) 4n 5n +--R (5b x + 4a x )(%e ) - 5b x x %e - 4a x x +--R (4) ---------------------------------------------------------------- +--R 4n 5n n log(x) 5 +--R 20n x x (%e ) +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 4n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1299 +r0:=1/4*a^2*x^(4*n)/n+2/5*a*b*x^(5*n)/n+1/6*b^2*x^(6*n)/n +--R +--R +--R 2 6n 5n 2 4n +--R 10b x + 24a b x + 15a x +--R (2) ----------------------------- +--R 60n +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 6 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 24a b (%e ) + 15a (%e ) +--R (3) ----------------------------------------------------------- +--R 60n +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 6 n log(x) 5 2 n log(x) 4 2 6n +--R 10b (%e ) + 24a b (%e ) + 15a (%e ) - 10b x +--R + +--R 5n 2 4n +--R - 24a b x - 15a x +--R / +--R 60n +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1299 +t0:=x^(-1+3*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 3n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1299 +r0:=1/3*a^2*x^(3*n)/n+1/2*a*b*x^(4*n)/n+1/5*b^2*x^(5*n)/n +--R +--R +--R 2 5n 4n 2 3n +--R 6b x + 15a b x + 10a x +--R (2) ---------------------------- +--R 30n +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 5 n log(x) 4 2 n log(x) 3 +--R 6b (%e ) + 15a b (%e ) + 10a (%e ) +--R (3) ---------------------------------------------------------- +--R 30n +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 5 n log(x) 4 2 n log(x) 3 2 5n +--R 6b (%e ) + 15a b (%e ) + 10a (%e ) - 6b x +--R + +--R 4n 2 3n +--R - 15a b x - 10a x +--R / +--R 30n +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1299 +t0:=x^(-1+2*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 2n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1299 +r0:=1/2*a^2*x^(2*n)/n+2/3*a*b*x^(3*n)/n+1/4*b^2*x^(4*n)/n +--R +--R +--R 2 4n 3n 2 2n +--R 3b x + 8a b x + 6a x +--R (2) -------------------------- +--R 12n +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 4 n log(x) 3 2 n log(x) 2 +--R 3b (%e ) + 8a b (%e ) + 6a (%e ) +--R (3) -------------------------------------------------------- +--R 12n +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 4 n log(x) 3 2 n log(x) 2 2 4n +--R 3b (%e ) + 8a b (%e ) + 6a (%e ) - 3b x +--R + +--R 3n 2 2n +--R - 8a b x - 6a x +--R / +--R 12n +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1299 +t0:=x^(-1+n)*(a+b*x^n)^2 +--R +--R +--R 2 n - 1 n 2 n - 1 n 2 n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1299 +r0:=1/3*(a+b*x^n)^3/(b*n) +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (2) ----------------------------------- +--R 3b n +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 3 n log(x) 2 2 n log(x) +--R b (%e ) + 3a b (%e ) + 3a %e +--R (3) ---------------------------------------------------- +--R 3n +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 n 3 +--R b (%e ) + 3a b (%e ) + 3a b %e - b (x ) +--R + +--R 2 n 2 2 n 3 +--R - 3a b (x ) - 3a b x - a +--R / +--R 3b n +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1299 +t0:=(a+b*x^n)^2/x +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1299 +r0:=2*a*b*x^n/n+1/2*b^2*x^(2*n)/n+a^2*log(x) +--R +--R +--R 2 2n n 2 +--R b x + 4a b x + 2a n log(x) +--R (2) ----------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 4a b %e + 2a n log(x) +--R (3) ----------------------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) 2 n log(x) 2 2n n +--R b (%e ) + 4a b %e - b x - 4a b x +--R (4) --------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1299 +t0:=x^(-1-n)*(a+b*x^n)^2 +--R +--R +--R 2 - n - 1 n 2 - n - 1 n 2 - n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1299 +r0:=-a^2/(n*x^n)+b^2*x^n/n+2*a*b*log(x) +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b n log(x)x - a +--R (2) ------------------------------ +--R n +--R n x +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b n log(x)%e - a +--R (3) ---------------------------------------------- +--R n log(x) +--R n %e +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n n log(x) 2 2 n 2 2 n log(x) 2 n +--R b x (%e ) + (- b (x ) + a )%e - a x +--R (4) ----------------------------------------------------- +--R n n log(x) +--R n x %e +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1299 +t0:=x^(-1-2*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 2n - 1 n 2 - 2n - 1 n 2 - 2n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1299 +r0:=-1/2*a^2/(n*x^(2*n))-2*a*b/(n*x^n)+b^2*log(x) +--R +--R +--R 2 n 2n 2 n +--R (2b n log(x)x - 4a b)x - a x +--R (2) -------------------------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) - 4a b %e - a +--R (3) ----------------------------------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1299 +m0:=a0-r0 +--R +--R +--R 2n 2 n n log(x) 2 n 2n n log(x) 2 n 2n +--R (4a b x + a x )(%e ) - 4a b x x %e - a x x +--R (4) --------------------------------------------------------------- +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1299 +t0:=x^(-1-3*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 3n - 1 n 2 - 3n - 1 n 2 - 3n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1299 +r0:=-1/3*(a+b*x^n)^3/(a*n*x^(3*n)) +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R - b (x ) - 3a b (x ) - 3a b x - a +--R (2) ------------------------------------- +--R 3n +--R 3a n x +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 3b (%e ) - 3a b %e - a +--R (3) ----------------------------------------- +--R n log(x) 3 +--R 3n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 3 2 n 2 2 n 3 n log(x) 3 +--R (b (x ) + 3a b (x ) + 3a b x + a )(%e ) +--R + +--R 2 3n n log(x) 2 2 3n n log(x) 3 3n +--R - 3a b x (%e ) - 3a b x %e - a x +--R / +--R 3n n log(x) 3 +--R 3a n x (%e ) +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1299 +t0:=x^(-1-4*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 4n - 1 n 2 - 4n - 1 n 2 - 4n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1299 +r0:=-1/4*a^2/(n*x^(4*n))-2/3*a*b/(n*x^(3*n))-1/2*b^2/(n*x^(2*n)) +--R +--R +--R 2 3n 2n 4n 2 2n 3n +--R (- 6b x - 8a b x )x - 3a x x +--R (2) ------------------------------------ +--R 2n 3n 4n +--R 12n x x x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 6b (%e ) - 8a b %e - 3a +--R (3) ------------------------------------------ +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3n 2n 4n 2 2n 3n n log(x) 4 +--R ((6b x + 8a b x )x + 3a x x )(%e ) +--R + +--R 2 2n 3n 4n n log(x) 2 2n 3n 4n n log(x) 2 2n 3n 4n +--R - 6b x x x (%e ) - 8a b x x x %e - 3a x x x +--R / +--R 2n 3n 4n n log(x) 4 +--R 12n x x x (%e ) +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1299 +t0:=x^(-1-5*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 5n - 1 n 2 - 5n - 1 n 2 - 5n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1299 +r0:=-1/5*a^2/(n*x^(5*n))-1/2*a*b/(n*x^(4*n))-1/3*b^2/(n*x^(3*n)) +--R +--R +--R 2 4n 3n 5n 2 3n 4n +--R (- 10b x - 15a b x )x - 6a x x +--R (2) -------------------------------------- +--R 3n 4n 5n +--R 30n x x x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 10b (%e ) - 15a b %e - 6a +--R (3) -------------------------------------------- +--R n log(x) 5 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4n 3n 5n 2 3n 4n n log(x) 5 +--R ((10b x + 15a b x )x + 6a x x )(%e ) +--R + +--R 2 3n 4n 5n n log(x) 2 3n 4n 5n n log(x) 2 3n 4n 5n +--R - 10b x x x (%e ) - 15a b x x x %e - 6a x x x +--R / +--R 3n 4n 5n n log(x) 5 +--R 30n x x x (%e ) +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1299 +t0:=x^(-1-6*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 6n - 1 n 2 - 6n - 1 n 2 - 6n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1299 +r0:=-1/6*a^2/(n*x^(6*n))-2/5*a*b/(n*x^(5*n))-1/4*b^2/(n*x^(4*n)) +--R +--R +--R 2 5n 4n 6n 2 4n 5n +--R (- 15b x - 24a b x )x - 10a x x +--R (2) --------------------------------------- +--R 4n 5n 6n +--R 60n x x x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 15b (%e ) - 24a b %e - 10a +--R (3) --------------------------------------------- +--R n log(x) 6 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5n 4n 6n 2 4n 5n n log(x) 6 +--R ((15b x + 24a b x )x + 10a x x )(%e ) +--R + +--R 2 4n 5n 6n n log(x) 2 4n 5n 6n n log(x) 2 4n 5n 6n +--R - 15b x x x (%e ) - 24a b x x x %e - 10a x x x +--R / +--R 4n 5n 6n n log(x) 6 +--R 60n x x x (%e ) +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 4n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1299 +r0:=1/4*a^3*x^(4*n)/n+3/5*a^2*b*x^(5*n)/n+1/2*a*b^2*x^(6*n)/n+1/7*b^3*x^(7*n)/n +--R +--R +--R 3 7n 2 6n 2 5n 3 4n +--R 20b x + 70a b x + 84a b x + 35a x +--R (2) ----------------------------------------- +--R 140n +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 7 2 n log(x) 6 2 n log(x) 5 +--R 20b (%e ) + 70a b (%e ) + 84a b (%e ) +--R + +--R 3 n log(x) 4 +--R 35a (%e ) +--R / +--R 140n +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 7 2 n log(x) 6 2 n log(x) 5 +--R 20b (%e ) + 70a b (%e ) + 84a b (%e ) +--R + +--R 3 n log(x) 4 3 7n 2 6n 2 5n 3 4n +--R 35a (%e ) - 20b x - 70a b x - 84a b x - 35a x +--R / +--R 140n +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4i.input.pdf b/src/axiom-website/CATS/rich4i.input.pdf new file mode 100644 index 0000000..cb45ee5 Binary files /dev/null and b/src/axiom-website/CATS/rich4i.input.pdf differ diff --git a/src/axiom-website/CATS/rich4j.input.pamphlet b/src/axiom-website/CATS/rich4j.input.pamphlet new file mode 100644 index 0000000..c5f485c --- /dev/null +++ b/src/axiom-website/CATS/rich4j.input.pamphlet @@ -0,0 +1,26659 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4j.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 268 integrals in this file. +\item 276 supplied "optimal results". +\item 239 matching answers. +\item 15 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4j.output +)spool rich4j.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 3n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1394 +r0:=1/3*a^3*x^(3*n)/n+3/4*a^2*b*x^(4*n)/n+3/5*a*b^2*x^(5*n)/n+1/6*b^3*x^(6*n)/n +--R +--R +--R 3 6n 2 5n 2 4n 3 3n +--R 10b x + 36a b x + 45a b x + 20a x +--R (2) ----------------------------------------- +--R 60n +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 6 2 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 36a b (%e ) + 45a b (%e ) +--R + +--R 3 n log(x) 3 +--R 20a (%e ) +--R / +--R 60n +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 6 2 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 36a b (%e ) + 45a b (%e ) +--R + +--R 3 n log(x) 3 3 6n 2 5n 2 4n 3 3n +--R 20a (%e ) - 10b x - 36a b x - 45a b x - 20a x +--R / +--R 60n +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 2n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1394 +r0:=-1/4*a*(a+b*x^n)^4/(b^2*n)+1/5*(a+b*x^n)^5/(b^2*n) +--R +--R +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 5 +--R 4b (x ) + 15a b (x ) + 20a b (x ) + 10a b (x ) - a +--R (2) ------------------------------------------------------- +--R 2 +--R 20b n +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 5 2 n log(x) 4 2 n log(x) 3 +--R 4b (%e ) + 15a b (%e ) + 20a b (%e ) +--R + +--R 3 n log(x) 2 +--R 10a (%e ) +--R / +--R 20n +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 4b (%e ) + 15a b (%e ) + 20a b (%e ) +--R + +--R 3 2 n log(x) 2 5 n 5 4 n 4 2 3 n 3 3 2 n 2 +--R 10a b (%e ) - 4b (x ) - 15a b (x ) - 20a b (x ) - 10a b (x ) +--R + +--R 5 +--R a +--R / +--R 2 +--R 20b n +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^3 +--R +--R +--R 3 n - 1 n 3 2 n - 1 n 2 2 n - 1 n 3 n - 1 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1394 +r0:=1/4*(a+b*x^n)^4/(b*n) +--R +--R +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R b (x ) + 4a b (x ) + 6a b (x ) + 4a b x + a +--R (2) ------------------------------------------------ +--R 4b n +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 4 2 n log(x) 3 2 n log(x) 2 3 n log(x) +--R b (%e ) + 4a b (%e ) + 6a b (%e ) + 4a %e +--R ------------------------------------------------------------------------- +--R 4n +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R b (%e ) + 4a b (%e ) + 6a b (%e ) +--R + +--R 3 n log(x) 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R 4a b %e - b (x ) - 4a b (x ) - 6a b (x ) - 4a b x - a +--R / +--R 4b n +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1394 +t0:=(a+b*x^n)^3/x +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1394 +r0:=3*a^2*b*x^n/n+3/2*a*b^2*x^(2*n)/n+1/3*b^3*x^(3*n)/n+a^3*log(x) +--R +--R +--R 3 3n 2 2n 2 n 3 +--R 2b x + 9a b x + 18a b x + 6a n log(x) +--R (2) ------------------------------------------ +--R 6n +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 9a b (%e ) + 18a b %e + 6a n log(x) +--R (3) ---------------------------------------------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 3n +--R 2b (%e ) + 9a b (%e ) + 18a b %e - 2b x +--R + +--R 2 2n 2 n +--R - 9a b x - 18a b x +--R / +--R 6n +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^3 +--R +--R +--R 3 - n - 1 n 3 2 - n - 1 n 2 2 - n - 1 n 3 - n - 1 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1394 +r0:=-a^3/(n*x^n)+3*a*b^2*x^n/n+1/2*b^3*x^(2*n)/n+3*a^2*b*log(x) +--R +--R +--R 3 n 2n 2 n 2 2 n 3 +--R b x x + 6a b (x ) + 6a b n log(x)x - 2a +--R (2) -------------------------------------------- +--R n +--R 2n x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R b (%e ) + 6a b (%e ) + 6a b n log(x)%e - 2a +--R (3) -------------------------------------------------------------------- +--R n log(x) +--R 2n %e +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n n log(x) 3 2 n n log(x) 2 +--R b x (%e ) + 6a b x (%e ) +--R + +--R 3 n 2n 2 n 2 3 n log(x) 3 n +--R (- b x x - 6a b (x ) + 2a )%e - 2a x +--R / +--R n n log(x) +--R 2n x %e +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 2n - 1 n 3 2 - 2n - 1 n 2 2 - 2n - 1 n 3 - 2n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1394 +r0:=-1/2*a^3/(n*x^(2*n))-3*a^2*b/(n*x^n)+b^3*x^n/n+3*a*b^2*log(x) +--R +--R +--R 3 n 2 2 n 2 2n 3 n +--R (2b (x ) + 6a b n log(x)x - 6a b)x - a x +--R (2) --------------------------------------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 6a b n log(x)(%e ) - 6a b %e - a +--R (3) -------------------------------------------------------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n n log(x) 3 3 n 2 2 2n 3 n n log(x) 2 +--R 2b x x (%e ) + ((- 2b (x ) + 6a b)x + a x )(%e ) +--R + +--R 2 n 2n n log(x) 3 n 2n +--R - 6a b x x %e - a x x +--R / +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 3n - 1 n 3 2 - 3n - 1 n 2 2 - 3n - 1 n 3 - 3n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1394 +r0:=-1/3*a^3/(n*x^(3*n))-3/2*a^2*b/(n*x^(2*n))-3*a*b^2/(n*x^n)+b^3*log(x) +--R +--R +--R 3 n 2 2n 2 n 3n 3 n 2n +--R ((6b n log(x)x - 18a b )x - 9a b x )x - 2a x x +--R (2) ----------------------------------------------------- +--R n 2n 3n +--R 6n x x x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 6b n log(x)(%e ) - 18a b (%e ) - 9a b %e - 2a +--R (3) ---------------------------------------------------------------------- +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((18a b x + 9a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 18a b x x x (%e ) - 9a b x x x %e - 2a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 6n x x x (%e ) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 4n - 1 n 3 2 - 4n - 1 n 2 2 - 4n - 1 n 3 - 4n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1394 +r0:=-1/4*(a+b*x^n)^4/(a*n*x^(4*n)) +--R +--R +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R - b (x ) - 4a b (x ) - 6a b (x ) - 4a b x - a +--R (2) -------------------------------------------------- +--R 4n +--R 4a n x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 4b (%e ) - 6a b (%e ) - 4a b %e - a +--R (3) -------------------------------------------------------------- +--R n log(x) 4 +--R 4n (%e ) +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 n log(x) 4 +--R (b (x ) + 4a b (x ) + 6a b (x ) + 4a b x + a )(%e ) +--R + +--R 3 4n n log(x) 3 2 2 4n n log(x) 2 3 4n n log(x) +--R - 4a b x (%e ) - 6a b x (%e ) - 4a b x %e +--R + +--R 4 4n +--R - a x +--R / +--R 4n n log(x) 4 +--R 4a n x (%e ) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 5n - 1 n 3 2 - 5n - 1 n 2 2 - 5n - 1 n 3 - 5n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1394 +r0:=-1/5*a^3/(n*x^(5*n))-3/4*a^2*b/(n*x^(4*n))-a*b^2/(n*x^(3*n))-_ + 1/2*b^3/(n*x^(2*n)) +--R +--R +--R 3 3n 2 2n 4n 2 2n 3n 5n 3 2n 3n 4n +--R ((- 10b x - 20a b x )x - 15a b x x )x - 4a x x x +--R (2) ------------------------------------------------------------- +--R 2n 3n 4n 5n +--R 20n x x x x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 10b (%e ) - 20a b (%e ) - 15a b %e - 4a +--R (3) ------------------------------------------------------------------ +--R n log(x) 5 +--R 20n (%e ) +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3n 2 2n 4n 2 2n 3n 5n 3 2n 3n 4n +--R (((10b x + 20a b x )x + 15a b x x )x + 4a x x x ) +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 3 2n 3n 4n 5n n log(x) 3 2 2n 3n 4n 5n n log(x) 2 +--R - 10b x x x x (%e ) - 20a b x x x x (%e ) +--R + +--R 2 2n 3n 4n 5n n log(x) 3 2n 3n 4n 5n +--R - 15a b x x x x %e - 4a x x x x +--R / +--R 2n 3n 4n 5n n log(x) 5 +--R 20n x x x x (%e ) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 6n - 1 n 3 2 - 6n - 1 n 2 2 - 6n - 1 n 3 - 6n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1394 +r0:=-1/6*a^3/(n*x^(6*n))-3/5*a^2*b/(n*x^(5*n))-3/4*a*b^2/(n*x^(4*n))-_ + 1/3*b^3/(n*x^(3*n)) +--R +--R +--R 3 4n 2 3n 5n 2 3n 4n 6n 3 3n 4n 5n +--R ((- 20b x - 45a b x )x - 36a b x x )x - 10a x x x +--R (2) -------------------------------------------------------------- +--R 3n 4n 5n 6n +--R 60n x x x x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 20b (%e ) - 45a b (%e ) - 36a b %e - 10a +--R (3) ------------------------------------------------------------------- +--R n log(x) 6 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4n 2 3n 5n 2 3n 4n 6n 3 3n 4n 5n +--R (((20b x + 45a b x )x + 36a b x x )x + 10a x x x ) +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 3 3n 4n 5n 6n n log(x) 3 2 3n 4n 5n 6n n log(x) 2 +--R - 20b x x x x (%e ) - 45a b x x x x (%e ) +--R + +--R 2 3n 4n 5n 6n n log(x) 3 3n 4n 5n 6n +--R - 36a b x x x x %e - 10a x x x x +--R / +--R 3n 4n 5n 6n n log(x) 6 +--R 60n x x x x (%e ) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 7n - 1 n 3 2 - 7n - 1 n 2 2 - 7n - 1 n 3 - 7n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1394 +r0:=-1/7*a^3/(n*x^(7*n))-1/2*a^2*b/(n*x^(6*n))-3/5*a*b^2/(n*x^(5*n))-_ + 1/4*b^3/(n*x^(4*n)) +--R +--R +--R 3 5n 2 4n 6n 2 4n 5n 7n 3 4n 5n 6n +--R ((- 35b x - 84a b x )x - 70a b x x )x - 20a x x x +--R (2) -------------------------------------------------------------- +--R 4n 5n 6n 7n +--R 140n x x x x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 35b (%e ) - 84a b (%e ) - 70a b %e - 20a +--R (3) ------------------------------------------------------------------- +--R n log(x) 7 +--R 140n (%e ) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5n 2 4n 6n 2 4n 5n 7n 3 4n 5n 6n +--R (((35b x + 84a b x )x + 70a b x x )x + 20a x x x ) +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 3 4n 5n 6n 7n n log(x) 3 2 4n 5n 6n 7n n log(x) 2 +--R - 35b x x x x (%e ) - 84a b x x x x (%e ) +--R + +--R 2 4n 5n 6n 7n n log(x) 3 4n 5n 6n 7n +--R - 70a b x x x x %e - 20a x x x x +--R / +--R 4n 5n 6n 7n n log(x) 7 +--R 140n x x x x (%e ) +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 4n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1394 +r0:=1/4*a^5*x^(4*n)/n+a^4*b*x^(5*n)/n+5/3*a^3*b^2*x^(6*n)/n+_ + 10/7*a^2*b^3*x^(7*n)/n+5/8*a*b^4*x^(8*n)/n+1/9*b^5*x^(9*n)/n +--R +--R +--R 5 9n 4 8n 2 3 7n 3 2 6n 4 5n 5 4n +--R 56b x + 315a b x + 720a b x + 840a b x + 504a b x + 126a x +--R (2) ---------------------------------------------------------------------- +--R 504n +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 9 4 n log(x) 8 2 3 n log(x) 7 +--R 56b (%e ) + 315a b (%e ) + 720a b (%e ) +--R + +--R 3 2 n log(x) 6 4 n log(x) 5 5 n log(x) 4 +--R 840a b (%e ) + 504a b (%e ) + 126a (%e ) +--R / +--R 504n +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 9 4 n log(x) 8 2 3 n log(x) 7 +--R 56b (%e ) + 315a b (%e ) + 720a b (%e ) +--R + +--R 3 2 n log(x) 6 4 n log(x) 5 5 n log(x) 4 +--R 840a b (%e ) + 504a b (%e ) + 126a (%e ) +--R + +--R 5 9n 4 8n 2 3 7n 3 2 6n 4 5n 5 4n +--R - 56b x - 315a b x - 720a b x - 840a b x - 504a b x - 126a x +--R / +--R 504n +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 3n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1394 +r0:=1/6*a^2*(a+b*x^n)^6/(b^3*n)-2/7*a*(a+b*x^n)^7/(b^3*n)+_ + 1/8*(a+b*x^n)^8/(b^3*n) +--R +--R +--R (2) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R 21b (x ) + 120a b (x ) + 280a b (x ) + 336a b (x ) + 210a b (x ) +--R + +--R 5 3 n 3 8 +--R 56a b (x ) + a +--R / +--R 3 +--R 168b n +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 8 4 n log(x) 7 2 3 n log(x) 6 +--R 21b (%e ) + 120a b (%e ) + 280a b (%e ) +--R + +--R 3 2 n log(x) 5 4 n log(x) 4 5 n log(x) 3 +--R 336a b (%e ) + 210a b (%e ) + 56a (%e ) +--R / +--R 168n +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 21b (%e ) + 120a b (%e ) + 280a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 336a b (%e ) + 210a b (%e ) + 56a b (%e ) +--R + +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R - 21b (x ) - 120a b (x ) - 280a b (x ) - 336a b (x ) - 210a b (x ) +--R + +--R 5 3 n 3 8 +--R - 56a b (x ) - a +--R / +--R 3 +--R 168b n +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 2n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1394 +r0:=-1/6*a*(a+b*x^n)^6/(b^2*n)+1/7*(a+b*x^n)^7/(b^2*n) +--R +--R +--R (2) +--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R 6b (x ) + 35a b (x ) + 84a b (x ) + 105a b (x ) + 70a b (x ) +--R + +--R 5 2 n 2 7 +--R 21a b (x ) - a +--R / +--R 2 +--R 42b n +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 7 4 n log(x) 6 2 3 n log(x) 5 +--R 6b (%e ) + 35a b (%e ) + 84a b (%e ) +--R + +--R 3 2 n log(x) 4 4 n log(x) 3 5 n log(x) 2 +--R 105a b (%e ) + 70a b (%e ) + 21a (%e ) +--R / +--R 42n +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 n log(x) 7 6 n log(x) 6 2 5 n log(x) 5 +--R 6b (%e ) + 35a b (%e ) + 84a b (%e ) +--R + +--R 3 4 n log(x) 4 4 3 n log(x) 3 5 2 n log(x) 2 +--R 105a b (%e ) + 70a b (%e ) + 21a b (%e ) +--R + +--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R - 6b (x ) - 35a b (x ) - 84a b (x ) - 105a b (x ) - 70a b (x ) +--R + +--R 5 2 n 2 7 +--R - 21a b (x ) + a +--R / +--R 2 +--R 42b n +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n - 1 n 5 4 n - 1 n 4 2 3 n - 1 n 3 3 2 n - 1 n 2 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) + 10a b x (x ) +--R + +--R 4 n - 1 n 5 n - 1 +--R 5a b x x + a x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1394 +r0:=1/6*(a+b*x^n)^6/(b*n) +--R +--R +--R (2) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 5 n 6 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) + 6a b x + a +--R ----------------------------------------------------------------------------- +--R 6b n +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 6 4 n log(x) 5 2 3 n log(x) 4 +--R b (%e ) + 6a b (%e ) + 15a b (%e ) +--R + +--R 3 2 n log(x) 3 4 n log(x) 2 5 n log(x) +--R 20a b (%e ) + 15a b (%e ) + 6a %e +--R / +--R 6n +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n log(x) 6 5 n log(x) 5 2 4 n log(x) 4 +--R b (%e ) + 6a b (%e ) + 15a b (%e ) +--R + +--R 3 3 n log(x) 3 4 2 n log(x) 2 5 n log(x) 6 n 6 +--R 20a b (%e ) + 15a b (%e ) + 6a b %e - b (x ) +--R + +--R 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 5 n 6 +--R - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) - 6a b x - a +--R / +--R 6b n +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1394 +t0:=(a+b*x^n)^5/x +--R +--R +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 +--R b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a +--R (1) --------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1394 +r0:=5*a^4*b*x^n/n+5*a^3*b^2*x^(2*n)/n+10/3*a^2*b^3*x^(3*n)/n+_ + 5/4*a*b^4*x^(4*n)/n+1/5*b^5*x^(5*n)/n+a^5*log(x) +--R +--R +--R (2) +--R 5 5n 4 4n 2 3 3n 3 2 2n 4 n 5 +--R 12b x + 75a b x + 200a b x + 300a b x + 300a b x + 60a n log(x) +--R ------------------------------------------------------------------------ +--R 60n +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 75a b (%e ) + 200a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 300a b (%e ) + 300a b %e + 60a n log(x) +--R / +--R 60n +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 75a b (%e ) + 200a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 5n 4 4n +--R 300a b (%e ) + 300a b %e - 12b x - 75a b x +--R + +--R 2 3 3n 3 2 2n 4 n +--R - 200a b x - 300a b x - 300a b x +--R / +--R 60n +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - n - 1 n 5 4 - n - 1 n 4 2 3 - n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - n - 1 n 2 4 - n - 1 n 5 - n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1394 +r0:=-a^5/(n*x^n)+10*a^3*b^2*x^n/n+5*a^2*b^3*x^(2*n)/n+_ + 5/3*a*b^4*x^(3*n)/n+1/4*b^5*x^(4*n)/n+5*a^4*b*log(x) +--R +--R +--R (2) +--R 5 n 4n 4 n 3n 2 3 n 2n 3 2 n 2 4 n 5 +--R 3b x x + 20a b x x + 60a b x x + 120a b (x ) + 60a b n log(x)x - 12a +--R ----------------------------------------------------------------------------- +--R n +--R 12n x +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 3b (%e ) + 20a b (%e ) + 60a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 120a b (%e ) + 60a b n log(x)%e - 12a +--R / +--R n log(x) +--R 12n %e +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n n log(x) 5 4 n n log(x) 4 2 3 n n log(x) 3 +--R 3b x (%e ) + 20a b x (%e ) + 60a b x (%e ) +--R + +--R 3 2 n n log(x) 2 +--R 120a b x (%e ) +--R + +--R 5 n 4n 4 n 3n 2 3 n 2n 3 2 n 2 5 n log(x) +--R (- 3b x x - 20a b x x - 60a b x x - 120a b (x ) + 12a )%e +--R + +--R 5 n +--R - 12a x +--R / +--R n n log(x) +--R 12n x %e +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 2n - 1 n 5 4 - 2n - 1 n 4 2 3 - 2n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 2n - 1 n 2 4 - 2n - 1 n 5 - 2n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1394 +r0:=-1/2*a^5/(n*x^(2*n))-5*a^4*b/(n*x^n)+10*a^2*b^3*x^n/n+_ + 5/2*a*b^4*x^(2*n)/n+1/3*b^5*x^(3*n)/n+10*a^3*b^2*log(x) +--R +--R +--R (2) +--R 5 n 2n 3n 4 n 2n 2 +--R 2b x x x + 15a b x (x ) +--R + +--R 2 3 n 2 3 2 n 4 2n 5 n +--R (60a b (x ) + 60a b n log(x)x - 30a b)x - 3a x +--R / +--R n 2n +--R 6n x x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 2b (%e ) + 15a b (%e ) + 60a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 60a b n log(x)(%e ) - 30a b %e - 3a +--R / +--R n log(x) 2 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n n log(x) 5 4 n 2n n log(x) 4 +--R 2b x x (%e ) + 15a b x x (%e ) +--R + +--R 2 3 n 2n n log(x) 3 +--R 60a b x x (%e ) +--R + +--R 5 n 2n 3n 4 n 2n 2 2 3 n 2 4 2n 5 n +--R (- 2b x x x - 15a b x (x ) + (- 60a b (x ) + 30a b)x + 3a x ) +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 4 n 2n n log(x) 5 n 2n +--R - 30a b x x %e - 3a x x +--R / +--R n 2n n log(x) 2 +--R 6n x x (%e ) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 3n - 1 n 5 4 - 3n - 1 n 4 2 3 - 3n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 3n - 1 n 2 4 - 3n - 1 n 5 - 3n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1394 +r0:=-1/3*a^5/(n*x^(3*n))-5/2*a^4*b/(n*x^(2*n))-10*a^3*b^2/(n*x^n)+_ + 5*a*b^4*x^n/n+1/2*b^5*x^(2*n)/n+10*a^2*b^3*log(x) +--R +--R +--R (2) +--R 5 n 2n 2 4 n 2 2 3 n 3 2 2n 4 n +--R (3b x (x ) + (30a b (x ) + 60a b n log(x)x - 60a b )x - 15a b x ) +--R * +--R 3n +--R x +--R + +--R 5 n 2n +--R - 2a x x +--R / +--R n 2n 3n +--R 6n x x x +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 3b (%e ) + 30a b (%e ) + 60a b n log(x)(%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 60a b (%e ) - 15a b %e - 2a +--R / +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n 3n n log(x) 5 4 n 2n 3n n log(x) 4 +--R 3b x x x (%e ) + 30a b x x x (%e ) +--R + +--R 5 n 2n 2 4 n 2 3 2 2n 4 n 3n +--R (- 3b x (x ) + (- 30a b (x ) + 60a b )x + 15a b x )x +--R + +--R 5 n 2n +--R 2a x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 3 2 n 2n 3n n log(x) 2 4 n 2n 3n n log(x) 5 n 2n 3n +--R - 60a b x x x (%e ) - 15a b x x x %e - 2a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 6n x x x (%e ) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 4n - 1 n 5 4 - 4n - 1 n 4 2 3 - 4n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 4n - 1 n 2 4 - 4n - 1 n 5 - 4n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1394 +r0:=-1/4*a^5/(n*x^(4*n))-5/3*a^4*b/(n*x^(3*n))-5*a^3*b^2/(n*x^(2*n))-_ + 10*a^2*b^3/(n*x^n)+b^5*x^n/n+5*a*b^4*log(x) +--R +--R +--R (2) +--R 5 n 2 4 n 2 3 2n 3 2 n 3n +--R ((12b (x ) + 60a b n log(x)x - 120a b )x - 60a b x )x +--R + +--R 4 n 2n +--R - 20a b x x +--R * +--R 4n +--R x +--R + +--R 5 n 2n 3n +--R - 3a x x x +--R / +--R n 2n 3n 4n +--R 12n x x x x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 60a b n log(x)(%e ) - 120a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 60a b (%e ) - 20a b %e - 3a +--R / +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n 3n 4n n log(x) 5 +--R 12b x x x x (%e ) +--R + +--R 5 n 2 2 3 2n 3 2 n 3n 4 n 2n 4n +--R (((- 12b (x ) + 120a b )x + 60a b x )x + 20a b x x )x +--R + +--R 5 n 2n 3n +--R 3a x x x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 2 3 n 2n 3n 4n n log(x) 3 3 2 n 2n 3n 4n n log(x) 2 +--R - 120a b x x x x (%e ) - 60a b x x x x (%e ) +--R + +--R 4 n 2n 3n 4n n log(x) 5 n 2n 3n 4n +--R - 20a b x x x x %e - 3a x x x x +--R / +--R n 2n 3n 4n n log(x) 4 +--R 12n x x x x (%e ) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 5n - 1 n 5 4 - 5n - 1 n 4 2 3 - 5n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 5n - 1 n 2 4 - 5n - 1 n 5 - 5n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1394 +r0:=-1/5*a^5/(n*x^(5*n))-5/4*a^4*b/(n*x^(4*n))-10/3*a^3*b^2/(n*x^(3*n))-_ + 5*a^2*b^3/(n*x^(2*n))-5*a*b^4/(n*x^n)+b^5*log(x) +--R +--R +--R (2) +--R 5 n 4 2n 2 3 n 3n 3 2 n 2n 4n +--R (((60b n log(x)x - 300a b )x - 300a b x )x - 200a b x x )x +--R + +--R 4 n 2n 3n +--R - 75a b x x x +--R * +--R 5n +--R x +--R + +--R 5 n 2n 3n 4n +--R - 12a x x x x +--R / +--R n 2n 3n 4n 5n +--R 60n x x x x x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 60b n log(x)(%e ) - 300a b (%e ) - 300a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 200a b (%e ) - 75a b %e - 12a +--R / +--R n log(x) 5 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2n 2 3 n 3n 3 2 n 2n 4n 4 n 2n 3n 5n +--R (((300a b x + 300a b x )x + 200a b x x )x + 75a b x x x )x +--R + +--R 5 n 2n 3n 4n +--R 12a x x x x +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 4 n 2n 3n 4n 5n n log(x) 4 2 3 n 2n 3n 4n 5n n log(x) 3 +--R - 300a b x x x x x (%e ) - 300a b x x x x x (%e ) +--R + +--R 3 2 n 2n 3n 4n 5n n log(x) 2 4 n 2n 3n 4n 5n n log(x) +--R - 200a b x x x x x (%e ) - 75a b x x x x x %e +--R + +--R 5 n 2n 3n 4n 5n +--R - 12a x x x x x +--R / +--R n 2n 3n 4n 5n n log(x) 5 +--R 60n x x x x x (%e ) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 6n - 1 n 5 4 - 6n - 1 n 4 2 3 - 6n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 6n - 1 n 2 4 - 6n - 1 n 5 - 6n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1394 +r0:=-1/6*(a+b*x^n)^6/(a*n*x^(6*n)) +--R +--R +--R (2) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) +--R + +--R 5 n 6 +--R - 6a b x - a +--R / +--R 6n +--R 6a n x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 6b (%e ) - 15a b (%e ) - 20a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 15a b (%e ) - 6a b %e - a +--R / +--R n log(x) 6 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) +--R + +--R 5 n 6 +--R 6a b x + a +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 5 6n n log(x) 5 2 4 6n n log(x) 4 3 3 6n n log(x) 3 +--R - 6a b x (%e ) - 15a b x (%e ) - 20a b x (%e ) +--R + +--R 4 2 6n n log(x) 2 5 6n n log(x) 6 6n +--R - 15a b x (%e ) - 6a b x %e - a x +--R / +--R 6n n log(x) 6 +--R 6a n x (%e ) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 7n - 1 n 5 4 - 7n - 1 n 4 2 3 - 7n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 7n - 1 n 2 4 - 7n - 1 n 5 - 7n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1394 +r0:=-1/7*(a+b*x^n)^6/(a*n*x^(7*n))+1/42*b*(a+b*x^n)^6/(a^2*n*x^(6*n)) +--R +--R +--R (2) +--R 7 n 6 6 n 5 2 5 n 4 3 4 n 3 4 3 n 2 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) +--R + +--R 5 2 n 6 +--R 6a b x + a b +--R * +--R 7n +--R x +--R + +--R 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 5 2 n 2 +--R - 6a b (x ) - 36a b (x ) - 90a b (x ) - 120a b (x ) - 90a b (x ) +--R + +--R 6 n 7 +--R - 36a b x - 6a +--R * +--R 6n +--R x +--R / +--R 2 6n 7n +--R 42a n x x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 21b (%e ) - 70a b (%e ) - 105a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 84a b (%e ) - 35a b %e - 6a +--R / +--R n log(x) 7 +--R 42n (%e ) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 n 6 6 n 5 2 5 n 4 3 4 n 3 4 3 n 2 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) +--R + +--R 5 2 n 6 +--R - 6a b x - a b +--R * +--R 7n +--R x +--R + +--R 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R 6a b (x ) + 36a b (x ) + 90a b (x ) + 120a b (x ) +--R + +--R 5 2 n 2 6 n 7 +--R 90a b (x ) + 36a b x + 6a +--R * +--R 6n +--R x +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 2 5 6n 7n n log(x) 5 3 4 6n 7n n log(x) 4 +--R - 21a b x x (%e ) - 70a b x x (%e ) +--R + +--R 4 3 6n 7n n log(x) 3 5 2 6n 7n n log(x) 2 +--R - 105a b x x (%e ) - 84a b x x (%e ) +--R + +--R 6 6n 7n n log(x) 7 6n 7n +--R - 35a b x x %e - 6a x x +--R / +--R 2 6n 7n n log(x) 7 +--R 42a n x x (%e ) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1394 +t0:=x^(-1-8*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 8n - 1 n 5 4 - 8n - 1 n 4 2 3 - 8n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 8n - 1 n 2 4 - 8n - 1 n 5 - 8n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1394 +r0:=-1/8*a^5/(n*x^(8*n))-5/7*a^4*b/(n*x^(7*n))-5/3*a^3*b^2/(n*x^(6*n))-_ + 2*a^2*b^3/(n*x^(5*n))-5/4*a*b^4/(n*x^(4*n))-1/3*b^5/(n*x^(3*n)) +--R +--R +--R (2) +--R 5 4n 4 3n 5n 2 3 3n 4n 6n +--R ((- 56b x - 210a b x )x - 336a b x x )x +--R + +--R 3 2 3n 4n 5n +--R - 280a b x x x +--R * +--R 7n +--R x +--R + +--R 4 3n 4n 5n 6n +--R - 120a b x x x x +--R * +--R 8n +--R x +--R + +--R 5 3n 4n 5n 6n 7n +--R - 21a x x x x x +--R / +--R 3n 4n 5n 6n 7n 8n +--R 168n x x x x x x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 56b (%e ) - 210a b (%e ) - 336a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 280a b (%e ) - 120a b %e - 21a +--R / +--R n log(x) 8 +--R 168n (%e ) +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4n 4 3n 5n 2 3 3n 4n 6n +--R ((56b x + 210a b x )x + 336a b x x )x +--R + +--R 3 2 3n 4n 5n +--R 280a b x x x +--R * +--R 7n +--R x +--R + +--R 4 3n 4n 5n 6n +--R 120a b x x x x +--R * +--R 8n +--R x +--R + +--R 5 3n 4n 5n 6n 7n +--R 21a x x x x x +--R * +--R n log(x) 8 +--R (%e ) +--R + +--R 5 3n 4n 5n 6n 7n 8n n log(x) 5 +--R - 56b x x x x x x (%e ) +--R + +--R 4 3n 4n 5n 6n 7n 8n n log(x) 4 +--R - 210a b x x x x x x (%e ) +--R + +--R 2 3 3n 4n 5n 6n 7n 8n n log(x) 3 +--R - 336a b x x x x x x (%e ) +--R + +--R 3 2 3n 4n 5n 6n 7n 8n n log(x) 2 +--R - 280a b x x x x x x (%e ) +--R + +--R 4 3n 4n 5n 6n 7n 8n n log(x) 5 3n 4n 5n 6n 7n 8n +--R - 120a b x x x x x x %e - 21a x x x x x x +--R / +--R 3n 4n 5n 6n 7n 8n n log(x) 8 +--R 168n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 9n - 1 n 5 4 - 9n - 1 n 4 2 3 - 9n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 9n - 1 n 2 4 - 9n - 1 n 5 - 9n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1394 +r0:=-1/9*a^5/(n*x^(9*n))-5/8*a^4*b/(n*x^(8*n))-10/7*a^3*b^2/(n*x^(7*n))-_ + 5/3*a^2*b^3/(n*x^(6*n))-a*b^4/(n*x^(5*n))-1/4*b^5/(n*x^(4*n)) +--R +--R +--R (2) +--R 5 5n 4 4n 6n 2 3 4n 5n 7n +--R ((- 126b x - 504a b x )x - 840a b x x )x +--R + +--R 3 2 4n 5n 6n +--R - 720a b x x x +--R * +--R 8n +--R x +--R + +--R 4 4n 5n 6n 7n +--R - 315a b x x x x +--R * +--R 9n +--R x +--R + +--R 5 4n 5n 6n 7n 8n +--R - 56a x x x x x +--R / +--R 4n 5n 6n 7n 8n 9n +--R 504n x x x x x x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 126b (%e ) - 504a b (%e ) - 840a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 720a b (%e ) - 315a b %e - 56a +--R / +--R n log(x) 9 +--R 504n (%e ) +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5n 4 4n 6n 2 3 4n 5n 7n +--R ((126b x + 504a b x )x + 840a b x x )x +--R + +--R 3 2 4n 5n 6n +--R 720a b x x x +--R * +--R 8n +--R x +--R + +--R 4 4n 5n 6n 7n +--R 315a b x x x x +--R * +--R 9n +--R x +--R + +--R 5 4n 5n 6n 7n 8n +--R 56a x x x x x +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 5 4n 5n 6n 7n 8n 9n n log(x) 5 +--R - 126b x x x x x x (%e ) +--R + +--R 4 4n 5n 6n 7n 8n 9n n log(x) 4 +--R - 504a b x x x x x x (%e ) +--R + +--R 2 3 4n 5n 6n 7n 8n 9n n log(x) 3 +--R - 840a b x x x x x x (%e ) +--R + +--R 3 2 4n 5n 6n 7n 8n 9n n log(x) 2 +--R - 720a b x x x x x x (%e ) +--R + +--R 4 4n 5n 6n 7n 8n 9n n log(x) 5 4n 5n 6n 7n 8n 9n +--R - 315a b x x x x x x %e - 56a x x x x x x +--R / +--R 4n 5n 6n 7n 8n 9n n log(x) 9 +--R 504n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1394 +t0:=x^(-1-10*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 10n - 1 n 5 4 - 10n - 1 n 4 2 3 - 10n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 10n - 1 n 2 4 - 10n - 1 n 5 - 10n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1394 +r0:=-1/10*a^5/(n*x^(10*n))-5/9*a^4*b/(n*x^(9*n))-5/4*a^3*b^2/(n*x^(8*n))-_ + 10/7*a^2*b^3/(n*x^(7*n))-5/6*a*b^4/(n*x^(6*n))-1/5*b^5/(n*x^(5*n)) +--R +--R +--R (2) +--R 5 6n 4 5n 7n 2 3 5n 6n 8n +--R ((- 252b x - 1050a b x )x - 1800a b x x )x +--R + +--R 3 2 5n 6n 7n +--R - 1575a b x x x +--R * +--R 9n +--R x +--R + +--R 4 5n 6n 7n 8n +--R - 700a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 5n 6n 7n 8n 9n +--R - 126a x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n +--R 1260n x x x x x x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 252b (%e ) - 1050a b (%e ) - 1800a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 1575a b (%e ) - 700a b %e - 126a +--R / +--R n log(x) 10 +--R 1260n (%e ) +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6n 4 5n 7n 2 3 5n 6n 8n +--R ((252b x + 1050a b x )x + 1800a b x x )x +--R + +--R 3 2 5n 6n 7n +--R 1575a b x x x +--R * +--R 9n +--R x +--R + +--R 4 5n 6n 7n 8n +--R 700a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 5n 6n 7n 8n 9n +--R 126a x x x x x +--R * +--R n log(x) 10 +--R (%e ) +--R + +--R 5 5n 6n 7n 8n 9n 10n n log(x) 5 +--R - 252b x x x x x x (%e ) +--R + +--R 4 5n 6n 7n 8n 9n 10n n log(x) 4 +--R - 1050a b x x x x x x (%e ) +--R + +--R 2 3 5n 6n 7n 8n 9n 10n n log(x) 3 +--R - 1800a b x x x x x x (%e ) +--R + +--R 3 2 5n 6n 7n 8n 9n 10n n log(x) 2 +--R - 1575a b x x x x x x (%e ) +--R + +--R 4 5n 6n 7n 8n 9n 10n n log(x) 5 5n 6n 7n 8n 9n 10n +--R - 700a b x x x x x x %e - 126a x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n n log(x) 10 +--R 1260n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1394 +t0:=x^(-1+9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 9n - 1 +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1394 +r0:=1/9*a^8*x^(9*n)/n+4/5*a^7*b*x^(10*n)/n+28/11*a^6*b^2*x^(11*n)/n+_ + 14/3*a^5*b^3*x^(12*n)/n+70/13*a^4*b^4*x^(13*n)/n+_ + 4*a^3*b^5*x^(14*n)/n+28/15*a^2*b^6*x^(15*n)/n+_ + 1/2*a*b^7*x^(16*n)/n+1/17*b^8*x^(17*n)/n +--R +--R +--R (2) +--R 8 17n 7 16n 2 6 15n 3 5 14n +--R 12870b x + 109395a b x + 408408a b x + 875160a b x +--R + +--R 4 4 13n 5 3 12n 6 2 11n 7 10n +--R 1178100a b x + 1021020a b x + 556920a b x + 175032a b x +--R + +--R 8 9n +--R 24310a x +--R / +--R 218790n +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 17 7 n log(x) 16 +--R 12870b (%e ) + 109395a b (%e ) +--R + +--R 2 6 n log(x) 15 3 5 n log(x) 14 +--R 408408a b (%e ) + 875160a b (%e ) +--R + +--R 4 4 n log(x) 13 5 3 n log(x) 12 +--R 1178100a b (%e ) + 1021020a b (%e ) +--R + +--R 6 2 n log(x) 11 7 n log(x) 10 8 n log(x) 9 +--R 556920a b (%e ) + 175032a b (%e ) + 24310a (%e ) +--R / +--R 218790n +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 17 7 n log(x) 16 +--R 12870b (%e ) + 109395a b (%e ) +--R + +--R 2 6 n log(x) 15 3 5 n log(x) 14 +--R 408408a b (%e ) + 875160a b (%e ) +--R + +--R 4 4 n log(x) 13 5 3 n log(x) 12 +--R 1178100a b (%e ) + 1021020a b (%e ) +--R + +--R 6 2 n log(x) 11 7 n log(x) 10 +--R 556920a b (%e ) + 175032a b (%e ) +--R + +--R 8 n log(x) 9 8 17n 7 16n 2 6 15n +--R 24310a (%e ) - 12870b x - 109395a b x - 408408a b x +--R + +--R 3 5 14n 4 4 13n 5 3 12n 6 2 11n +--R - 875160a b x - 1178100a b x - 1021020a b x - 556920a b x +--R + +--R 7 10n 8 9n +--R - 175032a b x - 24310a x +--R / +--R 218790n +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1394 +t0:=x^(-1+8*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 8n - 1 +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1394 +r0:=1/8*a^8*x^(8*n)/n+8/9*a^7*b*x^(9*n)/n+14/5*a^6*b^2*x^(10*n)/n+_ + 56/11*a^5*b^3*x^(11*n)/n+35/6*a^4*b^4*x^(12*n)/n+_ + 56/13*a^3*b^5*x^(13*n)/n+2*a^2*b^6*x^(14*n)/n+_ + 8/15*a*b^7*x^(15*n)/n+1/16*b^8*x^(16*n)/n +--R +--R +--R (2) +--R 8 16n 7 15n 2 6 14n 3 5 13n +--R 6435b x + 54912a b x + 205920a b x + 443520a b x +--R + +--R 4 4 12n 5 3 11n 6 2 10n 7 9n +--R 600600a b x + 524160a b x + 288288a b x + 91520a b x +--R + +--R 8 8n +--R 12870a x +--R / +--R 102960n +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 16 7 n log(x) 15 2 6 n log(x) 14 +--R 6435b (%e ) + 54912a b (%e ) + 205920a b (%e ) +--R + +--R 3 5 n log(x) 13 4 4 n log(x) 12 +--R 443520a b (%e ) + 600600a b (%e ) +--R + +--R 5 3 n log(x) 11 6 2 n log(x) 10 +--R 524160a b (%e ) + 288288a b (%e ) +--R + +--R 7 n log(x) 9 8 n log(x) 8 +--R 91520a b (%e ) + 12870a (%e ) +--R / +--R 102960n +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 16 7 n log(x) 15 2 6 n log(x) 14 +--R 6435b (%e ) + 54912a b (%e ) + 205920a b (%e ) +--R + +--R 3 5 n log(x) 13 4 4 n log(x) 12 +--R 443520a b (%e ) + 600600a b (%e ) +--R + +--R 5 3 n log(x) 11 6 2 n log(x) 10 +--R 524160a b (%e ) + 288288a b (%e ) +--R + +--R 7 n log(x) 9 8 n log(x) 8 8 16n +--R 91520a b (%e ) + 12870a (%e ) - 6435b x +--R + +--R 7 15n 2 6 14n 3 5 13n 4 4 12n +--R - 54912a b x - 205920a b x - 443520a b x - 600600a b x +--R + +--R 5 3 11n 6 2 10n 7 9n 8 8n +--R - 524160a b x - 288288a b x - 91520a b x - 12870a x +--R / +--R 102960n +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1394 +t0:=x^(-1+7*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 7n - 1 +--R x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1394 +r0:=1/7*a^8*x^(7*n)/n+a^7*b*x^(8*n)/n+28/9*a^6*b^2*x^(9*n)/n+_ + 28/5*a^5*b^3*x^(10*n)/n+70/11*a^4*b^4*x^(11*n)/n+_ + 14/3*a^3*b^5*x^(12*n)/n+28/13*a^2*b^6*x^(13*n)/n+_ + 4/7*a*b^7*x^(14*n)/n+1/15*b^8*x^(15*n)/n +--R +--R +--R (2) +--R 8 15n 7 14n 2 6 13n 3 5 12n +--R 3003b x + 25740a b x + 97020a b x + 210210a b x +--R + +--R 4 4 11n 5 3 10n 6 2 9n 7 8n 8 7n +--R 286650a b x + 252252a b x + 140140a b x + 45045a b x + 6435a x +--R / +--R 45045n +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 15 7 n log(x) 14 2 6 n log(x) 13 +--R 3003b (%e ) + 25740a b (%e ) + 97020a b (%e ) +--R + +--R 3 5 n log(x) 12 4 4 n log(x) 11 +--R 210210a b (%e ) + 286650a b (%e ) +--R + +--R 5 3 n log(x) 10 6 2 n log(x) 9 +--R 252252a b (%e ) + 140140a b (%e ) +--R + +--R 7 n log(x) 8 8 n log(x) 7 +--R 45045a b (%e ) + 6435a (%e ) +--R / +--R 45045n +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 15 7 n log(x) 14 2 6 n log(x) 13 +--R 3003b (%e ) + 25740a b (%e ) + 97020a b (%e ) +--R + +--R 3 5 n log(x) 12 4 4 n log(x) 11 +--R 210210a b (%e ) + 286650a b (%e ) +--R + +--R 5 3 n log(x) 10 6 2 n log(x) 9 +--R 252252a b (%e ) + 140140a b (%e ) +--R + +--R 7 n log(x) 8 8 n log(x) 7 8 15n 7 14n +--R 45045a b (%e ) + 6435a (%e ) - 3003b x - 25740a b x +--R + +--R 2 6 13n 3 5 12n 4 4 11n 5 3 10n +--R - 97020a b x - 210210a b x - 286650a b x - 252252a b x +--R + +--R 6 2 9n 7 8n 8 7n +--R - 140140a b x - 45045a b x - 6435a x +--R / +--R 45045n +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1394 +t0:=x^(-1+6*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 6n - 1 +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1394 +r0:=-1/9*a^5*(a+b*x^n)^9/(b^6*n)+1/2*a^4*(a+b*x^n)^10/(b^6*n)-_ + 10/11*a^3*(a+b*x^n)^11/(b^6*n)+5/6*a^2*(a+b*x^n)^12/(b^6*n)-_ + 5/13*a*(a+b*x^n)^13/(b^6*n)+1/14*(a+b*x^n)^14/(b^6*n) +--R +--R +--R (2) +--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11 +--R 1287b (x ) + 11088a b (x ) + 42042a b (x ) + 91728a b (x ) +--R + +--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7 +--R 126126a b (x ) + 112112a b (x ) + 63063a b (x ) + 20592a b (x ) +--R + +--R 8 6 n 6 14 +--R 3003a b (x ) - a +--R / +--R 6 +--R 18018b n +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 14 7 n log(x) 13 2 6 n log(x) 12 +--R 1287b (%e ) + 11088a b (%e ) + 42042a b (%e ) +--R + +--R 3 5 n log(x) 11 4 4 n log(x) 10 +--R 91728a b (%e ) + 126126a b (%e ) +--R + +--R 5 3 n log(x) 9 6 2 n log(x) 8 7 n log(x) 7 +--R 112112a b (%e ) + 63063a b (%e ) + 20592a b (%e ) +--R + +--R 8 n log(x) 6 +--R 3003a (%e ) +--R / +--R 18018n +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 14 n log(x) 14 13 n log(x) 13 +--R 1287b (%e ) + 11088a b (%e ) +--R + +--R 2 12 n log(x) 12 3 11 n log(x) 11 +--R 42042a b (%e ) + 91728a b (%e ) +--R + +--R 4 10 n log(x) 10 5 9 n log(x) 9 +--R 126126a b (%e ) + 112112a b (%e ) +--R + +--R 6 8 n log(x) 8 7 7 n log(x) 7 8 6 n log(x) 6 +--R 63063a b (%e ) + 20592a b (%e ) + 3003a b (%e ) +--R + +--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11 +--R - 1287b (x ) - 11088a b (x ) - 42042a b (x ) - 91728a b (x ) +--R + +--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7 +--R - 126126a b (x ) - 112112a b (x ) - 63063a b (x ) - 20592a b (x ) +--R + +--R 8 6 n 6 14 +--R - 3003a b (x ) + a +--R / +--R 6 +--R 18018b n +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1394 +t0:=x^(-1+5*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 5n - 1 +--R x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1394 +r0:=1/9*a^4*(a+b*x^n)^9/(b^5*n)-2/5*a^3*(a+b*x^n)^10/(b^5*n)+_ + 6/11*a^2*(a+b*x^n)^11/(b^5*n)-1/3*a*(a+b*x^n)^12/(b^5*n)+_ + 1/13*(a+b*x^n)^13/(b^5*n) +--R +--R +--R (2) +--R 13 n 13 12 n 12 2 11 n 11 3 10 n 10 +--R 495b (x ) + 4290a b (x ) + 16380a b (x ) + 36036a b (x ) +--R + +--R 4 9 n 9 5 8 n 8 6 7 n 7 7 6 n 6 +--R 50050a b (x ) + 45045a b (x ) + 25740a b (x ) + 8580a b (x ) +--R + +--R 8 5 n 5 13 +--R 1287a b (x ) + a +--R / +--R 5 +--R 6435b n +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 13 7 n log(x) 12 2 6 n log(x) 11 +--R 495b (%e ) + 4290a b (%e ) + 16380a b (%e ) +--R + +--R 3 5 n log(x) 10 4 4 n log(x) 9 5 3 n log(x) 8 +--R 36036a b (%e ) + 50050a b (%e ) + 45045a b (%e ) +--R + +--R 6 2 n log(x) 7 7 n log(x) 6 8 n log(x) 5 +--R 25740a b (%e ) + 8580a b (%e ) + 1287a (%e ) +--R / +--R 6435n +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 n log(x) 13 12 n log(x) 12 2 11 n log(x) 11 +--R 495b (%e ) + 4290a b (%e ) + 16380a b (%e ) +--R + +--R 3 10 n log(x) 10 4 9 n log(x) 9 +--R 36036a b (%e ) + 50050a b (%e ) +--R + +--R 5 8 n log(x) 8 6 7 n log(x) 7 7 6 n log(x) 6 +--R 45045a b (%e ) + 25740a b (%e ) + 8580a b (%e ) +--R + +--R 8 5 n log(x) 5 13 n 13 12 n 12 2 11 n 11 +--R 1287a b (%e ) - 495b (x ) - 4290a b (x ) - 16380a b (x ) +--R + +--R 3 10 n 10 4 9 n 9 5 8 n 8 6 7 n 7 +--R - 36036a b (x ) - 50050a b (x ) - 45045a b (x ) - 25740a b (x ) +--R + +--R 7 6 n 6 8 5 n 5 13 +--R - 8580a b (x ) - 1287a b (x ) - a +--R / +--R 5 +--R 6435b n +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 4n - 1 +--R x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1394 +r0:=-1/9*a^3*(a+b*x^n)^9/(b^4*n)+3/10*a^2*(a+b*x^n)^10/(b^4*n)-_ + 3/11*a*(a+b*x^n)^11/(b^4*n)+1/12*(a+b*x^n)^12/(b^4*n) +--R +--R +--R (2) +--R 12 n 12 11 n 11 2 10 n 10 3 9 n 9 +--R 165b (x ) + 1440a b (x ) + 5544a b (x ) + 12320a b (x ) +--R + +--R 4 8 n 8 5 7 n 7 6 6 n 6 7 5 n 5 +--R 17325a b (x ) + 15840a b (x ) + 9240a b (x ) + 3168a b (x ) +--R + +--R 8 4 n 4 12 +--R 495a b (x ) - a +--R / +--R 4 +--R 1980b n +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 12 7 n log(x) 11 2 6 n log(x) 10 +--R 165b (%e ) + 1440a b (%e ) + 5544a b (%e ) +--R + +--R 3 5 n log(x) 9 4 4 n log(x) 8 5 3 n log(x) 7 +--R 12320a b (%e ) + 17325a b (%e ) + 15840a b (%e ) +--R + +--R 6 2 n log(x) 6 7 n log(x) 5 8 n log(x) 4 +--R 9240a b (%e ) + 3168a b (%e ) + 495a (%e ) +--R / +--R 1980n +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 n log(x) 12 11 n log(x) 11 2 10 n log(x) 10 +--R 165b (%e ) + 1440a b (%e ) + 5544a b (%e ) +--R + +--R 3 9 n log(x) 9 4 8 n log(x) 8 5 7 n log(x) 7 +--R 12320a b (%e ) + 17325a b (%e ) + 15840a b (%e ) +--R + +--R 6 6 n log(x) 6 7 5 n log(x) 5 8 4 n log(x) 4 +--R 9240a b (%e ) + 3168a b (%e ) + 495a b (%e ) +--R + +--R 12 n 12 11 n 11 2 10 n 10 3 9 n 9 +--R - 165b (x ) - 1440a b (x ) - 5544a b (x ) - 12320a b (x ) +--R + +--R 4 8 n 8 5 7 n 7 6 6 n 6 7 5 n 5 +--R - 17325a b (x ) - 15840a b (x ) - 9240a b (x ) - 3168a b (x ) +--R + +--R 8 4 n 4 12 +--R - 495a b (x ) + a +--R / +--R 4 +--R 1980b n +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 3n - 1 +--R x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1394 +r0:=1/9*a^2*(a+b*x^n)^9/(b^3*n)-1/5*a*(a+b*x^n)^10/(b^3*n)+_ + 1/11*(a+b*x^n)^11/(b^3*n) +--R +--R +--R (2) +--R 11 n 11 10 n 10 2 9 n 9 3 8 n 8 +--R 45b (x ) + 396a b (x ) + 1540a b (x ) + 3465a b (x ) +--R + +--R 4 7 n 7 5 6 n 6 6 5 n 5 7 4 n 4 +--R 4950a b (x ) + 4620a b (x ) + 2772a b (x ) + 990a b (x ) +--R + +--R 8 3 n 3 11 +--R 165a b (x ) + a +--R / +--R 3 +--R 495b n +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 11 7 n log(x) 10 2 6 n log(x) 9 +--R 45b (%e ) + 396a b (%e ) + 1540a b (%e ) +--R + +--R 3 5 n log(x) 8 4 4 n log(x) 7 5 3 n log(x) 6 +--R 3465a b (%e ) + 4950a b (%e ) + 4620a b (%e ) +--R + +--R 6 2 n log(x) 5 7 n log(x) 4 8 n log(x) 3 +--R 2772a b (%e ) + 990a b (%e ) + 165a (%e ) +--R / +--R 495n +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 n log(x) 11 10 n log(x) 10 2 9 n log(x) 9 +--R 45b (%e ) + 396a b (%e ) + 1540a b (%e ) +--R + +--R 3 8 n log(x) 8 4 7 n log(x) 7 5 6 n log(x) 6 +--R 3465a b (%e ) + 4950a b (%e ) + 4620a b (%e ) +--R + +--R 6 5 n log(x) 5 7 4 n log(x) 4 8 3 n log(x) 3 +--R 2772a b (%e ) + 990a b (%e ) + 165a b (%e ) +--R + +--R 11 n 11 10 n 10 2 9 n 9 3 8 n 8 +--R - 45b (x ) - 396a b (x ) - 1540a b (x ) - 3465a b (x ) +--R + +--R 4 7 n 7 5 6 n 6 6 5 n 5 7 4 n 4 +--R - 4950a b (x ) - 4620a b (x ) - 2772a b (x ) - 990a b (x ) +--R + +--R 8 3 n 3 11 +--R - 165a b (x ) - a +--R / +--R 3 +--R 495b n +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 2n - 1 +--R x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1394 +r0:=-1/9*a*(a+b*x^n)^9/(b^2*n)+1/10*(a+b*x^n)^10/(b^2*n) +--R +--R +--R (2) +--R 10 n 10 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R 9b (x ) + 80a b (x ) + 315a b (x ) + 720a b (x ) + 1050a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 10 +--R 1008a b (x ) + 630a b (x ) + 240a b (x ) + 45a b (x ) - a +--R / +--R 2 +--R 90b n +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 10 7 n log(x) 9 2 6 n log(x) 8 +--R 9b (%e ) + 80a b (%e ) + 315a b (%e ) +--R + +--R 3 5 n log(x) 7 4 4 n log(x) 6 5 3 n log(x) 5 +--R 720a b (%e ) + 1050a b (%e ) + 1008a b (%e ) +--R + +--R 6 2 n log(x) 4 7 n log(x) 3 8 n log(x) 2 +--R 630a b (%e ) + 240a b (%e ) + 45a (%e ) +--R / +--R 90n +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 n log(x) 10 9 n log(x) 9 2 8 n log(x) 8 +--R 9b (%e ) + 80a b (%e ) + 315a b (%e ) +--R + +--R 3 7 n log(x) 7 4 6 n log(x) 6 5 5 n log(x) 5 +--R 720a b (%e ) + 1050a b (%e ) + 1008a b (%e ) +--R + +--R 6 4 n log(x) 4 7 3 n log(x) 3 8 2 n log(x) 2 +--R 630a b (%e ) + 240a b (%e ) + 45a b (%e ) +--R + +--R 10 n 10 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R - 9b (x ) - 80a b (x ) - 315a b (x ) - 720a b (x ) - 1050a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 10 +--R - 1008a b (x ) - 630a b (x ) - 240a b (x ) - 45a b (x ) + a +--R / +--R 2 +--R 90b n +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n - 1 n 8 7 n - 1 n 7 2 6 n - 1 n 6 3 5 n - 1 n 5 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) + 56a b x (x ) +--R + +--R 4 4 n - 1 n 4 5 3 n - 1 n 3 6 2 n - 1 n 2 7 n - 1 n +--R 70a b x (x ) + 56a b x (x ) + 28a b x (x ) + 8a b x x +--R + +--R 8 n - 1 +--R a x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1394 +r0:=1/9*(a+b*x^n)^9/(b*n) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R / +--R 9b n +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 9 7 n log(x) 8 2 6 n log(x) 7 +--R b (%e ) + 9a b (%e ) + 36a b (%e ) +--R + +--R 3 5 n log(x) 6 4 4 n log(x) 5 5 3 n log(x) 4 +--R 84a b (%e ) + 126a b (%e ) + 126a b (%e ) +--R + +--R 6 2 n log(x) 3 7 n log(x) 2 8 n log(x) +--R 84a b (%e ) + 36a b (%e ) + 9a %e +--R / +--R 9n +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n log(x) 9 8 n log(x) 8 2 7 n log(x) 7 +--R b (%e ) + 9a b (%e ) + 36a b (%e ) +--R + +--R 3 6 n log(x) 6 4 5 n log(x) 5 5 4 n log(x) 4 +--R 84a b (%e ) + 126a b (%e ) + 126a b (%e ) +--R + +--R 6 3 n log(x) 3 7 2 n log(x) 2 8 n log(x) 9 n 9 +--R 84a b (%e ) + 36a b (%e ) + 9a b %e - b (x ) +--R + +--R 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 5 4 n 4 +--R - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) - 126a b (x ) +--R + +--R 6 3 n 3 7 2 n 2 8 n 9 +--R - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9b n +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1394 +t0:=(a+b*x^n)^8/x +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1394 +r0:=8*a^7*b*x^n/n+14*a^6*b^2*x^(2*n)/n+56/3*a^5*b^3*x^(3*n)/n+_ + 35/2*a^4*b^4*x^(4*n)/n+56/5*a^3*b^5*x^(5*n)/n+_ + 14/3*a^2*b^6*x^(6*n)/n+8/7*a*b^7*x^(7*n)/n+1/8*b^8*x^(8*n)/n+a^8*log(x) +--R +--R +--R (2) +--R 8 8n 7 7n 2 6 6n 3 5 5n 4 4 4n +--R 105b x + 960a b x + 3920a b x + 9408a b x + 14700a b x +--R + +--R 5 3 3n 6 2 2n 7 n 8 +--R 15680a b x + 11760a b x + 6720a b x + 840a n log(x) +--R / +--R 840n +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 960a b (%e ) + 3920a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 9408a b (%e ) + 14700a b (%e ) + 15680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 11760a b (%e ) + 6720a b %e + 840a n log(x) +--R / +--R 840n +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 960a b (%e ) + 3920a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 9408a b (%e ) + 14700a b (%e ) + 15680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 8n 7 7n +--R 11760a b (%e ) + 6720a b %e - 105b x - 960a b x +--R + +--R 2 6 6n 3 5 5n 4 4 4n 5 3 3n 6 2 2n +--R - 3920a b x - 9408a b x - 14700a b x - 15680a b x - 11760a b x +--R + +--R 7 n +--R - 6720a b x +--R / +--R 840n +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - n - 1 n 8 7 - n - 1 n 7 2 6 - n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - n - 1 n 5 4 4 - n - 1 n 4 5 3 - n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - n - 1 n 2 7 - n - 1 n 8 - n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1394 +r0:=-a^8/(n*x^n)+28*a^6*b^2*x^n/n+28*a^5*b^3*x^(2*n)/n+_ + 70/3*a^4*b^4*x^(3*n)/n+14*a^3*b^5*x^(4*n)/n+_ + 28/5*a^2*b^6*x^(5*n)/n+4/3*a*b^7*x^(6*n)/n+1/7*b^8*x^(7*n)/n+_ + 8*a^7*b*log(x) +--R +--R +--R (2) +--R 8 n 7n 7 n 6n 2 6 n 5n 3 5 n 4n 4 4 n 3n +--R 15b x x + 140a b x x + 588a b x x + 1470a b x x + 2450a b x x +--R + +--R 5 3 n 2n 6 2 n 2 7 n 8 +--R 2940a b x x + 2940a b (x ) + 840a b n log(x)x - 105a +--R / +--R n +--R 105n x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 15b (%e ) + 140a b (%e ) + 588a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 1470a b (%e ) + 2450a b (%e ) + 2940a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 2940a b (%e ) + 840a b n log(x)%e - 105a +--R / +--R n log(x) +--R 105n %e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n n log(x) 8 7 n n log(x) 7 2 6 n n log(x) 6 +--R 15b x (%e ) + 140a b x (%e ) + 588a b x (%e ) +--R + +--R 3 5 n n log(x) 5 4 4 n n log(x) 4 +--R 1470a b x (%e ) + 2450a b x (%e ) +--R + +--R 5 3 n n log(x) 3 6 2 n n log(x) 2 +--R 2940a b x (%e ) + 2940a b x (%e ) +--R + +--R 8 n 7n 7 n 6n 2 6 n 5n 3 5 n 4n +--R - 15b x x - 140a b x x - 588a b x x - 1470a b x x +--R + +--R 4 4 n 3n 5 3 n 2n 6 2 n 2 8 +--R - 2450a b x x - 2940a b x x - 2940a b (x ) + 105a +--R * +--R n log(x) +--R %e +--R + +--R 8 n +--R - 105a x +--R / +--R n n log(x) +--R 105n x %e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 2n - 1 n 8 7 - 2n - 1 n 7 2 6 - 2n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 2n - 1 n 5 4 4 - 2n - 1 n 4 5 3 - 2n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 2n - 1 n 2 7 - 2n - 1 n 8 - 2n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1394 +r0:=-1/2*a^8/(n*x^(2*n))-8*a^7*b/(n*x^n)+56*a^5*b^3*x^n/n+_ + 35*a^4*b^4*x^(2*n)/n+56/3*a^3*b^5*x^(3*n)/n+_ + 7*a^2*b^6*x^(4*n)/n+8/5*a*b^7*x^(5*n)/n+1/6*b^8*x^(6*n)/n+_ + 28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 8 n 2n 6n 7 n 2n 5n 2 6 n 2n 4n 3 5 n 2n 3n +--R 5b x x x + 48a b x x x + 210a b x x x + 560a b x x x +--R + +--R 4 4 n 2n 2 5 3 n 2 6 2 n 7 2n 8 n +--R 1050a b x (x ) + (1680a b (x ) + 840a b n log(x)x - 240a b)x - 15a x +--R / +--R n 2n +--R 30n x x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 5b (%e ) + 48a b (%e ) + 210a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 560a b (%e ) + 1050a b (%e ) + 1680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 840a b n log(x)(%e ) - 240a b %e - 15a +--R / +--R n log(x) 2 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n n log(x) 8 7 n 2n n log(x) 7 +--R 5b x x (%e ) + 48a b x x (%e ) +--R + +--R 2 6 n 2n n log(x) 6 3 5 n 2n n log(x) 5 +--R 210a b x x (%e ) + 560a b x x (%e ) +--R + +--R 4 4 n 2n n log(x) 4 5 3 n 2n n log(x) 3 +--R 1050a b x x (%e ) + 1680a b x x (%e ) +--R + +--R 8 n 2n 6n 7 n 2n 5n 2 6 n 2n 4n 3 5 n 2n 3n +--R - 5b x x x - 48a b x x x - 210a b x x x - 560a b x x x +--R + +--R 4 4 n 2n 2 5 3 n 2 7 2n 8 n +--R - 1050a b x (x ) + (- 1680a b (x ) + 240a b)x + 15a x +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 7 n 2n n log(x) 8 n 2n +--R - 240a b x x %e - 15a x x +--R / +--R n 2n n log(x) 2 +--R 30n x x (%e ) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 3n - 1 n 8 7 - 3n - 1 n 7 2 6 - 3n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 3n - 1 n 5 4 4 - 3n - 1 n 4 5 3 - 3n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 3n - 1 n 2 7 - 3n - 1 n 8 - 3n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1394 +r0:=-1/3*a^8/(n*x^(3*n))-4*a^7*b/(n*x^(2*n))-28*a^6*b^2/(n*x^n)+_ + 70*a^4*b^4*x^n/n+28*a^3*b^5*x^(2*n)/n+28/3*a^2*b^6*x^(3*n)/n+_ + 2*a*b^7*x^(4*n)/n+1/5*b^8*x^(5*n)/n+56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 5n 7 n 2n 3n 4n 2 6 n 2n 3n 2 +--R 3b x x x x + 30a b x x x x + 140a b x x (x ) +--R + +--R 3 5 n 2n 2 4 4 n 2 5 3 n 6 2 2n +--R 420a b x (x ) + (1050a b (x ) + 840a b n log(x)x - 420a b )x +--R + +--R 7 n +--R - 60a b x +--R * +--R 3n +--R x +--R + +--R 8 n 2n +--R - 5a x x +--R / +--R n 2n 3n +--R 15n x x x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 3b (%e ) + 30a b (%e ) + 140a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 420a b (%e ) + 1050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R 840a b n log(x)(%e ) - 420a b (%e ) - 60a b %e +--R + +--R 8 +--R - 5a +--R / +--R n log(x) 3 +--R 15n (%e ) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n n log(x) 8 7 n 2n 3n n log(x) 7 +--R 3b x x x (%e ) + 30a b x x x (%e ) +--R + +--R 2 6 n 2n 3n n log(x) 6 3 5 n 2n 3n n log(x) 5 +--R 140a b x x x (%e ) + 420a b x x x (%e ) +--R + +--R 4 4 n 2n 3n n log(x) 4 +--R 1050a b x x x (%e ) +--R + +--R 8 n 2n 3n 5n 7 n 2n 3n 4n 2 6 n 2n 3n 2 +--R - 3b x x x x - 30a b x x x x - 140a b x x (x ) +--R + +--R 3 5 n 2n 2 4 4 n 2 6 2 2n 7 n 3n +--R (- 420a b x (x ) + (- 1050a b (x ) + 420a b )x + 60a b x )x +--R + +--R 8 n 2n +--R 5a x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 6 2 n 2n 3n n log(x) 2 7 n 2n 3n n log(x) 8 n 2n 3n +--R - 420a b x x x (%e ) - 60a b x x x %e - 5a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 15n x x x (%e ) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 4n - 1 n 8 7 - 4n - 1 n 7 2 6 - 4n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 4n - 1 n 5 4 4 - 4n - 1 n 4 5 3 - 4n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 4n - 1 n 2 7 - 4n - 1 n 8 - 4n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1394 +r0:=-1/4*a^8/(n*x^(4*n))-8/3*a^7*b/(n*x^(3*n))-14*a^6*b^2/(n*x^(2*n))-_ + 56*a^5*b^3/(n*x^n)+56*a^3*b^5*x^n/n+14*a^2*b^6*x^(2*n)/n+_ + 8/3*a*b^7*x^(3*n)/n+1/4*b^8*x^(4*n)/n+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 4n 2 +--R 3b x x x (x ) +--R + +--R 7 n 2n 3n 2 +--R 32a b x x (x ) +--R + +--R 2 6 n 2n 2 3 5 n 2 4 4 n 5 3 2n +--R 168a b x (x ) + (672a b (x ) + 840a b n log(x)x - 672a b )x +--R + +--R 6 2 n +--R - 168a b x +--R * +--R 3n +--R x +--R + +--R 7 n 2n +--R - 32a b x x +--R * +--R 4n +--R x +--R + +--R 8 n 2n 3n +--R - 3a x x x +--R / +--R n 2n 3n 4n +--R 12n x x x x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 3b (%e ) + 32a b (%e ) + 168a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 672a b (%e ) + 840a b n log(x)(%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) 8 +--R - 672a b (%e ) - 168a b (%e ) - 32a b %e - 3a +--R / +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n n log(x) 8 7 n 2n 3n 4n n log(x) 7 +--R 3b x x x x (%e ) + 32a b x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n n log(x) 6 3 5 n 2n 3n 4n n log(x) 5 +--R 168a b x x x x (%e ) + 672a b x x x x (%e ) +--R + +--R 8 n 2n 3n 4n 2 +--R - 3b x x x (x ) +--R + +--R 7 n 2n 3n 2 +--R - 32a b x x (x ) +--R + +--R 2 6 n 2n 2 3 5 n 2 5 3 2n 6 2 n +--R (- 168a b x (x ) + (- 672a b (x ) + 672a b )x + 168a b x ) +--R * +--R 3n +--R x +--R + +--R 7 n 2n +--R 32a b x x +--R * +--R 4n +--R x +--R + +--R 8 n 2n 3n +--R 3a x x x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 5 3 n 2n 3n 4n n log(x) 3 6 2 n 2n 3n 4n n log(x) 2 +--R - 672a b x x x x (%e ) - 168a b x x x x (%e ) +--R + +--R 7 n 2n 3n 4n n log(x) 8 n 2n 3n 4n +--R - 32a b x x x x %e - 3a x x x x +--R / +--R n 2n 3n 4n n log(x) 4 +--R 12n x x x x (%e ) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 5n - 1 n 8 7 - 5n - 1 n 7 2 6 - 5n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 5n - 1 n 5 4 4 - 5n - 1 n 4 5 3 - 5n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 5n - 1 n 2 7 - 5n - 1 n 8 - 5n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1394 +r0:=-1/5*a^8/(n*x^(5*n))-2*a^7*b/(n*x^(4*n))-28/3*a^6*b^2/(n*x^(3*n))-_ + 28*a^5*b^3/(n*x^(2*n))-70*a^4*b^4/(n*x^n)+28*a^2*b^6*x^n/n+_ + 4*a*b^7*x^(2*n)/n+1/3*b^8*x^(3*n)/n+56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 2 +--R 5b x x (x ) +--R + +--R 7 n 2n 2 +--R 60a b x (x ) +--R + +--R 2 6 n 2 3 5 n 4 4 2n 5 3 n +--R (420a b (x ) + 840a b n log(x)x - 1050a b )x - 420a b x +--R * +--R 3n +--R x +--R + +--R 6 2 n 2n +--R - 140a b x x +--R * +--R 4n +--R x +--R + +--R 7 n 2n 3n +--R - 30a b x x x +--R * +--R 5n +--R x +--R + +--R 8 n 2n 3n 4n +--R - 3a x x x x +--R / +--R n 2n 3n 4n 5n +--R 15n x x x x x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 5b (%e ) + 60a b (%e ) + 420a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 840a b n log(x)(%e ) - 1050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) 8 +--R - 420a b (%e ) - 140a b (%e ) - 30a b %e - 3a +--R / +--R n log(x) 5 +--R 15n (%e ) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n n log(x) 8 7 n 2n 3n 4n 5n n log(x) 7 +--R 5b x x x x x (%e ) + 60a b x x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n n log(x) 6 +--R 420a b x x x x x (%e ) +--R + +--R 8 n 2n 3n 2 +--R - 5b x x (x ) +--R + +--R 7 n 2n 2 2 6 n 2 4 4 2n +--R - 60a b x (x ) + (- 420a b (x ) + 1050a b )x +--R + +--R 5 3 n +--R 420a b x +--R * +--R 3n +--R x +--R + +--R 6 2 n 2n +--R 140a b x x +--R * +--R 4n +--R x +--R + +--R 7 n 2n 3n +--R 30a b x x x +--R * +--R 5n +--R x +--R + +--R 8 n 2n 3n 4n +--R 3a x x x x +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n n log(x) 4 +--R - 1050a b x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n n log(x) 3 6 2 n 2n 3n 4n 5n n log(x) 2 +--R - 420a b x x x x x (%e ) - 140a b x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n n log(x) 8 n 2n 3n 4n 5n +--R - 30a b x x x x x %e - 3a x x x x x +--R / +--R n 2n 3n 4n 5n n log(x) 5 +--R 15n x x x x x (%e ) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 6n - 1 n 8 7 - 6n - 1 n 7 2 6 - 6n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 6n - 1 n 5 4 4 - 6n - 1 n 4 5 3 - 6n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 6n - 1 n 2 7 - 6n - 1 n 8 - 6n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1394 +r0:=-1/6*a^8/(n*x^(6*n))-8/5*a^7*b/(n*x^(5*n))-7*a^6*b^2/(n*x^(4*n))-_ + 56/3*a^5*b^3/(n*x^(3*n))-35*a^4*b^4/(n*x^(2*n))-_ + 56*a^3*b^5/(n*x^n)+8*a*b^7*x^n/n+1/2*b^8*x^(2*n)/n+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 8 n 2n 2 +--R 15b x (x ) +--R + +--R 7 n 2 2 6 n 3 5 2n +--R (240a b (x ) + 840a b n log(x)x - 1680a b )x +--R + +--R 4 4 n +--R - 1050a b x +--R * +--R 3n +--R x +--R + +--R 5 3 n 2n +--R - 560a b x x +--R * +--R 4n +--R x +--R + +--R 6 2 n 2n 3n +--R - 210a b x x x +--R * +--R 5n +--R x +--R + +--R 7 n 2n 3n 4n +--R - 48a b x x x x +--R * +--R 6n +--R x +--R + +--R 8 n 2n 3n 4n 5n +--R - 5a x x x x x +--R / +--R n 2n 3n 4n 5n 6n +--R 30n x x x x x x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 15b (%e ) + 240a b (%e ) + 840a b n log(x)(%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 1680a b (%e ) - 1050a b (%e ) - 560a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 210a b (%e ) - 48a b %e - 5a +--R / +--R n log(x) 6 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n 6n n log(x) 8 +--R 15b x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n n log(x) 7 +--R 240a b x x x x x x (%e ) +--R + +--R 8 n 2n 2 7 n 2 3 5 2n +--R - 15b x (x ) + (- 240a b (x ) + 1680a b )x +--R + +--R 4 4 n +--R 1050a b x +--R * +--R 3n +--R x +--R + +--R 5 3 n 2n +--R 560a b x x +--R * +--R 4n +--R x +--R + +--R 6 2 n 2n 3n +--R 210a b x x x +--R * +--R 5n +--R x +--R + +--R 7 n 2n 3n 4n +--R 48a b x x x x +--R * +--R 6n +--R x +--R + +--R 8 n 2n 3n 4n 5n +--R 5a x x x x x +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n n log(x) 5 +--R - 1680a b x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n n log(x) 4 +--R - 1050a b x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n n log(x) 3 +--R - 560a b x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n n log(x) 2 +--R - 210a b x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n n log(x) 8 n 2n 3n 4n 5n 6n +--R - 48a b x x x x x x %e - 5a x x x x x x +--R / +--R n 2n 3n 4n 5n 6n n log(x) 6 +--R 30n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 7n - 1 n 8 7 - 7n - 1 n 7 2 6 - 7n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 7n - 1 n 5 4 4 - 7n - 1 n 4 5 3 - 7n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 7n - 1 n 2 7 - 7n - 1 n 8 - 7n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1394 +r0:=-1/7*a^8/(n*x^(7*n))-4/3*a^7*b/(n*x^(6*n))-28/5*a^6*b^2/(n*x^(5*n))-_ + 14*a^5*b^3/(n*x^(4*n))-70/3*a^4*b^4/(n*x^(3*n))-_ + 28*a^3*b^5/(n*x^(2*n))-28*a^2*b^6/(n*x^n)+b^8*x^n/n+8*a*b^7*log(x) +--R +--R +--R (2) +--R 8 n 2 7 n 2 6 2n +--R (105b (x ) + 840a b n log(x)x - 2940a b )x +--R + +--R 3 5 n +--R - 2940a b x +--R * +--R 3n +--R x +--R + +--R 4 4 n 2n +--R - 2450a b x x +--R * +--R 4n +--R x +--R + +--R 5 3 n 2n 3n +--R - 1470a b x x x +--R * +--R 5n +--R x +--R + +--R 6 2 n 2n 3n 4n +--R - 588a b x x x x +--R * +--R 6n +--R x +--R + +--R 7 n 2n 3n 4n 5n +--R - 140a b x x x x x +--R * +--R 7n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n +--R - 15a x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n +--R 105n x x x x x x x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 840a b n log(x)(%e ) - 2940a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 2940a b (%e ) - 2450a b (%e ) - 1470a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 588a b (%e ) - 140a b %e - 15a +--R / +--R n log(x) 7 +--R 105n (%e ) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n 6n 7n n log(x) 8 +--R 105b x x x x x x x (%e ) +--R + +--R 8 n 2 2 6 2n 3 5 n 3n +--R ((- 105b (x ) + 2940a b )x + 2940a b x )x +--R + +--R 4 4 n 2n +--R 2450a b x x +--R * +--R 4n +--R x +--R + +--R 5 3 n 2n 3n +--R 1470a b x x x +--R * +--R 5n +--R x +--R + +--R 6 2 n 2n 3n 4n +--R 588a b x x x x +--R * +--R 6n +--R x +--R + +--R 7 n 2n 3n 4n 5n +--R 140a b x x x x x +--R * +--R 7n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n +--R 15a x x x x x x +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n 6n 7n n log(x) 6 +--R - 2940a b x x x x x x x (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n 7n n log(x) 5 +--R - 2940a b x x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n 7n n log(x) 4 +--R - 2450a b x x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n 7n n log(x) 3 +--R - 1470a b x x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n 7n n log(x) 2 +--R - 588a b x x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n n log(x) 8 n 2n 3n 4n 5n 6n 7n +--R - 140a b x x x x x x x %e - 15a x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n n log(x) 7 +--R 105n x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1394 +t0:=x^(-1-8*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 8n - 1 n 8 7 - 8n - 1 n 7 2 6 - 8n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 8n - 1 n 5 4 4 - 8n - 1 n 4 5 3 - 8n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 8n - 1 n 2 7 - 8n - 1 n 8 - 8n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1394 +r0:=-1/8*a^8/(n*x^(8*n))-8/7*a^7*b/(n*x^(7*n))-14/3*a^6*b^2/(n*x^(6*n))-_ + 56/5*a^5*b^3/(n*x^(5*n))-35/2*a^4*b^4/(n*x^(4*n))-_ + 56/3*a^3*b^5/(n*x^(3*n))-14*a^2*b^6/(n*x^(2*n))-8*a*b^7/(n*x^n)+b^8*log(x) +--R +--R +--R (2) +--R 8 n 7 2n 2 6 n 3n +--R ((840b n log(x)x - 6720a b )x - 11760a b x )x +--R + +--R 3 5 n 2n +--R - 15680a b x x +--R * +--R 4n +--R x +--R + +--R 4 4 n 2n 3n +--R - 14700a b x x x +--R * +--R 5n +--R x +--R + +--R 5 3 n 2n 3n 4n +--R - 9408a b x x x x +--R * +--R 6n +--R x +--R + +--R 6 2 n 2n 3n 4n 5n +--R - 3920a b x x x x x +--R * +--R 7n +--R x +--R + +--R 7 n 2n 3n 4n 5n 6n +--R - 960a b x x x x x x +--R * +--R 8n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n 7n +--R - 105a x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n 8n +--R 840n x x x x x x x x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 +--R 840b n log(x)(%e ) - 6720a b (%e ) +--R + +--R 2 6 n log(x) 6 3 5 n log(x) 5 +--R - 11760a b (%e ) - 15680a b (%e ) +--R + +--R 4 4 n log(x) 4 5 3 n log(x) 3 6 2 n log(x) 2 +--R - 14700a b (%e ) - 9408a b (%e ) - 3920a b (%e ) +--R + +--R 7 n log(x) 8 +--R - 960a b %e - 105a +--R / +--R n log(x) 8 +--R 840n (%e ) +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 2n 2 6 n 3n 3 5 n 2n 4n +--R ((6720a b x + 11760a b x )x + 15680a b x x )x +--R + +--R 4 4 n 2n 3n +--R 14700a b x x x +--R * +--R 5n +--R x +--R + +--R 5 3 n 2n 3n 4n +--R 9408a b x x x x +--R * +--R 6n +--R x +--R + +--R 6 2 n 2n 3n 4n 5n +--R 3920a b x x x x x +--R * +--R 7n +--R x +--R + +--R 7 n 2n 3n 4n 5n 6n +--R 960a b x x x x x x +--R * +--R 8n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n 7n +--R 105a x x x x x x x +--R * +--R n log(x) 8 +--R (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n 8n n log(x) 7 +--R - 6720a b x x x x x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n 6n 7n 8n n log(x) 6 +--R - 11760a b x x x x x x x x (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n 7n 8n n log(x) 5 +--R - 15680a b x x x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n 7n 8n n log(x) 4 +--R - 14700a b x x x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n 7n 8n n log(x) 3 +--R - 9408a b x x x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n 7n 8n n log(x) 2 +--R - 3920a b x x x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n 8n n log(x) 8 n 2n 3n 4n 5n 6n 7n 8n +--R - 960a b x x x x x x x x %e - 105a x x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n 8n n log(x) 8 +--R 840n x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 9n - 1 n 8 7 - 9n - 1 n 7 2 6 - 9n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 9n - 1 n 5 4 4 - 9n - 1 n 4 5 3 - 9n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 9n - 1 n 2 7 - 9n - 1 n 8 - 9n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1394 +r0:=-1/9*(a+b*x^n)^9/(a*n*x^(9*n)) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R - 126a b (x ) - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9n +--R 9a n x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 9b (%e ) - 36a b (%e ) - 84a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 126a b (%e ) - 126a b (%e ) - 84a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 36a b (%e ) - 9a b %e - a +--R / +--R n log(x) 9 +--R 9n (%e ) +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 8 9n n log(x) 8 2 7 9n n log(x) 7 3 6 9n n log(x) 6 +--R - 9a b x (%e ) - 36a b x (%e ) - 84a b x (%e ) +--R + +--R 4 5 9n n log(x) 5 5 4 9n n log(x) 4 +--R - 126a b x (%e ) - 126a b x (%e ) +--R + +--R 6 3 9n n log(x) 3 7 2 9n n log(x) 2 8 9n n log(x) +--R - 84a b x (%e ) - 36a b x (%e ) - 9a b x %e +--R + +--R 9 9n +--R - a x +--R / +--R 9n n log(x) 9 +--R 9a n x (%e ) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1394 +t0:=x^(-1-10*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 10n - 1 n 8 7 - 10n - 1 n 7 2 6 - 10n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 10n - 1 n 5 4 4 - 10n - 1 n 4 5 3 - 10n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 10n - 1 n 2 7 - 10n - 1 n 8 - 10n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1394 +r0:=-1/10*(a+b*x^n)^9/(a*n*x^(10*n))+1/90*b*(a+b*x^n)^9/(a^2*n*x^(9*n)) +--R +--R +--R (2) +--R 10 n 9 9 n 8 2 8 n 7 3 7 n 6 4 6 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 5 n 4 6 4 n 3 7 3 n 2 8 2 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 n 10 +--R - 81a b x - 9a +--R * +--R 9n +--R x +--R / +--R 2 9n 10n +--R 90a n x x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 45b (%e ) - 240a b (%e ) - 630a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 1008a b (%e ) - 1050a b (%e ) - 720a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 315a b (%e ) - 80a b %e - 9a +--R / +--R n log(x) 10 +--R 90n (%e ) +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 n 9 9 n 8 2 8 n 7 3 7 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 6 n 5 5 5 n 4 6 4 n 3 7 3 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 2 n 9 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) + 324a b (x ) +--R + +--R 9 n 10 +--R 81a b x + 9a +--R * +--R 9n +--R x +--R * +--R n log(x) 10 +--R (%e ) +--R + +--R 2 8 9n 10n n log(x) 8 3 7 9n 10n n log(x) 7 +--R - 45a b x x (%e ) - 240a b x x (%e ) +--R + +--R 4 6 9n 10n n log(x) 6 5 5 9n 10n n log(x) 5 +--R - 630a b x x (%e ) - 1008a b x x (%e ) +--R + +--R 6 4 9n 10n n log(x) 4 7 3 9n 10n n log(x) 3 +--R - 1050a b x x (%e ) - 720a b x x (%e ) +--R + +--R 8 2 9n 10n n log(x) 2 9 9n 10n n log(x) 10 9n 10n +--R - 315a b x x (%e ) - 80a b x x %e - 9a x x +--R / +--R 2 9n 10n n log(x) 10 +--R 90a n x x (%e ) +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1394 +t0:=x^(-1-11*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 11n - 1 n 8 7 - 11n - 1 n 7 2 6 - 11n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 11n - 1 n 5 4 4 - 11n - 1 n 4 5 3 - 11n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 11n - 1 n 2 7 - 11n - 1 n 8 - 11n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1394 +r0:=-1/11*(a+b*x^n)^9/(a*n*x^(11*n))+1/55*b*(a+b*x^n)^9/(a^2*n*x^(10*n))-_ + 1/495*b^2*(a+b*x^n)^9/(a^3*n*x^(9*n)) +--R +--R +--R (2) +--R 11 n 9 10 n 8 2 9 n 7 3 8 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 7 n 5 5 6 n 4 6 5 n 3 7 4 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 3 n 9 2 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 10 n 9 2 9 n 8 3 8 n 7 4 7 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 6 n 5 6 5 n 4 7 4 n 3 8 3 n 2 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) + 324a b (x ) +--R + +--R 9 2 n 10 +--R 81a b x + 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 9 n 9 3 8 n 8 4 7 n 7 5 6 n 6 +--R - 45a b (x ) - 405a b (x ) - 1620a b (x ) - 3780a b (x ) +--R + +--R 6 5 n 5 7 4 n 4 8 3 n 3 9 2 n 2 +--R - 5670a b (x ) - 5670a b (x ) - 3780a b (x ) - 1620a b (x ) +--R + +--R 10 n 11 +--R - 405a b x - 45a +--R * +--R 9n 10n +--R x x +--R / +--R 3 9n 10n 11n +--R 495a n x x x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 165b (%e ) - 990a b (%e ) - 2772a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 4620a b (%e ) - 4950a b (%e ) - 3465a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 1540a b (%e ) - 396a b %e - 45a +--R / +--R n log(x) 11 +--R 495n (%e ) +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 n 9 10 n 8 2 9 n 7 3 8 n 6 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) +--R + +--R 4 7 n 5 5 6 n 4 6 5 n 3 7 4 n 2 +--R 126a b (x ) + 126a b (x ) + 84a b (x ) + 36a b (x ) +--R + +--R 8 3 n 9 2 +--R 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 10 n 9 2 9 n 8 3 8 n 7 4 7 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 6 n 5 6 5 n 4 7 4 n 3 8 3 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 2 n 10 +--R - 81a b x - 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 9 n 9 3 8 n 8 4 7 n 7 5 6 n 6 +--R 45a b (x ) + 405a b (x ) + 1620a b (x ) + 3780a b (x ) +--R + +--R 6 5 n 5 7 4 n 4 8 3 n 3 9 2 n 2 +--R 5670a b (x ) + 5670a b (x ) + 3780a b (x ) + 1620a b (x ) +--R + +--R 10 n 11 +--R 405a b x + 45a +--R * +--R 9n 10n +--R x x +--R * +--R n log(x) 11 +--R (%e ) +--R + +--R 3 8 9n 10n 11n n log(x) 8 4 7 9n 10n 11n n log(x) 7 +--R - 165a b x x x (%e ) - 990a b x x x (%e ) +--R + +--R 5 6 9n 10n 11n n log(x) 6 6 5 9n 10n 11n n log(x) 5 +--R - 2772a b x x x (%e ) - 4620a b x x x (%e ) +--R + +--R 7 4 9n 10n 11n n log(x) 4 8 3 9n 10n 11n n log(x) 3 +--R - 4950a b x x x (%e ) - 3465a b x x x (%e ) +--R + +--R 9 2 9n 10n 11n n log(x) 2 10 9n 10n 11n n log(x) +--R - 1540a b x x x (%e ) - 396a b x x x %e +--R + +--R 11 9n 10n 11n +--R - 45a x x x +--R / +--R 3 9n 10n 11n n log(x) 11 +--R 495a n x x x (%e ) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1394 +t0:=x^(-1-12*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 12n - 1 n 8 7 - 12n - 1 n 7 2 6 - 12n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 12n - 1 n 5 4 4 - 12n - 1 n 4 5 3 - 12n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 12n - 1 n 2 7 - 12n - 1 n 8 - 12n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1394 +r0:=-1/12*(a+b*x^n)^9/(a*n*x^(12*n))+1/44*b*(a+b*x^n)^9/(a^2*n*x^(11*n))-_ + 1/220*b^2*(a+b*x^n)^9/(a^3*n*x^(10*n))+_ + 1/1980*b^3*(a+b*x^n)^9/(a^4*n*x^(9*n)) +--R +--R +--R (2) +--R 12 n 9 11 n 8 2 10 n 7 3 9 n 6 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) +--R + +--R 4 8 n 5 5 7 n 4 6 6 n 3 7 5 n 2 +--R 126a b (x ) + 126a b (x ) + 84a b (x ) + 36a b (x ) +--R + +--R 8 4 n 9 3 +--R 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 11 n 9 2 10 n 8 3 9 n 7 4 8 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 7 n 5 6 6 n 4 7 5 n 3 8 4 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 3 n 10 2 +--R - 81a b x - 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 10 n 9 3 9 n 8 4 8 n 7 5 7 n 6 +--R 45a b (x ) + 405a b (x ) + 1620a b (x ) + 3780a b (x ) +--R + +--R 6 6 n 5 7 5 n 4 8 4 n 3 9 3 n 2 +--R 5670a b (x ) + 5670a b (x ) + 3780a b (x ) + 1620a b (x ) +--R + +--R 10 2 n 11 +--R 405a b x + 45a b +--R * +--R 9n 10n +--R x x +--R * +--R 12n +--R x +--R + +--R 3 9 n 9 4 8 n 8 5 7 n 7 6 6 n 6 +--R - 165a b (x ) - 1485a b (x ) - 5940a b (x ) - 13860a b (x ) +--R + +--R 7 5 n 5 8 4 n 4 9 3 n 3 10 2 n 2 +--R - 20790a b (x ) - 20790a b (x ) - 13860a b (x ) - 5940a b (x ) +--R + +--R 11 n 12 +--R - 1485a b x - 165a +--R * +--R 9n 10n 11n +--R x x x +--R / +--R 4 9n 10n 11n 12n +--R 1980a n x x x x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 495b (%e ) - 3168a b (%e ) - 9240a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 15840a b (%e ) - 17325a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 12320a b (%e ) - 5544a b (%e ) - 1440a b %e +--R + +--R 8 +--R - 165a +--R / +--R n log(x) 12 +--R 1980n (%e ) +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 n 9 11 n 8 2 10 n 7 3 9 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 8 n 5 5 7 n 4 6 6 n 3 7 5 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 4 n 9 3 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 11 n 9 2 10 n 8 3 9 n 7 4 8 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 7 n 5 6 6 n 4 7 5 n 3 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) +--R + +--R 8 4 n 2 9 3 n 10 2 +--R 324a b (x ) + 81a b x + 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 10 n 9 3 9 n 8 4 8 n 7 5 7 n 6 +--R - 45a b (x ) - 405a b (x ) - 1620a b (x ) - 3780a b (x ) +--R + +--R 6 6 n 5 7 5 n 4 8 4 n 3 +--R - 5670a b (x ) - 5670a b (x ) - 3780a b (x ) +--R + +--R 9 3 n 2 10 2 n 11 +--R - 1620a b (x ) - 405a b x - 45a b +--R * +--R 9n 10n +--R x x +--R * +--R 12n +--R x +--R + +--R 3 9 n 9 4 8 n 8 5 7 n 7 6 6 n 6 +--R 165a b (x ) + 1485a b (x ) + 5940a b (x ) + 13860a b (x ) +--R + +--R 7 5 n 5 8 4 n 4 9 3 n 3 10 2 n 2 +--R 20790a b (x ) + 20790a b (x ) + 13860a b (x ) + 5940a b (x ) +--R + +--R 11 n 12 +--R 1485a b x + 165a +--R * +--R 9n 10n 11n +--R x x x +--R * +--R n log(x) 12 +--R (%e ) +--R + +--R 4 8 9n 10n 11n 12n n log(x) 8 +--R - 495a b x x x x (%e ) +--R + +--R 5 7 9n 10n 11n 12n n log(x) 7 +--R - 3168a b x x x x (%e ) +--R + +--R 6 6 9n 10n 11n 12n n log(x) 6 +--R - 9240a b x x x x (%e ) +--R + +--R 7 5 9n 10n 11n 12n n log(x) 5 +--R - 15840a b x x x x (%e ) +--R + +--R 8 4 9n 10n 11n 12n n log(x) 4 +--R - 17325a b x x x x (%e ) +--R + +--R 9 3 9n 10n 11n 12n n log(x) 3 +--R - 12320a b x x x x (%e ) +--R + +--R 10 2 9n 10n 11n 12n n log(x) 2 +--R - 5544a b x x x x (%e ) +--R + +--R 11 9n 10n 11n 12n n log(x) 12 9n 10n 11n 12n +--R - 1440a b x x x x %e - 165a x x x x +--R / +--R 4 9n 10n 11n 12n n log(x) 12 +--R 1980a n x x x x (%e ) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1394 +t0:=x^(-1-13*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 13n - 1 n 8 7 - 13n - 1 n 7 2 6 - 13n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 13n - 1 n 5 4 4 - 13n - 1 n 4 5 3 - 13n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 13n - 1 n 2 7 - 13n - 1 n 8 - 13n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1394 +r0:=-1/13*a^8/(n*x^(13*n))-2/3*a^7*b/(n*x^(12*n))-_ + 28/11*a^6*b^2/(n*x^(11*n))-28/5*a^5*b^3/(n*x^(10*n))-_ + 70/9*a^4*b^4/(n*x^(9*n))-7*a^3*b^5/(n*x^(8*n))-_ + 4*a^2*b^6/(n*x^(7*n))-4/3*a*b^7/(n*x^(6*n))-1/5*b^8/(n*x^(5*n)) +--R +--R +--R (2) +--R 8 6n 7 5n 7n 2 6 5n 6n 8n +--R ((- 1287b x - 8580a b x )x - 25740a b x x )x +--R + +--R 3 5 5n 6n 7n +--R - 45045a b x x x +--R * +--R 9n +--R x +--R + +--R 4 4 5n 6n 7n 8n +--R - 50050a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 3 5n 6n 7n 8n 9n +--R - 36036a b x x x x x +--R * +--R 11n +--R x +--R + +--R 6 2 5n 6n 7n 8n 9n 10n +--R - 16380a b x x x x x x +--R * +--R 12n +--R x +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n +--R - 4290a b x x x x x x x +--R * +--R 13n +--R x +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n +--R - 495a x x x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n 11n 12n 13n +--R 6435n x x x x x x x x x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 1287b (%e ) - 8580a b (%e ) - 25740a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 45045a b (%e ) - 50050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 36036a b (%e ) - 16380a b (%e ) - 4290a b %e +--R + +--R 8 +--R - 495a +--R / +--R n log(x) 13 +--R 6435n (%e ) +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 6n 7 5n 7n +--R (1287b x + 8580a b x )x +--R + +--R 2 6 5n 6n +--R 25740a b x x +--R * +--R 8n +--R x +--R + +--R 3 5 5n 6n 7n +--R 45045a b x x x +--R * +--R 9n +--R x +--R + +--R 4 4 5n 6n 7n 8n +--R 50050a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 3 5n 6n 7n 8n 9n +--R 36036a b x x x x x +--R * +--R 11n +--R x +--R + +--R 6 2 5n 6n 7n 8n 9n 10n +--R 16380a b x x x x x x +--R * +--R 12n +--R x +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n +--R 4290a b x x x x x x x +--R * +--R 13n +--R x +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n +--R 495a x x x x x x x x +--R * +--R n log(x) 13 +--R (%e ) +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 8 +--R - 1287b x x x x x x x x x (%e ) +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 7 +--R - 8580a b x x x x x x x x x (%e ) +--R + +--R 2 6 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 6 +--R - 25740a b x x x x x x x x x (%e ) +--R + +--R 3 5 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 5 +--R - 45045a b x x x x x x x x x (%e ) +--R + +--R 4 4 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 4 +--R - 50050a b x x x x x x x x x (%e ) +--R + +--R 5 3 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 3 +--R - 36036a b x x x x x x x x x (%e ) +--R + +--R 6 2 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 2 +--R - 16380a b x x x x x x x x x (%e ) +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) +--R - 4290a b x x x x x x x x x %e +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n 13n +--R - 495a x x x x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 13 +--R 6435n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1394 +t0:=x^(-1-14*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 14n - 1 n 8 7 - 14n - 1 n 7 2 6 - 14n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 14n - 1 n 5 4 4 - 14n - 1 n 4 5 3 - 14n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 14n - 1 n 2 7 - 14n - 1 n 8 - 14n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1394 +r0:=-1/14*a^8/(n*x^(14*n))-8/13*a^7*b/(n*x^(13*n))-_ + 7/3*a^6*b^2/(n*x^(12*n))-56/11*a^5*b^3/(n*x^(11*n))-_ + 7*a^4*b^4/(n*x^(10*n))-56/9*a^3*b^5/(n*x^(9*n))-_ + 7/2*a^2*b^6/(n*x^(8*n))-8/7*a*b^7/(n*x^(7*n))-1/6*b^8/(n*x^(6*n)) +--R +--R +--R (2) +--R 8 7n 7 6n 8n 2 6 6n 7n +--R ((- 3003b x - 20592a b x )x - 63063a b x x ) +--R * +--R 9n +--R x +--R + +--R 3 5 6n 7n 8n +--R - 112112a b x x x +--R * +--R 10n +--R x +--R + +--R 4 4 6n 7n 8n 9n +--R - 126126a b x x x x +--R * +--R 11n +--R x +--R + +--R 5 3 6n 7n 8n 9n 10n +--R - 91728a b x x x x x +--R * +--R 12n +--R x +--R + +--R 6 2 6n 7n 8n 9n 10n 11n +--R - 42042a b x x x x x x +--R * +--R 13n +--R x +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n +--R - 11088a b x x x x x x x +--R * +--R 14n +--R x +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n +--R - 1287a x x x x x x x x +--R / +--R 6n 7n 8n 9n 10n 11n 12n 13n 14n +--R 18018n x x x x x x x x x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 3003b (%e ) - 20592a b (%e ) - 63063a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 112112a b (%e ) - 126126a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 91728a b (%e ) - 42042a b (%e ) - 11088a b %e +--R + +--R 8 +--R - 1287a +--R / +--R n log(x) 14 +--R 18018n (%e ) +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 7n 7 6n 8n +--R (3003b x + 20592a b x )x +--R + +--R 2 6 6n 7n +--R 63063a b x x +--R * +--R 9n +--R x +--R + +--R 3 5 6n 7n 8n +--R 112112a b x x x +--R * +--R 10n +--R x +--R + +--R 4 4 6n 7n 8n 9n +--R 126126a b x x x x +--R * +--R 11n +--R x +--R + +--R 5 3 6n 7n 8n 9n 10n +--R 91728a b x x x x x +--R * +--R 12n +--R x +--R + +--R 6 2 6n 7n 8n 9n 10n 11n +--R 42042a b x x x x x x +--R * +--R 13n +--R x +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n +--R 11088a b x x x x x x x +--R * +--R 14n +--R x +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n +--R 1287a x x x x x x x x +--R * +--R n log(x) 14 +--R (%e ) +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 8 +--R - 3003b x x x x x x x x x (%e ) +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 7 +--R - 20592a b x x x x x x x x x (%e ) +--R + +--R 2 6 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 6 +--R - 63063a b x x x x x x x x x (%e ) +--R + +--R 3 5 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 5 +--R - 112112a b x x x x x x x x x (%e ) +--R + +--R 4 4 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 4 +--R - 126126a b x x x x x x x x x (%e ) +--R + +--R 5 3 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 3 +--R - 91728a b x x x x x x x x x (%e ) +--R + +--R 6 2 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 2 +--R - 42042a b x x x x x x x x x (%e ) +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) +--R - 11088a b x x x x x x x x x %e +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n 14n +--R - 1287a x x x x x x x x x +--R / +--R 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 14 +--R 18018n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1394 +t0:=x^(-1-15*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 15n - 1 n 8 7 - 15n - 1 n 7 2 6 - 15n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 15n - 1 n 5 4 4 - 15n - 1 n 4 5 3 - 15n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 15n - 1 n 2 7 - 15n - 1 n 8 - 15n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1394 +r0:=-1/15*a^8/(n*x^(15*n))-4/7*a^7*b/(n*x^(14*n))-_ + 28/13*a^6*b^2/(n*x^(13*n))-14/3*a^5*b^3/(n*x^(12*n))-_ + 70/11*a^4*b^4/(n*x^(11*n))-28/5*a^3*b^5/(n*x^(10*n))-_ + 28/9*a^2*b^6/(n*x^(9*n))-a*b^7/(n*x^(8*n))-1/7*b^8/(n*x^(7*n)) +--R +--R +--R (2) +--R 8 8n 7 7n 9n +--R (- 6435b x - 45045a b x )x +--R + +--R 2 6 7n 8n +--R - 140140a b x x +--R * +--R 10n +--R x +--R + +--R 3 5 7n 8n 9n +--R - 252252a b x x x +--R * +--R 11n +--R x +--R + +--R 4 4 7n 8n 9n 10n +--R - 286650a b x x x x +--R * +--R 12n +--R x +--R + +--R 5 3 7n 8n 9n 10n 11n +--R - 210210a b x x x x x +--R * +--R 13n +--R x +--R + +--R 6 2 7n 8n 9n 10n 11n 12n +--R - 97020a b x x x x x x +--R * +--R 14n +--R x +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n +--R - 25740a b x x x x x x x +--R * +--R 15n +--R x +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n +--R - 3003a x x x x x x x x +--R / +--R 7n 8n 9n 10n 11n 12n 13n 14n 15n +--R 45045n x x x x x x x x x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 6435b (%e ) - 45045a b (%e ) - 140140a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 252252a b (%e ) - 286650a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 210210a b (%e ) - 97020a b (%e ) - 25740a b %e +--R + +--R 8 +--R - 3003a +--R / +--R n log(x) 15 +--R 45045n (%e ) +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8n 7 7n 9n +--R (6435b x + 45045a b x )x +--R + +--R 2 6 7n 8n +--R 140140a b x x +--R * +--R 10n +--R x +--R + +--R 3 5 7n 8n 9n +--R 252252a b x x x +--R * +--R 11n +--R x +--R + +--R 4 4 7n 8n 9n 10n +--R 286650a b x x x x +--R * +--R 12n +--R x +--R + +--R 5 3 7n 8n 9n 10n 11n +--R 210210a b x x x x x +--R * +--R 13n +--R x +--R + +--R 6 2 7n 8n 9n 10n 11n 12n +--R 97020a b x x x x x x +--R * +--R 14n +--R x +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n +--R 25740a b x x x x x x x +--R * +--R 15n +--R x +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n +--R 3003a x x x x x x x x +--R * +--R n log(x) 15 +--R (%e ) +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 8 +--R - 6435b x x x x x x x x x (%e ) +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 7 +--R - 45045a b x x x x x x x x x (%e ) +--R + +--R 2 6 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 6 +--R - 140140a b x x x x x x x x x (%e ) +--R + +--R 3 5 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 5 +--R - 252252a b x x x x x x x x x (%e ) +--R + +--R 4 4 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 4 +--R - 286650a b x x x x x x x x x (%e ) +--R + +--R 5 3 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 3 +--R - 210210a b x x x x x x x x x (%e ) +--R + +--R 6 2 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 2 +--R - 97020a b x x x x x x x x x (%e ) +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) +--R - 25740a b x x x x x x x x x %e +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n 15n +--R - 3003a x x x x x x x x x +--R / +--R 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 15 +--R 45045n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^m +--R +--R +--R n - 1 n m +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1394 +r0:=(a+b*x^n)^(1+m)/(b*(1+m)*n) +--R +--R +--R n m + 1 +--R (b x + a) +--R (2) --------------- +--R (b m + b)n +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R n log(x) m log(b %e + a) +--R (b %e + a)%e +--R (3) ------------------------------------------- +--R (b m + b)n +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) +--R n log(x) m log(b %e + a) n m + 1 +--R (b %e + a)%e - (b x + a) +--R (4) ------------------------------------------------------------- +--R (b m + b)n +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^16 +--R +--R +--R (1) +--R 16 n - 1 n 16 15 n - 1 n 15 2 14 n - 1 n 14 +--R b x (x ) + 16a b x (x ) + 120a b x (x ) +--R + +--R 3 13 n - 1 n 13 4 12 n - 1 n 12 5 11 n - 1 n 11 +--R 560a b x (x ) + 1820a b x (x ) + 4368a b x (x ) +--R + +--R 6 10 n - 1 n 10 7 9 n - 1 n 9 8 8 n - 1 n 8 +--R 8008a b x (x ) + 11440a b x (x ) + 12870a b x (x ) +--R + +--R 9 7 n - 1 n 7 10 6 n - 1 n 6 11 5 n - 1 n 5 +--R 11440a b x (x ) + 8008a b x (x ) + 4368a b x (x ) +--R + +--R 12 4 n - 1 n 4 13 3 n - 1 n 3 14 2 n - 1 n 2 +--R 1820a b x (x ) + 560a b x (x ) + 120a b x (x ) +--R + +--R 15 n - 1 n 16 n - 1 +--R 16a b x x + a x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1394 +r0:=1/17*(a+b*x^n)^17/(b*n) +--R +--R +--R (2) +--R 17 n 17 16 n 16 2 15 n 15 3 14 n 14 +--R b (x ) + 17a b (x ) + 136a b (x ) + 680a b (x ) +--R + +--R 4 13 n 13 5 12 n 12 6 11 n 11 7 10 n 10 +--R 2380a b (x ) + 6188a b (x ) + 12376a b (x ) + 19448a b (x ) +--R + +--R 8 9 n 9 9 8 n 8 10 7 n 7 11 6 n 6 +--R 24310a b (x ) + 24310a b (x ) + 19448a b (x ) + 12376a b (x ) +--R + +--R 12 5 n 5 13 4 n 4 14 3 n 3 15 2 n 2 +--R 6188a b (x ) + 2380a b (x ) + 680a b (x ) + 136a b (x ) +--R + +--R 16 n 17 +--R 17a b x + a +--R / +--R 17b n +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 n log(x) 17 15 n log(x) 16 2 14 n log(x) 15 +--R b (%e ) + 17a b (%e ) + 136a b (%e ) +--R + +--R 3 13 n log(x) 14 4 12 n log(x) 13 +--R 680a b (%e ) + 2380a b (%e ) +--R + +--R 5 11 n log(x) 12 6 10 n log(x) 11 +--R 6188a b (%e ) + 12376a b (%e ) +--R + +--R 7 9 n log(x) 10 8 8 n log(x) 9 9 7 n log(x) 8 +--R 19448a b (%e ) + 24310a b (%e ) + 24310a b (%e ) +--R + +--R 10 6 n log(x) 7 11 5 n log(x) 6 +--R 19448a b (%e ) + 12376a b (%e ) +--R + +--R 12 4 n log(x) 5 13 3 n log(x) 4 14 2 n log(x) 3 +--R 6188a b (%e ) + 2380a b (%e ) + 680a b (%e ) +--R + +--R 15 n log(x) 2 16 n log(x) +--R 136a b (%e ) + 17a %e +--R / +--R 17n +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 17 n log(x) 17 16 n log(x) 16 2 15 n log(x) 15 +--R b (%e ) + 17a b (%e ) + 136a b (%e ) +--R + +--R 3 14 n log(x) 14 4 13 n log(x) 13 +--R 680a b (%e ) + 2380a b (%e ) +--R + +--R 5 12 n log(x) 12 6 11 n log(x) 11 +--R 6188a b (%e ) + 12376a b (%e ) +--R + +--R 7 10 n log(x) 10 8 9 n log(x) 9 +--R 19448a b (%e ) + 24310a b (%e ) +--R + +--R 9 8 n log(x) 8 10 7 n log(x) 7 +--R 24310a b (%e ) + 19448a b (%e ) +--R + +--R 11 6 n log(x) 6 12 5 n log(x) 5 13 4 n log(x) 4 +--R 12376a b (%e ) + 6188a b (%e ) + 2380a b (%e ) +--R + +--R 14 3 n log(x) 3 15 2 n log(x) 2 16 n log(x) +--R 680a b (%e ) + 136a b (%e ) + 17a b %e +--R + +--R 17 n 17 16 n 16 2 15 n 15 3 14 n 14 +--R - b (x ) - 17a b (x ) - 136a b (x ) - 680a b (x ) +--R + +--R 4 13 n 13 5 12 n 12 6 11 n 11 7 10 n 10 +--R - 2380a b (x ) - 6188a b (x ) - 12376a b (x ) - 19448a b (x ) +--R + +--R 8 9 n 9 9 8 n 8 10 7 n 7 11 6 n 6 +--R - 24310a b (x ) - 24310a b (x ) - 19448a b (x ) - 12376a b (x ) +--R + +--R 12 5 n 5 13 4 n 4 14 3 n 3 15 2 n 2 +--R - 6188a b (x ) - 2380a b (x ) - 680a b (x ) - 136a b (x ) +--R + +--R 16 n 17 +--R - 17a b x - a +--R / +--R 17b n +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1394 +t0:=x^12*(a+b*x^13)^12 +--R +--R +--R (1) +--R 12 168 11 155 2 10 142 3 9 129 4 8 116 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 103 6 6 90 7 5 77 8 4 64 9 3 51 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 38 11 25 12 12 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 266 + +--S 267 of 1394 +r0:=1/169*(a+b*x^13)^13/b +--R +--R +--R (2) +--R 1 13 169 1 12 156 6 2 11 143 22 3 10 130 55 4 9 117 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 169 13 13 13 13 +--R + +--R 99 5 8 104 132 6 7 91 132 7 6 78 99 8 5 65 55 9 4 52 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 13 13 13 13 13 +--R + +--R 22 10 3 39 6 11 2 26 1 12 13 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 13 13 13 169 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 169 1 11 156 6 2 10 143 22 3 9 130 55 4 8 117 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 169 13 13 13 13 +--R + +--R 99 5 7 104 132 6 6 91 132 7 5 78 99 8 4 65 55 9 3 52 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 13 13 13 13 13 +--R + +--R 22 10 2 39 6 11 26 1 12 13 +--R -- a b x + -- a b x + -- a x +--R 13 13 13 +--R Type: Polynomial(Fraction(Integer)) +--E 268 + +--S 269 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 169 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 269 + +--S 270 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 270 + +)clear all + +--S 271 of 1394 +t0:=x^24*(a+b*x^25)^12 +--R +--R +--R (1) +--R 12 324 11 299 2 10 274 3 9 249 4 8 224 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 199 6 6 174 7 5 149 8 4 124 9 3 99 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 74 11 49 12 24 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 271 + +--S 272 of 1394 +r0:=1/325*(a+b*x^25)^13/b +--R +--R +--R (2) +--R 1 13 325 1 12 300 6 2 11 275 22 3 10 250 11 4 9 225 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 325 25 25 25 5 +--R + +--R 99 5 8 200 132 6 7 175 132 7 6 150 99 8 5 125 11 9 4 100 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 25 25 25 25 5 +--R + +--R 22 10 3 75 6 11 2 50 1 12 25 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 25 25 25 325 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 272 + +--S 273 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 325 1 11 300 6 2 10 275 22 3 9 250 11 4 8 225 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 325 25 25 25 5 +--R + +--R 99 5 7 200 132 6 6 175 132 7 5 150 99 8 4 125 11 9 3 100 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 25 25 25 25 5 +--R + +--R 22 10 2 75 6 11 50 1 12 25 +--R -- a b x + -- a b x + -- a x +--R 25 25 25 +--R Type: Polynomial(Fraction(Integer)) +--E 273 + +--S 274 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 325 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 274 + +--S 275 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 275 + +)clear all + +--S 276 of 1394 +t0:=x^36*(a+b*x^37)^12 +--R +--R +--R (1) +--R 12 480 11 443 2 10 406 3 9 369 4 8 332 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 295 6 6 258 7 5 221 8 4 184 9 3 147 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 110 11 73 12 36 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 276 + +--S 277 of 1394 +r0:=1/481*(a+b*x^37)^13/b +--R +--R +--R (2) +--R 1 13 481 1 12 444 6 2 11 407 22 3 10 370 55 4 9 333 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 481 37 37 37 37 +--R + +--R 99 5 8 296 132 6 7 259 132 7 6 222 99 8 5 185 55 9 4 148 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 37 37 37 37 37 +--R + +--R 22 10 3 111 6 11 2 74 1 12 37 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 37 37 37 481 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 277 + +--S 278 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 481 1 11 444 6 2 10 407 22 3 9 370 55 4 8 333 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 481 37 37 37 37 +--R + +--R 99 5 7 296 132 6 6 259 132 7 5 222 99 8 4 185 55 9 3 148 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 37 37 37 37 37 +--R + +--R 22 10 2 111 6 11 74 1 12 37 +--R -- a b x + -- a b x + -- a x +--R 37 37 37 +--R Type: Polynomial(Fraction(Integer)) +--E 278 + +--S 279 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 481 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 279 + +--S 280 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 280 + +)clear all + +--S 281 of 1394 +t0:=x^(12*m)*(a+b*x^(1+12*m))^12 +--R +--R +--R (1) +--R 12 12m 12m + 1 12 11 12m 12m + 1 11 2 10 12m 12m + 1 10 +--R b x (x ) + 12a b x (x ) + 66a b x (x ) +--R + +--R 3 9 12m 12m + 1 9 4 8 12m 12m + 1 8 5 7 12m 12m + 1 7 +--R 220a b x (x ) + 495a b x (x ) + 792a b x (x ) +--R + +--R 6 6 12m 12m + 1 6 7 5 12m 12m + 1 5 8 4 12m 12m + 1 4 +--R 924a b x (x ) + 792a b x (x ) + 495a b x (x ) +--R + +--R 9 3 12m 12m + 1 3 10 2 12m 12m + 1 2 11 12m 12m + 1 +--R 220a b x (x ) + 66a b x (x ) + 12a b x x +--R + +--R 12 12m +--R a x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1394 +r0:=1/13*(a+b*x^(1+12*m))^13/(b*(1+12*m)) +--R +--R +--R (2) +--R 13 12m + 1 13 12 12m + 1 12 2 11 12m + 1 11 +--R b (x ) + 13a b (x ) + 78a b (x ) +--R + +--R 3 10 12m + 1 10 4 9 12m + 1 9 5 8 12m + 1 8 +--R 286a b (x ) + 715a b (x ) + 1287a b (x ) +--R + +--R 6 7 12m + 1 7 7 6 12m + 1 6 8 5 12m + 1 5 +--R 1716a b (x ) + 1716a b (x ) + 1287a b (x ) +--R + +--R 9 4 12m + 1 4 10 3 12m + 1 3 11 2 12m + 1 2 +--R 715a b (x ) + 286a b (x ) + 78a b (x ) +--R + +--R 12 12m + 1 13 +--R 13a b x + a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 (12m + 1)log(x) 13 11 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 10 (12m + 1)log(x) 11 3 9 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 8 (12m + 1)log(x) 9 5 7 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 6 (12m + 1)log(x) 7 7 5 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 4 (12m + 1)log(x) 5 9 3 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 2 (12m + 1)log(x) 3 11 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) +--R 13a %e +--R / +--R 156m + 13 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 (12m + 1)log(x) 13 12 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 11 (12m + 1)log(x) 11 3 10 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 9 (12m + 1)log(x) 9 5 8 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 7 (12m + 1)log(x) 7 7 6 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 5 (12m + 1)log(x) 5 9 4 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 3 (12m + 1)log(x) 3 11 2 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) 13 12m + 1 13 12 12m + 1 12 +--R 13a b %e - b (x ) - 13a b (x ) +--R + +--R 2 11 12m + 1 11 3 10 12m + 1 10 4 9 12m + 1 9 +--R - 78a b (x ) - 286a b (x ) - 715a b (x ) +--R + +--R 5 8 12m + 1 8 6 7 12m + 1 7 7 6 12m + 1 6 +--R - 1287a b (x ) - 1716a b (x ) - 1716a b (x ) +--R + +--R 8 5 12m + 1 5 9 4 12m + 1 4 10 3 12m + 1 3 +--R - 1287a b (x ) - 715a b (x ) - 286a b (x ) +--R + +--R 11 2 12m + 1 2 12 12m + 1 13 +--R - 78a b (x ) - 13a b x - a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1394 +t0:=x^(12+12*(-1+m))*(a+b*x^(1+12*m))^12 +--R +--R +--R (1) +--R 12 12m 12m + 1 12 11 12m 12m + 1 11 2 10 12m 12m + 1 10 +--R b x (x ) + 12a b x (x ) + 66a b x (x ) +--R + +--R 3 9 12m 12m + 1 9 4 8 12m 12m + 1 8 5 7 12m 12m + 1 7 +--R 220a b x (x ) + 495a b x (x ) + 792a b x (x ) +--R + +--R 6 6 12m 12m + 1 6 7 5 12m 12m + 1 5 8 4 12m 12m + 1 4 +--R 924a b x (x ) + 792a b x (x ) + 495a b x (x ) +--R + +--R 9 3 12m 12m + 1 3 10 2 12m 12m + 1 2 11 12m 12m + 1 +--R 220a b x (x ) + 66a b x (x ) + 12a b x x +--R + +--R 12 12m +--R a x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1394 +r0:=1/13*(a+b*x^(1+12*m))^13/(b*(1+12*m)) +--R +--R +--R (2) +--R 13 12m + 1 13 12 12m + 1 12 2 11 12m + 1 11 +--R b (x ) + 13a b (x ) + 78a b (x ) +--R + +--R 3 10 12m + 1 10 4 9 12m + 1 9 5 8 12m + 1 8 +--R 286a b (x ) + 715a b (x ) + 1287a b (x ) +--R + +--R 6 7 12m + 1 7 7 6 12m + 1 6 8 5 12m + 1 5 +--R 1716a b (x ) + 1716a b (x ) + 1287a b (x ) +--R + +--R 9 4 12m + 1 4 10 3 12m + 1 3 11 2 12m + 1 2 +--R 715a b (x ) + 286a b (x ) + 78a b (x ) +--R + +--R 12 12m + 1 13 +--R 13a b x + a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 (12m + 1)log(x) 13 11 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 10 (12m + 1)log(x) 11 3 9 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 8 (12m + 1)log(x) 9 5 7 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 6 (12m + 1)log(x) 7 7 5 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 4 (12m + 1)log(x) 5 9 3 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 2 (12m + 1)log(x) 3 11 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) +--R 13a %e +--R / +--R 156m + 13 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 (12m + 1)log(x) 13 12 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 11 (12m + 1)log(x) 11 3 10 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 9 (12m + 1)log(x) 9 5 8 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 7 (12m + 1)log(x) 7 7 6 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 5 (12m + 1)log(x) 5 9 4 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 3 (12m + 1)log(x) 3 11 2 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) 13 12m + 1 13 12 12m + 1 12 +--R 13a b %e - b (x ) - 13a b (x ) +--R + +--R 2 11 12m + 1 11 3 10 12m + 1 10 4 9 12m + 1 9 +--R - 78a b (x ) - 286a b (x ) - 715a b (x ) +--R + +--R 5 8 12m + 1 8 6 7 12m + 1 7 7 6 12m + 1 6 +--R - 1287a b (x ) - 1716a b (x ) - 1716a b (x ) +--R + +--R 8 5 12m + 1 5 9 4 12m + 1 4 10 3 12m + 1 3 +--R - 1287a b (x ) - 715a b (x ) - 286a b (x ) +--R + +--R 11 2 12m + 1 2 12 12m + 1 13 +--R - 78a b (x ) - 13a b x - a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1394 +r0:=a^2*x^n/(b^3*n)-1/2*a*x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-_ + a^3*log(a+b*x^n)/(b^4*n) +--R +--R +--R 3 n 3 3n 2 2n 2 n +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 6a log(b %e + a) + 2b (%e ) - 3a b (%e ) +--R + +--R 2 n log(x) +--R 6a b %e +--R / +--R 4 +--R 6b n +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 n 3 n log(x) 3 +--R - 6a log(b %e + a) + 6a log(b x + a) + 2b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 3n 2 2n 2 n +--R - 3a b (%e ) + 6a b %e - 2b x + 3a b x - 6a b x +--R / +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1394 +r0:=-a*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+a^2*log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 2n n +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R 2a log(b %e + a) + b (%e ) - 2a b %e +--R (3) ------------------------------------------------------------ +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 2 n 2 n log(x) 2 +--R 2a log(b %e + a) - 2a log(b x + a) + b (%e ) +--R + +--R n log(x) 2 2n n +--R - 2a b %e - b x + 2a b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1394 +r0:=x^n/(b*n)-a*log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R b n +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - a log(b %e + a) + b %e +--R (3) ---------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - a log(b %e + a) + a log(b x + a) + b %e - b x +--R (4) ----------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1394 +t0:=x^(-1+n)/(a+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1394 +r0:=log(a+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + a) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + a) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + a) - log(b x + a) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1394 +r0:=(-1/2)/(a*n*x^(2*n))+b/(a^2*n*x^n)+b^2*log(x)/a^3-b^2*log(a+b*x^n)/(a^3*n) +--R +--R +--R 2 n 2n n 2 n 2n 2 n +--R - 2b x x log(b x + a) + (2b n log(x)x + 2a b)x - a x +--R (2) ---------------------------------------------------------- +--R 3 n 2n +--R 2a n x x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - 2b (%e ) log(b %e + a) + 2b n log(x)(%e ) +--R + +--R n log(x) 2 +--R 2a b %e - a +--R / +--R 3 n log(x) 2 +--R 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - 2b x x (%e ) log(b %e + a) +--R + +--R 2 n 2n n log(x) 2 n 2n 2 n n log(x) 2 +--R 2b x x (%e ) log(b x + a) + (- 2a b x + a x )(%e ) +--R + +--R n 2n n log(x) 2 n 2n +--R 2a b x x %e - a x x +--R / +--R 3 n 2n n log(x) 2 +--R 2a n x x (%e ) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1394 +r0:=(-1/3)/(a*n*x^(3*n))+1/2*b/(a^2*n*x^(2*n))-b^2/(a^3*n*x^n)-_ + b^3*log(x)/a^4+b^3*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2n 3n n 3 n 2 2n 2 n 3n +--R 6b x x x log(b x + a) + ((- 6b n log(x)x - 6a b )x + 3a b x )x +--R + +--R 3 n 2n +--R - 2a x x +--R / +--R 4 n 2n 3n +--R 6a n x x x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 6b (%e ) log(b %e + a) - 6b n log(x)(%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 6a b (%e ) + 3a b %e - 2a +--R / +--R 4 n log(x) 3 +--R 6a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 6b x x x (%e ) log(b %e + a) +--R + +--R 3 n 2n 3n n log(x) 3 n +--R - 6b x x x (%e ) log(b x + a) +--R + +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((6a b x - 3a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 6a b x x x (%e ) + 3a b x x x %e - 2a x x x +--R / +--R 4 n 2n 3n n log(x) 3 +--R 6a n x x x (%e ) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1394 +t0:=x^(3+4*(-1+n))/(a+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1394 +r0:=a^2*x^n/(b^3*n)-1/2*a*x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-_ + a^3*log(a+b*x^n)/(b^4*n) +--R +--R +--R 3 n 3 3n 2 2n 2 n +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 6a log(b %e + a) + 2b (%e ) - 3a b (%e ) +--R + +--R 2 n log(x) +--R 6a b %e +--R / +--R 4 +--R 6b n +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 n 3 n log(x) 3 +--R - 6a log(b %e + a) + 6a log(b x + a) + 2b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 3n 2 2n 2 n +--R - 3a b (%e ) + 6a b %e - 2b x + 3a b x - 6a b x +--R / +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1394 +t0:=x^(2+3*(-1+n))/(a+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1394 +r0:=-a*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+a^2*log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 2n n +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R 2a log(b %e + a) + b (%e ) - 2a b %e +--R (3) ------------------------------------------------------------ +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 2 n 2 n log(x) 2 +--R 2a log(b %e + a) - 2a log(b x + a) + b (%e ) +--R + +--R n log(x) 2 2n n +--R - 2a b %e - b x + 2a b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1394 +t0:=x^(1+2*(-1+n))/(a+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1394 +r0:=x^n/(b*n)-a*log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R b n +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - a log(b %e + a) + b %e +--R (3) ---------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - a log(b %e + a) + a log(b x + a) + b %e - b x +--R (4) ----------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1394 +t0:=x^(-1+n)/(a+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1394 +r0:=log(a+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + a) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + a) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + a) - log(b x + a) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1394 +t0:=x^(-3-2*(-1+n))/(a+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1394 +r0:=(-1/2)/(a*n*x^(2*n))+b/(a^2*n*x^n)+b^2*log(x)/a^3-b^2*log(a+b*x^n)/(a^3*n) +--R +--R +--R 2 n 2n n 2 n 2n 2 n +--R - 2b x x log(b x + a) + (2b n log(x)x + 2a b)x - a x +--R (2) ---------------------------------------------------------- +--R 3 n 2n +--R 2a n x x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - 2b (%e ) log(b %e + a) + 2b n log(x)(%e ) +--R + +--R n log(x) 2 +--R 2a b %e - a +--R / +--R 3 n log(x) 2 +--R 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - 2b x x (%e ) log(b %e + a) +--R + +--R 2 n 2n n log(x) 2 n 2n 2 n n log(x) 2 +--R 2b x x (%e ) log(b x + a) + (- 2a b x + a x )(%e ) +--R + +--R n 2n n log(x) 2 n 2n +--R 2a b x x %e - a x x +--R / +--R 3 n 2n n log(x) 2 +--R 2a n x x (%e ) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1394 +t0:=x^(-4-3*(-1+n))/(a+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1394 +r0:=(-1/3)/(a*n*x^(3*n))+1/2*b/(a^2*n*x^(2*n))-b^2/(a^3*n*x^n)-_ + b^3*log(x)/a^4+b^3*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2n 3n n 3 n 2 2n 2 n 3n +--R 6b x x x log(b x + a) + ((- 6b n log(x)x - 6a b )x + 3a b x )x +--R + +--R 3 n 2n +--R - 2a x x +--R / +--R 4 n 2n 3n +--R 6a n x x x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 6b (%e ) log(b %e + a) - 6b n log(x)(%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 6a b (%e ) + 3a b %e - 2a +--R / +--R 4 n log(x) 3 +--R 6a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 6b x x x (%e ) log(b %e + a) +--R + +--R 3 n 2n 3n n log(x) 3 n +--R - 6b x x x (%e ) log(b x + a) +--R + +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((6a b x - 3a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 6a b x x x (%e ) + 3a b x x x %e - 2a x x x +--R / +--R 4 n 2n 3n n log(x) 3 +--R 6a n x x x (%e ) +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1394 +t0:=x^(-1+4*n)/(2+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1394 +r0:=4*x^n/(b^3*n)-x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-8*log(2+b*x^n)/(b^4*n) +--R +--R +--R n 3 3n 2 2n n +--R - 24log(b x + 2) + b x - 3b x + 12b x +--R (2) ------------------------------------------- +--R 4 +--R 3b n +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 24log(b %e + 2) + b (%e ) - 3b (%e ) +--R + +--R n log(x) +--R 12b %e +--R / +--R 4 +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) n 3 n log(x) 3 +--R - 24log(b %e + 2) + 24log(b x + 2) + b (%e ) +--R + +--R 2 n log(x) 2 n log(x) 3 3n 2 2n n +--R - 3b (%e ) + 12b %e - b x + 3b x - 12b x +--R / +--R 4 +--R 3b n +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1394 +t0:=x^(-1+3*n)/(2+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1394 +r0:=-2*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+4*log(2+b*x^n)/(b^3*n) +--R +--R +--R n 2 2n n +--R 8log(b x + 2) + b x - 4b x +--R (2) ------------------------------ +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 2 n log(x) 2 n log(x) +--R 8log(b %e + 2) + b (%e ) - 4b %e +--R (3) -------------------------------------------------------- +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) n 2 n log(x) 2 n log(x) +--R 8log(b %e + 2) - 8log(b x + 2) + b (%e ) - 4b %e +--R + +--R 2 2n n +--R - b x + 4b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1394 +t0:=x^(-1+2*n)/(2+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1394 +r0:=x^n/(b*n)-2*log(2+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - 2log(b x + 2) + b x +--R (2) ----------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - 2log(b %e + 2) + b %e +--R (3) --------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - 2log(b %e + 2) + 2log(b x + 2) + b %e - b x +--R (4) --------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1394 +t0:=x^(-1+n)/(2+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1394 +r0:=log(2+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + 2) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + 2) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + 2) - log(b x + 2) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1394 +t0:=1/(x*(2+b*x^n)) +--R +--R +--R 1 +--R (1) ----------- +--R n +--R b x x + 2x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1394 +r0:=-atanh(1+b*x^n)/n +--R +--R +--R n +--R atanh(b x + 1) +--R (2) - --------------- +--R n +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + 2) + n log(x) +--R (3) ---------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + 2) + 2atanh(b x + 1) + n log(x) +--R (4) ----------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1394 +t0:=x^(-1-n)/(2+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1394 +r0:=(-1/2)/(n*x^n)+1/2*b*atanh(1+b*x^n)/n +--R +--R +--R n n +--R b x atanh(b x + 1) - 1 +--R (2) ----------------------- +--R n +--R 2n x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + 2) - b n log(x)%e - 2 +--R (3) ------------------------------------------------------------ +--R n log(x) +--R 4n %e +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) +--R b x %e log(b %e + 2) +--R + +--R n n n n log(x) n +--R (- 2b x atanh(b x + 1) - b n log(x)x + 2)%e - 2x +--R / +--R n n log(x) +--R 4n x %e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1394 +t0:=x^(-1-2*n)/(2+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1394 +r0:=(-1/4)/(n*x^(2*n))+1/4*b/(n*x^n)-1/4*b^2*atanh(1+b*x^n)/n +--R +--R +--R 2 n 2n n 2n n +--R - b x x atanh(b x + 1) + b x - x +--R (2) ------------------------------------- +--R n 2n +--R 4n x x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - b (%e ) log(b %e + 2) + b n log(x)(%e ) +--R + +--R n log(x) +--R 2b %e - 2 +--R / +--R n log(x) 2 +--R 8n (%e ) +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - b x x (%e ) log(b %e + 2) +--R + +--R 2 n 2n n 2 n 2n n n log(x) 2 +--R (2b x x atanh(b x + 1) + (b n log(x)x - 2b)x + 2x )(%e ) +--R + +--R n 2n n log(x) n 2n +--R 2b x x %e - 2x x +--R / +--R n 2n n log(x) 2 +--R 8n x x (%e ) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1394 +t0:=x^(-1-3*n)/(2+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1394 +r0:=(-1/6)/(n*x^(3*n))+1/8*b/(n*x^(2*n))-1/8*b^2/(n*x^n)+_ + 1/8*b^3*atanh(1+b*x^n)/n +--R +--R +--R 3 n 2n 3n n 2 2n n 3n n 2n +--R 3b x x x atanh(b x + 1) + (- 3b x + 3b x )x - 4x x +--R (2) ----------------------------------------------------------- +--R n 2n 3n +--R 24n x x x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 3b (%e ) log(b %e + 2) - 3b n log(x)(%e ) +--R + +--R 2 n log(x) 2 n log(x) +--R - 6b (%e ) + 6b %e - 8 +--R / +--R n log(x) 3 +--R 48n (%e ) +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 3b x x x (%e ) log(b %e + 2) +--R + +--R 3 n 2n 3n n +--R - 6b x x x atanh(b x + 1) +--R + +--R 3 n 2 2n n 3n n 2n +--R ((- 3b n log(x)x + 6b )x - 6b x )x + 8x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 n 2n 3n n log(x) 2 n 2n 3n n log(x) n 2n 3n +--R - 6b x x x (%e ) + 6b x x x %e - 8x x x +--R / +--R n 2n 3n n log(x) 3 +--R 48n x x x (%e ) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^2 +--R +--R +--R 4n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1394 +r0:=-2*a*x^n/(b^3*n)+1/2*x^(2*n)/(b^2*n)+a^3/(b^4*n*(a+b*x^n))+_ + 3*a^2*log(a+b*x^n)/(b^4*n) +--R +--R +--R (2) +--R 2 n 3 n 3 n 2 2n 2 n 2 2 n 3 +--R (6a b x + 6a )log(b x + a) + (b x + a b )x - 4a b (x ) - 4a b x + 2a +--R ---------------------------------------------------------------------------- +--R 5 n 4 +--R 2b n x + 2a b n +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 3 n log(x) 3 n log(x) 3 +--R (6a b %e + 6a )log(b %e + a) + b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 3a b (%e ) - 4a b %e + 2a +--R / +--R 5 n log(x) 4 +--R 2b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n 3 n log(x) 3 n 4 n log(x) +--R ((6a b x + 6a b)%e + 6a b x + 6a )log(b %e + a) +--R + +--R 2 2 n 3 n log(x) 3 n 4 n +--R ((- 6a b x - 6a b)%e - 6a b x - 6a )log(b x + a) +--R + +--R 4 n 3 n log(x) 3 3 n 2 2 n log(x) 2 +--R (b x + a b )(%e ) + (- 3a b x - 3a b )(%e ) +--R + +--R 4 n 3 2n 3 n 2 3 n log(x) 3 n 2 2 2n +--R ((- b x - a b )x + 4a b (x ) - 6a b)%e + (- a b x - a b )x +--R + +--R 2 2 n 2 3 n +--R 4a b (x ) + 6a b x +--R / +--R 6 n 5 n log(x) 5 n 2 4 +--R (2b n x + 2a b n)%e + 2a b n x + 2a b n +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^2 +--R +--R +--R 3n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1394 +r0:=x^n/(b^2*n)-a^2/(b^3*n*(a+b*x^n))-2*a*log(a+b*x^n)/(b^3*n) +--R +--R +--R n 2 n 2 n 2 n 2 +--R (- 2a b x - 2a )log(b x + a) + b (x ) + a b x - a +--R (2) ------------------------------------------------------ +--R 4 n 3 +--R b n x + a b n +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) 2 n log(x) 2 n log(x) 2 +--R (- 2a b %e - 2a )log(b %e + a) + b (%e ) +--R + +--R n log(x) 2 +--R a b %e - a +--R / +--R 4 n log(x) 3 +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2 n log(x) 2 n 3 n log(x) +--R ((- 2a b x - 2a b)%e - 2a b x - 2a )log(b %e + a) +--R + +--R 2 n 2 n log(x) 2 n 3 n +--R ((2a b x + 2a b)%e + 2a b x + 2a )log(b x + a) +--R + +--R 3 n 2 n log(x) 2 3 n 2 2 n log(x) 2 n 2 +--R (b x + a b )(%e ) + (- b (x ) + 2a b)%e - a b (x ) +--R + +--R 2 n +--R - 2a b x +--R / +--R 5 n 4 n log(x) 4 n 2 3 +--R (b n x + a b n)%e + a b n x + a b n +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^2 +--R +--R +--R 2n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1394 +r0:=a/(b^2*n*(a+b*x^n))+log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 n 2 +--R b n x + a b n +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R (b %e + a)log(b %e + a) + a +--R (3) ------------------------------------------- +--R 3 n log(x) 2 +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((b x + a b)%e + a b x + a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((- b x - a b)%e - a b x - a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 4 n 3 n log(x) 3 n 2 2 +--R (b n x + a b n)%e + a b n x + a b n +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^2 +--R +--R +--R n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1394 +r0:=(-1)/(b*n*(a+b*x^n)) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 n +--R b n x + a b n +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 2 n log(x) +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R %e - x +--R (4) ------------------------------------------- +--R 2 n n log(x) n 2 +--R (b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1394 +t0:=1/(x*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 n 2 n 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1394 +r0:=1/(a*n*(a+b*x^n))+log(x)/a^2-log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R (- b x - a)log(b x + a) + b n log(x)x + a n log(x) + a +--R (2) --------------------------------------------------------- +--R 2 n 3 +--R a b n x + a n +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) n log(x) n log(x) +--R (- b %e - a)log(b %e + a) + b n log(x)%e +--R + +--R a n log(x) + a +--R / +--R 2 n log(x) 3 +--R a b n %e + a n +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((- b x - a b)%e - a b x - a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((b x + a b)%e + a b x + a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 2 2 n 3 n log(x) 3 n 4 +--R (a b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^2 +--R +--R +--R - n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1394 +r0:=(-2)/(a^2*n*x^n)+1/(a*n*x^n*(a+b*x^n))-2*b*log(x)/a^3+_ + 2*b*log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n n 2 n 2 +--R (2b (x ) + 2a b x )log(b x + a) - 2b n log(x)(x ) +--R + +--R n 2 +--R (- 2a b n log(x) - 2a b)x - a +--R / +--R 3 n 2 4 n +--R a b n (x ) + a n x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) n log(x) +--R (2b (%e ) + 2a b %e )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R - 2b n log(x)(%e ) + (- 2a b n log(x) - 2a b)%e - a +--R / +--R 3 n log(x) 2 4 n log(x) +--R a b n (%e ) + a n %e +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2 2 n n log(x) 2 2 n 2 2 n n log(x) +--R ((2b (x ) + 2a b x )(%e ) + (2a b (x ) + 2a b x )%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 3 n 2 2 n n log(x) 2 +--R (- 2b (x ) - 2a b x )(%e ) +--R + +--R 2 n 2 2 n n log(x) +--R (- 2a b (x ) - 2a b x )%e +--R * +--R n +--R log(b x + a) +--R + +--R 2 n 2 n log(x) 2 2 n 2 3 n log(x) 2 n 2 +--R (2a b x + a b)(%e ) + (- 2a b (x ) + a )%e - a b (x ) +--R + +--R 3 n +--R - a x +--R / +--R 3 2 n 2 4 n n log(x) 2 4 n 2 5 n n log(x) +--R (a b n (x ) + a b n x )(%e ) + (a b n (x ) + a n x )%e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^2 +--R +--R +--R - 2n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1394 +r0:=(-3/2)/(a^2*n*x^(2*n))+3*b/(a^3*n*x^n)+1/(a*n*x^(2*n)*(a+b*x^n))+_ + 3*b^2*log(x)/a^4-3*b^2*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2 2 n 2n n +--R (- 6b (x ) - 6a b x )x log(b x + a) +--R + +--R 3 n 2 2 2 n 2 2n 2 n 2 +--R (6b n log(x)(x ) + (6a b n log(x) + 6a b )x + 6a b)x - 3a b (x ) +--R + +--R 3 n +--R - a x +--R / +--R 4 n 2 5 n 2n +--R (2a b n (x ) + 2a n x )x +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 n log(x) +--R (- 6b (%e ) - 6a b (%e ) )log(b %e + a) +--R + +--R 3 n log(x) 3 2 2 n log(x) 2 +--R 6b n log(x)(%e ) + (6a b n log(x) + 6a b )(%e ) +--R + +--R 2 n log(x) 3 +--R 3a b %e - a +--R / +--R 4 n log(x) 3 5 n log(x) 2 +--R 2a b n (%e ) + 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2n n log(x) 3 +--R (- 6b (x ) - 6a b x )x (%e ) +--R + +--R 3 n 2 2 2 n 2n n log(x) 2 +--R (- 6a b (x ) - 6a b x )x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2n n log(x) 3 +--R (6b (x ) + 6a b x )x (%e ) +--R + +--R 3 n 2 2 2 n 2n n log(x) 2 +--R (6a b (x ) + 6a b x )x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 2n 2 2 n 2 3 n n log(x) 3 +--R ((- 6a b x - 6a b )x + 3a b (x ) + a b x )(%e ) +--R + +--R 3 n 2 3 2n 3 n 2 4 n n log(x) 2 +--R ((6a b (x ) - 6a b)x + 3a b (x ) + a x )(%e ) +--R + +--R 2 2 n 2 3 n 2n n log(x) 3 n 2 4 n 2n +--R (3a b (x ) + 3a b x )x %e + (- a b (x ) - a x )x +--R / +--R 4 2 n 2 5 n 2n n log(x) 3 +--R (2a b n (x ) + 2a b n x )x (%e ) +--R + +--R 5 n 2 6 n 2n n log(x) 2 +--R (2a b n (x ) + 2a n x )x (%e ) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n)^2 +--R +--R +--R - 3n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1394 +r0:=(-4/3)/(a^2*n*x^(3*n))+2*b/(a^3*n*x^(2*n))-4*b^2/(a^4*n*x^n)+_ + 1/(a*n*x^(3*n)*(a+b*x^n))-4*b^3*log(x)/a^5+4*b^3*log(a+b*x^n)/(a^5*n) +--R +--R +--R (2) +--R 4 n 2 3 n 2n 3n n +--R (12b (x ) + 12a b x )x x log(b x + a) +--R + +--R 4 n 2 3 3 n 2 2 2n +--R (- 12b n log(x)(x ) + (- 12a b n log(x) - 12a b )x - 12a b )x +--R + +--R 2 2 n 2 3 n +--R 6a b (x ) + 6a b x +--R * +--R 3n +--R x +--R + +--R 3 n 2 4 n 2n +--R (- 4a b (x ) - a x )x +--R / +--R 5 n 2 6 n 2n 3n +--R (3a b n (x ) + 3a n x )x x +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 n log(x) +--R (12b (%e ) + 12a b (%e ) )log(b %e + a) +--R + +--R 4 n log(x) 4 3 3 n log(x) 3 +--R - 12b n log(x)(%e ) + (- 12a b n log(x) - 12a b )(%e ) +--R + +--R 2 2 n log(x) 2 3 n log(x) 4 +--R - 6a b (%e ) + 2a b %e - a +--R / +--R 5 n log(x) 4 6 n log(x) 3 +--R 3a b n (%e ) + 3a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2 4 n 2n 3n n log(x) 4 +--R (12b (x ) + 12a b x )x x (%e ) +--R + +--R 4 n 2 2 3 n 2n 3n n log(x) 3 +--R (12a b (x ) + 12a b x )x x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 5 n 2 4 n 2n 3n n log(x) 4 +--R (- 12b (x ) - 12a b x )x x (%e ) +--R + +--R 4 n 2 2 3 n 2n 3n n log(x) 3 +--R (- 12a b (x ) - 12a b x )x x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 4 n 2 3 2n 2 3 n 2 3 2 n 3n +--R ((12a b x + 12a b )x - 6a b (x ) - 6a b x )x +--R + +--R 3 2 n 2 4 n 2n +--R (4a b (x ) + a b x )x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 4 n 2 3 2 2n 3 2 n 2 4 n 3n +--R ((- 12a b (x ) + 12a b )x - 6a b (x ) - 6a b x )x +--R + +--R 4 n 2 5 n 2n +--R (4a b (x ) + a x )x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 3 n 2 3 2 n 2n 3n n log(x) 2 +--R (- 6a b (x ) - 6a b x )x x (%e ) +--R + +--R 3 2 n 2 4 n 2n 3n n log(x) 4 n 2 5 n 2n 3n +--R (2a b (x ) + 2a b x )x x %e + (- a b (x ) - a x )x x +--R / +--R 5 2 n 2 6 n 2n 3n n log(x) 4 +--R (3a b n (x ) + 3a b n x )x x (%e ) +--R + +--R 6 n 2 7 n 2n 3n n log(x) 3 +--R (3a b n (x ) + 3a n x )x x (%e ) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^3 +--R +--R +--R 4n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1394 +r0:=x^n/(b^3*n)+1/2*a^3/(b^4*n*(a+b*x^n)^2)-3*a^2/(b^4*n*(a+b*x^n))-_ + 3*a*log(a+b*x^n)/(b^4*n) +--R +--R +--R (2) +--R 2 n 2 2 n 3 n 3 n 3 2 n 2 +--R (- 6a b (x ) - 12a b x - 6a )log(b x + a) + 2b (x ) + 4a b (x ) +--R + +--R 2 n 3 +--R - 4a b x - 5a +--R / +--R 6 n 2 5 n 2 4 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 2 n log(x) 3 n log(x) +--R (- 6a b (%e ) - 12a b %e - 6a )log(b %e + a) +--R + +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 4a b (%e ) - 4a b %e - 5a +--R / +--R 6 n log(x) 2 5 n log(x) 2 4 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 2 3 n 3 2 n log(x) 2 +--R (- 6a b (x ) - 12a b x - 6a b )(%e ) +--R + +--R 2 3 n 2 3 2 n 4 n log(x) 3 2 n 2 4 n +--R (- 12a b (x ) - 24a b x - 12a b)%e - 6a b (x ) - 12a b x +--R + +--R 5 +--R - 6a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 2 3 n 3 2 n log(x) 2 +--R (6a b (x ) + 12a b x + 6a b )(%e ) +--R + +--R 2 3 n 2 3 2 n 4 n log(x) 3 2 n 2 4 n +--R (12a b (x ) + 24a b x + 12a b)%e + 6a b (x ) + 12a b x +--R + +--R 5 +--R 6a +--R * +--R n +--R log(b x + a) +--R + +--R 5 n 2 4 n 2 3 n log(x) 3 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 5 n 3 2 3 n 3 2 n log(x) 2 +--R (- 2b (x ) + 12a b x + 9a b )(%e ) +--R + +--R 4 n 3 2 3 n 2 4 n log(x) 2 3 n 3 3 2 n 2 +--R (- 4a b (x ) - 12a b (x ) + 6a b)%e - 2a b (x ) - 9a b (x ) +--R + +--R 4 n +--R - 6a b x +--R / +--R 8 n 2 7 n 2 6 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 7 n 2 2 6 n 3 5 n log(x) 2 6 n 2 3 5 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 4 +--R 2a b n +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^3 +--R +--R +--R 3n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1394 +r0:=-1/2*a^2/(b^3*n*(a+b*x^n)^2)+2*a/(b^3*n*(a+b*x^n))+log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 n 2 n n 2 +--R (2b (x ) + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ------------------------------------------------------- +--R 5 n 2 4 n 2 3 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (2b (%e ) + 4a b %e + 2a )log(b %e + a) +--R + +--R n log(x) 2 +--R 4a b %e + 3a +--R / +--R 5 n log(x) 2 4 n log(x) 2 3 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 4a b x - 3a b )(%e ) + (4a b (x ) - 2a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 2a b x +--R / +--R 7 n 2 6 n 2 5 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 6 n 2 2 5 n 3 4 n log(x) 2 5 n 2 3 4 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 3 +--R 2a b n +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^3 +--R +--R +--R 2n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1394 +r0:=1/2*x^(2*n)/(a*n*(a+b*x^n)^2) +--R +--R +--R 2n +--R x +--R (2) ------------------------------- +--R 2 n 2 2 n 3 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 2b %e - a +--R (3) ----------------------------------------------- +--R 4 n log(x) 2 3 n log(x) 2 2 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2n n log(x) 2 +--R - b x (%e ) +--R + +--R 3 2n 3 n 2 2 2 n 3 n log(x) 2 2 2n +--R (- 2a b x - 2a b (x ) - 4a b x - 2a b)%e - a b x +--R + +--R 2 2 n 2 3 n 4 +--R - a b (x ) - 2a b x - a +--R / +--R 6 n 2 2 5 n 3 4 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 2 5 n 2 3 4 n 4 3 n log(x) 3 4 n 2 4 3 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 5 2 +--R 2a b n +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^3 +--R +--R +--R n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1394 +r0:=(-1/2)/(b*n*(a+b*x^n)^2) +--R +--R +--R 1 +--R (2) - ------------------------------- +--R 3 n 2 2 n 2 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------------------------------- +--R 3 n log(x) 2 2 n log(x) 2 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) 2 n log(x) n 2 n +--R b (%e ) + 2a %e - b (x ) - 2a x +--R / +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 +--R 2a n +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1394 +t0:=1/(x*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------ +--R 3 n 3 2 n 2 2 n 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1394 +r0:=1/2/(a*n*(a+b*x^n)^2)+1/(a^2*n*(a+b*x^n))+log(x)/a^3-log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n 2 n 2 n 2 +--R (- 2b (x ) - 4a b x - 2a )log(b x + a) + 2b n log(x)(x ) +--R + +--R n 2 2 +--R (4a b n log(x) + 2a b)x + 2a n log(x) + 3a +--R / +--R 3 2 n 2 4 n 5 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (- 2b (%e ) - 4a b %e - 2a )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) + (4a b n log(x) + 2a b)%e + 2a n log(x) +--R + +--R 2 +--R 3a +--R / +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 2a b n (%e ) + 4a b n %e + 2a n +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 2a b x - 3a b )(%e ) + (2a b (x ) - 4a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 4a b x +--R / +--R 3 4 n 2 4 3 n 5 2 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 4 3 n 2 5 2 n 6 n log(x) 5 2 n 2 6 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 7 +--R 2a n +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^3 +--R +--R +--R - n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1394 +r0:=(-3)/(a^3*n*x^n)+1/2/(a*n*x^n*(a+b*x^n)^2)+3/2/(a^2*n*x^n*(a+b*x^n))-_ + 3*b*log(x)/a^4+3*b*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 3 2 n 2 2 n n 3 n 3 +--R (6b (x ) + 12a b (x ) + 6a b x )log(b x + a) - 6b n log(x)(x ) +--R + +--R 2 2 n 2 2 2 n 3 +--R (- 12a b n log(x) - 6a b )(x ) + (- 6a b n log(x) - 9a b)x - 2a +--R / +--R 4 2 n 3 5 n 2 6 n +--R 2a b n (x ) + 4a b n (x ) + 2a n x +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) +--R (6b (%e ) + 12a b (%e ) + 6a b %e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 3 n log(x) 3 2 2 n log(x) 2 +--R - 6b n log(x)(%e ) + (- 12a b n log(x) - 6a b )(%e ) +--R + +--R 2 2 n log(x) 3 +--R (- 6a b n log(x) - 9a b)%e - 2a +--R / +--R 4 2 n log(x) 3 5 n log(x) 2 6 n log(x) +--R 2a b n (%e ) + 4a b n (%e ) + 2a n %e +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 3 4 n 2 2 3 n n log(x) 3 +--R (6b (x ) + 12a b (x ) + 6a b x )(%e ) +--R + +--R 4 n 3 2 3 n 2 3 2 n n log(x) 2 +--R (12a b (x ) + 24a b (x ) + 12a b x )(%e ) +--R + +--R 2 3 n 3 3 2 n 2 4 n n log(x) +--R (6a b (x ) + 12a b (x ) + 6a b x )%e +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 5 n 3 4 n 2 2 3 n n log(x) 3 +--R (- 6b (x ) - 12a b (x ) - 6a b x )(%e ) +--R + +--R 4 n 3 2 3 n 2 3 2 n n log(x) 2 +--R (- 12a b (x ) - 24a b (x ) - 12a b x )(%e ) +--R + +--R 2 3 n 3 3 2 n 2 4 n n log(x) +--R (- 6a b (x ) - 12a b (x ) - 6a b x )%e +--R * +--R n +--R log(b x + a) +--R + +--R 4 n 2 2 3 n 3 2 n log(x) 3 +--R (6a b (x ) + 9a b x + 2a b )(%e ) +--R + +--R 4 n 3 3 2 n 4 n log(x) 2 +--R (- 6a b (x ) + 12a b x + 4a b)(%e ) +--R + +--R 2 3 n 3 3 2 n 2 5 n log(x) 3 2 n 3 4 n 2 +--R (- 9a b (x ) - 12a b (x ) + 2a )%e - 2a b (x ) - 4a b (x ) +--R + +--R 5 n +--R - 2a x +--R / +--R 4 4 n 3 5 3 n 2 6 2 n n log(x) 3 +--R (2a b n (x ) + 4a b n (x ) + 2a b n x )(%e ) +--R + +--R 5 3 n 3 6 2 n 2 7 n n log(x) 2 +--R (4a b n (x ) + 8a b n (x ) + 4a b n x )(%e ) +--R + +--R 6 2 n 3 7 n 2 8 n n log(x) +--R (2a b n (x ) + 4a b n (x ) + 2a n x )%e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^3 +--R +--R +--R - 2n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1394 +r0:=(-3)/(a^3*n*x^(2*n))+6*b/(a^4*n*x^n)+1/2/(a*n*x^(2*n)*(a+b*x^n)^2)+_ + 2/(a^2*n*x^(2*n)*(a+b*x^n))+6*b^2*log(x)/a^5-6*b^2*log(a+b*x^n)/(a^5*n) +--R +--R +--R (2) +--R 4 n 3 3 n 2 2 2 n 2n n +--R (- 12b (x ) - 24a b (x ) - 12a b x )x log(b x + a) +--R + +--R 4 n 3 3 3 n 2 +--R 12b n log(x)(x ) + (24a b n log(x) + 12a b )(x ) +--R + +--R 2 2 2 2 n 3 +--R (12a b n log(x) + 24a b )x + 12a b +--R * +--R 2n +--R x +--R + +--R 2 2 n 3 3 n 2 4 n +--R - 6a b (x ) - 8a b (x ) - a x +--R / +--R 5 2 n 3 6 n 2 7 n 2n +--R (2a b n (x ) + 4a b n (x ) + 2a n x )x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R (- 12b (%e ) - 24a b (%e ) - 12a b (%e ) ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n log(x) 4 3 3 n log(x) 3 +--R 12b n log(x)(%e ) + (24a b n log(x) + 12a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (12a b n log(x) + 18a b )(%e ) + 4a b %e - a +--R / +--R 5 2 n log(x) 4 6 n log(x) 3 7 n log(x) 2 +--R 2a b n (%e ) + 4a b n (%e ) + 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n 3 5 n 2 2 4 n 2n n log(x) 4 +--R (- 12b (x ) - 24a b (x ) - 12a b x )x (%e ) +--R + +--R 5 n 3 2 4 n 2 3 3 n 2n n log(x) 3 +--R (- 24a b (x ) - 48a b (x ) - 24a b x )x (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 2n n log(x) 2 +--R (- 12a b (x ) - 24a b (x ) - 12a b x )x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 6 n 3 5 n 2 2 4 n 2n n log(x) 4 +--R (12b (x ) + 24a b (x ) + 12a b x )x (%e ) +--R + +--R 5 n 3 2 4 n 2 3 3 n 2n n log(x) 3 +--R (24a b (x ) + 48a b (x ) + 24a b x )x (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 2n n log(x) 2 +--R (12a b (x ) + 24a b (x ) + 12a b x )x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 5 n 2 2 4 n 3 3 2n 2 4 n 3 3 3 n 2 +--R (- 12a b (x ) - 24a b x - 12a b )x + 6a b (x ) + 8a b (x ) +--R + +--R 4 2 n +--R a b x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 5 n 3 3 3 n 4 2 2n 3 3 n 3 4 2 n 2 +--R (12a b (x ) - 36a b x - 24a b )x + 12a b (x ) + 16a b (x ) +--R + +--R 5 n +--R 2a b x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 5 2n 4 2 n 3 +--R (18a b (x ) + 24a b (x ) - 6a b x - 12a b)x + 6a b (x ) +--R + +--R 5 n 2 6 n +--R 8a b (x ) + a x +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 3 3 n 3 4 2 n 2 5 n 2n n log(x) +--R (4a b (x ) + 8a b (x ) + 4a b x )x %e +--R + +--R 4 2 n 3 5 n 2 6 n 2n +--R (- a b (x ) - 2a b (x ) - a x )x +--R / +--R 5 4 n 3 6 3 n 2 7 2 n 2n n log(x) 4 +--R (2a b n (x ) + 4a b n (x ) + 2a b n x )x (%e ) +--R + +--R 6 3 n 3 7 2 n 2 8 n 2n n log(x) 3 +--R (4a b n (x ) + 8a b n (x ) + 4a b n x )x (%e ) +--R + +--R 7 2 n 3 8 n 2 9 n 2n n log(x) 2 +--R (2a b n (x ) + 4a b n (x ) + 2a n x )x (%e ) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1394 +t0:=x^(-1-1/2*n)/(a+b*x^n) +--R +--R +--R - n - 2 +--R ------- +--R 2 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1394 +r0:=(-2)/(a*n*x^(1/2*n))-2*atan(x^(1/2*n)*sqrt(b)/sqrt(a))*sqrt(b)/(a^(3/2)*n) +--R +--R +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R - 2x \|b atan(------) - 2\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R +---+ a x (%e ) + 2a x |- - %e - b +--R | b \| a +--R |- - log(----------------------------------------------------------) +--R \| a (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R (- n - 2)log(x) +--R --------------- +--R 2 +--R - 2x %e +--R / +--R a n +--R , +--R (- n - 2)log(x) +--R --------------- (- n - 2)log(x) +--R +-+ 2 --------------- +--R |b x %e 2 +--R 2 |- atan(------------------- - 2x %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -----------------------------------------------------] +--R a n +--R Type: Union(List(Expression(Integer)),...) +--E 488 + +--S 489 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R n +--R - +---+ +--R 2 | b +-+ +--R x |- - \|a +--R \| a +--R * +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R a x (%e ) + 2a x |- - %e - b +--R \| a +--R log(----------------------------------------------------------) +--R (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R n +--R n (- n - 2)log(x) n - +--R - --------------- - 2 +-+ +--R 2 +-+ 2 2 +-+ x \|b +-+ +--R - 2x x \|a %e + 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R (- n - 2)log(x) +--R n --------------- n (- n - 2)log(x) +--R - +-+ 2 - --------------- +--R 2 +-+ |b x %e 2 +-+ 2 +--R 2x \|a |- atan(-------------------) - 2x x \|a %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1394 +t0:=x^(-1-2/3*n)/(a+b*x^n) +--R +--R +--R - 2n - 3 +--R -------- +--R 3 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1394 +r0:=(-3/2)/(a*n*x^(2/3*n))-b^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3*n))/_ + (a^(5/3)*n)+1/2*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3*n)+_ + b^(2/3)*x^(2/3*n))/(a^(5/3)*n)+b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(5/3)*n) +--R +--R +--R (2) +--R 2n 2n n 2n n +--R -- -- - -- - +--R 3 3+-+2 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+2 3 3+-+ 3+-+ +--R x \|b log(x \|b - x \|a \|b + \|a - 2x \|b log(x \|b + \|a ) +--R + +--R n +--R 2n - +--R -- 3 3+-+ 3+-+ +--R +-+ 3 3+-+2 2x \|b - \|a 3+-+2 +--R - 2\|3 x \|b atan(-------------- - 3\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2n +--R -- +--R 3 3+-+2 +--R 2a n x \|a +--R Type: Expression(Integer) +--E 494 + +--R +--S 495 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 495 + +--S 496 of 1394 +--m0:=a0-r0 +--E 496 + +--S 497 of 1394 +--d0:=D(m0,x) +--E 497 + +)clear all + +--S 498 of 1394 +t0:=x^(-1-3/4*n)/(a+b*x^n) +--R +--R +--R - 3n - 4 +--R -------- +--R 4 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1394 +r0:=(-4/3)/(a*n*x^(3/4*n))+b^(3/4)*log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+_ + sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(7/4)*n*sqrt(2))-_ + b^(3/4)*log(a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+_ + x^(1/2*n)*sqrt(b))/(a^(7/4)*n*sqrt(2))+b^(3/4)*atan(1-_ + b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(7/4)*n)-_ + b^(3/4)*atan(1+b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(7/4)*n) +--R +--R +--R (2) +--R 3n n n +--R -- - - +--R 4 4+-+3 +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - 3x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R 3n n n +--R -- - - +--R 4 4+-+3 +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R 3x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n +--R 3n - 3n - +--R -- +-+ 4 4+-+ 4+-+ -- +-+ 4 4+-+ 4+-+ +--R 4 4+-+3 \|2 x \|b + \|a 4 4+-+3 \|2 x \|b - \|a +--R - 6x \|b atan(----------------- - 6x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 3n +--R -- +--R +-+ 4 4+-+3 +--R 3a n\|2 x \|a +--R Type: Expression(Integer) +--E 499 + +--R +--S 500 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 500 + +--S 501 of 1394 +--m0:=a0-r0 +--E 501 + +--S 502 of 1394 +--d0:=D(m0,x) +--E 502 + +)clear all + +--S 503 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1394 +t0:=x^(-1-1/2*n)/(a+b*x^n) +--R +--R +--R - n - 2 +--R ------- +--R 2 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1394 +r0:=(-2)/(a*n*x^(1/2*n))-2*atan(x^(1/2*n)*sqrt(b)/sqrt(a))*sqrt(b)/(a^(3/2)*n) +--R +--R +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R - 2x \|b atan(------) - 2\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R +---+ a x (%e ) + 2a x |- - %e - b +--R | b \| a +--R |- - log(----------------------------------------------------------) +--R \| a (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R (- n - 2)log(x) +--R --------------- +--R 2 +--R - 2x %e +--R / +--R a n +--R , +--R (- n - 2)log(x) +--R --------------- (- n - 2)log(x) +--R +-+ 2 --------------- +--R |b x %e 2 +--R 2 |- atan(------------------- - 2x %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -----------------------------------------------------] +--R a n +--R Type: Union(List(Expression(Integer)),...) +--E 510 + +--S 511 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R n +--R - +---+ +--R 2 | b +-+ +--R x |- - \|a +--R \| a +--R * +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R a x (%e ) + 2a x |- - %e - b +--R \| a +--R log(----------------------------------------------------------) +--R (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R n +--R n (- n - 2)log(x) n - +--R - --------------- - 2 +-+ +--R 2 +-+ 2 2 +-+ x \|b +-+ +--R - 2x x \|a %e + 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R (- n - 2)log(x) +--R n --------------- n (- n - 2)log(x) +--R - +-+ 2 - --------------- +--R 2 +-+ |b x %e 2 +-+ 2 +--R 2x \|a |- atan(-------------------) - 2x x \|a %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 514 + +)clear all + +--S 515 of 1394 +t0:=x^(-1-1/3*n)/(a+b*x^n) +--R +--R +--R - n - 3 +--R ------- +--R 3 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1394 +r0:=(-3)/(a*n*x^(1/3*n))+b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3*n))/_ + (a^(4/3)*n)-1/2*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3*n)+_ + b^(2/3)*x^(2/3*n))/(a^(4/3)*n)+b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(4/3)*n) +--R +--R +--R (2) +--R n 2n n n n +--R - -- - - - +--R 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+ 3 3+-+ 3+-+ +--R - x \|b log(x \|b - x \|a \|b + \|a + 2x \|b log(x \|b + \|a ) +--R + +--R n +--R n - +--R - 3 3+-+ 3+-+ +--R +-+ 3 3+-+ 2x \|b - \|a 3+-+ +--R - 2\|3 x \|b atan(-------------- - 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R n +--R - +--R 3 3+-+ +--R 2a n x \|a +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- n - 3)log(x) 2 (- n - 3)log(x) +--R --------------- +-+ --------------- +-+2 +--R 2 3 |b 3 |b +--R +-+ x (%e ) - x 3|- %e + 3|- +--R |b \|a \|a +--R - 3|- log(-------------------------------------------------------) +--R \|a 2 +--R x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R 3 |b +--R +-+ x %e + 3|- +--R |b \|a +--R 2 3|- log(--------------------------) +--R \|a x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R 3 |b (- n - 3)log(x) +--R +-+ 2x %e - 3|- --------------- +--R +-+ |b \|a 3 +--R 2\|3 3|- atan(--------------------------- - 6x %e +--R \|a +-+ +--R +-+ |b +--R \|3 3|- +--R \|a +--R / +--R 2a n +--R Type: Union(Expression(Integer),...) +--E 517 + +--S 518 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (- n - 3)log(x) 2 (- n - 3)log(x) +--R --------------- +-+ --------------- +-+2 +--R n 2 3 |b 3 |b +--R - +-+ x (%e ) - x 3|- %e + 3|- +--R 3 3+-+ |b \|a \|a +--R - x \|a 3|- log(-------------------------------------------------------) +--R \|a 2 +--R x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R n 3 |b +--R - +-+ x %e + 3|- +--R 3 3+-+ |b \|a +--R 2x \|a 3|- log(--------------------------) +--R \|a x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R n 3 |b +--R - +-+ 2x %e - 3|- +--R +-+ 3 3+-+ |b \|a +--R 2\|3 x \|a 3|- atan(---------------------------) +--R \|a +-+ +--R +-+ |b +--R \|3 3|- +--R \|a +--R + +--R n 2n n n n +--R - -- - - - +--R 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+ 3 3+-+ 3+-+ +--R x \|b log(x \|b - x \|a \|b + \|a - 2x \|b log(x \|b + \|a ) +--R + +--R n +--R n (- n - 3)log(x) n - +--R - --------------- - 3 3+-+ 3+-+ +--R 3 3+-+ 3 +-+ 3 3+-+ 2x \|b - \|a 3+-+ +--R - 6x x \|a %e + 2\|3 x \|b atan(-------------- + 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R n +--R - +--R 3 3+-+ +--R 2a n x \|a +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1394 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1394 +t0:=x^(-1-1/4*n)/(a+b*x^n) +--R +--R +--R - n - 4 +--R ------- +--R 4 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1394 +r0:=(-4)/(a*n*x^(1/4*n))-b^(1/4)*log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+_ + sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(5/4)*n*sqrt(2))+b^(1/4)*_ + log(a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*sqrt(b))/_ + (a^(5/4)*n*sqrt(2))+b^(1/4)*atan(1-b^(1/4)*x^(1/4*n)*sqrt(2)/_ + a^(1/4))*sqrt(2)/(a^(5/4)*n)-b^(1/4)*atan(1+b^(1/4)*_ + x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(5/4)*n) +--R +--R +--R (2) +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n +--R n - n - +--R - +-+ 4 4+-+ 4+-+ - +-+ 4 4+-+ 4+-+ +--R 4 4+-+ \|2 x \|b + \|a 4 4+-+ \|2 x \|b - \|a +--R - 2x \|b atan(----------------- - 2x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R n +--R - +--R +-+ 4 4+-+ +--R a n\|2 x \|a +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R x %e + a n |- ---- +--R +------+ 4| 5 4 +--R | b \| a n +--R a n |- ---- log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R x %e - a n |- ---- +--R +------+ 4| 5 4 +--R | b \| a n +--R - a n |- ---- log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R +------+ +--R | b +--R a n |- ---- (- n - 4)log(x) +--R +------+ 4| 5 4 --------------- +--R | b \| a n 4 +--R - 2a n |- ---- atan(------------------- - 4x %e +--R 4| 5 4 (- n - 4)log(x) +--R \| a n --------------- +--R 4 +--R x %e +--R / +--R a n +--R Type: Union(Expression(Integer),...) +--E 522 + +--S 523 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R n x %e + a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R a n\|2 x |- ---- \|a log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R n x %e - a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R - a n\|2 x |- ---- \|a log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R +------+ +--R | b +--R n a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R - 2a n\|2 x |- ---- \|a atan(-------------------) +--R 4| 5 4 (- n - 4)log(x) +--R \| a n --------------- +--R 4 +--R x %e +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n +--R n (- n - 4)log(x) n - +--R - --------------- - +-+ 4 4+-+ 4+-+ +--R +-+ 4 4+-+ 4 4 4+-+ \|2 x \|b + \|a +--R - 4x\|2 x \|a %e + 2x \|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R n +--R n - +--R - +-+ 4 4+-+ 4+-+ +--R 4 4+-+ \|2 x \|b - \|a +-+4+-+ +--R 2x \|b atan(----------------- + 4\|2 \|a +--R 4+-+ +--R \|a +--R / +--R n +--R - +--R +-+ 4 4+-+ +--R a n\|2 x \|a +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1394 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1394 +t0:=x^(-1-3/2*n)/(a+b*x^n) +--R +--R +--R - 3n - 2 +--R -------- +--R 2 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1394 +r0:=(-2/3)/(a*n*x^(3/2*n))+2*b/(a^2*n*x^(1/2*n))+2*b^(3/2)*_ + atan(x^(1/2*n)*sqrt(b)/sqrt(a))/(a^(5/2)*n) +--R +--R +--R n +--R n 3n - 3n n +--R - -- 2 +-+ -- - +--R 2 2 +-+ x \|b 2 2 +-+ +--R 6b x x \|b atan(------) + (6b x - 2a x )\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R n 3n +--R - -- +--R 2 2 2 +-+ +--R 3a n x x \|a +--R Type: Expression(Integer) +--E 526 + +--R +--S 527 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 527 + +--S 528 of 1394 +--m0:=a0-r0 +--E 528 + +--S 529 of 1394 +--d0:=D(m0,x) +--E 529 + +)clear all + +--S 530 of 1394 +t0:=x^(-1-4/3*n)/(a+b*x^n) +--R +--R +--R - 4n - 3 +--R -------- +--R 3 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1394 +r0:=(-3/4)/(a*n*x^(4/3*n))+3*b/(a^2*n*x^(1/3*n))-b^(4/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3*n))/(a^(7/3)*n)+1/2*b^(4/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3*n)+b^(2/3)*x^(2/3*n))/(a^(7/3)*n)-_ + b^(4/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*_ + sqrt(3)/(a^(7/3)*n) +--R +--R +--R (2) +--R n 4n 2n n +--R - -- -- - +--R 3 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 +--R 2b x x \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R n +--R n 4n n n 4n - +--R - -- - - -- 3 3+-+ 3+-+ +--R 3 3 3+-+ 3 3+-+ 3+-+ +-+ 3 3 3+-+ 2x \|b - \|a +--R - 4b x x \|b log(x \|b + \|a + 4b\|3 x x \|b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4n n +--R -- - +--R 3 3 3+-+ +--R (12b x - 3a x )\|a +--R / +--R n 4n +--R - -- +--R 2 3 3 3+-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 532 + +--S 533 of 1394 +--m0:=a0-r0 +--E 533 + +--S 534 of 1394 +--d0:=D(m0,x) +--E 534 + +)clear all + +--S 535 of 1394 +t0:=x^(-1-5/4*n)/(a+b*x^n) +--R +--R +--R - 5n - 4 +--R -------- +--R 4 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1394 +r0:=(-4/5)/(a*n*x^(5/4*n))+4*b/(a^2*n*x^(1/4*n))+b^(5/4)*_ + log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*_ + sqrt(b))/(a^(9/4)*n*sqrt(2))-b^(5/4)*log(a^(1/4)*b^(1/4)*_ + x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(9/4)*n*sqrt(2))-_ + b^(5/4)*atan(1-b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*_ + sqrt(2)/(a^(9/4)*n)+b^(5/4)*atan(1+b^(1/4)*x^(1/4*n)*_ + sqrt(2)/a^(1/4))*sqrt(2)/(a^(9/4)*n) +--R +--R +--R (2) +--R n 5n n n +--R - -- - - +--R 4 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - 5b x x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n 5n n n +--R - -- - - +--R 4 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R 5b x x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n +--R n 5n - +--R - -- +-+ 4 4+-+ 4+-+ +--R 4 4 4+-+ \|2 x \|b + \|a +--R 10b x x \|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R n +--R n 5n - 5n n +--R - -- +-+ 4 4+-+ 4+-+ -- - +--R 4 4 4+-+ \|2 x \|b - \|a +-+ 4 +-+ 4 4+-+ +--R 10b x x \|b atan(----------------- + (20b\|2 x - 4a\|2 x )\|a +--R 4+-+ +--R \|a +--R / +--R n 5n +--R - -- +--R 2 +-+ 4 4 4+-+ +--R 5a n\|2 x x \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 537 + +--S 538 of 1394 +--m0:=a0-r0 +--E 538 + +--S 539 of 1394 +--d0:=D(m0,x) +--E 539 + +)clear all + +--S 540 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 4n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1394 +r0:=-2/3*a^3*(a+b*x^n)^(3/2)/(b^4*n)+6/5*a^2*(a+b*x^n)^(5/2)/(b^4*n)-_ + 6/7*a*(a+b*x^n)^(7/2)/(b^4*n)+2/9*(a+b*x^n)^(9/2)/(b^4*n) +--R +--R +--R +--------+ +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 | n +--R (70b (x ) + 10a b (x ) - 12a b (x ) + 16a b x - 32a )\|b x + a +--R (2) -------------------------------------------------------------------- +--R 4 +--R 315b n +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R 70b (%e ) + 10a b (%e ) - 12a b (%e ) +--R + +--R 3 n log(x) 4 +--R 16a b %e - 32a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +--R 315b n +--R Type: Union(Expression(Integer),...) +--E 542 + +--S 543 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R 70b (%e ) + 10a b (%e ) - 12a b (%e ) +--R + +--R 3 n log(x) 4 +--R 16a b %e - 32a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 | n +--R (- 70b (x ) - 10a b (x ) + 12a b (x ) - 16a b x + 32a )\|b x + a +--R / +--R 4 +--R 315b n +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 3n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1394 +r0:=2/3*a^2*(a+b*x^n)^(3/2)/(b^3*n)-4/5*a*(a+b*x^n)^(5/2)/(b^3*n)+_ + 2/7*(a+b*x^n)^(7/2)/(b^3*n) +--R +--R +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (30b (x ) + 6a b (x ) - 8a b x + 16a )\|b x + a +--R (2) ---------------------------------------------------- +--R 3 +--R 105b n +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (30b (%e ) + 6a b (%e ) - 8a b %e + 16a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +--R 105b n +--R Type: Union(Expression(Integer),...) +--E 547 + +--S 548 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (30b (%e ) + 6a b (%e ) - 8a b %e + 16a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (- 30b (x ) - 6a b (x ) + 8a b x - 16a )\|b x + a +--R / +--R 3 +--R 105b n +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 2n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1394 +r0:=-2/3*a*(a+b*x^n)^(3/2)/(b^2*n)+2/5*(a+b*x^n)^(5/2)/(b^2*n) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (6b (x ) + 2a b x - 4a )\|b x + a +--R (2) ------------------------------------- +--R 2 +--R 15b n +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 2a b %e - 4a )\|b %e + a +--R (3) ------------------------------------------------------------- +--R 2 +--R 15b n +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 2a b %e - 4a )\|b %e + a +--R + +--R +--------+ +--R 2 n 2 n 2 | n +--R (- 6b (x ) - 2a b x + 4a )\|b x + a +--R / +--R 2 +--R 15b n +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1394 +r0:=2/3*(a+b*x^n)^(3/2)/(b*n) +--R +--R +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R (2) ----------------------- +--R 3b n +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 2a)\|b %e + a +--R (3) --------------------------------------- +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 557 + +--S 558 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R n log(x) | n log(x) n | n +--R (2b %e + 2a)\|b %e + a + (- 2b x - 2a)\|b x + a +--R (4) ------------------------------------------------------------------- +--R 3b n +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +)clear all + +--S 560 of 1394 +t0:=(a+b*x^n)^(1/2)/x +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1394 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))*sqrt(a)/n+2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 562 + +--S 563 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--------+ +--R | n log(x) +-+ \|b x + a | n +--R 2\|b %e + a + 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1394 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R + +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1394 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 566 + +)clear all + +--S 567 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1394 +r0:=-b*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a))-sqrt(a+b*x^n)/(n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R n \|b x + a +-+ | n +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R n +-+ +--R n x \|a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n log(x) - 2a\|b %e + a + b\|a %e + 2a\|a +--R b %e log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ | n log(x) +--R - 2\|a \|b %e + a +--R / +--R +-+ n log(x) +--R 2n\|a %e +--R , +--R +----------------+ +--R +---+ | n log(x) +----------------+ +--R n log(x) \|- a \|b %e + a +---+ | n log(x) +--R - b %e atan(-------------------------) - \|- a \|b %e + a +--R a +--R -------------------------------------------------------------------------] +--R +---+ n log(x) +--R n\|- a %e +--R Type: Union(List(Expression(Integer)),...) +--E 569 + +--S 570 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n n log(x) - 2a\|b %e + a + b\|a %e + 2a\|a +--R b x %e log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n +-+ | n log(x) n n log(x) \|b x + a +--R - 2x \|a \|b %e + a + 2b x %e atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ n log(x) | n +--R 2\|a %e \|b x + a +--R / +--R n +-+ n log(x) +--R 2n x \|a %e +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R n +-+ n log(x) \|- a \|b %e + a +--R - b x \|a %e atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n +---+ +-+ | n log(x) +--R - x \|- a \|a \|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R n +---+ n log(x) \|b x + a +---+ +-+ n log(x) | n +--R b x \|- a %e atanh(-----------) + \|- a \|a %e \|b x + a +--R +-+ +--R \|a +--R / +--R n +---+ +-+ n log(x) +--R n x \|- a \|a %e +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 2n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1394 +r0:=1/4*b^2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)-_ + 1/2*sqrt(a+b*x^n)/(n*x^(2*n))-1/4*b*sqrt(a+b*x^n)/(a*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 n 2n \|b x + a 2n n +-+ | n +--R b x x atanh(-----------) + (- b x - 2a x )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------ +--R n 2n +-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n log(x) 2 2a\|b %e + a + b\|a %e + 2a\|a +--R b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ n log(x) +-+ | n log(x) +--R (- 2b\|a %e - 4a\|a )\|b %e + a +--R / +--R +-+ n log(x) 2 +--R 8a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 2 n log(x) 2 \|- a \|b %e + a +--R b (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R +---+ n log(x) +---+ | n log(x) +--R (- b\|- a %e - 2a\|- a )\|b %e + a +--R / +--R +---+ n log(x) 2 +--R 4a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 576 + +--S 577 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n 2n n log(x) 2 2a\|b %e + a + b\|a %e + 2a\|a +--R b x x (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n 2n +-+ n log(x) n 2n +-+ | n log(x) +--R (- 2b x x \|a %e - 4a x x \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n n log(x) 2 \|b x + a +--R - 2b x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +-+ n log(x) 2 | n +--R (2b x + 4a x )\|a (%e ) \|b x + a +--R / +--R n 2n +-+ n log(x) 2 +--R 8a n x x \|a (%e ) +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 2 n 2n +-+ n log(x) 2 \|- a \|b %e + a +--R b x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n 2n +---+ +-+ n log(x) n 2n +---+ +-+ | n log(x) +--R (- b x x \|- a \|a %e - 2a x x \|- a \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n +---+ n log(x) 2 \|b x + a +--R - b x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +---+ +-+ n log(x) 2 | n +--R (b x + 2a x )\|- a \|a (%e ) \|b x + a +--R / +--R n 2n +---+ +-+ n log(x) 2 +--R 4a n x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 3n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1394 +r0:=-1/8*b^3*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)-_ + 1/3*sqrt(a+b*x^n)/(n*x^(3*n))-1/12*b*sqrt(a+b*x^n)/_ + (a*n*x^(2*n))+1/8*b^2*sqrt(a+b*x^n)/(a^2*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 3 n 2n 3n \|b x + a +--R - 3b x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ | n +--R ((3b x - 2a b x )x - 8a x x )\|a \|b x + a +--R / +--R 2 n 2n 3n +-+ +--R 24a n x x x \|a +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 3 n log(x) 3 - 2a\|b %e + a + b\|a %e + 2a\|a +--R 3b (%e ) log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 +-+ n log(x) 2 +-+ n log(x) 2 +-+ | n log(x) +--R (6b \|a (%e ) - 4a b\|a %e - 16a \|a )\|b %e + a +--R / +--R 2 +-+ n log(x) 3 +--R 48a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 3 n log(x) 3 \|- a \|b %e + a +--R - 3b (%e ) atan(-------------------------) +--R a +--R + +--R 2 +---+ n log(x) 2 +---+ n log(x) 2 +---+ +--R (3b \|- a (%e ) - 2a b\|- a %e - 8a \|- a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 2 +---+ n log(x) 3 +--R 24a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 583 + +--S 584 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 +--R 3b x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 n 2n 3n +-+ n log(x) 2 n 2n 3n +-+ n log(x) +--R 6b x x x \|a (%e ) - 4a b x x x \|a %e +--R + +--R 2 n 2n 3n +-+ +--R - 16a x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n n log(x) 3 \|b x + a +--R 6b x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ n log(x) 3 | n +--R ((- 6b x + 4a b x )x + 16a x x )\|a (%e ) \|b x + a +--R / +--R 2 n 2n 3n +-+ n log(x) 3 +--R 48a n x x x \|a (%e ) +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 3 n 2n 3n +-+ n log(x) 3 \|- a \|b %e + a +--R - 3b x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 2 n 2n 3n +---+ +-+ n log(x) 2 +--R 3b x x x \|- a \|a (%e ) +--R + +--R n 2n 3n +---+ +-+ n log(x) 2 n 2n 3n +---+ +-+ +--R - 2a b x x x \|- a \|a %e - 8a x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n +---+ n log(x) 3 \|b x + a +--R 3b x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +---+ +-+ n log(x) 3 | n +--R ((- 3b x + 2a b x )x + 8a x x )\|- a \|a (%e ) \|b x + a +--R / +--R 2 n 2n 3n +---+ +-+ n log(x) 3 +--R 24a n x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 4n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1394 +r0:=5/64*b^4*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(7/2)*n)-_ + 1/4*sqrt(a+b*x^n)/(n*x^(4*n))-1/24*b*sqrt(a+b*x^n)/_ + (a*n*x^(3*n))+5/96*b^2*sqrt(a+b*x^n)/(a^2*n*x^(2*n))-_ + 5/64*b^3*sqrt(a+b*x^n)/(a^3*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 4 n 2n 3n 4n \|b x + a +--R 15b x x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ | n +--R (((- 15b x + 10a b x )x - 8a b x x )x - 48a x x x )\|a \|b x + a +--R / +--R 3 n 2n 3n 4n +-+ +--R 192a n x x x x \|a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 4 n log(x) 4 2a\|b %e + a + b\|a %e + 2a\|a +--R 15b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 +-+ n log(x) 3 2 +-+ n log(x) 2 +--R - 30b \|a (%e ) + 20a b \|a (%e ) +--R + +--R 2 +-+ n log(x) 3 +-+ +--R - 16a b\|a %e - 96a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +-+ n log(x) 4 +--R 384a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 4 n log(x) 4 \|- a \|b %e + a +--R 15b (%e ) atan(-------------------------) +--R a +--R + +--R 3 +---+ n log(x) 3 2 +---+ n log(x) 2 +--R - 15b \|- a (%e ) + 10a b \|- a (%e ) +--R + +--R 2 +---+ n log(x) 3 +---+ +--R - 8a b\|- a %e - 48a \|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +---+ n log(x) 4 +--R 192a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 590 + +--S 591 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 n 2n 3n 4n n log(x) 4 +--R 15b x x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2a\|b %e + a + b\|a %e + 2a\|a +--R log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 n 2n 3n 4n +-+ n log(x) 3 +--R - 30b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 2 2 n 2n 3n 4n +-+ n log(x) +--R 20a b x x x x \|a (%e ) - 16a b x x x x \|a %e +--R + +--R 3 n 2n 3n 4n +-+ +--R - 96a x x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n n log(x) 4 \|b x + a +--R - 30b x x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ +--R (((30b x - 20a b x )x + 16a b x x )x + 96a x x x )\|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 3 n 2n 3n 4n +-+ n log(x) 4 +--R 384a n x x x x \|a (%e ) +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 4 n 2n 3n 4n +-+ n log(x) 4 \|- a \|b %e + a +--R 15b x x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 3 +--R - 15b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 2 +--R 10a b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 3 n 2n 3n 4n +---+ +-+ +--R - 8a b x x x x \|- a \|a %e - 48a x x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n +---+ n log(x) 4 \|b x + a +--R - 15b x x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +---+ +-+ +--R (((15b x - 10a b x )x + 8a b x x )x + 48a x x x )\|- a \|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 4 +--R 192a n x x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^(1/2) +--R +--R +--R 4n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1394 +r0:=2*a^2*(a+b*x^n)^(3/2)/(b^4*n)-6/5*a*(a+b*x^n)^(5/2)/(b^4*n)+_ + 2/7*(a+b*x^n)^(7/2)/(b^4*n)-2*a^3*sqrt(a+b*x^n)/(b^4*n) +--R +--R +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (10b (x ) - 12a b (x ) + 16a b x - 32a )\|b x + a +--R (2) ------------------------------------------------------ +--R 4 +--R 35b n +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (10b (%e ) - 12a b (%e ) + 16a b %e - 32a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +--R 35b n +--R Type: Union(Expression(Integer),...) +--E 597 + +--S 598 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (10b (%e ) - 12a b (%e ) + 16a b %e - 32a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (- 10b (x ) + 12a b (x ) - 16a b x + 32a )\|b x + a +--R / +--R 4 +--R 35b n +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 599 + +)clear all + +--S 600 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^(1/2) +--R +--R +--R 3n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1394 +r0:=-4/3*a*(a+b*x^n)^(3/2)/(b^3*n)+2/5*(a+b*x^n)^(5/2)/(b^3*n)+_ + 2*a^2*sqrt(a+b*x^n)/(b^3*n) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (6b (x ) - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------- +--R 3 +--R 15b n +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) - 8a b %e + 16a )\|b %e + a +--R (3) -------------------------------------------------------------- +--R 3 +--R 15b n +--R Type: Union(Expression(Integer),...) +--E 602 + +--S 603 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) - 8a b %e + 16a )\|b %e + a +--R + +--R +--------+ +--R 2 n 2 n 2 | n +--R (- 6b (x ) + 8a b x - 16a )\|b x + a +--R / +--R 3 +--R 15b n +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 604 + +)clear all + +--S 605 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^(1/2) +--R +--R +--R 2n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1394 +r0:=2/3*(a+b*x^n)^(3/2)/(b^2*n)-2*a*sqrt(a+b*x^n)/(b^2*n) +--R +--R +--R +--------+ +--R n | n +--R (2b x - 4a)\|b x + a +--R (2) ----------------------- +--R 2 +--R 3b n +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e - 4a)\|b %e + a +--R (3) --------------------------------------- +--R 2 +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 607 + +--S 608 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R n log(x) | n log(x) n | n +--R (2b %e - 4a)\|b %e + a + (- 2b x + 4a)\|b x + a +--R (4) ------------------------------------------------------------------- +--R 2 +--R 3b n +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^(1/2) +--R +--R +--R n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1394 +r0:=2*sqrt(a+b*x^n)/(b*n) +--R +--R +--R +--------+ +--R | n +--R 2\|b x + a +--R (2) ------------ +--R b n +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R (3) -------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 612 + +--S 613 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R | n log(x) | n +--R 2\|b %e + a - 2\|b x + a +--R (4) ----------------------------------- +--R b n +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1394 +t0:=1/(x*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | n +--R x\|b x + a +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1394 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a)) +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R [-------------------------------------------------------, +--R +-+ +--R n\|a +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R 2atan(-------------------------) +--R a +--R - --------------------------------] +--R +---+ +--R n\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 617 + +--S 618 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--------+ +--R | n log(x) +-+ n log(x) +-+ | n +--R - 2a\|b %e + a + b\|a %e + 2a\|a \|b x + a +--R log(--------------------------------------------------) + 2atanh(-----------) +--R n log(x) +-+ +--R %e \|a +--R ----------------------------------------------------------------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1394 +m0b:=a0.2-r0 +--R +--R +--R +----------------+ +--------+ +--R +---+ | n log(x) | n +--R +-+ \|- a \|b %e + a +---+ \|b x + a +--R - 2\|a atan(-------------------------) + 2\|- a atanh(-----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------------------------ +--R +---+ +-+ +--R n\|- a \|a +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^(1/2) +--R +--R +--R - n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1394 +r0:=b*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)-sqrt(a+b*x^n)/(a*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R n \|b x + a +-+ | n +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n log(x) 2a\|b %e + a + b\|a %e + 2a\|a +--R b %e log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ | n log(x) +--R - 2\|a \|b %e + a +--R / +--R +-+ n log(x) +--R 2a n\|a %e +--R , +--R +----------------+ +--R +---+ | n log(x) +----------------+ +--R n log(x) \|- a \|b %e + a +---+ | n log(x) +--R b %e atan(-------------------------) - \|- a \|b %e + a +--R a +--R -----------------------------------------------------------------------] +--R +---+ n log(x) +--R a n\|- a %e +--R Type: Union(List(Expression(Integer)),...) +--E 624 + +--S 625 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n n log(x) 2a\|b %e + a + b\|a %e + 2a\|a +--R b x %e log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n +-+ | n log(x) n n log(x) \|b x + a +--R - 2x \|a \|b %e + a - 2b x %e atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ n log(x) | n +--R 2\|a %e \|b x + a +--R / +--R n +-+ n log(x) +--R 2a n x \|a %e +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R n +-+ n log(x) \|- a \|b %e + a +--R b x \|a %e atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n +---+ +-+ | n log(x) +--R - x \|- a \|a \|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R n +---+ n log(x) \|b x + a +---+ +-+ n log(x) | n +--R - b x \|- a %e atanh(-----------) + \|- a \|a %e \|b x + a +--R +-+ +--R \|a +--R / +--R n +---+ +-+ n log(x) +--R a n x \|- a \|a %e +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 2n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1394 +r0:=-3/4*b^2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)-_ + 1/2*sqrt(a+b*x^n)/(a*n*x^(2*n))+3/4*b*sqrt(a+b*x^n)/(a^2*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 n 2n \|b x + a 2n n +-+ | n +--R - 3b x x atanh(-----------) + (3b x - 2a x )\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 n 2n +-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n log(x) 2 - 2a\|b %e + a + b\|a %e + 2a\|a +--R 3b (%e ) log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ n log(x) +-+ | n log(x) +--R (6b\|a %e - 4a\|a )\|b %e + a +--R / +--R 2 +-+ n log(x) 2 +--R 8a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 2 n log(x) 2 \|- a \|b %e + a +--R - 3b (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R +---+ n log(x) +---+ | n log(x) +--R (3b\|- a %e - 2a\|- a )\|b %e + a +--R / +--R 2 +---+ n log(x) 2 +--R 4a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 631 + +--S 632 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 +--R 3b x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n 2n +-+ n log(x) n 2n +-+ | n log(x) +--R (6b x x \|a %e - 4a x x \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n n log(x) 2 \|b x + a +--R 6b x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +-+ n log(x) 2 | n +--R (- 6b x + 4a x )\|a (%e ) \|b x + a +--R / +--R 2 n 2n +-+ n log(x) 2 +--R 8a n x x \|a (%e ) +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 2 n 2n +-+ n log(x) 2 \|- a \|b %e + a +--R - 3b x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n 2n +---+ +-+ n log(x) n 2n +---+ +-+ | n log(x) +--R (3b x x \|- a \|a %e - 2a x x \|- a \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n +---+ n log(x) 2 \|b x + a +--R 3b x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +---+ +-+ n log(x) 2 | n +--R (- 3b x + 2a x )\|- a \|a (%e ) \|b x + a +--R / +--R 2 n 2n +---+ +-+ n log(x) 2 +--R 4a n x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 3n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1394 +r0:=5/8*b^3*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(7/2)*n)-_ + 1/3*sqrt(a+b*x^n)/(a*n*x^(3*n))+5/12*b*sqrt(a+b*x^n)/_ + (a^2*n*x^(2*n))-5/8*b^2*sqrt(a+b*x^n)/(a^3*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 3 n 2n 3n \|b x + a +--R 15b x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ | n +--R ((- 15b x + 10a b x )x - 8a x x )\|a \|b x + a +--R / +--R 3 n 2n 3n +-+ +--R 24a n x x x \|a +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 3 n log(x) 3 2a\|b %e + a + b\|a %e + 2a\|a +--R 15b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 +-+ n log(x) 2 +-+ n log(x) 2 +-+ +--R (- 30b \|a (%e ) + 20a b\|a %e - 16a \|a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +-+ n log(x) 3 +--R 48a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 3 n log(x) 3 \|- a \|b %e + a +--R 15b (%e ) atan(-------------------------) +--R a +--R + +--R 2 +---+ n log(x) 2 +---+ n log(x) 2 +---+ +--R (- 15b \|- a (%e ) + 10a b\|- a %e - 8a \|- a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +---+ n log(x) 3 +--R 24a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 638 + +--S 639 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 +--R 15b x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2a\|b %e + a + b\|a %e + 2a\|a +--R log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 n 2n 3n +-+ n log(x) 2 n 2n 3n +-+ n log(x) +--R - 30b x x x \|a (%e ) + 20a b x x x \|a %e +--R + +--R 2 n 2n 3n +-+ +--R - 16a x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n n log(x) 3 \|b x + a +--R - 30b x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ n log(x) 3 | n +--R ((30b x - 20a b x )x + 16a x x )\|a (%e ) \|b x + a +--R / +--R 3 n 2n 3n +-+ n log(x) 3 +--R 48a n x x x \|a (%e ) +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 3 n 2n 3n +-+ n log(x) 3 \|- a \|b %e + a +--R 15b x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 2 n 2n 3n +---+ +-+ n log(x) 2 +--R - 15b x x x \|- a \|a (%e ) +--R + +--R n 2n 3n +---+ +-+ n log(x) 2 n 2n 3n +---+ +-+ +--R 10a b x x x \|- a \|a %e - 8a x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n +---+ n log(x) 3 \|b x + a +--R - 15b x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +---+ +-+ n log(x) 3 | n +--R ((15b x - 10a b x )x + 8a x x )\|- a \|a (%e ) \|b x + a +--R / +--R 3 n 2n 3n +---+ +-+ n log(x) 3 +--R 24a n x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1394 +t0:=x^(-1-4*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 4n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1394 +r0:=-35/64*b^4*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(9/2)*n)-_ + 1/4*sqrt(a+b*x^n)/(a*n*x^(4*n))+7/24*b*sqrt(a+b*x^n)/_ + (a^2*n*x^(3*n))-35/96*b^2*sqrt(a+b*x^n)/(a^3*n*x^(2*n))+_ + 35/64*b^3*sqrt(a+b*x^n)/(a^4*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 4 n 2n 3n 4n \|b x + a +--R - 105b x x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ | n +--R (((105b x - 70a b x )x + 56a b x x )x - 48a x x x )\|a \|b x + a +--R / +--R 4 n 2n 3n 4n +-+ +--R 192a n x x x x \|a +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 n log(x) 4 +--R 105b (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 +-+ n log(x) 3 2 +-+ n log(x) 2 +--R 210b \|a (%e ) - 140a b \|a (%e ) +--R + +--R 2 +-+ n log(x) 3 +-+ +--R 112a b\|a %e - 96a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +-+ n log(x) 4 +--R 384a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 4 n log(x) 4 \|- a \|b %e + a +--R - 105b (%e ) atan(-------------------------) +--R a +--R + +--R 3 +---+ n log(x) 3 2 +---+ n log(x) 2 +--R 105b \|- a (%e ) - 70a b \|- a (%e ) +--R + +--R 2 +---+ n log(x) 3 +---+ +--R 56a b\|- a %e - 48a \|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +---+ n log(x) 4 +--R 192a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 645 + +--S 646 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 n 2n 3n 4n n log(x) 4 +--R 105b x x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 n 2n 3n 4n +-+ n log(x) 3 +--R 210b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 2 +--R - 140a b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 3 n 2n 3n 4n +-+ +--R 112a b x x x x \|a %e - 96a x x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n n log(x) 4 \|b x + a +--R 210b x x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ +--R (((- 210b x + 140a b x )x - 112a b x x )x + 96a x x x )\|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 4 n 2n 3n 4n +-+ n log(x) 4 +--R 384a n x x x x \|a (%e ) +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 4 n 2n 3n 4n +-+ n log(x) 4 \|- a \|b %e + a +--R - 105b x x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 3 +--R 105b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 2 +--R - 70a b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 3 n 2n 3n 4n +---+ +-+ +--R 56a b x x x x \|- a \|a %e - 48a x x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n +---+ n log(x) 4 \|b x + a +--R 105b x x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +---+ +--R (((- 105b x + 70a b x )x - 56a b x x )x + 48a x x x )\|- a +--R * +--R +--------+ +--R +-+ n log(x) 4 | n +--R \|a (%e ) \|b x + a +--R / +--R 4 n 2n 3n 4n +---+ +-+ n log(x) 4 +--R 192a n x x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 649 + +)clear all + +--S 650 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^p +--R +--R +--R n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1394 +r0:=(a+b*x^n)^(1+p)/(b*n*(1+p)) +--R +--R +--R n p + 1 +--R (b x + a) +--R (2) --------------- +--R b n p + b n +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R n log(x) p log(b %e + a) +--R (b %e + a)%e +--R (3) ------------------------------------------- +--R b n p + b n +--R Type: Union(Expression(Integer),...) +--E 652 + +--S 653 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) +--R n log(x) p log(b %e + a) n p + 1 +--R (b %e + a)%e - (b x + a) +--R (4) ------------------------------------------------------------- +--R b n p + b n +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^p +--R +--R +--R 2n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1394 +r0:=-a*(a+b*x^n)^(1+p)/(b^2*n*(1+p))+(a+b*x^n)^(2+p)/(b^2*n*(2+p)) +--R +--R +--R n p + 2 n p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) +--R 2 2 n log(x) 2 n log(x) 2 p log(b %e + a) +--R ((b p + b )(%e ) + a b p %e - a )%e +--R -------------------------------------------------------------------------- +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Union(Expression(Integer),...) +--E 657 + +--S 658 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) 2 +--R ((b p + b )(%e ) + a b p %e - a ) +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R n p + 2 n p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 659 + +)clear all + +--S 660 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^p +--R +--R +--R 3n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1394 +r0:=a^2*(a+b*x^n)^(1+p)/(b^3*n*(1+p))-2*a*(a+b*x^n)^(2+p)/(b^3*n*(2+p))+_ + (a+b*x^n)^(3+p)/(b^3*n*(3+p)) +--R +--R +--R (2) +--R 2 n p + 3 2 n p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 n p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 2 2 2 n log(x) 2 +--R (b p + 3b p + 2b )(%e ) + (a b p + a b p)(%e ) +--R + +--R 2 n log(x) 3 +--R - 2a b p %e + 2a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Union(Expression(Integer),...) +--E 662 + +--S 663 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 2 2 2 n log(x) 2 +--R (b p + 3b p + 2b )(%e ) + (a b p + a b p)(%e ) +--R + +--R 2 n log(x) 3 +--R - 2a b p %e + 2a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R 2 n p + 3 2 n p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 n p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^p +--R +--R +--R 4n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1394 +r0:=-a^3*(a+b*x^n)^(1+p)/(b^4*n*(1+p))+3*a^2*(a+b*x^n)^(2+p)/(b^4*n*(2+p))-_ + 3*a*(a+b*x^n)^(3+p)/(b^4*n*(3+p))+(a+b*x^n)^(4+p)/(b^4*n*(4+p)) +--R +--R +--R (2) +--R 3 2 n p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 n p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 n log(x) 4 +--R (b p + 6b p + 11b p + 6b )(%e ) +--R + +--R 3 3 3 2 3 n log(x) 3 +--R (a b p + 3a b p + 2a b p)(%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (- 3a b p - 3a b p)(%e ) + 6a b p %e - 6a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 n log(x) 4 +--R (b p + 6b p + 11b p + 6b )(%e ) +--R + +--R 3 3 3 2 3 n log(x) 3 +--R (a b p + 3a b p + 2a b p)(%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (- 3a b p - 3a b p)(%e ) + 6a b p %e - 6a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R 3 2 n p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 n p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1394 +t0:=x^(-1-n-n*p)*(a+b*x^n)^p +--R +--R +--R - n p - n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1394 +r0:=-(a+b*x^n)^(1+p)/(a*n*(1+p)*x^(n*(1+p))) +--R +--R +--R n p + 1 +--R (b x + a) +--R (2) - --------------------- +--R n p + n +--R (a n p + a n)x +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1394 +--a0:=integrate(t0,x) +--E 672 + +--S 673 of 1394 +--m0:=a0-r0 +--E 673 + +--S 674 of 1394 +--d0:=D(m0,x) +--E 674 + +)clear all + +--S 675 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 9n - 1 n 8 7 - 9n - 1 n 7 2 6 - 9n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 9n - 1 n 5 4 4 - 9n - 1 n 4 5 3 - 9n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 9n - 1 n 2 7 - 9n - 1 n 8 - 9n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1394 +r0:=-1/9*(a+b*x^n)^9/(a*n*x^(9*n)) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R - 126a b (x ) - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9n +--R 9a n x +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 9b (%e ) - 36a b (%e ) - 84a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 126a b (%e ) - 126a b (%e ) - 84a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 36a b (%e ) - 9a b %e - a +--R / +--R n log(x) 9 +--R 9n (%e ) +--R Type: Union(Expression(Integer),...) +--E 677 + +--S 678 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 8 9n n log(x) 8 2 7 9n n log(x) 7 3 6 9n n log(x) 6 +--R - 9a b x (%e ) - 36a b x (%e ) - 84a b x (%e ) +--R + +--R 4 5 9n n log(x) 5 5 4 9n n log(x) 4 +--R - 126a b x (%e ) - 126a b x (%e ) +--R + +--R 6 3 9n n log(x) 3 7 2 9n n log(x) 2 8 9n n log(x) +--R - 84a b x (%e ) - 36a b x (%e ) - 9a b x %e +--R + +--R 9 9n +--R - a x +--R / +--R 9n n log(x) 9 +--R 9a n x (%e ) +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 679 + +)clear all + +--S 680 of 1394 +t0:=x^(-4-3*p)*(a+b*x^3)^p +--R +--R +--R - 3p - 4 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1394 +r0:=-1/3*(a+b*x^3)^(1+p)/(a*(1+p)*x^(3*(1+p))) +--R +--R +--R 3 p + 1 +--R (b x + a) +--R (2) - ------------------ +--R 3p + 3 +--R (3a p + 3a)x +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 4 (- 3p - 4)log(x) p log(b x + a) +--R (- b x - a x)%e %e +--R (3) ------------------------------------------------- +--R 3a p + 3a +--R Type: Union(Expression(Integer),...) +--E 682 + +--S 683 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R 4 3p + 3 (- 3p - 4)log(x) p log(b x + a) 3 p + 1 +--R (- b x - a x)x %e %e + (b x + a) +--R -------------------------------------------------------------------------- +--R 3p + 3 +--R (3a p + 3a)x +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1394 +t0:=(a+b*x^3)^8/x^28 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 685 + +--S 686 of 1394 +r0:=-1/27*(a+b*x^3)^9/(a*x^27) +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R - -- a b x - - a b x - - a b x - -- a +--R 9 3 3 27 +--R / +--R 27 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 686 + +--S 687 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 6 7 3 8 +--R - 36a b x - 9a b x - a +--R / +--R 27 +--R 27x +--R Type: Union(Expression(Integer),...) +--E 687 + +--S 688 of 1394 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 27a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 689 + +)clear all + +--S 690 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 692 + +--S 693 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 694 + +)clear all + +--S 695 of 1394 +t0:=1/(x*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 695 + +--S 696 of 1394 +r0:=log(x)/a-1/3*log(a+b*x^3)/a +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 697 + +--S 698 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1394 +t0:=1/(x*(a+b/x^n)) +--R +--R +--R n +--R x +--R (1) ------------ +--R n +--R a x x + b x +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1394 +r0:=log(b+a*x^n)/(a*n) +--R +--R +--R n +--R log(a x + b) +--R (2) ------------- +--R a n +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(a %e + b) +--R (3) --------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 702 + +--S 703 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(a %e + b) - log(a x + b) +--R (4) ------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 704 + +)clear all + +--S 705 of 1394 +t0:=x^m/(a+b*x^(1+m)) +--R +--R +--R m +--R x +--R (1) ------------ +--R m + 1 +--R b x + a +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1394 +r0:=log(a+b*x^(1+m))/(b*(1+m)) +--R +--R +--R m + 1 +--R log(b x + a) +--R (2) ----------------- +--R b m + b +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (m + 1)log(x) +--R log(b %e + a) +--R (3) -------------------------- +--R b m + b +--R Type: Union(Expression(Integer),...) +--E 707 + +--S 708 of 1394 +m0:=a0-r0 +--R +--R +--R (m + 1)log(x) m + 1 +--R log(b %e + a) - log(b x + a) +--R (4) ---------------------------------------------- +--R b m + b +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 709 + +)clear all + +--S 710 of 1394 +t0:=x^m*(a+b*x^(1+m))^n +--R +--R +--R m m + 1 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1394 +r0:=(a+b*x^(1+m))^(1+n)/(b*(1+m)*(1+n)) +--R +--R +--R m + 1 n + 1 +--R (b x + a) +--R (2) -------------------- +--R (b m + b)n + b m + b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (m + 1)log(x) +--R (m + 1)log(x) n log(b %e + a) +--R (b %e + a)%e +--R (3) ----------------------------------------------------- +--R (b m + b)n + b m + b +--R Type: Union(Expression(Integer),...) +--E 712 + +--S 713 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (m + 1)log(x) +--R (m + 1)log(x) n log(b %e + a) m + 1 n + 1 +--R (b %e + a)%e - (b x + a) +--R --------------------------------------------------------------------------- +--R (b m + b)n + b m + b +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^3 +--R +--R +--R 3 m 2m + 2 3 2 m 2m + 2 2 2 m 2m + 2 3 m +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1394 +r0:=a^3*x^(1+m)/(1+m)+a^2*b*x^(3*(1+m))/(1+m)+_ + 3/5*a*b^2*x^(5*(1+m))/(1+m)+1/7*b^3*x^(7*(1+m))/(1+m) +--R +--R +--R 3 7m + 7 2 5m + 5 2 3m + 3 3 m + 1 +--R 5b x + 21a b x + 35a b x + 35a x +--R (2) ------------------------------------------------------- +--R 35m + 35 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 m log(x) 7 2 5 m log(x) 5 2 3 m log(x) 3 +--R 5b x (%e ) + 21a b x (%e ) + 35a b x (%e ) +--R + +--R 3 m log(x) +--R 35a x %e +--R / +--R 35m + 35 +--R Type: Union(Expression(Integer),...) +--E 717 + +--S 718 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 m log(x) 7 2 5 m log(x) 5 2 3 m log(x) 3 +--R 5b x (%e ) + 21a b x (%e ) + 35a b x (%e ) +--R + +--R 3 m log(x) 3 7m + 7 2 5m + 5 2 3m + 3 3 m + 1 +--R 35a x %e - 5b x - 21a b x - 35a b x - 35a x +--R / +--R 35m + 35 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 719 + +)clear all + +--S 720 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^2 +--R +--R +--R 2 m 2m + 2 2 m 2m + 2 2 m +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1394 +r0:=a^2*x^(1+m)/(1+m)+2/3*a*b*x^(3*(1+m))/(1+m)+1/5*b^2*x^(5*(1+m))/(1+m) +--R +--R +--R 2 5m + 5 3m + 3 2 m + 1 +--R 3b x + 10a b x + 15a x +--R (2) --------------------------------------- +--R 15m + 15 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R 3b x (%e ) + 10a b x (%e ) + 15a x %e +--R (3) ------------------------------------------------------------- +--R 15m + 15 +--R Type: Union(Expression(Integer),...) +--E 722 + +--S 723 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R 3b x (%e ) + 10a b x (%e ) + 15a x %e +--R + +--R 2 5m + 5 3m + 3 2 m + 1 +--R - 3b x - 10a b x - 15a x +--R / +--R 15m + 15 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1394 +t0:=x^m*(a+b*x^(2+2*m)) +--R +--R +--R m 2m + 2 m +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1394 +r0:=a*x^(1+m)/(1+m)+1/3*b*x^(3*(1+m))/(1+m) +--R +--R +--R 3m + 3 m + 1 +--R b x + 3a x +--R (2) --------------------- +--R 3m + 3 +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 m log(x) 3 m log(x) +--R b x (%e ) + 3a x %e +--R (3) ----------------------------------- +--R 3m + 3 +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1394 +m0:=a0-r0 +--R +--R +--R 3 m log(x) 3 m log(x) 3m + 3 m + 1 +--R b x (%e ) + 3a x %e - b x - 3a x +--R (4) ----------------------------------------------------------- +--R 3m + 3 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1394 +t0:=x^m/(a+b*x^(2+2*m)) +--R +--R +--R m +--R x +--R (1) ------------- +--R 2m + 2 +--R b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1394 +r0:=atan(x^(1+m)*sqrt(b)/sqrt(a))/((1+m)*sqrt(a)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R (2) ---------------- +--R +-+ +-+ +--R (m + 1)\|a \|b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R [--------------------------------------------------------------, +--R +-----+ +--R (2m + 2)\|- a b +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R -----------------------] +--R +---+ +--R (m + 1)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R +-+ +-+ b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R \|a \|b log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R +-----+ x \|b +--R - 2\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R (2m + 2)\|- a b \|a \|b +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1394 +m0b:=a0.2-r0 +--R +--R +--R +---+ m log(x) m + 1 +-+ +--R +-+ +-+ x\|a b %e +---+ x \|b +--R \|a \|b atan(-----------------) - \|a b atan(----------) +--R a +-+ +--R \|a +--R (6) -------------------------------------------------------- +--R +-+ +-+ +---+ +--R (m + 1)\|a \|b \|a b +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^2 +--R +--R +--R m +--R x +--R (1) -------------------------------- +--R 2 2m + 2 2 2m + 2 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1394 +r0:=1/2*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m))))+_ + 1/2*atan(x^(1+m)*sqrt(b)/sqrt(a))/(a^(3/2)*(1+m)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R 2m + 2 x \|b m + 1 +-+ +-+ +--R (b x + a)atan(----------) + x \|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------ +--R 2m + 2 2 2 +-+ +-+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 m log(x) 2 +--R (b x (%e ) + a) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R +-----+ m log(x) +--R 2x\|- a b %e +--R / +--R 2 +-----+ m log(x) 2 2 2 +-----+ +--R (4a b m + 4a b)x \|- a b (%e ) + (4a m + 4a )\|- a b +--R , +--R +---+ m log(x) +--R 2 m log(x) 2 x\|a b %e +---+ m log(x) +--R (b x (%e ) + a)atan(-----------------) + x\|a b %e +--R a +--R ------------------------------------------------------------------] +--R 2 +---+ m log(x) 2 2 2 +---+ +--R (2a b m + 2a b)x \|a b (%e ) + (2a m + 2a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 739 + +--S 740 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +-----+ x \|b +--R (- 2b x x - 2a b x )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-----+ +-+ +-+ +--R - 2b x x \|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-----+ +-+ +-+ m log(x) +--R (2b x x + 2a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +-----+ x \|b m + 1 +-----+ +-+ +-+ +--R (- 2a b x - 2a )\|- a b atan(----------) - 2a x \|- a b \|a \|b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-----+ +-+ +-+ +--R ((4a b m + 4a b )x x + (4a b m + 4a b)x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-----+ +-+ +-+ +--R ((4a b m + 4a b)x + 4a m + 4a )\|- a b \|a \|b +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +---+ x \|b +--R (- b x x - a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-+ +-+ +---+ +--R - b x x \|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-+ +-+ +---+ m log(x) +--R (b x x + a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +---+ x \|b m + 1 +-+ +-+ +---+ +--R (- a b x - a )\|a b atan(----------) - a x \|a \|b \|a b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-+ +-+ +---+ +--R ((2a b m + 2a b )x x + (2a b m + 2a b)x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-+ +-+ +---+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b \|a b +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^3 +--R +--R +--R m +--R x +--R (1) -------------------------------------------------- +--R 3 2m + 2 3 2 2m + 2 2 2 2m + 2 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1394 +r0:=1/4*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^2)+_ + 3/8*x^(1+m)/(a^2*(1+m)*(a+b*x^(2*(1+m))))+_ + 3/8*atan(x^(1+m)*sqrt(b)/sqrt(a))/(a^(5/2)*(1+m)*sqrt(b)) +--R +--R +--R (2) +--R m + 1 +-+ +--R 2 2m + 2 2 2m + 2 2 x \|b +--R (3b (x ) + 6a b x + 3a )atan(----------) +--R +-+ +--R \|a +--R + +--R m + 1 2m + 2 m + 1 +-+ +-+ +--R (3b x x + 5a x )\|a \|b +--R / +--R 2 2 2 2 2m + 2 2 3 3 2m + 2 4 4 +-+ +--R ((8a b m + 8a b )(x ) + (16a b m + 16a b)x + 8a m + 8a )\|a +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 m log(x) 4 2 m log(x) 2 2 +--R (3b x (%e ) + 6a b x (%e ) + 3a ) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R 3 +-----+ m log(x) 3 +-----+ m log(x) +--R 6b x \|- a b (%e ) + 10a x\|- a b %e +--R / +--R 2 2 2 2 4 +-----+ m log(x) 4 +--R (16a b m + 16a b )x \|- a b (%e ) +--R + +--R 3 3 2 +-----+ m log(x) 2 4 4 +-----+ +--R (32a b m + 32a b)x \|- a b (%e ) + (16a m + 16a )\|- a b +--R , +--R +--R 2 4 m log(x) 4 2 m log(x) 2 2 +--R (3b x (%e ) + 6a b x (%e ) + 3a ) +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R 3 +---+ m log(x) 3 +---+ m log(x) +--R 3b x \|a b (%e ) + 5a x\|a b %e +--R / +--R 2 2 2 2 4 +---+ m log(x) 4 +--R (8a b m + 8a b )x \|a b (%e ) +--R + +--R 3 3 2 +---+ m log(x) 2 4 4 +---+ +--R (16a b m + 16a b)x \|a b (%e ) + (8a m + 8a )\|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 746 + +--S 747 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-+ +-+ m log(x) 4 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-+ +-+ m log(x) 2 +--R (6a b x (x ) + 12a b x x + 6a b x )\|a \|b (%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 +-+ +-+ +--R (3a b (x ) + 6a b x + 3a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-----+ +--R (- 6b x (x ) - 12a b x x - 6a b x )\|- a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 +-----+ +-+ +-+ +--R (- 6b x x x - 10a b x x )\|- a b \|a \|b +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 3 2m + 2 2 2 3 2m + 2 2 3 +-----+ +-+ +-+ +--R (6b x (x ) + 12a b x x + 6a b x )\|- a b \|a \|b +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-----+ +--R (- 12a b x (x ) - 24a b x x - 12a b x )\|- a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 +-----+ +-+ +-+ +--R (- 12a b x x x - 20a b x x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2m + 2 2 2 2m + 2 3 +-----+ +-+ +-+ m log(x) +--R (10a b x (x ) + 20a b x x + 10a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 3 2m + 2 4 +-----+ x \|b +--R (- 6a b (x ) - 12a b x - 6a )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 2m + 2 3 m + 1 +-----+ +-+ +-+ +--R (- 6a b x x - 10a x )\|- a b \|a \|b +--R / +--R 2 4 2 4 4 2m + 2 2 3 3 3 3 4 2m + 2 +--R (16a b m + 16a b )x (x ) + (32a b m + 32a b )x x +--R + +--R 4 2 4 2 4 +--R (16a b m + 16a b )x +--R * +--R +-----+ +-+ +-+ m log(x) 4 +--R \|- a b \|a \|b (%e ) +--R + +--R 3 3 3 3 2 2m + 2 2 4 2 4 2 2 2m + 2 +--R (32a b m + 32a b )x (x ) + (64a b m + 64a b )x x +--R + +--R 5 5 2 +--R (32a b m + 32a b)x +--R * +--R +-----+ +-+ +-+ m log(x) 2 +--R \|- a b \|a \|b (%e ) +--R + +--R 4 2 4 2 2m + 2 2 5 5 2m + 2 6 +--R (16a b m + 16a b )(x ) + (32a b m + 32a b)x + 16a m +--R + +--R 6 +--R 16a +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-+ +-+ m log(x) 4 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-+ +-+ m log(x) 2 +--R (6a b x (x ) + 12a b x x + 6a b x )\|a \|b (%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 +-+ +-+ +--R (3a b (x ) + 6a b x + 3a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +---+ x \|b +--R (- 3b x (x ) - 6a b x x - 3a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 +-+ +-+ +---+ +--R (- 3b x x x - 5a b x x )\|a \|b \|a b +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 3 2m + 2 2 2 3 2m + 2 2 3 +-+ +-+ +---+ m log(x) 3 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b \|a b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +---+ +--R (- 6a b x (x ) - 12a b x x - 6a b x )\|a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 +-+ +-+ +---+ +--R (- 6a b x x x - 10a b x x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2m + 2 2 2 2m + 2 3 +-+ +-+ +---+ m log(x) +--R (5a b x (x ) + 10a b x x + 5a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 3 2m + 2 4 +---+ x \|b +--R (- 3a b (x ) - 6a b x - 3a )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 2m + 2 3 m + 1 +-+ +-+ +---+ +--R (- 3a b x x - 5a x )\|a \|b \|a b +--R / +--R 2 4 2 4 4 2m + 2 2 3 3 3 3 4 2m + 2 +--R (8a b m + 8a b )x (x ) + (16a b m + 16a b )x x +--R + +--R 4 2 4 2 4 +--R (8a b m + 8a b )x +--R * +--R +-+ +-+ +---+ m log(x) 4 +--R \|a \|b \|a b (%e ) +--R + +--R 3 3 3 3 2 2m + 2 2 4 2 4 2 2 2m + 2 +--R (16a b m + 16a b )x (x ) + (32a b m + 32a b )x x +--R + +--R 5 5 2 +--R (16a b m + 16a b)x +--R * +--R +-+ +-+ +---+ m log(x) 2 +--R \|a \|b \|a b (%e ) +--R + +--R 4 2 4 2 2m + 2 2 5 5 2m + 2 6 6 +--R ((8a b m + 8a b )(x ) + (16a b m + 16a b)x + 8a m + 8a ) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(5/2) +--R +--R +--R +-------------+ +--R 2 m 2m + 2 2 m 2m + 2 2 m | 2m + 2 +--R (1) (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1394 +r0:=5/24*a*x^(1+m)*(a+b*x^(2*(1+m)))^(3/2)/(1+m)+_ + 1/6*x^(1+m)*(a+b*x^(2*(1+m)))^(5/2)/(1+m)+_ + 5/16*a^3*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b))+_ + 5/16*a^2*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R (2) +--R m + 1 +-+ +--R 3 x \|b +--R 15a atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R + +--R 2 m + 1 2m + 2 2 m + 1 2m + 2 2 m + 1 +-+ +--R (8b x (x ) + 26a b x x + 33a x )\|b +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R / +--R +-+ +--R (48m + 48)\|b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 753 + +--S 754 of 1394 +--m0:=a0-r0 +--E 754 + +--S 755 of 1394 +--d0:=D(m0,x) +--E 755 + +)clear all + +--S 756 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(3/2) +--R +--R +--R +-------------+ +--R m 2m + 2 m | 2m + 2 +--R (1) (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1394 +r0:=1/4*x^(1+m)*(a+b*x^(2*(1+m)))^(3/2)/(1+m)+_ + 3/8*a^2*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*_ + sqrt(b))+3/8*a*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R (2) +--R m + 1 +-+ +--R 2 x \|b +--R 3a atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R + +--R +-------------+ +--R m + 1 2m + 2 m + 1 +-+ | 2m + 2 +--R (2b x x + 5a x )\|b \|b x + a +--R / +--R +-+ +--R (8m + 8)\|b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 758 + +--S 759 of 1394 +--m0:=a0-r0 +--E 759 + +--S 760 of 1394 +--d0:=D(m0,x) +--E 760 + +)clear all + +--S 761 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(1/2) +--R +--R +--R +-------------+ +--R m | 2m + 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1394 +r0:=1/2*a*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b))+_ + 1/2*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R m + 1 +-+ +-------------+ +--R x \|b m + 1 +-+ | 2m + 2 +--R a atanh(----------------) + x \|b \|b x + a +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R (2m + 2)\|b +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 763 + +--S 764 of 1394 +--m0:=a0-r0 +--E 764 + +--S 765 of 1394 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(1/2) +--R +--R +--R m +--R x +--R (1) ---------------- +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1394 +r0:=atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R (2) ----------------------- +--R +-+ +--R (m + 1)\|b +--R Type: Expression(Integer) +--E 767 + +--R +--S 768 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1394 +--m0:=a0-r0 +--E 769 + +--S 770 of 1394 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(3/2) +--R +--R +--R m +--R x +--R (1) ------------------------------- +--R +-------------+ +--R 2m + 2 | 2m + 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1394 +r0:=x^(1+m)/(a*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R m + 1 +--R x +--R (2) ------------------------- +--R +-------------+ +--R | 2m + 2 +--R (a m + a)\|b x + a +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +---------------------+ +--R m log(x) | 2 m log(x) 2 +--R x %e \|b x (%e ) + a +--R (3) --------------------------------------- +--R 2 m log(x) 2 2 2 +--R (a b m + a b)x (%e ) + a m + a +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------------+ +---------------------+ +--R m log(x) | 2m + 2 | 2 m log(x) 2 +--R x %e \|b x + a \|b x (%e ) + a +--R + +--R 2 m + 1 m log(x) 2 m + 1 +--R - b x x (%e ) - a x +--R / +--R +-------------+ +--R 2 m log(x) 2 2 2 | 2m + 2 +--R ((a b m + a b)x (%e ) + a m + a )\|b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(5/2) +--R +--R +--R m +--R x +--R (1) -------------------------------------------------- +--R +-------------+ +--R 2 2m + 2 2 2m + 2 2 | 2m + 2 +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1394 +r0:=1/3*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^(3/2))+_ + 2/3*x^(1+m)/(a^2*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R m + 1 2m + 2 m + 1 +--R 2b x x + 3a x +--R (2) ----------------------------------------------------- +--R +-------------+ +--R 2 2 2m + 2 3 3 | 2m + 2 +--R ((3a b m + 3a b)x + 3a m + 3a )\|b x + a +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------------+ +--R 3 m log(x) 3 m log(x) | 2 m log(x) 2 +--R (2b x (%e ) + 3a x %e )\|b x (%e ) + a +--R ----------------------------------------------------------------------------- +--R 2 2 2 2 4 m log(x) 4 3 3 2 m log(x) 2 4 4 +--R (3a b m + 3a b )x (%e ) + (6a b m + 6a b)x (%e ) + 3a m + 3a +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2m + 2 3 m log(x) 3 +--R (2b x x + 2a b x )(%e ) +--R + +--R 2m + 2 2 m log(x) +--R (3a b x x + 3a x)%e +--R * +--R +-------------+ +---------------------+ +--R | 2m + 2 | 2 m log(x) 2 +--R \|b x + a \|b x (%e ) + a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 m log(x) 4 +--R (- 2b x x x - 3a b x x )(%e ) +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 m log(x) 2 +--R (- 4a b x x x - 6a b x x )(%e ) +--R + +--R 2 m + 1 2m + 2 3 m + 1 +--R - 2a b x x - 3a x +--R / +--R 2 3 2 3 4 2m + 2 3 2 3 2 4 m log(x) 4 +--R ((3a b m + 3a b )x x + (3a b m + 3a b )x )(%e ) +--R + +--R 3 2 3 2 2 2m + 2 4 4 2 m log(x) 2 +--R ((6a b m + 6a b )x x + (6a b m + 6a b)x )(%e ) +--R + +--R 4 4 2m + 2 5 5 +--R (3a b m + 3a b)x + 3a m + 3a +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(7/2) +--R +--R +--R m +--R x +--R (1) -------------------------------------------------------------------- +--R +-------------+ +--R 3 2m + 2 3 2 2m + 2 2 2 2m + 2 3 | 2m + 2 +--R (b (x ) + 3a b (x ) + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1394 +r0:=1/5*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^(5/2))+_ + 4/15*x^(1+m)/(a^2*(1+m)*(a+b*x^(2*(1+m)))^(3/2))+_ + 8/15*x^(1+m)/(a^3*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R (2) +--R 2 m + 1 2m + 2 2 m + 1 2m + 2 2 m + 1 +--R 8b x (x ) + 20a b x x + 15a x +--R / +--R 3 2 3 2 2m + 2 2 4 4 2m + 2 5 5 +--R ((15a b m + 15a b )(x ) + (30a b m + 30a b)x + 15a m + 15a ) +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R (8b x (%e ) + 20a b x (%e ) + 15a x %e ) +--R * +--R +---------------------+ +--R | 2 m log(x) 2 +--R \|b x (%e ) + a +--R / +--R 3 3 3 3 6 m log(x) 6 4 2 4 2 4 m log(x) 4 +--R (15a b m + 15a b )x (%e ) + (45a b m + 45a b )x (%e ) +--R + +--R 5 5 2 m log(x) 2 6 6 +--R (45a b m + 45a b)x (%e ) + 15a m + 15a +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 2m + 2 2 3 5 2m + 2 2 2 5 m log(x) 5 +--R (8b x (x ) + 16a b x x + 8a b x )(%e ) +--R + +--R 3 3 2m + 2 2 2 2 3 2m + 2 3 3 m log(x) 3 +--R (20a b x (x ) + 40a b x x + 20a b x )(%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 m log(x) +--R (15a b x (x ) + 30a b x x + 15a x)%e +--R * +--R +-------------+ +---------------------+ +--R | 2m + 2 | 2 m log(x) 2 +--R \|b x + a \|b x (%e ) + a +--R + +--R 5 6 m + 1 2m + 2 2 4 6 m + 1 2m + 2 2 3 6 m + 1 +--R (- 8b x x (x ) - 20a b x x x - 15a b x x ) +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 4 4 m + 1 2m + 2 2 2 3 4 m + 1 2m + 2 3 2 4 m + 1 +--R (- 24a b x x (x ) - 60a b x x x - 45a b x x ) +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 3 2 m + 1 2m + 2 2 3 2 2 m + 1 2m + 2 4 2 m + 1 +--R (- 24a b x x (x ) - 60a b x x x - 45a b x x ) +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 2 m + 1 2m + 2 2 4 m + 1 2m + 2 5 m + 1 +--R - 8a b x (x ) - 20a b x x - 15a x +--R / +--R 3 5 3 5 6 2m + 2 2 4 4 4 4 6 2m + 2 +--R (15a b m + 15a b )x (x ) + (30a b m + 30a b )x x +--R + +--R 5 3 5 3 6 +--R (15a b m + 15a b )x +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 4 4 4 4 4 2m + 2 2 5 3 5 3 4 2m + 2 +--R (45a b m + 45a b )x (x ) + (90a b m + 90a b )x x +--R + +--R 6 2 6 2 4 +--R (45a b m + 45a b )x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 5 3 5 3 2 2m + 2 2 6 2 6 2 2 2m + 2 +--R (45a b m + 45a b )x (x ) + (90a b m + 90a b )x x +--R + +--R 7 7 2 +--R (45a b m + 45a b)x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 6 2 6 2 2m + 2 2 7 7 2m + 2 8 8 +--R (15a b m + 15a b )(x ) + (30a b m + 30a b)x + 15a m + 15a +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1394 +t0:=x^n*sqrt(1+x^(1+n)) +--R +--R +--R +----------+ +--R n | n + 1 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1394 +r0:=2/3*(1+x^(1+n))^(3/2)/(1+n) +--R +--R +--R +----------+ +--R n + 1 | n + 1 +--R (2x + 2)\|x + 1 +--R (2) -------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------------------+ +--R (n + 1)log(x) | (n + 1)log(x) +--R (2%e + 2)\|%e + 1 +--R (3) -------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------------------+ +----------+ +--R (n + 1)log(x) | (n + 1)log(x) n + 1 | n + 1 +--R (2%e + 2)\|%e + 1 + (- 2x - 2)\|x + 1 +--R --------------------------------------------------------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 1394 +t0:=x^n*sqrt(a^2+x^(1+n)) +--R +--R +--R +-----------+ +--R n | n + 1 2 +--R (1) x \|x + a +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1394 +r0:=2/3*(a^2+x^(1+n))^(3/2)/(1+n) +--R +--R +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (2x + 2a )\|x + a +--R (2) ----------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R (3) ----------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R + +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (- 2x - 2a )\|x + a +--R / +--R 3n + 3 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 1394 +t0:=(c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1394 +r0:=1/6*c^2*(a+b*x)^5*sqrt(c*(a+b*x)^2)/b +--R +--R +--R (2) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R / +--R 6b +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 4 2 5 2 3 2 4 3 2 2 3 4 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a c x)\|c +--R ------------------------------------------------------------------------ +--R 6 +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (- b c x - 5a b c x - 10a b c x - 10a b c x - 5a b c x - a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x)\|c +--R / +--R 6b +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +-+ +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x - 6a b c x +--R + +--R 6 3 +--R - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 1394 +t0:=(c*(a+b*x)^2)^(3/2) +--R +--R +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (1) (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1394 +r0:=1/4*c*(a+b*x)^3*sqrt(c*(a+b*x)^2)/b +--R +--R +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 2a b c x + a c +--R (2) --------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a c x)\|c +--R (3) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + 2a b c x + a c +--R + +--R 4 4 3 3 2 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x)\|c +--R / +--R 4b +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------+ +--R 3 3 2 2 2 3 +-+ | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|c \|b c x + 2a b c x + a c +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 1394 +t0:=(c*(a+b*x)^2)^(1/2) +--R +--R +--R +-----------------------+ +--R | 2 2 2 +--R (1) \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1394 +r0a:=1/2*(a+b*x)*sqrt(c*(a+b*x)^2)/b +--R +--R +--R +-----------------------+ +--R | 2 2 2 +--R (b x + a)\|b c x + 2a b c x + a c +--R (2) ----------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1394 +r0b:=a*x*sqrt(c*(a+b*x)^2)/(a+b*x)+1/2*b*x^2*sqrt(c*(a+b*x)^2)/(a+b*x) +--R +--R +--R +-----------------------+ +--R 2 | 2 2 2 +--R (b x + 2a x)\|b c x + 2a b c x + a c +--R (3) --------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (b x + 2a x)\|c +--R (4) ----------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 809 + +--S 810 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------------------+ +--R | 2 2 2 2 2 +-+ +--R (- b x - a)\|b c x + 2a b c x + a c + (b x + 2a b x)\|c +--R (5) ----------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 2 2 2 +--R (b x + a)\|c \|b c x + 2a b c x + a c - b c x - 2a b c x - a c +--R (6) ----------------------------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) +--R +-----------------------+ +--R 2 | 2 2 2 2 3 2 2 +-+ +--R (- b x - 2a x)\|b c x + 2a b c x + a c + (b x + 3a b x + 2a x)\|c +--R ----------------------------------------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 2 2 2 +--R (b x + a)\|c \|b c x + 2a b c x + a c - b c x - 2a b c x - a c +--R (8) ----------------------------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1394 +t0:=1/(c*(a+b*x)^2)^(1/2) +--R +--R +--R 1 +--R (1) -------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1394 +r0:=(a+b*x)*log(a+b*x)/(b*sqrt(c*(a+b*x)^2)) +--R +--R +--R (b x + a)log(b x + a) +--R (2) --------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R b\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R +-+ +--R b\|c +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------+ +--R | 2 2 2 +-+ +--R log(b x + a)\|b c x + 2a b c x + a c + (- b x - a)log(b x + a)\|c +--R (4) -------------------------------------------------------------------- +--R +-----------------------+ +--R +-+ | 2 2 2 +--R b\|c \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R (5) -------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R (b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1394 +t0:=1/(c*(a+b*x)^2)^(3/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1394 +r0:=(-1/2)/(b*c*(a+b*x)*sqrt(c*(a+b*x)^2)) +--R +--R +--R 1 +--R (2) - ------------------------------------------- +--R +-----------------------+ +--R 2 | 2 2 2 +--R (2b c x + 2a b c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------------------- +--R 3 2 2 2 +-+ +--R (2b c x + 4a b c x + 2a b c)\|c +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------+ +--R | 2 2 2 +-+ +--R - \|b c x + 2a b c x + a c + (b x + a)\|c +--R (4) ----------------------------------------------------------- +--R +-----------------------+ +--R 3 2 2 2 +-+ | 2 2 2 +--R (2b c x + 4a b c x + 2a b c)\|c \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R (5) ---------------------------------------------------------------- +--R +-----------------------+ +--R 3 2 3 2 2 2 2 2 3 2 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1394 +t0:=1/(c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1394 +r0:=(-1/4)/(b*c^2*(a+b*x)^3*sqrt(c*(a+b*x)^2)) +--R +--R +--R (2) +--R 1 +--R - ---------------------------------------------------------------------- +--R +-----------------------+ +--R 4 2 3 3 2 2 2 2 2 3 2 | 2 2 2 +--R (4b c x + 12a b c x + 12a b c x + 4a b c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------------------- +--R 5 2 4 4 2 3 2 3 2 2 3 2 2 4 2 +-+ +--R (4b c x + 16a b c x + 24a b c x + 16a b c x + 4a b c )\|c +--R Type: Union(Expression(Integer),...) +--E 826 + +--S 827 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------+ +--R | 2 2 2 +-+ +--R - \|b c x + 2a b c x + a c + (b x + a)\|c +--R / +--R 5 2 4 4 2 3 2 3 2 2 3 2 2 4 2 +-+ +--R (4b c x + 16a b c x + 24a b c x + 16a b c x + 4a b c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R / +--R 5 3 5 4 3 4 2 3 3 3 3 2 3 2 4 3 5 3 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 828 + +)clear all + +--TPDHERE: factor(25*x^2+30*x+9) = (5*x+3)^2 +--S 829 of 1394 +t0:=sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1394 +r0a:=1/10*(3+5*x)*sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R (2) ------------------------- +--R 10 +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1394 +r0b:=3*x*sqrt((3+5*x)^2)/(3+5*x)+5/2*x^2*sqrt((3+5*x)^2)/(3+5*x) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (5x + 6x)\|25x + 30x + 9 +--R (3) --------------------------- +--R 10x + 6 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 5x + 6x +--R (4) -------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 832 + +--S 833 of 1394 +m0a:=a0-r0a +--R +--R +--R +--------------+ +--R | 2 2 +--R (- 5x - 3)\|25x + 30x + 9 + 25x + 30x +--R (5) ---------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (5x + 3)\|25x + 30x + 9 - 25x - 30x - 9 +--R (6) ------------------------------------------ +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1394 +m0b:=a0-r0b +--R +--R +--R +--------------+ +--R 2 | 2 3 2 +--R (- 5x - 6x)\|25x + 30x + 9 + 25x + 45x + 18x +--R (7) ------------------------------------------------- +--R 10x + 6 +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (5x + 3)\|25x + 30x + 9 - 25x - 30x - 9 +--R (8) ------------------------------------------ +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 836 + +)clear all + +--TPDHERE: factor(100*x^2+120*x+36) = 4*(5*x+3)^2 +--TPDHERE: why isn't the sqrt of a perfect square simplified? +--S 837 of 1394 +t0:=sqrt((6+10*x)^2) +--R +--R +--R +-----------------+ +--R | 2 +--R (1) \|100x + 120x + 36 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1394 +r0a:=1/5*(3+5*x)*sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R (2) ------------------------- +--R 5 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1394 +r0b:=6*x*sqrt((3+5*x)^2)/(3+5*x)+5*x^2*sqrt((3+5*x)^2)/(3+5*x) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (5x + 6x)\|25x + 30x + 9 +--R (3) --------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (4) 5x + 6x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1394 +m0a:=a0-r0a +--R +--R +--R +--------------+ +--R | 2 2 +--R (- 5x - 3)\|25x + 30x + 9 + 25x + 30x +--R (5) ---------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (10x + 6)\|25x + 30x + 9 - 50x - 60x - 18 +--R (6) -------------------------------------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1394 +m0b:=a0-r0b +--R +--R +--R +--------------+ +--R 2 | 2 3 2 +--R (- 5x - 6x)\|25x + 30x + 9 + 25x + 45x + 18x +--R (7) ------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (10x + 6)\|25x + 30x + 9 - 50x - 60x - 18 +--R (8) -------------------------------------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 844 + +)clear all + +--S 845 of 1394 +t0:=1/sqrt((3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1394 +r0:=1/5*(3+5*x)*log(3+5*x)/sqrt((3+5*x)^2) +--R +--R +--R (5x + 3)log(5x + 3) +--R (2) ------------------- +--R +--------------+ +--R | 2 +--R 5\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) +--R (3) ----------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 847 + +--S 848 of 1394 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +--R log(5x + 3)\|25x + 30x + 9 + (- 5x - 3)log(5x + 3) +--R (4) ---------------------------------------------------- +--R +--------------+ +--R | 2 +--R 5\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1394 +d0:=D(m0,x) +--R +--R +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 - 5x - 3 +--R (5) -------------------------- +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 849 + +)clear all + +--S 850 of 1394 +t0:=1/sqrt((6+10*x)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R +-----------------+ +--R | 2 +--R \|100x + 120x + 36 +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1394 +r0:=1/10*(3+5*x)*log(3+5*x)/sqrt((3+5*x)^2) +--R +--R +--R (5x + 3)log(5x + 3) +--R (2) ------------------- +--R +--------------+ +--R | 2 +--R 10\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) +--R (3) ----------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 852 + +--S 853 of 1394 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +--R log(5x + 3)\|25x + 30x + 9 + (- 5x - 3)log(5x + 3) +--R (4) ---------------------------------------------------- +--R +--------------+ +--R | 2 +--R 10\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1394 +d0:=D(m0,x) +--R +--R +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 - 5x - 3 +--R (5) -------------------------- +--R +--------------+ +--R | 2 +--R (10x + 6)\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1394 +t0:=1/sqrt(-(2+3*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R +---------------+ +--R | 2 +--R \|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1394 +r0:=1/3*(2+3*x)*log(2+3*x)/sqrt(-(2+3*x)^2) +--R +--R +--R (3x + 2)log(3x + 2) +--R (2) ------------------- +--R +---------------+ +--R | 2 +--R 3\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +---+ 3x + 2 +--R \|- 1 log(------) +--R 3 +--R (3) - ----------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1394 +m0:=a0-r0 +--R +--R +--R +---------------+ +--R +---+ 3x + 2 | 2 +--R - \|- 1 log(------)\|- 9x - 12x - 4 + (- 3x - 2)log(3x + 2) +--R 3 +--R (4) ------------------------------------------------------------- +--R +---------------+ +--R | 2 +--R 3\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1394 +d0:=D(m0,x) +--R +--R +--R +---------------+ +--R +---+ | 2 +--R - \|- 1 \|- 9x - 12x - 4 - 3x - 2 +--R (5) ----------------------------------- +--R +---------------+ +--R | 2 +--R (3x + 2)\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1394 +t0:=(c*(a+b*x)^3)^(5/2) +--R +--R +--R (1) +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 2 +--R a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1394 +r0:=2/17*c^2*(a+b*x)^7*sqrt(c*(a+b*x)^3)/b +--R +--R +--R (2) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 +--R 2b c x + 14a b c x + 42a b c x + 70a b c x + 70a b c x +--R + +--R 5 2 2 2 6 2 7 2 +--R 42a b c x + 14a b c x + 2a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R / +--R 17b +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 8 7 2 7 2 6 2 6 3 5 2 5 4 4 2 4 +--R 2b c x + 16a b c x + 56a b c x + 112a b c x + 140a b c x +--R + +--R 5 3 2 3 6 2 2 2 7 2 8 2 +--R 112a b c x + 56a b c x + 16a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 17b +--R Type: Union(Expression(Integer),...) +--E 862 + +--S 863 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 +--R - 2b c x - 14a b c x - 42a b c x - 70a b c x - 70a b c x +--R + +--R 5 2 2 2 6 2 7 2 +--R - 42a b c x - 14a b c x - 2a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 8 2 8 7 2 7 2 6 2 6 3 5 2 5 4 4 2 4 +--R 2b c x + 16a b c x + 56a b c x + 112a b c x + 140a b c x +--R + +--R 5 3 2 3 6 2 2 2 7 2 8 2 +--R 112a b c x + 56a b c x + 16a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 17b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 3 8 7 3 7 2 6 3 6 3 5 3 5 4 4 3 4 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x +--R + +--R 5 3 3 3 6 2 3 2 7 3 8 3 +--R 56a b c x + 28a b c x + 8a b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 9 3 9 8 3 8 2 7 3 7 3 6 3 6 4 5 3 5 +--R - b c x - 9a b c x - 36a b c x - 84a b c x - 126a b c x +--R + +--R 5 4 3 4 6 3 3 3 7 2 3 2 8 3 9 3 +--R - 126a b c x - 84a b c x - 36a b c x - 9a b c x - a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1394 +t0:=(c*(a+b*x)^3)^(3/2) +--R +--R +--R (1) +--R +-----------------------------------+ +--R 3 3 2 2 2 3 | 3 3 2 2 2 3 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1394 +r0:=2/11*c*(a+b*x)^4*sqrt(c*(a+b*x)^3)/b +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (2b c x + 8a b c x + 12a b c x + 8a b c x + 2a c) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R / +--R 11b +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b c x + 10a b c x + 20a b c x + 20a b c x + 10a b c x + 2a c) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 11b +--R Type: Union(Expression(Integer),...) +--E 867 + +--S 868 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b c x - 8a b c x - 12a b c x - 8a b c x - 2a c) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b c x + 10a b c x + 20a b c x + 20a b c x + 10a b c x + 2a c) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 11b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x +--R + +--R 5 2 6 2 +--R - 6a b c x - a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 869 + +)clear all + +--S 870 of 1394 +t0:=(c*(a+b*x)^3)^(1/2) +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (1) \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1394 +r0:=2/5*(a+b*x)*sqrt(c*(a+b*x)^3)/b +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (2b x + 2a)\|b c x + 3a b c x + 3a b c x + a c +--R (2) ------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R (3) ------------------------------------ +--R 5b +--R Type: Union(Expression(Integer),...) +--E 872 + +--S 873 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (- 2b x - 2a)\|b c x + 3a b c x + 3a b c x + a c +--R + +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R / +--R 5b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R 2 2 2 | 3 3 2 2 2 3 +--R (b c x + 2a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 874 + +)clear all + +--S 875 of 1394 +t0:=1/(c*(a+b*x)^3)^(1/2) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1394 +r0:=-2*(a+b*x)/(b*sqrt(c*(a+b*x)^3)) +--R +--R +--R - 2b x - 2a +--R (2) --------------------------------------- +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R b\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - --------------- +--R +-----------+ +--R b\|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 877 + +--S 878 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R (4) --------------------------------------------------------------------- +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R b\|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R (5) ------------------------------------------------------------------ +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R (b x + a)\|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 879 + +)clear all + +--S 880 of 1394 +t0:=1/(c*(a+b*x)^3)^(3/2) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +-----------------------------------+ +--R 3 3 2 2 2 3 | 3 3 2 2 2 3 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1394 +r0:=(-2/7)/(b*c*(a+b*x)^2*sqrt(c*(a+b*x)^3)) +--R +--R +--R 2 +--R (2) - -------------------------------------------------------------------- +--R +-----------------------------------+ +--R 3 2 2 2 | 3 3 2 2 2 3 +--R (7b c x + 14a b c x + 7a b c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - --------------------------------------------------------- +--R 4 3 3 2 2 2 3 +-----------+ +--R (7b c x + 21a b c x + 21a b c x + 7a b c)\|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 882 + +--S 883 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R / +--R 4 3 3 2 2 2 3 +-----------+ +--R (7b c x + 21a b c x + 21a b c x + 7a b c)\|b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R / +--R 4 4 3 3 2 2 2 3 4 +-----------+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c)\|b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 884 + +)clear all + +--S 885 of 1394 +t0:=1/(c*(a+b*x)^3)^(5/2) +--R +--R +--R (1) +--R 1 +--R / +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 2 +--R a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1394 +r0:=(-2/13)/(b*c^2*(a+b*x)^5*sqrt(c*(a+b*x)^3)) +--R +--R +--R (2) +--R - +--R 2 +--R / +--R 6 2 5 5 2 4 2 4 2 3 3 3 2 2 4 2 2 +--R 13b c x + 65a b c x + 130a b c x + 130a b c x + 65a b c x +--R + +--R 5 2 +--R 13a b c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R / +--R 7 2 6 6 2 5 2 5 2 4 3 4 2 3 4 3 2 2 +--R 13b c x + 78a b c x + 195a b c x + 260a b c x + 195a b c x +--R + +--R 5 2 2 6 2 +--R 78a b c x + 13a b c +--R * +--R +-----------+ +--R \|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 887 + +--S 888 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R / +--R 7 2 6 6 2 5 2 5 2 4 3 4 2 3 4 3 2 2 +--R 13b c x + 78a b c x + 195a b c x + 260a b c x + 195a b c x +--R + +--R 5 2 2 6 2 +--R 78a b c x + 13a b c +--R * +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R / +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 5 2 2 2 +--R b c x + 7a b c x + 21a b c x + 35a b c x + 35a b c x + 21a b c x +--R + +--R 6 2 7 2 +--R 7a b c x + a c +--R * +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 889 + +)clear all + +--S 890 of 1394 +t0:=(c/(a+b*x))^(5/2) +--R +--R +--R +-------+ +--R 2 | c +--R c |------- +--R \|b x + a +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1394 +r0:=-2/3*c^2*sqrt(c/(a+b*x))/(b*(a+b*x)) +--R +--R +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R (2) - ------------- +--R 2 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R (3) - ------------- +--R 2 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 892 + +--S 893 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1394 +t0:=(c/(a+b*x))^(3/2) +--R +--R +--R +-------+ +--R | c +--R c |------- +--R \|b x + a +--R (1) ----------- +--R b x + a +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1394 +r0:=-2*c*sqrt(c/(a+b*x))/b +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (2) - ------------ +--R b +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (3) - ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 897 + +--S 898 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1394 +t0:=(c/(a+b*x))^(1/2) +--R +--R +--R +-------+ +--R | c +--R (1) |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1394 +r0:=2*(a+b*x)*sqrt(c/(a+b*x))/b +--R +--R +--R +-------+ +--R | c +--R (2b x + 2a) |------- +--R \|b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2c +--R (3) ----------- +--R +-------+ +--R | c +--R b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 902 + +--S 903 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1394 +t0:=1/(c/(a+b*x))^(1/2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1394 +r0:=2/3*(a+b*x)/(b*sqrt(c/(a+b*x))) +--R +--R +--R 2b x + 2a +--R (2) ------------ +--R +-------+ +--R | c +--R 3b |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2b x + 2a +--R (3) ------------ +--R +-------+ +--R | c +--R 3b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 907 + +--S 908 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1394 +t0:=1/(c/(a+b*x))^(3/2) +--R +--R +--R b x + a +--R (1) ----------- +--R +-------+ +--R | c +--R c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1394 +r0:=2/5*(a+b*x)^2/(b*c*sqrt(c/(a+b*x))) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (2) -------------------- +--R +-------+ +--R | c +--R 5b c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (3) -------------------- +--R +-------+ +--R | c +--R 5b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 912 + +--S 913 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1394 +t0:=1/(c/(a+b*x))^(5/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-------+ +--R 2 | c +--R c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1394 +r0:=2/7*(a+b*x)^3/(b*c^2*sqrt(c/(a+b*x))) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 6a b x + 6a b x + 2a +--R (2) ------------------------------ +--R +-------+ +--R 2 | c +--R 7b c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 6a b x + 6a b x + 2a +--R (3) ------------------------------ +--R +-------+ +--R 2 | c +--R 7b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 917 + +--S 918 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +)clear all + +--S 920 of 1394 +t0:=(c/(a+b*x)^2)^(5/2) +--R +--R +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1394 +r0:=-1/4*c^2*sqrt(c/(a+b*x)^2)/(b*(a+b*x)^3) +--R +--R +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) - --------------------------------- +--R 4 3 3 2 2 2 3 +--R 4b x + 12a b x + 12a b x + 4a b +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R c \|c +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 922 + +--S 923 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R 2 +-+ 2 2 | c +--R - c \|c + (b c x + a c ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) ---------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R 2 +-+ 2 2 | c +--R c \|c + (- b c x - a c ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1394 +t0:=(c/(a+b*x)^2)^(3/2) +--R +--R +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (1) ---------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1394 +r0:=-1/2*c*sqrt(c/(a+b*x)^2)/(b*(a+b*x)) +--R +--R +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) - ---------------------- +--R 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R c\|c +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 927 + +--S 928 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-+ | c +--R - c\|c + (b c x + a c) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) -------------------------------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R +-+ | c +--R c\|c + (- b c x - a c) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) -------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1394 +t0:=(c/(a+b*x)^2)^(1/2) +--R +--R +--R +------------------+ +--R | c +--R (1) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1394 +r0:=(a+b*x)*log(a+b*x)*sqrt(c/(a+b*x)^2)/b +--R +--R +--R +------------------+ +--R | c +--R (b x + a)log(b x + a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) ------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R log(b x + a)\|c +--R (3) ---------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 932 + +--S 933 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-+ | c +--R log(b x + a)\|c + (- b x - a)log(b x + a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) --------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R | c +-+ +--R (b x + a) |------------------ \|c - c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | c +--R (b x + 2a b x + a ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1394 +t0:=1/(c/(a+b*x)^2)^(1/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1394 +r0a:=1/2*(a+b*x)/(b*sqrt(c/(a+b*x)^2)) +--R +--R +--R b x + a +--R (2) ----------------------- +--R +------------------+ +--R | c +--R 2b |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1394 +r0b:=a*x/((a+b*x)*sqrt(c/(a+b*x)^2))+1/2*b*x^2/((a+b*x)*sqrt(c/(a+b*x)^2)) +--R +--R +--R 2 +--R b x + 2a x +--R (3) -------------------------------- +--R +------------------+ +--R | c +--R (2b x + 2a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x + 2a x +--R (4) ----------- +--R +-+ +--R 2\|c +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 1394 +m0a:=a0-r0a +--R +--R +--R +------------------+ +--R +-+ 2 2 | c +--R (- b x - a)\|c + (b x + 2a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) ------------------------------------------------------ +--R +------------------+ +--R | c +-+ +--R 2b |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +------------------+ +--R | c +-+ +--R (b x + a) |------------------ \|c - c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (6) -------------------------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1394 +m0b:=a0-r0b +--R +--R +--R +------------------+ +--R 2 +-+ 2 3 2 2 | c +--R (- b x - 2a x)\|c + (b x + 3a b x + 2a x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (7) ------------------------------------------------------------------ +--R +------------------+ +--R | c +-+ +--R (2b x + 2a) |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +------------------+ +--R +-+ 2 2 2 | c +--R (b x + a)\|c + (- b x - 2a b x - a ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (8) ----------------------------------------------------------- +--R c +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1394 +t0:=1/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ---------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1394 +r0:=1/4*(a+b*x)^3/(b*c*sqrt(c/(a+b*x)^2)) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (2) ---------------------------- +--R +------------------+ +--R | c +--R 4b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (3) ------------------------------- +--R +-+ +--R 4c\|c +--R Type: Union(Expression(Integer),...) +--E 945 + +--S 946 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 3 +-+ +--R (- b x - 3a b x - 3a b x - a )\|c +--R + +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | c +--R (b x + 4a b x + 6a b x + 4a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R | c +-+ +--R 4b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | c +-+ 2 2 +--R (b x + 3a b x + 3a b x + a ) |------------------ \|c - b c x +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 +--R - 2a b c x - a c +--R / +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 947 + +)clear all + +--S 948 of 1394 +t0:=1/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1394 +r0:=1/6*(a+b*x)^5/(b*c^2*sqrt(c/(a+b*x)^2)) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (2) -------------------------------------------------- +--R +------------------+ +--R 2 | c +--R 6b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 5 6 4 5 2 3 4 3 2 3 4 2 5 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a x +--R (3) ------------------------------------------------------ +--R 2 +-+ +--R 6c \|c +--R Type: Union(Expression(Integer),...) +--E 950 + +--S 951 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|c +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x) +--R * +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R 2 | c +-+ +--R 6b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a ) +--R * +--R +------------------+ +--R | c +-+ +--R |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +------------------+ +--R 3 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 952 + +)clear all + +--S 953 of 1394 +t0:=(c/(a+b*x)^3)^(5/2) +--R +--R +--R +----------------------------+ +--R 2 | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1394 +r0:=-2/13*c^2*sqrt(c/(a+b*x)^3)/(b*(a+b*x)^5) +--R +--R +--R +----------------------------+ +--R 2 | c +--R 2c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) - ----------------------------------------------------------- +--R 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R 13b x + 65a b x + 130a b x + 130a b x + 65a b x + 13a b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R - ----------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 13b x + 78a b x + 195a b x + 260a b x + 195a b x + 78a b x + 13a b +--R Type: Union(Expression(Integer),...) +--E 955 + +--S 956 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +----------------------------+ +--R 2 | c 2 2 | c +--R - 2c |------- + (2b c x + 2a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R ----------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 13b x + 78a b x + 195a b x + 260a b x + 195a b x + 78a b x + 13a b +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R 3 | c 3 3 | c +--R - c |------- + (b c x + a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R * +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 957 + +)clear all + +--S 958 of 1394 +t0:=(c/(a+b*x)^3)^(3/2) +--R +--R +--R +----------------------------+ +--R | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (1) -------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1394 +r0:=-2/7*c*sqrt(c/(a+b*x)^3)/(b*(a+b*x)^2) +--R +--R +--R +----------------------------+ +--R | c +--R 2c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) - --------------------------------- +--R 3 2 2 2 +--R 7b x + 14a b x + 7a b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (3) - --------------------------------- +--R 4 3 3 2 2 2 3 +--R 7b x + 21a b x + 21a b x + 7a b +--R Type: Union(Expression(Integer),...) +--E 960 + +--S 961 of 1394 +m0:=a0-r0 +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - 2c |------- + (2b c x + 2a c) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (4) --------------------------------------------------------------- +--R 4 3 3 2 2 2 3 +--R 7b x + 21a b x + 21a b x + 7a b +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R 2 | c 2 2 | c +--R - c |------- + (b c x + a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 962 + +)clear all + +--S 963 of 1394 +t0:=(c/(a+b*x)^3)^(1/2) +--R +--R +--R +----------------------------+ +--R | c +--R (1) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1394 +r0:=-2*(a+b*x)*sqrt(c/(a+b*x)^3)/b +--R +--R +--R +----------------------------+ +--R | c +--R (- 2b x - 2a) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2 |------- +--R \|b x + a +--R (3) - ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 965 + +--S 966 of 1394 +m0:=a0-r0 +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - 2 |------- + (2b x + 2a) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (4) ---------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R | c | c +--R - c |------- + (b c x + a c) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R ----------------------------------------------------------------------- +--R +----------------------------+ +-------+ +--R 3 3 2 2 2 3 | c | c +--R (b x + 3a b x + 3a b x + a ) |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1394 +t0:=1/(c/(a+b*x)^3)^(1/2) +--R +--R +--R 1 +--R (1) ------------------------------- +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1394 +r0:=2/5*(a+b*x)/(b*sqrt(c/(a+b*x)^3)) +--R +--R +--R 2b x + 2a +--R (2) --------------------------------- +--R +----------------------------+ +--R | c +--R 5b |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (3) -------------------- +--R +-------+ +--R | c +--R 5b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 970 + +--S 971 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | c +--R (- 2b x - 2a) |------- +--R \|b x + a +--R + +--R +----------------------------+ +--R 2 2 2 | c +--R (2b x + 4a b x + 2a ) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R 5b |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1394 +d0:=D(m0,x) +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - |------- + (b x + a) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (5) ------------------------------------------------------- +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1394 +t0:=1/(c/(a+b*x)^3)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------- +--R +----------------------------+ +--R | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1394 +r0:=2/11*(a+b*x)^4/(b*c*sqrt(c/(a+b*x)^3)) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 2b x + 8a b x + 12a b x + 8a b x + 2a +--R (2) ----------------------------------------- +--R +----------------------------+ +--R | c +--R 11b c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R 2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a +--R (3) ------------------------------------------------------ +--R +-------+ +--R | c +--R 11b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 | c +--R (- 2b x - 8a b x - 12a b x - 8a b x - 2a ) |------- +--R \|b x + a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a ) +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R 11b c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +--R 3 3 2 2 2 3 | c +--R (- b x - 3a b x - 3a b x - a ) |------- +--R \|b x + a +--R + +--R +----------------------------+ +--R 4 4 3 3 2 2 2 3 4 | c +--R (b x + 4a b x + 6a b x + 4a b x + a ) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1394 +t0:=1/(c/(a+b*x)^3)^(5/2) +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (1) ------------------------------------------------------------- +--R +----------------------------+ +--R 2 | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1394 +r0:=2/17*(a+b*x)^7/(b*c^2*sqrt(c/(a+b*x)^3)) +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 2b x + 14a b x + 42a b x + 70a b x + 70a b x + 42a b x + 14a b x + 2a +--R ---------------------------------------------------------------------------- +--R +----------------------------+ +--R 2 | c +--R 17b c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 2b x + 16a b x + 56a b x + 112a b x + 140a b x + 112a b x +--R + +--R 6 2 2 7 8 +--R 56a b x + 16a b x + 2a +--R / +--R +-------+ +--R 2 | c +--R 17b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 980 + +--S 981 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 2b x - 14a b x - 42a b x - 70a b x - 70a b x - 42a b x +--R + +--R 6 7 +--R - 14a b x - 2a +--R * +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 2b x + 16a b x + 56a b x + 112a b x + 140a b x + 112a b x +--R + +--R 6 2 2 7 8 +--R 56a b x + 16a b x + 2a +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R 2 | c | c +--R 17b c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 +--R a +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R 2 | c | c +--R c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 982 + +)clear all + +--S 983 of 1394 +t0:=(c*(a+b*x)^(3/2))^(2/3) +--R +--R +--R +-----------------------+2 +--R 3| +-------+ +--R (1) \|(b c x + a c)\|b x + a +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1394 +r0a:=1/2*(a+b*x)*(c*(a+b*x)^(3/2))^(2/3)/b +--R +--R +--R +-----------------------+2 +--R 3| +-------+ +--R (b x + a)\|(b c x + a c)\|b x + a +--R (2) ------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1394 +r0b:=a*x*(c*(a+b*x)^(3/2))^(2/3)/(a+b*x)+_ + 1/2*b*x^2*(c*(a+b*x)^(3/2))^(2/3)/(a+b*x) +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R (b x + 2a x)\|(b c x + a c)\|b x + a +--R (3) ---------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R (b x + 2a x)\|(b c x + a c)\|b x + a +--R (4) ---------------------------------------- +--R 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 986 + +--S 987 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R a \|(b c x + a c)\|b x + a +--R (5) - ----------------------------- +--R 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1394 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1394 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1394 +t0:=(c*(a+b*x)^(2/3))^(3/2) +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 +--R (1) c \|b x + a \|c \|b x + a +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1394 +r0a:=1/2*c*(a+b*x)^(5/3)*sqrt(c*(a+b*x)^(2/3))/b +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 +--R (b c x + a c)\|b x + a \|c \|b x + a +--R (2) ---------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1394 +r0b:=a*c*x*sqrt(c*(a+b*x)^(2/3))/(a+b*x)^(1/3)+_ + 1/2*b*c*x^2*sqrt(c*(a+b*x)^(2/3))/(a+b*x)^(1/3) +--R +--R +--R +-------------+ +--R 2 | 3+-------+2 +--R (b c x + 2a c x)\|c \|b x + a +--R (3) --------------------------------- +--R 3+-------+ +--R 2\|b x + a +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (b c x + 2a c x)\|c +--R (4) --------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 994 + +--S 995 of 1394 +m0a:=a0-r0a +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 2 2 +-+ +--R (- b c x - a c)\|b x + a \|c \|b x + a + (b c x + 2a b c x)\|c +--R (5) -------------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-------------+ +--R +-+ | 3+-------+2 2 2 3+-------+ +--R (b c x + a c)\|c \|c \|b x + a + (- b c x - a c )\|b x + a +--R (6) -------------------------------------------------------------- +--R +-------------+ +--R | 3+-------+2 +--R \|c \|b x + a +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1394 +m0b:=a0-r0b +--R +--R +--R +-------------+ +--R 2 | 3+-------+2 2 +-+3+-------+ +--R (- b c x - 2a c x)\|c \|b x + a + (b c x + 2a c x)\|c \|b x + a +--R (7) --------------------------------------------------------------------- +--R 3+-------+ +--R 2\|b x + a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R +-------------+ +--R +-+ | 3+-------+2 2 2 3+-------+ +--R (b c x + a c)\|c \|c \|b x + a + (- b c x - a c )\|b x + a +--R (8) -------------------------------------------------------------- +--R +-------------+ +--R | 3+-------+2 +--R \|c \|b x + a +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1394 +t0:=1/(c/(a+b*x)^(3/2))^(2/3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------------------+2 +--R | c +--R |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1394 +r0a:=1/2*(a+b*x)/(b*(c/(a+b*x)^(3/2))^(2/3)) +--R +--R +--R b x + a +--R (2) -------------------------- +--R +-------------------+2 +--R | c +--R 2b |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1394 +r0b:=a*x/((c/(a+b*x)^(3/2))^(2/3)*(a+b*x))+_ + 1/2*b*x^2/((c/(a+b*x)^(3/2))^(2/3)*(a+b*x)) +--R +--R +--R 2 +--R b x + 2a x +--R (3) ---------------------------------- +--R +-------------------+2 +--R | c +--R (2b x + 2a) |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------------------+ +--R 2 3 2 2 | c +--R (b x + 3a b x + 2a x) |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R (4) --------------------------------------------- +--R +-------+ +--R 2c\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1002 + +--S 1003 of 1394 +m0a:=a0-r0a +--R +--R +--R 2 +--R a +--R (5) - ------------------------------------- +--R +-------------------+2 +--R +-------+2 | c +--R 2b \|b x + a |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1394 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1006 + +)clear all + +--S 1007 of 1394 +t0:=1/(c/(a+b*x)^(2/3))^(3/2) +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) --------------- +--R +-----------+ +--R | c +--R c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1394 +r0a:=1/2*(a+b*x)^(5/3)/(b*c*sqrt(c/(a+b*x)^(2/3))) +--R +--R +--R 3+-------+2 +--R (b x + a)\|b x + a +--R (2) -------------------- +--R +-----------+ +--R | c +--R 2b c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1394 +r0b:=a*x/(c*(a+b*x)^(1/3)*sqrt(c/(a+b*x)^(2/3)))+_ + 1/2*b*x^2/(c*(a+b*x)^(1/3)*sqrt(c/(a+b*x)^(2/3))) +--R +--R +--R 2 +--R b x + 2a x +--R (3) -------------------------- +--R +-----------+ +--R 3+-------+ | c +--R 2c\|b x + a |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x + 2a x +--R (4) ----------- +--R +-+ +--R 2c\|c +--R Type: Union(Expression(Integer),...) +--E 1010 + +--S 1011 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------+ +--R 2 2 | c +-+3+-------+2 +--R (b x + 2a b x) |----------- + (- b x - a)\|c \|b x + a +--R |3+-------+2 +--R \|\|b x + a +--R (5) ---------------------------------------------------------- +--R +-----------+ +--R +-+ | c +--R 2b c\|c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-----------+ +--R +-+ | c 3+-------+2 +--R (b x + a)\|c |----------- - c \|b x + a +--R |3+-------+2 +--R \|\|b x + a +--R (6) ------------------------------------------- +--R +-----------+ +--R 2 | c +--R c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1394 +m0b:=a0-r0b +--R +--R +--R +-----------+ +--R 2 3+-------+ | c 2 +-+ +--R (b x + 2a x)\|b x + a |----------- + (- b x - 2a x)\|c +--R |3+-------+2 +--R \|\|b x + a +--R (7) ----------------------------------------------------------- +--R +-----------+ +--R +-+3+-------+ | c +--R 2c\|c \|b x + a |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R +-----------+ +--R 3+-------+ | c +-+ +--R (- b x - a)\|b x + a |----------- + (b x + a)\|c +--R |3+-------+2 +--R \|\|b x + a +--R (8) --------------------------------------------------- +--R 2 +--R c +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 +--R b d x + 5b c d x + (10b c + a)d x + (10b c + 3a c)d x +--R + +--R 4 2 5 3 +--R (5b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1015 + +--S 1016 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/6*b*(c+d*x)^6/d +--R +--R +--R (2) +--R 1 6 6 5 5 5 2 1 4 4 10 3 3 3 +--R - b d x + b c d x + (- b c + - a)d x + (-- b c + a c)d x +--R 6 2 4 3 +--R + +--R 5 4 3 2 2 2 5 3 1 6 1 4 +--R (- b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 2 6 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1016 + +--S 1017 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 6 4 5 5 2 1 3 4 10 3 2 3 +--R - b d x + b c d x + (- b c + - a)d x + (-- b c + a c)d x +--R 6 2 4 3 +--R + +--R 5 4 3 2 2 5 3 +--R (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1017 + +--S 1018 of 1394 +m0:=a0-r0 +--R +--R +--R 1 6 1 4 +--R - - b c - - a c +--R 6 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1018 + +--S 1019 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1019 + +)clear all + +--S 1020 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^2 +--R +--R +--R (1) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d x + 7b c d x + (21b c + 2a b)d x + (35b c + 10a b c)d x +--R + +--R 2 4 2 2 3 3 2 5 3 2 2 2 +--R (35b c + 20a b c + a )d x + (21b c + 20a b c + 3a c)d x +--R + +--R 2 6 4 2 2 2 7 5 2 3 +--R (7b c + 10a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial(Integer) +--E 1020 + +--S 1021 of 1394 +r0:=1/4*a^2*(c+d*x)^4/d+1/3*a*b*(c+d*x)^6/d+1/8*b^2*(c+d*x)^8/d +--R +--R +--R (2) +--R 1 2 8 8 2 7 7 7 2 2 1 6 6 2 3 5 5 +--R - b d x + b c d x + (- b c + - a b)d x + (7b c + 2a b c)d x +--R 8 2 3 +--R + +--R 35 2 4 2 1 2 4 4 2 5 20 3 2 3 3 +--R (-- b c + 5a b c + - a )d x + (7b c + -- a b c + a c)d x +--R 4 4 3 +--R + +--R 7 2 6 4 3 2 2 2 2 2 7 5 2 3 1 2 8 +--R (- b c + 5a b c + - a c )d x + (b c + 2a b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 6 1 2 4 +--R - a b c + - a c +--R 3 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1021 + +--S 1022 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 8 2 6 7 7 2 2 1 5 6 2 3 4 5 +--R - b d x + b c d x + (- b c + - a b)d x + (7b c + 2a b c)d x +--R 8 2 3 +--R + +--R 35 2 4 2 1 2 3 4 2 5 20 3 2 2 3 +--R (-- b c + 5a b c + - a )d x + (7b c + -- a b c + a c)d x +--R 4 4 3 +--R + +--R 7 2 6 4 3 2 2 2 2 7 5 2 3 +--R (- b c + 5a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1022 + +--S 1023 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 8 1 6 1 2 4 +--R - - b c - - a b c - - a c +--R 8 3 4 +--R (4) ---------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1023 + +--S 1024 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1024 + +)clear all + +--S 1025 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^3 +--R +--R +--R (1) +--R 3 9 9 3 8 8 3 2 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + (36b c + 3a b )d x + (84b c + 21a b c)d x +--R + +--R 3 4 2 2 2 5 5 3 5 2 3 2 4 4 +--R (126b c + 63a b c + 3a b)d x + (126b c + 105a b c + 15a b c)d x +--R + +--R 3 6 2 4 2 2 3 3 3 +--R (84b c + 105a b c + 30a b c + a )d x +--R + +--R 3 7 2 5 2 3 3 2 2 +--R (36b c + 63a b c + 30a b c + 3a c)d x +--R + +--R 3 8 2 6 2 4 3 2 3 9 2 7 2 5 3 3 +--R (9b c + 21a b c + 15a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial(Integer) +--E 1025 + +--S 1026 of 1394 +r0:=-1/8*a*(a+b*(c+d*x)^2)^4/(b^2*d)+1/10*(a+b*(c+d*x)^2)^5/(b^2*d) +--R +--R +--R (2) +--R 1 5 10 10 5 9 9 9 5 2 3 4 8 8 5 3 4 7 7 +--R -- b d x + b c d x + (- b c + - a b )d x + (12b c + 3a b c)d x +--R 10 2 8 +--R + +--R 5 4 21 4 2 1 2 3 6 6 126 5 5 4 3 2 3 5 5 +--R (21b c + -- a b c + - a b )d x + (--- b c + 21a b c + 3a b c)d x +--R 2 2 5 +--R + +--R 5 6 105 4 4 15 2 3 2 1 3 2 4 4 +--R (21b c + --- a b c + -- a b c + - a b )d x +--R 4 2 4 +--R + +--R 5 7 4 5 2 3 3 3 2 3 3 +--R (12b c + 21a b c + 10a b c + a b c)d x +--R + +--R 9 5 8 21 4 6 15 2 3 4 3 3 2 2 2 2 +--R (- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 5 9 4 7 2 3 5 3 2 3 1 5 10 3 4 8 1 2 3 6 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c + - a b c +--R 10 8 2 +--R + +--R 1 3 2 4 1 5 +--R - a b c - -- a +--R 4 40 +--R / +--R 2 +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1026 + +--S 1027 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 10 3 8 9 9 3 2 3 2 7 8 3 3 2 6 7 +--R -- b d x + b c d x + (- b c + - a b )d x + (12b c + 3a b c)d x +--R 10 2 8 +--R + +--R 3 4 21 2 2 1 2 5 6 126 3 5 2 3 2 4 5 +--R (21b c + -- a b c + - a b)d x + (--- b c + 21a b c + 3a b c)d x +--R 2 2 5 +--R + +--R 3 6 105 2 4 15 2 2 1 3 3 4 +--R (21b c + --- a b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 3 7 2 5 2 3 3 2 3 +--R (12b c + 21a b c + 10a b c + a c)d x +--R + +--R 9 3 8 21 2 6 15 2 4 3 3 2 2 +--R (- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 9 2 7 2 5 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1027 + +--S 1028 of 1394 +m0:=a0-r0 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R - -- b c - - a b c - - a b c - - a b c + -- a +--R 10 8 2 4 40 +--R (4) --------------------------------------------------- +--R 2 +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1028 + +--S 1029 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1029 + +)clear all + +--S 1030 of 1394 +t0:=(2+x)/(1+(2+x)^2) +--R +--R +--R x + 2 +--R (1) ----------- +--R 2 +--R x + 4x + 5 +--R Type: Fraction(Polynomial(Integer)) +--E 1030 + +--S 1031 of 1394 +r0:=1/2*log(1+(2+x)^2) +--R +--R +--R 2 +--R log(x + 4x + 5) +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(x + 4x + 5) +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1394 +t0:=(2+x)/(1+(2+x)^2)^2 +--R +--R +--R x + 2 +--R (1) -------------------------- +--R 4 3 2 +--R x + 8x + 26x + 40x + 25 +--R Type: Fraction(Polynomial(Integer)) +--E 1035 + +--S 1036 of 1394 +r0:=(-1/2)/(1+(2+x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ----------- +--R 2 +--R x + 4x + 5 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1036 + +--S 1037 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R 2 +--R 2x + 8x + 10 +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1394 +t0:=(2+x)/(1+(2+x)^2)^3 +--R +--R +--R x + 2 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R x + 12x + 63x + 184x + 315x + 300x + 125 +--R Type: Fraction(Polynomial(Integer)) +--E 1040 + +--S 1041 of 1394 +r0:=(-1/4)/(1+(2+x)^2)^2 +--R +--R +--R 1 +--R - +--R 4 +--R (2) - -------------------------- +--R 4 3 2 +--R x + 8x + 26x + 40x + 25 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1041 + +--S 1042 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 2 +--R 4x + 32x + 104x + 160x + 100 +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1394 +t0:=(c+d*x)^5*(a+b*(c+d*x)^2)^p +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (d x + 5c d x + 10c d x + 10c d x + 5c d x + c ) +--R * +--R 2 2 2 p +--R (b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1394 +r0:=1/2*a^2*(a+b*(c+d*x)^2)^(1+p)/(b^3*d*(1+p))-_ + a*(a+b*(c+d*x)^2)^(2+p)/(b^3*d*(2+p))+1/2*(a+b*(c+d*x)^2)^(3+p)/_ + (b^3*d*(3+p)) +--R +--R +--R (2) +--R 2 2 2 2 p + 3 +--R (p + 3p + 2)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 p + 2 +--R (- 2a p - 8a p - 6a)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 2 2 2 p + 1 +--R (a p + 5a p + 6a )(b d x + 2b c d x + b c + a) +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 6 3 6 6 3 5 2 3 5 3 5 5 +--R (b d p + 3b d p + 2b d )x + (6b c d p + 18b c d p + 12b c d )x +--R + +--R 3 2 2 4 2 3 2 2 4 3 2 4 4 +--R ((15b c + a b )d p + (45b c + a b )d p + 30b c d )x +--R + +--R 3 3 2 3 2 3 3 2 3 3 3 3 3 +--R ((20b c + 4a b c)d p + (60b c + 4a b c)d p + 40b c d )x +--R + +--R 3 4 2 2 2 2 3 4 2 2 2 2 3 4 2 2 +--R ((15b c + 6a b c )d p + (45b c + 6a b c - 2a b)d p + 30b c d )x +--R + +--R 3 5 2 3 2 3 5 2 3 2 3 5 +--R ((6b c + 4a b c )d p + (18b c + 4a b c - 4a b c)d p + 12b c d)x +--R + +--R 3 6 2 4 2 3 6 2 4 2 2 3 6 3 +--R (b c + a b c )p + (3b c + a b c - 2a b c )p + 2b c + 2a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 2 3 6 3 6 6 3 5 2 3 5 3 5 5 +--R (b d p + 3b d p + 2b d )x + (6b c d p + 18b c d p + 12b c d )x +--R + +--R 3 2 2 4 2 3 2 2 4 3 2 4 4 +--R ((15b c + a b )d p + (45b c + a b )d p + 30b c d )x +--R + +--R 3 3 2 3 2 3 3 2 3 3 3 3 3 +--R ((20b c + 4a b c)d p + (60b c + 4a b c)d p + 40b c d )x +--R + +--R 3 4 2 2 2 2 3 4 2 2 2 2 3 4 2 2 +--R ((15b c + 6a b c )d p + (45b c + 6a b c - 2a b)d p + 30b c d )x +--R + +--R 3 5 2 3 2 3 5 2 3 2 3 5 +--R ((6b c + 4a b c )d p + (18b c + 4a b c - 4a b c)d p + 12b c d)x +--R + +--R 3 6 2 4 2 3 6 2 4 2 2 3 6 3 +--R (b c + a b c )p + (3b c + a b c - 2a b c )p + 2b c + 2a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R + +--R 2 2 2 2 p + 3 +--R (- p - 3p - 2)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 p + 2 +--R (2a p + 8a p + 6a)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 2 2 2 p + 1 +--R (- a p - 5a p - 6a )(b d x + 2b c d x + b c + a) +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1394 +t0:=(c+d*x)^4*(a+b*(c+d*x)^2)^p +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 2 2 2 p +--R (d x + 4c d x + 6c d x + 4c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1394 +--r0:=-3*a*(c+d*x)*(a+b*(c+d*x)^2)^(1+p)/(b^2*d*(3+2*p)*(5+2*p))+_ +-- (c+d*x)^3*(a+b*(c+d*x)^2)^(1+p)/(b*d*(5+2*p))+_ +-- 3*a^2*(c+d*x)*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*(c+d*x)^2/a)/(b^2*d*(3+2*p)*(5+2*p)*_ +-- ((a+b*(c+d*x)^2)/a)^p) +--E 1051 + +--S 1052 of 1394 +--a0:=integrate(t0,x) +--E 1052 + +--S 1053 of 1394 +--m0:=a0-r0 +--E 1053 + +--S 1054 of 1394 +--d0:=D(m0,x) +--E 1054 + +)clear all + +--S 1055 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^p +--R +--R +--R 3 3 2 2 2 3 2 2 2 p +--R (1) (d x + 3c d x + 3c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1394 +r0:=-1/2*a*(a+b*(c+d*x)^2)^(1+p)/(b^2*d*(1+p))+_ + 1/2*(a+b*(c+d*x)^2)^(2+p)/(b^2*d*(2+p)) +--R +--R +--R (2) +--R 2 2 2 p + 2 +--R (p + 1)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 p + 1 +--R (- a p - 2a)(b d x + 2b c d x + b c + a) +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 4 4 2 3 2 3 3 +--R (b d p + b d )x + (4b c d p + 4b c d )x +--R + +--R 2 2 2 2 2 2 2 2 3 2 3 +--R ((6b c + a b)d p + 6b c d )x + ((4b c + 2a b c)d p + 4b c d)x +--R + +--R 2 4 2 2 4 2 +--R (b c + a b c )p + b c - a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 4 4 2 3 2 3 3 +--R (b d p + b d )x + (4b c d p + 4b c d )x +--R + +--R 2 2 2 2 2 2 2 2 3 2 3 +--R ((6b c + a b)d p + 6b c d )x + ((4b c + 2a b c)d p + 4b c d)x +--R + +--R 2 4 2 2 4 2 +--R (b c + a b c )p + b c - a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R + +--R 2 2 2 p + 2 +--R (- p - 1)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 p + 1 +--R (a p + 2a)(b d x + 2b c d x + b c + a) +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1394 +t0:=(c+d*x)^2*(a+b*(c+d*x)^2)^p +--R +--R +--R 2 2 2 2 2 2 p +--R (1) (d x + 2c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1394 +--r0:=(c+d*x)*(a+b*(c+d*x)^2)^(1+p)/(b*d*(3+2*p))-_ +-- a*(c+d*x)*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*(c+d*x)^2/a)/(b*d*(3+2*p)*_ +-- ((a+b*(c+d*x)^2)/a)^p) +--E 1061 + +--S 1062 of 1394 +--a0:=integrate(t0,x) +--E 1062 + +--S 1063 of 1394 +--m0:=a0-r0 +--E 1063 + +--S 1064 of 1394 +--d0:=D(m0,x) +--E 1064 + +)clear all + +--S 1065 of 1394 +t0:=(c+d*x)*(a+b*(c+d*x)^2)^p +--R +--R +--R 2 2 2 p +--R (1) (d x + c)(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1394 +r0:=1/2*(a+b*(c+d*x)^2)^(1+p)/(b*d*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b d x + 2b c d x + b c + a) +--R (2) ----------------------------------- +--R 2b d p + 2b d +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2 2 2 p log(b d x + 2b c d x + b c + a) +--R (b d x + 2b c d x + b c + a)%e +--R (3) ------------------------------------------------------------------- +--R 2b d p + 2b d +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 +--R 2 2 2 p log(b d x + 2b c d x + b c + a) +--R (b d x + 2b c d x + b c + a)%e +--R + +--R 2 2 2 p + 1 +--R - (b d x + 2b c d x + b c + a) +--R / +--R 2b d p + 2b d +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1394 +t0:=(a+b*(c+d*x)^2)^p/(c+d*x) +--R +--R +--R 2 2 2 p +--R (b d x + 2b c d x + b c + a) +--R (1) ------------------------------- +--R d x + c +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1394 +--r0:=1/2*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(-p,-p,1-p,-a/(b*(c+d*x)^2))/_ +-- (d*p*((a+b*(c+d*x)^2)/(b*(c+d*x)^2))^p) +--E 1071 + +--S 1072 of 1394 +--a0:=integrate(t0,x) +--E 1072 + +--S 1073 of 1394 +--m0:=a0-r0 +--E 1073 + +--S 1074 of 1394 +--d0:=D(m0,x) +--E 1074 + +)clear all + +--S 1075 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (1) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1075 + +--S 1076 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/7*b*(c+d*x)^7/d +--R +--R +--R (2) +--R 1 7 7 6 6 2 5 5 3 1 4 4 4 3 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 2 6 3 1 7 1 4 +--R (3b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1076 + +--S 1077 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 6 7 5 6 2 4 5 3 1 3 4 4 2 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 6 3 +--R (3b c + - a c )d x + (b c + a c )x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1077 + +--S 1078 of 1394 +m0:=a0-r0 +--R +--R +--R 1 7 1 4 +--R - - b c - - a c +--R 7 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1078 + +--S 1079 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1079 + +)clear all + +--S 1080 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial(Integer) +--E 1080 + +--S 1081 of 1394 +r0:=1/4*a^2*(c+d*x)^4/d+2/7*a*b*(c+d*x)^7/d+1/10*b^2*(c+d*x)^10/d +--R +--R +--R (2) +--R 1 2 10 10 2 9 9 9 2 2 8 8 2 3 2 7 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 6 6 126 2 5 2 5 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 4 4 2 7 4 2 3 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 2 9 6 2 3 1 2 10 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )d x + -- b c +--R 2 2 10 +--R + +--R 2 7 1 2 4 +--R - a b c + - a c +--R 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1081 + +--S 1082 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 9 10 2 8 9 9 2 2 7 8 2 3 2 6 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 5 6 126 2 5 2 4 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 3 4 2 7 4 2 2 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 9 6 2 3 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1082 + +--S 1083 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R - -- b c - - a b c - - a c +--R 10 7 4 +--R (4) ------------------------------ +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1084 + +)clear all + +--S 1085 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 3 3 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial(Integer) +--E 1085 + +--S 1086 of 1394 +r0:=1/4*a^3*(c+d*x)^4/d+3/7*a^2*b*(c+d*x)^7/d+3/10*a*b^2*(c+d*x)^10/d+_ + 1/13*b^3*(c+d*x)^13/d +--R +--R +--R (2) +--R 1 3 13 13 3 12 12 3 2 11 11 3 3 3 2 10 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 9 9 3 5 27 2 2 8 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 7 7 3 7 2 4 2 6 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 1 3 13 3 2 10 3 2 7 +--R (b c + 3a b c + 3a b c + a c )d x + -- b c + -- a b c + - a b c +--R 13 10 7 +--R + +--R 1 3 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1086 + +--S 1087 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 12 13 3 11 12 3 2 10 11 3 3 3 2 9 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 8 9 3 5 27 2 2 7 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 6 7 3 7 2 4 2 5 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1087 + +--S 1088 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R - -- b c - -- a b c - - a b c - - a c +--R 13 10 7 4 +--R (4) ------------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1089 + +)clear all + +--S 1090 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (1) +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + a)d e x +--R + +--R 4 2 3 2 5 2 3 6 3 3 +--R (15b c + 3a c)d e x + (6b c + 3a c )d e x + (b c + a c )e +--R Type: Polynomial(Integer) +--E 1090 + +--S 1091 of 1394 +r0:=1/4*a*e^3*(c+d*x)^4/d+1/7*b*e^3*(c+d*x)^7/d +--R +--R +--R (2) +--R 1 7 3 7 6 3 6 2 5 3 5 3 1 4 3 4 +--R - b d e x + b c d e x + 3b c d e x + (5b c + - a)d e x +--R 7 4 +--R + +--R 4 3 3 3 5 3 2 2 3 2 6 3 3 +--R (5b c + a c)d e x + (3b c + - a c )d e x + (b c + a c )d e x +--R 2 +--R + +--R 1 7 1 4 3 +--R (- b c + - a c )e +--R 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1091 + +--S 1092 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 6 3 7 5 3 6 2 4 3 5 3 1 3 3 4 +--R - b d e x + b c d e x + 3b c d e x + (5b c + - a)d e x +--R 7 4 +--R + +--R 4 2 3 3 5 3 2 3 2 6 3 3 +--R (5b c + a c)d e x + (3b c + - a c )d e x + (b c + a c )e x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1092 + +--S 1093 of 1394 +m0:=a0-r0 +--R +--R +--R 1 7 1 4 3 +--R (- - b c - - a c )e +--R 7 4 +--R (4) --------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1094 + +)clear all + +--S 1095 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 9 3 9 2 8 3 8 2 2 7 3 7 2 3 6 3 6 +--R b d e x + 9b c d e x + 36b c d e x + (84b c + 2a b)d e x +--R + +--R 2 4 5 3 5 2 5 2 4 3 4 +--R (126b c + 12a b c)d e x + (126b c + 30a b c )d e x +--R + +--R 2 6 3 2 3 3 3 2 7 4 2 2 3 2 +--R (84b c + 40a b c + a )d e x + (36b c + 30a b c + 3a c)d e x +--R + +--R 2 8 5 2 2 3 2 9 6 2 3 3 +--R (9b c + 12a b c + 3a c )d e x + (b c + 2a b c + a c )e +--R Type: Polynomial(Integer) +--E 1095 + +--S 1096 of 1394 +r0:=1/4*a^2*e^3*(c+d*x)^4/d+2/7*a*b*e^3*(c+d*x)^7/d+1/10*b^2*e^3*(c+d*x)^10/d +--R +--R +--R (2) +--R 1 2 10 3 10 2 9 3 9 9 2 2 8 3 8 2 3 2 7 3 7 +--R -- b d e x + b c d e x + - b c d e x + (12b c + - a b)d e x +--R 10 2 7 +--R + +--R 2 4 6 3 6 126 2 5 2 5 3 5 +--R (21b c + 2a b c)d e x + (--- b c + 6a b c )d e x +--R 5 +--R + +--R 2 6 3 1 2 4 3 4 2 7 4 2 3 3 3 +--R (21b c + 10a b c + - a )d e x + (12b c + 10a b c + a c)d e x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 3 2 2 9 6 2 3 3 +--R (- b c + 6a b c + - a c )d e x + (b c + 2a b c + a c )d e x +--R 2 2 +--R + +--R 1 2 10 2 7 1 2 4 3 +--R (-- b c + - a b c + - a c )e +--R 10 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1096 + +--S 1097 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 9 3 10 2 8 3 9 9 2 2 7 3 8 2 3 2 6 3 7 +--R -- b d e x + b c d e x + - b c d e x + (12b c + - a b)d e x +--R 10 2 7 +--R + +--R 2 4 5 3 6 126 2 5 2 4 3 5 +--R (21b c + 2a b c)d e x + (--- b c + 6a b c )d e x +--R 5 +--R + +--R 2 6 3 1 2 3 3 4 2 7 4 2 2 3 3 +--R (21b c + 10a b c + - a )d e x + (12b c + 10a b c + a c)d e x +--R 4 +--R + +--R 9 2 8 5 3 2 2 3 2 2 9 6 2 3 3 +--R (- b c + 6a b c + - a c )d e x + (b c + 2a b c + a c )e x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1097 + +--S 1098 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 10 2 7 1 2 4 3 +--R (- -- b c - - a b c - - a c )e +--R 10 7 4 +--R (4) ---------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1098 + +--S 1099 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1099 + +)clear all + +--S 1100 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 12 3 12 3 11 3 11 3 2 10 3 10 3 3 2 9 3 9 +--R b d e x + 12b c d e x + 66b c d e x + (220b c + 3a b )d e x +--R + +--R 3 4 2 8 3 8 3 5 2 2 7 3 7 +--R (495b c + 27a b c)d e x + (792b c + 108a b c )d e x +--R + +--R 3 6 2 3 2 6 3 6 3 7 2 4 2 5 3 5 +--R (924b c + 252a b c + 3a b)d e x + (792b c + 378a b c + 18a b c)d e x +--R + +--R 3 8 2 5 2 2 4 3 4 +--R (495b c + 378a b c + 45a b c )d e x +--R + +--R 3 9 2 6 2 3 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 3 2 +--R (66b c + 108a b c + 45a b c + 3a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 3 +--R (12b c + 27a b c + 18a b c + 3a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Polynomial(Integer) +--E 1100 + +--S 1101 of 1394 +r0:=1/4*a^3*e^3*(c+d*x)^4/d+3/7*a^2*b*e^3*(c+d*x)^7/d+_ + 3/10*a*b^2*e^3*(c+d*x)^10/d+1/13*b^3*e^3*(c+d*x)^13/d +--R +--R +--R (2) +--R 1 3 13 3 13 3 12 3 12 3 2 11 3 11 3 3 3 2 10 3 10 +--R -- b d e x + b c d e x + 6b c d e x + (22b c + -- a b )d e x +--R 13 10 +--R + +--R 3 4 2 9 3 9 3 5 27 2 2 8 3 8 +--R (55b c + 3a b c)d e x + (99b c + -- a b c )d e x +--R 2 +--R + +--R 3 6 2 3 3 2 7 3 7 3 7 2 4 2 6 3 6 +--R (132b c + 36a b c + - a b)d e x + (132b c + 63a b c + 3a b c)d e x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 3 5 +--R (99b c + --- a b c + 9a b c )d e x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 3 4 +--R (55b c + 63a b c + 15a b c + - a )d e x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d e x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 3 2 +--R (6b c + -- a b c + 9a b c + - a c )d e x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )d e x +--R + +--R 1 3 13 3 2 10 3 2 7 1 3 4 3 +--R (-- b c + -- a b c + - a b c + - a c )e +--R 13 10 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1101 + +--S 1102 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 12 3 13 3 11 3 12 3 2 10 3 11 3 3 3 2 9 3 10 +--R -- b d e x + b c d e x + 6b c d e x + (22b c + -- a b )d e x +--R 13 10 +--R + +--R 3 4 2 8 3 9 3 5 27 2 2 7 3 8 +--R (55b c + 3a b c)d e x + (99b c + -- a b c )d e x +--R 2 +--R + +--R 3 6 2 3 3 2 6 3 7 3 7 2 4 2 5 3 6 +--R (132b c + 36a b c + - a b)d e x + (132b c + 63a b c + 3a b c)d e x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 3 5 +--R (99b c + --- a b c + 9a b c )d e x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d e x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 3 +--R (22b c + 36a b c + 15a b c + a c)d e x +--R + +--R 3 11 27 2 8 2 5 3 3 2 3 2 +--R (6b c + -- a b c + 9a b c + - a c )d e x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e x +--R Type: Polynomial(Fraction(Integer)) +--E 1102 + +--S 1103 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 3 +--R (- -- b c - -- a b c - - a b c - - a c )e +--R 13 10 7 4 +--R (4) ----------------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1104 + +)clear all + +--S 1105 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1105 + +--S 1106 of 1394 +r0:=1/2*(c+d*x)^2/(b*d)+1/3*a^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(b^(5/3)*d)-1/6*a^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(b^(5/3)*d)+_ + a^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 3+-+ 3+-+ 3+-+2 (2d x + 2c)\|b - \|a +--R 2\|3 \|a log((d x + c)\|b + \|a ) - 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+2 +--R (3d x + 6c d x + 3c )\|3 \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 2 2 +--R - \|3 |-- log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a \|b 2 2 +-+ +--R 6 |-- atan(----------------------------------- + (3d x + 6c d x)\|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R - 2\|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R +-+ |a 3+-+2 +--R \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a 3+-+2 \|b 2 +-+3+-+2 +--R 6 |-- \|b atan(----------------------------------- - 3c \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1110 + +--S 1111 of 1394 +r0:=x/b-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(b^(4/3)*d)+_ + 1/6*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(b^(4/3)*d)+a^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ 3+-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2\|3 \|a log((d x + c)\|b + \|a ) - 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+ +--R 6d x\|3 \|b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R +-+ | a | a | a 2 2 2 +--R - \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a | a +--R 2\|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(---------------------------- + 6d x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R 2\|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 2 2 +--R - \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +--R 2\|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(----------------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1115 + +--S 1116 of 1394 +r0:=1/3*log(a+b*(c+d*x)^3)/(b*d) +--R +--R +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R (2) --------------------------------------------- +--R 3b d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R (3) --------------------------------------------- +--R 3b d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3) +--R +--R +--R d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1120 + +--S 1121 of 1394 +r0:=-1/3*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(2/3)*d)+_ + 1/6*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(1/3)*_ + b^(2/3)*d)-atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2\|3 log((d x + c)\|b + \|a ) + 6atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6d\|3 \|a \|b +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + (4b c + a)d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1125 + +--S 1126 of 1394 +r0:=log(c+d*x)/(a*d)-1/3*log(a+b*(c+d*x)^3)/(a*d) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (2) --------------------------------------------------------------- +--R 3a d +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (3) --------------------------------------------------------------- +--R 3a d +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 +--R b d x + 5b c d x + 10b c d x + (10b c + a)d x + (5b c + 2a c)d x +--R + +--R 5 2 +--R b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1130 + +--S 1131 of 1394 +r0:=(-1)/(a*d*(c+d*x))+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*d)-1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(4/3)*d)+b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ +--R (- d x - c)\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R (2d x + 2c)\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +-+3+-+ +--R (- 6d x - 6c)\|b atan(----------------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R (6a d x + 6a c d)\|3 \|a +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R (6a d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1135 + +--S 1136 of 1394 +r0:=(-1/2)/(a*d*(c+d*x)^2)-1/3*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(5/3)*d)+1/6*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(5/3)*d)+_ + b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+2 +--R (d x + 2c d x + c )\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 2 2 +-+3+-+2 3+-+ 3+-+ +--R (- 2d x - 4c d x - 2c )\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (2d x + 2c)\|b - \|a +-+3+-+2 +--R (- 6d x - 12c d x - 6c )\|b atan(----------------------) - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 2 2 +-+3+-+2 +--R (6a d x + 12a c d x + 6a c d)\|3 \|a +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 2 2 2 +-+ +--R (6a d x + 12a c d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + (35b c + a)d x + (35b c + 4a c)d x +--R + +--R 5 2 2 2 6 3 7 4 +--R (21b c + 6a c )d x + (7b c + 4a c )d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1140 + +--S 1141 of 1394 +r0:=(-1/3)/(a*d*(c+d*x)^3)-b*log(c+d*x)/(a^2*d)+_ + 1/3*b*log(a+b*(c+d*x)^3)/(a^2*d) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3a d x + 9a c d x + 9a c d x + 3a c d +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3a d x + 9a c d x + 9a c d x + 3a c d +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1145 + +--S 1146 of 1394 +r0:=-1/3*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3))-_ + 2/9*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(5/3)*d)+_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(1/3)*b^(5/3)*d)-2/3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d x + 3b c d x + 3b c d x + b c + a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (- 3d x - 6c d x - 3c )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (- 3d x - 6c d x - 3c )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1150 + +--S 1151 of 1394 +r0:=1/3*(-c-d*x)/(b*d*(a+b*(c+d*x)^3))+1/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(2/3)*b^(4/3)*d)-1/18*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(2/3)*b^(4/3)*d)-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*_ + sqrt(3)))/(a^(2/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (- 6d x - 6c)\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (- 6d x - 6c)\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 2 2 +--R d x + 2c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1155 + +--S 1156 of 1394 +r0:=(-1/3)/(b*d*(a+b*(c+d*x)^3)) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - --------------------------------------------- +--R 2 4 3 2 3 2 2 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1156 + +--S 1157 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------ +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3b d x + 9b c d x + 9b c d x + (3b c + 3a b)d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1160 + +--S 1161 of 1394 +r0:=1/3*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3))-1/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(4/3)*b^(2/3)*d)+1/18*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(2/3)*d)-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d x + 3b c d x + 3b c d x + b c + a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (6d x + 12c d x + 6c )\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d x + 12c d x + 6c )\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1394 +t0:=1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1165 + +--S 1166 of 1394 +r0:=1/3*(c+d*x)/(a*d*(a+b*(c+d*x)^3))+2/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(5/3)*b^(1/3)*d)-1/9*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(1/3)*d)-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (3d x + 3c)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d x + 7b c d x + 21b c d x + (35b c + 2a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (35b c + 8a b c)d x + (21b c + 12a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (7b c + 8a b c + a )d x + b c + 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1170 + +--S 1171 of 1394 +r0:=1/3/(a*d*(a+b*(c+d*x)^3))+log(c+d*x)/(a^2*d)-1/3*log(a+b*(c+d*x)^3)/(a^2*d) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d x + 9a b c d x + 9a b c d x + (3a b c + 3a )d +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d x + 9a b c d x + 9a b c d x + (3a b c + 3a )d +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R b d x + 8b c d x + 28b c d x + (56b c + 2a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (70b c + 10a b c)d x + (56b c + 20a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 2 8 +--R (28b c + 20a b c + a )d x + (8b c + 10a b c + 2a c)d x + b c +--R + +--R 5 2 2 +--R 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1175 + +--S 1176 of 1394 +r0:=(-4/3)/(a^2*d*(c+d*x))+1/3/(a*d*(c+d*x)*(a+b*(c+d*x)^3))+_ + 4/9*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(7/3)*d)-_ + 2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(7/3)*d)+4/3*b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(7/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 12b d x - 48b c d x - 72b c d x + (- 48b c - 12a)d x - 12b c +--R + +--R - 12a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 \|a +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 4\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 12\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a d\|3 \|a +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1180 + +--S 1181 of 1394 +r0:=(-5/6)/(a^2*d*(c+d*x)^2)+1/3/(a*d*(c+d*x)^2*(a+b*(c+d*x)^3))-_ + 5/9*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(8/3)*d)+_ + 5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(8/3)*d)+5/3*b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(8/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 \|a +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 30\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a d\|3 \|a +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 10 10 2 9 9 2 2 8 8 2 3 7 7 +--R b d x + 10b c d x + 45b c d x + (120b c + 2a b)d x +--R + +--R 2 4 6 6 2 5 2 5 5 +--R (210b c + 14a b c)d x + (252b c + 42a b c )d x +--R + +--R 2 6 3 2 4 4 2 7 4 2 3 3 +--R (210b c + 70a b c + a )d x + (120b c + 70a b c + 4a c)d x +--R + +--R 2 8 5 2 2 2 2 2 9 6 2 3 2 10 +--R (45b c + 42a b c + 6a c )d x + (10b c + 14a b c + 4a c )d x + b c +--R + +--R 7 2 4 +--R 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1185 + +--S 1186 of 1394 +r0:=(-2/3)/(a^2*d*(c+d*x)^3)+1/3/(a*d*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 2*b*log(c+d*x)/(a^3*d)+2/3*b*log(a+b*(c+d*x)^3)/(a^3*d) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 4 4 3 +--R 3a b d x + 18a b c d x + 45a b c d x + (60a b c + 3a )d x +--R + +--R 3 4 4 3 2 3 5 4 2 2 3 6 4 3 +--R (45a b c + 9a c)d x + (18a b c + 9a c )d x + (3a b c + 3a c )d +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 4 4 3 +--R 3a b d x + 18a b c d x + 45a b c d x + (60a b c + 3a )d x +--R + +--R 3 4 4 3 2 3 5 4 2 2 3 6 4 3 +--R (45a b c + 9a c)d x + (18a b c + 9a c )d x + (3a b c + 3a c )d +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1190 + +--S 1191 of 1394 +r0:=-1/6*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3)^2)+1/9*(c+d*x)^2/_ + (a*b*d*(a+b*(c+d*x)^3))-1/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*b^(5/3)*d)+1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(5/3)*d)-1/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 90b c - 36a b c)d x + (- 36b c - 36a b c )d x - 6b c +--R + +--R 3 2 +--R - 12a b c - 6a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1195 + +--S 1196 of 1394 +r0:=1/6*(-c-d*x)/(b*d*(a+b*(c+d*x)^3)^2)+1/18*(c+d*x)/_ + (a*b*d*(a+b*(c+d*x)^3))+1/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(4/3)*d)-1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(4/3)*d)-1/9*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 2 2 2 +--R d x + 2c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1200 + +--S 1201 of 1394 +r0:=(-1/6)/(b*d*(a+b*(c+d*x)^3)^2) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 6 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 3 6 2 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1201 + +--S 1202 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x +--R + +--R 3 6 2 3 2 +--R (6b c + 12a b c + 6a b)d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1205 + +--S 1206 of 1394 +r0:=1/6*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3)^2)+2/9*(c+d*x)^2/(a^2*d*_ + (a+b*(c+d*x)^3))-2/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(7/3)*b^(2/3)*d)+1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(7/3)*b^(2/3)*d)-2/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d x - 24b c d x - 60b c d x + (- 80b c - 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 60b c - 24a b c)d x + (- 24b c - 24a b c )d x - 4b c - 8a b c +--R + +--R 2 +--R - 4a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 12b d x + 72b c d x + 180b c d x + (240b c + 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (180b c + 72a b c)d x + (72b c + 72a b c )d x + 12b c + 24a b c +--R + +--R 2 +--R 12a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 12b d x - 72b c d x - 180b c d x + (- 240b c - 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 180b c - 72a b c)d x + (- 72b c - 72a b c )d x - 12b c +--R + +--R 3 2 +--R - 24a b c - 12a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1394 +t0:=1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1394 +r0:=1/6*(c+d*x)/(a*d*(a+b*(c+d*x)^3)^2)+5/18*(c+d*x)/_ + (a^2*d*(a+b*(c+d*x)^3))+5/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(8/3)*b^(1/3)*d)-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(8/3)*b^(1/3)*d)-5/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 10\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 30\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 10 10 3 9 9 3 2 8 8 3 3 2 7 7 +--R b d x + 10b c d x + 45b c d x + (120b c + 3a b )d x +--R + +--R 3 4 2 6 6 3 5 2 2 5 5 +--R (210b c + 21a b c)d x + (252b c + 63a b c )d x +--R + +--R 3 6 2 3 2 4 4 3 7 2 4 2 3 3 +--R (210b c + 105a b c + 3a b)d x + (120b c + 105a b c + 12a b c)d x +--R + +--R 3 8 2 5 2 2 2 2 +--R (45b c + 63a b c + 18a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 3 +--R (10b c + 21a b c + 12a b c + a )d x + b c + 3a b c + 3a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1394 +r0:=1/6/(a*d*(a+b*(c+d*x)^3)^2)+1/3/(a^2*d*(a+b*(c+d*x)^3))+_ + log(c+d*x)/(a^3*d)-1/3*log(a+b*(c+d*x)^3)/(a^3*d) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d x + 36a b c d x + 90a b c d x + (120a b c + 12a b)d x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d x + (36a b c + 36a b c )d x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d x + 36a b c d x + 90a b c d x + (120a b c + 12a b)d x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d x + (36a b c + 36a b c )d x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 11 11 3 10 10 3 2 9 9 3 3 2 8 8 +--R b d x + 11b c d x + 55b c d x + (165b c + 3a b )d x +--R + +--R 3 4 2 7 7 3 5 2 2 6 6 +--R (330b c + 24a b c)d x + (462b c + 84a b c )d x +--R + +--R 3 6 2 3 2 5 5 3 7 2 4 2 4 4 +--R (462b c + 168a b c + 3a b)d x + (330b c + 210a b c + 15a b c)d x +--R + +--R 3 8 2 5 2 2 3 3 +--R (165b c + 168a b c + 30a b c )d x +--R + +--R 3 9 2 6 2 3 3 2 2 +--R (55b c + 84a b c + 30a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 11 2 8 2 5 +--R (11b c + 24a b c + 15a b c + 2a c)d x + b c + 3a b c + 3a b c +--R + +--R 3 2 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1394 +r0:=(-14/9)/(a^3*d*(c+d*x))+1/6/(a*d*(c+d*x)*(a+b*(c+d*x)^3)^2)+_ + 7/18/(a^2*d*(c+d*x)*(a+b*(c+d*x)^3))+14/27*b^(1/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(10/3)*d)-7/27*b^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(10/3)*d)+_ + 14/9*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(10/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 84b d x - 588b c d x - 1764b c d x + (- 2940b c - 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 2940b c - 672a b c)d x + (- 1764b c - 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 588b c - 672a b c - 84a )d x - 84b c - 168a b c - 84a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 7\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 14\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 42\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1394 +r0:=(-10/9)/(a^3*d*(c+d*x)^2)+1/6/(a*d*(c+d*x)^2*(a+b*(c+d*x)^3)^2)+_ + 4/9/(a^2*d*(c+d*x)^2*(a+b*(c+d*x)^3))-20/27*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(11/3)*d)+10/27*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(11/3)*d)+_ + 20/9*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(11/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+3+-+2 +--R \|3 \|a +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 10\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 20\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 60\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 13 13 3 12 12 3 2 11 11 3 3 2 10 10 +--R b d x + 13b c d x + 78b c d x + (286b c + 3a b )d x +--R + +--R 3 4 2 9 9 3 5 2 2 8 8 +--R (715b c + 30a b c)d x + (1287b c + 135a b c )d x +--R + +--R 3 6 2 3 2 7 7 3 7 2 4 2 6 6 +--R (1716b c + 360a b c + 3a b)d x + (1716b c + 630a b c + 21a b c)d x +--R + +--R 3 8 2 5 2 2 5 5 +--R (1287b c + 756a b c + 63a b c )d x +--R + +--R 3 9 2 6 2 3 3 4 4 +--R (715b c + 630a b c + 105a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (286b c + 360a b c + 105a b c + 4a c)d x +--R + +--R 3 11 2 8 2 5 3 2 2 2 +--R (78b c + 135a b c + 63a b c + 6a c )d x +--R + +--R 3 12 2 9 2 6 3 3 3 13 2 10 2 7 +--R (13b c + 30a b c + 21a b c + 4a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 4 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1394 +r0:=(-1)/(a^3*d*(c+d*x)^3)+1/6/(a*d*(c+d*x)^3*(a+b*(c+d*x)^3)^2)+_ + 1/2/(a^2*d*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 3*b*log(c+d*x)/(a^4*d)+b*log(a+b*(c+d*x)^3)/(a^4*d) +--R +--R +--R (2) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 9 4 2 9 8 4 2 2 8 7 4 2 3 5 7 6 +--R 6a b d x + 54a b c d x + 216a b c d x + (504a b c + 12a b)d x +--R + +--R 4 2 4 5 6 5 4 2 5 5 2 5 4 +--R (756a b c + 72a b c)d x + (756a b c + 180a b c )d x +--R + +--R 4 2 6 5 3 6 4 3 4 2 7 5 4 6 3 2 +--R (504a b c + 240a b c + 6a )d x + (216a b c + 180a b c + 18a c)d x +--R + +--R 4 2 8 5 5 6 2 2 4 2 9 5 6 6 3 +--R (54a b c + 72a b c + 18a c )d x + (6a b c + 12a b c + 6a c )d +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 9 4 2 9 8 4 2 2 8 7 4 2 3 5 7 6 +--R 6a b d x + 54a b c d x + 216a b c d x + (504a b c + 12a b)d x +--R + +--R 4 2 4 5 6 5 4 2 5 5 2 5 4 +--R (756a b c + 72a b c)d x + (756a b c + 180a b c )d x +--R + +--R 4 2 6 5 3 6 4 3 4 2 7 5 4 6 3 2 +--R (504a b c + 240a b c + 6a )d x + (216a b c + 180a b c + 18a c)d x +--R + +--R 4 2 8 5 5 6 2 2 4 2 9 5 6 6 3 +--R (54a b c + 72a b c + 18a c )d x + (6a b c + 12a b c + 6a c )d +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R (1) ------------------------------------------------ +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1394 +r0:=1/2*e^4*(c+d*x)^2/(b*d)+1/3*a^(2/3)*e^4*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (b^(5/3)*d)-1/6*a^(2/3)*e^4*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(b^(5/3)*d)+a^(2/3)*e^4*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 4 +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 +-+3+-+2 3+-+ 3+-+ +--R 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 4 3+-+2 (2d x + 2c)\|b - \|a +--R - 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 4 2 4 2 4 +-+3+-+2 +--R (3d e x + 6c d e x + 3c e )\|3 \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R 4 +-+ |a |a +--R 2e \|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R 4 +-+ |a +--R e \|3 |-- +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R 4 |a \|b +--R 6e |-- atan(-----------------------------------) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R + +--R 2 4 2 4 +-+ +--R (3d e x + 6c d e x)\|3 +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 +-+3+-+2 3+-+ 3+-+ +--R - 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R 4 +-+ |a 3+-+2 |a +--R 2e \|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R 4 +-+ |a 3+-+2 +--R e \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 3+-+ 3+-+ +--R 4 3+-+2 (2d x + 2c)\|b - \|a +--R 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R 4 |a 3+-+2 \|b 2 4 +-+3+-+2 +--R 6e |-- \|b atan(----------------------------------- - 3c e \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1394 +r0:=e^3*x/b-1/3*a^(1/3)*e^3*log(a^(1/3)+b^(1/3)*(c+d*x))/(b^(4/3)*d)+_ + 1/6*a^(1/3)*e^3*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*_ + (c+d*x)^2)/(b^(4/3)*d)+a^(1/3)*e^3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R - 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ (2d x + 2c)\|b - \|a 3 +-+3+-+ +--R - 6e \|a atan(---------------------- + 6d e x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R 3 +-+ | a | a | a 2 2 2 +--R - e \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R 3 +-+ | a | a +--R 2e \|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R 3 | a \| b 3 +-+ +--R - 6e 3|- - atan(---------------------------- + 6d e x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R 3 +-+ | a 3+-+ | a | a 2 2 2 +--R - e \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R 3 +-+ | a 3+-+ | a +--R 2e \|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ (2d x + 2c)\|b - \|a +--R 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R 3 | a 3+-+ \| b +--R - 6e 3|- - \|b atan(----------------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1394 +r0:=1/3*e^2*log(a+b*(c+d*x)^3)/(b*d) +--R +--R +--R 2 3 3 2 2 2 3 +--R e log(b d x + 3b c d x + 3b c d x + b c + a) +--R (2) ----------------------------------------------- +--R 3b d +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 2 2 2 3 +--R e log(b d x + 3b c d x + 3b c d x + b c + a) +--R (3) ----------------------------------------------- +--R 3b d +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3) +--R +--R +--R d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1394 +r0:=-1/3*e*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(2/3)*d)+_ + 1/6*e*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(1/3)*b^(2/3)*d)-e*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e\|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2e\|3 log((d x + c)\|b + \|a ) + 6e atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6d\|3 \|a \|b +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R e\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2e\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d e x + 4b c d e x + 6b c d e x + (4b c + a)d e x + (b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1394 +r0:=log(c+d*x)/(a*d*e)-1/3*log(a+b*(c+d*x)^3)/(a*d*e) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (2) --------------------------------------------------------------- +--R 3a d e +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (3) --------------------------------------------------------------- +--R 3a d e +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 +--R b d e x + 5b c d e x + 10b c d e x + (10b c + a)d e x +--R + +--R 4 2 5 2 2 +--R (5b c + 2a c)d e x + (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1394 +r0:=(-1)/(a*d*e^2*(c+d*x))+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*d*e^2)-1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*d*e^2)+b^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ +--R (- d x - c)\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R (2d x + 2c)\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +-+3+-+ +--R (- 6d x - 6c)\|b atan(----------------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 2 2 +-+3+-+ +--R (6a d e x + 6a c d e )\|3 \|a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 2 2 +-+ +--R (6a d e x + 6a c d e )\|3 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 6a d e \|3 \|a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + a)d e x +--R + +--R 4 2 3 2 5 2 3 6 3 3 +--R (15b c + 3a c)d e x + (6b c + 3a c )d e x + (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1394 +r0:=(-1/2)/(a*d*e^3*(c+d*x)^2)-1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*d*e^3)+1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*d*e^3)+b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+2 +--R (d x + 2c d x + c )\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 2 2 +-+3+-+2 3+-+ 3+-+ +--R (- 2d x - 4c d x - 2c )\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (2d x + 2c)\|b - \|a +-+3+-+2 +--R (- 6d x - 12c d x - 6c )\|b atan(----------------------) - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 3 2 2 3 2 3 +-+3+-+2 +--R (6a d e x + 12a c d e x + 6a c d e )\|3 \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 3 2 2 3 2 3 +-+ +--R (6a d e x + 12a c d e x + 6a c d e )\|3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 6a d e \|3 \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 4 7 6 4 6 2 5 4 5 3 4 4 4 +--R b d e x + 7b c d e x + 21b c d e x + (35b c + a)d e x +--R + +--R 4 3 4 3 5 2 2 4 2 6 3 4 +--R (35b c + 4a c)d e x + (21b c + 6a c )d e x + (7b c + 4a c )d e x +--R + +--R 7 4 4 +--R (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1394 +r0:=(-1/3)/(a*d*e^4*(c+d*x)^3)-b*log(c+d*x)/(a^2*d*e^4)+_ + 1/3*b*log(a+b*(c+d*x)^3)/(a^2*d*e^4) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 4 3 2 3 4 2 2 2 2 4 2 3 4 +--R 3a d e x + 9a c d e x + 9a c d e x + 3a c d e +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 4 3 2 3 4 2 2 2 2 4 2 3 4 +--R 3a d e x + 9a c d e x + 9a c d e x + 3a c d e +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1394 +r0:=-1/3*e^4*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3))-2/9*e^4*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(1/3)*b^(5/3)*d)+1/9*e^4*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(1/3)*b^(5/3)*d)-_ + 2/3*e^4*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (b d e x + 3b c d e x + 3b c d e x + (b c + a)e )\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (- 2b d e x - 6b c d e x - 6b c d e x + (- 2b c - 2a)e )\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 4 2 4 2 4 +-+3+-+3+-+2 +--R (- 3d e x - 6c d e x - 3c e )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +--R (- 6b d e x - 18b c d e x - 18b c d e x + (- 6b c - 6a)e ) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 4 2 4 2 4 +-+3| 2 +--R (- 3d e x - 6c d e x - 3c e )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R 4 +-+3| 2 +--R e \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R 4 +-+3| 2 3+-+ 3+-+ +--R 2e \|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R 4 +-+3+-+3+-+2 +--R e \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R 4 +-+3+-+3+-+2 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 4 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 4 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e \|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1394 +r0:=-1/3*e^3*(c+d*x)/(b*d*(a+b*(c+d*x)^3))+1/9*e^3*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(2/3)*b^(4/3)*d)-1/18*e^3*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(2/3)*b^(4/3)*d)-_ + 1/3*e^3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 +-+3+-+2 3+-+ +--R (- 6d e x - 6c e )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R +---+ +--R 3| 2 +--R log((d x + c)\|a b + a) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R 3 3 +-+3| 2 +--R (- 6d e x - 6c e )\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +-+3+-+2 3+-+ +--R e \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 +-+3+-+2 3+-+ 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R 3 +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R 3 +-+3| 2 3+-+ 3+-+ +--R - 2e \|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6e \|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1394 +r0:=-1/3*e^2/(b*d*(a+b*(c+d*x)^3)) +--R +--R +--R 1 2 +--R - e +--R 3 +--R (2) - --------------------------------------------- +--R 2 4 3 2 3 2 2 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1286 + +--S 1287 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R e +--R (3) - ------------------------------------------------ +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3b d x + 9b c d x + 9b c d x + (3b c + 3a b)d +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1394 +r0:=1/3*e*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3))-1/9*e*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(4/3)*b^(2/3)*d)+1/18*e*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(2/3)*d)-_ + 1/3*e*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d e x + 3b c d e x + 3b c d e x + (b c + a)e)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d e x - 6b c d e x - 6b c d e x + (- 2b c - 2a)e)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (6d e x + 12c d e x + 6c e)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d e x - 18b c d e x - 18b c d e x + (- 6b c - 6a)e) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d e x + 12c d e x + 6c e)\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1394 +t0:=1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1394 +r0:=1/3*(c+d*x)/(a*d*(a+b*(c+d*x)^3))+2/9*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(1/3)*d)-1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(1/3)*d)-2/3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (3d x + 3c)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d e x + 7b c d e x + 21b c d e x + (35b c + 2a b)d e x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (35b c + 8a b c)d e x + (21b c + 12a b c )d e x +--R + +--R 2 6 3 2 2 7 4 2 +--R (7b c + 8a b c + a )d e x + (b c + 2a b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1394 +r0:=1/3/(a*d*e*(a+b*(c+d*x)^3))+log(c+d*x)/(a^2*d*e)-_ + 1/3*log(a+b*(c+d*x)^3)/(a^2*d*e) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d e x + 9a b c d e x + 9a b c d e x + (3a b c + 3a )d e +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d e x + 9a b c d e x + 9a b c d e x + (3a b c + 3a )d e +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 8 2 8 2 7 2 7 2 2 6 2 6 2 3 5 2 5 +--R b d e x + 8b c d e x + 28b c d e x + (56b c + 2a b)d e x +--R + +--R 2 4 4 2 4 2 5 2 3 2 3 +--R (70b c + 10a b c)d e x + (56b c + 20a b c )d e x +--R + +--R 2 6 3 2 2 2 2 2 7 4 2 2 +--R (28b c + 20a b c + a )d e x + (8b c + 10a b c + 2a c)d e x +--R + +--R 2 8 5 2 2 2 +--R (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1394 +r0:=(-4/3)/(a^2*d*e^2*(c+d*x))+1/3/(a*d*e^2*(c+d*x)*(a+b*(c+d*x)^3))+_ + 4/9*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(7/3)*d*e^2)-_ + 2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(7/3)*d*e^2)+4/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 12b d x - 48b c d x - 72b c d x + (- 48b c - 12a)d x - 12b c +--R + +--R - 12a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 \|a +--R / +--R 2 5 2 4 2 4 2 3 2 2 3 2 2 2 3 3 2 2 +--R 9a b d e x + 36a b c d e x + 54a b c d e x + (36a b c + 9a )d e x +--R + +--R 2 4 3 2 +--R (9a b c + 9a c)d e +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 2 4 2 4 2 3 2 2 3 2 2 2 3 3 2 2 +--R 9a b d e x + 36a b c d e x + 54a b c d e x + (36a b c + 9a )d e x +--R + +--R 2 4 3 2 +--R (9a b c + 9a c)d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 4\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 12\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 2 +-+3+-+ +--R 9a d e \|3 \|a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 9 3 9 2 8 3 8 2 2 7 3 7 2 3 6 3 6 +--R b d e x + 9b c d e x + 36b c d e x + (84b c + 2a b)d e x +--R + +--R 2 4 5 3 5 2 5 2 4 3 4 +--R (126b c + 12a b c)d e x + (126b c + 30a b c )d e x +--R + +--R 2 6 3 2 3 3 3 2 7 4 2 2 3 2 +--R (84b c + 40a b c + a )d e x + (36b c + 30a b c + 3a c)d e x +--R + +--R 2 8 5 2 2 3 2 9 6 2 3 3 +--R (9b c + 12a b c + 3a c )d e x + (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1394 +r0:=(-5/6)/(a^2*d*e^3*(c+d*x)^2)+1/3/(a*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3))-_ + 5/9*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(8/3)*d*e^3)+_ + 5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(8/3)*d*e^3)+5/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 \|a +--R / +--R 2 6 3 5 2 5 3 4 2 2 4 3 3 +--R 18a b d e x + 90a b c d e x + 180a b c d e x +--R + +--R 2 3 3 3 3 2 2 4 3 2 3 +--R (180a b c + 18a )d e x + (90a b c + 36a c)d e x +--R + +--R 2 5 3 2 3 +--R (18a b c + 18a c )d e +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 3 5 2 5 3 4 2 2 4 3 3 +--R 18a b d e x + 90a b c d e x + 180a b c d e x +--R + +--R 2 3 3 3 3 2 2 4 3 2 3 +--R (180a b c + 18a )d e x + (90a b c + 36a c)d e x +--R + +--R 2 5 3 2 3 +--R (18a b c + 18a c )d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 30\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 3 +-+3+-+2 +--R 18a d e \|3 \|a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 10 4 10 2 9 4 9 2 2 8 4 8 2 3 7 4 7 +--R b d e x + 10b c d e x + 45b c d e x + (120b c + 2a b)d e x +--R + +--R 2 4 6 4 6 2 5 2 5 4 5 +--R (210b c + 14a b c)d e x + (252b c + 42a b c )d e x +--R + +--R 2 6 3 2 4 4 4 2 7 4 2 3 4 3 +--R (210b c + 70a b c + a )d e x + (120b c + 70a b c + 4a c)d e x +--R + +--R 2 8 5 2 2 2 4 2 2 9 6 2 3 4 +--R (45b c + 42a b c + 6a c )d e x + (10b c + 14a b c + 4a c )d e x +--R + +--R 2 10 7 2 4 4 +--R (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1315 + +--S 1316 of 1394 +r0:=(-2/3)/(a^2*d*e^4*(c+d*x)^3)+1/3/(a*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 2*b*log(c+d*x)/(a^3*d*e^4)+2/3*b*log(a+b*(c+d*x)^3)/(a^3*d*e^4) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 4 6 3 6 4 5 3 2 5 4 4 3 3 4 4 4 3 +--R 3a b d e x + 18a b c d e x + 45a b c d e x + (60a b c + 3a )d e x +--R + +--R 3 4 4 3 4 2 3 5 4 2 2 4 3 6 4 3 4 +--R (45a b c + 9a c)d e x + (18a b c + 9a c )d e x + (3a b c + 3a c )d e +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 4 6 3 6 4 5 3 2 5 4 4 3 3 4 4 4 3 +--R 3a b d e x + 18a b c d e x + 45a b c d e x + (60a b c + 3a )d e x +--R + +--R 3 4 4 3 4 2 3 5 4 2 2 4 3 6 4 3 4 +--R (45a b c + 9a c)d e x + (18a b c + 9a c )d e x + (3a b c + 3a c )d e +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1320 + +--S 1321 of 1394 +r0:=-1/6*e^4*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3)^2)+1/9*e^4*(c+d*x)^2/_ + (a*b*d*(a+b*(c+d*x)^3))-1/27*e^4*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*b^(5/3)*d)+1/54*e^4*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(5/3)*d)-1/9*e^4*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + 2a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (15b c + 6a b c)d e x + (6b c + 6a b c )d e x +--R + +--R 2 6 3 2 4 +--R (b c + 2a b c + a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - 2b d e x - 12b c d e x - 30b c d e x + (- 40b c - 4a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 30b c - 12a b c)d e x + (- 12b c - 12a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- 2b c - 4a b c - 2a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 4 +--R (6b c + 12a b c + 6a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 4 5 4 4 4 2 3 4 3 3 2 4 2 +--R 6b d e x + 30b c d e x + 60b c d e x + (60b c - 3a)d e x +--R + +--R 4 4 5 2 4 +--R (30b c - 6a c)d e x + (6b c - 3a c )e +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- b c - 2a b c - a )e +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 4 +--R (2b c + 4a b c + 2a )e +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - 6b d e x - 36b c d e x - 90b c d e x + (- 120b c - 12a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 90b c - 36a b c)d e x + (- 36b c - 36a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- 6b c - 12a b c - 6a )e +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 4 5 4 4 4 2 3 4 3 3 2 4 2 +--R 6b d e x + 30b c d e x + 60b c d e x + (60b c - 3a)d e x +--R + +--R 4 4 5 2 4 +--R (30b c - 6a c)d e x + (6b c - 3a c )e +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R 4 +-+3| 2 +--R e \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R 4 +-+3| 2 3+-+ 3+-+ +--R 2e \|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R 4 +-+3+-+3+-+2 +--R e \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R 4 +-+3+-+3+-+2 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 4 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 4 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e \|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1325 + +--S 1326 of 1394 +r0:=-1/6*e^3*(c+d*x)/(b*d*(a+b*(c+d*x)^3)^2)+1/18*e^3*(c+d*x)/_ + (a*b*d*(a+b*(c+d*x)^3))+1/27*e^3*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(4/3)*d)-1/54*e^3*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(4/3)*d)-1/9*e^3*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 3 +--R (- b c - 2a b c - a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 3 +--R (2b c + 4a b c + 2a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 3 +--R (6b c + 12a b c + 6a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 +--R 3b d e x + 12b c d e x + 18b c d e x + (12b c - 6a)d e x +--R + +--R 4 3 +--R (3b c - 6a c)e +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 3 +--R (- b c - 2a b c - a )e +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 3 +--R (2b c + 4a b c + 2a )e +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 3 +--R (6b c + 12a b c + 6a )e +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 +--R 3b d e x + 12b c d e x + 18b c d e x + (12b c - 6a)d e x +--R + +--R 4 3 +--R (3b c - 6a c)e +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +-+3+-+2 3+-+ +--R e \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 +-+3+-+2 3+-+ 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R 3 +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R 3 +-+3| 2 3+-+ 3+-+ +--R - 2e \|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6e \|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1330 + +--S 1331 of 1394 +r0:=-1/6*e^2/(b*d*(a+b*(c+d*x)^3)^2) +--R +--R +--R (2) +--R - +--R 1 2 +--R - e +--R 6 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 3 6 2 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1331 + +--S 1332 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R e +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x +--R + +--R 3 6 2 3 2 +--R (6b c + 12a b c + 6a b)d +--R Type: Union(Expression(Integer),...) +--E 1332 + +--S 1333 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1335 + +--S 1336 of 1394 +r0:=1/6*e*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3)^2)+2/9*e*(c+d*x)^2/_ + (a^2*d*(a+b*(c+d*x)^3))-2/27*e*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(7/3)*b^(2/3)*d)+1/27*e*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(7/3)*b^(2/3)*d)-2/9*e*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d e x - 24b c d e x - 60b c d e x + (- 80b c - 8a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (- 60b c - 24a b c)d e x + (- 24b c - 24a b c )d e x +--R + +--R 2 6 3 2 +--R (- 4b c - 8a b c - 4a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 12b d e x + 72b c d e x + 180b c d e x + (240b c + 24a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (180b c + 72a b c)d e x + (72b c + 72a b c )d e x +--R + +--R 2 6 3 2 +--R (12b c + 24a b c + 12a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d e x + 60b c d e x + 120b c d e x + (120b c + 21a)d e x +--R + +--R 4 5 2 +--R (60b c + 42a c)d e x + (12b c + 21a c )e +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d e x - 12b c d e x - 30b c d e x + (- 40b c - 4a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (- 30b c - 12a b c)d e x + (- 12b c - 12a b c )d e x +--R + +--R 2 6 3 2 +--R (- 2b c - 4a b c - 2a )e +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d e x + 24b c d e x + 60b c d e x + (80b c + 8a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (60b c + 24a b c)d e x + (24b c + 24a b c )d e x +--R + +--R 2 6 3 2 +--R (4b c + 8a b c + 4a )e +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 +--R - 12b d e x - 72b c d e x - 180b c d e x +--R + +--R 2 3 3 3 2 4 2 2 +--R (- 240b c - 24a b)d e x + (- 180b c - 72a b c)d e x +--R + +--R 2 5 2 2 6 3 2 +--R (- 72b c - 72a b c )d e x + (- 12b c - 24a b c - 12a )e +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d e x + 60b c d e x + 120b c d e x + (120b c + 21a)d e x +--R + +--R 4 5 2 +--R (60b c + 42a c)d e x + (12b c + 21a c )e +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1337 + +--S 1338 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1394 +t0:=1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1340 + +--S 1341 of 1394 +r0:=1/6*(c+d*x)/(a*d*(a+b*(c+d*x)^3)^2)+5/18*(c+d*x)/(a^2*d*_ + (a+b*(c+d*x)^3))+5/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(8/3)*b^(1/3)*d)-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(8/3)*b^(1/3)*d)-5/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1342 + +--S 1343 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 10\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 30\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 10 10 3 9 9 3 2 8 8 3 3 2 7 7 +--R b d e x + 10b c d e x + 45b c d e x + (120b c + 3a b )d e x +--R + +--R 3 4 2 6 6 3 5 2 2 5 5 +--R (210b c + 21a b c)d e x + (252b c + 63a b c )d e x +--R + +--R 3 6 2 3 2 4 4 +--R (210b c + 105a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 3 3 +--R (120b c + 105a b c + 12a b c)d e x +--R + +--R 3 8 2 5 2 2 2 2 +--R (45b c + 63a b c + 18a b c )d e x +--R + +--R 3 9 2 6 2 3 3 +--R (10b c + 21a b c + 12a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 +--R (b c + 3a b c + 3a b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1345 + +--S 1346 of 1394 +r0:=1/6/(a*d*e*(a+b*(c+d*x)^3)^2)+1/3/(a^2*d*e*(a+b*(c+d*x)^3))+_ + log(c+d*x)/(a^3*d*e)-1/3*log(a+b*(c+d*x)^3)/(a^3*d*e) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d e x + 36a b c d e x + 90a b c d e x + (120a b c + 12a b)d e x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d e x + (36a b c + 36a b c )d e x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d e +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d e x + 36a b c d e x + 90a b c d e x + (120a b c + 12a b)d e x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d e x + (36a b c + 36a b c )d e x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d e +--R Type: Union(Expression(Integer),...) +--E 1347 + +--S 1348 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1349 + +)clear all + +--S 1350 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 11 2 11 3 10 2 10 3 2 9 2 9 3 3 2 8 2 8 +--R b d e x + 11b c d e x + 55b c d e x + (165b c + 3a b )d e x +--R + +--R 3 4 2 7 2 7 3 5 2 2 6 2 6 +--R (330b c + 24a b c)d e x + (462b c + 84a b c )d e x +--R + +--R 3 6 2 3 2 5 2 5 +--R (462b c + 168a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 4 2 4 +--R (330b c + 210a b c + 15a b c)d e x +--R + +--R 3 8 2 5 2 2 3 2 3 +--R (165b c + 168a b c + 30a b c )d e x +--R + +--R 3 9 2 6 2 3 3 2 2 2 +--R (55b c + 84a b c + 30a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 +--R (11b c + 24a b c + 15a b c + 2a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 2 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1350 + +--S 1351 of 1394 +r0:=(-14/9)/(a^3*d*e^2*(c+d*x))+1/6/(a*d*e^2*(c+d*x)*(a+b*(c+d*x)^3)^2)+_ + 7/18/(a^2*d*e^2*(c+d*x)*(a+b*(c+d*x)^3))+14/27*b^(1/3)*_ + log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(10/3)*d*e^2)-7/27*b^(1/3)*_ + log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(10/3)*d*e^2)+14/9*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(10/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 84b d x - 588b c d x - 1764b c d x + (- 2940b c - 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 2940b c - 672a b c)d x + (- 1764b c - 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 588b c - 672a b c - 84a )d x - 84b c - 168a b c - 84a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 8 2 7 3 2 7 2 6 3 2 2 6 2 5 +--R 54a b d e x + 378a b c d e x + 1134a b c d e x +--R + +--R 3 2 3 4 5 2 4 3 2 4 4 4 2 3 +--R (1890a b c + 108a b)d e x + (1890a b c + 432a b c)d e x +--R + +--R 3 2 5 4 2 3 2 2 3 2 6 4 3 5 2 2 +--R (1134a b c + 648a b c )d e x + (378a b c + 432a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 +--R (54a b c + 108a b c + 54a c)d e +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 2 7 3 2 7 2 6 3 2 2 6 2 5 +--R 54a b d e x + 378a b c d e x + 1134a b c d e x +--R + +--R 3 2 3 4 5 2 4 3 2 4 4 4 2 3 +--R (1890a b c + 108a b)d e x + (1890a b c + 432a b c)d e x +--R + +--R 3 2 5 4 2 3 2 2 3 2 6 4 3 5 2 2 +--R (1134a b c + 648a b c )d e x + (378a b c + 432a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 +--R (54a b c + 108a b c + 54a c)d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1352 + +--S 1353 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 7\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 14\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 42\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 2 +-+3+-+ +--R 27a d e \|3 \|a +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1354 + +)clear all + +--S 1355 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 12 3 12 3 11 3 11 3 2 10 3 10 3 3 2 9 3 9 +--R b d e x + 12b c d e x + 66b c d e x + (220b c + 3a b )d e x +--R + +--R 3 4 2 8 3 8 3 5 2 2 7 3 7 +--R (495b c + 27a b c)d e x + (792b c + 108a b c )d e x +--R + +--R 3 6 2 3 2 6 3 6 +--R (924b c + 252a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 5 3 5 +--R (792b c + 378a b c + 18a b c)d e x +--R + +--R 3 8 2 5 2 2 4 3 4 +--R (495b c + 378a b c + 45a b c )d e x +--R + +--R 3 9 2 6 2 3 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 3 2 +--R (66b c + 108a b c + 45a b c + 3a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 3 +--R (12b c + 27a b c + 18a b c + 3a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1355 + +--S 1356 of 1394 +r0:=(-10/9)/(a^3*d*e^3*(c+d*x)^2)+1/6/(a*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3)^2)+_ + 4/9/(a^2*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3))-20/27*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(11/3)*d*e^3)+10/27*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(11/3)*d*e^3)+_ + 20/9*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(11/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+3+-+2 +--R \|3 \|a +--R / +--R 3 2 9 3 8 3 2 8 3 7 3 2 2 7 3 6 +--R 54a b d e x + 432a b c d e x + 1512a b c d e x +--R + +--R 3 2 3 4 6 3 5 3 2 4 4 5 3 4 +--R (3024a b c + 108a b)d e x + (3780a b c + 540a b c)d e x +--R + +--R 3 2 5 4 2 4 3 3 +--R (3024a b c + 1080a b c )d e x +--R + +--R 3 2 6 4 3 5 3 3 2 +--R (1512a b c + 1080a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 3 +--R (432a b c + 540a b c + 108a c)d e x +--R + +--R 3 2 8 4 5 5 2 3 +--R (54a b c + 108a b c + 54a c )d e +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 3 8 3 2 8 3 7 3 2 2 7 3 6 +--R 54a b d e x + 432a b c d e x + 1512a b c d e x +--R + +--R 3 2 3 4 6 3 5 3 2 4 4 5 3 4 +--R (3024a b c + 108a b)d e x + (3780a b c + 540a b c)d e x +--R + +--R 3 2 5 4 2 4 3 3 +--R (3024a b c + 1080a b c )d e x +--R + +--R 3 2 6 4 3 5 3 3 2 +--R (1512a b c + 1080a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 3 +--R (432a b c + 540a b c + 108a c)d e x +--R + +--R 3 2 8 4 5 5 2 3 +--R (54a b c + 108a b c + 54a c )d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1357 + +--S 1358 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 10\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 20\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 60\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 3 +-+3+-+2 +--R 27a d e \|3 \|a +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1359 + +)clear all + +--S 1360 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 13 4 13 3 12 4 12 3 2 11 4 11 3 3 2 10 4 10 +--R b d e x + 13b c d e x + 78b c d e x + (286b c + 3a b )d e x +--R + +--R 3 4 2 9 4 9 3 5 2 2 8 4 8 +--R (715b c + 30a b c)d e x + (1287b c + 135a b c )d e x +--R + +--R 3 6 2 3 2 7 4 7 +--R (1716b c + 360a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 6 4 6 +--R (1716b c + 630a b c + 21a b c)d e x +--R + +--R 3 8 2 5 2 2 5 4 5 +--R (1287b c + 756a b c + 63a b c )d e x +--R + +--R 3 9 2 6 2 3 3 4 4 4 +--R (715b c + 630a b c + 105a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 3 4 3 +--R (286b c + 360a b c + 105a b c + 4a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 2 4 2 +--R (78b c + 135a b c + 63a b c + 6a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 4 +--R (13b c + 30a b c + 21a b c + 4a c )d e x +--R + +--R 3 13 2 10 2 7 3 4 4 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1360 + +--S 1361 of 1394 +r0:=(-1)/(a^3*d*e^4*(c+d*x)^3)+1/6/(a*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3)^2)+_ + 1/2/(a^2*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3))-3*b*log(c+d*x)/(a^4*d*e^4)+_ + b*log(a+b*(c+d*x)^3)/(a^4*d*e^4) +--R +--R +--R (2) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 4 9 4 2 9 4 8 4 2 2 8 4 7 +--R 6a b d e x + 54a b c d e x + 216a b c d e x +--R + +--R 4 2 3 5 7 4 6 4 2 4 5 6 4 5 +--R (504a b c + 12a b)d e x + (756a b c + 72a b c)d e x +--R + +--R 4 2 5 5 2 5 4 4 4 2 6 5 3 6 4 4 3 +--R (756a b c + 180a b c )d e x + (504a b c + 240a b c + 6a )d e x +--R + +--R 4 2 7 5 4 6 3 4 2 +--R (216a b c + 180a b c + 18a c)d e x +--R + +--R 4 2 8 5 5 6 2 2 4 4 2 9 5 6 6 3 4 +--R (54a b c + 72a b c + 18a c )d e x + (6a b c + 12a b c + 6a c )d e +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 4 9 4 2 9 4 8 4 2 2 8 4 7 +--R 6a b d e x + 54a b c d e x + 216a b c d e x +--R + +--R 4 2 3 5 7 4 6 4 2 4 5 6 4 5 +--R (504a b c + 12a b)d e x + (756a b c + 72a b c)d e x +--R + +--R 4 2 5 5 2 5 4 4 4 2 6 5 3 6 4 4 3 +--R (756a b c + 180a b c )d e x + (504a b c + 240a b c + 6a )d e x +--R + +--R 4 2 7 5 4 6 3 4 2 +--R (216a b c + 180a b c + 18a c)d e x +--R + +--R 4 2 8 5 5 6 2 2 4 4 2 9 5 6 6 3 4 +--R (54a b c + 72a b c + 18a c )d e x + (6a b c + 12a b c + 6a c )d e +--R Type: Union(Expression(Integer),...) +--E 1362 + +--S 1363 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + 35b c d x + (35b c + a)d x +--R + +--R 5 2 2 6 2 7 3 +--R (21b c + 3a c)d x + (7b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1365 + +--S 1366 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/8*b*(c+d*x)^8/d +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 1 4 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 3 3 7 6 3 2 2 2 7 3 1 8 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1366 + +--S 1367 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 1 3 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 2 3 7 6 3 2 2 7 3 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1367 + +--S 1368 of 1394 +m0:=a0-r0 +--R +--R +--R 1 8 1 4 +--R - - b c - - a c +--R 8 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1368 + +--S 1369 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1369 + +)clear all + +--S 1370 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4)^2 +--R +--R +--R (1) +--R 2 11 11 2 10 10 2 2 9 9 2 3 8 8 2 4 7 7 +--R b d x + 11b c d x + 55b c d x + 165b c d x + (330b c + 2a b)d x +--R + +--R 2 5 6 6 2 6 2 5 5 +--R (462b c + 14a b c)d x + (462b c + 42a b c )d x +--R + +--R 2 7 3 4 4 2 8 4 2 3 3 +--R (330b c + 70a b c )d x + (165b c + 70a b c + a )d x +--R + +--R 2 9 5 2 2 2 2 10 6 2 2 2 11 +--R (55b c + 42a b c + 3a c)d x + (11b c + 14a b c + 3a c )d x + b c +--R + +--R 7 2 3 +--R 2a b c + a c +--R Type: Polynomial(Integer) +--E 1370 + +--S 1371 of 1394 +r0:=1/12*(a+b*(c+d*x)^4)^3/(b*d) +--R +--R +--R (2) +--R 1 3 12 12 3 11 11 11 3 2 10 10 55 3 3 9 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 3 4 1 2 8 8 3 5 2 7 7 3 6 2 2 6 6 +--R (--- b c + - a b )d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 3 7 2 3 5 5 165 3 8 35 2 4 1 2 4 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a b)d x +--R 4 2 4 +--R + +--R 55 3 9 2 5 2 3 3 11 3 10 2 6 3 2 2 2 2 +--R (-- b c + 14a b c + a b c)d x + (-- b c + 7a b c + - a b c )d x +--R 3 2 2 +--R + +--R 3 11 2 7 2 3 1 3 12 1 2 8 1 2 4 1 3 +--R (b c + 2a b c + a b c )d x + -- b c + - a b c + - a b c + -- a +--R 12 4 4 12 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1371 + +--S 1372 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 11 12 2 10 11 11 2 2 9 10 55 2 3 8 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 2 4 1 7 8 2 5 6 7 2 6 2 5 6 +--R (--- b c + - a b)d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 2 7 3 4 5 165 2 8 35 4 1 2 3 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 55 2 9 5 2 2 3 11 2 10 6 3 2 2 2 +--R (-- b c + 14a b c + a c)d x + (-- b c + 7a b c + - a c )d x +--R 3 2 2 +--R + +--R 2 11 7 2 3 +--R (b c + 2a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1372 + +--S 1373 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R - -- b c - - a b c - - a b c - -- a +--R 12 4 4 12 +--R (4) ---------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1373 + +--S 1374 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1374 + +)clear all + +--S 1375 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4)^3 +--R +--R +--R (1) +--R 3 15 15 3 14 14 3 2 13 13 3 3 12 12 +--R b d x + 15b c d x + 105b c d x + 455b c d x +--R + +--R 3 4 2 11 11 3 5 2 10 10 +--R (1365b c + 3a b )d x + (3003b c + 33a b c)d x +--R + +--R 3 6 2 2 9 9 3 7 2 3 8 8 +--R (5005b c + 165a b c )d x + (6435b c + 495a b c )d x +--R + +--R 3 8 2 4 2 7 7 3 9 2 5 2 6 6 +--R (6435b c + 990a b c + 3a b)d x + (5005b c + 1386a b c + 21a b c)d x +--R + +--R 3 10 2 6 2 2 5 5 +--R (3003b c + 1386a b c + 63a b c )d x +--R + +--R 3 11 2 7 2 3 4 4 +--R (1365b c + 990a b c + 105a b c )d x +--R + +--R 3 12 2 8 2 4 3 3 3 +--R (455b c + 495a b c + 105a b c + a )d x +--R + +--R 3 13 2 9 2 5 3 2 2 +--R (105b c + 165a b c + 63a b c + 3a c)d x +--R + +--R 3 14 2 10 2 6 3 2 3 15 2 11 2 7 +--R (15b c + 33a b c + 21a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Polynomial(Integer) +--E 1375 + +--S 1376 of 1394 +r0:=1/16*(a+b*(c+d*x)^4)^4/(b*d) +--R +--R +--R (2) +--R 1 4 16 16 4 15 15 15 4 2 14 14 4 3 13 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 4 4 1 3 12 12 4 5 3 11 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 4 6 33 3 2 10 10 4 7 3 3 9 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 4 8 495 3 4 3 2 2 8 8 +--R (---- b c + --- a b c + - a b )d x +--R 8 4 8 +--R + +--R 4 9 3 5 2 2 7 7 +--R (715b c + 198a b c + 3a b c)d x +--R + +--R 1001 4 10 3 6 21 2 2 2 6 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 4 11 3 7 2 2 3 5 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 4 12 495 3 8 105 2 2 4 1 3 4 4 +--R (--- b c + --- a b c + --- a b c + - a b)d x +--R 4 4 4 4 +--R + +--R 4 13 3 9 2 2 5 3 3 3 +--R (35b c + 55a b c + 21a b c + a b c)d x +--R + +--R 15 4 14 33 3 10 21 2 2 6 3 3 2 2 2 +--R (-- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 4 15 3 11 2 2 7 3 3 1 4 16 1 3 12 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c +--R 16 4 +--R + +--R 3 2 2 8 1 3 4 1 4 +--R - a b c + - a b c + -- a +--R 8 4 16 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1376 + +--S 1377 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 15 16 3 14 15 15 3 2 13 14 3 3 12 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 3 4 1 2 11 12 3 5 2 10 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 3 6 33 2 2 9 10 3 7 2 3 8 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 3 8 495 2 4 3 2 7 8 3 9 2 5 2 6 7 +--R (---- b c + --- a b c + - a b)d x + (715b c + 198a b c + 3a b c)d x +--R 8 4 8 +--R + +--R 1001 3 10 2 6 21 2 2 5 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 3 11 2 7 2 3 4 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 3 12 495 2 8 105 2 4 1 3 3 4 +--R (--- b c + --- a b c + --- a b c + - a )d x +--R 4 4 4 4 +--R + +--R 3 13 2 9 2 5 3 2 3 +--R (35b c + 55a b c + 21a b c + a c)d x +--R + +--R 15 3 14 33 2 10 21 2 6 3 3 2 2 +--R (-- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 15 2 11 2 7 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1377 + +--S 1378 of 1394 +m0:=a0-r0 +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R - -- b c - - a b c - - a b c - - a b c - -- a +--R 16 4 8 4 16 +--R (4) ---------------------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1378 + +--S 1379 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1379 + +)clear all + +--S 1380 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1380 + +--S 1381 of 1394 +r0:=1/4*log(a+b*(c+d*x)^4)/(b*d) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R (2) --------------------------------------------------------- +--R 4b d +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R (3) --------------------------------------------------------- +--R 4b d +--R Type: Union(Expression(Integer),...) +--E 1382 + +--S 1383 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1384 + +)clear all + +--S 1385 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4)^2 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 2 4 4 4 +--R b d x + 8b c d x + 28b c d x + 56b c d x + (70b c + 2a b)d x +--R + +--R 2 5 3 3 2 6 2 2 2 2 7 3 +--R (56b c + 8a b c)d x + (28b c + 12a b c )d x + (8b c + 8a b c )d x +--R + +--R 2 8 4 2 +--R b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1385 + +--S 1386 of 1394 +r0:=(-1/4)/(b*d*(a+b*(c+d*x)^4)) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------------------------- +--R 2 5 4 2 4 3 2 2 3 2 2 3 2 2 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1386 + +--S 1387 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------------------------------------------------- +--R 2 5 4 2 4 3 2 2 3 2 2 3 2 2 4 +--R 4b d x + 16b c d x + 24b c d x + 16b c d x + (4b c + 4a b)d +--R Type: Union(Expression(Integer),...) +--E 1387 + +--S 1388 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1389 + +)clear all + +--S 1390 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4)^3 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 9 9 +--R b d x + 12b c d x + 66b c d x + 220b c d x +--R + +--R 3 4 2 8 8 3 5 2 7 7 +--R (495b c + 3a b )d x + (792b c + 24a b c)d x +--R + +--R 3 6 2 2 6 6 3 7 2 3 5 5 +--R (924b c + 84a b c )d x + (792b c + 168a b c )d x +--R + +--R 3 8 2 4 2 4 4 3 9 2 5 2 3 3 +--R (495b c + 210a b c + 3a b)d x + (220b c + 168a b c + 12a b c)d x +--R + +--R 3 10 2 6 2 2 2 2 3 11 2 7 2 3 +--R (66b c + 84a b c + 18a b c )d x + (12b c + 24a b c + 12a b c )d x +--R + +--R 3 12 2 8 2 4 3 +--R b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1390 + +--S 1391 of 1394 +r0:=(-1/8)/(b*d*(a+b*(c+d*x)^4)^2) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 8 +--R / +--R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 3 4 2 5 4 +--R b d x + 8b c d x + 28b c d x + 56b c d x + (70b c + 2a b )d x +--R + +--R 3 5 2 4 3 3 6 2 2 3 2 3 7 2 3 2 +--R (56b c + 8a b c)d x + (28b c + 12a b c )d x + (8b c + 8a b c )d x +--R + +--R 3 8 2 4 2 +--R (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1391 + +--S 1392 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 +--R 8b d x + 64b c d x + 224b c d x + 448b c d x +--R + +--R 3 4 2 5 4 3 5 2 4 3 +--R (560b c + 16a b )d x + (448b c + 64a b c)d x +--R + +--R 3 6 2 2 3 2 3 7 2 3 2 +--R (224b c + 96a b c )d x + (64b c + 64a b c )d x +--R + +--R 3 8 2 4 2 +--R (8b c + 16a b c + 8a b)d +--R Type: Union(Expression(Integer),...) +--E 1392 + +--S 1393 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1394 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/rich4j.input.pdf b/src/axiom-website/CATS/rich4j.input.pdf new file mode 100644 index 0000000..329700a Binary files /dev/null and b/src/axiom-website/CATS/rich4j.input.pdf differ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 5cd6db4..e912f51 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -4252,6 +4252,8 @@ src/axiom-website/CATS/rich2, rich3a src/axiom-website/CATS/rich3b 20130727.01.tpd.patch src/axiom-website/CATS/rich3c +20130804.01.tpd.patch +src/axiom-website/CATS/rich4*, src/input/rich4* diff --git a/src/input/Makefile.pamphlet b/src/input/Makefile.pamphlet index 49f31b2..a14b944 100644 --- a/src/input/Makefile.pamphlet +++ b/src/input/Makefile.pamphlet @@ -432,8 +432,17 @@ CATSTESTS= \ These long-running tests have been split into a different group so we can run them in parallel. <>= -NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress \ - rich3a.regress rich3b.regress rich3c.regress +NEWRICHTESTS = rich1a.regress rich1b.regress rich2.regress \ + rich3a.regress rich3b.regress rich3c.regress \ + rich3d.regress rich3e.regress rich3f.regress \ + rich3g.regress rich3h.regress rich3i.regress \ + rich3j.regress rich3k.regress rich3l.regress \ + rich3m.regress rich3n.regress rich3o.regress \ + rich3p.regress rich3q.regress rich3r.regress \ + rich3s.regress rich3t.regress rich4a.regress \ + rich4b.regress rich4c.regress rich4d.regress \ + rich4e.regress rich4f.regress rich4g.regress \ + rich4h.regress rich4i.regress rich4j.regress RICHTESTS= \ richalgebraic000-099.regress \ @@ -789,7 +798,16 @@ FILES= ${OUT}/ackermann.input \ ${OUT}/ribbons.input ${OUT}/ribbonsnew.input \ ${OUT}/rich1a.input ${OUT}/rich1b.input \ ${OUT}/rich2.input ${OUT}/rich3a.input ${OUT}/rich3b.input \ - ${OUT}/rich3c.input \ + ${OUT}/rich3c.input ${OUT}/rich3d.input ${OUT}/rich3e.input \ + ${OUT}/rich3f.input ${OUT}/rich3g.input ${OUT}/rich3h.input \ + ${OUT}/rich3i.input ${OUT}/rich3j.input ${OUT}/rich3k.input \ + ${OUT}/rich3l.input ${OUT}/rich3m.input ${OUT}/rich3n.input \ + ${OUT}/rich3o.input ${OUT}/rich3p.input ${OUT}/rich3q.input \ + ${OUT}/rich3r.input ${OUT}/rich3s.input ${OUT}/rich3t.input \ + ${OUT}/rich4a.input ${OUT}/rich4b.input ${OUT}/rich4c.input \ + ${OUT}/rich4d.input ${OUT}/rich4e.input ${OUT}/rich4f.input \ + ${OUT}/rich4g.input ${OUT}/rich4h.input ${OUT}/rich4i.input \ + ${OUT}/rich4j.input \ ${OUT}/rk4draw.input \ ${OUT}/r20abugs.input \ ${OUT}/r20bugs.input ${OUT}/r21bugsbig.input \ @@ -876,7 +894,16 @@ FILES2=${OUT}/arith.input ${OUT}/bugs.input \ NEWRICHINPUT= ${OUT}/rich1a.input ${OUT}/rich1b.input \ ${OUT}/rich2.input ${OUT}/rich3a.input ${OUT}/rich3b.input \ - ${OUT}/rich3c.input + ${OUT}/rich3c.input ${OUT}/rich3d.input ${OUT}/rich3e.input \ + ${OUT}/rich3f.input ${OUT}/rich3g.input ${OUT}/rich3h.input \ + ${OUT}/rich3i.input ${OUT}/rich3j.input ${OUT}/rich3k.input \ + ${OUT}/rich3l.input ${OUT}/rich3m.input ${OUT}/rich3n.input \ + ${OUT}/rich3o.input ${OUT}/rich3p.input ${OUT}/rich3q.input \ + ${OUT}/rich3r.input ${OUT}/rich3s.input ${OUT}/rich3t.input \ + ${OUT}/rich4a.input ${OUT}/rich4b.input ${OUT}/rich4c.input \ + ${OUT}/rich4d.input ${OUT}/rich4e.input ${OUT}/rich4f.input \ + ${OUT}/rich4g.input ${OUT}/rich4h.input ${OUT}/rich4i.input \ + ${OUT}/rich4j.input RICHINPUT= \ ${OUT}/richalgebraic000-099.input \ @@ -1198,7 +1225,20 @@ DOCFILES= \ ${DOC}/rich1a.input.dvi ${DOC}/rich1b.input.dvi \ ${DOC}/rich2.input.dvi \ ${DOC}/rich3a.input.dvi ${DOC}/rich3b.input.dvi \ - ${DOC}/rich3c.input.dvi \ + ${DOC}/rich3c.input.dvi ${DOC}/rich3d.input.dvi \ + ${DOC}/rich3e.input.dvi ${DOC}/rich3f.input.dvi \ + ${DOC}/rich3g.input.dvi ${DOC}/rich3h.input.dvi \ + ${DOC}/rich3i.input.dvi ${DOC}/rich3j.input.dvi \ + ${DOC}/rich3k.input.dvi ${DOC}/rich3l.input.dvi \ + ${DOC}/rich3m.input.dvi ${DOC}/rich3n.input.dvi \ + ${DOC}/rich3o.input.dvi ${DOC}/rich3p.input.dvi \ + ${DOC}/rich3q.input.dvi ${DOC}/rich3r.input.dvi \ + ${DOC}/rich3s.input.dvi ${DOC}/rich3t.input.dvi \ + ${DOC}/rich4a.input.dvi ${DOC}/rich4b.input.dvi \ + ${DOC}/rich4c.input.dvi ${DOC}/rich4d.input.dvi \ + ${DOC}/rich4e.input.dvi ${DOC}/rich4f.input.dvi \ + ${DOC}/rich4g.input.dvi ${DOC}/rich4h.input.dvi \ + ${DOC}/rich4i.input.dvi ${DOC}/rich4j.input.dvi \ ${DOC}/richalgebraic000-099.input.dvi \ ${DOC}/richalgebraic100-199.input.dvi \ ${DOC}/richalgebraic200-299.input.dvi \ diff --git a/src/input/rich1a.input.pamphlet b/src/input/rich1a.input.pamphlet index 06f6586..b6a7a8b 100644 --- a/src/input/rich1a.input.pamphlet +++ b/src/input/rich1a.input.pamphlet @@ -33369,7 +33369,7 @@ r0000:=-2/3*(a+b*x)^(3/2)/(a*x^(3/2)) --R Type: Expression(Integer) --E 2555 ---S 2556 of 3333 +--S 2556 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33381,7 +33381,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2556 ---S 2557 of 3333 +--S 2557 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33426,7 +33426,7 @@ r0000:=-2/5*(a+b*x)^(3/2)/(a*x^(5/2))+4/15*b*(a+b*x)^(3/2)/(a^2*x^(3/2)) --R Type: Expression(Integer) --E 2560 ---S 2561 of 3333 +--S 2561 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33442,7 +33442,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2561 ---S 2562 of 3333 +--S 2562 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33489,7 +33489,7 @@ r0000:=-2/7*(a+b*x)^(3/2)/(a*x^(7/2))+8/35*b*(a+b*x)^(3/2)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2565 ---S 2566 of 3333 +--S 2566 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33505,7 +33505,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2566 ---S 2567 of 3333 +--S 2567 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33756,7 +33756,7 @@ r0000:=-2/3*(a-b*x)^(3/2)/(a*x^(3/2)) --R Type: Expression(Integer) --E 2595 ---S 2596 of 3333 +--S 2596 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33768,7 +33768,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2596 ---S 2597 of 3333 +--S 2597 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33813,7 +33813,7 @@ r0000:=-2/5*(a-b*x)^(3/2)/(a*x^(5/2))-4/15*b*(a-b*x)^(3/2)/(a^2*x^(3/2)) --R Type: Expression(Integer) --E 2600 ---S 2601 of 3333 +--S 2601 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33829,7 +33829,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2601 ---S 2602 of 3333 +--S 2602 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -33876,7 +33876,7 @@ r0000:=-2/7*(a-b*x)^(3/2)/(a*x^(7/2))-8/35*b*(a-b*x)^(3/2)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2605 ---S 2606 of 3333 +--S 2606 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -33892,7 +33892,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2606 ---S 2607 of 3333 +--S 2607 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34138,7 +34138,7 @@ r0000:=-1/3*(2+b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2635 ---S 2636 of 3333 +--S 2636 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34150,7 +34150,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2636 ---S 2637 of 3333 +--S 2637 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34195,7 +34195,7 @@ r0000:=-1/5*(2+b*x)^(3/2)/x^(5/2)+1/15*b*(2+b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2640 ---S 2641 of 3333 +--S 2641 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34207,7 +34207,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2641 ---S 2642 of 3333 +--S 2642 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34253,7 +34253,7 @@ r0000:=-1/7*(2+b*x)^(3/2)/x^(7/2)+2/35*b*(2+b*x)^(3/2)/x^(5/2)-_ --R Type: Expression(Integer) --E 2645 ---S 2646 of 3333 +--S 2646 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34269,7 +34269,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2646 ---S 2647 of 3333 +--S 2647 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34515,7 +34515,7 @@ r0000:=-1/3*(2-b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2675 ---S 2676 of 3333 +--S 2676 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34527,7 +34527,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2676 ---S 2677 of 3333 +--S 2677 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -34572,7 +34572,7 @@ r0000:=-1/5*(2-b*x)^(3/2)/x^(5/2)-1/15*b*(2-b*x)^(3/2)/x^(3/2) --R Type: Expression(Integer) --E 2680 ---S 2681 of 3333 +--S 2681 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -34584,7 +34584,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2681 ---S 2682 of 3333 +--S 2682 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36903,7 +36903,7 @@ r0000:=-2*sqrt(a+b*x)/(a*sqrt(x)) --R Type: Expression(Integer) --E 2950 ---S 2951 of 3333 +--S 2951 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -36914,7 +36914,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2951 ---S 2952 of 3333 +--S 2952 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36957,7 +36957,7 @@ r0000:=-2/3*sqrt(a+b*x)/(a*x^(3/2))+4/3*b*sqrt(a+b*x)/(a^2*sqrt(x)) --R Type: Expression(Integer) --E 2955 ---S 2956 of 3333 +--S 2956 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -36969,7 +36969,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2956 ---S 2957 of 3333 +--S 2957 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -36984,7 +36984,7 @@ m0000:=a0000 - r0000 --S 2958 of 3333 d0000:=D(m0000,x) --R ---R +--R --R (5) 0 --R Type: Expression(Integer) --E 2958 @@ -37077,7 +37077,7 @@ r0000:=-2/7*sqrt(a+b*x)/(a*x^(7/2))+12/35*b*sqrt(a+b*x)/(a^2*x^(5/2))-_ --R Type: Expression(Integer) --E 2965 ---S 2966 of 3333 +--S 2966 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37093,7 +37093,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2966 ---S 2967 of 3333 +--S 2967 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37264,7 +37264,7 @@ r0000:=2*sqrt(x)/(a*sqrt(a+b*x)) --R Type: Expression(Integer) --E 2985 ---S 2986 of 3333 +--S 2986 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37276,7 +37276,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2986 ---S 2987 of 3333 +--S 2987 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37381,7 +37381,7 @@ r0000:=2/(a*x^(3/2)*sqrt(a+b*x))-8/3*sqrt(a+b*x)/(a^2*x^(3/2))+_ --R Type: Expression(Integer) --E 2995 ---S 2996 of 3333 +--S 2996 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37400,7 +37400,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 2996 ---S 2997 of 3333 +--S 2997 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37446,7 +37446,7 @@ r0000:=2/(a*x^(5/2)*sqrt(a+b*x))-12/5*sqrt(a+b*x)/(a^2*x^(5/2))+_ --R Type: Expression(Integer) --E 3000 ---S 3001 of 3333 +--S 3001 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37477,7 +37477,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3001 ---S 3002 of 3333 +--S 3002 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37613,7 +37613,7 @@ r0000:=2/3*x^(3/2)/(a*(a+b*x)^(3/2)) --R Type: Expression(Integer) --E 3015 ---S 3016 of 3333 +--S 3016 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37632,7 +37632,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3016 ---S 3017 of 3333 +--S 3017 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37676,7 +37676,7 @@ r0000:=2/3*sqrt(x)/(a*(a+b*x)^(3/2))+4/3*sqrt(x)/(a^2*sqrt(a+b*x)) --R Type: Expression(Integer) --E 3020 ---S 3021 of 3333 +--S 3021 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37695,7 +37695,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3021 ---S 3022 of 3333 +--S 3022 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37741,7 +37741,7 @@ r0000:=2/3/(a*(a+b*x)^(3/2)*sqrt(x))+8/3/(a^2*sqrt(x)*sqrt(a+b*x))-_ --R Type: Expression(Integer) --E 3025 ---S 3026 of 3333 +--S 3026 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37772,7 +37772,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3026 ---S 3027 of 3333 +--S 3027 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -37818,7 +37818,7 @@ r0000:=2/3/(a*x^(3/2)*(a+b*x)^(3/2))+4/(a^2*x^(3/2)*sqrt(a+b*x))-_ --R Type: Expression(Integer) --E 3030 ---S 3031 of 3333 ok to fail, random algorithm +--S 3031 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -37867,7 +37867,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3031 ---S 3032 of 3333 ok to fail, random algorithm +--S 3032 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -40512,7 +40512,7 @@ r0000:=1/(x^(3/2)*sqrt(2-b*x))-2/3*sqrt(2-b*x)/x^(3/2)-_ --R Type: Expression(Integer) --E 3285 ---S 3286 of 3333 +--S 3286 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -40528,7 +40528,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3286 ---S 3287 of 3333 +--S 3287 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R @@ -40658,7 +40658,7 @@ r0000:=1/3*x^(3/2)/(2-b*x)^(3/2) --R Type: Expression(Integer) --E 3300 ---S 3301 of 3333 ok to fail, random algorithm +--S 3301 of 3333 ok to fail, differs by a constant a0000:=integrate(t0000,x) --R --R @@ -40673,7 +40673,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 3301 ---S 3302 of 3333 ok to fail, random algorithm +--S 3302 of 3333 ok to fail, differs by a constant m0000:=a0000 - r0000 --R --R diff --git a/src/input/rich1b.input.pamphlet b/src/input/rich1b.input.pamphlet index 7234288..1f09a0d 100644 --- a/src/input/rich1b.input.pamphlet +++ b/src/input/rich1b.input.pamphlet @@ -49865,7 +49865,7 @@ r0000:=2*asinh(sqrt(b*x)/sqrt(2))/b --R Type: Expression(Integer) --E 1964 ---S 1965 of 2952 +--S 1965 of 2952 ok to fail, (non-algebraic residues) a0000:=integrate(t0000,x) --R --R @@ -49876,7 +49876,7 @@ a0000:=integrate(t0000,x) --R Type: Union(Expression(Integer),...) --E 1965 ---S 1966 of 2952 +--S 1966 of 2952 m0000:=a0000 - r0000 --R --R diff --git a/src/input/rich3a.input.pamphlet b/src/input/rich3a.input.pamphlet index fc946de..29348ed 100644 --- a/src/input/rich3a.input.pamphlet +++ b/src/input/rich3a.input.pamphlet @@ -28,16 +28,16 @@ There are: )set message auto off )clear all ---S 1 of 1092 +--S 1 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x) --R --R --R 3 2 n --R (1) (d x + c x )(b x + a) --R Type: Expression(Integer) ---E 1 +--E 1 ---S 2 of 1092 +--S 2 of 1092 r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ a*(2*b*c-3*a*d)*(a+b*x)^(2+n)/(b^4*(2+n))+_ (b*c-3*a*d)*(a+b*x)^(3+n)/(b^4*(3+n))+d*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -75,9 +75,9 @@ r0:=a^2*(b*c-a*d)*(a+b*x)^(1+n)/(b^4*(1+n))-_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 2 +--E 2 ---S 3 of 1092 +--S 3 of 1092 a0:=integrate(t0,x) --R --R @@ -100,9 +100,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 3 +--E 3 ---S 4 of 1092 +--S 4 of 1092 m0:=a0-r0 --R --R @@ -152,28 +152,28 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 4 +--E 4 ---S 5 of 1092 +--S 5 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 5 +--E 5 )clear all ---S 6 of 1092 +--S 6 of 1092 t0:=x*(a+b*x)^n*(c+d*x) --R --R --R 2 n --R (1) (d x + c x)(b x + a) --R Type: Expression(Integer) ---E 6 +--E 6 ---S 7 of 1092 +--S 7 of 1092 r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ (b*c-2*a*d)*(a+b*x)^(2+n)/(b^3*(2+n))+d*(a+b*x)^(3+n)/(b^3*(3+n)) --R @@ -191,9 +191,9 @@ r0:=-a*(b*c-a*d)*(a+b*x)^(1+n)/(b^3*(1+n))+_ --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 7 +--E 7 ---S 8 of 1092 +--S 8 of 1092 a0:=integrate(t0,x) --R --R @@ -213,9 +213,9 @@ a0:=integrate(t0,x) --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Union(Expression(Integer),...) ---E 8 +--E 8 ---S 9 of 1092 +--S 9 of 1092 m0:=a0-r0 --R --R @@ -244,28 +244,28 @@ m0:=a0-r0 --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 9 +--E 9 ---S 10 of 1092 +--S 10 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 10 +--E 10 )clear all ---S 11 of 1092 +--S 11 of 1092 t0:=(a+b*x)^n*(c+d*x) --R --R --R n --R (1) (d x + c)(b x + a) --R Type: Expression(Integer) ---E 11 +--E 11 ---S 12 of 1092 +--S 12 of 1092 r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) --R --R @@ -275,9 +275,9 @@ r0:=(b*c-a*d)*(a+b*x)^(1+n)/(b^2*(1+n))+d*(a+b*x)^(2+n)/(b^2*(2+n)) --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Expression(Integer) ---E 12 +--E 12 ---S 13 of 1092 +--S 13 of 1092 a0:=integrate(t0,x) --R --R @@ -291,9 +291,9 @@ a0:=integrate(t0,x) --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Union(Expression(Integer),...) ---E 13 +--E 13 ---S 14 of 1092 +--S 14 of 1092 m0:=a0-r0 --R --R @@ -310,19 +310,19 @@ m0:=a0-r0 --R 2 2 2 2 --R b n + 3b n + 2b --R Type: Expression(Integer) ---E 14 +--E 14 ---S 15 of 1092 +--S 15 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 15 +--E 15 )clear all ---S 16 of 1092 +--S 16 of 1092 t0:=(a+b*x)^n*(c+d*x)/x --R --R @@ -331,28 +331,28 @@ t0:=(a+b*x)^n*(c+d*x)/x --R (1) ------------------- --R x --R Type: Expression(Integer) ---E 16 +--E 16 ---S 17 of 1092 +--S 17 of 1092 --r0:=d*(a+b*x)^(1+n)/(b*(1+n))-c*(a+b*x)^(1+n)*_ -- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 17 +--E 17 ---S 18 of 1092 +--S 18 of 1092 --a0:=integrate(t0,x) ---E 18 +--E 18 ---S 19 of 1092 +--S 19 of 1092 --m0:=a0-r0 ---E 19 +--E 19 ---S 20 of 1092 +--S 20 of 1092 --d0:=D(m0,x) ---E 20 +--E 20 )clear all ---S 21 of 1092 +--S 21 of 1092 t0:=x^m*(a+b*x)*(c+d*x)^5 --R --R @@ -366,9 +366,9 @@ t0:=x^m*(a+b*x)*(c+d*x)^5 --R m --R x --R Type: Expression(Integer) ---E 21 +--E 21 ---S 22 of 1092 +--S 22 of 1092 r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ 5*c^3*d*(b*c+2*a*d)*x^(3+m)/(3+m)+10*c^2*d^2*(b*c+a*d)*_ x^(4+m)/(4+m)+5*c*d^3*(2*b*c+a*d)*x^(5+m)/(5+m)+_ @@ -466,9 +466,9 @@ r0:=a*c^5*x^(1+m)/(1+m)+c^4*(b*c+5*a*d)*x^(2+m)/(2+m)+_ --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Expression(Integer) ---E 22 +--E 22 ---S 23 of 1092 +--S 23 of 1092 a0:=integrate(t0,x) --R --R @@ -568,9 +568,9 @@ a0:=integrate(t0,x) --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Union(Expression(Integer),...) ---E 23 +--E 23 ---S 24 of 1092 +--S 24 of 1092 m0:=a0-r0 --R --R @@ -766,19 +766,19 @@ m0:=a0-r0 --R 7 6 5 4 3 2 --R m + 28m + 322m + 1960m + 6769m + 13132m + 13068m + 5040 --R Type: Expression(Integer) ---E 24 +--E 24 ---S 25 of 1092 +--S 25 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 25 +--E 25 )clear all ---S 26 of 1092 +--S 26 of 1092 t0:=x^3*(a+b*x)*(c+d*x)^5 --R --R @@ -789,9 +789,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 6 3 2 4 5 4 5 4 5 3 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 26 +--E 26 ---S 27 of 1092 +--S 27 of 1092 r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ 10/7*c^2*d^2*(b*c+a*d)*x^7+5/8*c*d^3*(2*b*c+a*d)*x^8+_ 1/9*d^4*(5*b*c+a*d)*x^9+1/10*b*d^5*x^10 @@ -810,9 +810,9 @@ r0:=1/4*a*c^5*x^4+1/5*c^4*(b*c+5*a*d)*x^5+5/6*c^3*d*(b*c+2*a*d)*x^6+_ --R - a c x --R 4 --R Type: Polynomial(Fraction(Integer)) ---E 27 +--E 27 ---S 28 of 1092 +--S 28 of 1092 a0:=integrate(t0,x) --R --R @@ -829,27 +829,27 @@ a0:=integrate(t0,x) --R - a c x --R 4 --R Type: Polynomial(Fraction(Integer)) ---E 28 +--E 28 ---S 29 of 1092 +--S 29 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Polynomial(Fraction(Integer)) ---E 29 +--E 29 ---S 30 of 1092 +--S 30 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Polynomial(Fraction(Integer)) ---E 30 +--E 30 )clear all ---S 31 of 1092 +--S 31 of 1092 t0:=x^2*(a+b*x)*(c+d*x)^5 --R --R @@ -860,9 +860,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 5 3 2 4 4 4 5 3 5 2 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 31 +--E 31 ---S 32 of 1092 +--S 32 of 1092 r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ 1/8*(3*b*c-a*d)*(c+d*x)^8/d^4+1/9*b*(c+d*x)^9/d^4 --R @@ -883,9 +883,9 @@ r0:=-1/6*c^2*(b*c-a*d)*(c+d*x)^6/d^4+1/7*c*(3*b*c-2*a*d)*(c+d*x)^7/d^4-_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 32 +--E 32 ---S 33 of 1092 +--S 33 of 1092 a0:=integrate(t0,x) --R --R @@ -902,9 +902,9 @@ a0:=integrate(t0,x) --R - a c x --R 3 --R Type: Polynomial(Fraction(Integer)) ---E 33 +--E 33 ---S 34 of 1092 +--S 34 of 1092 m0:=a0-r0 --R --R @@ -915,19 +915,19 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 34 +--E 34 ---S 35 of 1092 +--S 35 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 35 +--E 35 )clear all ---S 36 of 1092 +--S 36 of 1092 t0:=x*(a+b*x)*(c+d*x)^5 --R --R @@ -938,9 +938,9 @@ t0:=x*(a+b*x)*(c+d*x)^5 --R 2 3 3 2 4 3 2 4 3 4 5 2 5 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 36 +--E 36 ---S 37 of 1092 +--S 37 of 1092 r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ 1/8*b*(c+d*x)^8/d^3 --R @@ -961,9 +961,9 @@ r0:=1/6*c*(b*c-a*d)*(c+d*x)^6/d^3-1/7*(2*b*c-a*d)*(c+d*x)^7/d^3+_ --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 37 +--E 37 ---S 38 of 1092 +--S 38 of 1092 a0:=integrate(t0,x) --R --R @@ -980,9 +980,9 @@ a0:=integrate(t0,x) --R - a c x --R 2 --R Type: Polynomial(Fraction(Integer)) ---E 38 +--E 38 ---S 39 of 1092 +--S 39 of 1092 m0:=a0-r0 --R --R @@ -993,19 +993,19 @@ m0:=a0-r0 --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 39 +--E 39 ---S 40 of 1092 +--S 40 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 40 +--E 40 )clear all ---S 41 of 1092 +--S 41 of 1092 t0:=(a+b*x)*(c+d*x)^5 --R --R @@ -1016,9 +1016,9 @@ t0:=(a+b*x)*(c+d*x)^5 --R 2 3 3 2 3 3 2 4 2 4 5 5 --R (10a c d + 10b c d )x + (10a c d + 5b c d)x + (5a c d + b c )x + a c --R Type: Polynomial(Integer) ---E 41 +--E 41 ---S 42 of 1092 +--S 42 of 1092 r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 --R --R @@ -1038,9 +1038,9 @@ r0:=-1/6*(b*c-a*d)*(c+d*x)^6/d^2+1/7*b*(c+d*x)^7/d^2 --R 2 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 42 +--E 42 ---S 43 of 1092 +--S 43 of 1092 a0:=integrate(t0,x) --R --R @@ -1056,9 +1056,9 @@ a0:=integrate(t0,x) --R 5 --R a c x --R Type: Polynomial(Fraction(Integer)) ---E 43 +--E 43 ---S 44 of 1092 +--S 44 of 1092 m0:=a0-r0 --R --R @@ -1069,19 +1069,19 @@ m0:=a0-r0 --R 2 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 44 +--E 44 ---S 45 of 1092 +--S 45 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 45 +--E 45 )clear all ---S 46 of 1092 +--S 46 of 1092 t0:=(a+b*x)*(c+d*x)^5/x --R --R @@ -1094,9 +1094,9 @@ t0:=(a+b*x)*(c+d*x)^5/x --R / --R x --R Type: Fraction(Polynomial(Integer)) ---E 46 +--E 46 ---S 47 of 1092 +--S 47 of 1092 r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ 5/4*a*c*d^4*x^4+1/5*a*d^5*x^5+1/6*b*(c+d*x)^6/d+a*c^5*log(x) --R @@ -1113,9 +1113,9 @@ r0:=5*a*c^4*d*x+5*a*c^3*d^2*x^2+10/3*a*c^2*d^3*x^3+_ --R / --R 60d --R Type: Expression(Integer) ---E 47 +--E 47 ---S 48 of 1092 +--S 48 of 1092 a0:=integrate(t0,x) --R --R @@ -1131,9 +1131,9 @@ a0:=integrate(t0,x) --R / --R 60 --R Type: Union(Expression(Integer),...) ---E 48 +--E 48 ---S 49 of 1092 +--S 49 of 1092 m0:=a0-r0 --R --R @@ -1142,19 +1142,19 @@ m0:=a0-r0 --R (4) - ---- --R 6d --R Type: Expression(Integer) ---E 49 +--E 49 ---S 50 of 1092 +--S 50 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 50 +--E 50 )clear all ---S 51 of 1092 +--S 51 of 1092 t0:=(a+b*x)*(c+d*x)^5/x^2 --R --R @@ -1168,9 +1168,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^2 --R 2 --R x --R Type: Fraction(Polynomial(Integer)) ---E 51 +--E 51 ---S 52 of 1092 +--S 52 of 1092 r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ 5/3*c*d^3*(2*b*c+a*d)*x^3+1/4*d^4*(5*b*c+a*d)*x^4+_ 1/5*b*d^5*x^5+c^4*(b*c+5*a*d)*log(x) @@ -1188,9 +1188,9 @@ r0:=-a*c^5/x+5*c^3*d*(b*c+2*a*d)*x+5*c^2*d^2*(b*c+a*d)*x^2+_ --R / --R 60x --R Type: Expression(Integer) ---E 52 +--E 52 ---S 53 of 1092 +--S 53 of 1092 a0:=integrate(t0,x) --R --R @@ -1206,27 +1206,27 @@ a0:=integrate(t0,x) --R / --R 60x --R Type: Union(Expression(Integer),...) ---E 53 +--E 53 ---S 54 of 1092 +--S 54 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 54 +--E 54 ---S 55 of 1092 +--S 55 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 55 +--E 55 )clear all ---S 56 of 1092 +--S 56 of 1092 t0:=(a+b*x)*(c+d*x)^5/x^3 --R --R @@ -1240,9 +1240,9 @@ t0:=(a+b*x)*(c+d*x)^5/x^3 --R 3 --R x --R Type: Fraction(Polynomial(Integer)) ---E 56 +--E 56 ---S 57 of 1092 +--S 57 of 1092 r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ 5/2*c*d^3*(2*b*c+a*d)*x^2+1/3*d^4*(5*b*c+a*d)*x^3+_ 1/4*b*d^5*x^4+5*c^3*d*(b*c+2*a*d)*log(x) @@ -1261,9 +1261,9 @@ r0:=-1/2*a*c^5/x^2-c^4*(b*c+5*a*d)/x+10*c^2*d^2*(b*c+a*d)*x+_ --R 2 --R 12x --R Type: Expression(Integer) ---E 57 +--E 57 ---S 58 of 1092 +--S 58 of 1092 a0:=integrate(t0,x) --R --R @@ -1280,27 +1280,27 @@ a0:=integrate(t0,x) --R 2 --R 12x --R Type: Union(Expression(Integer),...) ---E 58 +--E 58 ---S 59 of 1092 +--S 59 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 59 +--E 59 ---S 60 of 1092 +--S 60 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 60 +--E 60 )clear all ---S 61 of 1092 +--S 61 of 1092 t0:=x*(a+b*x)*(c+d*x)^16 --R --R @@ -1329,9 +1329,9 @@ t0:=x*(a+b*x)*(c+d*x)^16 --R 14 2 15 3 15 16 2 16 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 61 +--E 61 ---S 62 of 1092 +--S 62 of 1092 r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ 1/19*b*(c+d*x)^19/d^3 --R @@ -1374,9 +1374,9 @@ r0:=1/17*c*(b*c-a*d)*(c+d*x)^17/d^3-1/18*(2*b*c-a*d)*(c+d*x)^18/d^3+_ --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 62 +--E 62 ---S 63 of 1092 +--S 63 of 1092 a0:=integrate(t0,x) --R --R @@ -1411,9 +1411,9 @@ a0:=integrate(t0,x) --R (30a c d + 4b c d)x + (-- a c d + - b c )x + - a c x --R 3 3 2 --R Type: Polynomial(Fraction(Integer)) ---E 63 +--E 63 ---S 64 of 1092 +--S 64 of 1092 m0:=a0-r0 --R --R @@ -1424,19 +1424,19 @@ m0:=a0-r0 --R 3 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 64 +--E 64 ---S 65 of 1092 +--S 65 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 65 +--E 65 )clear all ---S 66 of 1092 +--S 66 of 1092 t0:=x^2*(a+b*x)*(c+d*x)^16 --R --R @@ -1465,9 +1465,9 @@ t0:=x^2*(a+b*x)*(c+d*x)^16 --R 14 2 15 4 15 16 3 16 2 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 66 +--E 66 ---S 67 of 1092 +--S 67 of 1092 r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ 1/19*(3*b*c-a*d)*(c+d*x)^19/d^4+1/20*b*(c+d*x)^20/d^4 --R @@ -1512,9 +1512,9 @@ r0:=-1/17*c^2*(b*c-a*d)*(c+d*x)^17/d^4+1/18*c*(3*b*c-2*a*d)*(c+d*x)^18/d^4-_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 67 +--E 67 ---S 68 of 1092 +--S 68 of 1092 a0:=integrate(t0,x) --R --R @@ -1551,9 +1551,9 @@ a0:=integrate(t0,x) --R (24a c d + -- b c d)x + (4a c d + - b c )x + - a c x --R 5 4 3 --R Type: Polynomial(Fraction(Integer)) ---E 68 +--E 68 ---S 69 of 1092 +--S 69 of 1092 m0:=a0-r0 --R --R @@ -1564,19 +1564,19 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 69 +--E 69 ---S 70 of 1092 +--S 70 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 70 +--E 70 )clear all ---S 71 of 1092 +--S 71 of 1092 t0:=x^3*(a+b*x)*(c+d*x)^16 --R --R @@ -1605,9 +1605,9 @@ t0:=x^3*(a+b*x)*(c+d*x)^16 --R 14 2 15 5 15 16 4 16 3 --R (120a c d + 16b c d)x + (16a c d + b c )x + a c x --R Type: Polynomial(Integer) ---E 71 +--E 71 ---S 72 of 1092 +--S 72 of 1092 r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ 3/19*c*(2*b*c-a*d)*(c+d*x)^19/d^5-1/20*(4*b*c-a*d)*(c+d*x)^20/d^5+_ 1/21*b*(c+d*x)^21/d^5 @@ -1653,9 +1653,9 @@ r0:=1/17*c^3*(b*c-a*d)*(c+d*x)^17/d^5-1/18*c^2*(4*b*c-3*a*d)*(c+d*x)^18/d^5+_ --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 72 +--E 72 ---S 73 of 1092 +--S 73 of 1092 a0:=integrate(t0,x) --R --R @@ -1692,9 +1692,9 @@ a0:=integrate(t0,x) --R (20a c d + - b c d)x + (-- a c d + - b c )x + - a c x --R 3 5 5 4 --R Type: Polynomial(Fraction(Integer)) ---E 73 +--E 73 ---S 74 of 1092 +--S 74 of 1092 m0:=a0-r0 --R --R @@ -1705,28 +1705,28 @@ m0:=a0-r0 --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 74 +--E 74 ---S 75 of 1092 +--S 75 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 75 +--E 75 )clear all ---S 76 of 1092 +--S 76 of 1092 t0:=x^2*(2+x)^5*(2+3*x) --R --R --R 8 7 6 5 4 3 2 --R (1) 3x + 32x + 140x + 320x + 400x + 256x + 64x --R Type: Polynomial(Integer) ---E 76 +--E 76 ---S 77 of 1092 +--S 77 of 1092 r0:=1/3*x^3*(2+x)^6 --R --R @@ -1734,9 +1734,9 @@ r0:=1/3*x^3*(2+x)^6 --R (2) - x + 4x + 20x + --- x + 80x + 64x + -- x --R 3 3 3 --R Type: Polynomial(Fraction(Integer)) ---E 77 +--E 77 ---S 78 of 1092 +--S 78 of 1092 a0:=integrate(t0,x) --R --R @@ -1744,36 +1744,36 @@ a0:=integrate(t0,x) --R (3) - x + 4x + 20x + --- x + 80x + 64x + -- x --R 3 3 3 --R Type: Polynomial(Fraction(Integer)) ---E 78 +--E 78 ---S 79 of 1092 +--S 79 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Polynomial(Fraction(Integer)) ---E 79 +--E 79 ---S 80 of 1092 +--S 80 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Polynomial(Fraction(Integer)) ---E 80 +--E 80 )clear all ---S 81 of 1092 +--S 81 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x)^2 --R --R --R 2 4 3 2 2 n --R (1) (d x + 2c d x + c x )(b x + a) --R Type: Expression(Integer) ---E 81 +--E 81 ---S 82 of 1092 +--S 82 of 1092 r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ (a+b*x)^(2+n)/(b^5*(2+n))+(b^2*c^2-6*a*b*c*d+6*a^2*d^2)*_ (a+b*x)^(3+n)/(b^5*(3+n))+2*d*(b*c-2*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ @@ -1838,9 +1838,9 @@ r0:=a^2*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^5*(1+n))-2*a*(b*c-2*a*d)*(b*c-a*d)*_ --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 82 +--E 82 ---S 83 of 1092 +--S 83 of 1092 a0:=integrate(t0,x) --R --R @@ -1898,9 +1898,9 @@ a0:=integrate(t0,x) --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Union(Expression(Integer),...) ---E 83 +--E 83 ---S 84 of 1092 +--S 84 of 1092 m0:=a0-r0 --R --R @@ -2009,28 +2009,28 @@ m0:=a0-r0 --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 84 +--E 84 ---S 85 of 1092 +--S 85 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 85 +--E 85 )clear all ---S 86 of 1092 +--S 86 of 1092 t0:=x*(a+b*x)^n*(c+d*x)^2 --R --R --R 2 3 2 2 n --R (1) (d x + 2c d x + c x)(b x + a) --R Type: Expression(Integer) ---E 86 +--E 86 ---S 87 of 1092 +--S 87 of 1092 r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ (a+b*x)^(2+n)/(b^4*(2+n))+d*(2*b*c-3*a*d)*(a+b*x)^(3+n)/_ (b^4*(3+n))+d^2*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -2070,9 +2070,9 @@ r0:=-a*(b*c-a*d)^2*(a+b*x)^(1+n)/(b^4*(1+n))+(b*c-3*a*d)*(b*c-a*d)*_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 87 +--E 87 ---S 88 of 1092 +--S 88 of 1092 a0:=integrate(t0,x) --R --R @@ -2115,9 +2115,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 88 +--E 88 ---S 89 of 1092 +--S 89 of 1092 m0:=a0-r0 --R --R @@ -2190,28 +2190,28 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 89 +--E 89 ---S 90 of 1092 +--S 90 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 90 +--E 90 )clear all ---S 91 of 1092 +--S 91 of 1092 t0:=(a+b*x)^n*(c+d*x)^2 --R --R --R 2 2 2 n --R (1) (d x + 2c d x + c )(b x + a) --R Type: Expression(Integer) ---E 91 +--E 91 ---S 92 of 1092 +--S 92 of 1092 r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ (b^3*(2+n))+d^2*(a+b*x)^(3+n)/(b^3*(3+n)) --R @@ -2238,9 +2238,9 @@ r0:=(b*c-a*d)^2*(a+b*x)^(1+n)/(b^3*(1+n))+2*d*(b*c-a*d)*(a+b*x)^(2+n)/_ --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 92 +--E 92 ---S 93 of 1092 +--S 93 of 1092 a0:=integrate(t0,x) --R --R @@ -2263,9 +2263,9 @@ a0:=integrate(t0,x) --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Union(Expression(Integer),...) ---E 93 +--E 93 ---S 94 of 1092 +--S 94 of 1092 m0:=a0-r0 --R --R @@ -2303,19 +2303,19 @@ m0:=a0-r0 --R 3 3 3 2 3 3 --R b n + 6b n + 11b n + 6b --R Type: Expression(Integer) ---E 94 +--E 94 ---S 95 of 1092 +--S 95 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 95 +--E 95 )clear all ---S 96 of 1092 +--S 96 of 1092 t0:=(a+b*x)^n*(c+d*x)^2/x --R --R @@ -2324,29 +2324,29 @@ t0:=(a+b*x)^n*(c+d*x)^2/x --R (1) ------------------------------ --R x --R Type: Expression(Integer) ---E 96 +--E 96 ---S 97 of 1092 +--S 97 of 1092 --r0:=-d*(a*d-b*c*(3+n))*(a+b*x)^(1+n)/(b^2*(1+n)*(2+n))+_ -- d*(a+b*x)^(1+n)*(c+d*x)/(b*(2+n))-c^2*(a+b*x)^(1+n)*_ -- hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 97 +--E 97 ---S 98 of 1092 +--S 98 of 1092 --a0:=integrate(t0,x) ---E 98 +--E 98 ---S 99 of 1092 +--S 99 of 1092 --m0:=a0-r0 ---E 99 +--E 99 ---S 100 of 1092 +--S 100 of 1092 --d0:=D(m0,x) ---E 100 +--E 100 )clear all ---S 101 of 1092 +--S 101 of 1092 t0:=x^m*(a+b*x)^2*(c+d*x)^5 --R --R @@ -2363,9 +2363,9 @@ t0:=x^m*(a+b*x)^2*(c+d*x)^5 --R m --R x --R Type: Expression(Integer) ---E 101 +--E 101 ---S 102 of 1092 +--S 102 of 1092 r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ c^3*(b^2*c^2+10*a*b*c*d+10*a^2*d^2)*x^(3+m)/(3+m)+_ 5*c^2*d*(b^2*c^2+4*a*b*c*d+2*a^2*d^2)*x^(4+m)/(4+m)+_ @@ -2531,9 +2531,9 @@ r0:=a^2*c^5*x^(1+m)/(1+m)+a*c^4*(2*b*c+5*a*d)*x^(2+m)/(2+m)+_ --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Expression(Integer) ---E 102 +--E 102 ---S 103 of 1092 +--S 103 of 1092 a0:=integrate(t0,x) --R --R @@ -2699,9 +2699,9 @@ a0:=integrate(t0,x) --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Union(Expression(Integer),...) ---E 103 +--E 103 ---S 104 of 1092 +--S 104 of 1092 m0:=a0-r0 --R --R @@ -3023,19 +3023,19 @@ m0:=a0-r0 --R 8 7 6 5 4 3 2 --R m + 36m + 546m + 4536m + 22449m + 67284m + 118124m + 109584m + 40320 --R Type: Expression(Integer) ---E 104 +--E 104 ---S 105 of 1092 +--S 105 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 105 +--E 105 )clear all ---S 106 of 1092 +--S 106 of 1092 t0:=x^3*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3088,9 +3088,9 @@ t0:=x^3*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 5 2 15 16 4 2 16 3 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 106 +--E 106 ---S 107 of 1092 +--S 107 of 1092 r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ (b*c-a*d)*(c+d*x)^18/d^6-1/19*c*(10*b^2*c^2-12*a*b*c*d+_ 3*a^2*d^2)*(c+d*x)^19/d^6+1/20*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ @@ -3169,9 +3169,9 @@ r0:=-1/17*c^3*(b*c-a*d)^2*(c+d*x)^17/d^6+1/18*c^2*(5*b*c-3*a*d)*_ --R 6 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 107 +--E 107 ---S 108 of 1092 +--S 108 of 1092 a0:=integrate(t0,x) --R --R @@ -3239,9 +3239,9 @@ a0:=integrate(t0,x) --R (20a c d + -- a b c d + - b c )x + (-- a c d + - a b c )x + - a c x --R 3 6 5 5 4 --R Type: Polynomial(Fraction(Integer)) ---E 108 +--E 108 ---S 109 of 1092 +--S 109 of 1092 m0:=a0-r0 --R --R @@ -3252,19 +3252,19 @@ m0:=a0-r0 --R 6 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 109 +--E 109 ---S 110 of 1092 +--S 110 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 110 +--E 110 )clear all ---S 111 of 1092 +--S 111 of 1092 t0:=x^2*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3317,9 +3317,9 @@ t0:=x^2*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 4 2 15 16 3 2 16 2 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 111 +--E 111 ---S 112 of 1092 +--S 112 of 1092 r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ (c+d*x)^18/d^5+1/19*(6*b^2*c^2-6*a*b*c*d+a^2*d^2)*(c+d*x)^19/d^5-_ 1/10*b*(2*b*c-a*d)*(c+d*x)^20/d^5+1/21*b^2*(c+d*x)^21/d^5 @@ -3394,9 +3394,9 @@ r0:=1/17*c^2*(b*c-a*d)^2*(c+d*x)^17/d^5-1/9*c*(b*c-a*d)*(2*b*c-a*d)*_ --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 112 +--E 112 ---S 113 of 1092 +--S 113 of 1092 a0:=integrate(t0,x) --R --R @@ -3462,9 +3462,9 @@ a0:=integrate(t0,x) --R (24a c d + -- a b c d + - b c )x + (4a c d + - a b c )x + - a c x --R 5 5 2 3 --R Type: Polynomial(Fraction(Integer)) ---E 113 +--E 113 ---S 114 of 1092 +--S 114 of 1092 m0:=a0-r0 --R --R @@ -3475,19 +3475,19 @@ m0:=a0-r0 --R 5 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 114 +--E 114 ---S 115 of 1092 +--S 115 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 115 +--E 115 )clear all ---S 116 of 1092 +--S 116 of 1092 t0:=x*(a+b*x)^2*(c+d*x)^16 --R --R @@ -3540,9 +3540,9 @@ t0:=x*(a+b*x)^2*(c+d*x)^16 --R 2 14 2 15 2 16 3 2 15 16 2 2 16 --R (120a c d + 32a b c d + b c )x + (16a c d + 2a b c )x + a c x --R Type: Polynomial(Integer) ---E 116 +--E 116 ---S 117 of 1092 +--S 117 of 1092 r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ (c+d*x)^18/d^4-1/19*b*(3*b*c-2*a*d)*(c+d*x)^19/d^4+_ 1/20*b^2*(c+d*x)^20/d^4 @@ -3616,9 +3616,9 @@ r0:=-1/17*c*(b*c-a*d)^2*(c+d*x)^17/d^4+1/18*(b*c-a*d)*(3*b*c-a*d)*_ --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 117 +--E 117 ---S 118 of 1092 +--S 118 of 1092 a0:=integrate(t0,x) --R --R @@ -3683,9 +3683,9 @@ a0:=integrate(t0,x) --R (30a c d + 8a b c d + - b c )x + (-- a c d + - a b c )x + - a c x --R 4 3 3 2 --R Type: Polynomial(Fraction(Integer)) ---E 118 +--E 118 ---S 119 of 1092 +--S 119 of 1092 m0:=a0-r0 --R --R @@ -3696,28 +3696,28 @@ m0:=a0-r0 --R 4 --R d --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 119 +--E 119 ---S 120 of 1092 +--S 120 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Fraction(Polynomial(Fraction(Integer))) ---E 120 +--E 120 )clear all ---S 121 of 1092 +--S 121 of 1092 t0:=x^2*(a+b*x)^n*(c+d*x)^3 --R --R --R 3 5 2 4 2 3 3 2 n --R (1) (d x + 3c d x + 3c d x + c x )(b x + a) --R Type: Expression(Integer) ---E 121 +--E 121 ---S 122 of 1092 +--S 122 of 1092 r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ (b*c-a*d)^2*(a+b*x)^(2+n)/(b^6*(2+n))+(b*c-a*d)*_ (b^2*c^2-8*a*b*c*d+10*a^2*d^2)*(a+b*x)^(3+n)/(b^6*(3+n))+_ @@ -3828,9 +3828,9 @@ r0:=a^2*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^6*(1+n))-a*(2*b*c-5*a*d)*_ --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Expression(Integer) ---E 122 +--E 122 ---S 123 of 1092 +--S 123 of 1092 a0:=integrate(t0,x) --R --R @@ -3921,9 +3921,9 @@ a0:=integrate(t0,x) --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Union(Expression(Integer),...) ---E 123 +--E 123 ---S 124 of 1092 +--S 124 of 1092 m0:=a0-r0 --R --R @@ -4113,28 +4113,28 @@ m0:=a0-r0 --R 6 6 6 5 6 4 6 3 6 2 6 6 --R b n + 21b n + 175b n + 735b n + 1624b n + 1764b n + 720b --R Type: Expression(Integer) ---E 124 +--E 124 ---S 125 of 1092 +--S 125 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 125 +--E 125 )clear all ---S 126 of 1092 +--S 126 of 1092 t0:=x*(a+b*x)^n*(c+d*x)^3 --R --R --R 3 4 2 3 2 2 3 n --R (1) (d x + 3c d x + 3c d x + c x)(b x + a) --R Type: Expression(Integer) ---E 126 +--E 126 ---S 127 of 1092 +--S 127 of 1092 r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ (a+b*x)^(2+n)/(b^5*(2+n))+3*d*(b*c-2*a*d)*(b*c-a*d)*(a+b*x)^(3+n)/_ (b^5*(3+n))+d^2*(3*b*c-4*a*d)*(a+b*x)^(4+n)/(b^5*(4+n))+_ @@ -4208,9 +4208,9 @@ r0:=-a*(b*c-a*d)^3*(a+b*x)^(1+n)/(b^5*(1+n))+(b*c-4*a*d)*(b*c-a*d)^2*_ --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 127 +--E 127 ---S 128 of 1092 +--S 128 of 1092 a0:=integrate(t0,x) --R --R @@ -4277,9 +4277,9 @@ a0:=integrate(t0,x) --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Union(Expression(Integer),...) ---E 128 +--E 128 ---S 129 of 1092 +--S 129 of 1092 m0:=a0-r0 --R --R @@ -4412,28 +4412,28 @@ m0:=a0-r0 --R 5 5 5 4 5 3 5 2 5 5 --R b n + 15b n + 85b n + 225b n + 274b n + 120b --R Type: Expression(Integer) ---E 129 +--E 129 ---S 130 of 1092 +--S 130 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 130 +--E 130 )clear all ---S 131 of 1092 +--S 131 of 1092 t0:=(a+b*x)^n*(c+d*x)^3 --R --R --R 3 3 2 2 2 3 n --R (1) (d x + 3c d x + 3c d x + c )(b x + a) --R Type: Expression(Integer) ---E 131 +--E 131 ---S 132 of 1092 +--S 132 of 1092 r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ (a+b*x)^(2+n)/(b^4*(2+n))+3*d^2*(b*c-a*d)*(a+b*x)^(3+n)/_ (b^4*(3+n))+d^3*(a+b*x)^(4+n)/(b^4*(4+n)) @@ -4479,9 +4479,9 @@ r0:=(b*c-a*d)^3*(a+b*x)^(1+n)/(b^4*(1+n))+3*d*(b*c-a*d)^2*_ --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 132 +--E 132 ---S 133 of 1092 +--S 133 of 1092 a0:=integrate(t0,x) --R --R @@ -4530,9 +4530,9 @@ a0:=integrate(t0,x) --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Union(Expression(Integer),...) ---E 133 +--E 133 ---S 134 of 1092 +--S 134 of 1092 m0:=a0-r0 --R --R @@ -4620,19 +4620,19 @@ m0:=a0-r0 --R 4 4 4 3 4 2 4 4 --R b n + 10b n + 35b n + 50b n + 24b --R Type: Expression(Integer) ---E 134 +--E 134 ---S 135 of 1092 +--S 135 of 1092 d0:=normalize m0 --R --R --R (5) 0 --R Type: Expression(Integer) ---E 135 +--E 135 )clear all ---S 136 of 1092 +--S 136 of 1092 t0:=(a+b*x)^n*(c+d*x)^3/x --R --R @@ -4641,30 +4641,30 @@ t0:=(a+b*x)^n*(c+d*x)^3/x --R (1) ---------------------------------------- --R x --R Type: Expression(Integer) ---E 136 +--E 136 ---S 137 of 1092 +--S 137 of 1092 --r0:=3*c^2*d*(a+b*x)^(1+n)/(b*(1+n))-3*a*c*d^2*(a+b*x)^(1+n)/(b^2*(1+n))+_ -- a^2*d^3*(a+b*x)^(1+n)/(b^3*(1+n))+3*c*d^2*(a+b*x)^(2+n)/(b^2*(2+n))-_ -- 2*a*d^3*(a+b*x)^(2+n)/(b^3*(2+n))+d^3*(a+b*x)^(3+n)/(b^3*(3+n))-_ -- c^3*(a+b*x)^(1+n)*hypergeometric(1,1+n,2+n,(a+b*x)/a)/(a*(1+n)) ---E 137 +--E 137 ---S 138 of 1092 +--S 138 of 1092 --a0:=integrate(t0,x) ---E 138 +--E 138 ---S 139 of 1092 +--S 139 of 1092 --m0:=a0-r0 ---E 139 +--E 139 ---S 140 of 1092 +--S 140 of 1092 --d0:=D(m0,x) ---E 140 +--E 140 )clear all ---S 141 of 1092 +--S 141 of 1092 t0:=x^m*(c+d*x)/(a+b*x) --R --R @@ -4673,28 +4673,28 @@ t0:=x^m*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Expression(Integer) ---E 141 +--E 141 ---S 142 of 1092 +--S 142 of 1092 --r0:=d*x^(1+m)/(b*(1+m))+(b*c-a*d)*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b*(1+m)) ---E 142 +--E 142 ---S 143 of 1092 +--S 143 of 1092 --a0:=integrate(t0,x) ---E 143 +--E 143 ---S 144 of 1092 +--S 144 of 1092 --m0:=a0-r0 ---E 144 +--E 144 ---S 145 of 1092 +--S 145 of 1092 --d0:=D(m0,x) ---E 145 +--E 145 )clear all ---S 146 of 1092 +--S 146 of 1092 t0:=x^4*(c+d*x)/(a+b*x) --R --R @@ -4703,9 +4703,9 @@ t0:=x^4*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 146 +--E 146 ---S 147 of 1092 +--S 147 of 1092 r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ 1/4*(b*c-a*d)*x^4/b^2+1/5*d*x^5/b+a^4*(b*c-a*d)*log(a+b*x)/b^6 --R @@ -4720,9 +4720,9 @@ r0:=-a^3*(b*c-a*d)*x/b^5+1/2*a^2*(b*c-a*d)*x^2/b^4-1/3*a*(b*c-a*d)*x^3/b^3+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 147 +--E 147 ---S 148 of 1092 +--S 148 of 1092 a0:=integrate(t0,x) --R --R @@ -4736,27 +4736,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 148 +--E 148 ---S 149 of 1092 +--S 149 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 149 +--E 149 ---S 150 of 1092 +--S 150 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 150 +--E 150 )clear all ---S 151 of 1092 +--S 151 of 1092 t0:=x^3*(c+d*x)/(a+b*x) --R --R @@ -4765,9 +4765,9 @@ t0:=x^3*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 151 +--E 151 ---S 152 of 1092 +--S 152 of 1092 r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ 1/4*d*x^4/b-a^3*(b*c-a*d)*log(a+b*x)/b^5 --R @@ -4782,9 +4782,9 @@ r0:=a^2*(b*c-a*d)*x/b^4-1/2*a*(b*c-a*d)*x^2/b^3+1/3*(b*c-a*d)*x^3/b^2+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 152 +--E 152 ---S 153 of 1092 +--S 153 of 1092 a0:=integrate(t0,x) --R --R @@ -4798,27 +4798,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 153 +--E 153 ---S 154 of 1092 +--S 154 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 154 +--E 154 ---S 155 of 1092 +--S 155 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 155 +--E 155 )clear all ---S 156 of 1092 +--S 156 of 1092 t0:=x^2*(c+d*x)/(a+b*x) --R --R @@ -4827,9 +4827,9 @@ t0:=x^2*(c+d*x)/(a+b*x) --R (1) ----------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 156 +--E 156 ---S 157 of 1092 +--S 157 of 1092 r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ a^2*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -4844,9 +4844,9 @@ r0:=-a*(b*c-a*d)*x/b^3+1/2*(b*c-a*d)*x^2/b^2+1/3*d*x^3/b+_ --R 4 --R 6b --R Type: Expression(Integer) ---E 157 +--E 157 ---S 158 of 1092 +--S 158 of 1092 a0:=integrate(t0,x) --R --R @@ -4860,27 +4860,27 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 158 +--E 158 ---S 159 of 1092 +--S 159 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 159 +--E 159 ---S 160 of 1092 +--S 160 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 160 +--E 160 )clear all ---S 161 of 1092 +--S 161 of 1092 t0:=x*(c+d*x)/(a+b*x) --R --R @@ -4889,9 +4889,9 @@ t0:=x*(c+d*x)/(a+b*x) --R (1) ---------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 161 +--E 161 ---S 162 of 1092 +--S 162 of 1092 r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 --R --R @@ -4901,9 +4901,9 @@ r0:=(b*c-a*d)*x/b^2+1/2*d*x^2/b-a*(b*c-a*d)*log(a+b*x)/b^3 --R 3 --R 2b --R Type: Expression(Integer) ---E 162 +--E 162 ---S 163 of 1092 +--S 163 of 1092 a0:=integrate(t0,x) --R --R @@ -4913,27 +4913,27 @@ a0:=integrate(t0,x) --R 3 --R 2b --R Type: Union(Expression(Integer),...) ---E 163 +--E 163 ---S 164 of 1092 +--S 164 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 164 +--E 164 ---S 165 of 1092 +--S 165 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 165 +--E 165 )clear all ---S 166 of 1092 +--S 166 of 1092 t0:=(c+d*x)/(a+b*x) --R --R @@ -4941,9 +4941,9 @@ t0:=(c+d*x)/(a+b*x) --R (1) ------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 166 +--E 166 ---S 167 of 1092 +--S 167 of 1092 r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 --R --R @@ -4952,9 +4952,9 @@ r0:=d*x/b+(b*c-a*d)*log(a+b*x)/b^2 --R 2 --R b --R Type: Expression(Integer) ---E 167 +--E 167 ---S 168 of 1092 +--S 168 of 1092 a0:=integrate(t0,x) --R --R @@ -4963,27 +4963,27 @@ a0:=integrate(t0,x) --R 2 --R b --R Type: Union(Expression(Integer),...) ---E 168 +--E 168 ---S 169 of 1092 +--S 169 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 169 +--E 169 ---S 170 of 1092 +--S 170 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 170 +--E 170 )clear all ---S 171 of 1092 +--S 171 of 1092 t0:=(c+d*x)/(x*(a+b*x)) --R --R @@ -4992,9 +4992,9 @@ t0:=(c+d*x)/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 171 +--E 171 ---S 172 of 1092 +--S 172 of 1092 r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) --R --R @@ -5002,9 +5002,9 @@ r0:=c*log(x)/a-(b*c-a*d)*log(a+b*x)/(a*b) --R (2) ------------------------------------ --R a b --R Type: Expression(Integer) ---E 172 +--E 172 ---S 173 of 1092 +--S 173 of 1092 a0:=integrate(t0,x) --R --R @@ -5012,27 +5012,27 @@ a0:=integrate(t0,x) --R (3) ------------------------------------ --R a b --R Type: Union(Expression(Integer),...) ---E 173 +--E 173 ---S 174 of 1092 +--S 174 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 174 +--E 174 ---S 175 of 1092 +--S 175 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 175 +--E 175 )clear all ---S 176 of 1092 +--S 176 of 1092 t0:=(c+d*x)/(x^2*(a+b*x)) --R --R @@ -5041,9 +5041,9 @@ t0:=(c+d*x)/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 176 +--E 176 ---S 177 of 1092 +--S 177 of 1092 r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 --R --R @@ -5052,9 +5052,9 @@ r0:=-c/(a*x)-(b*c-a*d)*log(x)/a^2+(b*c-a*d)*log(a+b*x)/a^2 --R 2 --R a x --R Type: Expression(Integer) ---E 177 +--E 177 ---S 178 of 1092 +--S 178 of 1092 a0:=integrate(t0,x) --R --R @@ -5063,27 +5063,27 @@ a0:=integrate(t0,x) --R 2 --R a x --R Type: Union(Expression(Integer),...) ---E 178 +--E 178 ---S 179 of 1092 +--S 179 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 179 +--E 179 ---S 180 of 1092 +--S 180 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 180 +--E 180 )clear all ---S 181 of 1092 +--S 181 of 1092 t0:=(c+d*x)/(x^3*(a+b*x)) --R --R @@ -5092,9 +5092,9 @@ t0:=(c+d*x)/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 181 +--E 181 ---S 182 of 1092 +--S 182 of 1092 r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ b*(b*c-a*d)*log(a+b*x)/a^3 --R @@ -5109,9 +5109,9 @@ r0:=-1/2*c/(a*x^2)+(b*c-a*d)/(a^2*x)+b*(b*c-a*d)*log(x)/a^3-_ --R 3 2 --R 2a x --R Type: Expression(Integer) ---E 182 +--E 182 ---S 183 of 1092 +--S 183 of 1092 a0:=integrate(t0,x) --R --R @@ -5125,27 +5125,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a x --R Type: Union(Expression(Integer),...) ---E 183 +--E 183 ---S 184 of 1092 +--S 184 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 184 +--E 184 ---S 185 of 1092 +--S 185 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 185 +--E 185 )clear all ---S 186 of 1092 +--S 186 of 1092 t0:=(c+d*x)/(x^4*(a+b*x)) --R --R @@ -5154,9 +5154,9 @@ t0:=(c+d*x)/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 186 +--E 186 ---S 187 of 1092 +--S 187 of 1092 r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ b^2*(b*c-a*d)*log(x)/a^4+b^2*(b*c-a*d)*log(a+b*x)/a^4 --R @@ -5171,9 +5171,9 @@ r0:=-1/3*c/(a*x^3)+1/2*(b*c-a*d)/(a^2*x^2)-b*(b*c-a*d)/(a^3*x)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 187 +--E 187 ---S 188 of 1092 +--S 188 of 1092 a0:=integrate(t0,x) --R --R @@ -5187,27 +5187,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 188 +--E 188 ---S 189 of 1092 +--S 189 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 189 +--E 189 ---S 190 of 1092 +--S 190 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 190 +--E 190 )clear all ---S 191 of 1092 +--S 191 of 1092 t0:=(c+d*x)/(x^5*(a+b*x)) --R --R @@ -5216,9 +5216,9 @@ t0:=(c+d*x)/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 191 +--E 191 ---S 192 of 1092 +--S 192 of 1092 r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ b^2*(b*c-a*d)/(a^4*x)+b^3*(b*c-a*d)*log(x)/a^5-_ b^3*(b*c-a*d)*log(a+b*x)/a^5 @@ -5234,9 +5234,9 @@ r0:=-1/4*c/(a*x^4)+1/3*(b*c-a*d)/(a^2*x^3)-1/2*b*(b*c-a*d)/(a^3*x^2)+_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 192 +--E 192 ---S 193 of 1092 +--S 193 of 1092 a0:=integrate(t0,x) --R --R @@ -5250,27 +5250,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 193 +--E 193 ---S 194 of 1092 +--S 194 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 194 +--E 194 ---S 195 of 1092 +--S 195 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 195 +--E 195 )clear all ---S 196 of 1092 +--S 196 of 1092 t0:=x^m*(c+d*x)^2/(a+b*x) --R --R @@ -5279,29 +5279,29 @@ t0:=x^m*(c+d*x)^2/(a+b*x) --R (1) ---------------------- --R b x + a --R Type: Expression(Integer) ---E 196 +--E 196 ---S 197 of 1092 +--S 197 of 1092 --r0:=-d*(a*d*(2+m)-b*c*(3+m))*x^(1+m)/(b^2*(1+m)*(2+m))+_ -- d*x^(1+m)*(c+d*x)/(b*(2+m))+(b*c-a*d)^2*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^2*(1+m)) ---E 197 +--E 197 ---S 198 of 1092 +--S 198 of 1092 --a0:=integrate(t0,x) ---E 198 +--E 198 ---S 199 of 1092 +--S 199 of 1092 --m0:=a0-r0 ---E 199 +--E 199 ---S 200 of 1092 +--S 200 of 1092 --d0:=D(m0,x) ---E 200 +--E 200 )clear all ---S 201 of 1092 +--S 201 of 1092 t0:=x^4*(c+d*x)^2/(a+b*x) --R --R @@ -5310,9 +5310,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 201 +--E 201 ---S 202 of 1092 +--S 202 of 1092 r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ 1/3*a*(b*c-a*d)^2*x^3/b^4+1/4*(b*c-a*d)^2*x^4/b^3+_ 1/5*d*(2*b*c-a*d)*x^5/b^2+1/6*d^2*x^6/b+a^4*(b*c-a*d)^2*log(a+b*x)/b^7 @@ -5334,9 +5334,9 @@ r0:=-a^3*(b*c-a*d)^2*x/b^6+1/2*a^2*(b*c-a*d)^2*x^2/b^5-_ --R 7 --R 60b --R Type: Expression(Integer) ---E 202 +--E 202 ---S 203 of 1092 +--S 203 of 1092 a0:=integrate(t0,x) --R --R @@ -5356,27 +5356,27 @@ a0:=integrate(t0,x) --R 7 --R 60b --R Type: Union(Expression(Integer),...) ---E 203 +--E 203 ---S 204 of 1092 +--S 204 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 204 +--E 204 ---S 205 of 1092 +--S 205 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 205 +--E 205 )clear all ---S 206 of 1092 +--S 206 of 1092 t0:=x^3*(c+d*x)^2/(a+b*x) --R --R @@ -5385,9 +5385,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 206 +--E 206 ---S 207 of 1092 +--S 207 of 1092 r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ 1/3*(b*c-a*d)^2*x^3/b^3+1/4*d*(2*b*c-a*d)*x^4/b^2+1/5*d^2*x^5/b-_ a^3*(b*c-a*d)^2*log(a+b*x)/b^6 @@ -5406,9 +5406,9 @@ r0:=a^2*(b*c-a*d)^2*x/b^5-1/2*a*(b*c-a*d)^2*x^2/b^4+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 207 +--E 207 ---S 208 of 1092 +--S 208 of 1092 a0:=integrate(t0,x) --R --R @@ -5425,27 +5425,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 208 +--E 208 ---S 209 of 1092 +--S 209 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 209 +--E 209 ---S 210 of 1092 +--S 210 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 210 +--E 210 )clear all ---S 211 of 1092 +--S 211 of 1092 t0:=x^2*(c+d*x)^2/(a+b*x) --R --R @@ -5454,9 +5454,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x) --R (1) --------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 211 +--E 211 ---S 212 of 1092 +--S 212 of 1092 r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ 1/4*d^2*x^4/b+a^2*(b*c-a*d)^2*log(a+b*x)/b^5 --R @@ -5474,9 +5474,9 @@ r0:=-a*(b*c-a*d)^2*x/b^4+1/2*(b*c-a*d)^2*x^2/b^3+1/3*d*(2*b*c-a*d)*x^3/b^2+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 212 +--E 212 ---S 213 of 1092 +--S 213 of 1092 a0:=integrate(t0,x) --R --R @@ -5493,27 +5493,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 213 +--E 213 ---S 214 of 1092 +--S 214 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 214 +--E 214 ---S 215 of 1092 +--S 215 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 215 +--E 215 )clear all ---S 216 of 1092 +--S 216 of 1092 t0:=x*(c+d*x)^2/(a+b*x) --R --R @@ -5522,9 +5522,9 @@ t0:=x*(c+d*x)^2/(a+b*x) --R (1) -------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 216 +--E 216 ---S 217 of 1092 +--S 217 of 1092 r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ a*(b*c-a*d)^2*log(a+b*x)/b^4 --R @@ -5539,9 +5539,9 @@ r0:=(b*c-a*d)^2*x/b^3+1/2*d*(2*b*c-a*d)*x^2/b^2+1/3*d^2*x^3/b-_ --R 4 --R 6b --R Type: Expression(Integer) ---E 217 +--E 217 ---S 218 of 1092 +--S 218 of 1092 a0:=integrate(t0,x) --R --R @@ -5555,27 +5555,27 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 218 +--E 218 ---S 219 of 1092 +--S 219 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 219 +--E 219 ---S 220 of 1092 +--S 220 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 220 +--E 220 )clear all ---S 221 of 1092 +--S 221 of 1092 t0:=(c+d*x)^2/(a+b*x) --R --R @@ -5584,9 +5584,9 @@ t0:=(c+d*x)^2/(a+b*x) --R (1) ------------------ --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 221 +--E 221 ---S 222 of 1092 +--S 222 of 1092 r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 --R --R @@ -5600,9 +5600,9 @@ r0:=d*(b*c-a*d)*x/b^2+1/2*(c+d*x)^2/b+(b*c-a*d)^2*log(a+b*x)/b^3 --R 3 --R 2b --R Type: Expression(Integer) ---E 222 +--E 222 ---S 223 of 1092 +--S 223 of 1092 a0:=integrate(t0,x) --R --R @@ -5613,9 +5613,9 @@ a0:=integrate(t0,x) --R 3 --R 2b --R Type: Union(Expression(Integer),...) ---E 223 +--E 223 ---S 224 of 1092 +--S 224 of 1092 m0:=a0-r0 --R --R @@ -5624,19 +5624,19 @@ m0:=a0-r0 --R (4) - -- --R 2b --R Type: Expression(Integer) ---E 224 +--E 224 ---S 225 of 1092 +--S 225 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 225 +--E 225 )clear all ---S 226 of 1092 +--S 226 of 1092 t0:=(c+d*x)^2/(x*(a+b*x)) --R --R @@ -5646,9 +5646,9 @@ t0:=(c+d*x)^2/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 226 +--E 226 ---S 227 of 1092 +--S 227 of 1092 r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) --R --R @@ -5658,9 +5658,9 @@ r0:=d^2*x/b+c^2*log(x)/a-(b*c-a*d)^2*log(a+b*x)/(a*b^2) --R 2 --R a b --R Type: Expression(Integer) ---E 227 +--E 227 ---S 228 of 1092 +--S 228 of 1092 a0:=integrate(t0,x) --R --R @@ -5670,27 +5670,27 @@ a0:=integrate(t0,x) --R 2 --R a b --R Type: Union(Expression(Integer),...) ---E 228 +--E 228 ---S 229 of 1092 +--S 229 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 229 +--E 229 ---S 230 of 1092 +--S 230 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 230 +--E 230 )clear all ---S 231 of 1092 +--S 231 of 1092 t0:=(c+d*x)^2/(x^2*(a+b*x)) --R --R @@ -5700,9 +5700,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 231 +--E 231 ---S 232 of 1092 +--S 232 of 1092 r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) --R --R @@ -5713,9 +5713,9 @@ r0:=-c^2/(a*x)-c*(b*c-2*a*d)*log(x)/a^2+(b*c-a*d)^2*log(a+b*x)/(a^2*b) --R 2 --R a b x --R Type: Expression(Integer) ---E 232 +--E 232 ---S 233 of 1092 +--S 233 of 1092 a0:=integrate(t0,x) --R --R @@ -5726,27 +5726,27 @@ a0:=integrate(t0,x) --R 2 --R a b x --R Type: Union(Expression(Integer),...) ---E 233 +--E 233 ---S 234 of 1092 +--S 234 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 234 +--E 234 ---S 235 of 1092 +--S 235 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 235 +--E 235 )clear all ---S 236 of 1092 +--S 236 of 1092 t0:=(c+d*x)^2/(x^3*(a+b*x)) --R --R @@ -5756,9 +5756,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 236 +--E 236 ---S 237 of 1092 +--S 237 of 1092 r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ (b*c-a*d)^2*log(a+b*x)/a^3 --R @@ -5773,9 +5773,9 @@ r0:=-1/2*c^2/(a*x^2)+c*(b*c-2*a*d)/(a^2*x)+(b*c-a*d)^2*log(x)/a^3-_ --R 3 2 --R 2a x --R Type: Expression(Integer) ---E 237 +--E 237 ---S 238 of 1092 +--S 238 of 1092 a0:=integrate(t0,x) --R --R @@ -5789,27 +5789,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a x --R Type: Union(Expression(Integer),...) ---E 238 +--E 238 ---S 239 of 1092 +--S 239 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 239 +--E 239 ---S 240 of 1092 +--S 240 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 240 +--E 240 )clear all ---S 241 of 1092 +--S 241 of 1092 t0:=(c+d*x)^2/(x^4*(a+b*x)) --R --R @@ -5819,9 +5819,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 241 +--E 241 ---S 242 of 1092 +--S 242 of 1092 r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ b*(b*c-a*d)^2*log(x)/a^4+b*(b*c-a*d)^2*log(a+b*x)/a^4 --R @@ -5839,9 +5839,9 @@ r0:=-1/3*c^2/(a*x^3)+1/2*c*(b*c-2*a*d)/(a^2*x^2)-(b*c-a*d)^2/(a^3*x)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 242 +--E 242 ---S 243 of 1092 +--S 243 of 1092 a0:=integrate(t0,x) --R --R @@ -5858,27 +5858,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 243 +--E 243 ---S 244 of 1092 +--S 244 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 244 +--E 244 ---S 245 of 1092 +--S 245 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 245 +--E 245 )clear all ---S 246 of 1092 +--S 246 of 1092 t0:=(c+d*x)^2/(x^5*(a+b*x)) --R --R @@ -5888,9 +5888,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 246 +--E 246 ---S 247 of 1092 +--S 247 of 1092 r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ 1/2*(b*c-a*d)^2/(a^3*x^2)+b*(b*c-a*d)^2/(a^4*x)+_ b^2*(b*c-a*d)^2*log(x)/a^5-b^2*(b*c-a*d)^2*log(a+b*x)/a^5 @@ -5912,9 +5912,9 @@ r0:=-1/4*c^2/(a*x^4)+1/3*c*(b*c-2*a*d)/(a^2*x^3)-_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 247 +--E 247 ---S 248 of 1092 +--S 248 of 1092 a0:=integrate(t0,x) --R --R @@ -5934,27 +5934,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 248 +--E 248 ---S 249 of 1092 +--S 249 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 249 +--E 249 ---S 250 of 1092 +--S 250 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 250 +--E 250 )clear all ---S 251 of 1092 +--S 251 of 1092 t0:=(c+d*x)^2/(x^6*(a+b*x)) --R --R @@ -5964,9 +5964,9 @@ t0:=(c+d*x)^2/(x^6*(a+b*x)) --R 7 6 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 251 +--E 251 ---S 252 of 1092 +--S 252 of 1092 r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ 1/3*(b*c-a*d)^2/(a^3*x^3)+1/2*b*(b*c-a*d)^2/(a^4*x^2)-_ b^2*(b*c-a*d)^2/(a^5*x)-b^3*(b*c-a*d)^2*log(x)/a^6+_ @@ -5992,9 +5992,9 @@ r0:=-1/5*c^2/(a*x^5)+1/4*c*(b*c-2*a*d)/(a^2*x^4)-_ --R 6 5 --R 60a x --R Type: Expression(Integer) ---E 252 +--E 252 ---S 253 of 1092 +--S 253 of 1092 a0:=integrate(t0,x) --R --R @@ -6017,27 +6017,27 @@ a0:=integrate(t0,x) --R 6 5 --R 60a x --R Type: Union(Expression(Integer),...) ---E 253 +--E 253 ---S 254 of 1092 +--S 254 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 254 +--E 254 ---S 255 of 1092 +--S 255 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 255 +--E 255 )clear all ---S 256 of 1092 +--S 256 of 1092 t0:=x^m*(c+d*x)^3/(a+b*x) --R --R @@ -6046,29 +6046,29 @@ t0:=x^m*(c+d*x)^3/(a+b*x) --R (1) -------------------------------- --R b x + a --R Type: Expression(Integer) ---E 256 +--E 256 ---S 257 of 1092 +--S 257 of 1092 --r0:=d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^(1+m)/(b^3*(1+m))+_ -- d^2*(3*b*c-a*d)*x^(2+m)/(b^2*(2+m))+d^3*x^(3+m)/(b*(3+m))+_ -- (b*c-a*d)^3*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*b^3*(1+m)) ---E 257 +--E 257 ---S 258 of 1092 +--S 258 of 1092 --a0:=integrate(t0,x) ---E 258 +--E 258 ---S 259 of 1092 +--S 259 of 1092 --m0:=a0-r0 ---E 259 +--E 259 ---S 260 of 1092 +--S 260 of 1092 --d0:=D(m0,x) ---E 260 +--E 260 )clear all ---S 261 of 1092 +--S 261 of 1092 t0:=x^4*(c+d*x)^3/(a+b*x) --R --R @@ -6077,9 +6077,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 261 +--E 261 ---S 262 of 1092 +--S 262 of 1092 r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ x^3/b^5+1/4*(b*c-a*d)^3*x^4/b^4+1/5*d*(3*b^2*c^2-_ 3*a*b*c*d+a^2*d^2)*x^5/b^3+1/6*d^2*(3*b*c-a*d)*x^6/b^2+_ @@ -6111,9 +6111,9 @@ r0:=-a^3*(b*c-a*d)^3*x/b^7+1/2*a^2*(b*c-a*d)^3*x^2/b^6-1/3*a*(b*c-a*d)^3*_ --R 8 --R 420b --R Type: Expression(Integer) ---E 262 +--E 262 ---S 263 of 1092 +--S 263 of 1092 a0:=integrate(t0,x) --R --R @@ -6142,27 +6142,27 @@ a0:=integrate(t0,x) --R 8 --R 420b --R Type: Union(Expression(Integer),...) ---E 263 +--E 263 ---S 264 of 1092 +--S 264 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 264 +--E 264 ---S 265 of 1092 +--S 265 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 265 +--E 265 )clear all ---S 266 of 1092 +--S 266 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x) --R --R @@ -6171,9 +6171,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 266 +--E 266 ---S 267 of 1092 +--S 267 of 1092 r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ 1/4*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^4/b^3+_ 1/5*d^2*(3*b*c-a*d)*x^5/b^2+1/6*d^3*x^6/b-a^3*(b*c-a*d)^3*log(a+b*x)/b^7 @@ -6198,9 +6198,9 @@ r0:=a^2*(b*c-a*d)^3*x/b^6-1/2*a*(b*c-a*d)^3*x^2/b^5+1/3*(b*c-a*d)^3*x^3/b^4+_ --R 7 --R 60b --R Type: Expression(Integer) ---E 267 +--E 267 ---S 268 of 1092 +--S 268 of 1092 a0:=integrate(t0,x) --R --R @@ -6223,27 +6223,27 @@ a0:=integrate(t0,x) --R 7 --R 60b --R Type: Union(Expression(Integer),...) ---E 268 +--E 268 ---S 269 of 1092 +--S 269 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 269 +--E 269 ---S 270 of 1092 +--S 270 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 270 +--E 270 )clear all ---S 271 of 1092 +--S 271 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x) --R --R @@ -6252,9 +6252,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x) --R (1) ------------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 271 +--E 271 ---S 272 of 1092 +--S 272 of 1092 r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ 1/3*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^3/b^3+_ 1/4*d^2*(3*b*c-a*d)*x^4/b^2+1/5*d^3*x^5/b+a^2*(b*c-a*d)^3*log(a+b*x)/b^6 @@ -6276,9 +6276,9 @@ r0:=-a*(b*c-a*d)^3*x/b^5+1/2*(b*c-a*d)^3*x^2/b^4+_ --R 6 --R 60b --R Type: Expression(Integer) ---E 272 +--E 272 ---S 273 of 1092 +--S 273 of 1092 a0:=integrate(t0,x) --R --R @@ -6298,27 +6298,27 @@ a0:=integrate(t0,x) --R 6 --R 60b --R Type: Union(Expression(Integer),...) ---E 273 +--E 273 ---S 274 of 1092 +--S 274 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 274 +--E 274 ---S 275 of 1092 +--S 275 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 275 +--E 275 )clear all ---S 276 of 1092 +--S 276 of 1092 t0:=x*(c+d*x)^3/(a+b*x) --R --R @@ -6327,9 +6327,9 @@ t0:=x*(c+d*x)^3/(a+b*x) --R (1) ------------------------------ --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 276 +--E 276 ---S 277 of 1092 +--S 277 of 1092 r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ 1/3*d^2*(3*b*c-a*d)*x^3/b^2+1/4*d^3*x^4/b-a*(b*c-a*d)^3*log(a+b*x)/b^5 --R @@ -6347,9 +6347,9 @@ r0:=(b*c-a*d)^3*x/b^4+1/2*d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*x^2/b^3+_ --R 5 --R 12b --R Type: Expression(Integer) ---E 277 +--E 277 ---S 278 of 1092 +--S 278 of 1092 a0:=integrate(t0,x) --R --R @@ -6366,27 +6366,27 @@ a0:=integrate(t0,x) --R 5 --R 12b --R Type: Union(Expression(Integer),...) ---E 278 +--E 278 ---S 279 of 1092 +--S 279 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 279 +--E 279 ---S 280 of 1092 +--S 280 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 280 +--E 280 )clear all ---S 281 of 1092 +--S 281 of 1092 t0:=(c+d*x)^3/(a+b*x) --R --R @@ -6395,9 +6395,9 @@ t0:=(c+d*x)^3/(a+b*x) --R (1) ---------------------------- --R b x + a --R Type: Fraction(Polynomial(Integer)) ---E 281 +--E 281 ---S 282 of 1092 +--S 282 of 1092 r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ 1/3*(c+d*x)^3/b+(b*c-a*d)^3*log(a+b*x)/b^4 --R @@ -6415,9 +6415,9 @@ r0:=d*(b*c-a*d)^2*x/b^3+1/2*(b*c-a*d)*(c+d*x)^2/b^2+_ --R 4 --R 6b --R Type: Expression(Integer) ---E 282 +--E 282 ---S 283 of 1092 +--S 283 of 1092 a0:=integrate(t0,x) --R --R @@ -6431,9 +6431,9 @@ a0:=integrate(t0,x) --R 4 --R 6b --R Type: Union(Expression(Integer),...) ---E 283 +--E 283 ---S 284 of 1092 +--S 284 of 1092 m0:=a0-r0 --R --R @@ -6443,19 +6443,19 @@ m0:=a0-r0 --R 2 --R 6b --R Type: Expression(Integer) ---E 284 +--E 284 ---S 285 of 1092 +--S 285 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 285 +--E 285 )clear all ---S 286 of 1092 +--S 286 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)) --R --R @@ -6465,9 +6465,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 286 +--E 286 ---S 287 of 1092 +--S 287 of 1092 r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ c^3*log(x)/a-(b*c-a*d)^3*log(a+b*x)/(a*b^3) --R @@ -6482,9 +6482,9 @@ r0:=d^2*(3*b*c-a*d)*x/b^2+1/2*d^3*x^2/b+_ --R 3 --R 2a b --R Type: Expression(Integer) ---E 287 +--E 287 ---S 288 of 1092 +--S 288 of 1092 a0:=integrate(t0,x) --R --R @@ -6498,27 +6498,27 @@ a0:=integrate(t0,x) --R 3 --R 2a b --R Type: Union(Expression(Integer),...) ---E 288 +--E 288 ---S 289 of 1092 +--S 289 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 289 +--E 289 ---S 290 of 1092 +--S 290 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 290 +--E 290 )clear all ---S 291 of 1092 +--S 291 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)) --R --R @@ -6528,9 +6528,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 291 +--E 291 ---S 292 of 1092 +--S 292 of 1092 r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ (b*c-a*d)^3*log(a+b*x)/(a^2*b^2) --R @@ -6545,9 +6545,9 @@ r0:=-c^3/(a*x)+d^3*x/b-c^2*(b*c-3*a*d)*log(x)/a^2+_ --R 2 2 --R a b x --R Type: Expression(Integer) ---E 292 +--E 292 ---S 293 of 1092 +--S 293 of 1092 a0:=integrate(t0,x) --R --R @@ -6561,27 +6561,27 @@ a0:=integrate(t0,x) --R 2 2 --R a b x --R Type: Union(Expression(Integer),...) ---E 293 +--E 293 ---S 294 of 1092 +--S 294 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 294 +--E 294 ---S 295 of 1092 +--S 295 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 295 +--E 295 )clear all ---S 296 of 1092 +--S 296 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)) --R --R @@ -6591,9 +6591,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 296 +--E 296 ---S 297 of 1092 +--S 297 of 1092 r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(x)/a^3-(b*c-a*d)^3*log(a+b*x)/(a^3*b) --R @@ -6608,9 +6608,9 @@ r0:=-1/2*c^3/(a*x^2)+c^2*(b*c-3*a*d)/(a^2*x)+_ --R 3 2 --R 2a b x --R Type: Expression(Integer) ---E 297 +--E 297 ---S 298 of 1092 +--S 298 of 1092 a0:=integrate(t0,x) --R --R @@ -6624,27 +6624,27 @@ a0:=integrate(t0,x) --R 3 2 --R 2a b x --R Type: Union(Expression(Integer),...) ---E 298 +--E 298 ---S 299 of 1092 +--S 299 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 299 +--E 299 ---S 300 of 1092 +--S 300 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 300 +--E 300 )clear all ---S 301 of 1092 +--S 301 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)) --R --R @@ -6654,9 +6654,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 301 +--E 301 ---S 302 of 1092 +--S 302 of 1092 r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x)-_ (b*c-a*d)^3*log(x)/a^4+(b*c-a*d)^3*log(a+b*x)/a^4 @@ -6675,9 +6675,9 @@ r0:=-1/3*c^3/(a*x^3)+1/2*c^2*(b*c-3*a*d)/(a^2*x^2)-_ --R 4 3 --R 6a x --R Type: Expression(Integer) ---E 302 +--E 302 ---S 303 of 1092 +--S 303 of 1092 a0:=integrate(t0,x) --R --R @@ -6694,27 +6694,27 @@ a0:=integrate(t0,x) --R 4 3 --R 6a x --R Type: Union(Expression(Integer),...) ---E 303 +--E 303 ---S 304 of 1092 +--S 304 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 304 +--E 304 ---S 305 of 1092 +--S 305 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 305 +--E 305 )clear all ---S 306 of 1092 +--S 306 of 1092 t0:=(c+d*x)^3/(x^5*(a+b*x)) --R --R @@ -6724,9 +6724,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x)) --R 6 5 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 306 +--E 306 ---S 307 of 1092 +--S 307 of 1092 r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ 1/2*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^2)+_ (b*c-a*d)^3/(a^4*x)+b*(b*c-a*d)^3*log(x)/a^5-b*(b*c-a*d)^3*log(a+b*x)/a^5 @@ -6748,9 +6748,9 @@ r0:=-1/4*c^3/(a*x^4)+1/3*c^2*(b*c-3*a*d)/(a^2*x^3)-_ --R 5 4 --R 12a x --R Type: Expression(Integer) ---E 307 +--E 307 ---S 308 of 1092 +--S 308 of 1092 a0:=integrate(t0,x) --R --R @@ -6770,27 +6770,27 @@ a0:=integrate(t0,x) --R 5 4 --R 12a x --R Type: Union(Expression(Integer),...) ---E 308 +--E 308 ---S 309 of 1092 +--S 309 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 309 +--E 309 ---S 310 of 1092 +--S 310 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 310 +--E 310 )clear all ---S 311 of 1092 +--S 311 of 1092 t0:=(c+d*x)^3/(x^6*(a+b*x)) --R --R @@ -6800,9 +6800,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x)) --R 7 6 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 311 +--E 311 ---S 312 of 1092 +--S 312 of 1092 r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ 1/3*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^3)+_ 1/2*(b*c-a*d)^3/(a^4*x^2)-b*(b*c-a*d)^3/(a^5*x)-_ @@ -6828,9 +6828,9 @@ r0:=-1/5*c^3/(a*x^5)+1/4*c^2*(b*c-3*a*d)/(a^2*x^4)-_ --R 6 5 --R 60a x --R Type: Expression(Integer) ---E 312 +--E 312 ---S 313 of 1092 +--S 313 of 1092 a0:=integrate(t0,x) --R --R @@ -6853,27 +6853,27 @@ a0:=integrate(t0,x) --R 6 5 --R 60a x --R Type: Union(Expression(Integer),...) ---E 313 +--E 313 ---S 314 of 1092 +--S 314 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 314 +--E 314 ---S 315 of 1092 +--S 315 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 315 +--E 315 )clear all ---S 316 of 1092 +--S 316 of 1092 t0:=(c+d*x)^3/(x^7*(a+b*x)) --R --R @@ -6883,9 +6883,9 @@ t0:=(c+d*x)^3/(x^7*(a+b*x)) --R 8 7 --R b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 316 +--E 316 ---S 317 of 1092 +--S 317 of 1092 r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ 1/4*c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)/(a^3*x^4)+_ 1/3*(b*c-a*d)^3/(a^4*x^3)-1/2*b*(b*c-a*d)^3/(a^5*x^2)+_ @@ -6915,9 +6915,9 @@ r0:=-1/6*c^3/(a*x^6)+1/5*c^2*(b*c-3*a*d)/(a^2*x^5)-_ --R 7 6 --R 60a x --R Type: Expression(Integer) ---E 317 +--E 317 ---S 318 of 1092 +--S 318 of 1092 a0:=integrate(t0,x) --R --R @@ -6943,27 +6943,27 @@ a0:=integrate(t0,x) --R 7 6 --R 60a x --R Type: Union(Expression(Integer),...) ---E 318 +--E 318 ---S 319 of 1092 +--S 319 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 319 +--E 319 ---S 320 of 1092 +--S 320 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 320 +--E 320 )clear all ---S 321 of 1092 +--S 321 of 1092 t0:=x^m/((a+b*x)*(c+d*x)) --R --R @@ -6973,28 +6973,28 @@ t0:=x^m/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Expression(Integer) ---E 321 +--E 321 ---S 322 of 1092 +--S 322 of 1092 --r0:=b*x^(1+m)*hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)*(1+m))-_ -- d*x^(1+m)*hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)*(1+m)) ---E 322 +--E 322 ---S 323 of 1092 +--S 323 of 1092 --a0:=integrate(t0,x) ---E 323 +--E 323 ---S 324 of 1092 +--S 324 of 1092 --m0:=a0-r0 ---E 324 +--E 324 ---S 325 of 1092 +--S 325 of 1092 --d0:=D(m0,x) ---E 325 +--E 325 )clear all ---S 326 of 1092 +--S 326 of 1092 t0:=x^5/((a+b*x)*(c+d*x)) --R --R @@ -7004,9 +7004,9 @@ t0:=x^5/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 326 +--E 326 ---S 327 of 1092 +--S 327 of 1092 r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ 1/2*(b^2*c^2+a*b*c*d+a^2*d^2)*x^2/(b^3*d^3)-_ 1/3*(b*c+a*d)*x^3/(b^2*d^2)+1/4*x^4/(b*d)-_ @@ -7023,9 +7023,9 @@ r0:=-(b*c+a*d)*(b^2*c^2+a^2*d^2)*x/(b^4*d^4)+_ --R 5 6 6 5 --R 12a b d - 12b c d --R Type: Expression(Integer) ---E 327 +--E 327 ---S 328 of 1092 +--S 328 of 1092 a0:=integrate(t0,x) --R --R @@ -7039,27 +7039,27 @@ a0:=integrate(t0,x) --R 5 6 6 5 --R 12a b d - 12b c d --R Type: Union(Expression(Integer),...) ---E 328 +--E 328 ---S 329 of 1092 +--S 329 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 329 +--E 329 ---S 330 of 1092 +--S 330 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 330 +--E 330 )clear all ---S 331 of 1092 +--S 331 of 1092 t0:=x^4/((a+b*x)*(c+d*x)) --R --R @@ -7069,9 +7069,9 @@ t0:=x^4/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 331 +--E 331 ---S 332 of 1092 +--S 332 of 1092 r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ 1/2*(b*c+a*d)*x^2/(b^2*d^2)+1/3*x^3/(b*d)+_ a^4*log(a+b*x)/(b^4*(b*c-a*d))-c^4*log(c+d*x)/(d^4*(b*c-a*d)) @@ -7087,9 +7087,9 @@ r0:=(b^2*c^2+a*b*c*d+a^2*d^2)*x/(b^3*d^3)-_ --R 4 5 5 4 --R 6a b d - 6b c d --R Type: Expression(Integer) ---E 332 +--E 332 ---S 333 of 1092 +--S 333 of 1092 a0:=integrate(t0,x) --R --R @@ -7103,27 +7103,27 @@ a0:=integrate(t0,x) --R 4 5 5 4 --R 6a b d - 6b c d --R Type: Union(Expression(Integer),...) ---E 333 +--E 333 ---S 334 of 1092 +--S 334 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 334 +--E 334 ---S 335 of 1092 +--S 335 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 335 +--E 335 )clear all ---S 336 of 1092 +--S 336 of 1092 t0:=x^3/((a+b*x)*(c+d*x)) --R --R @@ -7133,9 +7133,9 @@ t0:=x^3/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 336 +--E 336 ---S 337 of 1092 +--S 337 of 1092 r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ c^3*log(c+d*x)/(d^3*(b*c-a*d)) --R @@ -7150,9 +7150,9 @@ r0:=-(b*c+a*d)*x/(b^2*d^2)+1/2*x^2/(b*d)-a^3*log(a+b*x)/(b^3*(b*c-a*d))+_ --R 3 4 4 3 --R 2a b d - 2b c d --R Type: Expression(Integer) ---E 337 +--E 337 ---S 338 of 1092 +--S 338 of 1092 a0:=integrate(t0,x) --R --R @@ -7166,27 +7166,27 @@ a0:=integrate(t0,x) --R 3 4 4 3 --R 2a b d - 2b c d --R Type: Union(Expression(Integer),...) ---E 338 +--E 338 ---S 339 of 1092 +--S 339 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 339 +--E 339 ---S 340 of 1092 +--S 340 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 340 +--E 340 )clear all ---S 341 of 1092 +--S 341 of 1092 t0:=x^2/((a+b*x)*(c+d*x)) --R --R @@ -7196,9 +7196,9 @@ t0:=x^2/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 341 +--E 341 ---S 342 of 1092 +--S 342 of 1092 r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) --R --R @@ -7208,9 +7208,9 @@ r0:=x/(b*d)+a^2*log(a+b*x)/(b^2*(b*c-a*d))-c^2*log(c+d*x)/(d^2*(b*c-a*d)) --R 2 3 3 2 --R a b d - b c d --R Type: Expression(Integer) ---E 342 +--E 342 ---S 343 of 1092 +--S 343 of 1092 a0:=integrate(t0,x) --R --R @@ -7220,27 +7220,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 --R a b d - b c d --R Type: Union(Expression(Integer),...) ---E 343 +--E 343 ---S 344 of 1092 +--S 344 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 344 +--E 344 ---S 345 of 1092 +--S 345 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 345 +--E 345 )clear all ---S 346 of 1092 +--S 346 of 1092 t0:=x/((a+b*x)*(c+d*x)) --R --R @@ -7249,9 +7249,9 @@ t0:=x/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 346 +--E 346 ---S 347 of 1092 +--S 347 of 1092 r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) --R --R @@ -7260,9 +7260,9 @@ r0:=-a*log(a+b*x)/(b*(b*c-a*d))+c*log(c+d*x)/(d*(b*c-a*d)) --R 2 2 --R a b d - b c d --R Type: Expression(Integer) ---E 347 +--E 347 ---S 348 of 1092 +--S 348 of 1092 a0:=integrate(t0,x) --R --R @@ -7271,27 +7271,27 @@ a0:=integrate(t0,x) --R 2 2 --R a b d - b c d --R Type: Union(Expression(Integer),...) ---E 348 +--E 348 ---S 349 of 1092 +--S 349 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 349 +--E 349 ---S 350 of 1092 +--S 350 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 350 +--E 350 )clear all ---S 351 of 1092 +--S 351 of 1092 t0:=1/((a+b*x)*(c+d*x)) --R --R @@ -7300,9 +7300,9 @@ t0:=1/((a+b*x)*(c+d*x)) --R 2 --R b d x + (a d + b c)x + a c --R Type: Fraction(Polynomial(Integer)) ---E 351 +--E 351 ---S 352 of 1092 +--S 352 of 1092 r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) --R --R @@ -7310,9 +7310,9 @@ r0:=log(a+b*x)/(b*c-a*d)-log(c+d*x)/(b*c-a*d) --R (2) --------------------------- --R a d - b c --R Type: Expression(Integer) ---E 352 +--E 352 ---S 353 of 1092 +--S 353 of 1092 a0:=integrate(t0,x) --R --R @@ -7320,27 +7320,27 @@ a0:=integrate(t0,x) --R (3) --------------------------- --R a d - b c --R Type: Union(Expression(Integer),...) ---E 353 +--E 353 ---S 354 of 1092 +--S 354 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 354 +--E 354 ---S 355 of 1092 +--S 355 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 355 +--E 355 )clear all ---S 356 of 1092 +--S 356 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)) --R --R @@ -7349,9 +7349,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)) --R 3 2 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 356 +--E 356 ---S 357 of 1092 +--S 357 of 1092 r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) --R --R @@ -7360,9 +7360,9 @@ r0:=log(x)/(a*c)-b*log(a+b*x)/(a*(b*c-a*d))+d*log(c+d*x)/(c*(b*c-a*d)) --R 2 2 --R a c d - a b c --R Type: Expression(Integer) ---E 357 +--E 357 ---S 358 of 1092 +--S 358 of 1092 a0:=integrate(t0,x) --R --R @@ -7371,27 +7371,27 @@ a0:=integrate(t0,x) --R 2 2 --R a c d - a b c --R Type: Union(Expression(Integer),...) ---E 358 +--E 358 ---S 359 of 1092 +--S 359 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 359 +--E 359 ---S 360 of 1092 +--S 360 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 360 +--E 360 )clear all ---S 361 of 1092 +--S 361 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)) --R --R @@ -7400,9 +7400,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)) --R 4 3 2 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 361 +--E 361 ---S 362 of 1092 +--S 362 of 1092 r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ b^2*log(a+b*x)/(a^2*(b*c-a*d))-d^2*log(c+d*x)/(c^2*(b*c-a*d)) --R @@ -7417,9 +7417,9 @@ r0:=(-1)/(a*c*x)-(b*c+a*d)*log(x)/(a^2*c^2)+_ --R 3 2 2 3 --R (a c d - a b c )x --R Type: Expression(Integer) ---E 362 +--E 362 ---S 363 of 1092 +--S 363 of 1092 a0:=integrate(t0,x) --R --R @@ -7433,27 +7433,27 @@ a0:=integrate(t0,x) --R 3 2 2 3 --R (a c d - a b c )x --R Type: Union(Expression(Integer),...) ---E 363 +--E 363 ---S 364 of 1092 +--S 364 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 364 +--E 364 ---S 365 of 1092 +--S 365 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 365 +--E 365 )clear all ---S 366 of 1092 +--S 366 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)) --R --R @@ -7462,9 +7462,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)) --R 5 4 3 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 366 +--E 366 ---S 367 of 1092 +--S 367 of 1092 r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ log(x)/(a^3*c^3)-b^3*log(a+b*x)/(a^3*(b*c-a*d))+_ d^3*log(c+d*x)/(c^3*(b*c-a*d)) @@ -7480,9 +7480,9 @@ r0:=(-1/2)/(a*c*x^2)+(b*c+a*d)/(a^2*c^2*x)+(b^2*c^2+a*b*c*d+a^2*d^2)*_ --R 4 3 3 4 2 --R (2a c d - 2a b c )x --R Type: Expression(Integer) ---E 367 +--E 367 ---S 368 of 1092 +--S 368 of 1092 a0:=integrate(t0,x) --R --R @@ -7496,27 +7496,27 @@ a0:=integrate(t0,x) --R 4 3 3 4 2 --R (2a c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 368 +--E 368 ---S 369 of 1092 +--S 369 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 369 +--E 369 ---S 370 of 1092 +--S 370 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 370 +--E 370 )clear all ---S 371 of 1092 +--S 371 of 1092 t0:=1/(x^4*(a+b*x)*(c+d*x)) --R --R @@ -7525,9 +7525,9 @@ t0:=1/(x^4*(a+b*x)*(c+d*x)) --R 6 5 4 --R b d x + (a d + b c)x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 371 +--E 371 ---S 372 of 1092 +--S 372 of 1092 r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ (-b^2*c^2-a*b*c*d-a^2*d^2)/(a^3*c^3*x)-(b*c+a*d)*(b^2*c^2+a^2*d^2)*_ log(x)/(a^4*c^4)+b^4*log(a+b*x)/(a^4*(b*c-a*d))-_ @@ -7544,9 +7544,9 @@ r0:=(-1/3)/(a*c*x^3)+1/2*(b*c+a*d)/(a^2*c^2*x^2)+_ --R 5 4 4 5 3 --R (6a c d - 6a b c )x --R Type: Expression(Integer) ---E 372 +--E 372 ---S 373 of 1092 +--S 373 of 1092 a0:=integrate(t0,x) --R --R @@ -7560,27 +7560,27 @@ a0:=integrate(t0,x) --R 5 4 4 5 3 --R (6a c d - 6a b c )x --R Type: Union(Expression(Integer),...) ---E 373 +--E 373 ---S 374 of 1092 +--S 374 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 374 +--E 374 ---S 375 of 1092 +--S 375 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 375 +--E 375 )clear all ---S 376 of 1092 +--S 376 of 1092 t0:=x^m/((a+b*x)*(c+d*x)^2) --R --R @@ -7590,30 +7590,30 @@ t0:=x^m/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Expression(Integer) ---E 376 +--E 376 ---S 377 of 1092 +--S 377 of 1092 --r0:=-d*x^(1+m)/(c*(b*c-a*d)*(c+d*x))+b^2*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-b*x/a)/(a*(b*c-a*d)^2*(1+m))-b*d*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c*(b*c-a*d)^2*(1+m))+d*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)*(1+m)) ---E 377 +--E 377 ---S 378 of 1092 +--S 378 of 1092 --a0:=integrate(t0,x) ---E 378 +--E 378 ---S 379 of 1092 +--S 379 of 1092 --m0:=a0-r0 ---E 379 +--E 379 ---S 380 of 1092 +--S 380 of 1092 --d0:=D(m0,x) ---E 380 +--E 380 )clear all ---S 381 of 1092 +--S 381 of 1092 t0:=x^m/((1-a*x)^2*(1+a*x)) --R --R @@ -7623,30 +7623,30 @@ t0:=x^m/((1-a*x)^2*(1+a*x)) --R 3 3 2 2 --R a x - a x - a x + 1 --R Type: Expression(Integer) ---E 381 +--E 381 ---S 382 of 1092 +--S 382 of 1092 --r0:=1/2*x^(1+m)/(1-a*x)+1/4*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-a*x)/(1+m)+1/4*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,a*x)/(1+m)-1/2*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,a*x)/(1+m) ---E 382 +--E 382 ---S 383 of 1092 +--S 383 of 1092 --a0:=integrate(t0,x) ---E 383 +--E 383 ---S 384 of 1092 +--S 384 of 1092 --m0:=a0-r0 ---E 384 +--E 384 ---S 385 of 1092 +--S 385 of 1092 --d0:=D(m0,x) ---E 385 +--E 385 )clear all ---S 386 of 1092 +--S 386 of 1092 t0:=x^5/((a+b*x)*(c+d*x)^2) --R --R @@ -7656,9 +7656,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 386 +--E 386 ---S 387 of 1092 +--S 387 of 1092 r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ 1/2*(2*b*c+a*d)*x^2/(b^2*d^3)+1/3*x^3/(b*d^2)-_ c^5/(d^5*(b*c-a*d)*(c+d*x))-a^5*log(a+b*x)/(b^4*(b*c-a*d)^2)-_ @@ -7684,9 +7684,9 @@ r0:=(3*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^3*d^4)-_ --R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 --R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d --R Type: Expression(Integer) ---E 387 +--E 387 ---S 388 of 1092 +--S 388 of 1092 a0:=integrate(t0,x) --R --R @@ -7709,27 +7709,27 @@ a0:=integrate(t0,x) --R 2 4 8 5 7 6 2 6 2 4 7 5 2 6 6 3 5 --R (6a b d - 12a b c d + 6b c d )x + 6a b c d - 12a b c d + 6b c d --R Type: Union(Expression(Integer),...) ---E 388 +--E 388 ---S 389 of 1092 +--S 389 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 389 +--E 389 ---S 390 of 1092 +--S 390 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 390 +--E 390 )clear all ---S 391 of 1092 +--S 391 of 1092 t0:=x^4/((a+b*x)*(c+d*x)^2) --R --R @@ -7739,9 +7739,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 391 +--E 391 ---S 392 of 1092 +--S 392 of 1092 r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ c^4/(d^4*(b*c-a*d)*(c+d*x))+a^4*log(a+b*x)/(b^3*(b*c-a*d)^2)+_ c^3*(3*b*c-4*a*d)*log(c+d*x)/(d^4*(b*c-a*d)^2) @@ -7763,9 +7763,9 @@ r0:=-(2*b*c+a*d)*x/(b^2*d^3)+1/2*x^2/(b*d^2)+_ --R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 --R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d --R Type: Expression(Integer) ---E 392 +--E 392 ---S 393 of 1092 +--S 393 of 1092 a0:=integrate(t0,x) --R --R @@ -7785,27 +7785,27 @@ a0:=integrate(t0,x) --R 2 3 7 4 6 5 2 5 2 3 6 4 2 5 5 3 4 --R (2a b d - 4a b c d + 2b c d )x + 2a b c d - 4a b c d + 2b c d --R Type: Union(Expression(Integer),...) ---E 393 +--E 393 ---S 394 of 1092 +--S 394 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 394 +--E 394 ---S 395 of 1092 +--S 395 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 395 +--E 395 )clear all ---S 396 of 1092 +--S 396 of 1092 t0:=x^3/((a+b*x)*(c+d*x)^2) --R --R @@ -7815,9 +7815,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 396 +--E 396 ---S 397 of 1092 +--S 397 of 1092 r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ a^3*log(a+b*x)/(b^2*(b*c-a*d)^2)-c^2*(2*b*c-3*a*d)*log(c+d*x)/_ (d^3*(b*c-a*d)^2) @@ -7836,9 +7836,9 @@ r0:=x/(b*d^2)-c^3/(d^3*(b*c-a*d)*(c+d*x))-_ --R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 397 +--E 397 ---S 398 of 1092 +--S 398 of 1092 a0:=integrate(t0,x) --R --R @@ -7855,27 +7855,27 @@ a0:=integrate(t0,x) --R 2 2 6 3 5 4 2 4 2 2 5 3 2 4 4 3 3 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 398 +--E 398 ---S 399 of 1092 +--S 399 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 399 +--E 399 ---S 400 of 1092 +--S 400 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 400 +--E 400 )clear all ---S 401 of 1092 +--S 401 of 1092 t0:=x^2/((a+b*x)*(c+d*x)^2) --R --R @@ -7885,9 +7885,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 401 +--E 401 ---S 402 of 1092 +--S 402 of 1092 r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ c*(b*c-2*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^2) --R @@ -7902,9 +7902,9 @@ r0:=c^2/(d^2*(b*c-a*d)*(c+d*x))+a^2*log(a+b*x)/(b*(b*c-a*d)^2)+_ --R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 402 +--E 402 ---S 403 of 1092 +--S 403 of 1092 a0:=integrate(t0,x) --R --R @@ -7918,27 +7918,27 @@ a0:=integrate(t0,x) --R 2 5 2 4 3 2 3 2 4 2 2 3 3 3 2 --R (a b d - 2a b c d + b c d )x + a b c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 403 +--E 403 ---S 404 of 1092 +--S 404 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 404 +--E 404 ---S 405 of 1092 +--S 405 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 405 +--E 405 )clear all ---S 406 of 1092 +--S 406 of 1092 t0:=x/((a+b*x)*(c+d*x)^2) --R --R @@ -7947,9 +7947,9 @@ t0:=x/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 406 +--E 406 ---S 407 of 1092 +--S 407 of 1092 r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 --R --R @@ -7960,9 +7960,9 @@ r0:=-c/(d*(b*c-a*d)*(c+d*x))-a*log(a+b*x)/(b*c-a*d)^2+a*log(c+d*x)/(b*c-a*d)^2 --R 2 4 3 2 2 2 2 3 2 2 2 3 --R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d --R Type: Expression(Integer) ---E 407 +--E 407 ---S 408 of 1092 +--S 408 of 1092 a0:=integrate(t0,x) --R --R @@ -7973,27 +7973,27 @@ a0:=integrate(t0,x) --R 2 4 3 2 2 2 2 3 2 2 2 3 --R (a d - 2a b c d + b c d )x + a c d - 2a b c d + b c d --R Type: Union(Expression(Integer),...) ---E 408 +--E 408 ---S 409 of 1092 +--S 409 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 409 +--E 409 ---S 410 of 1092 +--S 410 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 410 +--E 410 )clear all ---S 411 of 1092 +--S 411 of 1092 t0:=1/((a+b*x)*(c+d*x)^2) --R --R @@ -8002,9 +8002,9 @@ t0:=1/((a+b*x)*(c+d*x)^2) --R 2 3 2 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 411 +--E 411 ---S 412 of 1092 +--S 412 of 1092 r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 --R --R @@ -8013,9 +8013,9 @@ r0:=1/((b*c-a*d)*(c+d*x))+b*log(a+b*x)/(b*c-a*d)^2-b*log(c+d*x)/(b*c-a*d)^2 --R 2 3 2 2 2 2 2 2 2 3 --R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c --R Type: Expression(Integer) ---E 412 +--E 412 ---S 413 of 1092 +--S 413 of 1092 a0:=integrate(t0,x) --R --R @@ -8024,27 +8024,27 @@ a0:=integrate(t0,x) --R 2 3 2 2 2 2 2 2 2 3 --R (a d - 2a b c d + b c d)x + a c d - 2a b c d + b c --R Type: Union(Expression(Integer),...) ---E 413 +--E 413 ---S 414 of 1092 +--S 414 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 414 +--E 414 ---S 415 of 1092 +--S 415 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 415 +--E 415 )clear all ---S 416 of 1092 +--S 416 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)^2) --R --R @@ -8053,9 +8053,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^2) --R 2 4 2 3 2 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 416 +--E 416 ---S 417 of 1092 +--S 417 of 1092 r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ b^2*log(a+b*x)/(a*(b*c-a*d)^2)+d*(2*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^2) --R @@ -8076,9 +8076,9 @@ r0:=-d/(c*(b*c-a*d)*(c+d*x))+log(x)/(a*c^2)-_ --R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 --R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c --R Type: Expression(Integer) ---E 417 +--E 417 ---S 418 of 1092 +--S 418 of 1092 a0:=integrate(t0,x) --R --R @@ -8098,27 +8098,27 @@ a0:=integrate(t0,x) --R 3 2 3 2 3 2 2 4 3 3 2 2 4 2 5 --R (a c d - 2a b c d + a b c d)x + a c d - 2a b c d + a b c --R Type: Union(Expression(Integer),...) ---E 418 +--E 418 ---S 419 of 1092 +--S 419 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 419 +--E 419 ---S 420 of 1092 +--S 420 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 420 +--E 420 )clear all ---S 421 of 1092 +--S 421 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)^2) --R --R @@ -8127,9 +8127,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^2) --R 2 5 2 4 2 3 2 2 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 421 +--E 421 ---S 422 of 1092 +--S 422 of 1092 r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ (b*c+2*a*d)*log(x)/(a^2*c^3)+b^3*log(a+b*x)/(a^2*(b*c-a*d)^2)-_ d^2*(3*b*c-2*a*d)*log(c+d*x)/(c^3*(b*c-a*d)^2) @@ -8151,9 +8151,9 @@ r0:=(-1)/(a*c^2*x)+d^2/(c^2*(b*c-a*d)*(c+d*x))-_ --R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 --R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x --R Type: Expression(Integer) ---E 422 +--E 422 ---S 423 of 1092 +--S 423 of 1092 a0:=integrate(t0,x) --R --R @@ -8173,27 +8173,27 @@ a0:=integrate(t0,x) --R 4 3 3 3 4 2 2 2 5 2 4 4 2 3 5 2 2 6 --R (a c d - 2a b c d + a b c d)x + (a c d - 2a b c d + a b c )x --R Type: Union(Expression(Integer),...) ---E 423 +--E 423 ---S 424 of 1092 +--S 424 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 424 +--E 424 ---S 425 of 1092 +--S 425 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 425 +--E 425 )clear all ---S 426 of 1092 +--S 426 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)^2) --R --R @@ -8202,9 +8202,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^2) --R 2 6 2 5 2 4 2 3 --R b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 426 +--E 426 ---S 427 of 1092 +--S 427 of 1092 r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ d^3/(c^3*(b*c-a*d)*(c+d*x))+(b^2*c^2+2*a*b*c*d+3*a^2*d^2)*log(x)/_ (a^3*c^4)-b^4*log(a+b*x)/(a^3*(b*c-a*d)^2)+d^3*(4*b*c-3*a*d)*_ @@ -8230,9 +8230,9 @@ r0:=(-1/2)/(a*c^2*x^2)+(b*c+2*a*d)/(a^2*c^3*x)-_ --R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 --R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x --R Type: Expression(Integer) ---E 427 +--E 427 ---S 428 of 1092 +--S 428 of 1092 a0:=integrate(t0,x) --R --R @@ -8255,27 +8255,27 @@ a0:=integrate(t0,x) --R 5 4 3 4 5 2 3 2 6 3 5 5 2 4 6 3 2 7 2 --R (2a c d - 4a b c d + 2a b c d)x + (2a c d - 4a b c d + 2a b c )x --R Type: Union(Expression(Integer),...) ---E 428 +--E 428 ---S 429 of 1092 +--S 429 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 429 +--E 429 ---S 430 of 1092 +--S 430 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 430 +--E 430 )clear all ---S 431 of 1092 +--S 431 of 1092 t0:=x^m/((a+b*x)*(c+d*x)^3) --R --R @@ -8286,9 +8286,9 @@ t0:=x^m/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Expression(Integer) ---E 431 +--E 431 ---S 432 of 1092 +--S 432 of 1092 --r0:=-1/2*d*x^(1+m)/(c*(b*c-a*d)*(c+d*x)^2)-_ -- b*d*x^(1+m)/(c*(b*c-a*d)^2*(c+d*x))-_ -- 1/2*d*(1-m)*x^(1+m)/(c^2*(b*c-a*d)*(c+d*x))+_ @@ -8298,23 +8298,23 @@ t0:=x^m/((a+b*x)*(c+d*x)^3) -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^2*(b*c-a*d)^2*(1+m))+_ -- 1/2*d*(1-m)*m*x^(1+m)*_ -- hypergeometric(1,1+m,2+m,-d*x/c)/(c^3*(b*c-a*d)*(1+m)) ---E 432 +--E 432 ---S 433 of 1092 +--S 433 of 1092 --a0:=integrate(t0,x) ---E 433 +--E 433 ---S 434 of 1092 +--S 434 of 1092 --m0:=a0-r0 ---E 434 +--E 434 ---S 435 of 1092 +--S 435 of 1092 --d0:=D(m0,x) ---E 435 +--E 435 )clear all ---S 436 of 1092 +--S 436 of 1092 t0:=x^6/((a+b*x)*(c+d*x)^3) --R --R @@ -8325,9 +8325,9 @@ t0:=x^6/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 436 +--E 436 ---S 437 of 1092 +--S 437 of 1092 r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ 1/2*(3*b*c+a*d)*x^2/(b^2*d^4)+1/3*x^3/(b*d^3)+_ 1/2*c^6/(d^6*(b*c-a*d)*(c+d*x)^2)-_ @@ -8378,9 +8378,9 @@ r0:=(6*b^2*c^2+3*a*b*c*d+a^2*d^2)*x/(b^3*d^5)-_ --R 2 5 3 8 6 4 7 7 5 6 --R - 18a b c d + 18a b c d - 6b c d --R Type: Expression(Integer) ---E 437 +--E 437 ---S 438 of 1092 +--S 438 of 1092 a0:=integrate(t0,x) --R --R @@ -8426,27 +8426,27 @@ a0:=integrate(t0,x) --R 2 5 3 8 6 4 7 7 5 6 --R - 18a b c d + 18a b c d - 6b c d --R Type: Union(Expression(Integer),...) ---E 438 +--E 438 ---S 439 of 1092 +--S 439 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 439 +--E 439 ---S 440 of 1092 +--S 440 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 440 +--E 440 )clear all ---S 441 of 1092 +--S 441 of 1092 t0:=x^5/((a+b*x)*(c+d*x)^3) --R --R @@ -8457,9 +8457,9 @@ t0:=x^5/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 441 +--E 441 ---S 442 of 1092 +--S 442 of 1092 r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ 1/2*c^5/(d^5*(b*c-a*d)*(c+d*x)^2)+c^4*(4*b*c-5*a*d)/_ (d^5*(b*c-a*d)^2*(c+d*x))-a^5*log(a+b*x)/(b^3*(b*c-a*d)^3)+_ @@ -8505,9 +8505,9 @@ r0:=-(3*b*c+a*d)*x/(b^2*d^4)+1/2*x^2/(b*d^3)-_ --R 5 4 6 6 5 5 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 442 +--E 442 ---S 443 of 1092 +--S 443 of 1092 a0:=integrate(t0,x) --R --R @@ -8550,27 +8550,27 @@ a0:=integrate(t0,x) --R 5 4 6 6 5 5 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 443 +--E 443 ---S 444 of 1092 +--S 444 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 444 +--E 444 ---S 445 of 1092 +--S 445 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 445 +--E 445 )clear all ---S 446 of 1092 +--S 446 of 1092 t0:=x^4/((a+b*x)*(c+d*x)^3) --R --R @@ -8581,9 +8581,9 @@ t0:=x^4/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 446 +--E 446 ---S 447 of 1092 +--S 447 of 1092 r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ c^3*(3*b*c-4*a*d)/(d^4*(b*c-a*d)^2*(c+d*x))+_ a^4*log(a+b*x)/(b^2*(b*c-a*d)^3)-_ @@ -8623,9 +8623,9 @@ r0:=x/(b*d^3)+1/2*c^4/(d^4*(b*c-a*d)*(c+d*x)^2)-_ --R 4 4 5 5 5 4 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 447 +--E 447 ---S 448 of 1092 +--S 448 of 1092 a0:=integrate(t0,x) --R --R @@ -8662,27 +8662,27 @@ a0:=integrate(t0,x) --R 4 4 5 5 5 4 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 448 +--E 448 ---S 449 of 1092 +--S 449 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 449 +--E 449 ---S 450 of 1092 +--S 450 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 450 +--E 450 )clear all ---S 451 of 1092 +--S 451 of 1092 t0:=x^3/((a+b*x)*(c+d*x)^3) --R --R @@ -8693,9 +8693,9 @@ t0:=x^3/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 451 +--E 451 ---S 452 of 1092 +--S 452 of 1092 r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ (d^3*(b*c-a*d)^2*(c+d*x))-a^3*log(a+b*x)/(b*(b*c-a*d)^3)+_ c*(b^2*c^2-3*a*b*c*d+3*a^2*d^2)*log(c+d*x)/(d^3*(b*c-a*d)^3) @@ -8725,9 +8725,9 @@ r0:=-1/2*c^3/(d^3*(b*c-a*d)*(c+d*x)^2)+c^2*(2*b*c-3*a*d)/_ --R 3 4 4 4 5 3 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 452 +--E 452 ---S 453 of 1092 +--S 453 of 1092 a0:=integrate(t0,x) --R --R @@ -8755,27 +8755,27 @@ a0:=integrate(t0,x) --R 3 4 4 4 5 3 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 453 +--E 453 ---S 454 of 1092 +--S 454 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 454 +--E 454 ---S 455 of 1092 +--S 455 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 455 +--E 455 )clear all ---S 456 of 1092 +--S 456 of 1092 t0:=x^2/((a+b*x)*(c+d*x)^3) --R --R @@ -8786,9 +8786,9 @@ t0:=x^2/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 456 +--E 456 ---S 457 of 1092 +--S 457 of 1092 r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ (d^2*(b*c-a*d)^2*(c+d*x))+a^2*log(a+b*x)/(b*c-a*d)^3-_ a^2*log(c+d*x)/(b*c-a*d)^3 @@ -8813,9 +8813,9 @@ r0:=1/2*c^2/(d^2*(b*c-a*d)*(c+d*x)^2)-c*(b*c-2*a*d)/_ --R 2 4 3 3 5 2 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 457 +--E 457 ---S 458 of 1092 +--S 458 of 1092 a0:=integrate(t0,x) --R --R @@ -8838,27 +8838,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 5 2 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 458 +--E 458 ---S 459 of 1092 +--S 459 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 459 +--E 459 ---S 460 of 1092 +--S 460 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 460 +--E 460 )clear all ---S 461 of 1092 +--S 461 of 1092 t0:=x/((a+b*x)*(c+d*x)^3) --R --R @@ -8868,9 +8868,9 @@ t0:=x/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 461 +--E 461 ---S 462 of 1092 +--S 462 of 1092 r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ a*b*log(a+b*x)/(b*c-a*d)^3+a*b*log(c+d*x)/(b*c-a*d)^3 --R @@ -8894,9 +8894,9 @@ r0:=-1/2*c/(d*(b*c-a*d)*(c+d*x)^2)-a/((b*c-a*d)^2*(c+d*x))-_ --R 2 4 2 3 5 --R 6a b c d - 2b c d --R Type: Expression(Integer) ---E 462 +--E 462 ---S 463 of 1092 +--S 463 of 1092 a0:=integrate(t0,x) --R --R @@ -8919,27 +8919,27 @@ a0:=integrate(t0,x) --R 2 4 2 3 5 --R 6a b c d - 2b c d --R Type: Union(Expression(Integer),...) ---E 463 +--E 463 ---S 464 of 1092 +--S 464 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 464 +--E 464 ---S 465 of 1092 +--S 465 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 465 +--E 465 )clear all ---S 466 of 1092 +--S 466 of 1092 t0:=1/((a+b*x)*(c+d*x)^3) --R --R @@ -8949,9 +8949,9 @@ t0:=1/((a+b*x)*(c+d*x)^3) --R 3 4 3 2 3 2 2 2 2 3 3 --R b d x + (a d + 3b c d )x + (3a c d + 3b c d)x + (3a c d + b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 466 +--E 466 ---S 467 of 1092 +--S 467 of 1092 r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ b^2*log(a+b*x)/(b*c-a*d)^3-b^2*log(c+d*x)/(b*c-a*d)^3 --R @@ -8975,9 +8975,9 @@ r0:=1/2/((b*c-a*d)*(c+d*x)^2)+b/((b*c-a*d)^2*(c+d*x))+_ --R 2 4 3 5 --R 6a b c d - 2b c --R Type: Expression(Integer) ---E 467 +--E 467 ---S 468 of 1092 +--S 468 of 1092 a0:=integrate(t0,x) --R --R @@ -9000,27 +9000,27 @@ a0:=integrate(t0,x) --R 2 4 3 5 --R 6a b c d - 2b c --R Type: Union(Expression(Integer),...) ---E 468 +--E 468 ---S 469 of 1092 +--S 469 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 469 +--E 469 ---S 470 of 1092 +--S 470 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 470 +--E 470 )clear all ---S 471 of 1092 +--S 471 of 1092 t0:=1/(x*(a+b*x)*(c+d*x)^3) --R --R @@ -9033,9 +9033,9 @@ t0:=1/(x*(a+b*x)*(c+d*x)^3) --R 3 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 471 +--E 471 ---S 472 of 1092 +--S 472 of 1092 r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ (c^2*(b*c-a*d)^2*(c+d*x))+log(x)/(a*c^3)-_ b^3*log(a+b*x)/(a*(b*c-a*d)^3)+d*(3*b^2*c^2-3*a*b*c*d+a^2*d^2)*_ @@ -9077,9 +9077,9 @@ r0:=-1/2*d/(c*(b*c-a*d)*(c+d*x)^2)-d*(2*b*c-a*d)/_ --R 2 2 7 3 8 --R 6a b c d - 2a b c --R Type: Expression(Integer) ---E 472 +--E 472 ---S 473 of 1092 +--S 473 of 1092 a0:=integrate(t0,x) --R --R @@ -9118,27 +9118,27 @@ a0:=integrate(t0,x) --R 2 2 7 3 8 --R 6a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 473 +--E 473 ---S 474 of 1092 +--S 474 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 474 +--E 474 ---S 475 of 1092 +--S 475 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 475 +--E 475 )clear all ---S 476 of 1092 +--S 476 of 1092 t0:=1/(x^2*(a+b*x)*(c+d*x)^3) --R --R @@ -9151,9 +9151,9 @@ t0:=1/(x^2*(a+b*x)*(c+d*x)^3) --R 3 2 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 476 +--E 476 ---S 477 of 1092 +--S 477 of 1092 r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ d^2*(3*b*c-2*a*d)/(c^3*(b*c-a*d)^2*(c+d*x))-(b*c+3*a*d)*_ log(x)/(a^2*c^4)+b^4*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ @@ -9204,9 +9204,9 @@ r0:=(-1)/(a*c^3*x)+1/2*d^2/(c^2*(b*c-a*d)*(c+d*x)^2)+_ --R 5 6 3 4 7 2 3 2 8 2 3 9 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 477 +--E 477 ---S 478 of 1092 +--S 478 of 1092 a0:=integrate(t0,x) --R --R @@ -9254,27 +9254,27 @@ a0:=integrate(t0,x) --R 5 6 3 4 7 2 3 2 8 2 3 9 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 478 +--E 478 ---S 479 of 1092 +--S 479 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 479 +--E 479 ---S 480 of 1092 +--S 480 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 480 +--E 480 )clear all ---S 481 of 1092 +--S 481 of 1092 t0:=1/(x^3*(a+b*x)*(c+d*x)^3) --R --R @@ -9287,9 +9287,9 @@ t0:=1/(x^3*(a+b*x)*(c+d*x)^3) --R 3 3 --R a c x --R Type: Fraction(Polynomial(Integer)) ---E 481 +--E 481 ---S 482 of 1092 +--S 482 of 1092 r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ (c+d*x)^2)-d^3*(4*b*c-3*a*d)/(c^4*(b*c-a*d)^2*(c+d*x))+_ (b^2*c^2+3*a*b*c*d+6*a^2*d^2)*log(x)/(a^3*c^5)-b^5*_ @@ -9344,9 +9344,9 @@ r0:=(-1/2)/(a*c^3*x^2)+(b*c+3*a*d)/(a^2*c^4*x)-1/2*d^3/(c^3*(b*c-a*d)*_ --R 6 7 3 5 8 2 4 2 9 3 3 10 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 482 +--E 482 ---S 483 of 1092 +--S 483 of 1092 a0:=integrate(t0,x) --R --R @@ -9397,27 +9397,27 @@ a0:=integrate(t0,x) --R 6 7 3 5 8 2 4 2 9 3 3 10 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 483 +--E 483 ---S 484 of 1092 +--S 484 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 484 +--E 484 ---S 485 of 1092 +--S 485 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 485 +--E 485 )clear all ---S 486 of 1092 +--S 486 of 1092 t0:=x^4*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9427,9 +9427,9 @@ t0:=x^4*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 486 +--E 486 ---S 487 of 1092 +--S 487 of 1092 r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ 1/3*(b*c-3*a*d)*(b*c-a*d)*x^3/b^4+1/2*d*(b*c-a*d)*x^4/b^3+_ 1/5*d^2*x^5/b^2-a^4*(b*c-a*d)^2/(b^7*(a+b*x))-_ @@ -9460,9 +9460,9 @@ r0:=a^2*(3*b*c-5*a*d)*(b*c-a*d)*x/b^6-a*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+_ --R 8 7 --R 30b x + 30a b --R Type: Expression(Integer) ---E 487 +--E 487 ---S 488 of 1092 +--S 488 of 1092 a0:=integrate(t0,x) --R --R @@ -9490,27 +9490,27 @@ a0:=integrate(t0,x) --R 8 7 --R 30b x + 30a b --R Type: Union(Expression(Integer),...) ---E 488 +--E 488 ---S 489 of 1092 +--S 489 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 489 +--E 489 ---S 490 of 1092 +--S 490 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 490 +--E 490 )clear all ---S 491 of 1092 +--S 491 of 1092 t0:=x^3*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9520,9 +9520,9 @@ t0:=x^3*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 491 +--E 491 ---S 492 of 1092 +--S 492 of 1092 r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ 2/3*d*(b*c-a*d)*x^3/b^3+1/4*d^2*x^4/b^2+_ a^3*(b*c-a*d)^2/(b^6*(a+b*x))+a^2*(3*b*c-5*a*d)*(b*c-a*d)*log(a+b*x)/b^6 @@ -9546,9 +9546,9 @@ r0:=-2*a*(b*c-2*a*d)*(b*c-a*d)*x/b^5+1/2*(b*c-3*a*d)*(b*c-a*d)*x^2/b^4+_ --R 7 6 --R 12b x + 12a b --R Type: Expression(Integer) ---E 492 +--E 492 ---S 493 of 1092 +--S 493 of 1092 a0:=integrate(t0,x) --R --R @@ -9570,27 +9570,27 @@ a0:=integrate(t0,x) --R 7 6 --R 12b x + 12a b --R Type: Union(Expression(Integer),...) ---E 493 +--E 493 ---S 494 of 1092 +--S 494 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 494 +--E 494 ---S 495 of 1092 +--S 495 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 495 +--E 495 )clear all ---S 496 of 1092 +--S 496 of 1092 t0:=x^2*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9600,9 +9600,9 @@ t0:=x^2*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 496 +--E 496 ---S 497 of 1092 +--S 497 of 1092 r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ a^2*(b*c-a*d)^2/(b^5*(a+b*x))-2*a*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 --R @@ -9622,9 +9622,9 @@ r0:=(b*c-3*a*d)*(b*c-a*d)*x/b^4+d*(b*c-a*d)*x^2/b^3+1/3*d^2*x^3/b^2-_ --R 6 5 --R 3b x + 3a b --R Type: Expression(Integer) ---E 497 +--E 497 ---S 498 of 1092 +--S 498 of 1092 a0:=integrate(t0,x) --R --R @@ -9643,27 +9643,27 @@ a0:=integrate(t0,x) --R 6 5 --R 3b x + 3a b --R Type: Union(Expression(Integer),...) ---E 498 +--E 498 ---S 499 of 1092 +--S 499 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 499 +--E 499 ---S 500 of 1092 +--S 500 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 500 +--E 500 )clear all ---S 501 of 1092 +--S 501 of 1092 t0:=x*(c+d*x)^2/(a+b*x)^2 --R --R @@ -9673,9 +9673,9 @@ t0:=x*(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 501 +--E 501 ---S 502 of 1092 +--S 502 of 1092 r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ (b*c-3*a*d)*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -9693,9 +9693,9 @@ r0:=2*d*(b*c-a*d)*x/b^3+1/2*d^2*x^2/b^2+a*(b*c-a*d)^2/(b^4*(a+b*x))+_ --R 5 4 --R 2b x + 2a b --R Type: Expression(Integer) ---E 502 +--E 502 ---S 503 of 1092 +--S 503 of 1092 a0:=integrate(t0,x) --R --R @@ -9712,27 +9712,27 @@ a0:=integrate(t0,x) --R 5 4 --R 2b x + 2a b --R Type: Union(Expression(Integer),...) ---E 503 +--E 503 ---S 504 of 1092 +--S 504 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 504 +--E 504 ---S 505 of 1092 +--S 505 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 505 +--E 505 )clear all ---S 506 of 1092 +--S 506 of 1092 t0:=(c+d*x)^2/(a+b*x)^2 --R --R @@ -9742,9 +9742,9 @@ t0:=(c+d*x)^2/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 506 +--E 506 ---S 507 of 1092 +--S 507 of 1092 r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 --R --R @@ -9758,9 +9758,9 @@ r0:=d^2*x/b^2-(b*c-a*d)^2/(b^3*(a+b*x))+2*d*(b*c-a*d)*log(a+b*x)/b^3 --R 4 3 --R b x + a b --R Type: Expression(Integer) ---E 507 +--E 507 ---S 508 of 1092 +--S 508 of 1092 a0:=integrate(t0,x) --R --R @@ -9774,27 +9774,27 @@ a0:=integrate(t0,x) --R 4 3 --R b x + a b --R Type: Union(Expression(Integer),...) ---E 508 +--E 508 ---S 509 of 1092 +--S 509 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 509 +--E 509 ---S 510 of 1092 +--S 510 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 510 +--E 510 )clear all ---S 511 of 1092 +--S 511 of 1092 t0:=(c+d*x)^2/(x*(a+b*x)^2) --R --R @@ -9804,9 +9804,9 @@ t0:=(c+d*x)^2/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 511 +--E 511 ---S 512 of 1092 +--S 512 of 1092 r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) --R --R @@ -9820,9 +9820,9 @@ r0:=(b*c-a*d)^2/(a*b^2*(a+b*x))+c^2*log(x)/a^2-(c^2/a^2-d^2/b^2)*log(a+b*x) --R 2 3 3 2 --R a b x + a b --R Type: Expression(Integer) ---E 512 +--E 512 ---S 513 of 1092 +--S 513 of 1092 a0:=integrate(t0,x) --R --R @@ -9836,27 +9836,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 --R a b x + a b --R Type: Union(Expression(Integer),...) ---E 513 +--E 513 ---S 514 of 1092 +--S 514 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 514 +--E 514 ---S 515 of 1092 +--S 515 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 515 +--E 515 )clear all ---S 516 of 1092 +--S 516 of 1092 t0:=(c+d*x)^2/(x^2*(a+b*x)^2) --R --R @@ -9866,9 +9866,9 @@ t0:=(c+d*x)^2/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 516 +--E 516 ---S 517 of 1092 +--S 517 of 1092 r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ log(x)/a^3+2*c*(b*c-a*d)*log(a+b*x)/a^3 --R @@ -9886,9 +9886,9 @@ r0:=-c^2/(a^2*x)-(b*c-a*d)^2/(a^2*b*(a+b*x))-2*c*(b*c-a*d)*_ --R 3 2 2 4 --R a b x + a b x --R Type: Expression(Integer) ---E 517 +--E 517 ---S 518 of 1092 +--S 518 of 1092 a0:=integrate(t0,x) --R --R @@ -9905,27 +9905,27 @@ a0:=integrate(t0,x) --R 3 2 2 4 --R a b x + a b x --R Type: Union(Expression(Integer),...) ---E 518 +--E 518 ---S 519 of 1092 +--S 519 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 519 +--E 519 ---S 520 of 1092 +--S 520 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 520 +--E 520 )clear all ---S 521 of 1092 +--S 521 of 1092 t0:=(c+d*x)^2/(x^3*(a+b*x)^2) --R --R @@ -9935,9 +9935,9 @@ t0:=(c+d*x)^2/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 521 +--E 521 ---S 522 of 1092 +--S 522 of 1092 r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ (b*c-a*d)*(3*b*c-a*d)*log(x)/a^4-(b*c-a*d)*(3*b*c-a*d)*log(a+b*x)/a^4 --R @@ -9957,9 +9957,9 @@ r0:=-1/2*c^2/(a^2*x^2)+2*c*(b*c-a*d)/(a^3*x)+(b*c-a*d)^2/(a^3*(a+b*x))+_ --R 4 3 5 2 --R 2a b x + 2a x --R Type: Expression(Integer) ---E 522 +--E 522 ---S 523 of 1092 +--S 523 of 1092 a0:=integrate(t0,x) --R --R @@ -9978,27 +9978,27 @@ a0:=integrate(t0,x) --R 4 3 5 2 --R 2a b x + 2a x --R Type: Union(Expression(Integer),...) ---E 523 +--E 523 ---S 524 of 1092 +--S 524 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 524 +--E 524 ---S 525 of 1092 +--S 525 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 525 +--E 525 )clear all ---S 526 of 1092 +--S 526 of 1092 t0:=(c+d*x)^2/(x^4*(a+b*x)^2) --R --R @@ -10008,9 +10008,9 @@ t0:=(c+d*x)^2/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 526 +--E 526 ---S 527 of 1092 +--S 527 of 1092 r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ (a^4*x)-b*(b*c-a*d)^2/(a^4*(a+b*x))-2*b*(b*c-a*d)*(2*b*c-a*d)*_ log(x)/a^5+2*b*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 @@ -10039,9 +10039,9 @@ r0:=-1/3*c^2/(a^2*x^3)+c*(b*c-a*d)/(a^3*x^2)-(b*c-a*d)*(3*b*c-a*d)/_ --R 5 4 6 3 --R 3a b x + 3a x --R Type: Expression(Integer) ---E 527 +--E 527 ---S 528 of 1092 +--S 528 of 1092 a0:=integrate(t0,x) --R --R @@ -10068,27 +10068,27 @@ a0:=integrate(t0,x) --R 5 4 6 3 --R 3a b x + 3a x --R Type: Union(Expression(Integer),...) ---E 528 +--E 528 ---S 529 of 1092 +--S 529 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 529 +--E 529 ---S 530 of 1092 +--S 530 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 530 +--E 530 )clear all ---S 531 of 1092 +--S 531 of 1092 t0:=(c+d*x)^2/(x^5*(a+b*x)^2) --R --R @@ -10098,9 +10098,9 @@ t0:=(c+d*x)^2/(x^5*(a+b*x)^2) --R 2 7 6 2 5 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 531 +--E 531 ---S 532 of 1092 +--S 532 of 1092 r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ (3*b*c-a*d)/(a^4*x^2)+2*b*(b*c-a*d)*(2*b*c-a*d)/(a^5*x)+_ b^2*(b*c-a*d)^2/(a^5*(a+b*x))+b^2*(5*b*c-3*a*d)*(b*c-a*d)*_ @@ -10133,9 +10133,9 @@ r0:=-1/4*c^2/(a^2*x^4)+2/3*c*(b*c-a*d)/(a^3*x^3)-1/2*(b*c-a*d)*_ --R 6 5 7 4 --R 12a b x + 12a x --R Type: Expression(Integer) ---E 532 +--E 532 ---S 533 of 1092 +--S 533 of 1092 a0:=integrate(t0,x) --R --R @@ -10165,27 +10165,27 @@ a0:=integrate(t0,x) --R 6 5 7 4 --R 12a b x + 12a x --R Type: Union(Expression(Integer),...) ---E 533 +--E 533 ---S 534 of 1092 +--S 534 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 534 +--E 534 ---S 535 of 1092 +--S 535 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 535 +--E 535 )clear all ---S 536 of 1092 +--S 536 of 1092 t0:=x^4*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10195,9 +10195,9 @@ t0:=x^4*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 536 +--E 536 ---S 537 of 1092 +--S 537 of 1092 r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ (b*c-a*d)^2*x^2/b^6+1/3*(b*c-4*a*d)*(b*c-a*d)^2*x^3/b^5+_ 3/4*d*(b*c-a*d)^2*x^4/b^4+1/5*d^2*(3*b*c-2*a*d)*x^5/b^3+_ @@ -10238,9 +10238,9 @@ r0:=3*a^2*(b*c-2*a*d)*(b*c-a*d)^2*x/b^7-1/2*a*(2*b*c-5*a*d)*_ --R 9 8 --R 60b x + 60a b --R Type: Expression(Integer) ---E 537 +--E 537 ---S 538 of 1092 +--S 538 of 1092 a0:=integrate(t0,x) --R --R @@ -10277,27 +10277,27 @@ a0:=integrate(t0,x) --R 9 8 --R 60b x + 60a b --R Type: Union(Expression(Integer),...) ---E 538 +--E 538 ---S 539 of 1092 +--S 539 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 539 +--E 539 ---S 540 of 1092 +--S 540 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 540 +--E 540 )clear all ---S 541 of 1092 +--S 541 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10307,9 +10307,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 541 +--E 541 ---S 542 of 1092 +--S 542 of 1092 r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ x^2/b^5+d*(b*c-a*d)^2*x^3/b^4+1/4*d^2*(3*b*c-2*a*d)*x^4/b^3+_ 1/5*d^3*x^5/b^2+a^3*(b*c-a*d)^3/(b^7*(a+b*x))+_ @@ -10343,9 +10343,9 @@ r0:=-a*(2*b*c-5*a*d)*(b*c-a*d)^2*x/b^6+1/2*(b*c-4*a*d)*(b*c-a*d)^2*_ --R 8 7 --R 20b x + 20a b --R Type: Expression(Integer) ---E 542 +--E 542 ---S 543 of 1092 +--S 543 of 1092 a0:=integrate(t0,x) --R --R @@ -10376,27 +10376,27 @@ a0:=integrate(t0,x) --R 8 7 --R 20b x + 20a b --R Type: Union(Expression(Integer),...) ---E 543 +--E 543 ---S 544 of 1092 +--S 544 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 544 +--E 544 ---S 545 of 1092 +--S 545 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 545 +--E 545 )clear all ---S 546 of 1092 +--S 546 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10406,9 +10406,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 546 +--E 546 ---S 547 of 1092 +--S 547 of 1092 r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ 1/3*d^2*(3*b*c-2*a*d)*x^3/b^3+1/4*d^3*x^4/b^2-a^2*_ (b*c-a*d)^3/(b^6*(a+b*x))-a*(2*b*c-5*a*d)*(b*c-a*d)^2*log(a+b*x)/b^6 @@ -10438,9 +10438,9 @@ r0:=(b*c-4*a*d)*(b*c-a*d)^2*x/b^5+3/2*d*(b*c-a*d)^2*x^2/b^4+_ --R 7 6 --R 12b x + 12a b --R Type: Expression(Integer) ---E 547 +--E 547 ---S 548 of 1092 +--S 548 of 1092 a0:=integrate(t0,x) --R --R @@ -10468,27 +10468,27 @@ a0:=integrate(t0,x) --R 7 6 --R 12b x + 12a b --R Type: Union(Expression(Integer),...) ---E 548 +--E 548 ---S 549 of 1092 +--S 549 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 549 +--E 549 ---S 550 of 1092 +--S 550 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 550 +--E 550 )clear all ---S 551 of 1092 +--S 551 of 1092 t0:=x*(c+d*x)^3/(a+b*x)^2 --R --R @@ -10498,7 +10498,7 @@ t0:=x*(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 551 +--E 551 --S 552 of 1092 r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ @@ -10528,7 +10528,7 @@ r0:=3*d*(b*c-a*d)^2*x/b^4+1/2*d^2*(3*b*c-2*a*d)*x^2/b^3+1/3*d^3*x^3/b^2+_ --R Type: Expression(Integer) --E 552 ---S 553 of 1092 +--S 553 of 1092 a0:=integrate(t0,x) --R --R @@ -10553,27 +10553,27 @@ a0:=integrate(t0,x) --R 6 5 --R 6b x + 6a b --R Type: Union(Expression(Integer),...) ---E 553 +--E 553 ---S 554 of 1092 +--S 554 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 554 +--E 554 ---S 555 of 1092 +--S 555 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 555 +--E 555 )clear all ---S 556 of 1092 +--S 556 of 1092 t0:=(c+d*x)^3/(a+b*x)^2 --R --R @@ -10583,9 +10583,9 @@ t0:=(c+d*x)^3/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 556 +--E 556 ---S 557 of 1092 +--S 557 of 1092 r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ 3*d*(b*c-a*d)^2*log(a+b*x)/b^4 --R @@ -10605,9 +10605,9 @@ r0:=d^2*(3*b*c-2*a*d)*x/b^3+1/2*d^3*x^2/b^2-(b*c-a*d)^3/(b^4*(a+b*x))+_ --R 5 4 --R 2b x + 2a b --R Type: Expression(Integer) ---E 557 +--E 557 ---S 558 of 1092 +--S 558 of 1092 a0:=integrate(t0,x) --R --R @@ -10626,27 +10626,27 @@ a0:=integrate(t0,x) --R 5 4 --R 2b x + 2a b --R Type: Union(Expression(Integer),...) ---E 558 +--E 558 ---S 559 of 1092 +--S 559 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 559 +--E 559 ---S 560 of 1092 +--S 560 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 560 +--E 560 )clear all ---S 561 of 1092 +--S 561 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)^2) --R --R @@ -10656,9 +10656,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 561 +--E 561 ---S 562 of 1092 +--S 562 of 1092 r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ (b*c-a*d)^2*(b*c+2*a*d)*log(a+b*x)/(a^2*b^3) --R @@ -10678,9 +10678,9 @@ r0:=d^3*x/b^2+(b*c-a*d)^3/(a*b^3*(a+b*x))+c^3*log(x)/a^2-_ --R 2 4 3 3 --R a b x + a b --R Type: Expression(Integer) ---E 562 +--E 562 ---S 563 of 1092 +--S 563 of 1092 a0:=integrate(t0,x) --R --R @@ -10699,27 +10699,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 --R a b x + a b --R Type: Union(Expression(Integer),...) ---E 563 +--E 563 ---S 564 of 1092 +--S 564 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 564 +--E 564 ---S 565 of 1092 +--S 565 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 565 +--E 565 )clear all ---S 566 of 1092 +--S 566 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)^2) --R --R @@ -10729,9 +10729,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 566 +--E 566 ---S 567 of 1092 +--S 567 of 1092 r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ log(x)/a^3+(b*c-a*d)^2*(2*b*c+a*d)*log(a+b*x)/(a^3*b^2) --R @@ -10751,9 +10751,9 @@ r0:=-c^3/(a^2*x)-(b*c-a*d)^3/(a^2*b^2*(a+b*x))-c^2*(2*b*c-3*a*d)*_ --R 3 3 2 4 2 --R a b x + a b x --R Type: Expression(Integer) ---E 567 +--E 567 ---S 568 of 1092 +--S 568 of 1092 a0:=integrate(t0,x) --R --R @@ -10772,27 +10772,27 @@ a0:=integrate(t0,x) --R 3 3 2 4 2 --R a b x + a b x --R Type: Union(Expression(Integer),...) ---E 568 +--E 568 ---S 569 of 1092 +--S 569 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 569 +--E 569 ---S 570 of 1092 +--S 570 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 570 +--E 570 )clear all ---S 571 of 1092 +--S 571 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)^2) --R --R @@ -10802,9 +10802,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 571 +--E 571 ---S 572 of 1092 +--S 572 of 1092 r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ (a^3*b*(a+b*x))+3*c*(b*c-a*d)^2*log(x)/a^4-3*c*(b*c-a*d)^2*log(a+b*x)/a^4 --R @@ -10835,9 +10835,9 @@ r0:=-1/2*c^3/(a^2*x^2)+c^2*(2*b*c-3*a*d)/(a^3*x)+(b*c-a*d)^3/_ --R 4 2 3 5 2 --R 2a b x + 2a b x --R Type: Expression(Integer) ---E 572 +--E 572 ---S 573 of 1092 +--S 573 of 1092 a0:=integrate(t0,x) --R --R @@ -10867,27 +10867,27 @@ a0:=integrate(t0,x) --R 4 2 3 5 2 --R 2a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 573 +--E 573 ---S 574 of 1092 +--S 574 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 574 +--E 574 ---S 575 of 1092 +--S 575 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 575 +--E 575 )clear all ---S 576 of 1092 +--S 576 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)^2) --R --R @@ -10897,9 +10897,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 576 +--E 576 ---S 577 of 1092 +--S 577 of 1092 r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ (a^4*x)-(b*c-a*d)^3/(a^4*(a+b*x))-(b*c-a*d)^2*(4*b*c-a*d)*log(x)/_ a^5+(b*c-a*d)^2*(4*b*c-a*d)*log(a+b*x)/a^5 @@ -10931,9 +10931,9 @@ r0:=-1/3*c^3/(a^2*x^3)+1/2*c^2*(2*b*c-3*a*d)/(a^3*x^2)-3*c*(b*c-a*d)^2/_ --R 5 4 6 3 --R 6a b x + 6a x --R Type: Expression(Integer) ---E 577 +--E 577 ---S 578 of 1092 +--S 578 of 1092 a0:=integrate(t0,x) --R --R @@ -10963,27 +10963,27 @@ a0:=integrate(t0,x) --R 5 4 6 3 --R 6a b x + 6a x --R Type: Union(Expression(Integer),...) ---E 578 +--E 578 ---S 579 of 1092 +--S 579 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 579 +--E 579 ---S 580 of 1092 +--S 580 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 580 +--E 580 )clear all ---S 581 of 1092 +--S 581 of 1092 t0:=(c+d*x)^3/(x^5*(a+b*x)^2) --R --R @@ -10993,9 +10993,9 @@ t0:=(c+d*x)^3/(x^5*(a+b*x)^2) --R 2 7 6 2 5 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 581 +--E 581 ---S 582 of 1092 +--S 582 of 1092 r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ 3/2*c*(b*c-a*d)^2/(a^4*x^2)+(b*c-a*d)^2*(4*b*c-a*d)/_ (a^5*x)+b*(b*c-a*d)^3/(a^5*(a+b*x))+b*(5*b*c-2*a*d)*_ @@ -11031,9 +11031,9 @@ r0:=-1/4*c^3/(a^2*x^4)+1/3*c^2*(2*b*c-3*a*d)/(a^3*x^3)-_ --R 6 5 7 4 --R 12a b x + 12a x --R Type: Expression(Integer) ---E 582 +--E 582 ---S 583 of 1092 +--S 583 of 1092 a0:=integrate(t0,x) --R --R @@ -11066,27 +11066,27 @@ a0:=integrate(t0,x) --R 6 5 7 4 --R 12a b x + 12a x --R Type: Union(Expression(Integer),...) ---E 583 +--E 583 ---S 584 of 1092 +--S 584 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 584 +--E 584 ---S 585 of 1092 +--S 585 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 585 +--E 585 )clear all ---S 586 of 1092 +--S 586 of 1092 t0:=(c+d*x)^3/(x^6*(a+b*x)^2) --R --R @@ -11096,9 +11096,9 @@ t0:=(c+d*x)^3/(x^6*(a+b*x)^2) --R 2 8 7 2 6 --R b x + 2a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 586 +--E 586 ---S 587 of 1092 +--S 587 of 1092 r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ (a^4*x^3)+1/2*(b*c-a*d)^2*(4*b*c-a*d)/(a^5*x^2)-_ b*(5*b*c-2*a*d)*(b*c-a*d)^2/(a^6*x)-b^2*(b*c-a*d)^3/_ @@ -11138,9 +11138,9 @@ r0:=-1/5*c^3/(a^2*x^5)+1/4*c^2*(2*b*c-3*a*d)/(a^3*x^4)-c*(b*c-a*d)^2/_ --R 7 6 8 5 --R 20a b x + 20a x --R Type: Expression(Integer) ---E 587 +--E 587 ---S 588 of 1092 +--S 588 of 1092 a0:=integrate(t0,x) --R --R @@ -11176,27 +11176,27 @@ a0:=integrate(t0,x) --R 7 6 8 5 --R 20a b x + 20a x --R Type: Union(Expression(Integer),...) ---E 588 +--E 588 ---S 589 of 1092 +--S 589 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 589 +--E 589 ---S 590 of 1092 +--S 590 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 590 +--E 590 )clear all ---S 591 of 1092 +--S 591 of 1092 t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 --R --R @@ -11206,9 +11206,9 @@ t0:=(2-3*x)^3*sqrt(x)/(1+x)^2 --R 2 --R x + 2x + 1 --R Type: Expression(Integer) ---E 591 +--E 591 ---S 592 of 1092 +--S 592 of 1092 r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ 125*sqrt(x)/(1+x) --R @@ -11218,9 +11218,9 @@ r0a:=72*x^(3/2)-54/5*x^(5/2)+575*atan(sqrt(x))-450*sqrt(x)-_ --R (2) -------------------------------------------------------------- --R 5x + 5 --R Type: Expression(Integer) ---E 592 +--E 592 ---S 593 of 1092 +--S 593 of 1092 r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ 1/5*(62-513*x)*sqrt(x)-21/5*(2-3*x)^2*sqrt(x)-(2-3*x)^3*sqrt(x)/(1+x) --R @@ -11230,9 +11230,9 @@ r0b:=575*atan(sqrt(x))-2689/5*sqrt(x)-_ --R (3) -------------------------------------------------------------- --R 5x + 5 --R Type: Expression(Integer) ---E 593 +--E 593 ---S 594 of 1092 +--S 594 of 1092 a0:=integrate(t0,x) --R --R @@ -11241,43 +11241,43 @@ a0:=integrate(t0,x) --R (4) -------------------------------------------------------------- --R 5x + 5 --R Type: Union(Expression(Integer),...) ---E 594 +--E 594 ---S 595 of 1092 +--S 595 of 1092 m0a:=a0-r0a --R --R --R (5) 0 --R Type: Expression(Integer) ---E 595 +--E 595 ---S 596 of 1092 +--S 596 of 1092 d0:=D(m0a,x) --R --R --R (6) 0 --R Type: Expression(Integer) ---E 596 +--E 596 ---S 597 of 1092 +--S 597 of 1092 m0b:=a0-r0b --R --R --R (7) 0 --R Type: Expression(Integer) ---E 597 +--E 597 ---S 598 of 1092 +--S 598 of 1092 d0:=D(m0b,x) --R --R --R (8) 0 --R Type: Expression(Integer) ---E 598 +--E 598 )clear all ---S 599 of 1092 +--S 599 of 1092 t0:=x^6/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11291,9 +11291,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 599 +--E 599 ---S 600 of 1092 +--S 600 of 1092 r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ 1/3*x^3/(b^2*d^2)-a^6/(b^5*(b*c-a*d)^2*(a+b*x))-_ c^6/(d^5*(b*c-a*d)^2*(c+d*x))-2*a^5*(3*b*c-2*a*d)*log(a+b*x)/_ @@ -11344,9 +11344,9 @@ r0:=(3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*x/(b^4*d^4)-(b*c+a*d)*x^2/(b^3*d^3)+_ --R 2 7 3 6 8 4 5 --R 9a b c d - 3a b c d --R Type: Expression(Integer) ---E 600 +--E 600 ---S 601 of 1092 +--S 601 of 1092 a0:=integrate(t0,x) --R --R @@ -11394,27 +11394,27 @@ a0:=integrate(t0,x) --R 2 7 3 6 8 4 5 --R 9a b c d - 3a b c d --R Type: Union(Expression(Integer),...) ---E 601 +--E 601 ---S 602 of 1092 +--S 602 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 602 +--E 602 ---S 603 of 1092 +--S 603 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 603 +--E 603 )clear all ---S 604 of 1092 +--S 604 of 1092 t0:=x^5/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11428,9 +11428,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 604 +--E 604 ---S 605 of 1092 +--S 605 of 1092 r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ (a+b*x))+c^5/(d^4*(b*c-a*d)^2*(c+d*x))+a^4*(5*b*c-3*a*d)*_ log(a+b*x)/(b^4*(b*c-a*d)^3)+c^4*(3*b*c-5*a*d)*log(c+d*x)/_ @@ -11478,9 +11478,9 @@ r0:=-2*(b*c+a*d)*x/(b^3*d^3)+1/2*x^2/(b^2*d^2)+a^5/(b^4*(b*c-a*d)^2*_ --R 2 6 3 5 7 4 4 --R 6a b c d - 2a b c d --R Type: Expression(Integer) ---E 605 +--E 605 ---S 606 of 1092 +--S 606 of 1092 a0:=integrate(t0,x) --R --R @@ -11525,27 +11525,27 @@ a0:=integrate(t0,x) --R 2 6 3 5 7 4 4 --R 6a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 606 +--E 606 ---S 607 of 1092 +--S 607 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 607 +--E 607 ---S 608 of 1092 +--S 608 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 608 +--E 608 )clear all ---S 609 of 1092 +--S 609 of 1092 t0:=x^4/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11559,9 +11559,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 609 +--E 609 ---S 610 of 1092 +--S 610 of 1092 r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ 2*a^3*(2*b*c-a*d)*log(a+b*x)/(b^3*(b*c-a*d)^3)-_ 2*c^3*(b*c-2*a*d)*log(c+d*x)/(d^3*(b*c-a*d)^3) @@ -11605,9 +11605,9 @@ r0:=x/(b^2*d^2)-a^4/(b^3*(b*c-a*d)^2*(a+b*x))-c^4/(d^3*(b*c-a*d)^2*(c+d*x))-_ --R 2 5 3 4 6 4 3 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 610 +--E 610 ---S 611 of 1092 +--S 611 of 1092 a0:=integrate(t0,x) --R --R @@ -11649,27 +11649,27 @@ a0:=integrate(t0,x) --R 2 5 3 4 6 4 3 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 611 +--E 611 ---S 612 of 1092 +--S 612 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 612 +--E 612 ---S 613 of 1092 +--S 613 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 613 +--E 613 )clear all ---S 614 of 1092 +--S 614 of 1092 t0:=x^3/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11683,9 +11683,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 614 +--E 614 ---S 615 of 1092 +--S 615 of 1092 r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ a^2*(3*b*c-a*d)*log(a+b*x)/(b^2*(b*c-a*d)^3)+_ c^2*(b*c-3*a*d)*log(c+d*x)/(d^2*(b*c-a*d)^3) @@ -11720,9 +11720,9 @@ r0:=a^3/(b^2*(b*c-a*d)^2*(a+b*x))+c^3/(d^2*(b*c-a*d)^2*(c+d*x))+_ --R 2 4 3 3 5 4 2 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 615 +--E 615 ---S 616 of 1092 +--S 616 of 1092 a0:=integrate(t0,x) --R --R @@ -11755,27 +11755,27 @@ a0:=integrate(t0,x) --R 2 4 3 3 5 4 2 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 616 +--E 616 ---S 617 of 1092 +--S 617 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 617 +--E 617 ---S 618 of 1092 +--S 618 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 618 +--E 618 )clear all ---S 619 of 1092 +--S 619 of 1092 t0:=x^2/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11789,9 +11789,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 619 +--E 619 ---S 620 of 1092 +--S 620 of 1092 r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ 2*a*c*log(a+b*x)/(b*c-a*d)^3+2*a*c*log(c+d*x)/(b*c-a*d)^3 --R @@ -11815,9 +11815,9 @@ r0:=-a^2/(b*(b*c-a*d)^2*(a+b*x))-c^2/(d*(b*c-a*d)^2*(c+d*x))-_ --R 2 3 3 2 4 4 --R 3a b c d - a b c d --R Type: Expression(Integer) ---E 620 +--E 620 ---S 621 of 1092 +--S 621 of 1092 a0:=integrate(t0,x) --R --R @@ -11840,27 +11840,27 @@ a0:=integrate(t0,x) --R 2 3 3 2 4 4 --R 3a b c d - a b c d --R Type: Union(Expression(Integer),...) ---E 621 +--E 621 ---S 622 of 1092 +--S 622 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 622 +--E 622 ---S 623 of 1092 +--S 623 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 623 +--E 623 )clear all ---S 624 of 1092 +--S 624 of 1092 t0:=x/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11873,9 +11873,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 624 +--E 624 ---S 625 of 1092 +--S 625 of 1092 r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ (b*c+a*d)*log(a+b*x)/(b*c-a*d)^3-(b*c+a*d)*log(c+d*x)/(b*c-a*d)^3 --R @@ -11903,9 +11903,9 @@ r0:=a/((b*c-a*d)^2*(a+b*x))+c/((b*c-a*d)^2*(c+d*x))+_ --R 3 4 --R - a b c --R Type: Expression(Integer) ---E 625 +--E 625 ---S 626 of 1092 +--S 626 of 1092 a0:=integrate(t0,x) --R --R @@ -11932,27 +11932,27 @@ a0:=integrate(t0,x) --R 3 4 --R - a b c --R Type: Union(Expression(Integer),...) ---E 626 +--E 626 ---S 627 of 1092 +--S 627 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 627 +--E 627 ---S 628 of 1092 +--S 628 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 628 +--E 628 )clear all ---S 629 of 1092 +--S 629 of 1092 t0:=1/((a+b*x)^2*(c+d*x)^2) --R --R @@ -11965,9 +11965,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 --R (2a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 629 +--E 629 ---S 630 of 1092 +--S 630 of 1092 r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ 2*b*d*log(a+b*x)/(b*c-a*d)^3+2*b*d*log(c+d*x)/(b*c-a*d)^3 --R @@ -11991,9 +11991,9 @@ r0:=-b/((b*c-a*d)^2*(a+b*x))-d/((b*c-a*d)^2*(c+d*x))-_ --R 3 4 --R - a b c --R Type: Expression(Integer) ---E 630 +--E 630 ---S 631 of 1092 +--S 631 of 1092 a0:=integrate(t0,x) --R --R @@ -12016,27 +12016,27 @@ a0:=integrate(t0,x) --R 3 4 --R - a b c --R Type: Union(Expression(Integer),...) ---E 631 +--E 631 ---S 632 of 1092 +--S 632 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 632 +--E 632 ---S 633 of 1092 +--S 633 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 633 +--E 633 )clear all ---S 634 of 1092 +--S 634 of 1092 t0:=1/(x*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12049,9 +12049,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^2) --R 2 2 2 2 2 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 634 +--E 634 ---S 635 of 1092 +--S 635 of 1092 r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ log(x)/(a^2*c^2)-b^2*(b*c-3*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^3)-_ d^2*(3*b*c-a*d)*log(c+d*x)/(c^2*(b*c-a*d)^3) @@ -12097,9 +12097,9 @@ r0:=b^2/(a*(b*c-a*d)^2*(a+b*x))+d^2/(c*(b*c-a*d)^2*(c+d*x))+_ --R 3 3 6 --R - a b c --R Type: Expression(Integer) ---E 635 +--E 635 ---S 636 of 1092 +--S 636 of 1092 a0:=integrate(t0,x) --R --R @@ -12143,27 +12143,27 @@ a0:=integrate(t0,x) --R 3 3 6 --R - a b c --R Type: Union(Expression(Integer),...) ---E 636 +--E 636 ---S 637 of 1092 +--S 637 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 637 +--E 637 ---S 638 of 1092 +--S 638 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 638 +--E 638 )clear all ---S 639 of 1092 +--S 639 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12176,9 +12176,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^2) --R 2 2 3 2 2 2 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 639 +--E 639 ---S 640 of 1092 +--S 640 of 1092 r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ d^3/(c^2*(b*c-a*d)^2*(c+d*x))-2*(b*c+a*d)*log(x)/(a^3*c^3)+_ 2*b^3*(b*c-2*a*d)*log(a+b*x)/(a^3*(b*c-a*d)^3)+_ @@ -12231,9 +12231,9 @@ r0:=(-1)/(a^2*c^2*x)-b^3/(a^2*(b*c-a*d)^2*(a+b*x))-_ --R 7 4 3 6 5 2 5 2 6 4 3 7 --R (a c d - 3a b c d + 3a b c d - a b c )x --R Type: Expression(Integer) ---E 640 +--E 640 ---S 641 of 1092 +--S 641 of 1092 a0:=integrate(t0,x) --R --R @@ -12283,27 +12283,27 @@ a0:=integrate(t0,x) --R 7 4 3 6 5 2 5 2 6 4 3 7 --R (a c d - 3a b c d + 3a b c d - a b c )x --R Type: Union(Expression(Integer),...) ---E 641 +--E 641 ---S 642 of 1092 +--S 642 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 642 +--E 642 ---S 643 of 1092 +--S 643 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 643 +--E 643 )clear all ---S 644 of 1092 +--S 644 of 1092 t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) --R --R @@ -12316,9 +12316,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^2) --R 2 2 4 2 2 3 --R (2a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 644 +--E 644 ---S 645 of 1092 +--S 645 of 1092 r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ b^4/(a^3*(b*c-a*d)^2*(a+b*x))+d^4/(c^3*(b*c-a*d)^2*(c+d*x))+_ (3*b^2*c^2+4*a*b*c*d+3*a^2*d^2)*log(x)/(a^4*c^4)-b^4*(3*b*c-5*a*d)*_ @@ -12375,9 +12375,9 @@ r0:=(-1/2)/(a^2*c^2*x^2)+2*(b*c+a*d)/(a^3*c^3*x)+_ --R 8 5 3 7 6 2 6 2 7 5 3 8 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Expression(Integer) ---E 645 +--E 645 ---S 646 of 1092 +--S 646 of 1092 a0:=integrate(t0,x) --R --R @@ -12430,27 +12430,27 @@ a0:=integrate(t0,x) --R 8 5 3 7 6 2 6 2 7 5 3 8 2 --R (2a c d - 6a b c d + 6a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 646 +--E 646 ---S 647 of 1092 +--S 647 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 647 +--E 647 ---S 648 of 1092 +--S 648 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 648 +--E 648 )clear all ---S 649 of 1092 +--S 649 of 1092 t0:=x^7/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12464,9 +12464,9 @@ t0:=x^7/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 649 +--E 649 ---S 650 of 1092 +--S 650 of 1092 r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ (b^3*d^4)+1/3*x^3/(b^2*d^3)+a^7/(b^5*(b*c-a*d)^3*(a+b*x))+1/2*c^7/_ (d^6*(b*c-a*d)^2*(c+d*x)^2)-c^6*(5*b*c-7*a*d)/(d^6*(b*c-a*d)^3*_ @@ -12570,9 +12570,9 @@ r0:=3*(2*b^2*c^2+2*a*b*c*d+a^2*d^2)*x/(b^4*d^5)-1/2*(3*b*c+2*a*d)*x^2/_ --R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 --R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d --R Type: Expression(Integer) ---E 650 +--E 650 ---S 651 of 1092 +--S 651 of 1092 a0:=integrate(t0,x) --R --R @@ -12672,27 +12672,27 @@ a0:=integrate(t0,x) --R 5 5 2 10 4 6 3 9 3 7 4 8 2 8 5 7 9 6 6 --R 6a b c d - 24a b c d + 36a b c d - 24a b c d + 6a b c d --R Type: Union(Expression(Integer),...) ---E 651 +--E 651 ---S 652 of 1092 +--S 652 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 652 +--E 652 ---S 653 of 1092 +--S 653 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 653 +--E 653 )clear all ---S 654 of 1092 +--S 654 of 1092 t0:=x^6/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12706,9 +12706,9 @@ t0:=x^6/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 654 +--E 654 ---S 655 of 1092 +--S 655 of 1092 r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ (a+b*x))-1/2*c^6/(d^5*(b*c-a*d)^2*(c+d*x)^2)+2*c^5*(2*b*c-3*a*d)/_ (d^5*(b*c-a*d)^3*(c+d*x))-3*a^5*(2*b*c-a*d)*log(a+b*x)/_ @@ -12786,9 +12786,9 @@ r0:=-(3*b*c+2*a*d)*x/(b^3*d^4)+1/2*x^2/(b^2*d^3)-a^6/(b^4*(b*c-a*d)^3*_ --R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 655 +--E 655 ---S 656 of 1092 +--S 656 of 1092 a0:=integrate(t0,x) --R --R @@ -12862,27 +12862,27 @@ a0:=integrate(t0,x) --R 5 4 2 9 4 5 3 8 3 6 4 7 2 7 5 6 8 6 5 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 656 +--E 656 ---S 657 of 1092 +--S 657 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 657 +--E 657 ---S 658 of 1092 +--S 658 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 658 +--E 658 )clear all ---S 659 of 1092 +--S 659 of 1092 t0:=x^5/((a+b*x)^2*(c+d*x)^3) --R --R @@ -12896,9 +12896,9 @@ t0:=x^5/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 659 +--E 659 ---S 660 of 1092 +--S 660 of 1092 r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ (c+d*x)^2)-c^4*(3*b*c-5*a*d)/(d^4*(b*c-a*d)^3*(c+d*x))+_ a^4*(5*b*c-2*a*d)*log(a+b*x)/(b^3*(b*c-a*d)^4)-c^3*_ @@ -12966,9 +12966,9 @@ r0:=x/(b^2*d^3)+a^5/(b^3*(b*c-a*d)^3*(a+b*x))+1/2*c^5/(d^4*(b*c-a*d)^2*_ --R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 660 +--E 660 ---S 661 of 1092 +--S 661 of 1092 a0:=integrate(t0,x) --R --R @@ -13033,27 +13033,27 @@ a0:=integrate(t0,x) --R 5 3 2 8 4 4 3 7 3 5 4 6 2 6 5 5 7 6 4 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 661 +--E 661 ---S 662 of 1092 +--S 662 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 662 +--E 662 ---S 663 of 1092 +--S 663 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 663 +--E 663 )clear all ---S 664 of 1092 +--S 664 of 1092 t0:=x^4/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13067,9 +13067,9 @@ t0:=x^4/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 664 +--E 664 ---S 665 of 1092 +--S 665 of 1092 r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ 2*c^3*(b*c-2*a*d)/(d^3*(b*c-a*d)^3*(c+d*x))-a^3*(4*b*c-a*d)*_ log(a+b*x)/(b^2*(b*c-a*d)^4)+c^2*(b^2*c^2-4*a*b*c*d+6*a^2*d^2)*_ @@ -13120,9 +13120,9 @@ r0:=-a^4/(b^2*(b*c-a*d)^3*(a+b*x))-1/2*c^4/(d^3*(b*c-a*d)^2*(c+d*x)^2)+_ --R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 665 +--E 665 ---S 666 of 1092 +--S 666 of 1092 a0:=integrate(t0,x) --R --R @@ -13170,27 +13170,27 @@ a0:=integrate(t0,x) --R 5 2 2 7 4 3 3 6 3 4 4 5 2 5 5 4 6 6 3 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 666 +--E 666 ---S 667 of 1092 +--S 667 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 667 +--E 667 ---S 668 of 1092 +--S 668 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 668 +--E 668 )clear all ---S 669 of 1092 +--S 669 of 1092 t0:=x^3/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13204,9 +13204,9 @@ t0:=x^3/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 669 +--E 669 ---S 670 of 1092 +--S 670 of 1092 r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ c^2*(b*c-3*a*d)/(d^2*(b*c-a*d)^3*(c+d*x))+3*a^2*c*log(a+b*x)/_ (b*c-a*d)^4-3*a^2*c*log(c+d*x)/(b*c-a*d)^4 @@ -13250,9 +13250,9 @@ r0:=a^3/(b*(b*c-a*d)^3*(a+b*x))+1/2*c^3/(d^2*(b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 670 +--E 670 ---S 671 of 1092 +--S 671 of 1092 a0:=integrate(t0,x) --R --R @@ -13294,27 +13294,27 @@ a0:=integrate(t0,x) --R 5 2 6 4 2 3 5 3 3 4 4 2 4 5 3 5 6 2 --R 2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 671 +--E 671 ---S 672 of 1092 +--S 672 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 672 +--E 672 ---S 673 of 1092 +--S 673 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 673 +--E 673 )clear all ---S 674 of 1092 +--S 674 of 1092 t0:=x^2/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13328,9 +13328,9 @@ t0:=x^2/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 674 +--E 674 ---S 675 of 1092 +--S 675 of 1092 r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ 2*a*c/((b*c-a*d)^3*(c+d*x))-a*(2*b*c+a*d)*log(a+b*x)/(b*c-a*d)^4+_ a*(2*b*c+a*d)*log(c+d*x)/(b*c-a*d)^4 @@ -13371,9 +13371,9 @@ r0:=-a^2/((b*c-a*d)^3*(a+b*x))-1/2*c^2/(d*(b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Expression(Integer) ---E 675 +--E 675 ---S 676 of 1092 +--S 676 of 1092 a0:=integrate(t0,x) --R --R @@ -13412,27 +13412,27 @@ a0:=integrate(t0,x) --R 5 2 5 4 3 4 3 2 4 3 2 3 5 2 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d --R Type: Union(Expression(Integer),...) ---E 676 +--E 676 ---S 677 of 1092 +--S 677 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 677 +--E 677 ---S 678 of 1092 +--S 678 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 678 +--E 678 )clear all ---S 679 of 1092 +--S 679 of 1092 t0:=x/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13445,9 +13445,9 @@ t0:=x/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 679 +--E 679 ---S 680 of 1092 +--S 680 of 1092 r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ ((b*c-a*d)^3*(c+d*x))+b*(b*c+2*a*d)*log(a+b*x)/(b*c-a*d)^4-_ b*(b*c+2*a*d)*log(c+d*x)/(b*c-a*d)^4 @@ -13488,9 +13488,9 @@ r0:=a*b/((b*c-a*d)^3*(a+b*x))+1/2*c/((b*c-a*d)^2*(c+d*x)^2)+(b*c+a*d)/_ --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 680 +--E 680 ---S 681 of 1092 +--S 681 of 1092 a0:=integrate(t0,x) --R --R @@ -13529,27 +13529,27 @@ a0:=integrate(t0,x) --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 681 +--E 681 ---S 682 of 1092 +--S 682 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 682 +--E 682 ---S 683 of 1092 +--S 683 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 683 +--E 683 )clear all ---S 684 of 1092 +--S 684 of 1092 t0:=1/((a+b*x)^2*(c+d*x)^3) --R --R @@ -13562,9 +13562,9 @@ t0:=1/((a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 2 2 2 3 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 684 +--E 684 ---S 685 of 1092 +--S 685 of 1092 r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ 2*b*d/((b*c-a*d)^3*(c+d*x))-3*b^2*d*log(a+b*x)/(b*c-a*d)^4+_ 3*b^2*d*log(c+d*x)/(b*c-a*d)^4 @@ -13602,9 +13602,9 @@ r0:=-b^2/((b*c-a*d)^3*(a+b*x))-1/2*d/((b*c-a*d)^2*(c+d*x)^2)-_ --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 685 +--E 685 ---S 686 of 1092 +--S 686 of 1092 a0:=integrate(t0,x) --R --R @@ -13640,27 +13640,27 @@ a0:=integrate(t0,x) --R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 686 +--E 686 ---S 687 of 1092 +--S 687 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 687 +--E 687 ---S 688 of 1092 +--S 688 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 688 +--E 688 )clear all ---S 689 of 1092 +--S 689 of 1092 t0:=1/(x*(a+b*x)^2*(c+d*x)^3) --R --R @@ -13673,9 +13673,9 @@ t0:=1/(x*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 3 2 2 3 2 2 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 689 +--E 689 ---S 690 of 1092 +--S 690 of 1092 r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ d^2*(3*b*c-a*d)/(c^2*(b*c-a*d)^3*(c+d*x))+log(x)/(a^2*c^3)-_ b^3*(b*c-4*a*d)*log(a+b*x)/(a^2*(b*c-a*d)^4)-d^2*(6*b^2*c^2-_ @@ -13740,9 +13740,9 @@ r0:=b^3/(a*(b*c-a*d)^3*(a+b*x))+1/2*d^2/(c*(b*c-a*d)^2*(c+d*x)^2)+_ --R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Expression(Integer) ---E 690 +--E 690 ---S 691 of 1092 +--S 691 of 1092 a0:=integrate(t0,x) --R --R @@ -13804,27 +13804,27 @@ a0:=integrate(t0,x) --R 7 5 4 6 6 3 5 2 7 2 4 3 8 3 4 9 --R 2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c --R Type: Union(Expression(Integer),...) ---E 691 +--E 691 ---S 692 of 1092 +--S 692 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 692 +--E 692 ---S 693 of 1092 +--S 693 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 693 +--E 693 )clear all ---S 694 of 1092 +--S 694 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) --R --R @@ -13837,9 +13837,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 4 2 2 3 3 2 3 2 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 694 +--E 694 ---S 695 of 1092 +--S 695 of 1092 r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ 1/2*d^3/(c^2*(b*c-a*d)^2*(c+d*x)^2)-2*d^3*(2*b*c-a*d)/_ (c^3*(b*c-a*d)^3*(c+d*x))-(2*b*c+3*a*d)*log(x)/(a^3*c^4)+_ @@ -13926,112 +13926,23 @@ r0:=(-1)/(a^2*c^3*x)-b^4/(a^2*(b*c-a*d)^3*(a+b*x))-_ --R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Expression(Integer) ---E 695 +--E 695 ---S 696 of 1092 -a0:=integrate(t0,x) ---R ---R ---R (3) ---R 5 7 4 2 6 3 3 2 5 4 ---R (6a b d - 20a b c d + 20a b c d )x ---R + ---R 6 7 5 6 4 2 2 5 3 3 3 4 3 ---R (6a d - 8a b c d - 20a b c d + 40a b c d )x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 ---R (12a c d - 34a b c d + 20a b c d + 20a b c d )x ---R + ---R 6 2 5 5 3 4 4 2 4 3 ---R (6a c d - 20a b c d + 20a b c d )x ---R * ---R log(d x + c) ---R + ---R 5 4 3 6 5 2 4 2 4 4 3 5 5 2 6 6 3 ---R (- 10a b c d + 4b c d )x + (- 10a b c d - 16a b c d + 8b c d)x ---R + ---R 2 4 5 2 5 6 6 7 2 2 4 6 5 7 ---R (- 20a b c d - 2a b c d + 4b c )x + (- 10a b c d + 4a b c )x ---R * ---R log(b x + a) ---R + ---R 5 7 4 2 6 3 3 2 5 5 4 3 6 5 2 4 ---R (- 6a b d + 20a b c d - 20a b c d + 10a b c d - 4b c d )x ---R + ---R 6 7 5 6 4 2 2 5 3 3 3 4 2 4 4 3 ---R - 6a d + 8a b c d + 20a b c d - 40a b c d + 10a b c d ---R + ---R 5 5 2 6 6 ---R 16a b c d - 8b c d ---R * ---R 3 ---R x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 ---R - 12a c d + 34a b c d - 20a b c d - 20a b c d + 20a b c d ---R + ---R 5 6 6 7 ---R 2a b c d - 4b c ---R * ---R 2 ---R x ---R + ---R 6 2 5 5 3 4 4 2 4 3 2 4 6 5 7 ---R (- 6a c d + 20a b c d - 20a b c d + 10a b c d - 4a b c )x ---R * ---R log(x) ---R + ---R 5 6 4 2 2 5 3 3 3 4 2 4 4 3 5 5 2 3 ---R (- 6a b c d + 20a b c d - 20a b c d + 10a b c d - 4a b c d )x ---R + ---R 6 6 5 2 5 4 2 3 4 3 3 4 3 2 4 5 2 ---R - 6a c d + 11a b c d + 10a b c d - 25a b c d + 18a b c d ---R + ---R 5 6 ---R - 8a b c d ---R * ---R 2 ---R x ---R + ---R 6 2 5 5 3 4 4 2 4 3 3 3 5 2 2 4 6 5 7 ---R (- 9a c d + 28a b c d - 25a b c d + 4a b c d + 6a b c d - 4a b c )x ---R + ---R 6 3 4 5 4 3 4 2 5 2 3 3 6 2 4 7 ---R - 2a c d + 8a b c d - 12a b c d + 8a b c d - 2a b c ---R / ---R 7 4 6 6 2 5 5 5 3 6 4 4 4 7 3 3 5 8 2 4 ---R (2a b c d - 8a b c d + 12a b c d - 8a b c d + 2a b c d )x ---R + ---R 8 4 6 7 5 5 6 2 6 4 5 3 7 3 4 4 8 2 3 5 9 3 ---R (2a c d - 4a b c d - 4a b c d + 16a b c d - 14a b c d + 4a b c d)x ---R + ---R 8 5 5 7 6 4 6 2 7 3 5 3 8 2 4 4 9 3 5 10 2 ---R (4a c d - 14a b c d + 16a b c d - 4a b c d - 4a b c d + 2a b c )x ---R + ---R 8 6 4 7 7 3 6 2 8 2 5 3 9 4 4 10 ---R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x ---R Type: Union(Expression(Integer),...) ---E 696 +--S 696 of 1092 +--a0:=integrate(t0,x) +--E 696 ---S 697 of 1092 -m0:=a0-r0 ---R ---R ---R (4) 0 ---R Type: Expression(Integer) ---E 697 +--S 697 of 1092 +--m0:=a0-r0 +--E 697 ---S 698 of 1092 -d0:=D(m0,x) ---R ---R ---R (5) 0 ---R Type: Expression(Integer) ---E 698 +--S 698 of 1092 +--d0:=D(m0,x) +--E 698 )clear all ---S 699 of 1092 +--S 699 of 1092 t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) --R --R @@ -14044,9 +13955,9 @@ t0:=1/(x^3*(a+b*x)^2*(c+d*x)^3) --R 2 2 2 2 3 5 2 2 3 4 2 3 3 --R (3a c d + 6a b c d + b c )x + (3a c d + 2a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 699 +--E 699 ---S 700 of 1092 +--S 700 of 1092 r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ (a+b*x))+1/2*d^4/(c^3*(b*c-a*d)^2*(c+d*x)^2)+d^4*(5*b*c-3*a*d)/_ (c^4*(b*c-a*d)^3*(c+d*x))+3*(b^2*c^2+2*a*b*c*d+2*a^2*d^2)*log(x)/_ @@ -14142,9 +14053,9 @@ r0:=(-1/2)/(a^2*c^3*x^2)+(2*b*c+3*a*d)/(a^3*c^4*x)+b^5/(a^3*(b*c-a*d)^3*_ --R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Expression(Integer) ---E 700 +--E 700 ---S 701 of 1092 +--S 701 of 1092 a0:=integrate(t0,x) --R --R @@ -14236,27 +14147,27 @@ a0:=integrate(t0,x) --R 9 7 4 8 8 3 7 2 9 2 6 3 10 5 4 11 2 --R (2a c d - 8a b c d + 12a b c d - 8a b c d + 2a b c )x --R Type: Union(Expression(Integer),...) ---E 701 +--E 701 ---S 702 of 1092 +--S 702 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 702 +--E 702 ---S 703 of 1092 +--S 703 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 703 +--E 703 )clear all ---S 704 of 1092 +--S 704 of 1092 t0:=x^2/((-1+x)^2*(1+x)^2) --R --R @@ -14266,9 +14177,9 @@ t0:=x^2/((-1+x)^2*(1+x)^2) --R 4 2 --R x - 2x + 1 --R Type: Fraction(Polynomial(Integer)) ---E 704 +--E 704 ---S 705 of 1092 +--S 705 of 1092 r0:=1/2*x/(1-x^2)-1/2*atanh(x) --R --R @@ -14278,9 +14189,9 @@ r0:=1/2*x/(1-x^2)-1/2*atanh(x) --R 2 --R 2x - 2 --R Type: Expression(Integer) ---E 705 +--E 705 ---S 706 of 1092 +--S 706 of 1092 a0:=integrate(t0,x) --R --R @@ -14290,9 +14201,9 @@ a0:=integrate(t0,x) --R 2 --R 4x - 4 --R Type: Union(Expression(Integer),...) ---E 706 +--E 706 ---S 707 of 1092 +--S 707 of 1092 m0:=a0-r0 --R --R @@ -14300,19 +14211,19 @@ m0:=a0-r0 --R (4) ------------------------------------- --R 4 --R Type: Expression(Integer) ---E 707 +--E 707 ---S 708 of 1092 +--S 708 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 708 +--E 708 )clear all ---S 709 of 1092 +--S 709 of 1092 t0:=b^2*x^m/(b+a*x^2)^2 --R --R @@ -14322,28 +14233,28 @@ t0:=b^2*x^m/(b+a*x^2)^2 --R 2 4 2 2 --R a x + 2a b x + b --R Type: Expression(Integer) ---E 709 +--E 709 ---S 710 of 1092 +--S 710 of 1092 --r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ -- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) ---E 710 +--E 710 ---S 711 of 1092 +--S 711 of 1092 --a0:=integrate(t0,x) ---E 711 +--E 711 ---S 712 of 1092 +--S 712 of 1092 --m0:=a0-r0 ---E 712 +--E 712 ---S 713 of 1092 +--S 713 of 1092 --d0:=D(m0,x) ---E 713 +--E 713 )clear all ---S 714 of 1092 +--S 714 of 1092 t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) --R --R @@ -14353,28 +14264,28 @@ t0:=x^m/((1-x*sqrt(a)/sqrt(-b))^2*(1+x*sqrt(a)/sqrt(-b))^2) --R 2 4 2 2 --R a x + 2a b x + b --R Type: Expression(Integer) ---E 714 +--E 714 ---S 715 of 1092 +--S 715 of 1092 --r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ -- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) ---E 715 +--E 715 ---S 716 of 1092 +--S 716 of 1092 --a0:=integrate(t0,x) ---E 716 +--E 716 ---S 717 of 1092 +--S 717 of 1092 --m0:=a0-r0 ---E 717 +--E 717 ---S 718 of 1092 +--S 718 of 1092 --d0:=D(m0,x) ---E 718 +--E 718 )clear all ---S 719 of 1092 +--S 719 of 1092 t0:=x^3*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14384,9 +14295,9 @@ t0:=x^3*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 719 +--E 719 ---S 720 of 1092 +--S 720 of 1092 r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ 3/2*d*(b*c-2*a*d)*(b*c-a*d)*x^2/b^5+d^2*(b*c-a*d)*x^3/b^4+_ 1/4*d^3*x^4/b^3+1/2*a^3*(b*c-a*d)^3/(b^7*(a+b*x)^2)-_ @@ -14424,9 +14335,9 @@ r0:=(b*c-a*d)*(b^2*c^2-8*a*b*c*d+10*a^2*d^2)*x/b^6+_ --R 9 2 8 2 7 --R 4b x + 8a b x + 4a b --R Type: Expression(Integer) ---E 720 +--E 720 ---S 721 of 1092 +--S 721 of 1092 a0:=integrate(t0,x) --R --R @@ -14460,27 +14371,27 @@ a0:=integrate(t0,x) --R 9 2 8 2 7 --R 4b x + 8a b x + 4a b --R Type: Union(Expression(Integer),...) ---E 721 +--E 721 ---S 722 of 1092 +--S 722 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 722 +--E 722 ---S 723 of 1092 +--S 723 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 723 +--E 723 )clear all ---S 724 of 1092 +--S 724 of 1092 t0:=x^2*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14490,9 +14401,9 @@ t0:=x^2*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 724 +--E 724 ---S 725 of 1092 +--S 725 of 1092 r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ 1/3*d^3*x^3/b^3-1/2*a^2*(b*c-a*d)^3/(b^6*(a+b*x)^2)+_ a*(2*b*c-5*a*d)*(b*c-a*d)^2/(b^6*(a+b*x))+(b*c-a*d)*_ @@ -14526,9 +14437,9 @@ r0:=3*d*(b*c-2*a*d)*(b*c-a*d)*x/b^5+3/2*d^2*(b*c-a*d)*x^2/b^4+_ --R 8 2 7 2 6 --R 6b x + 12a b x + 6a b --R Type: Expression(Integer) ---E 725 +--E 725 ---S 726 of 1092 +--S 726 of 1092 a0:=integrate(t0,x) --R --R @@ -14559,27 +14470,27 @@ a0:=integrate(t0,x) --R 8 2 7 2 6 --R 6b x + 12a b x + 6a b --R Type: Union(Expression(Integer),...) ---E 726 +--E 726 ---S 727 of 1092 +--S 727 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 727 +--E 727 ---S 728 of 1092 +--S 728 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 728 +--E 728 )clear all ---S 729 of 1092 +--S 729 of 1092 t0:=x*(c+d*x)^3/(a+b*x)^3 --R --R @@ -14589,9 +14500,9 @@ t0:=x*(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 729 +--E 729 ---S 730 of 1092 +--S 730 of 1092 r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ (b^5*(a+b*x)^2)-(b*c-4*a*d)*(b*c-a*d)^2/(b^5*(a+b*x))+_ 3*d*(b*c-2*a*d)*(b*c-a*d)*log(a+b*x)/b^5 @@ -14618,9 +14529,9 @@ r0:=3*d^2*(b*c-a*d)*x/b^4+1/2*d^3*x^2/b^3+1/2*a*(b*c-a*d)^3/_ --R 7 2 6 2 5 --R 2b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 730 +--E 730 ---S 731 of 1092 +--S 731 of 1092 a0:=integrate(t0,x) --R --R @@ -14645,27 +14556,27 @@ a0:=integrate(t0,x) --R 7 2 6 2 5 --R 2b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 731 +--E 731 ---S 732 of 1092 +--S 732 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 732 +--E 732 ---S 733 of 1092 +--S 733 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 733 +--E 733 )clear all ---S 734 of 1092 +--S 734 of 1092 t0:=(c+d*x)^3/(a+b*x)^3 --R --R @@ -14675,9 +14586,9 @@ t0:=(c+d*x)^3/(a+b*x)^3 --R 3 3 2 2 2 3 --R b x + 3a b x + 3a b x + a --R Type: Fraction(Polynomial(Integer)) ---E 734 +--E 734 ---S 735 of 1092 +--S 735 of 1092 r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ (b^4*(a+b*x))+3*d^2*(b*c-a*d)*log(a+b*x)/b^4 --R @@ -14700,9 +14611,9 @@ r0:=d^3*x/b^3-1/2*(b*c-a*d)^3/(b^4*(a+b*x)^2)-3*d*(b*c-a*d)^2/_ --R 6 2 5 2 4 --R 2b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 735 +--E 735 ---S 736 of 1092 +--S 736 of 1092 a0:=integrate(t0,x) --R --R @@ -14724,27 +14635,27 @@ a0:=integrate(t0,x) --R 6 2 5 2 4 --R 2b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 736 +--E 736 ---S 737 of 1092 +--S 737 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 737 +--E 737 ---S 738 of 1092 +--S 738 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 738 +--E 738 )clear all ---S 739 of 1092 +--S 739 of 1092 t0:=(c+d*x)^3/(x*(a+b*x)^3) --R --R @@ -14754,9 +14665,9 @@ t0:=(c+d*x)^3/(x*(a+b*x)^3) --R 3 4 2 3 2 2 3 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 739 +--E 739 ---S 740 of 1092 +--S 740 of 1092 r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ (a^2*b^3*(a+b*x))+c^3*log(x)/a^3-(c^3/a^3-d^3/b^3)*log(a+b*x) --R @@ -14776,9 +14687,9 @@ r0:=1/2*(b*c-a*d)^3/(a*b^3*(a+b*x)^2)+(b*c-a*d)^2*(b*c+2*a*d)/_ --R 3 5 2 4 4 5 3 --R 2a b x + 4a b x + 2a b --R Type: Expression(Integer) ---E 740 +--E 740 ---S 741 of 1092 +--S 741 of 1092 a0:=integrate(t0,x) --R --R @@ -14797,27 +14708,27 @@ a0:=integrate(t0,x) --R 3 5 2 4 4 5 3 --R 2a b x + 4a b x + 2a b --R Type: Union(Expression(Integer),...) ---E 741 +--E 741 ---S 742 of 1092 +--S 742 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 742 +--E 742 ---S 743 of 1092 +--S 743 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 743 +--E 743 )clear all ---S 744 of 1092 +--S 744 of 1092 t0:=(c+d*x)^3/(x^2*(a+b*x)^3) --R --R @@ -14827,9 +14738,9 @@ t0:=(c+d*x)^3/(x^2*(a+b*x)^3) --R 3 5 2 4 2 3 3 2 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 744 +--E 744 ---S 745 of 1092 +--S 745 of 1092 r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ (2*b*c+a*d)/(a^3*b^2*(a+b*x))-3*c^2*(b*c-a*d)*log(x)/a^4+_ 3*c^2*(b*c-a*d)*log(a+b*x)/a^4 @@ -14861,9 +14772,9 @@ r0:=-c^3/(a^3*x)-1/2*(b*c-a*d)^3/(a^2*b^2*(a+b*x)^2)-(b*c-a*d)^2*_ --R 4 4 3 5 3 2 6 2 --R 2a b x + 4a b x + 2a b x --R Type: Expression(Integer) ---E 745 +--E 745 ---S 746 of 1092 +--S 746 of 1092 a0:=integrate(t0,x) --R --R @@ -14893,27 +14804,27 @@ a0:=integrate(t0,x) --R 4 4 3 5 3 2 6 2 --R 2a b x + 4a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 746 +--E 746 ---S 747 of 1092 +--S 747 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 747 +--E 747 ---S 748 of 1092 +--S 748 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 748 +--E 748 )clear all ---S 749 of 1092 +--S 749 of 1092 t0:=(c+d*x)^3/(x^3*(a+b*x)^3) --R --R @@ -14923,9 +14834,9 @@ t0:=(c+d*x)^3/(x^3*(a+b*x)^3) --R 3 6 2 5 2 4 3 3 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 749 +--E 749 ---S 750 of 1092 +--S 750 of 1092 r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ (a^3*b*(a+b*x)^2)+3*c*(b*c-a*d)^2/(a^4*(a+b*x))+3*c*(b*c-a*d)*_ (2*b*c-a*d)*log(x)/a^5-3*c*(b*c-a*d)*(2*b*c-a*d)*log(a+b*x)/a^5 @@ -14966,9 +14877,9 @@ r0:=-1/2*c^3/(a^3*x^2)+3*c^2*(b*c-a*d)/(a^4*x)+1/2*(b*c-a*d)^3/_ --R 5 3 4 6 2 3 7 2 --R 2a b x + 4a b x + 2a b x --R Type: Expression(Integer) ---E 750 +--E 750 ---S 751 of 1092 +--S 751 of 1092 a0:=integrate(t0,x) --R --R @@ -15007,27 +14918,27 @@ a0:=integrate(t0,x) --R 5 3 4 6 2 3 7 2 --R 2a b x + 4a b x + 2a b x --R Type: Union(Expression(Integer),...) ---E 751 +--E 751 ---S 752 of 1092 +--S 752 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 752 +--E 752 ---S 753 of 1092 +--S 753 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 753 +--E 753 )clear all ---S 754 of 1092 +--S 754 of 1092 t0:=(c+d*x)^3/(x^4*(a+b*x)^3) --R --R @@ -15037,9 +14948,9 @@ t0:=(c+d*x)^3/(x^4*(a+b*x)^3) --R 3 7 2 6 2 5 3 4 --R b x + 3a b x + 3a b x + a x --R Type: Fraction(Polynomial(Integer)) ---E 754 +--E 754 ---S 755 of 1092 +--S 755 of 1092 r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ (2*b*c-a*d)/(a^5*x)-1/2*(b*c-a*d)^3/(a^4*(a+b*x)^2)-(b*c-a*d)^2*_ (4*b*c-a*d)/(a^5*(a+b*x))-(b*c-a*d)*(10*b^2*c^2-8*a*b*c*d+a^2*d^2)*_ @@ -15081,9 +14992,9 @@ r0:=-1/3*c^3/(a^3*x^3)+3/2*c^2*(b*c-a*d)/(a^4*x^2)-3*c*(b*c-a*d)*_ --R 6 2 5 7 4 8 3 --R 6a b x + 12a b x + 6a x --R Type: Expression(Integer) ---E 755 +--E 755 ---S 756 of 1092 +--S 756 of 1092 a0:=integrate(t0,x) --R --R @@ -15122,27 +15033,27 @@ a0:=integrate(t0,x) --R 6 2 5 7 4 8 3 --R 6a b x + 12a b x + 6a x --R Type: Union(Expression(Integer),...) ---E 756 +--E 756 ---S 757 of 1092 +--S 757 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 757 +--E 757 ---S 758 of 1092 +--S 758 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 758 +--E 758 )clear all ---S 759 of 1092 +--S 759 of 1092 t0:=x^7/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15159,9 +15070,9 @@ t0:=x^7/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 759 +--E 759 ---S 760 of 1092 +--S 760 of 1092 r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ (a+b*x)^2)-a^6*(7*b*c-4*a*d)/(b^5*(b*c-a*d)^4*(a+b*x))-1/2*c^7/_ (d^5*(b*c-a*d)^3*(c+d*x)^2)+c^6*(4*b*c-7*a*d)/(d^5*(b*c-a*d)^4*(c+d*x))-_ @@ -15292,9 +15203,9 @@ r0:=-3*(b*c+a*d)*x/(b^4*d^4)+1/2*x^2/(b^3*d^3)+1/2*a^7/(b^5*(b*c-a*d)^3*_ --R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 760 +--E 760 ---S 761 of 1092 +--S 761 of 1092 a0:=integrate(t0,x) --R --R @@ -15421,27 +15332,27 @@ a0:=integrate(t0,x) --R 7 5 2 10 6 6 3 9 5 7 4 8 4 8 5 7 3 9 6 6 2 10 7 5 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 761 +--E 761 ---S 762 of 1092 +--S 762 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 762 +--E 762 ---S 763 of 1092 +--S 763 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 763 +--E 763 )clear all ---S 764 of 1092 +--S 764 of 1092 t0:=x^6/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15458,9 +15369,9 @@ t0:=x^6/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 764 +--E 764 ---S 765 of 1092 +--S 765 of 1092 r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ (b^4*(b*c-a*d)^4*(a+b*x))+1/2*c^6/(d^4*(b*c-a*d)^3*(c+d*x)^2)-_ 3*c^5*(b*c-2*a*d)/(d^4*(b*c-a*d)^4*(c+d*x))+3*a^4*(5*b^2*c^2-_ @@ -15576,9 +15487,9 @@ r0:=x/(b^3*d^3)-1/2*a^6/(b^4*(b*c-a*d)^3*(a+b*x)^2)+3*a^5*(2*b*c-a*d)/_ --R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 765 +--E 765 ---S 766 of 1092 +--S 766 of 1092 a0:=integrate(t0,x) --R --R @@ -15690,27 +15601,27 @@ a0:=integrate(t0,x) --R 7 4 2 9 6 5 3 8 5 6 4 7 4 7 5 6 3 8 6 5 2 9 7 4 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 766 +--E 766 ---S 767 of 1092 +--S 767 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 767 +--E 767 ---S 768 of 1092 +--S 768 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 768 +--E 768 )clear all ---S 769 of 1092 +--S 769 of 1092 t0:=x^5/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15727,9 +15638,9 @@ t0:=x^5/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 769 +--E 769 ---S 770 of 1092 +--S 770 of 1092 r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ (b^3*(b*c-a*d)^4*(a+b*x))-1/2*c^5/(d^3*(b*c-a*d)^3*(c+d*x)^2)+_ c^4*(2*b*c-5*a*d)/(d^3*(b*c-a*d)^4*(c+d*x))-a^3*(10*b^2*c^2-_ @@ -15828,9 +15739,9 @@ r0:=1/2*a^5/(b^3*(b*c-a*d)^3*(a+b*x)^2)-a^4*(5*b*c-2*a*d)/_ --R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 770 +--E 770 ---S 771 of 1092 +--S 771 of 1092 a0:=integrate(t0,x) --R --R @@ -15925,27 +15836,27 @@ a0:=integrate(t0,x) --R 7 3 2 8 6 4 3 7 5 5 4 6 4 6 5 5 3 7 6 4 2 8 7 3 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 771 +--E 771 ---S 772 of 1092 +--S 772 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 772 +--E 772 ---S 773 of 1092 +--S 773 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 773 +--E 773 )clear all ---S 774 of 1092 +--S 774 of 1092 t0:=x^4/((a+b*x)^3*(c+d*x)^3) --R --R @@ -15962,9 +15873,9 @@ t0:=x^4/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 774 +--E 774 ---S 775 of 1092 +--S 775 of 1092 r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ (a+b*x))+1/2*c^4/(d^2*(b*c-a*d)^3*(c+d*x)^2)-c^3*(b*c-4*a*d)/_ (d^2*(b*c-a*d)^4*(c+d*x))+6*a^2*c^2*log(a+b*x)/(b*c-a*d)^5-_ @@ -16032,9 +15943,9 @@ r0:=-1/2*a^4/(b^2*(b*c-a*d)^3*(a+b*x)^2)+a^3*(4*b*c-a*d)/(b^2*(b*c-a*d)^4*_ --R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 775 +--E 775 ---S 776 of 1092 +--S 776 of 1092 a0:=integrate(t0,x) --R --R @@ -16099,27 +16010,27 @@ a0:=integrate(t0,x) --R 7 2 2 7 6 3 3 6 5 4 4 5 4 5 5 4 3 6 6 3 2 7 7 2 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 776 +--E 776 ---S 777 of 1092 +--S 777 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 777 +--E 777 ---S 778 of 1092 +--S 778 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 778 +--E 778 )clear all ---S 779 of 1092 +--S 779 of 1092 t0:=x^3/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16136,9 +16047,9 @@ t0:=x^3/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 779 +--E 779 ---S 780 of 1092 +--S 780 of 1092 r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ 1/2*c^3/(d*(b*c-a*d)^3*(c+d*x)^2)-3*a*c^2/((b*c-a*d)^4*(c+d*x))-_ 3*a*c*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*a*c*(b*c+a*d)*log(c+d*x)/_ @@ -16209,9 +16120,9 @@ r0:=1/2*a^3/(b*(b*c-a*d)^3*(a+b*x)^2)-3*a^2*c/((b*c-a*d)^4*(a+b*x))-_ --R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Expression(Integer) ---E 780 +--E 780 ---S 781 of 1092 +--S 781 of 1092 a0:=integrate(t0,x) --R --R @@ -16279,27 +16190,27 @@ a0:=integrate(t0,x) --R 7 2 6 6 2 3 5 5 3 4 4 4 4 5 3 3 5 6 2 2 6 7 --R 2a b c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c d --R Type: Union(Expression(Integer),...) ---E 781 +--E 781 ---S 782 of 1092 +--S 782 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 782 +--E 782 ---S 783 of 1092 +--S 783 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 783 +--E 783 )clear all ---S 784 of 1092 +--S 784 of 1092 t0:=x^2/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16316,9 +16227,9 @@ t0:=x^2/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 784 +--E 784 ---S 785 of 1092 +--S 785 of 1092 r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ 1/2*c^2/((b*c-a*d)^3*(c+d*x)^2)+c*(b*c+2*a*d)/((b*c-a*d)^4*(c+d*x))+_ (b^2*c^2+4*a*b*c*d+a^2*d^2)*log(a+b*x)/(b*c-a*d)^5-(b^2*c^2+4*a*b*c*d+_ @@ -16390,9 +16301,9 @@ r0:=-1/2*a^2/((b*c-a*d)^3*(a+b*x)^2)+a*(2*b*c+a*d)/((b*c-a*d)^4*(a+b*x))+_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 785 +--E 785 ---S 786 of 1092 +--S 786 of 1092 a0:=integrate(t0,x) --R --R @@ -16461,27 +16372,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 786 +--E 786 ---S 787 of 1092 +--S 787 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 787 +--E 787 ---S 788 of 1092 +--S 788 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 788 +--E 788 )clear all ---S 789 of 1092 +--S 789 of 1092 t0:=x/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16497,9 +16408,9 @@ t0:=x/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 789 +--E 789 ---S 790 of 1092 +--S 790 of 1092 r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ 1/2*c*d/((b*c-a*d)^3*(c+d*x)^2)-d*(2*b*c+a*d)/((b*c-a*d)^4*(c+d*x))-_ 3*b*d*(b*c+a*d)*log(a+b*x)/(b*c-a*d)^5+3*b*d*(b*c+a*d)*_ @@ -16559,9 +16470,9 @@ r0:=1/2*a*b/((b*c-a*d)^3*(a+b*x)^2)-b*(b*c+2*a*d)/((b*c-a*d)^4*(a+b*x))-_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 790 +--E 790 ---S 791 of 1092 +--S 791 of 1092 a0:=integrate(t0,x) --R --R @@ -16618,27 +16529,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 791 +--E 791 ---S 792 of 1092 +--S 792 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 792 +--E 792 ---S 793 of 1092 +--S 793 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 793 +--E 793 )clear all ---S 794 of 1092 +--S 794 of 1092 t0:=1/((a+b*x)^3*(c+d*x)^3) --R --R @@ -16654,9 +16565,9 @@ t0:=1/((a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 --R (3a c d + 3a b c )x + a c --R Type: Fraction(Polynomial(Integer)) ---E 794 +--E 794 ---S 795 of 1092 +--S 795 of 1092 r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ 1/2*d^2/((b*c-a*d)^3*(c+d*x)^2)+3*b*d^2/((b*c-a*d)^4*(c+d*x))+_ 6*b^2*d^2*log(a+b*x)/(b*c-a*d)^5-6*b^2*d^2*log(c+d*x)/(b*c-a*d)^5 @@ -16715,9 +16626,9 @@ r0:=-1/2*b^2/((b*c-a*d)^3*(a+b*x)^2)+3*b^2*d/((b*c-a*d)^4*(a+b*x))+_ --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 795 +--E 795 ---S 796 of 1092 +--S 796 of 1092 a0:=integrate(t0,x) --R --R @@ -16774,27 +16685,27 @@ a0:=integrate(t0,x) --R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 796 +--E 796 ---S 797 of 1092 +--S 797 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 797 +--E 797 ---S 798 of 1092 +--S 798 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 798 +--E 798 )clear all ---S 799 of 1092 +--S 799 of 1092 t0:=1/(x*(a+b*x)^3*(c+d*x)^3) --R --R @@ -16810,9 +16721,9 @@ t0:=1/(x*(a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 2 3 3 --R (3a c d + 3a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 799 +--E 799 ---S 800 of 1092 +--S 800 of 1092 r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ (a+b*x))-1/2*d^3/(c*(b*c-a*d)^3*(c+d*x)^2)-d^3*(4*b*c-a*d)/_ (c^2*(b*c-a*d)^4*(c+d*x))+log(x)/(a^3*c^3)-b^3*(b^2*c^2-_ @@ -16946,9 +16857,9 @@ r0:=1/2*b^3/(a*(b*c-a*d)^3*(a+b*x)^2)+b^3*(b*c-4*a*d)/(a^2*(b*c-a*d)^4*_ --R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Expression(Integer) ---E 800 +--E 800 ---S 801 of 1092 +--S 801 of 1092 a0:=integrate(t0,x) --R --R @@ -17078,27 +16989,27 @@ a0:=integrate(t0,x) --R 10 5 5 9 6 4 8 2 7 3 7 3 8 2 6 4 9 5 5 10 --R 2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c --R Type: Union(Expression(Integer),...) ---E 801 +--E 801 ---S 802 of 1092 +--S 802 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 802 +--E 802 ---S 803 of 1092 +--S 803 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 803 +--E 803 )clear all ---S 804 of 1092 +--S 804 of 1092 t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) --R --R @@ -17114,9 +17025,9 @@ t0:=1/(x^2*(a+b*x)^3*(c+d*x)^3) --R 3 2 2 3 3 3 3 2 --R (3a c d + 3a b c )x + a c x --R Type: Fraction(Polynomial(Integer)) ---E 804 +--E 804 ---S 805 of 1092 +--S 805 of 1092 r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ (a^3*(b*c-a*d)^4*(a+b*x))+1/2*d^4/(c^2*(b*c-a*d)^3*_ (c+d*x)^2)+d^4*(5*b*c-2*a*d)/(c^3*(b*c-a*d)^4*(c+d*x))-_ @@ -17278,9 +17189,9 @@ r0:=(-1)/(a^3*c^3*x)-1/2*b^4/(a^2*(b*c-a*d)^3*(a+b*x)^2)-b^4*(2*b*c-5*a*d)/_ --R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 --R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x --R Type: Expression(Integer) ---E 805 +--E 805 ---S 806 of 1092 +--S 806 of 1092 a0:=integrate(t0,x) --R --R @@ -17437,27 +17348,27 @@ a0:=integrate(t0,x) --R 11 6 5 10 7 4 9 2 8 3 8 3 9 2 7 4 10 6 5 11 --R (2a c d - 10a b c d + 20a b c d - 20a b c d + 10a b c d - 2a b c )x --R Type: Union(Expression(Integer),...) ---E 806 +--E 806 ---S 807 of 1092 +--S 807 of 1092 m0:=a0-r0 --R --R --R (4) 0 --R Type: Expression(Integer) ---E 807 +--E 807 ---S 808 of 1092 +--S 808 of 1092 d0:=D(m0,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 808 +--E 808 )clear all ---S 809 of 1092 +--S 809 of 1092 t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) --R --R @@ -17467,9 +17378,9 @@ t0:=(a+b*x)^2/(x^2*sqrt(c+d*x)) --R 2 +-------+ --R x \|d x + c --R Type: Expression(Integer) ---E 809 +--E 809 ---S 810 of 1092 +--S 810 of 1092 r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ a^2*sqrt(c+d*x)/(c*x) --R @@ -17483,9 +17394,9 @@ r0:=-a*(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/c^(3/2)+2*b^2*sqrt(c+d*x)/d-_ --R +-+ --R c d x\|c --R Type: Expression(Integer) ---E 810 +--E 810 ---S 811 of 1092 +--S 811 of 1092 a0:=integrate(t0,x) --R --R @@ -17510,9 +17421,9 @@ a0:=integrate(t0,x) --R +---+ --R c d x\|- c --R Type: Union(List(Expression(Integer)),...) ---E 811 +--E 811 ---S 812 of 1092 +--S 812 of 1092 m0a:=a0.1-r0 --R --R @@ -17531,17 +17442,17 @@ m0a:=a0.1-r0 --R +-+ --R 2c\|c --R Type: Expression(Integer) ---E 812 +--E 812 ---S 813 of 1092 +--S 813 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 813 +--E 813 ---S 814 of 1092 +--S 814 of 1092 m0b:=a0.2-r0 --R --R @@ -17560,19 +17471,19 @@ m0b:=a0.2-r0 --R +---+ +-+ --R c\|- c \|c --R Type: Expression(Integer) ---E 814 +--E 814 ---S 815 of 1092 +--S 815 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 815 +--E 815 )clear all ---S 816 of 1092 +--S 816 of 1092 t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) --R --R @@ -17582,9 +17493,9 @@ t0:=(c+d*x)^(3/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 816 +--E 816 ---S 817 of 1092 +--S 817 of 1092 r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ sqrt(c)/a^3-(4*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ sqrt(b*c-a*d)/(a^3*sqrt(b))-2*(b*c-a*d)*sqrt(c+d*x)/(a^2*(a+b*x)) @@ -17609,9 +17520,9 @@ r0:=-(c+d*x)^(3/2)/(a*x*(a+b*x))+(4*b*c-3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))*_ --R 3 2 4 +-+ --R (a b x + a x)\|b --R Type: Expression(Integer) ---E 817 +--E 817 ---S 818 of 1092 +--S 818 of 1092 a0:=integrate(t0,x) --R --R @@ -17713,9 +17624,9 @@ a0:=integrate(t0,x) --R a b x + a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 818 +--E 818 ---S 819 of 1092 +--S 819 of 1092 m0a:=a0.1-r0 --R --R @@ -17752,17 +17663,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 2a \|b --R Type: Expression(Integer) ---E 819 +--E 819 ---S 820 of 1092 +--S 820 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 820 +--E 820 ---S 821 of 1092 +--S 821 of 1092 m0b:=a0.2-r0 --R --R @@ -17795,19 +17706,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R 2a \|b --R Type: Expression(Integer) ---E 821 +--E 821 ---S 822 of 1092 +--S 822 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 822 +--E 822 )clear all ---S 823 of 1092 +--S 823 of 1092 t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) --R --R @@ -17817,9 +17728,9 @@ t0:=(c+d*x)^(1/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 823 +--E 823 ---S 824 of 1092 +--S 824 of 1092 r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/(a^3*sqrt(b*c-a*d))-_ 2*b*sqrt(c+d*x)/(a^2*(a+b*x))-sqrt(c+d*x)/(a*x*(a+b*x)) @@ -17844,9 +17755,9 @@ r0:=(4*b*c-a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*sqrt(c))-(4*b*c-3*a*d)*_ --R 3 2 4 +-----------+ +-+ --R (a b x + a x)\|- a d + b c \|c --R Type: Expression(Integer) ---E 824 +--E 824 ---S 825 of 1092 +--S 825 of 1092 a0:=integrate(t0,x) --R --R @@ -17956,9 +17867,9 @@ a0:=integrate(t0,x) --R (a b x + a x)\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 825 +--E 825 ---S 826 of 1092 +--S 826 of 1092 m0a:=a0.1-r0 --R --R @@ -17995,17 +17906,17 @@ m0a:=a0.1-r0 --R 3 +-----------+ +-+ --R 2a \|- a d + b c \|c --R Type: Expression(Integer) ---E 826 +--E 826 ---S 827 of 1092 +--S 827 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 827 +--E 827 ---S 828 of 1092 +--S 828 of 1092 m0b:=a0.2-r0 --R --R @@ -18038,19 +17949,19 @@ m0b:=a0.2-r0 --R 3 +-----------+ +-+ --R 2a \|- a d + b c \|c --R Type: Expression(Integer) ---E 828 +--E 828 ---S 829 of 1092 +--S 829 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 829 +--E 829 )clear all ---S 830 of 1092 +--S 830 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) --R --R @@ -18059,9 +17970,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(1/2)) --R 2 4 3 2 2 +-------+ --R (b x + 2a b x + a x )\|d x + c --R Type: Expression(Integer) ---E 830 +--E 830 ---S 831 of 1092 +--S 831 of 1092 r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ (4*b*c-5*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*_ (b*c-a*d)^(3/2))-b*(2*b*c-a*d)*sqrt(c+d*x)/(a^2*c*(b*c-a*d)*(a+b*x))-_ @@ -18093,9 +18004,9 @@ r0:=(4*b*c+a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(3/2))-b^(3/2)*_ --R 4 3 2 2 2 5 4 2 +-----------+ +-+ --R ((a b c d - a b c )x + (a c d - a b c )x)\|- a d + b c \|c --R Type: Expression(Integer) ---E 831 +--E 831 ---S 832 of 1092 +--S 832 of 1092 a0:=integrate(t0,x) --R --R @@ -18211,9 +18122,9 @@ a0:=integrate(t0,x) --R ((a b c d - a b c )x + (a c d - a b c )x)\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 832 +--E 832 ---S 833 of 1092 +--S 833 of 1092 m0a:=a0.1-r0 --R --R @@ -18250,17 +18161,17 @@ m0a:=a0.1-r0 --R 4 3 2 +-----------+ +-+ --R (2a c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 833 +--E 833 ---S 834 of 1092 +--S 834 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 834 +--E 834 ---S 835 of 1092 +--S 835 of 1092 m0b:=a0.2-r0 --R --R @@ -18298,19 +18209,19 @@ m0b:=a0.2-r0 --R 4 3 2 +-----------+ +-+ --R (2a c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 835 +--E 835 ---S 836 of 1092 +--S 836 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 836 +--E 836 )clear all ---S 837 of 1092 +--S 837 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) --R --R @@ -18319,9 +18230,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(3/2)) --R 2 5 2 4 2 3 2 2 +-------+ --R (b d x + (2a b d + b c)x + (a d + 2a b c)x + a c x )\|d x + c --R Type: Expression(Integer) ---E 837 +--E 837 ---S 838 of 1092 +--S 838 of 1092 r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ (4*b*c-7*a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a^3*(b*c-a*d)^(5/2))-d*(2*b^2*c^2-2*a*b*c*d+3*a^2*d^2)/_ @@ -18366,9 +18277,9 @@ r0:=(4*b*c+3*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/(a^3*c^(5/2))-b^(5/2)*_ --R +-----------+ +-+ +-------+ --R \|- a d + b c \|c \|d x + c --R Type: Expression(Integer) ---E 838 +--E 838 ---S 839 of 1092 +--S 839 of 1092 a0:=integrate(t0,x) --R --R @@ -18550,9 +18461,9 @@ a0:=integrate(t0,x) --R \|- c \|d x + c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 839 +--E 839 ---S 840 of 1092 +--S 840 of 1092 m0a:=a0.1-r0 --R --R @@ -18592,17 +18503,17 @@ m0a:=a0.1-r0 --R 5 2 2 4 3 3 2 4 +-----------+ +-+ --R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 840 +--E 840 ---S 841 of 1092 +--S 841 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 841 +--E 841 ---S 842 of 1092 +--S 842 of 1092 m0b:=a0.2-r0 --R --R @@ -18643,19 +18554,19 @@ m0b:=a0.2-r0 --R 5 2 2 4 3 3 2 4 +-----------+ +-+ --R (2a c d - 4a b c d + 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 842 +--E 842 ---S 843 of 1092 +--S 843 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 843 +--E 843 )clear all ---S 844 of 1092 +--S 844 of 1092 t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) --R --R @@ -18671,9 +18582,9 @@ t0:=1/(x^2*(a+b*x)^2*(c+d*x)^(5/2)) --R +-------+ --R \|d x + c --R Type: Expression(Integer) ---E 844 +--E 844 ---S 845 of 1092 +--S 845 of 1092 r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ (c+d*x)^(3/2))-b*(2*b*c-a*d)/(a^2*c*(b*c-a*d)*(a+b*x)*(c+d*x)^(3/2))+_ (-1)/(a*c*x*(a+b*x)*(c+d*x)^(3/2))+(4*b*c+5*a*d)*atanh(sqrt(c+d*x)/_ @@ -18737,9 +18648,9 @@ r0:=-1/3*d*(6*b^2*c^2-6*a*b*c*d+5*a^2*d^2)/(a^2*c^2*(b*c-a*d)^2*_ --R +-----------+ +-+ +-------+ --R \|- a d + b c \|c \|d x + c --R Type: Expression(Integer) ---E 845 +--E 845 ---S 846 of 1092 +--S 846 of 1092 a0:=integrate(t0,x) --R --R @@ -19001,9 +18912,9 @@ a0:=integrate(t0,x) --R \|- c \|d x + c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 846 +--E 846 ---S 847 of 1092 +--S 847 of 1092 m0a:=a0.1-r0 --R --R @@ -19046,17 +18957,17 @@ m0a:=a0.1-r0 --R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ --R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 847 +--E 847 ---S 848 of 1092 +--S 848 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 848 +--E 848 ---S 849 of 1092 +--S 849 of 1092 m0b:=a0.2-r0 --R --R @@ -19100,19 +19011,19 @@ m0b:=a0.2-r0 --R 6 3 3 5 4 2 4 2 5 3 3 6 +-----------+ +-+ --R (2a c d - 6a b c d + 6a b c d - 2a b c )\|- a d + b c \|c --R Type: Expression(Integer) ---E 849 +--E 849 ---S 850 of 1092 +--S 850 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 850 +--E 850 )clear all ---S 851 of 1092 +--S 851 of 1092 t0:=x^3*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19121,9 +19032,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x) --R (1) --------------------------------- --R b x + a --R Type: Expression(Integer) ---E 851 +--E 851 ---S 852 of 1092 +--S 852 of 1092 r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ 495*a^2*b*c*d^2-693*a^3*d^3)*(c+d*x)^(5/2)/(b^4*d^3)-2/693*_ (20*b^2*c^2+55*a*b*c*d-99*a^2*d^2)*x*(c+d*x)^(5/2)/(b^3*d^2)+_ @@ -19166,9 +19077,9 @@ r0:=-2/3*a^3*(b*c-a*d)*(c+d*x)^(3/2)/b^5+2/3465*(40*b^3*c^3+110*a*b^2*c^2*d+_ --R 6 3 +-+ --R 3465b d \|b --R Type: Expression(Integer) ---E 852 +--E 852 ---S 853 of 1092 +--S 853 of 1092 a0:=integrate(t0,x) --R --R @@ -19244,9 +19155,9 @@ a0:=integrate(t0,x) --R 3465b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 853 +--E 853 ---S 854 of 1092 +--S 854 of 1092 m0a:=a0.1-r0 --R --R @@ -19272,17 +19183,17 @@ m0a:=a0.1-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 854 +--E 854 ---S 855 of 1092 +--S 855 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 855 +--E 855 ---S 856 of 1092 +--S 856 of 1092 m0b:=a0.2-r0 --R --R @@ -19304,19 +19215,19 @@ m0b:=a0.2-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 856 +--E 856 ---S 857 of 1092 +--S 857 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 857 +--E 857 )clear all ---S 858 of 1092 +--S 858 of 1092 t0:=x^2*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19325,9 +19236,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x) --R (1) --------------------------------- --R b x + a --R Type: Expression(Integer) ---E 858 +--E 858 ---S 859 of 1092 +--S 859 of 1092 r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ 2/63*(2*b*c+9*a*d)*(c+d*x)^(7/2)/(b^2*d^2)+2/9*x*(c+d*x)^(7/2)/(b*d)-_ 2*a^2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/_ @@ -19362,9 +19273,9 @@ r0:=2/3*a^2*(b*c-a*d)*(c+d*x)^(3/2)/b^4+2/5*a^2*(c+d*x)^(5/2)/b^3-_ --R 5 2 +-+ --R 315b d \|b --R Type: Expression(Integer) ---E 859 +--E 859 ---S 860 of 1092 +--S 860 of 1092 a0:=integrate(t0,x) --R --R @@ -19428,9 +19339,9 @@ a0:=integrate(t0,x) --R 315b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 860 +--E 860 ---S 861 of 1092 +--S 861 of 1092 m0a:=a0.1-r0 --R --R @@ -19456,17 +19367,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 861 +--E 861 ---S 862 of 1092 +--S 862 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 862 +--E 862 ---S 863 of 1092 +--S 863 of 1092 m0b:=a0.2-r0 --R --R @@ -19488,19 +19399,19 @@ m0b:=a0.2-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 863 +--E 863 ---S 864 of 1092 +--S 864 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 864 +--E 864 )clear all ---S 865 of 1092 +--S 865 of 1092 t0:=x*(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19509,9 +19420,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x) --R (1) -------------------------------- --R b x + a --R Type: Expression(Integer) ---E 865 +--E 865 ---S 866 of 1092 +--S 866 of 1092 r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ 2/7*(c+d*x)^(7/2)/(b*d)+2*a*(b*c-a*d)^(5/2)*atanh(sqrt(b)*_ sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)-2*a*(b*c-a*d)^2*sqrt(c+d*x)/b^4 @@ -19539,9 +19450,9 @@ r0:=-2/3*a*(b*c-a*d)*(c+d*x)^(3/2)/b^3-2/5*a*(c+d*x)^(5/2)/b^2+_ --R 4 +-+ --R 105b d\|b --R Type: Expression(Integer) ---E 866 +--E 866 ---S 867 of 1092 +--S 867 of 1092 a0:=integrate(t0,x) --R --R @@ -19599,9 +19510,9 @@ a0:=integrate(t0,x) --R 105b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 867 +--E 867 ---S 868 of 1092 +--S 868 of 1092 m0a:=a0.1-r0 --R --R @@ -19627,17 +19538,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 868 +--E 868 ---S 869 of 1092 +--S 869 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 869 +--E 869 ---S 870 of 1092 +--S 870 of 1092 m0b:=a0.2-r0 --R --R @@ -19659,19 +19570,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 870 +--E 870 ---S 871 of 1092 +--S 871 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 871 +--E 871 )clear all ---S 872 of 1092 +--S 872 of 1092 t0:=(c+d*x)^(5/2)/(a+b*x) --R --R @@ -19680,9 +19591,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x) --R (1) ------------------------------ --R b x + a --R Type: Expression(Integer) ---E 872 +--E 872 ---S 873 of 1092 +--S 873 of 1092 r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+2*(b*c-a*d)^2*_ sqrt(c+d*x)/b^3 @@ -19704,9 +19615,9 @@ r0:=2/3*(b*c-a*d)*(c+d*x)^(3/2)/b^2+2/5*(c+d*x)^(5/2)/b-2*(b*c-a*d)^(5/2)*_ --R 3 +-+ --R 15b \|b --R Type: Expression(Integer) ---E 873 +--E 873 ---S 874 of 1092 +--S 874 of 1092 a0:=integrate(t0,x) --R --R @@ -19752,9 +19663,9 @@ a0:=integrate(t0,x) --R 15b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 874 +--E 874 ---S 875 of 1092 +--S 875 of 1092 m0a:=a0.1-r0 --R --R @@ -19780,17 +19691,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 875 +--E 875 ---S 876 of 1092 +--S 876 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 876 +--E 876 ---S 877 of 1092 +--S 877 of 1092 m0b:=a0.2-r0 --R --R @@ -19812,19 +19723,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 877 +--E 877 ---S 878 of 1092 +--S 878 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 878 +--E 878 )clear all ---S 879 of 1092 +--S 879 of 1092 t0:=(c+d*x)^(5/2)/(x*(a+b*x)) --R --R @@ -19834,9 +19745,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x)) --R 2 --R b x + a x --R Type: Expression(Integer) ---E 879 +--E 879 ---S 880 of 1092 +--S 880 of 1092 r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a*b^(5/2))+2*d*(2*b*c-a*d)*sqrt(c+d*x)/b^2 @@ -19861,9 +19772,9 @@ r0:=2/3*d*(c+d*x)^(3/2)/b-2*c^(5/2)*atanh(sqrt(c+d*x)/sqrt(c))/a+_ --R 2 +-+ --R 3a b \|b --R Type: Expression(Integer) ---E 880 +--E 880 ---S 881 of 1092 +--S 881 of 1092 a0:=integrate(t0,x) --R --R @@ -19956,9 +19867,9 @@ a0:=integrate(t0,x) --R 3a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 881 +--E 881 ---S 882 of 1092 +--S 882 of 1092 m0a:=a0.1-r0 --R --R @@ -19995,17 +19906,17 @@ m0a:=a0.1-r0 --R 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 882 +--E 882 ---S 883 of 1092 +--S 883 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 883 +--E 883 ---S 884 of 1092 +--S 884 of 1092 m0b:=a0.2-r0 --R --R @@ -20038,19 +19949,19 @@ m0b:=a0.2-r0 --R 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 884 +--E 884 ---S 885 of 1092 +--S 885 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 885 +--E 885 )clear all ---S 886 of 1092 +--S 886 of 1092 t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) --R --R @@ -20060,9 +19971,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)) --R 3 2 --R b x + a x --R Type: Expression(Integer) ---E 886 +--E 886 ---S 887 of 1092 +--S 887 of 1092 r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ atanh(sqrt(c+d*x)/sqrt(c))/a^2-2*(b*c-a*d)^(5/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(3/2))+_ @@ -20088,9 +19999,9 @@ r0:=d*(c+d*x)^(3/2)/a-(c+d*x)^(5/2)/(a*x)+c^(3/2)*(2*b*c-5*a*d)*_ --R 2 +-+ --R a b x\|b --R Type: Expression(Integer) ---E 887 +--E 887 ---S 888 of 1092 +--S 888 of 1092 a0:=integrate(t0,x) --R --R @@ -20183,9 +20094,9 @@ a0:=integrate(t0,x) --R a b x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 888 +--E 888 ---S 889 of 1092 +--S 889 of 1092 m0a:=a0.1-r0 --R --R @@ -20222,17 +20133,17 @@ m0a:=a0.1-r0 --R 2 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 889 +--E 889 ---S 890 of 1092 +--S 890 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 890 +--E 890 ---S 891 of 1092 +--S 891 of 1092 m0b:=a0.2-r0 --R --R @@ -20265,19 +20176,19 @@ m0b:=a0.2-r0 --R 2 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 891 +--E 891 ---S 892 of 1092 +--S 892 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 892 +--E 892 )clear all ---S 893 of 1092 +--S 893 of 1092 t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) --R --R @@ -20287,9 +20198,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)) --R 4 3 --R b x + a x --R Type: Expression(Integer) ---E 893 +--E 893 ---S 894 of 1092 +--S 894 of 1092 r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/_ (a^3*sqrt(b))-1/4*(8*b^2*c^2-20*a*b*c*d+15*a^2*d^2)*_ @@ -20316,9 +20227,9 @@ r0:=1/4*(4*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x)-1/2*(c+d*x)^(5/2)/(a*x^2)+_ --R 3 2 +-+ --R 4a x \|b --R Type: Expression(Integer) ---E 894 +--E 894 ---S 895 of 1092 +--S 895 of 1092 a0:=integrate(t0,x) --R --R @@ -20414,9 +20325,9 @@ a0:=integrate(t0,x) --R 4a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 895 +--E 895 ---S 896 of 1092 +--S 896 of 1092 m0a:=a0.1-r0 --R --R @@ -20453,17 +20364,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 896 +--E 896 ---S 897 of 1092 +--S 897 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 897 +--E 897 ---S 898 of 1092 +--S 898 of 1092 m0b:=a0.2-r0 --R --R @@ -20496,19 +20407,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 898 +--E 898 ---S 899 of 1092 +--S 899 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 899 +--E 899 )clear all ---S 900 of 1092 +--S 900 of 1092 t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) --R --R @@ -20518,9 +20429,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)) --R 5 4 --R b x + a x --R Type: Expression(Integer) ---E 900 +--E 900 ---S 901 of 1092 +--S 901 of 1092 r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ 2*(b*c-a*d)^(5/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))*_ sqrt(b)/a^4+1/8*(16*b^3*c^3-40*a*b^2*c^2*d+30*a^2*b*c*d^2-5*a^3*d^3)*_ @@ -20553,9 +20464,9 @@ r0:=1/12*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2)-1/3*(c+d*x)^(5/2)/(a*x^3)-_ --R 4 3 +-+ --R 24a x \|c --R Type: Expression(Integer) ---E 901 +--E 901 ---S 902 of 1092 +--S 902 of 1092 a0:=integrate(t0,x) --R --R @@ -20681,9 +20592,9 @@ a0:=integrate(t0,x) --R 24a x \|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 902 +--E 902 ---S 903 of 1092 +--S 903 of 1092 m0a:=a0.1-r0 --R --R @@ -20721,17 +20632,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 903 +--E 903 ---S 904 of 1092 +--S 904 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 904 +--E 904 ---S 905 of 1092 +--S 905 of 1092 m0b:=a0.2-r0 --R --R @@ -20766,19 +20677,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 905 +--E 905 ---S 906 of 1092 +--S 906 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 906 +--E 906 )clear all ---S 907 of 1092 +--S 907 of 1092 t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -20788,9 +20699,9 @@ t0:=x^3*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 907 +--E 907 ---S 908 of 1092 +--S 908 of 1092 r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ 180*a*b*c*d-693*a^2*d^2)*(c+d*x)^(5/2)/(b^4*d^2)+_ 1/63*(10*b*c-99*a*d)*x*(c+d*x)^(5/2)/(b^3*d)+11/9*x^2*(c+d*x)^(5/2)/_ @@ -20833,9 +20744,9 @@ r0:=1/3*a^2*(6*b*c-11*a*d)*(c+d*x)^(3/2)/b^5-1/315*(20*b^2*c^2+_ --R 7 2 6 2 +-+ --R (315b d x + 315a b d )\|b --R Type: Expression(Integer) ---E 908 +--E 908 ---S 909 of 1092 +--S 909 of 1092 a0:=integrate(t0,x) --R --R @@ -20912,9 +20823,9 @@ a0:=integrate(t0,x) --R 315b d x + 315a b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 909 +--E 909 ---S 910 of 1092 +--S 910 of 1092 m0a:=a0.1-r0 --R --R @@ -20940,17 +20851,17 @@ m0a:=a0.1-r0 --R 6 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 910 +--E 910 ---S 911 of 1092 +--S 911 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 911 +--E 911 ---S 912 of 1092 +--S 912 of 1092 m0b:=a0.2-r0 --R --R @@ -20972,19 +20883,19 @@ m0b:=a0.2-r0 --R 6 +-+ --R b \|b --R Type: Expression(Integer) ---E 912 +--E 912 ---S 913 of 1092 +--S 913 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 913 +--E 913 )clear all ---S 914 of 1092 +--S 914 of 1092 t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -20994,9 +20905,9 @@ t0:=x^2*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 914 +--E 914 ---S 915 of 1092 +--S 915 of 1092 r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ (c+d*x)^(5/2)/(b^3*(b*c-a*d))+2/7*(c+d*x)^(7/2)/(b^2*d)-_ a^2*(c+d*x)^(7/2)/(b^2*(b*c-a*d)*(a+b*x))+a*(4*b*c-9*a*d)*_ @@ -21035,9 +20946,9 @@ r0:=-1/3*a*(4*b*c-9*a*d)*(c+d*x)^(3/2)/b^4-1/5*a*(4*b*c-9*a*d)*_ --R 6 5 +-+ --R (105b d x + 105a b d)\|b --R Type: Expression(Integer) ---E 915 +--E 915 ---S 916 of 1092 +--S 916 of 1092 a0:=integrate(t0,x) --R --R @@ -21108,9 +21019,9 @@ a0:=integrate(t0,x) --R 105b d x + 105a b d --R ] --R Type: Union(List(Expression(Integer)),...) ---E 916 +--E 916 ---S 917 of 1092 +--S 917 of 1092 m0a:=a0.1-r0 --R --R @@ -21136,17 +21047,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 917 +--E 917 ---S 918 of 1092 +--S 918 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 918 +--E 918 ---S 919 of 1092 +--S 919 of 1092 m0b:=a0.2-r0 --R --R @@ -21168,19 +21079,19 @@ m0b:=a0.2-r0 --R 5 +-+ --R b \|b --R Type: Expression(Integer) ---E 919 +--E 919 ---S 920 of 1092 +--S 920 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 920 +--E 920 )clear all ---S 921 of 1092 +--S 921 of 1092 t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -21190,9 +21101,9 @@ t0:=x*(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 921 +--E 921 ---S 922 of 1092 +--S 922 of 1092 r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ (b^2*(b*c-a*d))+a*(c+d*x)^(7/2)/(b*(b*c-a*d)*(a+b*x))-(2*b*c-7*a*d)*_ (b*c-a*d)^(3/2)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(9/2)+_ @@ -21224,9 +21135,9 @@ r0:=1/3*(2*b*c-7*a*d)*(c+d*x)^(3/2)/b^3+1/5*(2*b*c-7*a*d)*(c+d*x)^(5/2)/_ --R 5 4 +-+ --R (15b x + 15a b )\|b --R Type: Expression(Integer) ---E 922 +--E 922 ---S 923 of 1092 +--S 923 of 1092 a0:=integrate(t0,x) --R --R @@ -21285,9 +21196,9 @@ a0:=integrate(t0,x) --R 15b x + 15a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 923 +--E 923 ---S 924 of 1092 +--S 924 of 1092 m0a:=a0.1-r0 --R --R @@ -21313,17 +21224,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 924 +--E 924 ---S 925 of 1092 +--S 925 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 925 +--E 925 ---S 926 of 1092 +--S 926 of 1092 m0b:=a0.2-r0 --R --R @@ -21345,19 +21256,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R b \|b --R Type: Expression(Integer) ---E 926 +--E 926 ---S 927 of 1092 +--S 927 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 927 +--E 927 )clear all ---S 928 of 1092 +--S 928 of 1092 t0:=(c+d*x)^(5/2)/(a+b*x)^2 --R --R @@ -21367,9 +21278,9 @@ t0:=(c+d*x)^(5/2)/(a+b*x)^2 --R 2 2 2 --R b x + 2a b x + a --R Type: Expression(Integer) ---E 928 +--E 928 ---S 929 of 1092 +--S 929 of 1092 r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/b^(7/2)+5*d*(b*c-a*d)*_ sqrt(c+d*x)/b^3 @@ -21394,9 +21305,9 @@ r0:=5/3*d*(c+d*x)^(3/2)/b^2-(c+d*x)^(5/2)/(b*(a+b*x))-5*d*(b*c-a*d)^(3/2)*_ --R 4 3 +-+ --R (3b x + 3a b )\|b --R Type: Expression(Integer) ---E 929 +--E 929 ---S 930 of 1092 +--S 930 of 1092 a0:=integrate(t0,x) --R --R @@ -21447,9 +21358,9 @@ a0:=integrate(t0,x) --R 3b x + 3a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 930 +--E 930 ---S 931 of 1092 +--S 931 of 1092 m0a:=a0.1-r0 --R --R @@ -21475,17 +21386,17 @@ m0a:=a0.1-r0 --R 3 +-+ --R 2b \|b --R Type: Expression(Integer) ---E 931 +--E 931 ---S 932 of 1092 +--S 932 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 932 +--E 932 ---S 933 of 1092 +--S 933 of 1092 m0b:=a0.2-r0 --R --R @@ -21507,19 +21418,19 @@ m0b:=a0.2-r0 --R 3 +-+ --R b \|b --R Type: Expression(Integer) ---E 933 +--E 933 ---S 934 of 1092 +--S 934 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 934 +--E 934 )clear all ---S 935 of 1092 +--S 935 of 1092 t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) --R --R @@ -21529,9 +21440,9 @@ t0:=(c+d*x)^(5/2)/(x*(a+b*x)^2) --R 2 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 935 +--E 935 ---S 936 of 1092 +--S 936 of 1092 r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ atanh(sqrt(c+d*x)/sqrt(c))/a^2+(b*c-a*d)^(3/2)*(2*b*c+3*a*d)*_ atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^2*b^(5/2))-_ @@ -21560,9 +21471,9 @@ r0:=-d*(c+d*x)^(3/2)/(a*b)+(c+d*x)^(5/2)/(a*(a+b*x))-2*c^(5/2)*_ --R 2 3 3 2 +-+ --R (a b x + a b )\|b --R Type: Expression(Integer) ---E 936 +--E 936 ---S 937 of 1092 +--S 937 of 1092 a0:=integrate(t0,x) --R --R @@ -21660,9 +21571,9 @@ a0:=integrate(t0,x) --R a b x + a b --R ] --R Type: Union(List(Expression(Integer)),...) ---E 937 +--E 937 ---S 938 of 1092 +--S 938 of 1092 m0a:=a0.1-r0 --R --R @@ -21699,17 +21610,17 @@ m0a:=a0.1-r0 --R 2 2 +-+ --R 2a b \|b --R Type: Expression(Integer) ---E 938 +--E 938 ---S 939 of 1092 +--S 939 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 939 +--E 939 ---S 940 of 1092 +--S 940 of 1092 m0b:=a0.2-r0 --R --R @@ -21742,19 +21653,19 @@ m0b:=a0.2-r0 --R 2 2 +-+ --R a b \|b --R Type: Expression(Integer) ---E 940 +--E 940 ---S 941 of 1092 +--S 941 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 941 +--E 941 )clear all ---S 942 of 1092 +--S 942 of 1092 t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) --R --R @@ -21764,9 +21675,9 @@ t0:=(c+d*x)^(5/2)/(x^2*(a+b*x)^2) --R 2 4 3 2 2 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 942 +--E 942 ---S 943 of 1092 +--S 943 of 1092 r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))-_ c^2*sqrt(c+d*x)/(a^2*x)-(b*c-a*d)^2*sqrt(c+d*x)/(a^2*b*(a+b*x)) @@ -21797,9 +21708,9 @@ r0a:=c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ --R 3 2 2 4 +-+ --R (a b x + a b x)\|b --R Type: Expression(Integer) ---E 943 +--E 943 ---S 944 of 1092 +--S 944 of 1092 r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ c^(3/2)*(4*b*c-5*a*d)*atanh(sqrt(c+d*x)/sqrt(c))/a^3-(b*c-a*d)^(3/2)*_ (4*b*c+a*d)*atanh(sqrt(b)*sqrt(c+d*x)/sqrt(b*c-a*d))/(a^3*b^(3/2))+_ @@ -21831,9 +21742,9 @@ r0b:=-2*(b*c-a*d)*(c+d*x)^(3/2)/(a^2*(a+b*x))-(c+d*x)^(5/2)/(a*x*(a+b*x))+_ --R 3 2 2 4 +-+ --R (a b x + a b x)\|b --R Type: Expression(Integer) ---E 944 +--E 944 ---S 945 of 1092 +--S 945 of 1092 a0:=integrate(t0,x) --R --R @@ -21943,9 +21854,9 @@ a0:=integrate(t0,x) --R a b x + a b x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 945 +--E 945 ---S 946 of 1092 +--S 946 of 1092 m0a:=a0.1-r0a --R --R @@ -21982,17 +21893,17 @@ m0a:=a0.1-r0a --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 946 +--E 946 ---S 947 of 1092 +--S 947 of 1092 d0a:=D(m0a,x) --R --R --R (6) 0 --R Type: Expression(Integer) ---E 947 +--E 947 ---S 948 of 1092 +--S 948 of 1092 m0b:=a0.1-r0b --R --R @@ -22029,17 +21940,17 @@ m0b:=a0.1-r0b --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 948 +--E 948 ---S 949 of 1092 +--S 949 of 1092 d0b:=D(m0b,x) --R --R --R (8) 0 --R Type: Expression(Integer) ---E 949 +--E 949 ---S 950 of 1092 +--S 950 of 1092 m0c:=a0.2-r0a --R --R @@ -22072,17 +21983,17 @@ m0c:=a0.2-r0a --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 950 +--E 950 ---S 951 of 1092 +--S 951 of 1092 d0c:=D(m0c,x) --R --R --R (10) 0 --R Type: Expression(Integer) ---E 951 +--E 951 ---S 952 of 1092 +--S 952 of 1092 m0d:=a0.2-r0b --R --R @@ -22115,19 +22026,19 @@ m0d:=a0.2-r0b --R 3 +-+ --R 2a b\|b --R Type: Expression(Integer) ---E 952 +--E 952 ---S 953 of 1092 +--S 953 of 1092 d0d:=D(m0d,x) --R --R --R (12) 0 --R Type: Expression(Integer) ---E 953 +--E 953 )clear all ---S 954 of 1092 +--S 954 of 1092 t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) --R --R @@ -22137,9 +22048,9 @@ t0:=(c+d*x)^(5/2)/(x^3*(a+b*x)^2) --R 2 5 4 2 3 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 954 +--E 954 ---S 955 of 1092 +--S 955 of 1092 r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ (a*x^2*(a+b*x))+(b*c-a*d)^(3/2)*(6*b*c-a*d)*atanh(sqrt(b)*sqrt(c+d*x)/_ sqrt(b*c-a*d))/(a^4*sqrt(b))-1/4*(24*b^2*c^2-40*a*b*c*d+15*a^2*d^2)*_ @@ -22178,9 +22089,9 @@ r0:=1/4*(6*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x*(a+b*x))-1/2*(c+d*x)^(5/2)/_ --R 4 3 5 2 +-+ --R (4a b x + 4a x )\|b --R Type: Expression(Integer) ---E 955 +--E 955 ---S 956 of 1092 +--S 956 of 1092 a0:=integrate(t0,x) --R --R @@ -22314,9 +22225,9 @@ a0:=integrate(t0,x) --R 4a b x + 4a x --R ] --R Type: Union(List(Expression(Integer)),...) ---E 956 +--E 956 ---S 957 of 1092 +--S 957 of 1092 m0a:=a0.1-r0 --R --R @@ -22353,17 +22264,17 @@ m0a:=a0.1-r0 --R 4 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 957 +--E 957 ---S 958 of 1092 +--S 958 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 958 +--E 958 ---S 959 of 1092 +--S 959 of 1092 m0b:=a0.2-r0 --R --R @@ -22396,19 +22307,19 @@ m0b:=a0.2-r0 --R 4 +-+ --R 8a \|b --R Type: Expression(Integer) ---E 959 +--E 959 ---S 960 of 1092 +--S 960 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 960 +--E 960 )clear all ---S 961 of 1092 +--S 961 of 1092 t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) --R --R @@ -22418,9 +22329,9 @@ t0:=(c+d*x)^(5/2)/(x^4*(a+b*x)^2) --R 2 6 5 2 4 --R b x + 2a b x + a x --R Type: Expression(Integer) ---E 961 +--E 961 ---S 962 of 1092 +--S 962 of 1092 r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ (a*x^3*(a+b*x))-(8*b*c-3*a*d)*(b*c-a*d)^(3/2)*atanh(sqrt(b)*_ sqrt(c+d*x)/sqrt(b*c-a*d))*sqrt(b)/a^5+1/8*(64*b^3*c^3-_ @@ -22467,9 +22378,9 @@ r0:=1/12*(8*b*c-5*a*d)*(c+d*x)^(3/2)/(a^2*x^2*(a+b*x))-1/3*(c+d*x)^(5/2)/_ --R 5 4 6 3 +-+ --R (24a b x + 24a x )\|c --R Type: Expression(Integer) ---E 962 +--E 962 ---S 963 of 1092 +--S 963 of 1092 a0:=integrate(t0,x) --R --R @@ -22635,9 +22546,9 @@ a0:=integrate(t0,x) --R (24a b x + 24a x )\|- c --R ] --R Type: Union(List(Expression(Integer)),...) ---E 963 +--E 963 ---S 964 of 1092 +--S 964 of 1092 m0a:=a0.1-r0 --R --R @@ -22678,17 +22589,17 @@ m0a:=a0.1-r0 --R 5 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 964 +--E 964 ---S 965 of 1092 +--S 965 of 1092 d0a:=D(m0a,x) --R --R --R (5) 0 --R Type: Expression(Integer) ---E 965 +--E 965 ---S 966 of 1092 +--S 966 of 1092 m0b:=a0.2-r0 --R --R @@ -22726,28 +22637,28 @@ m0b:=a0.2-r0 --R 5 +-+ --R 16a \|c --R Type: Expression(Integer) ---E 966 +--E 966 ---S 967 of 1092 +--S 967 of 1092 d0b:=D(m0b,x) --R --R --R (7) 0 --R Type: Expression(Integer) ---E 967 +--E 967 )clear all ---S 968 of 1092 +--S 968 of 1092 t0:=x^3*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R 3 +-------+ +-------+ --R (1) x \|b x + a \|d x + c --R Type: Expression(Integer) ---E 968 +--E 968 ---S 969 of 1092 +--S 969 of 1092 r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(9/2)*d^(9/2))-_ 1/960*(105*b^3*c^3-5*a*b^2*c^2*d-17*a^2*b*c*d^2-35*a^3*d^3)*_ @@ -22786,32 +22697,32 @@ r0:=1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ --R 4 4 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 969 +--E 969 ---S 970 of 1092 +--S 970 of 1092 --a0:=integrate(t0,x) ---E 970 +--E 970 ---S 971 of 1092 +--S 971 of 1092 --m0:=a0-r0 ---E 971 +--E 971 ---S 972 of 1092 +--S 972 of 1092 --d0:=D(m0,x) ---E 972 +--E 972 )clear all ---S 973 of 1092 +--S 973 of 1092 t0:=x^2*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R 2 +-------+ +-------+ --R (1) x \|b x + a \|d x + c --R Type: Expression(Integer) ---E 973 +--E 973 ---S 974 of 1092 +--S 974 of 1092 r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ (a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/64*(b*c-a*d)^2*_ (4*a*b*c*d-5*(b*c+a*d)^2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*_ @@ -22845,32 +22756,32 @@ r0:=-5/24*(b*c+a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d^2)+1/4*x*_ --R 3 3 +-+ +-+ --R 192b d \|b \|d --R Type: Expression(Integer) ---E 974 +--E 974 ---S 975 of 1092 +--S 975 of 1092 --a0:=integrate(t0,x) ---E 975 +--E 975 ---S 976 of 1092 +--S 976 of 1092 --m0:=a0-r0 ---E 976 +--E 976 ---S 977 of 1092 +--S 977 of 1092 --d0:=D(m0,x) ---E 977 +--E 977 )clear all ---S 978 of 1092 +--S 978 of 1092 t0:=x*sqrt(a+b*x)*sqrt(c+d*x) --R --R --R +-------+ +-------+ --R (1) x\|b x + a \|d x + c --R Type: Expression(Integer) ---E 978 +--E 978 ---S 979 of 1092 +--S 979 of 1092 r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(5/2))-_ 1/4*(b*c+a*d)*(a+b*x)^(3/2)*sqrt(c+d*x)/(b^2*d)+1/8*_ @@ -22893,32 +22804,32 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b*d)+1/8*(b*c-a*d)^2*(b*c+a*d)*_ --R 2 2 +-+ +-+ --R 24b d \|b \|d --R Type: Expression(Integer) ---E 979 +--E 979 ---S 980 of 1092 +--S 980 of 1092 --a0:=integrate(t0,x) ---E 980 +--E 980 ---S 981 of 1092 +--S 981 of 1092 --m0:=a0-r0 ---E 981 +--E 981 ---S 982 of 1092 +--S 982 of 1092 --d0:=D(m0,x) ---E 982 +--E 982 )clear all ---S 983 of 1092 +--S 983 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x) --R --R --R +-------+ +-------+ --R (1) \|b x + a \|d x + c --R Type: Expression(Integer) ---E 983 +--E 983 ---S 984 of 1092 +--S 984 of 1092 r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ (b^(3/2)*d^(3/2))+1/2*(a+b*x)^(3/2)*sqrt(c+d*x)/b+1/4*(b*c-a*d)*_ sqrt(a+b*x)*sqrt(c+d*x)/(b*d) @@ -22937,23 +22848,23 @@ r0:=-1/4*(b*c-a*d)^2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ --R +-+ +-+ --R 4b d\|b \|d --R Type: Expression(Integer) ---E 984 +--E 984 ---S 985 of 1092 +--S 985 of 1092 --a0:=integrate(t0,x) ---E 985 +--E 985 ---S 986 of 1092 +--S 986 of 1092 --m0:=a0-r0 ---E 986 +--E 986 ---S 987 of 1092 +--S 987 of 1092 --d0:=D(m0,x) ---E 987 +--E 987 )clear all ---S 988 of 1092 +--S 988 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x --R --R @@ -22962,9 +22873,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x --R (1) -------------------- --R x --R Type: Expression(Integer) ---E 988 +--E 988 ---S 989 of 1092 +--S 989 of 1092 r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ (b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ (sqrt(b)*sqrt(d))+sqrt(a+b*x)*sqrt(c+d*x) @@ -22983,23 +22894,23 @@ r0:=-2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)*sqrt(c)+_ --R +-+ +-+ --R \|b \|d --R Type: Expression(Integer) ---E 989 +--E 989 ---S 990 of 1092 (non-algebraic residues) +--S 990 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 990 +--E 990 ---S 991 of 1092 +--S 991 of 1092 --m0:=a0-r0 ---E 991 +--E 991 ---S 992 of 1092 +--S 992 of 1092 --d0:=D(m0,x) ---E 992 +--E 992 )clear all ---S 993 of 1092 +--S 993 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 --R --R @@ -23009,9 +22920,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 993 +--E 993 ---S 994 of 1092 +--S 994 of 1092 r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (sqrt(a)*sqrt(c))+2*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*_ sqrt(b)*sqrt(d)-sqrt(a+b*x)*sqrt(c+d*x)/x @@ -23033,23 +22944,23 @@ r0:=-(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R +-+ +-+ --R x\|a \|c --R Type: Expression(Integer) ---E 994 +--E 994 ---S 995 of 1092 +--S 995 of 1092 --a0:=integrate(t0,x) ---E 995 +--E 995 ---S 996 of 1092 +--S 996 of 1092 --m0:=a0-r0 ---E 996 +--E 996 ---S 997 of 1092 +--S 997 of 1092 --d0:=D(m0,x) ---E 997 +--E 997 )clear all ---S 998 of 1092 +--S 998 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 --R --R @@ -23059,9 +22970,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 998 +--E 998 ---S 999 of 1092 +--S 999 of 1092 r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (a^(3/2)*c^(3/2))-1/2*(c+d*x)^(3/2)*sqrt(a+b*x)/(c*x^2)-_ 1/4*(b*c-a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x) @@ -23080,23 +22991,23 @@ r0:=1/4*(b*c-a*d)^2*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R 2 +-+ +-+ --R 4a c x \|a \|c --R Type: Expression(Integer) ---E 999 +--E 999 ---S 1000 of 1092 +--S 1000 of 1092 --a0:=integrate(t0,x) ---E 1000 +--E 1000 ---S 1001 of 1092 +--S 1001 of 1092 --m0:=a0-r0 ---E 1001 +--E 1001 ---S 1002 of 1092 +--S 1002 of 1092 --d0:=D(m0,x) ---E 1002 +--E 1002 )clear all ---S 1003 of 1092 +--S 1003 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 --R --R @@ -23106,9 +23017,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^4 --R 4 --R x --R Type: Expression(Integer) ---E 1003 +--E 1003 ---S 1004 of 1092 +--S 1004 of 1092 r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ sqrt(c+d*x)))/(a^(5/2)*c^(5/2))-1/3*sqrt(a+b*x)*sqrt(c+d*x)/x^3-_ 1/12*(b*c+a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*c*x^2)+_ @@ -23131,23 +23042,23 @@ r0:=-1/8*(b*c-a*d)^2*(b*c+a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ --R 2 2 3 +-+ +-+ --R 24a c x \|a \|c --R Type: Expression(Integer) ---E 1004 +--E 1004 ---S 1005 of 1092 +--S 1005 of 1092 --a0:=integrate(t0,x) ---E 1005 +--E 1005 ---S 1006 of 1092 +--S 1006 of 1092 --m0:=a0-r0 ---E 1006 +--E 1006 ---S 1007 of 1092 +--S 1007 of 1092 --d0:=D(m0,x) ---E 1007 +--E 1007 )clear all ---S 1008 of 1092 +--S 1008 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 --R --R @@ -23157,9 +23068,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^5 --R 5 --R x --R Type: Expression(Integer) ---E 1008 +--E 1008 ---S 1009 of 1092 +--S 1009 of 1092 r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(7/2)*c^(7/2))-_ 1/4*sqrt(a+b*x)*sqrt(c+d*x)/x^4-1/24*(b*c+a*d)*sqrt(a+b*x)*_ @@ -23190,23 +23101,23 @@ r0:=1/64*(b*c-a*d)^2*(5*b^2*c^2+6*a*b*c*d+5*a^2*d^2)*atanh(sqrt(c)*_ --R 3 3 4 +-+ +-+ --R 192a c x \|a \|c --R Type: Expression(Integer) ---E 1009 +--E 1009 ---S 1010 of 1092 +--S 1010 of 1092 --a0:=integrate(t0,x) ---E 1010 +--E 1010 ---S 1011 of 1092 +--S 1011 of 1092 --m0:=a0-r0 ---E 1011 +--E 1011 ---S 1012 of 1092 +--S 1012 of 1092 --d0:=D(m0,x) ---E 1012 +--E 1012 )clear all ---S 1013 of 1092 +--S 1013 of 1092 t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 --R --R @@ -23216,9 +23127,9 @@ t0:=sqrt(a+b*x)*sqrt(c+d*x)/x^6 --R 6 --R x --R Type: Expression(Integer) ---E 1013 +--E 1013 ---S 1014 of 1092 +--S 1014 of 1092 r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(9/2))-_ 1/5*sqrt(a+b*x)*sqrt(c+d*x)/x^5-1/40*(b*c+a*d)*sqrt(a+b*x)*_ @@ -23258,32 +23169,32 @@ r0:=-1/128*(b*c-a*d)^2*(b*c+a*d)*(7*b^2*c^2+2*a*b*c*d+7*a^2*d^2)*_ --R 4 4 5 +-+ +-+ --R 1920a c x \|a \|c --R Type: Expression(Integer) ---E 1014 +--E 1014 ---S 1015 of 1092 +--S 1015 of 1092 --a0:=integrate(t0,x) ---E 1015 +--E 1015 ---S 1016 of 1092 +--S 1016 of 1092 --m0:=a0-r0 ---E 1016 +--E 1016 ---S 1017 of 1092 +--S 1017 of 1092 --d0:=D(m0,x) ---E 1017 +--E 1017 )clear all ---S 1018 of 1092 +--S 1018 of 1092 t0:=x^2*(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R 3 2 +-------+ +-------+ --R (1) (d x + c x )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1018 +--E 1018 ---S 1019 of 1092 +--S 1019 of 1092 r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ (b^3*d^2)-1/40*(5*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d^2)+_ 1/5*x*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)-1/128*(b*c-a*d)^3*_ @@ -23322,32 +23233,32 @@ r0:=1/48*(3*b^2*c^2+6*a*b*c*d+7*a^2*d^2)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/_ --R 4 3 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 1019 +--E 1019 ---S 1020 of 1092 +--S 1020 of 1092 --a0:=integrate(t0,x) ---E 1020 +--E 1020 ---S 1021 of 1092 +--S 1021 of 1092 --m0:=a0-r0 ---E 1021 +--E 1021 ---S 1022 of 1092 +--S 1022 of 1092 --d0:=D(m0,x) ---E 1022 +--E 1022 )clear all ---S 1023 of 1092 +--S 1023 of 1092 t0:=x*(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R 2 +-------+ +-------+ --R (1) (d x + c x)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1023 +--E 1023 ---S 1024 of 1092 +--S 1024 of 1092 r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b*d)+1/64*(b*c-a*d)^3*(3*b*c+5*a*d)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(5/2))-_ @@ -23380,32 +23291,32 @@ r0:=-1/24*(3*b*c+5*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^2*d)+1/4*_ --R 3 2 +-+ +-+ --R 192b d \|b \|d --R Type: Expression(Integer) ---E 1024 +--E 1024 ---S 1025 of 1092 +--S 1025 of 1092 --a0:=integrate(t0,x) ---E 1025 +--E 1025 ---S 1026 of 1092 +--S 1026 of 1092 --m0:=a0-r0 ---E 1026 +--E 1026 ---S 1027 of 1092 +--S 1027 of 1092 --d0:=D(m0,x) ---E 1027 +--E 1027 )clear all ---S 1028 of 1092 +--S 1028 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x) --R --R --R +-------+ +-------+ --R (1) (d x + c)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1028 +--E 1028 ---S 1029 of 1092 +--S 1029 of 1092 r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*d^(3/2))+1/4*(b*c-a*d)*_ (a+b*x)^(3/2)*sqrt(c+d*x)/b^2+1/8*(b*c-a*d)^2*sqrt(a+b*x)*_ @@ -23428,23 +23339,23 @@ r0:=1/3*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b-1/8*(b*c-a*d)^3*atanh(sqrt(d)*_ --R 2 +-+ +-+ --R 24b d\|b \|d --R Type: Expression(Integer) ---E 1029 +--E 1029 ---S 1030 of 1092 +--S 1030 of 1092 --a0:=integrate(t0,x) ---E 1030 +--E 1030 ---S 1031 of 1092 +--S 1031 of 1092 --m0:=a0-r0 ---E 1031 +--E 1031 ---S 1032 of 1092 +--S 1032 of 1092 --d0:=D(m0,x) ---E 1032 +--E 1032 )clear all ---S 1033 of 1092 +--S 1033 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x --R --R @@ -23453,9 +23364,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x --R (1) ----------------------------- --R x --R Type: Expression(Integer) ---E 1033 +--E 1033 ---S 1034 of 1092 +--S 1034 of 1092 r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ sqrt(a)+1/4*(3*b^2*c^2+6*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(3/2)*sqrt(d))+_ @@ -23481,23 +23392,23 @@ r0:=-2*c^(3/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ --R +-+ +-+ --R 4b\|b \|d --R Type: Expression(Integer) ---E 1034 +--E 1034 ---S 1035 of 1092 (non-algebraic residues) +--S 1035 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1035 +--E 1035 ---S 1036 of 1092 +--S 1036 of 1092 --m0:=a0-r0 ---E 1036 +--E 1036 ---S 1037 of 1092 +--S 1037 of 1092 --d0:=D(m0,x) ---E 1037 +--E 1037 )clear all ---S 1038 of 1092 +--S 1038 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 --R --R @@ -23507,9 +23418,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 1038 +--E 1038 ---S 1039 of 1092 +--S 1039 of 1092 r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ sqrt(c)/sqrt(a)+(3*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/_ (sqrt(b)*sqrt(c+d*x)))*sqrt(d)/sqrt(b)-(c+d*x)^(3/2)*_ @@ -23535,23 +23446,23 @@ r0:=-(b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*_ --R +-+ +-+ --R x\|a \|b --R Type: Expression(Integer) ---E 1039 +--E 1039 ---S 1040 of 1092 (non-algebraic residues) +--S 1040 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1040 +--E 1040 ---S 1041 of 1092 +--S 1041 of 1092 --m0:=a0-r0 ---E 1041 +--E 1041 ---S 1042 of 1092 +--S 1042 of 1092 --d0:=D(m0,x) ---E 1042 +--E 1042 )clear all ---S 1043 of 1092 +--S 1043 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 --R --R @@ -23561,9 +23472,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 1043 +--E 1043 ---S 1044 of 1092 +--S 1044 of 1092 r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ 1/4*(b^2*c^2-6*a*b*c*d-3*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(3/2)*sqrt(c))-_ @@ -23590,23 +23501,23 @@ r0:=2*d^(3/2)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(b)+_ --R 2 +-+ +-+ --R 4a x \|a \|c --R Type: Expression(Integer) ---E 1044 +--E 1044 ---S 1045 of 1092 (non-algebraic residues) +--S 1045 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1045 +--E 1045 ---S 1046 of 1092 +--S 1046 of 1092 --m0:=a0-r0 ---E 1046 +--E 1046 ---S 1047 of 1092 +--S 1047 of 1092 --d0:=D(m0,x) ---E 1047 +--E 1047 )clear all ---S 1048 of 1092 +--S 1048 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 --R --R @@ -23616,9 +23527,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^4 --R 4 --R x --R Type: Expression(Integer) ---E 1048 +--E 1048 ---S 1049 of 1092 +--S 1049 of 1092 r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ (a^(5/2)*c^(3/2))-1/12*(b*c-a*d)*(c+d*x)^(3/2)*sqrt(a+b*x)/(a*c*x^2)-_ 1/3*(c+d*x)^(5/2)*sqrt(a+b*x)/(c*x^3)+1/8*(b*c-a*d)^2*_ @@ -23641,23 +23552,23 @@ r0:=-1/8*(b*c-a*d)^3*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R 2 3 +-+ +-+ --R 24a c x \|a \|c --R Type: Expression(Integer) ---E 1049 +--E 1049 ---S 1050 of 1092 +--S 1050 of 1092 --a0:=integrate(t0,x) ---E 1050 +--E 1050 ---S 1051 of 1092 +--S 1051 of 1092 --m0:=a0-r0 ---E 1051 +--E 1051 ---S 1052 of 1092 +--S 1052 of 1092 --d0:=D(m0,x) ---E 1052 +--E 1052 )clear all ---S 1053 of 1092 +--S 1053 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 --R --R @@ -23667,9 +23578,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^5 --R 5 --R x --R Type: Expression(Integer) ---E 1053 +--E 1053 ---S 1054 of 1092 +--S 1054 of 1092 r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ sqrt(c+d*x)))/(a^(7/2)*c^(5/2))-1/4*(c+d*x)^(3/2)*_ sqrt(a+b*x)/x^4-1/24*(b*c+3*a*d)*sqrt(a+b*x)*sqrt(c+d*x)/(a*x^3)+_ @@ -23700,23 +23611,23 @@ r0:=1/64*(b*c-a*d)^3*(5*b*c+3*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*_ --R 3 2 4 +-+ +-+ --R 192a c x \|a \|c --R Type: Expression(Integer) ---E 1054 +--E 1054 ---S 1055 of 1092 +--S 1055 of 1092 --a0:=integrate(t0,x) ---E 1055 +--E 1055 ---S 1056 of 1092 +--S 1056 of 1092 --m0:=a0-r0 ---E 1056 +--E 1056 ---S 1057 of 1092 +--S 1057 of 1092 --d0:=D(m0,x) ---E 1057 +--E 1057 )clear all ---S 1058 of 1092 +--S 1058 of 1092 t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 --R --R @@ -23726,9 +23637,9 @@ t0:=(c+d*x)^(3/2)*sqrt(a+b*x)/x^6 --R 6 --R x --R Type: Expression(Integer) ---E 1058 +--E 1058 ---S 1059 of 1092 +--S 1059 of 1092 r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/(a^(9/2)*c^(7/2))-_ 1/5*(c+d*x)^(3/2)*sqrt(a+b*x)/x^5-1/40*(b*c+3*a*d)*_ @@ -23768,32 +23679,32 @@ r0:=-1/128*(b*c-a*d)^3*(7*b^2*c^2+6*a*b*c*d+3*a^2*d^2)*atanh(sqrt(c)*_ --R 4 3 5 +-+ +-+ --R 1920a c x \|a \|c --R Type: Expression(Integer) ---E 1059 +--E 1059 ---S 1060 of 1092 +--S 1060 of 1092 --a0:=integrate(t0,x) ---E 1060 +--E 1060 ---S 1061 of 1092 +--S 1061 of 1092 --m0:=a0-r0 ---E 1061 +--E 1061 ---S 1062 of 1092 +--S 1062 of 1092 --d0:=D(m0,x) ---E 1062 +--E 1062 )clear all ---S 1063 of 1092 +--S 1063 of 1092 t0:=x^2*(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 4 3 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c x )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1063 +--E 1063 ---S 1064 of 1092 +--S 1064 of 1092 r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ (c+d*x)^(3/2)/(b^4*d^2)+1/160*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*_ (a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^3*d^2)-1/60*(5*b*c+9*a*d)*_ @@ -23840,32 +23751,32 @@ r0:=1/192*(b*c-a*d)*(5*b^2*c^2+14*a*b*c*d+21*a^2*d^2)*(a+b*x)^(3/2)*_ --R 5 3 +-+ +-+ --R 7680b d \|b \|d --R Type: Expression(Integer) ---E 1064 +--E 1064 ---S 1065 of 1092 +--S 1065 of 1092 --a0:=integrate(t0,x) ---E 1065 +--E 1065 ---S 1066 of 1092 +--S 1066 of 1092 --m0:=a0-r0 ---E 1066 +--E 1066 ---S 1067 of 1092 +--S 1067 of 1092 --d0:=D(m0,x) ---E 1067 +--E 1067 )clear all ---S 1068 of 1092 +--S 1068 of 1092 t0:=x*(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 3 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c x)\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1068 +--E 1068 ---S 1069 of 1092 +--S 1069 of 1092 r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ 1/40*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(5/2)/(b^2*d)+_ 1/5*(a+b*x)^(3/2)*(c+d*x)^(7/2)/(b*d)+1/128*(b*c-a*d)^4*_ @@ -23906,32 +23817,32 @@ r0:=-1/48*(b*c-a*d)*(3*b*c+7*a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/(b^3*d)-_ --R 4 2 +-+ +-+ --R 1920b d \|b \|d --R Type: Expression(Integer) ---E 1069 +--E 1069 ---S 1070 of 1092 +--S 1070 of 1092 --a0:=integrate(t0,x) ---E 1070 +--E 1070 ---S 1071 of 1092 +--S 1071 of 1092 --m0:=a0-r0 ---E 1071 +--E 1071 ---S 1072 of 1092 +--S 1072 of 1092 --d0:=D(m0,x) ---E 1072 +--E 1072 )clear all ---S 1073 of 1092 +--S 1073 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x) --R --R --R 2 2 2 +-------+ +-------+ --R (1) (d x + 2c d x + c )\|b x + a \|d x + c --R Type: Expression(Integer) ---E 1073 +--E 1073 ---S 1074 of 1092 +--S 1074 of 1092 r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ (c+d*x)^(5/2)/b-5/64*(b*c-a*d)^4*atanh(sqrt(d)*sqrt(a+b*x)/_ (sqrt(b)*sqrt(c+d*x)))/(b^(7/2)*d^(3/2))+5/32*(b*c-a*d)^2*_ @@ -23964,23 +23875,23 @@ r0:=5/24*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(3/2)/b^2+1/4*(a+b*x)^(3/2)*_ --R 3 +-+ +-+ --R 192b d\|b \|d --R Type: Expression(Integer) ---E 1074 +--E 1074 ---S 1075 of 1092 +--S 1075 of 1092 --a0:=integrate(t0,x) ---E 1075 +--E 1075 ---S 1076 of 1092 +--S 1076 of 1092 --m0:=a0-r0 ---E 1076 +--E 1076 ---S 1077 of 1092 +--S 1077 of 1092 --d0:=D(m0,x) ---E 1077 +--E 1077 )clear all ---S 1078 of 1092 +--S 1078 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x --R --R @@ -23989,9 +23900,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x --R (1) ---------------------------------------- --R x --R Type: Expression(Integer) ---E 1078 +--E 1078 ---S 1079 of 1092 +--S 1079 of 1092 r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ 1/8*(5*b^3*c^3+15*a*b^2*c^2*d-5*a^2*b*c*d^2+a^3*d^3)*_ atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/(b^(5/2)*sqrt(d))+_ @@ -24021,23 +23932,23 @@ r0:=-2*c^(5/2)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(a)+_ --R 2 +-+ +-+ --R 24b \|b \|d --R Type: Expression(Integer) ---E 1079 +--E 1079 ---S 1080 of 1092 (non-algebraic residues) +--S 1080 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1080 +--E 1080 ---S 1081 of 1092 +--S 1081 of 1092 --m0:=a0-r0 ---E 1081 +--E 1081 ---S 1082 of 1092 +--S 1082 of 1092 --d0:=D(m0,x) ---E 1082 +--E 1082 )clear all ---S 1083 of 1092 +--S 1083 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 --R --R @@ -24047,9 +23958,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^2 --R 2 --R x --R Type: Expression(Integer) ---E 1083 +--E 1083 ---S 1084 of 1092 +--S 1084 of 1092 r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ sqrt(a)+1/4*(15*b^2*c^2+10*a*b*c*d-a^2*d^2)*atanh(sqrt(d)*_ sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))*sqrt(d)/b^(3/2)+3/2*d*_ @@ -24076,23 +23987,23 @@ r0:=-c^(3/2)*(b*c+5*a*d)*atanh(sqrt(c)*sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))/_ --R +-+ +-+ --R 4b x\|a \|b --R Type: Expression(Integer) ---E 1084 +--E 1084 ---S 1085 of 1092 (non-algebraic residues) +--S 1085 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1085 +--E 1085 ---S 1086 of 1092 +--S 1086 of 1092 --m0:=a0-r0 ---E 1086 +--E 1086 ---S 1087 of 1092 +--S 1087 of 1092 --d0:=D(m0,x) ---E 1087 +--E 1087 )clear all ---S 1088 of 1092 +--S 1088 of 1092 t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 --R --R @@ -24102,9 +24013,9 @@ t0:=(c+d*x)^(5/2)*sqrt(a+b*x)/x^3 --R 3 --R x --R Type: Expression(Integer) ---E 1088 +--E 1088 ---S 1089 of 1092 +--S 1089 of 1092 r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ sqrt(b)+1/4*(b^2*c^2-10*a*b*c*d-15*a^2*d^2)*atanh(sqrt(c)*_ sqrt(a+b*x)/(sqrt(a)*sqrt(c+d*x)))*sqrt(c)/a^(3/2)-_ @@ -24132,17 +24043,17 @@ r0:=d^(3/2)*(5*b*c+a*d)*atanh(sqrt(d)*sqrt(a+b*x)/(sqrt(b)*sqrt(c+d*x)))/_ --R 2 +-+ +-+ --R 4a x \|a \|b --R Type: Expression(Integer) ---E 1089 +--E 1089 ---S 1090 of 1092 (non-algebraic residues) +--S 1090 of 1092 (non-algebraic residues) --a0:=integrate(t0,x) ---E 1090 +--E 1090 ---S 1091 of 1092 +--S 1091 of 1092 --m0:=a0-r0 ---E 1091 +--E 1091 ---S 1092 of 1092 +--S 1092 of 1092 --d0:=D(m0,x) --E 1092 diff --git a/src/input/rich3c.input.pamphlet b/src/input/rich3c.input.pamphlet index 88bdf31..e55f406 100644 --- a/src/input/rich3c.input.pamphlet +++ b/src/input/rich3c.input.pamphlet @@ -4200,7 +4200,7 @@ r0:=sqrt(-1+x)*sqrt(1+x) --R Type: Expression(Integer) --E 267 ---S 268 of 500 +--S 268 of 500 ok to fail, differs by a constant a0:=integrate(t0,x) --R --R @@ -4209,7 +4209,7 @@ a0:=integrate(t0,x) --R Type: Union(Expression(Integer),...) --E 268 ---S 269 of 500 +--S 269 of 500 ok to fail, differs by a constant m0:=a0-r0 --R --R diff --git a/src/input/rich3d.input.pamphlet b/src/input/rich3d.input.pamphlet new file mode 100644 index 0000000..12ebaa2 --- /dev/null +++ b/src/input/rich3d.input.pamphlet @@ -0,0 +1,5940 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 95 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 5 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3d.output +)spool rich3d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^2) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 2 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 1 + +--S 2 of 500 +--r0:=(-3/37-18/37*%i)*2^(1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(%i*x)^(-1-1/6*%i)*_ +-- hypergeometric(1/6*%i,1+1/6*%i,2+1/6*%i,1/2*%i*(2-2*%i*x+%i*(%i+x))/x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-%i*x)^(1/6*%i)/((1+%i*x)^(1/6*%i)*x^3) +--R +--R +--R %i +--R -- +--R 6 +--R (- %i x + 1) +--R (1) -------------- +--R %i +--R -- +--R 3 6 +--R x (%i x + 1) +--R Type: Expression(Complex(Integer)) +--E 6 + +--S 7 of 500 +--r0:=(2/37-1/111*%i)*2^(-1-1/6*%i)*(1-%i*x)^(1+1/6*%i)*(3-18*%i+_ +-- 37*x+(3+19*%i)*x^2-2*%i*x^2*_ +-- hypergeometric(1,1+1/6*%i,2+1/6*%i,(%i+x)/(%i-x)))/_ +-- ((%i-x)*x^2*(1+1/2*%i*(%i+x))^(1/6*%i)) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x) +--R +--R +--R 2 m +--R (1) (- 10x - x + 3)(3x + 2) +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-7/27*(2+3*x)^(1+m)/(1+m)+37/27*(2+3*x)^(2+m)/(2+m)-_ + 10/27*(2+3*x)^(3+m)/(3+m) +--R +--R +--R (2) +--R 2 m + 3 2 m + 2 +--R (- 10m - 30m - 20)(3x + 2) + (37m + 148m + 111)(3x + 2) +--R + +--R 2 m + 1 +--R (- 7m - 35m - 42)(3x + 2) +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 2 +--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x +--R + +--R 2 2 +--R (63m + 591m + 486)x + 54m + 282m + 200 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2 2 +--R (- 270m - 810m - 540)x + (- 207m - 288m - 81)x +--R + +--R 2 2 +--R (63m + 591m + 486)x + 54m + 282m + 200 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 2 m + 3 2 m + 2 +--R (10m + 30m + 20)(3x + 2) + (- 37m - 148m - 111)(3x + 2) +--R + +--R 2 m + 1 +--R (7m + 35m + 42)(3x + 2) +--R / +--R 3 2 +--R 27m + 162m + 297m + 162 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 65610x - 356481x - 831789x - 1065312x - 771120x - 247968x +--R + +--R 4 3 2 +--R 62496x + 98304x + 42752x + 8960x + 768 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=-7/243*(2+3*x)^9+37/270*(2+3*x)^10-10/297*(2+3*x)^11 +--R +--R +--R (2) +--R 65610 11 356481 10 9 8 7 6 +--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x +--R 11 10 +--R + +--R 62496 5 4 42752 3 2 756736 +--R ----- x + 24576x + ----- x + 4480x + 768x + ------ +--R 5 3 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 65610 11 356481 10 9 8 7 6 +--R - ----- x - ------ x - 92421x - 133164x - 110160x - 41328x +--R 11 10 +--R + +--R 62496 5 4 42752 3 2 +--R ----- x + 24576x + ----- x + 4480x + 768x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 756736 +--R (4) - ------ +--R 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 21870x - 104247x - 207765x - 216594x - 112644x - 7560x + 25872x +--R + +--R 2 +--R 15520x + 3904x + 384 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=-7/216*(2+3*x)^8+37/243*(2+3*x)^9-1/27*(2+3*x)^10 +--R +--R +--R (2) +--R 10 9 207765 8 7 6 5 4 +--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x +--R 8 +--R + +--R 15520 3 2 7712 +--R ----- x + 1952x + 384x + ---- +--R 3 243 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 207765 8 7 6 5 4 +--R - 2187x - 11583x - ------ x - 30942x - 18774x - 1512x + 6468x +--R 8 +--R + +--R 15520 3 2 +--R ----- x + 1952x + 384x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 7712 +--R (4) - ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x + 1664x +--R + +--R 192 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=-1/27*(2+3*x)^7+37/216*(2+3*x)^8-10/243*(2+3*x)^9 +--R +--R +--R (2) +--R 9 29889 8 7 6 5 4 5264 3 2 +--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x +--R 8 3 +--R + +--R 4384 +--R 192x + ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 29889 8 7 6 5 4 5264 3 2 +--R - 810x - ----- x - 7047x - 6552x - 2268x + 1260x + ---- x + 832x +--R 8 3 +--R + +--R 192x +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 4384 +--R (4) - ---- +--R 243 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=96*x+344*x^2+1600/3*x^3+30*x^4-1170*x^5-3627/2*x^6-8343/7*x^7-1215/4*x^8 +--R +--R +--R 1215 8 8343 7 3627 6 5 4 1600 3 2 +--R (2) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x +--R 4 7 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1215 8 8343 7 3627 6 5 4 1600 3 2 +--R (3) - ---- x - ---- x - ---- x - 1170x + 30x + ---- x + 344x + 96x +--R 4 7 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) - 810x - 2241x - 2133x - 528x + 392x + 272x + 48 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=48*x+136*x^2+392/3*x^3-132*x^4-2133/5*x^5-747/2*x^6-810/7*x^7 +--R +--R +--R 810 7 747 6 2133 5 4 392 3 2 +--R (2) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x +--R 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 810 7 747 6 2133 5 4 392 3 2 +--R (3) - --- x - --- x - ---- x - 132x + --- x + 136x + 48x +--R 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) - 270x - 567x - 333x + 46x + 100x + 24 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=24*x+50*x^2+46/3*x^3-333/4*x^4-567/5*x^5-45*x^6 +--R +--R +--R 6 567 5 333 4 46 3 2 +--R (2) - 45x - --- x - --- x + -- x + 50x + 24x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 567 5 333 4 46 3 2 +--R (3) - 45x - --- x - --- x + -- x + 50x + 24x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) - 90x - 129x - 25x + 32x + 12 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=12*x+16*x^2-25/3*x^3-129/4*x^4-18*x^5 +--R +--R +--R 5 129 4 25 3 2 +--R (2) - 18x - --- x - -- x + 16x + 12x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 129 4 25 3 2 +--R (3) - 18x - --- x - -- x + 16x + 12x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x) +--R +--R +--R 3 2 +--R (1) - 30x - 23x + 7x + 6 +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 500 +r0:=6*x+7/2*x^2-23/3*x^3-15/2*x^4 +--R +--R +--R 15 4 23 3 7 2 +--R (2) - -- x - -- x + - x + 6x +--R 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 15 4 23 3 7 2 +--R (3) - -- x - -- x + - x + 6x +--R 2 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)*(3+5*x) +--R +--R +--R 2 +--R (1) - 10x - x + 3 +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 500 +r0:=3*x-1/2*x^2-10/3*x^3 +--R +--R +--R 10 3 1 2 +--R (2) - -- x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 10 3 1 2 +--R (3) - -- x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x) +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) -------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=17/9*x-5/3*x^2-7/27*log(2+3*x) +--R +--R +--R 2 +--R - 7log(3x + 2) - 45x + 51x +--R (2) --------------------------- +--R 27 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 7log(3x + 2) - 45x + 51x +--R (3) --------------------------- +--R 27 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) -------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=-10/9*x+7/27/(2+3*x)+37/27*log(2+3*x) +--R +--R +--R 2 +--R (111x + 74)log(3x + 2) - 90x - 60x + 7 +--R (2) --------------------------------------- +--R 81x + 54 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (111x + 74)log(3x + 2) - 90x - 60x + 7 +--R (3) --------------------------------------- +--R 81x + 54 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=7/54/(2+3*x)^2+(-37/27)/(2+3*x)-10/27*log(2+3*x) +--R +--R +--R 2 +--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141 +--R (2) --------------------------------------------- +--R 2 +--R 486x + 648x + 216 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 180x - 240x - 80)log(3x + 2) - 222x - 141 +--R (3) --------------------------------------------- +--R 2 +--R 486x + 648x + 216 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=7/81/(2+3*x)^3+(-37/54)/(2+3*x)^2+10/27/(2+3*x) +--R +--R +--R 10 2 43 16 +--R -- x + --- x + ---- +--R 81 486 2187 +--R (2) -------------------- +--R 3 2 4 8 +--R x + 2x + - x + -- +--R 3 27 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 540x + 387x + 32 +--R (3) ------------------------------ +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=7/108/(2+3*x)^4+(-37/81)/(2+3*x)^3+5/27/(2+3*x)^2 +--R +--R +--R 5 2 23 35 +--R --- x + ---- x - ----- +--R 243 2187 26244 +--R (2) ---------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 540x + 276x - 35 +--R (3) ------------------------------------------- +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--R - 10x - x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=7/135/(2+3*x)^5+(-37/108)/(2+3*x)^4+10/81/(2+3*x)^3 +--R +--R +--R 10 2 49 113 +--R ---- x + ----- x - ------ +--R 2187 26244 196830 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 1800x + 735x - 226 +--R (3) -------------------------------------------------------------- +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^2 +--R +--R +--R 3 2 m +--R (1) (- 50x - 35x + 12x + 9)(3x + 2) +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=7/81*(2+3*x)^(1+m)/(1+m)-8/9*(2+3*x)^(2+m)/(2+m)+_ + 65/27*(2+3*x)^(3+m)/(3+m)-50/81*(2+3*x)^(4+m)/(4+m) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (- 50m - 300m - 550m - 300)(3x + 2) +--R + +--R 3 2 m + 3 +--R (195m + 1365m + 2730m + 1560)(3x + 2) +--R + +--R 3 2 m + 2 +--R (- 72m - 576m - 1368m - 864)(3x + 2) +--R + +--R 3 2 m + 1 +--R (7m + 63m + 182m + 168)(3x + 2) +--R / +--R 4 3 2 +--R 81m + 810m + 2835m + 4050m + 1944 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 +--R (- 1350m - 8100m - 14850m - 8100)x +--R + +--R 3 2 3 +--R (- 1845m - 9315m - 15030m - 7560)x +--R + +--R 3 2 2 3 2 +--R (- 306m + 1242m + 5436m + 3888)x + (459m + 4539m + 9870m + 5832)x +--R + +--R 3 2 +--R 162m + 1314m + 2644m + 1520 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 4 3 2 +--R 27m + 270m + 945m + 1350m + 648 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 4 +--R (- 4050m - 24300m - 44550m - 24300)x +--R + +--R 3 2 3 +--R (- 5535m - 27945m - 45090m - 22680)x +--R + +--R 3 2 2 +--R (- 918m + 3726m + 16308m + 11664)x +--R + +--R 3 2 3 2 +--R (1377m + 13617m + 29610m + 17496)x + 486m + 3942m + 7932m + 4560 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 3 2 m + 4 +--R (50m + 300m + 550m + 300)(3x + 2) +--R + +--R 3 2 m + 3 +--R (- 195m - 1365m - 2730m - 1560)(3x + 2) +--R + +--R 3 2 m + 2 +--R (72m + 576m + 1368m + 864)(3x + 2) +--R + +--R 3 2 m + 1 +--R (- 7m - 63m - 182m - 168)(3x + 2) +--R / +--R 4 3 2 +--R 81m + 810m + 2835m + 4050m + 1944 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 328050x - 1979235x - 5228388x - 7821927x - 7051536x - 3553200x +--R + +--R 5 4 3 2 +--R - 431424x + 679008x + 508672x + 173056x + 30720x + 2304 +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 500 +r0:=7/729*(2+3*x)^9-4/45*(2+3*x)^10+65/297*(2+3*x)^11-25/486*(2+3*x)^12 +--R +--R +--R (2) +--R 54675 12 1979235 11 2614194 10 9 8 7 +--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x +--R 2 11 5 +--R + +--R 6 679008 5 4 173056 3 2 6070784 +--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x + ------- +--R 5 3 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 54675 12 1979235 11 2614194 10 9 8 7 +--R - ----- x - ------- x - ------- x - 869103x - 881442x - 507600x +--R 2 11 5 +--R + +--R 6 679008 5 4 173056 3 2 +--R - 71904x + ------ x + 127168x + ------ x + 15360x + 2304x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R 6070784 +--R (4) - ------- +--R 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 109350x - 586845x - 1351566x - 1706265x - 1213002x - 375732x +--R + +--R 4 3 2 +--R 106680x + 155216x + 66080x + 13632x + 1152 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=7/648*(2+3*x)^8-8/81*(2+3*x)^9+13/54*(2+3*x)^10-50/891*(2+3*x)^11 +--R +--R +--R (2) +--R 109350 11 117369 10 9 1706265 8 7 6 +--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x +--R 11 2 8 +--R + +--R 5 4 66080 3 2 74656 +--R 21336x + 38804x + ----- x + 6816x + 1152x + ----- +--R 3 891 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 109350 11 117369 10 9 1706265 8 7 6 +--R - ------ x - ------ x - 150174x - ------- x - 173286x - 62622x +--R 11 2 8 +--R + +--R 5 4 66080 3 2 +--R 21336x + 38804x + ----- x + 6816x + 1152x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 74656 +--R (4) - ----- +--R 891 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 36450x - 171315x - 336312x - 344547x - 174636x - 8820x + 41440x +--R + +--R 2 +--R 24112x + 5952x + 576 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=576*x+2976*x^2+24112/3*x^3+10360*x^4-1764*x^5-29106*x^6-_ + 49221*x^7-42039*x^8-19035*x^9-3645*x^10 +--R +--R +--R (2) +--R 10 9 8 7 6 5 4 +--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x +--R + +--R 24112 3 2 +--R ----- x + 2976x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 6 5 4 +--R - 3645x - 19035x - 42039x - 49221x - 29106x - 1764x + 10360x +--R + +--R 24112 3 2 +--R ----- x + 2976x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 12150x - 49005x - 79434x - 61893x - 16950x + 8360x + 8240x + 2544x +--R + +--R 288 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=288*x+1272*x^2+8240/3*x^3+2090*x^4-3390*x^5-20631/2*x^6-79434/7*x^7-_ + 49005/8*x^8-1350*x^9 +--R +--R +--R (2) +--R 9 49005 8 79434 7 20631 6 5 4 8240 3 +--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x +--R 8 7 2 3 +--R + +--R 2 +--R 1272x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 49005 8 79434 7 20631 6 5 4 8240 3 +--R - 1350x - ----- x - ----- x - ----- x - 3390x + 2090x + ---- x +--R 8 7 2 3 +--R + +--R 2 +--R 1272x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=144*x+528*x^2+2536/3*x^3+94*x^4-9039/5*x^5-2898*x^6-13635/7*x^7-2025/4*x^8 +--R +--R +--R (2) +--R 2025 8 13635 7 6 9039 5 4 2536 3 2 +--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x +--R 4 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2025 8 13635 7 6 9039 5 4 2536 3 2 +--R - ---- x - ----- x - 2898x - ---- x + 94x + ---- x + 528x + 144x +--R 4 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) - 1350x - 3645x - 3366x - 769x + 638x + 420x + 72 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=72*x+210*x^2+638/3*x^3-769/4*x^4-3366/5*x^5-1215/2*x^6-1350/7*x^7 +--R +--R +--R 1350 7 1215 6 3366 5 769 4 638 3 2 +--R (2) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x +--R 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1350 7 1215 6 3366 5 769 4 638 3 2 +--R (3) - ---- x - ---- x - ---- x - --- x + --- x + 210x + 72x +--R 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) - 450x - 915x - 512x + 85x + 156x + 36 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=36*x+78*x^2+85/3*x^3-128*x^4-183*x^5-75*x^6 +--R +--R +--R 6 5 4 85 3 2 +--R (2) - 75x - 183x - 128x + -- x + 78x + 36x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 85 3 2 +--R (3) - 75x - 183x - 128x + -- x + 78x + 36x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--R (1) - 150x - 205x - 34x + 51x + 18 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=18*x+51/2*x^2-34/3*x^3-205/4*x^4-30*x^5 +--R +--R +--R 5 205 4 34 3 51 2 +--R (2) - 30x - --- x - -- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 205 4 34 3 51 2 +--R (3) - 30x - --- x - -- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)*(3+5*x)^2 +--R +--R +--R 3 2 +--R (1) - 50x - 35x + 12x + 9 +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 500 +r0:=9*x+6*x^2-35/3*x^3-25/2*x^4 +--R +--R +--R 25 4 35 3 2 +--R (2) - -- x - -- x + 6x + 9x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 25 4 35 3 2 +--R (3) - -- x - -- x + 6x + 9x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x) +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=118/27*x-5/18*x^2-50/9*x^3+7/81*log(2+3*x) +--R +--R +--R 3 2 +--R 14log(3x + 2) - 900x - 45x + 708x +--R (2) ----------------------------------- +--R 162 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 14log(3x + 2) - 900x - 45x + 708x +--R (3) ----------------------------------- +--R 162 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=95/27*x-25/9*x^2+(-7/81)/(2+3*x)-8/9*log(2+3*x) +--R +--R +--R 3 2 +--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7 +--R (2) ---------------------------------------------------- +--R 243x + 162 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (- 216x - 144)log(3x + 2) - 675x + 405x + 570x - 7 +--R (3) ---------------------------------------------------- +--R 243x + 162 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=-50/27*x+(-7/162)/(2+3*x)^2+8/9/(2+3*x)+65/27*log(2+3*x) +--R +--R +--R 2 3 2 +--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281 +--R (2) ----------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (3510x + 4680x + 1560)log(3x + 2) - 2700x - 3600x - 768x + 281 +--R (3) ----------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-7/243)/(2+3*x)^3+4/9/(2+3*x)^2+(-65/27)/(2+3*x)-50/81*log(2+3*x) +--R +--R +--R 3 2 2 +--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131 +--R (2) --------------------------------------------------------------------- +--R 3 2 +--R 6561x + 13122x + 8748x + 1944 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +--R (- 4050x - 8100x - 5400x - 1200)log(3x + 2) - 5265x - 6696x - 2131 +--R (3) --------------------------------------------------------------------- +--R 3 2 +--R 6561x + 13122x + 8748x + 1944 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=7/12*(3+5*x)^3/(2+3*x)^4+3/4*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 125 4 2300 3 515 2 38 25 +--R --- x + ---- x + --- x + -- x + -- +--R 36 243 54 9 36 +--R (2) ------------------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 600x + 810x + 312x + 25 +--R (3) -------------------------------------- +--R 4 3 2 +--R 2916x + 7776x + 7776x + 3456x + 576 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R 125 +--R (4) - --- +--R 36 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-7/405)/(2+3*x)^5+2/9/(2+3*x)^4+(-65/81)/(2+3*x)^3+25/81/(2+3*x)^2 +--R +--R +--R 25 3 85 2 58 127 +--R --- x + ---- x + ---- x - ----- +--R 729 2187 6561 98415 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 3375x + 3825x + 870x - 127 +--R (3) --------------------------------------------------------- +--R 5 4 3 2 +--R 98415x + 328050x + 437400x + 291600x + 97200x + 12960 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-7/486)/(2+3*x)^6+8/45/(2+3*x)^5+(-65/108)/(2+3*x)^4+50/243/(2+3*x)^3 +--R +--R +--R 50 3 205 2 97 1021 +--R ---- x + ----- x + ----- x - ------- +--R 6561 26244 98415 1771470 +--R (2) ---------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 27000x + 27675x + 3492x - 2042 +--R / +--R 6 5 4 3 2 +--R 3542940x + 14171760x + 23619600x + 20995200x + 10497600x + 2799360x +--R + +--R 311040 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--R - 50x - 35x + 12x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=(-1/81)/(2+3*x)^7+4/27/(2+3*x)^6+(-13/27)/(2+3*x)^5+25/162/(2+3*x)^4 +--R +--R +--R 25 3 4 2 2 11 +--R ----- x + ---- x + ----- x - ----- +--R 13122 2187 19683 59049 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 225x + 216x + 12x - 22 +--R / +--R 7 6 5 4 3 2 +--R 118098x + 551124x + 1102248x + 1224720x + 816480x + 326592x +--R + +--R 72576x + 6912 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)*(2+3*x)^m*(3+5*x)^3 +--R +--R +--R 4 3 2 m +--R (1) (- 250x - 325x - 45x + 81x + 27)(3x + 2) +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-7/243*(2+3*x)^(1+m)/(1+m)+107/243*(2+3*x)^(2+m)/(2+m)-_ + 185/81*(2+3*x)^(3+m)/(3+m)+1025/243*(2+3*x)^(4+m)/(4+m)-_ + 250/243*(2+3*x)^(5+m)/(5+m) +--R +--R +--R (2) +--R 4 3 2 m + 5 +--R (- 250m - 2500m - 8750m - 12500m - 6000)(3x + 2) +--R + +--R 4 3 2 m + 4 +--R (1025m + 11275m + 42025m + 62525m + 30750)(3x + 2) +--R + +--R 4 3 2 m + 3 +--R (- 555m - 6660m - 27195m - 43290m - 22200)(3x + 2) +--R + +--R 4 3 2 m + 2 +--R (107m + 1391m + 6313m + 11449m + 6420)(3x + 2) +--R + +--R 4 3 2 m + 1 +--R (- 7m - 98m - 497m - 1078m - 840)(3x + 2) +--R / +--R 5 4 3 2 +--R 243m + 3645m + 20655m + 54675m + 66582m + 29160 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 5 +--R (- 20250m - 202500m - 708750m - 1012500m - 486000)x +--R + +--R 4 3 2 4 +--R (- 39825m - 370575m - 1227825m - 1686825m - 789750)x +--R + +--R 4 3 2 3 +--R (- 21195m - 148140m - 368955m - 387810m - 145800)x +--R + +--R 4 3 2 2 +--R (4131m + 96093m + 455229m + 756927m + 393660)x +--R + +--R 4 3 2 4 3 +--R (6561m + 86346m + 343215m + 526038m + 262440)x + 1458m + 17496m +--R + +--R 2 +--R 66366m + 99240m + 48800 +--R * +--R m log(3x + 2) +--R %e +--R / +--R 5 4 3 2 +--R 81m + 1215m + 6885m + 18225m + 22194m + 9720 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 2 5 +--R (- 60750m - 607500m - 2126250m - 3037500m - 1458000)x +--R + +--R 4 3 2 4 +--R (- 119475m - 1111725m - 3683475m - 5060475m - 2369250)x +--R + +--R 4 3 2 3 +--R (- 63585m - 444420m - 1106865m - 1163430m - 437400)x +--R + +--R 4 3 2 2 +--R (12393m + 288279m + 1365687m + 2270781m + 1180980)x +--R + +--R 4 3 2 4 +--R (19683m + 259038m + 1029645m + 1578114m + 787320)x + 4374m +--R + +--R 3 2 +--R 52488m + 199098m + 297720m + 146400 +--R * +--R m log(3x + 2) +--R %e +--R + +--R 4 3 2 m + 5 +--R (250m + 2500m + 8750m + 12500m + 6000)(3x + 2) +--R + +--R 4 3 2 m + 4 +--R (- 1025m - 11275m - 42025m - 62525m - 30750)(3x + 2) +--R + +--R 4 3 2 m + 3 +--R (555m + 6660m + 27195m + 43290m + 22200)(3x + 2) +--R + +--R 4 3 2 m + 2 +--R (- 107m - 1391m - 6313m - 11449m - 6420)(3x + 2) +--R + +--R 4 3 2 m + 1 +--R (7m + 98m + 497m + 1078m + 840)(3x + 2) +--R / +--R 5 4 3 2 +--R 243m + 3645m + 20655m + 54675m + 66582m + 29160 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)*(2+3*x)^8*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 +--R - 1640250x - 10880325x - 32079645x - 54794799x - 58723461x +--R + +--R 7 6 5 4 3 2 +--R - 38920608x - 12816720x + 2100768x + 4580384x + 2391296x + 672768x +--R + +--R 103680x + 6912 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=-7/2187*(2+3*x)^9+107/2430*(2+3*x)^10-185/891*(2+3*x)^11+_ + 1025/2916*(2+3*x)^12-250/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 1640250 13 3626775 12 32079645 11 54794799 10 9 +--R - ------- x - ------- x - -------- x - -------- x - 6524829x +--R 13 4 11 10 +--R + +--R 8 7 6 4580384 5 4 3 +--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x +--R 5 +--R + +--R 2 640642048 +--R 51840x + 6912x + --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1640250 13 3626775 12 32079645 11 54794799 10 9 +--R - ------- x - ------- x - -------- x - -------- x - 6524829x +--R 13 4 11 10 +--R + +--R 8 7 6 4580384 5 4 3 +--R - 4865076x - 1830960x + 350128x + ------- x + 597824x + 224256x +--R 5 +--R + +--R 2 +--R 51840x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 640642048 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 546750x - 3262275x - 8518365x - 12586023x - 11183805x - 5517666x +--R + +--R 5 4 3 2 +--R - 593796x + 1096120x + 796048x + 266400x + 46656x + 3456 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=3456*x+23328*x^2+88800*x^3+199012*x^4+219224*x^5-98966*x^6-_ + 788238*x^7-11183805/8*x^8-1398447*x^9-1703673/2*x^10-_ + 3262275/11*x^11-91125/2*x^12 +--R +--R +--R (2) +--R 91125 12 3262275 11 1703673 10 9 11183805 8 +--R - ----- x - ------- x - ------- x - 1398447x - -------- x +--R 2 11 2 8 +--R + +--R 7 6 5 4 3 2 +--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 91125 12 3262275 11 1703673 10 9 11183805 8 +--R - ----- x - ------- x - ------- x - 1398447x - -------- x +--R 2 11 2 8 +--R + +--R 7 6 5 4 3 2 +--R - 788238x - 98966x + 219224x + 199012x + 88800x + 23328x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 182250x - 965925x - 2195505x - 2731671x - 1906821x - 568008x +--R + +--R 4 3 2 +--R 180740x + 244880x + 102096x + 20736x + 1728 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=1728*x+10368*x^2+34032*x^3+61220*x^4+36148*x^5-94668*x^6-_ + 272403*x^7-2731671/8*x^8-243945*x^9-193185/2*x^10-182250/11*x^11 +--R +--R +--R (2) +--R 182250 11 193185 10 9 2731671 8 7 6 +--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x +--R 11 2 8 +--R + +--R 5 4 3 2 +--R 36148x + 61220x + 34032x + 10368x + 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 182250 11 193185 10 9 2731671 8 7 6 +--R - ------ x - ------ x - 243945x - ------- x - 272403x - 94668x +--R 11 2 8 +--R + +--R 5 4 3 2 +--R 36148x + 61220x + 34032x + 10368x + 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 60750x - 281475x - 544185x - 547767x - 270429x - 9050x + 66280x +--R + +--R 2 +--R 37440x + 9072x + 864 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=864*x+4536*x^2+12480*x^3+16570*x^4-1810*x^5-90143/2*x^6-_ + 547767/7*x^7-544185/8*x^8-31275*x^9-6075*x^10 +--R +--R +--R (2) +--R 10 9 544185 8 547767 7 90143 6 5 4 +--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x +--R 8 7 2 +--R + +--R 3 2 +--R 12480x + 4536x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 544185 8 547767 7 90143 6 5 4 +--R - 6075x - 31275x - ------ x - ------ x - ----- x - 1810x + 16570x +--R 8 7 2 +--R + +--R 3 2 +--R 12480x + 4536x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x +--R + +--R 3888x + 432 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=432*x+1944*x^2+4296*x^3+3452*x^4-25237/5*x^5-32453/2*x^6-_ + 127845/7*x^7-80325/8*x^8-2250*x^9 +--R +--R +--R (2) +--R 9 80325 8 127845 7 32453 6 25237 5 4 3 +--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x +--R 8 7 2 5 +--R + +--R 2 +--R 1944x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 80325 8 127845 7 32453 6 25237 5 4 3 +--R - 2250x - ----- x - ------ x - ----- x - ----- x + 3452x + 4296x +--R 8 7 2 5 +--R + +--R 2 +--R 1944x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=216*x+810*x^2+1338*x^3+883/4*x^4-13943/5*x^5-9255/2*x^6-_ + 22275/7*x^7-3375/4*x^8 +--R +--R +--R (2) +--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2 +--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x +--R 4 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3375 8 22275 7 9255 6 13943 5 883 4 3 2 +--R - ---- x - ----- x - ---- x - ----- x + --- x + 1338x + 810x + 216x +--R 4 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) - 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=108*x+324*x^2+345*x^3-1111/4*x^4-1061*x^5-1975/2*x^6-2250/7*x^7 +--R +--R +--R 2250 7 1975 6 5 1111 4 3 2 +--R (2) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x +--R 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2250 7 1975 6 5 1111 4 3 2 +--R (3) - ---- x - ---- x - 1061x - ---- x + 345x + 324x + 108x +--R 7 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R (1) - 750x - 1475x - 785x + 153x + 243x + 54 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=54*x+243/2*x^2+51*x^3-785/4*x^4-295*x^5-125*x^6 +--R +--R +--R 6 5 785 4 3 243 2 +--R (2) - 125x - 295x - --- x + 51x + --- x + 54x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 785 4 3 243 2 +--R (3) - 125x - 295x - --- x + 51x + --- x + 54x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)*(3+5*x)^3 +--R +--R +--R 4 3 2 +--R (1) - 250x - 325x - 45x + 81x + 27 +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 500 +r0:=27*x+81/2*x^2-15*x^3-325/4*x^4-50*x^5 +--R +--R +--R 5 325 4 3 81 2 +--R (2) - 50x - --- x - 15x + -- x + 27x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 325 4 3 81 2 +--R (3) - 50x - --- x - 15x + -- x + 27x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x) +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1097/81*x+545/54*x^2-475/27*x^3-125/6*x^4-7/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x +--R (2) --------------------------------------------------- +--R 486 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 14log(3x + 2) - 10125x - 8550x + 4905x + 6582x +--R (3) --------------------------------------------------- +--R 486 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=55/9*x+25/54*x^2-250/27*x^3+7/243/(2+3*x)+107/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14 +--R (2) ---------------------------------------------------------------- +--R 1458x + 972 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (642x + 428)log(3x + 2) - 13500x - 8325x + 9360x + 5940x + 14 +--R (3) ---------------------------------------------------------------- +--R 1458x + 972 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=175/27*x-125/27*x^2+7/486/(2+3*x)^2+(-107/243)/(2+3*x)-185/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x +--R + +--R 11958x - 421 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 9990x - 13320x - 4440)log(3x + 2) - 20250x + 1350x + 28800x +--R + +--R 11958x - 421 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=-250/81*x+7/729/(2+3*x)^3+(-107/486)/(2+3*x)^2+185/81/(2+3*x)+_ + 1025/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x +--R + +--R 2 +--R - 132030x + 2997x + 12692 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (166050x + 332100x + 221400x + 49200)log(3x + 2) - 121500x - 243000x +--R + +--R 2 +--R - 132030x + 2997x + 12692 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=7/972/(2+3*x)^4+(-107/729)/(2+3*x)^3+185/162/(2+3*x)^2+_ + (-1025/243)/(2+3*x)-250/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2) +--R + +--R 3 2 +--R - 332100x - 634230x - 404124x - 85915 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 243000x - 648000x - 648000x - 288000x - 48000)log(3x + 2) +--R + +--R 3 2 +--R - 332100x - 634230x - 404124x - 85915 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=7/15*(3+5*x)^4/(2+3*x)^5+5/12*(3+5*x)^4/(2+3*x)^4 +--R +--R +--R 3125 5 5375 4 2425 3 2 119 13 +--R ---- x + ---- x + ---- x + 10x + --- x + -- +--R 972 486 162 36 30 +--R (2) ----------------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 405000x + 803250x + 559800x + 153795x + 11758 +--R (3) ----------------------------------------------------------------- +--R 5 4 3 2 +--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R 3125 +--R (4) - ---- +--R 972 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=7/18*(3+5*x)^4/(2+3*x)^6+29/45*(3+5*x)^4/(2+3*x)^5+_ + 29/36*(3+5*x)^4/(2+3*x)^4 +--R +--R +--R 18125 6 18125 5 30250 4 8975 3 665 2 664 49 +--R ----- x + ----- x + ----- x + ---- x + --- x + --- x + -- +--R 2916 729 729 243 36 135 90 +--R (2) -------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 607500x + 1066500x + 587925x + 78048x - 13198 +--R / +--R 6 5 4 3 2 +--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x +--R + +--R 933120 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R 18125 +--R (4) - ----- +--R 2916 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R - 250x - 325x - 45x + 81x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=1/243/(2+3*x)^7+(-107/1458)/(2+3*x)^6+37/81/(2+3*x)^5+_ + (-1025/972)/(2+3*x)^4+250/729/(2+3*x)^3 +--R +--R +--R 250 4 4925 3 1147 2 107 922 +--R ----- x + ------ x + ------ x + ------- x - ------- +--R 19683 236196 118098 1062882 1594323 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 81000x + 132975x + 61938x + 642x - 3688 +--R / +--R 7 6 5 4 3 +--R 6377292x + 29760696x + 59521392x + 66134880x + 44089920x +--R + +--R 2 +--R 17635968x + 3919104x + 373248 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(5-2*x)^6*(2+3*x)^3*(-16+33*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 57024x - 768960x + 4070736x - 10051008x + 8647828x + 8983380x +--R + +--R 4 3 2 +--R - 19081125x - 196250x + 11962500x - 75000x - 2000000 +--R Type: Polynomial(Integer) +--E 271 + +--S 272 of 500 +r0:=-1/2*(5-2*x)^7*(2+3*x)^4 +--R +--R +--R (2) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x - 625000 +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 10 9 8 7 6 +--R 5184x - 76896x + 452304x - 1256376x + 1235404x + 1497230x +--R + +--R 5 98125 4 3 2 +--R - 3816225x - ----- x + 3987500x - 37500x - 2000000x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 625000 +--R Type: Polynomial(Fraction(Integer)) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x) +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=-2/15*(2+3*x)^(1+m)/(1+m)-11/5*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x) +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=1666663/78125*x+1777779/31250*x^2+152469/3125*x^3-_ + 152469/2500*x^4-106677/625*x^5-7047/50*x^6-1458/35*x^7+_ + 11/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x +--R + +--R 3 2 +--R 533641500x + 622222650x + 233332820x +--R / +--R 10937500 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 308log(5x + 3) - 455625000x - 1541531250x - 1866847500x - 667051875x +--R + +--R 3 2 +--R 533641500x + 622222650x + 233332820x +--R / +--R 10937500 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=166663/15625*x+127779/6250*x^2+2469/625*x^3-17469/500*x^4-_ + 5427/125*x^5-81/5*x^6+11/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x +--R + +--R 2 +--R 6388950x + 3333260x +--R / +--R 312500 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 44log(5x + 3) - 5062500x - 13567500x - 10918125x + 1234500x +--R + +--R 2 +--R 6388950x + 3333260x +--R / +--R 312500 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x) +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=16663/3125*x+7779/1250*x^2-531/125*x^3-1269/100*x^4-_ + 162/25*x^5+11/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x +--R (2) ------------------------------------------------------------------- +--R 62500 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 44log(5x + 3) - 405000x - 793125x - 265500x + 388950x + 333260x +--R (3) ------------------------------------------------------------------- +--R 62500 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x) +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=1663/625*x+279/250*x^2-81/25*x^3-27/10*x^4+11/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x +--R (2) --------------------------------------------------- +--R 6250 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 22log(5x + 3) - 16875x - 20250x + 6975x + 16630x +--R (3) --------------------------------------------------- +--R 6250 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x) +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ---------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=163/125*x-21/50*x^2-6/5*x^3+11/625*log(3+5*x) +--R +--R +--R 3 2 +--R 22log(5x + 3) - 1500x - 525x + 1630x +--R (2) -------------------------------------- +--R 1250 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 22log(5x + 3) - 1500x - 525x + 1630x +--R (3) -------------------------------------- +--R 1250 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x) +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) ------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=13/25*x-3/5*x^2+11/125*log(3+5*x) +--R +--R +--R 2 +--R 11log(5x + 3) - 75x + 65x +--R (2) -------------------------- +--R 125 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 11log(5x + 3) - 75x + 65x +--R (3) -------------------------- +--R 125 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)/(3+5*x) +--R +--R +--R - 2x + 1 +--R (1) -------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=-2/5*x+11/25*log(3+5*x) +--R +--R +--R 11log(5x + 3) - 10x +--R (2) ------------------- +--R 25 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R 11log(5x + 3) - 10x +--R (3) ------------------- +--R 25 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=-7/3*log(2+3*x)+11/5*log(3+5*x) +--R +--R +--R 33log(5x + 3) - 35log(3x + 2) +--R (2) ----------------------------- +--R 15 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R 33log(5x + 3) - 35log(3x + 2) +--R (3) ----------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=7/3/(2+3*x)-11*log(2+3*x)+11*log(3+5*x) +--R +--R +--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7 +--R (2) --------------------------------------------------- +--R 9x + 6 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (99x + 66)log(5x + 3) + (- 99x - 66)log(3x + 2) + 7 +--R (3) --------------------------------------------------- +--R 9x + 6 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=7/6/(2+3*x)^2+11/(2+3*x)-55*log(2+3*x)+55*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2) +--R + +--R 198x + 139 +--R / +--R 2 +--R 54x + 72x + 24 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (2970x + 3960x + 1320)log(5x + 3) + (- 2970x - 3960x - 1320)log(3x + 2) +--R + +--R 198x + 139 +--R / +--R 2 +--R 54x + 72x + 24 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=7/9/(2+3*x)^3+11/2/(2+3*x)^2+55/(2+3*x)-275*log(2+3*x)+275*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (133650x + 267300x + 178200x + 39600)log(5x + 3) +--R + +--R 3 2 2 +--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x +--R + +--R 4172 +--R / +--R 3 2 +--R 486x + 972x + 648x + 144 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (133650x + 267300x + 178200x + 39600)log(5x + 3) +--R + +--R 3 2 2 +--R (- 133650x - 267300x - 178200x - 39600)log(3x + 2) + 8910x + 12177x +--R + +--R 4172 +--R / +--R 3 2 +--R 486x + 972x + 648x + 144 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=7/12/(2+3*x)^4+11/3/(2+3*x)^3+55/2/(2+3*x)^2+275/(2+3*x)-_ + 1375*log(2+3*x)+1375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2) +--R + +--R 3 2 +--R 89100x + 181170x + 122892x + 27815 +--R / +--R 4 3 2 +--R 972x + 2592x + 2592x + 1152x + 192 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1336500x + 3564000x + 3564000x + 1584000x + 264000)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1336500x - 3564000x - 3564000x - 1584000x - 264000)log(3x + 2) +--R + +--R 3 2 +--R 89100x + 181170x + 122892x + 27815 +--R / +--R 4 3 2 +--R 972x + 2592x + 2592x + 1152x + 192 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=7/15/(2+3*x)^5+11/4/(2+3*x)^4+55/3/(2+3*x)^3+275/2/(2+3*x)^2+_ + 1375/(2+3*x)-6875*log(2+3*x)+6875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x +--R + +--R 4400000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x +--R + +--R - 4400000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2227500x + 6014250x + 6091800x + 2743565x + 463586 +--R / +--R 5 4 3 2 +--R 4860x + 16200x + 21600x + 14400x + 4800x + 640 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 33412500x + 111375000x + 148500000x + 99000000x + 33000000x +--R + +--R 4400000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 33412500x - 111375000x - 148500000x - 99000000x - 33000000x +--R + +--R - 4400000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2227500x + 6014250x + 6091800x + 2743565x + 463586 +--R / +--R 5 4 3 2 +--R 4860x + 16200x + 21600x + 14400x + 4800x + 640 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=7/18/(2+3*x)^6+11/5/(2+3*x)^5+55/4/(2+3*x)^4+275/3/(2+3*x)^3+_ + 1375/2/(2+3*x)^2+6875/(2+3*x)-34375*log(2+3*x)+34375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 4510687500x + 18042750000x + 30071250000x + 26730000000x +--R + +--R 2 +--R 13365000000x + 3564000000x + 396000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x +--R + +--R 2 +--R - 13365000000x - 3564000000x - 396000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x +--R + +--R 41722762 +--R / +--R 6 5 4 3 2 +--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 4510687500x + 18042750000x + 30071250000x + 26730000000x +--R + +--R 2 +--R 13365000000x + 3564000000x + 396000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 4510687500x - 18042750000x - 30071250000x - 26730000000x +--R + +--R 2 +--R - 13365000000x - 3564000000x - 396000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 300712500x + 1012398750x + 1363675500x + 918643275x + 309504888x +--R + +--R 41722762 +--R / +--R 6 5 4 3 2 +--R 131220x + 524880x + 874800x + 777600x + 388800x + 103680x + 11520 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^2 +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-11/5*(2+3*x)^(1+m)/(3+5*x)+1/5*(2-33*m)*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x +--R + +--R 128 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=5555478/390625*x+5740767/156250*x^2+92592/3125*x^3-_ + 513783/12500*x^4-336798/3125*x^5-21627/250*x^6-_ + 4374/175*x^7+(-11/1953125)/(3+5*x)+229/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 +--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x +--R + +--R 6 5 4 3 +--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x +--R + +--R 2 +--R 9916639950x + 2333300760x - 308 +--R / +--R 273437500x + 164062500 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (32060x + 19236)log(5x + 3) - 6834375000x - 27755156250x +--R + +--R 6 5 4 3 +--R - 43662543750x - 28920898125x + 1358398125x + 14907422250x +--R + +--R 2 +--R 9916639950x + 2333300760x - 308 +--R / +--R 273437500x + 164062500 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=555489/78125*x+40743/3125*x^2+5553/3125*x^3-14094/625*x^4-_ + 16767/625*x^5-243/25*x^6+(-11/390625)/(3+5*x)+196/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x +--R + +--R 4 3 2 +--R - 22955625x + 27546750x + 29165850x + 8332335x - 11 +--R / +--R 1953125x + 1171875 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (980x + 588)log(5x + 3) - 18984375x - 63787500x - 75481875x +--R + +--R 4 3 2 +--R - 22955625x + 27546750x + 29165850x + 8332335x - 11 +--R / +--R 1953125x + 1171875 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=444/125*x+24093/6250*x^2-1854/625*x^3-3969/500*x^4-_ + 486/125*x^5+(-11/78125)/(3+5*x)+163/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x +--R + +--R 3 2 +--R 3242250x + 9163950x + 3330000x - 44 +--R / +--R 1562500x + 937500 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (3260x + 1956)log(5x + 3) - 6075000x - 16048125x - 12076875x +--R + +--R 3 2 +--R 3242250x + 9163950x + 3330000x - 44 +--R / +--R 1562500x + 937500 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=5511/3125*x+378/625*x^2-261/125*x^3-81/50*x^4+(-11/15625)/(3+5*x)+_ + 26/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x +--R + +--R 165330x - 22 +--R / +--R 156250x + 93750 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1300x + 780)log(5x + 3) - 253125x - 478125x - 101250x + 332250x +--R + +--R 165330x - 22 +--R / +--R 156250x + 93750 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=522/625*x-81/250*x^2-18/25*x^3+(-11/3125)/(3+5*x)+97/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22 +--R (2) ------------------------------------------------------------------- +--R 31250x + 18750 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (970x + 582)log(5x + 3) - 22500x - 23625x + 20025x + 15660x - 22 +--R (3) ------------------------------------------------------------------- +--R 31250x + 18750 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ---------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=33/125*x-9/25*x^2+(-11/625)/(3+5*x)+64/625*log(3+5*x) +--R +--R +--R 3 2 +--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11 +--R (2) ---------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (320x + 192)log(5x + 3) - 1125x + 150x + 495x - 11 +--R (3) ---------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=-6/25*x+(-11/125)/(3+5*x)+31/125*log(3+5*x) +--R +--R +--R 2 +--R (155x + 93)log(5x + 3) - 150x - 90x - 11 +--R (2) ----------------------------------------- +--R 625x + 375 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (155x + 93)log(5x + 3) - 150x - 90x - 11 +--R (3) ----------------------------------------- +--R 625x + 375 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)/(3+5*x)^2 +--R +--R +--R - 2x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-11/25)/(3+5*x)-2/25*log(3+5*x) +--R +--R +--R (- 10x - 6)log(5x + 3) - 11 +--R (2) --------------------------- +--R 125x + 75 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 10x - 6)log(5x + 3) - 11 +--R (3) --------------------------- +--R 125x + 75 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-11/5)/(3+5*x)+7*log(2+3*x)-7*log(3+5*x) +--R +--R +--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11 +--R (2) -------------------------------------------------------- +--R 25x + 15 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 175x - 105)log(5x + 3) + (175x + 105)log(3x + 2) - 11 +--R (3) -------------------------------------------------------- +--R 25x + 15 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-7)/(2+3*x)+(-11)/(3+5*x)+68*log(2+3*x)-68*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2) +--R + +--R - 68x - 43 +--R / +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 1020x - 1292x - 408)log(5x + 3) + (1020x + 1292x + 408)log(3x + 2) +--R + +--R - 68x - 43 +--R / +--R 2 +--R 15x + 19x + 6 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-7/2)/(2+3*x)^2+(-68)/(2+3*x)+(-55)/(3+5*x)+505*log(2+3*x)-505*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3) +--R + +--R 3 2 2 +--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277 +--R / +--R 3 2 +--R 90x + 174x + 112x + 24 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 45450x - 87870x - 56560x - 12120)log(5x + 3) +--R + +--R 3 2 2 +--R (45450x + 87870x + 56560x + 12120)log(3x + 2) - 3030x - 3939x - 1277 +--R / +--R 3 2 +--R 90x + 174x + 112x + 24 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-7/3)/(2+3*x)^3+(-34)/(2+3*x)^2+(-505)/(2+3*x)+(-275)/(3+5*x)+_ + 3350*log(2+3*x)-3350*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3) +--R + +--R 4 3 2 +--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2) +--R + +--R 3 2 +--R - 90450x - 177885x - 116513x - 25413 +--R / +--R 4 3 2 +--R 405x + 1053x + 1026x + 444x + 72 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 1356750x - 3527550x - 3437100x - 1487400x - 241200)log(5x + 3) +--R + +--R 4 3 2 +--R (1356750x + 3527550x + 3437100x + 1487400x + 241200)log(3x + 2) +--R + +--R 3 2 +--R - 90450x - 177885x - 116513x - 25413 +--R / +--R 4 3 2 +--R 405x + 1053x + 1026x + 444x + 72 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-7/4)/(2+3*x)^4+(-68/3)/(2+3*x)^3+(-505/2)/(2+3*x)^2+_ + (-3350)/(2+3*x)+(-1375)/(3+5*x)+20875*log(2+3*x)-20875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x +--R + +--R - 12024000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x +--R + +--R 12024000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855 +--R / +--R 5 4 3 2 +--R 4860x + 15876x + 20736x + 13536x + 4416x + 576 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 101452500x - 331411500x - 432864000x - 282564000x - 92184000x +--R + +--R - 12024000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 101452500x + 331411500x + 432864000x + 282564000x + 92184000x +--R + +--R 12024000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 6763500x - 17810550x - 17580090x - 7708553x - 1266855 +--R / +--R 5 4 3 2 +--R 4860x + 15876x + 20736x + 13536x + 4416x + 576 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-7/5)/(2+3*x)^5+(-17)/(2+3*x)^4+(-505/3)/(2+3*x)^3+_ + (-1675)/(2+3*x)^2+(-20875)/(2+3*x)+(-6875)/(3+5*x)+_ + 125000*log(2+3*x)-125000*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x +--R + +--R 2 +--R - 6300000000x - 1650000000x - 180000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 2278125000x + 8960625000x + 14681250000x + 12825000000x +--R + +--R 2 +--R 6300000000x + 1650000000x + 180000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x +--R + +--R - 18964893 +--R / +--R 6 5 4 3 2 +--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 2278125000x - 8960625000x - 14681250000x - 12825000000x +--R + +--R 2 +--R - 6300000000x - 1650000000x - 180000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 2278125000x + 8960625000x + 14681250000x + 12825000000x +--R + +--R 2 +--R 6300000000x + 1650000000x + 180000000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 151875000x - 501187500x - 661387500x - 436271250x - 143844850x +--R + +--R - 18964893 +--R / +--R 6 5 4 3 2 +--R 18225x + 71685x + 117450x + 102600x + 50400x + 13200x + 1440 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-7/6)/(2+3*x)^6+(-68/5)/(2+3*x)^5+(-505/4)/(2+3*x)^4+_ + (-3350/3)/(2+3*x)^3+(-20875/2)/(2+3*x)^2+(-125000)/(2+3*x)+_ + (-34375)/(3+5*x)+728125*log(2+3*x)-728125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x +--R + +--R 3 2 +--R - 346005000000x - 136305000000x - 29824000000x - 2796000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R 53080312500x + 244169437500x + 481261500000x + 526871250000x +--R + +--R 3 2 +--R 346005000000x + 136305000000x + 29824000000x + 2796000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x +--R + +--R 2 +--R - 10128331755x - 2676272018x - 294588002 +--R / +--R 7 6 5 4 3 2 +--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x +--R + +--R 3840 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 53080312500x - 244169437500x - 481261500000x - 526871250000x +--R + +--R 3 2 +--R - 346005000000x - 136305000000x - 29824000000x - 2796000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R 53080312500x + 244169437500x + 481261500000x + 526871250000x +--R + +--R 3 2 +--R 346005000000x + 136305000000x + 29824000000x + 2796000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3538687500x - 14036793750x - 23195441250x - 20438672625x +--R + +--R 2 +--R - 10128331755x - 2676272018x - 294588002 +--R / +--R 7 6 5 4 3 2 +--R 72900x + 335340x + 660960x + 723600x + 475200x + 187200x + 40960x +--R + +--R 3840 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)*(2+3*x)^m/(3+5*x)^3 +--R +--R +--R m +--R (- 2x + 1)(3x + 2) +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-11/10*(2+3*x)^(1+m)/(3+5*x)^2+1/10*(37-33*m)*(2+3*x)^(1+m)/(3+5*x)+_ +-- 3/10*(37-33*m)*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 4374x - 18225x - 30618x - 24948x - 7560x + 3024x + 3360x + 1088x +--R + +--R 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=1851147/390625*x+129654/15625*x^2+2052/3125*x^3-181521/12500*x^4-_ + 51759/3125*x^5-729/125*x^6+(-11/3906250)/(3+5*x)^2+_ + (-229/1953125)/(3+5*x)+2037/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x +--R + +--R 6 5 4 3 2 +--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x +--R + +--R 333201880x - 2770 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (203700x + 244440x + 73332)log(5x + 3) - 1139062500x - 4601812500x +--R + +--R 6 5 4 3 2 +--R - 7128253125x - 4439846250x + 753519375x + 2916553500x + 1694131200x +--R + +--R 333201880x - 2770 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R 7 6 5 4 2 +--R - 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=36936/15625*x+297/125*x^2-6399/3125*x^3-12393/2500*x^4-_ + 1458/625*x^5+(-11/781250)/(3+5*x)^2+(-196/390625)/(3+5*x)+_ + 1449/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x +--R + +--R 5 4 3 2 +--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374 +--R / +--R 2 +--R 39062500x + 46875000x + 14062500 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (144900x + 173880x + 52164)log(5x + 3) - 91125000x - 302990625x +--R + +--R 5 4 3 2 +--R - 345161250x - 72883125x + 174919500x + 144220500x + 33238480x - 2374 +--R / +--R 2 +--R 39062500x + 46875000x + 14062500 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 486x - 1377x - 1350x - 360x + 240x + 176x + 32 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=3636/3125*x+1971/6250*x^2-837/625*x^3-243/250*x^4+_ + (-11/156250)/(3+5*x)^2+(-163/78125)/(3+5*x)+192/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 4 +--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x +--R + +--R 3 2 +--R 4140000x + 5897475x + 1634570x - 989 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 4 +--R (48000x + 57600x + 17280)log(5x + 3) - 3796875x - 9787500x - 6412500x +--R + +--R 3 2 +--R 4140000x + 5897475x + 1634570x - 989 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R - 162x - 351x - 216x + 24x + 64x + 16 +--R (1) ----------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=1647/3125*x-297/1250*x^2-54/125*x^3+(-11/31250)/(3+5*x)^2+_ + (-26/3125)/(3+5*x)+114/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x +--R + +--R 2 +--R 427275x + 146930x - 791 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (28500x + 34200x + 10260)log(5x + 3) - 337500x - 590625x + 67500x +--R + +--R 2 +--R 427275x + 146930x - 791 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R - 54x - 81x - 18x + 20x + 8 +--R (1) ------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=81/625*x-27/125*x^2+(-11/6250)/(3+5*x)^2+(-97/3125)/(3+5*x)+_ + 279/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x +--R + +--R 6320x - 593 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (13950x + 16740x + 5022)log(5x + 3) - 33750x - 20250x + 12150x +--R + +--R 6320x - 593 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 3 2 +--R - 18x - 15x + 4x + 4 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=-18/125*x+(-11/1250)/(3+5*x)^2+(-64/625)/(3+5*x)+87/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395 +--R (2) ------------------------------------------------------------------ +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (4350x + 5220x + 1566)log(5x + 3) - 4500x - 5400x - 2260x - 395 +--R (3) ------------------------------------------------------------------ +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 2 +--R - 6x - x + 2 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=(-11/250)/(3+5*x)^2+(-31/125)/(3+5*x)-6/125*log(3+5*x) +--R +--R +--R 2 +--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197 +--R (2) ---------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 300x - 360x - 108)log(5x + 3) - 310x - 197 +--R (3) ---------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)/(3+5*x)^3 +--R +--R +--R - 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=-1/22*(1-2*x)^2/(3+5*x)^2 +--R +--R +--R 2 2 2 1 +--R - --- x + --- x - --- +--R 275 275 550 +--R (2) ---------------------- +--R 2 6 9 +--R x + - x + -- +--R 5 25 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 20x + 1 +--R (3) -------------------- +--R 2 +--R 1250x + 1500x + 450 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) --- +--R 275 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)/((2+3*x)*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-11/10)/(3+5*x)^2+7/(3+5*x)-21*log(2+3*x)+21*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2) +--R + +--R 350x + 199 +--R / +--R 2 +--R 250x + 300x + 90 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (5250x + 6300x + 1890)log(5x + 3) + (- 5250x - 6300x - 1890)log(3x + 2) +--R + +--R 350x + 199 +--R / +--R 2 +--R 250x + 300x + 90 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=21/(2+3*x)+(-11/2)/(3+5*x)^2+68/(3+5*x)-309*log(2+3*x)+309*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (46350x + 86520x + 53766x + 11124)log(5x + 3) +--R + +--R 3 2 2 +--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172 +--R / +--R 3 2 +--R 150x + 280x + 174x + 36 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (46350x + 86520x + 53766x + 11124)log(5x + 3) +--R + +--R 3 2 2 +--R (- 46350x - 86520x - 53766x - 11124)log(3x + 2) + 3090x + 3811x + 1172 +--R / +--R 3 2 +--R 150x + 280x + 174x + 36 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R - 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=21/2/(2+3*x)^2+309/(2+3*x)+(-55/2)/(3+5*x)^2+505/(3+5*x)-_ + 3060*log(2+3*x)+3060*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2) +--R + +--R 3 2 +--R 91800x + 174420x + 110296x + 23213 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1377000x + 3488400x + 3310920x + 1395360x + 220320)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1377000x - 3488400x - 3310920x - 1395360x - 220320)log(3x + 2) +--R + +--R 3 2 +--R 91800x + 174420x + 110296x + 23213 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=7/(2+3*x)^3+309/2/(2+3*x)^2+3060/(2+3*x)+(-275/2)/(3+5*x)^2+3350/(3+5*x)-_ + 25350*log(2+3*x)+25350*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x +--R + +--R 3650400 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x +--R + +--R - 3650400 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2281500x + 5855850x + 5631080x + 2404363x + 384608 +--R / +--R 5 4 3 2 +--R 1350x + 4320x + 5526x + 3532x + 1128x + 144 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 34222500x + 109512000x + 140084100x + 89536200x + 28594800x +--R + +--R 3650400 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 34222500x - 109512000x - 140084100x - 89536200x - 28594800x +--R + +--R - 3650400 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 2281500x + 5855850x + 5631080x + 2404363x + 384608 +--R / +--R 5 4 3 2 +--R 1350x + 4320x + 5526x + 3532x + 1128x + 144 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=21/4/(2+3*x)^4+103/(2+3*x)^3+1530/(2+3*x)^2+25350/(2+3*x)+_ + (-1375/2)/(3+5*x)^2+20875/(3+5*x)-189375*log(2+3*x)+189375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 1533937500x + 5931225000x + 9551317500x + 8199180000x +--R + +--R 2 +--R 3957180000x + 1018080000x + 109080000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x +--R + +--R 2 +--R - 3957180000x - 1018080000x - 109080000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x +--R + +--R 11492725 +--R / +--R 6 5 4 3 2 +--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 1533937500x + 5931225000x + 9551317500x + 8199180000x +--R + +--R 2 +--R 3957180000x + 1018080000x + 109080000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 1533937500x - 5931225000x - 9551317500x - 8199180000x +--R + +--R 2 +--R - 3957180000x - 1018080000x - 109080000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 102262500x + 330648750x + 427381500x + 276035525x + 89085434x +--R + +--R 11492725 +--R / +--R 6 5 4 3 2 +--R 8100x + 31320x + 50436x + 43296x + 20896x + 5376x + 576 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3e.input.pamphlet b/src/input/rich3e.input.pamphlet new file mode 100644 index 0000000..9146b9c --- /dev/null +++ b/src/input/rich3e.input.pamphlet @@ -0,0 +1,6307 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 249 integrals in this file. +\item 249 supplied "optimal results". +\item 230 matching answers. +\item 24 cases where Axiom supplied 2 results. +\item 34 cases that Axiom failed to integrate. +\item 6 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3e.output +)spool rich3e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R - 2x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=21/5/(2+3*x)^5+309/4/(2+3*x)^4+1020/(2+3*x)^3+12675/(2+3*x)^2+_ + 189375/(2+3*x)+(-6875/2)/(3+5*x)^2+125000/(3+5*x)-_ + 1321875*log(2+3*x)+1321875*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x +--R + +--R 3 2 +--R 986647500000x + 382815000000x + 82485000000x + 7614000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x +--R + +--R 3 2 +--R - 986647500000x - 382815000000x - 82485000000x - 7614000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 10707187500x + 41758031250x + 67828050000x + 58733814375x +--R + +--R 2 +--R 28595335800x + 7421662135x + 802214966 +--R / +--R 7 6 5 4 3 2 +--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x +--R + +--R 62400x + 5760 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 160607812500x + 728088750000x + 1414062562500x + 1525179375000x +--R + +--R 3 2 +--R 986647500000x + 382815000000x + 82485000000x + 7614000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 4 +--R - 160607812500x - 728088750000x - 1414062562500x - 1525179375000x +--R + +--R 3 2 +--R - 986647500000x - 382815000000x - 82485000000x - 7614000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 10707187500x + 41758031250x + 67828050000x + 58733814375x +--R + +--R 2 +--R 28595335800x + 7421662135x + 802214966 +--R / +--R 7 6 5 4 3 2 +--R 121500x + 550800x + 1069740x + 1153800x + 746400x + 289600x +--R + +--R 62400x + 5760 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 131220x + 647352x + 1307097x + 1298835x + 476928x - 275184x +--R + +--R 5 4 3 2 +--R - 372960x - 134112x + 12800x + 24832x + 7424x + 768 +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 500 +r0:=-49/729*(2+3*x)^9+91/270*(2+3*x)^10-16/99*(2+3*x)^11+5/243*(2+3*x)^12 +--R +--R +--R (2) +--R 12 647352 11 1307097 10 9 8 7 +--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x +--R 11 10 +--R + +--R 6 134112 5 4 24832 3 2 2566144 +--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x + ------- +--R 5 3 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 647352 11 1307097 10 9 8 7 +--R 10935x + ------ x + ------- x + 144315x + 59616x - 39312x +--R 11 10 +--R + +--R 6 134112 5 4 24832 3 2 +--R - 62160x - ------ x + 3200x + ----- x + 3712x + 768x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R 2566144 +--R (4) - ------- +--R 40095 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 43740x + 186624x + 311283x + 225423x + 8694x - 97524x - 59304x +--R + +--R 3 2 +--R - 5168x + 7712x + 3136x + 384 +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 500 +r0:=-49/648*(2+3*x)^8+91/243*(2+3*x)^9-8/45*(2+3*x)^10+20/891*(2+3*x)^11 +--R +--R +--R (2) +--R 43740 11 93312 10 9 225423 8 7 6 59304 5 +--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x +--R 11 5 8 5 +--R + +--R 4 7712 3 2 485216 +--R - 1292x + ---- x + 1568x + 384x + ------ +--R 3 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 43740 11 93312 10 9 225423 8 7 6 59304 5 +--R ----- x + ----- x + 34587x + ------ x + 1242x - 16254x - ----- x +--R 11 5 8 5 +--R + +--R 4 7712 3 2 +--R - 1292x + ---- x + 1568x + 384x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R 485216 +--R (4) - ------ +--R 13365 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x + 1936x +--R + +--R 1280x + 192 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=192*x+640*x^2+1936/3*x^3-1372*x^4-4284*x^5-2772*x^6+4185*x^7+_ + 68769/8*x^8+5832*x^9+1458*x^10 +--R +--R +--R (2) +--R 10 9 68769 8 7 6 5 4 1936 3 +--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x +--R 8 3 +--R + +--R 2 +--R 640x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 68769 8 7 6 5 4 1936 3 +--R 1458x + 5832x + ----- x + 4185x - 2772x - 4284x - 1372x + ---- x +--R 8 3 +--R + +--R 2 +--R 640x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=96*x+248*x^2+224/3*x^3-770*x^4-1218*x^5+273/2*x^6+1917*x^7+1782*x^8+540*x^9 +--R +--R +--R (2) +--R 9 8 7 273 6 5 4 224 3 2 +--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 273 6 5 4 224 3 2 +--R 540x + 1782x + 1917x + --- x - 1218x - 770x + --- x + 248x + 96x +--R 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=48*x+88*x^2-152/3*x^3-328*x^4-1077/5*x^5+675/2*x^6+3672/7*x^7+405/2*x^8 +--R +--R +--R 405 8 3672 7 675 6 1077 5 4 152 3 2 +--R (2) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x +--R 2 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R 405 8 3672 7 675 6 1077 5 4 152 3 2 +--R (3) --- x + ---- x + --- x - ---- x - 328x - --- x + 88x + 48x +--R 2 7 2 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) 540x + 864x + 99x - 425x - 154x + 52x + 24 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=24*x+26*x^2-154/3*x^3-425/4*x^4+99/5*x^5+144*x^6+540/7*x^7 +--R +--R +--R 540 7 6 99 5 425 4 154 3 2 +--R (2) --- x + 144x + -- x - --- x - --- x + 26x + 24x +--R 7 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 540 7 6 99 5 425 4 154 3 2 +--R (3) --- x + 144x + -- x - --- x - --- x + 26x + 24x +--R 7 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) 180x + 168x - 79x - 89x + 8x + 12 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=12*x+4*x^2-89/3*x^3-79/4*x^4+168/5*x^5+30*x^6 +--R +--R +--R 6 168 5 79 4 89 3 2 +--R (2) 30x + --- x - -- x - -- x + 4x + 12x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 168 5 79 4 89 3 2 +--R (3) 30x + --- x - -- x - -- x + 4x + 12x +--R 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) 60x + 16x - 37x - 5x + 6 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=6*x-5/2*x^2-37/3*x^3+4*x^4+12*x^5 +--R +--R +--R 5 4 37 3 5 2 +--R (2) 12x + 4x - -- x - - x + 6x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 37 3 5 2 +--R (3) 12x + 4x - -- x - - x + 6x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^2*(3+5*x) +--R +--R +--R 3 2 +--R (1) 20x - 8x - 7x + 3 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=3*x-7/2*x^2-8/3*x^3+5*x^4 +--R +--R +--R 4 8 3 7 2 +--R (2) 5x - - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 8 3 7 2 +--R (3) 5x - - x - - x + 3x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x) +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=65/27*x-32/9*x^2+20/9*x^3-49/81*log(2+3*x) +--R +--R +--R 3 2 +--R - 49log(3x + 2) + 180x - 288x + 195x +--R (2) -------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 49log(3x + 2) + 180x - 288x + 195x +--R (3) -------------------------------------- +--R 81 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=-104/27*x+10/9*x^2+49/81/(2+3*x)+91/27*log(2+3*x) +--R +--R +--R 3 2 +--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49 +--R (2) --------------------------------------------------- +--R 243x + 162 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (819x + 546)log(3x + 2) + 270x - 756x - 624x + 49 +--R (3) --------------------------------------------------- +--R 243x + 162 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=20/27*x+49/162/(2+3*x)^2+(-91/27)/(2+3*x)-16/9*log(2+3*x) +--R +--R +--R 2 3 2 +--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043 +--R (2) --------------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 2592x - 3456x - 1152)log(3x + 2) + 1080x + 1440x - 1158x - 1043 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 1458x + 1944x + 648 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=49/243/(2+3*x)^3+(-91/54)/(2+3*x)^2+16/9/(2+3*x)+20/81*log(2+3*x) +--R +--R +--R 3 2 2 +--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916 +--R (2) ------------------------------------------------------------------ +--R 3 2 +--R 13122x + 26244x + 17496x + 3888 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +--R (3240x + 6480x + 4320x + 960)log(3x + 2) + 7776x + 7911x + 1916 +--R (3) ------------------------------------------------------------------ +--R 3 2 +--R 13122x + 26244x + 17496x + 3888 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=1/84*(1-2*x)^3/(2+3*x)^4-23/294*(1-2*x)^3/(2+3*x)^3 +--R +--R +--R 92 4 244 3 16 2 31 85 +--R ---- x - ----- x - ---- x + ---- x - ----- +--R 3969 11907 3969 3969 47628 +--R (2) --------------------------------------------- +--R 4 8 3 8 2 32 16 +--R x + - x + - x + -- x + -- +--R 3 3 27 81 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 2160x - 1728x - 516x - 167 +--R (3) ------------------------------------------- +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R 92 +--R (4) - ---- +--R 3969 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=49/405/(2+3*x)^5+(-91/108)/(2+3*x)^4+16/27/(2+3*x)^3+(-10/81)/(2+3*x)^2 +--R +--R +--R 10 3 4 2 5 49 +--R - --- x - --- x + ---- x - ----- +--R 729 729 8748 65610 +--R (2) --------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 1800x - 720x + 75x - 98 +--R (3) ----------------------------------------------------------- +--R 5 4 3 2 +--R 131220x + 437400x + 583200x + 388800x + 129600x + 17280 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--R 20x - 8x - 7x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=49/486/(2+3*x)^6+(-91/135)/(2+3*x)^5+4/9/(2+3*x)^4+(-20/243)/(2+3*x)^3 +--R +--R +--R 20 3 4 2 47 311 +--R - ---- x - ---- x + ----- x - ------- +--R 6561 6561 98415 1771470 +--R (2) ---------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R - 5400x - 1080x + 846x - 311 +--R / +--R 6 5 4 3 2 +--R 1771470x + 7085880x + 11809800x + 10497600x + 5248800x + 1399680x +--R + +--R 155520 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^2*(3+5*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--R 20x - 8x - 7x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=7/81/(2+3*x)^7+(-91/162)/(2+3*x)^6+16/45/(2+3*x)^5+(-5/81)/(2+3*x)^4 +--R +--R +--R 5 3 2 2 97 44 +--R - ---- x - ----- x + ------ x - ------ +--R 6561 32805 590490 885735 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R - 1350x - 108x + 291x - 88 +--R / +--R 7 6 5 4 3 2 +--R 1771470x + 8266860x + 16533720x + 18370800x + 12247200x + 4898880x +--R + +--R 1088640x + 103680 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R 656100x + 3630420x + 8477541x + 10415466x + 6281145x + 54864x +--R + +--R 6 5 4 3 2 +--R - 2690352x - 1789440x - 338336x + 162560x + 111616x + 26112x + 2304 +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 500 +r0:=49/2187*(2+3*x)^9-259/1215*(2+3*x)^10+503/891*(2+3*x)^11-_ + 185/729*(2+3*x)^12+100/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 656100 13 12 8477541 11 5207733 10 9 8 +--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x +--R 13 11 5 +--R + +--R 7 6 338336 5 4 111616 3 2 +--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x +--R 5 3 +--R + +--R 264616448 +--R --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 656100 13 12 8477541 11 5207733 10 9 8 +--R ------ x + 302535x + ------- x + ------- x + 697905x + 6858x +--R 13 11 5 +--R + +--R 7 6 338336 5 4 111616 3 2 +--R - 384336x - 298240x - ------ x + 40640x + ------ x + 13056x + 2304x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 264616448 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 218700x + 1064340x + 2116287x + 2060964x + 719739x - 461538x +--R + +--R 5 4 3 2 +--R - 589092x - 203752x + 23056x + 38816x + 11328x + 1152 +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 500 +r0:=1152*x+5664*x^2+38816/3*x^3+5764*x^4-203752/5*x^5-98182*x^6-65934*x^7+_ + 719739/8*x^8+228996*x^9+2116287/10*x^10+1064340/11*x^11+18225*x^12 +--R +--R +--R (2) +--R 12 1064340 11 2116287 10 9 719739 8 7 +--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x +--R 11 10 8 +--R + +--R 6 203752 5 4 38816 3 2 +--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 1064340 11 2116287 10 9 719739 8 7 +--R 18225x + ------- x + ------- x + 228996x + ------ x - 65934x +--R 11 10 8 +--R + +--R 6 203752 5 4 38816 3 2 +--R - 98182x - ------ x + 5764x + ----- x + 5664x + 1152x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 72900x + 306180x + 501309x + 352782x + 4725x - 156996x - 91700x +--R + +--R 3 2 +--R - 6784x + 12208x + 4800x + 576 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=576*x+2400*x^2+12208/3*x^3-1696*x^4-18340*x^5-26166*x^6+675*x^7+_ + 176391/4*x^8+55701*x^9+30618*x^10+72900/11*x^11 +--R +--R +--R (2) +--R 72900 11 10 9 176391 8 7 6 5 +--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x +--R 11 4 +--R + +--R 4 12208 3 2 +--R - 1696x + ----- x + 2400x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 72900 11 10 9 176391 8 7 6 5 +--R ----- x + 30618x + 55701x + ------ x + 675x - 26166x - 18340x +--R 11 4 +--R + +--R 4 12208 3 2 +--R - 1696x + ----- x + 2400x + 576x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x +--R + +--R 2 +--R 3152x + 1968x + 288 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=288*x+984*x^2+3152/3*x^3-2030*x^4-6734*x^5-9331/2*x^6+6336*x^7+_ + 109863/8*x^8+9540*x^9+2430*x^10 +--R +--R +--R (2) +--R 10 9 109863 8 7 9331 6 5 4 3152 3 +--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x +--R 8 2 3 +--R + +--R 2 +--R 984x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 109863 8 7 9331 6 5 4 3152 3 +--R 2430x + 9540x + ------ x + 6336x - ---- x - 6734x - 2030x + ---- x +--R 8 2 3 +--R + +--R 2 +--R 984x + 288x +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=144*x+384*x^2+424/3*x^3-1174*x^4-9791/5*x^5+115*x^6+21141/7*x^7+_ + 5805/2*x^8+900*x^9 +--R +--R +--R (2) +--R 9 5805 8 21141 7 6 9791 5 4 424 3 2 +--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x +--R 2 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 5805 8 21141 7 6 9791 5 4 424 3 2 +--R 900x + ---- x + ----- x + 115x - ---- x - 1174x + --- x + 384x + 144x +--R 2 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=72*x+138*x^2-202/3*x^3-2045/4*x^4-1828/5*x^5+1029/2*x^6+5940/7*x^7+_ + 675/2*x^8 +--R +--R +--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2 +--R (2) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x +--R 2 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 675 8 5940 7 1029 6 1828 5 2045 4 202 3 2 +--R (3) --- x + ---- x + ---- x - ---- x - ---- x - --- x + 138x + 72x +--R 2 7 2 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) 900x + 1380x + 109x - 682x - 227x + 84x + 36 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=36*x+42*x^2-227/3*x^3-341/2*x^4+109/5*x^5+230*x^6+900/7*x^7 +--R +--R +--R 900 7 6 109 5 341 4 227 3 2 +--R (2) --- x + 230x + --- x - --- x - --- x + 42x + 36x +--R 7 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 900 7 6 109 5 341 4 227 3 2 +--R (3) --- x + 230x + --- x - --- x - --- x + 42x + 36x +--R 7 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) 300x + 260x - 137x - 136x + 15x + 18 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=18*x+15/2*x^2-136/3*x^3-137/4*x^4+52*x^5+50*x^6 +--R +--R +--R 6 5 137 4 136 3 15 2 +--R (2) 50x + 52x - --- x - --- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 137 4 136 3 15 2 +--R (3) 50x + 52x - --- x - --- x + -- x + 18x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^2*(3+5*x)^2 +--R +--R +--R 4 3 2 +--R (1) 100x + 20x - 59x - 6x + 9 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=9*x-3*x^2-59/3*x^3+5*x^4+20*x^5 +--R +--R +--R 5 4 59 3 2 +--R (2) 20x + 5x - -- x - 3x + 9x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 59 3 2 +--R (3) 20x + 5x - -- x - 3x + 9x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x) +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=340/81*x-251/54*x^2-140/27*x^3+25/3*x^4+49/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x +--R (2) ------------------------------------------------ +--R 486 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 98log(3x + 2) + 4050x - 2520x - 2259x + 2040x +--R (3) ------------------------------------------------ +--R 486 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=143/27*x-170/27*x^2+100/27*x^3+(-49/243)/(2+3*x)-518/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49 +--R (2) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (- 1554x - 1036)log(3x + 2) + 2700x - 2790x + 801x + 2574x - 49 +--R (3) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ---------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=-20/3*x+50/27*x^2+(-49/486)/(2+3*x)^2+518/243/(2+3*x)+503/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x +--R + +--R - 9852x + 2023 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (27162x + 36216x + 12072)log(3x + 2) + 8100x - 18360x - 35280x +--R + +--R - 9852x + 2023 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=100/81*x+(-49/729)/(2+3*x)^3+259/243/(2+3*x)^2+(-503/81)/(2+3*x)-_ + 740/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x +--R + +--R 2 +--R - 8343x - 44793x - 16603 +--R / +--R 3 2 +--R 19683x + 39366x + 26244x + 5832 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (- 59940x - 119880x - 79920x - 17760)log(3x + 2) + 24300x + 48600x +--R + +--R 2 +--R - 8343x - 44793x - 16603 +--R / +--R 3 2 +--R 19683x + 39366x + 26244x + 5832 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-49/972)/(2+3*x)^4+518/729/(2+3*x)^3+(-503/162)/(2+3*x)^2+_ + 740/243/(2+3*x)+100/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x +--R + +--R 2 +--R 398034x + 217248x + 38821 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 3 +--R (97200x + 259200x + 259200x + 115200x + 19200)log(3x + 2) + 239760x +--R + +--R 2 +--R 398034x + 217248x + 38821 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=(-49/1215)/(2+3*x)^5+259/486/(2+3*x)^4+(-503/243)/(2+3*x)^3+_ + 370/243/(2+3*x)^2+(-100/243)/(2+3*x) +--R +--R +--R 100 4 430 3 683 2 1285 2014 +--R - --- x - ---- x - ---- x - ----- x - ------ +--R 729 2187 6561 39366 295245 +--R (2) ----------------------------------------------- +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 81000x - 116100x - 61470x - 19275x - 4028 +--R (3) -------------------------------------------------------------- +--R 5 4 3 2 +--R 590490x + 1968300x + 2624400x + 1749600x + 583200x + 77760 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-49/1458)/(2+3*x)^6+518/1215/(2+3*x)^5+(-503/324)/(2+3*x)^4+_ + 740/729/(2+3*x)^3+(-50/243)/(2+3*x)^2 +--R +--R +--R 50 4 460 3 389 2 227 4099 +--R - ---- x - ----- x - ----- x - ------ x - ------- +--R 2187 19683 78732 295245 5314410 +--R (2) ---------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 243000x - 248400x - 52515x - 8172x - 8198 +--R / +--R 6 5 4 3 2 +--R 10628820x + 42515280x + 70858800x + 62985600x + 31492800x + 8398080x +--R + +--R 933120 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^2*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-7/243)/(2+3*x)^7+259/729/(2+3*x)^6+(-503/405)/(2+3*x)^5+_ + 185/243/(2+3*x)^4+(-100/729)/(2+3*x)^3 +--R +--R +--R 100 4 245 3 41 2 487 1423 +--R - ----- x - ----- x + ------ x + ------- x - ------- +--R 19683 59049 295245 2657205 7971615 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 40500x - 33075x + 1107x + 1461x - 1423 +--R / +--R 7 6 5 4 3 +--R 7971615x + 37200870x + 74401740x + 82668600x + 55112400x +--R + +--R 2 +--R 22044960x + 4898880x + 466560 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^2*(2+3*x)^10*(3+5*x)^3 +--R +--R +--R (1) +--R 15 14 13 12 11 +--R 29524500x + 220449600x + 734077485x + 1417418757x + 1707104403x +--R + +--R 10 9 8 7 6 +--R 1233925083x + 360437040x - 236139300x - 320907744x - 154612896x +--R + +--R 5 4 3 2 +--R - 21254656x + 15928960x + 10576640x + 3002112x + 442368x + 27648 +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 500 +r0:=-49/8019*(2+3*x)^11+763/8748*(2+3*x)^12-4099/9477*(2+3*x)^13+_ + 8285/10206*(2+3*x)^14-760/2187*(2+3*x)^15+125/2916*(2+3*x)^16 +--R +--R +--R (2) +--R 7381125 16 15 734077485 14 1417418757 13 569034801 12 +--R ------- x + 14696640x + --------- x + ---------- x + --------- x +--R 4 14 13 4 +--R + +--R 1233925083 11 10 9 8 154612896 7 +--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x +--R 11 7 +--R + +--R 10627328 6 5 4 3 2 +--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x +--R 3 +--R + +--R 3336045568 +--R ---------- +--R 2189187 +--R Type: Polynomial(Fraction(Integer)) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7381125 16 15 734077485 14 1417418757 13 569034801 12 +--R ------- x + 14696640x + --------- x + ---------- x + --------- x +--R 4 14 13 4 +--R + +--R 1233925083 11 10 9 8 154612896 7 +--R ---------- x + 36043704x - 26237700x - 40113468x - --------- x +--R 11 7 +--R + +--R 10627328 6 5 4 3 2 +--R - -------- x + 3185792x + 2644160x + 1000704x + 221184x + 27648x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R 3336045568 +--R (4) - ---------- +--R 2189187 +--R Type: Polynomial(Fraction(Integer)) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^2*(2+3*x)^9*(3+5*x)^3 +--R +--R +--R (1) +--R 14 13 12 11 10 +--R 9841500x + 66922200x + 200077695x + 339087789x + 342976275x +--R + +--R 9 8 7 6 5 4 +--R 182657511x - 1625994x - 77629104x - 55216512x - 14726624x + 2732864x +--R + +--R 3 2 +--R 3487744x + 1200384x + 200448x + 13824 +--R Type: Polynomial(Integer) +--E 181 + +--S 182 of 500 +r0:=-49/7290*(2+3*x)^10+763/8019*(2+3*x)^11-4099/8748*(2+3*x)^12+_ + 8285/9477*(2+3*x)^13-1900/5103*(2+3*x)^14+100/2187*(2+3*x)^15 +--R +--R +--R (2) +--R 15 33461100 14 200077695 13 113029263 12 342976275 11 +--R 656100x + -------- x + --------- x + --------- x + --------- x +--R 7 13 4 11 +--R + +--R 182657511 10 9 8 55216512 7 7363312 6 +--R --------- x - 180666x - 9703638x - -------- x - ------- x +--R 10 7 3 +--R + +--R 2732864 5 4 3 2 9067849216 +--R ------- x + 871936x + 400128x + 100224x + 13824x + ---------- +--R 5 10945935 +--R Type: Polynomial(Fraction(Integer)) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 33461100 14 200077695 13 113029263 12 342976275 11 +--R 656100x + -------- x + --------- x + --------- x + --------- x +--R 7 13 4 11 +--R + +--R 182657511 10 9 8 55216512 7 7363312 6 +--R --------- x - 180666x - 9703638x - -------- x - ------- x +--R 10 7 3 +--R + +--R 2732864 5 4 3 2 +--R ------- x + 871936x + 400128x + 100224x + 13824x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R 9067849216 +--R (4) - ---------- +--R 10945935 +--R Type: Polynomial(Fraction(Integer)) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^2*(2+3*x)^8*(3+5*x)^3 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R 3280500x + 20120400x + 53278965x + 77509953x + 62652123x +--R + +--R 8 7 6 5 4 3 +--R 19117755x - 13287168x - 17018256x - 7060000x - 202208x + 1045760x +--R + +--R 2 +--R 465408x + 89856x + 6912 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=6912*x+44928*x^2+155136*x^3+261440*x^4-202208/5*x^5-3530000/3*x^6-_ + 17018256/7*x^7-1660896*x^8+2124195*x^9+62652123/10*x^10+_ + 77509953/11*x^11+17759655/4*x^12+20120400/13*x^13+1640250/7*x^14 +--R +--R +--R (2) +--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10 +--R ------- x + -------- x + -------- x + -------- x + -------- x +--R 7 13 4 11 10 +--R + +--R 9 8 17018256 7 3530000 6 202208 5 4 +--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x +--R 7 3 5 +--R + +--R 3 2 +--R 155136x + 44928x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1640250 14 20120400 13 17759655 12 77509953 11 62652123 10 +--R ------- x + -------- x + -------- x + -------- x + -------- x +--R 7 13 4 11 10 +--R + +--R 9 8 17018256 7 3530000 6 202208 5 4 +--R 2124195x - 1660896x - -------- x - ------- x - ------ x + 261440x +--R 7 3 5 +--R + +--R 3 2 +--R 155136x + 44928x + 6912x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^2*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R 1093500x + 5977800x + 13774455x + 16653681x + 9781587x - 148473x +--R + +--R 6 5 4 3 2 +--R - 4330074x - 2786036x - 495976x + 263248x + 173088x + 39744x + 3456 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=3456*x+19872*x^2+57696*x^3+65812*x^4-495976/5*x^5-1393018/3*x^6-_ + 618582*x^7-148473/8*x^8+1086843*x^9+16653681/10*x^10+_ + 13774455/11*x^11+498150*x^12+1093500/13*x^13 +--R +--R +--R (2) +--R 1093500 13 12 13774455 11 16653681 10 9 +--R ------- x + 498150x + -------- x + -------- x + 1086843x +--R 13 11 10 +--R + +--R 148473 8 7 1393018 6 495976 5 4 3 +--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x +--R 8 3 5 +--R + +--R 2 +--R 19872x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1093500 13 12 13774455 11 16653681 10 9 +--R ------- x + 498150x + -------- x + -------- x + 1086843x +--R 13 11 10 +--R + +--R 148473 8 7 1393018 6 495976 5 4 3 +--R - ------ x - 618582x - ------- x - ------ x + 65812x + 57696x +--R 8 3 5 +--R + +--R 2 +--R 19872x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^2*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R 364500x + 1749600x + 3425085x + 3267837x + 1081971x - 770805x +--R + +--R 5 4 3 2 +--R - 929488x - 309020x + 40688x + 60624x + 17280x + 1728 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=1728*x+8640*x^2+20208*x^3+10172*x^4-61804*x^5-464744/3*x^6-_ + 110115*x^7+1081971/8*x^8+363093*x^9+685017/2*x^10+1749600/11*x^11+_ + 30375*x^12 +--R +--R +--R (2) +--R 12 1749600 11 685017 10 9 1081971 8 7 +--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x +--R 11 2 8 +--R + +--R 464744 6 5 4 3 2 +--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 1749600 11 685017 10 9 1081971 8 7 +--R 30375x + ------- x + ------ x + 363093x + ------- x - 110115x +--R 11 2 8 +--R + +--R 464744 6 5 4 3 2 +--R - ------ x - 61804x + 10172x + 20208x + 8640x + 1728x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^2*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 121500x + 502200x + 806895x + 551349x - 6909x - 252329x - 141610x +--R + +--R 3 2 +--R - 8600x + 19296x + 7344x + 864 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=864*x+3672*x^2+6432*x^3-2150*x^4-28322*x^5-252329/6*x^6-987*x^7+_ + 551349/8*x^8+89655*x^9+50220*x^10+121500/11*x^11 +--R +--R +--R (2) +--R 121500 11 10 9 551349 8 7 252329 6 5 +--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x +--R 11 8 6 +--R + +--R 4 3 2 +--R - 2150x + 6432x + 3672x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 121500 11 10 9 551349 8 7 252329 6 5 +--R ------ x + 50220x + 89655x + ------ x - 987x - ------ x - 28322x +--R 11 8 6 +--R + +--R 4 3 2 +--R - 2150x + 6432x + 3672x + 864x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^2*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=432*x+1512*x^2+1704*x^3-2992*x^4-52853/5*x^5-46885/6*x^6+66873/7*x^7+_ + 175365/8*x^8+15600*x^9+4050*x^10 +--R +--R +--R (2) +--R 10 9 175365 8 66873 7 46885 6 52853 5 4 +--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x +--R 8 7 6 5 +--R + +--R 3 2 +--R 1704x + 1512x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 175365 8 66873 7 46885 6 52853 5 4 +--R 4050x + 15600x + ------ x + ----- x - ----- x - ----- x - 2992x +--R 8 7 6 5 +--R + +--R 3 2 +--R 1704x + 1512x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^2*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=216*x+594*x^2+258*x^3-7145/4*x^4-15709/5*x^5+121/6*x^6+33255/7*x^7+_ + 4725*x^8+1500*x^9 +--R +--R +--R (2) +--R 9 8 33255 7 121 6 15709 5 7145 4 3 2 +--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x +--R 7 6 5 4 +--R + +--R 216x +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 33255 7 121 6 15709 5 7145 4 3 2 +--R 1500x + 4725x + ----- x + --- x - ----- x - ---- x + 258x + 594x +--R 7 6 5 4 +--R + +--R 216x +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^2*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=108*x+216*x^2-87*x^3-3181/4*x^4-3083/5*x^5+4685/6*x^6+9600/7*x^7+1125/2*x^8 +--R +--R +--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2 +--R (2) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x +--R 2 7 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1125 8 9600 7 4685 6 3083 5 3181 4 3 2 +--R (3) ---- x + ---- x + ---- x - ---- x - ---- x - 87x + 216x + 108x +--R 2 7 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^2*(2+3*x)*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) 1500x + 2200x + 95x - 1091x - 333x + 135x + 54 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=54*x+135/2*x^2-111*x^3-1091/4*x^4+19*x^5+1100/3*x^6+1500/7*x^7 +--R +--R +--R 1500 7 1100 6 5 1091 4 3 135 2 +--R (2) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x +--R 7 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1500 7 1100 6 5 1091 4 3 135 2 +--R (3) ---- x + ---- x + 19x - ---- x - 111x + --- x + 54x +--R 7 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^2*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R (1) 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 500 +r0:=27*x+27/2*x^2-69*x^3-235/4*x^4+80*x^5+250/3*x^6 +--R +--R +--R 250 6 5 235 4 3 27 2 +--R (2) --- x + 80x - --- x - 69x + -- x + 27x +--R 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R 250 6 5 235 4 3 27 2 +--R (3) --- x + 80x - --- x - 69x + -- x + 27x +--R 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x) +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=3305/243*x-559/162*x^2-2515/81*x^3+50/9*x^4+100/3*x^5-49/729*log(2+3*x) +--R +--R +--R 5 4 3 2 +--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x +--R (2) -------------------------------------------------------------- +--R 1458 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 98log(3x + 2) + 48600x + 8100x - 45270x - 5031x + 19830x +--R (3) -------------------------------------------------------------- +--R 1458 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=1271/243*x-305/54*x^2-800/81*x^3+125/9*x^4+49/729/(2+3*x)+_ + 763/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98 +--R ----------------------------------------------------------------------------- +--R 4374x + 2916 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (4578x + 3052)log(3x + 2) + 60750x - 2700x - 53505x + 6408x + 15252x + 98 +--R ----------------------------------------------------------------------------- +--R 4374x + 2916 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=895/81*x-100/9*x^2+500/81*x^3+49/1458/(2+3*x)^2+(-763/729)/(2+3*x)-_ + 4099/729*log(2+3*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x +--R + +--R 2 +--R 128520x + 59862x - 3003 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 73782x - 98376x - 32792)log(3x + 2) + 81000x - 37800x - 13410x +--R + +--R 2 +--R 128520x + 59862x - 3003 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ---------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=-2800/243*x+250/81*x^2+49/2187/(2+3*x)^3+(-763/1458)/(2+3*x)^2+_ + 4099/729/(2+3*x)+8285/729*log(2+3*x) +--R +--R +--R (2) +--R 3 2 5 +--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x +--R + +--R 4 3 2 +--R - 631800x - 2235600x - 1485054x - 114939x + 93896 +--R / +--R 3 2 +--R 118098x + 236196x + 157464x + 34992 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 +--R (1342170x + 2684340x + 1789560x + 397680)log(3x + 2) + 364500x +--R + +--R 4 3 2 +--R - 631800x - 2235600x - 1485054x - 114939x + 93896 +--R / +--R 3 2 +--R 118098x + 236196x + 157464x + 34992 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=500/243*x+49/2916/(2+3*x)^4+(-763/2187)/(2+3*x)^3+4099/1458/(2+3*x)^2+_ + (-8285/729)/(2+3*x)-3800/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2) +--R + +--R 5 4 3 2 +--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 3693600x - 9849600x - 9849600x - 4377600x - 729600)log(3x + 2) +--R + +--R 5 4 3 2 +--R 1458000x + 3888000x + 1203660x - 3419334x - 3005148x - 702941 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=49/3645/(2+3*x)^5+(-763/2916)/(2+3*x)^4+4099/2187/(2+3*x)^3+_ + (-8285/1458)/(2+3*x)^2+3800/729/(2+3*x)+500/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218 +--R / +--R 5 4 3 2 +--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (7290000x + 24300000x + 32400000x + 21600000x + 7200000x + 960000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 18468000x + 42537150x + 36564120x + 13889625x + 1965218 +--R / +--R 5 4 3 2 +--R 10628820x + 35429400x + 47239200x + 31492800x + 10497600x + 1399680 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=49/4374/(2+3*x)^6+(-763/3645)/(2+3*x)^5+4099/2916/(2+3*x)^4+_ + (-8285/2187)/(2+3*x)^3+1900/729/(2+3*x)^2+(-500/729)/(2+3*x) +--R +--R +--R 500 5 3100 4 22685 3 39781 2 41968 116741 +--R - ---- x - ---- x - ----- x - ------ x - ------ x - -------- +--R 2187 6561 59049 236196 885735 15943230 +--R (2) ---------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 7290000x - 15066000x - 12249900x - 5370435x - 1510848x - 233482 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^2*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=7/729/(2+3*x)^7+(-763/4374)/(2+3*x)^6+4099/3645/(2+3*x)^5+_ + (-8285/2916)/(2+3*x)^4+3800/2187/(2+3*x)^3+(-250/729)/(2+3*x)^2 +--R +--R +--R 250 5 3700 4 23255 3 12077 2 35089 19072 +--R - ---- x - ----- x - ------ x - ------- x - -------- x - -------- +--R 6561 59049 708588 1771470 15943230 23914845 +--R (2) --------------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 3645000x - 5994000x - 3139425x - 652158x - 210534x - 76288 +--R / +--R 7 6 5 4 3 +--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x +--R + +--R 2 +--R 264539520x + 58786560x + 5598720 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=83333293/1953125*x+80555569/781250*x^2+1327159/78125*x^3-_ + 20577159/62500*x^4-7315947/15625*x^5+130383/1250*x^6+_ + 672867/875*x^7+16767/25*x^8+972/5*x^9+121/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x +--R + +--R 6 5 4 3 +--R 28521281250x - 128029072500x - 90025070625x + 4645056500x +--R + +--R 2 +--R 28194449150x + 11666661020x +--R / +--R 273437500 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 3388log(5x + 3) + 53156250000x + 183389062500x + 210270937500x +--R + +--R 6 5 4 3 +--R 28521281250x - 128029072500x - 90025070625x + 4645056500x +--R + +--R 2 +--R 28194449150x + 11666661020x +--R / +--R 273437500 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=8333293/390625*x+5555569/156250*x^2-422841/15625*x^3-_ + 1677159/12500*x^4-228447/3125*x^5+35883/250*x^6+34992/175*x^7+_ + 729/10*x^8+121/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x +--R + +--R 5 4 3 2 +--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x +--R / +--R 54687500 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 3388log(5x + 3) + 3986718750x + 10935000000x + 7849406250x +--R + +--R 5 4 3 2 +--R - 3997822500x - 7337570625x - 1479943500x + 1944449150x + 1166661020x +--R / +--R 54687500 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=833293/78125*x+305569/31250*x^2-72841/3125*x^3-102159/2500*x^4+_ + 7803/625*x^5+1404/25*x^6+972/35*x^7+121/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x +--R + +--R 3 2 +--R - 254943500x + 106949150x + 116661020x +--R / +--R 10937500 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 3388log(5x + 3) + 303750000x + 614250000x + 136552500x - 446945625x +--R + +--R 3 2 +--R - 254943500x + 106949150x + 116661020x +--R / +--R 10937500 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=83293/15625*x+5569/6250*x^2-7841/625*x^3-3159/500*x^4+1728/125*x^5+_ + 54/5*x^6+121/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x +--R + +--R 1665860x +--R / +--R 312500 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 484log(5x + 3) + 3375000x + 4320000x - 1974375x - 3920500x + 278450x +--R + +--R 1665860x +--R / +--R 312500 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x) +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=8293/3125*x-1931/1250*x^2-591/125*x^3+54/25*x^4+108/25*x^5+_ + 121/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x +--R (2) ----------------------------------------------------------------- +--R 31250 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 242log(5x + 3) + 135000x + 67500x - 147750x - 48275x + 82930x +--R (3) ----------------------------------------------------------------- +--R 31250 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x) +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=793/625*x-431/250*x^2-16/25*x^3+9/5*x^4+121/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x +--R (2) --------------------------------------------------- +--R 6250 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 242log(5x + 3) + 11250x - 4000x - 10775x + 7930x +--R (3) --------------------------------------------------- +--R 6250 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x) +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=43/125*x-28/25*x^2+4/5*x^3+121/625*log(3+5*x) +--R +--R +--R 3 2 +--R 121log(5x + 3) + 500x - 700x + 215x +--R (2) ------------------------------------- +--R 625 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 121log(5x + 3) + 500x - 700x + 215x +--R (3) ------------------------------------- +--R 625 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^2/(3+5*x) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------ +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-32/25*x+2/5*x^2+121/125*log(3+5*x) +--R +--R +--R 2 +--R 121log(5x + 3) + 50x - 160x +--R (2) ---------------------------- +--R 125 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 121log(5x + 3) + 50x - 160x +--R (3) ---------------------------- +--R 125 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=4/15*x-49/9*log(2+3*x)+121/25*log(3+5*x) +--R +--R +--R 1089log(5x + 3) - 1225log(3x + 2) + 60x +--R (2) --------------------------------------- +--R 225 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1089log(5x + 3) - 1225log(3x + 2) + 60x +--R (3) --------------------------------------- +--R 225 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=49/9/(2+3*x)-217/9*log(2+3*x)+121/5*log(3+5*x) +--R +--R +--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245 +--R (2) ------------------------------------------------------------- +--R 135x + 90 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3267x + 2178)log(5x + 3) + (- 3255x - 2170)log(3x + 2) + 245 +--R (3) ------------------------------------------------------------- +--R 135x + 90 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=49/18/(2+3*x)^2+217/9/(2+3*x)-121*log(2+3*x)+121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (19602x + 26136x + 8712)log(5x + 3) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917 +--R / +--R 2 +--R 162x + 216x + 72 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (19602x + 26136x + 8712)log(5x + 3) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(3x + 2) + 1302x + 917 +--R / +--R 2 +--R 162x + 216x + 72 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=49/27/(2+3*x)^3+217/18/(2+3*x)^2+121/(2+3*x)-605*log(2+3*x)+605*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3) +--R + +--R 3 2 2 +--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x +--R + +--R 80361x + 27536 +--R / +--R 3 2 +--R 1458x + 2916x + 1944x + 432 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (882090x + 1764180x + 1176120x + 261360)log(5x + 3) +--R + +--R 3 2 2 +--R (- 882090x - 1764180x - 1176120x - 261360)log(3x + 2) + 58806x +--R + +--R 80361x + 27536 +--R / +--R 3 2 +--R 1458x + 2916x + 1944x + 432 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=49/36/(2+3*x)^4+217/27/(2+3*x)^3+121/2/(2+3*x)^2+605/(2+3*x)-_ + 3025*log(2+3*x)+3025*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2) +--R + +--R 3 2 +--R 1764180x + 3587166x + 2433252x + 550739 +--R / +--R 4 3 2 +--R 8748x + 23328x + 23328x + 10368x + 1728 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (26462700x + 70567200x + 70567200x + 31363200x + 5227200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 26462700x - 70567200x - 70567200x - 31363200x - 5227200)log(3x + 2) +--R + +--R 3 2 +--R 1764180x + 3587166x + 2433252x + 550739 +--R / +--R 4 3 2 +--R 8748x + 23328x + 23328x + 10368x + 1728 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=49/45/(2+3*x)^5+217/36/(2+3*x)^4+121/3/(2+3*x)^3+605/2/(2+3*x)^2+_ + 3025/(2+3*x)-15125*log(2+3*x)+15125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x +--R + +--R 87120000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 661567500x - 2205225000x - 2940300000x - 1960200000x +--R + +--R - 653400000x - 87120000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006 +--R / +--R 5 4 3 2 +--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 661567500x + 2205225000x + 2940300000x + 1960200000x + 653400000x +--R + +--R 87120000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 661567500x - 2205225000x - 2940300000x - 1960200000x +--R + +--R - 653400000x - 87120000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 44104500x + 119082150x + 120617640x + 54322575x + 9179006 +--R / +--R 5 4 3 2 +--R 43740x + 145800x + 194400x + 129600x + 43200x + 5760 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=49/54/(2+3*x)^6+217/45/(2+3*x)^5+121/4/(2+3*x)^4+605/3/(2+3*x)^3+_ + 3025/2/(2+3*x)^2+15125/(2+3*x)-75625*log(2+3*x)+75625*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 29770537500x + 119082150000x + 198470250000x + 176418000000x +--R + +--R 2 +--R 88209000000x + 23522400000x + 2613600000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x +--R + +--R 2 +--R - 88209000000x - 23522400000x - 2613600000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x +--R + +--R 275370238 +--R / +--R 6 5 4 3 2 +--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 29770537500x + 119082150000x + 198470250000x + 176418000000x +--R + +--R 2 +--R 88209000000x + 23522400000x + 2613600000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 29770537500x - 119082150000x - 198470250000x - 176418000000x +--R + +--R 2 +--R - 88209000000x - 23522400000x - 2613600000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1984702500x + 6681831750x + 9000258300x + 6063045615x + 2042732232x +--R + +--R 275370238 +--R / +--R 6 5 4 3 2 +--R 393660x + 1574640x + 2624400x + 2332800x + 1166400x + 311040x + 34560 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=7/9/(2+3*x)^7+217/54/(2+3*x)^6+121/5/(2+3*x)^5+605/4/(2+3*x)^4+_ + 3025/3/(2+3*x)^3+15125/2/(2+3*x)^2+75625/(2+3*x)-378125*log(2+3*x)+_ + 378125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x +--R + +--R 3 2 +--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 446558062500x - 2083937625000x - 4167875250000x +--R + +--R 4 3 2 +--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x +--R + +--R - 26136000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 29770537500x + 120074501250x + 201822192000x + 180948267225x +--R + +--R 2 +--R 91271440062x + 24557875626x + 2753702432 +--R / +--R 7 6 5 4 3 2 +--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x +--R + +--R 725760x + 69120 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 446558062500x + 2083937625000x + 4167875250000x + 4630972500000x +--R + +--R 3 2 +--R 3087315000000x + 1234926000000x + 274428000000x + 26136000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 446558062500x - 2083937625000x - 4167875250000x +--R + +--R 4 3 2 +--R - 4630972500000x - 3087315000000x - 1234926000000x - 274428000000x +--R + +--R - 26136000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 29770537500x + 120074501250x + 201822192000x + 180948267225x +--R + +--R 2 +--R 91271440062x + 24557875626x + 2753702432 +--R / +--R 7 6 5 4 3 2 +--R 1180980x + 5511240x + 11022480x + 12247200x + 8164800x + 3265920x +--R + +--R 725760x + 69120 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=27776932/1953125*x+17592879/781250*x^2-1512378/78125*x^3-_ + 213867/2500*x^4-656424/15625*x^5+116397/1250*x^6+_ + 107892/875*x^7+2187/50*x^8+(-121/9765625)/(3+5*x)+2497/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 +--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x +--R + +--R 7 6 5 4 +--R 228457968750x + 18948431250x - 151420775625x - 96641724375x +--R + +--R 3 2 +--R 14907569250x + 37916375350x + 11666311440x - 3388 +--R / +--R 1367187500x + 820312500 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (349580x + 209748)log(5x + 3) + 59800781250x + 204461718750x +--R + +--R 7 6 5 4 +--R 228457968750x + 18948431250x - 151420775625x - 96641724375x +--R + +--R 3 2 +--R 14907569250x + 37916375350x + 11666311440x - 3388 +--R / +--R 1367187500x + 820312500 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=2777053/390625*x+463086/78125*x^2-48771/3125*x^3-_ + 157599/6250*x^4+28917/3125*x^5+4374/125*x^6+2916/175*x^7+_ + (-121/1953125)/(3+5*x)+2134/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x +--R + +--R 5 4 3 2 +--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x +--R + +--R - 1694 +--R / +--R 136718750x + 82031250 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R (149380x + 89628)log(5x + 3) + 2278125000x + 6150937500x + 4135556250x +--R + +--R 5 4 3 2 +--R - 2688406875x - 4202218125x - 469838250x + 1458208850x + 583181130x +--R + +--R - 1694 +--R / +--R 136718750x + 82031250 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=277174/78125*x+1893/6250*x^2-25332/3125*x^3-8721/2500*x^4+_ + 5508/625*x^5+162/25*x^6+(-121/390625)/(3+5*x)+1771/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x +--R + +--R 4 3 2 +--R - 79681875x - 35631750x + 29137150x + 16630440x - 484 +--R / +--R 7812500x + 4687500 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (35420x + 21252)log(5x + 3) + 50625000x + 99225000x + 14056875x +--R + +--R 4 3 2 +--R - 79681875x - 35631750x + 29137150x + 16630440x - 484 +--R / +--R 7812500x + 4687500 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=5459/3125*x-3621/3125*x^2-1809/625*x^3+189/125*x^4+324/125*x^5+_ + (-121/78125)/(3+5*x)+1408/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x +--R + +--R 2 +--R 410800x + 409425x - 121 +--R / +--R 390625x + 234375 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (7040x + 4224)log(5x + 3) + 1012500x + 1198125x - 776250x - 1131000x +--R + +--R 2 +--R 410800x + 409425x - 121 +--R / +--R 390625x + 234375 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=2416/3125*x-1449/1250*x^2-36/125*x^3+27/25*x^4+(-121/15625)/(3+5*x)+_ + 209/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x +--R + +--R 72480x - 242 +--R / +--R 156250x + 93750 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (10450x + 6270)log(5x + 3) + 168750x + 56250x - 208125x + 12125x +--R + +--R 72480x - 242 +--R / +--R 156250x + 93750 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=37/625*x-78/125*x^2+12/25*x^3+(-121/3125)/(3+5*x)+682/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121 +--R (2) ----------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (3410x + 2046)log(5x + 3) + 7500x - 5250x - 4925x + 555x - 121 +--R (3) ----------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=-92/125*x+6/25*x^2+(-121/625)/(3+5*x)+319/625*log(3+5*x) +--R +--R +--R 3 2 +--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121 +--R (2) ------------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (1595x + 957)log(5x + 3) + 750x - 1850x - 1380x - 121 +--R (3) ------------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^2/(3+5*x)^2 +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=4/25*x+(-121/125)/(3+5*x)-44/125*log(3+5*x) +--R +--R +--R 2 +--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121 +--R (2) --------------------------------------------- +--R 625x + 375 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 220x - 132)log(5x + 3) + 100x + 60x - 121 +--R (3) --------------------------------------------- +--R 625x + 375 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-121/25)/(3+5*x)+49/3*log(2+3*x)-407/25*log(3+5*x) +--R +--R +--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363 +--R (2) ------------------------------------------------------------- +--R 375x + 225 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 6105x - 3663)log(5x + 3) + (6125x + 3675)log(3x + 2) - 363 +--R (3) ------------------------------------------------------------- +--R 375x + 225 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-49/3)/(2+3*x)+(-121/5)/(3+5*x)+154*log(2+3*x)-154*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 34650x - 43890x - 13860)log(5x + 3) +--R + +--R 2 +--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461 +--R / +--R 2 +--R 225x + 285x + 90 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 34650x - 43890x - 13860)log(5x + 3) +--R + +--R 2 +--R (34650x + 43890x + 13860)log(3x + 2) - 2314x - 1461 +--R / +--R 2 +--R 225x + 285x + 90 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-49/6)/(2+3*x)^2+(-154)/(2+3*x)+(-121)/(3+5*x)+1133*log(2+3*x)-_ + 1133*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3) +--R + +--R 3 2 2 +--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x +--R + +--R - 8595 +--R / +--R 3 2 +--R 270x + 522x + 336x + 72 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 305910x - 591426x - 380688x - 81576)log(5x + 3) +--R + +--R 3 2 2 +--R (305910x + 591426x + 380688x + 81576)log(3x + 2) - 20394x - 26513x +--R + +--R - 8595 +--R / +--R 3 2 +--R 270x + 522x + 336x + 72 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-49/9)/(2+3*x)^3+(-77)/(2+3*x)^2+(-1133)/(2+3*x)+(-605)/(3+5*x)+_ + 7480*log(2+3*x)-7480*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3) +--R + +--R 4 3 2 +--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2) +--R + +--R 3 2 +--R - 605880x - 1191564x - 780464x - 170229 +--R / +--R 4 3 2 +--R 1215x + 3159x + 3078x + 1332x + 216 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 9088200x - 23629320x - 23023440x - 9963360x - 1615680)log(5x + 3) +--R + +--R 4 3 2 +--R (9088200x + 23629320x + 23023440x + 9963360x + 1615680)log(3x + 2) +--R + +--R 3 2 +--R - 605880x - 1191564x - 780464x - 170229 +--R / +--R 4 3 2 +--R 1215x + 3159x + 3078x + 1332x + 216 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-49/12)/(2+3*x)^4+(-154/3)/(2+3*x)^3+(-1133/2)/(2+3*x)^2+_ + (-7480)/(2+3*x)+(-3025)/(3+5*x)+46475*log(2+3*x)-46475*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x +--R + +--R - 8923200 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x +--R + +--R 8923200 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153 +--R / +--R 5 4 3 2 +--R 1620x + 5292x + 6912x + 4512x + 1472x + 192 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 75289500x - 245945700x - 321235200x - 209695200x - 68411200x +--R + +--R - 8923200 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 75289500x + 245945700x + 321235200x + 209695200x + 68411200x +--R + +--R 8923200 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 5019300x - 13217490x - 13046462x - 5720639x - 940153 +--R / +--R 5 4 3 2 +--R 1620x + 5292x + 6912x + 4512x + 1472x + 192 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-49/15)/(2+3*x)^5+(-77/2)/(2+3*x)^4+(-1133/3)/(2+3*x)^3+_ + (-3740)/(2+3*x)^2+(-46475)/(2+3*x)+(-15125)/(3+5*x)+_ + 277750*log(2+3*x)-277750*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x +--R + +--R 2 +--R - 27997200000x - 7332600000x - 799920000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 10123987500x + 39821017500x + 65243475000x + 56994300000x +--R + +--R 2 +--R 27997200000x + 7332600000x + 799920000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x +--R + +--R - 84279984 +--R / +--R 6 5 4 3 2 +--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 10123987500x - 39821017500x - 65243475000x - 56994300000x +--R + +--R 2 +--R - 27997200000x - 7332600000x - 799920000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 10123987500x + 39821017500x + 65243475000x + 56994300000x +--R + +--R 2 +--R 27997200000x + 7332600000x + 799920000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 674932500x - 2227277250x - 2939206050x - 1938789435x - 639246515x +--R + +--R - 84279984 +--R / +--R 6 5 4 3 2 +--R 36450x + 143370x + 234900x + 205200x + 100800x + 26400x + 2880 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-49/18)/(2+3*x)^6+(-154/5)/(2+3*x)^5+(-1133/4)/(2+3*x)^4+_ + (-7480/3)/(2+3*x)^3+(-46475/2)/(2+3*x)^2+(-277750)/(2+3*x)+_ + (-75625)/(3+5*x)+1615625*log(2+3*x)-1615625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 1060011562500x - 4876053187500x - 9610771500000x +--R + +--R 4 3 2 +--R - 10521596250000x - 6909705000000x - 2722005000000x +--R + +--R - 595584000000x - 55836000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 1060011562500x + 4876053187500x + 9610771500000x +--R + +--R 4 3 2 +--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x +--R + +--R 55836000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x +--R + +--R 2 +--R - 202262350455x - 53445037346x - 5882909754 +--R / +--R 7 6 5 4 3 2 +--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x +--R + +--R 368640x + 34560 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 1060011562500x - 4876053187500x - 9610771500000x +--R + +--R 4 3 2 +--R - 10521596250000x - 6909705000000x - 2722005000000x +--R + +--R - 595584000000x - 55836000000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 1060011562500x + 4876053187500x + 9610771500000x +--R + +--R 4 3 2 +--R 10521596250000x + 6909705000000x + 2722005000000x + 595584000000x +--R + +--R 55836000000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 70667437500x - 280314168750x - 463211966250x - 408159415125x +--R + +--R 2 +--R - 202262350455x - 53445037346x - 5882909754 +--R / +--R 7 6 5 4 3 2 +--R 656100x + 3018060x + 5948640x + 6512400x + 4276800x + 1684800x +--R + +--R 368640x + 34560 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-7/3)/(2+3*x)^7+(-77/3)/(2+3*x)^6+(-1133/5)/(2+3*x)^5+_ + (-1870)/(2+3*x)^4+(-46475/3)/(2+3*x)^3+(-138875)/(2+3*x)^2+_ + (-1615625)/(2+3*x)+(-378125)/(3+5*x)+9212500*log(2+3*x)-9212500*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 1511080312500x - 7958356312500x - 18334441125000x +--R + +--R 5 4 3 +--R - 24132512250000x - 19849252500000x - 10446975000000x +--R + +--R 2 +--R - 3435894000000x - 645612000000x - 53064000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 1511080312500x + 7958356312500x + 18334441125000x +--R + +--R 5 4 3 +--R 24132512250000x + 19849252500000x + 10446975000000x +--R + +--R 2 +--R 3435894000000x + 645612000000x + 53064000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x +--R + +--R 3 2 +--R - 676227617505x - 268408563588x - 59178013234x - 5590850403 +--R / +--R 8 7 6 5 4 3 +--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x +--R + +--R 2 +--R 372960x + 70080x + 5760 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 1511080312500x - 7958356312500x - 18334441125000x +--R + +--R 5 4 3 +--R - 24132512250000x - 19849252500000x - 10446975000000x +--R + +--R 2 +--R - 3435894000000x - 645612000000x - 53064000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 1511080312500x + 7958356312500x + 18334441125000x +--R + +--R 5 4 3 +--R 24132512250000x + 19849252500000x + 10446975000000x +--R + +--R 2 +--R 3435894000000x + 645612000000x + 53064000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 100738687500x - 466755918750x - 926721303750x - 1022059900125x +--R + +--R 3 2 +--R - 676227617505x - 268408563588x - 59178013234x - 5590850403 +--R / +--R 8 7 6 5 4 3 +--R 164025x + 863865x + 1990170x + 2619540x + 2154600x + 1134000x +--R + +--R 2 +--R 372960x + 70080x + 5760 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^2*(2+3*x)^8/(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=92582457/9765625*x+55559043/3906250*x^2-5350194/390625*x^3-_ + 1700919/31250*x^4-74601/3125*x^5+376407/6250*x^6+332424/4375*x^7+_ + 6561/250*x^8+(-121/97656250)/(3+5*x)^2+(-572/9765625)/(3+5*x)+_ + 5888/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 10 +--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x +--R + +--R 9 8 7 6 +--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x +--R + +--R 5 4 3 2 +--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x +--R + +--R 58326747710x - 120967 +--R / +--R 2 +--R 17089843750x + 20507812500x + 6152343750 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 +--R (10304000x + 12364800x + 3709440)log(5x + 3) + 448505859375x +--R + +--R 9 8 7 6 +--R 1836738281250x + 2748937500000x + 1294582500000x - 1049233500000x +--R + +--R 5 4 3 2 +--R - 1497169800000x - 372682800000x + 369438720000x + 281928652425x +--R + +--R 58326747710x - 120967 +--R / +--R 2 +--R 17089843750x + 20507812500x + 6152343750 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^2*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=9251661/1953125*x+1390203/390625*x^2-162612/15625*x^3-_ + 193833/12500*x^4+104247/15625*x^5+13608/625*x^6+8748/875*x^7+_ + (-121/19531250)/(3+5*x)^2+(-2497/9765625)/(3+5*x)+21949/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 9 +--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x +--R + +--R 8 7 6 5 +--R 230850000000x + 248816812500x + 2308753125x - 181926753750x +--R + +--R 4 3 2 +--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (15364300x + 18437160x + 5531148)log(5x + 3) + 68343750000x +--R + +--R 8 7 6 5 +--R 230850000000x + 248816812500x + 2308753125x - 181926753750x +--R + +--R 4 3 2 +--R - 99203619375x + 35963686500x + 47615255100x + 11656743280x - 211442 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^2*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R (1) ---------------------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=920502/390625*x+189/15625*x^2-16299/3125*x^3-23571/12500*x^4+_ + 17496/3125*x^5+486/125*x^6+(-121/3906250)/(3+5*x)^2+_ + (-2134/1953125)/(3+5*x)+15547/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x +--R + +--R 6 5 4 3 2 +--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x +--R + +--R 165647680x - 25850 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (1554700x + 1865640x + 559692)log(5x + 3) + 759375000x + 2004750000x +--R + +--R 6 5 4 3 2 +--R 1217278125x - 1066983750x - 1352649375x + 96358500x + 553151700x +--R + +--R 165647680x - 25850 +--R / +--R 2 +--R 195312500x + 234375000x + 70312500 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^2*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R (1) ----------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=17796/15625*x-5301/6250*x^2-5499/3125*x^3+648/625*x^4+972/625*x^5+_ + (-121/781250)/(3+5*x)^2+(-1771/390625)/(3+5*x)+10234/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x +--R + +--R 5 4 3 2 +--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (511700x + 614040x + 184212)log(5x + 3) + 30375000x + 56700000x +--R + +--R 5 4 3 2 +--R 866250x - 50518125x - 10006500x + 20730375x + 7990490x - 10747 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^2*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R (1) ----------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=1419/3125*x-4779/6250*x^2-72/625*x^3+81/125*x^4+(-121/156250)/(3+5*x)^2+_ + (-1408/78125)/(3+5*x)+1202/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 +--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x +--R + +--R 4 3 2 +--R - 2615625x - 1972500x + 1053225x + 624470x - 8569 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (300500x + 360600x + 108180)log(5x + 3) + 2531250x + 2587500x +--R + +--R 4 3 2 +--R - 2615625x - 1972500x + 1053225x + 624470x - 8569 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^2*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R (1) ------------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=-153/3125*x-216/625*x^2+36/125*x^3+(-121/31250)/(3+5*x)^2+_ + (-209/3125)/(3+5*x)+23/125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 3 2 +--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x +--R + +--R - 24220x - 6391 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 3 2 +--R (143750x + 172500x + 51750)log(5x + 3) + 225000x - 281250x - 143100x +--R + +--R - 24220x - 6391 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^2*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R (1) --------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=-264/625*x+18/125*x^2+(-121/6250)/(3+5*x)^2+(-682/3125)/(3+5*x)+_ + 829/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x +--R + +--R - 30580x - 4213 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (41450x + 49740x + 14922)log(5x + 3) + 22500x - 39000x - 71100x +--R + +--R - 30580x - 4213 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^2*(2+3*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--R 12x - 4x - 5x + 2 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=12/125*x+(-121/1250)/(3+5*x)^2+(-319/625)/(3+5*x)-128/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035 +--R (2) --------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 6400x - 7680x - 2304)log(5x + 3) + 3000x + 3600x - 2110x - 2035 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^2/(3+5*x)^3 +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=(-121/250)/(3+5*x)^2+44/125/(3+5*x)+4/125*log(3+5*x) +--R +--R +--R 2 +--R (200x + 240x + 72)log(5x + 3) + 440x + 143 +--R (2) ------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (200x + 240x + 72)log(5x + 3) + 440x + 143 +--R (3) ------------------------------------------- +--R 2 +--R 6250x + 7500x + 2250 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^2/((2+3*x)*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-121/50)/(3+5*x)^2+407/25/(3+5*x)-49*log(2+3*x)+49*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321 +--R / +--R 2 +--R 1250x + 1500x + 450 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(3x + 2) + 4070x + 2321 +--R / +--R 2 +--R 1250x + 1500x + 450 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^2/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=49/(2+3*x)+(-121/10)/(3+5*x)^2+154/(3+5*x)-707*log(2+3*x)+707*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (530250x + 989800x + 615090x + 127260)log(5x + 3) +--R + +--R 3 2 2 +--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x +--R + +--R 13408 +--R / +--R 3 2 +--R 750x + 1400x + 870x + 180 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (530250x + 989800x + 615090x + 127260)log(5x + 3) +--R + +--R 3 2 2 +--R (- 530250x - 989800x - 615090x - 127260)log(3x + 2) + 35350x + 43597x +--R + +--R 13408 +--R / +--R 3 2 +--R 750x + 1400x + 870x + 180 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^2/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--R 4x - 4x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=49/2/(2+3*x)^2+707/(2+3*x)+(-121/2)/(3+5*x)^2+1133/(3+5*x)-_ + 6934*log(2+3*x)+6934*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3) +--R + +--R 4 3 2 +--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2) +--R + +--R 3 2 +--R 208020x + 395238x + 249932x + 52601 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3120300x + 7904760x + 7502588x + 3161904x + 499248)log(5x + 3) +--R + +--R 4 3 2 +--R (- 3120300x - 7904760x - 7502588x - 3161904x - 499248)log(3x + 2) +--R + +--R 3 2 +--R 208020x + 395238x + 249932x + 52601 +--R / +--R 4 3 2 +--R 450x + 1140x + 1082x + 456x + 72 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^2/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=49/3/(2+3*x)^3+707/2/(2+3*x)^2+6934/(2+3*x)+(-605/2)/(3+5*x)^2+_ + 7480/(3+5*x)-57110*log(2+3*x)+57110*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x +--R + +--R 24671520 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x +--R + +--R - 24671520 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404 +--R / +--R 5 4 3 2 +--R 4050x + 12960x + 16578x + 10596x + 3384x + 432 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 231295500x + 740145600x + 946769580x + 605137560x + 193260240x +--R + +--R 24671520 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 231295500x - 740145600x - 946769580x - 605137560x - 193260240x +--R + +--R - 24671520 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 15419700x + 39577230x + 38058104x + 16250079x + 2599404 +--R / +--R 5 4 3 2 +--R 4050x + 12960x + 16578x + 10596x + 3384x + 432 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^2/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=49/4/(2+3*x)^4+707/3/(2+3*x)^3+3467/(2+3*x)^2+57110/(2+3*x)+_ + (-3025/2)/(3+5*x)^2+46475/(3+5*x)-424975*log(2+3*x)+424975*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 10326892500x + 39930651000x + 64302117300x + 55199152800x +--R + +--R 2 +--R 26640832800x + 6853996800x + 734356800 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x +--R + +--R 2 +--R - 26640832800x - 6853996800x - 734356800 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x +--R + +--R 77372211 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 10326892500x + 39930651000x + 64302117300x + 55199152800x +--R + +--R 2 +--R 26640832800x + 6853996800x + 734356800 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 10326892500x - 39930651000x - 64302117300x - 55199152800x +--R + +--R 2 +--R - 26640832800x - 6853996800x - 734356800 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 688459500x + 2226019050x + 2877250740x + 1858347679x + 599747838x +--R + +--R 77372211 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3f.input.pamphlet b/src/input/rich3f.input.pamphlet new file mode 100644 index 0000000..1311f46 --- /dev/null +++ b/src/input/rich3f.input.pamphlet @@ -0,0 +1,6798 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 99 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 1 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3f.output +)spool rich3f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^2/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=49/5/(2+3*x)^5+707/4/(2+3*x)^4+6934/3/(2+3*x)^3+28555/(2+3*x)^2+_ + 424975/(2+3*x)+(-15125/2)/(3+5*x)^2+277750/(3+5*x)-_ + 2958125*log(2+3*x)+2958125*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 1078236562500x + 4888005750000x + 9493273912500x +--R + +--R 4 3 2 +--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x +--R + +--R 51116400000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 1078236562500x - 4888005750000x - 9493273912500x +--R + +--R 4 3 2 +--R - 10239253875000x - 6623833500000x - 2570019000000x +--R + +--R - 553761000000x - 51116400000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 71882437500x + 280341506250x + 455361930000x + 394308004875x +--R + +--R 2 +--R 191974077080x + 49825144515x + 5385650262 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 1078236562500x + 4888005750000x + 9493273912500x +--R + +--R 4 3 2 +--R 10239253875000x + 6623833500000x + 2570019000000x + 553761000000x +--R + +--R 51116400000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 1078236562500x - 4888005750000x - 9493273912500x +--R + +--R 4 3 2 +--R - 10239253875000x - 6623833500000x - 2570019000000x +--R + +--R - 553761000000x - 51116400000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 71882437500x + 280341506250x + 455361930000x + 394308004875x +--R + +--R 2 +--R 191974077080x + 49825144515x + 5385650262 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^2/((2+3*x)^7*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=49/6/(2+3*x)^6+707/5/(2+3*x)^5+3467/2/(2+3*x)^4+57110/3/(2+3*x)^3+_ + 424975/2/(2+3*x)^2+2958125/(2+3*x)+(-75625/2)/(3+5*x)^2+_ + 1615625/(3+5*x)-19637500*log(2+3*x)+19637500*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 3578934375000x + 18610458750000x + 42326863875000x +--R + +--R 5 4 3 +--R 54993640500000x + 44643892500000x + 23187960000000x +--R + +--R 2 +--R 7525090000000x + 1395048000000x + 113112000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 3578934375000x - 18610458750000x - 42326863875000x +--R + +--R 5 4 3 +--R - 54993640500000x - 44643892500000x - 23187960000000x +--R + +--R 2 +--R - 7525090000000x - 1395048000000x - 113112000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x +--R + +--R 3 2 +--R 1509746867100x + 590188362770x + 128130976648x + 11917538647 +--R / +--R 8 7 6 5 4 3 +--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x +--R + +--R 2 +--R 383200x + 71040x + 5760 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 3578934375000x + 18610458750000x + 42326863875000x +--R + +--R 5 4 3 +--R 54993640500000x + 44643892500000x + 23187960000000x +--R + +--R 2 +--R 7525090000000x + 1395048000000x + 113112000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 3578934375000x - 18610458750000x - 42326863875000x +--R + +--R 5 4 3 +--R - 54993640500000x - 44643892500000x - 23187960000000x +--R + +--R 2 +--R - 7525090000000x - 1395048000000x - 113112000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 238595625000x + 1089586687500x + 2131807725000x + 2316445391250x +--R + +--R 3 2 +--R 1509746867100x + 590188362770x + 128130976648x + 11917538647 +--R / +--R 8 7 6 5 4 3 +--R 182250x + 947700x + 2155410x + 2800440x + 2273400x + 1180800x +--R + +--R 2 +--R 383200x + 71040x + 5760 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^2/((2+3*x)^8*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--R 4x - 4x + 1 +--R / +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=7/(2+3*x)^7+707/6/(2+3*x)^6+6934/5/(2+3*x)^5+28555/2/(2+3*x)^4+_ + 424975/3/(2+3*x)^3+2958125/2/(2+3*x)^2+19637500/(2+3*x)+_ + (-378125/2)/(3+5*x)^2+9212500/(3+5*x)-125825000*log(2+3*x)+_ + 125825000*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 68794818750000x + 403596270000000x + 1052102094750000x +--R + +--R 6 5 4 +--R 1599505015500000x + 1562882391000000x + 1017823590000000x +--R + +--R 3 2 +--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 68794818750000x - 403596270000000x - 1052102094750000x +--R + +--R 6 5 4 +--R - 1599505015500000x - 1562882391000000x - 1017823590000000x +--R + +--R 3 2 +--R - 441796740000000x - 123248104000000x - 20051472000000x +--R + +--R - 1449504000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x +--R + +--R 4 3 2 +--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x +--R + +--R 152720488888 +--R / +--R 9 8 7 6 5 4 +--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x +--R + +--R 3 2 +--R 3511200x + 979520x + 159360x + 11520 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 68794818750000x + 403596270000000x + 1052102094750000x +--R + +--R 6 5 4 +--R 1599505015500000x + 1562882391000000x + 1017823590000000x +--R + +--R 3 2 +--R 441796740000000x + 123248104000000x + 20051472000000x + 1449504000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 68794818750000x - 403596270000000x - 1052102094750000x +--R + +--R 6 5 4 +--R - 1599505015500000x - 1562882391000000x - 1017823590000000x +--R + +--R 3 2 +--R - 441796740000000x - 123248104000000x - 20051472000000x +--R + +--R - 1449504000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R 4586321250000x + 24001747875000x + 54940731300000x + 71845684942500x +--R + +--R 4 3 2 +--R 58705292494800x + 30691745453460x + 10026079791288x + 1871049429619x +--R + +--R 152720488888 +--R / +--R 9 8 7 6 5 4 +--R 546750x + 3207600x + 8361630x + 12712140x + 12421080x + 8089200x +--R + +--R 3 2 +--R 3511200x + 979520x + 159360x + 11520 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x) +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 262440x - 1163484x - 1966842x - 1290573x + 344979x + 1027296x +--R + +--R 6 5 4 3 2 +--R 470736x - 104736x - 159712x - 36864x + 9984x + 5888x + 768 +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 500 +r0:=-343/2187*(2+3*x)^9+2009/2430*(2+3*x)^10-518/891*(2+3*x)^11+_ + 107/729*(2+3*x)^12-40/3159*(2+3*x)^13 +--R +--R +--R (2) +--R 262440 13 12 1966842 11 1290573 10 9 8 +--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x +--R 13 11 10 +--R + +--R 7 6 159712 5 4 3 2 114328576 +--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x + --------- +--R 5 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 262440 13 12 1966842 11 1290573 10 9 8 +--R - ------ x - 96957x - ------- x - ------- x + 38331x + 128412x +--R 13 11 10 +--R + +--R 7 6 159712 5 4 3 2 +--R 67248x - 17456x - ------ x - 9216x + 3328x + 2944x + 768x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 114328576 +--R (4) - --------- +--R 1563705 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x) +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 87480x - 329508x - 435942x - 139563x + 208035x + 203742x +--R + +--R 5 4 3 2 +--R 21084x - 48968x - 20592x + 1440x + 2368x + 384 +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 500 +r0:=384*x+1184*x^2+480*x^3-5148*x^4-48968/5*x^5+3514*x^6+29106*x^7+_ + 208035/8*x^8-15507*x^9-217971/5*x^10-329508/11*x^11-7290*x^12 +--R +--R +--R (2) +--R 12 329508 11 217971 10 9 208035 8 7 +--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x +--R 11 5 8 +--R + +--R 6 48968 5 4 3 2 +--R 3514x - ----- x - 5148x + 480x + 1184x + 384x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 329508 11 217971 10 9 208035 8 7 +--R - 7290x - ------ x - ------ x - 15507x + ------ x + 29106x +--R 11 5 8 +--R + +--R 6 48968 5 4 3 2 +--R 3514x - ----- x - 5148x + 480x + 1184x + 384x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 29160x - 90396x - 85050x + 10179x + 62559x + 26208x - 10444x +--R + +--R 3 2 +--R - 9360x - 624x + 896x + 192 +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 500 +r0:=192*x+448*x^2-208*x^3-2340*x^4-10444/5*x^5+4368*x^6+8937*x^7+_ + 10179/8*x^8-9450*x^9-45198/5*x^10-29160/11*x^11 +--R +--R +--R (2) +--R 29160 11 45198 10 9 10179 8 7 6 10444 5 +--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x +--R 11 5 8 5 +--R + +--R 4 3 2 +--R - 2340x - 208x + 448x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 29160 11 45198 10 9 10179 8 7 6 10444 5 +--R - ----- x - ----- x - 9450x + ----- x + 8937x + 4368x - ----- x +--R 11 5 8 5 +--R + +--R 4 3 2 +--R - 2340x - 208x + 448x + 192x +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 9720x - 23652x - 12582x + 11781x + 12999x + 70x - 3528x - 768x +--R + +--R 304x + 96 +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 500 +r0:=96*x+152*x^2-256*x^3-882*x^4+14*x^5+4333/2*x^6+1683*x^7-6291/4*x^8-_ + 2628*x^9-972*x^10 +--R +--R +--R (2) +--R 10 9 6291 8 7 4333 6 5 4 3 +--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x +--R 4 2 +--R + +--R 2 +--R 152x + 96x +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 6291 8 7 4333 6 5 4 3 +--R - 972x - 2628x - ---- x + 1683x + ---- x + 14x - 882x - 256x +--R 4 2 +--R + +--R 2 +--R 152x + 96x +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 3240x - 5724x - 378x + 4179x + 1547x - 1008x - 504x + 80x + 48 +--R Type: Polynomial(Integer) +--E 36 + +--S 37 of 500 +r0:=48*x+40*x^2-168*x^3-252*x^4+1547/5*x^5+1393/2*x^6-54*x^7-1431/2*x^8-360*x^9 +--R +--R +--R (2) +--R 9 1431 8 7 1393 6 1547 5 4 3 2 +--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x +--R 2 2 5 +--R Type: Polynomial(Fraction(Integer)) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 1431 8 7 1393 6 1547 5 4 3 2 +--R - 360x - ---- x - 54x + ---- x + ---- x - 252x - 168x + 40x + 48x +--R 2 2 5 +--R Type: Polynomial(Fraction(Integer)) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 1080x - 1188x + 666x + 949x - 117x - 258x + 4x + 24 +--R Type: Polynomial(Integer) +--E 41 + +--S 42 of 500 +r0:=24*x+2*x^2-86*x^3-117/4*x^4+949/5*x^5+111*x^6-1188/7*x^7-135*x^8 +--R +--R +--R 8 1188 7 6 949 5 117 4 3 2 +--R (2) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 1188 7 6 949 5 117 4 3 2 +--R (3) - 135x - ---- x + 111x + --- x - --- x - 86x + 2x + 24x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R (1) - 360x - 156x + 326x + 99x - 105x - 16x + 12 +--R Type: Polynomial(Integer) +--E 46 + +--S 47 of 500 +r0:=12*x-8*x^2-35*x^3+99/4*x^4+326/5*x^5-26*x^6-360/7*x^7 +--R +--R +--R 360 7 6 326 5 99 4 3 2 +--R (2) - --- x - 26x + --- x + -- x - 35x - 8x + 12x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R 360 7 6 326 5 99 4 3 2 +--R (3) - --- x - 26x + --- x + -- x - 35x - 8x + 12x +--R 7 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x) +--R +--R +--R 5 4 3 2 +--R (1) - 120x + 28x + 90x - 27x - 17x + 6 +--R Type: Polynomial(Integer) +--E 51 + +--S 52 of 500 +r0:=6*x-17/2*x^2-9*x^3+45/2*x^4+28/5*x^5-20*x^6 +--R +--R +--R 6 28 5 45 4 3 17 2 +--R (2) - 20x + -- x + -- x - 9x - -- x + 6x +--R 5 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 28 5 45 4 3 17 2 +--R (3) - 20x + -- x + -- x - 9x - -- x + 6x +--R 5 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^3*(3+5*x) +--R +--R +--R 4 3 2 +--R (1) - 40x + 36x + 6x - 13x + 3 +--R Type: Polynomial(Integer) +--E 56 + +--S 57 of 500 +r0:=3*x-13/2*x^2+2*x^3+9*x^4-8*x^5 +--R +--R +--R 5 4 3 13 2 +--R (2) - 8x + 9x + 2x - -- x + 3x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 13 2 +--R (3) - 8x + 9x + 2x - -- x + 3x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x) +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=293/81*x-161/27*x^2+188/27*x^3-10/3*x^4-343/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x +--R (2) ------------------------------------------------- +--R 243 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 343log(3x + 2) - 810x + 1692x - 1449x + 879x +--R (3) ------------------------------------------------- +--R 243 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^2 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=-286/27*x+134/27*x^2-40/27*x^3+343/243/(2+3*x)+2009/243*log(2+3*x) +--R +--R +--R 4 3 2 +--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343 +--R (2) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (6027x + 4018)log(3x + 2) - 1080x + 2898x - 5310x - 5148x + 343 +--R (3) ------------------------------------------------------------------ +--R 729x + 486 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^3 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=116/27*x-20/27*x^2+343/486/(2+3*x)^2+(-2009/243)/(2+3*x)-518/81*log(2+3*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x +--R + +--R - 3702x - 7693 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 27972x - 37296x - 12432)log(3x + 2) - 3240x + 14472x + 23616x +--R + +--R - 3702x - 7693 +--R / +--R 2 +--R 4374x + 5832x + 1944 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^4 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=-40/81*x+343/729/(2+3*x)^3+(-2009/486)/(2+3*x)^2+518/81/(2+3*x)+_ + 428/243*log(2+3*x) +--R +--R +--R (2) +--R 3 2 4 3 +--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x +--R + +--R 2 +--R 57996x + 88047x + 25928 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 3 +--R (69336x + 138672x + 92448x + 20544)log(3x + 2) - 19440x - 38880x +--R + +--R 2 +--R 57996x + 88047x + 25928 +--R / +--R 3 2 +--R 39366x + 78732x + 52488x + 11664 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^5 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=343/972/(2+3*x)^4+(-2009/729)/(2+3*x)^3+259/81/(2+3*x)^2+_ + (-428/243)/(2+3*x)-40/243*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 3 +--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x +--R + +--R 2 +--R - 193428x - 97116x - 18835 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 3 +--R (- 38880x - 103680x - 103680x - 46080x - 7680)log(3x + 2) - 138672x +--R + +--R 2 +--R - 193428x - 97116x - 18835 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^6 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=1/105*(1-2*x)^4/(2+3*x)^5-173/2940*(1-2*x)^4/(2+3*x)^4 +--R +--R +--R 692 5 64 4 38 3 58 2 5 53 +--R - ----- x + ---- x - ----- x - ----- x + ---- x - ------ +--R 59535 3969 11907 11907 1764 119070 +--R (2) ------------------------------------------------------------ +--R 5 10 4 40 3 80 2 80 32 +--R x + -- x + -- x + -- x + -- x + --- +--R 3 9 27 81 243 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 64800x + 57240x + 34920x + 16905x + 1282 +--R (3) ----------------------------------------------------------------- +--R 5 4 3 2 +--R 1180980x + 3936600x + 5248800x + 3499200x + 1166400x + 155520 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R 692 +--R (4) ----- +--R 59535 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^7 +--R +--R +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=1/126*(1-2*x)^4/(2+3*x)^6-103/2205*(1-2*x)^4/(2+3*x)^5-_ + 103/30870*(1-2*x)^4/(2+3*x)^4 +--R +--R +--R (2) +--R 824 6 3296 5 44 4 316 3 659 2 349 +--R - ------- x - ------- x + ---- x - ------ x - ------ x + ------ x +--R 1250235 1250235 9261 250047 500094 416745 +--R + +--R 113 +--R - ------ +--R 833490 +--R / +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 48600x + 14040x + 3375x + 7218x - 413 +--R / +--R 6 5 4 3 2 +--R 5314410x + 21257640x + 35429400x + 31492800x + 15746400x + 4199040x +--R + +--R 466560 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 824 +--R (4) ------- +--R 1250235 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^3*(3+5*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--R - 40x + 36x + 6x - 13x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=49/243/(2+3*x)^7+(-2009/1458)/(2+3*x)^6+518/405/(2+3*x)^5+_ + (-107/243)/(2+3*x)^4+40/729/(2+3*x)^3 +--R +--R +--R 40 4 1 3 56 2 1531 302 +--R ----- x - ----- x - ------ x + ------- x - ------- +--R 19683 59049 295245 5314410 7971615 +--R (2) ------------------------------------------------------------ +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 32400x - 270x - 3024x + 4593x - 604 +--R / +--R 7 6 5 4 3 +--R 15943230x + 74401740x + 148803480x + 165337200x + 110224800x +--R + +--R 2 +--R 44089920x + 9797760x + 933120 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^3*(2+3*x)^8*(3+5*x)^2 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R - 1312200x - 6604740x - 13324662x - 12353391x - 2146824x +--R + +--R 8 7 6 5 4 3 2 +--R 6171417x + 5435568x + 888528x - 1112768x - 663456x - 60672x + 59392x +--R + +--R 21504x + 2304 +--R Type: Polynomial(Integer) +--E 101 + +--S 102 of 500 +r0:=2304*x+10752*x^2+59392/3*x^3-15168*x^4-663456/5*x^5-556384/3*x^6+_ + 888528/7*x^7+679446*x^8+685713*x^9-1073412/5*x^10-_ + 12353391/11*x^11-2220777/2*x^12-6604740/13*x^13-656100/7*x^14 +--R +--R +--R (2) +--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10 +--R - ------ x - ------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 5 +--R + +--R 9 8 888528 7 556384 6 663456 5 4 +--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x +--R 7 3 5 +--R + +--R 59392 3 2 +--R ----- x + 10752x + 2304x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 656100 14 6604740 13 2220777 12 12353391 11 1073412 10 +--R - ------ x - ------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 5 +--R + +--R 9 8 888528 7 556384 6 663456 5 4 +--R 685713x + 679446x + ------ x - ------ x - ------ x - 15168x +--R 7 3 5 +--R + +--R 59392 3 2 +--R ----- x + 10752x + 2304x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^2 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 437400x - 1909980x - 3168234x - 2005641x + 621486x + 1642815x +--R + +--R 6 5 4 3 2 +--R 716646x - 181588x - 249864x - 54576x + 16160x + 9024x + 1152 +--R Type: Polynomial(Integer) +--E 106 + +--S 107 of 500 +r0:=1152*x+4512*x^2+16160/3*x^3-13644*x^4-249864/5*x^5-90794/3*x^6+_ + 102378*x^7+1642815/8*x^8+69054*x^9-2005641/10*x^10-3168234/11*x^11-_ + 159165*x^12-437400/13*x^13 +--R +--R +--R (2) +--R 437400 13 12 3168234 11 2005641 10 9 1642815 8 +--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x +--R 13 11 10 8 +--R + +--R 7 90794 6 249864 5 4 16160 3 2 +--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 437400 13 12 3168234 11 2005641 10 9 1642815 8 +--R - ------ x - 159165x - ------- x - ------- x + 69054x + ------- x +--R 13 11 10 8 +--R + +--R 7 90794 6 249864 5 4 16160 3 2 +--R 102378x - ----- x - ------ x - 13644x + ----- x + 4512x + 1152x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 145800x - 539460x - 696438x - 204255x + 343332x + 318717x +--R + +--R 5 4 3 2 +--R 26404x - 78132x - 31200x + 2608x + 3648x + 576 +--R Type: Polynomial(Integer) +--E 111 + +--S 112 of 500 +r0:=576*x+1824*x^2+2608/3*x^3-7800*x^4-78132/5*x^5+13202/3*x^6+45531*x^7+_ + 85833/2*x^8-22695*x^9-348219/5*x^10-539460/11*x^11-12150*x^12 +--R +--R +--R (2) +--R 12 539460 11 348219 10 9 85833 8 7 +--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x +--R 11 5 2 +--R + +--R 13202 6 78132 5 4 2608 3 2 +--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 539460 11 348219 10 9 85833 8 7 +--R - 12150x - ------ x - ------ x - 22695x + ----- x + 45531x +--R 11 5 2 +--R + +--R 13202 6 78132 5 4 2608 3 2 +--R ----- x - ----- x - 7800x + ---- x + 1824x + 576x +--R 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 48600x - 147420x - 133866x + 21159x + 100338x + 39347x - 17430x +--R + +--R 3 2 +--R - 14424x - 784x + 1392x + 288 +--R Type: Polynomial(Integer) +--E 116 + +--S 117 of 500 +r0:=288*x+696*x^2-784/3*x^3-3606*x^4-3486*x^5+39347/6*x^6+14334*x^7+_ + 21159/8*x^8-14874*x^9-14742*x^10-48600/11*x^11 +--R +--R +--R (2) +--R 48600 11 10 9 21159 8 7 39347 6 5 +--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x +--R 11 8 6 +--R + +--R 4 784 3 2 +--R - 3606x - --- x + 696x + 288x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 48600 11 10 9 21159 8 7 39347 6 5 +--R - ----- x - 14742x - 14874x + ----- x + 14334x + ----- x - 3486x +--R 11 8 6 +--R + +--R 4 784 3 2 +--R - 3606x - --- x + 696x + 288x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 16200x - 38340x - 19062x + 19761x + 20272x - 399x - 5544x - 1112x +--R + +--R 480x + 144 +--R Type: Polynomial(Integer) +--E 121 + +--S 122 of 500 +r0:=144*x+240*x^2-1112/3*x^3-1386*x^4-399/5*x^5+10136/3*x^6+2823*x^7-_ + 9531/4*x^8-4260*x^9-1620*x^10 +--R +--R +--R (2) +--R 10 9 9531 8 7 10136 6 399 5 4 +--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x +--R 4 3 5 +--R + +--R 1112 3 2 +--R - ---- x + 240x + 144x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 9531 8 7 10136 6 399 5 4 +--R - 1620x - 4260x - ---- x + 2823x + ----- x - --- x - 1386x +--R 4 3 5 +--R + +--R 1112 3 2 +--R - ---- x + 240x + 144x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 5400x - 9180x - 234x + 6743x + 2262x - 1641x - 754x + 132x + 72 +--R Type: Polynomial(Integer) +--E 126 + +--S 127 of 500 +r0:=72*x+66*x^2-754/3*x^3-1641/4*x^4+2262/5*x^5+6743/6*x^6-234/7*x^7-_ + 2295/2*x^8-600*x^9 +--R +--R +--R (2) +--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2 +--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x +--R 2 7 6 5 4 3 +--R + +--R 72x +--R Type: Polynomial(Fraction(Integer)) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 2295 8 234 7 6743 6 2262 5 1641 4 754 3 2 +--R - 600x - ---- x - --- x + ---- x + ---- x - ---- x - --- x + 66x +--R 2 7 6 5 4 3 +--R + +--R 72x +--R Type: Polynomial(Fraction(Integer)) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 1800x - 1860x + 1162x + 1473x - 228x - 395x + 12x + 36 +--R Type: Polynomial(Integer) +--E 131 + +--S 132 of 500 +r0:=36*x+6*x^2-395/3*x^3-57*x^4+1473/5*x^5+581/3*x^6-1860/7*x^7-225*x^8 +--R +--R +--R 8 1860 7 581 6 1473 5 4 395 3 2 +--R (2) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x +--R 7 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 1860 7 581 6 1473 5 4 395 3 2 +--R (3) - 225x - ---- x + --- x + ---- x - 57x - --- x + 6x + 36x +--R 7 3 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R (1) - 600x - 220x + 534x + 135x - 166x - 21x + 18 +--R Type: Polynomial(Integer) +--E 136 + +--S 137 of 500 +r0:=18*x-21/2*x^2-166/3*x^3+135/4*x^4+534/5*x^5-110/3*x^6-600/7*x^7 +--R +--R +--R 600 7 110 6 534 5 135 4 166 3 21 2 +--R (2) - --- x - --- x + --- x + --- x - --- x - -- x + 18x +--R 7 3 5 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 600 7 110 6 534 5 135 4 166 3 21 2 +--R (3) - --- x - --- x + --- x + --- x - --- x - -- x + 18x +--R 7 3 5 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^3*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R (1) - 200x + 60x + 138x - 47x - 24x + 9 +--R Type: Polynomial(Integer) +--E 141 + +--S 142 of 500 +r0:=9*x-12*x^2-47/3*x^3+69/2*x^4+12*x^5-100/3*x^6 +--R +--R +--R 100 6 5 69 4 47 3 2 +--R (2) - --- x + 12x + -- x - -- x - 12x + 9x +--R 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R 100 6 5 69 4 47 3 2 +--R (3) - --- x + 12x + -- x - -- x - 12x + 9x +--R 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x) +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=922/243*x-1433/162*x^2+82/81*x^3+145/9*x^4-40/3*x^5+343/729*log(2+3*x) +--R +--R +--R 5 4 3 2 +--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x +--R (2) ------------------------------------------------------------- +--R 1458 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 686log(3x + 2) - 19440x + 23490x + 1476x - 12897x + 5532x +--R (3) ------------------------------------------------------------- +--R 1458 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=2323/243*x-313/27*x^2+980/81*x^3-50/9*x^4+(-343/729)/(2+3*x)-_ + 3724/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x +--R + +--R 13938x - 343 +--R / +--R 2187x + 1458 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 11172x - 7448)log(3x + 2) - 12150x + 18360x - 7713x + 4005x +--R + +--R 13938x - 343 +--R / +--R 2187x + 1458 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=-1546/81*x+230/27*x^2-200/81*x^3+(-343/1458)/(2+3*x)^2+3724/729/(2+3*x)+_ + 11599/729*log(2+3*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x +--R + +--R 2 +--R - 284256x - 88968x + 14553 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (208782x + 278376x + 92792)log(3x + 2) - 32400x + 68580x - 115812x +--R + +--R 2 +--R - 284256x - 88968x + 14553 +--R / +--R 2 +--R 13122x + 17496x + 5832 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1780/243*x-100/81*x^2+(-343/2187)/(2+3*x)^3+1862/729/(2+3*x)^2+_ + (-11599/729)/(2+3*x)-8198/729*log(2+3*x) +--R +--R +--R (2) +--R 3 2 5 +--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x +--R + +--R 4 3 2 +--R 286740x + 767880x + 241947x - 272646x - 128359 +--R / +--R 3 2 +--R 59049x + 118098x + 78732x + 17496 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 5 +--R (- 664038x - 1328076x - 885384x - 196752)log(3x + 2) - 72900x +--R + +--R 4 3 2 +--R 286740x + 767880x + 241947x - 272646x - 128359 +--R / +--R 3 2 +--R 59049x + 118098x + 78732x + 17496 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=-200/243*x+(-343/2916)/(2+3*x)^4+3724/2187/(2+3*x)^3+_ + (-11599/1458)/(2+3*x)^2+8198/729/(2+3*x)+2180/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2) +--R + +--R 5 4 3 2 +--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (2118960x + 5650560x + 5650560x + 2511360x + 418560)log(3x + 2) +--R + +--R 5 4 3 2 +--R - 583200x - 1555200x + 1100952x + 3994758x + 2635896x + 537395 +--R / +--R 4 3 2 +--R 708588x + 1889568x + 1889568x + 839808x + 139968 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-343/3645)/(2+3*x)^5+931/729/(2+3*x)^4+(-11599/2187)/(2+3*x)^3+_ + 4099/729/(2+3*x)^2+(-2180/729)/(2+3*x)-200/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399 +--R / +--R 5 4 3 2 +--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 729000x - 2430000x - 3240000x - 2160000x - 720000x - 96000) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 2648700x - 5403105x - 4264965x - 1579785x - 236399 +--R / +--R 5 4 3 2 +--R 2657205x + 8857350x + 11809800x + 7873200x + 2624400x + 349920 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=(-343/4374)/(2+3*x)^6+3724/3645/(2+3*x)^5+(-11599/2916)/(2+3*x)^4+_ + 8198/2187/(2+3*x)^3+(-1090/729)/(2+3*x)^2+200/729/(2+3*x) +--R +--R +--R 200 5 910 4 6038 3 13345 2 15289 19643 +--R ---- x + ---- x + ----- x + ------ x + ------ x + -------- +--R 2187 6561 59049 236196 885735 15943230 +--R (2) -------------------------------------------------------------- +--R 6 5 20 4 160 3 80 2 64 64 +--R x + 4x + -- x + --- x + -- x + -- x + --- +--R 3 27 27 81 729 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2916000x + 4422600x + 3260520x + 1801575x + 550404x + 39286 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^3*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--R - 200x + 60x + 138x - 47x - 24x + 9 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=(-49/729)/(2+3*x)^7+1862/2187/(2+3*x)^6+(-11599/3645)/(2+3*x)^5+_ + 4099/1458/(2+3*x)^4+(-2180/2187)/(2+3*x)^3+100/729/(2+3*x)^2 +--R +--R +--R 100 5 820 4 1417 3 2686 2 10232 1763 +--R ---- x + ----- x + ------ x + ------ x + ------- x - -------- +--R 6561 59049 354294 885735 7971615 23914845 +--R (2) ----------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 729000x + 664200x + 191295x + 145044x + 61392x - 3526 +--R / +--R 7 6 5 4 3 +--R 47829690x + 223205220x + 446410440x + 496011600x + 330674400x +--R + +--R 2 +--R 132269760x + 29393280x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^3*(2+3*x)^7*(3+5*x)^3 +--R +--R +--R (1) +--R 13 12 11 10 9 +--R - 2187000x - 10862100x - 21571110x - 19532907x - 2909493x +--R + +--R 8 7 6 5 4 3 +--R 10078533x + 8511675x + 1241998x - 1794084x - 1022472x - 82928x +--R + +--R 2 +--R 93600x + 32832x + 3456 +--R Type: Polynomial(Integer) +--E 186 + +--S 187 of 500 +r0:=3456*x+16416*x^2+31200*x^3-20732*x^4-1022472/5*x^5-299014*x^6+_ + 1241998/7*x^7+8511675/8*x^8+1119837*x^9-2909493/10*x^10-_ + 19532907/11*x^11-3595185/2*x^12-10862100/13*x^13-1093500/7*x^14 +--R +--R +--R (2) +--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10 +--R - ------- x - -------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 10 +--R + +--R 9 8511675 8 1241998 7 6 1022472 5 4 +--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x +--R 8 7 5 +--R + +--R 3 2 +--R 31200x + 16416x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1093500 14 10862100 13 3595185 12 19532907 11 2909493 10 +--R - ------- x - -------- x - ------- x - -------- x - ------- x +--R 7 13 2 11 10 +--R + +--R 9 8511675 8 1241998 7 6 1022472 5 4 +--R 1119837x + ------- x + ------- x - 299014x - ------- x - 20732x +--R 8 7 5 +--R + +--R 3 2 +--R 31200x + 16416x + 3456x +--R Type: Polynomial(Fraction(Integer)) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^3*(2+3*x)^6*(3+5*x)^3 +--R +--R +--R (1) +--R 12 11 10 9 8 7 +--R - 729000x - 3134700x - 5100570x - 3110589x + 1103895x + 2623581x +--R + +--R 6 5 4 3 2 +--R 1088171x - 311448x - 390396x - 80560x + 26064x + 13824x + 1728 +--R Type: Polynomial(Integer) +--E 191 + +--S 192 of 500 +r0:=1728*x+6912*x^2+8688*x^3-20140*x^4-390396/5*x^5-51908*x^6+_ + 155453*x^7+2623581/8*x^8+122655*x^9-3110589/10*x^10-5100570/11*x^11-_ + 261225*x^12-729000/13*x^13 +--R +--R +--R (2) +--R 729000 13 12 5100570 11 3110589 10 9 +--R - ------ x - 261225x - ------- x - ------- x + 122655x +--R 13 11 10 +--R + +--R 2623581 8 7 6 390396 5 4 3 2 +--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x +--R 8 5 +--R + +--R 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 729000 13 12 5100570 11 3110589 10 9 +--R - ------ x - 261225x - ------- x - ------- x + 122655x +--R 13 11 10 +--R + +--R 2623581 8 7 6 390396 5 4 3 2 +--R ------- x + 155453x - 51908x - ------ x - 20140x + 8688x + 6912x +--R 8 5 +--R + +--R 1728x +--R Type: Polynomial(Fraction(Integer)) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^3*(2+3*x)^5*(3+5*x)^3 +--R +--R +--R (1) +--R 11 10 9 8 7 6 +--R - 243000x - 882900x - 1111590x - 295803x + 565167x + 497749x +--R + +--R 5 4 3 2 +--R 30891x - 124410x - 47192x + 4608x + 5616x + 864 +--R Type: Polynomial(Integer) +--E 196 + +--S 197 of 500 +r0:=864*x+2808*x^2+1536*x^3-11798*x^4-24882*x^5+10297/2*x^6+_ + 71107*x^7+565167/8*x^8-32867*x^9-111159*x^10-882900/11*x^11-20250*x^12 +--R +--R +--R (2) +--R 12 882900 11 10 9 565167 8 7 +--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x +--R 11 8 +--R + +--R 10297 6 5 4 3 2 +--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 882900 11 10 9 565167 8 7 +--R - 20250x - ------ x - 111159x - 32867x + ------ x + 71107x +--R 11 8 +--R + +--R 10297 6 5 4 3 2 +--R ----- x - 24882x - 11798x + 1536x + 2808x + 864x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^3*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 81000x - 240300x - 210330x + 41619x + 160643x + 58821x - 28917x +--R + +--R 3 2 +--R - 22192x - 936x + 2160x + 432 +--R Type: Polynomial(Integer) +--E 201 + +--S 202 of 500 +r0:=432*x+1080*x^2-312*x^3-5548*x^4-28917/5*x^5+19607/2*x^6+22949*x^7+_ + 41619/8*x^8-23370*x^9-24030*x^10-81000/11*x^11 +--R +--R +--R (2) +--R 81000 11 10 9 41619 8 7 19607 6 28917 5 +--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x +--R 11 8 2 5 +--R + +--R 4 3 2 +--R - 5548x - 312x + 1080x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 81000 11 10 9 41619 8 7 19607 6 28917 5 +--R - ----- x - 24030x - 23370x + ----- x + 22949x + ----- x - ----- x +--R 11 8 2 5 +--R + +--R 4 3 2 +--R - 5548x - 312x + 1080x + 432x +--R Type: Polynomial(Fraction(Integer)) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^3*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R - 27000x - 62100x - 28710x + 33013x + 31539x - 1419x - 8693x +--R + +--R 2 +--R - 1602x + 756x + 216 +--R Type: Polynomial(Integer) +--E 206 + +--S 207 of 500 +r0:=216*x+378*x^2-534*x^3-8693/4*x^4-1419/5*x^5+10513/2*x^6+33013/7*x^7-_ + 14355/4*x^8-6900*x^9-2700*x^10 +--R +--R +--R (2) +--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4 +--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x +--R 4 7 2 5 4 +--R + +--R 3 2 +--R - 534x + 378x + 216x +--R Type: Polynomial(Fraction(Integer)) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 14355 8 33013 7 10513 6 1419 5 8693 4 +--R - 2700x - 6900x - ----- x + ----- x + ----- x - ---- x - ---- x +--R 4 7 2 5 4 +--R + +--R 3 2 +--R - 534x + 378x + 216x +--R Type: Polynomial(Fraction(Integer)) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^3*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 9000x - 14700x + 230x + 10851x + 3279x - 2659x - 1125x + 216x + 108 +--R Type: Polynomial(Integer) +--E 211 + +--S 212 of 500 +r0:=108*x+108*x^2-375*x^3-2659/4*x^4+3279/5*x^5+3617/2*x^6+230/7*x^7-_ + 3675/2*x^8-1000*x^9 +--R +--R +--R (2) +--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2 +--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x +--R 2 7 2 5 4 +--R + +--R 108x +--R Type: Polynomial(Fraction(Integer)) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3675 8 230 7 3617 6 3279 5 2659 4 3 2 +--R - 1000x - ---- x + --- x + ---- x + ---- x - ---- x - 375x + 108x +--R 2 7 2 5 4 +--R + +--R 108x +--R Type: Polynomial(Fraction(Integer)) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^3*(2+3*x)*(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R (1) - 3000x - 2900x + 2010x + 2277x - 425x - 603x + 27x + 54 +--R Type: Polynomial(Integer) +--E 216 + +--S 217 of 500 +r0:=54*x+27/2*x^2-201*x^3-425/4*x^4+2277/5*x^5+335*x^6-2900/7*x^7-375*x^8 +--R +--R +--R 8 2900 7 6 2277 5 425 4 3 27 2 +--R (2) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x +--R 7 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 8 2900 7 6 2277 5 425 4 3 27 2 +--R (3) - 375x - ---- x + 335x + ---- x - --- x - 201x + -- x + 54x +--R 7 5 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^3*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R (1) - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 500 +r0:=27*x-27/2*x^2-87*x^3+179/4*x^4+174*x^5-50*x^6-1000/7*x^7 +--R +--R +--R 1000 7 6 5 179 4 3 27 2 +--R (2) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x +--R 7 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 1000 7 6 5 179 4 3 27 2 +--R (3) - ---- x - 50x + 174x + --- x - 87x - -- x + 27x +--R 7 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x) +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=10013/729*x-8287/486*x^2-6427/243*x^3+2815/54*x^4+220/9*x^5-500/9*x^6-_ + 343/2187*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x +--R + +--R 60078x +--R / +--R 4374 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 686log(3x + 2) - 243000x + 106920x + 228015x - 115686x - 74583x +--R + +--R 60078x +--R / +--R 4374 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=2287/729*x-5287/486*x^2-190/81*x^3+775/27*x^4-200/9*x^5+343/2187/(2+3*x)+_ + 1813/729*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x +--R + +--R 2 +--R - 54000x + 27444x + 686 +--R / +--R 13122x + 8748 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (32634x + 21756)log(3x + 2) - 291600x + 182250x + 220320x - 163269x +--R + +--R 2 +--R - 54000x + 27444x + 686 +--R / +--R 13122x + 8748 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=16253/729*x-1795/81*x^2+1700/81*x^3-250/27*x^4+343/4374/(2+3*x)^2+_ + (-1813/729)/(2+3*x)-10073/729*log(2+3*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x +--R + +--R 4 3 2 +--R 67230x + 81702x + 782496x + 357438x - 21413 +--R / +--R 2 +--R 39366x + 52488x + 17496 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 543942x - 725256x - 241752)log(3x + 2) - 364500x + 340200x +--R + +--R 4 3 2 +--R 67230x + 81702x + 782496x + 357438x - 21413 +--R / +--R 2 +--R 39366x + 52488x + 17496 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=-24970/729*x+3550/243*x^2-1000/243*x^3+343/6561/(2+3*x)^3+_ + (-1813/1458)/(2+3*x)^2+10073/729/(2+3*x)+66193/2187*log(2+3*x) +--R +--R +--R (2) +--R 3 2 6 +--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x +--R + +--R 5 4 3 2 +--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308 +--R / +--R 3 2 +--R 354294x + 708588x + 472392x + 104976 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 6 +--R (10723266x + 21446532x + 14297688x + 3177264)log(3x + 2) - 1458000x +--R + +--R 5 4 3 2 +--R 2259900x - 3727620x - 17801640x - 13015134x - 1468863x + 693308 +--R / +--R 3 2 +--R 354294x + 708588x + 472392x + 104976 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=9100/729*x-500/243*x^2+343/8748/(2+3*x)^4+(-1813/2187)/(2+3*x)^3+_ + 10073/1458/(2+3*x)^2+(-66193/2187)/(2+3*x)-14390/729*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x +--R + +--R - 630195 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 4662360x - 12432960x - 12432960x - 5525760x - 920960)log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 486000x + 1652400x + 6566400x + 4903452x - 1186182x - 2360364x +--R + +--R - 630195 +--R / +--R 4 3 2 +--R 236196x + 629856x + 629856x + 279936x + 46656 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=-1000/729*x+343/10935/(2+3*x)^5+(-1813/2916)/(2+3*x)^4+_ + 10073/2187/(2+3*x)^3+(-66193/4374)/(2+3*x)^2+14390/729/(2+3*x)+_ + 3700/729*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x +--R + +--R 2368000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x +--R + +--R 19824285x + 3090594 +--R / +--R 5 4 3 2 +--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 17982000x + 59940000x + 79920000x + 53280000x + 17760000x +--R + +--R 2368000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 4860000x - 16200000x + 1711800x + 41807430x + 46054440x +--R + +--R 19824285x + 3090594 +--R / +--R 5 4 3 2 +--R 3542940x + 11809800x + 15746400x + 10497600x + 3499200x + 466560 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=343/13122/(2+3*x)^6+(-1813/3645)/(2+3*x)^5+10073/2916/(2+3*x)^4+_ + (-66193/6561)/(2+3*x)^3+7195/729/(2+3*x)^2+(-3700/729)/(2+3*x)-_ + 1000/2187*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x +--R + +--R - 11520000x - 1280000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 14580000x - 58320000x - 97200000x - 86400000x - 43200000x +--R + +--R - 11520000x - 1280000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 53946000x - 144852300x - 158427540x - 89062425x - 25975248x - 3165082 +--R / +--R 6 5 4 3 2 +--R 31886460x + 127545840x + 212576400x + 188956800x + 94478400x +--R + +--R 25194240x + 2799360 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^3*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 6 5 4 3 2 +--R - 1000x - 300x + 870x + 179x - 261x - 27x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=49/2187/(2+3*x)^7+(-1813/4374)/(2+3*x)^6+10073/3645/(2+3*x)^5+_ + (-66193/8748)/(2+3*x)^4+14390/2187/(2+3*x)^3+(-1850/729)/(2+3*x)^2+_ + 1000/2187/(2+3*x) +--R +--R +--R (2) +--R 1000 6 2150 5 18890 4 146287 3 160381 2 331697 33326 +--R ---- x + ---- x + ----- x + ------ x + ------- x + -------- x + -------- +--R 6561 6561 59049 708588 1771470 15943230 23914845 +--R ----------------------------------------------------------------------------- +--R 7 14 6 28 5 280 4 560 3 224 2 448 128 +--R x + -- x + -- x + --- x + --- x + --- x + --- x + ---- +--R 3 3 27 81 81 729 2187 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 14580000x + 31347000x + 30601800x + 19748745x + 8660574x + 1990182x +--R + +--R 133304 +--R / +--R 7 6 5 4 3 +--R 95659380x + 446410440x + 892820880x + 992023200x + 661348800x +--R + +--R 2 +--R 264539520x + 58786560x + 5598720 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=41666223/1953125*x+11111259/781250*x^2-17453753/234375*x^3-_ + 5848749/62500*x^4+2212083/15625*x^5+331713/1250*x^6-40338/875*x^7-_ + 13851/50*x^8-648/5*x^9+1331/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x +--R + +--R 6 5 4 3 +--R 217686656250x + 116134357500x - 76764830625x - 61088135500x +--R + +--R 2 +--R 11666821950x + 17499813660x +--R / +--R 820312500 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 111804log(5x + 3) - 106312500000x - 227242968750x - 37816875000x +--R + +--R 6 5 4 3 +--R 217686656250x + 116134357500x - 76764830625x - 61088135500x +--R + +--R 2 +--R 11666821950x + 17499813660x +--R / +--R 820312500 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x) +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=4166223/390625*x-138741/156250*x^2-1703753/46875*x^3-73749/12500*x^4+_ + 243333/3125*x^5+4419/125*x^6-11988/175*x^7-243/5*x^8+_ + 1331/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x +--R + +--R 5 4 3 2 +--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x +--R / +--R 164062500 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 111804log(5x + 3) - 7973437500x - 11238750000x + 5799937500x +--R + +--R 5 4 3 2 +--R 12774982500x - 967955625x - 5963135500x - 145678050x + 1749813660x +--R / +--R 164062500 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x) +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=416223/78125*x-138741/31250*x^2-128753/9375*x^3+31251/2500*x^4+_ + 14958/625*x^5-306/25*x^6-648/35*x^7+1331/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x +--R + +--R 3 2 +--R - 450635500x - 145678050x + 174813660x +--R / +--R 32812500 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 111804log(5x + 3) - 607500000x - 401625000x + 785295000x + 410169375x +--R + +--R 3 2 +--R - 450635500x - 145678050x + 174813660x +--R / +--R 32812500 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=41223/15625*x-26241/6250*x^2-5003/1875*x^3+2313/250*x^4+_ + 108/125*x^5-36/5*x^6+1331/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x +--R + +--R 2 +--R - 1968075x + 1236690x +--R / +--R 468750 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 7986log(5x + 3) - 3375000x + 405000x + 4336875x - 1250750x +--R + +--R 2 +--R - 1968075x + 1236690x +--R / +--R 468750 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x) +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=3723/3125*x-3741/1250*x^2+622/375*x^3+69/25*x^4-72/25*x^5+_ + 1331/15625*log(3+5*x) +--R +--R +--R 5 4 3 2 +--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x +--R (2) --------------------------------------------------------------------- +--R 93750 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 7986log(5x + 3) - 270000x + 258750x + 155500x - 280575x + 111690x +--R (3) --------------------------------------------------------------------- +--R 93750 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x) +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=-27/625*x-183/125*x^2+172/75*x^3-6/5*x^4+1331/3125*log(3+5*x) +--R +--R +--R 4 3 2 +--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x +--R (2) ---------------------------------------------------- +--R 9375 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 3993log(5x + 3) - 11250x + 21500x - 13725x - 405x +--R (3) ---------------------------------------------------- +--R 9375 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^3/(3+5*x) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 5x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=-402/125*x+42/25*x^2-8/15*x^3+1331/625*log(3+5*x) +--R +--R +--R 3 2 +--R 3993log(5x + 3) - 1000x + 3150x - 6030x +--R (2) ----------------------------------------- +--R 1875 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 3993log(5x + 3) - 1000x + 3150x - 6030x +--R (3) ----------------------------------------- +--R 1875 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=332/225*x-4/15*x^2-343/27*log(2+3*x)+1331/125*log(3+5*x) +--R +--R +--R 2 +--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x +--R (2) --------------------------------------------------- +--R 3375 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 35937log(5x + 3) - 42875log(3x + 2) - 900x + 4980x +--R (3) --------------------------------------------------- +--R 3375 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-8/45*x+343/27/(2+3*x)-1421/27*log(2+3*x)+1331/25*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x +--R + +--R - 240x + 8575 +--R / +--R 2025x + 1350 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (107811x + 71874)log(5x + 3) + (- 106575x - 71050)log(3x + 2) - 360x +--R + +--R - 240x + 8575 +--R / +--R 2025x + 1350 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=343/54/(2+3*x)^2+1421/27/(2+3*x)-7189/27*log(2+3*x)+1331/5*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (646866x + 862488x + 287496)log(5x + 3) +--R + +--R 2 +--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135 +--R / +--R 2 +--R 2430x + 3240x + 1080 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (646866x + 862488x + 287496)log(5x + 3) +--R + +--R 2 +--R (- 647010x - 862680x - 287560)log(3x + 2) + 42630x + 30135 +--R / +--R 2 +--R 2430x + 3240x + 1080 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=343/81/(2+3*x)^3+1421/54/(2+3*x)^2+7189/27/(2+3*x)-1331*log(2+3*x)+_ + 1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x +--R + +--R 530397x + 181748 +--R / +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(3x + 2) + 388206x +--R + +--R 530397x + 181748 +--R / +--R 3 2 +--R 4374x + 8748x + 5832x + 1296 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=343/108/(2+3*x)^4+1421/81/(2+3*x)^3+7189/54/(2+3*x)^2+1331/(2+3*x)-_ + 6655*log(2+3*x)+6655*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 11643588x + 23675382x + 16059444x + 3634885 +--R / +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (174653820x + 465743520x + 465743520x + 206997120x + 34499520) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 174653820x - 465743520x - 465743520x - 206997120x - 34499520) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 11643588x + 23675382x + 16059444x + 3634885 +--R / +--R 4 3 2 +--R 26244x + 69984x + 69984x + 31104x + 5184 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=343/135/(2+3*x)^5+1421/108/(2+3*x)^4+7189/81/(2+3*x)^3+1331/2/(2+3*x)^2+_ + 6655/(2+3*x)-33275*log(2+3*x)+33275*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 13099036500x + 43663455000x + 58217940000x + 38811960000x +--R + +--R 12937320000x + 1724976000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x +--R + +--R - 12937320000x - 1724976000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346 +--R / +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13099036500x + 43663455000x + 58217940000x + 38811960000x +--R + +--R 12937320000x + 1724976000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 13099036500x - 43663455000x - 58217940000x - 38811960000x +--R + +--R - 12937320000x - 1724976000 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 873269100x + 2357826570x + 2388229560x + 1075586865x + 181744346 +--R / +--R 5 4 3 2 +--R 393660x + 1312200x + 1749600x + 1166400x + 388800x + 51840 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=343/162/(2+3*x)^6+1421/135/(2+3*x)^5+7189/108/(2+3*x)^4+_ + 1331/3/(2+3*x)^3+6655/2/(2+3*x)^2+33275/(2+3*x)-166375*log(2+3*x)+_ + 166375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x +--R + +--R 2 +--R 582179400000x + 155247840000x + 17249760000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x +--R + +--R 2 +--R - 582179400000x - 155247840000x - 17249760000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 13099036500x + 44100089550x + 59401704780x + 40016101275x +--R + +--R 13482032616x + 1817443594 +--R / +--R 6 5 4 3 2 +--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x +--R + +--R 103680 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 196485547500x + 785942190000x + 1309903650000x + 1164358800000x +--R + +--R 2 +--R 582179400000x + 155247840000x + 17249760000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 196485547500x - 785942190000x - 1309903650000x - 1164358800000x +--R + +--R 2 +--R - 582179400000x - 155247840000x - 17249760000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 13099036500x + 44100089550x + 59401704780x + 40016101275x +--R + +--R 13482032616x + 1817443594 +--R / +--R 6 5 4 3 2 +--R 1180980x + 4723920x + 7873200x + 6998400x + 3499200x + 933120x +--R + +--R 103680 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=49/27/(2+3*x)^7+1421/162/(2+3*x)^6+7189/135/(2+3*x)^5+1331/4/(2+3*x)^4+_ + 6655/3/(2+3*x)^3+33275/2/(2+3*x)^2+166375/(2+3*x)-_ + 831875*log(2+3*x)+831875*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2947283212500x + 13753988325000x + 27507976650000x +--R + +--R 4 3 2 +--R 30564418500000x + 20376279000000x + 8150511600000x +--R + +--R 1811224800000x + 172497600000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2947283212500x - 13753988325000x - 27507976650000x +--R + +--R 4 3 2 +--R - 30564418500000x - 20376279000000x - 8150511600000x +--R + +--R - 1811224800000x - 172497600000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x +--R + +--R 2 +--R 602391504582x + 162081979026x + 18174436072 +--R / +--R 7 6 5 4 3 2 +--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x +--R + +--R 2177280x + 207360 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 2947283212500x + 13753988325000x + 27507976650000x +--R + +--R 4 3 2 +--R 30564418500000x + 20376279000000x + 8150511600000x +--R + +--R 1811224800000x + 172497600000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2947283212500x - 13753988325000x - 27507976650000x +--R + +--R 4 3 2 +--R - 30564418500000x - 20376279000000x - 8150511600000x +--R + +--R - 1811224800000x - 172497600000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 196485547500x + 792491708250x + 1332026467200x + 1194258563685x +--R + +--R 2 +--R 602391504582x + 162081979026x + 18174436072 +--R / +--R 7 6 5 4 3 2 +--R 3542940x + 16533720x + 33067440x + 36741600x + 24494400x + 9797760x +--R + +--R 2177280x + 207360 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=13880997/1953125*x-461623/390625*x^2-1836723/78125*x^3-5643/3125*x^4+_ + 774981/15625*x^5+12231/625*x^6-37908/875*x^7-729/25*x^8+_ + (-1331/9765625)/(3+5*x)+23232/9765625*log(3+5*x) +--R +--R +--R (2) +--R 9 8 +--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x +--R + +--R 7 6 5 4 +--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x +--R + +--R 3 2 +--R - 5225318000x + 2186822400x + 1457504685x - 9317 +--R / +--R 341796875x + 205078125 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (813120x + 487872)log(5x + 3) - 9966796875x - 20787890625x +--R + +--R 7 6 5 4 +--R - 2195859375x + 20966006250x + 9554422500x - 8405985000x +--R + +--R 3 2 +--R - 5225318000x + 2186822400x + 1457504685x - 9317 +--R / +--R 341796875x + 205078125 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=1382328/390625*x-507023/156250*x^2-26594/3125*x^3+108387/12500*x^4+_ + 44982/3125*x^5-1026/125*x^6-1944/175*x^7+(-1331/1953125)/(3+5*x)+_ + 19239/1953125*log(3+5*x) +--R +--R +--R (2) +--R 8 7 +--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x +--R + +--R 6 5 4 3 2 +--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x +--R + +--R 580577760x - 37268 +--R / +--R 273437500x + 164062500 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (2693460x + 1616076)log(5x + 3) - 3037500000x - 4066875000x +--R + +--R 6 5 4 3 2 +--R 2589300000x + 4732520625x - 904395625x - 2283475250x + 435255450x +--R + +--R 580577760x - 37268 +--R / +--R 273437500x + 164062500 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=133659/78125*x-1816/625*x^2-4217/3125*x^3+7317/1250*x^4+108/625*x^5-_ + 108/25*x^6+(-1331/390625)/(3+5*x)+15246/390625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x +--R + +--R 4 3 2 +--R 8448125x - 14512750x - 127050x + 4009770x - 2662 +--R / +--R 3906250x + 2343750 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (152460x + 91476)log(5x + 3) - 16875000x - 9450000x + 23270625x +--R + +--R 4 3 2 +--R 8448125x - 14512750x - 127050x + 4009770x - 2662 +--R / +--R 3906250x + 2343750 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=1998/3125*x-12077/6250*x^2+786/625*x^3+189/125*x^4-216/125*x^5+_ + (-1331/78125)/(3+5*x)+11253/78125*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x +--R + +--R 3 2 +--R - 920125x - 406275x + 299700x - 2662 +--R / +--R 781250x + 468750 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (112530x + 67518)log(5x + 3) - 1350000x + 371250x + 1691250x +--R + +--R 3 2 +--R - 920125x - 406275x + 299700x - 2662 +--R / +--R 781250x + 468750 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=-1179/3125*x-427/625*x^2+164/125*x^3-18/25*x^4+(-1331/15625)/(3+5*x)+_ + 1452/3125*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x +--R + +--R - 17685x - 1331 +--R / +--R 78125x + 46875 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (36300x + 21780)log(5x + 3) - 56250x + 68750x + 8125x - 61500x +--R + +--R - 17685x - 1331 +--R / +--R 78125x + 46875 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^2 +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=-1098/625*x+122/125*x^2-8/25*x^3+(-1331/3125)/(3+5*x)+3267/3125*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331 +--R ----------------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (16335x + 9801)log(5x + 3) - 5000x + 12250x - 18300x - 16470x - 1331 +--R ----------------------------------------------------------------------- +--R 15625x + 9375 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^3/(3+5*x)^2 +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=108/125*x-4/25*x^2+(-1331/625)/(3+5*x)-726/625*log(3+5*x) +--R +--R +--R 3 2 +--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331 +--R (2) ----------------------------------------------------------- +--R 3125x + 1875 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (- 3630x - 2178)log(5x + 3) - 500x + 2400x + 1620x - 1331 +--R (3) ----------------------------------------------------------- +--R 3125x + 1875 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=-8/75*x+(-1331/125)/(3+5*x)+343/9*log(2+3*x)-4719/125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x +--R + +--R - 360x - 11979 +--R / +--R 5625x + 3375 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 212355x - 127413)log(5x + 3) + (214375x + 128625)log(3x + 2) - 600x +--R + +--R - 360x - 11979 +--R / +--R 5625x + 3375 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=(-343/9)/(2+3*x)+(-1331/25)/(3+5*x)+3136/9*log(2+3*x)-8712/25*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 1176120x - 1489752x - 470448)log(5x + 3) +--R + +--R 2 +--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683 +--R / +--R 2 +--R 3375x + 4275x + 1350 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 1176120x - 1489752x - 470448)log(5x + 3) +--R + +--R 2 +--R (1176000x + 1489600x + 470400)log(3x + 2) - 78812x - 49683 +--R / +--R 2 +--R 3375x + 4275x + 1350 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=(-343/18)/(2+3*x)^2+(-3136/9)/(2+3*x)+(-1331/5)/(3+5*x)+_ + 2541*log(2+3*x)-2541*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3) +--R + +--R 3 2 2 +--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x +--R + +--R - 891911x - 289137 +--R / +--R 3 2 +--R 4050x + 7830x + 5040x + 1080 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 10291050x - 19896030x - 12806640x - 2744280)log(5x + 3) +--R + +--R 3 2 2 +--R (10291050x + 19896030x + 12806640x + 2744280)log(3x + 2) - 686022x +--R + +--R - 891911x - 289137 +--R / +--R 3 2 +--R 4050x + 7830x + 5040x + 1080 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-343/27)/(2+3*x)^3+(-1568/9)/(2+3*x)^2+(-2541)/(2+3*x)+_ + (-1331)/(3+5*x)+16698*log(2+3*x)-16698*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R - 4057614x - 7979967x - 5226815x - 1140033 +--R / +--R 4 3 2 +--R 3645x + 9477x + 9234x + 3996x + 648 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 60864210x - 158246946x - 154189332x - 66725208x - 10820304) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (60864210x + 158246946x + 154189332x + 66725208x + 10820304) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R - 4057614x - 7979967x - 5226815x - 1140033 +--R / +--R 4 3 2 +--R 3645x + 9477x + 9234x + 3996x + 648 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-343/36)/(2+3*x)^4+(-3136/27)/(2+3*x)^3+(-2541/2)/(2+3*x)^2+_ + (-16698)/(2+3*x)+(-6655)/(3+5*x)+103455*log(2+3*x)-103455*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x +--R + +--R - 4111715520x - 536310720 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 4525121700x + 14782064220x + 19307185920x + 12603301920x +--R + +--R 4111715520x + 536310720 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975 +--R / +--R 5 4 3 2 +--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 4525121700x - 14782064220x - 19307185920x - 12603301920x +--R + +--R - 4111715520x - 536310720 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 4525121700x + 14782064220x + 19307185920x + 12603301920x +--R + +--R 4111715520x + 536310720 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R - 301674780x - 794410254x - 784130946x - 343827337x - 56505975 +--R / +--R 5 4 3 2 +--R 43740x + 142884x + 186624x + 121824x + 39744x + 5184 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-343/45)/(2+3*x)^5+(-784/9)/(2+3*x)^4+(-847)/(2+3*x)^3+_ + (-8349)/(2+3*x)^2+(-103455)/(2+3*x)+(-33275)/(3+5*x)+_ + 617100*log(2+3*x)-617100*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x +--R + +--R 2 +--R - 93305520000x - 24437160000x - 2665872000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 33739942500x + 132710440500x + 217435185000x + 189943380000x +--R + +--R 2 +--R 93305520000x + 24437160000x + 2665872000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x +--R + +--R - 280877649 +--R / +--R 6 5 4 3 2 +--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 33739942500x - 132710440500x - 217435185000x - 189943380000x +--R + +--R 2 +--R - 93305520000x - 24437160000x - 2665872000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R 33739942500x + 132710440500x + 217435185000x + 189943380000x +--R + +--R 2 +--R 93305520000x + 24437160000x + 2665872000 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2249329500x - 7422787350x - 9795413430x - 6461351715x - 2130399775x +--R + +--R - 280877649 +--R / +--R 6 5 4 3 2 +--R 54675x + 215055x + 352350x + 307800x + 151200x + 39600x + 4320 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-343/54)/(2+3*x)^6+(-3136/45)/(2+3*x)^5+(-2541/4)/(2+3*x)^4+_ + (-5566)/(2+3*x)^3+(-103455/2)/(2+3*x)^2+(-617100)/(2+3*x)+_ + (-166375)/(3+5*x)+3584625*log(2+3*x)-3584625*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 7055617387500x - 32455839982500x - 63970930980000x +--R + +--R 4 3 2 +--R - 70033535550000x - 45992172600000x - 18118128600000x +--R + +--R - 3964308480000x - 371653920000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 7055617387500x + 32455839982500x + 63970930980000x +--R + +--R 4 3 2 +--R 70033535550000x + 45992172600000x + 18118128600000x +--R + +--R 3964308480000x + 371653920000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x +--R + +--R 2 +--R - 1346292632205x - 355739265638x - 39157648662 +--R / +--R 7 6 5 4 3 2 +--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x +--R + +--R 1105920x + 103680 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 7055617387500x - 32455839982500x - 63970930980000x +--R + +--R 4 3 2 +--R - 70033535550000x - 45992172600000x - 18118128600000x +--R + +--R - 3964308480000x - 371653920000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R 7055617387500x + 32455839982500x + 63970930980000x +--R + +--R 4 3 2 +--R 70033535550000x + 45992172600000x + 18118128600000x +--R + +--R 3964308480000x + 371653920000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 470374492500x - 1865818820250x - 3083217691950x - 2716778541015x +--R + +--R 2 +--R - 1346292632205x - 355739265638x - 39157648662 +--R / +--R 7 6 5 4 3 2 +--R 1968300x + 9054180x + 17845920x + 19537200x + 12830400x + 5054400x +--R + +--R 1105920x + 103680 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^2) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-49/9)/(2+3*x)^7+(-1568/27)/(2+3*x)^6+(-2541/5)/(2+3*x)^5+_ + (-8349/2)/(2+3*x)^4+(-34485)/(2+3*x)^3+(-308550)/(2+3*x)^2+_ + (-3584625)/(2+3*x)+(-831875)/(3+5*x)+20418750*log(2+3*x)-_ + 20418750*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 60285338437500x - 317502782437500x - 731462106375000x +--R + +--R 5 4 3 +--R - 962779182750000x - 791896297500000x - 416787525000000x +--R + +--R 2 +--R - 137076786000000x - 25757028000000x - 2117016000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 60285338437500x + 317502782437500x + 731462106375000x +--R + +--R 5 4 3 +--R 962779182750000x + 791896297500000x + 416787525000000x +--R + +--R 2 +--R 137076786000000x + 25757028000000x + 2117016000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 +--R - 4019022562500x - 18621471206250x - 36972030521250x +--R + +--R 4 3 2 +--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x +--R + +--R - 223049897418 +--R / +--R 8 7 6 5 4 +--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x +--R + +--R 3 2 +--R 20412000x + 6713280x + 1261440x + 103680 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 60285338437500x - 317502782437500x - 731462106375000x +--R + +--R 5 4 3 +--R - 962779182750000x - 791896297500000x - 416787525000000x +--R + +--R 2 +--R - 137076786000000x - 25757028000000x - 2117016000000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R 60285338437500x + 317502782437500x + 731462106375000x +--R + +--R 5 4 3 +--R 962779182750000x + 791896297500000x + 416787525000000x +--R + +--R 2 +--R 137076786000000x + 25757028000000x + 2117016000000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 +--R - 4019022562500x - 18621471206250x - 36972030521250x +--R + +--R 4 3 2 +--R - 40775613627375x - 26978454053595x - 10708299857748x - 2360937751874x +--R + +--R - 223049897418 +--R / +--R 8 7 6 5 4 +--R 2952450x + 15549570x + 35823060x + 47151720x + 38782800x +--R + +--R 3 2 +--R 20412000x + 6713280x + 1261440x + 103680 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^3*(2+3*x)^7/(3+5*x)^3 +--R +--R +--R (1) +--R 10 9 8 7 6 5 4 +--R - 17496x - 55404x - 53946x + 4455x + 38934x + 17388x - 6216x +--R + +--R 3 2 +--R - 6064x - 480x + 576x + 128 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=46214407/9765625*x-2300646/1953125*x^2-5918904/390625*x^3+_ + 6507/62500*x^4+491913/15625*x^5+33291/3125*x^6-119556/4375*x^7-_ + 2187/125*x^8+(-1331/97656250)/(3+5*x)^2+(-1089/1953125)/(3+5*x)+_ + 47289/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 10 +--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x +--R + +--R 9 8 7 6 +--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x +--R + +--R 5 4 3 2 +--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x +--R + +--R 58226341320x - 2305534 +--R / +--R 2 +--R 34179687500x + 41015625000x + 12304687500 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 +--R (165511500x + 198613800x + 59584140)log(5x + 3) - 598007812500x +--R + +--R 9 8 7 6 +--R - 1651640625000x - 972000000000x + 1176752812500x + 1425913453125x +--R + +--R 5 4 3 2 +--R - 126252393750x - 660465159375x - 73008617500x + 179606439600x +--R + +--R 58226341320x - 2305534 +--R / +--R 2 +--R 34179687500x + 41015625000x + 12304687500 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^3*(2+3*x)^6/(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 2 +--R - 5832x - 14580x - 8262x + 6993x + 8316x + 252x - 2240x - 528x +--R + +--R 192x + 64 +--R / +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=4571416/1953125*x-915777/390625*x^2-81747/15625*x^3+74223/12500*x^4+_ + 134622/15625*x^5-3402/625*x^6-5832/875*x^7+(-1331/19531250)/(3+5*x)^2+_ + (-23232/9765625)/(3+5*x)+166749/9765625*log(3+5*x) +--R +--R +--R (2) +--R 2 9 +--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x +--R + +--R 8 7 6 5 +--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x +--R + +--R 4 3 2 +--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (116724300x + 140069160x + 42020748)log(5x + 3) - 45562500000x +--R + +--R 8 7 6 5 +--R - 91884375000x - 2156625000x + 97871878125x + 34147496250x +--R + +--R 4 3 2 +--R - 44330619375x - 16106513500x + 13430552100x + 5756731680x - 1970122 +--R / +--R 2 +--R 6835937500x + 8203125000x + 2460937500 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^3*(2+3*x)^5/(3+5*x)^3 +--R +--R +--R 8 7 6 5 4 3 2 +--R - 1944x - 3564x - 378x + 2583x + 1050x - 616x - 336x + 48x + 32 +--R (1) ---------------------------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=424432/390625*x-62097/31250*x^2-393/625*x^3+22977/6250*x^4-_ + 324/3125*x^5-324/125*x^6+(-1331/3906250)/(3+5*x)^2+_ + (-19239/1953125)/(3+5*x)+109032/1953125*log(3+5*x) +--R +--R +--R (2) +--R 2 8 7 +--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x +--R + +--R 6 5 4 3 2 +--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x +--R + +--R 38006490x - 116765 +--R / +--R 2 +--R 97656250x + 117187500x + 35156250 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 +--R (5451600x + 6541920x + 1962576)log(5x + 3) - 253125000x - 313875000x +--R + +--R 6 5 4 3 2 +--R 255740625x + 365767500x - 138495000x - 148862000x + 57470475x +--R + +--R 38006490x - 116765 +--R / +--R 2 +--R 97656250x + 117187500x + 35156250 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^3*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 7 6 5 4 3 2 +--R - 648x - 756x + 378x + 609x - 56x - 168x + 16 +--R (1) --------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=4691/15625*x-7617/6250*x^2+2826/3125*x^3+513/625*x^4-648/625*x^5+_ + (-1331/781250)/(3+5*x)^2+(-15246/390625)/(3+5*x)+63294/390625*log(3+5*x) +--R +--R +--R (2) +--R 2 7 6 +--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x +--R + +--R 5 4 3 2 +--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (3164700x + 3797640x + 1139292)log(5x + 3) - 20250000x - 8268750x +--R + +--R 5 4 3 2 +--R 29610000x + 3163125x - 16341500x - 1532625x + 1958490x - 92807 +--R / +--R 2 +--R 19531250x + 23437500x + 7031250 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^3*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 216x - 108x + 198x + 71x - 66x - 12x + 8 +--R (1) ----------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=-1303/3125*x-927/3125*x^2+468/625*x^3-54/125*x^4+_ + (-1331/156250)/(3+5*x)^2+(-11253/78125)/(3+5*x)+5907/15625*log(3+5*x) +--R +--R +--R (2) +--R 2 6 5 +--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x +--R + +--R 4 3 2 +--R 1743750x - 1966250x - 2371650x - 698880x - 68849 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (1476750x + 1772100x + 531630)log(5x + 3) - 1687500x + 900000x +--R + +--R 4 3 2 +--R 1743750x - 1966250x - 2371650x - 698880x - 68849 +--R / +--R 2 +--R 3906250x + 4687500x + 1406250 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^3*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--R - 72x + 12x + 58x - 15x - 12x + 4 +--R (1) ------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=-2978/3125*x+354/625*x^2-24/125*x^3+(-1331/31250)/(3+5*x)^2+_ + (-1452/3125)/(3+5*x)+1551/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x +--R + +--R 2 +--R - 734100x - 340620x - 44891 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (387750x + 465300x + 139590)log(5x + 3) - 150000x + 262500x - 267500x +--R + +--R 2 +--R - 734100x - 340620x - 44891 +--R / +--R 2 +--R 781250x + 937500x + 281250 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^3*(2+3*x)/(3+5*x)^3 +--R +--R +--R 4 3 2 +--R - 24x + 20x + 6x - 9x + 2 +--R (1) ---------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=316/625*x-12/125*x^2+(-1331/6250)/(3+5*x)^2+(-3267/3125)/(3+5*x)-_ + 2046/3125*log(3+5*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x +--R + +--R - 4230x - 20933 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 102300x - 122760x - 36828)log(5x + 3) - 15000x + 61000x + 89400x +--R + +--R - 4230x - 20933 +--R / +--R 2 +--R 156250x + 187500x + 56250 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^3/(3+5*x)^3 +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=-8/125*x+(-1331/1250)/(3+5*x)^2+726/625/(3+5*x)+132/625*log(3+5*x) +--R +--R +--R 2 3 2 +--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025 +--R (2) ------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (6600x + 7920x + 2376)log(5x + 3) - 2000x - 2400x + 6540x + 3025 +--R (3) ------------------------------------------------------------------- +--R 2 +--R 31250x + 37500x + 11250 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^3/((2+3*x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=(-1331/250)/(3+5*x)^2+4719/125/(3+5*x)-343/3*log(2+3*x)+_ + 14289/125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2143350x + 2572020x + 771606)log(5x + 3) +--R + +--R 2 +--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949 +--R / +--R 2 +--R 18750x + 22500x + 6750 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2143350x + 2572020x + 771606)log(5x + 3) +--R + +--R 2 +--R (- 2143750x - 2572500x - 771750)log(3x + 2) + 141570x + 80949 +--R / +--R 2 +--R 18750x + 22500x + 6750 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^3/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=343/3/(2+3*x)+(-1331/50)/(3+5*x)^2+8712/25/(3+5*x)-1617*log(2+3*x)+_ + 1617*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3) +--R + +--R 3 2 2 +--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x +--R + +--R 1495689x + 459996 +--R / +--R 3 2 +--R 11250x + 21000x + 13050x + 2700 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (18191250x + 33957000x + 21101850x + 4365900)log(5x + 3) +--R + +--R 3 2 2 +--R (- 18191250x - 33957000x - 21101850x - 4365900)log(3x + 2) + 1212830x +--R + +--R 1495689x + 459996 +--R / +--R 3 2 +--R 11250x + 21000x + 13050x + 2700 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^3/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=343/6/(2+3*x)^2+1617/(2+3*x)+(-1331/10)/(3+5*x)^2+2541/(3+5*x)-_ + 15708*log(2+3*x)+15708*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 7068600x + 13430348x + 8492784x + 1787403 +--R / +--R 4 3 2 +--R 6750x + 17100x + 16230x + 6840x + 1080 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (106029000x + 268606800x + 254940840x + 107442720x + 16964640) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 106029000x - 268606800x - 254940840x - 107442720x - 16964640) +--R * +--R log(3x + 2) +--R + +--R 3 2 +--R 7068600x + 13430348x + 8492784x + 1787403 +--R / +--R 4 3 2 +--R 6750x + 17100x + 16230x + 6840x + 1080 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^3/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=343/9/(2+3*x)^3+1617/2/(2+3*x)^2+15708/(2+3*x)+(-1331/2)/(3+5*x)^2+_ + 16698/(3+5*x)-128634*log(2+3*x)+128634*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1562903100x + 5001289920x + 6397483356x + 4089017592x +--R + +--R 1305892368x + 166709664 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x +--R + +--R - 1305892368x - 166709664 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616 +--R / +--R 5 4 3 2 +--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1562903100x + 5001289920x + 6397483356x + 4089017592x +--R + +--R 1305892368x + 166709664 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 1562903100x - 5001289920x - 6397483356x - 4089017592x +--R + +--R - 1305892368x - 166709664 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R 104193540x + 267430086x + 257165096x + 109804551x + 17564616 +--R / +--R 5 4 3 2 +--R 12150x + 38880x + 49734x + 31788x + 10152x + 1296 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^3/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=343/12/(2+3*x)^4+539/(2+3*x)^3+7854/(2+3*x)^2+128634/(2+3*x)+_ + (-6655/2)/(3+5*x)^2+103455/(3+5*x)-953535*log(2+3*x)+953535*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 23170900500x + 89594148600x + 144277473780x + 123852754080x +--R + +--R 2 +--R 59775202080x + 15378612480x + 1647708480 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x +--R + +--R 2 +--R - 59775202080x - 15378612480x - 1647708480 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x +--R + +--R 173603415 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 23170900500x + 89594148600x + 144277473780x + 123852754080x +--R + +--R 2 +--R 59775202080x + 15378612480x + 1647708480 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 3 +--R - 23170900500x - 89594148600x - 144277473780x - 123852754080x +--R + +--R 2 +--R - 59775202080x - 15378612480x - 1647708480 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R 1544726700x + 4994616330x + 6455813364x + 4169655991x + 1345680462x +--R + +--R 173603415 +--R / +--R 6 5 4 3 2 +--R 24300x + 93960x + 151308x + 129888x + 62688x + 16128x + 1728 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^3/((2+3*x)^6*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=343/15/(2+3*x)^5+1617/4/(2+3*x)^4+5236/(2+3*x)^3+64317/(2+3*x)^2+_ + 953535/(2+3*x)+(-33275/2)/(3+5*x)^2+617100/(3+5*x)-_ + 6618975*log(2+3*x)+6618975*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2412616387500x + 10937194290000x + 21241746949500x +--R + +--R 4 3 2 +--R 22910920065000x + 14821208820000x + 5750565480000x +--R + +--R 1239072120000x + 114375888000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2412616387500x - 10937194290000x - 21241746949500x +--R + +--R 4 3 2 +--R - 22910920065000x - 14821208820000x - 5750565480000x +--R + +--R - 1239072120000x - 114375888000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x +--R + +--R 2 +--R 429553050280x + 111486629505x + 12050702538 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 2412616387500x + 10937194290000x + 21241746949500x +--R + +--R 4 3 2 +--R 22910920065000x + 14821208820000x + 5750565480000x +--R + +--R 1239072120000x + 114375888000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 2412616387500x - 10937194290000x - 21241746949500x +--R + +--R 4 3 2 +--R - 22910920065000x - 14821208820000x - 5750565480000x +--R + +--R - 1239072120000x - 114375888000 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R 160841092500x + 627280260750x + 1018898535600x + 882286862985x +--R + +--R 2 +--R 429553050280x + 111486629505x + 12050702538 +--R / +--R 7 6 5 4 3 2 +--R 364500x + 1652400x + 3209220x + 3461400x + 2239200x + 868800x +--R + +--R 187200x + 17280 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^3/((2+3*x)^7*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=343/18/(2+3*x)^6+1617/5/(2+3*x)^5+3927/(2+3*x)^4+42878/(2+3*x)^3+_ + 953535/2/(2+3*x)^2+6618975/(2+3*x)+(-166375/2)/(3+5*x)^2+_ + 3584625/(3+5*x)-43848750*log(2+3*x)+43848750*log(3+5*x) +--R +--R +--R (2) +--R 8 7 6 +--R 71922912187500x + 373999143375000x + 850608308137500x +--R + +--R 5 4 3 +--R 1105162141050000x + 897171734250000x + 465989436000000x +--R + +--R 2 +--R 151225569000000x + 28035136800000x + 2273119200000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 71922912187500x - 373999143375000x - 850608308137500x +--R + +--R 5 4 3 +--R - 1105162141050000x - 897171734250000x - 465989436000000x +--R + +--R 2 +--R - 151225569000000x - 28035136800000x - 2273119200000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x +--R + +--R 3 2 +--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063 +--R / +--R 8 7 6 5 4 3 +--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x +--R + +--R 2 +--R 3448800x + 639360x + 51840 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 71922912187500x + 373999143375000x + 850608308137500x +--R + +--R 5 4 3 +--R 1105162141050000x + 897171734250000x + 465989436000000x +--R + +--R 2 +--R 151225569000000x + 28035136800000x + 2273119200000 +--R * +--R log(5x + 3) +--R + +--R 8 7 6 +--R - 71922912187500x - 373999143375000x - 850608308137500x +--R + +--R 5 4 3 +--R - 1105162141050000x - 897171734250000x - 465989436000000x +--R + +--R 2 +--R - 151225569000000x - 28035136800000x - 2273119200000 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R 4794860812500x + 21896531043750x + 42841193422500x + 46551705341625x +--R + +--R 3 2 +--R 30340145968110x + 11860532030465x + 2574943269792x + 239497011063 +--R / +--R 8 7 6 5 4 3 +--R 1640250x + 8529300x + 19398690x + 25203960x + 20460600x + 10627200x +--R + +--R 2 +--R 3448800x + 639360x + 51840 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^3/((2+3*x)^8*(3+5*x)^3) +--R +--R +--R (1) +--R 3 2 +--R - 8x + 12x - 6x + 1 +--R / +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=49/3/(2+3*x)^7+539/2/(2+3*x)^6+15708/5/(2+3*x)^5+64317/2/(2+3*x)^4+_ + 317845/(2+3*x)^3+6618975/2/(2+3*x)^2+43848750/(2+3*x)+_ + (-831875/2)/(3+5*x)^2+20418750/(3+5*x)-280500000*log(2+3*x)+_ + 280500000*log(3+5*x) +--R +--R +--R (2) +--R 9 8 7 +--R 460090125000000x + 2699195400000000x + 7036311645000000x +--R + +--R 6 5 4 +--R 10697265810000000x + 10452338820000000x + 6807061800000000x +--R + +--R 3 2 +--R 2954674800000000x + 824266080000000x + 134101440000000x +--R + +--R 9694080000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 460090125000000x - 2699195400000000x - 7036311645000000x +--R + +--R 6 5 4 +--R - 10697265810000000x - 10452338820000000x - 6807061800000000x +--R + +--R 3 2 +--R - 2954674800000000x - 824266080000000x - 134101440000000x +--R + +--R - 9694080000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R 30672675000000x + 160520332500000x + 367435926000000x +--R + +--R 5 4 3 +--R 480493891350000x + 392612784696000x + 205262100529200x +--R + +--R 2 +--R 67053019228048x + 12513316868859x + 1021373267628 +--R / +--R 9 8 7 6 5 4 +--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x +--R + +--R 3 2 +--R 10533600x + 2938560x + 478080x + 34560 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R 460090125000000x + 2699195400000000x + 7036311645000000x +--R + +--R 6 5 4 +--R 10697265810000000x + 10452338820000000x + 6807061800000000x +--R + +--R 3 2 +--R 2954674800000000x + 824266080000000x + 134101440000000x +--R + +--R 9694080000000 +--R * +--R log(5x + 3) +--R + +--R 9 8 7 +--R - 460090125000000x - 2699195400000000x - 7036311645000000x +--R + +--R 6 5 4 +--R - 10697265810000000x - 10452338820000000x - 6807061800000000x +--R + +--R 3 2 +--R - 2954674800000000x - 824266080000000x - 134101440000000x +--R + +--R - 9694080000000 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R 30672675000000x + 160520332500000x + 367435926000000x +--R + +--R 5 4 3 +--R 480493891350000x + 392612784696000x + 205262100529200x +--R + +--R 2 +--R 67053019228048x + 12513316868859x + 1021373267628 +--R / +--R 9 8 7 6 5 4 +--R 1640250x + 9622800x + 25084890x + 38136420x + 37263240x + 24267600x +--R + +--R 3 2 +--R 10533600x + 2938560x + 478080x + 34560 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^m*(3+5*x)/(1-2*x) +--R +--R +--R m +--R (- 5x - 3)(3x + 2) +--R (1) ------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=-5/6*(2+3*x)^(1+m)/(1+m)+11/14*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3g.input.pamphlet b/src/input/rich3g.input.pamphlet new file mode 100644 index 0000000..fe9418d --- /dev/null +++ b/src/input/rich3g.input.pamphlet @@ -0,0 +1,6855 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3g.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 95 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 5 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3g.output +)spool rich3g.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x +--R + +--R 3 2 +--R - 225792x - 63744x - 10496x - 768 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=-63019595/512*x-60332619/512*x^2-17391129/128*x^3-37722699/256*x^4-_ + 21272139/160*x^5-2929689/32*x^6-353565/8*x^7-422091/32*x^8-_ + 3645/2*x^9-63412811/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 317064055log(- 2x + 1) - 9331200x - 67534560x - 226281600x +--R + +--R 6 5 4 3 2 +--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x +--R + +--R - 630195950x +--R / +--R 5120 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 317064055log(2x - 1) - 9331200x - 67534560x - 226281600x +--R + +--R 6 5 4 3 2 +--R - 468750240x - 680708448x - 754453980x - 695645160x - 603326190x +--R + +--R - 630195950x +--R / +--R 5120 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 63412811log(2x - 1) + 63412811log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=-8960669/256*x-8362653/256*x^2-2257119/64*x^3-4352157/128*x^4-_ + 2053917/80*x^5-218943/16*x^6-126117/28*x^7-10935/16*x^8-_ + 9058973/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 317064055log(- 2x + 1) - 12247200x - 80714880x - 245216160x +--R + +--R 5 4 3 2 +--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x +--R / +--R 17920 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 317064055log(2x - 1) - 12247200x - 80714880x - 245216160x +--R + +--R 5 4 3 2 +--R - 460077408x - 609301980x - 631993320x - 585385710x - 627246830x +--R / +--R 17920 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R - 9058973log(2x - 1) + 9058973log(- 2x + 1) +--R (4) ------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=-1269563/128*x-1138491/128*x^2-279657/32*x^3-458811/64*x^4-_ + 169371/40*x^5-12393/8*x^6-3645/14*x^7-1294139/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 45294865log(- 2x + 1) - 2332800x - 13880160x - 37939104x +--R + +--R 4 3 2 +--R - 64233540x - 78303960x - 79694370x - 88869410x +--R / +--R 8960 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 45294865log(2x - 1) - 2332800x - 13880160x - 37939104x - 64233540x +--R + +--R 3 2 +--R - 78303960x - 79694370x - 88869410x +--R / +--R 8960 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R - 1294139log(2x - 1) + 1294139log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=-178733/64*x-150573/64*x^2-32271/16*x^3-42093/32*x^4-10773/20*x^5-_ + 405/4*x^6-184877/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 924385log(- 2x + 1) - 64800x - 344736x - 841860x - 1290840x +--R + +--R 2 +--R - 1505730x - 1787330x +--R / +--R 640 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 924385log(2x - 1) - 64800x - 344736x - 841860x - 1290840x +--R + +--R 2 +--R - 1505730x - 1787330x +--R / +--R 640 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R - 184877log(2x - 1) + 184877log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=-24875/32*x-18987/32*x^2-3321/8*x^3-3051/16*x^4-81/2*x^5-_ + 26411/64*log(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 26411log(- 2x + 1) - 2592x - 12204x - 26568x - 37974x - 49750x +--R (2) -------------------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 26411log(2x - 1) - 2592x - 12204x - 26568x - 37974x - 49750x +--R (3) ------------------------------------------------------------------ +--R 64 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R - 26411log(2x - 1) + 26411log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x) +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=-3389/16*x-2205/16*x^2-279/4*x^3-135/8*x^4-3773/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 3773log(- 2x + 1) - 540x - 2232x - 4410x - 6778x +--R (2) ----------------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 3773log(2x - 1) - 540x - 2232x - 4410x - 6778x +--R (3) --------------------------------------------------- +--R 32 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R - 3773log(2x - 1) + 3773log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x) +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=-443/8*x-219/8*x^2-15/2*x^3-539/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 539log(- 2x + 1) - 120x - 438x - 886x +--R (2) ----------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 539log(2x - 1) - 120x - 438x - 886x +--R (3) --------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R - 539log(2x - 1) + 539log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x) +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ---------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=-53/4*x-15/4*x^2-77/8*log(1-2*x) +--R +--R +--R 2 +--R - 77log(- 2x + 1) - 30x - 106x +--R (2) ------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 77log(2x - 1) - 30x - 106x +--R (3) ----------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R - 77log(2x - 1) + 77log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)/(1-2*x) +--R +--R +--R - 5x - 3 +--R (1) -------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=-5/2*x-11/4*log(1-2*x) +--R +--R +--R - 11log(- 2x + 1) - 10x +--R (2) ----------------------- +--R 4 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 11log(2x - 1) - 10x +--R (3) --------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) ----------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=-11/14*log(1-2*x)-1/21*log(2+3*x) +--R +--R +--R - 2log(3x + 2) - 33log(- 2x + 1) +--R (2) -------------------------------- +--R 42 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 2log(3x + 2) - 33log(2x - 1) +--R (3) ------------------------------ +--R 42 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 14 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) -------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=1/21/(2+3*x)-11/49*log(1-2*x)+11/49*log(2+3*x) +--R +--R +--R (99x + 66)log(3x + 2) + (- 99x - 66)log(- 2x + 1) + 7 +--R (2) ----------------------------------------------------- +--R 441x + 294 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (99x + 66)log(3x + 2) + (- 99x - 66)log(2x - 1) + 7 +--R (3) --------------------------------------------------- +--R 441x + 294 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R - 11log(2x - 1) + 11log(- 2x + 1) +--R (4) --------------------------------- +--R 49 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=1/42/(2+3*x)^2+(-11/49)/(2+3*x)-22/343*log(1-2*x)+22/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(- 2x + 1) +--R + +--R - 1386x - 875 +--R / +--R 2 +--R 18522x + 24696x + 8232 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1188x + 1584x + 528)log(3x + 2) + (- 1188x - 1584x - 528)log(2x - 1) +--R + +--R - 1386x - 875 +--R / +--R 2 +--R 18522x + 24696x + 8232 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 22log(2x - 1) + 22log(- 2x + 1) +--R (4) --------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=1/63/(2+3*x)^3+(-11/98)/(2+3*x)^2+(-22/343)/(2+3*x)-_ + 44/2401*log(1-2*x)+44/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (21384x + 42768x + 28512x + 6336)log(3x + 2) +--R + +--R 3 2 2 +--R (- 21384x - 42768x - 28512x - 6336)log(- 2x + 1) - 24948x - 47817x +--R + +--R - 20104 +--R / +--R 3 2 +--R 1166886x + 2333772x + 1555848x + 345744 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (21384x + 42768x + 28512x + 6336)log(3x + 2) +--R + +--R 3 2 2 +--R (- 21384x - 42768x - 28512x - 6336)log(2x - 1) - 24948x - 47817x - 20104 +--R / +--R 3 2 +--R 1166886x + 2333772x + 1555848x + 345744 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 44log(2x - 1) + 44log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=1/84/(2+3*x)^4+(-11/147)/(2+3*x)^3+(-11/343)/(2+3*x)^2+_ + (-44/2401)/(2+3*x)-88/16807*log(1-2*x)+88/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(- 2x + 1) - 33264x +--R + +--R 2 +--R - 85932x - 85316x - 27741 +--R / +--R 4 3 2 +--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (28512x + 76032x + 76032x + 33792x + 5632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 28512x - 76032x - 76032x - 33792x - 5632)log(2x - 1) - 33264x +--R + +--R 2 +--R - 85932x - 85316x - 27741 +--R / +--R 4 3 2 +--R 5445468x + 14521248x + 14521248x + 6453888x + 1075648 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 88log(2x - 1) + 88log(- 2x + 1) +--R (4) --------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^6) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=1/105/(2+3*x)^5+(-11/196)/(2+3*x)^4+(-22/1029)/(2+3*x)^3+_ + (-22/2401)/(2+3*x)^2+(-88/16807)/(2+3*x)-176/117649*log(1-2*x)+_ + 176/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582 +--R / +--R 5 4 3 2 +--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x +--R + +--R 225886080 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2566080x + 8553600x + 11404800x + 7603200x + 2534400x + 337920) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2566080x - 8553600x - 11404800x - 7603200x - 2534400x - 337920) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2993760x - 9729720x - 12834360x - 8876175x - 2437582 +--R / +--R 5 4 3 2 +--R 1715322420x + 5717741400x + 7623655200x + 5082436800x + 1694145600x +--R + +--R 225886080 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 176log(2x - 1) + 176log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R - 5x - 3 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=1/126/(2+3*x)^6+(-11/245)/(2+3*x)^5+(-11/686)/(2+3*x)^4+_ + (-44/7203)/(2+3*x)^3+(-44/16807)/(2+3*x)^2+(-176/117649)/(2+3*x)-_ + 352/823543*log(1-2*x)+352/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x +--R + +--R 18247680x + 2027520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x +--R + +--R - 18247680x - 2027520 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x +--R + +--R - 21096187 +--R / +--R 6 5 4 3 +--R 54032656230x + 216130624920x + 360217708200x + 320193518400x +--R + +--R 2 +--R 160096759200x + 42692469120x + 4743607680 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 23094720x + 92378880x + 153964800x + 136857600x + 68428800x +--R + +--R 18247680x + 2027520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 23094720x - 92378880x - 153964800x - 136857600x - 68428800x +--R + +--R - 18247680x - 2027520 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 26943840x - 105530040x - 173887560x - 156891735x - 85783698x +--R + +--R - 21096187 +--R / +--R 6 5 4 3 +--R 54032656230x + 216130624920x + 360217708200x + 320193518400x +--R + +--R 2 +--R 160096759200x + 42692469120x + 4743607680 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 352log(2x - 1) + 352log(- 2x + 1) +--R (4) ----------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R - 5x - 3 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=1/147/(2+3*x)^7+(-11/294)/(2+3*x)^6+(-22/1715)/(2+3*x)^5+_ + (-11/2401)/(2+3*x)^4+(-88/50421)/(2+3*x)^3+(-88/117649)/(2+3*x)^2+_ + (-352/823543)/(2+3*x)-704/5764801*log(1-2*x)+704/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x +--R + +--R 2 +--R 127733760x + 28385280x + 2703360 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x +--R + +--R 2 +--R - 127733760x - 28385280x - 2703360 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x +--R + +--R - 177159213x - 40677476 +--R / +--R 7 6 5 4 +--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x +--R + +--R 3 2 +--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 46189440x + 215550720x + 431101440x + 479001600x + 319334400x +--R + +--R 2 +--R 127733760x + 28385280x + 2703360 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 46189440x - 215550720x - 431101440x - 479001600x - 319334400x +--R + +--R 2 +--R - 127733760x - 28385280x - 2703360 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 53887680x - 246985200x - 488481840x - 545633550x - 380756376x +--R + +--R - 177159213x - 40677476 +--R / +--R 7 6 5 4 +--R 378228593610x + 1765066770180x + 3530133540360x + 3922370600400x +--R + +--R 3 2 +--R 2614913733600x + 1045965493440x + 232436776320x + 22136835840 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 704log(2x - 1) + 704log(- 2x + 1) +--R (4) ----------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^m*(3+5*x)^2/(1-2*x) +--R +--R +--R 2 m +--R (- 25x - 30x - 9)(3x + 2) +--R (1) --------------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=-5/36*(64+33*m)*(2+3*x)^(1+m)/((1+m)*(2+m))-_ +-- 5/6*(2+3*x)^(1+m)*(3+5*x)/(2+m)+121/28*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 164025x - 1071630x - 3150009x - 5485968x - 6268752x - 4910976x +--R + +--R 4 3 2 +--R - 2671200x - 996096x - 243712x - 35328x - 2304 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=-695181625/1024*x-677093689/1024*x^2-204901139/256*x^3-_ + 487203129/512*x^4-316246329/320*x^5-53031699/64*x^6-8399295/16*x^7-_ + 14907321/64*x^8-256365/4*x^9-32805/4*x^10-697540921/2048*log(1-2*x) +--R +--R +--R (2) +--R 10 9 8 +--R - 3487704605log(- 2x + 1) - 83980800x - 656294400x - 2385171360x +--R + +--R 7 6 5 4 +--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x +--R + +--R 3 2 +--R - 8196045560x - 6770936890x - 6951816250x +--R / +--R 10240 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 +--R - 3487704605log(2x - 1) - 83980800x - 656294400x - 2385171360x +--R + +--R 7 6 5 4 +--R - 5375548800x - 8485071840x - 10119882528x - 9744062580x +--R + +--R 3 2 +--R - 8196045560x - 6770936890x - 6951816250x +--R / +--R 10240 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R - 697540921log(2x - 1) + 697540921log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 2048 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x +--R + +--R 3 2 +--R - 351120x - 97952x - 15936x - 1152 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=-99058879/512*x-94979263/512*x^2-27480469/128*x^3-59969727/256*x^4-_ + 34084287/160*x^5-4736853/32*x^6-4040847/56*x^7-696195/32*x^8-_ + 6075/2*x^9-99648703/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 3487704605log(- 2x + 1) - 108864000x - 779738400x - 2586142080x +--R + +--R 6 5 4 3 +--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x +--R + +--R 2 +--R - 6648548410x - 6934121530x +--R / +--R 35840 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 3487704605log(2x - 1) - 108864000x - 779738400x - 2586142080x +--R + +--R 6 5 4 3 +--R - 5305275360x - 7634880288x - 8395761780x - 7694531320x +--R + +--R 2 +--R - 6648548410x - 6934121530x +--R / +--R 35840 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R - 99648703log(2x - 1) + 99648703log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x +--R + +--R - 7104x - 576 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=-14088073/256*x-13178761/256*x^2-3575427/64*x^3-6947721/128*x^4-_ + 3310281/80*x^5-356643/16*x^6-207765/28*x^7-18225/16*x^8-_ + 14235529/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 498243515log(- 2x + 1) - 20412000x - 132969600x - 399440160x +--R + +--R 5 4 3 2 +--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x +--R / +--R 17920 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 498243515log(2x - 1) - 20412000x - 132969600x - 399440160x +--R + +--R 5 4 3 2 +--R - 741502944x - 972680940x - 1001119560x - 922513270x - 986165110x +--R / +--R 17920 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R - 14235529log(2x - 1) + 14235529log(- 2x + 1) +--R (4) --------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=-1996783/128*x-1797103/128*x^2-444581/32*x^3-736623/64*x^4-_ + 275103/40*x^5-20385/8*x^6-6075/14*x^7-2033647/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 71177645log(- 2x + 1) - 3888000x - 22831200x - 61623072x +--R + +--R 4 3 2 +--R - 103127220x - 124482680x - 125797210x - 139774810x +--R / +--R 8960 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 71177645log(2x - 1) - 3888000x - 22831200x - 61623072x - 103127220x +--R + +--R 3 2 +--R - 124482680x - 125797210x - 139774810x +--R / +--R 8960 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R - 2033647log(2x - 1) + 2033647log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=-281305/64*x-238297/64*x^2-51571/16*x^3-68121/32*x^4-3537/4*x^5-_ + 675/4*x^6-290521/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 290521log(- 2x + 1) - 21600x - 113184x - 272484x - 412568x +--R + +--R 2 +--R - 476594x - 562610x +--R / +--R 128 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 290521log(2x - 1) - 21600x - 113184x - 272484x - 412568x - 476594x +--R + +--R - 562610x +--R / +--R 128 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R - 290521log(2x - 1) + 290521log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=-39199/32*x-30175/32*x^2-5349/8*x^3-4995/16*x^4-135/2*x^5-_ + 41503/64*log(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 41503log(- 2x + 1) - 4320x - 19980x - 42792x - 60350x - 78398x +--R (2) -------------------------------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 41503log(2x - 1) - 4320x - 19980x - 42792x - 60350x - 78398x +--R (3) ------------------------------------------------------------------ +--R 64 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R - 41503log(2x - 1) + 41503log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x) +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=-5353/16*x-3529/16*x^2-455/4*x^3-225/8*x^4-5929/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 5929log(- 2x + 1) - 900x - 3640x - 7058x - 10706x +--R (2) ------------------------------------------------------ +--R 32 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 5929log(2x - 1) - 900x - 3640x - 7058x - 10706x +--R (3) ---------------------------------------------------- +--R 32 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R - 5929log(2x - 1) + 5929log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x) +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=-703/8*x-355/8*x^2-25/2*x^3-847/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 847log(- 2x + 1) - 200x - 710x - 1406x +--R (2) ------------------------------------------ +--R 16 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 847log(2x - 1) - 200x - 710x - 1406x +--R (3) ---------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R - 847log(2x - 1) + 847log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^2/(1-2*x) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=-85/4*x-25/4*x^2-121/8*log(1-2*x) +--R +--R +--R 2 +--R - 121log(- 2x + 1) - 50x - 170x +--R (2) -------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 121log(2x - 1) - 50x - 170x +--R (3) ------------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=-25/6*x-121/28*log(1-2*x)+1/63*log(2+3*x) +--R +--R +--R 4log(3x + 2) - 1089log(- 2x + 1) - 1050x +--R (2) ---------------------------------------- +--R 252 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4log(3x + 2) - 1089log(2x - 1) - 1050x +--R (3) -------------------------------------- +--R 252 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 28 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=(-1/63)/(2+3*x)-121/98*log(1-2*x)-68/441*log(2+3*x) +--R +--R +--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(- 2x + 1) - 14 +--R (2) -------------------------------------------------------------- +--R 2646x + 1764 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 408x - 272)log(3x + 2) + (- 3267x - 2178)log(2x - 1) - 14 +--R (3) ------------------------------------------------------------ +--R 2646x + 1764 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 98 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=(-1/126)/(2+3*x)^2+68/441/(2+3*x)-121/343*log(1-2*x)+121/343*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (19602x + 26136x + 8712)log(3x + 2) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(- 2x + 1) + 2856x + 1855 +--R / +--R 2 +--R 55566x + 74088x + 24696 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (19602x + 26136x + 8712)log(3x + 2) +--R + +--R 2 +--R (- 19602x - 26136x - 8712)log(2x - 1) + 2856x + 1855 +--R / +--R 2 +--R 55566x + 74088x + 24696 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 121log(2x - 1) + 121log(- 2x + 1) +--R (4) ----------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=(-1/189)/(2+3*x)^3+34/441/(2+3*x)^2+(-121/343)/(2+3*x)-_ + 242/2401*log(1-2*x)+242/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (176418x + 352836x + 235224x + 52272)log(3x + 2) +--R + +--R 3 2 2 +--R (- 176418x - 352836x - 235224x - 52272)log(- 2x + 1) - 205821x +--R + +--R - 259434x - 81823 +--R / +--R 3 2 +--R 1750329x + 3500658x + 2333772x + 518616 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (176418x + 352836x + 235224x + 52272)log(3x + 2) +--R + +--R 3 2 2 +--R (- 176418x - 352836x - 235224x - 52272)log(2x - 1) - 205821x - 259434x +--R + +--R - 81823 +--R / +--R 3 2 +--R 1750329x + 3500658x + 2333772x + 518616 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 242log(2x - 1) + 242log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=(-1/252)/(2+3*x)^4+68/1323/(2+3*x)^3+(-121/686)/(2+3*x)^2+(-242/2401)/_ + (2+3*x)-484/16807*log(1-2*x)+484/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2) +--R + +--R 4 3 2 +--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(- 2x + 1) +--R + +--R 3 2 +--R - 4939704x - 12760902x - 10148376x - 2564891 +--R / +--R 4 3 2 +--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (4234032x + 11290752x + 11290752x + 5018112x + 836352)log(3x + 2) +--R + +--R 4 3 2 +--R (- 4234032x - 11290752x - 11290752x - 5018112x - 836352)log(2x - 1) +--R + +--R 3 2 +--R - 4939704x - 12760902x - 10148376x - 2564891 +--R / +--R 4 3 2 +--R 147027636x + 392073696x + 392073696x + 174254976x + 29042496 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 484log(2x - 1) + 484log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^6) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=(-1/315)/(2+3*x)^5+17/441/(2+3*x)^4+(-121/1029)/(2+3*x)^3+(-121/2401)/_ + (2+3*x)^2+(-484/16807)/(2+3*x)-968/117649*log(1-2*x)+968/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x +--R + +--R 1393920 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x +--R + +--R - 1393920 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617 +--R / +--R 5 4 3 2 +--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x +--R + +--R 169414560 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 10585080x + 35283600x + 47044800x + 31363200x + 10454400x +--R + +--R 1393920 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 10585080x - 35283600x - 47044800x - 31363200x - 10454400x +--R + +--R - 1393920 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 12349260x - 40135095x - 52941735x - 31099425x - 6672617 +--R / +--R 5 4 3 2 +--R 1286491815x + 4288306050x + 5717741400x + 3811827600x + 1270609200x +--R + +--R 169414560 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 968log(2x - 1) + 968log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=(-1/378)/(2+3*x)^6+68/2205/(2+3*x)^5+(-121/1372)/(2+3*x)^4+_ + (-242/7203)/(2+3*x)^3+(-242/16807)/(2+3*x)^2+(-968/117649)/(2+3*x)-_ + 1936/823543*log(1-2*x)+1936/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 762125760x + 3048503040x + 5080838400x + 4516300800x +--R + +--R 2 +--R 2258150400x + 602173440x + 66908160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 762125760x - 3048503040x - 5080838400x - 4516300800x +--R + +--R 2 +--R - 2258150400x - 602173440x - 66908160 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x +--R + +--R - 469699846 +--R / +--R 6 5 4 3 +--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x +--R + +--R 2 +--R 960580555200x + 256154814720x + 28461646080 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 762125760x + 3048503040x + 5080838400x + 4516300800x +--R + +--R 2 +--R 2258150400x + 602173440x + 66908160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 762125760x - 3048503040x - 5080838400x - 4516300800x +--R + +--R 2 +--R - 2258150400x - 602173440x - 66908160 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 889146720x - 3482491320x - 5738289480x - 5177427255x - 2460267684x +--R + +--R - 469699846 +--R / +--R 6 5 4 3 +--R 324195937380x + 1296783749520x + 2161306249200x + 1921161110400x +--R + +--R 2 +--R 960580555200x + 256154814720x + 28461646080 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 1936log(2x - 1) + 1936log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(3+5*x)^2/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=(-1/441)/(2+3*x)^7+34/1323/(2+3*x)^6+(-121/1715)/(2+3*x)^5+_ + (-121/4802)/(2+3*x)^4+(-484/50421)/(2+3*x)^3+(-484/117649)/(2+3*x)^2+_ + (-1936/823543)/(2+3*x)-3872/5764801*log(1-2*x)+3872/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 2286377280x + 10669760640x + 21339521280x + 23710579200x +--R + +--R 3 2 +--R 15807052800x + 6322821120x + 1405071360x + 133816320 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x +--R + +--R 3 2 +--R - 15807052800x - 6322821120x - 1405071360x - 133816320 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x +--R + +--R 2 +--R - 18847440612x - 7688480856x - 1354700662 +--R / +--R 7 6 5 4 +--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x +--R + +--R 3 2 +--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 2286377280x + 10669760640x + 21339521280x + 23710579200x +--R + +--R 3 2 +--R 15807052800x + 6322821120x + 1405071360x + 133816320 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 2286377280x - 10669760640x - 21339521280x - 23710579200x +--R + +--R 3 2 +--R - 15807052800x - 6322821120x - 1405071360x - 133816320 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 2667440160x - 12225767400x - 24179851080x - 27008860725x +--R + +--R 2 +--R - 18847440612x - 7688480856x - 1354700662 +--R / +--R 7 6 5 4 +--R 3404057342490x + 15885600931620x + 31771201863240x + 35301335403600x +--R + +--R 3 2 +--R 23534223602400x + 9413689440960x + 2091930986880x + 199231522560 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R - 3872log(2x - 1) + 3872log(- 2x + 1) +--R (4) ------------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^m*(3+5*x)^3/(1-2*x) +--R +--R +--R 3 2 m +--R (- 125x - 225x - 135x - 27)(3x + 2) +--R (1) -------------------------------------- +--R 2x - 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=-5135/216*(2+3*x)^(1+m)/(1+m)-725/108*(2+3*x)^(2+m)/(2+m)-_ +-- 125/54*(2+3*x)^(3+m)/(3+m)+1331/56*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R - 273375x - 1767825x - 5143095x - 8864559x - 10024182x - 7770924x +--R + +--R 4 3 2 +--R - 4182360x - 1543120x - 373536x - 53568x - 3456 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=-1092596789/1024*x-1065169973/1024*x^2-969544757/768*x^3-_ + 772025397/512*x^4-504354357/320*x^5-85228263/64*x^6-_ + 95297877/112*x^7-24381405/64*x^8-423225/4*x^9-54675/4*x^10-_ + 1096135733/2048*log(1-2*x) +--R +--R +--R (2) +--R 10 9 +--R - 115094251965log(- 2x + 1) - 2939328000x - 22752576000x +--R + +--R 8 7 6 5 +--R - 81921520800x - 182971923840x - 286366963680x - 338926127904x +--R + +--R 4 3 2 +--R - 324250666740x - 271472531960x - 223685694330x - 229445325690x +--R / +--R 215040 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 +--R - 115094251965log(2x - 1) - 2939328000x - 22752576000x - 81921520800x +--R + +--R 7 6 5 4 +--R - 182971923840x - 286366963680x - 338926127904x - 324250666740x +--R + +--R 3 2 +--R - 271472531960x - 223685694330x - 229445325690x +--R / +--R 215040 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R - 1096135733log(2x - 1) + 1096135733log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 2048 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x +--R + +--R 3 2 +--R - 545840x - 150480x - 24192x - 1728 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=-155706083/512*x-149512931/512*x^2-130251491/384*x^3-95317731/256*x^4-_ + 54600291/160*x^5-7656993/32*x^6-6596235/56*x^7-1148175/32*x^8-_ + 10125/2*x^9-156590819/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 7 +--R - 16442035995log(- 2x + 1) - 544320000x - 3857868000x - 12664771200x +--R + +--R 6 5 4 3 +--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x +--R + +--R 2 +--R - 31397715510x - 32698277430x +--R / +--R 107520 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 +--R - 16442035995log(2x - 1) - 544320000x - 3857868000x - 12664771200x +--R + +--R 6 5 4 3 +--R - 25727496480x - 36691395552x - 40033447020x - 36470417480x +--R + +--R 2 +--R - 31397715510x - 32698277430x +--R / +--R 107520 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R - 156590819log(2x - 1) + 156590819log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 +--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x +--R + +--R 2 +--R - 59040x - 10800x - 864 +--R / +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=-22148933/256*x-20766533/256*x^2-16987973/192*x^3-11088453/128*x^4-_ + 5333733/80*x^5-580815/16*x^6-342225/28*x^7-30375/16*x^8-_ + 22370117/512*log(1-2*x) +--R +--R +--R (2) +--R 8 7 6 +--R - 2348862285log(- 2x + 1) - 102060000x - 657072000x - 1951538400x +--R + +--R 5 4 3 2 +--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x +--R / +--R 53760 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R - 2348862285log(2x - 1) - 102060000x - 657072000x - 1951538400x +--R + +--R 5 4 3 2 +--R - 3584268576x - 4657150260x - 4756632440x - 4360971930x - 4651275930x +--R / +--R 53760 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R - 22370117log(2x - 1) + 22370117log(- 2x + 1) +--R (4) --------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=-3140435/128*x-2836307/128*x^2-2119763/96*x^3-1182291/64*x^4-_ + 89343/8*x^5-33525/8*x^6-10125/14*x^7-3195731/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R - 67110351log(- 2x + 1) - 3888000x - 22528800x - 60038496x +--R + +--R 4 3 2 +--R - 99312444x - 118706728x - 119124894x - 131898270x +--R / +--R 5376 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R - 67110351log(2x - 1) - 3888000x - 22528800x - 60038496x - 99312444x +--R + +--R 3 2 +--R - 118706728x - 119124894x - 131898270x +--R / +--R 5376 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R - 3195731log(2x - 1) + 3195731log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=-442709/64*x-377045/64*x^2-247157/48*x^3-110205/32*x^4-5805/4*x^5-_ + 1125/4*x^6-456533/128*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R - 1369599log(- 2x + 1) - 108000x - 557280x - 1322460x - 1977256x +--R + +--R 2 +--R - 2262270x - 2656254x +--R / +--R 384 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 1369599log(2x - 1) - 108000x - 557280x - 1322460x - 1977256x +--R + +--R 2 +--R - 2262270x - 2656254x +--R / +--R 384 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R - 456533log(2x - 1) + 456533log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=-61763/32*x-47939/32*x^2-25835/24*x^3-8175/16*x^4-225/2*x^5-_ + 65219/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 195657log(- 2x + 1) - 21600x - 98100x - 206680x - 287634x - 370578x +--R ------------------------------------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 195657log(2x - 1) - 21600x - 98100x - 206680x - 287634x - 370578x +--R ----------------------------------------------------------------------- +--R 192 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R - 65219log(2x - 1) + 65219log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x) +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=-8453/16*x-5645/16*x^2-2225/12*x^3-375/8*x^4-9317/32*log(1-2*x) +--R +--R +--R 4 3 2 +--R - 27951log(- 2x + 1) - 4500x - 17800x - 33870x - 50718x +--R (2) ---------------------------------------------------------- +--R 96 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 27951log(2x - 1) - 4500x - 17800x - 33870x - 50718x +--R (3) -------------------------------------------------------- +--R 96 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R - 9317log(2x - 1) + 9317log(- 2x + 1) +--R (4) ------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^3/(1-2*x) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=-1115/8*x-575/8*x^2-125/6*x^3-1331/16*log(1-2*x) +--R +--R +--R 3 2 +--R - 3993log(- 2x + 1) - 1000x - 3450x - 6690x +--R (2) --------------------------------------------- +--R 48 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 3993log(2x - 1) - 1000x - 3450x - 6690x +--R (3) ------------------------------------------- +--R 48 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2 +--R 6x + x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=-1225/36*x-125/12*x^2-1331/56*log(1-2*x)-1/189*log(2+3*x) +--R +--R +--R 2 +--R - 8log(3x + 2) - 35937log(- 2x + 1) - 15750x - 51450x +--R (2) ------------------------------------------------------ +--R 1512 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 8log(3x + 2) - 35937log(2x - 1) - 15750x - 51450x +--R (3) ---------------------------------------------------- +--R 1512 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 56 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 3 2 +--R 18x + 15x - 4x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=-125/18*x+1/189/(2+3*x)-1331/196*log(1-2*x)+103/1323*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(- 2x + 1) - 110250x +--R + +--R - 73500x + 28 +--R / +--R 15876x + 10584 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1236x + 824)log(3x + 2) + (- 107811x - 71874)log(2x - 1) - 110250x +--R + +--R - 73500x + 28 +--R / +--R 15876x + 10584 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 196 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------- +--R 4 3 2 +--R 54x + 81x + 18x - 20x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1/378/(2+3*x)^2+(-103/1323)/(2+3*x)-1331/686*log(1-2*x)-_ + 3469/9261*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 62442x - 83256x - 27752)log(3x + 2) +--R + +--R 2 +--R (- 323433x - 431244x - 143748)log(- 2x + 1) - 4326x - 2835 +--R / +--R 2 +--R 166698x + 222264x + 74088 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 62442x - 83256x - 27752)log(3x + 2) +--R + +--R 2 +--R (- 323433x - 431244x - 143748)log(2x - 1) - 4326x - 2835 +--R / +--R 2 +--R 166698x + 222264x + 74088 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 686 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------- +--R 5 4 3 2 +--R 162x + 351x + 216x - 24x - 64x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=1/567/(2+3*x)^3+(-103/2646)/(2+3*x)^2+3469/9261/(2+3*x)-_ + 1331/2401*log(1-2*x)+1331/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(- 2x + 1) + 1311282x +--R + +--R 1702953x + 553196 +--R / +--R 3 2 +--R 10501974x + 21003948x + 14002632x + 3111696 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5821794x + 11643588x + 7762392x + 1724976)log(3x + 2) +--R + +--R 3 2 2 +--R (- 5821794x - 11643588x - 7762392x - 1724976)log(2x - 1) + 1311282x +--R + +--R 1702953x + 553196 +--R / +--R 3 2 +--R 10501974x + 21003948x + 14002632x + 3111696 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 1331log(2x - 1) + 1331log(- 2x + 1) +--R (4) ------------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 486x + 1377x + 1350x + 360x - 240x - 176x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=1/756/(2+3*x)^4+(-103/3969)/(2+3*x)^3+3469/18522/(2+3*x)^2+_ + (-1331/2401)/(2+3*x)-2662/16807*log(1-2*x)+2662/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808) +--R * +--R log(- 2x + 1) +--R + +--R 3 2 +--R - 81505116x - 153831258x - 96858804x - 20345549 +--R / +--R 4 3 2 +--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (69861528x + 186297408x + 186297408x + 82798848x + 13799808) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 69861528x - 186297408x - 186297408x - 82798848x - 13799808) +--R * +--R log(2x - 1) +--R + +--R 3 2 +--R - 81505116x - 153831258x - 96858804x - 20345549 +--R / +--R 4 3 2 +--R 441082908x + 1176221088x + 1176221088x + 522764928x + 87127488 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 2662log(2x - 1) + 2662log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^6) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ------------------------------------------------------ +--R 7 6 5 4 2 +--R 1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=1/945/(2+3*x)^5+(-103/5292)/(2+3*x)^4+3469/27783/(2+3*x)^3+_ + (-1331/4802)/(2+3*x)^2+(-2662/16807)/(2+3*x)-_ + 5324/117649*log(1-2*x)+5324/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 2095845840x + 6986152800x + 9314870400x + 6209913600x +--R + +--R 2069971200x + 275996160 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x +--R + +--R - 2069971200x - 275996160 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446 +--R / +--R 5 4 3 2 +--R 46313705340x + 154379017800x + 205838690400x + 137225793600x +--R + +--R 45741931200x + 6098924160 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2095845840x + 6986152800x + 9314870400x + 6209913600x +--R + +--R 2069971200x + 275996160 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 2095845840x - 6986152800x - 9314870400x - 6209913600x +--R + +--R - 2069971200x - 275996160 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2445153480x - 7946748810x - 9158912280x - 4525306275x - 817640446 +--R / +--R 5 4 3 2 +--R 46313705340x + 154379017800x + 205838690400x + 137225793600x +--R + +--R 45741931200x + 6098924160 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 5324log(2x - 1) + 5324log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^7) +--R +--R +--R (1) +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R ----------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 4374x + 18225x + 30618x + 24948x + 7560x - 3024x - 3360x - 1088x - 128 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=1/1134/(2+3*x)^6+(-103/6615)/(2+3*x)^5+3469/37044/(2+3*x)^4+_ + (-1331/7203)/(2+3*x)^3+(-1331/16807)/(2+3*x)^2+_ + (-5324/117649)/(2+3*x)-10648/823543*log(1-2*x)+10648/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 12575075040x + 50300300160x + 83833833600x + 74518963200x +--R + +--R 2 +--R 37259481600x + 9935861760x + 1103984640 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x +--R + +--R 2 +--R - 37259481600x - 9935861760x - 1103984640 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x +--R + +--R - 32070746736x - 5135298434 +--R / +--R 6 5 4 3 +--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x +--R + +--R 2 +--R 2881741665600x + 768464444160x + 85384938240 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 12575075040x + 50300300160x + 83833833600x + 74518963200x +--R + +--R 2 +--R 37259481600x + 9935861760x + 1103984640 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 12575075040x - 50300300160x - 83833833600x - 74518963200x +--R + +--R 2 +--R - 37259481600x - 9935861760x - 1103984640 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 14670920880x - 57461106780x - 94681776420x - 78478905645x +--R + +--R - 32070746736x - 5135298434 +--R / +--R 6 5 4 3 +--R 972587812140x + 3890351248560x + 6483918747600x + 5763483331200x +--R + +--R 2 +--R 2881741665600x + 768464444160x + 85384938240 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 10648log(2x - 1) + 10648log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^3/((1-2*x)*(2+3*x)^8) +--R +--R +--R (1) +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R / +--R 9 8 7 6 5 4 3 +--R 13122x + 63423x + 128304x + 136080x + 72576x + 6048x - 16128x +--R + +--R 2 +--R - 9984x - 2560x - 256 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=1/1323/(2+3*x)^7+(-103/7938)/(2+3*x)^6+3469/46305/(2+3*x)^5+_ + (-1331/9604)/(2+3*x)^4+(-2662/50421)/(2+3*x)^3+(-2662/117649)/(2+3*x)^2+_ + (-10648/823543)/(2+3*x)-21296/5764801*log(1-2*x)+21296/5764801*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 75450450240x + 352102101120x + 704204202240x + 782449113600x +--R + +--R 3 2 +--R 521632742400x + 208653096960x + 46367354880x + 4415938560 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x +--R + +--R 3 2 +--R - 521632742400x - 208653096960x - 46367354880x - 4415938560 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x +--R + +--R 2 +--R - 583053133446x - 206160259998x - 30169587896 +--R / +--R 7 6 5 +--R 20424344054940x + 95313605589720x + 190627211179440x +--R + +--R 4 3 2 +--R 211808012421600x + 141205341614400x + 56482136645760x +--R + +--R 12551585921280x + 1195389135360 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 75450450240x + 352102101120x + 704204202240x + 782449113600x +--R + +--R 3 2 +--R 521632742400x + 208653096960x + 46367354880x + 4415938560 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 75450450240x - 352102101120x - 704204202240x - 782449113600x +--R + +--R 3 2 +--R - 521632742400x - 208653096960x - 46367354880x - 4415938560 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 88025525280x - 403450324200x - 797935085640x - 891292403925x +--R + +--R 2 +--R - 583053133446x - 206160259998x - 30169587896 +--R / +--R 7 6 5 +--R 20424344054940x + 95313605589720x + 190627211179440x +--R + +--R 4 3 2 +--R 211808012421600x + 141205341614400x + 56482136645760x +--R + +--R 12551585921280x + 1195389135360 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R - 21296log(2x - 1) + 21296log(- 2x + 1) +--R (4) --------------------------------------- +--R 5764801 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(a+b*x)^3/((c+d*x)*(e+f*x)) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ---------------------------- +--R 2 +--R d f x + (c f + d e)x + c e +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=-b^2*(b*d*e+b*c*f-3*a*d*f)*x/(d^2*f^2)+1/2*b^3*x^2/(d*f)-_ + (b*c-a*d)^3*log(c+d*x)/(d^3*(d*e-c*f))+_ + (b*e-a*f)^3*log(e+f*x)/(f^3*(d*e-c*f)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 2 3 3 3 +--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c) +--R + +--R 3 2 3 3 3 2 2 +--R (b c d f - b d e f )x +--R + +--R 2 2 3 2 3 2 3 2 3 3 2 +--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x +--R / +--R 3 4 4 3 +--R 2c d f - 2d e f +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 2 3 3 3 +--R (2a d f - 6a b d e f + 6a b d e f - 2b d e )log(f x + e) +--R + +--R 3 3 2 2 2 2 3 3 3 +--R (- 2a d + 6a b c d - 6a b c d + 2b c )f log(d x + c) +--R + +--R 3 2 3 3 3 2 2 +--R (b c d f - b d e f )x +--R + +--R 2 2 3 2 3 2 3 2 3 3 2 +--R ((6a b c d - 2b c d)f - 6a b d e f + 2b d e f)x +--R / +--R 3 4 4 3 +--R 2c d f - 2d e f +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)) +--R +--R +--R m +--R (3x + 2) +--R (1) - ------------ +--R 2 +--R 10x + x - 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=2/77*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-5/11*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=-40089855591/10000000*x-7136193339/2000000*x^2-345533877/100000*x^3-_ + 111146499/40000*x^4-8018271/5000*x^5-114453/200*x^6-6561/70*x^7-_ + 5764801/2816*log(1-2*x)+1/4296875*log(3+5*x) +--R +--R +--R (2) +--R 7 +--R 1792log(5x + 3) - 15763127734375log(- 2x + 1) - 721710000000x +--R + +--R 6 5 4 +--R - 4406440500000x - 12348137340000x - 21395701057500x +--R + +--R 3 2 +--R - 26606108529000x - 27474344355150x - 30869188805070x +--R / +--R 7700000000 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +--R 1792log(5x + 3) - 15763127734375log(2x - 1) - 721710000000x +--R + +--R 6 5 4 +--R - 4406440500000x - 12348137340000x - 21395701057500x +--R + +--R 3 2 +--R - 26606108529000x - 27474344355150x - 30869188805070x +--R / +--R 7700000000 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 2816 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=-1127138733/1000000*x-187738857/200000*x^2-7889751/10000*x^3-_ + 2006937/4000*x^4-99873/500*x^5-729/20*x^6-823543/1408*log(1-2*x)+_ + 1/859375*log(3+5*x) +--R +--R +--R (2) +--R 6 5 +--R 128log(5x + 3) - 64339296875log(- 2x + 1) - 4009500000x - 21972060000x +--R + +--R 4 3 2 +--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x +--R / +--R 110000000 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 +--R 128log(5x + 3) - 64339296875log(2x - 1) - 4009500000x - 21972060000x +--R + +--R 4 3 2 +--R - 55190767500x - 86787261000x - 103256371350x - 123985260630x +--R / +--R 110000000 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1408 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=-31289679/100000*x-4693491/20000*x^2-159813/1000*x^3-_ + 28431/400*x^4-729/50*x^5-117649/704*log(1-2*x)+1/171875*log(3+5*x) +--R +--R +--R (2) +--R 5 4 +--R 64log(5x + 3) - 1838265625log(- 2x + 1) - 160380000x - 781852500x +--R + +--R 3 2 +--R - 1757943000x - 2581420050x - 3441864690x +--R / +--R 11000000 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 +--R 64log(5x + 3) - 1838265625log(2x - 1) - 160380000x - 781852500x +--R + +--R 3 2 +--R - 1757943000x - 2581420050x - 3441864690x +--R / +--R 11000000 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 704 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=-848277/10000*x-107433/2000*x^2-2619/100*x^3-243/40*x^4-_ + 16807/352*log(1-2*x)+1/34375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 +--R 32log(5x + 3) - 52521875log(- 2x + 1) - 6682500x - 28809000x +--R + +--R 2 +--R - 59088150x - 93310470x +--R / +--R 1100000 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 32log(5x + 3) - 52521875log(2x - 1) - 6682500x - 28809000x - 59088150x +--R + +--R - 93310470x +--R / +--R 1100000 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 352 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=-21951/1000*x-2079/200*x^2-27/10*x^3-2401/176*log(1-2*x)+1/6875*log(3+5*x) +--R +--R +--R 3 2 +--R 16log(5x + 3) - 1500625log(- 2x + 1) - 297000x - 1143450x - 2414610x +--R (2) ---------------------------------------------------------------------- +--R 110000 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 16log(5x + 3) - 1500625log(2x - 1) - 297000x - 1143450x - 2414610x +--R (3) -------------------------------------------------------------------- +--R 110000 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 176 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ----------------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=-513/100*x-27/20*x^2-343/88*log(1-2*x)+1/1375*log(3+5*x) +--R +--R +--R 2 +--R 8log(5x + 3) - 42875log(- 2x + 1) - 14850x - 56430x +--R (2) ---------------------------------------------------- +--R 11000 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 8log(5x + 3) - 42875log(2x - 1) - 14850x - 56430x +--R (3) -------------------------------------------------- +--R 11000 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 88 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------- +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=-9/10*x-49/44*log(1-2*x)+1/275*log(3+5*x) +--R +--R +--R 4log(5x + 3) - 1225log(- 2x + 1) - 990x +--R (2) --------------------------------------- +--R 1100 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4log(5x + 3) - 1225log(2x - 1) - 990x +--R (3) ------------------------------------- +--R 1100 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 44 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ------------ +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=-7/22*log(1-2*x)+1/55*log(3+5*x) +--R +--R +--R 2log(5x + 3) - 35log(- 2x + 1) +--R (2) ------------------------------ +--R 110 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2log(5x + 3) - 35log(2x - 1) +--R (3) ---------------------------- +--R 110 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - 7log(2x - 1) + 7log(- 2x + 1) +--R (4) ------------------------------- +--R 22 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------ +--R 2 +--R 10x + x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=-1/11*log(1-2*x)+1/11*log(3+5*x) +--R +--R +--R log(5x + 3) - log(- 2x + 1) +--R (2) --------------------------- +--R 11 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) - log(2x - 1) +--R (3) ------------------------- +--R 11 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 11 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - -------------------- +--R 3 2 +--R 30x + 23x - 7x - 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=-2/77*log(1-2*x)-3/7*log(2+3*x)+5/11*log(3+5*x) +--R +--R +--R 35log(5x + 3) - 33log(3x + 2) - 2log(- 2x + 1) +--R (2) ---------------------------------------------- +--R 77 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R 35log(5x + 3) - 33log(3x + 2) - 2log(2x - 1) +--R (3) -------------------------------------------- +--R 77 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 2log(2x - 1) + 2log(- 2x + 1) +--R (4) ------------------------------- +--R 77 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------ +--R 4 3 2 +--R 90x + 129x + 25x - 32x - 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=3/7/(2+3*x)-4/539*log(1-2*x)-111/49*log(2+3*x)+25/11*log(3+5*x) +--R +--R +--R (2) +--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2) +--R + +--R (- 12x - 8)log(- 2x + 1) + 231 +--R / +--R 1617x + 1078 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (3675x + 2450)log(5x + 3) + (- 3663x - 2442)log(3x + 2) +--R + +--R (- 12x - 8)log(2x - 1) + 231 +--R / +--R 1617x + 1078 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 539 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------- +--R 5 4 3 2 +--R 270x + 567x + 333x - 46x - 100x - 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=3/14/(2+3*x)^2+111/49/(2+3*x)-8/3773*log(1-2*x)-3897/343*log(2+3*x)+_ + 125/11*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (771750x + 1029000x + 343000)log(5x + 3) +--R + +--R 2 +--R (- 771606x - 1028808x - 342936)log(3x + 2) +--R + +--R 2 +--R (- 144x - 192x - 64)log(- 2x + 1) + 51282x + 35805 +--R / +--R 2 +--R 67914x + 90552x + 30184 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (771750x + 1029000x + 343000)log(5x + 3) +--R + +--R 2 +--R (- 771606x - 1028808x - 342936)log(3x + 2) +--R + +--R 2 +--R (- 144x - 192x - 64)log(2x - 1) + 51282x + 35805 +--R / +--R 2 +--R 67914x + 90552x + 30184 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 3773 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 6 5 4 3 2 +--R 810x + 2241x + 2133x + 528x - 392x - 272x - 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=1/7/(2+3*x)^3+111/98/(2+3*x)^2+3897/343/(2+3*x)-16/26411*log(1-2*x)-_ + 136419/2401*log(2+3*x)+625/11*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3) +--R + +--R 3 2 +--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2) +--R + +--R 3 2 2 +--R (- 864x - 1728x - 1152x - 256)log(- 2x + 1) + 5401242x + 7381143x +--R + +--R 2527756 +--R / +--R 3 2 +--R 1426194x + 2852388x + 1901592x + 422576 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (81033750x + 162067500x + 108045000x + 24010000)log(5x + 3) +--R + +--R 3 2 +--R (- 81032886x - 162065772x - 108043848x - 24009744)log(3x + 2) +--R + +--R 3 2 2 +--R (- 864x - 1728x - 1152x - 256)log(2x - 1) + 5401242x + 7381143x +--R + +--R 2527756 +--R / +--R 3 2 +--R 1426194x + 2852388x + 1901592x + 422576 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 26411 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2430x + 8343x + 10881x + 5850x - 120x - 1600x - 688x - 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=3/28/(2+3*x)^4+37/49/(2+3*x)^3+3897/686/(2+3*x)^2+136419/2401/(2+3*x)-_ + 32/184877*log(1-2*x)-4774713/16807*log(2+3*x)+3125/11*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 17017087500x + 45378900000x + 45378900000x + 20168400000x +--R + +--R 3361400000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x +--R + +--R - 3361397952 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(- 2x + 1) +--R + +--R 3 2 +--R 1134460404x + 2306729502x + 1564700676x + 354136321 +--R / +--R 4 3 2 +--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 17017087500x + 45378900000x + 45378900000x + 20168400000x +--R + +--R 3361400000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 17017077132x - 45378872352x - 45378872352x - 20168387712x +--R + +--R - 3361397952 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 10368x - 27648x - 27648x - 12288x - 2048)log(2x - 1) + 1134460404x +--R + +--R 2 +--R 2306729502x + 1564700676x + 354136321 +--R / +--R 4 3 2 +--R 59900148x + 159733728x + 159733728x + 70992768x + 11832128 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 184877 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 7290x + 29889x + 49329x + 39312x + 11340x - 5040x - 5264x +--R + +--R - 1664x - 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=3/35/(2+3*x)^5+111/196/(2+3*x)^4+1299/343/(2+3*x)^3+_ + 136419/4802/(2+3*x)^2+4774713/16807/(2+3*x)-64/1294139*log(1-2*x)-_ + 167115051/117649*log(2+3*x)+15625/11*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 8933970937500x + 29779903125000x + 39706537500000x +--R + +--R 2 +--R 26471025000000x + 8823675000000x + 1176490000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8933970626460x - 29779902088200x - 39706536117600x +--R + +--R 2 +--R - 26471024078400x - 8823674692800x - 1176489959040 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x +--R + +--R 123954940494 +--R / +--R 5 4 3 2 +--R 6289515540x + 20965051800x + 27953402400x + 18635601600x +--R + +--R 6211867200x + 828248960 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 8933970937500x + 29779903125000x + 39706537500000x +--R + +--R 2 +--R 26471025000000x + 8823675000000x + 1176490000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8933970626460x - 29779902088200x - 39706536117600x +--R + +--R 2 +--R - 26471024078400x - 8823674692800x - 1176489959040 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 311040x - 1036800x - 1382400x - 921600x - 307200x - 40960) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 595597699620x + 1608113589390x + 1628848849320x + 733584557475x +--R + +--R 123954940494 +--R / +--R 5 4 3 2 +--R 6289515540x + 20965051800x + 27953402400x + 18635601600x +--R + +--R 6211867200x + 828248960 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 1294139 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=1/((1-2*x)*(2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 21870x + 104247x + 207765x + 216594x + 112644x + 7560x - 25872x +--R + +--R 2 +--R - 15520x - 3904x - 384 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=1/14/(2+3*x)^6+111/245/(2+3*x)^5+3897/1372/(2+3*x)^4+_ + 45473/2401/(2+3*x)^3+4774713/33614/(2+3*x)^2+_ + 167115051/117649/(2+3*x)-128/9058973*log(1-2*x)-_ + 5849026977/823543*log(2+3*x)+78125/11*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 938066948437500x + 3752267793750000x + 6253779656250000x +--R + +--R 3 2 +--R 5558915250000000x + 2779457625000000x + 741188700000000x +--R + +--R 82354300000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 938066946571260x - 3752267786285040x - 6253779643808400x +--R + +--R 3 2 +--R - 5558915238940800x - 2779457619470400x - 741188698525440x +--R + +--R - 82354299836160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x +--R + +--R - 1474560x - 163840 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 62537794385220x + 210543906566070x + 283597312285980x +--R + +--R 2 +--R 191046007176255x + 64366302153384x + 8676887688546 +--R / +--R 6 5 4 3 +--R 132079826340x + 528319305360x + 880532175600x + 782695267200x +--R + +--R 2 +--R 391347633600x + 104359368960x + 11595485440 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 938066948437500x + 3752267793750000x + 6253779656250000x +--R + +--R 3 2 +--R 5558915250000000x + 2779457625000000x + 741188700000000x +--R + +--R 82354300000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 938066946571260x - 3752267786285040x - 6253779643808400x +--R + +--R 3 2 +--R - 5558915238940800x - 2779457619470400x - 741188698525440x +--R + +--R - 82354299836160 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1866240x - 7464960x - 12441600x - 11059200x - 5529600x +--R + +--R - 1474560x - 163840 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 62537794385220x + 210543906566070x + 283597312285980x +--R + +--R 2 +--R 191046007176255x + 64366302153384x + 8676887688546 +--R / +--R 6 5 4 3 +--R 132079826340x + 528319305360x + 880532175600x + 782695267200x +--R + +--R 2 +--R 391347633600x + 104359368960x + 11595485440 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 9058973 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^2) +--R +--R +--R m +--R (3x + 2) +--R (1) - --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-5/11*(2+3*x)^(1+m)/(3+5*x)+4/847*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-10/121*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-15/11*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=-3579885909/5000000*x-118543581/200000*x^2-24660207/50000*x^3-_ + 6194313/20000*x^4-303993/2500*x^5-2187/100*x^6+(-1/4296875)/(3+5*x)-_ + 5764801/15488*log(1-2*x)+266/47265625*log(3+5*x) +--R +--R +--R (2) +--R (170240x + 102144)log(5x + 3) +--R + +--R 7 +--R (- 11259376953125x - 6755626171875)log(- 2x + 1) - 661567500000x +--R + +--R 6 5 4 +--R - 4075255800000x - 11575887592500x - 20540764282500x +--R + +--R 3 2 +--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408 +--R / +--R 30250000000x + 18150000000 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (170240x + 102144)log(5x + 3) +--R + +--R 7 +--R (- 11259376953125x - 6755626171875)log(2x - 1) - 661567500000x +--R + +--R 6 5 4 +--R - 4075255800000x - 11575887592500x - 20540764282500x +--R + +--R 3 2 +--R - 26881371767250x - 32416139725200x - 12994985849670x - 1408 +--R / +--R 30250000000x + 18150000000 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 15488 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=-19846971/100000*x-14750667/100000*x^2-495477/5000*x^3-86751/2000*x^4-_ + 2187/250*x^5+(-1/859375)/(3+5*x)-823543/7744*log(1-2*x)+_ + 233/9453125*log(3+5*x) +--R +--R +--R (2) +--R (74560x + 44736)log(5x + 3) +--R + +--R 6 +--R (- 321696484375x - 193017890625)log(- 2x + 1) - 26462700000x +--R + +--R 5 4 3 2 +--R - 147088507500x - 378490117500x - 626065827750x - 868095478800x +--R + +--R - 360222523650x - 704 +--R / +--R 3025000000x + 1815000000 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (74560x + 44736)log(5x + 3) + (- 321696484375x - 193017890625)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 26462700000x - 147088507500x - 378490117500x - 626065827750x +--R + +--R 2 +--R - 868095478800x - 360222523650x - 704 +--R / +--R 3025000000x + 1815000000 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 7744 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=-2682909/50000*x-335097/10000*x^2-8019/500*x^3-729/200*x^4+_ + (-1/171875)/(3+5*x)-117649/3872*log(1-2*x)+8/75625*log(3+5*x) +--R +--R +--R (2) +--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x +--R + +--R - 9738959670x - 352 +--R / +--R 302500000x + 181500000 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (32000x + 19200)log(5x + 3) + (- 9191328125x - 5514796875)log(2x - 1) +--R + +--R 5 4 3 2 +--R - 1102612500x - 5513062500x - 13047581250x - 22313610000x +--R + +--R - 9738959670x - 352 +--R / +--R 302500000x + 181500000 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 3872 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=-69039/5000*x-6399/1000*x^2-81/50*x^3+(-1/34375)/(3+5*x)-_ + 16807/1936*log(1-2*x)+167/378125*log(3+5*x) +--R +--R +--R (2) +--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(- 2x + 1) +--R + +--R 4 3 2 +--R - 49005000x - 222972750x - 533827800x - 250611570x - 176 +--R / +--R 30250000x + 18150000 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (13360x + 8016)log(5x + 3) + (- 262609375x - 157565625)log(2x - 1) +--R + +--R 4 3 2 +--R - 49005000x - 222972750x - 533827800x - 250611570x - 176 +--R / +--R 30250000x + 18150000 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=-1593/500*x-81/100*x^2+(-1/6875)/(3+5*x)-2401/968*log(1-2*x)+_ + 134/75625*log(3+5*x) +--R +--R +--R (2) +--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(- 2x + 1) +--R + +--R 3 2 +--R - 2450250x - 11107800x - 5782590x - 88 +--R / +--R 3025000x + 1815000 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R (5360x + 3216)log(5x + 3) + (- 7503125x - 4501875)log(2x - 1) - 2450250x +--R + +--R 2 +--R - 11107800x - 5782590x - 88 +--R / +--R 3025000x + 1815000 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 968 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ----------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=-27/50*x+(-1/1375)/(3+5*x)-343/484*log(1-2*x)+101/15125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(- 2x + 1) - 163350x +--R + +--R - 98010x - 44 +--R / +--R 302500x + 181500 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2020x + 1212)log(5x + 3) + (- 214375x - 128625)log(2x - 1) - 163350x +--R + +--R - 98010x - 44 +--R / +--R 302500x + 181500 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 484 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=(-1/275)/(3+5*x)-49/242*log(1-2*x)+68/3025*log(3+5*x) +--R +--R +--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(- 2x + 1) - 22 +--R (2) ------------------------------------------------------------ +--R 30250x + 18150 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (680x + 408)log(5x + 3) + (- 6125x - 3675)log(2x - 1) - 22 +--R (3) ---------------------------------------------------------- +--R 30250x + 18150 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 242 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=(-1/55)/(3+5*x)-7/121*log(1-2*x)+7/121*log(3+5*x) +--R +--R +--R (175x + 105)log(5x + 3) + (- 175x - 105)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------------- +--R 3025x + 1815 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (175x + 105)log(5x + 3) + (- 175x - 105)log(2x - 1) - 11 +--R (3) -------------------------------------------------------- +--R 3025x + 1815 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R - 7log(2x - 1) + 7log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - --------------------- +--R 3 2 +--R 50x + 35x - 12x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=(-1/11)/(3+5*x)-2/121*log(1-2*x)+2/121*log(3+5*x) +--R +--R +--R (10x + 6)log(5x + 3) + (- 10x - 6)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------- +--R 605x + 363 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x + 6)log(5x + 3) + (- 10x - 6)log(2x - 1) - 11 +--R (3) -------------------------------------------------- +--R 605x + 363 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R - 2log(2x - 1) + 2log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 4 3 2 +--R 150x + 205x + 34x - 51x - 18 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=(-5/11)/(3+5*x)-4/847*log(1-2*x)+9/7*log(2+3*x)-155/121*log(3+5*x) +--R +--R +--R (2) +--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2) +--R + +--R (- 20x - 12)log(- 2x + 1) - 385 +--R / +--R 4235x + 2541 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- 5425x - 3255)log(5x + 3) + (5445x + 3267)log(3x + 2) +--R + +--R (- 20x - 12)log(2x - 1) - 385 +--R / +--R 4235x + 2541 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 847 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------------- +--R 5 4 3 2 +--R 450x + 915x + 512x - 85x - 156x - 36 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=(-9/7)/(2+3*x)+(-25/11)/(3+5*x)-8/5929*log(1-2*x)+648/49*log(2+3*x)-_ + 1600/121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 1176000x - 1489600x - 470400)log(5x + 3) +--R + +--R 2 +--R (1176120x + 1489752x + 470448)log(3x + 2) +--R + +--R 2 +--R (- 120x - 152x - 48)log(- 2x + 1) - 78540x - 49819 +--R / +--R 2 +--R 88935x + 112651x + 35574 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 1176000x - 1489600x - 470400)log(5x + 3) +--R + +--R 2 +--R (1176120x + 1489752x + 470448)log(3x + 2) +--R + +--R 2 +--R (- 120x - 152x - 48)log(2x - 1) - 78540x - 49819 +--R / +--R 2 +--R 88935x + 112651x + 35574 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 5929 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 6 5 4 3 2 +--R 1350x + 3645x + 3366x + 769x - 638x - 420x - 72 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=(-9/14)/(2+3*x)^2+(-648/49)/(2+3*x)+(-125/11)/(3+5*x)-_ + 16/41503*log(1-2*x)+34371/343*log(2+3*x)-12125/121*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3) +--R + +--R 3 2 +--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2) +--R + +--R 3 2 2 +--R (- 1440x - 2784x - 1792x - 384)log(- 2x + 1) - 24954930x - 32442333x +--R + +--R - 10519355 +--R / +--R 3 2 +--R 3735270x + 7221522x + 4648336x + 996072 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 374298750x - 723644250x - 465794000x - 99813000)log(5x + 3) +--R + +--R 3 2 +--R (374300190x + 723647034x + 465795792x + 99813384)log(3x + 2) +--R + +--R 3 2 2 +--R (- 1440x - 2784x - 1792x - 384)log(2x - 1) - 24954930x - 32442333x +--R + +--R - 10519355 +--R / +--R 3 2 +--R 3735270x + 7221522x + 4648336x + 996072 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 41503 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 4050x + 13635x + 17388x + 9039x - 376x - 2536x - 1056x - 144 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=(-3/7)/(2+3*x)^3+(-324/49)/(2+3*x)^2+(-34371/343)/(2+3*x)+_ + (-625/11)/(3+5*x)-32/290521*log(1-2*x)+1612242/2401*log(2+3*x)-_ + 81250/121*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x +--R + +--R - 4681950000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 26335973070x + 68473529982x + 66717798444x + 28872029736x +--R + +--R 4681950768 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 4320x - 11232x - 10944x - 4736x - 768)log(- 2x + 1) - 1755736290x +--R + +--R 2 +--R - 3452950809x - 2261654241x - 493301347 +--R / +--R 4 3 2 +--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 26335968750x - 68473518750x - 66717787500x - 28872025000x +--R + +--R - 4681950000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 26335973070x + 68473529982x + 66717798444x + 28872029736x +--R + +--R 4681950768 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 4320x - 11232x - 10944x - 4736x - 768)log(2x - 1) - 1755736290x +--R + +--R 2 +--R - 3452950809x - 2261654241x - 493301347 +--R / +--R 4 3 2 +--R 39220335x + 101972871x + 99358182x + 42997108x + 6972504 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 290521 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 12150x + 49005x + 79434x + 61893x + 16950x - 8360x - 8240x +--R + +--R - 2544x - 288 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=(-9/28)/(2+3*x)^4+(-216/49)/(2+3*x)^3+(-34371/686)/(2+3*x)^2+_ + (-1612242/2401)/(2+3*x)+(-3125/11)/(3+5*x)-64/2033647*log(1-2*x)+_ + 70752609/16807*log(2+3*x)-509375/121*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R - 13868926312500x - 45305159287500x - 59174085600000x +--R + +--R 2 +--R - 38627528100000x - 12601888600000x - 1643724600000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R 13868926416180x + 45305159626188x + 59174086042368x +--R + +--R 2 +--R 38627528388768x + 12601888694208x + 1643724612288 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x +--R + +--R - 173183872939 +--R / +--R 5 4 3 2 +--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x +--R + +--R 390460224 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 13868926312500x - 45305159287500x - 59174085600000x +--R + +--R 2 +--R - 38627528100000x - 12601888600000x - 1643724600000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R 13868926416180x + 45305159626188x + 59174086042368x +--R + +--R 2 +--R 38627528388768x + 12601888694208x + 1643724612288 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 103680x - 338688x - 442368x - 288768x - 94208x - 12288)log(2x - 1) +--R + +--R 4 3 2 +--R - 924595208460x - 2434767448806x - 2403262839978x - 1053787613109x +--R + +--R - 173183872939 +--R / +--R 5 4 3 2 +--R 3294508140x + 10762059924x + 14056568064x + 9175815264x + 2993528384x +--R + +--R 390460224 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 2033647 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=1/((1-2*x)*(2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 36450x + 171315x + 336312x + 344547x + 174636x + 8820x - 41440x +--R + +--R 2 +--R - 24112x - 5952x - 576 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=(-9/35)/(2+3*x)^5+(-162/49)/(2+3*x)^4+(-11457/343)/(2+3*x)^3+_ + (-806121/2401)/(2+3*x)^2+(-70752609/16807)/(2+3*x)+_ + (-15625/11)/(3+5*x)-128/14235529*log(1-2*x)+2977686468/117649*_ + log(2+3*x)-3062500/121*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 2188822879687500x - 8609369993437500x - 14105747446875000x +--R + +--R 3 2 +--R - 12322262137500000x - 6053041050000000x - 1585320275000000x +--R + +--R - 172944030000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 2188822880465100x + 8609369996496060x + 14105747451886200x +--R + +--R 3 2 +--R 12322262141877600x + 6053041052150400x + 1585320275563200x +--R + +--R 172944030061440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x +--R + +--R - 61440 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R - 145921526219700x - 481541037023970x - 635461225889490x +--R + +--R 2 +--R - 419169494735145x - 138206158563165x - 18221473659389 +--R / +--R 6 5 4 3 +--R 86480838675x + 340157965455x + 557320960350x + 486855091800x +--R + +--R 2 +--R 239156887200x + 62636327600x + 6833053920 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 2188822879687500x - 8609369993437500x - 14105747446875000x +--R + +--R 3 2 +--R - 12322262137500000x - 6053041050000000x - 1585320275000000x +--R + +--R - 172944030000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 2188822880465100x + 8609369996496060x + 14105747451886200x +--R + +--R 3 2 +--R 12322262141877600x + 6053041052150400x + 1585320275563200x +--R + +--R 172944030061440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 777600x - 3058560x - 5011200x - 4377600x - 2150400x - 563200x +--R + +--R - 61440 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R - 145921526219700x - 481541037023970x - 635461225889490x +--R + +--R 2 +--R - 419169494735145x - 138206158563165x - 18221473659389 +--R / +--R 6 5 4 3 +--R 86480838675x + 340157965455x + 557320960350x + 486855091800x +--R + +--R 2 +--R 239156887200x + 62636327600x + 6833053920 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 14235529 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^m/((1-2*x)*(3+5*x)^3) +--R +--R +--R m +--R (3x + 2) +--R (1) - ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-5/22*(2+3*x)^(1+m)/(3+5*x)^2-10/121*(2+3*x)^(1+m)/(3+5*x)+_ +-- 15/22*(1-m)*(2+3*x)^(1+m)/(3+5*x)+8/9317*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,2/7*(2+3*x))/(1+m)-20/1331*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)-30/121*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m)+45/22*(1-m)*m*(2+3*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,5*(2+3*x))/(1+m) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^8/((1-2*x)*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=-62934003/500000*x-9268263/100000*x^2-1535517/25000*x^3-_ + 264627/10000*x^4-6561/1250*x^5+(-1/8593750)/(3+5*x)^2+_ + (-266/47265625)/(3+5*x)-5764801/85184*log(1-2*x)+_ + 31024/519921875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (49638400x + 59566080x + 17869824)log(5x + 3) +--R + +--R 2 +--R (- 56296884765625x - 67556261718750x - 20266878515625)log(- 2x + 1) +--R + +--R 7 6 5 +--R - 4366345500000x - 27253273162500x - 79082602830000x +--R + +--R 4 3 2 +--R - 146338473723750x - 215620841031750x - 153403867608750x +--R + +--R - 37694322033170x - 565664 +--R / +--R 2 +--R 831875000000x + 998250000000x + 299475000000 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (49638400x + 59566080x + 17869824)log(5x + 3) +--R + +--R 2 +--R (- 56296884765625x - 67556261718750x - 20266878515625)log(2x - 1) +--R + +--R 7 6 5 +--R - 4366345500000x - 27253273162500x - 79082602830000x +--R + +--R 4 3 2 +--R - 146338473723750x - 215620841031750x - 153403867608750x +--R + +--R - 37694322033170x - 565664 +--R / +--R 2 +--R 831875000000x + 998250000000x + 299475000000 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R - 5764801log(2x - 1) + 5764801log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^7/((1-2*x)*(3+5*x)^3) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=-339309/10000*x-1044657/50000*x^2-24543/2500*x^3-2187/1000*x^4+_ + (-1/1718750)/(3+5*x)^2+(-233/9453125)/(3+5*x)-_ + 823543/42592*log(1-2*x)+4667/20796875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (18668000x + 22401600x + 6720480)log(5x + 3) +--R + +--R 2 +--R (- 1608482421875x - 1930178906250x - 579053671875)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x +--R + +--R 2 +--R - 4012849402650x - 1016146037830x - 247984 +--R / +--R 2 +--R 83187500000x + 99825000000x + 29947500000 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (18668000x + 22401600x + 6720480)log(5x + 3) +--R + +--R 2 +--R (- 1608482421875x - 1930178906250x - 579053671875)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 181931062500x - 1034985600000x - 2783545256250x - 5202285041250x +--R + +--R 2 +--R - 4012849402650x - 1016146037830x - 247984 +--R / +--R 2 +--R 83187500000x + 99825000000x + 29947500000 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R - 823543log(2x - 1) + 823543log(- 2x + 1) +--R (4) ----------------------------------------- +--R 42592 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^6/((1-2*x)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=-216999/25000*x-19683/5000*x^2-243/250*x^3+(-1/343750)/(3+5*x)^2+_ + (-8/75625)/(3+5*x)-117649/21296*log(1-2*x)+3347/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (6694000x + 8032800x + 2409840)log(5x + 3) +--R + +--R 2 +--R (- 45956640625x - 55147968750x - 16544390625)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 8085825000x - 42450581250x - 114414423750x - 98436833550x +--R + +--R - 25994486210x - 106568 +--R / +--R 2 +--R 8318750000x + 9982500000x + 2994750000 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (6694000x + 8032800x + 2409840)log(5x + 3) +--R + +--R 2 5 +--R (- 45956640625x - 55147968750x - 16544390625)log(2x - 1) - 8085825000x +--R + +--R 4 3 2 +--R - 42450581250x - 114414423750x - 98436833550x - 25994486210x - 106568 +--R / +--R 2 +--R 8318750000x + 9982500000x + 2994750000 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R - 117649log(2x - 1) + 117649log(- 2x + 1) +--R (4) ----------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^5/((1-2*x)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=-4941/2500*x-243/500*x^2+(-1/68750)/(3+5*x)^2+(-167/378125)/(3+5*x)-_ + 16807/10648*log(1-2*x)+11224/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2244800x + 2693760x + 808128)log(5x + 3) +--R + +--R 2 4 +--R (- 1313046875x - 1575656250x - 472696875)log(- 2x + 1) - 404291250x +--R + +--R 3 2 +--R - 2129267250x - 2118486150x - 591955870x - 44572 +--R / +--R 2 +--R 831875000x + 998250000x + 299475000 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2244800x + 2693760x + 808128)log(5x + 3) +--R + +--R 2 4 +--R (- 1313046875x - 1575656250x - 472696875)log(2x - 1) - 404291250x +--R + +--R 3 2 +--R - 2129267250x - 2118486150x - 591955870x - 44572 +--R / +--R 2 +--R 831875000x + 998250000x + 299475000 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R - 16807log(2x - 1) + 16807log(- 2x + 1) +--R (4) --------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^4/((1-2*x)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=-81/250*x+(-1/13750)/(3+5*x)^2+(-134/75625)/(3+5*x)-_ + 2401/5324*log(1-2*x)+6802/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (680200x + 816240x + 244872)log(5x + 3) +--R + +--R 2 3 +--R (- 37515625x - 45018750x - 13505625)log(- 2x + 1) - 26952750x +--R + +--R 2 +--R - 32343300x - 9732470x - 17930 +--R / +--R 2 +--R 83187500x + 99825000x + 29947500 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (680200x + 816240x + 244872)log(5x + 3) +--R + +--R 2 3 +--R (- 37515625x - 45018750x - 13505625)log(2x - 1) - 26952750x +--R + +--R 2 +--R - 32343300x - 9732470x - 17930 +--R / +--R 2 +--R 83187500x + 99825000x + 29947500 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R - 2401log(2x - 1) + 2401log(- 2x + 1) +--R (4) ------------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^3/((1-2*x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=(-1/2750)/(3+5*x)^2+(-101/15125)/(3+5*x)-343/2662*log(1-2*x)+_ + 3469/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (173450x + 208140x + 62442)log(5x + 3) +--R + +--R 2 +--R (- 1071875x - 1286250x - 385875)log(- 2x + 1) - 11110x - 6787 +--R / +--R 2 +--R 8318750x + 9982500x + 2994750 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (173450x + 208140x + 62442)log(5x + 3) +--R + +--R 2 +--R (- 1071875x - 1286250x - 385875)log(2x - 1) - 11110x - 6787 +--R / +--R 2 +--R 8318750x + 9982500x + 2994750 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R - 343log(2x - 1) + 343log(- 2x + 1) +--R (4) ----------------------------------- +--R 2662 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)^2/((1-2*x)*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=(-1/550)/(3+5*x)^2+(-68/3025)/(3+5*x)-49/1331*log(1-2*x)+49/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(- 2x + 1) - 7480x - 4609 +--R / +--R 2 +--R 1663750x + 1996500x + 598950 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (61250x + 73500x + 22050)log(5x + 3) +--R + +--R 2 +--R (- 61250x - 73500x - 22050)log(2x - 1) - 7480x - 4609 +--R / +--R 2 +--R 1663750x + 1996500x + 598950 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R - 49log(2x - 1) + 49log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(2+3*x)/((1-2*x)*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=(-1/110)/(3+5*x)^2+(-7/121)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (3500x + 4200x + 1260)log(5x + 3) +--R + +--R 2 +--R (- 3500x - 4200x - 1260)log(- 2x + 1) - 3850x - 2431 +--R / +--R 2 +--R 332750x + 399300x + 119790 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (3500x + 4200x + 1260)log(5x + 3) + (- 3500x - 4200x - 1260)log(2x - 1) +--R + +--R - 3850x - 2431 +--R / +--R 2 +--R 332750x + 399300x + 119790 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R - 14log(2x - 1) + 14log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=1/((1-2*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 4 3 2 +--R 250x + 325x + 45x - 81x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=(-1/22)/(3+5*x)^2+(-2/121)/(3+5*x)-4/1331*log(1-2*x)+4/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(- 2x + 1) +--R + +--R - 220x - 253 +--R / +--R 2 +--R 66550x + 79860x + 23958 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x + 240x + 72)log(5x + 3) + (- 200x - 240x - 72)log(2x - 1) - 220x +--R + +--R - 253 +--R / +--R 2 +--R 66550x + 79860x + 23958 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R - 4log(2x - 1) + 4log(- 2x + 1) +--R (4) ------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=1/((1-2*x)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 5 4 3 2 +--R 750x + 1475x + 785x - 153x - 243x - 54 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=(-5/22)/(3+5*x)^2+155/121/(3+5*x)-8/9317*log(1-2*x)-27/7*log(2+3*x)+_ + 5135/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (1797250x + 2156700x + 647010)log(5x + 3) +--R + +--R 2 +--R (- 1796850x - 2156220x - 646866)log(3x + 2) +--R + +--R 2 +--R (- 400x - 480x - 144)log(- 2x + 1) + 119350x + 67375 +--R / +--R 2 +--R 465850x + 559020x + 167706 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1797250x + 2156700x + 647010)log(5x + 3) +--R + +--R 2 +--R (- 1796850x - 2156220x - 646866)log(3x + 2) +--R + +--R 2 +--R (- 400x - 480x - 144)log(2x - 1) + 119350x + 67375 +--R / +--R 2 +--R 465850x + 559020x + 167706 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R - 8log(2x - 1) + 8log(- 2x + 1) +--R (4) ------------------------------- +--R 9317 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=1/((1-2*x)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 6 5 4 3 2 +--R 2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=27/7/(2+3*x)+(-25/22)/(3+5*x)^2+1600/121/(3+5*x)-16/65219*log(1-2*x)-_ + 2889/49*log(2+3*x)+78475/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3) +--R + +--R 3 2 +--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2400x - 4480x - 2784x - 576)log(- 2x + 1) + 38449950x + 47420065x +--R + +--R 14580412 +--R / +--R 3 2 +--R 9782850x + 18261320x + 11348106x + 2347884 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (576791250x + 1076677000x + 669077850x + 138429900)log(5x + 3) +--R + +--R 3 2 +--R (- 576788850x - 1076672520x - 669075066x - 138429324)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2400x - 4480x - 2784x - 576)log(2x - 1) + 38449950x + 47420065x +--R + +--R 14580412 +--R / +--R 3 2 +--R 9782850x + 18261320x + 11348106x + 2347884 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R - 16log(2x - 1) + 16log(- 2x + 1) +--R (4) --------------------------------- +--R 65219 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=1/((1-2*x)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=27/14/(2+3*x)^2+2889/49/(2+3*x)+(-125/22)/(3+5*x)^2+12125/121/(3+5*x)-_ + 32/456533*log(1-2*x)-204228/343*log(2+3*x)+792500/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 122322375000x + 309883350000x + 294117355000x + 123953340000x +--R + +--R 19571580000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x +--R + +--R - 19571577696 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(- 2x + 1) +--R + +--R 3 2 +--R 8154808200x + 15494126340x + 9797832352x + 2062044985 +--R / +--R 4 3 2 +--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 122322375000x + 309883350000x + 294117355000x + 123953340000x +--R + +--R 19571580000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 122322360600x - 309883313520x - 294117320376x - 123953325408x +--R + +--R - 19571577696 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 14400x - 36480x - 34624x - 14592x - 2304)log(2x - 1) + 8154808200x +--R + +--R 2 +--R 15494126340x + 9797832352x + 2062044985 +--R / +--R 4 3 2 +--R 205439850x + 520447620x + 493968706x + 208179048x + 32870376 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R - 32log(2x - 1) + 32log(- 2x + 1) +--R (4) --------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=1/((1-2*x)*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 20250x + 80325x + 127845x + 97359x + 25237x - 13808x - 12888x +--R + +--R - 3888x - 432 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=9/7/(2+3*x)^3+2889/98/(2+3*x)^2+204228/343/(2+3*x)+(-625/22)/(3+5*x)^2+_ + 81250/121/(3+5*x)-64/3195731*log(1-2*x)-11984706/2401*log(2+3*x)+_ + 6643750/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 21534719062500x + 68911101000000x + 88148783362500x +--R + +--R 2 +--R 56341205725000x + 17993454150000x + 2297036700000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 21534718976100x - 68911100723520x - 88148783008836x +--R + +--R 2 +--R - 56341205498952x - 17993454077808x - 2297036690784 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(- 2x + 1) +--R + +--R 4 3 2 +--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x +--R + +--R 242016815656 +--R / +--R 5 4 3 2 +--R 4314236850x + 13805557920x + 17659609506x + 11287321892x +--R + +--R 3604784568x + 460185264 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 21534719062500x + 68911101000000x + 88148783362500x +--R + +--R 2 +--R 56341205725000x + 17993454150000x + 2297036700000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 21534718976100x - 68911100723520x - 88148783008836x +--R + +--R 2 +--R - 56341205498952x - 17993454077808x - 2297036690784 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 86400x - 276480x - 353664x - 226048x - 72192x - 9216)log(2x - 1) +--R + +--R 4 3 2 +--R 1435647836700x + 3684829392090x + 3543391400472x + 1512959972293x +--R + +--R 242016815656 +--R / +--R 5 4 3 2 +--R 4314236850x + 13805557920x + 17659609506x + 11287321892x +--R + +--R 3604784568x + 460185264 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R - 64log(2x - 1) + 64log(- 2x + 1) +--R (4) --------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3h.input.pamphlet b/src/input/rich3h.input.pamphlet new file mode 100644 index 0000000..147824c --- /dev/null +++ b/src/input/rich3h.input.pamphlet @@ -0,0 +1,7356 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3h.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 97 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3h.output +)spool rich3h.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)*(2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 60750x + 281475x + 544185x + 547767x + 270429x + 9050x - 66280x +--R + +--R 2 +--R - 37440x - 9072x - 864 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=27/28/(2+3*x)^4+963/49/(2+3*x)^3+102114/343/(2+3*x)^2+_ + 11984706/2401/(2+3*x)+(-3125/22)/(3+5*x)^2+509375/121/(3+5*x)-_ + 128/22370117*log(1-2*x)-631722537/16807*log(2+3*x)+_ + 50028125/1331*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 6810663844687500x + 26334566866125000x + 42407733539587500x +--R + +--R 3 2 +--R 36404259483900000x + 17569831073900000x + 4520262818400000x +--R + +--R 484313873400000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 6810663843650700x - 26334566862116040x - 42407733533131692x +--R + +--R 3 2 +--R - 36404259478358112x - 17569831071225312x - 4520262817711872x +--R + +--R - 484313873326272 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x +--R + +--R - 73728 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 454044255102900x + 1468076424167430x + 1897568655019884x +--R + +--R 2 +--R 1225594367568417x + 395538240141506x + 51027557612801 +--R / +--R 6 5 4 3 +--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x +--R + +--R 2 +--R 467445964832x + 120261748992x + 12885187392 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 6810663844687500x + 26334566866125000x + 42407733539587500x +--R + +--R 3 2 +--R 36404259483900000x + 17569831073900000x + 4520262818400000x +--R + +--R 484313873400000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 6810663843650700x - 26334566862116040x - 42407733533131692x +--R + +--R 3 2 +--R - 36404259478358112x - 17569831071225312x - 4520262817711872x +--R + +--R - 484313873326272 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 1036800x - 4008960x - 6455808x - 5541888x - 2674688x - 688128x +--R + +--R - 73728 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 454044255102900x + 1468076424167430x + 1897568655019884x +--R + +--R 2 +--R 1225594367568417x + 395538240141506x + 51027557612801 +--R / +--R 6 5 4 3 +--R 181197947700x + 700632064440x + 1128259221012x + 968536585632x +--R + +--R 2 +--R 467445964832x + 120261748992x + 12885187392 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 32805x + 194643x + 513216x + 789264x + 780192x + 514080x + 225792x +--R + +--R 2 +--R 63744x + 10496x + 768 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=63412811/1024/(1-2*x)+91609881/256*x+122887143/512*x^2+5892813/32*x^3+_ + 32991057/256*x^4+5859459/80*x^5+976617/32*x^6+56862/7*x^7+_ + 32805/32*x^8+246239357/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (17236754990x - 8618377495)log(- 2x + 1) + 73483200x + 545525280x +--R + +--R 7 6 5 4 3 +--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x +--R + +--R 2 +--R 17048666670x - 12825383340x - 2219448385 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (17236754990x - 8618377495)log(2x - 1) + 73483200x + 545525280x +--R + +--R 7 6 5 4 3 +--R 1896488640x + 4156264224x + 6612458328x + 8581153140x + 10604249460x +--R + +--R 2 +--R 17048666670x - 12825383340x - 2219448385 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R 246239357log(2x - 1) - 246239357log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=9058973/512/(1-2*x)+22333965/256*x+873207/16*x^2+2399985/64*x^3+_ + 1423899/64*x^4+793881/80*x^5+11421/4*x^6+10935/28*x^7+_ + 15647317/256*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (2190624380x - 1095312190)log(- 2x + 1) + 13996800x + 95333760x +--R + +--R 6 5 4 3 2 +--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x +--R + +--R - 1563377550x - 317064055 +--R / +--R 35840x - 17920 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (2190624380x - 1095312190)log(2x - 1) + 13996800x + 95333760x +--R + +--R 6 5 4 3 2 +--R 304492608x + 619554096x + 945299880x + 1283987880x + 2148763260x +--R + +--R - 1563377550x - 317064055 +--R / +--R 35840x - 17920 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R 15647317log(2x - 1) - 15647317log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R (1) --------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=1294139/256/(1-2*x)+661617/32*x+1507977/128*x^2+111501/16*x^3+_ + 210195/64*x^4+5103/5*x^5+1215/8*x^6+3916031/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (39160310x - 19580155)log(- 2x + 1) + 388800x + 2418336x + 7101432x +--R + +--R 4 3 2 +--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695 +--R / +--R 2560x - 1280 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (39160310x - 19580155)log(2x - 1) + 388800x + 2418336x + 7101432x +--R + +--R 4 3 2 +--R 13636260x + 21239460x + 37849590x - 26464680x - 6470695 +--R / +--R 2560x - 1280 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R 3916031log(2x - 1) - 3916031log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=184877/128/(1-2*x)+301467/64*x+75447/32*x^2+18027/16*x^3+2997/8*x^4+_ + 243/4*x^5+60025/16*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R (960400x - 480200)log(- 2x + 1) + 15552x + 88128x + 240480x + 459360x +--R + +--R 2 +--R 904080x - 602934x - 184877 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (960400x - 480200)log(2x - 1) + 15552x + 88128x + 240480x + 459360x +--R + +--R 2 +--R 904080x - 602934x - 184877 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 60025log(2x - 1) - 60025log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=26411/64/(1-2*x)+16203/16*x+13419/32*x^2+144*x^3+405/16*x^4+_ + 57281/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (114562x - 57281)log(- 2x + 1) + 3240x + 16812x + 44460x + 102786x +--R + +--R - 64812x - 26411 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (114562x - 57281)log(2x - 1) + 3240x + 16812x + 44460x + 102786x +--R + +--R - 64812x - 26411 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 57281log(2x - 1) - 57281log(- 2x + 1) +--R (4) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=3773/32/(1-2*x)+3177/16*x+243/4*x^2+45/4*x^3+3283/16*log(1-2*x) +--R +--R +--R 4 3 2 +--R (13132x - 6566)log(- 2x + 1) + 720x + 3528x + 10764x - 6354x - 3773 +--R (2) ---------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R (13132x - 6566)log(2x - 1) + 720x + 3528x + 10764x - 6354x - 3773 +--R (3) -------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R 3283log(2x - 1) - 3283log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^2 +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ---------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=539/16/(1-2*x)+33*x+45/8*x^2+707/16*log(1-2*x) +--R +--R +--R 3 2 +--R (1414x - 707)log(- 2x + 1) + 180x + 966x - 528x - 539 +--R (2) ------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (1414x - 707)log(2x - 1) + 180x + 966x - 528x - 539 +--R (3) ----------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R 707log(2x - 1) - 707log(- 2x + 1) +--R (4) --------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^2 +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) -------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=77/8/(1-2*x)+15/4*x+17/2*log(1-2*x) +--R +--R +--R 2 +--R (136x - 68)log(- 2x + 1) + 60x - 30x - 77 +--R (2) ------------------------------------------ +--R 16x - 8 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (136x - 68)log(2x - 1) + 60x - 30x - 77 +--R (3) ---------------------------------------- +--R 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R 17log(2x - 1) - 17log(- 2x + 1) +--R (4) ------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/(1-2*x)^2 +--R +--R +--R 5x + 3 +--R (1) ------------ +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=11/4/(1-2*x)+5/4*log(1-2*x) +--R +--R +--R (10x - 5)log(- 2x + 1) - 11 +--R (2) --------------------------- +--R 8x - 4 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x - 5)log(2x - 1) - 11 +--R (3) ------------------------- +--R 8x - 4 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R 5log(2x - 1) - 5log(- 2x + 1) +--R (4) ----------------------------- +--R 4 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=11/14/(1-2*x)+1/49*log(1-2*x)-1/49*log(2+3*x) +--R +--R +--R (- 4x + 2)log(3x + 2) + (4x - 2)log(- 2x + 1) - 77 +--R (2) -------------------------------------------------- +--R 196x - 98 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (- 4x + 2)log(3x + 2) + (4x - 2)log(2x - 1) - 77 +--R (3) ------------------------------------------------ +--R 196x - 98 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R log(2x - 1) - log(- 2x + 1) +--R (4) --------------------------- +--R 49 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 5x + 3 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=11/49/(1-2*x)+1/49/(2+3*x)-31/343*log(1-2*x)+31/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(- 2x + 1) - 217x +--R + +--R - 161 +--R / +--R 2 +--R 2058x + 343x - 686 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (186x + 31x - 62)log(3x + 2) + (- 186x - 31x + 62)log(2x - 1) - 217x - 161 +--R ---------------------------------------------------------------------------- +--R 2 +--R 2058x + 343x - 686 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 31log(2x - 1) + 31log(- 2x + 1) +--R (4) --------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=22/343/(1-2*x)+1/98/(2+3*x)^2+(-31/343)/(2+3*x)-128/2401*log(1-2*x)+_ + 128/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (4608x + 3840x - 1024x - 1024)log(3x + 2) +--R + +--R 3 2 2 +--R (- 4608x - 3840x + 1024x + 1024)log(- 2x + 1) - 5376x - 4032x - 413 +--R / +--R 3 2 +--R 86436x + 72030x - 19208x - 19208 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (4608x + 3840x - 1024x - 1024)log(3x + 2) +--R + +--R 3 2 2 +--R (- 4608x - 3840x + 1024x + 1024)log(2x - 1) - 5376x - 4032x - 413 +--R / +--R 3 2 +--R 86436x + 72030x - 19208x - 19208 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 5x + 3 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=44/2401/(1-2*x)+1/147/(2+3*x)^3+(-31/686)/(2+3*x)^2+(-128/2401)/(2+3*x)-_ + 388/16807*log(1-2*x)+388/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2) +--R + +--R 4 3 2 +--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(- 2x + 1) +--R + +--R 3 2 +--R - 146664x - 207774x - 48209x + 15148 +--R / +--R 4 3 2 +--R 5445468x + 8168202x + 1815156x - 2016840x - 806736 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (125712x + 188568x + 41904x - 46560x - 18624)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 125712x - 188568x - 41904x + 46560x + 18624)log(2x - 1) - 146664x +--R + +--R 2 +--R - 207774x - 48209x + 15148 +--R / +--R 4 3 2 +--R 5445468x + 8168202x + 1815156x - 2016840x - 806736 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 388log(2x - 1) + 388log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 5x + 3 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=88/16807/(1-2*x)+1/196/(2+3*x)^4+(-31/1029)/(2+3*x)^3+_ + (-64/2401)/(2+3*x)^2+(-388/16807)/(2+3*x)-1040/117649*log(1-2*x)+_ + 1040/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2358720x - 4914000x - 3003000x + 64610x + 370853 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (2021760x + 4380480x + 2695680x - 299520x - 798720x - 199680) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 2021760x - 4380480x - 2695680x + 299520x + 798720x + 199680) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2358720x - 4914000x - 3003000x + 64610x + 370853 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 1040log(2x - 1) + 1040log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=176/117649/(1-2*x)+1/245/(2+3*x)^5+(-31/1372)/(2+3*x)^4+_ + (-128/7203)/(2+3*x)^3+(-194/16807)/(2+3*x)^2+_ + (-1040/117649)/(2+3*x)-2608/823543*log(1-2*x)+2608/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x +--R + +--R - 27540480x - 5007360 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x +--R + +--R 27540480x + 5007360 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x +--R + +--R 14729806 +--R / +--R 6 5 4 3 +--R 24014513880x + 68041122660x + 66706983000x + 17788528800x +--R + +--R 2 +--R - 11859019200x - 8696614080x - 1581202560 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 76049280x + 215472960x + 211248000x + 56332800x - 37555200x +--R + +--R - 27540480x - 5007360 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 76049280x - 215472960x - 211248000x - 56332800x + 37555200x +--R + +--R 27540480x + 5007360 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 88724160x - 243991440x - 236187000x - 72875670x + 24420823x +--R + +--R 14729806 +--R / +--R 6 5 4 3 +--R 24014513880x + 68041122660x + 66706983000x + 17788528800x +--R + +--R 2 +--R - 11859019200x - 8696614080x - 1581202560 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 2608log(2x - 1) + 2608log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 5x + 3 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=352/823543/(1-2*x)+1/294/(2+3*x)^6+(-31/1715)/(2+3*x)^5+_ + (-32/2401)/(2+3*x)^4+(-388/50421)/(2+3*x)^3+_ + (-520/117649)/(2+3*x)^2+(-2608/823543)/(2+3*x)-_ + 128/117649*log(1-2*x)+128/117649*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 2 +--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x +--R + +--R - 81920 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 2 +--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x +--R + +--R 81920 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x +--R + +--R 343917 +--R / +--R 7 6 5 4 2 +--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x +--R + +--R - 527067520x - 75295360 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 2 +--R 1866240x + 6531840x + 8709120x + 4838400x - 1290240x - 573440x +--R + +--R - 81920 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 2 +--R - 1866240x - 6531840x - 8709120x - 4838400x + 1290240x + 573440x +--R + +--R 81920 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 2177280x - 7439040x - 9787680x - 5652360x - 592956x + 929404x +--R + +--R 343917 +--R / +--R 7 6 5 4 2 +--R 1715322420x + 6003628470x + 8004837960x + 4447132200x - 1185901920x +--R + +--R - 527067520x - 75295360 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 128log(2x - 1) + 128log(- 2x + 1) +--R (4) ----------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^8*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 164025x + 1071630x + 3150009x + 5485968x + 6268752x + 4910976x +--R + +--R 4 3 2 +--R 2671200x + 996096x + 243712x + 35328x + 2304 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=697540921/2048/(1-2*x)+2330515357/1024*x+413355417/256*x^2+_ + 346239417/256*x^3+275757561/256*x^4+235268793/320*x^5+_ + 396738*x^6+17378631/112*x^7+1235655/32*x^8+18225/4*x^9+_ + 1512848491/1024*log(1-2*x) +--R +--R +--R (2) +--R 10 9 +--R (211798788740x - 105899394370)log(- 2x + 1) + 653184000x + 5209142400x +--R + +--R 8 7 6 5 +--R 19476780480x + 45754035840x + 76962239424x + 101724024528x +--R + +--R 4 3 2 +--R 116681956440x + 134531996760x + 210532633220x - 163136074990x +--R + +--R - 24413932235 +--R / +--R 143360x - 71680 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 +--R (211798788740x - 105899394370)log(2x - 1) + 653184000x + 5209142400x +--R + +--R 8 7 6 5 +--R 19476780480x + 45754035840x + 76962239424x + 101724024528x +--R + +--R 4 3 2 +--R 116681956440x + 134531996760x + 210532633220x - 163136074990x +--R + +--R - 24413932235 +--R / +--R 143360x - 71680 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R 1512848491log(2x - 1) - 1512848491log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R 54675x + 320760x + 836163x + 1271214x + 1242108x + 808920x +--R + +--R 3 2 +--R 351120x + 97952x + 15936x + 1152 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=99648703/1024/(1-2*x)+9077405/16*x+195497697/512*x^2+18842715/64*x^3+_ + 53086563/256*x^4+4750569/40*x^5+1597239/32*x^6+375435/28*x^7+_ + 54675/32*x^8+389535839/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (27267508730x - 13633754365)log(- 2x + 1) + 122472000x + 899877600x +--R + +--R 7 6 5 4 +--R 3097258560x + 6724111968x + 10607727816x + 13671721980x +--R + +--R 3 2 +--R 16817757180x + 26981935610x - 20333387200x - 3487704605 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (27267508730x - 13633754365)log(2x - 1) + 122472000x + 899877600x +--R + +--R 7 6 5 4 +--R 3097258560x + 6724111968x + 10607727816x + 13671721980x +--R + +--R 3 2 +--R 16817757180x + 26981935610x - 20333387200x - 3487704605 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R 389535839log(2x - 1) - 389535839log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=14235529/512/(1-2*x)+35458963/256*x+11140101/128*x^2+3851307/64*x^3+_ + 575775/16*x^4+1295919/80*x^5+37665/8*x^6+18225/28*x^7+_ + 12386759/128*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (3468292520x - 1734146260)log(- 2x + 1) + 23328000x + 157075200x +--R + +--R 6 5 4 3 2 +--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x +--R + +--R - 2482127410x - 498243515 +--R / +--R 35840x - 17920 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (3468292520x - 1734146260)log(2x - 1) + 23328000x + 157075200x +--R + +--R 6 5 4 3 2 +--R 496202112x + 999450144x + 1511863920x + 2040862320x + 3404640680x +--R + +--R - 2482127410x - 498243515 +--R / +--R 35840x - 17920 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R 12386759log(2x - 1) - 12386759log(- 2x + 1) +--R (4) ------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=2033647/256/(1-2*x)+2104901/64*x+2412699/128*x^2+89913/8*x^3+_ + 342333/64*x^4+6723/4*x^5+2025/8*x^6+6206585/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (12413170x - 6206585)log(- 2x + 1) + 129600x + 795744x + 2308392x +--R + +--R 4 3 2 +--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647 +--R / +--R 512x - 256 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (12413170x - 6206585)log(2x - 1) + 129600x + 795744x + 2308392x +--R + +--R 4 3 2 +--R 4385100x + 6773580x + 12013810x - 8419604x - 2033647 +--R / +--R 512x - 256 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 6206585log(2x - 1) - 6206585log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=290521/128/(1-2*x)+480841/64*x+15159/4*x^2+29277/16*x^3+9855/16*x^4+_ + 405/4*x^5+381073/64*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 +--R (1524292x - 762146)log(- 2x + 1) + 25920x + 144720x + 389592x +--R + +--R 3 2 +--R 735960x + 1438276x - 961682x - 290521 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R (1524292x - 762146)log(2x - 1) + 25920x + 144720x + 389592x + 735960x +--R + +--R 2 +--R 1438276x - 961682x - 290521 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R 381073log(2x - 1) - 381073log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=41503/64/(1-2*x)+12973/8*x+21717/32*x^2+945/4*x^3+675/16*x^4+_ + 91091/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (182182x - 91091)log(- 2x + 1) + 5400x + 27540x + 71748x + 164134x +--R + +--R - 103784x - 41503 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (182182x - 91091)log(2x - 1) + 5400x + 27540x + 71748x + 164134x +--R + +--R - 103784x - 41503 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R 91091log(2x - 1) - 91091log(- 2x + 1) +--R (4) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=5929/32/(1-2*x)+5119/16*x+795/8*x^2+75/4*x^3+1309/4*log(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (20944x - 10472)log(- 2x + 1) + 1200x + 5760x + 17296x - 10238x - 5929 +--R ------------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (20944x - 10472)log(2x - 1) + 1200x + 5760x + 17296x - 10238x - 5929 +--R ----------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R 1309log(2x - 1) - 1309log(- 2x + 1) +--R (4) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ----------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=847/16/(1-2*x)+215/4*x+75/8*x^2+1133/16*log(1-2*x) +--R +--R +--R 3 2 +--R (2266x - 1133)log(- 2x + 1) + 300x + 1570x - 860x - 847 +--R (2) --------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (2266x - 1133)log(2x - 1) + 300x + 1570x - 860x - 847 +--R (3) ------------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R 1133log(2x - 1) - 1133log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=121/8/(1-2*x)+25/4*x+55/4*log(1-2*x) +--R +--R +--R 2 +--R (220x - 110)log(- 2x + 1) + 100x - 50x - 121 +--R (2) --------------------------------------------- +--R 16x - 8 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (220x - 110)log(2x - 1) + 100x - 50x - 121 +--R (3) ------------------------------------------- +--R 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R 55log(2x - 1) - 55log(- 2x + 1) +--R (4) ------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=121/28/(1-2*x)+407/196*log(1-2*x)+1/147*log(2+3*x) +--R +--R +--R (8x - 4)log(3x + 2) + (2442x - 1221)log(- 2x + 1) - 2541 +--R (2) -------------------------------------------------------- +--R 1176x - 588 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (8x - 4)log(3x + 2) + (2442x - 1221)log(2x - 1) - 2541 +--R (3) ------------------------------------------------------ +--R 1176x - 588 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R 407log(2x - 1) - 407log(- 2x + 1) +--R (4) --------------------------------- +--R 196 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=121/98/(1-2*x)+(-1/147)/(2+3*x)+22/343*log(1-2*x)-22/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(- 2x + 1) +--R + +--R - 7651x - 5068 +--R / +--R 2 +--R 12348x + 2058x - 4116 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 792x - 132x + 264)log(3x + 2) + (792x + 132x - 264)log(2x - 1) +--R + +--R - 7651x - 5068 +--R / +--R 2 +--R 12348x + 2058x - 4116 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R 22log(2x - 1) - 22log(- 2x + 1) +--R (4) ------------------------------- +--R 343 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=121/343/(1-2*x)+(-1/294)/(2+3*x)^2+22/343/(2+3*x)-319/2401*log(1-2*x)+_ + 319/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (34452x + 28710x - 7656x - 7656)log(3x + 2) +--R + +--R 3 2 2 +--R (- 34452x - 28710x + 7656x + 7656)log(- 2x + 1) - 40194x - 60158x +--R + +--R - 22127 +--R / +--R 3 2 +--R 259308x + 216090x - 57624x - 57624 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (34452x + 28710x - 7656x - 7656)log(3x + 2) +--R + +--R 3 2 2 +--R (- 34452x - 28710x + 7656x + 7656)log(2x - 1) - 40194x - 60158x - 22127 +--R / +--R 3 2 +--R 259308x + 216090x - 57624x - 57624 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 319log(2x - 1) + 319log(- 2x + 1) +--R (4) ----------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=242/2401/(1-2*x)+(-1/441)/(2+3*x)^3+11/343/(2+3*x)^2+_ + (-319/2401)/(2+3*x)-1364/16807*log(1-2*x)+1364/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2) +--R + +--R 4 3 2 +--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(- 2x + 1) +--R + +--R 3 2 +--R - 773388x - 1095633x - 464303x - 50939 +--R / +--R 4 3 2 +--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (662904x + 994356x + 220968x - 245520x - 98208)log(3x + 2) +--R + +--R 4 3 2 +--R (- 662904x - 994356x - 220968x + 245520x + 98208)log(2x - 1) +--R + +--R 3 2 +--R - 773388x - 1095633x - 464303x - 50939 +--R / +--R 4 3 2 +--R 8168202x + 12252303x + 2722734x - 3025260x - 1210104 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 1364log(2x - 1) + 1364log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=484/16807/(1-2*x)+(-1/588)/(2+3*x)^4+22/1029/(2+3*x)^3+_ + (-319/4802)/(2+3*x)^2+(-1364/16807)/(2+3*x)-4180/117649*log(1-2*x)+_ + 4180/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (8125920x + 17606160x + 10834560x - 1203840x - 3210240x - 802560) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 8125920x - 17606160x - 10834560x + 1203840x + 3210240x + 802560) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 9480240x - 19750500x - 12069750x - 1210930x + 583289 +--R / +--R 5 4 3 2 +--R 228709656x + 495537588x + 304946208x - 33882912x - 90354432x - 22588608 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 4180log(2x - 1) + 4180log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=968/117649/(1-2*x)+(-1/735)/(2+3*x)^5+11/686/(2+3*x)^4+_ + (-319/7203)/(2+3*x)^3+(-682/16807)/(2+3*x)^2+(-4180/117649)/(2+3*x)-_ + 11264/823543*log(1-2*x)+11264/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x +--R + +--R - 19824640x - 3604480 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x +--R + +--R 19824640x + 3604480 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708 +--R / +--R 6 5 4 3 +--R 4002418980x + 11340187110x + 11117830500x + 2964754800x +--R + +--R 2 +--R - 1976503200x - 1449435680x - 263533760 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 54743040x + 155105280x + 152064000x + 40550400x - 27033600x +--R + +--R - 19824640x - 3604480 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 54743040x - 155105280x - 152064000x - 40550400x + 27033600x +--R + +--R 19824640x + 3604480 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 63866880x - 175633920x - 170016000x - 52458560x + 10716139x + 6392708 +--R / +--R 6 5 4 3 +--R 4002418980x + 11340187110x + 11117830500x + 2964754800x +--R + +--R 2 +--R - 1976503200x - 1449435680x - 263533760 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 11264log(2x - 1) + 11264log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1936/823543/(1-2*x)+(-1/882)/(2+3*x)^6+22/1715/(2+3*x)^5+_ + (-319/9604)/(2+3*x)^4+(-1364/50421)/(2+3*x)^3+(-2090/117649)/(2+3*x)^2+_ + (-11264/823543)/(2+3*x)-4048/823543*log(1-2*x)+4048/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 1062357120x + 3718249920x + 4957666560x + 2754259200x +--R + +--R 2 +--R - 734469120x - 326430720x - 46632960 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x +--R + +--R 2 +--R 734469120x + 326430720x + 46632960 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x +--R + +--R 426120352x + 132853546 +--R / +--R 7 6 5 4 +--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x +--R + +--R 2 +--R - 149423641920x - 66410507520x - 9487215360 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 1062357120x + 3718249920x + 4957666560x + 2754259200x +--R + +--R 2 +--R - 734469120x - 326430720x - 46632960 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 1062357120x - 3718249920x - 4957666560x - 2754259200x +--R + +--R 2 +--R 734469120x + 326430720x + 46632960 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 1239416640x - 4234673520x - 5571636840x - 3217605930x - 337540203x +--R + +--R 426120352x + 132853546 +--R / +--R 7 6 5 4 +--R 216130624920x + 756457187220x + 1008609582960x + 560338657200x +--R + +--R 2 +--R - 149423641920x - 66410507520x - 9487215360 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 4048log(2x - 1) + 4048log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^2/((1-2*x)^2*(2+3*x)^8) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R / +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=3872/5764801/(1-2*x)+(-1/1029)/(2+3*x)^7+11/1029/(2+3*x)^6+_ + (-319/12005)/(2+3*x)^5+(-341/16807)/(2+3*x)^4+(-4180/352947)/(2+3*x)^3+_ + (-5632/823543)/(2+3*x)^2+(-4048/823543)/(2+3*x)-_ + 68288/40353607*log(1-2*x)+68288/40353607*log(2+3*x) +--R +--R +--R (2) +--R 8 7 6 5 +--R 4480375680x + 18668232000x + 31362629760x + 25554735360x +--R + +--R 4 3 2 +--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x +--R + +--R 4 3 2 +--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x +--R + +--R 3 2 +--R - 10470141297x + 1282240575x + 2289114821x + 535775051 +--R / +--R 8 7 6 5 +--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x +--R + +--R 4 3 2 +--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x +--R + +--R - 77478925440 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 4480375680x + 18668232000x + 31362629760x + 25554735360x +--R + +--R 4 3 2 +--R 7743859200x - 3097543680x - 3441715200x - 1114460160x - 131112960 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 5 +--R - 4480375680x - 18668232000x - 31362629760x - 25554735360x +--R + +--R 4 3 2 +--R - 7743859200x + 3097543680x + 3441715200x + 1114460160x + 131112960 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 4 +--R - 5227104960x - 21344011920x - 35403956280x - 29235085110x +--R + +--R 3 2 +--R - 10470141297x + 1282240575x + 2289114821x + 535775051 +--R / +--R 8 7 6 5 +--R 2647600155270x + 11031667313625x + 18533201086890x + 15101126811540x +--R + +--R 4 3 2 +--R 4576099033800x - 1830439613520x - 2033821792800x - 658570866240x +--R + +--R - 77478925440 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 68288log(2x - 1) + 68288log(- 2x + 1) +--R (4) --------------------------------------- +--R 40353607 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^8*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 11 10 9 8 7 +--R 820125x + 5850225x + 18964935x + 36879867x + 47801664x +--R + +--R 6 5 4 3 2 +--R 43361136x + 28088928x + 12994080x + 4206848x + 907776x + 117504x +--R + +--R 6912 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=7672950131/4096/(1-2*x)+7277894263/512*x+21573106793/2048*x^2+_ + 2416569641/256*x^3+8502681987/1024*x^4+260574273/40*x^5+_ + 544462047/128*x^6+242570133/112*x^7+101721015/128*x^8+_ + 370575/2*x^9+164025/8*x^10+36770371407/4096*log(1-2*x) +--R +--R +--R (2) +--R 11 +--R (2573925998490x - 1286962999245)log(- 2x + 1) + 5878656000x +--R + +--R 10 9 8 7 +--R 50186304000x + 201292257600x + 507052003680x + 909105215040x +--R + +--R 6 5 4 3 +--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x +--R + +--R 2 +--R 2565503311770x - 2037810393640x - 268553254585 +--R / +--R 286720x - 143360 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 +--R (2573925998490x - 1286962999245)log(2x - 1) + 5878656000x +--R + +--R 10 9 8 7 +--R 50186304000x + 201292257600x + 507052003680x + 909105215040x +--R + +--R 6 5 4 3 +--R 1257998896224x + 1446852761928x + 1516182519740x + 1666955952060x +--R + +--R 2 +--R 2565503311770x - 2037810393640x - 268553254585 +--R / +--R 286720x - 143360 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R 36770371407log(2x - 1) - 36770371407log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 4096 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^7*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 10 9 8 7 6 5 +--R 273375x + 1767825x + 5143095x + 8864559x + 10024182x + 7770924x +--R + +--R 4 3 2 +--R 4182360x + 1543120x + 373536x + 53568x + 3456 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=1096135733/2048/(1-2*x)+3690540955/1024*x+1312685491/512*x^2+_ + 551942075/256*x^3+220950207/128*x^4+379446471/320*x^5+_ + 20626947/32*x^6+28463805/112*x^7+127575/2*x^8+30375/4*x^9+_ + 298946109/128*log(1-2*x) +--R +--R +--R (2) +--R 10 +--R (334819642080x - 167409821040)log(- 2x + 1) + 1088640000x +--R + +--R 9 8 7 6 +--R 8600256000x + 31861382400x + 74191887360x + 123787657728x +--R + +--R 5 4 3 2 +--R 162468222336x + 185355446080x + 213008156480x + 332899764960x +--R + +--R - 258337866850x - 38364750655 +--R / +--R 143360x - 71680 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 +--R (334819642080x - 167409821040)log(2x - 1) + 1088640000x + 8600256000x +--R + +--R 8 7 6 5 +--R 31861382400x + 74191887360x + 123787657728x + 162468222336x +--R + +--R 4 3 2 +--R 185355446080x + 213008156480x + 332899764960x - 258337866850x +--R + +--R - 38364750655 +--R / +--R 143360x - 71680 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R 298946109log(2x - 1) - 298946109log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R 91125x + 528525x + 1362015x + 2046843x + 1976832x + 1272420x +--R + +--R 3 2 +--R 545840x + 150480x + 24192x + 1728 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=156590819/1024/(1-2*x)+230244479/256*x+310976027/512*x^2+7530189/16*x^3+_ + 85406805/256*x^4+15403257/80*x^5+2611845/32*x^6+309825/14*x^7+_ + 91125/32*x^8+616195041/1024*log(1-2*x) +--R +--R +--R (2) +--R 9 8 +--R (43133652870x - 21566826435)log(- 2x + 1) + 204120000x + 1484244000x +--R + +--R 7 6 5 4 +--R 5057380800x + 10876051872x + 17013246264x + 21778294020x +--R + +--R 3 2 +--R 26669020420x + 42700132230x - 32234227060x - 5480678665 +--R / +--R 71680x - 35840 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 +--R (43133652870x - 21566826435)log(2x - 1) + 204120000x + 1484244000x +--R + +--R 7 6 5 4 +--R 5057380800x + 10876051872x + 17013246264x + 21778294020x +--R + +--R 3 2 +--R 26669020420x + 42700132230x - 32234227060x - 5480678665 +--R / +--R 71680x - 35840 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R 616195041log(2x - 1) - 616195041log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1024 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R / +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=22370117/512/(1-2*x)+56291737/256*x+8881301/64*x^2+6179077/64*x^3+_ + 3724389/64*x^4+423009/16*x^5+15525/2*x^6+30375/28*x^7+_ + 39220335/256*log(1-2*x) +--R +--R +--R (2) +--R 8 7 +--R (1098169380x - 549084690)log(- 2x + 1) + 7776000x + 51753600x +--R + +--R 6 5 4 3 2 +--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x +--R + +--R - 788084318x - 156590819 +--R / +--R 7168x - 3584 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 +--R (1098169380x - 549084690)log(2x - 1) + 7776000x + 51753600x +--R + +--R 6 5 4 3 2 +--R 161687232x + 322377552x + 483490840x + 648677400x + 1078815780x +--R + +--R - 788084318x - 156590819 +--R / +--R 7168x - 3584 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R 39220335log(2x - 1) - 39220335log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=3195731/256/(1-2*x)+209243/4*x+3859469/128*x^2+289951/16*x^3+_ + 557415/64*x^4+5535/2*x^5+3375/8*x^6+9836211/256*log(1-2*x) +--R +--R +--R (2) +--R 7 6 5 +--R (19672422x - 9836211)log(- 2x + 1) + 216000x + 1308960x + 3750840x +--R + +--R 4 3 2 +--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731 +--R / +--R 512x - 256 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R (19672422x - 9836211)log(2x - 1) + 216000x + 1308960x + 3750840x +--R + +--R 4 3 2 +--R 7048772x + 10798660x + 19064166x - 13391552x - 3195731 +--R / +--R 512x - 256 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R 9836211log(2x - 1) - 9836211log(- 2x + 1) +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=456533/128/(1-2*x)+766807/64*x+194881/32*x^2+47535/16*x^3+_ + 2025/2*x^4+675/4*x^5+302379/32*log(1-2*x) +--R +--R +--R (2) +--R 6 5 4 +--R (2419032x - 1209516)log(- 2x + 1) + 43200x + 237600x + 630960x +--R + +--R 3 2 +--R 1178768x + 2287704x - 1533614x - 456533 +--R / +--R 256x - 128 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R (2419032x - 1209516)log(2x - 1) + 43200x + 237600x + 630960x +--R + +--R 3 2 +--R 1178768x + 2287704x - 1533614x - 456533 +--R / +--R 256x - 128 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R 302379log(2x - 1) - 302379log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=65219/64/(1-2*x)+41537/16*x+35135/32*x^2+775/2*x^3+1125/16*x^4+_ + 144837/64*log(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (289674x - 144837)log(- 2x + 1) + 9000x + 45100x + 115740x + 262026x +--R + +--R - 166148x - 65219 +--R / +--R 128x - 64 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (289674x - 144837)log(2x - 1) + 9000x + 45100x + 115740x + 262026x +--R + +--R - 166148x - 65219 +--R / +--R 128x - 64 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R 144837log(2x - 1) - 144837log(- 2x + 1) +--R (4) --------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=9317/32/(1-2*x)+8245/16*x+325/2*x^2+125/4*x^3+8349/16*log(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (33396x - 16698)log(- 2x + 1) + 2000x + 9400x + 27780x - 16490x - 9317 +--R ------------------------------------------------------------------------- +--R 64x - 32 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (33396x - 16698)log(2x - 1) + 2000x + 9400x + 27780x - 16490x - 9317 +--R ----------------------------------------------------------------------- +--R 64x - 32 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R 8349log(2x - 1) - 8349log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^3/(1-2*x)^2 +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 2 +--R 4x - 4x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=1331/16/(1-2*x)+175/2*x+125/8*x^2+1815/16*log(1-2*x) +--R +--R +--R 3 2 +--R (3630x - 1815)log(- 2x + 1) + 500x + 2550x - 1400x - 1331 +--R (2) ----------------------------------------------------------- +--R 32x - 16 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R (3630x - 1815)log(2x - 1) + 500x + 2550x - 1400x - 1331 +--R (3) --------------------------------------------------------- +--R 32x - 16 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R 1815log(2x - 1) - 1815log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 3 2 +--R 12x - 4x - 5x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=1331/56/(1-2*x)+125/12*x+1089/49*log(1-2*x)-1/441*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(- 2x + 1) + 73500x +--R + +--R - 36750x - 83853 +--R / +--R 7056x - 3528 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 16x + 8)log(3x + 2) + (156816x - 78408)log(2x - 1) + 73500x - 36750x +--R + +--R - 83853 +--R / +--R 7056x - 3528 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R 1089log(2x - 1) - 1089log(- 2x + 1) +--R (4) ----------------------------------- +--R 49 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) --------------------------- +--R 4 3 2 +--R 36x + 12x - 23x - 4x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=1331/196/(1-2*x)+1/441/(2+3*x)+4719/1372*log(1-2*x)+101/3087*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (2424x + 404x - 808)log(3x + 2) +--R + +--R 2 +--R (254826x + 42471x - 84942)log(- 2x + 1) - 251503x - 167734 +--R / +--R 2 +--R 74088x + 12348x - 24696 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (2424x + 404x - 808)log(3x + 2) + (254826x + 42471x - 84942)log(2x - 1) +--R + +--R - 251503x - 167734 +--R / +--R 2 +--R 74088x + 12348x - 24696 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R 4719log(2x - 1) - 4719log(- 2x + 1) +--R (4) ----------------------------------- +--R 1372 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^3) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------ +--R 5 4 3 2 +--R 108x + 108x - 45x - 58x + 4x + 8 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=1331/686/(1-2*x)+1/882/(2+3*x)^2+(-101/3087)/(2+3*x)+_ + 363/2401*log(1-2*x)-363/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2) +--R + +--R 3 2 2 +--R (117612x + 98010x - 26136x - 26136)log(- 2x + 1) - 763161x - 1007552x +--R + +--R - 332633 +--R / +--R 3 2 +--R 777924x + 648270x - 172872x - 172872 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 117612x - 98010x + 26136x + 26136)log(3x + 2) +--R + +--R 3 2 2 +--R (117612x + 98010x - 26136x - 26136)log(2x - 1) - 763161x - 1007552x +--R + +--R - 332633 +--R / +--R 3 2 +--R 777924x + 648270x - 172872x - 172872 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R 363log(2x - 1) - 363log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^4) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 324x + 540x + 81x - 264x - 104x + 32x + 16 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1331/2401/(1-2*x)+1/1323/(2+3*x)^3+(-101/6174)/(2+3*x)^2+_ + 363/2401/(2+3*x)-3267/16807*log(1-2*x)+3267/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2) +--R + +--R 4 3 2 +--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(- 2x + 1) +--R + +--R 3 2 +--R - 11114334x - 25199244x - 18674579x - 4544792 +--R / +--R 4 3 2 +--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (9526572x + 14289858x + 3175524x - 3528360x - 1411344)log(3x + 2) +--R + +--R 4 3 2 +--R (- 9526572x - 14289858x - 3175524x + 3528360x + 1411344)log(2x - 1) +--R + +--R 3 2 +--R - 11114334x - 25199244x - 18674579x - 4544792 +--R / +--R 4 3 2 +--R 49009212x + 73513818x + 16336404x - 18151560x - 7260624 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 3267log(2x - 1) + 3267log(- 2x + 1) +--R (4) ------------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^5) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ----------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=2662/16807/(1-2*x)+1/1764/(2+3*x)^4+(-101/9261)/(2+3*x)^3+_ + 363/4802/(2+3*x)^2+(-3267/16807)/(2+3*x)-14520/117649*log(1-2*x)+_ + 14520/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x +--R + +--R - 25090560 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x +--R + +--R 25090560 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787 +--R / +--R 5 4 3 2 +--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x +--R + +--R - 203297472 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 254041920x + 550424160x + 338722560x - 37635840x - 100362240x +--R + +--R - 25090560 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 254041920x - 550424160x - 338722560x + 37635840x + 100362240x +--R + +--R 25090560 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 296382240x - 617463000x - 465575250x - 147766430x - 16012787 +--R / +--R 5 4 3 2 +--R 2058386904x + 4459838292x + 2744515872x - 304946208x - 813189888x +--R + +--R - 203297472 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 14520log(2x - 1) + 14520log(- 2x + 1) +--R (4) --------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^6) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=5324/117649/(1-2*x)+1/2205/(2+3*x)^5+(-101/12348)/(2+3*x)^4+_ + 121/2401/(2+3*x)^3+(-3267/33614)/(2+3*x)^2+(-14520/117649)/(2+3*x)-_ + 45012/823543*log(1-2*x)+45012/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 3937649760x + 11156674320x + 10937916000x + 2916777600x +--R + +--R 2 +--R - 1944518400x - 1425980160x - 259269120 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x +--R + +--R 2 +--R 1944518400x + 1425980160x + 259269120 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x +--R + +--R - 181895609x + 165794902 +--R / +--R 6 5 4 3 +--R 72043541640x + 204123367980x + 200120949000x + 53365586400x +--R + +--R 2 +--R - 35577057600x - 26089842240x - 4743607680 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 3937649760x + 11156674320x + 10937916000x + 2916777600x +--R + +--R 2 +--R - 1944518400x - 1425980160x - 259269120 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 3937649760x - 11156674320x - 10937916000x - 2916777600x +--R + +--R 2 +--R 1944518400x + 1425980160x + 259269120 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 4593924720x - 12633292980x - 12229197750x - 4545399390x +--R + +--R - 181895609x + 165794902 +--R / +--R 6 5 4 3 +--R 72043541640x + 204123367980x + 200120949000x + 53365586400x +--R + +--R 2 +--R - 35577057600x - 26089842240x - 4743607680 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 45012log(2x - 1) + 45012log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^7) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 9 8 7 6 5 4 3 2 +--R 8748x + 32076x + 43011x + 19278x - 9828x - 13608x - 3696x + 1184x +--R + +--R 832x + 128 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=10648/823543/(1-2*x)+1/2646/(2+3*x)^6+(-101/15435)/(2+3*x)^5+_ + 363/9604/(2+3*x)^4+(-1089/16807)/(2+3*x)^3+(-7260/117649)/(2+3*x)^2+_ + (-45012/823543)/(2+3*x)-17424/823543*log(1-2*x)+17424/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 +--R 13718263680x + 48013922880x + 64018563840x + 35565868800x +--R + +--R 2 +--R - 9484231680x - 4215214080x - 602173440 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x +--R + +--R 2 +--R 9484231680x + 4215214080x + 602173440 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x +--R + +--R 2 +--R - 6211643067x + 3228815828x + 1017833894 +--R / +--R 7 6 5 4 +--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x +--R + +--R 2 +--R - 448270925760x - 199231522560x - 28461646080 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 13718263680x + 48013922880x + 64018563840x + 35565868800x +--R + +--R 2 +--R - 9484231680x - 4215214080x - 602173440 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 13718263680x - 48013922880x - 64018563840x - 35565868800x +--R + +--R 2 +--R 9484231680x + 4215214080x + 602173440 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 16004640960x - 54682523280x - 71946788760x - 41549085270x +--R + +--R 2 +--R - 6211643067x + 3228815828x + 1017833894 +--R / +--R 7 6 5 4 +--R 648391874760x + 2269371561660x + 3025828748880x + 1681015971600x +--R + +--R 2 +--R - 448270925760x - 199231522560x - 28461646080 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 17424log(2x - 1) + 17424log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)^2*(2+3*x)^8) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 10 9 8 7 6 5 4 +--R 26244x + 113724x + 193185x + 143856x + 9072x - 60480x - 38304x +--R + +--R 3 2 +--R - 3840x + 4864x + 2048x + 256 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=21296/5764801/(1-2*x)+1/3087/(2+3*x)^7+(-101/18522)/(2+3*x)^6+_ + 363/12005/(2+3*x)^5+(-3267/67228)/(2+3*x)^4+(-4840/117649)/(2+3*x)^3+_ + (-22506/823543)/(2+3*x)^2+(-17424/823543)/(2+3*x)-_ + 307824/40353607*log(1-2*x)+307824/40353607*log(2+3*x) +--R +--R +--R (2) +--R 8 7 6 5 +--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x +--R + +--R 4 3 2 +--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x +--R + +--R - 21276794880 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R - 727067975040x - 3029449896000x - 5089475825280x +--R + +--R 5 4 3 2 +--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x +--R + +--R 180852756480x + 21276794880 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x +--R + +--R 3 2 +--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928 +--R / +--R 8 7 6 +--R 95313605589720x + 397140023290500x + 667195239128040x +--R + +--R 5 4 3 +--R 543640565215440x + 164739565216800x - 65895826086720x +--R + +--R 2 +--R - 73217584540800x - 23708551184640x - 2789241315840 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 +--R 727067975040x + 3029449896000x + 5089475825280x + 4146980302080x +--R + +--R 4 3 2 +--R 1256660697600x - 502664279040x - 558515865600x - 180852756480x +--R + +--R - 21276794880 +--R * +--R log(3x + 2) +--R + +--R 8 7 6 +--R - 727067975040x - 3029449896000x - 5089475825280x +--R + +--R 5 4 3 2 +--R - 4146980302080x - 1256660697600x + 502664279040x + 558515865600x +--R + +--R 180852756480x + 21276794880 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 4 +--R - 848245970880x - 3463671047760x - 5745295626840x - 4744221388830x +--R + +--R 3 2 +--R - 1699077259341x + 132416872350x + 278976950938x + 58668936928 +--R / +--R 8 7 6 +--R 95313605589720x + 397140023290500x + 667195239128040x +--R + +--R 5 4 3 +--R 543640565215440x + 164739565216800x - 65895826086720x +--R + +--R 2 +--R - 73217584540800x - 23708551184640x - 2789241315840 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 307824log(2x - 1) + 307824log(- 2x + 1) +--R (4) ----------------------------------------- +--R 40353607 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(a+b*x)^m/(e+f*x)^2 +--R +--R +--R m +--R (b x + a) +--R (1) ------------------ +--R 2 2 2 +--R f x + 2e f x + e +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=(a+b*x)^(1+m)/((b*e-a*f)*(e+f*x))-b*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)^2*(1+m)) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(a+b*x)^m/((c+d*x)*(e+f*x)^2) +--R +--R +--R m +--R (b x + a) +--R (1) ---------------------------------------------------- +--R 2 3 2 2 2 2 +--R d f x + (c f + 2d e f)x + (2c e f + d e )x + c e +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-f*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)*(e+f*x))+d^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/((b*c-a*d)*_ +-- (d*e-c*f)^2*(1+m))-d*f*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)*(d*e-c*f)^2*(1+m))+b*f*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)^2*(d*e-c*f)*(1+m)) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(a+b*x)^m/((c+d*x)^2*(e+f*x)^2) +--R +--R +--R (1) +--R m +--R (b x + a) +--R / +--R 2 2 4 2 2 3 2 2 2 2 2 +--R d f x + (2c d f + 2d e f)x + (c f + 4c d e f + d e )x +--R + +--R 2 2 2 2 +--R (2c e f + 2c d e )x + c e +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=d^2*(a+b*x)^(1+m)/((b*c-a*d)*(d*e-c*f)^2*(c+d*x))+_ +-- f^2*(a+b*x)^(1+m)/((b*e-a*f)*(d*e-c*f)^2*(e+f*x))-_ +-- 2*d^2*f*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*(d*e-c*f)^3*(1+m))-b*d^2*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)^2*(d*e-c*f)^2*(1+m))+2*d*f^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)*(d*e-c*f)^3*(1+m))-b*f^2*m*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/_ +-- ((b*e-a*f)^2*(d*e-c*f)^2*(1+m)) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=5764801/2816/(1-2*x)+2041906293/250000*x+1839811401/400000*x^2+_ + 26773659/10000*x^3+9899091/8000*x^4+94041/250*x^5+2187/40*x^6+_ + 188591347/30976*log(1-2*x)+1/9453125*log(3+5*x) +--R +--R +--R (2) +--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x +--R + +--R 3 2 +--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375 +--R / +--R 4840000000x - 2420000000 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (512x - 256)log(5x + 3) + (29467397968750x - 14733698984375)log(2x - 1) +--R + +--R 7 6 5 4 +--R 264627000000x + 1688320260000x + 5078633175000x + 9963975928500x +--R + +--R 3 2 +--R 15782492474100x + 28400446856430x - 19765652916240x - 4954125859375 +--R / +--R 4840000000x - 2420000000 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R 188591347log(2x - 1) - 188591347log(- 2x + 1) +--R (4) --------------------------------------------- +--R 30976 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=823543/1408/(1-2*x)+370109547/200000*x+18237069/20000*x^2+_ + 853659/2000*x^3+13851/100*x^4+2187/100*x^5+5764801/3872*log(1-2*x)+_ + 1/1890625*log(3+5*x) +--R +--R +--R (2) +--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 10585080000x + 61746300000x + 173066058000x + 338044330800x +--R + +--R 2 +--R 674996568840x - 447832551870x - 141546453125 +--R / +--R 484000000x - 242000000 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (256x - 128)log(5x + 3) + (720600125000x - 360300062500)log(2x - 1) +--R + +--R 6 5 4 3 +--R 10585080000x + 61746300000x + 173066058000x + 338044330800x +--R + +--R 2 +--R 674996568840x - 447832551870x - 141546453125 +--R / +--R 484000000x - 242000000 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R 5764801log(2x - 1) - 5764801log(- 2x + 1) +--R (4) ----------------------------------------- +--R 3872 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=117649/704/(1-2*x)+3946293/10000*x+639819/4000*x^2+2673/50*x^3+_ + 729/80*x^4+2739541/7744*log(1-2*x)+1/378125*log(3+5*x) +--R +--R +--R (2) +--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x +--R + +--R - 4044184375 +--R / +--R 48400000x - 24200000 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (128x - 64)log(5x + 3) + (17122131250x - 8561065625)log(2x - 1) +--R + +--R 5 4 3 2 +--R 441045000x + 2366941500x + 6448077900x + 15229153170x - 9550029060x +--R + +--R - 4044184375 +--R / +--R 48400000x - 24200000 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R 2739541log(2x - 1) - 2739541log(- 2x + 1) +--R (4) ----------------------------------------- +--R 7744 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=16807/352/(1-2*x)+152793/2000*x+567/25*x^2+81/20*x^3+_ + 156065/1936*log(1-2*x)+1/75625*log(3+5*x) +--R +--R +--R (2) +--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(- 2x + 1) +--R + +--R 4 3 2 +--R 19602000x + 99970200x + 314873460x - 184879530x - 115548125 +--R / +--R 4840000x - 2420000 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +--R (64x - 32)log(5x + 3) + (390162500x - 195081250)log(2x - 1) + 19602000x +--R + +--R 3 2 +--R 99970200x + 314873460x - 184879530x - 115548125 +--R / +--R 4840000x - 2420000 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R 156065log(2x - 1) - 156065log(- 2x + 1) +--R (4) --------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=2401/176/(1-2*x)+621/50*x+81/40*x^2+33271/1936*log(1-2*x)+_ + 1/15125*log(3+5*x) +--R +--R +--R (2) +--R 3 +--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(- 2x + 1) + 980100x +--R + +--R 2 +--R 5521230x - 3005640x - 3301375 +--R / +--R 484000x - 242000 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R (32x - 16)log(5x + 3) + (8317750x - 4158875)log(2x - 1) + 980100x +--R + +--R 2 +--R 5521230x - 3005640x - 3301375 +--R / +--R 484000x - 242000 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R 33271log(2x - 1) - 33271log(- 2x + 1) +--R (4) ------------------------------------- +--R 1936 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=343/88/(1-2*x)+27/20*x+392/121*log(1-2*x)+1/3025*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (16x - 8)log(5x + 3) + (156800x - 78400)log(- 2x + 1) + 65340x - 32670x +--R + +--R - 94325 +--R / +--R 48400x - 24200 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (16x - 8)log(5x + 3) + (156800x - 78400)log(2x - 1) + 65340x - 32670x +--R + +--R - 94325 +--R / +--R 48400x - 24200 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R 392log(2x - 1) - 392log(- 2x + 1) +--R (4) --------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=49/44/(1-2*x)+217/484*log(1-2*x)+1/605*log(3+5*x) +--R +--R +--R (8x - 4)log(5x + 3) + (2170x - 1085)log(- 2x + 1) - 2695 +--R (2) -------------------------------------------------------- +--R 4840x - 2420 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (8x - 4)log(5x + 3) + (2170x - 1085)log(2x - 1) - 2695 +--R (3) ------------------------------------------------------ +--R 4840x - 2420 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R 217log(2x - 1) - 217log(- 2x + 1) +--R (4) --------------------------------- +--R 484 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=7/22/(1-2*x)-1/121*log(1-2*x)+1/121*log(3+5*x) +--R +--R +--R (4x - 2)log(5x + 3) + (- 4x + 2)log(- 2x + 1) - 77 +--R (2) -------------------------------------------------- +--R 484x - 242 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (4x - 2)log(5x + 3) + (- 4x + 2)log(2x - 1) - 77 +--R (3) ------------------------------------------------ +--R 484x - 242 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 121 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R 3 2 +--R 20x - 8x - 7x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=1/11/(1-2*x)-5/121*log(1-2*x)+5/121*log(3+5*x) +--R +--R +--R (10x - 5)log(5x + 3) + (- 10x + 5)log(- 2x + 1) - 11 +--R (2) ---------------------------------------------------- +--R 242x - 121 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (10x - 5)log(5x + 3) + (- 10x + 5)log(2x - 1) - 11 +--R (3) -------------------------------------------------- +--R 242x - 121 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - 5log(2x - 1) + 5log(- 2x + 1) +--R (4) ------------------------------- +--R 121 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 4 3 2 +--R 60x + 16x - 37x - 5x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=2/77/(1-2*x)-136/5929*log(1-2*x)-9/49*log(2+3*x)+25/121*log(3+5*x) +--R +--R +--R (2) +--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2) +--R + +--R (- 272x + 136)log(- 2x + 1) - 154 +--R / +--R 11858x - 5929 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (2450x - 1225)log(5x + 3) + (- 2178x + 1089)log(3x + 2) +--R + +--R (- 272x + 136)log(2x - 1) - 154 +--R / +--R 11858x - 5929 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 136log(2x - 1) + 136log(- 2x + 1) +--R (4) ----------------------------------- +--R 5929 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 180x + 168x - 79x - 89x + 8x + 12 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=4/539/(1-2*x)+9/49/(2+3*x)-404/41503*log(1-2*x)-_ + 351/343*log(2+3*x)+125/121*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (257250x + 42875x - 85750)log(5x + 3) +--R + +--R 2 +--R (- 254826x - 42471x + 84942)log(3x + 2) +--R + +--R 2 +--R (- 2424x - 404x + 808)log(- 2x + 1) + 14322x - 8239 +--R / +--R 2 +--R 249018x + 41503x - 83006 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (257250x + 42875x - 85750)log(5x + 3) +--R + +--R 2 +--R (- 254826x - 42471x + 84942)log(3x + 2) +--R + +--R 2 +--R (- 2424x - 404x + 808)log(2x - 1) + 14322x - 8239 +--R / +--R 2 +--R 249018x + 41503x - 83006 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 404log(2x - 1) + 404log(- 2x + 1) +--R (4) ----------------------------------- +--R 41503 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------- +--R 6 5 4 3 2 +--R 540x + 864x + 99x - 425x - 154x + 52x + 24 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=8/3773/(1-2*x)+9/98/(2+3*x)^2+351/343/(2+3*x)-1072/290521*log(1-2*x)-_ + 12393/2401*log(2+3*x)+625/121*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3) +--R + +--R 3 2 +--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2) +--R + +--R 3 2 2 +--R (- 38592x - 32160x + 8576x + 8576)log(- 2x + 1) + 3556476x + 686532x +--R + +--R - 1247477 +--R / +--R 3 2 +--R 10458756x + 8715630x - 2324168x - 2324168 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (54022500x + 45018750x - 12005000x - 12005000)log(5x + 3) +--R + +--R 3 2 +--R (- 53983908x - 44986590x + 11996424x + 11996424)log(3x + 2) +--R + +--R 3 2 2 +--R (- 38592x - 32160x + 8576x + 8576)log(2x - 1) + 3556476x + 686532x +--R + +--R - 1247477 +--R / +--R 3 2 +--R 10458756x + 8715630x - 2324168x - 2324168 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 1072log(2x - 1) + 1072log(- 2x + 1) +--R (4) ------------------------------------- +--R 290521 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=16/26411/(1-2*x)+3/49/(2+3*x)^3+351/686/(2+3*x)^2+12393/2401/(2+3*x)-_ + 2672/2033647*log(1-2*x)-434043/16807*log(2+3*x)+3125/121*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x +--R + +--R 840307248 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(- 2x + 1) +--R + +--R 3 2 +--R 377820828x + 327259548x - 81484557x - 88405856 +--R / +--R 4 3 2 +--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5672362500x + 8508543750x + 1890787500x - 2100875000x - 840350000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 5672073924x - 8508110886x - 1890691308x + 2100768120x +--R + +--R 840307248 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 288576x - 432864x - 96192x + 106880x + 42752)log(2x - 1) +--R + +--R 3 2 +--R 377820828x + 327259548x - 81484557x - 88405856 +--R / +--R 4 3 2 +--R 219633876x + 329450814x + 73211292x - 81345880x - 32538352 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 2672log(2x - 1) + 2672log(- 2x + 1) +--R (4) ------------------------------------- +--R 2033647 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 8 7 6 5 4 3 2 +--R 4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=32/184877/(1-2*x)+9/196/(2+3*x)^4+117/343/(2+3*x)^3+_ + 12393/4802/(2+3*x)^2+434043/16807/(2+3*x)-6400/14235529*log(1-2*x)-_ + 15192225/117649*log(2+3*x)+15625/121*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x +--R + +--R - 470596000000x - 117649000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 1191191977800x - 2580915951900x - 1588255970400x +--R + +--R 2 +--R 176472885600x + 470594361600x + 117648590400 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441 +--R / +--R 5 4 3 2 +--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x +--R + +--R - 911073856 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1191196125000x + 2580924937500x + 1588261500000x - 176473500000x +--R + +--R - 470596000000x - 117649000000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 1191191977800x - 2580915951900x - 1588255970400x +--R + +--R 2 +--R 176472885600x + 470594361600x + 117648590400 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 4147200x - 8985600x - 5529600x + 614400x + 1638400x + 409600) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 79408236600x + 121756635000x + 28788432750x - 29974871850x - 12393745441 +--R / +--R 5 4 3 2 +--R 9224622792x + 19986682716x + 12299497056x - 1366610784x - 3644295424x +--R + +--R - 911073856 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 6400log(2x - 1) + 6400log(- 2x + 1) +--R (4) ------------------------------------- +--R 14235529 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^6*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x +--R + +--R 2 +--R 1936x + 1280x + 192 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=64/1294139/(1-2*x)+9/245/(2+3*x)^5+351/1372/(2+3*x)^4+_ + 4131/2401/(2+3*x)^3+434043/33614/(2+3*x)^2+15192225/117649/(2+3*x)-_ + 14912/99648703*log(1-2*x)-531729603/823543*log(2+3*x)+78125/121*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 625377965625000x + 1771904235937500x + 1737161015625000x +--R + +--R 3 2 +--R 463242937500000x - 308828625000000x - 226474325000000x +--R + +--R - 41177150000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 625377820680360x - 1771903825261020x - 1737160613001000x +--R + +--R 3 2 +--R - 463242830133600x + 308828553422400x + 226474272509760x +--R + +--R 41177140456320 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x +--R + +--R 52490240x + 9543680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x +--R + +--R - 16998574124301x - 4338387945122 +--R / +--R 6 5 4 3 +--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x +--R + +--R 2 +--R - 478313774400x - 350763434560x - 63775169920 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 625377965625000x + 1771904235937500x + 1737161015625000x +--R + +--R 3 2 +--R 463242937500000x - 308828625000000x - 226474325000000x +--R + +--R - 41177150000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 625377820680360x - 1771903825261020x - 1737160613001000x +--R + +--R 3 2 +--R - 463242830133600x + 308828553422400x + 226474272509760x +--R + +--R 41177140456320 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 144944640x - 410676480x - 402624000x - 107366400x + 71577600x +--R + +--R 52490240x + 9543680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R 41691695272920x + 91721636594280x + 57735061287750x - 5658908734710x +--R + +--R - 16998574124301x - 4338387945122 +--R / +--R 6 5 4 3 +--R 968585393160x + 2744325280620x + 2690514981000x + 717470661600x +--R + +--R 2 +--R - 478313774400x - 350763434560x - 63775169920 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 14912log(2x - 1) + 14912log(- 2x + 1) +--R (4) --------------------------------------- +--R 99648703 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=5764801/15488/(1-2*x)+231915717/200000*x+14171517/25000*x^2+_ + 2626101/10000*x^3+168399/2000*x^4+6561/500*x^5+(-1/9453125)/(3+5*x)+_ + 79883671/85184*log(1-2*x)+268/103984375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (343040x + 34304x - 102912)log(5x + 3) +--R + +--R 2 +--R (124818235937500x + 12481823593750x - 37445470781250)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x +--R + +--R 3 2 +--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717 +--R / +--R 2 +--R 133100000000x + 13310000000x - 39930000000 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (343040x + 34304x - 102912)log(5x + 3) +--R + +--R 2 +--R (124818235937500x + 12481823593750x - 37445470781250)log(2x - 1) +--R + +--R 7 6 5 4 +--R 1746538200000x + 11381607270000x + 35550138195000x + 75582410904000x +--R + +--R 3 2 +--R 151398804021300x - 7200755986050x - 71072602198741x - 14862377576717 +--R / +--R 2 +--R 133100000000x + 13310000000x - 39930000000 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R 79883671log(2x - 1) - 79883671log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=823543/7744/(1-2*x)+6156243/25000*x+1974861/20000*x^2+16281/500*x^3+_ + 2187/400*x^4+(-1/1890625)/(3+5*x)+18941489/85184*log(1-2*x)+_ + 47/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (150400x + 15040x - 45120)log(5x + 3) +--R + +--R 2 +--R (2959607656250x + 295960765625x - 887882296875)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x +--R + +--R 2 +--R - 66522621330x - 1691007398993x - 424639358671 +--R / +--R 2 +--R 13310000000x + 1331000000x - 3993000000 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (150400x + 15040x - 45120)log(5x + 3) +--R + +--R 2 +--R (2959607656250x + 295960765625x - 887882296875)log(2x - 1) +--R + +--R 6 5 4 3 +--R 72772425000x + 440677462500x + 1335778290000x + 3278990706750x +--R + +--R 2 +--R - 66522621330x - 1691007398993x - 424639358671 +--R / +--R 2 +--R 13310000000x + 1331000000x - 3993000000 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R 18941489log(2x - 1) - 18941489log(- 2x + 1) +--R (4) ------------------------------------------- +--R 85184 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=117649/3872/(1-2*x)+473607/10000*x+13851/1000*x^2+243/100*x^3+_ + (-1/378125)/(3+5*x)+67228/1331*log(1-2*x)+202/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (64640x + 6464x - 19392)log(5x + 3) +--R + +--R 2 5 +--R (67228000000x + 6722800000x - 20168400000)log(- 2x + 1) + 3234330000x +--R + +--R 4 3 2 +--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773 +--R / +--R 2 +--R 1331000000x + 133100000x - 399300000 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (64640x + 6464x - 19392)log(5x + 3) +--R + +--R 2 5 +--R (67228000000x + 6722800000x - 20168400000)log(2x - 1) + 3234330000x +--R + +--R 4 3 2 +--R 18759114000x + 63910360800x + 773004870x - 39132050089x - 12132552773 +--R / +--R 2 +--R 1331000000x + 133100000x - 399300000 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R 67228log(2x - 1) - 67228log(- 2x + 1) +--R (4) ------------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=16807/1936/(1-2*x)+3807/500*x+243/200*x^2+(-1/75625)/(3+5*x)+_ + 228095/21296*log(1-2*x)+169/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (27040x + 2704x - 8112)log(5x + 3) +--R + +--R 2 4 +--R (1425593750x + 142559375x - 427678125)log(- 2x + 1) + 161716500x +--R + +--R 3 2 +--R 1029595050x + 52827390x - 881767997x - 346644199 +--R / +--R 2 +--R 133100000x + 13310000x - 39930000 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (27040x + 2704x - 8112)log(5x + 3) +--R + +--R 2 4 +--R (1425593750x + 142559375x - 427678125)log(2x - 1) + 161716500x +--R + +--R 3 2 +--R 1029595050x + 52827390x - 881767997x - 346644199 +--R / +--R 2 +--R 133100000x + 13310000x - 39930000 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R 228095log(2x - 1) - 228095log(- 2x + 1) +--R (4) --------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=2401/968/(1-2*x)+81/100*x+(-1/15125)/(3+5*x)+10633/5324*log(1-2*x)+_ + 136/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (10880x + 1088x - 3264)log(5x + 3) +--R + +--R 2 3 2 +--R (26582500x + 2658250x - 7974750)log(- 2x + 1) + 10781100x + 1078110x +--R + +--R - 19741381x - 9904037 +--R / +--R 2 +--R 13310000x + 1331000x - 3993000 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (10880x + 1088x - 3264)log(5x + 3) +--R + +--R 2 3 2 +--R (26582500x + 2658250x - 7974750)log(2x - 1) + 10781100x + 1078110x +--R + +--R - 19741381x - 9904037 +--R / +--R 2 +--R 13310000x + 1331000x - 3993000 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R 10633log(2x - 1) - 10633log(- 2x + 1) +--R (4) ------------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=343/484/(1-2*x)+(-1/3025)/(3+5*x)+1421/5324*log(1-2*x)+103/33275*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (4120x + 412x - 1236)log(5x + 3) +--R + +--R 2 +--R (355250x + 35525x - 106575)log(- 2x + 1) - 471713x - 282931 +--R / +--R 2 +--R 1331000x + 133100x - 399300 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (4120x + 412x - 1236)log(5x + 3) +--R + +--R 2 +--R (355250x + 35525x - 106575)log(2x - 1) - 471713x - 282931 +--R / +--R 2 +--R 1331000x + 133100x - 399300 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R 1421log(2x - 1) - 1421log(- 2x + 1) +--R (4) ----------------------------------- +--R 5324 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=49/242/(1-2*x)+(-1/605)/(3+5*x)-14/1331*log(1-2*x)+14/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(- 2x + 1) +--R + +--R - 13519x - 8063 +--R / +--R 2 +--R 133100x + 13310x - 39930 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (1400x + 140x - 420)log(5x + 3) + (- 1400x - 140x + 420)log(2x - 1) +--R + +--R - 13519x - 8063 +--R / +--R 2 +--R 133100x + 13310x - 39930 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R - 14log(2x - 1) + 14log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 3x + 2 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=7/121/(1-2*x)+(-1/121)/(3+5*x)-37/1331*log(1-2*x)+37/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(- 2x + 1) +--R + +--R - 407x - 220 +--R / +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (370x + 37x - 111)log(5x + 3) + (- 370x - 37x + 111)log(2x - 1) - 407x +--R + +--R - 220 +--R / +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R - 37log(2x - 1) + 37log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((1-2*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 4 3 2 +--R 100x + 20x - 59x - 6x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 500 +r0:=2/121/(1-2*x)+(-5/121)/(3+5*x)-20/1331*log(1-2*x)+20/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(- 2x + 1) - 220x - 11 +--R ----------------------------------------------------------------------------- +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x + 20x - 60)log(5x + 3) + (- 200x - 20x + 60)log(2x - 1) - 220x - 11 +--R --------------------------------------------------------------------------- +--R 2 +--R 13310x + 1331x - 3993 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R - 20log(2x - 1) + 20log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 300x + 260x - 137x - 136x + 15x + 18 +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 500 +r0:=4/847/(1-2*x)+(-25/121)/(3+5*x)-412/65219*log(1-2*x)+27/49*log(2+3*x)-_ + 725/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (- 355250x - 35525x + 106575)log(5x + 3) +--R + +--R 2 +--R (359370x + 35937x - 107811)log(3x + 2) +--R + +--R 2 +--R (- 4120x - 412x + 1236)log(- 2x + 1) - 28490x + 12551 +--R / +--R 2 +--R 652190x + 65219x - 195657 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 355250x - 35525x + 106575)log(5x + 3) +--R + +--R 2 +--R (359370x + 35937x - 107811)log(3x + 2) +--R + +--R 2 +--R (- 4120x - 412x + 1236)log(2x - 1) - 28490x + 12551 +--R / +--R 2 +--R 652190x + 65219x - 195657 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R - 412log(2x - 1) + 412log(- 2x + 1) +--R (4) ----------------------------------- +--R 65219 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 900x + 1380x + 109x - 682x - 227x + 84x + 36 +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 500 +r0:=8/5929/(1-2*x)+(-27/49)/(2+3*x)+(-125/121)/(3+5*x)-_ + 1088/456533*log(1-2*x)+1998/343*log(2+3*x)-7750/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3) +--R + +--R 3 2 +--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2) +--R + +--R 3 2 2 +--R (- 32640x - 25024x + 7616x + 6528)log(- 2x + 1) - 5354580x - 734888x +--R + +--R 1694231 +--R / +--R 3 2 +--R 13695990x + 10500259x - 3195731x - 2739198 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 79747500x - 61139750x + 18607750x + 15949500)log(5x + 3) +--R + +--R 3 2 +--R (79780140x + 61164774x - 18615366x - 15956028)log(3x + 2) +--R + +--R 3 2 2 +--R (- 32640x - 25024x + 7616x + 6528)log(2x - 1) - 5354580x - 734888x +--R + +--R 1694231 +--R / +--R 3 2 +--R 13695990x + 10500259x - 3195731x - 2739198 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R - 1088log(2x - 1) + 1088log(- 2x + 1) +--R (4) ------------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72 +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 500 +r0:=16/41503/(1-2*x)+(-27/98)/(2+3*x)^2+(-1998/343)/(2+3*x)+_ + (-625/121)/(3+5*x)-2704/3195731*log(1-2*x)+107109/2401*log(2+3*x)-_ + 59375/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x +--R + +--R 3421425000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 25661174220x + 36781016382x + 7128103950x - 9123973056x +--R + +--R - 3421489896 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(- 2x + 1) +--R + +--R 3 2 +--R - 1711280340x - 1369336584x + 390771227x + 360692563 +--R / +--R 4 3 2 +--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 25660687500x - 36780318750x - 7127968750x + 9123800000x +--R + +--R 3421425000 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R 25661174220x + 36781016382x + 7128103950x - 9123973056x +--R + +--R - 3421489896 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 486720x - 697632x - 135200x + 173056x + 64896)log(2x - 1) +--R + +--R 3 2 +--R - 1711280340x - 1369336584x + 390771227x + 360692563 +--R / +--R 4 3 2 +--R 575231580x + 824498598x + 159786550x - 204526784x - 76697544 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R - 2704log(2x - 1) + 2704log(- 2x + 1) +--R (4) ------------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144 +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 500 +r0:=32/290521/(1-2*x)+(-9/49)/(2+3*x)^3+(-999/343)/(2+3*x)^2+_ + (-107109/2401)/(2+3*x)+(-3125/121)/(3+5*x)-6464/22370117*log(1-2*x)+_ + 5050944/16807*log(2+3*x)-400000/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R - 1815156000000x - 3811827600000x - 2238692400000x +--R + +--R 2 +--R 309248800000x + 672280000000x + 161347200000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x +--R + +--R - 672280646400x - 161347355136 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x +--R + +--R 17000329577 +--R / +--R 5 4 3 2 +--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x +--R + +--R - 536882808 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 1815156000000x - 3811827600000x - 2238692400000x +--R + +--R 2 +--R 309248800000x + 672280000000x + 161347200000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1815157745280x + 3811831265088x + 2238694552512x - 309249097344x +--R + +--R - 672280646400x - 161347355136 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1745280x - 3665088x - 2152512x + 297344x + 646400x + 155136) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 121012436160x - 177486026256x - 36888162696x + 43940321194x +--R + +--R 17000329577 +--R / +--R 5 4 3 2 +--R 6039931590x + 12683856339x + 7449248961x - 1029025382x - 2237011700x +--R + +--R - 536882808 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R - 6464log(2x - 1) + 6464log(- 2x + 1) +--R (4) ------------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^5*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 24300x + 85860x + 109863x + 44352x - 27993x - 33670x - 8120x +--R + +--R 2 +--R 3152x + 1968x + 288 +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 500 +r0:=64/2033647/(1-2*x)+(-27/196)/(2+3*x)^4+(-666/343)/(2+3*x)^3+_ + (-107109/4802)/(2+3*x)^2+(-5050944/16807)/(2+3*x)+(-15625/121)/(3+5*x)-_ + 15040/156590819*log(1-2*x)+222359715/117649*log(2+3*x)-_ + 2515625/1331*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 958912880625000x - 2652992303062500x - 2525137252312500x +--R + +--R 3 2 +--R - 625069137000000x + 464066480500000x + 322005313000000x +--R + +--R 56824467000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 958912929354600x + 2652992437881060x + 2525137380633780x +--R + +--R 3 2 +--R 625069168764480x - 464066504082720x - 322005329363520x +--R + +--R - 56824469887680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x +--R + +--R 16363520x + 2887680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R - 63927582226200x - 136378873350720x - 81993113952750x +--R + +--R 2 +--R 10222048359600x + 24455908667575x + 5987073080219 +--R / +--R 6 5 4 3 +--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x +--R + +--R 2 +--R - 245534404192x - 170370811072x - 30065437248 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 958912880625000x - 2652992303062500x - 2525137252312500x +--R + +--R 3 2 +--R - 625069137000000x + 464066480500000x + 322005313000000x +--R + +--R 56824467000000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 958912929354600x + 2652992437881060x + 2525137380633780x +--R + +--R 3 2 +--R 625069168764480x - 464066504082720x - 322005329363520x +--R + +--R - 56824469887680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 48729600x - 134818560x - 128321280x - 31764480x + 23582720x +--R + +--R 16363520x + 2887680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R - 63927582226200x - 136378873350720x - 81993113952750x +--R + +--R 2 +--R 10222048359600x + 24455908667575x + 5987073080219 +--R / +--R 6 5 4 3 +--R 507354253560x + 1403680101516x + 1336032867708x + 330719809728x +--R + +--R 2 +--R - 245534404192x - 170370811072x - 30065437248 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R - 15040log(2x - 1) + 15040log(- 2x + 1) +--R (4) --------------------------------------- +--R 156590819 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^8/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R / +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 500 +r0:=5764801/85184/(1-2*x)+7680987/50000*x+6093711/100000*x^2+12393/625*x^3+_ + 6561/2000*x^4+(-1/18906250)/(3+5*x)^2+(-268/103984375)/(3+5*x)+_ + 130943337/937024*log(1-2*x)+6312/228765625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3) +--R + +--R 3 2 +--R 511497410156250x + 358048187109375x - 122759378437500x +--R + +--R - 92069533828125 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R 12007450125000x + 80983580287500x + 270968124487500x +--R + +--R 4 3 2 +--R 698838044478750x + 327005737947900x - 298950055409445x +--R + +--R - 249835373577966x - 44587132164487 +--R / +--R 3 2 +--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (100992000x + 70694400x - 24238080x - 18178560)log(5x + 3) +--R + +--R 3 2 +--R 511497410156250x + 358048187109375x - 122759378437500x +--R + +--R - 92069533828125 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R 12007450125000x + 80983580287500x + 270968124487500x +--R + +--R 4 3 2 +--R 698838044478750x + 327005737947900x - 298950055409445x +--R + +--R - 249835373577966x - 44587132164487 +--R / +--R 3 2 +--R 3660250000000x + 2562175000000x - 878460000000x - 658845000000 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R 130943337log(2x - 1) - 130943337log(- 2x + 1) +--R (4) --------------------------------------------- +--R 937024 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)^7/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R (1) --------------------------------------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 500 +r0:=823543/42592/(1-2*x)+1467477/50000*x+21141/2500*x^2+729/500*x^3+_ + (-1/3781250)/(3+5*x)^2+(-47/4159375)/(3+5*x)+7411887/234256*log(1-2*x)+_ + 4761/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3) +--R + +--R 3 2 +--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750) +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x +--R + +--R 2 +--R - 6674047531965x - 6180073448472x - 1273917828029 +--R / +--R 3 2 +--R 366025000000x + 256217500000x - 87846000000x - 65884500000 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (38088000x + 26661600x - 9141120x - 6855840)log(5x + 3) +--R + +--R 3 2 +--R (11581073437500x + 8106751406250x - 2779457625000x - 2084593218750) +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R 533664450000x + 3468818925000x + 12781263577500x + 6680945249550x +--R + +--R 2 +--R - 6674047531965x - 6180073448472x - 1273917828029 +--R / +--R 3 2 +--R 366025000000x + 256217500000x - 87846000000x - 65884500000 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R 7411887log(2x - 1) - 7411887log(- 2x + 1) +--R (4) ----------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(2+3*x)^6/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 500 +r0:=117649/21296/(1-2*x)+2916/625*x+729/1000*x^2+(-1/756250)/(3+5*x)^2+_ + (-202/4159375)/(3+5*x)+1563051/234256*log(1-2*x)+17139/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3) +--R + +--R 3 2 +--R (244226718750x + 170958703125x - 58614412500x - 43960809375) +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 26683222500x + 189450879750x + 113136863400x - 146893374705x +--R + +--R - 152064641058x - 36397551751 +--R / +--R 3 2 +--R 36602500000x + 25621750000x - 8784600000x - 6588450000 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (13711200x + 9597840x - 3290688x - 2468016)log(5x + 3) +--R + +--R 3 2 +--R (244226718750x + 170958703125x - 58614412500x - 43960809375)log(2x - 1) +--R + +--R 5 4 3 2 +--R 26683222500x + 189450879750x + 113136863400x - 146893374705x +--R + +--R - 152064641058x - 36397551751 +--R / +--R 3 2 +--R 36602500000x + 25621750000x - 8784600000x - 6588450000 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R 1563051log(2x - 1) - 1563051log(- 2x + 1) +--R (4) ----------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^5/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 500 +r0:=16807/10648/(1-2*x)+243/500*x+(-1/151250)/(3+5*x)^2+_ + (-169/831875)/(3+5*x)+36015/29282*log(1-2*x)+11562/9150625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3) +--R + +--R 3 2 +--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(- 2x + 1) +--R + +--R 4 3 2 +--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025 +--R / +--R 3 2 +--R 3660250000x + 2562175000x - 878460000x - 658845000 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (4624800x + 3237360x - 1109952x - 832464)log(5x + 3) +--R + +--R 3 2 +--R (4501875000x + 3151312500x - 1080450000x - 810337500)log(2x - 1) +--R + +--R 4 3 2 +--R 1778881500x + 1245217050x - 3315783405x - 3786658260x - 1039888025 +--R / +--R 3 2 +--R 3660250000x + 2562175000x - 878460000x - 658845000 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R 36015log(2x - 1) - 36015log(- 2x + 1) +--R (4) ------------------------------------- +--R 29282 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^4/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 436 + +--S 437 of 500 +r0:=2401/5324/(1-2*x)+(-1/30250)/(3+5*x)^2+(-136/166375)/(3+5*x)+_ + 9261/58564*log(1-2*x)+7074/1830125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (1414800x + 990360x - 339552x - 254664)log(5x + 3) +--R + +--R 3 2 +--R (57881250x + 40516875x - 13891500x - 10418625)log(- 2x + 1) +--R + +--R 2 +--R - 82594215x - 99047718x - 29694181 +--R / +--R 3 2 +--R 366025000x + 256217500x - 87846000x - 65884500 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1414800x + 990360x - 339552x - 254664)log(5x + 3) +--R + +--R 3 2 2 +--R (57881250x + 40516875x - 13891500x - 10418625)log(2x - 1) - 82594215x +--R + +--R - 99047718x - 29694181 +--R / +--R 3 2 +--R 366025000x + 256217500x - 87846000x - 65884500 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R 9261log(2x - 1) - 9261log(- 2x + 1) +--R (4) ----------------------------------- +--R 58564 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^3/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 441 + +--S 442 of 500 +r0:=343/2662/(1-2*x)+(-1/6050)/(3+5*x)^2+(-103/33275)/(3+5*x)-_ + 147/14641*log(1-2*x)+147/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (367500x + 257250x - 88200x - 66150)log(5x + 3) +--R + +--R 3 2 2 +--R (- 367500x - 257250x + 88200x + 66150)log(- 2x + 1) - 2380785x +--R + +--R - 2832258x - 842006 +--R / +--R 3 2 +--R 36602500x + 25621750x - 8784600x - 6588450 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (367500x + 257250x - 88200x - 66150)log(5x + 3) +--R + +--R 3 2 2 +--R (- 367500x - 257250x + 88200x + 66150)log(2x - 1) - 2380785x +--R + +--R - 2832258x - 842006 +--R / +--R 3 2 +--R 36602500x + 25621750x - 8784600x - 6588450 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R - 147log(2x - 1) + 147log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^2/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 446 + +--S 447 of 500 +r0:=49/1331/(1-2*x)+(-1/1210)/(3+5*x)^2+(-14/1331)/(3+5*x)-_ + 273/14641*log(1-2*x)+273/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (136500x + 95550x - 32760x - 24570)log(5x + 3) +--R + +--R 3 2 2 +--R (- 136500x - 95550x + 32760x + 24570)log(- 2x + 1) - 150150x - 163482x +--R + +--R - 43769 +--R / +--R 3 2 +--R 7320500x + 5124350x - 1756920x - 1317690 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (136500x + 95550x - 32760x - 24570)log(5x + 3) +--R + +--R 3 2 2 +--R (- 136500x - 95550x + 32760x + 24570)log(2x - 1) - 150150x - 163482x +--R + +--R - 43769 +--R / +--R 3 2 +--R 7320500x + 5124350x - 1756920x - 1317690 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R - 273log(2x - 1) + 273log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 3x + 2 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 451 + +--S 452 of 500 +r0:=14/1331/(1-2*x)+(-1/242)/(3+5*x)^2+(-37/1331)/(3+5*x)-_ + 144/14641*log(1-2*x)+144/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (14400x + 10080x - 3456x - 2592)log(5x + 3) +--R + +--R 3 2 2 +--R (- 14400x - 10080x + 3456x + 2592)log(- 2x + 1) - 15840x - 10296x - 209 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (14400x + 10080x - 3456x - 2592)log(5x + 3) +--R + +--R 3 2 2 +--R (- 14400x - 10080x + 3456x + 2592)log(2x - 1) - 15840x - 10296x - 209 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R - 144log(2x - 1) + 144log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/((1-2*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 5 4 3 2 +--R 500x + 400x - 235x - 207x + 27x + 27 +--R Type: Fraction(Polynomial(Integer)) +--E 456 + +--S 457 of 500 +r0:=4/1331/(1-2*x)+(-5/242)/(3+5*x)^2+(-20/1331)/(3+5*x)-_ + 60/14641*log(1-2*x)+60/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (6000x + 4200x - 1440x - 1080)log(5x + 3) +--R + +--R 3 2 2 +--R (- 6000x - 4200x + 1440x + 1080)log(- 2x + 1) - 6600x - 4290x + 1133 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (6000x + 4200x - 1440x - 1080)log(5x + 3) +--R + +--R 3 2 2 +--R (- 6000x - 4200x + 1440x + 1080)log(2x - 1) - 6600x - 4290x + 1133 +--R / +--R 3 2 +--R 1464100x + 1024870x - 351384x - 263538 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R - 60log(2x - 1) + 60log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/((1-2*x)^2*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R 6 5 4 3 2 +--R 1500x + 2200x + 95x - 1091x - 333x + 135x + 54 +--R Type: Fraction(Polynomial(Integer)) +--E 461 + +--S 462 of 500 +r0:=8/9317/(1-2*x)+(-25/242)/(3+5*x)^2+725/1331/(3+5*x)-_ + 1104/717409*log(1-2*x)-81/49*log(2+3*x)+24225/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3) +--R + +--R 3 2 +--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2) +--R + +--R 3 2 2 +--R (- 110400x - 77280x + 26496x + 19872)log(- 2x + 1) + 7784700x +--R + +--R 448140x - 2207513 +--R / +--R 3 2 +--R 71740900x + 50218630x - 17217816x - 12913362 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (118702500x + 83091750x - 28488600x - 21366450)log(5x + 3) +--R + +--R 3 2 +--R (- 118592100x - 83014470x + 28462104x + 21346578)log(3x + 2) +--R + +--R 3 2 2 +--R (- 110400x - 77280x + 26496x + 19872)log(2x - 1) + 7784700x + 448140x +--R + +--R - 2207513 +--R / +--R 3 2 +--R 71740900x + 50218630x - 17217816x - 12913362 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R - 1104log(2x - 1) + 1104log(- 2x + 1) +--R (4) ------------------------------------- +--R 717409 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108 +--R Type: Fraction(Polynomial(Integer)) +--E 466 + +--S 467 of 500 +r0:=16/65219/(1-2*x)+81/49/(2+3*x)+(-125/242)/(3+5*x)^2+7750/1331/(3+5*x)-_ + 2736/5021863*log(1-2*x)-8829/343*log(2+3*x)+376875/14641*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 38780437500x + 52999931250x + 8790232500x - 13185348750x +--R + +--R - 4653652500 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x +--R + +--R 4653554004 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(- 2x + 1) +--R + +--R 3 2 +--R 2584404900x + 1894703580x - 614007471x - 489983648 +--R / +--R 4 3 2 +--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 38780437500x + 52999931250x + 8790232500x - 13185348750x +--R + +--R - 4653652500 +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 38779616700x - 52998809490x - 8790046452x + 13185069678x +--R + +--R 4653554004 +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 820800x - 1121760x - 186048x + 279072x + 98496)log(2x - 1) +--R + +--R 3 2 +--R 2584404900x + 1894703580x - 614007471x - 489983648 +--R / +--R 4 3 2 +--R 1506558900x + 2058963830x + 341486684x - 512230026x - 180787068 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R - 2736log(2x - 1) + 2736log(- 2x + 1) +--R (4) ------------------------------------- +--R 5021863 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x + 216 +--R Type: Fraction(Polynomial(Integer)) +--E 471 + +--S 472 of 500 +r0:=32/456533/(1-2*x)+81/98/(2+3*x)^2+8829/343/(2+3*x)+(-625/242)/(3+5*x)^2+_ + 59375/1331/(3+5*x)-6528/35153041*log(1-2*x)-_ + 630342/2401*log(2+3*x)+3843750/14641*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 8305959375000x + 16888784062500x + 9450336000000x +--R + +--R 2 +--R - 1568903437500x - 2879399250000x - 664476750000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8305953499800x - 16888772116260x - 9450329315328x +--R + +--R 2 +--R 1568902327740x + 2879397213264x + 664476279984 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 553723770600x + 775209508920x + 139245535506x - 192629430378x +--R + +--R - 70007419097 +--R / +--R 5 4 3 2 +--R 31637736900x + 64330065030x + 35996713984x - 5976016970x +--R + +--R - 10967748792x - 2531018952 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 8305959375000x + 16888784062500x + 9450336000000x +--R + +--R 2 +--R - 1568903437500x - 2879399250000x - 664476750000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 8305953499800x - 16888772116260x - 9450329315328x +--R + +--R 2 +--R 1568902327740x + 2879397213264x + 664476279984 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 5875200x - 11946240x - 6684672x + 1109760x + 2036736x + 470016) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 553723770600x + 775209508920x + 139245535506x - 192629430378x +--R + +--R - 70007419097 +--R / +--R 5 4 3 2 +--R 31637736900x + 64330065030x + 35996713984x - 5976016970x +--R + +--R - 10967748792x - 2531018952 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R - 6528log(2x - 1) + 6528log(- 2x + 1) +--R (4) ------------------------------------- +--R 35153041 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=1/((1-2*x)^2*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 500 +r0:=64/3195731/(1-2*x)+27/49/(2+3*x)^3+8829/686/(2+3*x)^2+_ + 630342/2401/(2+3*x)+(-3125/242)/(3+5*x)^2+400000/1331/(3+5*x)-_ + 15168/246071287*log(1-2*x)-37214802/16807*log(2+3*x)+_ + 32418750/14641*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 1471127214375000x + 3972043478812500x + 3668010521175000x +--R + +--R 3 2 +--R 837997650262500x - 695243824275000x - 457684022250000x +--R + +--R - 78460118100000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 1471127173421400x - 3972043368237780x - 3668010419064024x +--R + +--R 3 2 +--R - 837997626934116x + 695243804920632x + 457684009508880x +--R + +--R 78460115915808 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x +--R + +--R 12741120x + 2184192 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 +--R 98075099845800x + 202688513402760x + 116200773740898x +--R + +--R 2 +--R - 17675352484482x - 35145131488467x - 8266584593036 +--R / +--R 6 5 4 3 +--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x +--R + +--R 2 +--R - 313986962212x - 206699881080x - 35434265328 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 1471127214375000x + 3972043478812500x + 3668010521175000x +--R + +--R 3 2 +--R 837997650262500x - 695243824275000x - 457684022250000x +--R + +--R - 78460118100000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 1471127173421400x - 3972043368237780x - 3668010419064024x +--R + +--R 3 2 +--R - 837997626934116x + 695243804920632x + 457684009508880x +--R + +--R 78460115915808 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 40953600x - 110574720x - 102110976x - 23328384x + 19354368x +--R + +--R 12741120x + 2184192 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 +--R 98075099845800x + 202688513402760x + 116200773740898x +--R + +--R 2 +--R - 17675352484482x - 35145131488467x - 8266584593036 +--R / +--R 6 5 4 3 +--R 664392474900x + 1793859682230x + 1656551904084x + 378457639406x +--R + +--R 2 +--R - 313986962212x - 206699881080x - 35434265328 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R - 15168log(2x - 1) + 15168log(- 2x + 1) +--R (4) --------------------------------------- +--R 246071287 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^8*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 32805x - 194643x - 513216x - 789264x - 780192x - 514080x +--R + +--R 3 2 +--R - 225792x - 63744x - 10496x - 768 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 500 +r0:=63412811/2048/(1-2*x)^2+(-246239357/1024)/(1-2*x)-120864213/256*x-_ + 118841283/512*x^2-16042509/128*x^3-7568235/128*x^4-213597/10*x^5-_ + 162567/32*x^6-32805/56*x^7-106237047/256*log(1-2*x) +--R +--R +--R (2) +--R 2 +--R (- 118985492640x + 118985492640x - 29746373160)log(- 2x + 1) +--R + +--R 9 8 7 6 +--R - 167961600x - 1288638720x - 4709643264x - 11192743296x +--R + +--R 5 4 3 2 +--R - 20513437056x - 34854109920x - 77800605120x + 118730138940x +--R + +--R 631530340x - 15017306605 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 118985492640x + 118985492640x - 29746373160)log(2x - 1) - 167961600x +--R + +--R 8 7 6 5 +--R - 1288638720x - 4709643264x - 11192743296x - 20513437056x +--R + +--R 4 3 2 +--R - 34854109920x - 77800605120x + 118730138940x + 631530340x - 15017306605 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R - 106237047log(2x - 1) + 106237047log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 500 +r0:=9058973/1024/(1-2*x)^2+(-15647317/256)/(1-2*x)-24960933/256*x-_ + 10989621/256*x^2-631611/32*x^3-235467/32*x^4-147987/80*x^5-_ + 3645/16*x^6-23647449/256*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 1891795920x + 1891795920x - 472948980)log(- 2x + 1) - 4665600x +--R + +--R 7 6 5 4 3 +--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x +--R + +--R 2 +--R 1777082220x + 126674020x - 267651475 +--R / +--R 2 +--R 20480x - 20480x + 5120 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 1891795920x + 1891795920x - 472948980)log(2x - 1) - 4665600x +--R + +--R 7 6 5 4 3 +--R - 33219072x - 113980608x - 263003328x - 512613360x - 1218762720x +--R + +--R 2 +--R 1777082220x + 126674020x - 267651475 +--R / +--R 2 +--R 20480x - 20480x + 5120 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R - 23647449log(2x - 1) + 23647449log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 500 +r0:=1294139/512/(1-2*x)^2+(-3916031/256)/(1-2*x)-2431647/128*x-_ + 461835/64*x^2-10611/4*x^3-44469/64*x^4-729/8*x^5-5078115/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 6 +--R (- 40624920x + 40624920x - 10156230)log(- 2x + 1) - 186624x - 1236384x +--R + +--R 5 4 3 2 +--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 40624920x + 40624920x - 10156230)log(2x - 1) - 186624x - 1236384x +--R + +--R 5 4 3 2 +--R - 4056480x - 9701640x - 25485840x + 35211672x + 5937536x - 6537923 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R - 5078115log(2x - 1) + 5078115log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 500 +r0:=184877/256/(1-2*x)^2+(-60025/16)/(1-2*x)-109089/32*x-16821/16*x^2-_ + 4401/16*x^3-1215/32*x^4-519645/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 4157160x + 4157160x - 1039290)log(- 2x + 1) - 38880x - 242784x +--R + +--R 4 3 2 +--R - 804600x - 2484720x + 3221712x + 1048088x - 775523 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 4157160x + 4157160x - 1039290)log(2x - 1) - 38880x - 242784x +--R + +--R 4 3 2 +--R - 804600x - 2484720x + 3221712x + 1048088x - 775523 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R - 519645log(2x - 1) + 519645log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/input/rich3i.input.pamphlet b/src/input/rich3i.input.pamphlet new file mode 100644 index 0000000..8e4ecb1 --- /dev/null +++ b/src/input/rich3i.input.pamphlet @@ -0,0 +1,7464 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3i.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 92 matching answers. +\item 8 cases where Axiom differed from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3i.output +)spool rich3i.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 500 +r0:=26411/128/(1-2*x)^2+(-57281/64)/(1-2*x)-540*x-3861/32*x^2-_ + 135/8*x^3-24843/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 3 +--R (- 397488x + 397488x - 99372)log(- 2x + 1) - 8640x - 53136x - 216864x +--R + +--R 2 +--R 261036x + 160004x - 88151 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 397488x + 397488x - 99372)log(2x - 1) - 8640x - 53136x - 216864x +--R + +--R 2 +--R 261036x + 160004x - 88151 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R - 24843log(2x - 1) + 24843log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 500 +r0:=3773/64/(1-2*x)^2+(-3283/16)/(1-2*x)-1107/16*x-135/16*x^2-1071/8*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 34272x + 34272x - 8568)log(- 2x + 1) - 2160x - 15552x + 17172x +--R + +--R 21836x - 9359 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 34272x + 34272x - 8568)log(2x - 1) - 2160x - 15552x + 17172x +--R + +--R 21836x - 9359 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R - 1071log(2x - 1) + 1071log(- 2x + 1) +--R (4) ------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 500 +r0:=539/32/(1-2*x)^2+(-707/16)/(1-2*x)-45/8*x-309/16*log(1-2*x) +--R +--R +--R 2 3 2 +--R (- 2472x + 2472x - 618)log(- 2x + 1) - 720x + 720x + 2648x - 875 +--R (2) ------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 2472x + 2472x - 618)log(2x - 1) - 720x + 720x + 2648x - 875 +--R (3) ----------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R - 309log(2x - 1) + 309log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^3 +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 500 +r0:=77/16/(1-2*x)^2+(-17/2)/(1-2*x)-15/8*log(1-2*x) +--R +--R +--R 2 +--R (- 120x + 120x - 30)log(- 2x + 1) + 272x - 59 +--R (2) ---------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 120x + 120x - 30)log(2x - 1) + 272x - 59 +--R (3) -------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R - 15log(2x - 1) + 15log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)/(1-2*x)^3 +--R +--R +--R - 5x - 3 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 500 +r0:=1/22*(3+5*x)^2/(1-2*x)^2 +--R +--R +--R 25 2 15 9 +--R -- x + -- x + -- +--R 88 44 88 +--R (2) ----------------- +--R 2 1 +--R x - x + - +--R 4 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R 20x + 1 +--R (3) -------------- +--R 2 +--R 32x - 32x + 8 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R 25 +--R (4) - -- +--R 88 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) -------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 500 +r0:=11/28/(1-2*x)^2+(-1/49)/(1-2*x)+3/343*log(1-2*x)-3/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(- 2x + 1) + 56x + 511 +--R --------------------------------------------------------------------------- +--R 2 +--R 5488x - 5488x + 1372 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (- 48x + 48x - 12)log(3x + 2) + (48x - 48x + 12)log(2x - 1) + 56x + 511 +--R ------------------------------------------------------------------------- +--R 2 +--R 5488x - 5488x + 1372 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R 3log(2x - 1) - 3log(- 2x + 1) +--R (4) ----------------------------- +--R 343 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 500 +r0:=11/98/(1-2*x)^2+31/343/(1-2*x)+3/343/(2+3*x)-87/2401*log(1-2*x)+_ + 87/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (2088x - 696x - 870x + 348)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2088x + 696x + 870x - 348)log(- 2x + 1) - 2436x + 1015x + 1988 +--R / +--R 3 2 +--R 57624x - 19208x - 24010x + 9604 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (2088x - 696x - 870x + 348)log(3x + 2) +--R + +--R 3 2 2 +--R (- 2088x + 696x + 870x - 348)log(2x - 1) - 2436x + 1015x + 1988 +--R / +--R 3 2 +--R 57624x - 19208x - 24010x + 9604 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R - 87log(2x - 1) + 87log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 500 +r0:=11/343/(1-2*x)^2+128/2401/(1-2*x)+3/686/(2+3*x)^2+(-87/2401)/(2+3*x)-_ + 558/16807*log(1-2*x)+558/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(- 2x + 1) - 46872x +--R + +--R 2 +--R - 11718x + 25606x + 9191 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (40176x + 13392x - 25668x - 4464x + 4464)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 40176x - 13392x + 25668x + 4464x - 4464)log(2x - 1) - 46872x +--R + +--R 2 +--R - 11718x + 25606x + 9191 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R - 558log(2x - 1) + 558log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 500 +r0:=22/2401/(1-2*x)^2+388/16807/(1-2*x)+1/343/(2+3*x)^3+_ + (-87/4802)/(2+3*x)^2+(-558/16807)/(2+3*x)-2280/117649*log(1-2*x)+_ + 2280/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 574560x - 526680x + 218120x + 236075x + 21616 +--R / +--R 5 4 3 2 +--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (492480x + 492480x - 205200x - 264480x + 18240x + 36480)log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 492480x - 492480x + 205200x + 264480x - 18240x - 36480)log(2x - 1) +--R + +--R 4 3 2 +--R - 574560x - 526680x + 218120x + 236075x + 21616 +--R / +--R 5 4 3 2 +--R 25412184x + 25412184x - 10588410x - 13647284x + 941192x + 1882384 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R - 2280log(2x - 1) + 2280log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 500 +r0:=44/16807/(1-2*x)^2+1040/117649/(1-2*x)+3/1372/(2+3*x)^4+_ + (-29/2401)/(2+3*x)^3+(-279/16807)/(2+3*x)^2+(-2280/117649)/(2+3*x)-_ + 7680/823543*log(1-2*x)+7680/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x +--R + +--R 491520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x +--R + +--R - 983040x - 491520 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925 +--R / +--R 6 5 4 3 2 +--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x +--R + +--R 105413504x + 52706752 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 9953280x + 16588800x + 2488320x - 8110080x - 3194880x + 983040x +--R + +--R 491520 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 9953280x - 16588800x - 2488320x + 8110080x + 3194880x +--R + +--R - 983040x - 491520 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 11612160x - 18385920x - 2688000x + 7710080x + 2825088x - 197925 +--R / +--R 6 5 4 3 2 +--R 1067311728x + 1778852880x + 266827932x - 869661408x - 342593888x +--R + +--R 105413504x + 52706752 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R - 7680log(2x - 1) + 7680log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)/((1-2*x)^3*(2+3*x)^6) +--R +--R +--R (1) +--R - 5x - 3 +--R / +--R 9 8 7 6 5 4 3 2 +--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x +--R + +--R - 192x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 500 +r0:=88/117649/(1-2*x)^2+2608/823543/(1-2*x)+3/1715/(2+3*x)^5+_ + (-87/9604)/(2+3*x)^4+(-186/16807)/(2+3*x)^3+(-1140/117649)/(2+3*x)^2+_ + (-7680/823543)/(2+3*x)-3312/823543*log(1-2*x)+3312/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x +--R + +--R 2 +--R - 7418880x + 7418880x + 2119680 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x +--R + +--R 2 +--R 7418880x - 7418880x - 2119680 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x +--R + +--R 7943257x - 2669758 +--R / +--R 7 6 5 4 +--R 16009675920x + 37355910480x + 21790947780x - 10376641800x +--R + +--R 3 2 +--R - 13835522400x - 1844736320x + 1844736320x + 527067520 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 64385280x + 150232320x + 87635520x - 41731200x - 55641600x +--R + +--R 2 +--R - 7418880x + 7418880x + 2119680 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 64385280x - 150232320x - 87635520x + 41731200x + 55641600x +--R + +--R 2 +--R 7418880x - 7418880x - 2119680 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 75116160x - 169011360x - 96677280x + 38282580x + 51524508x +--R + +--R 7943257x - 2669758 +--R / +--R 7 6 5 4 +--R 16009675920x + 37355910480x + 21790947780x - 10376641800x +--R + +--R 3 2 +--R - 13835522400x - 1844736320x + 1844736320x + 527067520 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R - 3312log(2x - 1) + 3312log(- 2x + 1) +--R (4) ------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^7*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 54675x - 320760x - 836163x - 1271214x - 1242108x - 808920x +--R + +--R 3 2 +--R - 351120x - 97952x - 15936x - 1152 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 500 +r0:=99648703/2048/(1-2*x)^2+(-389535839/1024)/(1-2*x)-48280011/64*x-_ + 190742391/512*x^2-25895367/128*x^3-12299769/128*x^4-2798631/80*x^5-_ + 268515/32*x^6-54675/56*x^7-84589631/128*log(1-2*x) +--R +--R +--R (2) +--R 2 +--R (- 189480773440x + 189480773440x - 47370193360)log(- 2x + 1) +--R + +--R 9 8 7 6 +--R - 279936000x - 2125958400x - 7694383104x - 18122662656x +--R + +--R 5 4 3 2 +--R - 32961712896x - 55697987520x - 123980115840x + 189590514540x +--R + +--R 461405140x - 23779804125 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 189480773440x + 189480773440x - 47370193360)log(2x - 1) - 279936000x +--R + +--R 8 7 6 5 +--R - 2125958400x - 7694383104x - 18122662656x - 32961712896x +--R + +--R 4 3 2 +--R - 55697987520x - 123980115840x + 189590514540x + 461405140x +--R + +--R - 23779804125 +--R / +--R 2 +--R 286720x - 286720x + 71680 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R - 84589631log(2x - 1) + 84589631log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^6*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 18225x - 94770x - 215541x - 280044x - 227340x - 118080x - 38320x +--R + +--R - 7104x - 576 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 500 +r0:=14235529/1024/(1-2*x)^2+(-12386759/128)/(1-2*x)-39980457/256*x-_ + 17700255/256*x^2-1024389/32*x^3-770067/64*x^4-48843/16*x^5-_ + 6075/16*x^6-18859855/128*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 603515360x + 603515360x - 150878840)log(- 2x + 1) - 1555200x +--R + +--R 7 6 5 4 3 +--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x +--R + +--R 2 +--R 568886292x + 38266316x - 84858543 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 603515360x + 603515360x - 150878840)log(2x - 1) - 1555200x +--R + +--R 7 6 5 4 3 +--R - 10948608x - 37169280x - 84963456x - 164403360x - 389263680x +--R + +--R 2 +--R 568886292x + 38266316x - 84858543 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R - 18859855log(2x - 1) + 18859855log(- 2x + 1) +--R (4) --------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 500 +r0:=2033647/512/(1-2*x)^2+(-6206585/256)/(1-2*x)-3907293/128*x-_ + 747297/64*x^2-69273/16*x^3-73305/64*x^4-1215/8*x^5-8117095/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 6 +--R (- 64936760x + 64936760x - 16234190)log(- 2x + 1) - 311040x - 2034720x +--R + +--R 5 4 3 2 +--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 64936760x + 64936760x - 16234190)log(2x - 1) - 311040x - 2034720x +--R + +--R 5 4 3 2 +--R - 6598944x - 15633000x - 40819920x + 56538312x + 9197168x - 10379523 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R - 8117095log(2x - 1) + 8117095log(- 2x + 1) +--R (4) ------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 500 +r0:=290521/256/(1-2*x)^2+(-381073/64)/(1-2*x)-176055/32*x-_ + 54783/32*x^2-7245/16*x^3-2025/32*x^4-832951/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 6663608x + 6663608x - 1665902)log(- 2x + 1) - 64800x - 398880x +--R + +--R 4 3 2 +--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 6663608x + 6663608x - 1665902)log(2x - 1) - 64800x - 398880x +--R + +--R 4 3 2 +--R - 1305576x - 3996624x + 5195496x + 1640144x - 1233771 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R - 832951log(2x - 1) + 832951log(- 2x + 1) +--R (4) ----------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 500 +r0:=41503/128/(1-2*x)^2+(-91091/64)/(1-2*x)-14031/16*x-6345/32*x^2-_ + 225/8*x^3-39977/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 +--R (- 639632x + 639632x - 159908)log(- 2x + 1) - 14400x - 87120x +--R + +--R 3 2 +--R - 351072x + 423612x + 252116x - 140679 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 3 +--R (- 639632x + 639632x - 159908)log(2x - 1) - 14400x - 87120x - 351072x +--R + +--R 2 +--R 423612x + 252116x - 140679 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R - 39977log(2x - 1) + 39977log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 81 + +--S 82 of 500 +r0:=5929/64/(1-2*x)^2+(-1309/4)/(1-2*x)-1815/16*x-225/16*x^2-3467/16*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 55472x + 55472x - 13868)log(- 2x + 1) - 3600x - 25440x + 28140x +--R + +--R 34628x - 15015 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 55472x + 55472x - 13868)log(2x - 1) - 3600x - 25440x + 28140x +--R + +--R 34628x - 15015 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R - 3467log(2x - 1) + 3467log(- 2x + 1) +--R (4) ------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 86 + +--S 87 of 500 +r0:=847/32/(1-2*x)^2+(-1133/16)/(1-2*x)-75/8*x-505/16*log(1-2*x) +--R +--R +--R (2) +--R 2 3 2 +--R (- 4040x + 4040x - 1010)log(- 2x + 1) - 1200x + 1200x + 4232x - 1419 +--R ----------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 4040x + 4040x - 1010)log(2x - 1) - 1200x + 1200x + 4232x - 1419 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R - 505log(2x - 1) + 505log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^2/(1-2*x)^3 +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 91 + +--S 92 of 500 +r0:=121/16/(1-2*x)^2+(-55/4)/(1-2*x)-25/8*log(1-2*x) +--R +--R +--R 2 +--R (- 200x + 200x - 50)log(- 2x + 1) + 440x - 99 +--R (2) ---------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (- 200x + 200x - 50)log(2x - 1) + 440x - 99 +--R (3) -------------------------------------------- +--R 2 +--R 64x - 64x + 16 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R - 25log(2x - 1) + 25log(- 2x + 1) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 96 + +--S 97 of 500 +r0:=121/56/(1-2*x)^2+(-407/196)/(1-2*x)-1/343*log(1-2*x)+1/343*log(2+3*x) +--R +--R +--R (2) +--R 2 2 +--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(- 2x + 1) + 11396x + 231 +--R ---------------------------------------------------------------------------- +--R 2 +--R 10976x - 10976x + 2744 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (32x - 32x + 8)log(3x + 2) + (- 32x + 32x - 8)log(2x - 1) + 11396x + 231 +--R -------------------------------------------------------------------------- +--R 2 +--R 10976x - 10976x + 2744 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 343 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 500 +r0:=121/196/(1-2*x)^2+(-22/343)/(1-2*x)+(-1/343)/(2+3*x)+_ + 64/2401*log(1-2*x)-64/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (- 3072x + 1024x + 1280x - 512)log(3x + 2) +--R + +--R 3 2 2 +--R (3072x - 1024x - 1280x + 512)log(- 2x + 1) + 3584x + 18515x + 10598 +--R / +--R 3 2 +--R 115248x - 38416x - 48020x + 19208 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 3072x + 1024x + 1280x - 512)log(3x + 2) +--R + +--R 3 2 2 +--R (3072x - 1024x - 1280x + 512)log(2x - 1) + 3584x + 18515x + 10598 +--R / +--R 3 2 +--R 115248x - 38416x - 48020x + 19208 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R 64log(2x - 1) - 64log(- 2x + 1) +--R (4) ------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 500 +r0:=121/686/(1-2*x)^2+319/2401/(1-2*x)+(-1/686)/(2+3*x)^2+_ + 64/2401/(2+3*x)-829/16807*log(1-2*x)+829/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(- 2x + 1) - 69636x +--R + +--R 2 +--R - 17409x + 84728x + 43323 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (59688x + 19896x - 38134x - 6632x + 6632)log(3x + 2) +--R + +--R 4 3 2 3 +--R (- 59688x - 19896x + 38134x + 6632x - 6632)log(2x - 1) - 69636x +--R + +--R 2 +--R - 17409x + 84728x + 43323 +--R / +--R 4 3 2 +--R 1210104x + 403368x - 773122x - 134456x + 134456 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R - 829log(2x - 1) + 829log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 500 +r0:=121/2401/(1-2*x)^2+1364/16807/(1-2*x)+(-1/1029)/(2+3*x)^3+_ + 32/2401/(2+3*x)^2+(-829/16807)/(2+3*x)-5750/117649*log(1-2*x)+_ + 5750/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 2173500x - 1992375x + 825125x + 1260700x + 310877 +--R / +--R 5 4 3 2 +--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1863000x + 1863000x - 776250x - 1000500x + 69000x + 138000) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 1863000x - 1863000x + 776250x + 1000500x - 69000x - 138000) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 2173500x - 1992375x + 825125x + 1260700x + 310877 +--R / +--R 5 4 3 2 +--R 38118276x + 38118276x - 15882615x - 20470926x + 1411788x + 2823576 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R - 5750log(2x - 1) + 5750log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 500 +r0:=242/16807/(1-2*x)^2+4180/117649/(1-2*x)+(-1/1372)/(2+3*x)^4+_ + 64/7203/(2+3*x)^3+(-829/33614)/(2+3*x)^2+(-5750/117649)/(2+3*x)-_ + 24040/823543*log(1-2*x)+24040/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x +--R + +--R 9231360x + 4615680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x +--R + +--R - 9231360x - 4615680 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 93467520x + 155779200x + 23366880x - 76158720x - 30001920x +--R + +--R 9231360x + 4615680 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 93467520x - 155779200x - 23366880x + 76158720x + 30001920x +--R + +--R - 9231360x - 4615680 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 109045440x - 172655280x - 25242000x + 72402470x + 34764772x + 3224165 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R - 24040log(2x - 1) + 24040log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(3+5*x)^2/((1-2*x)^3*(2+3*x)^6) +--R +--R +--R (1) +--R 2 +--R - 25x - 30x - 9 +--R / +--R 9 8 7 6 5 4 3 2 +--R 5832x + 14580x + 8262x - 6993x - 8316x - 252x + 2240x + 528x +--R + +--R - 192x - 64 +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 500 +r0:=484/117649/(1-2*x)^2+11264/823543/(1-2*x)+(-1/1715)/(2+3*x)^5+_ + 16/2401/(2+3*x)^4+(-829/50421)/(2+3*x)^3+(-2875/117649)/(2+3*x)^2+_ + (-24040/823543)/(2+3*x)-11696/823543*log(1-2*x)+11696/823543*log(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x +--R + +--R 2 +--R - 19649280x + 19649280x + 5614080 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x +--R + +--R 2 +--R 19649280x - 19649280x - 5614080 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 2 +--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x +--R + +--R 29616692x - 1806623 +--R / +--R 7 6 5 4 +--R 12007256940x + 28016932860x + 16343210835x - 7782481350x +--R + +--R 3 2 +--R - 10376641800x - 1383552240x + 1383552240x + 395300640 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 170527680x + 397897920x + 232107120x - 110527200x - 147369600x +--R + +--R 2 +--R - 19649280x + 19649280x + 5614080 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 3 +--R - 170527680x - 397897920x - 232107120x + 110527200x + 147369600x +--R + +--R 2 +--R 19649280x - 19649280x - 5614080 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 2 +--R - 198948960x - 447635160x - 256054680x + 101393355x + 136465273x +--R + +--R 29616692x - 1806623 +--R / +--R 7 6 5 4 +--R 12007256940x + 28016932860x + 16343210835x - 7782481350x +--R + +--R 3 2 +--R - 10376641800x - 1383552240x + 1383552240x + 395300640 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R - 11696log(2x - 1) + 11696log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^6*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 91125x - 528525x - 1362015x - 2046843x - 1976832x - 1272420x +--R + +--R 3 2 +--R - 545840x - 150480x - 24192x - 1728 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 500 +r0:=156590819/2048/(1-2*x)^2+(-616195041/1024)/(1-2*x)-308539921/256*x-_ + 306103815/512*x^2-41793093/128*x^3-19986237/128*x^4-_ + 229149/4*x^5-443475/32*x^6-91125/56*x^7-33674025/32*log(1-2*x) +--R +--R +--R (2) +--R 2 9 +--R (- 60343852800x + 60343852800x - 15085963200)log(- 2x + 1) - 93312000x +--R + +--R 8 7 6 5 +--R - 701395200x - 2513700864x - 5867430912x - 10590741504x +--R + +--R 4 3 2 +--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841 +--R / +--R 2 +--R 57344x - 57344x + 14336 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 +--R (- 60343852800x + 60343852800x - 15085963200)log(2x - 1) - 93312000x +--R + +--R 8 7 6 5 +--R - 701395200x - 2513700864x - 5867430912x - 10590741504x +--R + +--R 4 3 2 +--R - 17798780160x - 39510141440x + 60542035484x - 24774428x - 7530594841 +--R / +--R 2 +--R 57344x - 57344x + 14336 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R - 33674025log(2x - 1) + 33674025log(- 2x + 1) +--R (4) --------------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 +--R - 30375x - 155925x - 350055x - 448911x - 359670x - 184360x +--R + +--R 2 +--R - 59040x - 10800x - 864 +--R / +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 500 +r0:=22370117/1024/(1-2*x)^2+(-39220335/256)/(1-2*x)-64029233/256*x-_ + 28504029/256*x^2-1661133/32*x^3-629505/32*x^4-80595/16*x^5-_ + 10125/16*x^6-60160485/256*log(1-2*x) +--R +--R +--R (2) +--R 2 8 +--R (- 962567760x + 962567760x - 240641940)log(- 2x + 1) - 2592000x +--R + +--R 7 6 5 4 3 +--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x +--R + +--R 2 +--R 910451612x + 57645748x - 134511223 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 +--R (- 962567760x + 962567760x - 240641940)log(2x - 1) - 2592000x +--R + +--R 7 6 5 4 3 +--R - 18040320x - 60592320x - 137206464x - 263583600x - 621559520x +--R + +--R 2 +--R 910451612x + 57645748x - 134511223 +--R / +--R 2 +--R 4096x - 4096x + 1024 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R - 60160485log(2x - 1) + 60160485log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 500 +r0:=3195731/512/(1-2*x)^2+(-9836211/256)/(1-2*x)-6277415/128*x-_ + 1208973/64*x^2-7065*x^3-120825/64*x^4-2025/8*x^5-12973191/256*log(1-2*x) +--R +--R +--R (2) +--R 2 7 +--R (- 103785528x + 103785528x - 25946382)log(- 2x + 1) - 518400x +--R + +--R 6 5 4 3 2 +--R - 3348000x - 10732320x - 25184616x - 65368784x + 90766856x +--R + +--R 14235184x - 16476691 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 6 +--R (- 103785528x + 103785528x - 25946382)log(2x - 1) - 518400x - 3348000x +--R + +--R 5 4 3 2 +--R - 10732320x - 25184616x - 65368784x + 90766856x + 14235184x - 16476691 +--R / +--R 2 +--R 2048x - 2048x + 512 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R - 12973191log(2x - 1) + 12973191log(- 2x + 1) +--R (4) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 500 +r0:=456533/256/(1-2*x)^2+(-302379/32)/(1-2*x)-284071/32*x-44595/16*x^2-_ + 11925/16*x^3-3375/32*x^4-1334949/128*log(1-2*x) +--R +--R +--R (2) +--R 2 6 5 +--R (- 10679592x + 10679592x - 2669898)log(- 2x + 1) - 108000x - 655200x +--R + +--R 4 3 2 +--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 5 +--R (- 10679592x + 10679592x - 2669898)log(2x - 1) - 108000x - 655200x +--R + +--R 4 3 2 +--R - 2117880x - 6426992x + 8376752x + 2565496x - 1962499 +--R / +--R 2 +--R 1024x - 1024x + 256 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R - 1334949log(2x - 1) + 1334949log(- 2x + 1) +--R (4) ------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 500 +r0:=65219/128/(1-2*x)^2+(-144837/64)/(1-2*x)-5695/4*x-10425/32*x^2-_ + 375/8*x^3-64317/32*log(1-2*x) +--R +--R +--R (2) +--R 2 5 4 +--R (- 1029072x + 1029072x - 257268)log(- 2x + 1) - 24000x - 142800x +--R + +--R 3 2 +--R - 568160x + 687260x + 397108x - 224455 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 4 +--R (- 1029072x + 1029072x - 257268)log(2x - 1) - 24000x - 142800x +--R + +--R 3 2 +--R - 568160x + 687260x + 397108x - 224455 +--R / +--R 2 +--R 512x - 512x + 128 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R - 64317log(2x - 1) + 64317log(- 2x + 1) +--R (4) --------------------------------------- +--R 32 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 500 +r0:=9317/64/(1-2*x)^2+(-8349/16)/(1-2*x)-2975/16*x-375/16*x^2-2805/8*log(1-2*x) +--R +--R +--R (2) +--R 2 4 3 2 +--R (- 89760x + 89760x - 22440)log(- 2x + 1) - 6000x - 41600x + 46100x +--R + +--R 54892x - 24079 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 3 2 +--R (- 89760x + 89760x - 22440)log(2x - 1) - 6000x - 41600x + 46100x +--R + +--R 54892x - 24079 +--R / +--R 2 +--R 256x - 256x + 64 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R - 2805log(2x - 1) + 2805log(- 2x + 1) +--R (4) ------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)^3/(1-2*x)^3 +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 3 2 +--R 8x - 12x + 6x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 500 +r0:=1331/32/(1-2*x)^2+(-1815/16)/(1-2*x)-125/8*x-825/16*log(1-2*x) +--R +--R +--R (2) +--R 2 3 2 +--R (- 6600x + 6600x - 1650)log(- 2x + 1) - 2000x + 2000x + 6760x - 2299 +--R ----------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 +--R (- 6600x + 6600x - 1650)log(2x - 1) - 2000x + 2000x + 6760x - 2299 +--R (3) --------------------------------------------------------------------- +--R 2 +--R 128x - 128x + 32 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R - 825log(2x - 1) + 825log(- 2x + 1) +--R (4) ----------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 4 3 2 +--R 24x - 20x - 6x + 9x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 500 +r0:=1331/112/(1-2*x)^2+(-1089/49)/(1-2*x)-14289/2744*log(1-2*x)-_ + 1/1029*log(2+3*x) +--R +--R +--R (2) +--R 2 +--R (- 64x + 64x - 16)log(3x + 2) +--R + +--R 2 +--R (- 342936x + 342936x - 85734)log(- 2x + 1) + 731808x - 170247 +--R / +--R 2 +--R 65856x - 65856x + 16464 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (- 64x + 64x - 16)log(3x + 2) +--R + +--R 2 +--R (- 342936x + 342936x - 85734)log(2x - 1) + 731808x - 170247 +--R / +--R 2 +--R 65856x - 65856x + 16464 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R - 14289log(2x - 1) + 14289log(- 2x + 1) +--R (4) --------------------------------------- +--R 2744 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ----------------------------------- +--R 5 4 3 2 +--R 72x - 12x - 58x + 15x + 12x - 4 +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 500 +r0:=1331/392/(1-2*x)^2+(-4719/1372)/(1-2*x)+1/1029/(2+3*x)-_ + 33/2401*log(1-2*x)+33/2401*log(2+3*x) +--R +--R +--R (2) +--R 3 2 +--R (9504x - 3168x - 3960x + 1584)log(3x + 2) +--R + +--R 3 2 2 +--R (- 9504x + 3168x + 3960x - 1584)log(- 2x + 1) + 1189412x + 784945x +--R + +--R - 5026 +--R / +--R 3 2 +--R 691488x - 230496x - 288120x + 115248 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (9504x - 3168x - 3960x + 1584)log(3x + 2) +--R + +--R 3 2 2 +--R (- 9504x + 3168x + 3960x - 1584)log(2x - 1) + 1189412x + 784945x - 5026 +--R / +--R 3 2 +--R 691488x - 230496x - 288120x + 115248 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R - 33log(2x - 1) + 33log(- 2x + 1) +--R (4) --------------------------------- +--R 2401 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R 216x + 108x - 198x - 71x + 66x + 12x - 8 +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 500 +r0:=1331/1372/(1-2*x)^2+(-363/2401)/(1-2*x)+1/2058/(2+3*x)^2+_ + (-33/2401)/(2+3*x)+1023/16807*log(1-2*x)-1023/16807*log(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2) +--R + +--R 4 3 2 3 +--R (441936x + 147312x - 282348x - 49104x + 49104)log(- 2x + 1) + 515592x +--R + +--R 2 +--R 2229773x + 2239384x + 655214 +--R / +--R 4 3 2 +--R 7260624x + 2420208x - 4638732x - 806736x + 806736 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 441936x - 147312x + 282348x + 49104x - 49104)log(3x + 2) +--R + +--R 4 3 2 3 +--R (441936x + 147312x - 282348x - 49104x + 49104)log(2x - 1) + 515592x +--R + +--R 2 +--R 2229773x + 2239384x + 655214 +--R / +--R 4 3 2 +--R 7260624x + 2420208x - 4638732x - 806736x + 806736 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R 1023log(2x - 1) - 1023log(- 2x + 1) +--R (4) ----------------------------------- +--R 16807 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ------------------------------------------------- +--R 7 6 5 4 3 2 +--R 648x + 756x - 378x - 609x + 56x + 168x - 16 +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 500 +r0:=1331/4802/(1-2*x)^2+3267/16807/(1-2*x)+1/3087/(2+3*x)^3+_ + (-33/4802)/(2+3*x)^2+1023/16807/(2+3*x)-7755/117649*log(1-2*x)+_ + 7755/117649*log(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720) +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076 +--R / +--R 5 4 3 2 +--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (15075720x + 15075720x - 6281550x - 8096220x + 558360x + 1116720) +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R (- 15075720x - 15075720x + 6281550x + 8096220x - 558360x - 1116720) +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 17588340x - 16122645x + 21383180x + 28918225x + 8476076 +--R / +--R 5 4 3 2 +--R 228709656x + 228709656x - 95295690x - 122825556x + 8470728x + 16941456 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R - 7755log(2x - 1) + 7755log(- 2x + 1) +--R (4) ------------------------------------- +--R 117649 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(3+5*x)^3/((1-2*x)^3*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) -------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 1944x + 3564x + 378x - 2583x - 1050x + 616x + 336x - 48x - 32 +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 500 +r0:=1331/16807/(1-2*x)^2+14520/117649/(1-2*x)+1/4116/(2+3*x)^4+_ + (-11/2401)/(2+3*x)^3+1023/33614/(2+3*x)^2+(-7755/117649)/(2+3*x)-_ + 59070/823543*log(1-2*x)+59070/823543*log(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x +--R + +--R 22682880x + 11341440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x +--R + +--R - 22682880x - 11341440 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x +--R + +--R 27940465 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 229664160x + 382773600x + 57416040x - 187133760x - 73719360x +--R + +--R 22682880x + 11341440 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 229664160x - 382773600x - 57416040x + 187133760x + 73719360x +--R + +--R - 22682880x - 11341440 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 267941520x - 424240740x - 62023500x + 229375510x + 149599856x +--R + +--R 27940465 +--R / +--R 6 5 4 3 2 +--R 3201935184x + 5336558640x + 800483796x - 2608984224x - 1027781664x +--R + +--R 316240512x + 158120256 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R - 59070log(2x - 1) + 59070log(- 2x + 1) +--R (4) --------------------------------------- +--R 823543 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 500 +r0:=5764801/5632/(1-2*x)^2+(-188591347/30976)/(1-2*x)-2941619571/400000*x-_ + 110180817/40000*x^2-124416/125*x^3-408969/1600*x^4-6561/200*x^5-_ + 2644396573/340736*log(1-2*x)+1/20796875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (2048x - 2048x + 512)log(5x + 3) +--R + +--R 2 +--R (- 330549571625000x + 330549571625000x - 82637392906250)log(- 2x + 1) +--R + +--R 7 6 5 4 +--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x +--R + +--R 3 2 +--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625 +--R / +--R 2 +--R 42592000000x - 42592000000x + 10648000000 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (2048x - 2048x + 512)log(5x + 3) +--R + +--R 2 +--R (- 330549571625000x + 330549571625000x - 82637392906250)log(2x - 1) +--R + +--R 7 6 5 4 +--R - 1397230560000x - 9489524220000x - 31855563036000x - 77649212460600x +--R + +--R 3 2 +--R - 206501370522480x + 283893518434680x + 51350638082480x - 53929198640625 +--R / +--R 2 +--R 42592000000x - 42592000000x + 10648000000 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R - 2644396573log(2x - 1) + 2644396573log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 340736 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 500 +r0:=823543/2816/(1-2*x)^2+(-5764801/3872)/(1-2*x)-26161299/20000*x-_ + 792423/2000*x^2-40581/400*x^3-2187/160*x^4-269063263/170368*_ + log(1-2*x)+1/4159375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (1024x - 1024x + 256)log(5x + 3) +--R + +--R 2 +--R (- 6726581575000x + 6726581575000x - 1681645393750)log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x +--R + +--R 2 +--R 5149424229840x + 1777812991240x - 1273918078125 +--R / +--R 2 +--R 4259200000x - 4259200000x + 1064800000 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (1024x - 1024x + 256)log(5x + 3) +--R + +--R 2 +--R (- 6726581575000x + 6726581575000x - 1681645393750)log(2x - 1) +--R + +--R 6 5 4 3 +--R - 58217940000x - 373888548000x - 1269992017800x - 3991792836240x +--R + +--R 2 +--R 5149424229840x + 1777812991240x - 1273918078125 +--R / +--R 2 +--R 4259200000x - 4259200000x + 1064800000 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R - 269063263log(2x - 1) + 269063263log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 170368 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 500 +r0:=117649/1408/(1-2*x)^2+(-2739541/7744)/(1-2*x)-102303/500*x-35721/800*x^2-_ + 243/40*x^3-12761315/42592*log(1-2*x)+1/831875*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (512x - 512x + 128)log(5x + 3) +--R + +--R 2 +--R (- 127613150000x + 127613150000x - 31903287500)log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x +--R + +--R 53550930620x - 28771483125 +--R / +--R 2 +--R 425920000x - 425920000x + 106480000 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (512x - 512x + 128)log(5x + 3) +--R + +--R 2 +--R (- 127613150000x + 127613150000x - 31903287500)log(2x - 1) +--R + +--R 5 4 3 2 +--R - 2587464000x - 16430396400x - 68774793120x + 82391322420x +--R + +--R 53550930620x - 28771483125 +--R / +--R 2 +--R 425920000x - 425920000x + 106480000 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R - 12761315log(2x - 1) + 12761315log(- 2x + 1) +--R (4) --------------------------------------------- +--R 42592 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 500 +r0:=16807/704/(1-2*x)^2+(-156065/1936)/(1-2*x)-10287/400*x-243/80*x^2-_ + 543655/10648*log(1-2*x)+1/166375*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (256x - 256x + 64)log(5x + 3) +--R + +--R 2 4 +--R (- 2174620000x + 2174620000x - 543655000)log(- 2x + 1) - 129373200x +--R + +--R 3 2 +--R - 965986560x + 1063016460x + 1442875060x - 604151625 +--R / +--R 2 +--R 42592000x - 42592000x + 10648000 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (256x - 256x + 64)log(5x + 3) +--R + +--R 2 4 +--R (- 2174620000x + 2174620000x - 543655000)log(2x - 1) - 129373200x +--R + +--R 3 2 +--R - 965986560x + 1063016460x + 1442875060x - 604151625 +--R / +--R 2 +--R 42592000x - 42592000x + 10648000 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R - 543655log(2x - 1) + 543655log(- 2x + 1) +--R (4) ----------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 500 +r0:=2401/352/(1-2*x)^2+(-33271/1936)/(1-2*x)-81/40*x-_ + 153811/21296*log(1-2*x)+1/33275*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (128x - 128x + 32)log(5x + 3) +--R + +--R 2 3 2 +--R (- 30762200x + 30762200x - 7690550)log(- 2x + 1) - 8624880x + 8624880x +--R + +--R 34441880x - 11036025 +--R / +--R 2 +--R 4259200x - 4259200x + 1064800 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (128x - 128x + 32)log(5x + 3) +--R + +--R 2 3 2 +--R (- 30762200x + 30762200x - 7690550)log(2x - 1) - 8624880x + 8624880x +--R + +--R 34441880x - 11036025 +--R / +--R 2 +--R 4259200x - 4259200x + 1064800 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R - 153811log(2x - 1) + 153811log(- 2x + 1) +--R (4) ----------------------------------------- +--R 21296 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 500 +r0:=343/176/(1-2*x)^2+(-392/121)/(1-2*x)-7189/10648*log(1-2*x)+_ + 1/6655*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (64x - 64x + 16)log(5x + 3) +--R + +--R 2 +--R (- 287560x + 287560x - 71890)log(- 2x + 1) + 689920x - 137445 +--R / +--R 2 +--R 425920x - 425920x + 106480 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (64x - 64x + 16)log(5x + 3) + (- 287560x + 287560x - 71890)log(2x - 1) +--R + +--R 689920x - 137445 +--R / +--R 2 +--R 425920x - 425920x + 106480 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R - 7189log(2x - 1) + 7189log(- 2x + 1) +--R (4) ------------------------------------- +--R 10648 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 500 +r0:=49/88/(1-2*x)^2+(-217/484)/(1-2*x)-1/1331*log(1-2*x)+1/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(- 2x + 1) + 9548x + 1155 +--R ---------------------------------------------------------------------------- +--R 2 +--R 42592x - 42592x + 10648 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (32x - 32x + 8)log(5x + 3) + (- 32x + 32x - 8)log(2x - 1) + 9548x + 1155 +--R -------------------------------------------------------------------------- +--R 2 +--R 42592x - 42592x + 10648 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R - log(2x - 1) + log(- 2x + 1) +--R (4) ----------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 500 +r0:=7/44/(1-2*x)^2+1/121/(1-2*x)-5/1331*log(1-2*x)+5/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(- 2x + 1) - 88x + 891 +--R --------------------------------------------------------------------------- +--R 2 +--R 21296x - 21296x + 5324 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (80x - 80x + 20)log(5x + 3) + (- 80x + 80x - 20)log(2x - 1) - 88x + 891 +--R ------------------------------------------------------------------------- +--R 2 +--R 21296x - 21296x + 5324 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R - 5log(2x - 1) + 5log(- 2x + 1) +--R (4) ------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=1/((1-2*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------- +--R 4 3 2 +--R 40x - 36x - 6x + 13x - 3 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 500 +r0:=1/22/(1-2*x)^2+5/121/(1-2*x)-25/1331*log(1-2*x)+25/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 2 +--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(- 2x + 1) +--R + +--R - 220x + 231 +--R / +--R 2 +--R 10648x - 10648x + 2662 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 +--R (200x - 200x + 50)log(5x + 3) + (- 200x + 200x - 50)log(2x - 1) - 220x +--R + +--R 231 +--R / +--R 2 +--R 10648x - 10648x + 2662 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R - 25log(2x - 1) + 25log(- 2x + 1) +--R (4) --------------------------------- +--R 1331 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------ +--R 5 4 3 2 +--R 120x - 28x - 90x + 27x + 17x - 6 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 500 +r0:=1/77/(1-2*x)^2+136/5929/(1-2*x)-6938/456533*log(1-2*x)-_ + 27/343*log(2+3*x)+125/1331*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (171500x - 171500x + 42875)log(5x + 3) +--R + +--R 2 +--R (- 143748x + 143748x - 35937)log(3x + 2) +--R + +--R 2 +--R (- 27752x + 27752x - 6938)log(- 2x + 1) - 20944x + 16401 +--R / +--R 2 +--R 1826132x - 1826132x + 456533 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (171500x - 171500x + 42875)log(5x + 3) +--R + +--R 2 +--R (- 143748x + 143748x - 35937)log(3x + 2) +--R + +--R 2 +--R (- 27752x + 27752x - 6938)log(2x - 1) - 20944x + 16401 +--R / +--R 2 +--R 1826132x - 1826132x + 456533 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R - 6938log(2x - 1) + 6938log(- 2x + 1) +--R (4) ------------------------------------- +--R 456533 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------- +--R 6 5 4 3 2 +--R 360x + 156x - 326x - 99x + 105x + 16x - 12 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 500 +r0:=2/539/(1-2*x)^2+404/41503/(1-2*x)+27/343/(2+3*x)-_ + 27208/3195731*log(1-2*x)-1107/2401*log(2+3*x)+625/1331*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3) +--R + +--R 3 2 +--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2) +--R + +--R 3 2 2 +--R (- 326496x + 108832x + 136040x - 54416)log(- 2x + 1) + 819588x +--R + +--R - 1001770x + 337491 +--R / +--R 3 2 +--R 38348772x - 12782924x - 15978655x + 6391462 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (18007500x - 6002500x - 7503125x + 3001250)log(5x + 3) +--R + +--R 3 2 +--R (- 17681004x + 5893668x + 7367085x - 2946834)log(3x + 2) +--R + +--R 3 2 2 +--R (- 326496x + 108832x + 136040x - 54416)log(2x - 1) + 819588x +--R + +--R - 1001770x + 337491 +--R / +--R 3 2 +--R 38348772x - 12782924x - 15978655x + 6391462 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R - 27208log(2x - 1) + 27208log(- 2x + 1) +--R (4) --------------------------------------- +--R 3195731 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 1080x + 1188x - 666x - 949x + 117x + 258x - 4x - 24 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 500 +r0:=4/3773/(1-2*x)^2+1072/290521/(1-2*x)+27/686/(2+3*x)^2+1107/2401/(2+3*x)-_ + 89792/22370117*log(1-2*x)-39393/16807*log(2+3*x)+3125/1331*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(- 2x + 1) +--R + +--R 3 2 +--R 244562472x - 77517132x - 108953306x + 43866669 +--R / +--R 4 3 2 +--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3781575000x + 1260525000x - 2416006250x - 420175000x + 420175000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 3775109976x - 1258369992x + 2411875818x + 419456664x - 419456664) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 6465024x - 2155008x + 4130432x + 718336x - 718336)log(2x - 1) +--R + +--R 3 2 +--R 244562472x - 77517132x - 108953306x + 43866669 +--R / +--R 4 3 2 +--R 1610648424x + 536882808x - 1029025382x - 178960936x + 178960936 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R - 89792log(2x - 1) + 89792log(- 2x + 1) +--R (4) --------------------------------------- +--R 22370117 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R - --------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 3240x + 5724x + 378x - 4179x - 1547x + 1008x + 504x - 80x - 48 +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 500 +r0:=8/26411/(1-2*x)^2+2672/2033647/(1-2*x)+9/343/(2+3*x)^3+_ + 1107/4802/(2+3*x)^2+39393/16807/(2+3*x)-267760/156590819*log(1-2*x)-_ + 1380915/117649*log(2+3*x)+15625/1331*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 397065375000x + 397065375000x - 165443906250x - 213238812500x +--R + +--R 14706125000x + 29412250000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x +--R + +--R - 14703982920x - 29407965840 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x +--R + +--R - 4284160 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924 +--R / +--R 5 4 3 2 +--R 33823616904x + 33823616904x - 14093173710x - 18164535004x +--R + +--R 1252726552x + 2505453104 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 397065375000x + 397065375000x - 165443906250x - 213238812500x +--R + +--R 14706125000x + 29412250000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R - 397007538840x - 397007538840x + 165419807850x + 213207752340x +--R + +--R - 14703982920x - 29407965840 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 57836160x - 57836160x + 24098400x + 31060160x - 2142080x +--R + +--R - 4284160 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 26403549480x + 9644189940x - 17141334210x - 3318409325x + 3092859924 +--R / +--R 5 4 3 2 +--R 33823616904x + 33823616904x - 14093173710x - 18164535004x +--R + +--R 1252726552x + 2505453104 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R - 267760log(2x - 1) + 267760log(- 2x + 1) +--R (4) ----------------------------------------- +--R 156590819 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 500 +r0:=5764801/30976/(1-2*x)^2+(-79883671/85184)/(1-2*x)-81001863/100000*x-_ + 4863159/20000*x^2-123201/2000*x^3-6561/800*x^4+(-1/20796875)/(3+5*x)-_ + 1845559863/1874048*log(1-2*x)+54/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (1382400x - 552960x - 483840x + 207360)log(5x + 3) +--R + +--R 3 2 +--R - 1153474914375000x + 461389965750000x + 403716220031250x +--R + +--R - 173021237156250 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R - 9605960100000x - 68309049600000x - 252583384185000x +--R + +--R 4 3 2 +--R - 811024095717000x + 468362848619160x + 838544848893576x +--R + +--R - 32898384865071x - 132062840768441 +--R / +--R 3 2 +--R 1171280000000x - 468512000000x - 409948000000x + 175692000000 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1382400x - 552960x - 483840x + 207360)log(5x + 3) +--R + +--R 3 2 +--R - 1153474914375000x + 461389965750000x + 403716220031250x +--R + +--R - 173021237156250 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R - 9605960100000x - 68309049600000x - 252583384185000x +--R + +--R 4 3 2 +--R - 811024095717000x + 468362848619160x + 838544848893576x +--R + +--R - 32898384865071x - 132062840768441 +--R / +--R 3 2 +--R 1171280000000x - 468512000000x - 409948000000x + 175692000000 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R - 1845559863log(2x - 1) + 1845559863log(- 2x + 1) +--R (4) ------------------------------------------------- +--R 1874048 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 500 +r0:=823543/15488/(1-2*x)^2+(-18941489/85184)/(1-2*x)-1258983/10000*x-_ + 108621/4000*x^2-729/200*x^3+(-1/4159375)/(3+5*x)-_ + 87177909/468512*log(1-2*x)+237/45753125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (606720x - 242688x - 212352x + 91008)log(5x + 3) +--R + +--R 3 2 +--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500) +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x +--R + +--R 2 +--R 17706353292408x + 647305946397x - 2972475517033 +--R / +--R 3 2 +--R 117128000000x - 46851200000x - 40994800000x + 17569200000 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (606720x - 242688x - 212352x + 91008)log(5x + 3) +--R + +--R 3 2 +--R (- 21794477250000x + 8717790900000x + 7628067037500x - 3269171587500) +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 426931560000x - 3009867498000x - 13324533987600x + 6947670741660x +--R + +--R 2 +--R 17706353292408x + 647305946397x - 2972475517033 +--R / +--R 3 2 +--R 117128000000x - 46851200000x - 40994800000x + 17569200000 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R - 87177909log(2x - 1) + 87177909log(- 2x + 1) +--R (4) --------------------------------------------- +--R 468512 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 500 +r0:=117649/7744/(1-2*x)^2+(-67228/1331)/(1-2*x)-31347/2000*x-729/400*x^2+_ + (-1/831875)/(3+5*x)-7383075/234256*log(1-2*x)+204/9150625*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (261120x - 104448x - 91392x + 39168)log(5x + 3) +--R + +--R 3 2 +--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500) +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x +--R + +--R 46529265321x - 62049343829 +--R / +--R 3 2 +--R 11712800000x - 4685120000x - 4099480000x + 1756920000 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (261120x - 104448x - 91392x + 39168)log(5x + 3) +--R + +--R 3 2 +--R (- 369153750000x + 147661500000x + 129203812500x - 55373062500) +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 21346578000x - 175041939600x + 80903530620x + 356854410264x +--R + +--R 46529265321x - 62049343829 +--R / +--R 3 2 +--R 11712800000x - 4685120000x - 4099480000x + 1756920000 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R - 7383075log(2x - 1) + 7383075log(- 2x + 1) +--R (4) ------------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 500 +r0:=16807/3872/(1-2*x)^2+(-228095/21296)/(1-2*x)-243/200*x+_ + (-1/166375)/(3+5*x)-1034145/234256*log(1-2*x)+171/1830125*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (109440x - 43776x - 38304x + 16416)log(5x + 3) +--R + +--R 3 2 +--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(- 2x + 1) +--R + +--R 4 3 2 +--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477 +--R / +--R 3 2 +--R 1171280000x - 468512000x - 409948000x + 175692000 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (109440x - 43776x - 38304x + 16416)log(5x + 3) +--R + +--R 3 2 +--R (- 5170725000x + 2068290000x + 1809753750x - 775608750)log(2x - 1) +--R + +--R 4 3 2 +--R - 1423105200x + 569242080x + 6770697912x + 1684826253x - 1119166477 +--R / +--R 3 2 +--R 1171280000x - 468512000x - 409948000x + 175692000 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R - 1034145log(2x - 1) + 1034145log(- 2x + 1) +--R (4) ------------------------------------------- +--R 234256 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 500 +r0:=2401/1936/(1-2*x)^2+(-10633/5324)/(1-2*x)+(-1/33275)/(3+5*x)-_ + 47481/117128*log(1-2*x)+138/366025*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (44160x - 17664x - 15456x + 6624)log(5x + 3) +--R + +--R 3 2 +--R (- 47481000x + 18992400x + 16618350x - 7122150)log(- 2x + 1) +--R + +--R 2 +--R 116962296x + 48012129x - 13300001 +--R / +--R 3 2 +--R 117128000x - 46851200x - 40994800x + 17569200 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (44160x - 17664x - 15456x + 6624)log(5x + 3) +--R + +--R 3 2 +--R (- 47481000x + 18992400x + 16618350x - 7122150)log(2x - 1) +--R + +--R 2 +--R 116962296x + 48012129x - 13300001 +--R / +--R 3 2 +--R 117128000x - 46851200x - 40994800x + 17569200 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R - 47481log(2x - 1) + 47481log(- 2x + 1) +--R (4) --------------------------------------- +--R 117128 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 500 +r0:=343/968/(1-2*x)^2+(-1421/5324)/(1-2*x)+(-1/6655)/(3+5*x)-_ + 21/14641*log(1-2*x)+21/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (16800x - 6720x - 5880x + 2520)log(5x + 3) +--R + +--R 3 2 2 +--R (- 16800x + 6720x + 5880x - 2520)log(- 2x + 1) + 1562748x + 1194237x +--R + +--R 153527 +--R / +--R 3 2 +--R 11712800x - 4685120x - 4099480x + 1756920 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (16800x - 6720x - 5880x + 2520)log(5x + 3) +--R + +--R 3 2 2 +--R (- 16800x + 6720x + 5880x - 2520)log(2x - 1) + 1562748x + 1194237x +--R + +--R 153527 +--R / +--R 3 2 +--R 11712800x - 4685120x - 4099480x + 1756920 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R - 21log(2x - 1) + 21log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 500 +r0:=49/484/(1-2*x)^2+14/1331/(1-2*x)+(-1/1331)/(3+5*x)-_ + 72/14641*log(1-2*x)+72/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (5760x - 2304x - 2016x + 864)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5760x + 2304x + 2016x - 864)log(- 2x + 1) - 6336x + 29205x + 19591 +--R / +--R 3 2 +--R 1171280x - 468512x - 409948x + 175692 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (5760x - 2304x - 2016x + 864)log(5x + 3) +--R + +--R 3 2 2 +--R (- 5760x + 2304x + 2016x - 864)log(2x - 1) - 6336x + 29205x + 19591 +--R / +--R 3 2 +--R 1171280x - 468512x - 409948x + 175692 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R - 72log(2x - 1) + 72log(- 2x + 1) +--R (4) --------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 500 +r0:=7/242/(1-2*x)^2+37/1331/(1-2*x)+(-5/1331)/(3+5*x)-_ + 195/14641*log(1-2*x)+195/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (7800x - 3120x - 2730x + 1170)log(5x + 3) +--R + +--R 3 2 2 +--R (- 7800x + 3120x + 2730x - 1170)log(- 2x + 1) - 8580x + 3861x + 4873 +--R / +--R 3 2 +--R 585640x - 234256x - 204974x + 87846 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (7800x - 3120x - 2730x + 1170)log(5x + 3) +--R + +--R 3 2 2 +--R (- 7800x + 3120x + 2730x - 1170)log(2x - 1) - 8580x + 3861x + 4873 +--R / +--R 3 2 +--R 585640x - 234256x - 204974x + 87846 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R - 195log(2x - 1) + 195log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/((1-2*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R 5 4 3 2 +--R 200x - 60x - 138x + 47x + 24x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 500 +r0:=1/121/(1-2*x)^2+20/1331/(1-2*x)+(-25/1331)/(3+5*x)-_ + 150/14641*log(1-2*x)+150/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (3000x - 1200x - 1050x + 450)log(5x + 3) +--R + +--R 3 2 2 +--R (- 3000x + 1200x + 1050x - 450)log(- 2x + 1) - 3300x + 1485x + 748 +--R / +--R 3 2 +--R 292820x - 117128x - 102487x + 43923 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (3000x - 1200x - 1050x + 450)log(5x + 3) +--R + +--R 3 2 2 +--R (- 3000x + 1200x + 1050x - 450)log(2x - 1) - 3300x + 1485x + 748 +--R / +--R 3 2 +--R 292820x - 117128x - 102487x + 43923 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R - 150log(2x - 1) + 150log(- 2x + 1) +--R (4) ----------------------------------- +--R 14641 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------ +--R 6 5 4 3 2 +--R 600x + 220x - 534x - 135x + 166x + 21x - 18 +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 500 +r0:=2/847/(1-2*x)^2+412/65219/(1-2*x)+(-125/1331)/(3+5*x)-_ + 28296/5021863*log(1-2*x)+81/343*log(2+3*x)-3375/14641*log(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3) +--R + +--R 3 2 +--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2) +--R + +--R 3 2 2 +--R (- 565920x + 226368x + 198072x - 84888)log(- 2x + 1) - 2203740x +--R + +--R 1914066x - 340879 +--R / +--R 3 2 +--R 100437260x - 40174904x - 35153041x + 15065589 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (- 23152500x + 9261000x + 8103375x - 3472875)log(5x + 3) +--R + +--R 3 2 +--R (23718420x - 9487368x - 8301447x + 3557763)log(3x + 2) +--R + +--R 3 2 2 +--R (- 565920x + 226368x + 198072x - 84888)log(2x - 1) - 2203740x +--R + +--R 1914066x - 340879 +--R / +--R 3 2 +--R 100437260x - 40174904x - 35153041x + 15065589 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R - 28296log(2x - 1) + 28296log(- 2x + 1) +--R (4) --------------------------------------- +--R 5021863 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 1800x + 1860x - 1162x - 1473x + 228x + 395x - 12x - 36 +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 500 +r0:=4/5929/(1-2*x)^2+1088/456533/(1-2*x)+(-81/343)/(2+3*x)+_ + (-625/1331)/(3+5*x)-92496/35153041*log(1-2*x)+_ + 6156/2401*log(2+3*x)-37500/14641*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(- 2x + 1) +--R + +--R 3 2 +--R - 366624720x + 130867968x + 141681540x - 57273139 +--R / +--R 4 3 2 +--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 5402250000x - 1440600000x + 3331387500x + 450187500x - 540225000) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (5407799760x + 1442079936x - 3334809852x - 450649980x + 540779976) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 5549760x - 1479936x + 3422352x + 462480x - 554976)log(2x - 1) +--R + +--R 3 2 +--R - 366624720x + 130867968x + 141681540x - 57273139 +--R / +--R 4 3 2 +--R 2109182460x + 562448656x - 1300662517x - 175765205x + 210918246 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R - 92496log(2x - 1) + 92496log(- 2x + 1) +--R (4) --------------------------------------- +--R 35153041 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R - ---------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 5400x + 9180x + 234x - 6743x - 2262x + 1641x + 754x - 132x - 72 +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 500 +r0:=8/41503/(1-2*x)^2+2704/3195731/(1-2*x)+(-81/686)/(2+3*x)^2+_ + (-6156/2401)/(2+3*x)+(-3125/1331)/(3+5*x)-_ + 274224/246071287*log(1-2*x)+333639/16807*log(2+3*x)-_ + 290625/14641*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x +--R + +--R - 78152550000x - 117228825000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x +--R + +--R 78156937584x + 117235406376 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x +--R + +--R - 6581376 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x +--R + +--R - 12361039691 +--R / +--R 5 4 3 2 +--R 88585663320x + 82679952432x - 38879263346x - 43800689086x +--R + +--R 3937140592x + 5905710888 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1758432375000x - 1641203550000x + 771756431250x + 869447118750x +--R + +--R - 78152550000x - 117228825000 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 2 +--R 1758531095640x + 1641295689264x - 771799758642x - 869495930622x +--R + +--R 78156937584x + 117235406376 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 98720640x - 92139264x + 43327392x + 48811872x - 4387584x +--R + +--R - 6581376 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R - 117343999080x - 35266545468x + 73726130478x + 11356433319x +--R + +--R - 12361039691 +--R / +--R 5 4 3 2 +--R 88585663320x + 82679952432x - 38879263346x - 43800689086x +--R + +--R 3937140592x + 5905710888 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R - 274224log(2x - 1) + 274224log(- 2x + 1) +--R (4) ----------------------------------------- +--R 246071287 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^2) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 16200x + 38340x + 19062x - 19761x - 20272x + 399x + 5544x +--R + +--R 2 +--R 1112x - 480x - 144 +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 500 +r0:=16/290521/(1-2*x)^2+6464/22370117/(1-2*x)+(-27/343)/(2+3*x)^3+_ + (-3078/2401)/(2+3*x)^2+(-333639/16807)/(2+3*x)+_ + (-15625/1331)/(3+5*x)-761760/1722499009*log(1-2*x)+_ + 15820110/117649*log(2+3*x)-1968750/14641*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R - 125075593125000x - 200120949000000x - 22930525406250x +--R + +--R 3 2 +--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 125076004475400x + 200121607160640x + 22930600820490x +--R + +--R 3 2 +--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x +--R + +--R - 39611520x - 18282240 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x +--R + +--R - 342379099755x - 585732955423 +--R / +--R 6 5 4 3 +--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x +--R + +--R 2 +--R - 265264847386x + 89569948468x + 41339976216 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 125075593125000x - 200120949000000x - 22930525406250x +--R + +--R 3 2 +--R 98439124218750x + 35669706187500x - 12044316375000x - 5558915250000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R 125076004475400x + 200121607160640x + 22930600820490x +--R + +--R 3 2 +--R - 98439447966750x - 35669823498540x + 12044355986520x + 5558933532240 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 2 +--R - 411350400x - 658160640x - 75414240x + 323748000x + 117311040x +--R + +--R - 39611520x - 18282240 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 8338852783800x - 8061154974180x + 3573065429010x + 4298892128685x +--R + +--R - 342379099755x - 585732955423 +--R / +--R 6 5 4 3 +--R 930149464860x + 1488239143776x + 170527401891x - 732062078825x +--R + +--R 2 +--R - 265264847386x + 89569948468x + 41339976216 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R - 761760log(2x - 1) + 761760log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1722499009 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^9/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 9 8 7 6 5 4 +--R - 19683x - 118098x - 314928x - 489888x - 489888x - 326592x +--R + +--R 3 2 +--R - 145152x - 41472x - 6912x - 512 +--R / +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 500 +r0:=40353607/340736/(1-2*x)^2+(-17294403/29282)/(1-2*x)-_ + 50150097/100000*x-7459857/50000*x^2-373977/10000*x^3-_ + 19683/4000*x^4+(-1/207968750)/(3+5*x)^2+(-303/1143828125)/(3+5*x)-_ + 12657032367/20614528*log(1-2*x)+8202/2516421875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 197766130734375000x - 39553226146875000x + 116682017133281250x +--R + +--R 11865967844062500x - 17798951766093750 +--R * +--R log(- 2x + 1) +--R + +--R 8 7 6 +--R - 1584983416500000x - 12362870648700000x - 49530731765625000x +--R + +--R 5 4 3 +--R - 163943640232020000x - 3373337816263800x + 192223824266320440x +--R + +--R 2 +--R 81487109015452107x - 25922683108313662x - 13688249752028357 +--R / +--R 4 3 2 +--R 322102000000000x + 64420400000000x - 190040180000000x +--R + +--R - 19326120000000x + 28989180000000 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1049856000x + 209971200x - 619415040x - 62991360x + 94487040) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 197766130734375000x - 39553226146875000x + 116682017133281250x +--R + +--R 11865967844062500x - 17798951766093750 +--R * +--R log(2x - 1) +--R + +--R 8 7 6 +--R - 1584983416500000x - 12362870648700000x - 49530731765625000x +--R + +--R 5 4 3 +--R - 163943640232020000x - 3373337816263800x + 192223824266320440x +--R + +--R 2 +--R 81487109015452107x - 25922683108313662x - 13688249752028357 +--R / +--R 4 3 2 +--R 322102000000000x + 64420400000000x - 190040180000000x +--R + +--R - 19326120000000x + 28989180000000 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R - 12657032367log(2x - 1) + 12657032367log(- 2x + 1) +--R (4) --------------------------------------------------- +--R 20614528 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)^8/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 6561x - 34992x - 81648x - 108864x - 90720x - 48384x - 16128x +--R + +--R - 3072x - 256 +--R / +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 500 +r0:=5764801/170368/(1-2*x)^2+(-130943337/937024)/(1-2*x)-242028/3125*x-_ + 330237/20000*x^2-2187/1000*x^3+(-1/41593750)/(3+5*x)^2+_ + (-54/45753125)/(3+5*x)-595421589/5153632*log(1-2*x)+_ + 1284/100656875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 3721384931250000x - 744276986250000x + 2195617109437500x +--R + +--R 223283095875000x - 334924643812500 +--R * +--R log(- 2x + 1) +--R + +--R 7 6 5 +--R - 70443707400000x - 545938732350000x - 2559454702200000x +--R + +--R 4 3 2 +--R - 180911181221100x + 3748001092791780x + 1949701238862399x +--R + +--R - 437687139939434x - 307014257976349 +--R / +--R 4 3 2 +--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x +--R + +--R 2898918000000 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (410880000x + 82176000x - 242419200x - 24652800x + 36979200) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R - 3721384931250000x - 744276986250000x + 2195617109437500x +--R + +--R 223283095875000x - 334924643812500 +--R * +--R log(2x - 1) +--R + +--R 7 6 5 +--R - 70443707400000x - 545938732350000x - 2559454702200000x +--R + +--R 4 3 2 +--R - 180911181221100x + 3748001092791780x + 1949701238862399x +--R + +--R - 437687139939434x - 307014257976349 +--R / +--R 4 3 2 +--R 32210200000000x + 6442040000000x - 19004018000000x - 1932612000000x +--R + +--R 2898918000000 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R - 595421589log(2x - 1) + 595421589log(- 2x + 1) +--R (4) ----------------------------------------------- +--R 5153632 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(2+3*x)^7/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 2187x - 10206x - 20412x - 22680x - 15120x - 6048x - 1344x - 128 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 500 +r0:=823543/85184/(1-2*x)^2+(-7411887/234256)/(1-2*x)-95499/10000*x-_ + 2187/2000*x^2+(-1/8318750)/(3+5*x)^2+(-237/45753125)/(3+5*x)-_ + 25059237/1288408*log(1-2*x)+24279/503284375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3) +--R + +--R 4 3 2 +--R - 62648092500000x - 12529618500000x + 36962374575000x +--R + +--R 3758885550000x - 5638328325000 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 3 +--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x +--R + +--R 2 +--R 44983390879251x - 5655984161146x - 6369590895041 +--R / +--R 4 3 2 +--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x +--R + +--R 289891800000 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (155385600x + 31077120x - 91677504x - 9323136x + 13984704)log(5x + 3) +--R + +--R 4 3 2 +--R - 62648092500000x - 12529618500000x + 36962374575000x +--R + +--R 3758885550000x - 5638328325000 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 3 +--R - 3522185370000x - 31464855972000x - 4073994411300x + 69316698060060x +--R + +--R 2 +--R 44983390879251x - 5655984161146x - 6369590895041 +--R / +--R 4 3 2 +--R 3221020000000x + 644204000000x - 1900401800000x - 193261200000x +--R + +--R 289891800000 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R - 25059237log(2x - 1) + 25059237log(- 2x + 1) +--R (4) --------------------------------------------- +--R 1288408 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(2+3*x)^6/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 500 +r0:=117649/42592/(1-2*x)^2+(-1563051/234256)/(1-2*x)-729/1000*x+_ + (-1/1663750)/(3+5*x)^2+(-204/9150625)/(3+5*x)-_ + 6950895/2576816*log(1-2*x)+17547/100656875*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3) +--R + +--R 4 3 2 +--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x +--R + +--R - 78197568750 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x +--R + +--R - 12119848070x - 113352927985 +--R / +--R 4 3 2 +--R 322102000000x + 64420400000x - 190040180000x - 19326120000x +--R + +--R 28989180000 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (56150400x + 11230080x - 33128736x - 3369024x + 5053536)log(5x + 3) +--R + +--R 4 3 2 +--R - 868861875000x - 173772375000x + 512628506250x + 52131712500x +--R + +--R - 78197568750 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R - 234812358000x - 46962471600x + 1213135417560x + 988737742575x +--R + +--R - 12119848070x - 113352927985 +--R / +--R 4 3 2 +--R 322102000000x + 64420400000x - 190040180000x - 19326120000x +--R + +--R 28989180000 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R - 6950895log(2x - 1) + 6950895log(- 2x + 1) +--R (4) ------------------------------------------- +--R 2576816 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^5/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 500 +r0:=16807/21296/(1-2*x)^2+(-36015/29282)/(1-2*x)+(-1/332750)/(3+5*x)^2+_ + (-171/1830125)/(3+5*x)-313845/1288408*log(1-2*x)+11904/20131375*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3) +--R + +--R 4 3 2 +--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250) +--R * +--R log(- 2x + 1) +--R + +--R 3 2 +--R 19807648080x + 20221158771x + 2872410794x - 1277723381 +--R / +--R 4 3 2 +--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (19046400x + 3809280x - 11237376x - 1142784x + 1714176)log(5x + 3) +--R + +--R 4 3 2 +--R (- 7846125000x - 1569225000x + 4629213750x + 470767500x - 706151250) +--R * +--R log(2x - 1) +--R + +--R 3 2 +--R 19807648080x + 20221158771x + 2872410794x - 1277723381 +--R / +--R 4 3 2 +--R 32210200000x + 6442040000x - 19004018000x - 1932612000x + 2898918000 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R - 313845log(2x - 1) + 313845log(- 2x + 1) +--R (4) ----------------------------------------- +--R 1288408 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^4/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 500 +r0:=2401/10648/(1-2*x)^2+(-9261/58564)/(1-2*x)+(-1/66550)/(3+5*x)^2+_ + (-138/366025)/(3+5*x)-294/161051*log(1-2*x)+294/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(- 2x + 1) +--R + +--R 3 2 +--R 254434620x + 359945091x + 156855094x + 19488359 +--R / +--R 4 3 2 +--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5880000x + 1176000x - 3469200x - 352800x + 529200)log(5x + 3) +--R + +--R 4 3 2 +--R (- 5880000x - 1176000x + 3469200x + 352800x - 529200)log(2x - 1) +--R + +--R 3 2 +--R 254434620x + 359945091x + 156855094x + 19488359 +--R / +--R 4 3 2 +--R 3221020000x + 644204000x - 1900401800x - 193261200x + 289891800 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R - 294log(2x - 1) + 294log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^3/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 500 +r0:=343/5324/(1-2*x)^2+147/14641/(1-2*x)+(-1/13310)/(3+5*x)^2+_ + (-21/14641)/(3+5*x)-777/161051*log(1-2*x)+777/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(- 2x + 1) +--R + +--R 3 2 +--R - 1709400x + 4091967x + 6646838x + 2144593 +--R / +--R 4 3 2 +--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1554000x + 310800x - 916860x - 93240x + 139860)log(5x + 3) +--R + +--R 4 3 2 +--R (- 1554000x - 310800x + 916860x + 93240x - 139860)log(2x - 1) +--R + +--R 3 2 +--R - 1709400x + 4091967x + 6646838x + 2144593 +--R / +--R 4 3 2 +--R 322102000x + 64420400x - 190040180x - 19326120x + 28989180 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R - 777log(2x - 1) + 777log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^2/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 500 +r0:=49/2662/(1-2*x)^2+273/14641/(1-2*x)+(-1/2662)/(3+5*x)^2+_ + (-72/14641)/(3+5*x)-1509/161051*log(1-2*x)+1509/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3) +--R + +--R 4 3 2 +--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(- 2x + 1) +--R + +--R 3 2 +--R - 331980x - 49797x + 261514x + 102542 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (301800x + 60360x - 178062x - 18108x + 27162)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 301800x - 60360x + 178062x + 18108x - 27162)log(2x - 1) - 331980x +--R + +--R 2 +--R - 49797x + 261514x + 102542 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R - 1509log(2x - 1) + 1509log(- 2x + 1) +--R (4) ------------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 500 +r0:=7/1331/(1-2*x)^2+144/14641/(1-2*x)+(-5/2662)/(3+5*x)^2+_ + (-195/14641)/(3+5*x)-1110/161051*log(1-2*x)+1110/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3) +--R + +--R 4 3 2 +--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(- 2x + 1) +--R + +--R 3 2 +--R - 244200x - 36630x + 121286x + 30283 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (222000x + 44400x - 130980x - 13320x + 19980)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 222000x - 44400x + 130980x + 13320x - 19980)log(2x - 1) - 244200x +--R + +--R 2 +--R - 36630x + 121286x + 30283 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R - 1110log(2x - 1) + 1110log(- 2x + 1) +--R (4) ------------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=1/((1-2*x)^3*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------- +--R 6 5 4 3 2 +--R 1000x + 300x - 870x - 179x + 261x + 27x - 27 +--R Type: Fraction(Polynomial(Integer)) +--E 361 + +--S 362 of 500 +r0:=2/1331/(1-2*x)^2+60/14641/(1-2*x)+(-25/2662)/(3+5*x)^2+_ + (-150/14641)/(3+5*x)-600/161051*log(1-2*x)+600/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(- 2x + 1) - 132000x +--R + +--R 2 +--R - 19800x + 65560x + 3311 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (120000x + 24000x - 70800x - 7200x + 10800)log(5x + 3) +--R + +--R 4 3 2 3 +--R (- 120000x - 24000x + 70800x + 7200x - 10800)log(2x - 1) - 132000x +--R + +--R 2 +--R - 19800x + 65560x + 3311 +--R / +--R 4 3 2 +--R 32210200x + 6442040x - 19004018x - 1932612x + 2898918 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R - 600log(2x - 1) + 600log(- 2x + 1) +--R (4) ----------------------------------- +--R 161051 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=1/((1-2*x)^3*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------ +--R 7 6 5 4 3 2 +--R 3000x + 2900x - 2010x - 2277x + 425x + 603x - 27x - 54 +--R Type: Fraction(Polynomial(Integer)) +--E 366 + +--S 367 of 500 +r0:=4/9317/(1-2*x)^2+1104/717409/(1-2*x)+(-125/2662)/(3+5*x)^2+_ + 3375/14641/(3+5*x)-95232/55240493*log(1-2*x)-243/343*log(2+3*x)+_ + 114375/161051*log(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(- 2x + 1) +--R + +--R 3 2 +--R 500854200x - 229258260x - 154059598x + 73172407 +--R / +--R 4 3 2 +--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7846125000x + 1569225000x - 4629213750x - 470767500x + 706151250) +--R * +--R log(5x + 3) +--R + +--R 4 3 2 +--R (- 7827078600x - 1565415720x + 4617976374x + 469624716x - 704437074) +--R * +--R log(3x + 2) +--R + +--R 4 3 2 +--R (- 19046400x - 3809280x + 11237376x + 1142784x - 1714176)log(2x - 1) +--R + +--R 3 2 +--R 500854200x - 229258260x - 154059598x + 73172407 +--R / +--R 4 3 2 +--R 11048098600x + 2209619720x - 6518378174x - 662885916x + 994328874 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R - 95232log(2x - 1) + 95232log(- 2x + 1) +--R (4) --------------------------------------- +--R 55240493 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R - -------------------------------------------------------------------------- +--R 8 7 6 5 4 3 2 +--R 9000x + 14700x - 230x - 10851x - 3279x + 2659x + 1125x - 216x - 108 +--R Type: Fraction(Polynomial(Integer)) +--E 371 + +--S 372 of 500 +r0:=8/65219/(1-2*x)^2+2736/5021863/(1-2*x)+243/343/(2+3*x)+_ + (-625/2662)/(3+5*x)^2+37500/14641/(3+5*x)-280752/386683451*log(1-2*x)-_ + 26973/2401*log(2+3*x)+1809375/161051*log(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 2606585625000x + 2259040875000x - 1190340768750x - 1181652150000x +--R + +--R 130329281250x + 156395137500 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 2606417173800x - 2258894883960x + 1190263842702x +--R + +--R 2 +--R 1181575785456x - 130320858690x - 156385030428 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 168451200x - 145991040x + 76926048x + 76364544x - 8422560x +--R + +--R - 10107072 +--R * +--R log(- 2x + 1) +--R + +--R 4 3 2 +--R 173575848600x + 40392941820x - 104891101854x - 12253878175x +--R + +--R 16462150012 +--R / +--R 5 4 3 2 +--R 232010070600x + 201075394520x - 105951265574x - 105177898672x +--R + +--R 11600503530x + 13920604236 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2606585625000x + 2259040875000x - 1190340768750x - 1181652150000x +--R + +--R 130329281250x + 156395137500 +--R * +--R log(5x + 3) +--R + +--R 5 4 3 +--R - 2606417173800x - 2258894883960x + 1190263842702x +--R + +--R 2 +--R 1181575785456x - 130320858690x - 156385030428 +--R * +--R log(3x + 2) +--R + +--R 5 4 3 2 +--R - 168451200x - 145991040x + 76926048x + 76364544x - 8422560x +--R + +--R - 10107072 +--R * +--R log(2x - 1) +--R + +--R 4 3 2 +--R 173575848600x + 40392941820x - 104891101854x - 12253878175x +--R + +--R 16462150012 +--R / +--R 5 4 3 2 +--R 232010070600x + 201075394520x - 105951265574x - 105177898672x +--R + +--R 11600503530x + 13920604236 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R - 280752log(2x - 1) + 280752log(- 2x + 1) +--R (4) ----------------------------------------- +--R 386683451 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 9 8 7 6 5 4 3 +--R 27000x + 62100x + 28710x - 33013x - 31539x + 1419x + 8693x +--R + +--R 2 +--R 1602x - 756x - 216 +--R Type: Fraction(Polynomial(Integer)) +--E 376 + +--S 377 of 500 +r0:=16/456533/(1-2*x)^2+6528/35153041/(1-2*x)+243/686/(2+3*x)^2+_ + 26973/2401/(2+3*x)+(-3125/2662)/(3+5*x)^2+290625/14641/(3+5*x)-_ + 776928/2706784157*log(1-2*x)-1944972/16807*log(2+3*x)+_ + 18637500/161051*log(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 563832832500000x + 864543676500000x + 68286420825000x +--R + +--R 3 2 +--R - 427259990850000x - 142211169975000x + 52624397700000x +--R + +--R 22553313300000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 563831434029600x - 864541532178720x - 68286251454696x +--R + +--R 3 2 +--R 427258931120208x + 142210817249688x - 52624267176096x +--R + +--R - 22553257361184 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 1398470400x - 2144321280x - 169370304x + 1059729792x +--R + +--R 2 +--R 352725312x - 130523904x - 55938816 +--R * +--R log(- 2x + 1) +--R + +--R 5 4 3 2 +--R 37587223951200x + 33827604204240x - 16859483294808x - 17801732753112x +--R + +--R 1786038929444x + 2376093430249 +--R / +--R 6 5 4 3 +--R 4872211482600x + 7470724273320x + 590078946226x - 3692053590148x +--R + +--R 2 +--R - 1228880007278x + 454739738376x + 194888459304 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 563832832500000x + 864543676500000x + 68286420825000x +--R + +--R 3 2 +--R - 427259990850000x - 142211169975000x + 52624397700000x +--R + +--R 22553313300000 +--R * +--R log(5x + 3) +--R + +--R 6 5 4 +--R - 563831434029600x - 864541532178720x - 68286251454696x +--R + +--R 3 2 +--R 427258931120208x + 142210817249688x - 52624267176096x +--R + +--R - 22553257361184 +--R * +--R log(3x + 2) +--R + +--R 6 5 4 3 +--R - 1398470400x - 2144321280x - 169370304x + 1059729792x +--R + +--R 2 +--R 352725312x - 130523904x - 55938816 +--R * +--R log(2x - 1) +--R + +--R 5 4 3 2 +--R 37587223951200x + 33827604204240x - 16859483294808x - 17801732753112x +--R + +--R 1786038929444x + 2376093430249 +--R / +--R 6 5 4 3 +--R 4872211482600x + 7470724273320x + 590078946226x - 3692053590148x +--R + +--R 2 +--R - 1228880007278x + 454739738376x + 194888459304 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R - 776928log(2x - 1) + 776928log(- 2x + 1) +--R (4) ----------------------------------------- +--R 2706784157 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((1-2*x)^3*(2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 10 9 8 7 6 5 +--R 81000x + 240300x + 210330x - 41619x - 160643x - 58821x +--R + +--R 4 3 2 +--R 28917x + 22192x + 936x - 2160x - 432 +--R Type: Fraction(Polynomial(Integer)) +--E 381 + +--S 382 of 500 +r0:=32/3195731/(1-2*x)^2+15168/246071287/(1-2*x)+81/343/(2+3*x)^3+_ + 26973/4802/(2+3*x)^2+1944972/16807/(2+3*x)+(-15625/2662)/(3+5*x)^2+_ + 1968750/14641/(3+5*x)-2054400/18947489099*log(1-2*x)-_ + 115534350/117649*log(2+3*x)+158156250/161051*log(3+5*x) +--R +--R +--R (2) +--R 7 6 5 +--R 100477393143750000x + 221050264916250000x + 114879152827687500x +--R + +--R 4 3 2 +--R - 68026916543250000x - 76102321844062500x - 7517197561125000x +--R + +--R 10271022410250000x + 2679397150500000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 100477382049990000x - 221050240509978000x - 114879140143821900x +--R + +--R 4 3 2 +--R 68026909032363600x + 76102313441566500x + 7517196731147400x +--R + +--R - 10271021276221200x - 2679396854666400 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 11093760000x - 24406272000x - 12683865600x + 7510886400x +--R + +--R 3 2 +--R 8402496000x + 829977600x - 1134028800x - 295833600 +--R * +--R log(- 2x + 1) +--R + +--R 6 5 4 +--R 6698479933530000x + 10494278110701000x + 1014683641656300x +--R + +--R 3 2 +--R - 5175447127123350x - 1796782743686700x + 635595472278305x +--R + +--R 282301665291184 +--R / +--R 7 6 5 +--R 102316441134600x + 225096170496120x + 116981797697226x +--R + +--R 4 3 2 +--R - 69272020145944x - 77495230414910x - 7654785595996x + 10459013982648x +--R + +--R 2728438430256 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 100477393143750000x + 221050264916250000x + 114879152827687500x +--R + +--R 4 3 2 +--R - 68026916543250000x - 76102321844062500x - 7517197561125000x +--R + +--R 10271022410250000x + 2679397150500000 +--R * +--R log(5x + 3) +--R + +--R 7 6 5 +--R - 100477382049990000x - 221050240509978000x - 114879140143821900x +--R + +--R 4 3 2 +--R 68026909032363600x + 76102313441566500x + 7517196731147400x +--R + +--R - 10271021276221200x - 2679396854666400 +--R * +--R log(3x + 2) +--R + +--R 7 6 5 4 +--R - 11093760000x - 24406272000x - 12683865600x + 7510886400x +--R + +--R 3 2 +--R 8402496000x + 829977600x - 1134028800x - 295833600 +--R * +--R log(2x - 1) +--R + +--R 6 5 4 +--R 6698479933530000x + 10494278110701000x + 1014683641656300x +--R + +--R 3 2 +--R - 5175447127123350x - 1796782743686700x + 635595472278305x +--R + +--R 282301665291184 +--R / +--R 7 6 5 +--R 102316441134600x + 225096170496120x + 116981797697226x +--R + +--R 4 3 2 +--R - 69272020145944x - 77495230414910x - 7654785595996x + 10459013982648x +--R + +--R 2728438430256 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R - 2054400log(2x - 1) + 2054400log(- 2x + 1) +--R (4) ------------------------------------------- +--R 18947489099 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^6*(3+5*x)*sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1294139/384*(1-2*x)^(3/2)+3916031/640*(1-2*x)^(5/2)-_ + 725445/128*(1-2*x)^(7/2)+406455/128*(1-2*x)^(9/2)-_ + 1580985/1408*(1-2*x)^(11/2)+409941/1664*(1-2*x)^(13/2)-_ + 19683/640*(1-2*x)^(15/2)+3645/2176*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x +--R + +--R 3 2 +--R 72883440x + 5339712x - 16666112x - 23667392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 15637050x + 80999919x + 181983186x + 229582836x + 173491920x +--R + +--R 3 2 +--R 72883440x + 5339712x - 16666112x - 23667392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)^5*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-184877/192*(1-2*x)^(3/2)+12005/8*(1-2*x)^(5/2)-74235/64*(1-2*x)^(7/2)+_ + 4165/8*(1-2*x)^(9/2)-97335/704*(1-2*x)^(11/2)+81/4*(1-2*x)^(13/2)-_ + 81/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 33 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R (5346x + 24057x + 45765x + 46875x + 26220x + 5172x - 4120x - 7288) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 33 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^4*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-26411/96*(1-2*x)^(3/2)+57281/160*(1-2*x)^(5/2)-3549/16*(1-2*x)^(7/2)+_ + 1197/16*(1-2*x)^(9/2)-4671/352*(1-2*x)^(11/2)+405/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R (133650x + 509895x + 791640x + 614160x + 200328x - 60928x - 163888) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^3*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-3773/48*(1-2*x)^(3/2)+3283/40*(1-2*x)^(5/2)-153/4*(1-2*x)^(7/2)+_ + 69/8*(1-2*x)^(9/2)-135/176*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1 +--R (2) -------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (4050x + 12645x + 15075x + 7527x - 482x - 4442)\|- 2x + 1 +--R (3) -------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^2*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-539/24*(1-2*x)^(3/2)+707/40*(1-2*x)^(5/2)-309/56*(1-2*x)^(7/2)+_ + 5/8*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1050x + 2535x + 2046x + 244x - 1016)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)*(3+5*x)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-77/12*(1-2*x)^(3/2)+17/5*(1-2*x)^(5/2)-15/28*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (450x + 753x + 257x - 373)\|- 2x + 1 +--R (2) --------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (450x + 753x + 257x - 373)\|- 2x + 1 +--R (3) --------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(3+5*x)*sqrt(1-2*x) +--R +--R +--R +--------+ +--R (1) (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-11/6*(1-2*x)^(3/2)+1/2*(1-2*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (6x + 5x - 4)\|- 2x + 1 +--R (2) ------------------------- +--R 3 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (6x + 5x - 4)\|- 2x + 1 +--R (3) ------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-5/9*(1-2*x)^(3/2)+2/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 2/9*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--------+ +--R 2\|7 atanh(---------------) + (10x - 7)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------ +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +--------+ +--R \|7 log(---------------------------------) + (10x - 7)\|3 \|- 2x + 1 +--R 3x + 2 +--R (3) --------------------------------------------------------------------- +--R +-+ +--R 9\|3 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(---------------------------------) - 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/21*(1-2*x)^(3/2)/(2+3*x)-8*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 8/7*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (- 72x - 48)atanh(---------------) + (10x + 7)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) -------------------------------------------------------------- +--R +--+ +--R (9x + 6)\|21 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (36x + 24)log(-----------------------------) + (10x + 7)\|21 \|- 2x + 1 +--R 3x + 2 +--R ------------------------------------------------------------------------ +--R +--+ +--R (9x + 6)\|21 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4log(-----------------------------) + 8atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------- +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 12x + 20)\|21 + (12x - 20)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 8x + 4)\|3 \|7 \|21 + 168x - 84 +--R / +--R 2 +--------+ 3 2 +--+ +--R (126x + 21x - 42)\|- 2x + 1 + (18x - 27x - 11x + 10)\|21 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1/42*(1-2*x)^(3/2)/(2+3*x)^2+23/21*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-23/42*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--+ +--------+ +--R (414x + 552x + 184)atanh(---------------) + (- 71x - 45)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R 2 +--+ +--R (378x + 504x + 168)\|21 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (207x + 276x + 92)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 71x - 45)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (378x + 504x + 168)\|21 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23log(-------------------------------) - 46atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 42\|21 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (46x - 23)\|3 \|7 \|21 - 966x + 483 +--R / +--R 2 +--------+ 3 2 +--+ +--R (5292x + 882x - 1764)\|- 2x + 1 + (- 756x + 1134x + 462x - 420)\|21 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=1/63*(1-2*x)^(3/2)/(2+3*x)^3+34/441*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-17/63*sqrt(1-2*x)/(2+3*x)^2+17/441*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (918x + 1836x + 1224x + 272)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (153x - 167x - 163)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (11907x + 23814x + 15876x + 3528)\|21 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (459x + 918x + 612x + 136)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (153x - 167x - 163)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (11907x + 23814x + 15876x + 3528)\|21 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 17log(-------------------------------) - 34atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 441\|21 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (34x - 17)\|3 \|7 \|21 - 714x + 357 +--R / +--R 2 +--------+ +--R (55566x + 9261x - 18522)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 7938x + 11907x + 4851x - 4410)\|21 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=1/84*(1-2*x)^(3/2)/(2+3*x)^4+5/1372*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-5/28*sqrt(1-2*x)/(2+3*x)^3+5/392*sqrt(1-2*x)/(2+3*x)^2+_ + 15/2744*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 +-+ \|3 \|- 2x + 1 +--R (2430x + 6480x + 6480x + 2880x + 480)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (1215x + 3240x + 3240x + 1440x + 240)\|3 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (1215x + 3375x - 1726x - 2062)\|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|7 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 5\|3 log(---------------------------------) - 10\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 2744\|7 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(3+5*x)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=1/105*(1-2*x)^(3/2)/(2+3*x)^5+2/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-2/15*sqrt(1-2*x)/(2+3*x)^4+2/315*sqrt(1-2*x)/(2+3*x)^3+_ + 1/441*sqrt(1-2*x)/(2+3*x)^2+1/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 5 4 3 2 \|3 \|- 2x + 1 +--R (2430x + 8100x + 10800x + 7200x + 2400x + 320)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (1215x + 4050x + 5400x + 3600x + 1200x + 160) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (405x + 1395x + 2004x - 864x - 1019)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1250235x + 4167450x + 5556600x + 3704400x + 1234800x + 164640)\|21 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 18522x + 27783x + 11319x - 10290)\|21 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^4*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-290521/192*(1-2*x)^(3/2)+381073/160*(1-2*x)^(5/2)-118993/64*_ + (1-2*x)^(7/2)+40453/48*(1-2*x)^(9/2)-159111/704*(1-2*x)^(11/2)+_ + 13905/416*(1-2*x)^(13/2)-135/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x +--R + +--R - 426024x - 734904 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 579150x + 2561625x + 4787910x + 4814245x + 2635780x + 493524x +--R + +--R - 426024x - 734904 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^3*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-41503/96*(1-2*x)^(3/2)+91091/160*(1-2*x)^(5/2)-5711/16*(1-2*x)^(7/2)+_ + 1949/16*(1-2*x)^(9/2)-7695/352*(1-2*x)^(11/2)+675/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R (222750x + 832275x + 1264605x + 958275x + 301263x - 99458x - 253898) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^2*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-5929/48*(1-2*x)^(3/2)+1309/10*(1-2*x)^(5/2)-3467/56*(1-2*x)^(7/2)+_ + 85/6*(1-2*x)^(9/2)-225/176*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (47250x + 143675x + 166580x + 80313x - 6518x - 48098)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)*(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-847/24*(1-2*x)^(3/2)+1133/40*(1-2*x)^(5/2)-505/56*(1-2*x)^(7/2)+_ + 25/24*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 4075x + 3159x + 321x - 1569)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-121/12*(1-2*x)^(3/2)+11/2*(1-2*x)^(5/2)-25/28*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (150x + 237x + 74x - 115)\|- 2x + 1 +--R (2) -------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (150x + 237x + 74x - 115)\|- 2x + 1 +--R (3) -------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-28/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(3/2)*(3+5*x)-2/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+2/27*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+ +--R - 2\|7 atanh(---------------) + (90x + 65x - 53)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 2 +-+ +--------+ +--R \|7 log(-------------------------------) + (90x + 65x - 53)\|3 \|- 2x + 1 +--R 3x + 2 +--R --------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(-------------------------------) + 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-25/27*(1-2*x)^(3/2)-1/63*(1-2*x)^(3/2)/(2+3*x)+142/27*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-142/189*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 2 +--+ +--------+ +--R (426x + 284)atanh(---------------) + (150x - 35x - 91)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R (81x + 54)\|21 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R (213x + 142)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (150x - 35x - 91)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (81x + 54)\|21 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 71log(-------------------------------) - 142atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491 +--R / +--R 2 +--------+ 3 2 +--+ +--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/126*(1-2*x)^(3/2)/(2+3*x)^2+139/882*(1-2*x)^(3/2)/(2+3*x)-_ + 863/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+863/441*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 15534x - 20712x - 6904)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (2100x + 2941x + 1025)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1134x + 1512x + 504)\|21 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (7767x + 10356x + 3452)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (2100x + 2941x + 1025)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1134x + 1512x + 504)\|21 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 863log(-----------------------------) + 1726atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 126\|21 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2589x + 4315)\|21 + (2589x - 4315)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1726x + 863)\|3 \|7 \|21 + 36246x - 18123 +--R / +--R 2 +--------+ 3 2 +--+ +--R (15876x + 2646x - 5292)\|- 2x + 1 + (2268x - 3402x - 1386x + 1260)\|21 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-1/189*(1-2*x)^(3/2)/(2+3*x)^3+23/294*(1-2*x)^(3/2)/(2+3*x)^2+_ + 2381/1323*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 2381/2646*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (128574x + 257148x + 171432x + 38096)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (71442x + 142884x + 95256x + 21168)\|21 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (64287x + 128574x + 85716x + 19048)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 22671x - 28751x - 9124)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (71442x + 142884x + 95256x + 21168)\|21 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2381log(-------------------------------) - 4762atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 2646\|21 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001 +--R / +--R 2 +--------+ +--R (333396x + 55566x - 111132)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 47628x + 71442x + 29106x - 26460)\|21 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-1/252*(1-2*x)^(3/2)/(2+3*x)^4+275/5292*(1-2*x)^(3/2)/(2+3*x)^3+_ + 4625/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 4625/10584*sqrt(1-2*x)/(2+3*x)^2+4625/74088*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (749250x + 1998000x + 1998000x + 888000x + 148000) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (374625x + 999000x + 999000x + 444000x + 74000) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (124875x - 64725x - 225262x - 85094)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4625log(-------------------------------) - 9250atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 74088\|21 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13875x + 23125)\|21 + (13875x - 23125)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (9250x - 4625)\|3 \|7 \|21 - 194250x + 97125 +--R / +--R 2 +--------+ +--R (9335088x + 1555848x - 3111696)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 1333584x + 2000376x + 814968x - 740880)\|21 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3j.input.pamphlet b/src/input/rich3j.input.pamphlet new file mode 100644 index 0000000..7bfb8f5 --- /dev/null +++ b/src/input/rich3j.input.pamphlet @@ -0,0 +1,9134 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3j.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 55 matching answers. +\item 45 cases where Axiom differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3j.output +)spool rich3j.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-1/315*(1-2*x)^(3/2)/(2+3*x)^5+7/180*(1-2*x)^(3/2)/(2+3*x)^4+_ + 31/1764*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 31/108*sqrt(1-2*x)/(2+3*x)^3+31/1512*sqrt(1-2*x)/(2+3*x)^2+_ + 31/3528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (75330x + 251100x + 334800x + 223200x + 74400x + 9920) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (37665x + 125550x + 167400x + 111600x + 37200x + 4960) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (12555x + 43245x + 3324x - 33434x - 13564)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (4286520x + 14288400x + 19051200x + 12700800x + 4233600x + 564480)\|21 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 31log(-------------------------------) - 62atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3528\|21 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 93x + 155)\|21 + (93x - 155)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (62x - 31)\|3 \|7 \|21 - 1302x + 651 +--R / +--R 2 +--------+ +--R (444528x + 74088x - 148176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 63504x + 95256x + 38808x - 35280)\|21 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-1/378*(1-2*x)^(3/2)/(2+3*x)^6+137/4410*(1-2*x)^(3/2)/(2+3*x)^5+_ + 1613/518616*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1613/7560*sqrt(1-2*x)/(2+3*x)^4+1613/158760*sqrt(1-2*x)/(2+3*x)^3+_ + 1613/444528*sqrt(1-2*x)/(2+3*x)^2+1613/1037232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 11758770x + 47035080x + 78391800x + 69681600x + 34840800x +--R + +--R 9290880x + 1032320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 3780710640x + 15122842560x + 25204737600x + 22404211200x +--R + +--R 2 +--R 11202105600x + 2987228160x + 331914240 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 5879385x + 23517540x + 39195900x + 34840800x + 17420400x +--R + +--R 4645440x + 516160 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (1959795x + 8056935x + 14197626x + 1791558x - 7772840x - 3136864) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 3780710640x + 15122842560x + 25204737600x + 22404211200x +--R + +--R 2 +--R 11202105600x + 2987228160x + 331914240 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1613log(-------------------------------) - 3226atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 1037232\|21 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 4839x + 8065)\|21 + (4839x - 8065)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (3226x - 1613)\|3 \|7 \|21 - 67746x + 33873 +--R / +--R 2 +--------+ +--R (130691232x + 21781872x - 43563744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 18670176x + 28005264x + 11409552x - 10372320)\|21 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^4*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-3195731/384*(1-2*x)^(3/2)+9836211/640*(1-2*x)^(5/2)-_ + 1853313/128*(1-2*x)^(7/2)+9504551/1152*(1-2*x)^(9/2)-_ + 4177401/1408*(1-2*x)^(11/2)+1101465/1664*(1-2*x)^(13/2)-_ + 10755/128*(1-2*x)^(15/2)+10125/2176*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x +--R + +--R 3 2 +--R 514265240x + 26582592x - 124054192x - 171312832 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 130308750x + 655308225x + 1428673950x + 1747511955x + 1277595710x +--R + +--R 3 2 +--R 514265240x + 26582592x - 124054192x - 171312832 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^3*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-456533/192*(1-2*x)^(3/2)+302379/80*(1-2*x)^(5/2)-_ + 190707/64*(1-2*x)^(7/2)+98209/72*(1-2*x)^(9/2)-_ + 260055/704*(1-2*x)^(11/2)+11475/208*(1-2*x)^(13/2)-225/64*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x +--R + +--R 2 +--R 2166357x - 2030662x - 3420622 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 2895750x + 12585375x + 23107275x + 22806620x + 12220625x +--R + +--R 2 +--R 2166357x - 2030662x - 3420622 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^2*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-65219/96*(1-2*x)^(3/2)+144837/160*(1-2*x)^(5/2)-_ + 64317/112*(1-2*x)^(7/2)+28555/144*(1-2*x)^(9/2)-_ + 12675/352*(1-2*x)^(11/2)+1125/416*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x +--R + +--R - 8261156 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 45045 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 7796250x + 28515375x + 42393400x + 31374085x + 9500136x - 3396296x +--R + +--R - 8261156 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 45045 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (375x + 925x + 855x + 351x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-9317/48*(1-2*x)^(3/2)+8349/40*(1-2*x)^(5/2)-2805/28*(1-2*x)^(7/2)+_ + 1675/72*(1-2*x)^(9/2)-375/176*(1-2*x)^(11/2) +--R +--R +--R (2) +--R 5 4 3 2 +--------+ +--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1 +--R ------------------------------------------------------------------------ +--R 3465 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--------+ +--R (236250x + 699125x + 788075x + 366816x - 36121x - 223231)\|- 2x + 1 +--R ------------------------------------------------------------------------ +--R 3465 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (1) (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-1331/24*(1-2*x)^(3/2)+363/8*(1-2*x)^(5/2)-825/56*(1-2*x)^(7/2)+_ + 125/72*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1 +--R (2) --------------------------------------------------- +--R 63 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (1750x + 3925x + 2922x + 247x - 1454)\|- 2x + 1 +--R (3) --------------------------------------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=2/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-6946/945*sqrt(1-2*x)-_ + 47/315*(3+5*x)^2*sqrt(1-2*x)+2/21*(3+5*x)^3*sqrt(1-2*x)-_ + 1/567*(1333+1877*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 14\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 10035x + 2875x - 4804)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R \|7 log(---------------------------------) - 2\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-212/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-124/27*sqrt(1-2*x)+_ + 7/9*(3+5*x)^2*sqrt(1-2*x)-1/3*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)-_ + 10/81*(5+34*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (- 636x - 424)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (243x + 162)\|21 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R (318x + 212)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 1725x - 110x - 439)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (243x + 162)\|21 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 106log(-----------------------------) + 212atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 81\|21 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 318x + 530)\|21 + (318x - 530)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 212x + 106)\|3 \|7 \|21 + 4452x - 2226 +--R / +--R 2 +--------+ 3 2 +--+ +--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=7559/567*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+115/27*sqrt(1-2*x)-_ + 5/1134*(643-2815*x)*sqrt(1-2*x)-53/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-_ + 1/6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (136062x + 181416x + 60472)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (10206x + 13608x + 4536)\|21 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (68031x + 90708x + 30236)log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (31500x + 7350x - 32833x - 15815)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (10206x + 13608x + 4536)\|21 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 7559log(-------------------------------) - 15118atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 1134\|21 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739 +--R / +--R 2 +--------+ +--R (142884x + 23814x - 47628)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 20412x + 30618x + 12474x - 11340)\|21 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) -------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-92996/3969*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+23710/3969*sqrt(1-2*x)-_ + 3796/3969*(3+5*x)*sqrt(1-2*x)/(2+3*x)-53/189*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2510892x - 5021784x - 3347856x - 743968)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (107163x + 214326x + 142884x + 31752)\|21 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1255446x + 2510892x + 1673928x + 371984) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (330750x + 695043x + 484618x + 112187)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (107163x + 214326x + 142884x + 31752)\|21 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 46498log(-----------------------------) + 92996atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3969\|21 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 139494x + 232490)\|21 + (139494x - 232490)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 92996x + 46498)\|3 \|7 \|21 + 1952916x - 976458 +--R / +--R 2 +--------+ +--R (500094x + 83349x - 166698)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (71442x - 107163x - 43659x + 39690)\|21 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=328715/111132*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-48005/111132*_ + sqrt(1-2*x)/(2+3*x)-7625/31752*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2-_ + 53/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-1/12*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 4 3 2 +--R (53251830x + 142004880x + 142004880x + 63113280x + 10518880) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (26625915x + 71002440x + 71002440x + 31556640x + 5259440) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 9646695x - 18358575x - 11657098x - 2469626)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (18003384x + 48009024x + 48009024x + 21337344x + 3556224)\|21 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 328715log(-------------------------------) - 657430atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +--+ +--R 222264\|21 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 986145x + 1643575)\|21 + (986145x - 1643575)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (657430x - 328715)\|3 \|7 \|21 - 13806030x + 6903015 +--R / +--R 2 +--------+ +--R (28005264x + 4667544x - 9335088)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 4000752x + 6001128x + 2444904x - 2222640)\|21 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=11237/55566*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 475/5292*sqrt(1-2*x)/(2+3*x)^2+11237/111132*sqrt(1-2*x)/(2+3*x)-_ + 547/5670*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3-53/630*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 5 4 3 2 +--R 27305910x + 91019700x + 121359600x + 80906400x + 26968800x +--R + +--R 3595840 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x +--R + +--R 17781120 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13652955x + 45509850x + 60679800x + 40453200x + 13484400x +--R + +--R 1797920 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (4550985x + 240615x - 10100352x - 8471518x - 1984928)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 135025380x + 450084600x + 600112800x + 400075200x + 133358400x +--R + +--R 17781120 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 11237log(-------------------------------) - 22474atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 111132\|21 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 33711x + 56185)\|21 + (33711x - 56185)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (22474x - 11237)\|3 \|7 \|21 - 471954x + 235977 +--R / +--R 2 +--------+ +--R (14002632x + 2333772x - 4667544)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2000376x + 3000564x + 1222452x - 1111320)\|21 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=43957/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1861/59535*sqrt(1-2*x)/(2+3*x)^3+43957/1333584*sqrt(1-2*x)/(2+_ + 3*x)^2+43957/3111696*sqrt(1-2*x)/(2+3*x)-7691/158760*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)^4-53/945*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5-_ + 1/18*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R (2) +--R 6 5 4 3 +--R 320446530x + 1281786120x + 2136310200x + 1898942400x +--R + +--R 2 +--R 949471200x + 253192320x + 28132480 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x +--R + +--R - 36741296 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 11342131920x + 45368527680x + 75614212800x + 67212633600x +--R + +--R 2 +--R 33606316800x + 8961684480x + 995742720 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 160223265x + 640893060x + 1068155100x + 949471200x + 474735600x +--R + +--R 126596160x + 14066240 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 53407755x + 219565215x + 127601514x - 139462938x - 150340360x +--R + +--R - 36741296 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 11342131920x + 45368527680x + 75614212800x + 67212633600x +--R + +--R 2 +--R 33606316800x + 8961684480x + 995742720 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 43957log(-------------------------------) - 87914atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 3111696\|21 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 131871x + 219785)\|21 + (131871x - 219785)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (87914x - 43957)\|3 \|7 \|21 - 1846194x + 923097 +--R / +--R 2 +--------+ +--R (392073696x + 65345616x - 130691232)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=47434/9529569*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 13676/972405*sqrt(1-2*x)/(2+3*x)^4+47434/2917215*_ + sqrt(1-2*x)/(2+3*x)^3+23717/4084101*sqrt(1-2*x)/(2+3*x)^2+_ + 23717/9529569*sqrt(1-2*x)/(2+3*x)-3862/138915*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)^5-53/1323*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^6-_ + 1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R (2) +--R 7 6 5 4 +--R 518690790x + 2420557020x + 4841114040x + 5379015600x +--R + +--R 3 2 +--R 3586010400x + 1434404160x + 318756480x + 30357760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x +--R + +--R - 361589428x - 88036937 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x +--R + +--R 3 2 +--R 720435416400x + 288174166560x + 64038703680x + 6098924160 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 +--R 259345395x + 1210278510x + 2420557020x + 2689507800x +--R + +--R 3 2 +--R 1793005200x + 717202080x + 159378240x + 15178880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 86448465x + 413031555x + 863203932x + 473987484x - 306463011x +--R + +--R - 361589428x - 88036937 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 104205837015x + 486293906070x + 972587812140x + 1080653124600x +--R + +--R 3 2 +--R 720435416400x + 288174166560x + 64038703680x + 6098924160 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23717log(-------------------------------) - 47434atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 9529569\|21 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 71151x + 118585)\|21 + (71151x - 118585)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (47434x - 23717)\|3 \|7 \|21 - 996114x + 498057 +--R / +--R 2 +--------+ +--R (1200725694x + 200120949x - 400241898)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 171532242x + 257298363x + 104825259x - 95295690)\|21 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-93922/28125*_ + sqrt(1-2*x)-107/225*(2+3*x)*sqrt(1-2*x)-184/1875*(2+3*x)^2*_ + sqrt(1-2*x)-17/1575*(2+3*x)^3*sqrt(1-2*x)+2/45*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 14\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 21875\|5 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (78750x + 203625x + 177930x + 27865x - 88776)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 21875\|5 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 922/625*sqrt(1-2*x)-3/125*(2+3*x)^2*sqrt(1-2*x)+2/35*(2+3*x)^3*_ + sqrt(1-2*x)-1/625*(236+375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 14\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 4375\|5 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (6750x + 12555x + 5115x - 6526)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 4375\|5 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-8/25*(1-2*x)^(3/2)-3/25*(1-2*x)^(3/2)*(2+3*x)-2/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+2/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 2\|11 atanh(---------------) + (90x + 95x - 68)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 2 +-+ +--------+ +--R \|11 log(--------------------------------) + (90x + 95x - 68)\|5 \|- 2x + 1 +--R 5x + 3 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-1/5*(1-2*x)^(3/2)-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/25*_ + sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 2\|11 atanh(---------------) + (10x - 3)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R \|11 log(--------------------------------) + (10x - 3)\|5 \|- 2x + 1 +--R 5x + 3 +--R (3) --------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=sqrt(1-2*x)/(3+5*x) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2/5*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 2\|11 atanh(---------------) + 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R \|11 log(--------------------------------) + 2\|5 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R \|11 log(--------------------------------) + 2\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +-+ +--R 5\|5 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+2*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3) +--R +--R +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2\|5 \|7 atanh(---------------) - 2\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +-+ +--R \|3 \|5 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R \|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R \|5 \|7 log(---------------------------------) +--R 3x + 2 +--R / +--R +-+ +-+ +--R \|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R \|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R \|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 2\|5 \|7 atanh(---------------) + 2\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R \|3 \|5 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=68*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-2*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (204x + 136)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--+ +--------+ +--R (- 6x - 4)\|21 \|55 atanh(---------------) + \|21 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +--+ +--R (3x + 2)\|21 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (3x + 2)\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (102x + 68)log(-------------------------------) + \|21 \|- 2x + 1 +--R 3x + 2 +--R / +--R +--+ +--R (3x + 2)\|21 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-------------------------------) - 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (45x - 117x + 22x + 80)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 340x - 34x + 102)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 210x - 441x + 168 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ 2 +-+ +--+ +--R (75x - 365x + 592x - 320)\|21 + (6930x + 1155x - 2310)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2550x + 6800x - 1802x - 4080)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 30x + 113x - 129x + 40)\|21 +--R + +--R 3 2 +-+ +--+ +--R (630x - 903x - 378x + 336)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1020x - 1598x - 476x + 510)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 990x + 1485x + 605x - 550)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1700x + 2550x + 782x - 816)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1050x - 3885x + 4368x - 1344 +--R / +--R 4 3 2 +--+ +--+ 4 3 2 +--R (90x - 81x - 136x + 17x + 30)\|21 \|55 - 3150x + 2625x + 4599x +--R + +--R - 546x - 1008 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (1260x + 336x - 777x - 105x + 126)\|55 +--R + +--R 5 4 3 2 +--+ +--R (450x - 1125x - 32x + 1173x + 14x - 240)\|21 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=793/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+1/2*sqrt(1-2*x)/(2+3*x)^2+69/14*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (14274x + 19032x + 6344)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 1260x - 1680x - 560)\|7 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (207x + 145)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +--R (126x + 168x + 56)\|7 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R 2 +-+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (630x + 840x + 280)\|7 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (7137x + 9516x + 3172)\|3 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R (207x + 145)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +--R (126x + 168x + 56)\|7 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +-+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 70\|7 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 793\|3 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 1586\|3 atanh(---------------) + 140\|7 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +-+ +--+ +-+ +--+ +--R ((75x - 245x + 200)\|5 \|7 \|11 + (- 3850x + 1925)\|3 )\|55 +--R + +--R +-+ +-+ +--+ 2 +-+ +--R (3850x - 1925)\|3 \|5 \|11 + (- 4125x + 13475x - 11000)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ 2 +-+ +--+ +--R ((350x - 735x + 280)\|3 \|5 \|11 + (1650x - 3575x + 1375)\|7 )\|55 +--R + +--R 2 +-+ +-+ +--+ 2 +-+ +--R (- 1650x + 3575x - 1375)\|5 \|7 \|11 + (- 19250x + 40425x - 15400)\|3 +--R / +--R 3 2 +-+ +--+ +--R (30x - 47x - 14x + 15)\|7 \|55 +--R + +--R 3 2 +-+ +--R (- 350x + 525x + 161x - 168)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--+ +--R (140x - 56x - 49x + 21)\|3 \|55 +--R + +--R 4 3 2 +-+ +--R (150x - 475x + 306x + 187x - 120)\|7 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=83264/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(55)+1/3*sqrt(1-2*x)/(2+3*x)^3+52/21*_ + sqrt(1-2*x)/(2+3*x)^2+1207/49*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (2248128x + 4496256x + 2997504x + 666112)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 66150x - 132300x - 88200x - 19600)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (10863x + 14848x + 5087)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (1323x + 2646x + 1764x + 392)\|21 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (33075x + 66150x + 44100x + 9800)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (1124064x + 2248128x + 1498752x + 333056) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (10863x + 14848x + 5087)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (1323x + 2646x + 1764x + 392)\|21 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1225\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 41632log(-------------------------------) - 83264atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2450\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (55125x - 143325x + 26950x + 98000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 416320x - 41632x + 124896)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 253470x - 540603x + 206934 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (90525x - 443525x + 724246x - 394160)\|21 +--R + +--R 2 +-+ +--+ +--R (8489250x + 1414875x - 2829750)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 3122400x + 8326400x - 2206496x - 4995840)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 36210x + 137579x - 158277x + 49270)\|21 +--R + +--R 3 2 +-+ +--+ +--R (771750x - 1106175x - 463050x + 411600)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1248960x - 1956704x - 582848x + 624480)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1212750x + 1819125x + 741125x - 673750)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2081600x + 3122400x + 957536x - 999168)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1267350x - 4730775x + 5359494x - 1655472 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (4410x - 3969x - 6664x + 833x + 1470)\|21 \|55 - 154350x +--R + +--R 3 2 +--R 128625x + 225351x - 26754x - 49392 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (61740x + 16464x - 38073x - 5145x + 6174)\|55 +--R + +--R 5 4 3 2 +--+ +--R (22050x - 55125x - 1568x + 57477x + 686x - 11760)\|21 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^5*(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=11656955/1372*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-250*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1/4*sqrt(1-2*x)/(2+3*x)^4+_ + 139/84*sqrt(1-2*x)/(2+3*x)^3+14555/1176*sqrt(1-2*x)/(2+3*x)^2+_ + 337955/2744*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1888426710x + 5035804560x + 5035804560x + 2238135360x + 373022560) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 55566000x - 148176000x - 148176000x - 65856000x - 10976000)\|21 +--R * +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (222264x + 592704x + 592704x + 263424x + 43904)\|21 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--+ +--R (27783000x + 74088000x + 74088000x + 32928000x + 5488000)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (944213355x + 2517902280x + 2517902280x + 1119067680x + 186511280) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (9124785x + 18555225x + 12587542x + 2849254)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (222264x + 592704x + 592704x + 263424x + 43904)\|21 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 343000\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 11656955log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 23313910atanh(---------------) + 686000\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2744\|21 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (15435000x - 40131000x + 7546000x + 27440000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 116569550x - 11656955x + 34970865)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 70970550x - 151368945x + 57941835 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (25346625x - 124186000x + 202788615x - 110365400)\|21 +--R + +--R 2 +-+ +--+ +--R (2376990000x + 396165000x - 792330000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 874271625x + 2331391000x - 617818615x - 1398834600)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 10138650x + 38521885x - 44317630x + 13795675)\|21 +--R + +--R 3 2 +-+ +--+ +--R (216090000x - 309729000x - 129654000x + 115248000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (349708650x - 547876885x - 163197370x + 174854325)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 339570000x + 509355000x + 207515000x - 188650000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 582847750x + 874271625x + 268109965x - 279766920)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 354852750x - 1324609125x + 1500660735x - 463534680 +--R / +--R 4 3 2 +--+ +--+ +--R (246960x - 222264x - 373184x + 46648x + 82320)\|21 \|55 +--R + +--R 4 3 2 +--R - 8643600x + 7203000x + 12619656x - 1498224x - 2765952 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (3457440x + 921984x - 2132088x - 288120x + 345744)\|55 +--R + +--R 5 4 3 2 +--+ +--R (1234800x - 3087000x - 87808x + 3218712x + 38416x - 658560)\|21 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-328/15625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-35128/15625*_ + sqrt(1-2*x)-172/3125*(2+3*x)^2*sqrt(1-2*x)+64/2625*(2+3*x)^3*_ + sqrt(1-2*x)+11/75*(2+3*x)^4*sqrt(1-2*x)-1/5*(2+3*x)^5*_ + sqrt(1-2*x)/(3+5*x)-4/15625*(2216+3625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 11480x - 6888)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072) +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (546875x + 328125)\|55 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (5740x + 3444)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R (1181250x + 3864375x + 4760100x + 2225760x - 1133340x - 862072) +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (546875x + 328125)\|55 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 164log(-----------------------------) + 328atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 15625\|55 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 820x + 1312)\|55 + (820x - 1312)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 328x + 164)\|5 \|11 \|55 + 18040x - 9020 +--R / +--R 2 +--------+ +--R (8593750x + 859375x - 2578125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (781250x - 1171875x - 359375x + 375000)\|55 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=-262/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3018/3125*sqrt(1-2*x)-_ + 3/25*(2+3*x)*sqrt(1-2*x)+12/625*(2+3*x)^2*sqrt(1-2*x)+_ + 27/175*(2+3*x)^3*sqrt(1-2*x)-1/5*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 9170x - 5502)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (109375x + 65625)\|55 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (4585x + 2751)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (101250x + 258525x + 206415x - 52485x - 63088)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (109375x + 65625)\|55 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 131log(-----------------------------) + 262atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3125\|55 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 655x + 1048)\|55 + (655x - 1048)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 262x + 131)\|5 \|11 \|55 + 14410x - 7205 +--R / +--R 2 +--------+ +--R (1718750x + 171875x - 515625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (156250x - 234375x - 71875x + 75000)\|55 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-196/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-294/625*sqrt(1-2*x)+_ + 21/125*(2+3*x)^2*sqrt(1-2*x)-1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 980x - 588)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (3125x + 1875)\|55 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (490x + 294)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (1350x + 2385x - 90x - 622)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (3125x + 1875)\|55 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 98log(-----------------------------) + 196atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 625\|55 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 490x + 784)\|55 + (490x - 784)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 196x + 98)\|5 \|11 \|55 + 10780x - 5390 +--R / +--R 2 +--------+ +--R (343750x + 34375x - 103125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (31250x - 46875x - 14375x + 15000)\|55 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-3/25*(1-2*x)^(3/2)-1/275*(1-2*x)^(3/2)/(3+5*x)-_ + 26/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+26/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R (- 130x - 78)atanh(---------------) + (30x + 15x - 2)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (65x + 39)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (30x + 15x - 2)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (125x + 75)\|55 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 13log(-----------------------------) + 26atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 65x + 104)\|55 + (65x - 104)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 26x + 13)\|5 \|11 \|55 + 1430x - 715 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-1/55*(1-2*x)^(3/2)/(3+5*x)-64/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+64/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 320x - 192)atanh(---------------) + (30x + 17)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (160x + 96)log(-----------------------------) + (30x + 17)\|55 \|- 2x + 1 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +--+ +--R (125x + 75)\|55 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 32log(-----------------------------) + 64atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 160x + 256)\|55 + (160x - 256)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 64x + 32)\|5 \|11 \|55 + 3520x - 1760 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^2 +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/5*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (10x + 6)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------- +--R +--+ +--R (25x + 15)\|55 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (5x + 3)log(-------------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) --------------------------------------------------------------- +--R +--+ +--R (25x + 15)\|55 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55 +--R + +--R - 110x + 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2750x + 275x - 825)\|- 2x + 1 + (- 250x + 375x + 115x - 120)\|55 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=-2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)+68*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 +--R (- 10x - 6)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (340x + 204)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +--+ +--R (5x + 3)\|55 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5 +--R (5x + 3)\|21 \|55 log(-------------------------) +--R 3x + 2 +--R + +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (170x + 102)log(-------------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R / +--R +--+ +--R (5x + 3)\|55 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|21 \|- 2x + 1 + 3x - 5 +--R \|21 \|55 log(-------------------------) +--R 3x + 2 +--R + +--R +--------+ +--+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 +--R 34log(-------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R 2\|21 \|55 atanh(---------------) - 68atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 204x - 34x + 68)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (75x - 200x + 53x + 120)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 45x + 222x - 365x + 200 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 330x + 715x - 275)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 1530x + 3978x - 748x - 2720)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (11550x + 1155x - 3465)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30x - 113x + 129x - 40)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 612x + 918x + 374x - 340)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1050x + 1575x + 483x - 504)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (1020x - 1462x - 612x + 544)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1650x - 2585x - 770x + 825)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 990x + 3795x - 4400x + 1375 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (150x - 125x - 219x + 26x + 48)\|21 \|55 - 4950x + 4455x +--R + +--R 2 +--R 7480x - 935x - 1650 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (450x - 1125x - 32x + 1173x + 14x - 240)\|55 +--R + +--R 4 3 2 +--+ +--R (3300x + 880x - 2035x - 275x + 330)\|21 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-138*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+134*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-10*sqrt(1-2*x)/(3+5*x)+sqrt(1-2*x)/_ + ((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (- 2070x - 2622x - 828)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (2010x + 2546x + 804)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (- 30x - 19)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (15x + 19x + 6)\|7 \|11 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (1035x + 1311x + 414)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (1005x + 1273x + 402)\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R (- 30x - 19)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (15x + 19x + 6)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 69\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 67\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 138\|3 \|11 atanh(---------------) - 134\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-7209/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1000*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-1045/14*sqrt(1-2*x)/(3+5*x)+_ + 1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+52/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 648810x - 1254366x - 807408x - 173016)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|5 \|- 2x + 1 +--R (630000x + 1218000x + 784000x + 168000)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (630x + 1218x + 784x + 168)\|7 \|11 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (324405x + 627183x + 403704x + 86508)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--R (315000x + 609000x + 392000x + 84000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 9405x - 12228x - 3965)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (630x + 1218x + 784x + 168)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7209\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7000\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 14418\|3 \|11 atanh(---------------) - 14000\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 14\|7 \|11 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-335579/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+6650*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-48645/98*sqrt(1-2*x)/_ + (3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+139/42*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+7261/147*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +-+ +--R (- 90606330x - 235576458x - 229536036x - 99331384x - 16107792)\|3 +--R * +--R +-+ +--------+ +--R +--+ \|3 \|- 2x + 1 +--R \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (87979500x + 228746700x + 222881400x + 96451600x + 15640800)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--+ +--R (45303165x + 117788229x + 114768018x + 49665692x + 8053896)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +-+ +--R (43989750x + 114373350x + 111440700x + 48225800x + 7820400)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 1313415x - 2583264x - 1692159x - 369116)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (13230x + 34398x + 33516x + 14504x + 2352)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 335579\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 325850\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 671158\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 651700\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 98\|7 \|11 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-12803/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-10017/34375*_ + sqrt(1-2*x)+21/550*(2+3*x)*sqrt(1-2*x)+1428/6875*(2+3*x)^2*_ + sqrt(1-2*x)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2-131/550*_ + (2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 640150x - 768180x - 230454)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1718750x + 2062500x + 618750)\|55 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (320075x + 384090x + 115227)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (445500x + 1103850x + 506880x - 200305x - 121976)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1718750x + 2062500x + 618750)\|55 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 12803log(-----------------------------) + 25606atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 68750\|55 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 64015x + 102424)\|55 + (64015x - 102424)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 25606x + 12803)\|5 \|11 \|55 + 1408330x - 704165 +--R / +--R 2 +--------+ +--R (37812500x + 3781250x - 11343750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3437500x - 5156250x - 1581250x + 1650000)\|55 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-1267/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+623/1375*sqrt(1-2*x)-_ + 7/2750*(46-225*x)*sqrt(1-2*x)-1/10*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 49/275*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 63350x - 76020x - 22806)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (68750x + 82500x + 24750)\|55 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (31675x + 38010x + 11403)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (9900x + 12870x + 4555x + 236)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (68750x + 82500x + 24750)\|55 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 1267log(-----------------------------) + 2534atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 2750\|55 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 6335x + 10136)\|55 + (6335x - 10136)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2534x + 1267)\|5 \|11 \|55 + 139370x - 69685 +--R / +--R 2 +--------+ +--R (1512500x + 151250x - 453750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (137500x - 206250x - 63250x + 66000)\|55 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-1/550*(1-2*x)^(3/2)/(3+5*x)^2-133/6050*(1-2*x)^(3/2)/(3+5*x)-_ + 409/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+409/3025*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 20450x - 24540x - 7362)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (1980x + 2245x + 632)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (10225x + 12270x + 3681)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (1980x + 2245x + 632)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 409log(-----------------------------) + 818atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 550\|55 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 2045x + 3272)\|55 + (2045x - 3272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 818x + 409)\|5 \|11 \|55 + 44990x - 22495 +--R / +--R 2 +--------+ +--R (302500x + 30250x - 90750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (27500x - 41250x - 12650x + 13200)\|55 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-1/110*(1-2*x)^(3/2)/(3+5*x)^2+67/275*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-67/550*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (3350x + 4020x + 1206)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 325x - 206)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (1675x + 2010x + 603)log(-------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 325x - 206)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (13750x + 16500x + 4950)\|55 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 67log(-------------------------------) - 134atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 550\|55 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (134x - 67)\|5 \|11 \|55 - 7370x + 3685 +--R / +--R 2 +--------+ +--R (302500x + 30250x - 90750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 27500x + 41250x + 12650x - 13200)\|55 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^3 +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=1/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/10*sqrt(1-2*x)/(3+5*x)^2+_ + 1/110*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (50x + 60x + 18)atanh(---------------) + (5x - 8)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R 2 +--+ +--R (2750x + 3300x + 990)\|55 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (25x + 30x + 9)log(-------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (5x - 8)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2750x + 3300x + 990)\|55 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 110\|55 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +-+ +--+ +--+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 + (2x - 1)\|5 \|11 \|55 +--R + +--R - 110x + 55 +--R / +--R 2 +--------+ +--R (60500x + 6050x - 18150)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 5500x + 8250x + 2530x - 2640)\|55 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-2243/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-1/2*sqrt(1-2*x)/(3+5*x)^2+67/22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ +--+ \|3 \|- 2x + 1 +--R (3300x + 3960x + 1188)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 112150x - 134580x - 40374)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (335x + 190)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (550x + 660x + 198)\|55 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (56075x + 67290x + 20187)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R (1650x + 1980x + 594)\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (335x + 190)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (550x + 660x + 198)\|55 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 2243log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 66\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 132\|21 \|55 atanh(---------------) + 4486atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 22\|55 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 13458x - 2243x + 4486)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (4950x - 13200x + 3498x + 7920)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 3015x + 14769x - 24112x + 13120 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 22110x + 47135x - 18040)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 100935x + 262431x - 49346x - 179440)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (762300x + 76230x - 228690)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2010x + 7501x - 8496x + 2624)\|21 +--R + +--R 3 2 +-+ +--+ +--R (40374x - 60561x - 24673x + 22430)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (69300x - 103950x - 31878x + 33264)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 67290x + 96449x + 40374x - 35888)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 108900x + 170610x + 50820x - 54450)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 66330x - 251955x + 289795x - 90200 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (3300x - 2750x - 4818x + 572x + 1056)\|21 \|55 - 108900x +--R + +--R 3 2 +--R 98010x + 164560x - 20570x - 36300 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 9900x + 24750x + 704x - 25806x - 308x + 5280)\|55 +--R + +--R 4 3 2 +--+ +--R (- 72600x - 19360x + 44770x + 6050x - 7260)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=624*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-6665/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-15/2*sqrt(1-2*x)/_ + (3+5*x)^2+sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+995/22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (1029600x + 1921920x + 1194336x + 247104)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 999750x - 1866200x - 1159710x - 239940)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (1650x + 3080x + 1914x + 396)\|7 \|11 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (499875x + 933100x + 579855x + 119970)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (514800x + 960960x + 597168x + 123552)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (14925x + 18410x + 5662)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (1650x + 3080x + 1914x + 396)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 6665\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 6864\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 13728\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 13330\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 22\|7 \|11 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=43467/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-66325/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1045/14*_ + sqrt(1-2*x)/(3+5*x)^2+1/2*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 139/14*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+34655/77*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--R (215161650x + 545076180x + 517344234x + 218030472x + 34425864)\|3 +--R * +--R +-+ +--------+ +--R +--+ \|3 \|- 2x + 1 +--R \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--R (- 208923750x - 529273500x - 502345550x - 211709400x - 33427800)\|5 +--R * +--R +-+ +--------+ +--R +-+ \|5 \|- 2x + 1 +--R \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (104461875x + 264636750x + 251172775x + 105854700x + 16713900)\|5 +--R * +--R +-+ +--------+ +--+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--R (107580825x + 272538090x + 258672117x + 109015236x + 17212932)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (3118950x + 5926515x + 3748007x + 788875)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (34650x + 87780x + 83314x + 35112x + 5544)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 464275\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 478137\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 956274\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 928550\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 154\|7 \|11 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=2528082/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 551075/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_ + 182335/294*sqrt(1-2*x)/(3+5*x)^2+1/3*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^2)+_ + 29/7*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+4042/49*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^2)+4031135/1078*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 37542017700x + 120134456640x + 153671992452x + 98221041864x +--R + +--R 31368441456x + 4004481888 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 36453611250x - 116651556000x - 149216782050x - 95373448100x +--R + +--R - 30459017400x - 3888385200 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 18226805625x + 58325778000x + 74608391025x + 47686724050x +--R + +--R 15229508700x + 1944192600 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 18771008850x + 60067228320x + 76835996226x + 49110520932x +--R + +--R 15684220728x + 2002240944 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (544203225x + 1396877220x + 1343346156x + 573620246x + 91763734)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (727650x + 2328480x + 2978514x + 1903748x + 607992x + 77616)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 27002675\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 27808902\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 55617804\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 54005350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1078\|7 \|11 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 7290x - 29889x - 49329x - 39312x - 11340x + 5040x + 5264x +--R + +--R 1664x + 192 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-1294139/640*(1-2*x)^(5/2)+559433/128*(1-2*x)^(7/2)-_ + 564235/128*(1-2*x)^(9/2)+3658095/1408*(1-2*x)^(11/2)-_ + 1580985/1664*(1-2*x)^(13/2)+136647/640*(1-2*x)^(15/2)-_ + 59049/2176*(1-2*x)^(17/2)+3645/2432*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x +--R + +--R 4 3 2 +--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 230945 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R - 177219900x - 806871780x - 1489122063x - 1322260632x - 372044232x +--R + +--R 4 3 2 +--R 342957860x + 377036800x + 136800176x - 7336416x - 51677856 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 230945 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 2430x - 8343x - 10881x - 5850x + 120x + 1600x + 688x + 96) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-184877/320*(1-2*x)^(5/2)+8575/8*(1-2*x)^(7/2)-173215/192*(1-2*x)^(9/2)+_ + 37485/88*(1-2*x)^(11/2)-97335/832*(1-2*x)^(13/2)+_ + 351/20*(1-2*x)^(15/2)-1215/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x +--R + +--R 3 2 +--R 19014940x + 9775332x + 488008x - 3012632 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 10424700x - 40216176x - 59295159x - 35057799x + 5198095x +--R + +--R 3 2 +--R 19014940x + 9775332x + 488008x - 3012632 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 810x - 2241x - 2133x - 528x + 392x + 272x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-26411/160*(1-2*x)^(5/2)+8183/32*(1-2*x)^(7/2)-8281/48*(1-2*x)^(9/2)+_ + 10773/176*(1-2*x)^(11/2)-4671/416*(1-2*x)^(13/2)+27/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x +--R + +--R 36368x - 66592 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 231660x - 730620x - 793395x - 184090x + 296840x + 243312x +--R + +--R 36368x - 66592 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=-3773/80*(1-2*x)^(5/2)+469/8*(1-2*x)^(7/2)-119/4*(1-2*x)^(9/2)+_ + 621/88*(1-2*x)^(11/2)-135/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 715 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (- 29700x - 72360x - 48065x + 15945x + 31589x + 8666x - 8494)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 715 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-539/40*(1-2*x)^(5/2)+101/8*(1-2*x)^(7/2)-103/24*(1-2*x)^(9/2)+_ + 45/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1 +--R (2) ------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 2700x - 4580x - 755x + 2484x + 1216x - 764)\|- 2x + 1 +--R (3) ------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-77/20*(1-2*x)^(5/2)+17/7*(1-2*x)^(7/2)-5/12*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1 +--R (2) ------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 700x - 640x + 393x + 437x - 193)\|- 2x + 1 +--R (3) ------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x) +--R +--R +--R 2 +--------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-11/10*(1-2*x)^(5/2)+5/14*(1-2*x)^(7/2) +--R +--R +--R 3 2 +--------+ +--R (- 100x - 4x + 79x - 26)\|- 2x + 1 +--R (2) ------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 100x - 4x + 79x - 26)\|- 2x + 1 +--R (3) ------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x) +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-2/27*(1-2*x)^(3/2)-1/3*(1-2*x)^(5/2)+14/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)-14/27*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 2 +-+ +--------+ +--R 14\|7 atanh(---------------) + (- 36x + 40x - 25)\|3 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--------+ +--R (- 36x + 40x - 25)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 27\|3 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=76/189*(1-2*x)^(3/2)+1/21*(1-2*x)^(5/2)/(2+3*x)-76/27*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+76/27*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 228x - 152)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--------+ +--R (- 60x + 212x + 175)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (81x + 54)\|3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (114x + 76)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--------+ +--R (- 60x + 212x + 175)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (81x + 54)\|3 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 38\|7 log(-------------------------------) + 76\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 27\|3 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) --------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=1/42*(1-2*x)^(5/2)/(2+3*x)^2-71/126*(1-2*x)^(3/2)/(2+3*x)+_ + 71/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-71/63*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (1278x + 1704x + 568)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 235x - 101)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (162x + 216x + 72)\|21 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (639x + 852x + 284)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 235x - 101)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (162x + 216x + 72)\|21 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 71log(-------------------------------) - 142atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 18\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 213x + 355)\|21 + (213x - 355)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (142x - 71)\|3 \|7 \|21 - 2982x + 1491 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2268x + 378x - 756)\|- 2x + 1 + (- 324x + 486x + 198x - 180)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=1/63*(1-2*x)^(5/2)/(2+3*x)^3-52/189*(1-2*x)^(3/2)/(2+3*x)^2-_ + 104/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+52/189*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2808x - 5616x - 3744x - 832)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (792x + 664x + 107)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (5103x + 10206x + 6804x + 1512)\|21 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (1404x + 2808x + 1872x + 416)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (792x + 664x + 107)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (5103x + 10206x + 6804x + 1512)\|21 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 52log(-----------------------------) + 104atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 189\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 156x + 260)\|21 + (156x - 260)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 104x + 52)\|3 \|7 \|21 + 2184x - 1092 +--R / +--R 2 +--------+ 3 2 +--+ +--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=1/84*(1-2*x)^(5/2)/(2+3*x)^4-137/756*(1-2*x)^(3/2)/(2+3*x)^3-_ + 137/5292*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+137/1512*_ + sqrt(1-2*x)/(2+3*x)^2-137/10584*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (- 22194x - 59184x - 59184x - 26304x - 4384)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (11097x + 29592x + 29592x + 13152x + 2192) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 3699x + 13245x + 7990x - 970)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (857304x + 2286144x + 2286144x + 1016064x + 169344)\|21 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 137log(-----------------------------) + 274atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 10584\|21 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 411x + 685)\|21 + (411x - 685)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 274x + 137)\|3 \|7 \|21 + 5754x - 2877 +--R / +--R 2 +--------+ +--R (1333584x + 222264x - 444528)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (190512x - 285768x - 116424x + 105840)\|21 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +--R (- 10x - x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=1/105*(1-2*x)^(5/2)/(2+3*x)^5-17/126*(1-2*x)^(3/2)/(2+3*x)^4-_ + 17/6174*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+17/378*_ + sqrt(1-2*x)/(2+3*x)^3-17/5292*sqrt(1-2*x)/(2+3*x)^2-17/12348*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 41310x - 137700x - 183600x - 122400x - 40800x - 5440) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (20655x + 68850x + 91800x + 61200x + 20400x + 2720) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 6885x - 23715x + 48252x + 23998x - 7912)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (15002820x + 50009400x + 66679200x + 44452800x + 14817600x + 1975680) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 17log(-----------------------------) + 34atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 12348\|21 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 51x + 85)\|21 + (51x - 85)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 34x + 17)\|3 \|7 \|21 + 714x - 357 +--R / +--R 2 +--------+ +--R (1555848x + 259308x - 518616)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (222264x - 333396x - 135828x + 123480)\|21 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 4050x - 13635x - 17388x - 9039x + 376x + 2536x + 1056x + 144) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-290521/320*(1-2*x)^(5/2)+54439/32*(1-2*x)^(7/2)-832951/576*_ + (1-2*x)^(9/2)+121359/176*(1-2*x)^(11/2)-159111/832*(1-2*x)^(13/2)+_ + 927/32*(1-2*x)^(15/2)-2025/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x +--R + +--R 3 2 +--R 90028420x + 44740356x + 1821784x - 13931096 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 52123500x - 197142660x - 284055255x - 161801280x + 29120005x +--R + +--R 3 2 +--R 90028420x + 44740356x + 1821784x - 13931096 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=-41503/160*(1-2*x)^(5/2)+13013/32*(1-2*x)^(7/2)-39977/144*(1-2*x)^(9/2)+_ + 17541/176*(1-2*x)^(11/2)-7695/416*(1-2*x)^(13/2)+45/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x +--R + +--R 155842x - 307478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 1158300x - 3564000x - 3749895x - 776255x + 1436365x + 1121793x +--R + +--R 155842x - 307478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=-5929/80*(1-2*x)^(5/2)+187/2*(1-2*x)^(7/2)-3467/72*(1-2*x)^(9/2)+_ + 255/22*(1-2*x)^(11/2)-225/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x +--R + +--R - 117478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 445500x - 1050300x - 661435x + 248990x + 441543x + 114182x +--R + +--R - 117478 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6435 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-847/40*(1-2*x)^(5/2)+1133/56*(1-2*x)^(7/2)-505/72*(1-2*x)^(9/2)+_ + 75/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1 +--R (2) ---------------------------------------------------------------------- +--R 3465 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 94500x - 152600x - 19385x + 82617x + 37753x - 24617)\|- 2x + 1 +--R (3) ---------------------------------------------------------------------- +--R 3465 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-121/20*(1-2*x)^(5/2)+55/14*(1-2*x)^(7/2)-25/36*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1 +--R (2) ----------------------------------------------------- +--R 315 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 3500x - 2900x + 1977x + 1948x - 887)\|- 2x + 1 +--R (3) ----------------------------------------------------- +--R 315 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2/81*(1-2*x)^(3/2)-26/63*(1-2*x)^(5/2)-5/21*(1-2*x)^(5/2)*(3+5*x)-_ + 14/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+14/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 98\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 49\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (- 2700x + 144x + 1853x - 527)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 567\|3 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(-------------------------------) + 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-146/567*(1-2*x)^(3/2)-5/9*(1-2*x)^(5/2)-1/63*(1-2*x)^(5/2)/(2+3*x)+_ + 146/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-146/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (438x + 292)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (219x + 146)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (- 540x + 300x - 187x - 425)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 73\|7 log(---------------------------------) - 146\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=2873/3969*(1-2*x)^(3/2)-1/126*(1-2*x)^(5/2)/(2+3*x)^2+_ + 47/294*(1-2*x)^(5/2)/(2+3*x)-2873/81*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+2873/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 51714x - 68952x - 22984)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1458x + 1944x + 648)\|21 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (25857x + 34476x + 11492)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 1800x + 5520x + 10195x + 3803)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1458x + 1944x + 648)\|21 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2873log(-----------------------------) + 5746atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 162\|21 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 8619x + 14365)\|21 + (8619x - 14365)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 5746x + 2873)\|3 \|7 \|21 + 120666x - 60333 +--R / +--R 2 +--------+ 3 2 +--+ +--R (20412x + 3402x - 6804)\|- 2x + 1 + (2916x - 4374x - 1782x + 1620)\|21 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/189*(1-2*x)^(5/2)/(2+3*x)^3+209/2646*(1-2*x)^(5/2)/(2+3*x)^2-_ + 7559/7938*(1-2*x)^(3/2)/(2+3*x)+7559/567*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-7559/3969*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (408186x + 816372x + 544248x + 120944)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (30618x + 61236x + 40824x + 9072)\|21 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (204093x + 408186x + 272124x + 60472) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 37800x - 100809x - 82493x - 21424)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (30618x + 61236x + 40824x + 9072)\|21 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 7559log(-------------------------------) - 15118atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 1134\|21 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 22677x + 37795)\|21 + (22677x - 37795)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (15118x - 7559)\|3 \|7 \|21 - 317478x + 158739 +--R / +--R 2 +--------+ +--R (142884x + 23814x - 47628)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 20412x + 30618x + 12474x - 11340)\|21 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1/252*(1-2*x)^(5/2)/(2+3*x)^4+277/5292*(1-2*x)^(5/2)/(2+3*x)^3-_ + 14423/31752*(1-2*x)^(3/2)/(2+3*x)^2-14423/15876*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+14423/31752*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 2336526x - 6230736x - 6230736x - 2769216x - 461536) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1168263x + 3115368x + 3115368x + 1384608x + 230768) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (668979x + 988035x + 453730x + 60890)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (2571912x + 6858432x + 6858432x + 3048192x + 508032)\|21 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 14423log(-----------------------------) + 28846atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 31752\|21 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 43269x + 72115)\|21 + (43269x - 72115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 28846x + 14423)\|3 \|7 \|21 + 605766x - 302883 +--R / +--R 2 +--------+ +--R (4000752x + 666792x - 1333584)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (571536x - 857304x - 349272x + 317520)\|21 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-1/315*(1-2*x)^(5/2)/(2+3*x)^5+23/588*(1-2*x)^(5/2)/(2+3*x)^4-_ + 4693/15876*(1-2*x)^(3/2)/(2+3*x)^3-4693/111132*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+4693/31752*sqrt(1-2*x)/(2+3*x)^2-_ + 4693/222264*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 11403990x - 38013300x - 50684400x - 33789600x - 11263200x +--R + +--R - 1501760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x +--R + +--R 35562240 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (5701995x + 19006650x + 25342200x + 16894800x + 5631600x + 750880) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 1900665x + 5801265x + 8540988x + 2143262x - 292028)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 270050760x + 900169200x + 1200225600x + 800150400x + 266716800x +--R + +--R 35562240 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4693log(-----------------------------) + 9386atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 222264\|21 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 14079x + 23465)\|21 + (14079x - 23465)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 9386x + 4693)\|3 \|7 \|21 + 197106x - 98553 +--R / +--R 2 +--------+ +--R (28005264x + 4667544x - 9335088)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (4000752x - 6001128x - 2444904x + 2222640)\|21 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-1/378*(1-2*x)^(5/2)/(2+3*x)^6+59/1890*(1-2*x)^(5/2)/(2+3*x)^5-_ + 991/4536*(1-2*x)^(3/2)/(2+3*x)^4-991/222264*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+991/13608*sqrt(1-2*x)/(2+3*x)^3-_ + 991/190512*sqrt(1-2*x)/(2+3*x)^2-991/444528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 7224390x - 28897560x - 48162600x - 42811200x - 21405600x +--R + +--R - 5708160x - 634240 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 3612195x + 14448780x + 24081300x + 21405600x + 10702800x +--R + +--R 2854080x + 317120 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (- 1204065x - 4950045x + 6094818x + 9658494x + 1262200x - 858112) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 991log(-----------------------------) + 1982atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2973x + 4955)\|21 + (2973x - 4955)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1982x + 991)\|3 \|7 \|21 + 41622x - 20811 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8001504x - 12002256x - 4889808x + 4445280)\|21 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 20250x - 80325x - 127845x - 97359x - 25237x + 13808x + 12888x +--R + +--R 3888x + 432 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-3195731/640*(1-2*x)^(5/2)+1405173/128*(1-2*x)^(7/2)-_ + 4324397/384*(1-2*x)^(9/2)+9504551/1408*(1-2*x)^(11/2)-_ + 4177401/1664*(1-2*x)^(13/2)+73431/128*(1-2*x)^(15/2)-_ + 161325/2176*(1-2*x)^(17/2)+10125/2432*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 +--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x +--R + +--R 5 4 3 2 +--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x +--R + +--R - 369438704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 692835 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 +--R - 1476832500x - 6503854500x - 11568656385x - 9793273050x +--R + +--R 5 4 3 2 +--R - 2388733575x + 2741637820x + 2751200080x + 942365544x - 70133984x +--R + +--R - 369438704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 692835 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R (- 6750x - 22275x - 27765x - 13943x + 883x + 4014x + 1620x + 216) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-456533/320*(1-2*x)^(5/2)+43197/16*(1-2*x)^(7/2)-_ + 444983/192*(1-2*x)^(9/2)+98209/88*(1-2*x)^(11/2)-_ + 260055/832*(1-2*x)^(13/2)+765/16*(1-2*x)^(15/2)-3375/1088*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x +--R + +--R 3 2 +--R 47302655x + 22736811x + 717734x - 7158706 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R - 28957500x - 107335800x - 151076475x - 82806465x + 17644040x +--R + +--R 3 2 +--R 47302655x + 22736811x + 717734x - 7158706 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 36465 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (- 2250x - 5925x - 5305x - 1111x + 1035x + 648x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-65219/160*(1-2*x)^(5/2)+20691/32*(1-2*x)^(7/2)-_ + 21439/48*(1-2*x)^(9/2)+28555/176*(1-2*x)^(11/2)-975/32*(1-2*x)^(13/2)+_ + 75/32*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x +--R + +--R - 12136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 165 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 49500x - 148500x - 151275x - 27520x + 59255x + 44166x + 5684x +--R + +--R - 12136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 165 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (- 750x - 1475x - 785x + 153x + 243x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-9317/80*(1-2*x)^(5/2)+8349/56*(1-2*x)^(7/2)-935/12*(1-2*x)^(9/2)+_ + 1675/88*(1-2*x)^(11/2)-375/208*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x +--R + +--R - 421301 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 15015 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 1732500x - 3948000x - 2351825x + 996295x + 1597776x + 389509x +--R + +--R - 421301 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 15015 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (1) (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-1331/40*(1-2*x)^(5/2)+1815/56*(1-2*x)^(7/2)-275/24*(1-2*x)^(9/2)+_ + 125/88*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 52500x - 80500x - 7225x + 43482x + 18593x - 12592)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=2/27*(1-2*x)^(3/2)*(3+5*x)^3+14/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-72742/14175*sqrt(1-2*x)-919/4725*(3+5*x)^2*_ + sqrt(1-2*x)+26/315*(3+5*x)^3*sqrt(1-2*x)-1/8505*(14711+17779*x)*_ + sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 98\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 1701\|3 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 49\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 31500x - 23400x + 17649x + 15679x - 7456)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 1701\|3 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 7\|7 log(---------------------------------) - 14\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 243\|3 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)-8/9*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-1832/315*sqrt(1-2*x)+2/63*(4-239*x)*sqrt(1-2*x)+_ + 67/35*(3+5*x)^2*sqrt(1-2*x)-2/7*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 168x - 112)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (189x + 126)\|3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (84x + 56)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 1500x - 780x + 1005x + 442x - 85)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (189x + 126)\|3 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 4\|7 log(-------------------------------) + 8\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +-+ +--R 9\|3 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^2+887/27*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+13*sqrt(1-2*x)-5/54*(67-343*x)*sqrt(1-2*x)-_ + 31/3*(3+5*x)^2*sqrt(1-2*x)+6*(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (15966x + 21288x + 7096)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 2 +--+ +--------+ +--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (486x + 648x + 216)\|21 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (7983x + 10644x + 3548)log(-------------------------------) +--R 3x + 2 +--R + +--R 4 2 +--+ +--------+ +--R (- 1800x - 570x - 2965x - 1367)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (486x + 648x + 216)\|21 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 887log(-------------------------------) - 1774atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 54\|21 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2661x + 4435)\|21 + (2661x - 4435)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1774x - 887)\|3 \|7 \|21 - 37254x + 18627 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6804x + 1134x - 2268)\|- 2x + 1 + (- 972x + 1458x + 594x - 540)\|21 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^3-36038/567*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-830/27*sqrt(1-2*x)+5/567*(1163-7265*x)*_ + sqrt(1-2*x)+251/63*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)+2*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 973026x - 1946052x - 1297368x - 288304)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (15309x + 30618x + 20412x + 4536)\|21 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (486513x + 973026x + 648684x + 144152) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 31500x + 81900x + 259614x + 199243x + 47939)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (15309x + 30618x + 20412x + 4536)\|21 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 18019log(-----------------------------) + 36038atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 567\|21 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 54057x + 90095)\|21 + (54057x - 90095)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 36038x + 18019)\|3 \|7 \|21 + 756798x - 378399 +--R / +--R 2 +--------+ +--R (71442x + 11907x - 23814)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (10206x - 15309x - 6237x + 5670)\|21 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^4+13243/588*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-5305/588*sqrt(1-2*x)+337/392*(3+5*x)*_ + sqrt(1-2*x)/(2+3*x)+13/56*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+_ + (3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 4 3 2 +--R (2145366x + 5720976x + 5720976x + 2542656x + 423776) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1072683x + 2860488x + 2860488x + 1271328x + 211888) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 196000x - 661639x - 788415x - 401850x - 74810)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 13243log(-------------------------------) - 26486atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 39729x + 66215)\|21 + (39729x - 66215)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (26486x - 13243)\|3 \|7 \|21 - 556206x + 278103 +--R / +--R 2 +--------+ +--R (148176x + 24696x - 49392)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 21168x + 31752x + 12936x - 11760)\|21 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^5-13892/9261*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+1/1323*(136-19*x)*sqrt(1-2*x)/(2+3*x)^2-_ + 3335/3087*sqrt(1-2*x)/(2+3*x)-67/315*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3+_ + 3/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 16878780x - 56262600x - 75016800x - 50011200x - 16670400x +--R + +--R - 2222720 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (8439390x + 28131300x + 37508400x + 25005600x + 8335200x + 1111360) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (4904370x + 10375830x + 7992771x + 2619854x + 300049)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (11252115x + 37507050x + 50009400x + 33339600x + 11113200x + 1481760) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 6946log(-----------------------------) + 13892atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 9261\|21 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 20838x + 34730)\|21 + (20838x - 34730)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 13892x + 6946)\|3 \|7 \|21 + 291732x - 145866 +--R / +--R 2 +--------+ +--R (1166886x + 194481x - 388962)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (166698x - 250047x - 101871x + 92610)\|21 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^6-15313/222264*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/158760*(9323-8405*x)*_ + sqrt(1-2*x)/(2+3*x)^3-43207/63504*sqrt(1-2*x)/(2+3*x)^2-_ + 15313/444528*sqrt(1-2*x)/(2+3*x)-653/2520*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^4+2/5*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 111631770x - 446527080x - 744211800x - 661521600x - 330760800x +--R + +--R - 88202880x - 9800320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x +--R + +--R - 1660816 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 55815885x + 223263540x + 372105900x + 330760800x + 165380400x +--R + +--R 44101440x + 4900160 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 18605295x + 46991565x + 122053374x + 75153042x + 10947400x +--R + +--R - 1660816 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 +--R 1620304560x + 6481218240x + 10802030400x + 9601804800x +--R + +--R 2 +--R 4800902400x + 1280240640x + 142248960 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 15313log(-----------------------------) + 30626atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 45939x + 76565)\|21 + (45939x - 76565)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 30626x + 15313)\|3 \|7 \|21 + 643146x - 321573 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8001504x - 12002256x - 4889808x + 4445280)\|21 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +--R (- 250x - 325x - 45x + 81x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^3/(2+3*x)^7-4369/605052*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/61740*(2201-2675*x)*_ + sqrt(1-2*x)/(2+3*x)^4-5471/13230*sqrt(1-2*x)/(2+3*x)^3-_ + 4369/518616*sqrt(1-2*x)/(2+3*x)^2-4369/1210104*sqrt(1-2*x)/_ + (2+3*x)-173/735*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^5+2/7*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 95550030x - 445900140x - 891800280x - 990889200x - 660592800x +--R + +--R 2 +--R - 264237120x - 58719360x - 5592320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x +--R + +--R - 606784x - 7033976 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 13232487240x + 61751607120x + 123503214240x + 137225793600x +--R + +--R 3 2 +--R 91483862400x + 36593544960x + 8131898880x + 774466560 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 47775015x + 222950070x + 445900140x + 495444600x + 330296400x +--R + +--R 2 +--R 132118560x + 29359680x + 2796160 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R - 15925005x - 76086135x + 42669876x + 182748162x + 98441652x +--R + +--R - 606784x - 7033976 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 13232487240x + 61751607120x + 123503214240x + 137225793600x +--R + +--R 3 2 +--R 91483862400x + 36593544960x + 8131898880x + 774466560 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4369log(-----------------------------) + 8738atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 1210104\|21 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13107x + 21845)\|21 + (13107x - 21845)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 8738x + 4369)\|3 \|7 \|21 + 183498x - 91749 +--R / +--R 2 +--------+ +--R (152473104x + 25412184x - 50824368)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (21781872x - 32672808x - 13311144x + 12101040)\|21 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^6/(3+5*x) +--R +--R +--R 7 6 5 4 2 +--------+ +--R (- 1458x - 5103x - 6804x - 3780x + 1008x + 448x + 64)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^6-22/390625*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-16097737918/1508203125*sqrt(1-2*x)-18395813/12065625*(2+3*x)*_ + sqrt(1-2*x)-32816296/100546875*(2+3*x)^2*sqrt(1-2*x)-_ + 6469823/84459375*(2+3*x)^3*sqrt(1-2*x)-36202/2413125*(2+3*x)^4*_ + sqrt(1-2*x)+683/53625*(2+3*x)^5*sqrt(1-2*x)+2/195*(2+3*x)^6*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 66066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x +--R + +--R 3 2 +--R 61883481375x + 56176961670x + 9645684935x - 15379193944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 1173046875\|5 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33033\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 7 6 5 4 +--R - 45608062500x - 150857437500x - 174123928125x - 49094797500x +--R + +--R 3 2 +--R 61883481375x + 56176961670x + 9645684935x - 15379193944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 1173046875\|5 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 390625\|5 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^5-22/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-158985118/33515625*sqrt(1-2*x)-2803796/20109375*(2+3*x)^2*_ + sqrt(1-2*x)-467323/16891875*(2+3*x)^3*sqrt(1-2*x)+_ + 6673/482625*(2+3*x)^4*sqrt(1-2*x)+158/10725*(2+3*x)^5*sqrt(1-2*x)-_ + 1/100546875*(119316702+198601625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 66066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x +--R + +--R 2 +--R 4276774170x + 1321809935x - 1180568944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33033\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R - 3508312500x - 9100350000x - 6683000625x + 1659418875x +--R + +--R 2 +--R 4276774170x + 1321809935x - 1180568944 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^4-22/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-10083686/4640625*sqrt(1-2*x)-11401/37125*(2+3*x)*_ + sqrt(1-2*x)-17792/309375*(2+3*x)^2*sqrt(1-2*x)+3629/259875*(2+3*x)^3*_ + sqrt(1-2*x)+166/7425*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x +--R + +--R - 7095688 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 21262500x - 39532500x - 9559125x + 21433590x + 12144995x +--R + +--R - 7095688 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^3-22/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-10826/9375*sqrt(1-2*x)+53/5625*(2+3*x)^2*sqrt(1-2*x)+_ + 58/1575*(2+3*x)^3*sqrt(1-2*x)-1/28125*(8664+12625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 462\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 231\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 157500x - 171000x + 83565x + 123295x - 50858)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=2/375*(1-2*x)^(3/2)-18/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(5/2)*(2+3*x)-_ + 22/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+22/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 462\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 231\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (- 13500x - 3060x + 13045x - 3608)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=2/75*(1-2*x)^(3/2)-3/25*(1-2*x)^(5/2)-22/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+22/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 66\|11 atanh(---------------) + (- 180x + 160x + 31)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +--R 375\|5 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 180x + 160x + 31)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 375\|5 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2/15*(1-2*x)^(3/2)-22/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 22/25*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R - 66\|11 atanh(---------------) + (- 20x + 76)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------- +--R +-+ +--R 75\|5 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +-+ +--------+ +--R 33\|11 log(--------------------------------) + (- 20x + 76)\|5 \|- 2x + 1 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +-+ +--R 75\|5 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 11\|11 log(--------------------------------) + 22\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-22/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+14/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)-4/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 70\|5 \|7 atanh(---------------) - 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R + +--R +-+ +-+ +--------+ +--R - 4\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ +-+ +--------+ +--R 35\|5 \|7 log(---------------------------------) - 4\|3 \|5 \|- 2x + 1 +--R 3x + 2 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 35\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 70\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x)/(6+9*x),(1-2*x)^(3/2)/(2+3*x)-_ + 22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+64/3*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(7/3)+2/3*sqrt(1-2*x) +--R +--R +--R (2) +--R [ +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (192x + 128)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R , +--R +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (192x + 128)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (- 198x - 132)\|3 \|11 atanh(---------------) + 7\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (99x + 66)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (96x + 64)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R 7\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (9x + 6)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 33\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 32\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 64\|5 \|7 atanh(---------------) + 66\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 3\|3 \|5 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=1/2*(1-2*x)^(3/2)/(2+3*x)^2+2243/3*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-22*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+67/6*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (40374x + 53832x + 17944)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 1188x - 1584x - 528)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (195x + 137)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (54x + 72x + 24)\|21 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +--R 2 +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R (594x + 792x + 264)\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (20187x + 26916x + 8972)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (195x + 137)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (54x + 72x + 24)\|21 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 66\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2243log(-------------------------------) - 4486atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 132\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 6\|21 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (2970x - 7722x + 1452x + 5280)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 22430x - 2243x + 6729)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 13650x - 29127x + 11151 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (4875x - 23890x + 39019x - 21240)\|21 +--R + +--R 2 +-+ +--+ +--R (457380x + 76230x - 152460)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 168225x + 448600x - 118879x - 269160)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 1950x + 7411x - 8528x + 2655)\|21 +--R + +--R 3 2 +-+ +--+ +--R (41580x - 59598x - 24948x + 22176)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (67290x - 105421x - 31402x + 33645)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 65340x + 98010x + 39930x - 36300)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 112150x + 168225x + 51589x - 53832)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 68250x - 254835x + 288771x - 89208 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (540x - 486x - 816x + 102x + 180)\|21 \|55 - 18900x + 15750x +--R + +--R 2 +--R 27594x - 3276x - 6048 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (7560x + 2016x - 4662x - 630x + 756)\|55 +--R + +--R 5 4 3 2 +--+ +--R (2700x - 6750x - 192x + 7038x + 84x - 1440)\|21 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=1/3*(1-2*x)^(3/2)/(2+3*x)^3+78506/21*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-110*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+17/3*_ + sqrt(1-2*x)/(2+3*x)^2+1138/21*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (2119662x + 4239324x + 2826216x + 628048)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 62370x - 124740x - 83160x - 18480)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (10242x + 13999x + 4797)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (567x + 1134x + 756x + 168)\|21 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (31185x + 62370x + 41580x + 9240)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (1059831x + 2119662x + 1413108x + 314024) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (10242x + 13999x + 4797)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (567x + 1134x + 756x + 168)\|21 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1155\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39253log(-------------------------------) - 78506atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2310\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (51975x - 135135x + 25410x + 92400)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 392530x - 39253x + 117759)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 238980x - 509712x + 195111 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (85350x - 418175x + 682859x - 371640)\|21 +--R + +--R 2 +-+ +--+ +--R (8004150x + 1334025x - 2668050)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2943975x + 7850600x - 2080409x - 4710360)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 34140x + 129716x - 149233x + 46455)\|21 +--R + +--R 3 2 +-+ +--+ +--R (727650x - 1042965x - 436590x + 388080)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1177590x - 1844891x - 549542x + 588795)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1143450x + 1715175x + 698775x - 635250)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1962650x + 2943975x + 902819x - 942072)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1194900x - 4460400x + 5053251x - 1560888 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (1890x - 1701x - 2856x + 357x + 630)\|21 \|55 - 66150x + 55125x +--R + +--R 2 +--R 96579x - 11466x - 21168 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (26460x + 7056x - 16317x - 2205x + 2646)\|55 +--R + +--R 5 4 3 2 +--+ +--R (9450x - 23625x - 672x + 24633x + 294x - 5040)\|21 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=1/4*(1-2*x)^(3/2)/(2+3*x)^4+10990843/588*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-550*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+137/36*_ + sqrt(1-2*x)/(2+3*x)^3+13723/504*sqrt(1-2*x)/(2+3*x)^2+_ + 318643/1176*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1780516566x + 4748044176x + 4748044176x + 2110241856x + 351706976) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 52390800x - 139708800x - 139708800x - 62092800x - 10348800)\|21 +--R * +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (8603361x + 17494905x + 11868230x + 2686470)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--+ +--R (26195400x + 69854400x + 69854400x + 31046400x + 5174400)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (890258283x + 2374022088x + 2374022088x + 1055120928x + 175853488) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (8603361x + 17494905x + 11868230x + 2686470)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (95256x + 254016x + 254016x + 112896x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 323400\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 10990843log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 21981686atanh(---------------) + 646800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (14553000x - 37837800x + 7114800x + 25872000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 109908430x - 10990843x + 32972529)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 66915030x - 142719297x + 54630891 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (23898225x - 117089600x + 191200679x - 104058840)\|21 +--R + +--R 2 +-+ +--+ +--R (2241162000x + 373527000x - 747054000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 824313225x + 2198168600x - 582514679x - 1318901160)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 9559290x + 36320621x - 41785198x + 13007355)\|21 +--R + +--R 3 2 +-+ +--+ +--R (203742000x - 292030200x - 122245200x + 108662400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (329725290x - 516569621x - 153871802x + 164862645)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 320166000x + 480249000x + 195657000x - 177870000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 549542150x + 824313225x + 252789389x - 263780232)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 334575150x - 1248916725x + 1414908831x - 437047128 +--R / +--R 4 3 2 +--+ +--+ +--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55 +--R + +--R 4 3 2 +--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (1481760x + 395136x - 913752x - 123480x + 148176)\|55 +--R + +--R 5 4 3 2 +--+ +--R (529200x - 1323000x - 37632x + 1379448x + 16464x - 282240)\|21 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^6*(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Expression(Integer) +--E 471 + 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Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3438146250x + 11460487500x + 15280650000x + 10187100000x +--R + +--R 3395700000x + 452760000 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 116846400555x + 389488001850x + 519317335800x + 346211557200x +--R + +--R 115403852400x + 15387180320 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1129191435x + 3049001415x + 3088510878x + 1391064622x + 235067382) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (2500470x + 8334900x + 11113200x + 7408800x + 2469600x + 329280)\|21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 2829750\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 96169877log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 192339754atanh(---------------) + 5659500\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (127338750x - 331080750x + 62254500x + 226380000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 961698770x - 96169877x + 288509631)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 585506670x - 1248793833x + 478020249 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (209109525x - 1024534150x + 1673005981x - 910514760)\|21 +--R + +--R 2 +-+ +--+ +--R (19610167500x + 3268361250x - 6536722500)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 7212740775x + 19233975400x - 5097003481x - 11540385240)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 83643810x + 317805469x - 365620472x + 113814345)\|21 +--R + +--R 3 2 +-+ +--+ +--R (1782742500x - 2555264250x - 1069645500x + 950796000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (2885096310x - 4519984219x - 1346378278x + 1442548155)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 2801452500x + 4202178750x + 1711998750x - 1556362500)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4808493850x + 7212740775x + 2211907171x - 2308077048)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 2927533350x - 10928022525x + 12380451909x - 3824161992 +--R / +--R 4 3 2 +--+ +--+ +--R (185220x - 166698x - 279888x + 34986x + 61740)\|21 \|55 +--R + +--R 4 3 2 +--R - 6482700x + 5402250x + 9464742x - 1123668x - 2074464 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (2593080x + 691488x - 1599066x - 216090x + 259308)\|55 +--R + +--R 5 4 3 2 +--+ +--R (926100x - 2315250x - 65856x + 2414034x + 28812x - 493920)\|21 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (- 486x - 1377x - 1350x - 360x + 240x + 176x + 32)\|- 2x + 1 +--R (1) ------------------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^5/(3+5*x)-324/78125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-1270604/859375*sqrt(1-2*x)-9388/515625*_ + (2+3*x)^2*sqrt(1-2*x)+33406/433125*(2+3*x)^3*sqrt(1-2*x)+_ + 4019/12375*(2+3*x)^4*sqrt(1-2*x)-26/275*(2+3*x)^5*sqrt(1-2*x)-_ + 2/2578125*(491178+769625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 124740x - 74844)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x +--R + +--R 2532130x - 23061496 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (30078125x + 18046875)\|5 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (62370x + 37422)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R - 106312500x - 270112500x - 181738125x + 76760550x + 135193430x +--R + +--R 2532130x - 23061496 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (30078125x + 18046875)\|5 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 162\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 324\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)-258/15625*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-110938/140625*sqrt(1-2*x)-83/1125*(2+3*x)*_ + sqrt(1-2*x)+764/9375*(2+3*x)^2*sqrt(1-2*x)+2707/7875*(2+3*x)^3*_ + sqrt(1-2*x)-22/225*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 9030x - 5418)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (546875x + 328125)\|5 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (4515x + 2709)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (- 787500x - 1395000x - 157275x + 924335x + 143235x - 161312)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (546875x + 328125)\|5 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 129\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 258\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-1/5*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)-192/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-1418/3125*sqrt(1-2*x)+2/25*(2+3*x)*_ + sqrt(1-2*x)+237/625*(2+3*x)^2*sqrt(1-2*x)-18/175*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 6720x - 4032)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (109375x + 65625)\|5 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (3360x + 2016)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 67500x - 62100x + 57165x + 27640x - 8738)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (109375x + 65625)\|5 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 96\|11 log(--------------------------------) + 192\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=42/1375*(1-2*x)^(3/2)-9/125*(1-2*x)^(5/2)-1/275*(1-2*x)^(5/2)/(3+5*x)-_ + 126/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+126/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 630x - 378)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (3125x + 1875)\|5 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (315x + 189)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (- 900x + 160x + 935x + 298)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (3125x + 1875)\|5 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 63\|11 log(--------------------------------) + 126\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=4/55*(1-2*x)^(3/2)-1/55*(1-2*x)^(5/2)/(3+5*x)-12/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+12/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R (- 60x - 36)\|11 atanh(---------------) + (- 20x + 60x + 41)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R (125x + 75)\|5 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (30x + 18)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 20x + 60x + 41)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (125x + 75)\|5 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 6\|11 log(--------------------------------) + 12\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} + diff --git a/src/input/rich3k.input.pamphlet b/src/input/rich3k.input.pamphlet new file mode 100644 index 0000000..5349e5c --- /dev/null +++ b/src/input/rich3k.input.pamphlet @@ -0,0 +1,9833 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3k.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 61 matching answers. +\item 39 results where Axiom differs from Rubi +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3k.output +)spool rich3k.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^2 +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-1/5*(1-2*x)^(3/2)/(3+5*x)+6/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-6/25*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +-+ +--------+ +--R (30x + 18)\|11 atanh(---------------) + (- 20x - 23)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +-+ +--R (125x + 75)\|5 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (15x + 9)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R (- 20x - 23)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (125x + 75)\|5 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 3\|11 log(----------------------------------) - 6\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-(1-2*x)^(3/2)/(3+5*x)+72/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)_ + -14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2/5*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (- 350x - 210)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +-+ +-+ +--------+ +--R (360x + 216)\|3 \|11 atanh(---------------) - 11\|3 \|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R (25x + 15)\|3 \|5 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (175x + 105)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (180x + 108)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R - 11\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (25x + 15)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 35\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 36\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 70\|5 \|7 atanh(---------------) - 72\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 5\|3 \|5 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x))+138*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)-134*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 22*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 2010x - 2546x - 804)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (2070x + 2622x + 828)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (- 68x - 43)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (15x + 19x + 6)\|3 \|5 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (1005x + 1273x + 402)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1035x + 1311x + 414)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (- 68x - 43)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (15x + 19x + 6)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 67\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 69\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 134\|5 \|7 atanh(---------------) - 138\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R \|3 \|5 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x))-2311*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)+204*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-335/2*_ + sqrt(1-2*x)/(3+5*x)+17*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ \|3 \|- 2x + 1 +--R (- 207990x - 402114x - 258832x - 55464)\|3 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +--+ \|5 \|- 2x + 1 +--R (18360x + 35496x + 22848x + 4896)\|7 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +--R (90x + 174x + 112x + 24)\|7 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (103995x + 201057x + 129416x + 27732)\|3 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (9180x + 17748x + 11424x + 2448)\|7 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (- 3015x - 3920x - 1271)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +--R (90x + 174x + 112x + 24)\|7 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2311\|3 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +-+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 204\|7 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 4622\|3 atanh(---------------) - 408\|7 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 2\|7 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +-+ +--+ +-+ +--+ +--R ((1530x - 4998x + 4080)\|5 \|7 \|11 + (- 78540x + 39270)\|3 )\|55 +--R + +--R +-+ +-+ +--+ 2 +-+ +--R (78540x - 39270)\|3 \|5 \|11 + (- 84150x + 274890x - 224400)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ +--R (- 7140x + 14994x - 5712)\|3 \|5 \|11 +--R + +--R 2 +-+ +--R (- 33660x + 72930x - 28050)\|7 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +-+ +-+ +--+ 2 +-+ +--R (33660x - 72930x + 28050)\|5 \|7 \|11 + (392700x - 824670x + 314160)\|3 +--R / +--R 3 2 +-+ +--+ +--R (30x - 47x - 14x + 15)\|7 \|55 +--R + +--R 3 2 +-+ +--R (- 350x + 525x + 161x - 168)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--+ +--R (- 140x + 56x + 49x - 21)\|3 \|55 +--R + +--R 4 3 2 +-+ +--R (- 150x + 475x - 306x - 187x + 120)\|7 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x))-321161/7*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+1350*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 46555/42*sqrt(1-2*x)/(3+5*x)+137/18*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 6949/63*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R (- 86713470x - 225455022x - 219674124x - 95063656x - 15415728) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--+ +--R (2551500x + 6633900x + 6463800x + 2797200x + 453600)\|21 \|55 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 418995x - 824092x - 539819x - 117752)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1890x + 4914x + 4788x + 2072x + 336)\|21 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (43356735x + 112727511x + 109837062x + 47531828x + 7707864) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--+ +--R (1275750x + 3316950x + 3231900x + 1398600x + 226800)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 418995x - 824092x - 539819x - 117752)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1890x + 4914x + 4788x + 2072x + 336)\|21 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 321161log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 9450\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 642322atanh(---------------) - 18900\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 14\|21 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (425250x - 1105650x + 207900x + 756000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 3211610x - 321161x + 963483)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 1955310x - 4170369x + 1596357 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (698325x - 3421450x + 5587033x - 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3 2 +--+ +--R (- 6300x + 15750x + 448x - 16422x - 196x + 3360)\|21 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=1/4*(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x))-55953383/196*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+8400*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(55)-8110915/1176*sqrt(1-2*x)/(3+5*x)+43/9*sqrt(1-2*x)/_ + ((2+3*x)^3*(3+5*x))+23173/504*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 302668/441*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 45322240230x - 148052651418x - 193374891648x - 126230832048x +--R + +--R - 41181689888x - 5371524768 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 1333584000x + 4356374400x + 5689958400x + 3714278400x +--R + +--R 1211750400x + 158054400 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 218994705x - 576721848x - 569295605x - 249642200x - 41029970) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (158760x + 518616x + 677376x + 442176x + 144256x + 18816)\|21 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 22661120115x + 74026325709x + 96687445824x + 63115416024x +--R + +--R 20590844944x + 2685762384 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 666792000x + 2178187200x + 2844979200x + 1857139200x + 605875200x +--R + +--R 79027200 +--R * +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (- 218994705x - 576721848x - 569295605x - 249642200x - 41029970) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (158760x + 518616x + 677376x + 442176x + 144256x + 18816)\|21 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 55953383log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 1646400\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 111906766atanh(---------------) - 3292800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 392\|21 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (74088000x - 192628800x + 36220800x + 131712000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 559533830x - 55953383x + 167860149)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 340658430x - 726570957x + 278120871 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (121663725x - 596092600x + 973385299x - 529754040)\|21 +--R + +--R 2 +-+ +--+ +--R (11409552000x + 1901592000x - 3803184000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4196503725x + 11190676600x - 2965529299x - 6714405960)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (48665490x - 184905001x + 212724638x - 66219255)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 1037232000x + 1486699200x + 622339200x - 553190400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1678601490x + 2629809001x + 783347362x - 839300745)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (1629936000x - 2444904000x - 996072000x + 905520000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (2797669150x - 4196503725x - 1286927809x + 1342881192)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 1703292150x + 6358122225x - 7203172011x + 2224966968 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (35280x - 31752x - 53312x + 6664x + 11760)\|21 \|55 - 1234800x +--R + +--R 3 2 +--R 1029000x + 1802808x - 214032x - 395136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 493920x - 131712x + 304584x + 41160x - 49392)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 176400x + 441000x + 12544x - 459816x - 5488x + 94080)\|21 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (- 162x - 351x - 216x + 24x + 64x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^4/(3+5*x)^2-12279/15625*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+2571/15625*sqrt(1-2*x)-3/31250*(1618-4125*x)*_ + sqrt(1-2*x)+1404/3125*(2+3*x)^2*sqrt(1-2*x)+2643/1750*(2+3*x)^3*_ + sqrt(1-2*x)-129/50*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 4297650x - 5157180x - 1547154)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--+ +--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (5468750x + 6562500x + 1968750)\|55 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (2148825x + 2578590x + 773577)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--+ +--R (- 2025000x - 3267000x + 496350x + 2120880x + 489445x - 96776)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (5468750x + 6562500x + 1968750)\|55 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 12279log(-----------------------------) + 24558atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 31250\|55 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 61395x + 98232)\|55 + (61395x - 98232)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 24558x + 12279)\|5 \|11 \|55 + 1350690x - 675345 +--R / +--R 2 +--------+ +--R (17187500x + 1718750x - 5156250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1562500x - 2343750x - 718750x + 750000)\|55 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^2-5943/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+273/3125*sqrt(1-2*x)+21/50*(2+3*x)*_ + sqrt(1-2*x)+693/625*(2+3*x)^2*sqrt(1-2*x)-48/25*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 297150x - 356580x - 106974)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (156250x + 187500x + 56250)\|55 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (148575x + 178290x + 53487)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 27000x - 14400x + 37530x + 36295x + 8644)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (156250x + 187500x + 56250)\|55 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 5943log(-----------------------------) + 11886atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 6250\|55 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 29715x + 47544)\|55 + (29715x - 47544)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 11886x + 5943)\|5 \|11 \|55 + 653730x - 326865 +--R / +--R 2 +--------+ +--R (3437500x + 343750x - 1031250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (312500x - 468750x - 143750x + 150000)\|55 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=119/3025*(1-2*x)^(3/2)-1/550*(1-2*x)^(5/2)/(3+5*x)^2-131/6050*_ + (1-2*x)^(5/2)/(3+5*x)-357/125*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+357/1375*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 17850x - 21420x - 6426)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6250x + 7500x + 2250)\|55 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (8925x + 10710x + 3213)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 600x + 1320x + 2105x + 656)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6250x + 7500x + 2250)\|55 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 357log(-----------------------------) + 714atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 250\|55 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1785x + 2856)\|55 + (1785x - 2856)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 714x + 357)\|5 \|11 \|55 + 39270x - 19635 +--R / +--R 2 +--------+ +--R (137500x + 13750x - 41250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (12500x - 18750x - 5750x + 6000)\|55 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-1/110*(1-2*x)^(5/2)/(3+5*x)^2-13/110*(1-2*x)^(3/2)/(3+5*x)+_ + 39/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-39/275*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (1950x + 2340x + 702)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 205x - 82)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 55\|- 2x + 1 + (5x - 8)\|55 +--R (975x + 1170x + 351)log(-------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 120x - 205x - 82)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 39log(-------------------------------) - 78atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 50\|55 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 195x + 312)\|55 + (195x - 312)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (78x - 39)\|5 \|11 \|55 - 4290x + 2145 +--R / +--R 2 +--------+ +--R (27500x + 2750x - 8250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2500x + 3750x + 1150x - 1200)\|55 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^3 +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-1/10*(1-2*x)^(3/2)/(3+5*x)^2-3/25*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+3/50*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (- 150x - 180x - 54)atanh(---------------) + (25x + 4)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (75x + 90x + 27)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (25x + 4)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (1250x + 1500x + 450)\|55 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 3log(-----------------------------) + 6atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 50\|55 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165 +--R / +--R 2 +--------+ 3 2 +--+ +--R (27500x + 2750x - 8250)\|- 2x + 1 + (2500x - 3750x - 1150x + 1200)\|55 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-1/2*(1-2*x)^(3/2)/(3+5*x)^2+14*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-_ + 2379/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+69/10*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ +--+ \|3 \|- 2x + 1 +--R (3500x + 4200x + 1260)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 118950x - 142740x - 42822)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (355x + 202)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (250x + 300x + 90)\|55 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (59475x + 71370x + 21411)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R 2 +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R (1750x + 2100x + 630)\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (355x + 202)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (250x + 300x + 90)\|55 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 2379log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 70\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 140\|21 \|55 atanh(---------------) + 4758atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 10\|55 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 14274x - 2379x + 4758)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (5250x - 14000x + 3710x + 8400)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 3195x + 15657x - 25572x + 13920 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 23430x + 49995x - 19140)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 107055x + 278343x - 52338x - 190320)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (808500x + 80850x - 242550)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2130x + 7953x - 9012x + 2784)\|21 +--R + +--R 3 2 +-+ +--+ +--R (42822x - 64233x - 26169x + 23790)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (73500x - 110250x - 33810x + 35280)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 71370x + 102297x + 42822x - 38064)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 115500x + 180950x + 53900x - 57750)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 70290x - 267135x + 307395x - 95700 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (1500x - 1250x - 2190x + 260x + 480)\|21 \|55 - 49500x + 44550x +--R + +--R 2 +--R 74800x - 9350x - 16500 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 4500x + 11250x + 320x - 11730x - 140x + 2400)\|55 +--R + +--R 4 3 2 +--+ +--R (- 33000x - 8800x + 20350x + 2750x - 3300)\|21 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^2)+204*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(21)-6933*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 33/2*sqrt(1-2*x)/(3+5*x)^2+207/2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|3 \|- 2x + 1 +--R (30600x + 57120x + 35496x + 7344)\|21 \|55 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 \|5 \|- 2x + 1 +--R (- 1039950x - 1941240x - 1206342x - 249588)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (3105x + 3830x + 1178)\|55 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (150x + 280x + 174x + 36)\|55 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (519975x + 970620x + 603171x + 124794) +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--+ +--R (15300x + 28560x + 17748x + 3672)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|21 \|- 2x + 1 + 3x - 5 +--R log(---------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (3105x + 3830x + 1178)\|55 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (150x + 280x + 174x + 36)\|55 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 6933log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 204\|21 \|55 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +--+ +--+ \|3 \|- 2x + 1 \|5 \|- 2x + 1 +--R - 408\|21 \|55 atanh(---------------) + 13866atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2\|55 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 +-+ +--+ +--R (- 41598x - 6933x + 13866)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (15300x - 40800x + 10812x + 24480)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 9315x + 45639x - 74526x + 40560 +--R * +--R +--+ +--R \|55 +--R + +--R 2 +--+ +--R (- 68310x + 145695x - 55770)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 311985x + 811161x - 152526x - 554640)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (2356200x + 235620x - 706860)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 6210x + 23181x - 26262x + 8112)\|21 +--R + +--R 3 2 +-+ +--+ +--R (124794x - 187191x - 76263x + 69330)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (214200x - 321300x - 98532x + 102816)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 207990x + 298119x + 124794x - 110928)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 336600x + 527340x + 157080x - 168300)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 204930x - 778635x + 895785x - 278850 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (300x - 250x - 438x + 52x + 96)\|21 \|55 - 9900x + 8910x +--R + +--R 2 +--R 14960x - 1870x - 3300 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--+ +--R (- 900x + 2250x + 64x - 2346x - 28x + 480)\|55 +--R + +--R 4 3 2 +--+ +--R (- 6600x - 1760x + 4070x + 550x - 660)\|21 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^2)+14073*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-13665*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)-1015/6*sqrt(1-2*x)/(3+5*x)^2+137/6*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^2)+1020*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (6332850x + 16043220x + 15226986x + 6417288x + 1013256)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (- 6149250x - 15578100x - 14785530x - 6231240x - 983880)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (3074625x + 7789050x + 7392765x + 3115620x + 491940)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (91800x + 174435x + 110315x + 23219)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (450x + 1140x + 1082x + 456x + 72)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 13665\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 14073\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 28146\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 27330\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 2\|7 \|11 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^2)+813716/7*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-112875*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)-176065/126*sqrt(1-2*x)/(3+5*x)^2+86/9*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+1301/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 117955/14*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1098516600x + 3515253120x + 4496594616x + 2874044912x +--R + +--R 917871648x + 117175104 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 1066668750x - 3413340000x - 4366230750x - 2790721500x +--R + +--R - 891261000x - 113778000 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 533334375x + 1706670000x + 2183115375x + 1395360750x + 445630500x +--R + +--R 56889000 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 549258300x + 1757626560x + 2248297308x + 1437022456x + 458935824x +--R + +--R 58587552 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (15923925x + 40874010x + 39307638x + 16784696x + 2685098)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--+ +--R (9450x + 30240x + 38682x + 24724x + 7896x + 1008)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 790125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 813716\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1627432\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1580250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 14\|7 \|11 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^6*(3+5*x) +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 14580x + 52488x + 68769x + 29295x - 16632x - 21420x - 5488x +--R + +--R 2 +--R 1936x + 1280x + 192 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-184877/128*(1-2*x)^(7/2)+3916031/1152*(1-2*x)^(9/2)-_ + 5078115/1408*(1-2*x)^(11/2)+3658095/1664*(1-2*x)^(13/2)-_ + 105399/128*(1-2*x)^(15/2)+409941/2176*(1-2*x)^(17/2)-_ + 59049/2432*(1-2*x)^(19/2)+1215/896*(1-2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 +--R 4040613720x + 15971057388x + 23013359226x + 10299128697x +--R + +--R 6 5 4 3 +--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x +--R + +--R 2 +--R 1656222432x + 235056064x - 323646080 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2909907 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 +--R 4040613720x + 15971057388x + 23013359226x + 10299128697x +--R + +--R 6 5 4 3 +--R - 8457459318x - 11546145324x - 3037739768x + 2155110064x +--R + +--R 2 +--R 1656222432x + 235056064x - 323646080 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2909907 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^5*(3+5*x) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (4860x + 14256x + 13419x + 819x - 6090x - 3080x + 224x + 496x + 96) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-26411/64*(1-2*x)^(7/2)+60025/72*(1-2*x)^(9/2)-519645/704*(1-2*x)^(11/2)+_ + 37485/104*(1-2*x)^(13/2)-6489/64*(1-2*x)^(15/2)+1053/68*(1-2*x)^(17/2)-_ + 1215/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x +--R + +--R 4 3 2 +--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 415701 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R 212663880x + 690949116x + 717196194x + 9461529x - 486084375x +--R + +--R 4 3 2 +--R - 273280105x + 53353244x + 95863620x + 21784712x - 18122584 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 415701 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-3773/32*(1-2*x)^(7/2)+57281/288*(1-2*x)^(9/2)-24843/176*(1-2*x)^(11/2)+_ + 10773/208*(1-2*x)^(13/2)-1557/160*(1-2*x)^(15/2)+405/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x +--R + +--R 3 2 +--R - 2705920x + 9403464x + 3351776x - 1899184 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 20849400x + 52864812x + 31646538x - 24298407x - 32302900x +--R + +--R 3 2 +--R - 2705920x + 9403464x + 3351776x - 1899184 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 109395 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-539/16*(1-2*x)^(7/2)+3283/72*(1-2*x)^(9/2)-1071/44*(1-2*x)^(11/2)+_ + 621/104*(1-2*x)^(13/2)-9/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x +--R + +--R - 9038 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 92664x + 167508x + 13446x - 128237x - 51767x + 35349x + 21850x +--R + +--R - 9038 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=-77/8*(1-2*x)^(7/2)+707/72*(1-2*x)^(9/2)-309/88*(1-2*x)^(11/2)+_ + 45/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1 +--R --------------------------------------------------------------------------- +--R 1287 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (35640x + 37692x - 25678x - 32875x + 7302x + 11732x - 3712)\|- 2x + 1 +--R --------------------------------------------------------------------------- +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=-11/4*(1-2*x)^(7/2)+17/9*(1-2*x)^(9/2)-15/44*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1 +--R (2) --------------------------------------------------------- +--R 99 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (1080x + 292x - 1106x - 129x + 475x - 119)\|- 2x + 1 +--R (3) --------------------------------------------------------- +--R 99 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=-11/14*(1-2*x)^(7/2)+5/18*(1-2*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1 +--R (2) ---------------------------------------------- +--R 63 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (280x - 164x - 174x + 157x - 32)\|- 2x + 1 +--R (3) ---------------------------------------------- +--R 63 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x) +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=-14/81*(1-2*x)^(3/2)-2/45*(1-2*x)^(5/2)-5/21*(1-2*x)^(7/2)+_ + 98/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-98/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 3430\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 2835\|3 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1715\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (5400x - 8604x + 5534x - 4721)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 2835\|3 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=80/81*(1-2*x)^(3/2)+16/63*(1-2*x)^(5/2)+1/21*(1-2*x)^(7/2)/(2+3*x)-_ + 560/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+560/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 1680x - 1120)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (840x + 560)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (216x - 516x + 1474x + 1325)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (243x + 162)\|3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 280\|7 log(-------------------------------) + 560\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-365/567*(1-2*x)^(3/2)+1/42*(1-2*x)^(7/2)/(2+3*x)^2-_ + 73/126*(1-2*x)^(5/2)/(2+3*x)+365/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-365/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (6570x + 8760x + 2920)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--------+ +--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (3285x + 4380x + 1460)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (720x - 4584x - 8731x - 3521)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 365\|7 log(---------------------------------) - 730\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) -------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=1/63*(1-2*x)^(7/2)/(2+3*x)^3-53/189*(1-2*x)^(5/2)/(2+3*x)^2+_ + 265/567*(1-2*x)^(3/2)/(2+3*x)-530/81*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+530/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 14310x - 28620x - 19080x - 4240)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (2187x + 4374x + 2916x + 648)\|21 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (7155x + 14310x + 9540x + 2120)log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (1080x + 3627x + 2983x + 713)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (2187x + 4374x + 2916x + 648)\|21 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 265log(-----------------------------) + 530atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 81\|21 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 795x + 1325)\|21 + (795x - 1325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 530x + 265)\|3 \|7 \|21 + 11130x - 5565 +--R / +--R 2 +--------+ 3 2 +--+ +--R (10206x + 1701x - 3402)\|- 2x + 1 + (1458x - 2187x - 891x + 810)\|21 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=1/84*(1-2*x)^(7/2)/(2+3*x)^4-139/756*(1-2*x)^(5/2)/(2+3*x)^3+_ + 695/4536*(1-2*x)^(3/2)/(2+3*x)^2+695/2268*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-695/4536*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (112590x + 300240x + 300240x + 133440x + 22240)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (56295x + 150120x + 150120x + 66720x + 11120) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 41715x - 43971x - 18394x - 4394)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 695log(-------------------------------) - 1390atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 4536\|21 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2085x + 3475)\|21 + (2085x - 3475)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1390x - 695)\|3 \|7 \|21 - 29190x + 14595 +--R / +--R 2 +--------+ +--R (571536x + 95256x - 190512)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 81648x + 122472x + 49896x - 45360)\|21 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=1/105*(1-2*x)^(7/2)/(2+3*x)^5-43/315*(1-2*x)^(5/2)/(2+3*x)^4+_ + 43/567*(1-2*x)^(3/2)/(2+3*x)^3+43/3969*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-43/1134*sqrt(1-2*x)/(2+3*x)^2+43/7938*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (104490x + 348300x + 464400x + 309600x + 103200x + 13760) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (52245x + 174150x + 232200x + 154800x + 51600x + 6880) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (17415x - 116415x - 53772x + 3322x - 7018)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (9644670x + 32148900x + 42865200x + 28576800x + 9525600x + 1270080) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 43log(-------------------------------) - 86atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 7938\|21 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 129x + 215)\|21 + (129x - 215)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (86x - 43)\|3 \|7 \|21 - 1806x + 903 +--R / +--R 2 +--------+ +--R (1000188x + 166698x - 333396)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 142884x + 214326x + 87318x - 79380)\|21 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=1/126*(1-2*x)^(7/2)/(2+3*x)^6-41/378*(1-2*x)^(5/2)/(2+3*x)^5+_ + 205/4536*(1-2*x)^(3/2)/(2+3*x)^4+205/222264*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-205/13608*sqrt(1-2*x)/(2+3*x)^3+_ + 205/190512*sqrt(1-2*x)/(2+3*x)^2+205/444528*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 298890x + 1195560x + 1992600x + 1771200x + 885600x + 236160x +--R + +--R 26240 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x +--R + +--R 256048128x + 28449792 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 149445x + 597780x + 996300x + 885600x + 442800x + 118080x +--R + +--R 13120 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (49815x + 204795x - 824526x - 176850x + 154312x - 51904)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 324060912x + 1296243648x + 2160406080x + 1920360960x + 960180480x +--R + +--R 256048128x + 28449792 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 205log(-------------------------------) - 410atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 444528\|21 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 615x + 1025)\|21 + (615x - 1025)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (410x - 205)\|3 \|7 \|21 - 8610x + 4305 +--R / +--R 2 +--------+ +--R (56010528x + 9335088x - 18670176)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 8001504x + 12002256x + 4889808x - 4445280)\|21 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^2 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R (8100x + 23220x + 21141x + 690x - 9791x - 4696x + 424x + 768x + 144) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-41503/64*(1-2*x)^(7/2)+381073/288*(1-2*x)^(9/2)-_ + 832951/704*(1-2*x)^(11/2)+121359/208*(1-2*x)^(13/2)-_ + 53037/320*(1-2*x)^(15/2)+13905/544*(1-2*x)^(17/2)-2025/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 +--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x +--R + +--R 4 3 2 +--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2078505 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 +--R 1772199000x + 5625863100x + 5641824474x - 121581999x - 3896813214x +--R + +--R 4 3 2 +--R - 2072749175x + 461747860x + 739308228x + 160311352x - 138993368 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2078505 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-5929/32*(1-2*x)^(7/2)+91091/288*(1-2*x)^(9/2)-_ + 39977/176*(1-2*x)^(11/2)+17541/208*(1-2*x)^(13/2)-_ + 513/32*(1-2*x)^(15/2)+675/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 +--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x +--R + +--R 2 +--R 2934177x + 993442x - 581846 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 21879 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 +--R 6949800x + 17096508x + 9599634x - 8175663x - 10040957x - 608627x +--R + +--R 2 +--R 2934177x + 993442x - 581846 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 21879 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=-847/16*(1-2*x)^(7/2)+1309/18*(1-2*x)^(9/2)-3467/88*(1-2*x)^(11/2)+_ + 255/26*(1-2*x)^(13/2)-15/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x +--R + +--R - 13826 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 154440x + 267300x + 9846x - 205169x - 75320x + 56481x + 32506x +--R + +--R - 13826 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-121/8*(1-2*x)^(7/2)+1133/72*(1-2*x)^(9/2)-505/88*(1-2*x)^(11/2)+_ + 75/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R 1287 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (59400x + 58140x - 44062x - 49999x + 12729x + 17495x - 5671)\|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R 1287 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-121/28*(1-2*x)^(7/2)+55/18*(1-2*x)^(9/2)-25/44*(1-2*x)^(11/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1 +--R (2) -------------------------------------------------------------- +--R 693 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (12600x + 2380x - 12302x - 867x + 4966x - 1271)\|- 2x + 1 +--R (3) -------------------------------------------------------------- +--R 693 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=14/243*(1-2*x)^(3/2)+2/135*(1-2*x)^(5/2)-40/189*(1-2*x)^(7/2)-_ + 5/27*(1-2*x)^(7/2)*(3+5*x)-98/243*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)+98/243*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 3430\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 8505\|3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1715\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (63000x - 42300x - 30546x + 29791x - 2479)\|3 \|- 2x + 1 +--R / +--R +-+ +--R 8505\|3 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(-------------------------------) + 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 243\|3 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-50/81*(1-2*x)^(3/2)-10/63*(1-2*x)^(5/2)-25/63*(1-2*x)^(7/2)-_ + 1/63*(1-2*x)^(7/2)/(2+3*x)+350/81*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-350/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (7350x + 4900)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (1701x + 1134)\|3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (3675x + 2450)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (5400x - 5508x + 1002x - 4471x - 6239)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (1701x + 1134)\|3 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 175\|7 log(---------------------------------) - 350\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 81\|3 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=1055/567*(1-2*x)^(3/2)+211/441*(1-2*x)^(5/2)-1/126*(1-2*x)^(7/2)/_ + (2+3*x)^2+143/882*(1-2*x)^(7/2)/(2+3*x)-1055/81*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+1055/81*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (- 18990x - 25320x - 8440)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (9495x + 12660x + 4220)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (2160x - 3960x + 12828x + 25987x + 10007)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1458x + 1944x + 648)\|3 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 1055\|7 log(-------------------------------) + 2110\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-4435/3969*(1-2*x)^(3/2)-1/189*(1-2*x)^(7/2)/(2+3*x)^3+_ + 211/2646*(1-2*x)^(7/2)/(2+3*x)^2-887/882*(1-2*x)^(5/2)/(2+3*x)+_ + 4435/81*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-4435/567*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (239490x + 478980x + 319320x + 70960)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (4374x + 8748x + 5832x + 1296)\|21 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (119745x + 239490x + 159660x + 35480) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (3600x - 21240x - 61353x - 48697x - 12212)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (4374x + 8748x + 5832x + 1296)\|21 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4435log(-------------------------------) - 8870atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 162\|21 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13305x + 22175)\|21 + (13305x - 22175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (8870x - 4435)\|3 \|7 \|21 - 186270x + 93135 +--R / +--R 2 +--------+ +--R (20412x + 3402x - 6804)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2916x + 4374x + 1782x - 1620)\|21 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-1/252*(1-2*x)^(7/2)/(2+3*x)^4+31/588*(1-2*x)^(7/2)/(2+3*x)^3-_ + 4993/10584*(1-2*x)^(5/2)/(2+3*x)^2+24965/31752*(1-2*x)^(3/2)/(2+3*x)-_ + 24965/2268*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+24965/15876*sqrt(1-2*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 4044330x - 10784880x - 10784880x - 4793280x - 798880) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (2022165x + 5392440x + 5392440x + 2396640x + 399440) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (302400x + 1231065x + 1526937x + 762598x + 134558)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (367416x + 979776x + 979776x + 435456x + 72576)\|21 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 24965log(-----------------------------) + 49930atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 4536\|21 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 74895x + 124825)\|21 + (74895x - 124825)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 49930x + 24965)\|3 \|7 \|21 + 1048530x - 524265 +--R / +--R 2 +--------+ +--R (571536x + 95256x - 190512)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (81648x - 122472x - 49896x + 45360)\|21 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-1/315*(1-2*x)^(7/2)/(2+3*x)^5+347/8820*(1-2*x)^(7/2)/(2+3*x)^4-_ + 8051/26460*(1-2*x)^(5/2)/(2+3*x)^3+8051/31752*(1-2*x)^(3/2)/(2+3*x)^2+_ + 8051/15876*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 8051/31752*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 19563930x + 65213100x + 86950800x + 57967200x + 19322400x +--R + +--R 2576320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x +--R + +--R 5080320 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (9781965x + 32606550x + 43475400x + 28983600x + 9661200x + 1288160) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 7323345x - 12406455x - 8277204x - 2919346x - 503276)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 38578680x + 128595600x + 171460800x + 114307200x + 38102400x +--R + +--R 5080320 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 8051log(-------------------------------) - 16102atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 31752\|21 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 24153x + 40255)\|21 + (24153x - 40255)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (16102x - 8051)\|3 \|7 \|21 - 338142x + 169071 +--R / +--R 2 +--------+ +--R (4000752x + 666792x - 1333584)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 571536x + 857304x + 349272x - 317520)\|21 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1/378*(1-2*x)^(7/2)/(2+3*x)^6+83/2646*(1-2*x)^(7/2)/(2+3*x)^5-_ + 263/1176*(1-2*x)^(5/2)/(2+3*x)^4+1315/10584*(1-2*x)^(3/2)/(2+3*x)^3+_ + 1315/74088*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1315/21168*sqrt(1-2*x)/(2+3*x)^2+1315/148176*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 1917270x + 7669080x + 12781800x + 11361600x + 5680800x +--R + +--R 1514880x + 168320 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x +--R + +--R 85349376x + 9483264 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 958635x + 3834540x + 6390900x + 5680800x + 2840400x + 757440x +--R + +--R 84160 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (319545x - 1979115x - 2360850x - 587502x - 106808x - 81568)\|21 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 108020304x + 432081216x + 720135360x + 640120320x + 320060160x +--R + +--R 85349376x + 9483264 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1315log(-------------------------------) - 2630atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 148176\|21 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 3945x + 6575)\|21 + (3945x - 6575)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (2630x - 1315)\|3 \|7 \|21 - 55230x + 27615 +--R / +--R 2 +--------+ +--R (18670176x + 3111696x - 6223392)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2667168x + 4000752x + 1629936x - 1481760)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^2/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-1/441*(1-2*x)^(7/2)/(2+3*x)^7+23/882*(1-2*x)^(7/2)/(2+3*x)^6-_ + 467/2646*(1-2*x)^(5/2)/(2+3*x)^5+2335/31752*(1-2*x)^(3/2)/(2+3*x)^4+_ + 2335/1555848*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 2335/95256*sqrt(1-2*x)/(2+3*x)^3+2335/1333584*sqrt(1-2*x)/(2+3*x)^2+_ + 2335/3111696*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 10213290x + 47662020x + 95324040x + 105915600x + 70610400x +--R + +--R 2 +--R 28244160x + 6276480x + 597760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x +--R + +--R 1415408x - 1107536 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 6805279152x + 31757969376x + 63515938752x + 70573265280x +--R + +--R 3 2 +--R 47048843520x + 18819537408x + 4182119424x + 398297088 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 5106645x + 23831010x + 47662020x + 52957800x + 35305200x +--R + +--R 2 +--R 14122080x + 3138240x + 298880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 1702215x + 8132805x - 24492348x - 23950566x + 1405308x +--R + +--R 1415408x - 1107536 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 6805279152x + 31757969376x + 63515938752x + 70573265280x +--R + +--R 3 2 +--R 47048843520x + 18819537408x + 4182119424x + 398297088 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2335log(-------------------------------) - 4670atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3111696\|21 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7005x + 11675)\|21 + (7005x - 11675)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4670x - 2335)\|3 \|7 \|21 - 98070x + 49035 +--R / +--R 2 +--------+ +--R (392073696x + 65345616x - 130691232)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 56010528x + 84015792x + 34228656x - 31116960)\|21 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)^3 +--R +--R +--R (1) +--R 9 8 7 6 5 4 3 +--R 40500x + 140400x + 175365x + 66873x - 46885x - 52853x - 11968x +--R + +--R 2 +--R 5112x + 3024x + 432 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-456533/128*(1-2*x)^(7/2)+3278737/384*(1-2*x)^(9/2)-_ + 1179381/128*(1-2*x)^(11/2)+9504551/1664*(1-2*x)^(13/2)-_ + 1392467/640*(1-2*x)^(15/2)+1101465/2176*(1-2*x)^(17/2)-_ + 161325/2432*(1-2*x)^(19/2)+3375/896*(1-2*x)^(21/2) +--R +--R +--R (2) +--R 10 9 8 7 +--R 1700595000x + 6471211500x + 8880844050x + 3513142893x +--R + +--R 6 5 4 3 2 +--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x +--R + +--R 74758064x - 115708576 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 440895 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 9 8 7 +--R 1700595000x + 6471211500x + 8880844050x + 3513142893x +--R + +--R 6 5 4 3 2 +--R - 3556515018x - 4297543173x - 970928350x + 842946920x + 588303696x +--R + +--R 74758064x - 115708576 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 440895 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3 +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x +--R + +--R 216 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-65219/64*(1-2*x)^(7/2)+100793/48*(1-2*x)^(9/2)-_ + 121359/64*(1-2*x)^(11/2)+98209/104*(1-2*x)^(13/2)-_ + 17337/64*(1-2*x)^(15/2)+675/16*(1-2*x)^(17/2)-3375/1216*(1-2*x)^(19/2) +--R +--R +--R (2) +--R 9 8 7 6 5 4 +--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x +--R + +--R 3 2 +--R 281231x + 406155x + 84038x - 76018 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 741 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 7 6 5 4 +--R 1053000x + 3264300x + 3159234x - 180615x - 2223099x - 1118224x +--R + +--R 3 2 +--R 281231x + 406155x + 84038x - 76018 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 741 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3 +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-9317/32*(1-2*x)^(7/2)+16093/32*(1-2*x)^(9/2)-5847/16*(1-2*x)^(11/2)+_ + 28555/208*(1-2*x)^(13/2)-845/32*(1-2*x)^(15/2)+1125/544*(1-2*x)^(17/2) +--R +--R +--R (2) +--R 8 7 6 5 4 3 2 +--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x +--R + +--R 14864x - 9004 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 221 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 2 +--R 117000x + 278980x + 146310x - 138201x - 157296x - 5935x + 46164x +--R + +--R 14864x - 9004 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 221 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (1) (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-1331/16*(1-2*x)^(7/2)+2783/24*(1-2*x)^(9/2)-255/4*(1-2*x)^(11/2)+_ + 1675/104*(1-2*x)^(13/2)-25/16*(1-2*x)^(15/2) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--------+ +--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 39 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--------+ +--R (7800x + 12900x - 90x - 9917x - 3299x + 2724x + 1465x - 641)\|- 2x + 1 +--R ----------------------------------------------------------------------------- +--R 39 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (1) (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-1331/56*(1-2*x)^(7/2)+605/24*(1-2*x)^(9/2)-75/8*(1-2*x)^(11/2)+_ + 125/104*(1-2*x)^(13/2) +--R +--R +--R (2) +--R 6 5 4 3 2 +--------+ +--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 273 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--------+ +--R (21000x + 18900x - 15890x - 16061x + 4614x + 5533x - 1838)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 273 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=34/405*(1-2*x)^(3/2)*(3+5*x)^3+2/33*(1-2*x)^(5/2)*(3+5*x)^3+_ + 98/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 1012658/212625*sqrt(1-2*x)-25631/70875*(3+5*x)^2*sqrt(1-2*x)+_ + 514/4725*(3+5*x)^3*sqrt(1-2*x)-1/127575*(227389+191021*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R 37730\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R 280665\|3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 18865\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (8505000x + 913500x - 7838550x - 249219x + 3024349x - 830656)\|3 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R 280665\|3 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 49\|7 log(---------------------------------) - 98\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 729\|3 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-22/81*(1-2*x)^(3/2)*(3+5*x)^3-1/3*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)-_ + 1540/729*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+_ + 138578/127575*sqrt(1-2*x)-416152/127575*(3+5*x)*sqrt(1-2*x)+_ + 65153/14175*(3+5*x)^2*sqrt(1-2*x)-682/945*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R (- 32340x - 21560)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (15309x + 10206)\|3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (16170x + 10780)\|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (189000x - 17100x - 159714x + 25275x + 65558x + 13759)\|3 \|- 2x + 1 +--R / +--R +-+ +--R (15309x + 10206)\|3 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +-+ \|3 \|- 2x + 1 +--R 770\|7 log(-------------------------------) + 1540\|7 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ---------------------------------------------------------------------------- +--R +-+ +--R 729\|3 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^2+55/9*(1-2*x)^(3/2)*_ + (3+5*x)^3/(2+3*x)+935/81*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-_ + 78947/2835*sqrt(1-2*x)+89771/5670*(3+5*x)*sqrt(1-2*x)-_ + 7997/315*(3+5*x)^2*sqrt(1-2*x)+88/21*(3+5*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ \|3 \|- 2x + 1 +--R (117810x + 157080x + 52360)\|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (10206x + 13608x + 4536)\|3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (58905x + 78540x + 26180)\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--------+ +--R (54000x - 24120x - 17460x - 67962x - 152833x - 64943)\|3 \|- 2x + 1 +--R / +--R 2 +-+ +--R (10206x + 13608x + 4536)\|3 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 935\|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ \|3 \|- 2x + 1 +--R - 1870\|7 atanh(---------------) +--R +-+ +--R \|7 +--R / +--R +-+ +--R 162\|3 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^3+55/27*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^2-41360/243*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 12166/243*sqrt(1-2*x)-8294/243*(3+5*x)*sqrt(1-2*x)+_ + 1441/27*(3+5*x)^2*sqrt(1-2*x)-275/9*(3+5*x)^3*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 1116720x - 2233440x - 1488960x - 330880)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--------+ +--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (6561x + 13122x + 8748x + 1944)\|21 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (558360x + 1116720x + 744480x + 165440) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--------+ +--R (16200x - 20700x + 87030x + 289719x + 229336x + 56141)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (6561x + 13122x + 8748x + 1944)\|21 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 20680log(-----------------------------) + 41360atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 243\|21 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 62040x + 103400)\|21 + (62040x - 103400)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 41360x + 20680)\|3 \|7 \|21 + 868560x - 434280 +--R / +--R 2 +--------+ +--R (30618x + 5103x - 10206)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (4374x - 6561x - 2673x + 2430)\|21 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^4+55/54*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^3+645865/6804*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 224675/6804*sqrt(1-2*x)+252725/13608*(3+5*x)*sqrt(1-2*x)-_ + 2255/378*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)-55/24*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R 4 3 2 +--R (104630130x + 279013680x + 279013680x + 124006080x + 20667680) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (52315065x + 139506840x + 139506840x + 62003040x + 10333840) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R (1512000x - 8215200x - 32946525x - 39158517x - 19526798x - 3553918) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (1102248x + 2939328x + 2939328x + 1306368x + 217728)\|21 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 645865log(-------------------------------) - 1291730atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +--+ +--R 13608\|21 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1937595x + 3229325)\|21 + (1937595x - 3229325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1291730x - 645865)\|3 \|7 \|21 - 27126330x + 13563165 +--R / +--R 2 +--------+ +--R (1714608x + 285768x - 571536)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 244944x + 367416x + 149688x - 136080)\|21 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^5+11/18*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^4-146971/7938*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 715/7938*sqrt(1-2*x)-13387/15876*(3+5*x)*sqrt(1-2*x)/(2+3*x)-_ + 209/756*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2+11/9*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 357139530x - 1190465100x - 1587286800x - 1058191200x +--R + +--R - 352730400x - 47030720 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x +--R + +--R 7933096 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 178569765x + 595232550x + 793643400x + 529095600x + 176365200x +--R + +--R 23515360 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 26460000x + 126578745x + 207486855x + 157178184x + 56745266x +--R + +--R 7933096 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (19289340x + 64297800x + 85730400x + 57153600x + 19051200x + 2540160) +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 146971log(-----------------------------) + 293942atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 15876\|21 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 440913x + 734855)\|21 + (440913x - 734855)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 293942x + 146971)\|3 \|7 \|21 + 6172782x - 3086391 +--R / +--R 2 +--------+ +--R (2000376x + 333396x - 666792)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (285768x - 428652x - 174636x + 158760)\|21 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7 +--R +--R +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-121/4536*(1-2*x)^(3/2)/(2+3*x)^4+33275/95256*(1-2*x)^(3/2)/(2+3*x)^3-_ + 1/18*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^6+11/27*(1-2*x)^(3/2)*_ + (3+5*x)^3/(2+3*x)^5+559625/666792*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)-559625/190512*sqrt(1-2*x)/(2+3*x)^2+559625/1333584*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 815933250x + 3263733000x + 5439555000x + 4835160000x +--R + +--R 2 +--R 2417580000x + 644688000x + 71632000 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x +--R + +--R - 13847024 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x +--R + +--R 768144384x + 85349376 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 407966625x + 1631866500x + 2719777500x + 2417580000x +--R + +--R 2 +--R 1208790000x + 322344000x + 35816000 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 308539125x - 720187425x - 687940758x - 352611738x - 102558856x +--R + +--R - 13847024 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 972182736x + 3888730944x + 6481218240x + 5761082880x + 2880541440x +--R + +--R 768144384x + 85349376 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 559625log(-------------------------------) - 1119250atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +--+ +--R 1333584\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1678875x + 2798125)\|21 + (1678875x - 2798125)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1119250x - 559625)\|3 \|7 \|21 - 23504250x + 11752125 +--R / +--R 2 +--------+ +--R (168031584x + 28005264x - 56010528)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 24004512x + 36006768x + 14669424x - 13335840)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^8 +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^3/(2+3*x)^7+55/189*(1-2*x)^(3/2)*(3+5*x)^3/_ + (2+3*x)^6+33935/1166886*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 11/166698*(3833-4355*x)*sqrt(1-2*x)/(2+3*x)^3-153505/47628*_ + sqrt(1-2*x)/(2+3*x)^2+33935/2333772*sqrt(1-2*x)/(2+3*x)-_ + 3223/2646*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4+11/7*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 7 6 5 4 +--R 148431690x + 692681220x + 1385362440x + 1539291600x +--R + +--R 3 2 +--R 1026194400x + 410477760x + 91217280x + 8687360 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x +--R + +--R - 12384752x - 4005436 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 5103959364x + 23818477032x + 47636954064x + 52929948960x +--R + +--R 3 2 +--R 35286632640x + 14114653056x + 3136589568x + 298722816 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 74215845x + 346340610x + 692681220x + 769645800x + 513097200x +--R + +--R 2 +--R 205238880x + 45608640x + 4343680 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 24738615x - 141112395x - 283697388x - 164222766x - 39606312x +--R + +--R - 12384752x - 4005436 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 7 6 5 4 +--R 5103959364x + 23818477032x + 47636954064x + 52929948960x +--R + +--R 3 2 +--R 35286632640x + 14114653056x + 3136589568x + 298722816 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 33935log(-------------------------------) - 67870atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 2333772\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 101805x + 169675)\|21 + (101805x - 169675)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (67870x - 33935)\|3 \|7 \|21 - 1425270x + 712635 +--R / +--R 2 +--------+ +--R (294055272x + 49009212x - 98018424)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 42007896x + 63011844x + 25671492x - 23337720)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=298/10725*(1-2*x)^(3/2)*(2+3*x)^4+2/65*(1-2*x)^(5/2)*(2+3*x)^4-_ + 242/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 601617098/301640625*sqrt(1-2*x)-669943/2413125*(2+3*x)*_ + sqrt(1-2*x)-829256/20109375*(2+3*x)^2*sqrt(1-2*x)+_ + 861947/16891875*(2+3*x)^3*sqrt(1-2*x)+4138/482625*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 726726\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 2338875000x + 2842087500x - 1540428750x - 2556079875x +--R + +--R 2 +--R 399578370x + 960784285x - 289133384 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363363\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R 2338875000x + 2842087500x - 1540428750x - 2556079875x +--R + +--R 2 +--R 399578370x + 960784285x - 289133384 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 234609375\|5 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=34/825*(1-2*x)^(3/2)*(2+3*x)^3+2/55*(1-2*x)^(5/2)*(2+3*x)^3-242/15625*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-207982/171875*_ + sqrt(1-2*x)+6221/103125*(2+3*x)^2*sqrt(1-2*x)+706/28875*_ + (2+3*x)^3*sqrt(1-2*x)-1/515625*(177948+223375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 55902\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318) +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 27951\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R (14175000x + 6142500x - 15572250x - 3564885x + 7726195x - 1796318) +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R 3609375\|5 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=22/1875*(1-2*x)^(3/2)+2/625*(1-2*x)^(5/2)-44/525*(1-2*x)^(7/2)-_ + 1/15*(1-2*x)^(7/2)*(2+3*x)-242/3125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+242/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (105000x - 43500x - 91410x + 69995x - 8188)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 65625\|5 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=22/375*(1-2*x)^(3/2)+2/125*(1-2*x)^(5/2)-3/35*(1-2*x)^(7/2)-_ + 242/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 5082\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2541\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (9000x - 12660x + 4370x + 4937)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 13125\|5 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=22/75*(1-2*x)^(3/2)+2/25*(1-2*x)^(5/2)-242/125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+242/125*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R - 726\|11 atanh(---------------) + (120x - 340x + 866)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +--R 375\|5 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (120x - 340x + 866)\|5 \|- 2x + 1 +--R / +--R +-+ +--R 375\|5 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 121\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 242\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 125\|5 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +--R 15x + 19x + 6 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=-4/45*(1-2*x)^(3/2)-242/25*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)+98/9*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-272/225*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2450\|5 \|7 atanh(---------------) - 2178\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R + +--R +-+ +-+ +--------+ +--R (40x - 292)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1089\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (40x - 292)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1089\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 2450\|5 \|7 atanh(---------------) + 2178\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 225\|3 \|5 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 45x + 87x + 56x + 12 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=2/3*(1-2*x)^(3/2)+(1-2*x)^(5/2)/(2+3*x)-242/5*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)+140/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)+26/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (2100x + 1400)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R (- 2178x - 1452)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (8x + 87)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (45x + 30)\|3 \|5 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1089x + 726)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (1050x + 700)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (8x + 87)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (45x + 30)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 363\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 350\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 700\|5 \|7 atanh(---------------) + 726\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=1/2*(1-2*x)^(5/2)/(2+3*x)^2+65/6*(1-2*x)^(3/2)/(2+3*x)-_ + 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 235*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+7*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (12690x + 16920x + 5640)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 13068x - 17424x - 5808)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (427x + 301)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (54x + 72x + 24)\|3 \|5 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (6534x + 8712x + 2904)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (6345x + 8460x + 2820)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (427x + 301)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (54x + 72x + 24)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 242\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 235\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 470\|5 \|7 atanh(---------------) + 484\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 2\|3 \|5 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=1/3*(1-2*x)^(5/2)/(2+3*x)^3+50/9*(1-2*x)^(3/2)/(2+3*x)^2+_ + 74020/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 242*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+1105/9*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (1998540x + 3997080x + 2664720x + 592160)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +--+ +--+ \|5 \|- 2x + 1 +--R (- 58806x - 117612x - 78408x - 17424)\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (9657x + 13198x + 4523)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (243x + 486x + 324x + 72)\|21 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--+ +--+ +--R (29403x + 58806x + 39204x + 8712)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 3 2 +--R (999270x + 1998540x + 1332360x + 296080) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (9657x + 13198x + 4523)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (243x + 486x + 324x + 72)\|21 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 1089\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 37010log(-------------------------------) - 74020atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 2178\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 9\|21 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (49005x - 127413x + 23958x + 87120)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 370100x - 37010x + 111030)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 225330x - 480585x + 183960 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (80475x - 394285x + 643840x - 350400)\|21 +--R + +--R 2 +-+ +--+ +--R (7546770x + 1257795x - 2515590)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 2775750x + 7402000x - 1961530x - 4441200)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 32190x + 122305x - 140705x + 43800)\|21 +--R + +--R 3 2 +-+ +--+ +--R (686070x - 983367x - 411642x + 365904)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (1110300x - 1739470x - 518140x + 555150)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 1078110x + 1617165x + 658845x - 598950)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1850500x + 2775750x + 851230x - 888240)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 1126650x - 4205565x + 4764480x - 1471680 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (810x - 729x - 1224x + 153x + 270)\|21 \|55 - 28350x + 23625x +--R + +--R 2 +--R 41391x - 4914x - 9072 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (11340x + 3024x - 6993x - 945x + 1134)\|55 +--R + +--R 5 4 3 2 +--+ +--R (4050x - 10125x - 288x + 10557x + 126x - 2160)\|21 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------ +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=1/4*(1-2*x)^(5/2)/(2+3*x)^4+15/4*(1-2*x)^(3/2)/(2+3*x)^3+_ + 3454265/84*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1210*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+_ + 1495/24*sqrt(1-2*x)/(2+3*x)^2+100145/168*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (559590930x + 1492242480x + 1492242480x + 663218880x + 110536480) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 16465680x - 43908480x - 43908480x - 19514880x - 3252480)\|21 +--R * +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (2703915x + 5498403x + 3730002x + 844322)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (13608x + 36288x + 36288x + 16128x + 2688)\|21 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--+ +--R (8232840x + 21954240x + 21954240x + 9757440x + 1626240)\|21 \|55 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 + 5x - 8 +--R log(-------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (279795465x + 746121240x + 746121240x + 331609440x + 55268240) +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (2703915x + 5498403x + 3730002x + 844322)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (13608x + 36288x + 36288x + 16128x + 2688)\|21 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 101640\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 3454265log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 6908530atanh(---------------) + 203280\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 168\|21 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (4573800x - 11891880x + 2236080x + 8131200)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 34542650x - 3454265x + 10362795)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 21030450x - 44854635x + 17169705 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (7510875x - 36799600x + 60091645x - 32704200)\|21 +--R + +--R 2 +-+ +--+ +--R (704365200x + 117394200x - 234788400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 259069875x + 690853000x - 183076045x - 414511800)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 3004350x + 11415055x - 13132490x + 4088025)\|21 +--R + +--R 3 2 +-+ +--+ +--R (64033200x - 91780920x - 38419920x + 34151040)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (103627950x - 162350455x - 48359710x + 51813975)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 100623600x + 150935400x + 61492200x - 55902000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 172713250x + 259069875x + 79448095x - 82902360)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 105152250x - 392516775x + 444685605x - 137357640 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (15120x - 13608x - 22848x + 2856x + 5040)\|21 \|55 - 529200x +--R + +--R 3 2 +--R 441000x + 772632x - 91728x - 169344 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (211680x + 56448x - 130536x - 17640x + 21168)\|55 +--R + +--R 5 4 3 2 +--+ +--R (75600x - 189000x - 5376x + 197064x + 2352x - 40320)\|21 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192 +--R Type: Expression(Integer) +--E 326 + 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Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 2161120500x + 7203735000x + 9604980000x + 6403320000x +--R + +--R 2134440000x + 284592000 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 73446308955x + 244821029850x + 326428039800x + 217618693200x +--R + +--R 72539564400x + 9671941920 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (709777485x + 1916515215x + 1941349752x + 874383298x + 147756688) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (714420x + 2381400x + 3175200x + 2116800x + 705600x + 94080)\|21 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 592900\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 20149879log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 40299758atanh(---------------) + 1185800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 196\|21 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (26680500x - 69369300x + 13043800x + 47432000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 201498790x - 20149879x + 60449637)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 122677590x - 261652041x + 100156623 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (43813425x - 214664300x + 350534587x - 190774520)\|21 +--R + +--R 2 +-+ +--+ +--R (4108797000x + 684799500x - 1369599000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1511240925x + 4029975800x - 1067943587x - 2417985480)\|3 \|7 +--R * 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+)clear all + +--S 331 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^7*(3+5*x)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 10935x + 57591x + 132678x + 174636x + 143640x + 75600x + 24864x +--R + +--R 4672x + 384 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=1/6*(1-2*x)^(5/2)/(2+3*x)^6+41/18*(1-2*x)^(3/2)/(2+3*x)^5+_ + 25388847535/24696*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 30250*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)+_ + 2269/72*sqrt(1-2*x)/(2+3*x)^4+302651/1512*sqrt(1-2*x)/(2+3*x)^3+_ + 31700335/21168*sqrt(1-2*x)/(2+3*x)^2+736065535/49392*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R 37016939706030x + 148067758824120x + 246779598040200x +--R + +--R 3 2 +--R 219359642702400x + 109679821351200x + 29247952360320x + 3249772484480 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 +--R - 1089204732000x - 4356818928000x - 7261364880000x +--R + +--R 3 2 +--R - 6454546560000x - 3227273280000x - 860606208000x - 95622912000 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 178863925005x + 602204446665x + 811194684822x + 546491397114x +--R + +--R 184131053992x + 24823128464 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 36006768x + 144027072x + 240045120x + 213373440x + 106686720x +--R + +--R 28449792x + 3161088 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 544602366000x + 2178409464000x + 3630682440000x + 3227273280000x +--R + +--R 2 +--R 1613636640000x + 430303104000x + 47811456000 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 6 5 4 +--R 18508469853015x + 74033879412060x + 123389799020100x +--R + +--R 3 2 +--R 109679821351200x + 54839910675600x + 14623976180160x + 1624886242240 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 178863925005x + 602204446665x + 811194684822x + 546491397114x +--R + +--R 184131053992x + 24823128464 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 36006768x + 144027072x + 240045120x + 213373440x + 106686720x +--R + +--R 28449792x + 3161088 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 747054000\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 25388847535log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R - 50777695070atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R 1494108000\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 49392\|21 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +--R 33617430000x - 87405318000x + 16435188000x +--R + +--R 59764320000 +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 253888475350x - 25388847535x + 76166542605)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 154573762350x - 329681571765x + 126197345295 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (55204915125x - 270477017000x + 441673579355x - 240375895800)\|21 +--R + +--R 2 +-+ +--+ +--R (5177084220000x + 862847370000x - 1725694740000)\|5 \|11 +--R + +--R 3 2 +--R - 1904163565125x + 5077769507000x - 1345608919355x +--R + +--R - 3046661704200 +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 22081966050x + 83900644145x - 96523804510x + 30046986975)\|21 +--R + +--R 3 2 +--R (470644020000x - 674589762000x - 282386412000x + 251010144000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 3 2 +--R (761665426050x - 1193275834145x - 355443865490x + 380832713025) +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--R (- 739583460000x + 1109375190000x + 451967670000x - 410879700000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 3 2 +--R - 1269442376750x + 1904163565125x + 583943493305x +--R + +--R - 609332340840 +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 772868811750x - 2884997957625x + 3268439300595x - 1009578762360 +--R / +--R 4 3 2 +--+ +--+ +--R (4445280x - 4000752x - 6717312x + 839664x + 1481760)\|21 \|55 +--R + +--R 4 3 2 +--R - 155584800x + 129654000x + 227153808x - 26968032x - 49787136 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (62233920x + 16595712x - 38377584x - 5186160x + 6223392)\|55 +--R + +--R 5 4 3 2 +--R (22226400x - 55566000x - 1580544x + 57936816x + 691488x - 11854080) +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-26/275*(1-2*x)^(3/2)*(2+3*x)^4-1/5*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)-_ + 2794/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 20103122/23203125*sqrt(1-2*x)-7327/185625*(2+3*x)*sqrt(1-2*x)+_ + 312916/1546875*(2+3*x)^2*sqrt(1-2*x)+975383/1299375*(2+3*x)^3*_ + sqrt(1-2*x)-8318/37125*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 3227070x - 1936242)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x +--R + +--R 50081215x - 15982128 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (90234375x + 54140625)\|5 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1613535x + 968121)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R 212625000x + 237037500x - 173598750x - 214071975x + 85482115x +--R + +--R 50081215x - 15982128 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R +-+ +--R (90234375x + 54140625)\|5 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1397\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 2794\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 78125\|5 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2 +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-22/225*(1-2*x)^(3/2)*(2+3*x)^3-1/5*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)-_ + 2068/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 224794/421875*sqrt(1-2*x)+796/3375*(2+3*x)*sqrt(1-2*x)+_ + 23357/28125*(2+3*x)^2*sqrt(1-2*x)-1898/7875*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 217140x - 130284)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (1640625x + 984375)\|5 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (108570x + 65142)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (1575000x + 427500x - 1858950x + 152105x + 680930x + 16794)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +-+ +--R (1640625x + 984375)\|5 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1034\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 2068\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 15625\|5 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^2 +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=122/1875*(1-2*x)^(3/2)+122/6875*(1-2*x)^(5/2)-9/175*(1-2*x)^(7/2)-_ + 1/275*(1-2*x)^(7/2)/(3+5*x)-1342/3125*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(11/5)+1342/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 140910x - 84546)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (328125x + 196875)\|5 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (70455x + 42273)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (135000x - 96300x - 75130x + 173795x + 90486)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (328125x + 196875)\|5 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 671\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 1342\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 3125\|5 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^2 +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=56/375*(1-2*x)^(3/2)+56/1375*(1-2*x)^(5/2)-1/55*(1-2*x)^(7/2)/(3+5*x)-_ + 616/625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+616/625*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R (- 9240x - 5544)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (9375x + 5625)\|5 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (4620x + 2772)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (1800x - 3820x + 8630x + 6579)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (9375x + 5625)\|5 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 308\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 616\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 625\|5 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^2 +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +--R 25x + 30x + 9 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2/15*(1-2*x)^(3/2)-1/5*(1-2*x)^(5/2)/(3+5*x)+22/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-22/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 2 +-+ +--------+ +--R (330x + 198)\|11 atanh(---------------) + (40x - 260x - 243)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +-+ +--R (375x + 225)\|5 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (165x + 99)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (40x - 260x - 243)\|5 \|- 2x + 1 +--R / +--R +-+ +--R (375x + 225)\|5 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 11\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 22\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 25\|5 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 75x + 140x + 87x + 18 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-2/5*(1-2*x)^(3/2)-(1-2*x)^(5/2)/(3+5*x)+836/25*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-98/3*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(7/3)-58/75*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R (- 12250x - 7350)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R (12540x + 7524)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (40x - 339)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (375x + 225)\|3 \|5 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (6125x + 3675)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (6270x + 3762)\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (40x - 339)\|3 \|5 \|- 2x + 1 +--R / +--R +-+ +-+ +--R (375x + 225)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 1225\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1254\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 2450\|5 \|7 atanh(---------------) - 2508\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 75\|3 \|5 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-22*(1-2*x)^(3/2)/(3+5*x)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x))+_ + 1562/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 910/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-136/15*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 68250x - 86450x - 27300)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (70290x + 89034x + 28116)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (225x + 285x + 90)\|3 \|5 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (34125x + 43225x + 13650)\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (35145x + 44517x + 14058)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +-+ +--------+ +--R (- 2314x - 1461)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (225x + 285x + 90)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 2275\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2343\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 4550\|5 \|7 atanh(---------------) - 4686\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 15\|3 \|5 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x))+50/3*(1-2*x)^(3/2)/((2+3*x)*_ + (3+5*x))+2288*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)-_ + 6665/3*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)-2189/6*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|3 \|- 2x + 1 +--R (- 599850x - 1159710x - 746480x - 159960)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 3 2 +-+ +--+ \|5 \|- 2x + 1 +--R (617760x + 1194336x + 768768x + 164736)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (270x + 522x + 336x + 72)\|3 \|5 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (299925x + 579855x + 373240x + 79980)\|5 \|7 +--R * +--R +-+ +--------+ +-+ +--R 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (308880x + 597168x + 384384x + 82368)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 20289x - 26380x - 8553)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (270x + 522x + 336x + 72)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +-+ 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 6665\|5 \|7 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +-+ +--R +-+ +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 6864\|3 \|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R 13330\|5 \|7 atanh(---------------) - 13728\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 6\|3 \|5 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------- +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x))+15/2*(1-2*x)^(3/2)/((2+3*x)^2*_ + (3+5*x))-307295/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 3014*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 44545/18*sqrt(1-2*x)/(3+5*x)+2260/9*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R (- 82969650x - 215721090x - 210189780x - 90959320x - 14750160) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--+ +--R (2441340x + 6347484x + 6184728x + 2676432x + 434016)\|21 \|55 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (810x + 2106x + 2052x + 888x + 144)\|21 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (41484825x + 107860545x + 105094890x + 45479660x + 7375080) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--+ +--R (1220670x + 3173742x + 3092364x + 1338216x + 217008)\|21 \|55 +--R * +--R +--+ +--------+ +--R - \|55 \|- 2x + 1 + 5x - 8 +--R log(---------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 400905x - 788512x - 516513x - 112668)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (810x + 2106x + 2052x + 888x + 144)\|21 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 307295log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 9042\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 614590atanh(---------------) - 18084\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 6\|21 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (406890x - 1057914x + 198924x + 723360)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 3072950x - 307295x + 921885)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 1870890x - 3990315x + 1527435 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (668175x - 3273730x + 5345815x - 2909400)\|21 +--R + +--R 2 +-+ +--+ +--R (62661060x + 10443510x - 20887020)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 23047125x + 61459000x - 16286635x - 36875400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (267270x - 1015495x + 1168280x - 363675)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 5696460x + 8164926x + 3417876x - 3038112)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 9218850x + 14442865x + 4302130x - 4609425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (8951580x - 13427370x - 5470410x + 4973100)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (15364750x - 23047125x - 7067785x + 7375080)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 9354450x + 34918695x - 39559695x + 12219480 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (540x - 486x - 816x + 102x + 180)\|21 \|55 - 18900x + 15750x +--R + +--R 2 +--R 27594x - 3276x - 6048 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 7560x - 2016x + 4662x + 630x - 756)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 2700x + 6750x + 192x - 7038x - 84x + 1440)\|21 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x))+85/18*(1-2*x)^(3/2)/((2+3*x)^3*_ + (3+5*x))-53384095/84*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 18700*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 7738475/504*sqrt(1-2*x)/(3+5*x)+22765/216*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+288770/189*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 43241116950x - 141254315370x - 184495432320x - 120434518320x +--R + +--R - 39290693920x - 5124873120 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 1272348000x + 4156336800x + 5428684800x + 3543724800x +--R + +--R 1156108800x + 150796800 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 208938825x - 550239720x - 543154477x - 238179048x - 39145938) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (68040x + 222264x + 290304x + 189504x + 61824x + 8064)\|21 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 21620558475x + 70627157685x + 92247716160x + 60217259160x +--R + +--R 19645346960x + 2562436560 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 636174000x + 2078168400x + 2714342400x + 1771862400x + 578054400x +--R + +--R 75398400 +--R * +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (- 208938825x - 550239720x - 543154477x - 238179048x - 39145938) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (68040x + 222264x + 290304x + 189504x + 61824x + 8064)\|21 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 53384095log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 1570800\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R 106768190atanh(---------------) - 3141600\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 168\|21 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (70686000x - 183783600x + 34557600x + 125664000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 533840950x - 53384095x + 160152285)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 325015950x - 693208005x + 265350015 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (116077125x - 568721000x + 928689035x - 505428600)\|21 +--R + +--R 2 +-+ +--+ +--R (10885644000x + 1814274000x - 3628548000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 4003807125x + 10676819000x - 2829357035x - 6406091400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (46430850x - 176414465x + 202956670x - 63178575)\|21 +--R + +--R 3 2 +-+ +--+ +--R (- 989604000x + 1418432400x + 593762400x - 527788800)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 1601522850x + 2509052465x + 747377330x - 800761425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (1555092000x - 2332638000x - 950334000x + 863940000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (2669204750x - 4003807125x - 1227834185x + 1281218280)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 1625079750x + 6066167625x - 6872414115x + 2122800120 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (15120x - 13608x - 22848x + 2856x + 5040)\|21 \|55 - 529200x +--R + +--R 3 2 +--R 441000x + 772632x - 91728x - 169344 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 211680x - 56448x + 130536x + 17640x - 21168)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 75600x + 189000x + 5376x - 197064x - 2352x + 40320)\|21 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^2) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=1/5*(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x))+41/12*(1-2*x)^(3/2)/((2+3*x)^4*_ + (3+5*x))-2231141147/588*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 111650*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-323422735/3528*_ + sqrt(1-2*x)/(3+5*x)+1714/27*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+_ + 924025/1512*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+12068887/1323*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 6 5 4 +--R - 27108364936050x - 106626235415130x - 174698351810100x +--R + +--R 3 2 +--R - 152610054454800x - 74966342539200x - 19634042093600x +--R + +--R - 2141895501120 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 +--R 797649930000x + 3137423058000x + 5140410660000x + 4490473680000x +--R + +--R 2 +--R 2205846720000x + 577721760000x + 63024192000 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 130986207675x - 432275892930x - 570477768855x - 376323861626x +--R + +--R - 124085884254x - 16360698684 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 7144200x + 28100520x + 46040400x + 40219200x + 19756800x +--R + +--R 5174400x + 564480 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 13554182468025x + 53313117707565x + 87349175905050x +--R + +--R 3 2 +--R 76305027227400x + 37483171269600x + 9817021046800x + 1070947750560 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 +--R 398824965000x + 1568711529000x + 2570205330000x + 2245236840000x +--R + +--R 2 +--R 1102923360000x + 288860880000x + 31512096000 +--R * +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 130986207675x - 432275892930x - 570477768855x - 376323861626x +--R + +--R - 124085884254x - 16360698684 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 7144200x + 28100520x + 46040400x + 40219200x + 19756800x +--R + +--R 5174400x + 564480 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R 2231141147log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R +--+ +--+ - \|55 \|- 2x + 1 + 5x - 8 +--R 65650200\|21 \|55 log(---------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R 4462282294atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R - 131300400\|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +--+ +--R 1176\|21 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +--R (2954259000x - 7681073400x + 1444304400x + 5252016000) +--R * +--R +-+ +--+ +--R \|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 22311411470x - 2231141147x + 6693423441)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 13583754870x - 28972016913x + 11090069739 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (4851341025x - 23769192400x + 38813738791x - 21123942360)\|21 +--R + +--R 2 +-+ +--+ +--R (454955886000x + 75825981000x - 151651962000)\|5 \|11 +--R + +--R 3 2 +--R (- 167335586025x + 446228229400x - 118250480791x - 267736937640) +--R * +--R +-+ +-+ +--R \|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1940536410x - 7373086909x + 8482394942x - 2640492795)\|21 +--R + +--R 3 2 +-+ +--R (- 41359626000x + 59282130600x + 24815775600x - 22058467200)\|5 +--R * +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 66934234410x + 104863633909x + 31235976058x - 33467117205)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (64993698000x - 97490547000x - 39718371000x + 36107610000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (111557057350x - 167335586025x - 51316246381x + 53547387528)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R - 67918774350x + 253530123525x - 287226483999x + 88720557912 +--R / +--R 4 3 2 +--+ +--+ +--R (105840x - 95256x - 159936x + 19992x + 35280)\|21 \|55 +--R + +--R 4 3 2 +--R - 3704400x + 3087000x + 5408424x - 642096x - 1185408 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (- 1481760x - 395136x + 913752x + 123480x - 148176)\|55 +--R + +--R 5 4 3 2 +--+ +--R (- 529200x + 1323000x + 37632x - 1379448x - 16464x + 282240)\|21 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^3 +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^2-127/50*(1-2*x)^(3/2)*(2+3*x)^4/_ + (3+5*x)-11763/78125*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 50557/78125*sqrt(1-2*x)-1/468750*(118254-449875*x)*sqrt(1-2*x)+_ + 44804/46875*(2+3*x)^2*sqrt(1-2*x)+250829/78750*(2+3*x)^3*_ + sqrt(1-2*x)-1117/1125*(2+3*x)^4*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 4117050x - 4940460x - 1482138)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 2 +--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x +--R + +--R 6891315x + 871208 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (27343750x + 32812500x + 9843750)\|5 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (2058525x + 2470230x + 741069)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 2 +--R 15750000x + 15075000x - 16051500x - 11139550x + 9372960x +--R + +--R 6891315x + 871208 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (27343750x + 32812500x + 9843750)\|5 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 11763\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 23526\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 156250\|5 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^3 +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/10*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^2-47/25*(1-2*x)^(3/2)*(2+3*x)^3/_ + (3+5*x)-5559/15625*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 5839/15625*sqrt(1-2*x)+223/250*(2+3*x)*sqrt(1-2*x)+_ + 7149/3125*(2+3*x)^2*sqrt(1-2*x)-636/875*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 1945650x - 2334780x - 700434)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +-+ +--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +-+ +--R (5468750x + 6562500x + 1968750)\|5 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (972825x + 1167390x + 350217)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +-+ +--R (1350000x - 27000x - 1506900x + 1651030x + 2637795x + 770444)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +-+ +--R (5468750x + 6562500x + 1968750)\|5 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 5559\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 11118\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 31250\|5 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^3 +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=511/6875*(1-2*x)^(3/2)+1533/75625*(1-2*x)^(5/2)-1/550*(1-2*x)^(7/2)/_ + (3+5*x)^2-129/6050*(1-2*x)^(7/2)/(3+5*x)-1533/3125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+1533/3125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 76650x - 91980x - 27594)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (156250x + 187500x + 56250)\|5 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (38325x + 45990x + 13797)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--------+ +--R (18000x - 25400x + 51980x + 98595x + 32504)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (156250x + 187500x + 56250)\|5 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 1533\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R 3066\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 6250\|5 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^3 +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=-21/275*(1-2*x)^(3/2)-1/110*(1-2*x)^(7/2)/(3+5*x)^2-_ + 63/550*(1-2*x)^(5/2)/(3+5*x)+63/125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(11/5)-63/125*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (3150x + 3780x + 1134)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (6250x + 7500x + 2250)\|5 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (1575x + 1890x + 567)\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--------+ +--R (400x - 2280x - 3795x - 1394)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (6250x + 7500x + 2250)\|5 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ - 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 63\|11 log(----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +--+ \|5 \|- 2x + 1 +--R - 126\|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--R 250\|5 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^3 +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 3 2 +--R 125x + 225x + 135x + 27 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/10*(1-2*x)^(5/2)/(3+5*x)^2+1/10*(1-2*x)^(3/2)/(3+5*x)-_ + 3/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+3/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--+ \|5 \|- 2x + 1 +--R (- 150x - 180x - 54)\|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (80x + 195x + 64)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1250x + 1500x + 450)\|5 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (75x + 90x + 27)\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--------+ +--R (80x + 195x + 64)\|5 \|- 2x + 1 +--R / +--R 2 +-+ +--R (1250x + 1500x + 450)\|5 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +-+ +--------+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--+ \|5 \|- 2x + 1 +--R 3\|11 log(--------------------------------) + 6\|11 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +-+ +--R 50\|5 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/2*(1-2*x)^(5/2)/(3+5*x)^2+71/10*(1-2*x)^(3/2)/(3+5*x)-_ + 2523/25*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 98*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+73/25*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +-+ \|3 \|- 2x + 1 +--R (122500x + 147000x + 44100)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +--+ \|5 \|- 2x + 1 +--R (- 126150x - 151380x - 45414)\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +--R (4125x + 2354)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (1250x + 1500x + 450)\|3 \|5 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+ +-+ +--R 2 +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R (63075x + 75690x + 22707)\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R (61250x + 73500x + 22050)\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +-+ +--------+ +--R (4125x + 2354)\|3 \|5 \|- 2x + 1 +--R / +--R 2 +-+ +-+ +--R (1250x + 1500x + 450)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 2523\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 2450\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +-+ +--+ \|5 \|- 2x + 1 +--R - 4900\|5 \|7 atanh(---------------) + 5046\|3 \|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +-+ +--R 50\|3 \|5 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------- +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-33/2*(1-2*x)^(3/2)/(3+5*x)^2+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^2)-_ + 7209/5*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 1400*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(7/3)+2299/10*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +-+ \|3 \|- 2x + 1 +--R (1050000x + 1960000x + 1218000x + 252000)\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--+ +--R (- 1081350x - 2018520x - 1254366x - 259524)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (750x + 1400x + 870x + 180)\|3 \|5 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (540675x + 1009260x + 627183x + 129762)\|3 \|11 +--R * +--R +--+ +--------+ +-+ +--R 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(--------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +-+ +--R (525000x + 980000x + 609000x + 126000)\|5 \|7 +--R * +--R +-+ +--------+ +-+ +--R - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (35515x + 43806x + 13474)\|3 \|5 \|- 2x + 1 +--R / +--R 3 2 +-+ +-+ +--R (750x + 1400x + 870x + 180)\|3 \|5 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +-+ +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 7209\|3 \|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +-+ - 3\|7 \|- 2x + 1 + (3x - 5)\|3 +--R 7000\|5 \|7 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|3 \|- 2x + 1 +--R - 14000\|5 \|7 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|5 \|- 2x + 1 +--R 14418\|3 \|11 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--R 10\|3 \|5 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^3) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------- +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^2)+45/2*(1-2*x)^(3/2)/((2+3*x)*_ + (3+5*x)^2)-14073*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(11/5)+_ + 4555*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(21)-737/2*sqrt(1-2*x)/_ + (3+5*x)^2+2311*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (2049750x + 5192700x + 4928510x + 2077080x + 327960)\|5 \|21 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (- 6332850x - 16043220x - 15226986x - 6417288x - 1013256)\|11 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (450x + 1140x + 1082x + 456x + 72)\|5 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--+ +--R (3166425x + 8021610x + 7613493x + 3208644x + 506628)\|11 +--R * +--R +--+ +--------+ +-+ +--R 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R log(--------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (1024875x + 2596350x + 2464255x + 1038540x + 163980)\|5 \|21 +--R * +--R +--+ +--------+ +--R - \|21 \|- 2x + 1 + 3x - 5 +--R log(---------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--------+ +--R (207990x + 395215x + 249939x + 52607)\|5 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (450x + 1140x + 1082x + 456x + 72)\|5 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +-+ +--R +--+ 5\|11 \|- 2x + 1 + (5x - 8)\|5 +--R 14073\|11 log(--------------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R +-+ +--+ - \|21 \|- 2x + 1 + 3x - 5 +--R 4555\|5 \|21 log(---------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--+ \|5 \|- 2x + 1 +--R - 9110\|5 \|21 atanh(---------------) + 28146\|11 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--R 2\|5 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +--R (- 956550x + 478275)\|11 +--R + +--R 2 +-+ +-+ +-+ +--R (68325x - 223195x + 182200)\|3 \|5 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R +-+ +-+ +--+ +--R (956550x - 478275)\|3 \|7 \|11 +--R + +--R 2 +-+ +--R (- 1434825x + 4687095x - 3826200)\|5 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +-+ +--+ +--R (- 136650x + 296075x - 113875)\|3 \|7 \|11 +--R + +--R 2 +-+ +--R (- 956550x + 2008755x - 765240)\|5 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--+ +--R (2869650x - 6217575x + 2391375)\|11 +--R + +--R 2 +-+ +-+ +-+ +--R (956550x - 2008755x + 765240)\|3 \|5 \|7 +--R / +--R 3 2 +-+ +--+ +--R (60x - 86x - 36x + 32)\|5 \|21 +--R + +--R 3 2 +--+ +--R (- 180x + 270x + 110x - 100)\|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--+ +--R (- 120x + 40x + 50x - 20)\|11 \|21 +--R + +--R 4 3 2 +-+ +--R (- 180x + 558x - 322x - 276x + 160)\|5 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R ----------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^2)+85/9*(1-2*x)^(3/2)/((2+3*x)^2*_ + (3+5*x)^2)+785570*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 23115*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-169975/54*_ + sqrt(1-2*x)/(3+5*x)^2+11470/27*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 113875/6*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1060519500x + 3393662400x + 4341059820x + 2774633240x +--R + +--R 886122960x + 113122080 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R - 31205250x - 99856800x - 127733490x - 81642180x - 26073720x +--R + +--R - 3328560 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 15602625x + 49928400x + 63866745x + 40821090x + 13036860x +--R + +--R 1664280 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 530259750x + 1696831200x + 2170529910x + 1387316620x + 443061480x +--R + +--R 56561040 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (5124375x + 13153400x + 12649336x + 5401374x + 864074)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--+ +--R (1350x + 4320x + 5526x + 3532x + 1128x + 144)\|21 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 23115\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 785570log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 1571140atanh(---------------) + 46230\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 2\|21 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (1040175x - 2704455x + 508530x + 1849200)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 7855700x - 785570x + 2356710)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 4782750x - 10200855x + 3904740 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (1708125x - 8368975x + 13666060x - 7437600)\|21 +--R + +--R 2 +-+ +--+ +--R (160186950x + 26697825x - 53395650)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 58917750x + 157114000x - 41635210x - 94268400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 683250x + 2596015x - 2986595x + 929700)\|21 +--R + +--R 3 2 +-+ +--+ +--R (14562450x - 20872845x - 8737470x + 7766640)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (23567100x - 36921790x - 10997980x + 11783550)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 22883850x + 34325775x + 13984575x - 12713250)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 39278500x + 58917750x + 18068110x - 18853680)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 23913750x - 89266275x + 101130540x - 31237920 +--R / +--R 4 3 2 +--+ +--+ 4 3 +--R (180x - 162x - 272x + 34x + 60)\|21 \|55 - 6300x + 5250x +--R + +--R 2 +--R 9198x - 1092x - 2016 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (2520x + 672x - 1554x - 210x + 252)\|55 +--R + +--R 5 4 3 2 +--+ +--R (900x - 2250x - 64x + 2346x + 28x - 480)\|21 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^3) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^2)+205/36*(1-2*x)^(3/2)/((2+3*x)^3*_ + (3+5*x)^2)+163363895/28*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 171675*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(55)-_ + 8836825/378*sqrt(1-2*x)/(3+5*x)^2+34525/216*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+522385/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 23680975/168*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 661623774750x + 2558278595700x + 4119710704110x + 3536501598960x +--R + +--R 2 +--R 1706825974960x + 439122149760x + 47048801760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 +--R - 19467945000x - 75276054000x - 121220404200x - 104059771200x +--R + +--R 2 +--R - 50222491200x - 12920947200x - 1384387200 +--R * +--R +-+ +--------+ +--R +--+ +--+ \|5 \|- 2x + 1 +--R \|21 \|55 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 3196931625x + 10337268075x + 13362164665x + 8630749831x +--R + +--R 2785562634x + 359378534 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--+ +--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 9733972500x + 37638027000x + 60610202100x + 52029885600x +--R + +--R 2 +--R 25111245600x + 6460473600x + 692193600 +--R * +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R \|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R 6 5 4 3 +--R 330811887375x + 1279139297850x + 2059855352055x + 1768250799480x +--R + +--R 2 +--R 853412987480x + 219561074880x + 23524400880 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 3196931625x + 10337268075x + 13362164665x + 8630749831x +--R + +--R 2785562634x + 359378534 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--+ +--R (113400x + 438480x + 706104x + 606144x + 292544x + 75264x + 8064)\|21 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+ +--R +--+ +--+ \|55 \|- 2x + 1 + 5x - 8 +--R 4806900\|21 \|55 log(-------------------------) +--R 5x + 3 +--R + +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R 163363895log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--+ \|5 \|- 2x + 1 +--R - 326727790atanh(---------------) + 9613800\|21 \|55 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +--+ +--R 56\|21 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 2 +-+ +--+ +--R (216310500x - 562407300x + 105751800x + 384552000)\|5 \|11 +--R + +--R 2 +-+ +-+ +--R (- 1633638950x - 163363895x + 490091685)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 2 +--R 994600950x - 2121327705x + 812013615 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +--+ +--R (355214625x - 1740377500x + 2841937435x - 1546692600)\|21 +--R + +--R 2 +-+ +--+ +--R (33311817000x + 5551969500x - 11103939000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 12252292125x + 32672779000x - 8658286435x - 19603667400)\|3 \|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 142085850x + 539856565x - 621079970x + 193336575)\|21 +--R + +--R 3 2 +-+ +--+ +--R (3028347000x - 4340630700x - 1817008200x + 1615118400)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (4900916850x - 7678103065x - 2287094530x + 2450458425)\|3 \|7 +--R * +--R +--+ +--R \|55 +--R + +--R 3 2 +-+ +--+ +--R (- 4758831000x + 7138246500x + 2908174500x - 2643795000)\|5 \|11 +--R + +--R 3 2 +-+ +-+ +--R (- 8168194750x + 12252292125x + 3757369585x - 3920733480)\|3 \|7 +--R * +--R +--+ +--R \|21 +--R + +--R 3 2 +--R 4973004750x - 18563446125x + 21030689715x - 6496108920 +--R / +--R 4 3 2 +--+ +--+ 4 +--R (5040x - 4536x - 7616x + 952x + 1680)\|21 \|55 - 176400x +--R + +--R 3 2 +--R 147000x + 257544x - 30576x - 56448 +--R * +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--+ +--R (70560x + 18816x - 43512x - 5880x + 7056)\|55 +--R + +--R 5 4 3 2 +--+ +--R (25200x - 63000x - 1792x + 65688x + 784x - 13440)\|21 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^5*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=60025/24*(1-2*x)^(3/2)-103929/64*(1-2*x)^(5/2)+5355/8*(1-2*x)^(7/2)-_ + 10815/64*(1-2*x)^(9/2)+1053/44*(1-2*x)^(11/2)-_ + 1215/832*(1-2*x)^(13/2)-184877/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x +--R + +--R - 638648 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 40095x - 208251x - 488925x - 698580x - 707436x - 597464x +--R + +--R - 638648 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^4*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=57281/96*(1-2*x)^(3/2)-24843/80*(1-2*x)^(5/2)+1539/16*(1-2*x)^(7/2)-_ + 519/32*(1-2*x)^(9/2)+405/352*(1-2*x)^(11/2)-26411/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--------+ +--R (- 6075x - 27630x - 56520x - 71136x - 67664x - 75584)\|- 2x + 1 +--R (3) -------------------------------------------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)^3*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=3283/24*(1-2*x)^(3/2)-1071/20*(1-2*x)^(5/2)+621/56*(1-2*x)^(7/2)-_ + 15/16*(1-2*x)^(9/2)-3773/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1 +--R (2) --------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 1575x - 6165x - 10881x - 12434x - 14954)\|- 2x + 1 +--R (3) --------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^2*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ---------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=707/24*(1-2*x)^(3/2)-309/40*(1-2*x)^(5/2)+45/56*(1-2*x)^(7/2)-_ + 539/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1 +--R (2) -------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 675x - 2232x - 3448x - 4708)\|- 2x + 1 +--R (3) -------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)*(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) -------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=17/3*(1-2*x)^(3/2)-3/4*(1-2*x)^(5/2)-77/4*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (- 9x - 25x - 43)\|- 2x + 1 +--R (2) ----------------------------- +--R 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (- 9x - 25x - 43)\|- 2x + 1 +--R (3) ----------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(3+5*x)/sqrt(1-2*x) +--R +--R +--R 5x + 3 +--R (1) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=5/6*(1-2*x)^(3/2)-11/2*sqrt(1-2*x) +--R +--R +--R +--------+ +--R (- 5x - 14)\|- 2x + 1 +--R (2) ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R (- 5x - 14)\|- 2x + 1 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=2/3*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/3*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R 2atanh(---------------) - 5\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R log(-------------------------------) - 5\|21 \|- 2x + 1 +--R 3x + 2 +--R (3) -------------------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 3\|21 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (378x + 63x - 126)\|- 2x + 1 + (- 54x + 81x + 33x - 30)\|21 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-68/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/21*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (- 204x - 136)atanh(---------------) + \|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------- +--R +--+ +--R (63x + 42)\|21 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R (102x + 68)log(-----------------------------) + \|21 \|- 2x + 1 +--R 3x + 2 +--R (3) ---------------------------------------------------------------- +--R +--+ +--R (63x + 42)\|21 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-67/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/42*sqrt(1-2*x)/(2+3*x)^2-_ + 67/294*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 1206x - 1608x - 536)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +--+ +--------+ +--R (- 201x - 127)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (603x + 804x + 268)log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 201x - 127)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 67log(-----------------------------) + 134atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 294\|21 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 134x + 67)\|3 \|7 \|21 + 2814x - 1407 +--R / +--R 2 +--------+ +--R (37044x + 6174x - 12348)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (5292x - 7938x - 3234x + 2940)\|21 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-100/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 1/63*sqrt(1-2*x)/(2+3*x)^3-50/441*sqrt(1-2*x)/(2+3*x)^2-_ + 50/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2700x - 5400x - 3600x - 800)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 450x - 950x - 417)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (27783x + 55566x + 37044x + 8232)\|21 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (1350x + 2700x + 1800x + 400)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 450x - 950x - 417)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (27783x + 55566x + 37044x + 8232)\|21 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 50log(-----------------------------) + 100atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 150x + 250)\|21 + (150x - 250)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 100x + 50)\|3 \|7 \|21 + 2100x - 1050 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18522x - 27783x - 11319x + 10290)\|21 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=-95/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 1/84*sqrt(1-2*x)/(2+3*x)^4-19/252*sqrt(1-2*x)/(2+3*x)^3-_ + 95/3528*sqrt(1-2*x)/(2+3*x)^2-95/8232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 3 2 \|3 \|- 2x + 1 +--R (- 15390x - 41040x - 41040x - 18240x - 3040)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (7695x + 20520x + 20520x + 9120x + 1520) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 2565x - 7125x - 7942x - 2790)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 95log(-----------------------------) + 190atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 8232\|21 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 285x + 475)\|21 + (285x - 475)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 190x + 95)\|3 \|7 \|21 + 3990x - 1995 +--R / +--R 2 +--------+ +--R (1037232x + 172872x - 345744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (148176x - 222264x - 90552x + 82320)\|21 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=6206585/384*(1-2*x)^(3/2)-1623419/128*(1-2*x)^(5/2)+_ + 842415/128*(1-2*x)^(7/2)-285565/128*(1-2*x)^(9/2)+_ + 672003/1408*(1-2*x)^(11/2)-97605/1664*(1-2*x)^(13/2)+_ + 405/128*(1-2*x)^(15/2)-2033647/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x +--R + +--R - 3152152x - 3275704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 173745x - 1002375x - 2632743x - 4212525x - 4694340x - 4058988x +--R + +--R - 3152152x - 3275704 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 429 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3l.input.pamphlet b/src/input/rich3l.input.pamphlet new file mode 100644 index 0000000..86bc6fd --- /dev/null +++ b/src/input/rich3l.input.pamphlet @@ -0,0 +1,8152 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3l.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 50 matching answers. +\item 51 cases where the Axiom result differs from Rubi +\item 1 case where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3l.output +)spool rich3l.output +)set message test on +)set message auto off +)clear all + +--S 1 of 502 +t0:=(2+3*x)^4*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 502 +r0:=381073/96*(1-2*x)^(3/2)-832951/320*(1-2*x)^(5/2)+17337/16*(1-2*x)^(7/2)-_ + 17679/64*(1-2*x)^(9/2)+13905/352*(1-2*x)^(11/2)-2025/832*(1-2*x)^(13/2)-_ + 290521/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x +--R + +--R - 4994536 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 334125x - 1709100x - 3954645x - 5576580x - 5587044x - 4685656x +--R + +--R - 4994536 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 502 +t0:=(2+3*x)^3*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 502 +r0:=91091/96*(1-2*x)^(3/2)-39977/80*(1-2*x)^(5/2)+17541/112*(1-2*x)^(7/2)-_ + 855/32*(1-2*x)^(9/2)+675/352*(1-2*x)^(11/2)-41503/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--------+ +--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--------+ +--R (- 70875x - 316575x - 636795x - 790023x - 743822x - 826982)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 502 +t0:=(2+3*x)^2*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 502 +r0:=1309/6*(1-2*x)^(3/2)-3467/40*(1-2*x)^(5/2)+255/14*(1-2*x)^(7/2)-_ + 25/16*(1-2*x)^(9/2)-5929/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1 +--R (2) ---------------------------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 2625x - 10050x - 17391x - 19574x - 23354)\|- 2x + 1 +--R (3) ---------------------------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 502 +t0:=(2+3*x)*(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ----------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 502 +r0:=1133/24*(1-2*x)^(3/2)-101/8*(1-2*x)^(5/2)+75/56*(1-2*x)^(7/2)-_ + 847/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1 +--R (2) ------------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 225x - 723x - 1091x - 1469)\|- 2x + 1 +--R (3) ------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 502 +t0:=(3+5*x)^2/sqrt(1-2*x) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 502 +r0:=55/6*(1-2*x)^(3/2)-5/4*(1-2*x)^(5/2)-121/4*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +--R (- 15x - 40x - 67)\|- 2x + 1 +--R (2) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--------+ +--R (- 15x - 40x - 67)\|- 2x + 1 +--R (3) ------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 502 +t0:=(3+5*x)^2/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 502 +r0:=-2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-5/9*(13+5*x)*sqrt(1-2*x),_ + -2/9*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-50/9*sqrt(1-2*x)-_ + 5/9*(3+5*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R [--------------------------------------------------------, +--R +--+ +--R 9\|21 +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R --------------------------------------------------------] +--R +--+ +--R 9\|21 +--R Type: Tuple(Expression(Integer)) +--E 27 + +--S 28 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--------+ +--R log(-----------------------------) + (- 25x - 65)\|21 \|- 2x + 1 +--R 3x + 2 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R 9\|21 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 9\|21 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (1134x + 189x - 378)\|- 2x + 1 + (162x - 243x - 99x + 90)\|21 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 502 +t0:=(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 502 +r0:=46/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-25/9*sqrt(1-2*x)-_ + 1/63*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--+ +--------+ +--R (138x + 92)atanh(---------------) + (- 175x - 117)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--R (63x + 42)\|21 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R (69x + 46)log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (- 175x - 117)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (63x + 42)\|21 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 23log(-------------------------------) - 46atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 69x + 115)\|21 + (69x - 115)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (46x - 23)\|3 \|7 \|21 - 966x + 483 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (- 378x + 567x + 231x - 210)\|21 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 502 +t0:=(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 502 +r0:=-257/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/126*sqrt(1-2*x)/(2+3*x)^2+137/882*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (- 13878x - 18504x - 6168)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +--+ +--------+ +--R (137x + 89)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (6939x + 9252x + 3084)log(-----------------------------) +--R 3x + 2 +--R + +--R +--+ +--------+ +--R (137x + 89)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (2646x + 3528x + 1176)\|21 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 257log(-----------------------------) + 514atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 98\|21 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 771x + 1285)\|21 + (771x - 1285)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 514x + 257)\|3 \|7 \|21 + 10794x - 5397 +--R / +--R 2 +--------+ 3 2 +--+ +--R (12348x + 2058x - 4116)\|- 2x + 1 + (1764x - 2646x - 1078x + 980)\|21 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 502 +t0:=(3+5*x)^2/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 502 +r0:=-2245/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/189*sqrt(1-2*x)/(2+3*x)^3+205/2646*sqrt(1-2*x)/(2+3*x)^2-_ + 2245/6174*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 121230x - 242460x - 161640x - 35920)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (166698x + 333396x + 222264x + 49392)\|21 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 21\|- 2x + 1 + (3x - 5)\|21 +--R (60615x + 121230x + 80820x + 17960)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 20205x - 25505x - 8056)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (166698x + 333396x + 222264x + 49392)\|21 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2245log(-----------------------------) + 4490atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6174\|21 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 4490x + 2245)\|3 \|7 \|21 + 94290x - 47145 +--R / +--R 2 +--------+ +--R (777924x + 129654x - 259308)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (111132x - 166698x - 67914x + 61740)\|21 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 502 +t0:=(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 502 +r0:=-635/4116*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 1/252*sqrt(1-2*x)/(2+3*x)^4+13/252*sqrt(1-2*x)/(2+3*x)^3-_ + 635/3528*sqrt(1-2*x)/(2+3*x)^2-635/8232*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 102870x - 274320x - 274320x - 121920x - 20320) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (51435x + 137160x + 137160x + 60960x + 10160) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 17145x - 47625x - 39366x - 10190)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (666792x + 1778112x + 1778112x + 790272x + 131712)\|21 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 635log(-----------------------------) + 1270atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 8232\|21 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1905x + 3175)\|21 + (1905x - 3175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1270x + 635)\|3 \|7 \|21 + 26670x - 13335 +--R / +--R 2 +--------+ +--R (1037232x + 172872x - 345744)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (148176x - 222264x - 90552x + 82320)\|21 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 502 +t0:=(3+5*x)^2/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 502 +r0:=-117/9604*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1/315*sqrt(1-2*x)/(2+3*x)^5+341/8820*sqrt(1-2*x)/(2+3*x)^4-_ + 117/980*sqrt(1-2*x)/(2+3*x)^3-117/2744*sqrt(1-2*x)/(2+3*x)^2-_ + 351/19208*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 852930x - 2843100x - 3790800x - 2527200x - 842400x - 112320)\|3 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x +--R + +--R 9219840 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (426465x + 1421550x + 1895400x + 1263600x + 421200x + 56160)\|3 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--------+ +--R (- 426465x - 1468935x - 2110212x - 1327058x - 298748)\|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 70013160x + 233377200x + 311169600x + 207446400x + 69148800x +--R + +--R 9219840 +--R * +--R +-+ +--R \|7 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 117\|3 log(-------------------------------) + 234\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 19208\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 502 +t0:=(2+3*x)^4*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 502 +r0:=3278737/128*(1-2*x)^(3/2)-12973191/640*(1-2*x)^(5/2)+_ + 1357793/128*(1-2*x)^(7/2)-1392467/384*(1-2*x)^(9/2)+_ + 1101465/1408*(1-2*x)^(11/2)-161325/1664*(1-2*x)^(13/2)+_ + 675/128*(1-2*x)^(15/2)-3195731/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x +--R + +--R 2 +--R - 31962552x - 24706048x - 25632688 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R - 1447875x - 8241750x - 21369825x - 33786160x - 37260640x +--R + +--R 2 +--R - 31962552x - 24706048x - 25632688 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2145 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 502 +t0:=(2+3*x)^3*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 502 +r0:=100793/16*(1-2*x)^(3/2)-1334949/320*(1-2*x)^(5/2)+_ + 98209/56*(1-2*x)^(7/2)-28895/64*(1-2*x)^(9/2)+_ + 11475/176*(1-2*x)^(11/2)-3375/832*(1-2*x)^(13/2)-456533/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x +--R + +--R - 17147586x - 18228666 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5005 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 1299375x - 6544125x - 14921900x - 20766885x - 20586249x +--R + +--R - 17147586x - 18228666 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 5005 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 502 +t0:=(2+3*x)^2*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 502 +r0:=48279/32*(1-2*x)^(3/2)-64317/80*(1-2*x)^(5/2)+28555/112*(1-2*x)^(7/2)-_ + 4225/96*(1-2*x)^(9/2)+1125/352*(1-2*x)^(11/2)-65219/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1155 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (- 118125x - 518000x - 1024475x - 1252938x - 1167932x - 1292672) +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 502 +t0:=(2+3*x)*(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 502 +r0:=2783/8*(1-2*x)^(3/2)-561/4*(1-2*x)^(5/2)+1675/56*(1-2*x)^(7/2)-_ + 125/48*(1-2*x)^(9/2)-9317/16*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1 +--R (2) ----------------------------------------------------- +--R 21 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--------+ +--R (- 875x - 3275x - 5556x - 6161x - 7295)\|- 2x + 1 +--R (3) ----------------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 502 +t0:=(3+5*x)^3/sqrt(1-2*x) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 502 +r0:=605/8*(1-2*x)^(3/2)-165/8*(1-2*x)^(5/2)+125/56*(1-2*x)^(7/2)-_ + 1331/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +--R (- 125x - 390x - 575x - 764)\|- 2x + 1 +--R (2) ----------------------------------------- +--R 7 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--------+ +--R (- 125x - 390x - 575x - 764)\|- 2x + 1 +--R (3) ----------------------------------------- +--R 7 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 502 +t0:=(3+5*x)^3/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 502 +r0:=2/27*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-218/9*sqrt(1-2*x)-_ + 1/3*(3+5*x)^2*sqrt(1-2*x)-5/27*(41+61*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|3 \|- 2x + 1 2 +--+ +--------+ +--R 2atanh(---------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 2 +--+ +--------+ +--R log(-------------------------------) + (- 225x - 575x - 940)\|21 \|- 2x + 1 +--R 3x + 2 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 27\|21 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (3402x + 567x - 1134)\|- 2x + 1 + (- 486x + 729x + 297x - 270)\|21 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 502 +t0:=(3+5*x)^3/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 502 +r0:=-208/189*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-1570/189*sqrt(1-2*x)-_ + 38/189*(3+5*x)*sqrt(1-2*x)/(2+3*x)-5/9*(3+5*x)^2*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R (- 624x - 416)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (567x + 378)\|21 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R (312x + 208)log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 2625x - 8050x - 4199)\|21 \|- 2x + 1 +--R / +--R +--+ +--R (567x + 378)\|21 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 104log(-----------------------------) + 208atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 189\|21 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 312x + 520)\|21 + (312x - 520)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 208x + 104)\|3 \|7 \|21 + 4368x - 2184 +--R / +--R 2 +--------+ 3 2 +--+ +--R (23814x + 3969x - 7938)\|- 2x + 1 + (3402x - 5103x - 2079x + 1890)\|21 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 502 +t0:=(3+5*x)^3/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 502 +r0:=2381/441*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/126*(7-25*x)*_ + sqrt(1-2*x)/(2+3*x)^2-274/147*sqrt(1-2*x)/(2+3*x)-_ + 5/3*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|3 \|- 2x + 1 +--R (42858x + 57144x + 19048)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (7938x + 10584x + 3528)\|21 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 - 21\|- 2x + 1 + (3x - 5)\|21 +--R (21429x + 28572x + 9524)log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (- 36750x - 49207x - 16469)\|21 \|- 2x + 1 +--R / +--R 2 +--+ +--R (7938x + 10584x + 3528)\|21 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2381log(-------------------------------) - 4762atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 882\|21 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 7143x + 11905)\|21 + (7143x - 11905)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4762x - 2381)\|3 \|7 \|21 - 100002x + 50001 +--R / +--R 2 +--------+ +--R (111132x + 18522x - 37044)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 15876x + 23814x + 9702x - 8820)\|21 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 502 +t0:=(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 502 +r0:=-78710/9261*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+10600/9261*_ + sqrt(1-2*x)-3385/9261*(3+5*x)*sqrt(1-2*x)/(2+3*x)-50/441*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 \|3 \|- 2x + 1 +--R (- 2125170x - 4250340x - 2833560x - 629680)atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--------+ +--R (31680x + 41155x + 13373)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (250047x + 500094x + 333396x + 74088)\|21 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R (1062585x + 2125170x + 1416780x + 314840) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--------+ +--R (31680x + 41155x + 13373)\|21 \|- 2x + 1 +--R / +--R 3 2 +--+ +--R (250047x + 500094x + 333396x + 74088)\|21 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39355log(-----------------------------) + 78710atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 9261\|21 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 118065x + 196775)\|21 + (118065x - 196775)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 78710x + 39355)\|3 \|7 \|21 + 1652910x - 826455 +--R / +--R 2 +--------+ +--R (1166886x + 194481x - 388962)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (166698x - 250047x - 101871x + 92610)\|21 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 502 +t0:=(3+5*x)^3/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 502 +r0:=-42995/37044*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 3275/12348*sqrt(1-2*x)/(2+3*x)-1/18*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3-_ + 1/28*(3+5*x)^3*sqrt(1-2*x)/(2+3*x)^4+5/10584*(79+29*x)*_ + sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R (2) +--R 4 3 2 +--R (- 6965190x - 18573840x - 18573840x - 8255040x - 1375840) +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--------+ +--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3482595x + 9286920x + 9286920x + 4127520x + 687920) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--------+ +--R (- 1160865x - 2195625x - 1385462x - 291670)\|21 \|- 2x + 1 +--R / +--R 4 3 2 +--+ +--R (6001128x + 16003008x + 16003008x + 7112448x + 1185408)\|21 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 42995log(-----------------------------) + 85990atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 74088\|21 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 128985x + 214975)\|21 + (128985x - 214975)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 85990x + 42995)\|3 \|7 \|21 + 1805790x - 902895 +--R / +--R 2 +--------+ +--R (9335088x + 1555848x - 3111696)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1333584x - 2000376x - 814968x + 740880)\|21 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 502 +t0:=(3+5*x)^3/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 502 +r0:=-5293/21609*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)-_ + 61/882*sqrt(1-2*x)/(2+3*x)^2-5293/43218*sqrt(1-2*x)/(2+3*x)-_ + 8/245*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^3*_ + sqrt(1-2*x)/(2+3*x)^5+1/15435*(353+295*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 12861990x - 42873300x - 57164400x - 38109600x - 12703200x +--R + +--R - 1693760 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x +--R + +--R 6914880 +--R * +--R +--+ +--R \|21 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (6430995x + 21436650x + 28582200x + 19054800x + 6351600x + 846880) +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 2143665x - 7383735x - 8806422x - 4450198x - 816938)\|21 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 52509870x + 175032900x + 233377200x + 155584800x + 51861600x +--R + +--R 6914880 +--R * +--R +--+ +--R \|21 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 5293log(-----------------------------) + 10586atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 43218\|21 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 15879x + 26465)\|21 + (15879x - 26465)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 10586x + 5293)\|3 \|7 \|21 + 222306x - 111153 +--R / +--R 2 +--------+ +--R (5445468x + 907578x - 1815156)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (777924x - 1166886x - 475398x + 432180)\|21 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 502 +t0:=(a+b*x)^2/((c+d*x)^2*sqrt(e+f*x)) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------------------ +--R 2 2 2 +-------+ +--R (d x + 2c d x + c )\|f x + e +--R Type: Expression(Integer) +--E 111 + +--S 112 of 502 +r0:=(b*c-a*d)*(4*b*d*e-3*b*c*f-a*d*f)*atanh(sqrt(d)*sqrt(e+f*x)/_ + sqrt(d*e-c*f))/(d^(5/2)*(d*e-c*f)^(3/2))+2*b^2*sqrt(e+f*x)/_ + (d^2*f)-(b*c-a*d)^2*sqrt(e+f*x)/(d^2*(d*e-c*f)*(c+d*x)) +--R +--R +--R (2) +--R 2 3 2 2 2 2 3 2 2 +--R ((- a d - 2a b c d + 3b c d)f + (4a b d - 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (- a c d - 2a b c d + 3b c )f + (4a b c d - 4b c d)e f +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R + +--R 2 2 2 2 2 2 2 2 +--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e) +--R * +--R +-----------+ +-+ +-------+ +--R \|- c f + d e \|d \|f x + e +--R / +--R 3 2 4 2 2 2 3 +-----------+ +-+ +--R ((c d f - d e f)x + c d f - c d e f)\|- c f + d e \|d +--R Type: Expression(Integer) +--E 112 + +--S 113 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 3 2 2 2 2 3 2 2 +--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e +--R log(----------------------------------------------------------------) +--R d x + c +--R + +--R 2 2 2 2 2 2 2 2 +--R ((4b c d f - 4b d e)x + (2a d - 4a b c d + 6b c )f - 4b c d e) +--R * +--R +-------------+ +--R | 2 +-------+ +--R \|- c d f + d e \|f x + e +--R / +--R +-------------+ +--R 3 2 4 2 2 2 3 | 2 +--R ((2c d f - 2d e f)x + 2c d f - 2c d e f)\|- c d f + d e +--R , +--R +--R 2 3 2 2 2 2 3 2 2 +--R ((a d + 2a b c d - 3b c d)f + (- 4a b d + 4b c d )e f)x +--R + +--R 2 2 2 2 3 2 2 2 2 +--R (a c d + 2a b c d - 3b c )f + (- 4a b c d + 4b c d)e f +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R atan(------------------------) +--R c f - d e +--R + +--R 2 2 2 2 2 2 2 2 +--R ((2b c d f - 2b d e)x + (a d - 2a b c d + 3b c )f - 2b c d e) +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R / +--R +-----------+ +--R 3 2 4 2 2 2 3 | 2 +--R ((c d f - d e f)x + c d f - c d e f)\|c d f - d e +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 113 + +--S 114 of 502 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 +-----------+ +-+ +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d +--R * +--R +-------------+ +--R 2 +-------+ | 2 +--R (2c d f - 2d e)\|f x + e + (d f x - c f + 2d e)\|- c d f + d e +--R log(----------------------------------------------------------------) +--R d x + c +--R + +--R +-------------+ +--R 2 2 2 2 2 2 | 2 +--R ((2a d + 4a b c d - 6b c )f + (- 8a b d + 8b c d)e)\|- c d f + d e +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R / +--R +-------------+ +--R 2 3 | 2 +-----------+ +-+ +--R (2c d f - 2d e)\|- c d f + d e \|- c f + d e \|d +--R Type: Expression(Integer) +--E 114 + +--S 115 of 502 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 502 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-----------+ +--R 2 2 2 2 2 2 | 2 +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|c d f - d e +--R * +--R +-+ +-------+ +--R \|d \|f x + e +--R atanh(--------------) +--R +-----------+ +--R \|- c f + d e +--R + +--R 2 2 2 2 2 2 +-----------+ +-+ +--R ((a d + 2a b c d - 3b c )f + (- 4a b d + 4b c d)e)\|- c f + d e \|d +--R * +--R +-----------+ +--R | 2 +-------+ +--R \|c d f - d e \|f x + e +--R atan(------------------------) +--R c f - d e +--R / +--R +-----------+ +--R 2 3 +-----------+ +-+ | 2 +--R (c d f - d e)\|- c f + d e \|d \|c d f - d e +--R Type: Expression(Integer) +--E 116 + +--S 117 of 502 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 502 +t0:=(2+3*x)^5/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 118 + +--S 119 of 502 +r0:=-2/3125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 125702/3125*sqrt(1-2*x)-748/625*(2+3*x)^2*sqrt(1-2*x)-_ + 149/525*(2+3*x)^3*sqrt(1-2*x)-1/15*(2+3*x)^4*sqrt(1-2*x)-_ + 1/3125*(31426+52375*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R - 14atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 21875\|55 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 7log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 118125x - 482625x - 885870x - 1044285x - 1277616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 21875\|55 +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 3125\|55 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (1718750x + 171875x - 515625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (156250x - 234375x - 71875x + 75000)\|55 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 502 +t0:=(2+3*x)^4/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 502 +r0:=-2/625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7878/625*sqrt(1-2*x)-_ + 9/5*(2+3*x)*sqrt(1-2*x)-48/125*(2+3*x)^2*sqrt(1-2*x)-_ + 3/35*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R - 14atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 4375\|55 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R 7log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 10125x - 35370x - 57285x - 80616)\|55 \|- 2x + 1 +--R / +--R +--+ +--R 4375\|55 +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 625\|55 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (343750x + 34375x - 103125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (31250x - 46875x - 14375x + 15000)\|55 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 502 +t0:=(2+3*x)^3/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 502 +r0:=-2/125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-542/125*sqrt(1-2*x)-_ + 3/25*(2+3*x)^2*sqrt(1-2*x)-1/125*(136+225*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R - 2atanh(---------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--R 125\|55 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 2 +--+ +--------+ +--R log(-----------------------------) + (- 135x - 405x - 738)\|55 \|- 2x + 1 +--R 5x + 3 +--R --------------------------------------------------------------------------- +--R +--+ +--R 125\|55 +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 125\|55 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (68750x + 6875x - 20625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6250x - 9375x - 2875x + 3000)\|55 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 502 +t0:=(2+3*x)^2/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 133 + +--S 134 of 502 +r0:=-2/25*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-38/25*sqrt(1-2*x)-_ + 1/5*(2+3*x)*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) + (- 15x - 48)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R log(-----------------------------) + (- 15x - 48)\|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R 25\|55 +--R Type: Union(Expression(Integer),...) +--E 135 + +--S 136 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 25\|55 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (13750x + 1375x - 4125)\|- 2x + 1 + (1250x - 1875x - 575x + 600)\|55 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 502 +t0:=(2+3*x)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 138 + +--S 139 of 502 +r0:=-2/5*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-3/5*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R - 2atanh(---------------) - 3\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------- +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R log(-----------------------------) - 3\|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------ +--R +--+ +--R 5\|55 +--R Type: Union(Expression(Integer),...) +--E 140 + +--S 141 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 5\|55 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2750x + 275x - 825)\|- 2x + 1 + (250x - 375x - 115x + 120)\|55 +--R Type: Expression(Integer) +--E 142 + +)clear all + +--S 143 of 502 +t0:=1/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------- +--R +--------+ +--R (5x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 502 +r0:=-2*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R 2atanh(---------------) +--R +--+ +--R \|11 +--R (2) - ----------------------- +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R (3) ---------------------------------- +--R +--+ +--R \|55 +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R \|55 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (550x + 55x - 165)\|- 2x + 1 + (50x - 75x - 23x + 24)\|55 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 502 +t0:=1/((2+3*x)*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--------+ +--R (15x + 19x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 502 +r0:=2*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11) +--R +--R +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 2\|3 \|11 atanh(---------------) - 2\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2\|3 \|11 atanh(---------------) + 2\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 152 + +)clear all + +--S 153 of 502 +t0:=1/((2+3*x)^2*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 2 +--------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 502 +r0:=72/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+3/7*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R (216x + 144)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+ +--R (- 210x - 140)\|5 \|7 atanh(---------------) + 3\|7 \|11 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R (21x + 14)\|7 \|11 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (105x + 70)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (108x + 72)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R 3\|7 \|11 \|- 2x + 1 +--R / +--R +-+ +--+ +--R (21x + 14)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 36\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 72\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 7\|7 \|11 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 502 +t0:=1/((2+3*x)^3*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 502 +r0:=2523/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+3/14*sqrt(1-2*x)/(2+3*x)^2+_ + 219/98*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (45414x + 60552x + 20184)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (- 44100x - 58800x - 19600)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (657x + 459)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (882x + 1176x + 392)\|7 \|11 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (22050x + 29400x + 9800)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (22707x + 30276x + 10092)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R (657x + 459)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (882x + 1176x + 392)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2450\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2523\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 5046\|3 \|11 atanh(---------------) + 4900\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 98\|7 \|11 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 502 +t0:=1/((2+3*x)^4*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 502 +r0:=88310/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-250*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1/7*sqrt(1-2*x)/(2+3*x)^3+_ + 55/49*sqrt(1-2*x)/(2+3*x)^2+3840/343*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (2384370x + 4768740x + 3179160x + 706480)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 2315250x - 4630500x - 3087000x - 686000)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (9261x + 18522x + 12348x + 2744)\|7 \|11 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (1157625x + 2315250x + 1543500x + 343000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (1192185x + 2384370x + 1589580x + 353240)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (34560x + 47235x + 16179)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (9261x + 18522x + 12348x + 2744)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 42875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 44155\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 88310\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 85750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 343\|7 \|11 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 502 +t0:=1/((2+3*x)^5*(3+5*x)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|- 2x + 1 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 502 +r0:=36045/28*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1250*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 3/28*sqrt(1-2*x)/(2+3*x)^4+3/4*sqrt(1-2*x)/(2+3*x)^3+_ + 45/8*sqrt(1-2*x)/(2+3*x)^2+3135/56*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--+ +--R (5839290x + 15571440x + 15571440x + 6920640x + 1153440)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +-+ +--R (- 5670000x - 15120000x - 15120000x - 6720000x - 1120000)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +-+ +--R (2835000x + 7560000x + 7560000x + 3360000x + 560000)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (2919645x + 7785720x + 7785720x + 3460320x + 576720)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (84645x + 172125x + 116766x + 26430)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (4536x + 12096x + 12096x + 5376x + 896)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35000\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 36045\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 72090\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 70000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 56\|7 \|11 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 502 +t0:=(2+3*x)^6/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 502 +r0:=-398/171875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 4434698/171875*sqrt(1-2*x)-26352/34375*(2+3*x)^2*sqrt(1-2*x)-_ + 1717/9625*(2+3*x)^3*sqrt(1-2*x)+8/825*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)-_ + 1/15*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)-1/171875*(1108774+_ + 1847625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 13930x - 8358)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x +--R + +--R - 135011752 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (6015625x + 3609375)\|55 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (6965x + 4179)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 19490625x - 92998125x - 200942775x - 273540465x - 334366065x +--R + +--R - 135011752 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R +--+ +--R (6015625x + 3609375)\|55 +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 199log(-----------------------------) + 398atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 171875\|55 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 995x + 1592)\|55 + (995x - 1592)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 398x + 199)\|5 \|11 \|55 + 21890x - 10945 +--R / +--R 2 +--------+ +--R (94531250x + 9453125x - 28359375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (8593750x - 12890625x - 3953125x + 4125000)\|55 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 502 +t0:=(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 502 +r0:=-332/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 278748/34375*sqrt(1-2*x)-318/275*(2+3*x)*sqrt(1-2*x)-_ + 1668/6875*(2+3*x)^2*sqrt(1-2*x)+26/1925*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)-3/35*(2+3*x)^4*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 11620x - 6972)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +--+ +--R (1203125x + 721875)\|55 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (5810x + 3486)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 1670625x - 6994350x - 13532310x - 20175210x - 8527768)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R +--+ +--R (1203125x + 721875)\|55 +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 166log(-----------------------------) + 332atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 34375\|55 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 830x + 1328)\|55 + (830x - 1328)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 332x + 166)\|5 \|11 \|55 + 18260x - 9130 +--R / +--R 2 +--------+ +--R (18906250x + 1890625x - 5671875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1718750x - 2578125x - 790625x + 825000)\|55 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 502 +t0:=(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 502 +r0:=-266/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 19166/6875*sqrt(1-2*x)+28/1375*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)-_ + 3/25*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)-7/6875*(694+1125*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R (- 1330x - 798)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (34375x + 20625)\|55 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (665x + 399)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 22275x - 82665x - 171765x - 78112)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (34375x + 20625)\|55 +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 133log(-----------------------------) + 266atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 6875\|55 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 665x + 1064)\|55 + (665x - 1064)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 266x + 133)\|5 \|11 \|55 + 14630x - 7315 +--R / +--R 2 +--------+ +--R (3781250x + 378125x - 1134375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (343750x - 515625x - 158125x + 165000)\|55 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 502 +t0:=(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 502 +r0:=-8/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-54/55*sqrt(1-2*x)+_ + 2/55*(2+3*x)*sqrt(1-2*x)/(3+5*x)-1/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R \|5 \|- 2x + 1 2 +--+ +--------+ +--R (- 40x - 24)atanh(---------------) + (- 99x - 396x - 202)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (20x + 12)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 99x - 396x - 202)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (275x + 165)\|55 +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4log(-----------------------------) + 8atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 20x + 32)\|55 + (20x - 32)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 8x + 4)\|5 \|11 \|55 + 440x - 220 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 502 +t0:=(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 502 +r0:=-134/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-9/25*sqrt(1-2*x)-_ + 1/275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 670x - 402)atanh(---------------) + (- 495x - 298)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------------- +--R +--+ +--R (1375x + 825)\|55 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R (335x + 201)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 495x - 298)\|55 \|- 2x + 1 +--R / +--R +--+ +--R (1375x + 825)\|55 +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 67log(-----------------------------) + 134atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 275\|55 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 335x + 536)\|55 + (335x - 536)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 134x + 67)\|5 \|11 \|55 + 7370x - 3685 +--R / +--R 2 +--------+ +--R (151250x + 15125x - 45375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (13750x - 20625x - 6325x + 6600)\|55 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 502 +t0:=(2+3*x)/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 502 +r0:=-68/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/55*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 340x - 204)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (170x + 102)log(-----------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ----------------------------------------------------------------- +--R +--+ +--R (275x + 165)\|55 +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 502 +t0:=1/((3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 +--------+ +--R (25x + 30x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/11*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--+ +--------+ +--R (- 10x - 6)atanh(---------------) - \|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +--+ +--R (55x + 33)\|55 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--------+ +--R (5x + 3)log(-----------------------------) - \|55 \|- 2x + 1 +--R 5x + 3 +--R (3) ------------------------------------------------------------- +--R +--+ +--R (55x + 33)\|55 +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 11\|55 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 502 +t0:=1/((2+3*x)*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 2 +--------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 502 +r0:=-6*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-5/11*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R (- 330x - 198)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +-+ +--+ +--------+ +--R (320x + 192)\|5 \|7 atanh(---------------) - 5\|7 \|11 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R (55x + 33)\|7 \|11 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (165x + 99)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (160x + 96)\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R - 5\|7 \|11 \|- 2x + 1 +--R / +--R +-+ +--+ +--R (55x + 33)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 33\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 32\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 66\|3 \|11 atanh(---------------) - 64\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 11\|7 \|11 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 502 +t0:=1/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 502 +r0:=-426/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+650/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-340/77*sqrt(1-2*x)/(3+5*x)+3/7*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (- 70290x - 89034x - 28116)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (68250x + 86450x + 27300)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (- 1020x - 647)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (1155x + 1463x + 462)\|7 \|11 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (35145x + 44517x + 14058)\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--R (34125x + 43225x + 13650)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--------+ +--R (- 1020x - 647)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (1155x + 1463x + 462)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2343\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2275\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 4686\|3 \|11 atanh(---------------) - 4550\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 77\|7 \|11 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 502 +t0:=1/((2+3*x)^3*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 502 +r0:=-22479/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+4900/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35845/1078*_ + sqrt(1-2*x)/(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 162/49*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 22254210x - 43024806x - 27694128x - 5934456)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (21609000x + 41777400x + 26891200x + 5762400)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (48510x + 93786x + 60368x + 12936)\|7 \|11 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (11127105x + 21512403x + 13847064x + 2967228)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--R (10804500x + 20888700x + 13445600x + 2881200)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (- 322605x - 419448x - 136021)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (48510x + 93786x + 60368x + 12936)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 247269\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 240100\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 494538\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 480200\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1078\|7 \|11 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 502 +t0:=1/((2+3*x)^4*(3+5*x)^2*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 502 +r0:=-1051695/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+32750/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-1676975/7546*_ + sqrt(1-2*x)/(3+5*x)+1/7*sqrt(1-2*x)/((2+3*x)^3*(3+5*x))+_ + 145/98*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+7585/343*sqrt(1-2*x)/_ + ((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 3123534150x - 8121188790x - 7912953180x - 3424318920x +--R + +--R - 555294960 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (3032977500x + 7885741500x + 7683543000x + 3325042000x + 539196000) +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1561767075x + 4060594395x + 3956476590x + 1712159460x + 277647480) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1516488750x + 3942870750x + 3841771500x + 1662521000x + 269598000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (- 45278325x - 89054820x - 58335165x - 12724912)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (1018710x + 2648646x + 2580732x + 1116808x + 181104)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 11568645\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 11233250\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 23137290\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 22466500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 7546\|7 \|11 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 502 +t0:=(2+3*x)^6/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 502 +r0:=-33069/1890625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 9865791/1890625*sqrt(1-2*x)-22437/30250*(2+3*x)*sqrt(1-2*x)-_ + 56556/378125*(2+3*x)^2*sqrt(1-2*x)+59/3850*(2+3*x)^4*_ + sqrt(1-2*x)/(3+5*x)^2-3/35*(2+3*x)^5*sqrt(1-2*x)/(3+5*x)^2+_ + 309/211750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 11574150x - 13888980x - 4166694)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 551306250x - 2690374500x - 6078090150x - 9876010320x +--R + +--R - 7254126105x - 1804176536 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (661718750x + 794062500x + 238218750)\|55 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (5787075x + 6944490x + 2083347)log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 551306250x - 2690374500x - 6078090150x - 9876010320x +--R + +--R - 7254126105x - 1804176536 +--R * +--R +--+ +--------+ +--R \|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (661718750x + 794062500x + 238218750)\|55 +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 33069log(-----------------------------) + 66138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 3781250\|55 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 165345x + 264552)\|55 + (165345x - 264552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 66138x + 33069)\|5 \|11 \|55 + 3637590x - 1818795 +--R / +--R 2 +--------+ +--R (2079687500x + 207968750x - 623906250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (189062500x - 283593750x - 86968750x + 90750000)\|55 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 502 +t0:=(2+3*x)^5/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 502 +r0:=-22113/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 674163/378125*sqrt(1-2*x)+61/2750*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 3/25*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^2+504/75625*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)-189/756250*(1842+2875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 1105650x - 1326780x - 398034)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (18906250x + 22687500x + 6806250)\|55 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (552825x + 663390x + 199017)log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 7350750x - 32506650x - 76970520x - 63610155x - 16525496)\|55 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 2 +--+ +--R (18906250x + 22687500x + 6806250)\|55 +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 22113log(-----------------------------) + 44226atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 756250\|55 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 110565x + 176904)\|55 + (110565x - 176904)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 44226x + 22113)\|5 \|11 \|55 + 2432430x - 1216215 +--R / +--R 2 +--------+ +--R (415937500x + 41593750x - 124781250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37812500x - 56718750x - 17393750x + 18150000)\|55 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 502 +t0:=(2+3*x)^4/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 502 +r0:=-2667/15125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 9513/15125*sqrt(1-2*x)+21/550*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2-_ + 1/5*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2+21/1210*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 133350x - 160020x - 48006)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (756250x + 907500x + 272250)\|55 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (66675x + 80010x + 24003)log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--------+ +--R (- 163350x - 784080x - 764745x - 211864)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (756250x + 907500x + 272250)\|55 +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2667log(-----------------------------) + 5334atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 30250\|55 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 13335x + 21336)\|55 + (13335x - 21336)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5334x + 2667)\|5 \|11 \|55 + 293370x - 146685 +--R / +--R 2 +--------+ +--R (16637500x + 1663750x - 4991250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1512500x - 2268750x - 695750x + 726000)\|55 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 502 +t0:=(2+3*x)^3/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 502 +r0:=-1347/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+13/110*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x)^2-3/5*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 201/3025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 67350x - 80820x - 24246)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (33675x + 40410x + 12123)log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--------+ +--R (- 32670x - 39405x - 11884)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 1347log(-----------------------------) + 2694atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6050\|55 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 6735x + 10776)\|55 + (6735x - 10776)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2694x + 1347)\|5 \|11 \|55 + 148170x - 74085 +--R / +--R 2 +--------+ +--R (3327500x + 332750x - 998250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (302500x - 453750x - 139150x + 145200)\|55 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 502 +t0:=(2+3*x)^2/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 502 +r0:=-2313/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/550*sqrt(1-2*x)/_ + (3+5*x)^2-27/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 115650x - 138780x - 41634)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 675x - 416)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (57825x + 69390x + 20817)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 675x - 416)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (151250x + 181500x + 54450)\|55 +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2313log(-----------------------------) + 4626atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 6050\|55 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 11565x + 18504)\|55 + (11565x - 18504)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 4626x + 2313)\|5 \|11 \|55 + 254430x - 127215 +--R / +--R 2 +--------+ +--R (3327500x + 332750x - 998250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (302500x - 453750x - 139150x + 145200)\|55 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 502 +t0:=(2+3*x)/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 502 +r0:=-69/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/110*sqrt(1-2*x)/_ + (3+5*x)^2-69/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--R (- 3450x - 4140x - 1242)atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +--+ +--------+ +--R (- 345x - 218)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (30250x + 36300x + 10890)\|55 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (1725x + 2070x + 621)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 345x - 218)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (30250x + 36300x + 10890)\|55 +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 69log(-----------------------------) + 138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1210\|55 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795 +--R / +--R 2 +--------+ +--R (665500x + 66550x - 199650)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (60500x - 90750x - 27830x + 29040)\|55 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 502 +t0:=1/((3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 3 2 +--------+ +--R (125x + 225x + 135x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 502 +r0:=-3/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-1/22*sqrt(1-2*x)/_ + (3+5*x)^2-3/242*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 \|5 \|- 2x + 1 +--+ +--------+ +--R (- 150x - 180x - 54)atanh(---------------) + (- 15x - 20)\|55 \|- 2x + 1 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R 2 +--+ +--R (6050x + 7260x + 2178)\|55 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 55\|- 2x + 1 + (5x - 8)\|55 +--R (75x + 90x + 27)log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--------+ +--R (- 15x - 20)\|55 \|- 2x + 1 +--R / +--R 2 +--+ +--R (6050x + 7260x + 2178)\|55 +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 3log(-----------------------------) + 6atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------- +--R +--+ +--R 242\|55 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 15x + 24)\|55 + (15x - 24)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 6x + 3)\|5 \|11 \|55 + 330x - 165 +--R / +--R 2 +--------+ +--R (133100x + 13310x - 39930)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (12100x - 18150x - 5566x + 5808)\|55 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 502 +t0:=1/((2+3*x)*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------- +--R 4 3 2 +--------+ +--R (375x + 925x + 855x + 351x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 502 +r0:=18*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-2115/121*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)-5/22*sqrt(1-2*x)/(3+5*x)^2+_ + 315/242*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ \|3 \|- 2x + 1 +--R (108900x + 130680x + 39204)\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ \|5 \|- 2x + 1 +--R (- 105750x - 126900x - 38070)\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--------+ +--R (1575x + 890)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (6050x + 7260x + 2178)\|7 \|11 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (52875x + 63450x + 19035)\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R 2 +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (54450x + 65340x + 19602)\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--------+ +--R (1575x + 890)\|7 \|11 \|- 2x + 1 +--R / +--R 2 +-+ +--+ +--R (6050x + 7260x + 2178)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2115\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2178\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 4356\|3 \|11 atanh(---------------) + 4230\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 242\|7 \|11 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 502 +t0:=1/((2+3*x)^2*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (1125x + 3525x + 4415x + 2763x + 864x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 502 +r0:=1908/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-32025/121*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-505/154*sqrt(1-2*x)/(3+5*x)^2+_ + 3/7*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+33465/1694*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (34630200x + 64643040x + 40171032x + 8311248)\|3 \|11 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 33626250x - 62769000x - 39006450x - 8070300)\|5 \|7 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--------+ +--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (127050x + 237160x + 147378x + 30492)\|7 \|11 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (16813125x + 31384500x + 19503225x + 4035150)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (17315100x + 32321520x + 20085516x + 4155624)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--------+ +--R (501975x + 619170x + 190406)\|7 \|11 \|- 2x + 1 +--R / +--R 3 2 +-+ +--+ +--R (127050x + 237160x + 147378x + 30492)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 224175\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 230868\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 461736\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 448350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1694\|7 \|11 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 502 +t0:=1/((2+3*x)^3*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R ------------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216)\|- 2x + 1 +--R Type: Expression(Integer) +--E 273 + +--S 274 of 502 +r0:=134217/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-321825/121*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-35495/1078*_ + sqrt(1-2*x)/(3+5*x)^2+3/14*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 429/98*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1177080/5929*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 7308115650x + 18513892980x + 17571958074x + 7405557192x +--R + +--R 1169298504 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 7096241250x - 17977144500x - 17062517850x - 7190857800x +--R + +--R - 1135398600 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (3548120625x + 8988572250x + 8531258925x + 3595428900x + 567699300) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (3654057825x + 9256946490x + 8785979037x + 3702778596x + 584649252) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (105937200x + 201297915x + 127303347x + 26794499)\|7 \|11 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--+ +--R (2668050x + 6759060x + 6415178x + 2703624x + 426888)\|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 15769425\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 16240257\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 32480514\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 31538850\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 11858\|7 \|11 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 502 +t0:=1/((2+3*x)^4*(3+5*x)^3*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 502 +r0:=7852680/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 2689875/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)-_ + 2076675/7546*sqrt(1-2*x)/(3+5*x)^2+1/7*sqrt(1-2*x)/((2+3*x)^3*_ + (3+5*x)^2)+90/49*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 12555/343*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+137735775/83006*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1282735278000x + 4104752889600x + 5250663071280x + 3356015556960x +--R + +--R 1071796587840x + 136825096320 +--R * +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R \|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 +--R - 1245546618750x - 3985749180000x - 5098437492750x +--R + +--R 2 +--R - 3258719005500x - 1040723397000x - 132858306000 +--R * +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R \|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R 18594329625x + 47728484550x + 45899434890x + 19599448500x +--R + +--R 3135381218 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x +--R + +--R 5976432 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 622773309375x + 1992874590000x + 2549218746375x + 1629359502750x +--R + +--R 520361698500x + 66429153000 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 641367639000x + 2052376444800x + 2625331535640x + 1678007778480x +--R + +--R 535898293920x + 68412548160 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R 18594329625x + 47728484550x + 45899434890x + 19599448500x +--R + +--R 3135381218 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R 56029050x + 179292960x + 229345578x + 146588596x + 46815384x +--R + +--R 5976432 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 922627125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 950174280\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1900348560\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1845254250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 502 +t0:=(2+3*x)^7*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R - 10935x - 57591x - 132678x - 174636x - 143640x - 75600x - 24864x +--R + +--R - 4672x - 384 +--R / +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 502 +r0:=-7882483/128*(1-2*x)^(3/2)+4084101/128*(1-2*x)^(5/2)-_ + 787185/64*(1-2*x)^(7/2)+422919/128*(1-2*x)^(9/2)-_ + 821583/1408*(1-2*x)^(11/2)+101331/1664*(1-2*x)^(13/2)-_ + 729/256*(1-2*x)^(15/2)+9058973/256/sqrt(1-2*x)+15647317/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 8 7 6 5 4 3 +--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x +--R + +--R 2 +--R - 8106616x - 16881328x + 16936240 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 3 +--R - 104247x - 697653x - 2168775x - 4220622x - 5949090x - 6921432x +--R + +--R 2 +--R - 8106616x - 16881328x + 16936240 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 502 +t0:=(2+3*x)^6*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 3645x - 16767x - 33048x - 36180x - 23760x - 9360x - 2048x - 192 +--R ----------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 502 +r0:=-1692705/128*(1-2*x)^(3/2)+731619/128*(1-2*x)^(5/2)-_ + 225855/128*(1-2*x)^(7/2)+45549/128*(1-2*x)^(9/2)-_ + 59049/1408*(1-2*x)^(11/2)+3645/1664*(1-2*x)^(13/2)+_ + 1294139/128/sqrt(1-2*x)+3916031/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x +--R + +--R - 4512448x + 4539904 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 40095x - 243486x - 687420x - 1230120x - 1663632x - 2109792x +--R + +--R - 4512448x + 4539904 +--R / +--R +--------+ +--R 143\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 502 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 4779x - 7830x - 6840x - 3360x - 880x - 96 +--R (1) -------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 502 +r0:=-173215/64*(1-2*x)^(3/2)+7497/8*(1-2*x)^(5/2)-13905/64*(1-2*x)^(7/2)+_ + 117/4*(1-2*x)^(9/2)-1215/704*(1-2*x)^(11/2)+_ + 184877/64/sqrt(1-2*x)+60025/8*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760 +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 502 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R - 1215x - 6651x - 17055x - 28692x - 41012x - 91704x + 92760 +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 502 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 405x - 1323x - 1728x - 1128x - 368x - 48 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 502 +r0:=-8281/16*(1-2*x)^(3/2)+10773/80*(1-2*x)^(5/2)-4671/224*(1-2*x)^(7/2)+_ + 45/32*(1-2*x)^(9/2)+26411/32/sqrt(1-2*x)+57281/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456 +--R (2) ------------------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 1575x - 7740x - 18288x - 31448x - 75776x + 77456 +--R (3) ------------------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 502 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 135x - 351x - 342x - 148x - 24 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 502 +r0:=-357/4*(1-2*x)^(3/2)+621/40*(1-2*x)^(5/2)-135/112*(1-2*x)^(7/2)+_ + 3773/16/sqrt(1-2*x)+3283/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 675x - 2997x - 6987x - 19154x + 19994 +--R (2) ------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 675x - 2997x - 6987x - 19154x + 19994 +--R (3) ------------------------------------------ +--R +--------+ +--R 35\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 502 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 45x - 87x - 56x - 12 +--R (1) ------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 502 +r0:=-103/8*(1-2*x)^(3/2)+9/8*(1-2*x)^(5/2)+539/8/sqrt(1-2*x)+707/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 9x - 38x - 132x + 144 +--R (2) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 9x - 38x - 132x + 144 +--R (3) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 502 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +--R - 15x - 19x - 6 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 502 +r0:=-5/4*(1-2*x)^(3/2)+77/4/sqrt(1-2*x)+17*sqrt(1-2*x) +--R +--R +--R 2 +--R - 5x - 29x + 35 +--R (2) ---------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5x - 29x + 35 +--R (3) ---------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 502 +t0:=(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R - 5x - 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 502 +r0:=11/2/sqrt(1-2*x)+5/2*sqrt(1-2*x) +--R +--R +--R - 5x + 8 +--R (2) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 502 +a0:=integrate(t0,x) +--R +--R +--R - 5x + 8 +--R (3) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R - 5x - 3 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 502 +r0:=2/7*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+11/7/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R 2\|- 2x + 1 atanh(---------------) + 11\|21 +--R +-+ +--R \|7 +--R (2) -------------------------------------------- +--R +--+ +--------+ +--R 7\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R \|- 2x + 1 log(-------------------------------) + 11\|21 +--R 3x + 2 +--R (3) --------------------------------------------------------- +--R +--+ +--------+ +--R 7\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 7\|21 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (882x + 147x - 294)\|- 2x + 1 + (- 126x + 189x + 77x - 70)\|21 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R - 5x - 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 502 +r0:=-64/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+64/147/sqrt(1-2*x)+_ + 1/21/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (- 192x - 128)\|- 2x + 1 atanh(---------------) + (64x + 45)\|21 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (147x + 98)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R (96x + 64)\|- 2x + 1 log(-----------------------------) + (64x + 45)\|21 +--R 3x + 2 +--R ------------------------------------------------------------------------- +--R +--+ +--------+ +--R (147x + 98)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 32log(-----------------------------) + 64atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 96x + 160)\|21 + (96x - 160)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 64x + 32)\|3 \|7 \|21 + 1344x - 672 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R - 5x - 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 502 +r0:=-65/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/42/((2+3*x)^2*_ + sqrt(1-2*x))+65/147/((2+3*x)*sqrt(1-2*x))-195/686*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 1170x - 1560x - 520)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--R (1170x + 1105x + 233)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 8232x + 2744)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (585x + 780x + 260)\|3 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (1170x + 1105x + 233)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 8232x + 2744)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 65\|3 log(-------------------------------) + 130\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 338 + +--S 339 of 502 +r0:=-10/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/63/((2+3*x)^3*_ + sqrt(1-2*x))+4/9/((2+3*x)^2*sqrt(1-2*x))-5/21*sqrt(1-2*x)/_ + (2+3*x)^2-5/49*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (- 270x - 540x - 360x - 80)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (90x + 145x + 57x + 1)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 3 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (135x + 270x + 180x + 40)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (90x + 145x + 57x + 1)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (1323x + 2646x + 1764x + 392)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 5log(-----------------------------) + 10atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 15x + 25)\|21 + (15x - 25)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 10x + 5)\|3 \|7 \|21 + 210x - 105 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R - 5x - 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 502 +r0:=-655/9604*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+1/84/((2+3*x)^4*_ + sqrt(1-2*x))+131/294/((2+3*x)^3*sqrt(1-2*x))-131/588*_ + sqrt(1-2*x)/(2+3*x)^3-655/8232*sqrt(1-2*x)/(2+3*x)^2-_ + 655/19208*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 106110x - 282960x - 282960x - 125760x - 20960)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (35370x + 80565x + 60391x + 10742x - 2566)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (53055x + 141480x + 141480x + 62880x + 10480)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (35370x + 80565x + 60391x + 10742x - 2566)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (1555848x + 4148928x + 4148928x + 1843968x + 307328)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 655log(-----------------------------) + 1310atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 19208\|21 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 1965x + 3275)\|21 + (1965x - 3275)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1310x + 655)\|3 \|7 \|21 + 27510x - 13755 +--R / +--R 2 +--------+ +--R (2420208x + 403368x - 806736)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (345744x - 518616x - 211288x + 192080)\|21 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 502 +t0:=(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^6) +--R +--R +--R - 5x - 3 +--R (1) ------------------------------------------------------------------- +--R 7 6 5 4 2 +--------+ +--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 502 +r0:=-123/16807*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+1/105/((2+3*x)^5*_ + sqrt(1-2*x))+328/735/((2+3*x)^4*sqrt(1-2*x))-369/1715*sqrt(1-2*x)/_ + (2+3*x)^4-123/1715*sqrt(1-2*x)/(2+3*x)^3-123/4802*sqrt(1-2*x)/_ + (2+3*x)^2-369/33614*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 298890x - 996300x - 1328400x - 885600x - 295200x - 39360)\|3 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7 +--R / +--R 5 4 3 2 +--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x +--R + +--R 5378240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (149445x + 498150x + 664200x + 442800x + 147600x + 19680)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (298890x + 880065x + 964197x + 430992x + 8774x - 32894)\|7 +--R / +--R 5 4 3 2 +--R 40841010x + 136136700x + 181515600x + 121010400x + 40336800x +--R + +--R 5378240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 123\|3 log(-------------------------------) + 246\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R --------------------------------------------------------------------------- +--R +-+ +--R 33614\|7 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 502 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 6075x - 27540x - 53487x - 57690x - 37320x - 14480x - 3120x - 288 +--R ------------------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 502 +r0:=-8117095/384*(1-2*x)^(3/2)+1179381/128*(1-2*x)^(5/2)-_ + 367155/128*(1-2*x)^(7/2)+74667/128*(1-2*x)^(9/2)-_ + 97605/1408*(1-2*x)^(11/2)+6075/1664*(1-2*x)^(13/2)+_ + 2033647/128/sqrt(1-2*x)+6206585/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x +--R + +--R - 21370088x + 21493640 +--R / +--R +--------+ +--R 429\|- 2x + 1 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R - 200475x - 1201635x - 3350637x - 5928885x - 7945164x - 10015804x +--R + +--R - 21370088x + 21493640 +--R / +--R +--------+ +--R 429\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 502 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144 +--R (1) ------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 502 +r0:=-832951/192*(1-2*x)^(3/2)+121359/80*(1-2*x)^(5/2)-_ + 159111/448*(1-2*x)^(7/2)+1545/32*(1-2*x)^(9/2)-_ + 2025/704*(1-2*x)^(11/2)+290521/64/sqrt(1-2*x)+381073/32*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x +--R + +--R 15380984 +--R / +--R +--------+ +--R 1155\|- 2x + 1 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 212625x - 1146600x - 2899485x - 4819932x - 6831172x - 15214664x +--R + +--R 15380984 +--R / +--R +--------+ +--R 1155\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 502 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 675x - 2160x - 2763x - 1766x - 564x - 72 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 502 +r0:=-39977/48*(1-2*x)^(3/2)+17541/80*(1-2*x)^(5/2)-_ + 7695/224*(1-2*x)^(7/2)+75/32*(1-2*x)^(9/2)+_ + 41503/32/sqrt(1-2*x)+91091/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286 +--R (2) ---------------------------------------------------------- +--R +--------+ +--R 105\|- 2x + 1 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 7875x - 38025x - 88443x - 150253x - 359726x + 367286 +--R (3) ---------------------------------------------------------- +--R +--------+ +--R 105\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 502 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 225x - 570x - 541x - 228x - 36 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 502 +r0:=-3467/24*(1-2*x)^(3/2)+51/2*(1-2*x)^(5/2)-225/112*(1-2*x)^(7/2)+_ + 5929/16/sqrt(1-2*x)+1309/2*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 675x - 2934x - 6721x - 18230x + 18986 +--R (2) ------------------------------------------ +--R +--------+ +--R 21\|- 2x + 1 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 675x - 2934x - 6721x - 18230x + 18986 +--R (3) ------------------------------------------ +--R +--------+ +--R 21\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 502 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 75x - 140x - 87x - 18 +--R (1) ------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 373 + +--S 374 of 502 +r0:=-505/24*(1-2*x)^(3/2)+15/8*(1-2*x)^(5/2)+847/8/sqrt(1-2*x)+_ + 1133/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 45x - 185x - 631x + 685 +--R (2) --------------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 45x - 185x - 631x + 685 +--R (3) --------------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 502 +t0:=(3+5*x)^2/(1-2*x)^(3/2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 502 +r0:=-25/12*(1-2*x)^(3/2)+121/4/sqrt(1-2*x)+55/2*sqrt(1-2*x) +--R +--R +--R 2 +--R - 25x - 140x + 167 +--R (2) ------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 502 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 25x - 140x + 167 +--R (3) ------------------- +--R +--------+ +--R 3\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 502 +r0:=-2/21*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/sqrt(1-2*x)+_ + 25/6*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 175x + 269)\|21 +--R +-+ +--R \|7 +--R (2) ---------------------------------------------------------- +--R +--+ +--------+ +--R 21\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 175x + 269)\|21 +--R 3x + 2 +--R (3) ------------------------------------------------------------------- +--R +--+ +--------+ +--R 21\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 21\|21 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (2646x + 441x - 882)\|- 2x + 1 + (378x - 567x - 231x + 210)\|21 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 502 +r0:=134/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)*_ + sqrt(1-2*x))-1091/294*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (402x + 268)\|- 2x + 1 atanh(---------------) + (1091x + 725)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (201x + 134)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R +--+ +--R (1091x + 725)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 67log(-------------------------------) - 134atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 201x + 335)\|21 + (201x - 335)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (134x - 67)\|3 \|7 \|21 - 2814x + 1407 +--R / +--R 2 +--------+ +--R (18522x + 3087x - 6174)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2646x + 3969x + 1617x - 1470)\|21 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 502 +r0:=-2045/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^2*_ + sqrt(1-2*x))-545/147*sqrt(1-2*x)/(2+3*x)^2-2045/2058*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (- 36810x - 49080x - 16360)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (12270x + 17305x + 6067)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (18405x + 24540x + 8180)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (12270x + 17305x + 6067)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2045log(-----------------------------) + 4090atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6135x + 10225)\|21 + (6135x - 10225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 4090x + 2045)\|3 \|7 \|21 + 85890x - 42945 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37044x - 55566x - 22638x + 20580)\|21 +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 502 +r0:=-905/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^3*_ + sqrt(1-2*x))-467/126*sqrt(1-2*x)/(2+3*x)^3-905/882*_ + sqrt(1-2*x)/(2+3*x)^2-905/2058*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (- 48870x - 97740x - 65160x - 14480)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (16290x + 26245x + 13747x + 2316)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (24435x + 48870x + 32580x + 7240)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (16290x + 26245x + 13747x + 2316)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (55566x + 111132x + 74088x + 16464)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 905log(-----------------------------) + 1810atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 1810x + 905)\|3 \|7 \|21 + 38010x - 19005 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (37044x - 55566x - 22638x + 20580)\|21 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 502 +t0:=(3+5*x)^2/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 2 +--R - 25x - 30x - 9 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 502 +r0:=-9145/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+121/14/((2+3*x)^4*_ + sqrt(1-2*x))-2179/588*sqrt(1-2*x)/(2+3*x)^4-1829/1764*_ + sqrt(1-2*x)/(2+3*x)^3-9145/24696*sqrt(1-2*x)/(2+3*x)^2-_ + 9145/57624*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 1481490x - 3950640x - 3950640x - 1755840x - 292640)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (740745x + 1975320x + 1975320x + 877920x + 146320)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (493830x + 1124835x + 843169x + 218578x + 6486)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 9145log(-----------------------------) + 18290atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 57624\|21 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 27435x + 45725)\|21 + (27435x - 45725)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 18290x + 9145)\|3 \|7 \|21 + 384090x - 192045 +--R / +--R 2 +--------+ +--R (7260624x + 1210104x - 2420208)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1037232x - 1555848x - 633864x + 576240)\|21 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 502 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R - 10125x - 45225x - 86535x - 91947x - 58592x - 22392x - 4752x - 432 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 502 +r0:=-4324397/128*(1-2*x)^(3/2)+9504551/640*(1-2*x)^(5/2)-_ + 4177401/896*(1-2*x)^(7/2)+122385/128*(1-2*x)^(9/2)-_ + 161325/1408*(1-2*x)^(11/2)+10125/1664*(1-2*x)^(13/2)+_ + 3195731/128/sqrt(1-2*x)+9836211/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x +--R + +--R 2 +--R - 184884496x - 393552752x + 395714912 +--R / +--R +--------+ +--R 5005\|- 2x + 1 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R - 3898125x - 23058000x - 63495075x - 111095730x - 147527176x +--R + +--R 2 +--R - 184884496x - 393552752x + 395714912 +--R / +--R +--------+ +--R 5005\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 502 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--R - 3375x - 12825x - 20295x - 17119x - 8118x - 2052x - 216 +--R (1) ------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 502 +r0:=-444983/64*(1-2*x)^(3/2)+98209/40*(1-2*x)^(5/2)-260055/448*(1-2*x)^(7/2)+_ + 1275/16*(1-2*x)^(9/2)-3375/704*(1-2*x)^(11/2)+456533/64/sqrt(1-2*x)+_ + 302379/16*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x +--R + +--R 8096086 +--R / +--R +--------+ +--R 385\|- 2x + 1 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R - 118125x - 627375x - 1564350x - 2569643x - 3611453x - 8012926x +--R + +--R 8096086 +--R / +--R +--------+ +--R 385\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 502 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +--R - 1125x - 3525x - 4415x - 2763x - 864x - 108 +--R (1) ------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 502 +r0:=-21439/16*(1-2*x)^(3/2)+5711/16*(1-2*x)^(5/2)-12675/224*(1-2*x)^(7/2)+_ + 125/32*(1-2*x)^(9/2)+65219/32/sqrt(1-2*x)+144837/32*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700 +--R (2) ---------------------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 502 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R - 875x - 4150x - 9501x - 15948x - 37944x + 38700 +--R (3) ---------------------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 502 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +--R - 375x - 925x - 855x - 351x - 54 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 502 +r0:=-935/4*(1-2*x)^(3/2)+335/8*(1-2*x)^(5/2)-375/112*(1-2*x)^(7/2)+_ + 9317/16/sqrt(1-2*x)+8349/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R - 375x - 1595x - 3590x - 9637x + 10015 +--R (2) ----------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 502 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R - 375x - 1595x - 3590x - 9637x + 10015 +--R (3) ----------------------------------------- +--R +--------+ +--R 7\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 502 +t0:=(3+5*x)^3/(1-2*x)^(3/2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 502 +r0:=-275/8*(1-2*x)^(3/2)+25/8*(1-2*x)^(5/2)+1331/8/sqrt(1-2*x)+_ + 1815/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R - 25x - 100x - 335x + 362 +--R (2) --------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 502 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R - 25x - 100x - 335x + 362 +--R (3) --------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 502 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------- +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 502 +r0:=2/63*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+737/63*(3+5*x)/sqrt(1-2*x)-_ + 5/9*(3+5*x)^2/sqrt(1-2*x)+3680/63*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 2 +--+ +--R 2\|- 2x + 1 atanh(---------------) + (- 875x - 4725x + 5576)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R 63\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 875x - 4725x + 5576)\|21 +--R / +--R +--+ +--------+ +--R 63\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 63\|21 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (7938x + 1323x - 2646)\|- 2x + 1 + (- 1134x + 1701x + 693x - 630)\|21 +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 502 +r0:=-68/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+374/21*(3+5*x)/((2+3*x)*_ + sqrt(1-2*x))-5/3*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))+386/147*_ + sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R (- 204x - 136)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 6125x + 4968x + 6035)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (102x + 68)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 6125x + 4968x + 6035)\|21 +--R / +--R +--+ +--------+ +--R (441x + 294)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 102x + 170)\|21 + (102x - 170)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 68x + 34)\|3 \|7 \|21 + 1428x - 714 +--R / +--R 2 +--------+ 3 2 +--+ +--R (18522x + 3087x - 6174)\|- 2x + 1 + (2646x - 3969x - 1617x + 1470)\|21 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 502 +r0:=2245/1029*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_ + ((2+3*x)^2*sqrt(1-2*x))+650/343*sqrt(1-2*x)+5/98*(3+5*x)^2*_ + sqrt(1-2*x)/(2+3*x)^2-5/2058*(61+65*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (40410x + 53880x + 17960)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (72280x + 95895x + 31811)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (20205x + 26940x + 8980)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (72280x + 95895x + 31811)\|21 +--R / +--R 2 +--+ +--------+ +--R (18522x + 24696x + 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 2245log(-------------------------------) - 4490atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 6735x + 11225)\|21 + (6735x - 11225)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (4490x - 2245)\|3 \|7 \|21 - 94290x + 47145 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 37044x + 55566x + 22638x - 20580)\|21 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 502 +r0:=-9320/3087*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+2/7*(3+5*x)^3/_ + ((2+3*x)^3*sqrt(1-2*x))+590/3087*sqrt(1-2*x)/(2+3*x)+_ + 40/441*(3+5*x)*sqrt(1-2*x)/(2+3*x)^2+1/21*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 251640x - 503280x - 335520x - 74560)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (83880x + 178015x + 125154x + 29177)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (125820x + 251640x + 167760x + 37280)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (83880x + 178015x + 125154x + 29177)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (83349x + 166698x + 111132x + 24696)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 4660log(-----------------------------) + 9320atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 3087\|21 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 13980x + 23300)\|21 + (13980x - 23300)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 9320x + 4660)\|3 \|7 \|21 + 195720x - 97860 +--R / +--R 2 +--------+ +--R (388962x + 64827x - 129654)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (55566x - 83349x - 33957x + 30870)\|21 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 502 +t0:=(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 3 2 +--R - 125x - 225x - 135x - 27 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 502 +r0:=-39185/28812*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + 2/7*(3+5*x)^3/((2+3*x)^4*sqrt(1-2*x))+375/2744*sqrt(1-2*x)/(2+3*x)^2-_ + 39185/57624*sqrt(1-2*x)/(2+3*x)+47/588*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3+_ + 9/196*(3+5*x)^2*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 6347970x - 16927920x - 16927920x - 7523520x - 1253920)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (3173985x + 8463960x + 8463960x + 3761760x + 626960)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (2115990x + 4819755x + 4093057x + 1534434x + 213998)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (4667544x + 12446784x + 12446784x + 5531904x + 921984)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 39185log(-----------------------------) + 78370atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 57624\|21 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 117555x + 195925)\|21 + (117555x - 195925)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 78370x + 39185)\|3 \|7 \|21 + 1645770x - 822885 +--R / +--R 2 +--------+ +--R (7260624x + 1210104x - 2420208)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1037232x - 1555848x - 633864x + 576240)\|21 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 502 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 502 +r0:=-2/34375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+406/165*(2+3*x)^4/_ + sqrt(1-2*x)-1/15*(2+3*x)^5/sqrt(1-2*x)+19886122/34375*sqrt(1-2*x)+_ + 22727/275*(2+3*x)*sqrt(1-2*x)+121752/6875*(2+3*x)^2*sqrt(1-2*x)+_ + 8117/1925*(2+3*x)^3*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 14\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x +--R + +--R 213097384 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R 240625\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R 7\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 3898125x - 19824750x - 48323385x - 85159800x - 207964053x +--R + +--R 213097384 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R 240625\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 34375\|55 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (18906250x + 1890625x - 5671875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1718750x - 2578125x - 790625x + 825000)\|55 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 502 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 502 +r0:=-2/6875*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+139/55*(2+3*x)^3/_ + sqrt(1-2*x)-3/35*(2+3*x)^4/sqrt(1-2*x)+1050298/6875*sqrt(1-2*x)+_ + 6252/1375*(2+3*x)^2*sqrt(1-2*x)+1/6875*(262574+437625*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 14\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55 +--R / +--R +--+ +--------+ +--R 48125\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R 7\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 334125x - 1545885x - 3732300x - 10459053x + 10972384)\|55 +--R / +--R +--+ +--------+ +--R 48125\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 6875\|55 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (3781250x + 378125x - 1134375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (343750x - 515625x - 158125x + 165000)\|55 +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 502 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 502 +r0:=-2/1375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+728/275*(2+3*x)^2/_ + sqrt(1-2*x)-3/25*(2+3*x)^3/sqrt(1-2*x)+50922/1375*sqrt(1-2*x)+_ + 291/55*(2+3*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R - 2\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 4455x - 19800x - 71379x + 78712)\|55 +--R / +--R +--+ +--------+ +--R 1375\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R \|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 4455x - 19800x - 71379x + 78712)\|55 +--R / +--R +--+ +--------+ +--R 1375\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 1375\|55 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (756250x + 75625x - 226875)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (68750x - 103125x - 31625x + 33000)\|55 +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 502 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 502 +r0:=-2/275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+161/55*(2+3*x)/_ + sqrt(1-2*x)-1/5*(2+3*x)^2/sqrt(1-2*x)+2412/275*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 2 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 495x - 3069x + 3802)\|55 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +--------+ +--R 275\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 2 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 495x - 3069x + 3802)\|55 +--R 5x + 3 +--R ----------------------------------------------------------------------------- +--R +--+ +--------+ +--R 275\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 275\|55 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (151250x + 15125x - 45375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (13750x - 20625x - 6325x + 6600)\|55 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 502 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 502 +r0:=-2/55*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/sqrt(1-2*x)+_ + 9/10*sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + (- 99x + 172)\|55 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------- +--R +--+ +--------+ +--R 55\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R \|- 2x + 1 log(-----------------------------) + (- 99x + 172)\|55 +--R 5x + 3 +--R (3) ------------------------------------------------------------------ +--R +--+ +--------+ +--R 55\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 55\|55 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (30250x + 3025x - 9075)\|- 2x + 1 + (2750x - 4125x - 1265x + 1320)\|55 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 502 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+7/11/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|- 2x + 1 atanh(---------------) + 7\|55 +--R +--+ +--R \|11 +--R (2) --------------------------------------------- +--R +--+ +--------+ +--R 11\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 502 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R \|- 2x + 1 log(-----------------------------) + 7\|55 +--R 5x + 3 +--R (3) ------------------------------------------------------ +--R +--+ +--------+ +--R 11\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 502 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 11\|55 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 502 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6050x + 605x - 1815)\|- 2x + 1 + (550x - 825x - 253x + 264)\|55 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 502 +t0:=1/((1-2*x)^(3/2)*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------- +--R 2 +--------+ +--R (10x + x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 502 +r0:=-2/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R - 2\|5 \|- 2x + 1 atanh(---------------) + 2\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--------+ +--R 11\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 502 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--+ +--R \|5 \|- 2x + 1 log(---------------------------------) + 2\|11 +--R 5x + 3 +--R (3) -------------------------------------------------------------- +--R +--+ +--------+ +--R 11\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R \|5 log(---------------------------------) + 2\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 11\|11 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 502 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------- +--R 3 2 +--------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 502 +r0:=6/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-10/11*atanh(sqrt(5/11)*_ + sqrt(1-2*x))*sqrt(5/11)+4/77/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R 66\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +-+ +--+ +--R - 70\|5 \|7 \|- 2x + 1 atanh(---------------) + 4\|7 \|11 +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--------+ +--R 77\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ +--+ +--R 33\|3 \|11 \|- 2x + 1 log(---------------------------------) + 4\|7 \|11 +--R 3x + 2 +--R / +--R +-+ +--+ +--------+ +--R 77\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 35\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 33\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 66\|3 \|11 atanh(---------------) + 70\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 77\|7 \|11 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 502 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 4 3 2 +--------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 502 +r0:=228/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-50/11*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((2+3*x)*_ + sqrt(1-2*x))+87/539*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (7524x + 5016)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 7350x - 4900)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (- 174x + 115)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (1617x + 1078)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 502 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (3675x + 2450)\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (3762x + 2508)\|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--R (- 174x + 115)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (1617x + 1078)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 502 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1225\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1254\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2508\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 539\|7 \|11 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 502 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 502 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3m.input.pamphlet b/src/input/rich3m.input.pamphlet new file mode 100644 index 0000000..ade3647 --- /dev/null +++ b/src/input/rich3m.input.pamphlet @@ -0,0 +1,8548 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3m.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 55 matching answers. +\item 37 cases where Axiom supplied 2 results. +\item 8 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3m.output +)spool rich3m.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=8025/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*sqrt(1-2*x))+75/1078*sqrt(1-2*x)/(2+3*x)^2+_ + 7575/7546*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (1588950x + 2118600x + 706200)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 1543500x - 2058000x - 686000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 45450x - 8625x + 16067)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (771750x + 1029000x + 343000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (794475x + 1059300x + 353100)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 45450x - 8625x + 16067)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (67914x + 90552x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 85750\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 88275\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 176550\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 171500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 7546\|7 \|11 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=40140/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1250/11*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^3*sqrt(1-2*x))+3/77*sqrt(1-2*x)/(2+3*x)^3+_ + 270/539*sqrt(1-2*x)/(2+3*x)^2+19185/3773*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--------+ +--R (11921580x + 23843160x + 15895440x + 3532320)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (- 11576250x - 23152500x - 15435000x - 3430000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (5788125x + 11576250x + 7717500x + 1715000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (5960790x + 11921580x + 7947720x + 1766160)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 345330x - 299115x + 74556x + 80863)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (101871x + 203742x + 135828x + 30184)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 214375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 220770\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 441540\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 428750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 3773\|7 \|11 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-402/378125*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 139/55*(2+3*x)^4/((3+5*x)*sqrt(1-2*x))-3/35*(2+3*x)^5/((3+5*x)*_ + sqrt(1-2*x))+36473898/378125*sqrt(1-2*x)+217152/75625*(2+3*x)^2*_ + sqrt(1-2*x)-4839/21175*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)+_ + 3/378125*(3039458+5065875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 14070x - 8442)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x +--R + +--R 1143572552 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (13234375x + 7940625)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (7035x + 4221)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 55130625x - 293294925x - 795400155x - 2195407665x + 818846961x +--R + +--R 1143572552 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (13234375x + 7940625)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 201log(-----------------------------) + 402atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 378125\|55 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1005x + 1608)\|55 + (1005x - 1608)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 402x + 201)\|5 \|11 \|55 + 22110x - 11055 +--R / +--R 2 +--------+ +--R (207968750x + 20796875x - 62390625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18906250x - 28359375x - 8696875x + 9075000)\|55 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-336/75625*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 728/275*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-3/25*(2+3*x)^4/((3+5*x)*_ + sqrt(1-2*x))+1763496/75625*sqrt(1-2*x)+2016/605*(2+3*x)*_ + sqrt(1-2*x)-3612/15125*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 1680x - 1008)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55 +--R / +--R +--+ +--------+ +--R (378125x + 226875)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (840x + 504)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 735075x - 3789720x - 14309460x + 6264264x + 8186648)\|55 +--R / +--R +--+ +--------+ +--R (378125x + 226875)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 168log(-----------------------------) + 336atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 75625\|55 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 840x + 1344)\|55 + (840x - 1344)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 336x + 168)\|5 \|11 \|55 + 18480x - 9240 +--R / +--R 2 +--------+ +--R (41593750x + 4159375x - 12478125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3781250x - 5671875x - 1739375x + 1815000)\|55 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-54/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 161/55*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 1/5*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))+_ + 15648/3025*sqrt(1-2*x)+3/3025*(436+815*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 270x - 162)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 16335x - 114345x + 68661x + 78832)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (135x + 81)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 16335x - 114345x + 68661x + 78832)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 27log(-----------------------------) + 54atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 135x + 216)\|55 + (135x - 216)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 54x + 27)\|5 \|11 \|55 + 2970x - 1485 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-204/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 238/55*(2+3*x)/((3+5*x)*sqrt(1-2*x))-3/5*(2+3*x)^2/_ + ((3+5*x)*sqrt(1-2*x))-1158/3025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 1020x - 612)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 16335x + 19806x + 17762)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (510x + 306)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (- 16335x + 19806x + 17762)\|55 +--R / +--R +--+ +--------+ +--R (15125x + 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 102log(-----------------------------) + 204atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 510x + 816)\|55 + (510x - 816)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 204x + 102)\|5 \|11 \|55 + 11220x - 5610 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-138/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 49/22/((3+5*x)*sqrt(1-2*x))-1227/1210*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 690x - 414)\|- 2x + 1 atanh(---------------) + (1227x + 734)\|55 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +--------+ +--R (3025x + 1815)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (345x + 207)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (1227x + 734)\|55 +--R / +--R +--+ +--------+ +--R (3025x + 1815)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 69log(-----------------------------) + 138atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 605\|55 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 345x + 552)\|55 + (345x - 552)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 138x + 69)\|5 \|11 \|55 + 7590x - 3795 +--R / +--R 2 +--------+ +--R (332750x + 33275x - 99825)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30250x - 45375x - 13915x + 14520)\|55 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-72/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 72/605/sqrt(1-2*x)+(-1/55)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 360x - 216)\|- 2x + 1 atanh(---------------) + (72x + 41)\|55 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (605x + 363)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R (180x + 108)\|- 2x + 1 log(-----------------------------) + (72x + 41)\|55 +--R 5x + 3 +--R --------------------------------------------------------------------------- +--R +--+ +--------+ +--R (605x + 363)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 36log(-----------------------------) + 72atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 121\|55 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 180x + 288)\|55 + (180x - 288)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 72x + 36)\|5 \|11 \|55 + 3960x - 1980 +--R / +--R 2 +--------+ +--R (66550x + 6655x - 19965)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6050x - 9075x - 2783x + 2904)\|55 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ---------------------------------- +--R 3 2 +--------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=-6/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 2/11/((3+5*x)*sqrt(1-2*x))-15/121*sqrt(1-2*x)/(3+5*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 30x - 18)\|5 \|- 2x + 1 atanh(---------------) + (30x + 7)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (605x + 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (15x + 9)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (30x + 7)\|11 +--R / +--R +--+ +--------+ +--R (605x + 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 3\|5 log(---------------------------------) + 6\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - -------------------------------------------- +--R 4 3 2 +--------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=-18/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 300/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((3+5*x)*sqrt(1-2*x))-195/847*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (- 10890x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (10500x + 6300)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (390x - 151)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (4235x + 2541)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (5445x + 3267)\|3 \|11 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (5250x + 3150)\|5 \|7 \|- 2x + 1 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--+ +--R (390x - 151)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (4235x + 2541)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1089\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1050\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 2178\|3 \|11 atanh(---------------) - 2100\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 847\|7 \|11 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=-1314/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 3150/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)*(3+5*x)*sqrt(1-2*x))-11610/5929*sqrt(1-2*x)/(3+5*x)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (- 2384910x - 3020886x - 953964)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (2315250x + 2932650x + 926100)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (69660x + 9696x - 21955)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--+ +--------+ +--R (1192455x + 1510443x + 476982)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (1157625x + 1466325x + 463050)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--R (69660x + 9696x - 21955)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (88935x + 112651x + 35574)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 79497\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 77175\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 158994\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 154350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 5929\|7 \|11 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=-70065/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + 24000/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_ + 1229325/83006*sqrt(1-2*x)/(3+5*x)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x))+_ + 5520/3773*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 763007850x - 1475148510x - 949520880x - 203468760)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (740880000x + 1432368000x + 921984000x + 197568000)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--R (381503925x + 737574255x + 474760440x + 101734380)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (370440000x + 716184000x + 460992000x + 98784000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (22127850x + 17711235x - 5050290x - 4664333)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (3735270x + 7221522x + 4648336x + 996072)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 8477865\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 8232000\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 16955730\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 16464000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^6/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R - 729x - 2916x - 4860x - 4320x - 2160x - 576x - 64 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=-33873/4159375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 728/275*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))-_ + 3/25*(2+3*x)^5/((3+5*x)^2*sqrt(1-2*x))+_ + 61055253/4159375*sqrt(1-2*x)+139671/66550*(2+3*x)*sqrt(1-2*x)-_ + 7219/30250*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^2-_ + 125916/831875*(2+3*x)^2*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 1693650x - 2032380x - 609714)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 242574750x - 1423105200x - 5682717810x - 762244410x +--R + +--R 4150263077x + 1702670584 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +--R (846825x + 1016190x + 304857)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R - 242574750x - 1423105200x - 5682717810x - 762244410x +--R + +--R 4150263077x + 1702670584 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (207968750x + 249562500x + 74868750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 33873log(-----------------------------) + 67746atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 8318750\|55 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 169365x + 270984)\|55 + (169365x - 270984)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 67746x + 33873)\|5 \|11 \|55 + 3726030x - 1863015 +--R / +--R 2 +--------+ +--R (4575312500x + 457531250x - 1372593750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (415937500x - 623906250x - 191331250x + 199650000)\|55 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-4557/166375*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 161/55*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_ + 1/5*(2+3*x)^4/((3+5*x)^2*sqrt(1-2*x))+_ + 538608/166375*sqrt(1-2*x)-1589/6050*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 147/332750*(612+1145*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 227850x - 273420x - 82026)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55 +--R / +--R 2 +--+ +--------+ +--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (113925x + 136710x + 41013)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (- 5390550x - 42046290x + 764310x + 41668993x + 16342856)\|55 +--R / +--R 2 +--+ +--------+ +--R (8318750x + 9982500x + 2994750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4557log(-----------------------------) + 9114atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 332750\|55 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 22785x + 36456)\|55 + (22785x - 36456)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 9114x + 4557)\|5 \|11 \|55 + 501270x - 250635 +--R / +--R 2 +--------+ +--R (183012500x + 18301250x - 54903750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (16637500x - 24956250x - 7653250x + 7986000)\|55 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=-111/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 238/55*(2+3*x)^2/((3+5*x)^2*sqrt(1-2*x))-3/5*(2+3*x)^3/((3+5*x)^2*_ + sqrt(1-2*x))-1/6050*(346-195*x)*sqrt(1-2*x)/(3+5*x)^2-_ + 15759/33275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 27750x - 33300x - 9990)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 215622x + 149298x + 411911x + 146824)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (13875x + 16650x + 4995)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 215622x + 149298x + 411911x + 146824)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 111log(-----------------------------) + 222atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 2662\|55 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 555x + 888)\|55 + (555x - 888)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 222x + 111)\|5 \|11 \|55 + 12210x - 6105 +--R / +--R 2 +--------+ +--R (1464100x + 146410x - 439230)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (133100x - 199650x - 61226x + 63888)\|55 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-7143/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + 2/11*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))+_ + 3408/33275*sqrt(1-2*x)-5/242*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+_ + 3/13310*(24+71*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 357150x - 428580x - 128574)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (430800x + 514727x + 153724)\|55 +--R / +--R 2 +--+ +--------+ +--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (178575x + 214290x + 64287)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (430800x + 514727x + 153724)\|55 +--R / +--R 2 +--+ +--------+ +--R (1663750x + 1996500x + 598950)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 7143log(-----------------------------) + 14286atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 66550\|55 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 35715x + 57144)\|55 + (35715x - 57144)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 14286x + 7143)\|5 \|11 \|55 + 785730x - 392865 +--R / +--R 2 +--------+ +--R (36602500x + 3660250x - 10980750)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3327500x - 4991250x - 1530650x + 1597200)\|55 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=-2589/6655*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+49/22/((3+5*x)^2*_ + sqrt(1-2*x))-613/605*sqrt(1-2*x)/(3+5*x)^2-2589/13310*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 129450x - 155340x - 46602)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (25890x + 29561x + 8392)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (64725x + 77670x + 23301)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (25890x + 29561x + 8392)\|55 +--R / +--R 2 +--+ +--------+ +--R (332750x + 399300x + 119790)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2589log(-----------------------------) + 5178atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 13310\|55 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 12945x + 20712)\|55 + (12945x - 20712)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5178x + 2589)\|5 \|11 \|55 + 284790x - 142395 +--R / +--R 2 +--------+ +--R (7320500x + 732050x - 2196150)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (665500x - 998250x - 306130x + 319440)\|55 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R - 3x - 2 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=-213/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-1/110)/((3+5*x)^2*_ + sqrt(1-2*x))+71/605/((3+5*x)*sqrt(1-2*x))-213/2662*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 10650x - 12780x - 3834)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (2130x + 1775x + 274)\|55 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (5325x + 6390x + 1917)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (2130x + 1775x + 274)\|55 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 213log(-----------------------------) + 426atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 2662\|55 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1065x + 1704)\|55 + (1065x - 1704)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 426x + 213)\|5 \|11 \|55 + 23430x - 11715 +--R / +--R 2 +--------+ +--R (1464100x + 146410x - 439230)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (133100x - 199650x - 61226x + 63888)\|55 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - -------------------------------------------- +--R 4 3 2 +--------+ +--R (250x + 325x + 45x - 81x - 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=-15/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+2/11/((3+5*x)^2*_ + sqrt(1-2*x))-25/242*sqrt(1-2*x)/(3+5*x)^2-75/2662*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 750x - 900x - 270)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (750x + 625x - 16)\|11 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (375x + 450x + 135)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (750x + 625x - 16)\|11 +--R / +--R 2 +--+ +--------+ +--R (66550x + 79860x + 23958)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 15\|5 log(---------------------------------) + 30\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 2662\|11 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (750x + 1475x + 785x - 153x - 243x - 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=54/7*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-9975/1331*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+4/77/((3+5*x)^2*_ + sqrt(1-2*x))-215/1694*sqrt(1-2*x)/(3+5*x)^2+10245/18634*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (3593700x + 4312440x + 1293732)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +-+ +--------+ +--R (- 3491250x - 4189500x - 1256850)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 102450x - 5515x + 29338)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (1745625x + 2094750x + 628425)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (1796850x + 2156220x + 646866)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 102450x - 5515x + 29338)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (465850x + 559020x + 167706)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 69825\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 71874\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 143748\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 139650\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 18634\|7 \|11 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (2250x + 5925x + 5305x + 1111x - 1035x - 648x - 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=5832/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 153825/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-_ + 17095/11858*sqrt(1-2*x)/(3+5*x)^2+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+1124835/130438*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (1164358800x + 2173469760x + 1350656208x + 279446112)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 1130613750x - 2110479000x - 1311511950x - 271347300)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--R (565306875x + 1055239500x + 655755975x + 135673650)\|5 \|7 +--R * +--R +-+ +--------+ +--+ +--R +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (582179400x + 1086734880x + 675328104x + 139723056)\|3 \|11 +--R * +--R +-+ +--------+ +-+ +--R +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 33745050x - 24742935x + 8019782x + 6400750)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (9782850x + 18261320x + 11348106x + 2347884)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7537425\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7762392\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 15524784\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 15074850\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 130438\|7 \|11 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (6750x + 22275x + 27765x + 13943x - 883x - 4014x - 1620x - 216) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=414315/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 1561125/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 4/77/((2+3*x)^2*(3+5*x)^2*sqrt(1-2*x))-_ + 1205525/83006*sqrt(1-2*x)/(3+5*x)^2+75/1078*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^2)+14505/7546*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 39968475/456533*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 248153969250x + 628656722100x + 596672432730x + 251462688840x +--R + +--R 39704635080 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 240959643750x - 610431097500x - 579374076750x - 244172439000x +--R + +--R - 38553543000 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x +--R + +--R 909821467 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +-+ +--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 120479821875x + 305215548750x + 289687038375x + 122086219500x +--R + +--R 19276771500 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R 124076984625x + 314328361050x + 298336216365x + 125731344420x +--R + +--R 19852317540 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R - 7194325500x - 10073172600x - 1810042755x + 2503057145x +--R + +--R 909821467 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +-+ +--R (205439850x + 520447620x + 493968706x + 208179048x + 32870376)\|7 +--R * +--R +--+ +--------+ +--R \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 535465875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 551453265\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 1102906530\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 1070931750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 913066\|7 \|11 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^5*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96 +--R (1) ------------------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=184877/192/(1-2*x)^(3/2)+12495/8*(1-2*x)^(3/2)-19467/64*(1-2*x)^(5/2)+_ + 1053/28*(1-2*x)^(7/2)-135/64*(1-2*x)^(9/2)+(-60025/8)/sqrt(1-2*x)-_ + 519645/64*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696 +--R (2) ------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R 2835x + 16767x + 49653x + 114084x + 412812x - 844104x + 280696 +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^4*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 405x + 1323x + 1728x + 1128x + 368x + 48 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=26411/96/(1-2*x)^(3/2)+3591/16*(1-2*x)^(3/2)-4671/160*(1-2*x)^(5/2)+_ + 405/224*(1-2*x)^(7/2)+(-57281/32)/sqrt(1-2*x)-24843/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408 +--R (2) --------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 6075x + 33858x + 105624x + 435312x - 909264x + 301408 +--R (3) --------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^3*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 135x + 351x + 342x + 148x + 24 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=3773/48/(1-2*x)^(3/2)+207/8*(1-2*x)^(3/2)-27/16*(1-2*x)^(5/2)+_ + (-3283/8)/sqrt(1-2*x)-1071/4*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 81x + 459x + 2403x - 5250x + 1726 +--R (2) ------------------------------------ +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 81x + 459x + 2403x - 5250x + 1726 +--R (3) ------------------------------------ +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^2*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 45x + 87x + 56x + 12 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=539/24/(1-2*x)^(3/2)+15/8*(1-2*x)^(3/2)+(-707/8)/sqrt(1-2*x)-_ + 309/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 45x + 396x - 960x + 308 +--R (2) ------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 45x + 396x - 960x + 308 +--R (3) ------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)*(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +--R 15x + 19x + 6 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=77/12/(1-2*x)^(3/2)+(-17)/sqrt(1-2*x)-15/4*sqrt(1-2*x) +--R +--R +--R 2 +--R 45x - 147x + 43 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 45x - 147x + 43 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=11/6/(1-2*x)^(3/2)+(-5/2)/sqrt(1-2*x) +--R +--R +--R - 15x + 2 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +a0:=integrate(t0,x) +--R +--R +--R - 15x + 2 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=11/21/(1-2*x)^(3/2)+2/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+_ + (-2/49)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|3 \|- 2x + 1 +-+ +--R (12x - 6)\|3 \|- 2x + 1 atanh(---------------) + (- 12x - 71)\|7 +--R +-+ +--R \|7 +--R (2) ----------------------------------------------------------------- +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R +-+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (6x - 3)\|3 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--R (- 12x - 71)\|7 +--R / +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R \|3 log(---------------------------------) - 2\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------ +--R +-+ +--R 49\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=20/147/(1-2*x)^(3/2)+1/21/((1-2*x)^(3/2)*(2+3*x))-_ + 60/343*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+60/343/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 1080x - 180x + 360)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +-+ +--R (1080x - 240x - 689)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +-+ +--R 2 +-+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (540x + 90x - 180)\|3 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--R (1080x - 240x - 689)\|7 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 30\|3 log(-------------------------------) + 60\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 343\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=5/49/(1-2*x)^(3/2)+1/42/((1-2*x)^(3/2)*(2+3*x)^2)+_ + (-3/14)/((1-2*x)^(3/2)*(2+3*x))-45/343*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+45/343/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 4860x - 4050x + 1080x + 1080)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--R (4860x + 2160x - 2277x - 1087)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (2430x + 2025x - 540x - 540)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--R (4860x + 2160x - 2277x - 1087)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 45\|3 log(-------------------------------) + 90\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/63/((1-2*x)^(3/2)*(2+3*x)^3)+64/441/((1-2*x)^(3/2)*(2+3*x)^2)-_ + 160/2401*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+64/147/((2+3*x)^2*_ + sqrt(1-2*x))-80/343*sqrt(1-2*x)/(2+3*x)^2-240/2401*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +-+ +--------+ +--R (- 25920x - 38880x - 8640x + 9600x + 3840)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +-+ +--R (25920x + 28800x - 4464x - 11280x - 2237)\|7 +--R / +--R 4 3 2 +-+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--------+ +--R (12960x + 19440x + 4320x - 4800x - 1920)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--R (25920x + 28800x - 4464x - 11280x - 2237)\|7 +--R / +--R 4 3 2 +-+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 80\|3 log(-------------------------------) + 160\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 2401\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 5x + 3 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=1/84/((1-2*x)^(3/2)*(2+3*x)^4)+43/294/((1-2*x)^(3/2)*(2+3*x)^3)-_ + 1935/67228*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)+387/686/((2+3*x)^3*_ + sqrt(1-2*x))-387/1372*sqrt(1-2*x)/(2+3*x)^3-1935/19208*_ + sqrt(1-2*x)/(2+3*x)^2-5805/134456*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +-+ +--R (- 1880820x - 4075110x - 2507760x + 278640x + 743040x + 185760)\|3 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +-+ +--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (940410x + 2037555x + 1253880x - 139320x - 371520x - 92880)\|3 +--R * +--R +-+ +--------+ +-+ +--R +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +-+ +--R (1880820x + 3343680x + 1069281x - 1034451x - 611202x - 48490)\|7 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 1935\|3 log(-------------------------------) + 3870\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 134456\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^5*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 7 6 5 4 3 2 +--R 6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288 +--R (1) ---------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=2033647/384/(1-2*x)^(3/2)+1965635/128*(1-2*x)^(3/2)-_ + 514017/128*(1-2*x)^(5/2)+672003/896*(1-2*x)^(7/2)-_ + 10845/128*(1-2*x)^(9/2)+6075/1408*(1-2*x)^(11/2)+_ + (-6206585/128)/sqrt(1-2*x)-8117095/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 2 +--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x +--R + +--R - 65622552x + 21852008 +--R / +--R +--------+ +--R (462x - 231)\|- 2x + 1 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 2 +--R 127575x + 806085x + 2456001x + 5121279x + 9702012x + 32450916x +--R + +--R - 65622552x + 21852008 +--R / +--R +--------+ +--R (462x - 231)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^4*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144 +--R (1) ---------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=290521/192/(1-2*x)^(3/2)+40453/16*(1-2*x)^(3/2)-_ + 159111/320*(1-2*x)^(5/2)+13905/224*(1-2*x)^(7/2)-_ + 225/64*(1-2*x)^(9/2)+(-381073/32)/sqrt(1-2*x)-832951/64*sqrt(1-2*x) +--R +--R +--R (2) +--R 6 5 4 3 2 +--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 23625x + 137700x + 402489x + 915492x + 3294996x - 6731112x + 2238664 +--R ------------------------------------------------------------------------- +--R +--------+ +--R (210x - 105)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^3*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 675x + 2160x + 2763x + 1766x + 564x + 72 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=41503/96/(1-2*x)^(3/2)+5847/16*(1-2*x)^(3/2)-_ + 1539/32*(1-2*x)^(5/2)+675/224*(1-2*x)^(7/2)+(-91091/32)/sqrt(1-2*x)-_ + 39977/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442 +--R (2) ------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 2025x + 11097x + 34137x + 139497x - 290838x + 96442 +--R (3) ------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^2*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 225x + 570x + 541x + 228x + 36 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=5929/48/(1-2*x)^(3/2)+85/2*(1-2*x)^(3/2)-45/16*(1-2*x)^(5/2)+_ + (-1309/2)/sqrt(1-2*x)-3467/8*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 135x + 750x + 3873x - 8430x + 2774 +--R (2) ------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 135x + 750x + 3873x - 8430x + 2774 +--R (3) ------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(2+3*x)*(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 75x + 140x + 87x + 18 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=847/24/(1-2*x)^(3/2)+25/8*(1-2*x)^(3/2)+(-1133/8)/sqrt(1-2*x)-_ + 505/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 75x + 645x - 1551x + 499 +--R (2) -------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 75x + 645x - 1551x + 499 +--R (3) -------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(3+5*x)^2/(1-2*x)^(5/2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=121/12/(1-2*x)^(3/2)+(-55/2)/sqrt(1-2*x)-25/4*sqrt(1-2*x) +--R +--R +--R 2 +--R 75x - 240x + 71 +--R (2) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 75x - 240x + 71 +--R (3) ------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=121/42/(1-2*x)^(3/2)-2/49*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+_ + (-407/98)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 1221x + 187)\|21 +--R +-+ +--R \|7 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--+ +--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 1221x + 187)\|21 +--R 3x + 2 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 49\|21 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (- 2x + 1)\|3 \|7 \|21 +--R + +--R 42x - 21 +--R / +--R 2 +--------+ 3 2 +--+ +--R (6174x + 1029x - 2058)\|- 2x + 1 + (882x - 1323x - 539x + 490)\|21 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x))+130/343*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+(-130/1029)/sqrt(1-2*x)+(-365/294)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (2340x + 390x - 780)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 780x - 2685x - 1427)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (1170x + 195x - 390)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 780x - 2685x - 1427)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 65log(-------------------------------) - 130atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------ +--R +--+ +--R 343\|21 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 195x + 325)\|21 + (195x - 325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (130x - 65)\|3 \|7 \|21 - 2730x + 1365 +--R / +--R 2 +--------+ +--R (43218x + 7203x - 14406)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 6174x + 9261x + 3773x - 3430)\|21 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^2)-85/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)+(-26/21)/((2+3*x)^2*sqrt(1-2*x))+85/147/((2+3*x)*_ + sqrt(1-2*x))-255/686*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +-+ +--------+ \|3 \|- 2x + 1 +--R (- 9180x - 7650x + 2040x + 2040)\|3 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +--R (9180x + 4080x - 7731x - 4231)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (4590x + 3825x - 1020x - 1020)\|3 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--R (9180x + 4080x - 7731x - 4231)\|7 +--R / +--R 3 2 +-+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|7 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +-+ +--------+ +--R +-+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +-+ \|3 \|- 2x + 1 +--R 85\|3 log(-------------------------------) + 170\|3 atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R -------------------------------------------------------------------------- +--R +-+ +--R 686\|7 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 2 +--R 25x + 30x + 9 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^3)-1415/2401*atanh(sqrt(3/7)*sqrt(1-2*x))/_ + sqrt(21)+(-1091/882)/((2+3*x)^3*sqrt(1-2*x))+566/441/((2+3*x)^2*_ + sqrt(1-2*x))-1415/2058*sqrt(1-2*x)/(2+3*x)^2-1415/4802*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 458460x - 687690x - 152820x + 169800x + 67920)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (152820x + 169800x - 26319x - 83655x - 23872)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (229230x + 343845x + 76410x - 84900x - 33960)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (152820x + 169800x - 26319x - 83655x - 23872)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (777924x + 1166886x + 259308x - 288120x - 115248)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 1415log(-----------------------------) + 2830atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 4802\|21 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 4245x + 7075)\|21 + (4245x - 7075)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 2830x + 1415)\|3 \|7 \|21 + 59430x - 29715 +--R / +--R 2 +--------+ +--R (605052x + 100842x - 201684)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (86436x - 129654x - 52822x + 48020)\|21 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(3+5*x)^2/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 2 +--R 25x + 30x + 9 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=121/42/((1-2*x)^(3/2)*(2+3*x)^4)-20465/67228*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+(-727/588)/((2+3*x)^4*sqrt(1-2*x))+_ + 4093/2058/((2+3*x)^3*sqrt(1-2*x))-4093/4116*sqrt(1-2*x)/(2+3*x)^3-_ + 20465/57624*sqrt(1-2*x)/(2+3*x)^2-20465/134456*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R - 19891980x - 43099290x - 26522640x + 2946960x + 7858560x +--R + +--R 1964640 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--+ +--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R (9945990x + 21549645x + 13261320x - 1473480x - 3929280x - 982320) +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--+ +--R (6630660x + 11787840x + 3769653x - 3646863x - 2528226x - 401410)\|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 20465log(-----------------------------) + 40930atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 134456\|21 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 61395x + 102325)\|21 + (61395x - 102325)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 40930x + 20465)\|3 \|7 \|21 + 859530x - 429765 +--R / +--R 2 +--------+ +--R (16941456x + 2823576x - 5647152)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (2420208x - 3630312x - 1479016x + 1344560)\|21 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)^5*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R (1) +--R 8 7 6 5 4 3 2 +--R 30375x + 155925x + 350055x + 448911x + 359670x + 184360x + 59040x +--R + +--R 10800x + 864 +--R / +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=22370117/768/(1-2*x)^(3/2)+52725715/384*(1-2*x)^(3/2)-_ + 2887773/64*(1-2*x)^(5/2)+10121229/896*(1-2*x)^(7/2)-_ + 246315/128*(1-2*x)^(9/2)+277425/1408*(1-2*x)^(11/2)-_ + 30375/3328*(1-2*x)^(13/2)+(-39220335/128)/sqrt(1-2*x)-_ + 60160485/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 8 7 6 5 4 +--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x +--R + +--R 3 2 +--R 905206628x + 2892917004x - 5818266408x + 1938557272 +--R / +--R +--------+ +--R (6006x - 3003)\|- 2x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 5 4 +--R 7016625x + 47670525x + 153878760x + 324478899x + 540496701x +--R + +--R 3 2 +--R 905206628x + 2892917004x - 5818266408x + 1938557272 +--R / +--R +--------+ +--R (6006x - 3003)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(2+3*x)^4*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--R 10125x + 45225x + 86535x + 91947x + 58592x + 22392x + 4752x + 432 +--R ----------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=3195731/384/(1-2*x)^(3/2)+9504551/384*(1-2*x)^(3/2)-_ + 4177401/640*(1-2*x)^(5/2)+1101465/896*(1-2*x)^(7/2)-_ + 17925/128*(1-2*x)^(9/2)+10125/1408*(1-2*x)^(11/2)+_ + (-9836211/128)/sqrt(1-2*x)-12973191/128*sqrt(1-2*x) +--R +--R +--R (2) +--R 7 6 5 4 3 +--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x +--R + +--R 2 +--R 258342648x - 522173856x + 173891632 +--R / +--R +--------+ +--R (2310x - 1155)\|- 2x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 4 3 +--R 1063125x + 6630750x + 19961775x + 41201532x + 77493296x +--R + +--R 2 +--R 258342648x - 522173856x + 173891632 +--R / +--R +--------+ +--R (2310x - 1155)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(2+3*x)^3*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--R 3375x + 12825x + 20295x + 17119x + 8118x + 2052x + 216 +--R (1) ----------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=456533/192/(1-2*x)^(3/2)+98209/24*(1-2*x)^(3/2)-52011/64*(1-2*x)^(5/2)+_ + 11475/112*(1-2*x)^(7/2)-375/64*(1-2*x)^(9/2)+(-302379/16)/sqrt(1-2*x)-_ + 1334949/64*sqrt(1-2*x) +--R +--R +--R 6 5 4 3 2 +--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074 +--R (2) ---------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 +a0:=integrate(t0,x) +--R +--R +--R 6 5 4 3 2 +--R 7875x + 45225x + 130464x + 293785x + 1051833x - 2146758x + 714074 +--R (3) ---------------------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(2+3*x)^2*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +--R 1125x + 3525x + 4415x + 2763x + 864x + 108 +--R (1) ---------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=65219/96/(1-2*x)^(3/2)+28555/48*(1-2*x)^(3/2)-2535/32*(1-2*x)^(5/2)+_ + 1125/224*(1-2*x)^(7/2)+(-144837/32)/sqrt(1-2*x)-64317/16*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264 +--R (2) -------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +a0:=integrate(t0,x) +--R +--R +--R 5 4 3 2 +--R 3375x + 18180x + 55145x + 223458x - 465060x + 154264 +--R (3) -------------------------------------------------------- +--R +--------+ +--R (42x - 21)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(2+3*x)*(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +--R 375x + 925x + 855x + 351x + 54 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=9317/48/(1-2*x)^(3/2)+1675/24*(1-2*x)^(3/2)-75/16*(1-2*x)^(5/2)+_ + (-8349/8)/sqrt(1-2*x)-2805/4*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--R 225x + 1225x + 6240x - 13533x + 4457 +--R (2) --------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +a0:=integrate(t0,x) +--R +--R +--R 4 3 2 +--R 225x + 1225x + 6240x - 13533x + 4457 +--R (3) --------------------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^3/(1-2*x)^(5/2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=1331/24/(1-2*x)^(3/2)+125/24*(1-2*x)^(3/2)+(-1815/8)/sqrt(1-2*x)-_ + 825/8*sqrt(1-2*x) +--R +--R +--R 3 2 +--R 125x + 1050x - 2505x + 808 +--R (2) ---------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 125x + 1050x - 2505x + 808 +--R (3) ---------------------------- +--R +--------+ +--R (6x - 3)\|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=253/21*(3+5*x)/(1-2*x)^(3/2)-5/3*(3+5*x)^2/(1-2*x)^(3/2)+_ + 2/147*atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+(-2948/49)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 2 +--+ +--R (4x - 2)\|- 2x + 1 atanh(---------------) + (6125x - 19193x + 5736)\|21 +--R +-+ +--R \|7 +--R ------------------------------------------------------------------------- +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ - 21\|- 2x + 1 + (3x - 5)\|21 +--R (2x - 1)\|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (6125x - 19193x + 5736)\|21 +--R / +--R +--+ +--------+ +--R (294x - 147)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R log(-------------------------------) - 2atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------- +--R +--+ +--R 147\|21 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +-+ +-+ +--+ +--R ((- 3x + 5)\|21 + (3x - 5)\|3 \|7 )\|- 2x + 1 + (2x - 1)\|3 \|7 \|21 +--R + +--R - 42x + 21 +--R / +--R 2 +--------+ +--R (18522x + 3087x - 6174)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 2646x + 3969x + 1617x - 1470)\|21 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x))-200/1029*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)-15/49*(3+5*x)^2/((2+3*x)*sqrt(1-2*x))-_ + 750/343*sqrt(1-2*x)-50/1029*(3+5*x)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|3 \|- 2x + 1 +--R (- 1200x - 200x + 400)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 2 +--+ +--R (- 42475x - 21050x + 4839)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R (600x + 100x - 200)\|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 2 +--+ +--R (- 42475x - 21050x + 4839)\|21 +--R / +--R 2 +--+ +--------+ +--R (6174x + 1029x - 2058)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 100log(-----------------------------) + 200atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 1029\|21 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 300x + 500)\|21 + (300x - 500)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 200x + 100)\|3 \|7 \|21 + 4200x - 2100 +--R / +--R 2 +--------+ +--R (129654x + 21609x - 43218)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (18522x - 27783x - 11319x + 10290)\|21 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^2)+905/1029*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+1/7*(3+5*x)^2/((2+3*x)^2*sqrt(1-2*x))-_ + 5/294*(1+x)*sqrt(1-2*x)/(2+3*x)^2+50/1029*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 3 2 +--------+ \|3 \|- 2x + 1 +--R (32580x + 27150x - 7240x - 7240)\|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +--+ +--R (- 10860x - 33410x - 29593x - 8103)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (16290x + 13575x - 3620x - 3620)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +--+ +--R (- 10860x - 33410x - 29593x - 8103)\|21 +--R / +--R 3 2 +--+ +--------+ +--R (37044x + 30870x - 8232x - 8232)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R - 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 905log(-------------------------------) - 1810atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 2058\|21 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 2715x + 4525)\|21 + (2715x - 4525)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (1810x - 905)\|3 \|7 \|21 - 38010x + 19005 +--R / +--R 2 +--------+ +--R (259308x + 43218x - 86436)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (- 37044x + 55566x + 22638x - 20580)\|21 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 3 2 +--R 125x + 225x + 135x + 27 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^3)-7510/7203*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+29/49*(3+5*x)^2/((2+3*x)^3*sqrt(1-2*x))+_ + 125/1029*sqrt(1-2*x)/(2+3*x)^2-3755/7203*sqrt(1-2*x)/(2+3*x)+_ + 4/49*(3+5*x)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (- 405540x - 608310x - 135180x + 150200x + 60080)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--+ +--R (135180x + 150200x - 83306x - 150295x - 45383)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--------+ +--R (202770x + 304155x + 67590x - 75100x - 30040)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 21\|- 2x + 1 + (3x - 5)\|21 +--R log(-----------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--+ +--R (135180x + 150200x - 83306x - 150295x - 45383)\|21 +--R / +--R 4 3 2 +--+ +--------+ +--R (388962x + 583443x + 129654x - 144060x - 57624)\|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 3755log(-----------------------------) + 7510atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 7203\|21 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 11265x + 18775)\|21 + (11265x - 18775)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 7510x + 3755)\|3 \|7 \|21 + 157710x - 78855 +--R / +--R 2 +--------+ +--R (907578x + 151263x - 302526)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (129654x - 194481x - 79233x + 72030)\|21 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^4)-177635/201684*_ + atanh(sqrt(3/7)*sqrt(1-2*x))/sqrt(21)+51/49*(3+5*x)^2/((2+3*x)^4*_ + sqrt(1-2*x))+692/3087*sqrt(1-2*x)/(2+3*x)^3-177635/172872*_ + sqrt(1-2*x)/(2+3*x)^2-177635/403368*sqrt(1-2*x)/(2+3*x)+_ + 601/4116*(3+5*x)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R (2) +--R 5 4 3 2 +--R - 57553740x - 124699770x - 76738320x + 8526480x + 22737280x +--R + +--R 5684320 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 2 +--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x +--R + +--R - 2094250 +--R * +--R +--+ +--R \|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 28776870x + 62349885x + 38369160x - 4263240x - 11368640x +--R + +--R - 2842160 +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R 19184580x + 34105920x + 10906789x - 12952519x - 10307138x +--R + +--R - 2094250 +--R * +--R +--+ +--R \|21 +--R / +--R 5 4 3 2 +--R (65345616x + 141582168x + 87127488x - 9680832x - 25815552x - 6453888) +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 177635log(-----------------------------) + 355270atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R ----------------------------------------------------------------------- +--R +--+ +--R 403368\|21 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 532905x + 888175)\|21 + (532905x - 888175)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 355270x + 177635)\|3 \|7 \|21 + 7460670x - 3730335 +--R / +--R 2 +--------+ +--R (50824368x + 8470728x - 16941456)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (7260624x - 10890936x - 4437048x + 4033680)\|21 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(3+5*x)^3/((1-2*x)^(5/2)*(2+3*x)^6) +--R +--R +--R (1) +--R 3 2 +--R 125x + 225x + 135x + 27 +--R / +--R 8 7 6 5 4 3 2 +--R (2916x + 8748x + 8505x + 756x - 3780x - 2016x + 112x + 320x + 64) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2/21*(3+5*x)^3/((1-2*x)^(3/2)*(2+3*x)^5)-163474/352947*atanh(sqrt(3/7)*_ + sqrt(1-2*x))/sqrt(21)+73/49*(3+5*x)^2/((2+3*x)^5*sqrt(1-2*x))+_ + 3912/12005*sqrt(1-2*x)/(2+3*x)^4-163474/108045*sqrt(1-2*x)/(2+3*x)^3-_ + 81737/151263*sqrt(1-2*x)/(2+3*x)^2-81737/352947*sqrt(1-2*x)/(2+3*x)+_ + 1082/5145*(3+5*x)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R (2) +--R 6 5 4 3 +--R - 397241820x - 1125518490x - 1103449500x - 294253200x +--R + +--R 2 +--R 196168800x + 143857120x + 26155840 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 6 5 4 3 2 +--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x +--R + +--R - 42553376x - 5615203 +--R * +--R +--+ +--R \|21 +--R / +--R 6 5 4 3 2 +--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x +--R + +--R - 310593360x - 56471520 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 198620910x + 562759245x + 551724750x + 147126600x - 98084400x +--R + +--R - 71928560x - 13077920 +--R * +--R +--------+ +--+ +--R +--------+ 21\|- 2x + 1 + (3x - 5)\|21 +--R \|- 2x + 1 log(-----------------------------) +--R 3x + 2 +--R + +--R 6 5 4 3 2 +--R 132413940x + 323678520x + 232214817x - 22641149x - 99751837x +--R + +--R - 42553376x - 5615203 +--R * +--R +--+ +--R \|21 +--R / +--R 6 5 4 3 2 +--R 857661210x + 2430040095x + 2382392250x + 635304600x - 423536400x +--R + +--R - 310593360x - 56471520 +--R * +--R +--+ +--------+ +--R \|21 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 21\|- 2x + 1 + (3x - 5)\|21 \|3 \|- 2x + 1 +--R 81737log(-----------------------------) + 163474atanh(---------------) +--R 3x + 2 +-+ +--R \|7 +--R (4) ---------------------------------------------------------------------- +--R +--+ +--R 352947\|21 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +-+ +--------+ +--R ((- 245211x + 408685)\|21 + (245211x - 408685)\|3 \|7 )\|- 2x + 1 +--R + +--R +-+ +-+ +--+ +--R (- 163474x + 81737)\|3 \|7 \|21 + 3432954x - 1716477 +--R / +--R 2 +--------+ +--R (44471322x + 7411887x - 14823774)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6353046x - 9529569x - 3882417x + 3529470)\|21 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=172/165*(2+3*x)^4/(1-2*x)^(3/2)-3/35*(2+3*x)^5/(1-2*x)^(3/2)-2/75625*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-7561/605*(2+3*x)^3/_ + sqrt(1-2*x)-55573878/75625*sqrt(1-2*x)-63513/605*(2+3*x)*_ + sqrt(1-2*x)-340248/15125*(2+3*x)^2*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 84x + 42)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x +--R + +--R 1780047848 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (3176250x - 1588125)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (42x - 21)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 33078375x + 190531440x + 611141355x + 2562785082x - 5374023537x +--R + +--R 1780047848 +--R * +--R +--+ +--R \|55 +--R / +--R +--+ +--------+ +--R (3176250x - 1588125)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 75625\|55 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (41593750x + 4159375x - 12478125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (3781250x - 5671875x - 1739375x + 1815000)\|55 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=959/825*(2+3*x)^3/(1-2*x)^(3/2)-3/25*(2+3*x)^4/(1-2*x)^(3/2)-2/15125*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-31612/3025*(2+3*x)^2/_ + sqrt(1-2*x)-2276102/15125*sqrt(1-2*x)-1/15125*(569026+948375*x)*_ + sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55 +--R / +--R +--+ +--------+ +--R (90750x - 45375)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (441045x + 2597265x + 13976226x - 30775791x + 10097264)\|55 +--R / +--R +--+ +--------+ +--R (90750x - 45375)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 15125\|55 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (8318750x + 831875x - 2495625)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (756250x - 1134375x - 347875x + 363000)\|55 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=238/165*(2+3*x)^2/(1-2*x)^(3/2)-1/5*(2+3*x)^3/(1-2*x)^(3/2)-_ + 2/3025*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 7/605*(1426+2377*x)/sqrt(1-2*x)-80818/3025*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (49005x + 450846x - 1111431x + 354344)\|55 +--R / +--R +--+ +--------+ +--R (18150x - 9075)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (49005x + 450846x - 1111431x + 354344)\|55 +--R / +--R +--+ +--------+ +--R (18150x - 9075)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 3025\|55 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (1663750x + 166375x - 499125)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (151250x - 226875x - 69575x + 72600)\|55 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=469/165*(2+3*x)/(1-2*x)^(3/2)-3/5*(2+3*x)^2/(1-2*x)^(3/2)-_ + 2/605*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+(-5152/605)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 2 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (9801x - 33321x + 9494)\|55 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (3630x - 1815)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6x - 3)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (9801x - 33321x + 9494)\|55 +--R / +--R +--+ +--------+ +--R (3630x - 1815)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 605\|55 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (332750x + 33275x - 99825)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (30250x - 45375x - 13915x + 14520)\|55 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=49/66/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+_ + (-217/242)/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--+ +--R (- 12x + 6)\|- 2x + 1 atanh(---------------) + (- 651x + 56)\|55 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--+ +--R (6x - 3)\|- 2x + 1 log(-----------------------------) + (- 651x + 56)\|55 +--R 5x + 3 +--R -------------------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R log(-----------------------------) + 2atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------ +--R +--+ +--R 121\|55 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 5x + 8)\|55 + (5x - 8)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 2x + 1)\|5 \|11 \|55 + 110x - 55 +--R / +--R 2 +--------+ +--R (66550x + 6655x - 19965)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (6050x - 9075x - 2783x + 2904)\|55 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=7/33/(1-2*x)^(3/2)-2/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 2/121/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 12x + 6)\|5 \|- 2x + 1 atanh(---------------) + (12x - 83)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (6x - 3)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (12x - 83)\|11 +--R / +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R \|5 log(---------------------------------) + 2\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2/33/(1-2*x)^(3/2)-10/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 10/121/sqrt(1-2*x) +--R +--R +--R +-+ +--------+ +--R +-+ +--------+ \|5 \|- 2x + 1 +--+ +--R (- 60x + 30)\|5 \|- 2x + 1 atanh(---------------) + (60x - 52)\|11 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (30x - 15)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +--+ +--R (60x - 52)\|11 +--R / +--R +--+ +--------+ +--R (726x - 363)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 5\|5 log(---------------------------------) + 10\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +--+ +--R 121\|11 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=4/231/(1-2*x)^(3/2)+18/49*atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-_ + 50/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/5929/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (13068x - 6534)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 14700x + 7350)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--+ +--R (1632x - 1124)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (35574x - 17787)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (7350x - 3675)\|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R (6534x - 3267)\|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--+ +--R (1632x - 1124)\|7 \|11 +--R / +--R +-+ +--+ +--------+ +--R (35574x - 17787)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 1225\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 1089\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R - 2178\|3 \|11 atanh(---------------) + 2450\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 5929\|7 \|11 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x))+720/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 360/5929/((2+3*x)*sqrt(1-2*x))+2055/41503*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R (1568160x + 261360x - 522720)\|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (- 1543500x - 257250x + 514500)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (- 24660x + 39780x - 15881)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +--------+ +--R (771750x + 128625x - 257250)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--------+ +--R (784080x + 130680x - 261360)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +--+ +--R (- 24660x + 39780x - 15881)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 42875\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 43560\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 87120\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 85750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 41503\|7 \|11 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2)+3645/343*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-1250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 64/847/((2+3*x)^2*sqrt(1-2*x))+45/11858*sqrt(1-2*x)/(2+3*x)^2+_ + 36885/83006*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--------+ +--R (47632860x + 39694050x - 10585080x - 10585080)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (- 46305000x - 38587500x + 10290000x + 10290000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (23152500x + 19293750x - 5145000x - 5145000)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (23816430x + 19847025x - 5292540x - 5292540)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 1327860x + 438840x + 594687x - 245383)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (4482324x + 3735270x - 996072x - 996072)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 428750\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 441045\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 882090\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 857500\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 83006\|7 \|11 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*(3+5*x)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (1620x + 3672x + 2025x - 1077x - 1312x - 152x + 176x + 48)\|- 2x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^3)+127710/2401*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)-6250/121*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+536/5929/((2+3*x)^3*sqrt(1-2*x))-93/5929*_ + sqrt(1-2*x)/(2+3*x)^3+8955/41503*sqrt(1-2*x)/(2+3*x)^2+_ + 669990/290521*sqrt(1-2*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (2503371420x + 3755057130x + 834457140x - 927174600x - 370869840) +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (- 2431012500x - 3646518750x - 810337500x + 900375000x + 360150000) +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1215506250x + 1823259375x + 405168750x - 450187500x - 180075000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R (1251685710x + 1877528565x + 417228570x - 463587300x - 185434920) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +-+ +--+ +--R (- 72358920x - 26376300x + 47036214x + 9083055x - 8496203)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (47064402x + 70596603x + 15688134x - 17431260x - 6972504)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 7503125\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 7726455\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 15452910\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 15006250\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 290521\|7 \|11 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=959/825*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x))-3/25*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x))-406/831875*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-93611/9075*(2+3*x)^3/((3+5*x)*sqrt(1-2*x))-_ + 77849506/831875*sqrt(1-2*x)+154448/166375*(2+3*x)^2*sqrt(1-2*x)/_ + (3+5*x)-7/831875*(2780354+4633875*x)*sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 12180x - 1218x + 3654)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x +--R + +--R 1035652776 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (6090x + 609x - 1827)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 72772425x + 480298005x + 2644064775x - 3837745731x - 1434109759x +--R + +--R 1035652776 +--R * +--R +--+ +--R \|55 +--R / +--R 2 +--+ +--------+ +--R (24956250x + 2495625x - 7486875)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 203log(-----------------------------) + 406atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 831875\|55 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 1015x + 1624)\|55 + (1015x - 1624)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 406x + 203)\|5 \|11 \|55 + 22330x - 11165 +--R / +--R 2 +--------+ +--R (457531250x + 45753125x - 137259375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (41593750x - 62390625x - 19133125x + 19965000)\|55 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=238/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-1/5*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x))-68/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)-15442/1815*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 532452/33275*sqrt(1-2*x)+1014/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 2040x - 204x + 612)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (1020x + 102x - 306)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (1617165x + 16171650x - 28677318x - 10671002x + 7204728)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 34log(-----------------------------) + 68atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------- +--R +--+ +--R 33275\|55 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 170x + 272)\|55 + (170x - 272)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 68x + 34)\|5 \|11 \|55 + 3740x - 1870 +--R / +--R 2 +--------+ +--R (18301250x + 1830125x - 5490375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1663750x - 2495625x - 765325x + 798600)\|55 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=469/165*(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x))-3/5*(2+3*x)^3/((1-2*x)^(3/2)*_ + (3+5*x))-274/33275*atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-_ + 7/1815*(3944+7323*x)/((3+5*x)*sqrt(1-2*x))-26988/33275*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 8220x - 822x + 2466)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (1617165x - 4634229x - 1790101x + 943584)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (4110x + 411x - 1233)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (1617165x - 4634229x - 1790101x + 943584)\|55 +--R / +--R 2 +--+ +--------+ +--R (998250x + 99825x - 299475)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 137log(-----------------------------) + 274atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 33275\|55 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 685x + 1096)\|55 + (685x - 1096)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 274x + 137)\|5 \|11 \|55 + 15070x - 7535 +--R / +--R 2 +--------+ +--R (18301250x + 1830125x - 5490375)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1663750x - 2495625x - 765325x + 798600)\|55 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x))-208/6655*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-23/363*(2+3*x)^2/((3+5*x)*sqrt(1-2*x))-_ + 942/6655*sqrt(1-2*x)+6/1331*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 6240x - 624x + 1872)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 106563x - 57832x + 3678)\|55 +--R / +--R 2 +--+ +--------+ +--R (199650x + 19965x - 59895)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (3120x + 312x - 936)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (- 106563x - 57832x + 3678)\|55 +--R / +--R 2 +--+ +--------+ +--R (199650x + 19965x - 59895)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 104log(-----------------------------) + 208atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ----------------------------------------------------------------- +--R +--+ +--R 6655\|55 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 520x + 832)\|55 + (520x - 832)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 208x + 104)\|5 \|11 \|55 + 11440x - 5720 +--R / +--R 2 +--------+ +--R (3660250x + 366025x - 1098075)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (332750x - 499125x - 153065x + 159720)\|55 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x))-142/1331*atanh(sqrt(5/11)*sqrt(1-2*x))/_ + sqrt(55)+142/6655/sqrt(1-2*x)+(-1231/3630)/((3+5*x)*sqrt(1-2*x)) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +--------+ \|5 \|- 2x + 1 +--R (- 4260x - 426x + 1278)\|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (852x - 2623x - 1866)\|55 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--+ +--R 2 +--------+ 55\|- 2x + 1 + (5x - 8)\|55 +--R (2130x + 213x - 639)\|- 2x + 1 log(-----------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (852x - 2623x - 1866)\|55 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 71log(-----------------------------) + 142atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ---------------------------------------------------------------- +--R +--+ +--R 1331\|55 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 355x + 568)\|55 + (355x - 568)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 142x + 71)\|5 \|11 \|55 + 7810x - 3905 +--R / +--R 2 +--------+ +--R (732050x + 73205x - 219615)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (66550x - 99825x - 30613x + 31944)\|55 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=76/1815/(1-2*x)^(3/2)+(-1/55)/((1-2*x)^(3/2)*(3+5*x))-_ + 76/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+76/1331/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 2280x - 228x + 684)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (2280x - 608x - 1113)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--------+ +--R (1140x + 114x - 342)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (2280x - 608x - 1113)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 38\|5 log(---------------------------------) + 76\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 1331\|11 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=10/363/(1-2*x)^(3/2)+(-1/11)/((1-2*x)^(3/2)*(3+5*x))-_ + 50/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+50/1331/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +--------+ +--R 2 +-+ +--------+ \|5 \|- 2x + 1 +--R (- 1500x - 150x + 450)\|5 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (1500x - 400x - 417)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +--+ +--R 2 +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R (750x + 75x - 225)\|5 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 2 +--+ +--R (1500x - 400x - 417)\|11 +--R / +--R 2 +--+ +--------+ +--R (39930x + 3993x - 11979)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 25\|5 log(---------------------------------) + 50\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--R 1331\|11 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x))-54/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)+1400/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+_ + 1096/17787/((3+5*x)*sqrt(1-2*x))-8185/65219*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 2 +-+ +--+ +--------+ +--R (- 2156220x - 215622x + 646866)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|3 \|- 2x + 1 +--R atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R 2 +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R (2058000x + 205800x - 617400)\|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--+ +--R (98220x - 74108x + 9111)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--+ +--------+ +--R (1078110x + 107811x - 323433)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 2 +-+ +-+ +--------+ +--R (1029000x + 102900x - 308700)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 2 +-+ +--+ +--R (98220x - 74108x + 9111)\|7 \|11 +--R / +--R 2 +-+ +--+ +--------+ +--R (1956570x + 195657x - 586971)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 35937\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 34300\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +-+ +-+ \|5 \|- 2x + 1 +--R 71874\|3 \|11 atanh(---------------) - 68600\|5 \|7 atanh(---------------) +--R +-+ +--+ +--R \|7 \|11 +--R / +--R +-+ +--+ +--R 65219\|7 \|11 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^2) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x))-4050/343*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+15250/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+1360/17787/((2+3*x)*(3+5*x)*sqrt(1-2*x))-_ + 399500/456533*sqrt(1-2*x)/(3+5*x)+1775/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (- 485149500x - 371947950x + 113201550x + 97029900)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (470767500x + 360921750x - 109845750x - 94153500)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--+ +--------+ +--R (242574750x + 185973975x - 56600775x - 48514950)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(-------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +-+ +--------+ +--R (235383750x + 180460875x - 54922875x - 47076750)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(-----------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--R (14382000x - 5028300x - 5548760x + 2209989)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (41087970x + 31500777x - 9587193x - 8217594)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2695275\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2615375\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 5390550\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 5230750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 456533\|7 \|11 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^2) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x))-4455/49*atanh(sqrt(3/7)*_ + sqrt(1-2*x))*sqrt(3/7)+117500/1331*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+232/2541/((2+3*x)^2*(3+5*x)*sqrt(1-2*x))-_ + 860525/130438*sqrt(1-2*x)/(3+5*x)-5/1694*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x))+3790/5929*sqrt(1-2*x)/((2+3*x)*(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R (- 3201986700x - 4589514270x - 889440750x + 1138484160x + 426931560) +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R (3109050000x + 4456305000x + 863625000x - 1105440000x - 414540000) +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--+ +--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (1600993350x + 2294757135x + 444720375x - 569242080x - 213465780) +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(-------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (1554525000x + 2228152500x + 431812500x - 552720000x - 207270000) +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(-----------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +-+ +--+ +--R (92936700x + 27977220x - 58371045x - 9008764x + 9784671)\|7 \|11 +--R / +--R 4 3 2 +-+ +--+ +--R (35218260x + 50479506x + 9782850x - 12522048x - 4695768)\|7 \|11 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +-+ +--R +-+ +--+ 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 5929605\|3 \|11 log(-------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--+ +--R +-+ +-+ - 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 5757500\|5 \|7 log(-----------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R 11859210\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R - 11515000\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 130438\|7 \|11 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=238/165*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-1/5*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x)^2)-6937/1830125*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-15197/1815*(2+3*x)^3/((3+5*x)^2*sqrt(1-2*x))-_ + 18063843/1830125*sqrt(1-2*x)+149653/199650*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)^2+13755/29282*(2+3*x)*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 2081100x - 1456770x + 499464x + 374598)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x +--R + +--R 1463964312 +--R * +--R +--+ +--R \|55 +--R / +--R 3 2 +--+ +--------+ +--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (1040550x + 728385x - 249732x - 187299)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 533664450x + 5763576060x - 6510290070x - 9509366452x + 253794537x +--R + +--R 1463964312 +--R * +--R +--+ +--R \|55 +--R / +--R 3 2 +--+ +--------+ +--R (549037500x + 384326250x - 131769000x - 98826750)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 6937log(-----------------------------) + 13874atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 3660250\|55 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 34685x + 55496)\|55 + (34685x - 55496)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 13874x + 6937)\|5 \|11 \|55 + 763070x - 381535 +--R / +--R 2 +--------+ +--R (2013137500x + 201313750x - 603941250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (183012500x - 274518750x - 84185750x + 87846000)\|55 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=469/165*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-3/5*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x)^2)-4693/366025*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)-14966/1815*(2+3*x)^2/((3+5*x)^2*_ + sqrt(1-2*x))+29033/39930*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2+_ + 164309/366025*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 1407900x - 985530x + 337896x + 253422)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (703950x + 492765x - 168948x - 126711)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--+ +--R (106732890x - 248761830x - 309826828x - 10907307x + 37428168)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 4693log(-----------------------------) + 9386atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 732050\|55 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 23465x + 37544)\|55 + (23465x - 37544)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 9386x + 4693)\|5 \|11 \|55 + 516230x - 258115 +--R / +--R 2 +--------+ +--R (402627500x + 40262750x - 120788250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (36602500x - 54903750x - 16837150x + 17569200)\|55 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^2)-14423/366025*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)-19/363*(2+3*x)^3/_ + ((3+5*x)^2*sqrt(1-2*x))-29037/366025*sqrt(1-2*x)+_ + 31/7986*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^2+141/146410*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 4326900x - 3028830x + 1038456x + 778842)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 34712250x - 40823468x - 11479257x + 311208)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (2163450x + 1514415x - 519228x - 389421)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (- 34712250x - 40823468x - 11479257x + 311208)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (109807500x + 76865250x - 26353800x - 19765350)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 14423log(-----------------------------) + 28846atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) --------------------------------------------------------------------- +--R +--+ +--R 732050\|55 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 72115x + 115384)\|55 + (72115x - 115384)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 28846x + 14423)\|5 \|11 \|55 + 1586530x - 793265 +--R / +--R 2 +--------+ +--R (402627500x + 40262750x - 120788250)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (36602500x - 54903750x - 16837150x + 17569200)\|55 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^2)-7559/73205*_ + atanh(sqrt(5/11)*sqrt(1-2*x))/sqrt(55)+47/363*(2+3*x)^2/_ + ((3+5*x)^2*sqrt(1-2*x))-101/7986*(2+3*x)*sqrt(1-2*x)/(3+5*x)^2-_ + 683/73205*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 2267700x - 1587390x + 544248x + 408186)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (453540x - 639434x - 1242261x - 417036)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (1133850x + 793695x - 272124x - 204093)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (453540x - 639434x - 1242261x - 417036)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (21961500x + 15373050x - 5270760x - 3953070)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 7559log(-----------------------------) + 15118atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) -------------------------------------------------------------------- +--R +--+ +--R 146410\|55 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 37795x + 60472)\|55 + (37795x - 60472)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 15118x + 7559)\|5 \|11 \|55 + 831490x - 415745 +--R / +--R 2 +--------+ +--R (80525500x + 8052550x - 24157650)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (7320500x - 10980750x - 3367430x + 3513840)\|55 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^2)-2873/14641*atanh(sqrt(5/11)*_ + sqrt(1-2*x))/sqrt(55)+(-614/1815)/((3+5*x)^2*sqrt(1-2*x))+_ + 2873/19965/((3+5*x)*sqrt(1-2*x))-2873/29282*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 861900x - 603330x + 206856x + 155142)\|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (172380x + 57460x - 107127x - 47568)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +--R (430950x + 301665x - 103428x - 77571)\|- 2x + 1 +--R * +--R +--------+ +--+ +--R 55\|- 2x + 1 + (5x - 8)\|55 +--R log(-----------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (172380x + 57460x - 107127x - 47568)\|55 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|55 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 +m0:=a0-r0 +--R +--R +--R +--------+ +--+ +-+ +--------+ +--R 55\|- 2x + 1 + (5x - 8)\|55 \|5 \|- 2x + 1 +--R 2873log(-----------------------------) + 5746atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R (4) ------------------------------------------------------------------- +--R +--+ +--R 29282\|55 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +-+ +--+ +--------+ +--R ((- 14365x + 22984)\|55 + (14365x - 22984)\|5 \|11 )\|- 2x + 1 +--R + +--R +-+ +--+ +--+ +--R (- 5746x + 2873)\|5 \|11 \|55 + 316030x - 158015 +--R / +--R 2 +--------+ +--R (16105100x + 1610510x - 4831530)\|- 2x + 1 +--R + +--R 3 2 +--+ +--R (1464100x - 2196150x - 673486x + 702768)\|55 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=73/3993/(1-2*x)^(3/2)+(-1/110)/((1-2*x)^(3/2)*(3+5*x)^2)+(-73/1210)/_ + ((1-2*x)^(3/2)*(3+5*x))-365/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+365/14641/sqrt(1-2*x) +--R +--R +--R (2) +--R 3 2 +-+ +--------+ +--R (- 109500x - 76650x + 26280x + 19710)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (109500x + 36500x - 47961x - 17466)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (54750x + 38325x - 13140x - 9855)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (109500x + 36500x - 47961x - 17466)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 365\|5 log(---------------------------------) + 730\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 29282\|11 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (500x + 400x - 235x - 207x + 27x + 27)\|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^2)-175/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+70/363/((3+5*x)^2*sqrt(1-2*x))-875/7986*sqrt(1-2*x)/_ + (3+5*x)^2-875/29282*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--------+ +--R (- 52500x - 36750x + 12600x + 9450)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--R \|5 \|- 2x + 1 +--R atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (52500x + 17500x - 22995x - 4764)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--------+ +--R (26250x + 18375x - 6300x - 4725)\|5 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +--+ +--R (52500x + 17500x - 22995x - 4764)\|11 +--R / +--R 3 2 +--+ +--------+ +--R (4392300x + 3074610x - 1054152x - 790614)\|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +-+ +--------+ +--R +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +-+ \|5 \|- 2x + 1 +--R 175\|5 log(---------------------------------) + 350\|5 atanh(---------------) +--R 5x + 3 +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 29282\|11 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^3) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (1500x + 2200x + 95x - 1091x - 333x + 135x + 54)\|- 2x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^2)+162/49*atanh(sqrt(3/7)*sqrt(1-2*x))*_ + sqrt(3/7)-47075/14641*atanh(sqrt(5/11)*sqrt(1-2*x))*_ + sqrt(5/11)+1376/17787/((3+5*x)^2*sqrt(1-2*x))-_ + 33535/391314*sqrt(1-2*x)/(3+5*x)^2+325835/1434818*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +--+ +--R (711552600x + 498086820x - 170772624x - 128079468)\|3 \|11 +--R * +--R +-+ +--------+ +--R +--------+ \|3 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 3 2 +-+ +-+ +--R (- 692002500x - 484401750x + 166080600x + 124560450)\|5 \|7 +--R * +--R +-+ +--------+ +--R +--------+ \|5 \|- 2x + 1 +--R \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--+ +--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +-+ +--------+ +--R (346001250x + 242200875x - 83040300x - 62280225)\|5 \|7 \|- 2x + 1 +--R * +--R +-+ +--------+ +--+ +--R 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R log(---------------------------------) +--R 5x + 3 +--R + +--R 3 2 +-+ +--+ +--------+ +--R (355776300x + 249043410x - 85386312x - 64039734)\|3 \|11 \|- 2x + 1 +--R * +--R +-+ +--------+ +-+ +--R - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R log(---------------------------------) +--R 3x + 2 +--R + +--R 3 2 +-+ +--+ +--R (- 19550100x + 9295580x + 6032979x - 2971158)\|7 \|11 +--R / +--R 3 2 +-+ +--+ +--------+ +--R (215222700x + 150655890x - 51653448x - 38740086)\|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2306675\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2371842\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 4743684\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 4613350\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 1434818\|7 \|11 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--------+ +--R (4500x + 9600x + 4685x - 3083x - 3181x - 261x + 432x + 108)\|- 2x + 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^2)+17820/343*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-738625/14641*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+1640/17787/_ + ((2+3*x)*(3+5*x)^2*sqrt(1-2*x))-1759475/2739198*_ + sqrt(1-2*x)/(3+5*x)^2+1495/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 37771225/10043726*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 234812358000x + 320910222600x + 53224134480x - 79836201720x +--R + +--R - 28177482960 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 4 3 2 +--R - 228013537500x - 311618501250x - 51683068500x + 77524602750x +--R + +--R 27361624500 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882) +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204) +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 114006768750x + 155809250625x + 25841534250x - 38762301375x +--R + +--R - 13680812250 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 4 3 2 +--R 117406179000x + 160455111300x + 26612067240x - 39918100860x +--R + +--R - 14088741480 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 4 3 2 +--R (- 6798820500x - 1580768100x + 4110847595x + 479695050x - 645558882) +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 4 3 2 +--R (4519676700x + 6176891490x + 1024460052x - 1536690078x - 542361204) +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 253348375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 260902620\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 521805240\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 506696750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 10043726\|7 \|11 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 8 7 6 5 4 3 2 +--R 13500x + 37800x + 33255x + 121x - 15709x - 7145x + 774x + 1188x +--R + +--R 216 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^2)+182655/343*_ + atanh(sqrt(3/7)*sqrt(1-2*x))*sqrt(3/7)-7570625/14641*_ + atanh(sqrt(5/11)*sqrt(1-2*x))*sqrt(5/11)+272/2541/((2+3*x)^2*(3+5*x)^2*_ + sqrt(1-2*x))-17552275/2739198*sqrt(1-2*x)/(3+5*x)^2-_ + 115/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^2)+_ + 69235/83006*sqrt(1-2*x)/((2+3*x)*(3+5*x)^2)+_ + 193818700/5021863*sqrt(1-2*x)/(3+5*x) +--R +--R +--R (2) +--R 5 4 3 +--R 7220480008500x + 14681642683950x + 8215301698560x +--R + +--R 2 +--R - 1363868446050x - 2503099736280x - 577638400680 +--R * +--R +-+ +--------+ +--R +-+ +--+ +--------+ \|3 \|- 2x + 1 +--R \|3 \|11 \|- 2x + 1 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R 5 4 3 +--R - 7011155812500x - 14256016818750x - 7977137280000x +--R + +--R 2 +--R 1324329431250x + 2430534015000x + 560892465000 +--R * +--R +-+ +--------+ +--R +-+ +-+ +--------+ \|5 \|- 2x + 1 +--R \|5 \|7 \|- 2x + 1 atanh(---------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x +--R + +--R - 9944654283x - 13236365823 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 5 4 3 2 +--R 13559030100x + 27570027870x + 15427163136x - 2561150130x +--R + +--R - 4700463768x - 1084722408 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 3505577906250x + 7128008409375x + 3988568640000x - 662164715625x +--R + +--R - 1215267007500x - 280446232500 +--R * +--R +-+ +--------+ +--+ +--R +-+ +-+ +--------+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R \|5 \|7 \|- 2x + 1 log(---------------------------------) +--R 5x + 3 +--R + +--R 5 4 3 2 +--R 3610240004250x + 7340821341975x + 4107650849280x - 681934223025x +--R + +--R - 1251549868140x - 288819200340 +--R * +--R +-+ +--------+ +-+ +--R +-+ +--+ +--------+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R \|3 \|11 \|- 2x + 1 log(---------------------------------) +--R 3x + 2 +--R + +--R 5 4 3 2 +--R - 209324196000x - 188418548700x + 93885376440x + 99160158305x +--R + +--R - 9944654283x - 13236365823 +--R * +--R +-+ +--+ +--R \|7 \|11 +--R / +--R 5 4 3 2 +--R 13559030100x + 27570027870x + 15427163136x - 2561150130x +--R + +--R - 4700463768x - 1084722408 +--R * +--R +-+ +--+ +--------+ +--R \|7 \|11 \|- 2x + 1 +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 500 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +--------+ +--+ +--R +-+ +-+ 11\|5 \|- 2x + 1 + (5x - 8)\|11 +--R 2596724375\|5 \|7 log(---------------------------------) +--R 5x + 3 +--R + +--R +-+ +--------+ +-+ +--R +-+ +--+ - 7\|3 \|- 2x + 1 + (3x - 5)\|7 +--R 2674251855\|3 \|11 log(---------------------------------) +--R 3x + 2 +--R + +--R +-+ +--------+ +--R +-+ +--+ \|3 \|- 2x + 1 +--R - 5348503710\|3 \|11 atanh(---------------) +--R +-+ +--R \|7 +--R + +--R +-+ +--------+ +--R +-+ +-+ \|5 \|- 2x + 1 +--R 5193448750\|5 \|7 atanh(---------------) +--R +--+ +--R \|11 +--R / +--R +-+ +--+ +--R 10043726\|7 \|11 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=4122385421/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 32497997/38400000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 186473/960000*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3731/80000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 17/3000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)+1/30*(2+3*x)^4*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-374762311/51200000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 4122385421asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 2218752000x + 2739830400x + 1468973920x + 45781940x +--R + +--R - 518122939 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 51200000\|10 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=39142411/1280000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 104377/320000*(3+5*x)^(3/2)*sqrt(1-2*x)-21/2000*(2+3*x)^2*_ + (3+5*x)^(3/2)*sqrt(1-2*x)+1/25*(2+3*x)^3*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-7/40000*(3+5*x)^(3/2)*(802+1245*x)*sqrt(1-2*x)-_ + 3558401/1280000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 39142411asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x + 17366400x + 14946720x + 3002540x - 4282349)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1280000\|10 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (9x + 12x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-37/160*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(2+3*x)*_ + (3+5*x)^(3/2)+158873/12800*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-1313/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+14443/12800*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 158873asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (28800x + 51680x + 22500x - 13327)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 12800\|10 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) (3x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-1/10*(1-2*x)^(3/2)*(3+5*x)^(3/2)+4477/800*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-37/80*(1-2*x)^(3/2)*sqrt(3+5*x)+407/800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 4477asin(-------------) + (800x + 820x - 203)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 800\|10 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=121/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+11/40*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 121asin(-------------) + (20x + 1)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------- +--R +--+ +--R 40\|10 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 37/9*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 2\|7 \|10 atan(-------------) + 37asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R 3\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9\|10 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=37/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 2/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/3*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3 +--R (111x + 74)atan(-------------) + (- 6x - 4)\|7 \|10 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R - 3\|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (27x + 18)\|7 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) --------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=121/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/28*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (1089x + 1452x + 484)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (37x + 20)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (252x + 336x + 112)\|7 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 2178x - 2904x - 968)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ 2 +--R (1036x + 560)\|- 2x + 1 \|5x + 3 + 2205x + 2940x + 980 +--R / +--R 2 +--R 7056x + 9408x + 3136 +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 484atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R - 242atan(-----------------------------------------------------) + 35\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=4477/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+37/252*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+3547/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (120879x + 241758x + 161172x + 35816)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (3547x + 4902x + 1648)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (10584x + 21168x + 14112x + 3136)\|7 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 120879x - 241758x - 161172x - 35816)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (49658x + 68628x + 23072)\|- 2x + 1 \|5x + 3 - 155736x - 311472x +--R + +--R - 207648x - 46144 +--R / +--R 3 2 +--R 148176x + 296352x + 197568x + 43904 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 8954atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 4477atan(--------------------------------------------------) - 824\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=794365/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+37/504*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+6005/14112*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2+625115/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1875345x + 3834760x + 2617388x + 594416)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (64343565x + 171582840x + 171582840x + 76259040x + 12709840)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (26254830x + 53686640x + 36643432x + 8321824)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 84258468x + 224689248x + 224689248x + 99861888x + 16643648 +--R / +--R 4 3 2 +--R 24893568x + 66382848x + 66382848x + 29503488x + 4917248 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1588730atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 794365atan(------------------------------------------------) + 148604\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 43904\|7 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=5591773/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+37/840*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4+403/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 14023/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1466281/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 6794004195x + 22646680650x + 30195574200x + 20130382800x +--R + +--R 6710127600x + 894683680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (197947935x + 536695650x + 546004068x + 247045192x + 41933792)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 13588008390x + 45293361300x + 60391148400x + 40260765600x +--R + +--R 13420255200x + 1789367360 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R 5542542180x + 15027478200x + 15288113904x + 6917265376x +--R + +--R 1174146176 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 15603301917x - 52011006390x - 69348008520x - 46232005680x +--R + +--R - 15410668560x - 2054755808 +--R / +--R 5 4 3 2 +--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x +--R + +--R 196689920 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 111835460atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 55917730atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 9173017\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^7 +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=588912203/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^6+37/1260*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^5+10921/70560*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 126799/141120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 4429459/790272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 463266973/11063808*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R 2146584979935x + 8586339919740x + 14310566532900x +--R + +--R 3 2 +--R 12720503584800x + 6360251792400x + 1696067144640x + 188451904960 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 62541041355x + 211260697020x + 285550790544x + 193055073632x +--R + +--R 65287037520x + 8835086144 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 4480842240x + 17923368960x + 29872281600x + 26553139200x +--R + +--R 2 +--R 13276569600x + 3540418560x + 393379840 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 8586339919740x - 34345359678960x - 57242266131600x +--R + +--R 3 2 +--R - 50882014339200x - 25441007169600x - 6784268578560x - 753807619840 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 3502298315880x + 11830599033120x + 15990844270464x +--R + +--R 2 +--R 10811084123392x + 3656074101120x + 494764824064 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 13384741363497x + 53538965453988x + 89231609089980x + 79316985857760x +--R + +--R 2 +--R 39658492928880x + 10575598114368x + 1175066457152 +--R / +--R 6 5 4 3 +--R 250927165440x + 1003708661760x + 1672847769600x + 1486975795200x +--R + +--R 2 +--R 743487897600x + 198263439360x + 22029271040 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 23556488120atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 11778244060 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 2622916199\|7 +--R / +--R +-+ +--R 49172480\|7 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=70224051139/204800000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 580364059/153600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 10031801/19200000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 8223/64000*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 643/20000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 17/4200*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 1/35*(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 6384004649/204800000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1474705073919asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000000x + 950400000000x + 1480681728000x + 1161696585600x +--R + +--R 2 +--R 402838062880x - 72932734340x - 201521732121 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4300800000\|10 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3n.input.pamphlet b/src/input/rich3n.input.pamphlet new file mode 100644 index 0000000..a358a8f --- /dev/null +++ b/src/input/rich3n.input.pamphlet @@ -0,0 +1,6756 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3n.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 34 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 66 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3n.output +)spool rich3n.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=1269748711/10240000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 10493791/7680000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 183701/960000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 7/1000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 1/30*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 49/80000*(3+5*x)^(5/2)*(146+225*x)*sqrt(1-2*x)-_ + 115431701/10240000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 3809246133asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 2163456000x + 2600899200x + 1349400160x + 21761620x +--R + +--R - 483864147 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 30720000\|10 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-9007/9600*(1-2*x)^(3/2)*(3+5*x)^(3/2)-153/800*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 11988317/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 99077/25600*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1089847/256000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 35964951asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x + 16790400x + 13913120x + 2552540x - 4015809)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 768000\|10 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-181/480*(1-2*x)^(3/2)*(3+5*x)^(3/2)-3/40*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_ + 240911/12800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 1991/1280*(1-2*x)^(3/2)*sqrt(3+5*x)+21901/12800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 722733asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (144000x + 245600x + 99380x - 63387)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 38400\|10 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R +--------+ +------+ +--R (1) (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1331/160*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-11/16*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 121/160*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (800x + 740x - 207)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 480\|10 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=2/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 793/216*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)-41/72*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 16\|7 \|10 atan(-------------) + 793asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (180x - 15)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 216\|10 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=41/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_ + 107/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+10/9*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (- 321x - 214)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (123x + 82)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (45x + 33)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (81x + 54)\|2 \|7 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=4091/756*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 1/6*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 107/252*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (36819x + 49092x + 16364)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (- 2520x - 3360x - 1120)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (- 1593x - 1020)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (6804x + 9072x + 3024)\|7 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=1331/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 11/84*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 121/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (107811x + 215622x + 143748x + 31944)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (4223x + 4478x + 1152)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (31752x + 63504x + 42336x + 9408)\|7 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (107811x + 215622x + 143748x + 31944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (59122x + 62692x + 16128)\|- 2x + 1 \|5x + 3 - 129276x - 258552x +--R + +--R - 172368x - 38304 +--R / +--R 3 2 +--R 444528x + 889056x + 592704x + 131712 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 1331atan(------------------------------------------------------) - 228\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=153065/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 107/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 4355/42336*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 368045/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (37194795x + 99186120x + 99186120x + 44082720x + 7347120) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1104135x + 2269240x + 1512052x + 328464)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 185973975x - 495930600x - 495930600x - 220413600x - 36735600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (77289450x + 158846800x + 105843640x + 22992480)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 325918404x + 869115744x + 869115744x + 386273664x + 64378944 +--R / +--R 4 3 2 +--R 373403520x + 995742720x + 995742720x + 442552320x + 73758720 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1530650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 765325atan(-----------------------------------------------) + 191604\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 219520\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=783959/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-_ + 107/2520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 641/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 17981/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1852307/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 2857530555x + 9525101850x + 12700135800x + 8466757200x +--R + +--R 2822252400x + 376300320 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (83353815x + 226052850x + 230080132x + 103856008x + 17507808)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 14287652775x - 47625509250x - 63500679000x - 42333786000x +--R + +--R - 14111262000x - 1881501600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R 5834767050x + 15823699500x + 16105609240x + 7269920560x +--R + +--R 1225546560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 26058183732x + 86860612440x + 115814149920x + 77209433280x +--R + +--R 25736477760x + 3431530368 +--R / +--R 5 4 3 2 +--R 11202105600x + 37340352000x + 49787136000x + 33191424000x +--R + +--R 11063808000x + 1475174400 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 39197950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 19598975atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 5106444\|7 +--R / +--R +-+ +--R 2195200\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=64645339/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_ + 107/3780*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 4619/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 42461/423360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1460201/2370816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 152571047/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 706896781965x + 2827587127860x + 4712645213100x + 4189017967200x +--R + +--R 2 +--R 2094508983600x + 558535728960x + 62059525440 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 20597091345x + 69576897780x + 94045700016x + 63585046048x +--R + +--R 21497808880x + 2906375616 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 13442526720x + 53770106880x + 89616844800x + 79659417600x +--R + +--R 2 +--R 39829708800x + 10621255680x + 1180139520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 706896781965x - 2827587127860x - 4712645213100x +--R + +--R 3 2 +--R - 4189017967200x - 2094508983600x - 558535728960x - 62059525440 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 288359278830x + 974076568920x + 1316639800224x + 890190644672x +--R + +--R 300969324320x + 40689258624 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 926952173028x + 3707808692112x + 6179681153520x + 5493049914240x +--R + +--R 2 +--R 2746524957120x + 732406655232x + 81378517248 +--R / +--R 6 5 4 3 +--R 188195374080x + 752781496320x + 1254635827200x + 1115231846400x +--R + +--R 2 +--R 557615923200x + 148697579520x + 16521953280 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 646453390atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 323226695atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 60549492\|7 +--R / +--R +-+ +--R 12293120\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=1988505613369/1310720000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 16433930689/983040000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1493993699/614400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 18411711/51200000*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 58671/640000*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 753/32000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 17/5600*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 1/40*(2+3*x)^4*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 180773237579/1310720000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 41758617880749asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 +--R 6967296000000x + 30838579200000x + 57746856960000x +--R + +--R 4 3 2 +--R 58346097408000x + 32457421737600x + 6882844528480x +--R + +--R - 3991703112140x - 5973304472091 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 27525120000\|10 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=4343003753/8192000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 35892593/6144000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3262963/3840000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 8131/64000*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/200*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 1/35*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 3/20000*(3+5*x)^(7/2)*(414+635*x)*sqrt(1-2*x)-_ + 394818523/8192000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 91203078813asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 16588800000x + 62069760000x + 94673664000x + 72591427200x +--R + +--R 2 +--R 24336990560x - 4902803980x - 12531569067 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 172032000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-11759/3072*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1069/1280*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-13/80*(1-2*x)^(3/2)*(3+5*x)^(7/2)-1/20*(1-2*x)^(3/2)*_ + (2+3*x)*(3+5*x)^(7/2)+15651229/81920*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-129349/8192*(1-2*x)^(3/2)*sqrt(3+5*x)+1422839/81920*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 46953687asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (9216000x + 28108800x + 32887680x + 16507936x + 17884x - 6023169) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 245760\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=-2761/1920*(1-2*x)^(3/2)*(3+5*x)^(3/2)-251/800*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)-3/50*(1-2*x)^(3/2)*(3+5*x)^(7/2)+_ + 3674891/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 30371/5120*(1-2*x)^(3/2)*sqrt(3+5*x)+334081/51200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 11024673asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (2304000x + 5404800x + 4310240x + 718340x - 1254087)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 153600\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-55/96*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/8*(1-2*x)^(3/2)*(3+5*x)^(5/2)+_ + 14641/512*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 605/256*(1-2*x)^(3/2)*sqrt(3+5*x)+1331/512*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (9600x + 15520x + 5836x - 4005)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1536\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=6553/2592*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/81*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-5/24*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+1/9*(3+5*x)^(5/2)*sqrt(1-2*x)-925/864*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R - 64\|2 \|7 atan(-------------) + 6553\|5 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (7200x + 5940x - 1803)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 2592\|2 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=155/216*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+59/27*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/6*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/3*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-_ + 95/72*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (1416x + 944)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (465x + 310)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +------+ +--R (900x + 405x - 138)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (648x + 432)\|2 \|7 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2119/252*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-59/84*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 215/84*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ \|7 \|5x + 3 +--R (- 19071x - 25428x - 8476)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +-+ \|2 \|5x + 3 +--R (6300x + 8400x + 2800)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +-+ +--------+ +------+ +--R (2100x + 3117x + 1140)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +-+ +--R (2268x + 3024x + 1008)\|2 \|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=250433/31752*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 50/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-59/252*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-1/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 6401/10584*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (6761691x + 13523382x + 9015588x + 2003464)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 529200x - 1058400x - 705600x - 156800)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 372537x - 477522x - 153168)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (857304x + 1714608x + 1143072x + 254016)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=73205/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 605/4704*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-11/168*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^3+1/4*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 6655/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (814395x + 1285720x + 654436x + 105552)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (5334336x + 14224896x + 14224896x + 6322176x + 1053696)\|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (11401530x + 18000080x + 9162104x + 1477728)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 14961996x - 39898656x - 39898656x - 17732736x - 2955456 +--R / +--R 4 3 2 +--R 74680704x + 199148544x + 199148544x + 88510464x + 14751744 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 146410atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 73205atan(------------------------------------------------) - 8796\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 43904\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=248897/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/840*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/15*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-103/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 947/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+67709/131712*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 907229565x + 3024098550x + 4032131400x + 2688087600x + 896029200x +--R + +--R 119470560 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (27422145x + 74915550x + 74550556x + 32206264x + 5112864)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1814459130x + 6048197100x + 8064262800x + 5376175200x +--R + +--R 1792058400x + 238941120 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R (767820060x + 2097635400x + 2087415568x + 901775392x + 143160192) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 1902464739x - 6341549130x - 8455398840x - 5636932560x - 1878977520x +--R + +--R - 250530336 +--R / +--R 5 4 3 2 +--R 4480842240x + 14936140800x + 19914854400x + 13276569600x +--R + +--R 4425523200x + 590069760 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4977940atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 2488970atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 372813\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=15036307/1229312*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/1260*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/18*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-6533/211680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 47279/1270080*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1057139/7112448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 106751933/99574272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 164422017045x + 657688068180x + 1096146780300x + 974352693600x +--R + +--R 2 +--R 487176346800x + 129913692480x + 14434854720 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 4803836985x + 16234789140x + 21960917808x + 14818971424x +--R + +--R 4978384240x + 665270208 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 13442526720x + 53770106880x + 89616844800x + 79659417600x +--R + +--R 2 +--R 39829708800x + 10621255680x + 1180139520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 822110085225x - 3288440340900x - 5480733901500x +--R + +--R 3 2 +--R - 4871763468000x - 2435881734000x - 649568462400x - 72174273600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 5 4 3 2 +--R 336268588950x + 1136435239800x + 1537264246560x + 1037327999680x +--R + +--R 348486896800x + 46568914560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 1485257318748x + 5941029274992x + 9901715458320x + 8801524851840x +--R + +--R 2 +--R 4400762425920x + 1173536646912x + 130392960768 +--R / +--R 6 5 4 3 +--R 940976870400x + 3763907481600x + 6273179136000x + 5576159232000x +--R + +--R 2 +--R 2788079616000x + 743487897600x + 82609766400 +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 751815350atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 375907675atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 97018572\|7 +--R / +--R +-+ +--R 61465600\|7 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^8 +--R +--R +--R (1) +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=3735929329/120472576*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 59/1764*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-1/21*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^7-6577/370440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 369409/20744640*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 2524471/41489280*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 84539611/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 8818415317/3252759552*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 122557161637845x + 571933420976610x + 1143866841953220x +--R + +--R 4 3 2 +--R 1270963157725800x + 847308771817200x + 338923508726880x +--R + +--R 75316335272640x + 7172984311680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 3571458203385x + 14445612678330x + 24351227238888x +--R + +--R 3 2 +--R 21898948566336x + 11077661454896x + 2987299350368x + 335335888512 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 +--R 3952102855680x + 18443146659840x + 36886293319680x +--R + +--R 4 3 2 +--R 40984770355200x + 27323180236800x + 10929272094720x + 2428727132160x +--R + +--R 231307345920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 122557161637845x - 571933420976610x - 1143866841953220x +--R + +--R 4 3 2 +--R - 1270963157725800x - 847308771817200x - 338923508726880x +--R + +--R - 75316335272640x - 7172984311680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 6 5 4 +--R 50000414847390x + 202238577496620x + 340917181344432x +--R + +--R 3 2 +--R 306585279928704x + 155087260368544x + 41822190905152x + 4694702439168 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 160426784913444x - 748658329596072x - 1497316659192144x +--R + +--R 4 3 2 +--R - 1663685176880160x - 1109123451253440x - 443649380501376x +--R + +--R - 98588751222528x - 9389404878336 +--R / +--R 7 6 5 +--R 55329439979520x + 258204053237760x + 516408106475520x +--R + +--R 4 3 2 +--R 573786784972800x + 382524523315200x + 153009809326080x +--R + +--R 34002179850240x + 3238302842880 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 37359293290atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 18679646645atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 3493082172\|7 +--R / +--R +-+ +--R 1204725760\|7 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=525371/64000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 46613/64000*sqrt(1-2*x)*sqrt(3+5*x)-7/400*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)+1/20*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/16000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 525371asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (86400x + 162720x + 76140x - 41789)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 64000\|10 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=3047/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-23/80*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-1/10*(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)+277/800*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3047asin(-------------) + (480x + 540x - 113)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 800\|10 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=451/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+41/200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 451asin(-------------) + (60x + 11)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------ +--R +--+ +--R 200\|10 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=11/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/5*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 11asin(-------------) + \|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--R 5\|10 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-2/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+2/3*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7) +--R +--R +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R 2\|5 \|7 atan(-------------) - 2\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R (2) ------------------------------------------------------- +--R +-+ +--R 3\|5 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=11*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (33x + 22)atan(-------------) + \|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------- +--R +-+ +--R (3x + 2)\|7 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 33x - 22)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R 14\|- 2x + 1 \|5x + 3 + 42x + 28 +--R / +--R 42x + 28 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 22atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 11atan(--------------------------------------------------) + 2\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=1177/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/2*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+103/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (10593x + 14124x + 4708)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (309x + 220)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (252x + 336x + 112)\|7 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 10593x - 14124x - 4708)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (4326x + 3080)\|- 2x + 1 \|5x + 3 + 13860x + 18480x + 6160 +--R / +--R 2 +--R 3528x + 4704x + 1568 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2354atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 1177atan(--------------------------------------------------) + 220\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 56\|7 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=68959/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+173/84*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+18083/1176*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (1861893x + 3723786x + 2482524x + 551672)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (54249x + 74754x + 25856)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (10584x + 21168x + 14112x + 3136)\|7 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 9309465x - 18618930x - 12412620x - 2758360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (3797430x + 5232780x + 1809920)\|- 2x + 1 \|5x + 3 + 17103744x +--R + +--R 2 +--R 34207488x + 22804992x + 5067776 +--R / +--R 3 2 +--R 740880x + 1481760x + 987840x + 219520 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 689590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 344795atan(-----------------------------------------------) + 90496\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 3920\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=16925425/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+81/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+14145/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1479375/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1370959425x + 3655891800x + 3655891800x + 1624840800x + 270806800) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (39943125x + 81668520x + 55729116x + 12696112)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 6854797125x - 18279459000x - 18279459000x - 8124204000x +--R + +--R - 1354034000 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (2796018750x + 5716796400x + 3901038120x + 888727840)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 12597717132x + 33593912352x + 33593912352x + 14930627712x + 2488437952 +--R / +--R 4 3 2 +--R 124467840x + 331914240x + 331914240x + 147517440x + 24586240 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 169254250atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 84627125atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 22218196\|7 +--R / +--R +-+ +--R 219520\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=10409/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(2+3*x)^3*_ + sqrt(1-2*x)/sqrt(3+5*x)-791/4000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 7/200*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+7/25*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 10409\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (7200x + 13140x + 3825x - 893)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 4000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=317/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(3/2)/_ + sqrt(3+5*x)-9/100*(1-2*x)^(3/2)*sqrt(3+5*x)+317/2200*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R 317\|5x + 3 asin(-------------) + (180x + 165x + 31)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------------- +--R +--+ +------+ +--R 200\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=29/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(3/2)/_ + sqrt(3+5*x)+29/275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--+ +--------+ +--R 29\|5x + 3 asin(-------------) + (15x + 7)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------- +--R +--+ +------+ +--R 25\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-2/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/5*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R - 2\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------ +--R +-+ +------+ +--R 5\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R - 2\|7 \|5x + 3 atan(-------------) - 2\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R (- 60x - 36)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +--------+ +------+ +--R - 24\|- 2x + 1 \|5x + 3 + 95x + 57 +--R / +--R 60x + 36 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 24\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 12\|7 atan(------------------------------------------------------) + 19 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R 12 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=-103*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-15*sqrt(1-2*x)/_ + sqrt(3+5*x)+sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R (- 309x - 206)\|5x + 3 atan(-------------) + (- 45x - 29)\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ------------------------------------------------------------------------ +--R +-+ +------+ +--R (3x + 2)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 37080x - 46968x - 14832)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +--------+ +------+ 2 +--R (- 15120x - 9744)\|- 2x + 1 \|5x + 3 + 57855x + 73283x + 23142 +--R / +--R 2 +--R 5040x + 6384x + 2016 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 4944atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 2472atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R 551\|7 +--R / +--R +-+ +--R 48\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-17951/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 2615/28*sqrt(1-2*x)/sqrt(3+5*x)+1/2*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+173/28*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 161559x - 215412x - 71804)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 23535x - 30861x - 10100)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (252x + 336x + 112)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (9693540x + 18740844x + 12063072x + 2584944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 3953880x - 5184648x - 1696800)\|- 2x + 1 \|5x + 3 - 15112125x +--R + +--R 2 +--R - 29216775x - 18806200x - 4029900 +--R / +--R 3 2 +--R 211680x + 409248x + 263424x + 56448 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 430824atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 215412atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 47975\|7 +--R / +--R +-+ +--R 672\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1463447/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 639565/1176*sqrt(1-2*x)/sqrt(3+5*x)+1/3*sqrt(1-2*x)/((2+3*x)^3*_ + sqrt(3+5*x))+81/28*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 14101/392*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 39513069x - 79026138x - 52684092x - 11707576)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 5756085x - 11385261x - 7502166x - 1646704)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (10584x + 21168x + 14112x + 3136)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (592696035x + 1541009691x + 1501496622x + 649770468x + 105368184) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (- 241755570x - 478180962x - 315090972x - 69161568)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 778067640x + 2022975864x + 1971104688x + 852992672x + 138323136 +--R / +--R 4 3 2 +--R 2222640x + 5778864x + 5630688x + 2436672x + 395136 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 8780682atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 4390341atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 823352\|7 +--R / +--R +-+ +--R 2352\|7 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=35511/20000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^4*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-524/825*(2+3*x)^3*sqrt(1-2*x)/_ + sqrt(3+5*x)-23779/220000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 1043/11000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 623/1375*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (5859315x + 3515589)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (3564000x + 8999100x + 6384015x + 995870x - 218953)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3300000x + 1980000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=1071/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/15*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-392/825*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_ + 11557/11000*sqrt(1-2*x)*sqrt(3+5*x)-21/2750*(34-145*x)*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (176715x + 106029)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (89100x + 147015x + 75470x + 11567)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (165000x + 99000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-2/825*(1-2*x)^(3/2)/(3+5*x)^(3/2)+3/5*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-12/275*(1-2*x)^(3/2)/sqrt(3+5*x)+3/55*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (495x + 297)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (297x + 278x + 59)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (825x + 495)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-2/165*(1-2*x)^(3/2)/(3+5*x)^(3/2)-6/25*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)-6/25*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 990x - 594)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 970x - 604)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (4125x + 2475)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-2/33*(1-2*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (4x - 2)\|- 2x + 1 +--R (2) -------------------- +--R +------+ +--R (165x + 99)\|5x + 3 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (36x - 18)\|- 2x + 1 \|5x + 3 - 100x - 120x - 36 +--R (3) -------------------------------------------------- +--R 2 +--R 7425x + 8910x + 2673 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - --- +--R 297 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=sqrt(1-2*x)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2/3*sqrt(1-2*x)/(3+5*x)^(3/2)+202/33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (990x + 594)\|7 \|5x + 3 atan(-------------) + (1010x + 584)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R +------+ +--R (165x + 99)\|5x + 3 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (22275x + 26730x + 8019)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (9090x + 5256)\|- 2x + 1 \|5x + 3 + 29200x + 35040x + 10512 +--R / +--R 2 +--R 7425x + 8910x + 2673 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 1782\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 891\|7 atan(------------------------------------------------) + 1168 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 297 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=519*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 25/3*sqrt(1-2*x)/(3+5*x)^(3/2)+sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2495/33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (256905x + 325413x + 102762)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (37425x + 46580x + 14453)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (495x + 627x + 198)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 11560725x - 21580020x - 13410441x - 2774574)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (4715550x + 5869080x + 1821078)\|- 2x + 1 \|5x + 3 + 15175650x +--R + +--R 2 +--R 28327880x + 17603754x + 3642156 +--R / +--R 3 2 +--R 311850x + 582120x + 361746x + 74844 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 308286atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 154143atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 28906\|7 +--R / +--R +-+ +--R 594\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=126513/28*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 6095/84*sqrt(1-2*x)/(3+5*x)^(3/2)+1/2*sqrt(1-2*x)/((2+3*x)^2*_ + (3+5*x)^(3/2))+243/28*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 608185/924*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +------+ +--R (187871805x + 363218823x + 233796024x + 50099148)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (27368325x + 52308690x + 33277877x + 7046540)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (41580x + 80388x + 51744x + 11088)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 8454231225x + 21417385770x + 20327729301x + 8566954308x +--R + +--R 1352676996 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +--R (3448408950x + 6590894940x + 4193012502x + 887864040)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R - 11098300500x - 28115694600x - 26685246980x - 11246277840x - 1775728080 +--R / +--R 4 3 2 +--R 26195400x + 66361680x + 62985384x + 26544672x + 4191264 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 75148722atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 37574361atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 7046540\|7 +--R / +--R +-+ +--R 16632\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=13246251/392*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 638165/1176*sqrt(1-2*x)/(3+5*x)^(3/2)+1/3*sqrt(1-2*x)/((2+3*x)^3*_ + (3+5*x)^(3/2))+313/84*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 25441/392*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 63678595/12936*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 59012048205x + 153431325333x + 149497188786x + 64694689884x +--R + +--R 10491030792 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 8596610325x + 22161651840x + 21406565457x + 9181937962x +--R + +--R 1475586688 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (1746360x + 4540536x + 4424112x + 1914528x + 310464)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 2655542169225x - 8497734941520x - 10870019279361x +--R + +--R 2 +--R - 6947685142002x - 2218853012508x - 283257831384 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 1083172900950x + 2792368131840x + 2697227247582x + 1156924183212x +--R + +--R 185923922688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 3486073550400x + 11155435361280x + 14269661066304x + 9120601318528x +--R + +--R 2912808122112x + 371847845376 +--R / +--R 5 4 3 2 +--R 1100206800x + 3520661760x + 4503513168x + 2878466976x + 919283904x +--R + +--R 117355392 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7868273094atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 3934136547atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 737793344\|7 +--R / +--R +-+ +--R 232848\|7 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1/30*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 452517373/25600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 3501533/19200000*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 791/120000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 29/1500*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 7/2400000*(3+5*x)^(3/2)*(28458+41105*x)*sqrt(1-2*x)-_ + 41137943/25600000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1357552119asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 691200000x - 1251072000x - 308534400x + 623566880x + 374573660x +--R + +--R - 81405921 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 76800000\|10 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-567/4000*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*_ + (2+3*x)*(3+5*x)^(3/2)+5487713/640000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+45353/192000*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 4123/9600*(1-2*x)^(5/2)*sqrt(3+5*x)+498883/640000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 16463139asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 7286400x + 3141280x + 4872460x - 382101)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1920000\|10 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (- 6x - x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-3/40*(1-2*x)^(5/2)*(3+5*x)^(3/2)+30613/6400*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+253/1920*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 23/96*(1-2*x)^(5/2)*sqrt(3+5*x)+2783/6400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 91839asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 6880x + 23420x + 1959)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 19200\|10 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (1) (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=1331/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/120*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-1/6*(1-2*x)^(5/2)*sqrt(3+5*x)+121/400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (- 800x + 580x + 273)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ------------------------------------------------------------------------- +--R +--+ +--R 1200\|10 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-14/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 4091/540*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/6*(1-2*x)^(3/2)*sqrt(3+5*x)+107/180*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 280\|7 \|10 atan(-------------) + 4091asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (- 180x + 411)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 540\|10 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-107/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+41/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/_ + (2+3*x)-4/9*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (123x + 82)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R (- 321x - 214)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (- 18x - 33)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (81x + 54)\|5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=793/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/6*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^2+41/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (7137x + 9516x + 3172)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (144x + 192x + 64)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (405x + 228)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|7 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+_ + 1331/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 11/4*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-121/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (107811x + 215622x + 143748x + 31944)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (3103x + 4366x + 1488)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (4536x + 9072x + 6048x + 1344)\|7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (107811x + 215622x + 143748x + 31944)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (43442x + 61124x + 20832)\|- 2x + 1 \|5x + 3 + 140616x + 281232x +--R + +--R 187488x + 41664 +--R / +--R 3 2 +--R 63504x + 127008x + 84672x + 18816 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1331atan(------------------------------------------------) + 248\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=240911/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+41/216*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+5413/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 568363/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (58541373x + 156110328x + 156110328x + 69382368x + 11563728) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (1705089x + 3485960x + 2381420x + 541680)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 58541373x - 156110328x - 156110328x - 69382368x - 11563728)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (23871246x + 48803440x + 33339880x + 7583520)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 76783140x + 204755040x + 204755040x + 91002240x + 15167040 +--R / +--R 4 3 2 +--R 10668672x + 28449792x + 28449792x + 12644352x + 2107392 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 481822atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 240911atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 45140\|7 +--R / +--R +-+ +--R 6272\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=11988317/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+41/360*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4+7723/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 270463/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 28291441/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 43697415465x + 145658051550x + 194210735400x + 129473823600x +--R + +--R 43157941200x + 5754392160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (1273114845x + 3451770150x + 3511594796x + 1588955864x + 269759904) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 160030080x + 533433600x + 711244800x + 474163200x + 158054400x +--R + +--R 21073920 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 43697415465x - 145658051550x - 194210735400x - 129473823600x +--R + +--R - 43157941200x - 5754392160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 17823607830x + 48324782100x + 49162327144x + 22245382096x +--R + +--R 3776638656 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 57357699588x - 191192331960x - 254923109280x - 169948739520x +--R + +--R - 56649579840x - 7553277312 +--R / +--R 5 4 3 2 +--R 2240421120x + 7468070400x + 9957427200x + 6638284800x + 2212761600x +--R + +--R 295034880 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 119883170atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 59941585atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 11239996\|7 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (- 270x - 567x - 333x + 46x + 100x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=1/35*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+_ + 6219452877/102400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 17133479/25600000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 870407/9600000*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 51/10000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+29/2100*(2+3*x)^3*_ + (3+5*x)^(5/2)*sqrt(1-2*x)-1/800000*(3+5*x)^(5/2)*_ + (35878+51675*x)*sqrt(1-2*x)-565404807/102400000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43536170139asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 27648000000x - 67968000000x - 46732032000x + 12527113600x +--R + +--R 2 +--R 28707557280x + 9288436460x - 3952411101 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 716800000\|10 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-3101/6400*(1-2*x)^(5/2)*(3+5*x)^(3/2)-259/2000*(1-2*x)^(5/2)*_ + (3+5*x)^(5/2)-1/20*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 136205223/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 375221/512000*(1-2*x)^(3/2)*sqrt(3+5*x)-34111/25600*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+12382293/5120000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 136205223asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 76800000x - 132864000x - 27804800x + 66492960x + 37288220x +--R + +--R - 8705457 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5120000\|10 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=-37/160*(1-2*x)^(5/2)*(3+5*x)^(3/2)-3/50*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_ + 1625151/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 4477/12800*(1-2*x)^(3/2)*sqrt(3+5*x)-407/640*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+147741/128000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1625151asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 768000x - 745600x + 364320x + 489340x - 46809)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 128000\|10 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-1/8*(1-2*x)^(5/2)*(3+5*x)^(3/2)+43923/6400*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+121/640*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 11/32*(1-2*x)^(5/2)*sqrt(3+5*x)+3993/6400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 16000x - 2400x + 11980x + 603)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6400\|10 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)+14/81*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+19573/6480*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)+37/180*(3+5*x)^(3/2)*sqrt(1-2*x)-1781/2160*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 1120\|7 \|10 atan(-------------) + 19573asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (- 7200x + 5940x + 813)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6480\|10 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)-37/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1649/108*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-1/3*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 107/36*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (- 444x - 296)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (4947x + 3298)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (- 180x + 315x + 318)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (324x + 216)\|10 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^2+1649/108*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-37/27*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)+37/12*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)-205/36*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (14841x + 19788x + 6596)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (- 1332x - 1776x - 592)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 360x - 1035x - 516)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|7 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^3+19573/4536*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/81*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+37/36*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-661/1512*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (528471x + 1056942x + 704628x + 156584)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (30240x + 60480x + 40320x + 8960)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (57123x + 65286x + 18528)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (122472x + 244944x + 163296x + 36288)\|7 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=1/4*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+_ + 43923/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)-121/224*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 11/8*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 3993/3136*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (3557763x + 9487368x + 9487368x + 4216608x + 702768) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (100159x + 213240x + 145940x + 32400)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3557763x + 9487368x + 9487368x + 4216608x + 702768)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (1402226x + 2985360x + 2043160x + 453600)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 4592700x - 12247200x - 12247200x - 5443200x - 907200 +--R / +--R 4 3 2 +--R 3556224x + 9483264x + 9483264x + 4214784x + 702464 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 87846atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 43923atan(------------------------------------------------) - 8100\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 6272\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-1/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^5+_ + 1625151/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+37/120*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-_ + 5281/15120*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 36149/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 3831323/1185408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 1974558465x + 6581861550x + 8775815400x + 5850543600x +--R + +--R 1950181200x + 260024160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (57469845x + 155783350x + 158785356x + 71866904x + 12157344)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 1974558465x - 6581861550x - 8775815400x - 5850543600x +--R + +--R - 1950181200x - 260024160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R (804577830x + 2180966900x + 2222994984x + 1006136656x + 170202816) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 2584955268x - 8616517560x - 11488690080x - 7659126720x +--R + +--R - 2553042240x - 340405632 +--R / +--R 5 4 3 2 +--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x +--R + +--R 98344960 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16251510atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 8125755atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 1519668\|7 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^6+19457889/175616*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+37/180*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5-7591/30240*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 37333/181440*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 1316353/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 137752591/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 70924005405x + 283696021620x + 472826702700x + 420290402400x +--R + +--R 2 +--R 210145201200x + 56038720320x + 6226524480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 2066288865x + 6979774260x + 9434103472x + 6379024416x +--R + +--R 2157325040x + 291805632 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x +--R + +--R 505774080x + 56197120 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 70924005405x + 283696021620x + 472826702700x + 420290402400x +--R + +--R 2 +--R 210145201200x + 56038720320x + 6226524480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 28928044110x + 97716839640x + 132077448608x + 89306341824x +--R + +--R 30202550560x + 4085278848 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 93067758756x - 372271035024x - 620451725040x - 551512644480x +--R + +--R 2 +--R - 275756322240x - 73535019264x - 8170557696 +--R / +--R 6 5 4 3 +--R 8961684480x + 35846737920x + 59744563200x + 53106278400x +--R + +--R 2 +--R 26553139200x + 7080837120x + 786759680 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 194578890atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 97289445atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 18237852\|7 +--R / +--R +-+ +--R 1756160\|7 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^7+_ + 6219452877/17210368*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 37/252*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^6-_ + 9901/52920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^5+_ + 341917/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 4014523/5927040*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 140331343/33191424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 14677525921/464679936*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 68009717209995x + 317378680313310x + 634757360626620x +--R + +--R 4 3 2 +--R 705285956251800x + 470190637501200x + 188076255000480x +--R + +--R 41794723333440x + 3980449841280 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 1981465999335x + 8014272743430x + 13509190228248x +--R + +--R 3 2 +--R 12147806104256x + 6146173476816x + 1658923773088x + 186609267072 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x +--R + +--R 3 2 +--R 1301103820800x + 520441528320x + 115653672960x + 11014635520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 68009717209995x - 317378680313310x - 634757360626620x +--R + +--R 4 3 2 +--R - 705285956251800x - 470190637501200x - 188076255000480x +--R + +--R - 41794723333440x - 3980449841280 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 6 5 4 +--R 27740523990690x + 112199818408020x + 189128663195472x +--R + +--R 3 2 +--R 170069285459584x + 86046428675424x + 23224932823232x + 2612529739008 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 89275039675164x - 416616851817432x - 833233703634864x +--R + +--R 4 3 2 +--R - 925815226260960x - 617210150840640x - 246884060336256x +--R + +--R - 54863124519168x - 5225059478016 +--R / +--R 7 6 5 4 +--R 2634735237120x + 12295431106560x + 24590862213120x + 27323180236800x +--R + +--R 3 2 +--R 18215453491200x + 7286181396480x + 1619151421440x + 154204897280 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 62194528770atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 31097264385atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 5831539596\|7 +--R / +--R +-+ +--R 172103680\|7 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +------+ +--R (- 1350x - 3645x - 3366x - 769x + 638x + 420x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=1/40*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+_ + 147858829437/655360000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 407324599/163840000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 37029509/102400000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 803549/15360000*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 193/48000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 29/2800*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/1600000*(3+5*x)^(7/2)*(43298+62245*x)*sqrt(1-2*x)-_ + 13441711767/655360000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1035011806059asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R - 774144000000x - 2394316800000x - 2554199040000x - 592093952000x +--R + +--R 3 2 +--R 910419721600x + 749541131680x + 138459209260x - 116041578381 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4587520000\|10 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-8613/5120*(1-2*x)^(5/2)*(3+5*x)^(3/2)-783/1600*(1-2*x)^(5/2)*_ + (3+5*x)^(5/2)-47/400*(1-2*x)^(5/2)*(3+5*x)^(7/2)-_ + 3/70*(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(7/2)+_ + 378308799/4096000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1042173/409600*(1-2*x)^(3/2)*sqrt(3+5*x)-94743/20480*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+34391709/4096000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 2648161593asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 1843200000x - 4387840000x - 2867456000x + 887043200x +--R + +--R 2 +--R 1789716960x + 549624420x - 247243887 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 28672000\|10 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-187/256*(1-2*x)^(5/2)*(3+5*x)^(3/2)-17/80*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_ + 1/20*(1-2*x)^(5/2)*(3+5*x)^(7/2)+8213601/204800*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+22627/20480*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-2057/1024*(1-2*x)^(5/2)*sqrt(3+5*x)+_ + 746691/204800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 8213601asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (- 5120000x - 8448000x - 1456000x + 4238560x + 2224900x - 555399) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 204800\|10 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-11/32*(1-2*x)^(5/2)*(3+5*x)^(3/2)-1/10*(1-2*x)^(5/2)*(3+5*x)^(5/2)+_ + 483153/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1331/2560*(1-2*x)^(3/2)*sqrt(3+5*x)-121/128*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+43923/25600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 483153asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 256000x - 227200x + 124640x + 147140x - 16407)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 25600\|10 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)-14/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+648919/62208*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-53/192*(3+5*x)^(3/2)*sqrt(1-2*x)+23/216*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-15863/20736*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 3584\|7 \|10 atan(-------------) + 648919asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 259200x - 15840x + 175068x + 7167)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 62208\|10 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=-1/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)-43/3888*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)+181/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+25/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 8/27*(3+5*x)^(5/2)*sqrt(1-2*x)-3065/1296*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (8688x + 5792)\|2 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R (- 129x - 86)\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (- 21600x + 5580x + 10539x - 2190)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (11664x + 7776)\|2 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=-1/6*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^2+1945/324*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-6829/324*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-35/4*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+181/36*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)+_ + 185/27*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ \|7 \|5x + 3 +--R (- 61461x - 81948x - 27316)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +-+ \|2 \|5x + 3 +--R (17505x + 23340x + 7780)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +-+ +--------+ +------+ +--R (- 2700x + 3285x + 8955x + 3696)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +-+ +--R (2916x + 3888x + 1296)\|2 \|7 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=-1/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^3+326717/13608*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-575/243*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)+331/168*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)+181/108*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 39745/4536*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (8821359x + 17642718x + 11761812x + 2613736)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 869400x - 1738800x - 1159200x - 257600)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (- 226800x - 860373x - 825066x - 235248)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (367416x + 734832x + 489888x + 108864)\|7 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=-1/12*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^4+1922677/762048*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+100/243*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-871/6048*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2+181/216*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 77269/254016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (155736837x + 415298232x + 415298232x + 184576992x + 30762832) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--+ +--R (25401600x + 67737600x + 67737600x + 30105600x + 5017600)\|7 \|10 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (39870441x + 69556680x + 40302540x + 7751280)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (61725888x + 164602368x + 164602368x + 73156608x + 12192768)\|7 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=1/5*(1-2*x)^(3/2)*(3+5*x)^(7/2)/(2+3*x)^5+483153/43904*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-1331/3136*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^2-121/560*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 33/40*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-43923/43904*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (15899035x + 46076650x + 47906548x + 21437032x + 3507552)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R (222586490x + 645073100x + 670691672x + 300118448x + 49105728) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 745793244x - 2485977480x - 3314636640x - 2209757760x - 736585920x +--R + +--R - 98211456 +--R / +--R 5 4 3 2 +--R 746807040x + 2489356800x + 3319142400x + 2212761600x + 737587200x +--R + +--R 98344960 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4831530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2415765atan(------------------------------------------------) - 438444\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 439040\|7 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=-1/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^6+4348377/175616*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2857/10080*_ + (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+181/540*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-126463/544320*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^3+852587/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 92126789/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 15849834165x + 63399336660x + 105665561100x + 93924943200x +--R + +--R 2 +--R 46962471600x + 12523325760x + 1391480640 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 460633945x + 1555340180x + 2108117296x + 1428134688x + 482263920x +--R + +--R 64829376 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 640120320x + 2560481280x + 4267468800x + 3793305600x + 1896652800x +--R + +--R 505774080x + 56197120 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 ok to fail, differs by a constant +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 ok to fail, differs by a constant +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-1/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^7+1104970911/17210368*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-12421/52920*_ + (3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5+181/756*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-1289227/8890560*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^4+6249601/53343360*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 224018941/298722816*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 23466191827/4182119424*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 12082856911785x + 56386665588330x + 112773331176660x +--R + +--R 4 3 2 +--R 125303701307400x + 83535800871600x + 33414320348640x +--R + +--R 7425404521920x + 707181383040 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 351992877405x + 1423652835490x + 2399706883464x + 2158260396608x +--R + +--R 2 +--R 1092179419888x + 294736348384x + 33120084096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 188195374080x + 878245079040x + 1756490158080x + 1951655731200x +--R + +--R 3 2 +--R 1301103820800x + 520441528320x + 115653672960x + 11014635520 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=18648399/3200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/25*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)-_ + 4802371/9600000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 511/60000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 29/1000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 7/800000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 18648399asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 7862400x + 2952480x + 5372860x - 314441)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 3200000\|10 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=109263/32000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 301/3200*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 119/800*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 3/40*(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)+9933/32000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 109263asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 9440x + 25020x + 3383)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 32000\|10 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=1089/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 3/40*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 1/10*(1-2*x)^(5/2)*sqrt(3+5*x)+99/400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 1089asin(-------------) + (- 160x + 100x + 89)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ------------------------------------------------------------------------ +--R +--+ +--R 400\|10 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=363/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/10*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+33/100*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 363asin(-------------) + (- 20x + 43)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------- +--R +--+ +--R 100\|10 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=-103/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_ + 14/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2/15*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R 70\|5 \|7 atan(-------------) - 103\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R - 6\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 45\|5 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=4/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+29/9*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)+2/3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +-+ \|2 \|5x + 3 +--R (87x + 58)\|5 \|7 atan(-------------) + (12x + 8)\|2 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +--------+ +------+ +--R 21\|5 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R (27x + 18)\|5 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=363/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+33/4*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (3267x + 4356x + 1452)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (95x + 68)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (36x + 48x + 16)\|7 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 13068x - 17424x - 5808)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (5320x + 3808)\|- 2x + 1 \|5x + 3 + 20349x + 27132x + 9044 +--R / +--R 2 +--R 2016x + 2688x + 896 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2904atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 1452atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 323\|7 +--R / +--R +-+ +--R 32\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=21417/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^3+_ + 169/36*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 16847/504*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (578259x + 1156518x + 771012x + 171336)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (16847x + 23214x + 8032)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (1512x + 3024x + 2016x + 448)\|7 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (578259x + 1156518x + 771012x + 171336)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (235858x + 324996x + 112448)\|- 2x + 1 \|5x + 3 - 759024x - 1518048x +--R + +--R - 1012032x - 224896 +--R / +--R 3 2 +--R 21168x + 42336x + 28224x + 6272 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 42834atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 21417atan(------------------------------------------------) - 4016\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 112\|7 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=5274027/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_ + 239/72*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 39667/2016*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 4148797/28224*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (427196187x + 1139189832x + 1139189832x + 506306592x + 84384432) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12446391x + 25448120x + 17365300x + 3956240)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 854392374x - 2278379664x - 2278379664x - 1012613184x - 168768864) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 3 2 +--------+ +------+ +--R (348498948x + 712547360x + 486228400x + 110774720)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 981394785x + 2617052760x + 2617052760x + 1163134560x + 193855760 +--R / +--R 4 3 2 +--R 7112448x + 18966528x + 18966528x + 8429568x + 1404928 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 21096108atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 10548054atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 1730855\|7 +--R / +--R +-+ +--R 12544\|7 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^6*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=333216939/43904*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 103/40*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 23909/1680*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 835409/9408*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 87374783/131712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 404858580885x + 1349528602950x + 1799371470600x + 1199580980400x +--R + +--R 399860326800x + 53314710240 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 11795595705x + 31981229550x + 32535654204x + 14720806136x +--R + +--R 2499608096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 53343360x + 177811200x + 237081600x + 158054400x + 52684800x +--R + +--R 7024640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 809717161770x - 2699057205900x - 3598742941200x +--R + +--R 2 +--R - 2399161960800x - 799720653600x - 106629420480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120 +--R + +--R 4 3 2 +--R 330276679740x + 895474427400x + 910998317712x + 412182571808x +--R + +--R 69989026688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 1727307307089x + 5757691023630x + 7676921364840x + 5117947576560x +--R + +--R 1705982525520x + 227464336736 +--R / +--R 5 4 3 2 +--R 1493614080x + 4978713600x + 6638284800x + 4425523200x + 1475174400x +--R + +--R 196689920 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 6664338780atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 112\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 3332169390atan(------------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 2072x + 1120 +--R + +--R +-+ +--R 1015465789\|7 +--R / +--R +-+ +--R 878080\|7 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=390621/160000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/5*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)-_ + 23779/160000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 1043/8000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 623/1000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 9/50*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 390621\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 432000x - 439200x + 287460x + 317125x + 46783)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 160000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=3927/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/275*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 119/2200*(1-2*x)^(3/2)*sqrt(3+5*x)-_ + 3/50*(1-2*x)^(5/2)*sqrt(3+5*x)+357/2000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 3927\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2400x - 180x + 2575x + 1021)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 2000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=33/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/55*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 1/22*(1-2*x)^(3/2)*sqrt(3+5*x)+3/20*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R 33\|5x + 3 asin(-------------) + (- 12x + 17x + 11)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------------- +--R +--+ +------+ +--R 20\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=-33/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 2/5*(1-2*x)^(3/2)/sqrt(3+5*x)-6/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R - 33\|2 \|5x + 3 asin(-------------) + (- 10x - 28)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +------+ +--R 25\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=4/15*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 14/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2*(1-2*x)^(3/2)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R - 70\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 4\|2 \|5x + 3 asin(-------------) - 66\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +------+ +--R 15\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=-33*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + (1-2*x)^(3/2)/((2+3*x)*sqrt(3+5*x))-33*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (- 99x - 66)\|7 \|5x + 3 atan(-------------) + (- 101x - 65)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ----------------------------------------------------------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 1485x - 1881x - 594)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (- 606x - 390)\|- 2x + 1 \|5x + 3 - 1950x - 2470x - 780 +--R / +--R 2 +--R 90x + 114x + 36 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 198\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R - 99\|7 atan(------------------------------------------------) - 130 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 6 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3o.input.pamphlet b/src/input/rich3o.input.pamphlet new file mode 100644 index 0000000..fada68f --- /dev/null +++ b/src/input/rich3o.input.pamphlet @@ -0,0 +1,7197 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3o.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 36 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 64 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3o.output +)spool rich3o.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=-5709/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/2*(1-2*x)^(3/2)/((2+3*x)^2*sqrt(3+5*x))-_ + 2495/12*sqrt(1-2*x)/sqrt(3+5*x)+169/12*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 51381x - 68508x - 22836)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 7485x - 9815x - 3212)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (36x + 48x + 16)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (3082860x + 5960196x + 3836448x + 822096)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 1257480x - 1648920x - 539616)\|- 2x + 1 \|5x + 3 - 4805955x +--R + +--R 2 +--R - 9291513x - 5980744x - 1281588 +--R / +--R 3 2 +--R 30240x + 58464x + 37632x + 8064 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 137016atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 68508atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 15257\|7 +--R / +--R +-+ +--R 96\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=-463881/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(3/2)/((2+3*x)^3*sqrt(3+5*x))-_ + 608185/504*sqrt(1-2*x)/sqrt(3+5*x)+_ + 239/36*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 13409/168*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 12524787x - 25049574x - 16699716x - 3711048)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 1824555x - 3608883x - 2378026x - 521968)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (1512x + 3024x + 2016x + 448)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 187871805x - 488466693x - 475941906x - 205963164x - 33399432)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 3 2 +--------+ +------+ +--R (- 76631310x - 151573086x - 99877092x - 21922656)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 215801145x + 561082977x + 546696234x + 236581996x + 38364648 +--R / +--R 4 3 2 +--R 317520x + 825552x + 804384x + 348096x + 56448 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 2783286atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R - 1391643atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R 228361\|7 +--R / +--R +-+ +--R 336\|7 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^5*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=-145708761/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(3/2)/((2+3*x)^4*sqrt(3+5*x))-_ + 63678595/9408*sqrt(1-2*x)/sqrt(3+5*x)+_ + 103/24*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_ + 8063/224*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 1403963/3136*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 11802409641x - 31473092376x - 31473092376x - 13988041056x +--R + +--R - 2331340176 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R - 1719322065x - 4546951839x - 4508028900x - 1985778980x +--R + +--R - 327908240 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (254016x + 677376x + 677376x + 301056x + 50176)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 177036144615x + 578318072409x + 755354217024x + 493078447224x +--R + +--R 160862472144x + 20982061584 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 72211526730x - 190971977238x - 189337213800x - 83402717160x +--R + +--R - 13772146080 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 325366951140x - 1062865373724x - 1388232324864x - 906207212064x +--R + +--R - 295642069184x - 38562009024 +--R / +--R 5 4 3 2 +--R 53343360x + 174254976x + 227598336x + 148571136x + 48470016x + 6322176 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 874252566atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 437126283atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 114767884\|7 +--R / +--R +-+ +--R 18816\|7 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^3/(3+5*x)^(3/2)+_ + 13153/10000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 128/25*(2+3*x)^3*sqrt(1-2*x)/sqrt(3+5*x)+_ + 1953/10000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 399/500*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 378/125*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (197295x + 118377)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (- 108000x - 83700x + 118395x + 129910x + 31171)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (150000x + 90000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^2/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=-2/825*(1-2*x)^(5/2)/(3+5*x)^(3/2)+_ + 343/500*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 388/9075*(1-2*x)^(5/2)/sqrt(3+5*x)+_ + 343/18150*(1-2*x)^(3/2)*sqrt(3+5*x)+343/5500*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (5145x + 3087)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2700x + 1845x + 3610x + 901)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (7500x + 4500)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (- 6x - x + 2)\|- 2x + 1 +--R (1) -------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=-2/165*(1-2*x)^(5/2)/(3+5*x)^(3/2)-_ + 19/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-_ + 38/165*(1-2*x)^(3/2)/sqrt(3+5*x)-38/275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 285x - 171)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (- 90x - 290x - 146)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=-2/15*(1-2*x)^(3/2)/(3+5*x)^(3/2)+_ + 4/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+4/25*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R (60x + 36)\|2 \|5x + 3 asin(-------------) + (80x + 26)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-2/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+14*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+14*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|7 \|5x + 3 +--------+ +--R (210x + 126)\|7 \|5x + 3 atan(-------------) + (214x + 124)\|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------------------- +--R +------+ +--R (15x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 9450x - 11340x - 3402)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (3852x + 2232)\|- 2x + 1 \|5x + 3 + 14725x + 17670x + 5301 +--R / +--R 2 +--R 1350x + 1620x + 486 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 756\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 378\|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 589 +--R / +--R 54 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=(1-2*x)^(3/2)/((2+3*x)*(3+5*x)^(3/2))+_ + 169*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 55/3*sqrt(1-2*x)/(3+5*x)^(3/2)+517/3*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (7605x + 9633x + 3042)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (7755x + 9652x + 2995)\|- 2x + 1 +--R / +--R 2 +------+ +--R (45x + 57x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (342225x + 638820x + 396981x + 82134)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (139590x + 173736x + 53910)\|- 2x + 1 \|5x + 3 + 449250x + 838600x +--R + +--R 521130x + 107820 +--R / +--R 3 2 +--R 4050x + 7560x + 4698x + 972 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 9126\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 4563\|7 atan(------------------------------------------------) + 5990 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 54 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=1/2*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 40787/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 655/4*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 239/12*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 17825/12*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +------+ \|7 \|5x + 3 +--R (5506245x + 10645407x + 6852216x + 1468332)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (802125x + 1533090x + 975325x + 206524)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (540x + 1044x + 672x + 144)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (247781025x + 627711930x + 595775709x + 251084772x + 39644964)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (101067750x + 193169340x + 122890950x + 26022024)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 325275300x + 824030760x + 782106388x + 329612304x + 52044048 +--R / +--R 4 3 2 +--R 340200x + 861840x + 817992x + 344736x + 54432 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2202498atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1101249atan(------------------------------------------------) + 206524\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 216\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=1/3*(1-2*x)^(3/2)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 4246733/56*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 204595/168*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 103/12*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 24469/168*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 618645/56*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1719926865x + 4471809849x + 4357148058x + 1885549452x + 305764776) +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (250551225x + 645909120x + 623901861x + 267610802x + 43006496)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (22680x + 58968x + 57456x + 24864x + 4032)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 77396708925x - 247669468560x - 316810528533x - 202492722906x +--R + +--R - 64669250124x - 8255648952 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 31569454350x + 81384549120x + 78611634486x + 33718961052x +--R + +--R 5418818496 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 120653380575x + 386090817840x + 493874504487x + 315664992734x +--R + +--R 100812602436x + 12869693928 +--R / +--R 5 4 3 2 +--R 14288400x + 45722880x + 58487184x + 37382688x + 11938752x + 1524096 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 229323582atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 114661791atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 25535107\|7 +--R / +--R +-+ +--R 3024\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=17/700*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 1/35*(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)+_ + 3735929329/256000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 26653009/192000000*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 35443/1200000*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 919/105000*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/24000000*(3+5*x)^(3/2)*(1730238+2099155*x)*_ + sqrt(1-2*x)-339629939/256000000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 78454515909asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 82944000000x + 97459200000x - 52468992000x - 85095638400x +--R + +--R 2 +--R 9906627680x + 29819034260x - 679278531 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5376000000\|10 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=-193/2000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*_ + (2+3*x)*(3+5*x)^(3/2)+105254149/12800000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+869869/3840000*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+79079/960000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 7189/32000*(1-2*x)^(7/2)*sqrt(3+5*x)+9568559/12800000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 315762447asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 230400000x + 94464000x - 237187200x - 61262560x + 102523580x +--R + +--R 9303927 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 38400000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=-3/50*(1-2*x)^(7/2)*(3+5*x)^(3/2)+1742279/320000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)+14399/96000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1309/24000*(1-2*x)^(5/2)*sqrt(3+5*x)-119/800*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+158389/320000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5226837asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (2304000x - 931200x - 1849760x + 1108180x + 355917)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R 960000\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (1) (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=14641/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 121/960*(1-2*x)^(3/2)*sqrt(3+5*x)+11/240*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-1/8*(1-2*x)^(7/2)*sqrt(3+5*x)+1331/3200*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 43923asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (9600x - 12640x + 3020x + 4443)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9600\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=-98/81*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 250433/16200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 59/180*(1-2*x)^(3/2)*sqrt(3+5*x)+1/9*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+6401/5400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 19600\|7 \|10 atan(-------------) + 250433asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (7200x - 17820x + 26313)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 16200\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=35/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 2119/90*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 1/3*(1-2*x)^(3/2)*sqrt(3+5*x)-1/3*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)-43/30*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (1050x + 700)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (- 6357x - 4238)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +------+ +--R (60x - 237x - 348)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (270x + 180)\|10 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=118/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+_ + 155/108*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 5/4*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)+19/18*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (1395x + 1860x + 620)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (4248x + 5664x + 1888)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (144x + 1305x + 708)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|5 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=32765/648*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 8/81*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 1/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^3+_ + 5/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 925/216*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (884655x + 1769310x + 1179540x + 262120)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (- 1728x - 3456x - 2304x - 512)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (23067x + 33318x + 11568)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (17496x + 34992x + 23328x + 5184)\|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=1/4*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+55/24*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^3+73205/448*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)+605/32*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 6655/448*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (17788815x + 47436840x + 47436840x + 21083040x + 3513840) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (518715x + 1059032x + 723428x + 164688)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (108864x + 290304x + 290304x + 129024x + 21504)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 88944075x - 237184200x - 237184200x - 105415200x - 17569200)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (36310050x + 74132240x + 50639960x + 11528160)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 163411668x + 435764448x + 435764448x + 193673088x + 32278848 +--R / +--R 4 3 2 +--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 732050atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 366025atan(-----------------------------------------------) + 96068\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 4480\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=3674891/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+1/8*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^4+493/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 82937/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 8672663/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 13394977695x + 44649925650x + 59533234200x + 39688822800x +--R + +--R 13229607600x + 1763947680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (390269835x + 1058136330x + 1076423732x + 487066088x + 82697568)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x +--R + +--R 3010560 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 53579910780x - 178599702600x - 238132936800x - 158755291200x +--R + +--R - 52918430400x - 7055790720 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 21855110760x + 59255634480x + 60279728992x + 27275700928x +--R + +--R 4631063808 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 83521959381x + 278406531270x + 371208708360x + 247472472240x +--R + +--R 82490824080x + 10998776544 +--R / +--R 5 4 3 2 +--R 1280240640x + 4267468800x + 5689958400x + 3793305600x + 1264435200x +--R + +--R 168591360 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 146995640atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 73497820atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 16367227\|7 +--R / +--R +-+ +--R 250880\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^7 +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=391280725/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/18*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+1/12*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^5+647/864*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 151621/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 26486645/1016064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 2770202075/14224896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 855730945575x + 3422923782300x + 5704872970500x + 5070998196000x +--R + +--R 2 +--R 2535499098000x + 676133092800x + 75125899200 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 24931818675x + 84218501340x + 113834022672x + 76960600672x +--R + +--R 26026519504x + 3522190656 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 1711461891150x - 6845847564600x - 11409745941000x +--R + +--R 3 2 +--R - 10141996392000x - 5070998196000x - 1352266185600x - 150251798400 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 5 4 3 2 +--R 698090922900x + 2358118037520x + 3187352634816x + 2154896818816x +--R + +--R 728742546112x + 98621338368 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 1965877694109x + 7863510776436x + 13105851294060x + 11649645594720x +--R + +--R 2 +--R 5824822797360x + 1553286079296x + 172587342144 +--R / +--R 6 5 4 3 +--R 10754021376x + 43016085504x + 71693475840x + 63727534080x +--R + +--R 2 +--R 31863767040x + 8497004544x + 944111616 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1565122900atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 782561450atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 128413201\|7 +--R / +--R +-+ +--R 702464\|7 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--------+ +------+ +--R (1) (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=51/2800*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)+1/40*(1-2*x)^(5/2)*_ + (2+3*x)^3*(3+5*x)^(5/2)+355329559167/8192000000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-978869309/2048000000*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-135322391/2304000000*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+16321/800000*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 2477/504000*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-1/192000000*_ + (3+5*x)^(5/2)*(6543814+7759275*x)*sqrt(1-2*x)-_ + 32302687197/8192000000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 2487306914169asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R 3870720000000x + 7105536000000x + 808627200000x - 5264367872000x +--R + +--R 3 2 +--R - 2347326614400x + 1304824422880x + 942468770660x - 115416461871 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 57344000000\|10 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=-2287/8000*(1-2*x)^(7/2)*(3+5*x)^(3/2)-263/2800*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(5/2)+_ + 1104970911/51200000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 3043997/5120000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 276727/1280000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 75471/128000*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 100451901/51200000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 7734796377asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 9216000000x + 10112000000x - 6123776000x - 8717155200x +--R + +--R 2 +--R 1291331040x + 2994263780x - 104420943 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 358400000\|10 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=-63/400*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/20*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_ + 30438639/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 83853/256000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 7623/64000*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 2079/6400*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 2767149/2560000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 30438639asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (25600000x + 8448000x - 25526400x - 5162720x + 10406460x + 717399) +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2560000\|10 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-1/10*(1-2*x)^(7/2)*(3+5*x)^(3/2)+483153/64000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1331/6400*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+121/1600*(1-2*x)^(5/2)*sqrt(3+5*x)-33/160*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+43923/64000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 483153asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +------+ +--R (256000x - 124800x - 177440x + 116420x + 29673)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 64000\|10 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=181/1080*(1-2*x)^(3/2)*(3+5*x)^(3/2)+1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)+_ + 98/243*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 1922677/777600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 7093/21600*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 390869/259200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 313600\|7 \|10 atan(-------------) + 1922677asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (1296000x - 1821600x + 692820x + 178797)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 777600\|10 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-8/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)-1/3*(1-2*x)^(5/2)*_ + (3+5*x)^(3/2)/(2+3*x)-805/243*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)+326717/9720*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-247/270*(3+5*x)^(3/2)*sqrt(1-2*x)+24251/3240*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (- 96600x - 64400)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (980151x + 653434)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (21600x - 41220x + 51831x + 65154)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R (29160x + 19440)\|10 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^2+115/36*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)+1945/324*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)-6829/162*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)+41/18*(3+5*x)^(3/2)*sqrt(1-2*x)-1649/108*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +--+ \|7 \|5x + 3 +--R (17505x + 23340x + 7780)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 \|2 \|5x + 3 +--R (- 122922x - 163896x - 54632)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (1080x - 3690x - 10413x - 4884)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +--+ +--R (2916x + 3888x + 1296)\|10 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^3+115/108*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^2-215/1944*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)+362/243*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(10)+365/216*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-_ + 845/648*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (- 5805x - 11610x - 7740x - 1720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +--+ \|2 \|5x + 3 +--R (78192x + 156384x + 104256x + 23168)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12960x + 103023x + 108702x + 30912)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (52488x + 104976x + 69984x + 15552)\|7 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^5 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^4+115/216*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^3+3244595/108864*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-40/243*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(10)+2675/864*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-_ + 97235/36288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (262812195x + 700832520x + 700832520x + 311481120x + 51913520) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--+ +--R (- 1451520x - 3870720x - 3870720x - 1720320x - 286720)\|7 \|10 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (5370975x + 12310776x + 8842644x + 2031504)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (8817984x + 23514624x + 23514624x + 10450944x + 1741824)\|7 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=1/5*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+11/8*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^4+483153/6272*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-1331/448*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2+121/16*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 43923/6272*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (17153435x + 46327530x + 47166452x + 21361768x + 3620448)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +-+ +--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520)\|7 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 587030895x + 1956769650x + 2609026200x + 1739350800x + 579783600x +--R + +--R 77304480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R (240148090x + 648585420x + 660330328x + 299064752x + 50686272) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 769797756x - 2565992520x - 3421323360x - 2280882240x - 760294080x +--R + +--R - 101372544 +--R / +--R 5 4 3 2 +--R 106686720x + 355622400x + 474163200x + 316108800x + 105369600x +--R + +--R 14049280 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4831530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2415765atan(------------------------------------------------) - 452556\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 62720\|7 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7 +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=-1/18*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^6+23/108*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^5+41068005/175616*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1459/864*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^4-241207/108864*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^3+8346895/3048192*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 872316385/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 29938575645x + 119754302580x + 199590504300x + 177413781600x +--R + +--R 2 +--R 88706890800x + 23655170880x + 2628352320 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 872316385x + 2946673460x + 3982356144x + 2692519968x + 910641904x +--R + +--R 123208128 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 128024064x + 512096256x + 853493760x + 758661120x + 379330560x +--R + +--R 101154816x + 11239424 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 29938575645x - 119754302580x - 199590504300x - 177413781600x +--R + +--R 2 +--R - 88706890800x - 23655170880x - 2628352320 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 12212429390x + 41253428440x + 55752986016x + 37695279552x +--R + +--R 12748986656x + 1724913792 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 39295692324x - 157182769296x - 261971282160x - 232863361920x +--R + +--R 2 +--R - 116431680960x - 31048448256x - 3449827584 +--R / +--R 6 5 4 3 +--R 1792336896x + 7169347584x + 11948912640x + 10621255680x +--R + +--R 2 +--R 5310627840x + 1416167424x + 157351936 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 82136010atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 41068005atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 7700508\|7 +--R / +--R +-+ +--R 351232\|7 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^7+115/756*(1-2*x)^(3/2)*_ + (3+5*x)^(3/2)/(2+3*x)^6+1891543995/2458624*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1921/1512*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5-443563/254016*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^4+2199649/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 384136145/42674688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 40175505215/597445632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 4136806717065x + 19305098012970x + 38610196025940x +--R + +--R 4 3 2 +--R 42900217806600x + 28600145204400x + 11440058081760x +--R + +--R 2542235129280x + 242117631360 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 120526515645x + 487483968610x + 821723878536x + 738910550592x +--R + +--R 2 +--R 373848853744x + 100906793184x + 11351210112 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 5377010688x + 25092716544x + 50185433088x + 55761592320x +--R + +--R 3 2 +--R 37174394880x + 14869757952x + 3304390656x + 314703872 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 8273613434130x + 38610196025940x + 77220392051880x +--R + +--R 4 3 2 +--R 85800435613200x + 57200290408800x + 22880116163520x +--R + +--R 5084470258560x + 484235262720 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 6 5 4 +--R 3374742438060x + 13649551121080x + 23008268599008x +--R + +--R 3 2 +--R 20689495416576x + 10467767904832x + 2825390209152x + 317833883136 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 9503357259627x - 44349000544926x - 88698001089852x +--R + +--R 4 3 2 +--R - 98553334544280x - 65702223029520x - 26280889211808x - 5840197602624x +--R + +--R - 556209295488 +--R / +--R 7 6 5 4 +--R 150556299264x + 702596063232x + 1405192126464x + 1561324584960x +--R + +--R 3 2 +--R 1040883056640x + 416353222656x + 92522938368x + 8811708416 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7566175980atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 3783087990atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 620769303\|7 +--R / +--R +-+ +--R 9834496\|7 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 7 6 5 4 3 2 +--------+ +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=17/1200*(1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(7/2)+1/45*(1-2*x)^(5/2)*_ + (2+3*x)^3*(3+5*x)^(7/2)+932023556783/6553600000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 7702674023/4915200000*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 700243093/3072000000*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 122147797/4147200000*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 193049/12960000*(2+3*x)^2*(3+5*x)^(7/2)*sqrt(1-2*x)+_ + 2197/756000*(2+3*x)^3*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 1/432000000*(3+5*x)^(7/2)*(7919314+9176285*x)*sqrt(1-2*x)-_ + 84729414253/6553600000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 19572494692443asin(-------------) +--R +--+ +--R \|11 +--R + +--R 8 7 6 +--R 41287680000000x + 102445056000000x + 59625676800000x +--R + +--R 5 4 3 +--R - 46327577600000x - 60250198784000x - 5712426076800x +--R + +--R 2 +--R 16445681555360x + 6397508631020x - 1496712721437 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 137625600000\|10 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-132451/153600*(1-2*x)^(7/2)*(3+5*x)^(3/2)-12041/38400*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-999/11200*(1-2*x)^(7/2)*(3+5*x)^(7/2)-3/80*_ + (1-2*x)^(7/2)*(2+3*x)*(3+5*x)^(7/2)+21331366001/327680000*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+176292281/98304000*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+16026571/24576000*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-1456961/819200*(1-2*x)^(7/2)*sqrt(3+5*x)+_ + 1939215091/327680000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 447958686021asin(-------------) +--R +--+ +--R \|11 +--R + +--R 7 6 5 4 +--R 774144000000x + 1362124800000x + 97008640000x - 1013681408000x +--R + +--R 3 2 +--R - 413675529600x + 252700365920x + 169330465940x - 22414998339 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 6881280000\|10 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (1) (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=-407/960*(1-2*x)^(7/2)*(3+5*x)^(3/2)-37/240*(1-2*x)^(7/2)*_ + (3+5*x)^(5/2)-3/70*(1-2*x)^(7/2)*(3+5*x)^(7/2)+_ + 65547757/2048000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 541717/614400*(1-2*x)^(3/2)*sqrt(3+5*x)+49247/153600*_ + (1-2*x)^(5/2)*sqrt(3+5*x)-4477/5120*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+5958887/2048000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1376502897asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 1843200000x + 1879040000x - 1272064000x - 1600483200x +--R + +--R 2 +--R 287177440x + 540576580x - 24901623 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 43008000\|10 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=-11/48*(1-2*x)^(7/2)*(3+5*x)^(3/2)-1/12*(1-2*x)^(7/2)*(3+5*x)^(5/2)+_ + 1771561/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 14641/30720*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 1331/7680*(1-2*x)^(5/2)*sqrt(3+5*x)-121/256*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+161051/102400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5314683asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--+ +--R (5120000x + 1280000x - 4905600x - 748640x + 1895020x + 96003)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 307200\|10 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=37/360*(1-2*x)^(3/2)*(3+5*x)^(5/2)+1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)-_ + 98/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 109715471/9331200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 14557/28800*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 4783/32400*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1994287/3110400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R - 1254400\|7 \|10 atan(-------------) + 109715471asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R 4 3 2 +--+ +--R (62208000x - 35510400x - 35831520x + 25518780x + 6495351)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 9331200\|10 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 2 +--R 9x + 12x + 4 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=-5/18*(1-2*x)^(3/2)*(3+5*x)^(5/2)-1/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/_ + (2+3*x)+1295/729*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 660959/93312*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1453/288*(3+5*x)^(3/2)*sqrt(1-2*x)-247/324*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-155777/31104*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 +--R (497280x + 331520)\|7 \|10 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R \|2 \|5x + 3 +--R (- 1982877x - 1321918)asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (777600x - 643680x - 181044x + 218547x - 136974)\|10 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--R (279936x + 186624)\|10 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3 2 +--R 27x + 54x + 36x + 8 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-1/6*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^2+185/36*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)+81733/5832*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-21935/2916*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*_ + sqrt(7)-785/36*(3+5*x)^(3/2)*sqrt(1-2*x)+575/162*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+34145/1944*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (- 394830x - 526440x - 175480)\|2 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (735597x + 980796x + 326932)\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--------+ +------+ +--R (64800x - 86940x + 95193x + 361602x + 159612)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (52488x + 69984x + 23328)\|2 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-1/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^3+185/108*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^2-21935/1458*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)+408665/5832*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+2075/72*(3+5*x)^(3/2)*sqrt(1-2*x)-10385/648*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)-48625/1944*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +-+ \|7 \|5x + 3 +--R (11033955x + 22067910x + 14711940x + 3269320)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 3 2 +-+ +-+ \|2 \|5x + 3 +--R (- 2368980x - 4737960x - 3158640x - 701920)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +-+ +--------+ +--R (97200x - 280260x - 1261593x - 1173042x - 323952)\|2 \|7 \|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R 3 2 +-+ +-+ +--R (157464x + 314928x + 209952x + 46656)\|2 \|7 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1/12*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^4+185/216*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^3-3304795/326592*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1850/729*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)-3485/4032*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)+1165/2592*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 249575/108864*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (- 267688395x - 713835720x - 713835720x - 317260320x - 52876720) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (67132800x + 179020800x + 179020800x + 79564800x + 13260800)\|7 +--R * +--R +-+ +------+ +--R +--+ \|2 \|5x + 3 +--R \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +--R (10886400x + 88425945x + 136691784x + 77996556x + 15279216)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (26453952x + 70543872x + 70543872x + 31352832x + 5225472)\|7 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^6 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-1/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^5+37/72*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^4+109715471/4572288*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-200/729*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(10)-32453/36288*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2+2543/1296*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3-_ + 3248687/1524096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 133304297265x + 444347657550x + 592463543400x + 394975695600x +--R + +--R 131658565200x + 17554475360 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 1524096000x - 5080320000x - 6773760000x - 4515840000x +--R + +--R - 1505280000x - 200704000 +--R * +--R +-+ +------+ +--R +-+ +--+ \|2 \|5x + 3 +--R \|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (1471239045x + 5428407510x + 6440871564x + 3132020376x + 542283936) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 5555329920x + 18517766400x + 24690355200x + 16460236800x +--R + +--R 5486745600x + 731566080 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7 +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 7 6 5 4 3 2 +--R 2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=1/6*(1-2*x)^(5/2)*(3+5*x)^(7/2)/(2+3*x)^6+11/12*(1-2*x)^(3/2)*_ + (3+5*x)^(7/2)/(2+3*x)^5+8857805/175616*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-73205/37632*(3+5*x)^(3/2)*sqrt(1-2*x)/_ + (2+3*x)^2-1331/1344*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 121/32*(3+5*x)^(7/2)*sqrt(1-2*x)/(2+3*x)^4-805255/175616*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 19372019535x + 77488078140x + 129146796900x + 114797152800x +--R + +--R 2 +--R 57398576400x + 15306287040x + 1700698560 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 568572155x + 1905431420x + 2573967504x + 1743189856x + 589734736x +--R + +--R 79536960 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R - 19372019535x - 77488078140x - 129146796900x - 114797152800x +--R + +--R 2 +--R - 57398576400x - 15306287040x - 1700698560 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 2 +--R 7960010170x + 26676039880x + 36035545056x + 24404657984x +--R + +--R 8256286304x + 1113517440 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 25367319180x - 101469276720x - 169115461200x - 150324854400x +--R + +--R 2 +--R - 75162427200x - 20043313920x - 2227034880 +--R / +--R 6 5 4 3 +--R 5377010688x + 21508042752x + 35846737920x + 31863767040x +--R + +--R 2 +--R 15931883520x + 4248502272x + 472055808 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 17715610atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 8857805atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 1657020\|7 +--R / +--R +-+ +--R 351232\|7 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8 +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-1/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^7+185/756*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^6+327738785/2458624*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-129911/84672*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^4+7163/4536*(3+5*x)^(5/2)*sqrt(1-2*x)/_ + (2+3*x)^5-5777249/4572288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 200146505/128024064*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 20886641735/1792336896*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 7 6 5 +--R 2150294168385x + 10034706119130x + 20069412238260x +--R + +--R 4 3 2 +--R 22299346931400x + 14866231287600x + 5946492515040x +--R + +--R 1321442781120x + 125851693440 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 3 +--R 62659925205x + 253441751890x + 427105196104x + 384048502848x +--R + +--R 2 +--R 194338741616x + 52456780256x + 5897927808 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 +--R 16131032064x + 75278149632x + 150556299264x + 167284776960x +--R + +--R 3 2 +--R 111523184640x + 44609273856x + 9913171968x + 944111616 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R 8601176673540x + 40138824476520x + 80277648953040x +--R + +--R 4 3 2 +--R 89197387725600x + 59464925150400x + 23785970060160x +--R + +--R 5285771124480x + 503406773760 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 6 5 4 +--R 3508955811480x + 14192738105840x + 23917890981824x +--R + +--R 3 2 +--R 21506716159488x + 10882969530496x + 2937579694336x + 330283957248 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R - 13402626245631x - 62545589146278x - 125091178292556x +--R + +--R 4 3 2 +--R - 138990198102840x - 92660132068560x - 37064052827424x +--R + +--R - 8236456183872x - 784424398464 +--R / +--R 7 6 5 4 +--R 903337795584x + 4215576379392x + 8431152758784x + 9367947509760x +--R + +--R 3 2 +--R 6245298339840x + 2498119335936x + 555137630208x + 52870250496 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2621910280atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 1310955140atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 291824553\|7 +--R / +--R +-+ +--R 19668992\|7 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^9 +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 9 8 7 6 5 4 3 +--R 19683x + 118098x + 314928x + 489888x + 489888x + 326592x + 145152x +--R + +--R 2 +--R 41472x + 6912x + 512 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-1/24*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^8+185/1008*(1-2*x)^(3/2)*_ + (3+5*x)^(5/2)/(2+3*x)^7+106656830005/275365888*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-720833/508032*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5+47365/36288*(3+5*x)^(5/2)*sqrt(1-2*x)/_ + (2+3*x)^6-75045071/85349376*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 372439373/512096256*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 64983635965/14338695168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 6796051494355/200741732352*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 8 7 6 +--R 2099326384988415x + 11196407386604880x + 26124950568744720x +--R + +--R 5 4 3 +--R 34833267424992960x + 29027722854160800x + 15481452188885760x +--R + +--R 2 +--R 5160484062961920x + 982949345326080x + 81912445443840 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 7 6 5 +--R 61164463449195x + 288163475473440x + 581931572602156x +--R + +--R 4 3 2 +--R 652979564561296x + 439702534402320x + 177688060285568x +--R + +--R 39899303549504x + 3840133416192 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 +--R 5420026773504x + 28906809458688x + 67449222070272x +--R + +--R 5 4 3 +--R 89932296093696x + 74943580078080x + 39969909374976x +--R + +--R 2 +--R 13323303124992x + 2537772023808x + 211481001984 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 7 6 +--R 2099326384988415x + 11196407386604880x + 26124950568744720x +--R + +--R 5 4 3 +--R 34833267424992960x + 29027722854160800x + 15481452188885760x +--R + +--R 2 +--R 5160484062961920x + 982949345326080x + 81912445443840 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 7 6 5 +--R 856302488288730x + 4034288656628160x + 8147042016430184x +--R + +--R 4 3 2 +--R 9141713903858144x + 6155835481632480x + 2487632843997952x +--R + +--R 558590249693056x + 53761867826688 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 8 7 6 +--R - 2755715740710156x - 14697150617120832x - 34293351439948608x +--R + +--R 5 4 3 +--R - 45724468586598144x - 38103723822165120x - 20321986038488064x +--R + +--R 2 +--R - 6773995346162688x - 1290284827840512x - 107523735653376 +--R / +--R 8 7 6 +--R 75880374829056x + 404695332421632x + 944289108983808x +--R + +--R 5 4 3 +--R 1259052145311744x + 1049210121093120x + 559578731249664x +--R + +--R 2 +--R 186526243749888x + 35528808333312x + 2960734027776 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 213313660010atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 106656830005atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 20000694876\|7 +--R / +--R +-+ +--R 550731776\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=12679836719/1280000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 149/6300*(1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)+1/35*(1-2*x)^(5/2)*_ + (2+3*x)^4*sqrt(3+5*x)-29880867787/34560000000*sqrt(1-2*x)*_ + sqrt(3+5*x)-280447621/1728000000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 5575081/216000000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 3090401/75600000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+_ + 5647/945000*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 266276571099asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000000x + 311731200000x - 147923712000x - 275707382400x +--R + +--R 2 +--R 23172376480x + 98827130860x - 920643741 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 26880000000\|10 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=368012183/64000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 17/500*(1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)+1/30*(1-2*x)^(5/2)*_ + (2+3*x)^3*sqrt(3+5*x)-800452163/1728000000*sqrt(1-2*x)*_ + sqrt(3+5*x)+499583/10800000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 3037/180000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-7/144000000*_ + (3860014+4790855*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1104036549asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 691200000x + 338688000x - 729302400x - 233839520x + 334643860x +--R + +--R 39899709 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 192000000\|10 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=6531217/1600000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+53977/480000*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+4907/120000*(1-2*x)^(5/2)*_ + sqrt(3+5*x)-369/4000*(1-2*x)^(7/2)*sqrt(3+5*x)-_ + 3/50*(1-2*x)^(7/2)*(2+3*x)*sqrt(3+5*x)+593747/1600000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 19593651asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (6912000x - 2217600x - 6256480x + 3384140x + 1498491)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 4800000\|10 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=65219/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+539/4800*_ + (1-2*x)^(3/2)*sqrt(3+5*x)+49/1200*(1-2*x)^(5/2)*sqrt(3+5*x)-_ + 3/40*(1-2*x)^(7/2)*sqrt(3+5*x)+5929/16000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 195657asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (28800x - 35360x + 2980x + 21537)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 48000\|10 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=1331/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+11/60*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+1/15*(1-2*x)^(5/2)*sqrt(3+5*x)+121/200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 3993asin(-------------) + (160x - 380x + 513)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +--+ +--R 600\|10 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R (3x + 2)\|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=98/27*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-_ + 17687/1350*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/15*(1-2*x)^(3/2)*_ + sqrt(3+5*x)-239/450*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ +--+ \|7 \|5x + 3 \|2 \|5x + 3 +--R 4900\|7 \|10 atan(-------------) - 17687asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +--+ +--------+ +------+ +--R (180x - 807)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 1350\|10 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=346/135*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+175/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + (1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)+74/45*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ \|7 \|5x + 3 +--R (2625x + 1750)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +-+ +--------+ +------+ +--R (1038x + 692)\|2 asin(-------------) + (36x + 759)\|5 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +--R (405x + 270)\|5 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-8/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)+3035/108*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)^2+95/12*(1-2*x)^(3/2)*sqrt(3+5*x)/_ + (2+3*x)+91/18*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +-+ \|7 \|5x + 3 +--R (27315x + 36420x + 12140)\|5 \|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ \|2 \|5x + 3 +--R (- 288x - 384x - 128)\|2 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (5481x + 3948)\|5 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (972x + 1296x + 432)\|5 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=6655/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*(1-2*x)^(5/2)*_ + sqrt(3+5*x)/(2+3*x)^3+55/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^2+_ + 605/8*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (539055x + 1078110x + 718740x + 159720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (15707x + 21638x + 7488)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (648x + 1296x + 864x + 192)\|7 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 2695275x - 5390550x - 3593700x - 798600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (1099490x + 1514660x + 524160)\|- 2x + 1 \|5x + 3 + 4953312x +--R + +--R 2 +--R 9906624x + 6604416x + 1467648 +--R / +--R 3 2 +--R 45360x + 90720x + 60480x + 13440 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 66550atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 33275atan(-----------------------------------------------) + 8736\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 80\|7 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=1643785/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^4+235/72*(1-2*x)^(3/2)*_ + sqrt(3+5*x)/(2+3*x)^3+38875/864*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+3879245/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (399439755x + 1065172680x + 1065172680x + 473410080x + 78901680) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (11637735x + 23794744x + 16236916x + 3699216)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (108864x + 290304x + 290304x + 129024x + 21504)\|7 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 1997198775x - 5325863400x - 5325863400x - 2367050400x +--R + +--R - 394508400 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (814641450x + 1665632080x + 1136584120x + 258945120)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 3670547076x + 9788125536x + 9788125536x + 4350278016x + 725046336 +--R / +--R 4 3 2 +--R 7620480x + 20321280x + 20321280x + 9031680x + 1505280 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16437850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 8218925atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 2157876\|7 +--R / +--R +-+ +--R 4480\|7 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=104040277/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 61/24*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^4+_ + 14131/432*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 2347559/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 245529161/169344*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 379226809665x + 1264089365550x + 1685452487400x + 1123634991600x +--R + +--R 374544997200x + 49939332960 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 11048812245x + 29956486710x + 30475811404x + 13788819736x +--R + +--R 2341358496 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 22861440x + 76204800x + 101606400x + 67737600x + 22579200x +--R + +--R 3010560 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 1896134048325x - 6320446827750x - 8427262437000x +--R + +--R 2 +--R - 5618174958000x - 1872724986000x - 249696664800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R 773416857150x + 2096954069700x + 2133306798280x + 965217381520x +--R + +--R 163895094720 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 3484819451484x + 11616064838280x + 15488086451040x + 10325390967360x +--R + +--R 3441796989120x + 458906265216 +--R / +--R 5 4 3 2 +--R 1600300800x + 5334336000x + 7112448000x + 4741632000x + 1580544000x +--R + +--R 210739200 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5202013850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 2601006925atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 682896228\|7 +--R / +--R +-+ +--R 313600\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^7*sqrt(3+5*x)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=13391796605/175616*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/6*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^6+_ + 25/12*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^5+_ + 7445/288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 1729615/12096*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 302171615/338688*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 31603880465/4741632*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 +--R 29287859175135x + 117151436700540x + 195252394500900x +--R + +--R 3 2 +--R 173557684000800x + 86778842000400x + 23141024533440x + 2571224948160 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 853304772555x + 2882422865340x + 3896029345680x + 2634024494432x +--R + +--R 890768460368x + 120549503808 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 2 +--R 384072192x + 1536288768x + 2560481280x + 2275983360x + 1137991680x +--R + +--R 303464448x + 33718272 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 117151436700540x - 468605746802160x - 781009578003600x +--R + +--R 3 2 +--R - 694230736003200x - 347115368001600x - 92564098133760x +--R + +--R - 10284899792640 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 47785067263080x + 161415680459040x + 218177643358080x +--R + +--R 2 +--R 147505371688192x + 49883033780608x + 6750772213248 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R 182626847511129x + 730507390044516x + 1217512316740860x +--R + +--R 3 2 +--R 1082233170436320x + 541116585218160x + 144297756058176x + 16033084006464 +--R / +--R 6 5 4 3 +--R 21508042752x + 86032171008x + 143386951680x + 127455068160x +--R + +--R 2 +--R 63727534080x + 16994009088x + 1888223232 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 107134372840atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 53567186420 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 11929377981\|7 +--R / +--R +-+ +--R 1404928\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=1298595837/320000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2/5*(1-2*x)^(5/2)*(2+3*x)^4/sqrt(3+5*x)-13/75*(1-2*x)^(3/2)*_ + (2+3*x)^4*sqrt(3+5*x)-320899019/2880000000*sqrt(1-2*x)*_ + sqrt(3+5*x)-7/240000000*(6000382-1842385*x)*sqrt(1-2*x)*_ + sqrt(3+5*x)+5421479/18000000*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)+1178663/900000*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 4439/11250*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 1298595837\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 3456000000x + 4043520000x - 2530224000x - 3673002400x +--R + +--R 2 +--R 938891620x + 1366129125x + 168414751 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 320000000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=24319911/8000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*_ + (1-2*x)^(5/2)*(2+3*x)^3/sqrt(3+5*x)-22/125*(1-2*x)^(3/2)*_ + (2+3*x)^3*sqrt(3+5*x)-2987467/24000000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 386939/1200000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 205079/150000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 1019/2500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 24319911\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 34560000x + 12528000x - 39487200x - 4101140x + 20337375x +--R + +--R 6089453 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 8000000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=236313/80000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*(1-2*x)^(7/2)/_ + sqrt(3+5*x)+651/8000*(1-2*x)^(3/2)*sqrt(3+5*x)+_ + 651/22000*(1-2*x)^(5/2)*sqrt(3+5*x)-9/200*(1-2*x)^(7/2)*_ + sqrt(3+5*x)+21483/80000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 236313\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (144000x - 77600x - 112620x + 134625x + 79699)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 80000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=2541/1000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/55*(1-2*x)^(7/2)/_ + sqrt(3+5*x)+7/100*(1-2*x)^(3/2)*sqrt(3+5*x)+7/275*(1-2*x)^(5/2)*_ + sqrt(3+5*x)+231/1000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 2541\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (800x - 1340x + 1125x + 943)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 1000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-363/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/5*(1-2*x)^(5/2)/_ + sqrt(3+5*x)-1/5*(1-2*x)^(3/2)*sqrt(3+5*x)-33/50*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 2 +--+ +--------+ +--R - 363\|5x + 3 asin(-------------) + (20x - 75x - 149)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------------- +--R +--+ +------+ +--R 50\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=338/225*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-98/9*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-2*(1-2*x)^(5/2)/sqrt(3+5*x)-_ + 4/5*(1-2*x)^(3/2)*sqrt(3+5*x)-128/75*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R - 2450\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 338\|2 \|5x + 3 asin(-------------) + (60x - 2142)\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R / +--R +-+ +------+ +--R 225\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-8/45*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-665/9*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)-33*(1-2*x)^(3/2)/sqrt(3+5*x)+_ + (1-2*x)^(5/2)/((2+3*x)*sqrt(3+5*x))-202/15*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R (- 9975x - 6650)\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 24x - 16)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 10209x - 6561)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (135x + 90)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-1815/4*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+1/2*_ + (1-2*x)^(5/2)/((2+3*x)^2*sqrt(3+5*x))+55/4*(1-2*x)^(3/2)/((2+3*x)*_ + sqrt(3+5*x))-1815/4*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (- 16335x - 21780x - 7260)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (- 16657x - 21843x - 7148)\|- 2x + 1 +--R / +--R 2 +------+ +--R (36x + 48x + 16)\|5x + 3 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 980100x - 1894860x - 1219680x - 261360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 399768x - 524232x - 171552)\|- 2x + 1 \|5x + 3 + 1527885x +--R + +--R 2 +--R 2953911x + 1901368x + 407436 +--R / +--R 3 2 +--R 4320x + 8352x + 5376x + 1152 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R 43560\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 21780\|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 33953 +--R / +--R 96 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-147015/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/3*(1-2*x)^(5/2)/((2+3*x)^3*sqrt(3+5*x))+235/36*(1-2*x)^(3/2)/_ + ((2+3*x)^2*sqrt(3+5*x))-578245/216*sqrt(1-2*x)/sqrt(3+5*x)+_ + 39155/216*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 3969405x - 7938810x - 5292540x - 1176120)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 578245x - 1143741x - 753654x - 165424)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (216x + 432x + 288x + 64)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (59541075x + 154806795x + 150837390x + 65274660x + 10585080)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 3 2 +--------+ +------+ +--R (- 24286290x - 48037122x - 31653468x - 6947808)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 68392485x - 177820461x - 173260962x - 74978428x - 12158664 +--R / +--R 4 3 2 +--R 45360x + 117936x + 114912x + 49728x + 8064 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 882090atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R 441045atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R - 72373\|7 +--R / +--R +-+ +--R 48\|7 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-46095555/448*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/4*(1-2*x)^(5/2)/((2+3*x)^4*sqrt(3+5*x))+305/72*(1-2*x)^(3/2)/_ + ((2+3*x)^3*sqrt(3+5*x))-181304825/12096*sqrt(1-2*x)/sqrt(3+5*x)+_ + 71215/864*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+3997345/4032*_ + sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 4 3 2 +--R - 3733739955x - 9956639880x - 9956639880x - 4425173280x +--R + +--R - 737528880 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (- 543914475x - 1438446565x - 1426133132x - 628209228x - 103735088) +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (36288x + 96768x + 96768x + 43008x + 7168)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 280030496625x + 914766288975x + 1194796785600x + 779936790600x +--R + +--R 254447463600x + 33188799600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 114222039750x - 302073778650x - 299487957720x - 131923937880x +--R + +--R - 21784368480 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 514655705340x - 1681208637444x - 2195864342784x - 1433411445984x +--R + +--R - 467637776704x - 60996231744 +--R / +--R 5 4 3 2 +--R 38102400x + 124467840x + 162570240x + 106122240x + 34621440x + 4515840 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 1382866650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 691433325atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 181536404\|7 +--R / +--R +-+ +--R 13440\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (3645x + 16767x + 33048x + 36180x + 23760x + 9360x + 2048x + 192) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=-3538809681/6272*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/5*(1-2*x)^(5/2)/((2+3*x)^5*sqrt(3+5*x))+25/8*(1-2*x)^(3/2)/_ + ((2+3*x)^4*sqrt(3+5*x))-4639661185/56448*sqrt(1-2*x)/sqrt(3+5*x)+_ + 7501/144*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+587477/1344*_ + sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+102293609/18816*sqrt(1-2*x)/_ + ((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 5 4 3 +--R - 4299653762415x - 14332179208050x - 19109572277400x +--R + +--R 2 +--R - 12739714851600x - 4246571617200x - 566209548960 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 +--R - 626354259975x - 2074037896035x - 2746600901250x +--R + +--R 2 +--R - 1818284414692x - 601741553688x - 79638637088 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +--R (7620480x + 25401600x + 33868800x + 22579200x + 7526400x + 1003520) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 64494806436225x + 253679571982485x + 415633197033450x +--R + +--R 3 2 +--R 363081873270600x + 178356007922400x + 46712287789200x + 5095885940640 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 5 4 3 +--R - 26306878918950x - 87109591633470x - 115357237852500x +--R + +--R 2 +--R - 76367945417064x - 25273145254896x - 3344822757696 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R - 84665826054180x - 333018915813108x - 545624212349160x +--R + +--R 3 2 +--R - 476637242971680x - 234137593038720x - 61321750557760x - 6689645515392 +--R / +--R 6 5 4 3 2 +--R 1600300800x + 6294516480x + 10313049600x + 9009100800x + 4425523200x +--R + +--R 1159065600x + 126443520 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 106164290430atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 53082145215atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 9954829636\|7 +--R / +--R +-+ +--R 188160\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R (1) ------------------------------------------------------------ +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^4/(3+5*x)^(3/2)+_ + 88296593/40000000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 508/75*(1-2*x)^(3/2)*(2+3*x)^4/sqrt(3+5*x)+_ + 59754401/40000000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/10000000*(191622-763085*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 525259/250000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 109323/12500*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)-_ + 1676/625*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (1324448895x + 794669337)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 1555200000x + 1626480000x - 1419228000x - 1405199700x +--R + +--R 2 +--R 865945995x + 980658710x + 210855251 +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (600000000x + 360000000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R (1) ------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^3/(3+5*x)^(3/2)+_ + 766843/400000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 376/75*(1-2*x)^(3/2)*(2+3*x)^3/sqrt(3+5*x)+_ + 195643/400000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 34069/20000*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+_ + 16009/2500*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 247/125*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (11502645x + 6901587)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R (6480000x + 972000x - 7724700x + 3074745x + 7876210x + 2322001) +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (6000000x + 3600000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^2/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R (1) ---------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-2/825*(1-2*x)^(7/2)/(3+5*x)^(3/2)+_ + 3619/5000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 76/1815*(1-2*x)^(7/2)/sqrt(3+5*x)+329/16500*(1-2*x)^(3/2)*_ + sqrt(3+5*x)+329/45375*(1-2*x)^(5/2)*sqrt(3+5*x)+_ + 329/5000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (54285x + 32571)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--------+ +--R (36000x - 35100x + 3585x + 40930x + 10633)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (75000x + 45000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R (1) -------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-2/165*(1-2*x)^(7/2)/(3+5*x)^(3/2)-1001/250*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-182/825*(1-2*x)^(5/2)/sqrt(3+5*x)-_ + 91/825*(1-2*x)^(3/2)*sqrt(3+5*x)-91/250*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (- 15015x - 9009)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (900x - 2715x - 7970x - 3707)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3750x + 2250)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-2/15*(1-2*x)^(5/2)/(3+5*x)^(3/2)+22/25*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)+4/15*(1-2*x)^(3/2)/sqrt(3+5*x)+4/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (330x + 198)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +--R (60x + 380x + 158)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-2/3*(1-2*x)^(5/2)/(3+5*x)^(3/2)-8/75*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(2/5)+98/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+_ + 218/15*(1-2*x)^(3/2)/sqrt(3+5*x)+148/25*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +-+ +------+ \|7 \|5x + 3 +--R (12250x + 7350)\|5 \|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (- 40x - 24)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (12430x + 7216)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (375x + 225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------- +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-55/3*(1-2*x)^(3/2)/(3+5*x)^(3/2)+(1-2*x)^(5/2)/((2+3*x)*(3+5*x)^(3/2))+_ + 385*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))*sqrt(7)+385*sqrt(1-2*x)/_ + sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +-+ +------+ \|7 \|5x + 3 +--R (17325x + 21945x + 6930)\|7 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +--------+ +--R (17667x + 21988x + 6823)\|- 2x + 1 +--R / +--R 2 +------+ +--R (45x + 57x + 18)\|5x + 3 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (779625x + 1455300x + 904365x + 187110)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (318006x + 395784x + 122814)\|- 2x + 1 \|5x + 3 + 1023450x + 1910440x +--R + +--R 1187202x + 245628 +--R / +--R 3 2 +--R 4050x + 7560x + 4698x + 972 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 20790\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 10395\|7 atan(------------------------------------------------) + 13646 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R 54 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=1/2*(1-2*x)^(5/2)/((2+3*x)^2*(3+5*x)^(3/2))+235/12*(1-2*x)^(3/2)/_ + ((2+3*x)*(3+5*x)^(3/2))+13145/4*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))*sqrt(7)-4279/12*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 40213/12*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +-+ +------+ +--R (1774575x + 3430845x + 2208360x + 473220)\|7 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +--------+ +--R (1809585x + 3458634x + 2200321x + 465916)\|- 2x + 1 +--R / +--R 3 2 +------+ +--R (540x + 1044x + 672x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 79855875x - 202301550x - 192009015x - 80920620x - 12776940)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (32572530x + 62255412x + 39605778x + 8386488)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 104831100x + 265572120x + 252060556x + 106228848x + 16772976 +--R / +--R 4 3 2 +--R 48600x + 123120x + 116856x + 49248x + 7776 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R - 709830\|7 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 354915\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 465916 +--R / +--R 216 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=1/3*(1-2*x)^(5/2)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 305/36*(1-2*x)^(3/2)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 1361195/8*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 196735/72*sqrt(1-2*x)/(3+5*x)^(3/2)+7975/24*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+1784635/72*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R (551283975x + 1433338335x + 1396586070x + 604370580x + 98006040) +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (80308575x + 207031680x + 199977747x + 85776638x + 13784768)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R / +--R 4 3 2 +-+ +------+ +--R (3240x + 8424x + 8208x + 3552x + 576)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 24807778875x + 79384892400x + 101546508195x + 64904499990x +--R + +--R 20728277460x + 2646163080 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R 10118880450x + 26085991680x + 25197196122x + 10807856388x +--R + +--R 1736880768 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 32566514400x + 104212846080x + 133305598944x + 85203651008x +--R + +--R 27211132032x + 3473761536 +--R / +--R 5 4 3 2 +--R 2041200x + 6531840x + 8355312x + 5340384x + 1705536x + 217728 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 73504530atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 36752265atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 6892384\|7 +--R / +--R +-+ +--R 432\|7 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 7 6 5 4 3 2 +--R (6075x + 27540x + 53487x + 57690x + 37320x + 14480x + 3120x + 288) +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=1/4*(1-2*x)^(5/2)/((2+3*x)^4*(3+5*x)^(3/2))+125/24*(1-2*x)^(3/2)/_ + ((2+3*x)^3*(3+5*x)^(3/2))+519421265/448*atan(sqrt(7)*sqrt(3+5*x)/_ + sqrt(1-2*x))/sqrt(7)-25024175/1344*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 12595/96*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+2992825/1344*_ + sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+227000875/1344*_ + sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 631096836975x + 2061583000785x + 2692679837760x + 1757721560760x +--R + +--R 573441076560x + 74796662160 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 91935354375x + 298295199450x + 386933096475x + 250814924064x +--R + +--R 81243850516x + 10520317456 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 5 4 3 2 +-+ +--R (544320x + 1778112x + 2322432x + 1516032x + 494592x + 64512)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R 28399357663875x + 109810849633650x + 176833333720395x +--R + +--R 3 2 +--R 151799825853720x + 73263330585720x + 18848758864320x + 2019509878320 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 +--R 11583854651250x + 37585195130700x + 48753570155850x +--R + +--R 2 +--R 31602680432064x + 10236725165016x + 1325559999456 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R - 37281374984700x - 144154649940840x - 232138694904732x +--R + +--R 3 2 +--R - 199275853251552x - 96176742182752x - 24743786656512x - 2651119998912 +--R / +--R 6 5 4 3 2 +--R 342921600x + 1325963520x + 2135258496x + 1832979456x + 884653056x +--R + +--R 227598336x + 24385536 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 28048748310atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 14024374155atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 2630079364\|7 +--R / +--R +-+ +--R 24192\|7 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^6*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 8 7 6 5 4 3 2 +--R 18225x + 94770x + 215541x + 280044x + 227340x + 118080x + 38320x +--R + +--R 7104x + 576 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=1/5*(1-2*x)^(5/2)/((2+3*x)^5*(3+5*x)^(3/2))+89/24*(1-2*x)^(3/2)/_ + ((2+3*x)^4*(3+5*x)^(3/2))+46975917593/6272*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-754386765/6272*sqrt(1-2*x)/_ + (3+5*x)^(3/2)+10945/144*sqrt(1-2*x)/((2+3*x)^3*(3+5*x)^(3/2))+_ + 3329689/4032*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 270667969/18816*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 20529722435/18816*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 6 5 4 +--R 856136098132425x + 3367468652654205x + 5517321521297850x +--R + +--R 3 2 +--R 4819729145041800x + 2367586246687200x + 620082112227600x +--R + +--R 67645321333920 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 6 5 4 +--R 124718063792625x + 487807977825900x + 794682454662945x +--R + +--R 3 2 +--R 690189860794590x + 337048538999244x + 87747789308536x + 9514465420576 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 6 5 4 3 2 +--R 114307200x + 449608320x + 736646400x + 643507200x + 316108800x +--R + +--R 82790400x + 9031680 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 6 5 +--R - 77052248831918250x - 349303528038029400x - 678402244160133570x +--R + +--R 4 3 2 +--R - 731710985203845900x - 473348136034105200x - 183657047421592800x +--R + +--R - 39572512980343200x - 3652847352031680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 6 5 4 +--R 31428952075741500x + 122927610412126800x + 200259978575062140x +--R + +--R 3 2 +--R 173927844920236680x + 84936231827809488x + 22112442905751072x +--R + +--R 2397645285985152 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 7 6 5 +--R 88506827939686275x + 401230953326577780x + 779253449548971159x +--R + +--R 4 3 2 +--R 840487062360576330x + 543716019540591240x + 210959484537721360x +--R + +--R 45455358546801840x + 4195879250474016 +--R / +--R 7 6 5 4 +--R 144027072000x + 652922726400x + 1268078353920x + 1367723750400x +--R + +--R 3 2 +--R 884788531200x + 343294156800x + 73969459200x + 6827950080 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 25366995500220atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 12683497750110 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 2081289310751\|7 +--R / +--R +-+ +--R 3386880\|7 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R (1) ------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=1067352517/2560000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 96151531/2560000*sqrt(1-2*x)*sqrt(3+5*x)-25529/16000*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x)-313/800*(2+3*x)^3*sqrt(1-2*x)*_ + sqrt(3+5*x)-1/10*(2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/640000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 1067352517asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 20736000x - 82339200x - 146144160x - 163168620x - 157419203)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2560000\|10 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R (1) -------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=677017/5120*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 11835/1024*sqrt(1-2*x)*sqrt(3+5*x)-2829/1280*(2+3*x)*_ + sqrt(1-2*x)*sqrt(3+5*x)-81/160*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)-1/8*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 677017asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 17280x - 57888x - 88092x - 97295)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 5120\|10 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R (1) ------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=68959/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 181/400*(3+5*x)^(3/2)*sqrt(1-2*x)-1/10*(2+3*x)*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-6269/1600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 68959asin(-------------) + (- 2400x - 6660x - 9401)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 1600\|10 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (3x + 2)\|5x + 3 +--R (1) ----------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=1177/80*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/20*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-107/80*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 1177asin(-------------) + (- 60x - 143)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------------------- +--R +--+ +--R 80\|10 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=11/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 11asin(-------------) - \|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------- +--R +--+ +--R 2\|10 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-2/3*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+1/3*_ + asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10) +--R +--R +--R +-+ +------+ +-+ +------+ +--R \|7 \|5x + 3 +-+ +--+ \|2 \|5x + 3 +--R - 2atan(-------------) + \|7 \|10 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R (2) ----------------------------------------------------- +--R +-+ +--R 3\|7 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=11/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (33x + 22)atan(-------------) - \|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------- +--R +-+ +--R (21x + 14)\|7 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 33x - 22)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R - 14\|- 2x + 1 \|5x + 3 + 42x + 28 +--R / +--R 294x + 196 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 22atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 11atan(--------------------------------------------------) + 2\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=451/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+29/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (4059x + 5412x + 1804)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (87x + 44)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (4059x + 5412x + 1804)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (1218x + 616)\|- 2x + 1 \|5x + 3 + 2772x + 3696x + 1232 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 902atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 451atan(------------------------------------------------) + 44\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=15235/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 25/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 3895/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (411345x + 822690x + 548460x + 121880)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (11685x + 15930x + 5296)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 411345x - 822690x - 548460x - 121880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (163590x + 223020x + 74144)\|- 2x + 1 \|5x + 3 + 437913x + 875826x +--R + +--R 583884x + 129752 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 30470atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 15235atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 2317\|7 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=375265/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/28*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+1/56*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+305/1568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 32735/21952*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (30396465x + 81057240x + 81057240x + 36025440x + 6004240) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (883845x + 1806120x + 1230876x + 278960)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 121585860x - 324228960x - 324228960x - 144101760x - 24016960)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 3 2 +--------+ +------+ +--R (49495320x + 101142720x + 68929056x + 15621760)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 187827255x + 500872680x + 500872680x + 222610080x + 37101680 +--R / +--R 4 3 2 +--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 3002120atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 1501060atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 331265\|7 +--R / +--R +-+ +--R 175616\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=333216939/512000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 875641/128000*(3+5*x)^(3/2)*sqrt(1-2*x)-5029/3200*(2+3*x)*_ + (3+5*x)^(3/2)*sqrt(1-2*x)-309/800*(2+3*x)^2*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/10*(2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 30292449/512000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 333216939asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 26870400x - 46785120x - 51453140x - 49229901)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 512000\|10 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=5274027/25600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 14529/6400*(3+5*x)^(3/2)*sqrt(1-2*x)-251/800*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-3/40*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 479457/25600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 5274027asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 144000x - 469600x - 698580x - 760653)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 25600\|10 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=21417/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-59/80*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/10*(3+5*x)^(5/2)*sqrt(1-2*x)-1947/320*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 21417asin(-------------) + (- 800x - 2140x - 2943)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--R 320\|10 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=363/16*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-1/4*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-33/16*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 363asin(-------------) + (- 20x - 45)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------------------- +--R +--+ +--R 16\|10 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=29/18*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 2/9*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/6*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3 +--R 4\|2 atan(-------------) + 29\|5 \|7 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R - 15\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R 18\|2 \|7 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=-103/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 5/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-1/7*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)+5/21*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R (- 309x - 206)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +--+ \|2 \|5x + 3 +-+ +--------+ +------+ +--R (105x + 70)\|7 \|10 asin(-------------) + 3\|7 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +--R (189x + 126)\|7 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=363/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/14*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-33/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (3267x + 4356x + 1452)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (- 169x - 108)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 3267x - 4356x - 1452)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 2366x - 1512)\|- 2x + 1 \|5x + 3 - 6804x - 9072x - 3024 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 726atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 363atan(--------------------------------------------------) - 108\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=5445/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-95/1764*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+2195/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (147015x + 294030x + 196020x + 43560)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (2195x + 1830x + 288)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 147015x - 294030x - 196020x - 43560)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (30730x + 25620x + 4032)\|- 2x + 1 \|5x + 3 - 27216x - 54432x +--R + +--R - 36288x - 8064 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10890atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 5445atan(--------------------------------------------------) - 144\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=78045/21952*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/28*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-13/504*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+85/14112*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 57595/197568*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (6321645x + 16857720x + 16857720x + 7492320x + 1248720) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (172785x + 346760x + 226348x + 48240)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (1778112x + 4741632x + 4741632x + 2107392x + 351232)\|7 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (25286580x + 67430880x + 67430880x + 29969280x + 4994880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ +--R (9675960x + 19418560x + 12675488x + 2701440)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 32480595x - 86614920x - 86614920x - 38495520x - 6415920 +--R / +--R 4 3 2 +--R 99574272x + 265531392x + 265531392x + 118013952x + 19668992 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 624360atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 312180atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 57285\|7 +--R / +--R +-+ +--R 175616\|7 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3p.input.pamphlet b/src/input/rich3p.input.pamphlet new file mode 100644 index 0000000..a65f92d --- /dev/null +++ b/src/input/rich3p.input.pamphlet @@ -0,0 +1,6785 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3p.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 49 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 51 cases that Axiom failed to integrate. +\item 0 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3p.output +)spool rich3p.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=2664057/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 1/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-29/1960*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-73/11760*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 6107/65856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+694229/921984*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3236829255x + 10789430850x + 14385907800x + 9590605200x +--R + +--R 3196868400x + 426249120 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (93720915x + 253769850x + 257531412x + 115804328x + 19437408)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 373403520x + 1244678400x + 1659571200x + 1106380800x + 368793600x +--R + +--R 49172480 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 6473658510x - 21578861700x - 28771815600x - 19181210400x +--R + +--R - 6393736800x - 852498240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 4 3 2 +--R (2624185620x + 7105555800x + 7210879536x + 3242521184x + 544247424) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 7232538033x + 24108460110x + 32144613480x + 21429742320x +--R + +--R 7143247440x + 952432992 +--R / +--R 5 4 3 2 +--R 10455298560x + 34850995200x + 46467993600x + 30978662400x +--R + +--R 10326220800x + 1376829440 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 53281140atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 26640570atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 4251933\|7 +--R / +--R +-+ +--R 6146560\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=2678359321/819200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 22135201/614400*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 382619/76800*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1569/1280*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 5/16*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 1/12*(2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 243487211/819200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 8035077963asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 138240000x - 615168000x - 1229558400x - 1505007200x +--R + +--R - 1362715220x - 1202896557 +--R * +--R +--+ +--------+ +------+ +--R \|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 2457600\|10 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=104040277/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 859837/76800*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 78167/48000*(3+5*x)^(5/2)*sqrt(1-2*x)-963/4000*(3+5*x)^(7/2)*_ + sqrt(1-2*x)-3/50*(2+3*x)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ + 9458207/102400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 312120831asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 6912000x - 26294400x - 44906720x - 48658820x - 46187289)\|10 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 307200\|10 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=328757/1024*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 2717/768*(3+5*x)^(3/2)*sqrt(1-2*x)-247/480*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-3/40*(3+5*x)^(7/2)*sqrt(1-2*x)-29887/1024*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 986271asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 28800x - 91360x - 132868x - 142713)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 3072\|10 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=1331/64*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-55/48*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-1/6*(3+5*x)^(5/2)*sqrt(1-2*x)-605/64*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R 3993\|5 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 800x - 2060x - 2763)\|2 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +--R 192\|2 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +--R (3x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=3035/432*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-2/27*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-5/12*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 455/144*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +-+ +------+ +--R +-+ \|7 \|5x + 3 +-+ +-+ \|2 \|5x + 3 +--R - 32\|2 atan(-------------) + 3035\|5 \|7 asin(-------------) +--R +--------+ +--+ +--R \|- 2x + 1 \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (- 900x - 1905)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R 432\|2 \|7 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (9x + 12x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=125/54*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+173/189*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+5/21*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/7*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)-185/126*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ \|7 \|5x + 3 +--R (1038x + 692)\|2 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ \|2 \|5x + 3 +--R (2625x + 1750)\|5 \|7 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +--------+ +------+ +--R (- 1575x - 1056)\|2 \|7 \|- 2x + 1 \|5x + 3 +--R / +--R +-+ +-+ +--R (1134x + 756)\|2 \|7 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +--------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-17687/5292*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 25/27*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(10)-_ + 169/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)-1/14*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^2+1195/1764*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (- 159183x - 212244x - 70748)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R 2 +-+ +--+ \|2 \|5x + 3 +--R (44100x + 58800x + 19600)\|7 \|10 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +------+ +--R (2781x + 1812)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (47628x + 63504x + 21168)\|7 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------------------------- +--R 4 3 2 +--------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=6655/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 55/588*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2-1/21*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^3-605/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (539055x + 1078110x + 718740x + 159720)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (- 37685x - 48170x - 15408)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (222264x + 444528x + 296352x + 65856)\|7 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (539055x + 1078110x + 718740x + 159720)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (- 527590x - 674380x - 215712)\|- 2x + 1 \|5x + 3 + 1456056x +--R + +--R 2 +--R 2912112x + 1941408x + 431424 +--R / +--R 3 2 +--R 3111696x + 6223392x + 4148928x + 921984 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 13310atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 6655atan(------------------------------------------------) + 2568\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=6655/3136*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 23/504*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3-1/28*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^4-295/6048*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 4315/84672*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (1617165x + 4312440x + 4312440x + 1916640x + 319440) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +------+ +--R (12945x + 6920x - 6484x - 3600)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (762048x + 2032128x + 2032128x + 903168x + 150528)\|7 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (3234330x + 8624880x + 8624880x + 3833280x + 638880)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (362460x + 193760x - 181552x - 100800)\|- 2x + 1 \|5x + 3 + 893025x +--R + +--R 3 2 +--R 2381400x + 2381400x + 1058400x + 176400 +--R / +--R 4 3 2 +--R 21337344x + 56899584x + 56899584x + 25288704x + 4214784 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 26620atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 13310atan(---------------------------------------------------) + 525\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 12544\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^6*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=933031/307328*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 157/5880*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4-1/35*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^5-1721/105840*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 12371/592704*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 1948963/8297856*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 3400897995x + 11336326650x + 15115102200x + 10076734800x +--R + +--R 3358911600x + 447854880 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (87703335x + 231277650x + 222865988x + 93291272x + 14330592)\|7 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R / +--R 5 4 3 2 +--R 1120210560x + 3734035200x + 4978713600x + 3319142400x + 1106380800x +--R + +--R 147517440 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 13603591980x - 45345306600x - 60460408800x - 40306939200x +--R + +--R - 13435646400x - 1791419520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R 4911386760x + 12951548400x + 12480495328x + 5224311232x +--R + +--R 802513152 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 14473450089x + 48244833630x + 64326444840x + 42884296560x +--R + +--R 14294765520x + 1905968736 +--R / +--R 5 4 3 2 +--R 62731791360x + 209105971200x + 278807961600x + 185871974400x +--R + +--R 61957324800x + 8260976640 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 37321240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 18660620atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 2836263\|7 +--R / +--R +-+ +--R 12293120\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^7*sqrt(1-2*x)) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=52573169/8605184*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 17/980*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^5-1/42*(3+5*x)^(5/2)*_ + sqrt(1-2*x)/(2+3*x)^6-3037/493920*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 71369/2963520*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 958171/16595712*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 122343637/232339968*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 6 5 4 3 +--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x +--R + +--R 2 +--R 1703370675600x + 454232180160x + 50470242240 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 16516390995x + 55658284380x + 74931979536x + 50261760608x +--R + +--R 16771747280x + 2225100096 +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R / +--R 6 5 4 3 +--R 94097687040x + 376390748160x + 627317913600x + 557615923200x +--R + +--R 2 +--R 278807961600x + 74348789760x + 8260976640 +--R * +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 574887603015x + 2299550412060x + 3832584020100x + 3406741351200x +--R + +--R 2 +--R 1703370675600x + 454232180160x + 50470242240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 231229473930x + 779215981320x + 1049047713504x + 703664648512x +--R + +--R 234804461920x + 31151401344 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R 709667861868x + 2838671447472x + 4731119079120x + 4205439181440x +--R + +--R 2 +--R 2102719590720x + 560725224192x + 62302802688 +--R / +--R 6 5 4 3 +--R 1317367618560x + 5269470474240x + 8782450790400x + 7806622924800x +--R + +--R 2 +--R 3903311462400x + 1040883056640x + 115653672960 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 525731690atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 262865845atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 46356252\|7 +--R / +--R +-+ +--R 86051840\|7 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=10866247/128000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 949753/128000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 9079/6400*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 259/800*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)-_ + 3/40*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 +--R 10866247asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +------+ +--R (- 259200x - 891360x - 1387620x - 1555473)\|10 \|- 2x + 1 \|5x + 3 +--R / +--R +--+ +--R 128000\|10 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) --------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=44437/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 799/320*sqrt(1-2*x)*sqrt(3+5*x)-1/10*(2+3*x)^2*sqrt(1-2*x)*_ + sqrt(3+5*x)-3/400*(114+185*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R \|2 \|5x + 3 2 +--+ +--------+ +------+ +--R 44437asin(-------------) + (- 1440x - 4140x - 6003)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------------- +--R +--+ +--R 1600\|10 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=3827/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 333/400*sqrt(1-2*x)*sqrt(3+5*x)-3/20*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 3827asin(-------------) + (- 180x - 453)\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +--R 400\|10 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=37/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-3/10*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R \|2 \|5x + 3 +--+ +--------+ +------+ +--R 37asin(-------------) - 3\|10 \|- 2x + 1 \|5x + 3 +--R +--+ +--R \|11 +--R (2) -------------------------------------------------- +--R +--+ +--R 10\|10 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=1/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5) +--R +--R +--R +-+ +------+ +--R +-+ \|2 \|5x + 3 +--R \|2 asin(-------------) +--R +--+ +--R \|11 +--R (2) ----------------------- +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=1/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=2*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------- +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R (3) - ------------------------------------------------------------------ +--R 7 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R / +--R +-+ +--R \|7 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=1/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=37/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 3/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R \|7 \|5x + 3 +-+ +--------+ +------+ +--R (111x + 74)atan(-------------) + 3\|7 \|- 2x + 1 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------- +--R +-+ +--R (21x + 14)\|7 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 111x - 74)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R 42\|- 2x + 1 \|5x + 3 - 126x - 84 +--R / +--R 294x + 196 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 74atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 37atan(--------------------------------------------------) - 6\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=1/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=3827/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 3/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+333/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 \|7 \|5x + 3 +--R (34443x + 45924x + 15308)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +--R (999x + 708)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 2 +-+ +--R (1764x + 2352x + 784)\|7 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (34443x + 45924x + 15308)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (13986x + 9912)\|- 2x + 1 \|5x + 3 - 44604x - 59472x - 19824 +--R / +--R 2 +--R 24696x + 32928x + 10976 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 7654atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 3827atan(------------------------------------------------) - 708\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 392\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=1/((2+3*x)^4*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=222185/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 1/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+185/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+19415/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 \|7 \|5x + 3 +--R (5998995x + 11997990x + 7998660x + 1777480)atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +------+ +--R (174735x + 240750x + 83232)\|7 \|- 2x + 1 \|5x + 3 +--R / +--R 3 2 +-+ +--R (74088x + 148176x + 98784x + 21952)\|7 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 5998995x - 11997990x - 7998660x - 1777480)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (2446290x + 3370500x + 1165248)\|- 2x + 1 \|5x + 3 + 7865424x +--R + +--R 2 +--R 15730848x + 10487232x + 2330496 +--R / +--R 3 2 +--R 1037232x + 2074464x + 1382976x + 307328 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 444370atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 222185atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 41616\|7 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=143283/8000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 7/550*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-1/10*(2+3*x)^3*_ + sqrt(1-2*x)/sqrt(3+5*x)-139839/88000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 63/22000*(194+305*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 1576113\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 237600x - 849420x - 1477575x - 632101)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 88000\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=2493/400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/44*(2+3*x)*_ + sqrt(1-2*x)/sqrt(3+5*x)-3/20*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_ + 2337/4400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R 27423\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 5940x - 19305x - 9451)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R 4400\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=123/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-2/275*sqrt(1-2*x)/_ + sqrt(3+5*x)-9/50*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--+ +--------+ +--R 1353\|5x + 3 asin(-------------) + (- 495x - 301)\|10 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------------------- +--R +--+ +------+ +--R 550\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=3/5*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/55*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +-+ +--------+ +--R 33\|2 \|5x + 3 asin(-------------) - 2\|5 \|- 2x + 1 +--R +--+ +--R \|11 +--R (2) ----------------------------------------------------- +--R +-+ +------+ +--R 55\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=-2/11*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R 2\|- 2x + 1 +--R (2) - ------------ +--R +------+ +--R 11\|5x + 3 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ +--R - 6\|- 2x + 1 \|5x + 3 - 20x - 12 +--R (3) ---------------------------------- +--R 165x + 99 +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 33 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 500 +t0:=1/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (15x + 19x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=-6*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/11*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R - 66\|5x + 3 atan(-------------) - 10\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------- +--R +-+ +------+ +--R 11\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R (495x + 297)\|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +--------+ +------+ +--R - 210\|- 2x + 1 \|5x + 3 - 980x - 588 +--R / +--R 1155x + 693 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 198atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R 99atan(-----------------------------------------------) - 28\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 33\|7 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=1/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=-321/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 515/77*sqrt(1-2*x)/sqrt(3+5*x)+3/7*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R (- 10593x - 7062)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +--R (- 1545x - 997)\|7 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (231x + 154)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (158895x + 201267x + 63558)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 64890x - 41874)\|- 2x + 1 \|5x + 3 + 209370x + 265202x + 83748 +--R / +--R 2 +--R 48510x + 61446x + 19404 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 21186atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 10593atan(--------------------------------------------------) + 1994\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 462\|7 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=1/((2+3*x)^3*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=-56421/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 90415/2156*sqrt(1-2*x)/sqrt(3+5*x)+3/14*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+543/196*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (- 5585679x - 7447572x - 2482524)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (- 813735x - 1067061x - 349252)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (19404x + 25872x + 8624)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (335140740x + 647938764x + 417064032x + 89370864)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 136707480x - 179266248x - 58674336)\|- 2x + 1 \|5x + 3 - 522568305x +--R + +--R 2 +--R - 1010298723x - 650307224x - 139351548 +--R / +--R 3 2 +--R 16299360x + 31512096x + 20283648x + 4346496 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 14895144atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 7447572atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 1658947\|7 +--R / +--R +-+ +--R 51744\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=1/((2+3*x)^4*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------ +--R 5 4 3 2 +--------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=-4616025/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 7396875/30184*sqrt(1-2*x)/sqrt(3+5*x)+1/7*sqrt(1-2*x)/_ + ((2+3*x)^3*sqrt(3+5*x))+255/196*sqrt(1-2*x)/((2+3*x)^2*_ + sqrt(3+5*x))+44475/2744*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +------+ +--R (- 1370959425x - 2741918850x - 1827945900x - 406210200)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (- 199715625x - 395028225x - 260298990x - 57135248)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (814968x + 1629936x + 1086624x + 241472)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 20564391375x - 53467417575x - 52096458150x - 22544666100x +--R + +--R - 3655891800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +--R (- 8388056250x - 16591185450x - 10932557580x - 2399680416)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 26996404680x + 70190652168x + 68390891856x + 29596058464x + 4799360832 +--R / +--R 4 3 2 +--R 171143280x + 444972528x + 433562976x + 187623744x + 30425472 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 304657650atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R - 152328825atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R 28567624\|7 +--R / +--R +-+ +--R 181104\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)^5/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=462357/40000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+29/1650*(2+3*x)^3*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-1/10*(2+3*x)^4*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 511/90750*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)-_ + 4802371/4840000*sqrt(1-2*x)*sqrt(3+5*x)-_ + 21/1210000*(21038+30535*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (839177955x + 503506773)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--R (- 117612000x - 502791300x - 1030526145x - 795297410x - 199549721) +--R * +--R +--+ +--------+ +--R \|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (72600000x + 43560000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(2+3*x)^4/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=8127/2000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+91/3300*(2+3*x)^2*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-3/20*(2+3*x)^3*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 119/36300*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-80633/242000*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (14750505x + 8850303)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--------+ +--R (- 2940300x - 11712195x - 10891910x - 2953931)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (3630000x + 2178000)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(2+3*x)^3/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=81/50*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+19/330*(2+3*x)*_ + sqrt(1-2*x)/(3+5*x)^(3/2)-3/10*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 439/18150*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|2 \|5x + 3 +--R (147015x + 88209)\|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--------+ +--R (- 49005x - 60010x - 18373)\|10 \|- 2x + 1 +--R / +--R +--+ +------+ +--R (90750x + 54450)\|10 \|5x + 3 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^2/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=9/25*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(2/5)-2/825*sqrt(1-2*x)/_ + (3+5*x)^(3/2)-404/9075*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +------+ \|2 \|5x + 3 +--R (16335x + 9801)\|2 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +--------+ +--R (- 2020x - 1234)\|5 \|- 2x + 1 +--R / +--R +-+ +------+ +--R (45375x + 27225)\|5 \|5x + 3 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=-2/165*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 206x - 128)\|- 2x + 1 +--R (2) ------------------------- +--R +------+ +--R (1815x + 1089)\|5x + 3 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 1854x - 1152)\|- 2x + 1 \|5x + 3 - 6400x - 7680x - 2304 +--R (3) ------------------------------------------------------------ +--R 2 +--R 81675x + 98010x + 29403 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 256 +--R (4) - ---- +--R 3267 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=-2/33*sqrt(1-2*x)/(3+5*x)^(3/2)-8/363*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +--R (- 40x - 46)\|- 2x + 1 +--R (2) ----------------------- +--R +------+ +--R (1815x + 1089)\|5x + 3 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 360x - 414)\|- 2x + 1 \|5x + 3 - 2300x - 2760x - 828 +--R (3) --------------------------------------------------------- +--R 2 +--R 81675x + 98010x + 29403 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 92 +--R (4) - ---- +--R 3267 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=1/((2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 3 2 +--------+ +------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=18*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 10/33*sqrt(1-2*x)/(3+5*x)^(3/2)+950/363*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +-+ +--------+ +--R (32670x + 19602)\|5x + 3 atan(-------------) + (4750x + 2740)\|7 \|- 2x + 1 +--R +--------+ +--R \|- 2x + 1 +--R ---------------------------------------------------------------------------- +--R +-+ +------+ +--R (1815x + 1089)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (735075x + 882090x + 264627)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (299250x + 172620)\|- 2x + 1 \|5x + 3 - 959000x - 1150800x - 345240 +--R / +--R 2 +--R 571725x + 686070x + 205821 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 58806atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 29403atan(------------------------------------------------) - 5480\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 3267\|7 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=1/((2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=1593/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 845/231*sqrt(1-2*x)/(3+5*x)^(3/2)+3/7*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^(3/2))+84235/2541*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +------+ \|7 \|5x + 3 +--R (8673885x + 10986921x + 3469554)\|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--------+ +--R (1263525x + 1572580x + 487909)\|7 \|- 2x + 1 +--R / +--R 2 +-+ +------+ +--R (38115x + 48279x + 15246)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 390324825x - 728606340x - 452776797x - 93677958)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (159204150x + 198145080x + 61476534)\|- 2x + 1 \|5x + 3 + 512304450x +--R + +--R 2 +--R 956301640x + 594273162x + 122953068 +--R / +--R 3 2 +--R 24012450x + 44823240x + 27854442x + 5762988 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10408662atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 5204331atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 975818\|7 +--R / +--R +-+ +--R 45738\|7 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=1/((2+3*x)^3*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------ +--R 5 4 3 2 +--------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=392283/196*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 207895/6468*sqrt(1-2*x)/(3+5*x)^(3/2)+3/14*sqrt(1-2*x)/_ + ((2+3*x)^2*(3+5*x)^(3/2))+753/196*sqrt(1-2*x)/((2+3*x)*_ + (3+5*x)^(3/2))+20743985/71148*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +------+ +--R (6407942805x + 12388689423x + 7974328824x + 1708784748)\|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--------+ +--R (933479325x + 1784145090x + 1135041037x + 240342364)\|7 \|- 2x + 1 +--R / +--R 3 2 +-+ +------+ +--R (3201660x + 6189876x + 3984288x + 853776)\|7 \|5x + 3 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R 288357426225x + 730505479770x + 693339411501x + 292202191908x +--R + +--R 46137188196 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--R (117618394950x + 224802281340x + 143015170662x + 30283137864) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 378539223300x - 958966032360x - 910176532468x - 383586412944x +--R + +--R - 60566275728 +--R / +--R 4 3 2 +--R 2017045800x + 5109849360x + 4849874568x + 2043939744x + 322727328 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2563177122atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 1281588561atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 240342364\|7 +--R / +--R +-+ +--R 1280664\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=1/((2+3*x)^4*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=41307885/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-_ + 21891025/90552*sqrt(1-2*x)/(3+5*x)^(3/2)+1/7*sqrt(1-2*x)/_ + ((2+3*x)^3*(3+5*x)^(3/2))+325/196*sqrt(1-2*x)/((2+3*x)^2*_ + (3+5*x)^(3/2))+79335/2744*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2184369575/996072*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 2024292904425x + 5263161551505x + 5128208691210x + 2219224813740x +--R + +--R 359874294120 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R 294889892625x + 760212086400x + 734310313245x + 314968389410x +--R + +--R 50617099616 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R / +--R 4 3 2 +-+ +--R (134469720x + 349621272x + 340656624x + 147418656x + 23905728)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R 91093180699125x + 291498178237200x + 372874752995085x +--R + +--R 2 +--R 238326751280970x + 76113413206380x + 9716605941240 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R 37156126470750x + 95786722886400x + 92523099468870x +--R + +--R 39686017065660x + 6377754551616 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 +--R - 104635035612450x - 334832113959840x - 428306079106962x +--R + +--R 2 +--R - 273756256135684x - 87428385311736x - 11161070465328 +--R / +--R 5 4 3 2 +--R 84715923600x + 271090955520x + 346770513936x + 221641957152x +--R + +--R 70784860608x + 9036365184 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 269905720590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 134952860295atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 22144981082\|7 +--R / +--R +-+ +--R 17929296\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=-35439958001/5120000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^5*_ + sqrt(3+5*x)/sqrt(1-2*x)+3192575743/5120000*sqrt(1-2*x)*_ + sqrt(3+5*x)+847637/32000*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 10389/1600*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x)+33/20*(2+3*x)^4*_ + sqrt(1-2*x)*sqrt(3+5*x)+147/1280000*(1853322+3022165*x)*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 35439958001\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 124416000x - 613267200x - 1429191360x - 2297649240x +--R + +--R - 3810769458x + 5389783159 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 5120000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=-92108287/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_ + sqrt(3+5*x)/sqrt(1-2*x)+8050753/51200*sqrt(1-2*x)*sqrt(3+5*x)+_ + 15395/512*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)+2203/320*(2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x)+27/16*(2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 92108287\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 518400x - 2283840x - 5020200x - 9587886x + 14050073)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 51200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=-1463447/3200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_ + sqrt(3+5*x)/sqrt(1-2*x)+131833/3200*sqrt(1-2*x)*sqrt(3+5*x)+7/4*_ + (2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+3/160*(750+1223*x)*sqrt(1-2*x)*_ + sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 1463447\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 14400x - 57960x - 142686x + 224833)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 3200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=-17951/160*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(3/2)/_ + sqrt(1-2*x)+9/40*(3+5*x)^(3/2)*sqrt(1-2*x)+17951/1760*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 17951\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (- 360x - 1518x + 2809)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 160\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 3x - 2)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=-103/4*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(3/2)/_ + sqrt(1-2*x)+103/44*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 103\|- 2x + 1 asin(-------------) + (- 6x + 17)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) --------------------------------------------------------------- +--R +--+ +--------+ +--R 4\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=-asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R - \|5 \|- 2x + 1 asin(-------------) + \|2 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +-+ +--------+ +--R \|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-2/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R - 2\|- 2x + 1 atan(-------------) + 2\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------- +--R +-+ +--------+ +--R 7\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R (4x - 2)\|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ +--R - 28\|- 2x + 1 \|5x + 3 + 98x - 49 +--R / +--R 196x - 98 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 4atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R 2atan(-----------------------------------------------------) + 7\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 14\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=29/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))-9/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (87x + 58)\|- 2x + 1 atan(-------------) + (18x + 5)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ----------------------------------------------------------------- +--R +-+ +--------+ +--R (147x + 98)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 1392x - 232x + 464)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +--------+ +------+ 2 +--R (- 2016x - 560)\|- 2x + 1 \|5x + 3 + 3990x + 665x - 1330 +--R / +--R 2 +--R 32928x + 5488x - 10976 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 464atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 232atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 95\|7 +--R / +--R +-+ +--R 784\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=1585/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))-15/98*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+15/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (14265x + 19020x + 6340)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 90x + 405x + 212)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 142650x - 118875x + 31700x + 31700)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 2 +--R (6300x - 28350x - 14840)\|- 2x + 1 \|5x + 3 + 186984x + 155820x +--R + +--R - 41552x - 41552 +--R / +--R 3 2 +--R 1728720x + 1440600x - 384160x - 384160 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 15850atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 7925atan(-----------------------------------------------) + 1484\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 13720\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=7435/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-1/7*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3-5/196*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 565/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (200745x + 401490x + 267660x + 59480)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 10170x - 8055x + 3114x + 2512)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (802980x + 1204470x + 267660x - 297400x - 118960)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (284760x + 225540x - 87192x - 70336)\|- 2x + 1 \|5x + 3 - 1127574x +--R + +--R 3 2 +--R - 1691361x - 375858x + 417620x + 167048 +--R / +--R 4 3 2 +--R 4148928x + 6223392x + 1382976x - 1536640x - 614656 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 29740atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 14870atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 2983\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1244755/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))-27/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-13/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 835/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+107245/153664*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (100825155x + 268867080x + 268867080x + 119496480x + 19916080) +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 5791230x - 8897265x - 2075184x + 2239092x + 917264)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 403300620x + 873818010x + 537734160x - 59748240x - 159328640x +--R + +--R - 39832160 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--R (162154440x + 249123420x + 58105152x - 62694576x - 25683392) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 455077602x - 986001471x - 606770136x + 67418904x + 179783744x +--R + +--R 44945936 +--R / +--R 5 4 3 2 +--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x +--R + +--R - 68841472 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 4979020atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 2489510atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 401303\|7 +--R / +--R +-+ +--R 614656\|7 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 405x - 1323x - 1728x - 1128x - 368x - 48)\|5x + 3 +--R (1) --------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=-11199264087/1024000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^4*_ + (3+5*x)^(3/2)/sqrt(1-2*x)+29429853/256000*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+169017/6400*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 10377/1600*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+33/20*(2+3*x)^3*_ + (3+5*x)^(3/2)*sqrt(1-2*x)+1018114917/1024000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 11199264087\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 41472000x - 200966400x - 461171520x - 732415080x - 1206337246x +--R + +--R 1702927233 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 1024000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 135x - 351x - 342x - 148x - 24)\|5x + 3 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=-145708761/51200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+(2+3*x)^3*_ + (3+5*x)^(3/2)/sqrt(1-2*x)+392979/12800*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+27/16*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 3/320*(3+5*x)^(3/2)*(1382+2199*x)*sqrt(1-2*x)+_ + 13246251/51200*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 145708761\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 864000x - 3729600x - 8057880x - 15218818x + 22217679)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 51200\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 45x - 87x - 56x - 12)\|5x + 3 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=-463881/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/22*(3+5*x)^(5/2)/_ + sqrt(1-2*x)+14057/1760*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 3/20*(3+5*x)^(5/2)*sqrt(1-2*x)+42171/640*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 463881\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 4800x - 18840x - 45538x + 71199)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 640\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 15x - 19x - 6)\|5x + 3 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=-5709/32*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*(3+5*x)^(5/2)/_ + sqrt(1-2*x)+173/88*(3+5*x)^(3/2)*sqrt(1-2*x)+519/32*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 2 +--+ +------+ +--R - 5709\|- 2x + 1 asin(-------------) + (- 120x - 490x + 891)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R --------------------------------------------------------------------------- +--R +--+ +--------+ +--R 32\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=-33/4*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(3/2)/_ + sqrt(1-2*x)+15/4*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R - 33\|5 \|- 2x + 1 asin(-------------) + (- 10x + 27)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +-+ +--------+ +--R 4\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------ +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=-5/3*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 2/21*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R 2\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +-+ +-+ +------+ +--R - 35\|5 \|7 \|- 2x + 1 asin(-------------) + 33\|2 \|7 \|5x + 3 +--R +--+ +--R \|11 +--R / +--R +-+ +-+ +--------+ +--R 21\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=-33/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)*sqrt(1-2*x))+3/49*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (- 99x - 66)\|- 2x + 1 atan(-------------) + (64x + 45)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) -------------------------------------------------------------------- +--R +-+ +--------+ +--R (147x + 98)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 198x - 33x + 66)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +--------+ +------+ 2 +--R (- 896x - 630)\|- 2x + 1 \|5x + 3 - 3780x - 630x + 1260 +--R / +--R 2 +--R 4116x + 686x - 1372 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R - 33atan(------------------------------------------------) - 90\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 98\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=825/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^2*sqrt(1-2*x))+_ + 5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 425/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (7425x + 9900x + 3300)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (2550x + 2245x + 396)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 59400x - 49500x + 13200x + 13200)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 142800x - 125720x - 22176)\|- 2x + 1 \|5x + 3 + 237006x + 197505x +--R + +--R - 52668x - 52668 +--R / +--R 3 2 +--R 1382976x + 1152480x - 307328x - 307328 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 6600atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 3300atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 1881\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +r0:=2805/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^3*sqrt(1-2*x))+_ + 1/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 145/588*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 415/8232*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (75735x + 151470x + 100980x + 22440)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (2490x + 6135x + 3782x + 576)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 151470x - 227205x - 50490x + 56100x + 22440)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 34860x - 85890x - 52948x - 8064)\|- 2x + 1 \|5x + 3 + 108864x +--R + +--R 3 2 +--R 163296x + 36288x - 40320x - 16128 +--R / +--R 4 3 2 +--R 2074464x + 3111696x + 691488x - 768320x - 307328 +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5610atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 2805atan(--------------------------------------------------) + 288\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +r0:=279015/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(3/2)/((2+3*x)^4*sqrt(1-2*x))+9/196*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^4-89/392*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 745/10976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+16985/153664*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (22600215x + 60267240x + 60267240x + 26785440x + 4464240)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 917190x - 1188045x + 60048x + 538276x + 163152)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 302 + +--S 303 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 90400860x + 195868530x + 120534480x - 13392720x - 35713920x +--R + +--R - 8928480 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 4 3 2 +--------+ +--R (25681320x + 33265260x - 1681344x - 15071728x - 4568256)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R - 80943786x - 175378203x - 107925048x + 11991672x + 31977792x + 7994448 +--R / +--R 5 4 3 2 +--R 697019904x + 1510209792x + 929359872x - 103262208x - 275365888x +--R + +--R - 68841472 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1116060atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 558030atan(---------------------------------------------------) - 71379\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 614656\|7 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R (1) +--R 6 5 4 3 2 +------+ +--R (- 2025x - 7830x - 12609x - 10824x - 5224x - 1344x - 144)\|5x + 3 +--R ----------------------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +r0:=-107121749031/1638400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + (2+3*x)^4*(3+5*x)^(5/2)/sqrt(1-2*x)+295101237/409600*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+5100983/51200*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 62751/2560*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)+999/160*(2+3*x)^2*_ + (3+5*x)^(5/2)*sqrt(1-2*x)+13/8*(2+3*x)^3*(3+5*x)^(5/2)*_ + sqrt(1-2*x)+9738340821/1638400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 107121749031\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R - 276480000x - 1479168000x - 3687379200x - 5945485120x +--R + +--R 2 +--R - 7755469800x - 11734056318x + 16267424049 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 1638400\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|5x + 3 +--R (1) --------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +r0:=-3538809681/204800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + (2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)+9748787/51200*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+172209/6400*(3+5*x)^(5/2)*sqrt(1-2*x)+33/20*_ + (2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)+3/1600*(3+5*x)^(5/2)*_ + (6602+10365*x)*sqrt(1-2*x)+321709971/204800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 3538809681\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R - 13824000x - 65836800x - 148751040x - 233394520x - 381820658x +--R + +--R 538018839 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 204800\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +--R (- 225x - 570x - 541x - 228x - 36)\|5x + 3 +--R (1) ---------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +r0:=-9219111/2048*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22*(3+5*x)^(7/2)/sqrt(1-2*x)+25397/512*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+25397/3520*(3+5*x)^(5/2)*sqrt(1-2*x)+_ + 9/80*(3+5*x)^(7/2)*sqrt(1-2*x)+838101/2048*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 9219111\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (- 57600x - 243520x - 517096x - 966014x + 1405233)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 2048\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +--R (- 75x - 140x - 87x - 18)\|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +r0:=-29403/128*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 7/11*(3+5*x)^(7/2)/sqrt(1-2*x)+405/32*(3+5*x)^(3/2)*_ + sqrt(1-2*x)+81/44*(3+5*x)^(5/2)*sqrt(1-2*x)+13365/128*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R - 29403\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +------+ +--R (- 1600x - 6120x - 14526x + 22545)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R 128\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +r0:=-1815/32*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+(3+5*x)^(5/2)/_ + sqrt(1-2*x)+25/8*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 825/32*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R - 1815\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (- 200x - 790x + 1413)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R 32\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------- +--R 2 +--------+ +--R (6x + x - 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +r0:=-475/36*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)-_ + 2/63*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*sqrt(1-2*x)+_ + 505/84*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R - 8\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R - 3325\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (- 1050x + 2703)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R 252\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------------- +--R 3 2 +--------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +r0:=-25/9*asin(sqrt(2/11)*sqrt(3+5*x))*sqrt(5/2)+_ + 169/441*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)*sqrt(1-2*x))+_ + 3/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)+160/147*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R (507x + 338)\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R (- 3675x - 2450)\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (3273x + 2175)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R (1323x + 882)\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ----------------------------------------- +--R 4 3 2 +--------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +r0:=-1815/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^2*sqrt(1-2*x))+_ + 5/98*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^2+_ + 165/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (- 16335x - 21780x - 7260)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (8110x + 11525x + 4068)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (12348x + 16464x + 5488)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (32670x + 27225x - 7260x - 7260)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 113540x - 161350x - 56952)\|- 2x + 1 \|5x + 3 - 512568x - 427140x +--R + +--R 113904x + 113904 +--R / +--R 3 2 +--R 345744x + 288120x - 76832x - 76832 +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 3630atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 1815atan(--------------------------------------------------) - 4068\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2744\|7 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +r0:=1815/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^3*sqrt(1-2*x))+_ + 1/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^3+_ + 155/1764*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 12335/24696*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (49005x + 98010x + 65340x + 14520)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (24670x + 37405x + 17666x + 2448)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 148176x + 98784x + 21952)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 490050x - 735075x - 163350x + 181500x + 72600)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +------+ +--R (- 1726900x - 2618350x - 1236620x - 171360)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 3238704x + 4858056x + 1079568x - 1199520x - 479808 +--R / +--R 4 3 2 +--R 10372320x + 15558480x + 3457440x - 3841600x - 1536640 +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 18150atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 9075atan(-----------------------------------------------) + 8568\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 27440\|7 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^5) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +r0:=168795/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^4*sqrt(1-2*x))+_ + 9/196*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^4+_ + 277/3528*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 38365/98784*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-_ + 167155/1382976*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (13672395x + 36459720x + 36459720x + 16204320x + 2700720)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (1002930x + 2578615x + 2184144x + 687828x + 53136)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (12446784x + 33191424x + 33191424x + 14751744x + 2458624)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 109379160x + 236988180x + 145838880x - 16204320x - 43211520x +--R + +--R - 10802880 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 4 3 2 +--R (- 56164080x - 144402440x - 122312064x - 38518368x - 2975616) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 71554266x - 155034243x - 95405688x + 10600632x + 28268352x + 7067088 +--R / +--R 5 4 3 2 +--R 1394039808x + 3020419584x + 1858719744x - 206524416x - 550731776x +--R + +--R - 137682944 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1350360atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R 675180atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 63099\|7 +--R / +--R +-+ +--R 1229312\|7 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^6) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------------------------------- +--R 7 6 5 4 2 +--------+ +--R (1458x + 5103x + 6804x + 3780x - 1008x - 448x - 64)\|- 2x + 1 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +r0:=3474273/2151296*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/7*(3+5*x)^(5/2)/((2+3*x)^5*sqrt(1-2*x))+11/245*(3+5*x)^(3/2)*_ + sqrt(1-2*x)/(2+3*x)^5+1019/13720*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 29297/82320*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-55277/460992*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+426781/6453888*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 4221241695x + 14070805650x + 18761074200x + 12507382800x +--R + +--R 4169127600x + 555883680 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 115230870x - 180017865x + 19738914x + 164918884x + 95331368x +--R + +--R 16456032 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 5 4 3 2 +--R 2613824640x + 8712748800x + 11616998400x + 7744665600x +--R + +--R 2581555200x + 344207360 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 +--R 8442483390x + 23920369605x + 23451342750x + 6253691400x +--R + +--R 2 +--R - 4169127600x - 3057360240x - 555883680 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 5 4 3 2 +--R 1613232180x + 2520250110x - 276344796x - 2308864376x +--R + +--R - 1334639152x - 230384448 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 +--R - 6997927608x - 19827461556x - 19438687800x - 5183650080x +--R + +--R 2 +--R 3455766720x + 2534228928x + 460768896 +--R / +--R 6 5 4 3 +--R 73187089920x + 207363421440x + 203297472000x + 54212659200x +--R + +--R 2 +--R - 36141772800x - 26503966720x - 4818903040 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 34742730atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 17371365atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 2057004\|7 +--R / +--R +-+ +--R 21512960\|7 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +r0:=-291096141/256000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 2191/880*(2+3*x)^3*sqrt(3+5*x)/sqrt(1-2*x)-3/40*(2+3*x)^4*_ + sqrt(3+5*x)/sqrt(1-2*x)+288454593/2816000*sqrt(1-2*x)*_ + sqrt(3+5*x)+76587/17600*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x)+_ + 63/704000*(390718+637135*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 3202057551\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 17107200x - 76887360x - 171939240x - 332129358x + 488641609)\|10 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--------+ +--R 2816000\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) --------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +r0:=-184641/640*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 567/220*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-1/10*(2+3*x)^3*_ + sqrt(3+5*x)/sqrt(1-2*x)+35505/1408*sqrt(1-2*x)*sqrt(3+5*x)+_ + 8487/1760*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 2031051\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (- 19008x - 78408x - 196614x + 312365)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 7040\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +r0:=-56421/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x)-3/20*(2+3*x)^2*_ + sqrt(3+5*x)/sqrt(1-2*x)+54249/8800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R - 620631\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (- 11880x - 51678x + 97409)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R 8800\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +r0:=-321/20*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22*sqrt(3+5*x)/sqrt(1-2*x)+9/20*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 3531\|- 2x + 1 asin(-------------) + (- 198x + 589)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------- +--R +--+ +--------+ +--R 220\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +r0:=-3*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+7/11*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R - 33\|- 2x + 1 asin(-------------) + 7\|10 \|5x + 3 +--R +--+ +--R \|11 +--R (2) ---------------------------------------------------- +--R +--+ +--------+ +--R 11\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +r0:=2/11*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R 2\|5x + 3 +--R (2) ------------- +--R +--------+ +--R 11\|- 2x + 1 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ +--R - 2\|- 2x + 1 \|5x + 3 - 8x + 4 +--R (3) -------------------------------- +--R 22x - 11 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 11 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +r0:=6/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R 66\|- 2x + 1 atan(-------------) + 4\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ------------------------------------------------- +--R +-+ +--------+ +--R 77\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R (- 66x + 33)\|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ +--R - 28\|- 2x + 1 \|5x + 3 + 112x - 56 +--R / +--R 1078x - 539 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 33atan(--------------------------------------------------) + 8\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 77\|7 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +r0:=123/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)*sqrt(1-2*x))+87/539*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (4059x + 2706)\|- 2x + 1 atan(-------------) + (- 174x + 115)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (1617x + 1078)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (32472x + 5412x - 10824)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +--------+ +------+ 2 +--R (9744x - 6440)\|- 2x + 1 \|5x + 3 - 33810x - 5635x + 11270 +--R / +--R 2 +--R 181104x + 30184x - 60368 +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 10824atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 5412atan(---------------------------------------------------) - 805\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 4312\|7 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +r0:=12465/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+_ + 75/1078*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 11685/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (1234035x + 1645380x + 548460)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 70110x - 13785x + 25204)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (135828x + 181104x + 60368)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (4936140x + 4113450x - 1096920x - 1096920)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 2 +--------+ +------+ 3 +--R (1963080x + 385980x - 705712)\|- 2x + 1 \|5x + 3 - 5557482x +--R + +--R 2 +--R - 4631235x + 1234996x + 1234996 +--R / +--R 3 2 +--R 7606368x + 6338640x - 1690304x - 1690304 +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 548460atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +-+ +--R 274230atan(---------------------------------------------------) - 44107\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R / +--R +-+ +--R 60368\|7 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +r0:=102345/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))+_ + 3/77*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 915/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 98205/30184*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (30396465x + 60792930x + 40528620x + 9006360)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 1767690x - 1549935x + 377658x + 421184)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (814968x + 1629936x + 1086624x + 241472)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (60792930x + 91189395x + 20264310x - 22515900x - 9006360)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ +--R (24747660x + 21699090x - 5287212x - 5896576)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R - 79603776x - 119405664x - 26534592x + 29482880x + 11793152 +--R / +--R 4 3 2 +--R 22819104x + 34228656x + 7606368x - 8451520x - 3380608 +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2251590atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 1125795atan(------------------------------------------------) - 210592\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 60368\|7 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^5*sqrt(3+5*x)) +--R +--R +--R (1) +--R 1 +--R - ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +r0:=24922335/153664*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77*sqrt(3+5*x)/((2+3*x)^4*sqrt(1-2*x))+_ + 51/2156*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4+_ + 1269/4312*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3+_ + 228645/120736*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 23958315/1690304*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R 22205800485x + 59215467960x + 59215467960x + 26317985760x +--R + +--R 4386330960 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R (- 1293749010x - 1998242055x - 482249808x + 491393004x + 205593328) +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (136914624x + 365105664x + 365105664x + 162269184x + 27044864)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 88823201940x - 192450270870x - 118430935920x + 13158992880x +--R + +--R 35090647680x + 8772661920 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R \|7 atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R 4 3 2 +--R 36224972280x + 55950777540x + 13502994624x - 13759004112x +--R + +--R - 5756613184 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 101999989854x + 220999978017x + 135999986472x - 15111109608x +--R + +--R - 40296292288x - 10074073072 +--R / +--R 5 4 3 2 +--R 7667218944x + 16612307712x + 10222958592x - 1135884288x - 3029024768x +--R + +--R - 757256192 +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1096582740atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R - 548291370atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +-+ +--R 89947081\|7 +--R / +--R +-+ +--R 6761216\|7 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +r0:=-2911419/16000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 567/220*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 1/10*(2+3*x)^4/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 2821/12100*(2+3*x)^2*sqrt(1-2*x)/sqrt(3+5*x)+_ + 30791901/1936000*sqrt(1-2*x)*sqrt(3+5*x)+_ + 294483/96800*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 352281699\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 15681600x - 75663720x - 208989990x + 169670279x + 162727423)\|10 +--R / +--R +--+ +--------+ +------+ +--R 1936000\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +r0:=-35451/800*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3/20*(2+3*x)^3/(sqrt(1-2*x)*sqrt(3+5*x))+_ + 1/24200*(31586+54645*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 316941/96800*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 4289571\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 392040x - 1992870x + 2323271x + 2026687)\|10 +--R / +--R +--+ +--------+ +------+ +--R 96800\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +r0:=-999/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 721/220*(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3/10*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 3547/12100*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R - 120879\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 32670x + 82499x + 61243)\|10 +--R / +--R +--+ +--------+ +------+ +--R 12100\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +r0:=-9/5*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 49/22/(sqrt(1-2*x)*sqrt(3+5*x))-1229/1210*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--+ +--R - 1089\|- 2x + 1 \|5x + 3 asin(-------------) + (1229x + 733)\|10 +--R +--+ +--R \|11 +--R (2) ------------------------------------------------------------------ +--R +--+ +--------+ +------+ +--R 605\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R - 3x - 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +r0:=(-2/55)/(sqrt(1-2*x)*sqrt(3+5*x))+74/605*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 74x + 40 +--R (2) ----------------------- +--R +--------+ +------+ +--R 121\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 222x - 120)\|- 2x + 1 \|5x + 3 - 950x - 95x + 285 +--R (3) ------------------------------------------------------ +--R 2 +--R 3630x + 363x - 1089 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 95 +--R (4) - --- +--R 363 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +r0:=2/11/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 40x + 2 +--R (2) ----------------------- +--R +--------+ +------+ +--R 121\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 120x - 6)\|- 2x + 1 \|5x + 3 - 40x - 4x + 12 +--R (3) ------------------------------------------------- +--R 2 +--R 3630x + 363x - 1089 +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - --- +--R 363 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +r0:=-18/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/(sqrt(1-2*x)*sqrt(3+5*x))-370/847*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +-+ +--R - 2178\|- 2x + 1 \|5x + 3 atan(-------------) + (740x - 326)\|7 +--R +--------+ +--R \|- 2x + 1 +--R (2) ---------------------------------------------------------------- +--R +-+ +--------+ +------+ +--R 847\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (32670x + 3267x - 9801)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 15540x + 6846)\|- 2x + 1 \|5x + 3 + 45640x + 4564x - 13692 +--R / +--R 2 +--R 177870x + 17787x - 53361 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 6534atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 3267atan(--------------------------------------------------) + 652\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 2541\|7 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +r0:=-999/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_ + 17735/5929*sqrt(1-2*x)/sqrt(3+5*x)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (- 362637x - 241758)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (106410x + 15821x - 34205)\|7 +--R / +--R +-+ +--------+ +------+ +--R (17787x + 11858)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (87032880x + 66725208x - 20307672x - 17406576)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 35753760x - 5315856x + 11492880)\|- 2x + 1 \|5x + 3 - 136477950x +--R + +--R 2 +--R - 104633095x + 31844855x + 27295590 +--R / +--R 3 2 +--R 59764320x + 45819312x - 13945008x - 11952864 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 5802192atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R 2901096atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R - 649895\|7 +--R / +--R +-+ +--R 284592\|7 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +r0:=-177255/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x))-_ + 3125575/166012*sqrt(1-2*x)/sqrt(3+5*x)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 18615/15092*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (- 193030695x - 257374260x - 85791420)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (56260350x + 45655035x - 12730165x - 12072596)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (1494108x + 1992144x + 664048)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (5790920850x + 8300319885x + 1608589125x - 2058994080x - 772122780) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +--R (- 2362934700x - 1917511470x + 534666930x + 507049032)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R - 7605735480x - 10901554188x - 2112704300x + 2704261504x + 1014098064 +--R / +--R 4 3 2 +--R 627525360x + 899453016x + 174312600x - 223120128x - 83670048 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 128687130atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R 64343565atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 12072596\|7 +--R / +--R +-+ +--R 996072\|7 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^4*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R - ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (810x + 2241x + 2133x + 528x - 392x - 272x - 48)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +r0:=-2079585/2744*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^3*sqrt(1-2*x)*sqrt(3+5*x))-_ + 36657025/332024*sqrt(1-2*x)/sqrt(3+5*x)+_ + 3/77*sqrt(1-2*x)/((2+3*x)^3*sqrt(3+5*x))+_ + 1245/2156*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 220305/30184*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 6794004195x - 13588008390x - 9058672260x - 2013038280)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (1979479350x + 2925598635x + 622325745x - 723664682x - 283149136)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (8964648x + 17929296x + 11952864x + 2656192)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1019100629250x + 2140111321425x + 1256890776075x - 173624551650x +--R + +--R - 377444677500x - 90586722600 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 415690663500x - 614375713350x - 130688406450x + 151969583220x +--R + +--R 59461318560 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 1873031534640x - 3933366222744x - 2310072226056x + 319109076272x +--R + +--R 693715383200x + 166491691968 +--R / +--R 5 4 3 2 +--R 18825760800x + 39534097680x + 23218438320x - 3207351840x +--R + +--R - 6972504000x - 1673400960 +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 7548893550atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 3774446775atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 991021976\|7 +--R / +--R +-+ +--R 9960720\|7 +--R Type: Expression(Integer) +--E 464 + +--S 465 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(2+3*x)^5/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +--R - 243x - 810x - 1080x - 720x - 240x - 32 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +r0:=-111321/4000*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1211/440*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3/20*(2+3*x)^4/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 17983/72600*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 7/3993000*(467578+809265*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 10952053/5324000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 2222523765x - 1333514259)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (- 194059800x - 1128781170x + 612106475x + 1785872944x + 632498543)\|10 +--R / +--R +--+ +--------+ +------+ +--R (79860000x + 47916000)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +--R - 81x - 216x - 216x - 96x - 16 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +r0:=-621/100*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 721/220*(2+3*x)^2/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3/10*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))+_ + 1/36300*(4706+11385*x)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 168781/399300*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 12398265x - 7438959)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 3234330x + 6746215x + 11581424x + 3821563)\|10 +--R / +--R +--+ +--------+ +------+ +--R (1996500x + 1197900)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +--R - 27x - 54x - 36x - 8 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +r0:=-27/25*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 2/11*(2+3*x)^3/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 8/363*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 4/19965*(158+321*x)*sqrt(1-2*x)/sqrt(3+5*x)+_ + 3103/33275*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (- 539055x - 323433)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (649265x + 772408x + 229661)\|10 +--R / +--R +--+ +--------+ +------+ +--R (499125x + 299475)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^2/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--R - 9x - 12x - 4 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +r0:=49/22/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 3679/3630*sqrt(1-2*x)/(3+5*x)^(3/2)-4091/19965*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 8182x + 8912x + 2392 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 73638x - 80208x - 21528)\|- 2x + 1 \|5x + 3 - 209300x - 146510x +--R + +--R 50232x + 37674 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4186 +--R (4) - ----- +--R 35937 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R - 3x - 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +r0:=7/11/((3+5*x)^(3/2)*sqrt(1-2*x))-107/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 428/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 4280x + 2782x + 80 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 38520x - 25038x - 720)\|- 2x + 1 \|5x + 3 + 7000x + 4900x - 1680x +--R + +--R - 1260 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 140 +--R (4) ----- +--R 35937 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 500 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +r0:=2/11/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 160/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 1600x + 1040x - 194 +--R (2) ------------------------------------ +--R +--------+ +------+ +--R (19965x + 11979)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 14400x - 9360x + 1746)\|- 2x + 1 \|5x + 3 - 19400x - 13580x +--R + +--R 4656x + 3492 +--R / +--R 3 2 +--R 1796850x + 1257795x - 431244x - 323433 +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 388 +--R (4) - ----- +--R 35937 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +r0:=54/7*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 410/2541*sqrt(1-2*x)/(3+5*x)^(3/2)+31030/27951*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (1078110x + 646866)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (- 310300x - 22010x + 90032)\|7 +--R / +--R +-+ +--------+ +------+ +--R (139755x + 83853)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 48514950x - 33960465x + 11643588x + 8732691)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 2 +--------+ +------+ 3 +--R (19548900x + 1386630x - 5672016)\|- 2x + 1 \|5x + 3 - 63022400x +--R + +--R 2 +--R - 44115680x + 15125376x + 11344032 +--R / +--R 3 2 +--R 88045650x + 61631955x - 21130956x - 15848217 +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1940598atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 970299atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 180064\|7 +--R / +--R +-+ +--R 251559\|7 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3q.input.pamphlet b/src/input/rich3q.input.pamphlet new file mode 100644 index 0000000..ee96be1 --- /dev/null +++ b/src/input/rich3q.input.pamphlet @@ -0,0 +1,5581 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3q.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 34 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 25 cases that Axiom failed to integrate. +\item 41 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3q.output +)spool rich3q.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +r0:=4887/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x))-_ + 28705/17787*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 87/539*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 2841815/195657*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (292706865x + 370762029x + 117082746)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (- 85254450x - 63467215x + 20145298x + 16461125)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (2934855x + 3717483x + 1173942)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R - 26343617850x - 36002944395x - 5971220046x + 8956830069x +--R + +--R 3161234142 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 3 2 +--------+ +--R (10742060700x + 7996869090x - 2538307548x - 2074101750)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 48395707500x + 66140800250x + 10969693700x - 16454540550x - 5807484900 +--R / +--R 4 3 2 +--R 3697917300x + 5053820310x + 838194588x - 1257291882x - 443750076 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 351248238atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R - 175624119atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R 46091150\|7 +--R / +--R +-+ +--R 3521826\|7 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 500 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R - -------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +r0:=1215945/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/77/((2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x))-_ + 7090175/498036*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 75/1078*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 25545/15092*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 707286025/5478396*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +--R (218487077325x + 422408349495x + 271895029560x + 58263220620) +--R * +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R \|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +--R - 63655742250x - 89836042575x - 16567908760x + 22311149965x +--R + +--R 8194676012 +--R * +--R +-+ +--R \|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (246527820x + 476620452x + 306790176x + 65740752)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 +--R - 19663836959250x - 39983135150475x - 22373076718080x +--R + +--R 2 +--R 3714280314525x + 6816796812540x + 1573106956740 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 4 3 2 +--R 8020623523500x + 11319341364450x + 2087556503760x - 2811204895590x +--R + +--R - 1032529177512 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 +--R - 25813229437800x - 52486899856860x - 29369718827008x +--R + +--R 2 +--R 4875832227140x + 8948586205104x + 2065058355024 +--R / +--R 5 4 3 2 +--R 310625053200x + 631604274840x + 353422282752x - 58673621160x +--R + +--R - 107683351776x - 24850004256 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 87394830930atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 43697415465atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R - 8194676012\|7 +--R / +--R +-+ +--R 98611128\|7 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|5x + 3 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +r0:=13246251/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1/3*(2+3*x)^4*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-299/66*(2+3*x)^3*sqrt(3+5*x)/_ + sqrt(1-2*x)-12735719/70400*sqrt(1-2*x)*sqrt(3+5*x)-_ + 121769/3520*(2+3*x)*sqrt(1-2*x)*sqrt(3+5*x)-_ + 697/88*(2+3*x)^2*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (874252566x - 437126283)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (2851200x + 15040080x + 52700868x - 183672928x + 66038637)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (422400x - 211200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|5x + 3 +--R (1) -------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +r0:=126513/320*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+_ + 1/3*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-233/66*(2+3*x)^2*_ + sqrt(3+5*x)/sqrt(1-2*x)-25073/704*sqrt(1-2*x)*sqrt(3+5*x)-_ + 3/880*(3566+5815*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (8349858x - 4174929)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (71280x + 431244x - 1786144x + 625431)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (21120x - 10560)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +r0:=49/66*(3+5*x)^(3/2)/(1-2*x)^(3/2)+519/8*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-21/11*(3+5*x)^(3/2)/sqrt(1-2*x)-519/88*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (34254x - 17127)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (1188x - 7712x + 2481)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (528x - 264)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R (3x + 2)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +r0:=7/33*(3+5*x)^(3/2)/(1-2*x)^(3/2)+3/2*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-3/2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R (198x - 99)\|5 \|- 2x + 1 asin(-------------) + (- 268x + 57)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (132x - 66)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +r0:=2/33*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R +------+ +--R (- 10x - 6)\|5x + 3 +--R (2) --------------------- +--R +--------+ +--R (66x - 33)\|- 2x + 1 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (10x + 6)\|- 2x + 1 \|5x + 3 - 48x + 48x - 12 +--R (3) ----------------------------------------------- +--R 2 +--R 132x - 132x + 33 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 4 +--R (4) - -- +--R 11 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +r0:=-6/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*sqrt(3+5*x)/_ + (1-2*x)^(3/2)+128/1617*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (- 396x + 198)\|- 2x + 1 atan(-------------) + (256x - 282)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R ------------------------------------------------------------------------ +--R +-+ +--------+ +--R (3234x - 1617)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (396x - 396x + 99)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 1792x + 1974)\|- 2x + 1 \|5x + 3 + 15792x - 15792x + 3948 +--R / +--R 2 +--R 45276x - 45276x + 11319 +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 66atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R 33atan(--------------------------------------------------) + 188\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 539\|7 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +r0:=75/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+260/1617*sqrt(3+5*x)/_ + ((2+3*x)*sqrt(1-2*x))-425/3773*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (14850x + 2475x - 4950)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (5100x - 1460x - 1623)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (67914x + 11319x - 22638)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 42 + +--S 43 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 148500x + 49500x + 61875x - 24750)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 2 +--------+ +------+ 3 +--R (- 357000x + 102200x + 113610)\|- 2x + 1 \|5x + 3 + 1908648x +--R + +--R 2 +--R - 636216x - 795270x + 318108 +--R / +--R 3 2 +--R 9507960x - 3169320x - 3961650x + 1584660 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 8250atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 4125atan(-----------------------------------------------) + 7574\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 37730\|7 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +r0:=765/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+2/21*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+8/33*sqrt(3+5*x)/_ + ((2+3*x)^2*sqrt(1-2*x))-145/1078*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2-415/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (454410x + 378675x - 100980x - 100980)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (14940x + 19380x - 8633x - 6708)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (814968x + 679140x - 181104x - 181104)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (908820x + 302940x - 580635x - 100980x + 100980)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 209160x - 271320x + 120862x + 93912)\|- 2x + 1 \|5x + 3 - 1690416x +--R + +--R 3 2 +--R - 563472x + 1079988x + 187824x - 187824 +--R / +--R 4 3 2 +--R 22819104x + 7606368x - 14578872x - 2535456x + 2535456 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 16830atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 8415atan(------------------------------------------------) - 2236\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 30184\|7 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +r0:=25365/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+_ + 524/1617*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_ + 89/539*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-_ + 745/15092*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2+_ + 16985/211288*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (45200430x + 67800645x + 15066810x - 16740900x - 6696360)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (- 1834380x - 235980x + 1465461x + 39530x - 302352)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (34228656x + 51342984x + 11409552x - 12677280x - 5070912)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 52 + +--S 53 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 452004300x - 452004300x + 188335125x + 242743050x - 16740900x +--R + +--R - 33481800 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R (128406600x + 16518600x - 102582270x - 2767100x + 21164640) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 800023392x + 800023392x - 333343080x - 429642192x + 29630496x +--R + +--R 59260992 +--R / +--R 5 4 3 2 +--R 4792011840x + 4792011840x - 1996671600x - 2573487840x + 177481920x +--R + +--R 354963840 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2790150atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +-+ +--R - 1395075atan(-----------------------------------------------) + 352744\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R / +--R +-+ +--R 2112880\|7 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +r0:=1/3*(2+3*x)^4*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ + 1626211523/102400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 123/22*(2+3*x)^3*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 47007627/281600*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 269967/7040*(2+3*x)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 3315/352*(2+3*x)^2*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1626211523/1126400*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (9757269138x - 4878634569)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 15552000x + 83548800x + 236669040x + 633940524x - 2034703904x +--R + +--R 739060191 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (614400x - 307200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (135x + 351x + 342x + 148x + 24)\|5x + 3 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +r0:=1/3*(2+3*x)^3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ + 4246733/1280*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 101/22*(2+3*x)^2*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 125989/3520*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 1/440*(3+5*x)^(3/2)*(6646+10575*x)*sqrt(1-2*x)-_ + 4246733/14080*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (25480398x - 12740199)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +------+ +--R (86400x + 447120x + 1544724x - 5349344x + 1925361)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (7680x - 3840)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(2+3*x)^2*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (45x + 87x + 56x + 12)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +r0:=49/66*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ + 40787/64*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-_ + 938/363*(3+5*x)^(5/2)/sqrt(1-2*x)-_ + 40787/5808*(3+5*x)^(3/2)*sqrt(1-2*x)-40787/704*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (244722x - 122361)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (2160x + 12780x - 52256x + 18351)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (384x - 192)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(2+3*x)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (15x + 19x + 6)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +r0:=7/33*(3+5*x)^(5/2)/(1-2*x)^(3/2)+169/8*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)-169/66*(3+5*x)^(3/2)/sqrt(1-2*x)-_ + 845/88*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1014x - 507)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (180x - 1136x + 369)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (48x - 24)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +r0:=1/3*(3+5*x)^(3/2)/(1-2*x)^(3/2)+5/2*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-5/2*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +-+ +------+ +--R (30x - 15)\|5 \|- 2x + 1 asin(-------------) + (- 40x + 9)\|2 \|5x + 3 +--R +--+ +--R \|11 +--R ----------------------------------------------------------------------- +--R +-+ +--------+ +--R (12x - 6)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +r0:=2/21*(3+5*x)^(3/2)/(1-2*x)^(3/2)+2/49*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-2/49*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (12x - 6)\|- 2x + 1 atan(-------------) + (- 82x - 36)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R (2) ------------------------------------------------------------------- +--R +-+ +--------+ +--R (294x - 147)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 12x + 12x - 3)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +--R atan(-----------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R + +--R +--------+ +------+ 2 +--R (574x + 252)\|- 2x + 1 \|5x + 3 + 1764x - 1764x + 441 +--R / +--R 2 +--R 4116x - 4116x + 1029 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (- 71373x - 38580)\|7 +-+ +--R - atan(-----------------------------------------------------) + 21\|7 +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 + 22792x + 12320 +--R / +--R +-+ +--R 49\|7 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x))-95/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+20/49*sqrt(3+5*x)/((2+3*x)*_ + sqrt(1-2*x))-55/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (- 1710x - 285x + 570)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (660x - 310x - 549)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 87 + +--S 88 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 17100x + 5700x + 7125x - 2850)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7 +--R atan(---------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700 +--R + +--R 2 +--------+ +------+ 3 2 +--R (- 46200x + 21700x + 38430)\|- 2x + 1 \|5x + 3 - 645624x + 215208x +--R + +--R 269010x - 107604 +--R / +--R 3 2 +--R 864360x - 288120x - 360150x + 144060 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (333x + 180)\|7 +-+ +--R - 475atan(---------------------------------------------) - 2562\|7 +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 - 1295x - 700 +--R / +--R +-+ +--R 3430\|7 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^2)+5/28*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+6/7*sqrt(3+5*x)/((2+3*x)^2*_ + sqrt(1-2*x))-5/14*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-5/28*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (270x + 225x - 60x - 60)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (180x + 60x - 91x - 36)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (1512x + 1260x - 336x - 336)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (2160x + 720x - 1380x - 240x + 240)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 10080x - 3360x + 5096x + 2016)\|- 2x + 1 \|5x + 3 - 43092x +--R + +--R 3 2 +--R - 14364x + 27531x + 4788x - 4788 +--R / +--R 4 3 2 +--R 169344x + 56448x - 108192x - 18816x + 18816 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 40atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 20atan(------------------------------------------------------) - 57\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 224\|7 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^3)+_ + 9395/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)+64/49*sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-_ + 27/49*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-285/1372*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-1395/19208*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (1521990x + 2282985x + 507330x - 563700x - 225480)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (150660x + 193860x - 17127x - 80510x - 19296)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 97 + +--S 98 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (3043980x + 3043980x - 1268325x - 1634730x + 112740x + 225480)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--------+ +--R (- 2109240x - 2714040x + 239778x + 1127140x + 270144)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R - 7293888x - 7293888x + 3039120x + 3917088x - 270144x - 540288 +--R / +--R 5 4 3 2 +--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 18790atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 9395atan(------------------------------------------------) - 3216\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 38416\|7 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +r0:=1/3*(2+3*x)^4*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ + 46975917593/409600*asin(sqrt(2/11)*sqrt(3+5*x))/_ + sqrt(10)-439/66*(2+3*x)^3*(3+5*x)^(5/2)/sqrt(1-2*x)-_ + 4270537963/3379200*(3+5*x)^(3/2)*sqrt(1-2*x)-_ + 24606179/140800*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 302699/7040*(2+3*x)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 4819/440*(2+3*x)^2*(3+5*x)^(5/2)*sqrt(1-2*x)-_ + 4270537963/409600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (281855505558x - 140927752779)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 6 5 4 3 +--R 248832000x + 1423526400x + 4002203520x + 8217694800x +--R + +--R 2 +--R 18987469764x - 58600061024x + 21368105901 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (2457600x - 1228800)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|5x + 3 +--R (1) ------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +r0:=1/3*(2+3*x)^3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+103884253/4096*_ + asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)-373/66*(2+3*x)^2*_ + (3+5*x)^(5/2)/sqrt(1-2*x)-9444023/33792*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-278043/7040*(3+5*x)^(5/2)*sqrt(1-2*x)-1/1760*_ + (3+5*x)^(5/2)*(31978+50205*x)*sqrt(1-2*x)-9444023/4096*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (623305518x - 311652759)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 1036800x + 5477760x + 15301008x + 40614996x - 129940960x +--R + +--R 47216961 +--R * +--R +--+ +------+ +--R \|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (24576x - 12288)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(2+3*x)^2*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +--R (225x + 570x + 541x + 228x + 36)\|5x + 3 +--R (1) -------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +r0:=49/66*(3+5*x)^(7/2)/(1-2*x)^(3/2)+272239/256*asin(sqrt(2/11)*_ + sqrt(3+5*x))*sqrt(5/2)-1183/363*(3+5*x)^(7/2)/sqrt(1-2*x)-_ + 123745/2112*(3+5*x)^(3/2)*sqrt(1-2*x)-24749/2904*(3+5*x)^(5/2)*_ + sqrt(1-2*x)-123745/256*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1633434x - 816717)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +-+ +------+ +--R (28800x + 146160x + 497868x - 1713440x + 617319)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (1536x - 768)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(2+3*x)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +--R (75x + 140x + 87x + 18)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +r0:=7/33*(3+5*x)^(7/2)/(1-2*x)^(3/2)+13145/64*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-239/66*(3+5*x)^(5/2)/sqrt(1-2*x)-5975/528*(3+5*x)^(3/2)*_ + sqrt(1-2*x)-5975/64*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (78870x - 39435)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +-+ +------+ +--R (3600x + 20820x - 84064x + 29601)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (384x - 192)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +r0:=1/3*(3+5*x)^(5/2)/(1-2*x)^(3/2)+275/8*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-25/6*(3+5*x)^(3/2)/sqrt(1-2*x)-125/8*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|2 \|5x + 3 +--R (1650x - 825)\|5 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +-+ +------+ +--R (300x - 1840x + 603)\|2 \|5x + 3 +--R / +--R +-+ +--------+ +--R (48x - 24)\|2 \|- 2x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) -------------------------------- +--R 3 2 +--------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +r0:=2/21*(3+5*x)^(5/2)/(1-2*x)^(3/2)+25/6*asin(sqrt(2/11)*sqrt(3+5*x))*_ + sqrt(5/2)-2/147*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/_ + sqrt(7)-76/147*(3+5*x)^(3/2)/sqrt(1-2*x)-185/98*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +-+ +--------+ \|7 \|5x + 3 +--R (- 8x + 4)\|2 \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +------+ +--R +-+ +-+ +--------+ \|2 \|5x + 3 +--R (2450x - 1225)\|5 \|7 \|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R +-+ +-+ +------+ +--R (- 3212x + 759)\|2 \|7 \|5x + 3 +--R / +--R +-+ +-+ +--------+ +--R (588x - 294)\|2 \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 127 + +--S 128 of 500 (residue poly has multiple non-linear factors) +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^2) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------- +--R 4 3 2 +--------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x))+55/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)-10/147*(3+5*x)^(3/2)/((2+3*x)*_ + sqrt(1-2*x))-5/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (990x + 165x - 330)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 3090x - 3070x - 657)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (6174x + 1029x - 2058)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 132 + +--S 133 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (15840x - 5280x - 6600x + 2640)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 2 +--------+ +------+ 3 2 +--R (346080x + 343840x + 73584)\|- 2x + 1 \|5x + 3 - 1048572x + 349524x +--R + +--R 436905x - 174762 +--R / +--R 3 2 +--R 1382976x - 460992x - 576240x + 230496 +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 880atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +-+ +--R 440atan(------------------------------------------------------) - 4161\|7 +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R / +--R +-+ +--R 5488\|7 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^3) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------- +--R 5 4 3 2 +--------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^2)-715/1372*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+8/21*(3+5*x)^(3/2)/((2+3*x)^2*_ + sqrt(1-2*x))+5/98*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-285/1372*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 3 2 +--------+ \|7 \|5x + 3 +--R (- 38610x - 32175x + 8580x + 8580)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (10260x + 1620x - 13627x - 6732)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (74088x + 61740x - 16464x - 16464)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 308880x - 102960x + 197340x + 34320x - 34320)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +------+ 4 +--R (- 574560x - 90720x + 763112x + 376992)\|- 2x + 1 \|5x + 3 - 8058204x +--R + +--R 3 2 +--R - 2686068x + 5148297x + 895356x - 895356 +--R / +--R 4 3 2 +--R 8297856x + 2765952x - 5301408x - 921984x + 921984 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 5720atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 2860atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R - 10659\|7 +--R / +--R +-+ +--R 10976\|7 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^4) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------------------ +--R 6 5 4 3 2 +--------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^3)+2585/19208*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+122/147*(3+5*x)^(3/2)/((2+3*x)^3*_ + sqrt(1-2*x))+17/147*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-2165/4116*_ + sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^2-15755/57624*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--------+ +--R (418770x + 628155x + 139590x - 155100x - 62040)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +------+ +--R (567180x + 552780x - 169221x - 304730x - 75888)\|7 \|5x + 3 +--R / +--R 4 3 2 +-+ +--------+ +--R (3111696x + 4667544x + 1037232x - 1152480x - 460992)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +-+ +--R (837540x + 837540x - 348975x - 449790x + 31020x + 62040)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--------+ +--R (- 7940520x - 7738920x + 2369094x + 4266220x + 1062432)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 5 4 3 2 +--R 28685664x + 28685664x - 11952360x - 15405264x + 1062432x + 2124864 +--R / +--R 5 4 3 2 +--R 87127488x + 87127488x - 36303120x - 46790688x + 3226944x + 6453888 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5170atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +-+ +--R 2585atan(------------------------------------------------) + 12648\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R / +--R +-+ +--R 38416\|7 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^5) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R ------------------------------------------------------------------------ +--R 7 6 5 4 3 2 +--------+ +--R (972x + 2268x + 1323x - 630x - 840x - 112x + 112x + 32)\|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^4)+547745/1075648*_ + atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+188/147*(3+5*x)^(3/2)/_ + ((2+3*x)^4*sqrt(1-2*x))+247/1372*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^4-_ + 2287/2744*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^3-24335/76832*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2-139745/1075648*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 5 4 3 2 +--R 266204070x + 576775485x + 354938760x - 39437640x - 105167040x +--R + +--R - 26291760 +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R 45277380x + 82071900x + 25673409x - 27318504x - 18627988x +--R + +--R - 2906640 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R / +--R 5 4 3 2 +--R 522764928x + 1132657344x + 697019904x - 77446656x - 206524416x +--R + +--R - 51631104 +--R * +--R +-+ +--------+ +--R \|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 3 2 +--R 1064816280x + 1774693800x + 266204070x - 867628080x - 341792880x +--R + +--R 105167040x + 52583520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R \|7 atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 5 4 3 2 +--R - 1267766640x - 2298013200x - 718855452x + 764918112x +--R + +--R 521583664x + 81385920 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 3 2 +--R - 2884113540x - 4806855900x - 721028385x + 2350018440x + 925764840x +--R + +--R - 284850720x - 142425360 +--R / +--R 6 5 4 3 +--R 29274835968x + 48791393280x + 7318708992x - 23853570048x +--R + +--R 2 +--R - 9396860928x + 2891341824x + 1445670912 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2190980atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R 1095490atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R - 423885\|7 +--R / +--R +-+ +--R 4302592\|7 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +r0:=8261577/6400*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+721/660*(2+3*x)^3*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-1/10*(2+3*x)^4*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 167363/14520*(2+3*x)^2*sqrt(3+5*x)/sqrt(1-2*x)-_ + 90052591/774400*sqrt(1-2*x)*sqrt(3+5*x)-3/193600*_ + (2561546+4177045*x)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (5997904902x - 2998952451)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (18817920x + 101146320x + 359461476x - 1261070176x + 452899509)\|10 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R +--+ +--------+ +--R (4646400x - 2323200)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +r0:=392283/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^2*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-3/20*(2+3*x)^3*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 7/29040*(76466+124737*x)*sqrt(3+5*x)/sqrt(1-2*x)-_ + 4282637/193600*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (284797458x - 142398729)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +------+ +--R (2352240x + 14544684x - 61036064x + 21305631)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (1161600x - 580800)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +r0:=1593/40*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-3/10*(2+3*x)^2*sqrt(3+5*x)/(1-2*x)^(3/2)-_ + 117929/14520*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--R (1156518x - 578259)\|- 2x + 1 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +------+ +--R (39204x - 261664x + 83301)\|10 \|5x + 3 +--R / +--R +--+ +--------+ +--R (29040x - 14520)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +r0:=9/2*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+49/66*_ + sqrt(3+5*x)/(1-2*x)^(3/2)-448/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|2 \|5x + 3 +--+ +------+ +--R (6534x - 3267)\|- 2x + 1 asin(-------------) + (- 1792x + 357)\|10 \|5x + 3 +--R +--+ +--R \|11 +--R ---------------------------------------------------------------------------- +--R +--+ +--------+ +--R (1452x - 726)\|10 \|- 2x + 1 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +r0:=7/33*sqrt(3+5*x)/(1-2*x)^(3/2)-29/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (- 58x - 48)\|5x + 3 +--R (2) ----------------------- +--R +--------+ +--R (726x - 363)\|- 2x + 1 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (58x + 48)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84 +--R (3) -------------------------------------------------- +--R 2 +--R 1452x - 1452x + 363 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 28 +--R (4) --- +--R 121 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 500 +t0:=1/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +r0:=2/33*sqrt(3+5*x)/(1-2*x)^(3/2)+20/363*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +--R (40x - 42)\|5x + 3 +--R (2) ----------------------- +--R +--------+ +--R (726x - 363)\|- 2x + 1 +--R Type: Expression(Integer) +--E 177 + +--S 178 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +------+ 2 +--R (- 40x + 42)\|- 2x + 1 \|5x + 3 + 336x - 336x + 84 +--R (3) ---------------------------------------------------- +--R 2 +--R 1452x - 1452x + 363 +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 28 +--R (4) --- +--R 121 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +r0:=18/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_ + sqrt(3+5*x)/(1-2*x)^(3/2)+676/17787*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +-+ +------+ +--R (13068x - 6534)\|- 2x + 1 atan(-------------) + (1352x - 984)\|7 \|5x + 3 +--R +--------+ +--R \|- 2x + 1 +--R -------------------------------------------------------------------------- +--R +-+ +--------+ +--R (35574x - 17787)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R (- 13068x + 13068x - 3267)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +--------+ +------+ 2 +--R (- 9464x + 6888)\|- 2x + 1 \|5x + 3 + 55104x - 55104x + 13776 +--R / +--R 2 +--R 498036x - 498036x + 124509 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 2178atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +-+ +--R - 1089atan(--------------------------------------------------) + 656\|7 +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R / +--R +-+ +--R 5929\|7 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +r0:=405/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+4/231*_ + sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x))+940/17787*sqrt(3+5*x)/_ + ((2+3*x)*sqrt(1-2*x))+2195/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ \|7 \|5x + 3 +--R (882090x + 147015x - 294030)\|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +------+ +--R (- 26340x + 39500x - 15321)\|7 \|5x + 3 +--R / +--R 2 +-+ +--------+ +--R (747054x + 124509x - 249018)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 187 + +--S 188 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 14113440x + 4704480x + 5880600x - 2352240)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 2 +--------+ +------+ 3 +--R (2950080x - 4424000x + 1715952)\|- 2x + 1 \|5x + 3 + 24452316x +--R + +--R 2 +--R - 8150772x - 10188465x + 4075386 +--R / +--R 3 2 +--R 167340096x - 55780032x - 69725040x + 27890016 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 784080atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 392040atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 97033\|7 +--R / +--R +-+ +--R 664048\|7 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +r0:=5805/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^2)+172/2541*_ + sqrt(3+5*x)/((2+3*x)^2*sqrt(1-2*x))+85/11858*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^2+57595/166012*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (37929870x + 31608225x - 8428860x - 8428860)\|- 2x + 1 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +------+ +--R (- 2073420x + 676860x + 945629x - 391476)\|7 \|5x + 3 +--R / +--R 3 2 +-+ +--------+ +--R (8964648x + 7470540x - 1992144x - 1992144)\|7 \|- 2x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +-+ +--R (- 303438960x - 101146320x + 193863780x + 33715440x - 33715440)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 3 2 +--------+ +------+ +--R (116111520x - 37904160x - 52955224x + 21922656)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 468596772x + 156198924x - 299381271x - 52066308x + 52066308 +--R / +--R 4 3 2 +--R 1004040576x + 334680192x - 641470368x - 111560064x + 111560064 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 5619240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 2809620atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 619837\|7 +--R / +--R +-+ +--R 1328096\|7 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^4*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +r0:=330255/19208*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^3)+1468/17787*_ + sqrt(3+5*x)/((2+3*x)^3*sqrt(1-2*x))-73/5929*sqrt(1-2*x)*_ + sqrt(3+5*x)/(2+3*x)^3+30535/166012*sqrt(1-2*x)*sqrt(3+5*x)/_ + (2+3*x)^2+3471145/2324168*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x) +--R +--R +--R (2) +--R 4 3 2 +--R (6473658510x + 9710487765x + 2157886170x - 2397651300x - 959060520) +--R * +--R +-+ +------+ +--R +--------+ \|7 \|5x + 3 +--R \|- 2x + 1 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (- 374883660x - 140350860x + 244982277x + 48873610x - 44829024)\|7 +--R * +--R +------+ +--R \|5x + 3 +--R / +--R 4 3 2 +-+ +--R (376515216x + 564772824x + 125505072x - 139450080x - 55780032)\|7 +--R * +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R - 12947317020x - 12947317020x + 5394715425x + 6953188770x +--R + +--R - 479530260x - 959060520 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 4 3 2 +--R (5248371240x + 1964912040x - 3429751878x - 684230540x + 627606336) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R 20122628148x + 20122628148x - 8384428395x - 10806596598x + 745282524x +--R + +--R 1490565048 +--R / +--R 5 4 3 2 +--R 10542426048x + 10542426048x - 4392677520x - 5661673248x + 390460224x +--R + +--R 780920448 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 79921710atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R - 39960855atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 8872411\|7 +--R / +--R +-+ +--R 4648336\|7 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +r0:=243189/1600*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1673/1320*(2+3*x)^3/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-3/20*(2+3*x)^4/((1-2*x)^(3/2)*_ + sqrt(3+5*x))-273749/29040*(2+3*x)^2/(sqrt(1-2*x)*sqrt(3+5*x))+_ + 270463/319440*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-28291441/2129600*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (1942107354x - 971053677)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (77623920x + 536898780x - 1790987404x - 525679641x + 435258129)\|10 +--R / +--R +--+ +--------+ +------+ +--R (12777600x - 6388800)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +r0:=4887/200*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+1183/660*(2+3*x)^2/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-3/10*(2+3*x)^3/((1-2*x)^(3/2)*_ + sqrt(3+5*x))-7/14520*(31106+53757*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 212417/798600*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (39027582x - 19513791)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (6468660x - 40488772x - 12657123x + 8379147)\|10 +--R / +--R +--+ +--------+ +------+ +--R (1597200x - 798600)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +r0:=27/10*asin(sqrt(2/11)*sqrt(3+5*x))/sqrt(10)+2/33*(2+3*x)^3/_ + ((1-2*x)^(3/2)*sqrt(3+5*x))-58/363*(2+3*x)^2/(sqrt(1-2*x)*_ + sqrt(3+5*x))+50/3993*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_ + 3103/13310*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|2 \|5x + 3 +--R (215622x - 107811)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 2 +--+ +--R (- 298852x - 124263x + 33087)\|10 +--R / +--R +--+ +--------+ +------+ +--R (79860x - 39930)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +r0:=49/66/((1-2*x)^(3/2)*sqrt(3+5*x))+(-1237/3630)/(sqrt(1-2*x)*_ + sqrt(3+5*x))-793/19965*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R - 1586x - 2880x - 1128 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (1586x + 2880x + 1128)\|- 2x + 1 \|5x + 3 + 13160x - 5264x - 4606x + 1974 +--R ----------------------------------------------------------------------------- +--R 3 2 +--R 79860x - 31944x - 27951x + 11979 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 658 +--R (4) ---- +--R 3993 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +r0:=(-2/55)/((1-2*x)^(3/2)*sqrt(3+5*x))+82/1815*sqrt(3+5*x)/(1-2*x)^(3/2)+_ + 164/3993*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +--R 1640x - 738x - 888 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 1640x + 738x + 888)\|- 2x + 1 \|5x + 3 + 14060x - 5624x - 4921x + 2109 +--R ----------------------------------------------------------------------------- +--R 3 2 +--R 79860x - 31944x - 27951x + 11979 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 703 +--R (4) ---- +--R 3993 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +r0:=2/33/((1-2*x)^(3/2)*sqrt(3+5*x))+40/363/(sqrt(1-2*x)*sqrt(3+5*x))-_ + 400/3993*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--R 1600x - 720x - 282 +--R (2) ---------------------------------- +--R +--------+ +------+ +--R (7986x - 3993)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--------+ +------+ 3 2 +--R (- 3200x + 1440x + 564)\|- 2x + 1 \|5x + 3 + 6580x - 2632x - 2303x + 987 +--R ---------------------------------------------------------------------------- +--R 3 2 +--R 159720x - 63888x - 55902x + 23958 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 329 +--R (4) ---- +--R 7986 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +r0:=-54/49*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*sqrt(3+5*x))+_ + 956/17787/(sqrt(1-2*x)*sqrt(3+5*x))-42230/195657*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R (- 431244x + 215622)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 2 +-+ +--R (168920x - 147888x + 28326)\|7 +--R / +--R +-+ +--------+ +------+ +--R (391314x - 195657)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +-+ +--R (- 4312440x + 1724976x + 1509354x - 646866)\|7 +--R * +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R 2 +--------+ +------+ 3 +--R (- 2364880x + 2070432x - 396564)\|- 2x + 1 \|5x + 3 + 4626580x +--R + +--R 2 +--R - 1850632x - 1619303x + 693987 +--R / +--R 3 2 +--R 54783960x - 21913584x - 19174386x + 8217594 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 431244atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 1232\|7 \|- 2x + 1 \|5x + 3 + (71373x + 38580)\|7 +--R - 215622atan(---------------------------------------------------) +--R +--------+ +------+ +--R 27006\|- 2x + 1 \|5x + 3 - 22792x - 12320 +--R + +--R +-+ +--R 33047\|7 +--R / +--R +-+ +--R 391314\|7 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +r0:=-3105/343*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*(2+3*x)*sqrt(3+5*x))+_ + 1220/17787/((2+3*x)*sqrt(1-2*x)*sqrt(3+5*x))-_ + 1840225/1369599*sqrt(1-2*x)/sqrt(3+5*x)+_ + 1915/41503*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (- 74389590x - 12398265x + 24796530)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|7 \|5x + 3 +--R atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (22082700x - 7613680x - 8760465x + 3499599)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (8217594x + 1369599x - 2739198)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 5951167200x - 1586977920x + 3669886440x + 495930600x - 595116720) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R \|7 atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R 3 2 +--------+ +--R (- 2473262400x + 852732160x + 981172080x - 391955088)\|- 2x + 1 +--R * +--R +------+ +--R \|5x + 3 +--R + +--R 4 3 2 +--R 9308933340x + 2482382224x - 5740508893x - 775744445x + 930893334 +--R / +--R 4 3 2 +--R 9203705280x + 2454321408x - 5675618256x - 766975440x + 920370528 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 198372240atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (242757x + 131220)\|7 +--R - 99186120atan(------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 - 592592x - 320320 +--R + +--R +-+ +--R 22164127\|7 +--R / +--R +-+ +--R 21913584\|7 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +r0:=-79515/1372*atan(sqrt(7)*sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+_ + 4/231/((1-2*x)^(3/2)*(2+3*x)^2*sqrt(3+5*x))+212/2541/((2+3*x)^2*_ + sqrt(1-2*x)*sqrt(3+5*x))-46307675/5478396*sqrt(1-2*x)/sqrt(3+5*x)+_ + 5/11858*sqrt(1-2*x)/((2+3*x)^2*sqrt(3+5*x))+_ + 89945/166012*sqrt(1-2*x)/((2+3*x)*sqrt(3+5*x)) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (- 5715061110x - 4762550925x + 1270013580x + 1270013580)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (1667076300x + 520073880x - 1053213025x - 169466391x + 178740084)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (98611128x + 82175940x - 21913584x - 21913584)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 285753055500x + 266702851800x - 125413841025x - 141289010775x +--R + +--R 12700135800x + 19050203700 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R \|7 atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R 4 3 2 +--R - 116695341000x - 36405171600x + 73724911750x + 11862647370x +--R + +--R - 12511805880 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 525495846960x - 490462790496x + 230634288388x + 259828502108x +--R + +--R - 23355370976x - 35033056464 +--R / +--R 5 4 3 2 +--R 69027789600x + 64425936960x - 30295529880x - 34130407080x +--R + +--R 3067901760x + 4601852640 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R 3175033950atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 70\|7 \|- 2x + 1 \|5x + 3 + (- 333x - 180)\|7 +--R 1587516975atan(-----------------------------------------------) +--R +--------+ +------+ +--R 126\|- 2x + 1 \|5x + 3 + 1295x + 700 +--R + +--R +-+ +--R - 417060196\|7 +--R / +--R +-+ +--R 54783960\|7 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(2+3*x)^6/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 6 5 4 3 2 +--R 729x + 2916x + 4860x + 4320x + 2160x + 576x + 64 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +r0:=1673/1320*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/20*(2+3*x)^5/_ + ((1-2*x)^(3/2)*(3+5*x)^(3/2))+753543/8000*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-89943/9680*(2+3*x)^3/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+1332779/1597200*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 9214471/17569200*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-_ + 964268137/117128000*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (330978691890x + 33097869189x - 99293607567)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 5 4 3 2 +--R 12807946800x + 97980793020x - 252342435560x - 274128335769x +--R + +--R 19932058554x + 44437106459 +--R * +--R +--+ +--R \|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (3513840000x + 351384000x - 1054152000)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(2+3*x)^5/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +--R 243x + 810x + 1080x + 720x + 240x + 32 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +r0:=1183/660*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))-3/10*(2+3*x)^4/_ + ((1-2*x)^(3/2)*(3+5*x)^(3/2))+2997/200*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-38003/4840*(2+3*x)^2/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+111719/159720*(2+3*x)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 3831323/8784600*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 2 +--------+ +------+ +--R (1316372310x + 131637231x - 394911693)\|- 2x + 1 \|5x + 3 +--R * +--R +-+ +------+ +--R \|2 \|5x + 3 +--R asin(-------------) +--R +--+ +--R \|11 +--R + +--R 4 3 2 +--+ +--R (213465780x - 1247811640x - 1260430251x + 19593966x + 168318961)\|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (87846000x + 8784600x - 26353800)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(2+3*x)^4/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +--R 81x + 216x + 216x + 96x + 16 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +r0:=2/33*(2+3*x)^4/((1-2*x)^(3/2)*(3+5*x)^(3/2))+81/50*asin(sqrt(2/11)*_ + sqrt(3+5*x))/sqrt(10)-18/121*(2+3*x)^3/((3+5*x)^(3/2)*_ + sqrt(1-2*x))+50/3993*(2+3*x)^2*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1058/219615*(2+3*x)*sqrt(1-2*x)/sqrt(3+5*x)-100159/732050*_ + sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ +------+ \|2 \|5x + 3 +--R (35577630x + 3557763x - 10673289)\|- 2x + 1 \|5x + 3 asin(-------------) +--R +--+ +--R \|11 +--R + +--R 3 2 +--+ +--R (- 49702040x - 51334383x - 7883562x + 3014813)\|10 +--R / +--R 2 +--+ +--------+ +------+ +--R (21961500x + 2196150x - 6588450)\|10 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(2+3*x)^3/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +--R 27x + 54x + 36x + 8 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +r0:=2/33*(2+3*x)^3/((1-2*x)^(3/2)*(3+5*x)^(3/2))+49/121/((3+5*x)^(3/2)*_ + sqrt(1-2*x))-3679/19965*sqrt(1-2*x)/(3+5*x)^(3/2)-8182/_ + 219615*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R - 39146x - 124464x - 104088x - 26080 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (352314x + 1120176x + 936792x + 234720)\|- 2x + 1 \|5x + 3 + 5216000x +--R + +--R 3 2 +--R 1043200x - 3077440x - 312960x + 469440 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 52160 +--R (4) ------ +--R 395307 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(2+3*x)^2/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--R 9x + 12x + 4 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +r0:=49/66/((1-2*x)^(3/2)*(3+5*x)^(3/2))+14/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 1649/7986*sqrt(1-2*x)/(3+5*x)^(3/2)-3298/43923*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 65960x + 9894x - 49200x - 18728 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ +--R (- 2968200x - 445230x + 2214000x + 842760)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 26219200x + 5243840x - 15469328x - 1573152x + 2359728 +--R / +--R 4 3 2 +--R 197653500x + 39530700x - 116615565x - 11859210x + 17788815 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 262192 +--R (4) ------- +--R 1976535 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +r0:=(-2/165)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+74/1815/((1-2*x)^(3/2)*_ + sqrt(3+5*x))+296/3993/(sqrt(1-2*x)*sqrt(3+5*x))-2960/43923*_ + sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 59200x + 8880x - 26418x - 5728 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (- 532800x - 79920x + 237762x + 51552)\|- 2x + 1 \|5x + 3 - 1145600x +--R + +--R 3 2 +--R - 229120x + 675904x + 68736x - 103104 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 11456 +--R (4) - ------ +--R 395307 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 500 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +r0:=2/33/((1-2*x)^(3/2)*(3+5*x)^(3/2))+20/121/((3+5*x)^(3/2)*sqrt(1-2*x))-_ + 400/3993*sqrt(1-2*x)/(3+5*x)^(3/2)-1600/43923*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 3 2 +--R 32000x + 4800x - 14280x - 722 +--R (2) ------------------------------------------------ +--R 2 +--------+ +------+ +--R (439230x + 43923x - 131769)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--------+ +------+ 4 +--R (- 288000x - 43200x + 128520x + 6498)\|- 2x + 1 \|5x + 3 + 144400x +--R + +--R 3 2 +--R 28880x - 85196x - 8664x + 12996 +--R / +--R 4 3 2 +--R 39530700x + 7906140x - 23323113x - 2371842x + 3557763 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 1444 +--R (4) ------ +--R 395307 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +r0:=4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2))+162/49*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+412/5929/((3+5*x)^(3/2)*_ + sqrt(1-2*x))-19130/195657*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1001590/2152227*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R +-+ +------+ +--R 2 +--------+ +------+ \|7 \|5x + 3 +--R (71155260x + 7115526x - 21346578)\|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 3 2 +-+ +--R (- 20031800x + 8854440x + 6468522x - 2981164)\|7 +--R / +--R 2 +-+ +--------+ +------+ +--R (21522270x + 2152227x - 6456681)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 2 +--R (- 3201986700x - 640397340x + 1889172153x + 192119202x - 288178803) +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R \|7 atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R 3 2 +--------+ +------+ +--R (1262003400x - 557829720x - 407516886x + 187813332)\|- 2x + 1 \|5x + 3 +--R + +--R 4 3 2 +--R 4173629600x + 834725920x - 2462441464x - 250417776x + 375626664 +--R / +--R 4 3 2 +--R 13559030100x + 2711806020x - 7999827759x - 813541806x + 1220312709 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 64039734atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (- 2109x - 1140)\|7 +--R - 32019867atan(--------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 + 2849x + 1540 +--R + +--R +-+ +--R 5962328\|7 +--R / +--R +-+ +--R 19370043\|7 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^2*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)*(3+5*x)^(3/2))+14985/343*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+500/5929/((2+3*x)*(3+5*x)^(3/2)*_ + sqrt(1-2*x))-985525/1369599*sqrt(1-2*x)/(3+5*x)^(3/2)+_ + 1635/41503*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 95783075/15065589*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 3 2 +--------+ +--R (19745584650x + 15138281565x - 4607303085x - 3949116930)\|- 2x + 1 +--R * +--R +-+ +------+ +--R +------+ \|7 \|5x + 3 +--R \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 4 3 2 +-+ +--R (- 5746984500x - 1402439900x + 3498236655x + 429626520x - 555141781)\|7 +--R / +--R 3 2 +-+ +--------+ +------+ +--R (451967670x + 346508547x - 105459123x - 90393534)\|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 +--R 1777102618500x + 1540155602700x - 811543529115x - 805619853720x +--R + +--R 88855130925x + 106626157110 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R \|7 atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R 4 3 2 +--R 724120047000x + 176707427400x - 440777818530x - 54132941520x +--R + +--R 69947864406 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 5 4 3 2 +--R - 2331595480200x - 2020716082840x + 1064761935958x + 1056989951024x +--R + +--R - 116579774010x - 139895728812 +--R / +--R 5 4 3 2 +--R 569479264200x + 493548695640x - 260062197318x - 258163933104x +--R + +--R 28473963210x + 34168755852 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 11847350790atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R +-+ +--------+ +------+ +-+ +--R 154\|7 \|- 2x + 1 \|5x + 3 + (2109x + 1140)\|7 +--R 5923675395atan(------------------------------------------------) +--R +--------+ +------+ +--R 798\|- 2x + 1 \|5x + 3 - 2849x - 1540 +--R + +--R +-+ +--R - 1110283562\|7 +--R / +--R +-+ +--R 271180602\|7 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^3*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72) +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^2*(3+5*x)^(3/2))+538245/1372*atan(sqrt(7)*_ + sqrt(3+5*x)/sqrt(1-2*x))/sqrt(7)+12/121/((2+3*x)^2*(3+5*x)^(3/2)*_ + sqrt(1-2*x))-34551425/5478396*sqrt(1-2*x)/(3+5*x)^(3/2)-_ + 75/11858*sqrt(1-2*x)/((2+3*x)^2*(3+5*x)^(3/2))+_ + 122295/166012*sqrt(1-2*x)/((2+3*x)*(3+5*x)^(3/2))+_ + 3443814775/60262356*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R (2) +--R 4 3 2 +--R 2127720162150x + 3049732232415x + 591033378375x - 756522724320x +--R + +--R - 283696021620 +--R * +--R +-+ +------+ +--R +--------+ +------+ \|7 \|5x + 3 +--R \|- 2x + 1 \|5x + 3 atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R 5 4 3 2 +--R - 619886659500x - 564878517900x + 276089438305x + 297937101390x +--R + +--R - 28838387211x - 39900939556 +--R * +--R +-+ +--R \|7 +--R / +--R 4 3 2 +--R (5423612040x + 7773843924x + 1506558900x - 1928395392x - 723148272) +--R * +--R +-+ +--------+ +------+ +--R \|7 \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 500 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 5 4 +--R - 765979258374000x - 1174501529506800x - 92768599069740x +--R + +--R 3 2 +--R 580442060234520x + 193196990723220x - 71491397448240x +--R + +--R - 30639170334960 +--R * +--R +-+ +--------+ +------+ +-+ +--R +-+ 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R \|7 atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R 5 4 3 +--R 312422876388000x + 284698773021600x - 139149076905720x +--R + +--R 2 +--R - 150160299100560x + 14534547154344x + 20110073536224 +--R * +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R + +--R 6 5 4 +--R 1194035616213300x + 1830854611527060x + 144610980185833x +--R + +--R 3 2 +--R - 904813655841634x - 301162316533799x + 111443324179908x + 47761424648532 +--R / +--R 6 5 4 3 +--R 27335004681600x + 41913673845120x + 3310572789216x - 20713859103168x +--R + +--R 2 +--R - 6894495625248x + 2551267103616x + 1093400187264 +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 500 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +------+ +--R \|7 \|5x + 3 +--R - 1702176129720atan(-------------) +--R +--------+ +--R \|- 2x + 1 +--R + +--R - +--R 851088064860 +--R * +--R +-+ +--------+ +------+ +-+ +--R 32032\|7 \|- 2x + 1 \|5x + 3 + (- 242757x - 131220)\|7 +--R atan(--------------------------------------------------------) +--R +--------+ +------+ +--R 91854\|- 2x + 1 \|5x + 3 + 592592x + 320320 +--R + +--R +-+ +--R 189529462891\|7 +--R / +--R +-+ +--R 4338889632\|7 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 500 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=167647/101250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2911577/50625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),_ +-- 33/35)/sqrt(35)-23/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)+2/45*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 1244/13125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 175111/236250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=796/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 55019/2250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/35*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-27/875*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-823/2625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=-1159/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 259/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/25*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-31/225*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=-37/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=-74/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-74/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 40/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/9*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+74/63*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=148/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4636/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/15*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+74/315*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+4636/2205*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=6368/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 220076/3087*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+74/735*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+3184/5145*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+220076/36015*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=21713939/3341250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1508889271/6682500*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 23/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+2/55*(2+3*x)^(5/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)-342971/866250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-543/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 11346991/3898125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=153319/60750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5327983/60750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/45*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1208/7875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 3/175*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 160297/141750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=2129/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 148831/4050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-31/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2/35*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-2252/4725*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-974/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 119/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 41/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=362/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 49/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/3*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+40/27*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1150/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/9*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 214/189*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=1252/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 8314/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/15*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-214/945*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+8314/6615*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=17156/27783*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 475592/27783*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_ +-- 214/2205*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8578/46305*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+475592/324135*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(11/2) +--R +--R +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=664744/583443*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 22738708/583443*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/27*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 214/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+8842/138915*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+332372/972405*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+22738708/6806835*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=472506679/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-16416987253/17374500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-23/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)+2/65*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 1865989/1126125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 564731/2252250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2014/53625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 493825477/40540500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=222527/22275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 30926081/89100*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/55*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 7031/11550*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 177/1925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 3/275*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 465127/103950*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=28109/7290*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 488149/3645*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-223/945*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 31/945*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+2/45*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-29357/17010*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=134/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 9013/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-1/7*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 131/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=-3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/3*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+4/3*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=-2209/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2960/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/9*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 118/63*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+2470/567*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-13834/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 31588/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-118/315*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 2/15*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-12758/6615*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=32176/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 173482/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-118/735*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-4282/15435*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+173482/108045*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=1136636/1750329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-27198452/1750329*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-118/1323*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-2/27*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-12934/138915*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+568318/2917215*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+27198452/20420505*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=38834192/44925111*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1305025844/44925111*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-118/2079*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(9/2)-2/33*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(11/2)-13022/305613*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(7/2)+627806/10696455*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+19417096/74875185*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+1305025844/524126295*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(a+b*x)^(1/2)/((c+d*x)^(1/2)*(e+f*x)^(1/2)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) -------------------- +--R +-------+ +-------+ +--R \|d x + c \|f x + e +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=2*elliptic_e(asin(sqrt(f)*sqrt(c+d*x)/sqrt(-d*e+c*f)),-b*(d*e-c*f)/_ +-- ((b*c-a*d)*f))*sqrt(-d*e+c*f)*sqrt(a+b*x)*sqrt(d*(e+f*x)/_ +-- (d*e-c*f))/(d*sqrt(f)*sqrt(-d*(a+b*x)/(b*c-a*d))*sqrt(e+f*x)) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +--R +--R +--R (2) tpdhere +--R Type: Variable(tpdhere) +)clear all + +--S 436 of 500 +t0:=(a+b*x)^(1/2)/((c+d*x)^(3/2)*(e+f*x)^(1/2)) +--R +--R +--R +-------+ +--R \|b x + a +--R (1) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|d x + c \|f x + e +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-2*sqrt(a+b*x)*sqrt(e+f*x)/((d*e-c*f)*sqrt(c+d*x))+_ +-- 2*elliptic_e(asin(sqrt(d)*sqrt(a+b*x)/sqrt(-b*c+a*d)),_ +-- (b*c-a*d)*f/(d*(b*e-a*f)))*sqrt(-b*c+a*d)*sqrt(b*(c+d*x)/_ +-- (b*c-a*d))*sqrt(e+f*x)/((d*e-c*f)*sqrt(d)*sqrt(c+d*x)*_ +-- sqrt(b*(e+f*x)/(b*e-a*f))) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=859/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 61151/3750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-23/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2/35*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-859/4375*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=7/125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 146/125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 9/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) -------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=-31/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------ +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=-2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_ +-- 2*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=-136/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 136/21*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=184/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 6388/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+92/35*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+6388/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=226/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_ +-- sqrt(11/3)-203179/18750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(2+3*x)^(7/2)*sqrt(1-2*x)/_ +-- sqrt(3+5*x)+183/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 48/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2486/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-1409/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-91/1875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 36/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+13/625*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-19/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-56/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 8/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) -------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=4/5*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/5*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3r.input.pamphlet b/src/input/rich3r.input.pamphlet new file mode 100644 index 0000000..e83adb6 --- /dev/null +++ b/src/input/rich3r.input.pamphlet @@ -0,0 +1,3527 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3r.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 0 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3r.output +)spool rich3r.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +--r0:=-4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-20*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +--r0:=556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-80/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 92/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2780/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +--r0:=-3352/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 116464/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 416/105*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 19268/245*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 116464/147*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +--r0:=12601/103125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1473539/206250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/15*(2+3*x)^(9/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-118/165*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 5153/48125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 958/1925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 12601/240625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +--r0:=-47342/103125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-19033/103125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/15*(2+3*x)^(7/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-458/825*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 2818/6875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2719/34375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +--r0:=-169/4125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 3206/4125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 326/825*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 458/1375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +--r0:=458/825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1358/825*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/15*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 194/825*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R (1) ------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +--r0:=62/165*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/165*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/15*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-_ +-- 62/165*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=sqrt(1-2*x)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +--r0:=-136/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+28/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 136/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +--r0:=536/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 532/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-40/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+2660/33*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +--r0:=-36968/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5320/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+416/21*_ +-- sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-2780/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+184840/231*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=sqrt(1-2*x)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R \|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +--r0:=296816/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-10312712/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 556/105*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 116044/735*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 155104/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 10312712/1617*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+17427983/16706250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 604915631/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+1103/259875*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ +-- 178/7425*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 124891/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 18177329/38981250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (- 6x - x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +--r0:=2/45*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+83093/151875*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5684677/303750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+62/1575*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 347/39375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 84134/354375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +------+ +--R (1) (- 2x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +--r0:=4289/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 118898/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/35*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 194/2625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2657/23625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +--r0:=-4157/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+4382/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+214/675*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +--r0:=494/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1610/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)-16/27*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=724/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 98/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 2/9*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+82/27*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +--r0:=68/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/15*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 82/135*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+3896/945*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +--r0:=17032/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-595324/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/21*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 82/315*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+8516/6615*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+595324/46305*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(11/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +--r0:=1226552/83349*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-42623864/83349*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/27*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(9/2)+82/567*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(7/2)+13136/19845*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+613276/138915*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+42623864/972405*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (- 90x - 129x - 25x + 32x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+_ +-- 371279941/108590625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-51601293223/434362500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+601/160875*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+178/10725*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-11725073/56306250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-18034/625625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 776112041/506756250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 30x - 23x + 7x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +--r0:=2/55*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+5199979/3341250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 90397364/1670625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+62/2475*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 40703/433125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 23/9625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 5442127/7796250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (- 10x - x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +--r0:=70226/91125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4971289/182250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/45*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 839/23625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 194/4725*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 76163/212625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +--r0:=-31/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 29933/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 74/525*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1847/4725*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +--r0:=-2209/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+4144/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_ +-- 8/15*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+494/135*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_ +-- 8774/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 592/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+74/9*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 1150/81*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------ +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_ +-- 1184/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 4418/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+74/45*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_ +-- 988/945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_ +-- 124/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 119732/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+74/105*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-_ +-- 3632/6615*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 119732/46305*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_ +-- 561808/250047*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-19885156/250047*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/189*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-8252/19845*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+280904/416745*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+19885156/2917215*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 10x - x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_ +-- 41599832/6417873*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1446357824/6417873*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/297*(3+5*x)^(3/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-12872/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 442076/1528065*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 20799916/10696455*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 1446357824/74875185*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +------+ +------+ +--R (- 450x - 915x - 512x + 85x + 156x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +--r0:=2/75*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(7/2)+_ +-- 48128081531/3909262500*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-836091184171/1954631250*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2503/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)+_ +-- 178/14625*(2+3*x)^(5/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 380132617/506756250*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 57509209/506756250*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 199721/12065625*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 50299451003/9121612500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (- 150x - 205x - 34x + 51x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +--r0:=2/65*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 134992031/26061750*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-9380126059/52123500*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 62/3575*(2+3*x)^(3/2)*(3+5*x)^(7/2)*sqrt(1-2*x)-_ +-- 2133359/6756750*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 160084/3378375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 67/160875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 70536439/30405375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (- 50x - 35x + 12x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +--r0:=2810993/1202850*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-97540001/1202850*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2/55*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(2+3*x)-22576/155925*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2377/155925*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 194/7425*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2930159/2806650*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +--r0:=14101/10935*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 886499/21870*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 499/2835*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 46/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 11908/25515*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=-835/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2894/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)+_ +-- 202/63*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 32/63*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1061/567*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +--r0:=-2/9*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)-_ +-- 9587/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+21206/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+362/27*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 614/27*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+2632/243*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-_ +-- 47422/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+116854/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+362/135*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)+_ +-- 9808/945*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)-_ +-- 43214/1701*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) --------------------------------------------- +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +--r0:=-2/21*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_ +-- 290204/11907*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-962678/11907*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2108/6615*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+362/315*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+249448/138915*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 192 + +--S 193 of 500 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +--r0:=-2/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_ +-- 600868/750141*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-17830424/750141*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-1864/6615*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+362/567*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-558524/1250235*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+17830424/8751645*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 197 + +--S 198 of 500 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +--r0:=-2/33*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_ +-- 91496584/57760857*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-3316711588/57760857*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-13292/43659*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)+362/891*(3+5*x)^(5/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-1366496/4584195*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)+45748292/96268095*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+3316711588/673876665*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (- 50x - 35x + 12x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +--r0:=-2/39*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 7046965448/1752079329*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-245282464136/1752079329*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-20992/81081*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(9/2)+362/1287*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(11/2)-2174468/11918907*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(7/2)+73596464/417161745*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+3523482724/2920132215*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+245282464136/20440925505*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +--r0:=87476/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6515539/506250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+2/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x)+403/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 178/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/590625*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +--r0:=487/5625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 46159/5625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/35*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_ +-- 62/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/13125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +--r0:=-2797/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-2828/3375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/25*(1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)+194/1125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------- +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +--r0:=272/135*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1442/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-4/45*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +--r0:=-74/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 56/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +--r0:=116/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 124/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/3*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 128/9*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +--r0:=512/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 268/45*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+17804/315*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*sqrt(3+5*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +--r0:=36136/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1255552/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 136/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18068/735*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+1255552/5145*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +--r0:=12601/84375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1473539/168750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(7/2)/_ +-- sqrt(3+5*x)+5153/39375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 958/1575*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-8/45*(2+3*x)^(7/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-12601/196875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=-2719/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 47342/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/5*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_ +-- 2818/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 32/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 2719/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-169/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-3206/1875*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/5*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-24/125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 458/625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=458/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1358/225*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-_ +-- 16/75*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +--r0:=62/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2*(1-2*x)^(3/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=136/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 28/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +--r0:=-536/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 532/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 268/9*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-2660/9*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 282 + +--S 283 of 500 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +--r0:=-1064/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 36968/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 136/15*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+6116/35*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-36968/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 287 + +--S 288 of 500 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 500 +--m0:=a0-r0 +--E 289 + +--S 290 of 500 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +--r0:=-296816/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 10312712/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_ +-- 548/105*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+12276/245*_ +-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+1706144/1715*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-10312712/1029*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 292 + +--S 293 of 500 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 500 +--m0:=a0-r0 +--E 294 + +--S 295 of 500 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (- 54x - 81x - 18x + 20x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_ +-- 4801/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 25643/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-6*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 3872/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 622/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4801/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (- 18x - 15x + 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) -------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)+_ +-- 1973/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-15848/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-106/25*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 1558/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+2264/3125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (- 6x - x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=-2/15*(1-2*x)^(3/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)+_ +-- 496/375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-1246/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-62/25*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 178/125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R +--------+ +------+ +--R (- 2x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------ +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=38/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 112/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-_ +-- 18/25*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(1-2*x)^(3/2)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=-148/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 28/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/3*(1-2*x)^(3/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+48/5*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-556/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 112/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+556/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=2/3*(1-2*x)^(3/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 1096/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1088/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 136/3*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-300*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+5440/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=(1-2*x)^(3/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R +--------+ +--R (- 2x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=2/5*(1-2*x)^(3/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 8672/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 301304/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+548/45*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 111884/315*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 16616/7*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 301304/21*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=62/2145*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_ +-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)+_ +-- 67138787/72393750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1163388067/36196875*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+32717/1126125*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+34/2475*(2+3*x)^(5/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)-445024/9384375*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-69808931/168918750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=106/2475*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)+2/55*(1-2*x)^(5/2)*_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)+4854274/8353125*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 326256461/16706250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2866/86625*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+_ +-- 38729/2165625*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 4738087/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +------+ +--R (1) (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=284159/455625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6799613/455625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+326/4725*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 2/45*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 10214/118125*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 110717/1063125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=16088/3375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 86741/3375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 118/525*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)+2/21*(1-2*x)^(5/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+4282/7875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=31588/2025*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-96838/2025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)-_ +-- 8/15*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-1076/675*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2) +--E 361 + +--S 362 of 500 +--r0:=-4418/243*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+8288/243*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 10/3*(1-2*x)^(3/2)*sqrt(3+5*x)/sqrt(2+3*x)+196/81*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 362 + +--S 363 of 500 +--Ra0:=integrate(t0,x) +--R +--R +--R (1) t0 x +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 500 +--Rm0:=a0-r0 +--R +--R +--R (2) t0 x - r0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 500 +--Rd0:=D(m0,x) +--R +--R +--R (3) t0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=-12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+2/3*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+8*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=-36052/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5360/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/21*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+2/7*_ +-- (1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+524/189*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+36052/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(11/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=-7810384/35721*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+1124360/35721*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/27*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 10/63*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+832/567*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+112436/11907*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+7810384/83349*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(13/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=-247408648/305613*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+35604320/305613*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(11/2)+10/99*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 1900/2079*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 76492/14553*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 3560432/101871*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 247408648/713097*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +------+ +--R (1) (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=62/2925*(1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)+2/75*(1-2*x)^(5/2)*_ +-- (2+3*x)^(5/2)*(3+5*x)^(5/2)+25385346787/9773156250*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1764163292393/19546312500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+142391/7239375*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+3698/482625*(2+3*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-400516993/2533781250*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-569519/28153125*(3+5*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-13267820528/11402015625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=106/3575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_ +-- 2/65*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)+_ +-- 880870681/651543750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-30660308017/651543750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+8318/482625*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-6794792/84459375*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+25603/1876875*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 923943703/1520268750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +------+ +--R (1) (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=11437073/15035625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-829177897/30071250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/7425*(1-2*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(2+3*x)+2/55*(1-2*x)^(5/2)*(3+5*x)^(5/2)*_ +-- sqrt(2+3*x)-78797/3898125*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+30362/779625*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 12996374/35083125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=-150217/273375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-4457606/273375*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+362/2835*(1-2*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x)+2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)+_ +-- 14318/70875*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 429479/637875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=145102/6075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 481339/6075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(3/2)/sqrt(2+3*x)-_ +-- 32/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)-_ +-- 2108/1575*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 124724/14175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)+116854/3645*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 331954/3645*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+230/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/sqrt(2+3*x)+_ +-- 788/135*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-43214/1215*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)+_ +-- 46/27*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(3/2)-_ +-- 19174/729*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+42412/729*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-316/27*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+5264/243*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ------------------------------------------ +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)+_ +-- 46/63*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(5/2)-_ +-- 11576/1701*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-16700/1701*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+608/189*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 4244/3969*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)+_ +-- 230/567*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(7/2)-_ +-- 3545996/107163*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+564040/107163*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+1532/567*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-104036/35721*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+3545996/250047*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)+_ +-- 230/891*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(9/2)-_ +-- 780320008/8251551*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+112439720/8251551*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+12280/6237*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-325796/130977*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+11243972/2750517*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+780320008/19253619*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(3/2)/(2+3*x)^(13/2)+_ +-- 230/1287*(1-2*x)^(3/2)*(3+5*x)^(3/2)/(2+3*x)^(11/2)-_ +-- 75041008472/250297047*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+10799362480/250297047*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1300/891*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 3347620/1702701*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 23210828/11918907*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 1079936248/83432349*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 75041008472/584026443*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2) +--R +--R +--R (1) +--R 5 4 3 2 +--------+ +------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=106/4875*(1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 2/75*(1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(7/2)+_ +-- 11371367372/2931946875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1580201444291/11727787500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+8038/804375*(2+3*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(1-2*x)-359748241/1520268750*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-26534891/760134375*(3+5*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+364267/36196875*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 23763809947/13682418750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +------+ +--R (1) (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=469049629/234555750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-8120161139/117277875*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/10725*(1-2*x)^(3/2)*(3+5*x)^(7/2)*_ +-- sqrt(2+3*x)+2/65*(1-2*x)^(5/2)*(3+5*x)^(7/2)*sqrt(2+3*x)-_ +-- 3872003/30405375*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 121031/30405375*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 2314/111375*(3+5*x)^(7/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 486785077/547296750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=2617892/1804275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-146222113/3608550*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+74/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(2+3*x)+2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)-_ +-- 146963/467775*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 9698/93555*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1654421/4209975*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R +------+ +--R (3x + 2)\|3x + 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=-291227/32805*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-25111/32805*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-2/3*(1-2*x)^(5/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_ +-- 40/81*(1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)+_ +-- 64628/8505*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 2108/1701*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 310399/76545*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=-2/9*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_ +-- 153452/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-452399/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+370/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/sqrt(2+3*x)-_ +-- 31298/567*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 5260/567*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 135334/5103*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)+_ +-- 74/27*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(3/2)+_ +-- 136028/2187*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-374366/2187*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-6464/81*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+_ +-- 11036/81*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 48478/729*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=-2/21*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)+_ +-- 74/63*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(5/2)-904798/15309*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 1534520/15309*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1844/567*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-_ +-- 62596/3969*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+_ +-- 1353340/35721*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=-2/27*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)+_ +-- 370/567*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(7/2)-_ +-- 100444/321489*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-5824540/321489*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-13316/35721*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+2776/1701*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-1241596/750141*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-2/33*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)+_ +-- 370/891*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(9/2)-_ +-- 584888452/24754653*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+104715680/24754653*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-55772/43659*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+36980/18711*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-17089252/8251551*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+584888452/57760857*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2) +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 7 6 5 4 3 2 +--R (2187x + 10206x + 20412x + 22680x + 15120x + 6048x + 1344x + 128) +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-2/39*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 370/1287*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(11/2)-_ +-- 129922578224/2252673423*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+18761985160/2252673423*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2622980/1702701*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+_ +-- 60080/34749*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-_ +-- 54281308/35756721*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 1876198516/750891141*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 129922578224/5256237987*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(17/2) +--R +--R +--R (1) +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R / +--R 8 7 6 5 4 3 2 +--R 6561x + 34992x + 81648x + 108864x + 90720x + 48384x + 16128x +--R + +--R 3072x + 256 +--R * +--R +------+ +--R \|3x + 2 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=-2/45*(1-2*x)^(5/2)*(3+5*x)^(5/2)/(2+3*x)^(15/2)+_ +-- 74/351*(1-2*x)^(3/2)*(3+5*x)^(5/2)/(2+3*x)^(13/2)+_ +-- 363883755904/15768713961*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-12641611554328/15768713961*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 1085156/729729*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_ +-- 16636/11583*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_ +-- 112817764/107270163*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 3914701972/3754455705*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 181941877952/26281189935*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 12641611554328/183968329545*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/sqrt(3+5*x) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=2865161/8353125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-231061879/16706250*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+62/1485*(1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x)+2/55*(1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_ +-- 181333/3898125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4258/155925*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2865161/19490625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3s.input.pamphlet b/src/input/rich3s.input.pamphlet new file mode 100644 index 0000000..41adf97 --- /dev/null +++ b/src/input/rich3s.input.pamphlet @@ -0,0 +1,3401 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3s.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 100 integrals in this file. +\item 100 supplied "optimal results". +\item 0 matching answers. +\item 0 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3s.output +)spool rich3s.output +)set message test on +)set message auto off +)clear all + +--S 1 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/sqrt(3+5*x) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 500 +--r0:=-21547/759375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-8024546/759375*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+106/1575*(1-2*x)^(3/2)*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x)+2/45*(1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)+_ +-- 8878/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 21547/1771875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 2 + +--S 3 of 500 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 500 +--m0:=a0-r0 +--E 4 + +--S 5 of 500 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 500 +--r0:=-101902/50625*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-408311/50625*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+326/2625*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+2/35*(1-2*x)^(5/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)+30922/118125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 7 + +--S 8 of 500 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 500 +--m0:=a0-r0 +--E 9 + +--S 10 of 500 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 500 +t0:=(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------- +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 500 +--r0:=53194/10125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-246694/10125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-4/75*(1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x)-1088/3375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 12 + +--S 13 of 500 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 500 +--m0:=a0-r0 +--E 14 + +--S 15 of 500 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 500 +--r0:=-8314/405*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 8764/405*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)*sqrt(3+5*x)/sqrt(2+3*x)+4/3*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)+428/135*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 17 + +--S 18 of 500 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 500 +--m0:=a0-r0 +--E 19 + +--S 20 of 500 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------- +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 500 +--r0:=-3896/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 476/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(3/2)+40/3*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/sqrt(2+3*x)+232/27*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 22 + +--S 23 of 500 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 500 +--m0:=a0-r0 +--E 24 + +--S 25 of 500 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------- +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 500 +--r0:=-16564/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 3352/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/5*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(5/2)+52/9*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+3412/27*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 27 + +--S 28 of 500 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 500 +--m0:=a0-r0 +--E 29 + +--S 30 of 500 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) --------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 500 +--r0:=-703480/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 101240/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(1-2*x)^(5/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+80/21*(1-2*x)^(3/2)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+10580/189*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+703480/1323*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 32 + +--S 33 of 500 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 500 +--m0:=a0-r0 +--E 34 + +--S 35 of 500 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*sqrt(3+5*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 500 +--r0:=-66055016/11907*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+9505840/11907*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(9/2)+20/7*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 7148/189*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 950584/3969*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 66055016/27783*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 37 + +--S 38 of 500 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 500 +--m0:=a0-r0 +--E 39 + +--S 40 of 500 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(13/2)*sqrt(3+5*x)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R ------------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 500 +--r0:=-23204503328/916839*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+3339309520/916839*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(1-2*x)^(5/2)*sqrt(3+5*x)/_ +-- (2+3*x)^(11/2)+680/297*(1-2*x)^(3/2)*sqrt(3+5*x)/(2+3*x)^(9/2)+_ +-- 180020/6237*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)+_ +-- 7173272/43659*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 333930952/305613*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 23204503328/2139291*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 42 + +--S 43 of 500 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 500 +--m0:=a0-r0 +--E 44 + +--S 45 of 500 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 500 +--r0:=703672/13921875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-264260033/27843750*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(7/2)/_ +-- sqrt(3+5*x)-48/275*(1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)+_ +-- 2020841/6496875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 346636/259875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 2972/7425*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 703672/32484375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 47 + +--S 48 of 500 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 500 +--m0:=a0-r0 +--E 49 + +--S 50 of 500 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 500 +--r0:=-196499/253125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-1509007/253125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(5/2)/_ +-- sqrt(3+5*x)-8/45*(1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)+_ +-- 167228/118125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 1972/4725*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 196499/590625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 52 + +--S 53 of 500 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 500 +--m0:=a0-r0 +--E 54 + +--S 55 of 500 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 500 +--r0:=-106772/28125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+53279/28125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-2/5*(1-2*x)^(5/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-32/175*(1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)-_ +-- 1972/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 106772/65625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 57 + +--S 58 of 500 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 500 +--m0:=a0-r0 +--E 59 + +--S 60 of 500 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R +------+ +--R (5x + 3)\|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 500 +--r0:=81164/16875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 218414/16875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/5*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-_ +-- 24/125*(1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)-_ +-- 3028/5625*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 62 + +--S 63 of 500 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 500 +--m0:=a0-r0 +--E 64 + +--S 65 of 500 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 500 +t0:=(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) -------------------------- +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 500 +--r0:=5594/675*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 5656/675*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2*(1-2*x)^(5/2)*sqrt(2+3*x)/sqrt(3+5*x)-4/5*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)*sqrt(3+5*x)-388/225*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 67 + +--S 68 of 500 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 500 +--m0:=a0-r0 +--E 69 + +--S 70 of 500 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 500 +--r0:=4636/45*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1036/45*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)/(sqrt(2+3*x)*sqrt(3+5*x))-44*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)-272/15*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 500 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 500 +--m0:=a0-r0 +--E 74 + +--S 75 of 500 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------ +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 500 +--r0:=17804/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 3584/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*sqrt(3+5*x))+260/9*(1-2*x)^(3/2)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-5764/9*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 77 + +--S 78 of 500 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 500 +--m0:=a0-r0 +--E 79 + +--S 80 of 500 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 500 +--r0:=105584/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 21272/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*sqrt(3+5*x))+80/9*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(3/2)*sqrt(3+5*x))+10636/27*sqrt(1-2*x)/(sqrt(2+3*x)*_ +-- sqrt(3+5*x))-105584/27*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 82 + +--S 83 of 500 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 500 +--m0:=a0-r0 +--E 84 + +--S 85 of 500 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (405x + 1323x + 1728x + 1128x + 368x + 48)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 500 +--r0:=1959032/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 281920/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+36/7*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(5/2)*sqrt(3+5*x))+7204/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_ +-- sqrt(3+5*x))+324104/147*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 9795160/441*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 87 + +--S 88 of 500 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 500 +--m0:=a0-r0 +--E 89 + +--S 90 of 500 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(11/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R -------------------------------------------------------------------------- +--R 6 5 4 3 2 +------+ +------+ +--R (1215x + 4779x + 7830x + 6840x + 3360x + 880x + 96)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 500 +--r0:=683150096/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-98310640/3969*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/9*(1-2*x)^(5/2)/((2+3*x)^(9/2)*_ +-- sqrt(3+5*x))+680/189*(1-2*x)^(3/2)/((2+3*x)^(7/2)*sqrt(3+5*x))+_ +-- 36284/567*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 813208/1323*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 113020952/9261*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 3415750480/27783*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 92 + +--S 93 of 500 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 500 +--m0:=a0-r0 +--E 94 + +--S 95 of 500 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(5/2) +--R +--R +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(7/2)/(3+5*x)^(3/2)-_ +-- 500501/421875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1065118/421875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-442/75*(1-2*x)^(3/2)*(2+3*x)^(7/2)/sqrt(3+5*x)+_ +-- 373022/196875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 59662/7875*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 524/225*(2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 500501/984375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 97 + +--S 98 of 500 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 500 +--m0:=a0-r0 +--E 99 + +--S 100 of 500 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(5/2) +--R +--R +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R (1) ------------------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(5/2)/(3+5*x)^(3/2)-_ +-- 33778/9375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 49321/9375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 62/15*(1-2*x)^(3/2)*(2+3*x)^(5/2)/sqrt(3+5*x)+_ +-- 22866/4375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 284/175*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 33778/21875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 102 + +--S 103 of 500 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 500 +--m0:=a0-r0 +--E 104 + +--S 105 of 500 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 500 +t0:=(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(5/2) +--R +--R +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R (1) ----------------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 500 +--r0:=-2/15*(1-2*x)^(5/2)*(2+3*x)^(3/2)/(3+5*x)^(3/2)-_ +-- 6902/3125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*_ +-- sqrt(3/11)+9206/3125*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)-178/75*(1-2*x)^(3/2)*(2+3*x)^(3/2)/_ +-- sqrt(3+5*x)-572/625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 8874/3125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 107 + +--S 108 of 500 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 500 +--m0:=a0-r0 +--E 109 + +--S 110 of 500 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 500 +t0:=(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(5/2) +--R +--R +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R (1) ---------------------------------- +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 500 +--r0:=338/1125*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 6412/1125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/15*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)-46/75*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)-76/375*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 112 + +--S 113 of 500 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 500 +--m0:=a0-r0 +--E 114 + +--S 115 of 500 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 500 +t0:=(1-2*x)^(5/2)/((3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------- +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 500 +--r0:=28/25*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 584/25*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2/3*(1-2*x)^(5/2)*sqrt(2+3*x)/(3+5*x)^(3/2)+152/15*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(3+5*x)+104/25*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 500 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 500 +--m0:=a0-r0 +--E 119 + +--S 120 of 500 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ------------------------------------------- +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 500 +--r0:=-6388/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1288/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2*(1-2*x)^(5/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-88/3*(1-2*x)^(3/2)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+2068/5*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 122 + +--S 123 of 500 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 500 +--m0:=a0-r0 +--E 124 + +--S 125 of 500 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ----------------------------------------------------- +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 500 +--r0:=2/3*(1-2*x)^(5/2)/((2+3*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 36968/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7448/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 400/9*(1-2*x)^(3/2)/((3+5*x)^(3/2)*sqrt(2+3*x))-5852/9*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+36968/9*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 127 + +--S 128 of 500 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 500 +--m0:=a0-r0 +--E 129 + +--S 130 of 500 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 500 +--r0:=2/5*(1-2*x)^(5/2)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+12*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(3/2)*(3+5*x)^(3/2))-96808/3*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)+19504/3*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2420/3*sqrt(1-2*x)/((3+5*x)^(3/2)*_ +-- sqrt(2+3*x))-16016/3*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 96808/3*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 132 + +--S 133 of 500 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 500 +--m0:=a0-r0 +--E 134 + +--S 135 of 500 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 500 +t0:=(1-2*x)^(5/2)/((2+3*x)^(9/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R / +--R 6 5 4 3 2 +------+ +--R (2025x + 7830x + 12609x + 10824x + 5224x + 1344x + 144)\|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 500 +--r0:=2/7*(1-2*x)^(5/2)/((2+3*x)^(7/2)*(3+5*x)^(3/2))+136/21*(1-2*x)^(3/2)/_ +-- ((2+3*x)^(5/2)*(3+5*x)^(3/2))-2234208/7*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+321520/7*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+12188/63*sqrt(1-2*x)/((2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2))+2488904/441*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 5544440/147*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+11171040/49*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 137 + +--S 138 of 500 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 500 +--m0:=a0-r0 +--E 139 + +--S 140 of 500 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 500 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R (1) --------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 500 +--r0:=1613/250*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 56041/250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 104/175*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-1/7*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-4839/1750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 142 + +--S 143 of 500 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 500 +--m0:=a0-r0 +--E 144 + +--S 145 of 500 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 500 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 500 +--r0:=-1597/150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 161/75*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-23/25*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 147 + +--S 148 of 500 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 500 +--m0:=a0-r0 +--E 149 + +--S 150 of 500 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 500 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) ------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 500 +--r0:=-34/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/3*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 152 + +--S 153 of 500 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 500 +--m0:=a0-r0 +--E 154 + +--S 155 of 500 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 500 +t0:=sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 500 +--r0:=-elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3) +--E 157 + +--S 158 of 500 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 500 +--m0:=a0-r0 +--E 159 + +--S 160 of 500 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 500 +--r0:=2/3*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)-2/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 162 + +--S 163 of 500 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 500 +--m0:=a0-r0 +--E 164 + +--S 165 of 500 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 500 +--r0:=-62/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+62/147*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 167 + +--S 168 of 500 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 500 +--m0:=a0-r0 +--E 169 + +--S 170 of 500 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 500 +t0:=sqrt(3+5*x)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 500 +--r0:=4/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 584/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+18/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+1752/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 172 + +--S 173 of 500 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 500 +--m0:=a0-r0 +--E 174 + +--S 175 of 500 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------ +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 500 +--r0:=317384/10125*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 44109377/40500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-137/315*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-_ +-- 1/9*(2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-9547/5250*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-663409/47250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 500 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 500 +--m0:=a0-r0 +--E 179 + +--S 180 of 500 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 500 +--r0:=4517/450*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 78472/225*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 1/7*(2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)-102/175*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-4721/1050*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 182 + +--S 183 of 500 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 500 +--m0:=a0-r0 +--E 184 + +--S 185 of 500 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 500 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x) +--R +--R +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 500 +--r0:=-4451/270*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 448/135*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-67/45*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 187 + +--S 188 of 500 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 500 +--m0:=a0-r0 +--E 189 + +--S 190 of 500 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 500 +t0:=(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 500 +--r0:=29/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 31/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 5/9*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 192 + +--S 193 of 500 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 500 +--m0:=a0-r0 +--E 194 + +--S 195 of 500 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 500 +--r0:=-37/9*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/7*(3+5*x)^(3/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 197 + +--S 198 of 500 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 500 +--m0:=a0-r0 +--E 199 + +--S 200 of 500 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 500 +--r0:=272/189*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1030/189*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-202/441*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 500 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 500 +--m0:=a0-r0 +--E 204 + +--S 205 of 500 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 500 +--r0:=-808/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5594/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/35*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-194/2205*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+5594/15435*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 500 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 500 +--m0:=a0-r0 +--E 209 + +--S 210 of 500 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 500 +t0:=(3+5*x)^(3/2)/((2+3*x)^(9/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 500 +--r0:=1948/21609*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 184636/21609*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 2/49*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-62/1715*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+974/36015*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+184636/252105*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 212 + +--S 213 of 500 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 500 +--m0:=a0-r0 +--E 214 + +--S 215 of 500 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 500 +--r0:=8787401429/17374500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-610627101631/34749000*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-14303/12870*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-41/143*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1/13*(2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-138809831/4504500*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-221673/50050*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-2295970088/10135125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 500 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 500 +--m0:=a0-r0 +--E 219 + +--S 220 of 500 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 500 +--r0:=41741369/267300*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-725140729/133650*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)-34/99*(2+3*x)^(3/2)*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)-1/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 329683/34650*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1053/770*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 43624697/623700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 500 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 500 +--m0:=a0-r0 +--E 224 + +--S 225 of 500 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x) +--R +--R +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 500 +--r0:=118823/2430*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 8256877/4860*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-1/9*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-_ +-- 1877/630*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-3/7*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-62092/2835*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 227 + +--S 228 of 500 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 500 +--m0:=a0-r0 +--E 229 + +--S 230 of 500 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 500 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x) +--R +--R +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R +--------+ +--R \|- 2x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 500 +--r0:=-17587/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2531/162*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 20/21*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-1/7*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-2645/378*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 232 + +--S 233 of 500 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 500 +--m0:=a0-r0 +--E 234 + +--S 235 of 500 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 500 +t0:=(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 500 +--r0:=-4141/162*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 419/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/3*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-62/27*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 237 + +--S 238 of 500 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 500 +--m0:=a0-r0 +--E 239 + +--S 240 of 500 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 500 +--r0:=-974/81*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 85/81*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/7*(3+5*x)^(5/2)*sqrt(1-2*x)/sqrt(2+3*x)+10/21*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-205/189*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 242 + +--S 243 of 500 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 500 +--m0:=a0-r0 +--E 244 + +--S 245 of 500 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------- +--R 2 +--------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 500 +--r0:=-4157/567*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 3130/567*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/21*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-38/49*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(2+3*x)+2060/1323*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 247 + +--S 248 of 500 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 500 +--m0:=a0-r0 +--E 249 + +--S 250 of 500 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 500 +--r0:=-35242/3969*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 53194/3969*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 334/2205*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(3/2)-2/35*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)-34154/46305*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 252 + +--S 253 of 500 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 500 +--m0:=a0-r0 +--E 254 + +--S 255 of 500 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(9/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 500 +--r0:=-203804/194481*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 816622/194481*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 326/5145*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(5/2)-2/49*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(7/2)-30922/324135*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+816622/2268945*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 257 + +--S 258 of 500 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 500 +--m0:=a0-r0 +--E 259 + +--S 260 of 500 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(11/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 500 +--r0:=-86188/4084101*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 32098184/4084101*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-106/3087*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)-_ +-- 2/63*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(9/2)-8878/324135*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-43094/6806835*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+32098184/47647845*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 262 + +--S 263 of 500 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 500 +--m0:=a0-r0 +--E 264 + +--S 265 of 500 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 500 +t0:=(3+5*x)^(5/2)/((2+3*x)^(13/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R --------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 500 +--r0:=-924247516/314475777*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+114606440/314475777*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-310/14553*(3+5*x)^(3/2)*sqrt(1-2*x)/_ +-- (2+3*x)^(9/2)-2/77*(3+5*x)^(5/2)*sqrt(1-2*x)/(2+3*x)^(11/2)-_ +-- 21290/2139291*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_ +-- 362666/14975037*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 11460644/104825259*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 924247516/733776813*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 267 + +--S 268 of 500 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 500 +--m0:=a0-r0 +--E 269 + +--S 270 of 500 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 500 +t0:=(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 500 +--r0:=15553/3750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 270248/1875*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 333/875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-3/35*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-15553/8750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 500 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 500 +--m0:=a0-r0 +--E 274 + +--S 275 of 500 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 500 +t0:=(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ------------------------ +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 500 +--r0:=-5161/750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 518/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 3/25*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-74/125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 277 + +--S 278 of 500 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 500 +--m0:=a0-r0 +--E 279 + +--S 280 of 500 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 500 +t0:=(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 500 +--r0:=-37/15*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 7/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 1/5*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 282 + +--S 283 of 500 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 500 +--m0:=a0-r0 +--E 284 + +--S 285 of 500 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 500 +t0:=sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) -------------------- +--R +--------+ +------+ +--R \|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 500 +--r0:=-elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5) +--E 287 + +--S 288 of 500 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 500 +--m0:=a0-r0 +--E 289 + +--S 290 of 500 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 500 +t0:=1/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ----------------------------- +--R +--------+ +------+ +------+ +--R \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 500 +--r0:=-2*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33) +--E 292 + +--S 293 of 500 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 500 +--m0:=a0-r0 +--E 294 + +--S 295 of 500 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 500 +t0:=1/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +------+ +------+ +--R (3x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 500 +--r0:=-2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 6/7*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 297 + +--S 298 of 500 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 500 +--m0:=a0-r0 +--E 299 + +--S 300 of 500 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 500 +t0:=1/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (9x + 12x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 500 +--r0:=-148/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 20/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+148/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 302 + +--S 303 of 500 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 500 +--m0:=a0-r0 +--E 304 + +--S 305 of 500 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 500 +t0:=1/((2+3*x)^(7/2)*sqrt(1-2*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (27x + 54x + 36x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 500 +--r0:=592/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 20644/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 6/35*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+296/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+20644/1715*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 307 + +--S 308 of 500 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 500 +--m0:=a0-r0 +--E 309 + +--S 310 of 500 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 500 +t0:=(2+3*x)^(7/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 500 +--r0:=-61151/13750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+6013/6875*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/11*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 69/1375*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+6/55*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-2577/6875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 312 + +--S 313 of 500 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 500 +--m0:=a0-r0 +--E 314 + +--S 315 of 500 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 500 +t0:=(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 500 +--r0:=21/275*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 438/275*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2/11*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-27/275*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 317 + +--S 318 of 500 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 500 +--m0:=a0-r0 +--E 319 + +--S 320 of 500 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 500 +t0:=(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 500 +--r0:=-31/55*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/11*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+6/55*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 322 + +--S 323 of 500 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 500 +--m0:=a0-r0 +--E 324 + +--S 325 of 500 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 500 +t0:=sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (5x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 500 +--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(7/5)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)-2/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 327 + +--S 328 of 500 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 500 +--m0:=a0-r0 +--E 329 + +--S 330 of 500 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 500 +t0:=1/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +------+ +------+ +--R (5x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 500 +--r0:=2*elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 10/11*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 332 + +--S 333 of 500 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 500 +--m0:=a0-r0 +--E 334 + +--S 335 of 500 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 500 +t0:=1/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (15x + 19x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 500 +--r0:=136/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 6/7*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-680/77*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 337 + +--S 338 of 500 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 500 +--m0:=a0-r0 +--E 339 + +--S 340 of 500 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 500 +t0:=1/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (45x + 87x + 56x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 500 +--r0:=6388/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 920/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+288/49*sqrt(1-2*x)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-31940/539*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 342 + +--S 343 of 500 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 500 +--m0:=a0-r0 +--E 344 + +--S 345 of 500 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 500 +t0:=1/((2+3*x)^(7/2)*(3+5*x)^(3/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 500 +--r0:=-12904/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 1344984/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+436/245*sqrt(1-2*x)/_ +-- ((2+3*x)^(3/2)*sqrt(3+5*x))+60684/1715*sqrt(1-2*x)/(sqrt(2+3*x)*_ +-- sqrt(3+5*x))-1344984/3773*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 347 + +--S 348 of 500 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 500 +--m0:=a0-r0 +--E 349 + +--S 350 of 500 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 500 +t0:=(2+3*x)^(9/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 500 +--r0:=-6515539/2268750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+612332/1134375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-2/33*(2+3*x)^(9/2)*sqrt(1-2*x)/_ +-- (3+5*x)^(3/2)-602/1815*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 403/75625*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+668/3025*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-87476/378125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 500 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 500 +--m0:=a0-r0 +--E 354 + +--S 355 of 500 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 500 +t0:=(2+3*x)^(7/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 500 +--r0:=-46159/45375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+3409/45375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-2/33*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 94/363*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+536/3025*_ +-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-487/15125*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 357 + +--S 358 of 500 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 500 +--m0:=a0-r0 +--E 359 + +--S 360 of 500 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 500 +t0:=(2+3*x)^(5/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 500 +--r0:=-2797/9075*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2828/9075*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-338/1815*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+404/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 362 + +--S 363 of 500 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 500 +--m0:=a0-r0 +--E 364 + +--S 365 of 500 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 500 +t0:=(2+3*x)^(3/2)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 500 +--r0:=272/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1442/1815*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-206/1815*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 367 + +--S 368 of 500 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 500 +--m0:=a0-r0 +--E 369 + +--S 370 of 500 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 500 +t0:=sqrt(2+3*x)/((3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ------------------------------------ +--R 2 +--------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 500 +--r0:=74/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 56/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 2/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-74/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 372 + +--S 373 of 500 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 500 +--m0:=a0-r0 +--E 374 + +--S 375 of 500 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 500 +t0:=1/((3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) --------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (25x + 30x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 500 +--r0:=116/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 124/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 10/33*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+620/363*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 377 + +--S 378 of 500 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 500 +--m0:=a0-r0 +--E 379 + +--S 380 of 500 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 500 +t0:=1/((2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------ +--R 3 2 +--------+ +------+ +------+ +--R (75x + 140x + 87x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 500 +--r0:=-17804/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2560/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 6/7*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-1340/231*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+89020/2541*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 382 + +--S 383 of 500 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 500 +--m0:=a0-r0 +--E 384 + +--S 385 of 500 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 500 +t0:=1/((2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 500 +--r0:=-1255552/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+180680/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/7*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 428/49*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 94420/1617*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 6277760/17787*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 387 + +--S 388 of 500 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 500 +--m0:=a0-r0 +--E 389 + +--S 390 of 500 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 500 +t0:=1/((2+3*x)^(7/2)*(3+5*x)^(5/2)*sqrt(1-2*x)) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 500 +--r0:=10156288/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 352875016/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+6/35*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 576/245*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 120324/1715*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 5307272/11319*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 352875016/124509*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 392 + +--S 393 of 500 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 500 +--m0:=a0-r0 +--E 394 + +--S 395 of 500 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 500 +t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 500 +--r0:=-2663/375*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(11/3)+_ +-- 4071079/1500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+2517/350*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+12/7*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 29293/875*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 500 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 500 +--m0:=a0-r0 +--E 399 + +--S 400 of 500 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 500 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 9x - 12x - 4)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 500 +--r0:=7279/75*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2933/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+9/5*(2+3*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)+419/50*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 500 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 500 +--m0:=a0-r0 +--E 404 + +--S 405 of 500 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 500 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R (- 3x - 2)\|3x + 2 \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 500 +--r0:=139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 14/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+2*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 407 + +--S 408 of 500 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 500 +--m0:=a0-r0 +--E 409 + +--S 410 of 500 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 500 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) - ------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 500 +--r0:=-elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 412 + +--S 413 of 500 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 500 +--m0:=a0-r0 +--E 414 + +--S 415 of 500 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 500 +--r0:=elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2/7*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 417 + +--S 418 of 500 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 500 +--m0:=a0-r0 +--E 419 + +--S 420 of 500 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 500 +--r0:=4/7*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 10/7*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))-12/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 422 + +--S 423 of 500 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 500 +--m0:=a0-r0 +--E 424 + +--S 425 of 500 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 500 +--r0:=-38/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 80/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-8/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+38/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 427 + +--S 428 of 500 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 500 +--m0:=a0-r0 +--E 429 + +--S 430 of 500 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 500 +t0:=sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) - -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 500 +--r0:=-52/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 5636/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-36/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-26/1715*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+5636/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 432 + +--S 433 of 500 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 500 +--m0:=a0-r0 +--E 434 + +--S 435 of 500 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (- 135x - 351x - 342x - 148x - 24)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 500 +--r0:=-6478333/13500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 112543103/6750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+1397/210*_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x)+5/3*(2+3*x)^(5/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+24358/875*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+6770629/31500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 437 + +--S 438 of 500 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 500 +--m0:=a0-r0 +--E 439 + +--S 440 of 500 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 45x - 87x - 56x - 12)\|3x + 2 \|5x + 3 +--R (1) -------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 500 +--r0:=-18551/150*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1289089/300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+12/7*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)+2511/350*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+9694/175*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 442 + +--S 443 of 500 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 500 +--m0:=a0-r0 +--E 444 + +--S 445 of 500 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 15x - 19x - 6)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 500 +--r0:=4621/30*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 931/30*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)+9/5*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+139/10*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 447 + +--S 448 of 500 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 500 +--m0:=a0-r0 +--E 449 + +--S 450 of 500 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 500 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2) +--R +--R +--R +------+ +------+ +--R (- 5x - 3)\|3x + 2 \|5x + 3 +--R (1) ---------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 500 +--r0:=-67/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 133/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- (3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+10/3*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 452 + +--S 453 of 500 +--a0:=integrate(t0,x) +--E 453 + +--S 454 of 500 +--m0:=a0-r0 +--E 454 + +--S 455 of 500 +--d0:=D(m0,x) +--E 455 + +)clear all + +--S 456 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 500 +--r0:=34/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 5/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 457 + +--S 458 of 500 +--a0:=integrate(t0,x) +--E 458 + +--S 459 of 500 +--m0:=a0-r0 +--E 459 + +--S 460 of 500 +--d0:=D(m0,x) +--E 460 + +)clear all + +--S 461 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 500 +--r0:=31/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 462 + +--S 463 of 500 +--a0:=integrate(t0,x) +--E 463 + +--S 464 of 500 +--m0:=a0-r0 +--E 464 + +--S 465 of 500 +--d0:=D(m0,x) +--E 465 + +)clear all + +--S 466 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 500 +--r0:=458/441*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 970/441*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-458/1029*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 467 + +--S 468 of 500 +--a0:=integrate(t0,x) +--E 468 + +--S 469 of 500 +--m0:=a0-r0 +--E 469 + +--S 470 of 500 +--d0:=D(m0,x) +--E 470 + +)clear all + +--S 471 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 500 +--r0:=-916/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 338/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-458/1715*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+338/12005*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 472 + +--S 473 of 500 +--a0:=integrate(t0,x) +--E 473 + +--S 474 of 500 +--m0:=a0-r0 +--E 474 + +--S 475 of 500 +--d0:=D(m0,x) +--E 475 + +)clear all + +--S 476 of 500 +t0:=(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)) +--R +--R +--R +------+ +--R (- 5x - 3)\|5x + 3 +--R (1) ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 500 +--r0:=-10876/50421*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 189368/50421*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+16/343*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-2818/12005*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)-5438/84035*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+189368/588245*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 477 + +--S 478 of 500 +--a0:=integrate(t0,x) +--E 478 + +--S 479 of 500 +--m0:=a0-r0 +--E 479 + +--S 480 of 500 +--d0:=D(m0,x) +--E 480 + +)clear all + +--S 481 of 500 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (- 675x - 2160x - 2763x - 1766x - 564x - 72)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 500 +--r0:=-128715331/44550*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+17888580643/178200*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+(2+3*x)^(7/2)*(3+5*x)^(5/2)/_ +-- sqrt(1-2*x)+419/66*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+_ +-- 18/11*(2+3*x)^(5/2)*(3+5*x)^(5/2)*sqrt(1-2*x)+4066493/23100*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)+9741/385*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+269045681/207900*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 482 + +--S 483 of 500 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 500 +--m0:=a0-r0 +--E 484 + +--S 485 of 500 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 500 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (- 225x - 570x - 541x - 228x - 36)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 500 +--r0:=-1228883/1620*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 42696881/1620*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+5/3*(2+3*x)^(3/2)*_ +-- (3+5*x)^(5/2)*sqrt(1-2*x)+4853/105*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+93/14*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 1284329/3780*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 487 + +--S 488 of 500 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 500 +--m0:=a0-r0 +--E 489 + +--S 490 of 500 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 500 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2) +--R +--R +--R 3 2 +------+ +------+ +--R (- 75x - 140x - 87x - 18)\|3x + 2 \|5x + 3 +--R (1) --------------------------------------------- +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 500 +--r0:=-1762/9*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 244879/36*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- (2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)+167/14*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+12/7*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)+_ +-- 3683/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 492 + +--S 493 of 500 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 500 +--m0:=a0-r0 +--E 494 + +--S 495 of 500 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 500 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2) +--R +--R +--R 2 +------+ +------+ +--R (- 25x - 30x - 9)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------ +--R +--------+ +--R (2x - 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 500 +--r0:=6599/27*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 2659/54*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- (3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+3*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)+397/18*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 497 + +--S 498 of 500 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 500 +--m0:=a0-r0 +--E 499 + +--S 500 of 500 +--d0:=D(m0,x) +--E 500 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich3t.input.pamphlet b/src/input/rich3t.input.pamphlet new file mode 100644 index 0000000..8134e56 --- /dev/null +++ b/src/input/rich3t.input.pamphlet @@ -0,0 +1,5009 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich3t.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|(a+b x)^m (c+d)^n (e+f x)^p| +There are: +\begin{itemize} +\item 119 integrals in this file. +\item 119 supplied "optimal results". +\item 7 matching answers. +\item 3 cases where Axiom's result differs from Rubi +\item 1 case where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 100 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich3t.output +)spool rich3t.output +)set message test on +)set message auto off +)clear all + +--S 1 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 597 +--r0:=4451/54*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 320/27*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)+5/7*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)+335/63*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 2 + +--S 3 of 597 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 597 +--m0:=a0-r0 +--E 4 + +--S 5 of 597 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 597 +--r0:=1159/63*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 185/63*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)/(sqrt(1-2*x)*sqrt(2+3*x))+4/49*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(2+3*x)+155/147*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 7 + +--S 8 of 597 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 597 +--m0:=a0-r0 +--E 9 + +--S 10 of 597 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 597 +--r0:=2797/1323*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2020/1323*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+8/147*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(3/2)+598/3087*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 12 + +--S 13 of 597 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 597 +--m0:=a0-r0 +--E 14 + +--S 15 of 597 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 597 +--r0:=-31202/9261*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 81164/9261*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/7*(3+5*x)^(5/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+12/245*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)/(2+3*x)^(5/2)+1514/15435*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)-81164/108045*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 17 + +--S 18 of 597 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 597 +--m0:=a0-r0 +--E 19 + +--S 20 of 597 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(9/2)) +--R +--R +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R (1) ------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (162x + 351x + 216x - 24x - 64x - 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 597 +--r0:=-213544/151263*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+106558/151263*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+2/7*(3+5*x)^(5/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_ +-- 16/343*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(7/2)+986/12005*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-106772/252105*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-106558/1764735*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 22 + +--S 23 of 597 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 597 +--m0:=a0-r0 +--E 24 + +--S 25 of 597 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(11/2)) +--R +--R +--R (1) +--R 2 +------+ +--R (- 25x - 30x - 9)\|5x + 3 +--R ------------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (486x + 1377x + 1350x + 360x - 240x - 176x - 32)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 597 +--r0:=-6036028/9529569*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-3929980/9529569*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/7*(3+5*x)^(5/2)/((2+3*x)^(9/2)*_ +-- sqrt(1-2*x))+20/441*(3+5*x)^(3/2)*sqrt(1-2*x)/(2+3*x)^(9/2)+_ +-- 4930/64827*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-167228/453789*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-392998/3176523*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+6036028/22235661*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 27 + +--S 28 of 597 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 597 +--m0:=a0-r0 +--E 29 + +--S 30 of 597 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ---------------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 597 +--r0:=-11291/2750*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 168123/2750*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2/11*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)+_ +-- 312/275*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+3/11*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+14517/2750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 32 + +--S 33 of 597 +--a0:=integrate(t0,x) +--E 33 + +--S 34 of 597 +--m0:=a0-r0 +--E 34 + +--S 35 of 597 +--d0:=D(m0,x) +--E 35 + +)clear all + +--S 36 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 36 + +--S 37 of 597 +--r0:=1597/110*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 161/55*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)+69/55*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 37 + +--S 38 of 597 +--a0:=integrate(t0,x) +--E 38 + +--S 39 of 597 +--m0:=a0-r0 +--E 39 + +--S 40 of 597 +--d0:=D(m0,x) +--E 40 + +)clear all + +--S 41 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 597 +--r0:=34/11*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 7/11*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)+3/11*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 42 + +--S 43 of 597 +--a0:=integrate(t0,x) +--E 43 + +--S 44 of 597 +--m0:=a0-r0 +--E 44 + +--S 45 of 597 +--d0:=D(m0,x) +--E 45 + +)clear all + +--S 46 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ---------------------------- +--R +--------+ +------+ +--R (2x - 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 597 +--r0:=elliptic_e(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 2/11*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 47 + +--S 48 of 597 +--a0:=integrate(t0,x) +--E 48 + +--S 49 of 597 +--m0:=a0-r0 +--E 49 + +--S 50 of 597 +--d0:=D(m0,x) +--E 50 + +)clear all + +--S 51 of 597 +t0:=1/((1-2*x)^(3/2)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------- +--R +--------+ +------+ +------+ +--R (2x - 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 597 +--r0:=2/11*elliptic_e(asin(sqrt(5)*sqrt(2+3*x)),2/35)*sqrt(5/7)*_ +-- sqrt(-3-5*x)/sqrt(3+5*x)+4/77*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 52 + +--S 53 of 597 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 597 +--m0:=a0-r0 +--E 54 + +--S 55 of 597 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------ +--R 2 +--------+ +------+ +------+ +--R (6x + x - 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 597 +--r0:=-62/77*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/77*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+186/539*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 57 + +--S 58 of 597 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 597 +--m0:=a0-r0 +--E 59 + +--S 60 of 597 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (18x + 15x - 4x - 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 597 +--r0:=60/539*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 1752/539*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 4/77*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+54/539*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+5256/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 62 + +--S 63 of 597 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 597 +--m0:=a0-r0 +--E 64 + +--S 65 of 597 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (54x + 81x + 18x - 20x - 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 597 +--r0:=6872/3773*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 244604/3773*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 4/77*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))+138/2695*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(5/2)+10308/18865*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(3/2)+733812/132055*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 67 + +--S 68 of 597 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 597 +--m0:=a0-r0 +--E 69 + +--S 70 of 597 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2 +--R (1) -------------------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 597 +--r0:=2911577/75625*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-1173529/151250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/(sqrt(1-2*x)*_ +-- sqrt(3+5*x))-4/121*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 10851/15125*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+111/605*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+502941/151250*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 72 + +--S 73 of 597 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 597 +--m0:=a0-r0 +--E 74 + +--S 75 of 597 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 597 +--r0:=55019/6050*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 5572/3025*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(5/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*(2+3*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)+2388/3025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 77 + +--S 78 of 597 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 597 +--m0:=a0-r0 +--E 79 + +--S 80 of 597 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 597 +--r0:=1159/605*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 259/605*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))-4/121*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/sqrt(3+5*x)+111/605*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 82 + +--S 83 of 597 +--a0:=integrate(t0,x) +--E 83 + +--S 84 of 597 +--m0:=a0-r0 +--E 84 + +--S 85 of 597 +--d0:=D(m0,x) +--E 85 + +)clear all + +--S 86 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 597 +--r0:=37/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 28/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 4/121*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 87 + +--S 88 of 597 +--a0:=integrate(t0,x) +--E 88 + +--S 89 of 597 +--m0:=a0-r0 +--E 89 + +--S 90 of 597 +--d0:=D(m0,x) +--E 90 + +)clear all + +--S 91 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ---------------------------------- +--R 2 +--------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 597 +--r0:=-74/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/11*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-20/121*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 92 + +--S 93 of 597 +--a0:=integrate(t0,x) +--E 93 + +--S 94 of 597 +--m0:=a0-r0 +--E 94 + +--S 95 of 597 +--d0:=D(m0,x) +--E 95 + +)clear all + +--S 96 of 597 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) - ------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (10x + x - 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 597 +--r0:=74/121*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 40/121*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 370/847*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 97 + +--S 98 of 597 +--a0:=integrate(t0,x) +--E 98 + +--S 99 of 597 +--m0:=a0-r0 +--E 99 + +--S 100 of 597 +--d0:=D(m0,x) +--E 100 + +)clear all + +--S 101 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - --------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (30x + 23x - 7x - 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 597 +--r0:=4636/847*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 740/847*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+186/539*_ +-- sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-23180/5929*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 102 + +--S 103 of 597 +--a0:=integrate(t0,x) +--E 103 + +--S 104 of 597 +--m0:=a0-r0 +--E 104 + +--S 105 of 597 +--d0:=D(m0,x) +--E 105 + +)clear all + +--S 106 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (90x + 129x + 25x - 32x - 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 597 +--r0:=220076/5929*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 31840/5929*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+54/539*_ +-- sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+9876/3773*sqrt(1-2*x)/_ +-- (sqrt(2+3*x)*sqrt(3+5*x))-1100380/41503*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 107 + +--S 108 of 597 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 597 +--m0:=a0-r0 +--E 109 + +--S 110 of 597 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R - ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (270x + 567x + 333x - 46x - 100x - 24)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 597 +--r0:=-1341176/41503*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+46585232/41503*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 14928/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 2101332/132055*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 46585232/290521*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 112 + +--S 113 of 597 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 597 +--m0:=a0-r0 +--E 114 + +--S 115 of 597 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (- 243x - 810x - 1080x - 720x - 240x - 32)\|3x + 2 +--R (1) ------------------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 597 +--r0:=604915631/24956250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-121995881/24956250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(11/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 1022/19965*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)+_ +-- 380188/831875*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 4553/33275*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)+_ +-- 17427983/8318750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 117 + +--S 118 of 597 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 597 +--m0:=a0-r0 +--E 119 + +--S 120 of 597 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +------+ +--R (- 81x - 216x - 216x - 96x - 16)\|3x + 2 +--R (1) -------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 597 +--r0:=5684677/998250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-581651/499125*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 178/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)+4421/33275*_ +-- (2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)+83093/166375*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 122 + +--S 123 of 597 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 597 +--m0:=a0-r0 +--E 124 + +--S 125 of 597 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +------+ +--R (- 27x - 54x - 36x - 8)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 597 +--r0:=118898/99825*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-30023/99825*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/11*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))-8/363*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-_ +-- 758/19965*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)+4289/33275*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 127 + +--S 128 of 597 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 597 +--m0:=a0-r0 +--E 129 + +--S 130 of 597 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (- 9x - 12x - 4)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 597 +--r0:=4157/19965*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 4382/19965*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)/(3+5*x)^(3/2)-626/19965*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 132 + +--S 133 of 597 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 597 +--m0:=a0-r0 +--E 134 + +--S 135 of 597 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R (- 3x - 2)\|3x + 2 +--R (1) ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 597 +--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)-_ +-- 1610/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/11*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-8/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-494/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 137 + +--S 138 of 597 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 597 +--m0:=a0-r0 +--E 139 + +--S 140 of 597 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) - ------------------------------------------- +--R 3 2 +--------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 597 +--r0:=-724/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 98/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/11*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-40/363*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-490/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 142 + +--S 143 of 597 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 597 +--m0:=a0-r0 +--E 144 + +--S 145 of 597 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 597 +t0:=1/((1-2*x)^(3/2)*(3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (50x + 35x - 12x - 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 597 +--r0:=-3896/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 340/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/77*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-410/2541*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)+19480/27951*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 147 + +--S 148 of 597 +--a0:=integrate(t0,x) +--E 148 + +--S 149 of 597 +--m0:=a0-r0 +--E 149 + +--S 150 of 597 +--d0:=D(m0,x) +--E 150 + +)clear all + +--S 151 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R 1 +--R (1) - -------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (150x + 205x + 34x - 51x - 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 597 +--r0:=-595324/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+85160/27951*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x))+186/539*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 45040/17787*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 2976620/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 152 + +--S 153 of 597 +--a0:=integrate(t0,x) +--E 153 + +--S 154 of 597 +--m0:=a0-r0 +--E 154 + +--S 155 of 597 +--d0:=D(m0,x) +--E 155 + +)clear all + +--S 156 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R - ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (450x + 915x + 512x - 85x - 156x - 36)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 597 +--r0:=-42623864/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+6132760/195657*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/77/((2+3*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+54/539*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 14496/3773*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 3205940/124509*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 213119320/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 157 + +--S 158 of 597 +--a0:=integrate(t0,x) +--E 158 + +--S 159 of 597 +--m0:=a0-r0 +--E 159 + +--S 160 of 597 +--d0:=D(m0,x) +--E 160 + +)clear all + +--S 161 of 597 +t0:=1/((1-2*x)^(3/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R - +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +--R (1350x + 3645x + 3366x + 769x - 638x - 420x - 72)\|- 2x + 1 +--R * +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 597 +--r0:=347423024/1369599*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-12071114168/1369599*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/77/((2+3*x)^(5/2)*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+138/2695*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 19548/18865*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 4115652/132055*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 181551856/871563*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 12071114168/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 162 + +--S 163 of 597 +--a0:=integrate(t0,x) +--E 163 + +--S 164 of 597 +--m0:=a0-r0 +--E 164 + +--S 165 of 597 +--d0:=D(m0,x) +--E 165 + +)clear all + +--S 166 of 597 +t0:=(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 \|5x + 3 +--R (1) --------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 597 +--r0:=6478333/16500*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 112543103/8250*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+1/3*(2+3*x)^(9/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-166/33*_ +-- (2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-139163/3850*(2+3*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(3+5*x)-1327/154*(2+3*x)^(5/2)*sqrt(1-2*x)*_ +-- sqrt(3+5*x)-6478333/38500*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 167 + +--S 168 of 597 +--a0:=integrate(t0,x) +--E 168 + +--S 169 of 597 +--m0:=a0-r0 +--E 169 + +--S 170 of 597 +--d0:=D(m0,x) +--E 170 + +)clear all + +--S 171 of 597 +t0:=(2+3*x)^(7/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 597 +--r0:=-1289089/3300*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+129857/1650*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+1/3*(2+3*x)^(7/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-133/33*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 797/110*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-18551/550*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 172 + +--S 173 of 597 +--a0:=integrate(t0,x) +--E 173 + +--S 174 of 597 +--m0:=a0-r0 +--E 174 + +--S 175 of 597 +--d0:=D(m0,x) +--E 175 + +)clear all + +--S 176 of 597 +t0:=(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (9x + 12x + 4)\|3x + 2 \|5x + 3 +--R (1) --------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 597 +--r0:=-4621/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 931/66*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-100/33*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x)/sqrt(1-2*x)-133/22*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 177 + +--S 178 of 597 +--a0:=integrate(t0,x) +--E 178 + +--S 179 of 597 +--m0:=a0-r0 +--E 179 + +--S 180 of 597 +--d0:=D(m0,x) +--E 180 + +)clear all + +--S 181 of 597 +t0:=(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R (3x + 2)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 597 +--r0:=67/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 133/66*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 1/3*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-67/33*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 182 + +--S 183 of 597 +--a0:=integrate(t0,x) +--E 183 + +--S 184 of 597 +--m0:=a0-r0 +--E 184 + +--S 185 of 597 +--d0:=D(m0,x) +--E 185 + +)clear all + +--S 186 of 597 +t0:=sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R \|3x + 2 \|5x + 3 +--R (1) ------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 597 +--r0:=-34/33*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5/33*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)-68/231*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 187 + +--S 188 of 597 +--a0:=integrate(t0,x) +--E 188 + +--S 189 of 597 +--m0:=a0-r0 +--E 189 + +--S 190 of 597 +--d0:=D(m0,x) +--E 190 + +)clear all + +--S 191 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 597 +--r0:=31/231*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/231*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+62/1617*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 192 + +--S 193 of 597 +--a0:=integrate(t0,x) +--E 193 + +--S 194 of 597 +--m0:=a0-r0 +--E 194 + +--S 195 of 597 +--d0:=D(m0,x) +--E 195 + +)clear all + +--S 196 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 597 +--r0:=458/1617*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 970/1617*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+194/1617*sqrt(3+5*x)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-458/3773*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 197 + +--S 198 of 597 +--a0:=integrate(t0,x) +--E 198 + +--S 199 of 597 +--m0:=a0-r0 +--E 199 + +--S 200 of 597 +--d0:=D(m0,x) +--E 200 + +)clear all + +--S 201 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 597 +--r0:=-338/11319*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 4580/11319*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+326/1617*sqrt(3+5*x)/_ +-- ((2+3*x)^(3/2)*sqrt(1-2*x))-458/3773*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)+338/26411*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 202 + +--S 203 of 597 +--a0:=integrate(t0,x) +--E 203 + +--S 204 of 597 +--m0:=a0-r0 +--E 204 + +--S 205 of 597 +--d0:=D(m0,x) +--E 205 + +)clear all + +--S 206 of 597 +t0:=sqrt(3+5*x)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R \|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 597 +--r0:=-10876/79233*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 189368/79233*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 2/21*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+458/1617*sqrt(3+5*x)/_ +-- ((2+3*x)^(5/2)*sqrt(1-2*x))-2818/18865*sqrt(1-2*x)*sqrt(3+5*x)/_ +-- (2+3*x)^(5/2)-5438/132055*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 189368/924385*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 207 + +--S 208 of 597 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 597 +--m0:=a0-r0 +--E 209 + +--S 210 of 597 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 597 +t0:=(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (135x + 351x + 342x + 148x + 24)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 597 +--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+188443/300*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-6547351/300*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-56/11*_ +-- (2+3*x)^(5/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-1341/154*(2+3*x)^(3/2)*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)-140289/3850*(3+5*x)^(3/2)*sqrt(1-2*x)*_ +-- sqrt(2+3*x)-2166399/7700*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 212 + +--S 213 of 597 +--a0:=integrate(t0,x) +--E 213 + +--S 214 of 597 +--m0:=a0-r0 +--E 214 + +--S 215 of 597 +--d0:=D(m0,x) +--E 215 + +)clear all + +--S 216 of 597 +t0:=(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (45x + 87x + 56x + 12)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------ +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 597 +--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)-37663/60*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1897/15*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 45/11*(2+3*x)^(3/2)*(3+5*x)^(3/2)/sqrt(1-2*x)-807/110*(3+5*x)^(3/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-6231/110*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 217 + +--S 218 of 597 +--a0:=integrate(t0,x) +--E 218 + +--S 219 of 597 +--m0:=a0-r0 +--E 219 + +--S 220 of 597 +--d0:=D(m0,x) +--E 220 + +)clear all + +--S 221 of 597 +t0:=(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (15x + 19x + 6)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 597 +--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(3/2)/(1-2*x)^(3/2)+_ +-- 137/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 68/3*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)-_ +-- 34/11*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-225/22*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 222 + +--S 223 of 597 +--a0:=integrate(t0,x) +--E 223 + +--S 224 of 597 +--m0:=a0-r0 +--E 224 + +--S 225 of 597 +--d0:=D(m0,x) +--E 225 + +)clear all + +--S 226 of 597 +t0:=(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(5/2) +--R +--R +--R +------+ +------+ +--R (5x + 3)\|3x + 2 \|5x + 3 +--R (1) -------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 597 +--r0:=-139/6*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 10/3*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-23/7*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 227 + +--S 228 of 597 +--a0:=integrate(t0,x) +--E 228 + +--S 229 of 597 +--m0:=a0-r0 +--E 229 + +--S 230 of 597 +--d0:=D(m0,x) +--E 230 + +)clear all + +--S 231 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 597 +--r0:=-37/21*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 5/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(3/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-13/49*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 232 + +--S 233 of 597 +--a0:=integrate(t0,x) +--E 233 + +--S 234 of 597 +--m0:=a0-r0 +--E 234 + +--S 235 of 597 +--d0:=D(m0,x) +--E 235 + +)clear all + +--S 236 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 597 +--r0:=19/147*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 40/147*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*sqrt(2+3*x))+9/49*sqrt(3+5*x)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-19/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 237 + +--S 238 of 597 +--a0:=integrate(t0,x) +--E 238 + +--S 239 of 597 +--m0:=a0-r0 +--E 239 + +--S 240 of 597 +--d0:=D(m0,x) +--E 240 + +)clear all + +--S 241 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 597 +--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_ +-- 496/1029*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-890/1029*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+31/49*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))-_ +-- 89/343*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-496/2401*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 242 + +--S 243 of 597 +--a0:=integrate(t0,x) +--E 243 + +--S 244 of 597 +--m0:=a0-r0 +--E 244 + +--S 245 of 597 +--d0:=D(m0,x) +--E 245 + +)clear all + +--S 246 of 597 +t0:=(3+5*x)^(3/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R +------+ +--R (5x + 3)\|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 597 +--r0:=2/21*(3+5*x)^(3/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_ +-- 4528/7203*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 3946/7203*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 53/49*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_ +-- 779/1715*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_ +-- 2264/12005*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_ +-- 3946/84035*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 247 + +--S 248 of 597 +--a0:=integrate(t0,x) +--E 248 + +--S 249 of 597 +--m0:=a0-r0 +--E 249 + +--S 250 of 597 +--d0:=D(m0,x) +--E 250 + +)clear all + +--S 251 of 597 +t0:=(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 5 4 3 2 +------+ +------+ +--R (675x + 2160x + 2763x + 1766x + 564x + 72)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 597 +--r0:=1/3*(2+3*x)^(7/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ +-- 2513419/540*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 174654791/1080*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)-203/33*(2+3*x)^(5/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_ +-- 225/22*(2+3*x)^(3/2)*(3+5*x)^(5/2)*sqrt(1-2*x)-1310203/4620*_ +-- (3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-6277/154*(3+5*x)^(5/2)*_ +-- sqrt(1-2*x)*sqrt(2+3*x)-1313411/630*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 252 + +--S 253 of 597 +--a0:=integrate(t0,x) +--E 253 + +--S 254 of 597 +--m0:=a0-r0 +--E 254 + +--S 255 of 597 +--d0:=D(m0,x) +--E 255 + +)clear all + +--S 256 of 597 +t0:=(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 4 3 2 +------+ +------+ +--R (225x + 570x + 541x + 228x + 36)\|3x + 2 \|5x + 3 +--R (1) ----------------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 597 +--r0:=1/3*(2+3*x)^(5/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)+_ +-- 4019/4*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 69819/2*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)-_ +-- 170/33*(2+3*x)^(3/2)*(3+5*x)^(5/2)/sqrt(1-2*x)-_ +-- 28283/462*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 1355/154*(3+5*x)^(5/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 12601/28*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 257 + +--S 258 of 597 +--a0:=integrate(t0,x) +--E 258 + +--S 259 of 597 +--m0:=a0-r0 +--E 259 + +--S 260 of 597 +--d0:=D(m0,x) +--E 260 + +)clear all + +--S 261 of 597 +t0:=(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(5/2) +--R +--R +--R 3 2 +------+ +------+ +--R (75x + 140x + 87x + 18)\|3x + 2 \|5x + 3 +--R (1) ------------------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 597 +--r0:=1/3*(2+3*x)^(3/2)*(3+5*x)^(5/2)/(1-2*x)^(3/2)-_ +-- 12101/12*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 1219/6*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 137/33*(3+5*x)^(5/2)*sqrt(2+3*x)/sqrt(1-2*x)-_ +-- 817/66*(3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x)-_ +-- 91*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 262 + +--S 263 of 597 +--a0:=integrate(t0,x) +--E 263 + +--S 264 of 597 +--m0:=a0-r0 +--E 264 + +--S 265 of 597 +--d0:=D(m0,x) +--E 265 + +)clear all + +--S 266 of 597 +t0:=(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(5/2) +--R +--R +--R 2 +------+ +------+ +--R (25x + 30x + 9)\|3x + 2 \|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +--R (4x - 4x + 1)\|- 2x + 1 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 597 +--r0:=-4621/18*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 665/18*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 1/3*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-104/21*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x)/sqrt(1-2*x)-695/42*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 267 + +--S 268 of 597 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 597 +--m0:=a0-r0 +--E 269 + +--S 270 of 597 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 271 + +--S 272 of 597 +--r0:=-1597/42*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 115/21*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/21*(3+5*x)^(5/2)*sqrt(2+3*x)/(1-2*x)^(3/2)-_ +-- 109/147*(3+5*x)^(3/2)*sqrt(2+3*x)/sqrt(1-2*x)-_ +-- 120/49*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 272 + +--S 273 of 597 +--a0:=integrate(t0,x) +--E 273 + +--S 274 of 597 +--m0:=a0-r0 +--E 274 + +--S 275 of 597 +--d0:=D(m0,x) +--E 275 + +)clear all + +--S 276 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 597 +--r0:=5/49*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)-_ +-- 146/49*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*sqrt(2+3*x))-43/147*(3+5*x)^(3/2)/_ +-- (sqrt(1-2*x)*sqrt(2+3*x))-17/343*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 277 + +--S 278 of 597 +--a0:=integrate(t0,x) +--E 278 + +--S 279 of 597 +--m0:=a0-r0 +--E 279 + +--S 280 of 597 +--d0:=D(m0,x) +--E 280 + +)clear all + +--S 281 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+169/3087*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)+_ +-- 2290/3087*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 23/147*(3+5*x)^(3/2)/((2+3*x)^(3/2)*sqrt(1-2*x))+19/1029*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-169/7203*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 282 + +--S 283 of 597 +--a0:=integrate(t0,x) +--E 283 + +--S 284 of 597 +--m0:=a0-r0 +--E 284 + +--S 285 of 597 +--d0:=D(m0,x) +--E 285 + +)clear all + +--S 286 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(7/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) ---------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(5/2))-_ +-- 986/2401*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)*sqrt(3/11)+_ +-- 9206/2401*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 89/147*(3+5*x)^(3/2)/((2+3*x)^(5/2)*sqrt(1-2*x))+143/1715*_ +-- sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-4437/12005*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/(2+3*x)^(3/2)-27618/84035*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 287 + +--S 288 of 597 +--a0:=integrate(t0,x) +--E 288 + +--S 289 of 597 +--m0:=a0-r0 +--E 289 + +--S 290 of 597 +--d0:=D(m0,x) +--E 290 + +)clear all + +--S 291 of 597 +t0:=(3+5*x)^(5/2)/((1-2*x)^(5/2)*(2+3*x)^(9/2)) +--R +--R +--R 2 +------+ +--R (25x + 30x + 9)\|5x + 3 +--R (1) --------------------------------------------------------------------- +--R 6 5 4 3 2 +--------+ +------+ +--R (324x + 540x + 81x - 264x - 104x + 32x + 16)\|- 2x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 597 +--r0:=2/21*(3+5*x)^(5/2)/((1-2*x)^(3/2)*(2+3*x)^(7/2))+_ +-- 98642/352947*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-337780/352947*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+155/147*(3+5*x)^(3/2)/((2+3*x)^(7/2)*sqrt(1-2*x))+_ +-- 355/2401*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(7/2)-_ +-- 11433/16807*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)-_ +-- 33778/117649*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)-_ +-- 98642/823543*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 292 + +--S 293 of 597 +--a0:=integrate(t0,x) +--E 293 + +--S 294 of 597 +--m0:=a0-r0 +--E 294 + +--S 295 of 597 +--d0:=D(m0,x) +--E 295 + +)clear all + +--S 296 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 597 +--r0:=-44109377/181500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+2221688/45375*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-227/363*(2+3*x)^(7/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 27271/6050*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-130/121*_ +-- (2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-317384/15125*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 297 + +--S 298 of 597 +--a0:=integrate(t0,x) +--E 298 + +--S 299 of 597 +--m0:=a0-r0 +--E 299 + +--S 300 of 597 +--d0:=D(m0,x) +--E 300 + +)clear all + +--S 301 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 597 +--r0:=-78472/1815*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+31619/3630*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)*sqrt(3+5*x)/_ +-- (1-2*x)^(3/2)-161/363*(2+3*x)^(5/2)*sqrt(3+5*x)/sqrt(1-2*x)-_ +-- 97/121*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-4517/1210*_ +-- sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 302 + +--S 303 of 597 +--a0:=integrate(t0,x) +--E 303 + +--S 304 of 597 +--m0:=a0-r0 +--E 304 + +--S 305 of 597 +--d0:=D(m0,x) +--E 305 + +)clear all + +--S 306 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 597 +--r0:=-4451/726*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+448/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/33*(2+3*x)^(5/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_ +-- 95/363*(2+3*x)^(3/2)*sqrt(3+5*x)/sqrt(1-2*x)-64/121*sqrt(1-2*x)*_ +-- sqrt(2+3*x)*sqrt(3+5*x) +--E 307 + +--S 308 of 597 +--a0:=integrate(t0,x) +--E 308 + +--S 309 of 597 +--m0:=a0-r0 +--E 309 + +--S 310 of 597 +--d0:=D(m0,x) +--E 310 + +)clear all + +--S 311 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 597 +--r0:=29/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 31/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+2/33*(2+3*x)^(3/2)*sqrt(3+5*x)/(1-2*x)^(3/2)-_ +-- 29/363*sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 312 + +--S 313 of 597 +--a0:=integrate(t0,x) +--E 313 + +--S 314 of 597 +--m0:=a0-r0 +--E 314 + +--S 315 of 597 +--d0:=D(m0,x) +--E 315 + +)clear all + +--S 316 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ---------------------------------- +--R 2 +--------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 597 +--r0:=37/363*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 20/363*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+74/2541*sqrt(2+3*x)*_ +-- sqrt(3+5*x)/sqrt(1-2*x) +--E 317 + +--S 318 of 597 +--a0:=integrate(t0,x) +--E 318 + +--S 319 of 597 +--m0:=a0-r0 +--E 319 + +--S 320 of 597 +--d0:=D(m0,x) +--E 320 + +)clear all + +--S 321 of 597 +t0:=1/((1-2*x)^(5/2)*sqrt(2+3*x)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 2 +--------+ +------+ +------+ +--R (4x - 4x + 1)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 597 +--r0:=272/2541*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1030/2541*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(2+3*x)*sqrt(3+5*x)/(1-2*x)^(3/2)+544/17787*_ +-- sqrt(2+3*x)*sqrt(3+5*x)/sqrt(1-2*x) +--E 322 + +--S 323 of 597 +--a0:=integrate(t0,x) +--E 323 + +--S 324 of 597 +--m0:=a0-r0 +--E 324 + +--S 325 of 597 +--d0:=D(m0,x) +--E 325 + +)clear all + +--S 326 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (12x - 4x - 5x + 2)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 597 +--r0:=-5594/17787*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 4040/17787*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*sqrt(2+3*x))+808/17787*_ +-- sqrt(3+5*x)/(sqrt(1-2*x)*sqrt(2+3*x))+5594/41503*sqrt(1-2*x)*_ +-- sqrt(3+5*x)/sqrt(2+3*x) +--E 327 + +--S 328 of 597 +--a0:=integrate(t0,x) +--E 328 + +--S 329 of 597 +--m0:=a0-r0 +--E 329 + +--S 330 of 597 +--d0:=D(m0,x) +--E 330 + +)clear all + +--S 331 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (36x + 12x - 23x - 4x + 4)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 597 +--r0:=-184636/124509*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+9740/124509*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(3/2))+_ +-- 1072/17787*sqrt(3+5*x)/((2+3*x)^(3/2)*sqrt(1-2*x))+_ +-- 974/41503*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 184636/290521*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 332 + +--S 333 of 597 +--a0:=integrate(t0,x) +--E 333 + +--S 334 of 597 +--m0:=a0-r0 +--E 334 + +--S 335 of 597 +--d0:=D(m0,x) +--E 335 + +)clear all + +--S 336 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*sqrt(3+5*x)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (108x + 108x - 45x - 58x + 4x + 8)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 597 +--r0:=699808/871563*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 26062156/871563*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/_ +-- sqrt(35)+4/231*sqrt(3+5*x)/((1-2*x)^(3/2)*(2+3*x)^(5/2))+_ +-- 1336/17787*sqrt(3+5*x)/((2+3*x)^(5/2)*sqrt(1-2*x))-_ +-- 806/207515*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(5/2)+_ +-- 349904/1452605*sqrt(1-2*x)*sqrt(3+5*x)/(2+3*x)^(3/2)+_ +-- 26062156/10168235*sqrt(1-2*x)*sqrt(3+5*x)/sqrt(2+3*x) +--E 337 + +--S 338 of 597 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 597 +--m0:=a0-r0 +--E 339 + +--S 340 of 597 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 597 +--r0:=-1508889271/9982500*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+151997573/4991250*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-223/363*(2+3*x)^(9/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 215/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 932783/332750*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 4439/6655*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 21713939/1663750*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 342 + +--S 343 of 597 +--a0:=integrate(t0,x) +--E 343 + +--S 344 of 597 +--m0:=a0-r0 +--E 344 + +--S 345 of 597 +--d0:=D(m0,x) +--E 345 + +)clear all + +--S 346 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) ------------------------------------------ +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 597 +--r0:=-5327983/199650*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+1073233/199650*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-157/363*(2+3*x)^(7/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 149/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 3284/6655*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 153319/66550*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 347 + +--S 348 of 597 +--a0:=integrate(t0,x) +--E 348 + +--S 349 of 597 +--m0:=a0-r0 +--E 349 + +--S 350 of 597 +--d0:=D(m0,x) +--E 350 + +)clear all + +--S 351 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 597 +--r0:=-148831/39930*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+14903/19965*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*_ +-- sqrt(3+5*x))-91/363*(2+3*x)^(5/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 83/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 2129/6655*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 352 + +--S 353 of 597 +--a0:=integrate(t0,x) +--E 353 + +--S 354 of 597 +--m0:=a0-r0 +--E 354 + +--S 355 of 597 +--d0:=D(m0,x) +--E 355 + +)clear all + +--S 356 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 597 +--r0:=-974/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(7/5)+_ +-- 119/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*sqrt(3+5*x))-_ +-- 25/363*(2+3*x)^(3/2)/(sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 17/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 357 + +--S 358 of 597 +--a0:=integrate(t0,x) +--E 358 + +--S 359 of 597 +--m0:=a0-r0 +--E 359 + +--S 360 of 597 +--d0:=D(m0,x) +--E 360 + +)clear all + +--S 361 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 597 +--r0:=-362/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 49/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(35)+_ +-- 2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*sqrt(3+5*x))+_ +-- 41/363*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 245/3993*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 362 + +--S 363 of 597 +--a0:=integrate(t0,x) +--E 363 + +--S 364 of 597 +--m0:=a0-r0 +--E 364 + +--S 365 of 597 +--d0:=D(m0,x) +--E 365 + +)clear all + +--S 366 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) ----------------------------------------- +--R 3 2 +--------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 597 +--r0:=494/3993*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 1150/3993*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+214/2541*sqrt(2+3*x)/_ +-- (sqrt(1-2*x)*sqrt(3+5*x))-2470/27951*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 367 + +--S 368 of 597 +--a0:=integrate(t0,x) +--E 368 + +--S 369 of 597 +--m0:=a0-r0 +--E 369 + +--S 370 of 597 +--d0:=D(m0,x) +--E 370 + +)clear all + +--S 371 of 597 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(3/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) -------------------------------------------------- +--R 3 2 +--------+ +------+ +------+ +--R (20x - 8x - 7x + 3)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 597 +--r0:=8314/27951*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*sqrt(5/7)-_ +-- 6260/27951*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*sqrt(3+5*x))+_ +-- 824/17787*sqrt(2+3*x)/(sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 41570/195657*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 372 + +--S 373 of 597 +--a0:=integrate(t0,x) +--E 373 + +--S 374 of 597 +--m0:=a0-r0 +--E 374 + +--S 375 of 597 +--d0:=D(m0,x) +--E 375 + +)clear all + +--S 376 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (60x + 16x - 37x - 5x + 6)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 597 +--r0:=475592/195657*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-85780/195657*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*sqrt(2+3*x)*_ +-- sqrt(3+5*x))+1088/17787/(sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x))+_ +-- 5314/41503*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 2377960/1369599*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 377 + +--S 378 of 597 +--a0:=integrate(t0,x) +--E 378 + +--S 379 of 597 +--m0:=a0-r0 +--E 379 + +--S 380 of 597 +--d0:=D(m0,x) +--E 380 + +)clear all + +--S 381 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (180x + 168x - 79x - 89x + 8x + 12)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 597 +--r0:=22738708/1369599*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-3323720/1369599*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*_ +-- sqrt(3+5*x))+1352/17787/((2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x))+_ +-- 694/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 336536/290521*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 113693540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 382 + +--S 383 of 597 +--a0:=integrate(t0,x) +--E 383 + +--S 384 of 597 +--m0:=a0-r0 +--E 384 + +--S 385 of 597 +--d0:=D(m0,x) +--E 385 + +)clear all + +--S 386 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(3/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +------+ +--R (540x + 864x + 99x - 425x - 154x + 52x + 24)\|- 2x + 1 \|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 597 +--r0:=-139423864/9587193*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4839325048/9587193*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)/sqrt(35)+4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*_ +-- sqrt(3+5*x))+1616/17787/((2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x))-_ +-- 2206/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*sqrt(3+5*x))+_ +-- 499564/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*sqrt(3+5*x))+_ +-- 72709316/10168235*sqrt(1-2*x)/(sqrt(2+3*x)*sqrt(3+5*x))-_ +-- 4839325048/67110351*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 387 + +--S 388 of 597 +--a0:=integrate(t0,x) +--E 388 + +--S 389 of 597 +--m0:=a0-r0 +--E 389 + +--S 390 of 597 +--d0:=D(m0,x) +--E 390 + +)clear all + +--S 391 of 597 +t0:=(2+3*x)^(13/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 6 5 4 3 2 +------+ +--R (729x + 2916x + 4860x + 4320x + 2160x + 576x + 64)\|3x + 2 +--R (1) ---------------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 597 +--r0:=2/33*(2+3*x)^(13/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 51601293223/549037500*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(7/5)+2598959587/137259375*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)-_ +-- 73/121*(2+3*x)^(11/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 215/3993*(2+3*x)^(9/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 6503/219615*(2+3*x)^(7/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 31887029/18301250*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 150812/366025*(2+3*x)^(5/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 371279941/45753125*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 392 + +--S 393 of 597 +--a0:=integrate(t0,x) +--E 393 + +--S 394 of 597 +--m0:=a0-r0 +--E 394 + +--S 395 of 597 +--d0:=D(m0,x) +--E 395 + +)clear all + +--S 396 of 597 +t0:=(2+3*x)^(11/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 5 4 3 2 +------+ +--R (243x + 810x + 1080x + 720x + 240x + 32)\|3x + 2 +--R (1) ----------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 597 +--r0:=2/33*(2+3*x)^(11/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 90397364/5490375*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+36399853/10980750*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-51/121*(2+3*x)^(9/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+149/3993*(2+3*x)^(7/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 865/43923*(2+3*x)^(5/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 110519/366025*(2+3*x)^(3/2)*sqrt(1-2*x)*sqrt(3+5*x)-_ +-- 5199979/3660250*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 397 + +--S 398 of 597 +--a0:=integrate(t0,x) +--E 398 + +--S 399 of 597 +--m0:=a0-r0 +--E 399 + +--S 400 of 597 +--d0:=D(m0,x) +--E 400 + +)clear all + +--S 401 of 597 +t0:=(2+3*x)^(9/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 4 3 2 +------+ +--R (81x + 216x + 216x + 96x + 16)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 597 +--r0:=2/33*(2+3*x)^(9/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 4971289/2196150*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)+491582/1098075*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-29/121*(2+3*x)^(7/2)/((3+5*x)^(3/2)*_ +-- sqrt(1-2*x))+83/3993*(2+3*x)^(5/2)*sqrt(1-2*x)/(3+5*x)^(3/2)+_ +-- 2147/219615*(2+3*x)^(3/2)*sqrt(1-2*x)/sqrt(3+5*x)-_ +-- 70226/366025*sqrt(1-2*x)*sqrt(2+3*x)*sqrt(3+5*x) +--E 402 + +--S 403 of 597 +--a0:=integrate(t0,x) +--E 403 + +--S 404 of 597 +--m0:=a0-r0 +--E 404 + +--S 405 of 597 +--d0:=D(m0,x) +--E 405 + +)clear all + +--S 406 of 597 +t0:=(2+3*x)^(7/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 3 2 +------+ +--R (27x + 54x + 36x + 8)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 597 +--r0:=2/33*(2+3*x)^(7/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 29933/219615*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-217/219615*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)-7/121*(2+3*x)^(5/2)/((3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 17/3993*(2+3*x)^(3/2)*sqrt(1-2*x)/(3+5*x)^(3/2)-31/219615*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 407 + +--S 408 of 597 +--a0:=integrate(t0,x) +--E 408 + +--S 409 of 597 +--m0:=a0-r0 +--E 409 + +--S 410 of 597 +--d0:=D(m0,x) +--E 410 + +)clear all + +--S 411 of 597 +t0:=(2+3*x)^(5/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R 2 +------+ +--R (9x + 12x + 4)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 597 +--r0:=2/33*(2+3*x)^(5/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 2209/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(7/5)-4144/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+15/121*(2+3*x)^(3/2)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 49/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2209/43923*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 412 + +--S 413 of 597 +--a0:=integrate(t0,x) +--E 413 + +--S 414 of 597 +--m0:=a0-r0 +--E 414 + +--S 415 of 597 +--d0:=D(m0,x) +--E 415 + +)clear all + +--S 416 of 597 +t0:=(2+3*x)^(3/2)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R (3x + 2)\|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 597 +--r0:=2/33*(2+3*x)^(3/2)/((1-2*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 8774/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+592/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(35)+37/121*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 575/3993*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)-2960/43923*_ +-- sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 417 + +--S 418 of 597 +--a0:=integrate(t0,x) +--E 418 + +--S 419 of 597 +--m0:=a0-r0 +--E 419 + +--S 420 of 597 +--d0:=D(m0,x) +--E 420 + +)clear all + +--S 421 of 597 +t0:=sqrt(2+3*x)/((1-2*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R +------+ +--R \|3x + 2 +--R (1) -------------------------------------------------- +--R 4 3 2 +--------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|5x + 3 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 597 +--r0:=4418/43923*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-5920/43923*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+2/33*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+118/847*_ +-- sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-2470/27951*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/(3+5*x)^(3/2)-22090/307461*sqrt(1-2*x)*_ +-- sqrt(2+3*x)/sqrt(3+5*x) +--E 422 + +--S 423 of 597 +--a0:=integrate(t0,x) +--E 423 + +--S 424 of 597 +--m0:=a0-r0 +--E 424 + +--S 425 of 597 +--d0:=D(m0,x) +--E 425 + +)clear all + +--S 426 of 597 +t0:=1/((1-2*x)^(5/2)*(3+5*x)^(5/2)*sqrt(2+3*x)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------------- +--R 4 3 2 +--------+ +------+ +------+ +--R (100x + 20x - 59x - 6x + 9)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 597 +--r0:=-119732/307461*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)-620/307461*elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/_ +-- sqrt(33)+4/231*sqrt(2+3*x)/((1-2*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 368/5929*sqrt(2+3*x)/((3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 18470/195657*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 598660/2152227*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 427 + +--S 428 of 597 +--a0:=integrate(t0,x) +--E 428 + +--S 429 of 597 +--m0:=a0-r0 +--E 429 + +--S 430 of 597 +--d0:=D(m0,x) +--E 430 + +)clear all + +--S 431 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(3/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 5 4 3 2 +--------+ +------+ +------+ +--R (300x + 260x - 137x - 136x + 15x + 18)\|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 597 +--r0:=-19885156/2152227*elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)*_ +-- sqrt(5/7)+2809040/2152227*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)+4/231/((1-2*x)^(3/2)*(3+5*x)^(3/2)*_ +-- sqrt(2+3*x))+456/5929/((3+5*x)^(3/2)*sqrt(1-2*x)*sqrt(2+3*x))+_ +-- 5034/41503*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 1523260/1369599*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 99425780/15065589*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 432 + +--S 433 of 597 +--a0:=integrate(t0,x) +--E 433 + +--S 434 of 597 +--m0:=a0-r0 +--E 434 + +--S 435 of 597 +--d0:=D(m0,x) +--E 435 + +)clear all + +--S 436 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(5/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 5 4 3 2 +--------+ +------+ +--R (900x + 1380x + 109x - 682x - 227x + 84x + 36)\|- 2x + 1 \|3x + 2 +--R * +--R +------+ +--R \|5x + 3 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 597 +--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(3/2)*(3+5*x)^(3/2))-_ +-- 1446357824/15065589*elliptic_e(asin(sqrt(5/11)*_ +-- sqrt(1-2*x)),33/35)*sqrt(5/7)+207999160/15065589*_ +-- elliptic_f(asin(sqrt(3/7)*sqrt(1-2*x)),35/33)/sqrt(33)+_ +-- 544/5929/((2+3*x)^(3/2)*(3+5*x)^(3/2)*sqrt(1-2*x))+_ +-- 414/41503*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 488436/290521*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 108842540/9587193*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 7231789120/105459123*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 437 + +--S 438 of 597 +--a0:=integrate(t0,x) +--E 438 + +--S 439 of 597 +--m0:=a0-r0 +--E 439 + +--S 440 of 597 +--d0:=D(m0,x) +--E 440 + +)clear all + +--S 441 of 597 +t0:=1/((1-2*x)^(5/2)*(2+3*x)^(7/2)*(3+5*x)^(5/2)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 6 5 4 3 2 +--R (2700x + 5940x + 3087x - 1828x - 2045x - 202x + 276x + 72) +--R * +--R +--------+ +------+ +------+ +--R \|- 2x + 1 \|3x + 2 \|5x + 3 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 597 +--r0:=4/231/((1-2*x)^(3/2)*(2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 11880958112/105459123*elliptic_f(asin(sqrt(3/7)*_ +-- sqrt(1-2*x)),35/33)/sqrt(33)-412810345784/105459123*_ +-- elliptic_e(asin(sqrt(5/11)*sqrt(1-2*x)),33/35)/sqrt(35)+_ +-- 632/5929/((2+3*x)^(5/2)*(3+5*x)^(3/2)*sqrt(1-2*x))-_ +-- 3606/207515*sqrt(1-2*x)/((2+3*x)^(5/2)*(3+5*x)^(3/2))+_ +-- 649224/1452605*sqrt(1-2*x)/((2+3*x)^(3/2)*(3+5*x)^(3/2))+_ +-- 140700876/10168235*sqrt(1-2*x)/((3+5*x)^(3/2)*sqrt(2+3*x))-_ +-- 6208896328/67110351*sqrt(1-2*x)*sqrt(2+3*x)/(3+5*x)^(3/2)+_ +-- 412810345784/738213861*sqrt(1-2*x)*sqrt(2+3*x)/sqrt(3+5*x) +--E 442 + +--S 443 of 597 +--a0:=integrate(t0,x) +--E 443 + +--S 444 of 597 +--m0:=a0-r0 +--E 444 + +--S 445 of 597 +--d0:=D(m0,x) +--E 445 + +)clear all + +--S 446 of 597 +t0:=(a+b*x)*(A+B*x)*sqrt(c+d*x)/x +--R +--R +--R 2 +-------+ +--R (B b x + (A b + B a)x + A a)\|d x + c +--R (1) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 446 + +--S 447 of 597 +r0:=-2/15*(2*b*B*c-5*A*b*d-2*a*B*d)*(c+d*x)^(3/2)/d^2+_ + 2/5*B*(a+b*x)*(c+d*x)^(3/2)/d-2*a*A*atanh(sqrt(c+d*x)/sqrt(c))*_ + sqrt(c)+2*a*A*sqrt(c+d*x) +--R +--R +--R (2) +--R +-------+ +--R 2 +-+ \|d x + c +--R - 30A a d \|c atanh(----------) +--R +-+ +--R \|c +--R + +--R 2 2 2 2 +--R 6B b d x + ((10A b + 10B a)d + 2B b c d)x + 30A a d +--R + +--R 2 +--R (10A b + 10B a)c d - 4B b c +--R * +--R +-------+ +--R \|d x + c +--R / +--R 2 +--R 15d +--R Type: Expression(Integer) +--E 447 + +--S 448 of 597 +--a0:=integrate(t0,x) +--E 448 + +--S 449 of 597 +--m0:=a0-r0 +--E 449 + +--S 450 of 597 +--d0:=D(m0,x) +--E 450 + +)clear all + +--S 451 of 597 +t0:=(A+B*x)*(c+d*x)*sqrt(a+b*x)/x +--R +--R +--R 2 +-------+ +--R (B d x + (A d + B c)x + A c)\|b x + a +--R (1) --------------------------------------- +--R x +--R Type: Expression(Integer) +--E 451 + +--S 452 of 597 +r0:=2/15*(5*b*B*c+2*A*b*d-2*a*B*d)*(a+b*x)^(3/2)/b^2+_ + 2/5*d*(a+b*x)^(3/2)*(A+B*x)/b-2*A*c*atanh(sqrt(a+b*x)/sqrt(a))*_ + sqrt(a)+2*A*c*sqrt(a+b*x) +--R +--R +--R (2) +--R +-------+ +--R 2 +-+ \|b x + a +--R - 30A b c\|a atanh(----------) +--R +-+ +--R \|a +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 452 + +--S 453 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-------+ +--R 2 +-+ - 2\|a \|b x + a + b x + 2a +--R 15A b c\|a log(----------------------------) +--R x +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R , +--R +--R +-------+ +--R 2 +---+ \|b x + a +--R - 30A b c\|- a atan(----------) +--R +---+ +--R \|- a +--R + +--R 2 2 2 2 2 +--R 6B b d x + ((10A b + 2B a b)d + 10B b c)x + (10A a b - 4B a )d +--R + +--R 2 +--R (30A b + 10B a b)c +--R * +--R +-------+ +--R \|b x + a +--R / +--R 2 +--R 15b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 453 + +--S 454 of 597 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-------+ +-------+ +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R (4) A c\|a log(----------------------------) + 2A c\|a atanh(----------) +--R x +-+ +--R \|a +--R Type: Expression(Integer) +--E 454 + +--S 455 of 597 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 597 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R +-+ \|b x + a +---+ \|b x + a +--R (6) 2A c\|a atanh(----------) - 2A c\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 597 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 597 +t0:=x^3*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 4 3 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 597 +r0:=-75/128*asin(1-2*a*x)/a^4-75/64*sqrt(a*x-a^2*x^2)/a^4-_ + 25/32*x*sqrt(a*x-a^2*x^2)/a^3-5/8*x^2*sqrt(a*x-a^2*x^2)/a^2-_ + 1/4*x^3*sqrt(a*x-a^2*x^2)/a +--R +--R +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (- 32a x - 80a x - 100a x - 150)\|- a x + a x + 75asin(2a x - 1) +--R (2) -------------------------------------------------------------------- +--R 4 +--R 128a +--R Type: Expression(Integer) +--E 459 + +--S 460 of 597 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 597 +--m0:=a0-r0 +--E 461 + +--S 462 of 597 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 597 +t0:=x^2*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 3 2 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 597 +r0:=-11/16*asin(1-2*a*x)/a^3-11/8*sqrt(a*x-a^2*x^2)/a^3-_ + 11/12*x*sqrt(a*x-a^2*x^2)/a^2-1/3*x^2*sqrt(a*x-a^2*x^2)/a +--R +--R +--R +------------+ +--R 2 2 | 2 2 +--R (- 16a x - 44a x - 66)\|- a x + a x + 33asin(2a x - 1) +--R (2) --------------------------------------------------------- +--R 3 +--R 48a +--R Type: Expression(Integer) +--E 464 + +--S 465 of 597 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 597 +--m0:=a0-r0 +--E 466 + +--S 467 of 597 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 597 +t0:=x*(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R 2 +--R a x + x +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 597 +r0:=-7/8*asin(1-2*a*x)/a^2-5/4*sqrt(a*x)*sqrt(1-a*x)/a^2-_ + 1/2*(1+a*x)*sqrt(a*x)*sqrt(1-a*x)/a^2 +--R +--R +--R +---------+ +---+ +--R (- 4a x - 14)\|- a x + 1 \|a x + 7asin(2a x - 1) +--R (2) ------------------------------------------------- +--R 2 +--R 8a +--R Type: Expression(Integer) +--E 469 + +--S 470 of 597 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 597 +--m0:=a0-r0 +--E 471 + +--S 472 of 597 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 597 +t0:=(1+a*x)/(sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) ------------------ +--R +---------+ +---+ +--R \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 473 + +--S 474 of 597 +r0:=-3/2*asin(1-2*a*x)/a-sqrt(a*x)*sqrt(1-a*x)/a +--R +--R +--R +---------+ +---+ +--R - 2\|- a x + 1 \|a x + 3asin(2a x - 1) +--R (2) --------------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 474 + +--S 475 of 597 +--a0:=integrate(t0,x) +--E 475 + +--S 476 of 597 +--m0:=a0-r0 +--E 476 + +--S 477 of 597 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 of 597 +t0:=(1+a*x)/(x*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) ------------------- +--R +---------+ +---+ +--R x\|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 478 + +--S 479 of 597 +r0:=-asin(1-2*a*x)-2*sqrt(a*x-a^2*x^2)/(a*x) +--R +--R +--R +------------+ +--R | 2 2 +--R - 2\|- a x + a x + a x asin(2a x - 1) +--R (2) --------------------------------------- +--R a x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 597 +--a0:=integrate(t0,x) +--E 480 + +--S 481 of 597 +--m0:=a0-r0 +--E 481 + +--S 482 of 597 +--d0:=D(m0,x) +--E 482 + +)clear all + +--S 483 of 597 +t0:=(1+a*x)/(x^2*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 2 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 483 + +--S 484 of 597 +r0:=-2/3*sqrt(a*x-a^2*x^2)/(a*x^2)-10/3*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R | 2 2 +--R (- 10a x - 2)\|- a x + a x +--R (2) ---------------------------- +--R 2 +--R 3a x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 597 +--a0:=integrate(t0,x) +--E 485 + +--S 486 of 597 +--m0:=a0-r0 +--E 486 + +--S 487 of 597 +--d0:=D(m0,x) +--E 487 + +)clear all + +--S 488 of 597 +t0:=(1+a*x)/(x^3*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 3 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 597 +r0:=-2/5*sqrt(a*x-a^2*x^2)/(a*x^3)-6/5*sqrt(a*x-a^2*x^2)/x^2-_ + 12/5*a*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 2 2 | 2 2 +--R (- 12a x - 6a x - 2)\|- a x + a x +--R (2) ------------------------------------ +--R 3 +--R 5a x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 597 +--a0:=integrate(t0,x) +--E 490 + +--S 491 of 597 +--m0:=a0-r0 +--E 491 + +--S 492 of 597 +--d0:=D(m0,x) +--E 492 + +)clear all + +--S 493 of 597 +t0:=(1+a*x)/(x^4*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 4 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 493 + +--S 494 of 597 +r0:=-2/7*sqrt(a*x-a^2*x^2)/(a*x^4)-26/35*sqrt(a*x-a^2*x^2)/x^3-_ + 104/105*a*sqrt(a*x-a^2*x^2)/x^2-208/105*a^2*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (- 208a x - 104a x - 78a x - 30)\|- a x + a x +--R (2) ------------------------------------------------- +--R 4 +--R 105a x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 597 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 +---------+ +---+ +--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x +--R + +--R 3 2 4 +--R (104a + 52a + 39a + 15)x +--R / +--R 4 +--R 105a x +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 597 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 +---------+ +---+ +--R (- 208a x - 104a x - 78a x - 30)\|- a x + 1 \|a x +--R + +--R +------------+ +--R 3 3 2 2 | 2 2 +--R (208a x + 104a x + 78a x + 30)\|- a x + a x +--R + +--R 3 2 4 +--R (104a + 52a + 39a + 15)x +--R / +--R 4 +--R 105a x +--R Type: Expression(Integer) +--E 496 + +--S 497 of 597 +d0:=D(m0,x) +--R +--R +--R +------------+ +--R +---------+ +---+ | 2 2 +--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x +--R (5) -------------------------------------------------------- +--R +------------+ +--R 4 | 2 2 +---------+ +---+ +--R x \|- a x + a x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 597 +t0:=(1+a*x)/(x^5*sqrt(a*x)*sqrt(1-a*x)) +--R +--R +--R a x + 1 +--R (1) -------------------- +--R 5 +---------+ +---+ +--R x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 498 + +--S 499 of 597 +r0:=-2/9*sqrt(a*x-a^2*x^2)/(a*x^5)-34/63*sqrt(a*x-a^2*x^2)/x^4-_ + 68/105*a*sqrt(a*x-a^2*x^2)/x^3-272/315*a^2*sqrt(a*x-a^2*x^2)/x^2-_ + 544/315*a^3*sqrt(a*x-a^2*x^2)/x +--R +--R +--R +------------+ +--R 4 4 3 3 2 2 | 2 2 +--R (- 544a x - 272a x - 204a x - 170a x - 70)\|- a x + a x +--R (2) ------------------------------------------------------------ +--R 5 +--R 315a x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 597 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 +---------+ +---+ +--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x +--R + +--R 5 4 3 2 5 +--R (816a - 680a - 238a - 153a - 235a - 140)x +--R / +--R 5 +--R 630a x +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 597 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 +---------+ +---+ +--R (- 1088a x - 544a x - 408a x - 340a x - 140)\|- a x + 1 \|a x +--R + +--R +------------+ +--R 4 4 3 3 2 2 | 2 2 +--R (1088a x + 544a x + 408a x + 340a x + 140)\|- a x + a x +--R + +--R 5 4 3 2 5 +--R (816a - 680a - 238a - 153a - 235a - 140)x +--R / +--R 5 +--R 630a x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 597 +d0:=D(m0,x) +--R +--R +--R +------------+ +--R +---------+ +---+ | 2 2 +--R (- a x - 1)\|- a x + 1 \|a x + (a x + 1)\|- a x + a x +--R (5) -------------------------------------------------------- +--R +------------+ +--R 5 | 2 2 +---------+ +---+ +--R x \|- a x + a x \|- a x + 1 \|a x +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 597 +t0:=x^m*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R m n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 503 + +--S 504 of 597 +--r0:=b*x^(1+m)*(e+f*x)^n*_ +-- AppellF1(1+m,1,-n,2+m,-b*x/a,-f*x/e)/(a*(b*c-a*d)*(1+m)*_ +-- ((e+f*x)/e)^n)-d*x^(1+m)*(e+f*x)^n*_ +-- AppellF1(1+m,1,-n,2+m,-d*x/c,-f*x/e)/(c*(b*c-a*d)*(1+m)*_ +-- ((e+f*x)/e)^n) +--E 504 + +--S 505 of 597 +--a0:=integrate(t0,x) +--E 505 + +--S 506 of 597 +--m0:=a0-r0 +--E 506 + +--S 507 of 597 +--d0:=D(m0,x) +--E 507 + +)clear all + +--S 508 of 597 +t0:=x^4*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 4 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 508 + +--S 509 of 597 +--r0:=e^2*(e+f*x)^(1+n)/(b*d*f^3*(1+n))+(b*c+a*d)*e*(e+f*x)^(1+n)/_ +-- (b^2*d^2*f^2*(1+n))+(b^2*c^2+a*b*c*d+a^2*d^2)*(e+f*x)^(1+n)/_ +-- (b^3*d^3*f*(1+n))-2*e*(e+f*x)^(2+n)/(b*d*f^3*(2+n))-_ +-- (b*c+a*d)*(e+f*x)^(2+n)/(b^2*d^2*f^2*(2+n))+(e+f*x)^(3+n)/_ +-- (b*d*f^3*(3+n))-a^4*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b^3*(b*c-a*d)*(b*e-a*f)*(1+n))+c^4*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d^3*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 509 + +--S 510 of 597 +--a0:=integrate(t0,x) +--E 510 + +--S 511 of 597 +--m0:=a0-r0 +--E 511 + +--S 512 of 597 +--d0:=D(m0,x) +--E 512 + +)clear all + +--S 513 of 597 +t0:=x^3*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 3 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 513 + +--S 514 of 597 +--r0:=-e*(e+f*x)^(1+n)/(b*d*f^2*(1+n))-(b*c+a*d)*(e+f*x)^(1+n)/_ +-- (b^2*d^2*f*(1+n))+(e+f*x)^(2+n)/(b*d*f^2*(2+n))+a^3*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b^2*(b*c-a*d)*(b*e-a*f)*(1+n))-c^3*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d^2*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 514 + +--S 515 of 597 +--a0:=integrate(t0,x) +--E 515 + +--S 516 of 597 +--m0:=a0-r0 +--E 516 + +--S 517 of 597 +--d0:=D(m0,x) +--E 517 + +)clear all + +--S 518 of 597 +t0:=x^2*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R 2 n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 518 + +--S 519 of 597 +--r0:=(e+f*x)^(1+n)/(b*d*f*(1+n))-a^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (b*(b*c-a*d)*(b*e-a*f)*(1+n))+c^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (d*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 519 + +--S 520 of 597 +--a0:=integrate(t0,x) +--E 520 + +--S 521 of 597 +--m0:=a0-r0 +--E 521 + +--S 522 of 597 +--d0:=D(m0,x) +--E 522 + +)clear all + +--S 523 of 597 +t0:=x*(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R n +--R x (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 523 + +--S 524 of 597 +--r0:=a*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- ((b*c-a*d)*(b*e-a*f)*(1+n))-c*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- ((b*c-a*d)*(d*e-c*f)*(1+n)) +--E 524 + +--S 525 of 597 +--a0:=integrate(t0,x) +--E 525 + +--S 526 of 597 +--m0:=a0-r0 +--E 526 + +--S 527 of 597 +--d0:=D(m0,x) +--E 527 + +)clear all + +--S 528 of 597 +t0:=(e+f*x)^n/((a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) --------------------------- +--R 2 +--R b d x + (a d + b c)x + a c +--R Type: Expression(Integer) +--E 528 + +--S 529 of 597 +--r0:=-b*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/_ +-- (b*e-a*f))/((b*c-a*d)*(b*e-a*f)*(1+n))+d*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- ((b*c-a*d)*(d*e-c*f)*(1+n)) +--E 529 + +--S 530 of 597 +--a0:=integrate(t0,x) +--E 530 + +--S 531 of 597 +--m0:=a0-r0 +--E 531 + +--S 532 of 597 +--d0:=D(m0,x) +--E 532 + +)clear all + +--S 533 of 597 +t0:=(e+f*x)^n/(x*(a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) ------------------------------ +--R 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 597 +--r0:=-(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a*c*e*(1+n))+_ +-- b^2*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,b*(e+f*x)/(b*e-a*f))/_ +-- (a*(b*c-a*d)*(b*e-a*f)*(1+n))-d^2*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,d*(e+f*x)/(d*e-c*f))/_ +-- (c*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 534 + +--S 535 of 597 +--a0:=integrate(t0,x) +--E 535 + +--S 536 of 597 +--m0:=a0-r0 +--E 536 + +--S 537 of 597 +--d0:=D(m0,x) +--E 537 + +)clear all + +--S 538 of 597 +t0:=(e+f*x)^n/(x^2*(a+b*x)*(c+d*x)) +--R +--R +--R n +--R (f x + e) +--R (1) ------------------------------- +--R 4 3 2 +--R b d x + (a d + b c)x + a c x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 597 +--r0:=-(e+f*x)^(1+n)/(a*c*e*x)+(b*c+a*d)*(e+f*x)^(1+n)*_ +-- hypergeometric(1,1+n,2+n,(e+f*x)/e)/(a^2*c^2*e*(1+n))-_ +-- f*n*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,(e+f*x)/e)/_ +-- (a*c*e^2*(1+n))-b^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,_ +-- 2+n,b*(e+f*x)/(b*e-a*f))/(a^2*(b*c-a*d)*(b*e-a*f)*(1+n))_ +-- +d^3*(e+f*x)^(1+n)*hypergeometric(1,1+n,2+n,d*(e+f*x)/_ +-- (d*e-c*f))/(c^2*(b*c-a*d)*(d*e-c*f)*(1+n)) +--E 539 + +--S 540 of 597 +--a0:=integrate(t0,x) +--E 540 + +--S 541 of 597 +--m0:=a0-r0 +--E 541 + +--S 542 of 597 +--d0:=D(m0,x) +--E 542 + +)clear all + +--S 543 of 597 +t0:=(a+b*x)*(c+d*x)*(e+f*x)*(g+h*x) +--R +--R +--R (1) +--R 4 3 +--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x +--R + +--R 2 +--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x +--R + +--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g +--R Type: Polynomial(Integer) +--E 543 + +--S 544 of 597 +r0:=a*c*e*g*x+1/2*(b*c*e*g+a*(d*e*g+c*f*g+c*e*h))*x^2+_ + 1/3*(b*(d*e*g+c*f*g+c*e*h)+a*(d*f*g+d*e*h+c*f*h))*x^3+_ + 1/4*(a*d*f*h+b*(d*f*g+d*e*h+c*f*h))*x^4+1/5*b*d*f*h*x^5 +--R +--R +--R (2) +--R 1 5 1 1 1 1 4 +--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x +--R 5 4 4 4 4 +--R + +--R 1 1 1 1 1 1 3 +--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x +--R 3 3 3 3 3 3 +--R + +--R 1 1 1 1 2 +--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x +--R 2 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 544 + +--S 545 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 1 1 1 1 4 +--R - b d f h x + (((- a d + - b c)f + - b d e)h + - b d f g)x +--R 5 4 4 4 4 +--R + +--R 1 1 1 1 1 1 3 +--R ((- a c f + (- a d + - b c)e)h + ((- a d + - b c)f + - b d e)g)x +--R 3 3 3 3 3 3 +--R + +--R 1 1 1 1 2 +--R (- a c e h + (- a c f + (- a d + - b c)e)g)x + a c e g x +--R 2 2 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 545 + +--S 546 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 546 + +--S 547 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 547 + +)clear all + +--S 548 of 597 +t0:=(a+b*x)*(c+d*x)*(e+f*x)/(g+h*x) +--R +--R +--R 3 2 +--R b d f x + ((a d + b c)f + b d e)x + (a c f + (a d + b c)e)x + a c e +--R (1) --------------------------------------------------------------------- +--R h x + g +--R Type: Fraction(Polynomial(Integer)) +--E 548 + +--S 549 of 597 +r0:=(b*(d*g-c*h)*(f*g-e*h)-a*h*(d*f*g-d*e*h-c*f*h))*x/h^3+_ + 1/2*(a*d*f*h-b*(d*f*g-d*e*h-c*f*h))*x^2/h^2+_ + 1/3*b*d*f*x^3/h-(b*g-a*h)*(d*g-c*h)*(f*g-e*h)*log(g+h*x)/h^4 +--R +--R +--R (2) +--R 3 2 +--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h +--R + +--R 2 3 +--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g +--R * +--R log(h x + g) +--R + +--R 3 3 3 2 2 +--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x +--R + +--R 3 2 +--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h +--R + +--R 2 +--R 6b d f g h +--R * +--R x +--R / +--R 4 +--R 6h +--R Type: Expression(Integer) +--E 549 + +--S 550 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 +--R 6a c e h + (- 6a c f + (- 6a d - 6b c)e)g h +--R + +--R 2 3 +--R ((6a d + 6b c)f + 6b d e)g h - 6b d f g +--R * +--R log(h x + g) +--R + +--R 3 3 3 2 2 +--R 2b d f h x + (((3a d + 3b c)f + 3b d e)h - 3b d f g h )x +--R + +--R 3 2 +--R (6a c f + (6a d + 6b c)e)h + ((- 6a d - 6b c)f - 6b d e)g h +--R + +--R 2 +--R 6b d f g h +--R * +--R x +--R / +--R 4 +--R 6h +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 597 +t0:=(a+b*x)*(c+d*x)/((e+f*x)*(g+h*x)) +--R +--R +--R 2 +--R b d x + (a d + b c)x + a c +--R (1) --------------------------- +--R 2 +--R f h x + (e h + f g)x + e g +--R Type: Fraction(Polynomial(Integer)) +--E 553 + +--S 554 of 597 +r0:=b*d*x/(f*h)+(b*e-a*f)*(d*e-c*f)*log(e+f*x)/(f^2*(f*g-e*h))-_ + (b*g-a*h)*(d*g-c*h)*log(g+h*x)/(h^2*(f*g-e*h)) +--R +--R +--R (2) +--R 2 2 2 2 2 +--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )h log(f x + e) +--R + +--R 2 2 +--R (b d e f h - b d f g h)x +--R / +--R 2 3 3 2 +--R e f h - f g h +--R Type: Expression(Integer) +--E 554 + +--S 555 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 +--R (a c f h + (- a d - b c)f g h + b d f g )log(h x + g) +--R + +--R 2 2 2 +--R (- a c f + (a d + b c)e f - b d e )h log(f x + e) +--R + +--R 2 2 +--R (b d e f h - b d f g h)x +--R / +--R 2 3 3 2 +--R e f h - f g h +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 597 +t0:=(a+b*x)/((c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R b x + a +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g +--R Type: Fraction(Polynomial(Integer)) +--E 558 + +--S 559 of 597 +r0:=-(b*c-a*d)*log(c+d*x)/((d*e-c*f)*(d*g-c*h))+_ + (b*e-a*f)*log(e+f*x)/((d*e-c*f)*(f*g-e*h))-_ + (b*g-a*h)*log(g+h*x)/((d*g-c*h)*(f*g-e*h)) +--R +--R +--R (2) +--R ((a c f - a d e)h + (- b c f + b d e)g)log(h x + g) +--R + +--R ((- a c f + b c e)h + (a d f - b d e)g)log(f x + e) +--R + +--R ((a d - b c)e h + (- a d + b c)f g)log(d x + c) +--R / +--R 2 2 2 2 2 2 2 2 2 2 +--R (c e f - c d e )h + (- c f + d e )g h + (c d f - d e f)g +--R Type: Expression(Integer) +--E 559 + +--S 560 of 597 +--a0:=integrate(t0,x) +--E 560 + +--S 561 of 597 +--m0:=a0-r0 +--E 561 + +--S 562 of 597 +--d0:=D(m0,x) +--E 562 + +)clear all + +--S 563 of 597 +t0:=1/((a+b*x)*(c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R (1) +--R 1 +--R / +--R 4 3 +--R b d f h x + (((a d + b c)f + b d e)h + b d f g)x +--R + +--R 2 +--R ((a c f + (a d + b c)e)h + ((a d + b c)f + b d e)g)x +--R + +--R (a c e h + (a c f + (a d + b c)e)g)x + a c e g +--R Type: Fraction(Polynomial(Integer)) +--E 563 + +--S 564 of 597 +r0:=b^2*log(a+b*x)/((b*c-a*d)*(b*e-a*f)*(b*g-a*h))-_ + d^2*log(c+d*x)/((b*c-a*d)*(d*e-c*f)*(d*g-c*h))+_ + f^2*log(e+f*x)/((b*e-a*f)*(d*e-c*f)*(f*g-e*h))-_ + h^2*log(g+h*x)/((b*g-a*h)*(d*g-c*h)*(f*g-e*h)) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2 2 2 2 2 +--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d)e )h +--R * +--R log(h x + g) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 2 2 +--R ((- a c d + a b c )f h + (a d - b c )f g h + (- a b d + b c d)f g ) +--R * +--R log(f x + e) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (a d e f - a b d e )h + (- a d f + b d e )g h +--R + +--R 2 2 2 2 2 +--R (a b d f - b d e f)g +--R * +--R log(d x + c) +--R + +--R 2 2 2 2 2 2 2 2 2 2 2 +--R (- b c e f + b c d e )h + (b c f - b d e )g h +--R + +--R 2 2 2 2 2 +--R (- b c d f + b d e f)g +--R * +--R log(b x + a) +--R / +--R 3 2 2 3 2 3 2 2 3 2 +--R (a c d - a b c )e f + (- a c d + a b c )e f +--R + +--R 2 2 2 2 3 +--R (a b c d - a b c d)e +--R * +--R 3 +--R h +--R + +--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2 +--R ((- a c d + a b c )f + (a d - b c )e f + (- a b d + b c d)e )g h +--R + +--R 3 2 2 3 3 3 3 3 3 2 2 3 3 2 3 2 +--R ((a c d - a b c )f + (- a d + b c )e f + (a b d - b c d )e )g h +--R + +--R 2 2 2 2 3 2 3 3 2 2 +--R (- a b c d + a b c d)f + (a b d - b c d)e f +--R + +--R 2 3 3 2 2 +--R (- a b d + b c d )e f +--R * +--R 3 +--R g +--R Type: Expression(Integer) +--E 564 + +--S 565 of 597 +--a0:=integrate(t0,x) +--E 565 + +--S 566 of 597 +--m0:=a0-r0 +--E 566 + +--S 567 of 597 +--d0:=D(m0,x) +--E 567 + +)clear all + +--S 568 of 597 +t0:=(a+b*x)^m*(c+d*x)*(e+f*x)*(g+h*x) +--R +--R +--R (1) +--R 3 2 +--R (d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g) +--R * +--R m +--R (b x + a) +--R Type: Expression(Integer) +--E 568 + +--S 569 of 597 +r0:=(b*c-a*d)*(b*e-a*f)*(b*g-a*h)*(a+b*x)^(1+m)/(b^4*(1+m))+_ + (3*a^2*d*f*h+b^2*(d*e*g+c*f*g+c*e*h)-_ + 2*a*b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(2+m)/(b^4*(2+m))-_ + (3*a*d*f*h-b*(d*f*g+d*e*h+c*f*h))*(a+b*x)^(3+m)/(b^4*(3+m))+_ + d*f*h*(a+b*x)^(4+m)/(b^4*(4+m)) +--R +--R +--R (2) +--R 3 2 m + 4 +--R (d f h m + 6d f h m + 11d f h m + 6d f h)(b x + a) +--R + +--R 3 +--R (((- 3a d + b c)f + b d e)h + b d f g)m +--R + +--R 2 +--R (((- 21a d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R (((- 42a d + 14b c)f + 14b d e)h + 14b d f g)m +--R + +--R ((- 24a d + 8b c)f + 8b d e)h + 8b d f g +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 2 +--R ((3a d - 2a b c)f + (- 2a b d + b c)e)h +--R + +--R 2 2 +--R ((- 2a b d + b c)f + b d e)g +--R * +--R 3 +--R m +--R + +--R 2 2 +--R ((24a d - 16a b c)f + (- 16a b d + 8b c)e)h +--R + +--R 2 2 +--R ((- 16a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 +--R ((57a d - 38a b c)f + (- 38a b d + 19b c)e)h +--R + +--R 2 2 +--R ((- 38a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 2 2 +--R ((36a d - 24a b c)f + (- 24a b d + 12b c)e)h +--R + +--R 2 2 +--R ((- 24a b d + 12b c)f + 12b d e)g +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((- a d + a b c)f + (a b d - a b c)e)h +--R + +--R 2 2 2 3 +--R ((a b d - a b c)f + (- a b d + b c)e)g +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 +--R ((- 9a d + 9a b c)f + (9a b d - 9a b c)e)h +--R + +--R 2 2 2 3 +--R ((9a b d - 9a b c)f + (- 9a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 +--R ((- 26a d + 26a b c)f + (26a b d - 26a b c)e)h +--R + +--R 2 2 2 3 +--R ((26a b d - 26a b c)f + (- 26a b d + 26b c)e)g +--R * +--R m +--R + +--R 3 2 2 2 +--R ((- 24a d + 24a b c)f + (24a b d - 24a b c)e)h +--R + +--R 2 2 2 3 +--R ((24a b d - 24a b c)f + (- 24a b d + 24b c)e)g +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 569 + +--S 570 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 4 +--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x +--R + +--R 3 4 4 4 3 +--R (((a b d + b c)f + b d e)h + b d f g)m +--R + +--R 3 4 4 4 2 +--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R 3 4 4 4 4 4 +--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m + (8b c f + 8b d e)h +--R + +--R 4 +--R 8b d f g +--R * +--R 3 +--R x +--R + +--R 3 3 4 3 4 4 3 +--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h +--R + +--R 3 4 4 +--R ((5a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h +--R + +--R 3 4 4 +--R ((4a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 4 4 4 +--R 12b c e h + (12b c f + 12b d e)g +--R * +--R 2 +--R x +--R + +--R 3 3 3 4 3 +--R (a b c e h + (a b c f + (a b d + b c)e)g)m +--R + +--R 2 2 2 2 3 +--R (- 2a b c f + (- 2a b d + 7a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 2 3 +--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g +--R * +--R m +--R + +--R 4 +--R 24b c e g +--R * +--R x +--R + +--R 3 3 2 2 2 2 2 2 3 2 +--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m +--R + +--R 3 3 2 2 +--R (2a b c f + (2a b d - 7a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g +--R * +--R m +--R + +--R 4 3 3 2 2 +--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g +--R * +--R m log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 597 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 4 +--R (b d f h m + 6b d f h m + 11b d f h m + 6b d f h)x +--R + +--R 3 4 4 4 3 +--R (((a b d + b c)f + b d e)h + b d f g)m +--R + +--R 3 4 4 4 2 +--R (((3a b d + 7b c)f + 7b d e)h + 7b d f g)m +--R + +--R 3 4 4 4 +--R (((2a b d + 14b c)f + 14b d e)h + 14b d f g)m +--R + +--R 4 4 4 +--R (8b c f + 8b d e)h + 8b d f g +--R * +--R 3 +--R x +--R + +--R 3 3 4 3 4 4 3 +--R ((a b c f + (a b d + b c)e)h + ((a b d + b c)f + b d e)g)m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 5a b c)f + (5a b d + 8b c)e)h +--R + +--R 3 4 4 +--R ((5a b d + 8b c)f + 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 3 3 4 +--R ((- 3a b d + 4a b c)f + (4a b d + 19b c)e)h +--R + +--R 3 4 4 +--R ((4a b d + 19b c)f + 19b d e)g +--R * +--R m +--R + +--R 4 4 4 +--R 12b c e h + (12b c f + 12b d e)g +--R * +--R 2 +--R x +--R + +--R 3 3 3 4 3 +--R (a b c e h + (a b c f + (a b d + b c)e)g)m +--R + +--R 2 2 2 2 3 +--R (- 2a b c f + (- 2a b d + 7a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 2a b d + 7a b c)f + (7a b d + 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 2 3 +--R ((6a b d - 8a b c)f + (- 8a b d + 12a b c)e)h +--R + +--R 2 2 3 3 4 +--R ((- 8a b d + 12a b c)f + (12a b d + 26b c)e)g +--R * +--R m +--R + +--R 4 +--R 24b c e g +--R * +--R x +--R + +--R 3 3 2 2 2 2 2 2 3 2 +--R a b c e g m + (- a b c e h + (- a b c f + (- a b d + 9a b c)e)g)m +--R + +--R 3 3 2 2 +--R (2a b c f + (2a b d - 7a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((2a b d - 7a b c)f + (- 7a b d + 26a b c)e)g +--R * +--R m +--R + +--R 4 3 3 2 2 +--R ((- 6a d + 8a b c)f + (8a b d - 12a b c)e)h +--R + +--R 3 2 2 2 2 3 +--R ((8a b d - 12a b c)f + (- 12a b d + 24a b c)e)g +--R * +--R m log(b x + a) +--R %e +--R + +--R 3 2 m + 4 +--R (- d f h m - 6d f h m - 11d f h m - 6d f h)(b x + a) +--R + +--R 3 +--R (((3a d - b c)f - b d e)h - b d f g)m +--R + +--R 2 +--R (((21a d - 7b c)f - 7b d e)h - 7b d f g)m +--R + +--R (((42a d - 14b c)f - 14b d e)h - 14b d f g)m +--R + +--R ((24a d - 8b c)f - 8b d e)h - 8b d f g +--R * +--R m + 3 +--R (b x + a) +--R + +--R 2 2 +--R ((- 3a d + 2a b c)f + (2a b d - b c)e)h +--R + +--R 2 2 +--R ((2a b d - b c)f - b d e)g +--R * +--R 3 +--R m +--R + +--R 2 2 +--R ((- 24a d + 16a b c)f + (16a b d - 8b c)e)h +--R + +--R 2 2 +--R ((16a b d - 8b c)f - 8b d e)g +--R * +--R 2 +--R m +--R + +--R 2 2 +--R ((- 57a d + 38a b c)f + (38a b d - 19b c)e)h +--R + +--R 2 2 +--R ((38a b d - 19b c)f - 19b d e)g +--R * +--R m +--R + +--R 2 2 +--R ((- 36a d + 24a b c)f + (24a b d - 12b c)e)h +--R + +--R 2 2 +--R ((24a b d - 12b c)f - 12b d e)g +--R * +--R m + 2 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((a d - a b c)f + (- a b d + a b c)e)h +--R + +--R 2 2 2 3 +--R ((- a b d + a b c)f + (a b d - b c)e)g +--R * +--R 3 +--R m +--R + +--R 3 2 2 2 +--R ((9a d - 9a b c)f + (- 9a b d + 9a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 9a b d + 9a b c)f + (9a b d - 9b c)e)g +--R * +--R 2 +--R m +--R + +--R 3 2 2 2 +--R ((26a d - 26a b c)f + (- 26a b d + 26a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 26a b d + 26a b c)f + (26a b d - 26b c)e)g +--R * +--R m +--R + +--R 3 2 2 2 +--R ((24a d - 24a b c)f + (- 24a b d + 24a b c)e)h +--R + +--R 2 2 2 3 +--R ((- 24a b d + 24a b c)f + (24a b d - 24b c)e)g +--R * +--R m + 1 +--R (b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b m + 10b m + 35b m + 50b m + 24b +--R Type: Expression(Integer) +--E 571 + +--S 572 of 597 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 3 3 3 3 2 +--R b d f h x + ((b c f + b d e)h + b d f g)x +--R + +--R 3 3 3 3 +--R (b c e h + (b c f + b d e)g)x + b c e g +--R * +--R m log(b x + a) +--R %e +--R + +--R m + 3 +--R - d f h (b x + a) +--R + +--R m + 2 +--R (((3a d - b c)f - b d e)h - b d f g)(b x + a) +--R + +--R 2 2 2 2 +--R (((- 3a d + 2a b c)f + (2a b d - b c)e)h + ((2a b d - b c)f - b d e)g) +--R * +--R m + 1 +--R (b x + a) +--R + +--R 3 2 2 2 +--R ((a d - a b c)f + (- a b d + a b c)e)h +--R + +--R 2 2 2 3 +--R ((- a b d + a b c)f + (a b d - b c)e)g +--R * +--R m +--R (b x + a) +--R / +--R 3 +--R b +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 597 +t0:=(a+b*x)^m*(c+d*x)*(e+f*x)/(g+h*x) +--R +--R +--R 2 m +--R (d f x + (c f + d e)x + c e)(b x + a) +--R (1) --------------------------------------- +--R h x + g +--R Type: Expression(Integer) +--E 573 + +--S 574 of 597 +--r0:=(b*d*e*h*(2+m)+f*(b*c*h-d*(a*h+b*g*(2+m))))*(a+b*x)^(1+m)/_ +-- (b^2*h^2*(1+m)*(2+m))+f*(a+b*x)^(1+m)*(c+d*x)/(b*h*(2+m))+_ +-- (d*g-c*h)*(f*g-e*h)*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,_ +-- -h*(a+b*x)/(b*g-a*h))/(h^2*(b*g-a*h)*(1+m)) +--E 574 + +--S 575 of 597 +--a0:=integrate(t0,x) +--E 575 + +--S 576 of 597 +--m0:=a0-r0 +--E 576 + +--S 577 of 597 +--d0:=D(m0,x) +--E 577 + +)clear all + +--S 578 of 597 +t0:=(a+b*x)^m*(c+d*x)/((e+f*x)*(g+h*x)) +--R +--R +--R m +--R (d x + c)(b x + a) +--R (1) --------------------------- +--R 2 +--R f h x + (e h + f g)x + e g +--R Type: Expression(Integer) +--E 578 + +--S 579 of 597 +--r0:=-(d*e-c*f)*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_ +-- (f*g-e*h)*(1+m))+(d*g-c*h)*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_ +-- (f*g-e*h)*(1+m)) +--E 579 + +--S 580 of 597 +--a0:=integrate(t0,x) +--E 580 + +--S 581 of 597 +--m0:=a0-r0 +--E 581 + +--S 582 of 597 +--d0:=D(m0,x) +--E 582 + +)clear all + +--S 583 of 597 +t0:=(a+b*x)^m/((c+d*x)*(e+f*x)*(g+h*x)) +--R +--R +--R m +--R (b x + a) +--R (1) --------------------------------------------------------------------- +--R 3 2 +--R d f h x + ((c f + d e)h + d f g)x + (c e h + (c f + d e)g)x + c e g +--R Type: Expression(Integer) +--E 583 + +--S 584 of 597 +--r0:=d^2*(a+b*x)^(1+m)*hypergeometric(1,1+m,2+m,-d*(a+b*x)/(b*c-a*d))/_ +-- ((b*c-a*d)*(d*e-c*f)*(d*g-c*h)*(1+m))-f^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-f*(a+b*x)/(b*e-a*f))/((b*e-a*f)*_ +-- (d*e-c*f)*(f*g-e*h)*(1+m))+h^2*(a+b*x)^(1+m)*_ +-- hypergeometric(1,1+m,2+m,-h*(a+b*x)/(b*g-a*h))/((b*g-a*h)*_ +-- (d*g-c*h)*(f*g-e*h)*(1+m)) +--E 584 + +--S 585 of 597 +--a0:=integrate(t0,x) +--E 585 + +--S 586 of 597 +--m0:=a0-r0 +--E 586 + +--S 587 of 597 +--d0:=D(m0,x) +--E 587 + +)clear all + +--S 588 of 597 +t0:=x/((1+x)*(2+x)*(3+x)) +--R +--R +--R x +--R (1) ------------------ +--R 3 2 +--R x + 6x + 11x + 6 +--R Type: Fraction(Polynomial(Integer)) +--E 588 + +--S 589 of 597 +r0:=-1/2*log(1+x)+2*log(2+x)-3/2*log(3+x) +--R +--R +--R - 3log(x + 3) + 4log(x + 2) - log(x + 1) +--R (2) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 597 +a0:=integrate(t0,x) +--R +--R +--R - 3log(x + 3) + 4log(x + 2) - log(x + 1) +--R (3) ---------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 597 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 597 +t0:=(-x^2+x^3)/((-6+x)*(3+5*x)^3) +--R +--R +--R 3 2 +--R x - x +--R (1) ----------------------------------- +--R 4 3 2 +--R 125x - 525x - 1215x - 783x - 162 +--R Type: Fraction(Polynomial(Integer)) +--E 593 + +--S 594 of 597 +r0:=(-12/1375)/(3+5*x)^2+201/15125/(3+5*x)+_ + 20/3993*log(6-x)+1493/499125*log(3+5*x) +--R +--R +--R (2) +--R 2 +--R (37325x + 44790x + 13437)log(5x + 3) +--R + +--R 2 +--R (62500x + 75000x + 22500)log(- x + 6) + 33165x + 15543 +--R / +--R 2 +--R 12478125x + 14973750x + 4492125 +--R Type: Expression(Integer) +--E 594 + +--S 595 of 597 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R (37325x + 44790x + 13437)log(5x + 3) +--R + +--R 2 +--R (62500x + 75000x + 22500)log(x - 6) + 33165x + 15543 +--R / +--R 2 +--R 12478125x + 14973750x + 4492125 +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 597 +m0:=a0-r0 +--R +--R +--R 20log(x - 6) - 20log(- x + 6) +--R (4) ----------------------------- +--R 3993 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 597 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4a.input.pamphlet b/src/input/rich4a.input.pamphlet new file mode 100644 index 0000000..45696d2 --- /dev/null +++ b/src/input/rich4a.input.pamphlet @@ -0,0 +1,20344 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4a.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 311 matching answers. +\item 59 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4a.output +)spool rich4a.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1393 +t0:=x^m*(a+b*x^2) +--R +--R +--R 2 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1393 +r0:=a*x^(1+m)/(1+m)+b*x^(3+m)/(3+m) +--R +--R +--R m + 3 m + 1 +--R (b m + b)x + (a m + 3a)x +--R (2) ---------------------------------- +--R 2 +--R m + 4m + 3 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 m log(x) +--R ((b m + b)x + (a m + 3a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 4m + 3 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 m log(x) m + 3 +--R ((b m + b)x + (a m + 3a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 3a)x +--R / +--R 2 +--R m + 4m + 3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1393 +t0:=x^4*(a+b*x^2) +--R +--R +--R 6 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 6 + +--S 7 of 1393 +r0:=1/5*a*x^5+1/7*b*x^7 +--R +--R +--R 1 7 1 5 +--R (2) - b x + - a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 7 + +--S 8 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 5 +--R (3) - b x + - a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 8 + +--S 9 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 9 + +--S 10 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 10 + +)clear all + +--S 11 of 1393 +t0:=x^3*(a+b*x^2) +--R +--R +--R 5 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 11 + +--S 12 of 1393 +r0:=1/4*a*x^4+1/6*b*x^6 +--R +--R +--R 1 6 1 4 +--R (2) - b x + - a x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 12 + +--S 13 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 4 +--R (3) - b x + - a x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 13 + +--S 14 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 14 + +--S 15 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 15 + +)clear all + +--S 16 of 1393 +t0:=x^2*(a+b*x^2) +--R +--R +--R 4 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 16 + +--S 17 of 1393 +r0:=1/3*a*x^3+1/5*b*x^5 +--R +--R +--R 1 5 1 3 +--R (2) - b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 17 + +--S 18 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 3 +--R (3) - b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 18 + +--S 19 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 19 + +--S 20 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 20 + +)clear all + +--S 21 of 1393 +t0:=x*(a+b*x^2) +--R +--R +--R 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 21 + +--S 22 of 1393 +r0:=1/2*a*x^2+1/4*b*x^4 +--R +--R +--R 1 4 1 2 +--R (2) - b x + - a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 22 + +--S 23 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 4 1 2 +--R (3) - b x + - a x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 23 + +--S 24 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 24 + +--S 25 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 25 + +)clear all + +--S 26 of 1393 +t0:=a+b*x^2 +--R +--R +--R 2 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 26 + +--S 27 of 1393 +r0:=a*x+1/3*b*x^3 +--R +--R +--R 1 3 +--R (2) - b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 27 + +--S 28 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 +--R (3) - b x + a x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 28 + +--S 29 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 29 + +--S 30 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 30 + +)clear all + +--S 31 of 1393 +t0:=(a+b*x^2)/x +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1393 +r0:=1/2*b*x^2+a*log(x) +--R +--R +--R 2 +--R 2a log(x) + b x +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2a log(x) + b x +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1393 +t0:=(a+b*x^2)/x^2 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1393 +r0:=-a/x+b*x +--R +--R +--R 2 +--R b x - a +--R (2) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 37 + +--S 38 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x - a +--R (3) -------- +--R x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1393 +t0:=(a+b*x^2)/x^3 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1393 +r0:=-1/2*a/x^2+b*log(x) +--R +--R +--R 2 +--R 2b x log(x) - a +--R (2) --------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x log(x) - a +--R (3) --------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1393 +t0:=(a+b*x^2)/x^4 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1393 +r0:=-1/3*a/x^3-b/x +--R +--R +--R 2 1 +--R - b x - - a +--R 3 +--R (2) ------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3b x - a +--R (3) ----------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1393 +t0:=(a+b*x^2)/x^5 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1393 +r0:=-1/4*a/x^4-1/2*b/x^2 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 2 4 +--R (2) -------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2b x - a +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1393 +t0:=(a+b*x^2)/x^6 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1393 +r0:=-1/5*a/x^5-1/3*b/x^3 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 3 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5b x - 3a +--R (3) ------------ +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1393 +t0:=(a+b*x^2)/x^7 +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1393 +r0:=-1/6*a/x^6-1/4*b/x^4 +--R +--R +--R 1 2 1 +--R - - b x - - a +--R 4 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3b x - 2a +--R (3) ------------ +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1393 +t0:=x^m*(a+b*x^2)^2 +--R +--R +--R 2 4 2 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1393 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(3+m)/(3+m)+b^2*x^(5+m)/(5+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 5 2 m + 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 8a m + 15a )x +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 5 2 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 +--R (a m + 8a m + 15a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 5 2 3 +--R (b m + 4b m + 3b )x + (2a b m + 12a b m + 10a b)x +--R + +--R 2 2 2 2 +--R (a m + 8a m + 15a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 5 2 m + 3 +--R (- b m - 4b m - 3b )x + (- 2a b m - 12a b m - 10a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 8a m - 15a )x +--R / +--R 3 2 +--R m + 9m + 23m + 15 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1393 +t0:=x^5*(a+b*x^2)^2 +--R +--R +--R 2 9 7 2 5 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 71 + +--S 72 of 1393 +r0:=1/6*a^2*x^6+1/4*a*b*x^8+1/10*b^2*x^10 +--R +--R +--R 1 2 10 1 8 1 2 6 +--R (2) -- b x + - a b x + - a x +--R 10 4 6 +--R Type: Polynomial(Fraction(Integer)) +--E 72 + +--S 73 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 1 8 1 2 6 +--R (3) -- b x + - a b x + - a x +--R 10 4 6 +--R Type: Polynomial(Fraction(Integer)) +--E 73 + +--S 74 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 74 + +--S 75 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 75 + +)clear all + +--S 76 of 1393 +t0:=x^4*(a+b*x^2)^2 +--R +--R +--R 2 8 6 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 76 + +--S 77 of 1393 +r0:=1/5*a^2*x^5+2/7*a*b*x^7+1/9*b^2*x^9 +--R +--R +--R 1 2 9 2 7 1 2 5 +--R (2) - b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 77 + +--S 78 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 2 7 1 2 5 +--R (3) - b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 78 + +--S 79 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 79 + +--S 80 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 80 + +)clear all + +--S 81 of 1393 +t0:=x^3*(a+b*x^2)^2 +--R +--R +--R 2 7 5 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1393 +r0:=1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8 +--R +--R +--R 1 2 8 1 6 1 2 4 +--R (2) - b x + - a b x + - a x +--R 8 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 1 6 1 2 4 +--R (3) - b x + - a b x + - a x +--R 8 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1393 +t0:=x^2*(a+b*x^2)^2 +--R +--R +--R 2 6 4 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1393 +r0:=1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7 +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (2) - b x + - a b x + - a x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (3) - b x + - a b x + - a x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1393 +t0:=x*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1393 +r0:=1/6*(a+b*x^2)^3/b +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - b x + - a b x + - a b x + - a +--R 6 2 2 6 +--R (2) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 92 + +--S 93 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 6 1 4 1 2 2 +--R (3) - b x + - a b x + - a x +--R 6 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1393 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - a +--R 6 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 94 + +--S 95 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 95 + +)clear all + +--S 96 of 1393 +t0:=(a+b*x^2)^2 +--R +--R +--R 2 4 2 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1393 +r0:=a^2*x+2/3*a*b*x^3+1/5*b^2*x^5 +--R +--R +--R 1 2 5 2 3 2 +--R (2) - b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 2 5 2 3 2 +--R (3) - b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1393 +t0:=(a+b*x^2)^2/x +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1393 +r0:=a*b*x^2+1/4*b^2*x^4+a^2*log(x) +--R +--R +--R 2 2 4 2 +--R 4a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1393 +t0:=(a+b*x^2)^2/x^2 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1393 +r0:=-a^2/x+2*a*b*x+1/3*b^2*x^3 +--R +--R +--R 2 4 2 2 +--R b x + 6a b x - 3a +--R (2) -------------------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 107 + +--S 108 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R b x + 6a b x - 3a +--R (3) -------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1393 +t0:=(a+b*x^2)^2/x^3 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1393 +r0:=-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*log(x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + b x - a +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + b x - a +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1393 +t0:=(a+b*x^2)^2/x^4 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1393 +r0:=-1/3*a^2/x^3-2*a*b/x+b^2*x +--R +--R +--R 2 4 2 1 2 +--R b x - 2a b x - - a +--R 3 +--R (2) --------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 3b x - 6a b x - a +--R (3) -------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1393 +t0:=(a+b*x^2)^2/x^5 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1393 +r0:=-1/4*a^2/x^4-a*b/x^2+b^2*log(x) +--R +--R +--R 2 4 2 2 +--R 4b x log(x) - 4a b x - a +--R (2) -------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 4b x log(x) - 4a b x - a +--R (3) -------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1393 +t0:=(a+b*x^2)^2/x^6 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1393 +r0:=-1/5*a^2/x^5-2/3*a*b/x^3-b^2/x +--R +--R +--R 2 4 2 2 1 2 +--R - b x - - a b x - - a +--R 3 5 +--R (2) ------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 15b x - 10a b x - 3a +--R (3) ------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1393 +t0:=(a+b*x^2)^2/x^7 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 1393 +r0:=-1/6*(a+b*x^2)^3/(a*x^6) +--R +--R +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 6 2 2 6 +--R (2) ------------------------------------- +--R 6 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 132 + +--S 133 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 3b x - 3a b x - a +--R (3) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1393 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R 6a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1393 +t0:=(a+b*x^2)^2/x^8 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 1393 +r0:=-1/7*a^2/x^7-2/5*a*b/x^5-1/3*b^2/x^3 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - b x - - a b x - - a +--R 3 5 7 +--R (2) -------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 137 + +--S 138 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 35b x - 42a b x - 15a +--R (3) -------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1393 +t0:=(a+b*x^2)^2/x^9 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 1393 +r0:=-1/8*a^2/x^8-1/3*a*b/x^6-1/4*b^2/x^4 +--R +--R +--R 1 2 4 1 2 1 2 +--R - - b x - - a b x - - a +--R 4 3 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 142 + +--S 143 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 6b x - 8a b x - 3a +--R (3) ----------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1393 +t0:=(a+b*x^2)^2/x^10 +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1393 +r0:=-1/9*a^2/x^9-2/7*a*b/x^7-1/5*b^2/x^5 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - b x - - a b x - - a +--R 5 7 9 +--R (2) -------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 147 + +--S 148 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 63b x - 90a b x - 35a +--R (3) -------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1393 +t0:=x^m*(a+b*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1393 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(3+m)/(3+m)+3*a*b^2*x^(5+m)/(5+m)+_ + b^3*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 15a m + 71a m + 105a )x +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 15a m + 71a m + 105a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 7 +--R (b m + 9b m + 23b m + 15b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 33a b m + 93a b m + 63a b )x +--R + +--R 2 3 2 2 2 2 3 +--R (3a b m + 39a b m + 141a b m + 105a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 15a m + 71a m + 105a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 7 +--R (- b m - 9b m - 23b m - 15b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (- 3a b m - 33a b m - 93a b m - 63a b )x +--R + +--R 2 3 2 2 2 2 m + 3 +--R (- 3a b m - 39a b m - 141a b m - 105a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 15a m - 71a m - 105a )x +--R / +--R 4 3 2 +--R m + 16m + 86m + 176m + 105 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1393 +t0:=x^9*(a+b*x^2)^3 +--R +--R +--R 3 15 2 13 2 11 3 9 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 156 + +--S 157 of 1393 +r0:=1/10*a^3*x^10+1/4*a^2*b*x^12+3/14*a*b^2*x^14+1/16*b^3*x^16 +--R +--R +--R 1 3 16 3 2 14 1 2 12 1 3 10 +--R (2) -- b x + -- a b x + - a b x + -- a x +--R 16 14 4 10 +--R Type: Polynomial(Fraction(Integer)) +--E 157 + +--S 158 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 16 3 2 14 1 2 12 1 3 10 +--R (3) -- b x + -- a b x + - a b x + -- a x +--R 16 14 4 10 +--R Type: Polynomial(Fraction(Integer)) +--E 158 + +--S 159 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 159 + +--S 160 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 160 + +)clear all + +--S 161 of 1393 +t0:=x^7*(a+b*x^2)^3 +--R +--R +--R 3 13 2 11 2 9 3 7 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 161 + +--S 162 of 1393 +r0:=1/8*a^3*x^8+3/10*a^2*b*x^10+1/4*a*b^2*x^12+1/14*b^3*x^14 +--R +--R +--R 1 3 14 1 2 12 3 2 10 1 3 8 +--R (2) -- b x + - a b x + -- a b x + - a x +--R 14 4 10 8 +--R Type: Polynomial(Fraction(Integer)) +--E 162 + +--S 163 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 1 2 12 3 2 10 1 3 8 +--R (3) -- b x + - a b x + -- a b x + - a x +--R 14 4 10 8 +--R Type: Polynomial(Fraction(Integer)) +--E 163 + +--S 164 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 164 + +--S 165 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 165 + +)clear all + +--S 166 of 1393 +t0:=x^5*(a+b*x^2)^3 +--R +--R +--R 3 11 2 9 2 7 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 166 + +--S 167 of 1393 +r0:=1/6*a^3*x^6+3/8*a^2*b*x^8+3/10*a*b^2*x^10+1/12*b^3*x^12 +--R +--R +--R 1 3 12 3 2 10 3 2 8 1 3 6 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 12 10 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 167 + +--S 168 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 12 3 2 10 3 2 8 1 3 6 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 12 10 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 168 + +--S 169 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 169 + +--S 170 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 170 + +)clear all + +--S 171 of 1393 +t0:=x^3*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 171 + +--S 172 of 1393 +r0:=-1/8*a*(a+b*x^2)^4/b^2+1/10*(a+b*x^2)^5/b^2 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 10 8 2 4 40 +--R (2) ------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 172 + +--S 173 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 10 3 2 8 1 2 6 1 3 4 +--R (3) -- b x + - a b x + - a b x + - a x +--R 10 8 2 4 +--R Type: Polynomial(Fraction(Integer)) +--E 173 + +--S 174 of 1393 +m0:=a0-r0 +--R +--R +--R 1 5 +--R -- a +--R 40 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 174 + +--S 175 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 175 + +)clear all + +--S 176 of 1393 +t0:=x*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 176 + +--S 177 of 1393 +r0:=1/8*(a+b*x^2)^4/b +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - b x + - a b x + - a b x + - a b x + - a +--R 8 2 4 2 8 +--R (2) ---------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 177 + +--S 178 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 8 1 2 6 3 2 4 1 3 2 +--R (3) - b x + - a b x + - a b x + - a x +--R 8 2 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 178 + +--S 179 of 1393 +m0:=a0-r0 +--R +--R +--R 1 4 +--R - a +--R 8 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 179 + +--S 180 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 180 + +)clear all + +--S 181 of 1393 +t0:=(a+b*x^2)^3/x +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1393 +r0:=3/2*a^2*b*x^2+3/4*a*b^2*x^4+1/6*b^3*x^6+a^3*log(x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12a log(x) + 2b x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12a log(x) + 2b x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1393 +t0:=(a+b*x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1393 +r0:=-1/2*a^3/x^2+3/2*a*b^2*x^2+1/4*b^3*x^4+3*a^2*b*log(x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1393 +t0:=(a+b*x^2)^3/x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1393 +r0:=-1/4*a^3/x^4-3/2*a^2*b/x^2+1/2*b^3*x^2+3*a*b^2*log(x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2b x - 6a b x - a +--R (2) ------------------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2b x - 6a b x - a +--R (3) ------------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1393 +t0:=(a+b*x^2)^3/x^7 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1393 +r0:=-1/6*a^3/x^6-3/4*a^2*b/x^4-3/2*a*b^2/x^2+b^3*log(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12b x log(x) - 18a b x - 9a b x - 2a +--R (2) --------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12b x log(x) - 18a b x - 9a b x - 2a +--R (3) --------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1393 +t0:=(a+b*x^2)^3/x^9 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1393 +r0:=-1/8*(a+b*x^2)^4/(a*x^8) +--R +--R +--R 1 4 8 1 3 6 3 2 2 4 1 3 2 1 4 +--R - - b x - - a b x - - a b x - - a b x - - a +--R 8 2 4 2 8 +--R (2) ------------------------------------------------ +--R 8 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 202 + +--S 203 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1393 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) -- +--R 8a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1393 +t0:=(a+b*x^2)^3/x^11 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1393 +r0:=-1/10*a^3/x^10-3/8*a^2*b/x^8-1/2*a*b^2/x^6-1/4*b^3/x^4 +--R +--R +--R 1 3 6 1 2 4 3 2 2 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 4 2 8 10 +--R (2) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 207 + +--S 208 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ------------------------------------ +--R 10 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1393 +t0:=(a+b*x^2)^3/x^13 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1393 +r0:=-1/12*a^3/x^12-3/10*a^2*b/x^10-3/8*a*b^2/x^8-1/6*b^3/x^6 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - b x - - a b x - -- a b x - -- a +--R 6 8 10 12 +--R (2) --------------------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 212 + +--S 213 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------- +--R 12 +--R 120x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1393 +t0:=(a+b*x^2)^3/x^15 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1393 +r0:=-1/14*a^3/x^14-1/4*a^2*b/x^12-3/10*a*b^2/x^10-1/8*b^3/x^8 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - b x - -- a b x - - a b x - -- a +--R 8 10 4 14 +--R (2) --------------------------------------- +--R 14 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 217 + +--S 218 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------- +--R 14 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1393 +t0:=x^6*(a+b*x^2)^3 +--R +--R +--R 3 12 2 10 2 8 3 6 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 221 + +--S 222 of 1393 +r0:=1/7*a^3*x^7+1/3*a^2*b*x^9+3/11*a*b^2*x^11+1/13*b^3*x^13 +--R +--R +--R 1 3 13 3 2 11 1 2 9 1 3 7 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 13 11 3 7 +--R Type: Polynomial(Fraction(Integer)) +--E 222 + +--S 223 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 3 2 11 1 2 9 1 3 7 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 13 11 3 7 +--R Type: Polynomial(Fraction(Integer)) +--E 223 + +--S 224 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 224 + +--S 225 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 225 + +)clear all + +--S 226 of 1393 +t0:=x^4*(a+b*x^2)^3 +--R +--R +--R 3 10 2 8 2 6 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 226 + +--S 227 of 1393 +r0:=1/5*a^3*x^5+3/7*a^2*b*x^7+1/3*a*b^2*x^9+1/11*b^3*x^11 +--R +--R +--R 1 3 11 1 2 9 3 2 7 1 3 5 +--R (2) -- b x + - a b x + - a b x + - a x +--R 11 3 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 227 + +--S 228 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 11 1 2 9 3 2 7 1 3 5 +--R (3) -- b x + - a b x + - a b x + - a x +--R 11 3 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 228 + +--S 229 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 229 + +--S 230 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 230 + +)clear all + +--S 231 of 1393 +t0:=x^2*(a+b*x^2)^3 +--R +--R +--R 3 8 2 6 2 4 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 231 + +--S 232 of 1393 +r0:=1/3*a^3*x^3+3/5*a^2*b*x^5+3/7*a*b^2*x^7+1/9*b^3*x^9 +--R +--R +--R 1 3 9 3 2 7 3 2 5 1 3 3 +--R (2) - b x + - a b x + - a b x + - a x +--R 9 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 232 + +--S 233 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 9 3 2 7 3 2 5 1 3 3 +--R (3) - b x + - a b x + - a b x + - a x +--R 9 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 233 + +--S 234 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 234 + +--S 235 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 235 + +)clear all + +--S 236 of 1393 +t0:=(a+b*x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 236 + +--S 237 of 1393 +r0:=a^3*x+a^2*b*x^3+3/5*a*b^2*x^5+1/7*b^3*x^7 +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (2) - b x + - a b x + a b x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 237 + +--S 238 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (3) - b x + - a b x + a b x + a x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 238 + +--S 239 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 239 + +--S 240 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 240 + +)clear all + +--S 241 of 1393 +t0:=(a+b*x^2)^3/x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1393 +r0:=-a^3/x+3*a^2*b*x+a*b^2*x^3+1/5*b^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 5a b x + 15a b x - 5a +--R (2) ------------------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 242 + +--S 243 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 5a b x + 15a b x - 5a +--R (3) ------------------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1393 +t0:=(a+b*x^2)^3/x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1393 +r0:=-1/3*a^3/x^3-3*a^2*b/x+3*a*b^2*x+1/3*b^3*x^3 +--R +--R +--R 1 3 6 2 4 2 2 1 3 +--R - b x + 3a b x - 3a b x - - a +--R 3 3 +--R (2) --------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 247 + +--S 248 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 9a b x - 9a b x - a +--R (3) ----------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1393 +t0:=(a+b*x^2)^3/x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1393 +r0:=-1/5*a^3/x^5-a^2*b/x^3-3*a*b^2/x+b^3*x +--R +--R +--R 3 6 2 4 2 2 1 3 +--R b x - 3a b x - a b x - - a +--R 5 +--R (2) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 252 + +--S 253 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 5b x - 15a b x - 5a b x - a +--R (3) ------------------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1393 +t0:=(a+b*x^2)^3/x^8 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1393 +r0:=-1/7*a^3/x^7-3/5*a^2*b/x^5-a*b^2/x^3-b^3/x +--R +--R +--R 3 6 2 4 3 2 2 1 3 +--R - b x - a b x - - a b x - - a +--R 5 7 +--R (2) --------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 257 + +--S 258 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 35a b x - 21a b x - 5a +--R (3) ------------------------------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1393 +t0:=(a+b*x^2)^3/x^10 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1393 +r0:=-1/9*a^3/x^9-3/7*a^2*b/x^7-3/5*a*b^2/x^5-1/3*b^3/x^3 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - b x - - a b x - - a b x - - a +--R 3 5 7 9 +--R (2) ------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 105b x - 189a b x - 135a b x - 35a +--R (3) ---------------------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1393 +t0:=(a+b*x^2)^3/x^12 +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1393 +r0:=-1/11*a^3/x^11-1/3*a^2*b/x^9-3/7*a*b^2/x^7-1/5*b^3/x^5 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 5 7 3 11 +--R (2) -------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 231b x - 495a b x - 385a b x - 105a +--R (3) ----------------------------------------- +--R 11 +--R 1155x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1393 +t0:=x^m*(a+b*x^2)^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1393 +r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(3+m)/(3+m)+10*a^3*b^2*x^(5+m)/(5+m)+_ + 10*a^2*b^3*x^(7+m)/(7+m)+5*a*b^4*x^(9+m)/(9+m)+b^5*x^(11+m)/(11+m) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m + 5775a b ) +--R * +--R m + 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R m + 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R m + 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R m + 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m +--R + +--R 4 +--R 5775a b +--R * +--R 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R * +--R m log(x) +--R %e +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 3 5 2 5 5 11 +--R (b m + 25b m + 230b m + 950b m + 1689b m + 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 135a b m + 1310a b m + 5610a b m + 10205a b m +--R + +--R 4 +--R 5775a b +--R * +--R 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 290a b m + 3020a b m + 13660a b m + 25770a b m +--R + +--R 2 3 +--R 14850a b +--R * +--R 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 310a b m + 3500a b m + 17300a b m + 34890a b m +--R + +--R 3 2 +--R 20790a b +--R * +--R 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 165a b m + 2030a b m + 11310a b m + 26765a b m +--R + +--R 4 +--R 17325a b +--R * +--R 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 35a m + 470a m + 3010a m + 9129a m + 10395a )x +--R * +--R m log(x) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 11 +--R (- b m - 25b m - 230b m - 950b m - 1689b m - 945b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 135a b m - 1310a b m - 5610a b m - 10205a b m +--R + +--R 4 +--R - 5775a b +--R * +--R m + 9 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R - 10a b m - 290a b m - 3020a b m - 13660a b m - 25770a b m +--R + +--R 2 3 +--R - 14850a b +--R * +--R m + 7 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R - 10a b m - 310a b m - 3500a b m - 17300a b m - 34890a b m +--R + +--R 3 2 +--R - 20790a b +--R * +--R m + 5 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 165a b m - 2030a b m - 11310a b m - 26765a b m +--R + +--R 4 +--R - 17325a b +--R * +--R m + 3 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (- a m - 35a m - 470a m - 3010a m - 9129a m - 10395a )x +--R / +--R 6 5 4 3 2 +--R m + 36m + 505m + 3480m + 12139m + 19524m + 10395 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1393 +t0:=x^11*(a+b*x^2)^5 +--R +--R +--R 5 21 4 19 2 3 17 3 2 15 4 13 5 11 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 276 + +--S 277 of 1393 +r0:=1/12*a^5*x^12+5/14*a^4*b*x^14+5/8*a^3*b^2*x^16+5/9*a^2*b^3*x^18+_ + 1/4*a*b^4*x^20+1/22*b^5*x^22 +--R +--R +--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12 +--R (2) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x +--R 22 4 9 8 14 12 +--R Type: Polynomial(Fraction(Integer)) +--E 277 + +--S 278 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 22 1 4 20 5 2 3 18 5 3 2 16 5 4 14 1 5 12 +--R (3) -- b x + - a b x + - a b x + - a b x + -- a b x + -- a x +--R 22 4 9 8 14 12 +--R Type: Polynomial(Fraction(Integer)) +--E 278 + +--S 279 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 279 + +--S 280 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 280 + +)clear all + +--S 281 of 1393 +t0:=x^9*(a+b*x^2)^5 +--R +--R +--R 5 19 4 17 2 3 15 3 2 13 4 11 5 9 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 281 + +--S 282 of 1393 +r0:=1/10*a^5*x^10+5/12*a^4*b*x^12+5/7*a^3*b^2*x^14+5/8*a^2*b^3*x^16+_ + 5/18*a*b^4*x^18+1/20*b^5*x^20 +--R +--R +--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10 +--R (2) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x +--R 20 18 8 7 12 10 +--R Type: Polynomial(Fraction(Integer)) +--E 282 + +--S 283 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 20 5 4 18 5 2 3 16 5 3 2 14 5 4 12 1 5 10 +--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a x +--R 20 18 8 7 12 10 +--R Type: Polynomial(Fraction(Integer)) +--E 283 + +--S 284 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 284 + +--S 285 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 285 + +)clear all + +--S 286 of 1393 +t0:=x^7*(a+b*x^2)^5 +--R +--R +--R 5 17 4 15 2 3 13 3 2 11 4 9 5 7 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 286 + +--S 287 of 1393 +r0:=1/8*a^5*x^8+1/2*a^4*b*x^10+5/6*a^3*b^2*x^12+5/7*a^2*b^3*x^14+_ + 5/16*a*b^4*x^16+1/18*b^5*x^18 +--R +--R +--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8 +--R (2) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 18 16 7 6 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 287 + +--S 288 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 18 5 4 16 5 2 3 14 5 3 2 12 1 4 10 1 5 8 +--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 18 16 7 6 2 8 +--R Type: Polynomial(Fraction(Integer)) +--E 288 + +--S 289 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 289 + +--S 290 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 290 + +)clear all + +--S 291 of 1393 +t0:=x^5*(a+b*x^2)^5 +--R +--R +--R 5 15 4 13 2 3 11 3 2 9 4 7 5 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 291 + +--S 292 of 1393 +r0:=1/12*a^2*(a+b*x^2)^6/b^3-1/7*a*(a+b*x^2)^7/b^3+1/16*(a+b*x^2)^8/b^3 +--R +--R +--R (2) +--R 1 8 16 5 7 14 5 2 6 12 3 5 10 5 4 4 8 1 5 3 6 1 8 +--R -- b x + -- a b x + - a b x + a b x + - a b x + - a b x + --- a +--R 16 14 6 8 6 336 +--R -------------------------------------------------------------------------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 292 + +--S 293 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 16 5 4 14 5 2 3 12 3 2 10 5 4 8 1 5 6 +--R (3) -- b x + -- a b x + - a b x + a b x + - a b x + - a x +--R 16 14 6 8 6 +--R Type: Polynomial(Fraction(Integer)) +--E 293 + +--S 294 of 1393 +m0:=a0-r0 +--R +--R +--R 1 8 +--R --- a +--R 336 +--R (4) - ------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 294 + +--S 295 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 295 + +)clear all + +--S 296 of 1393 +t0:=x^3*(a+b*x^2)^5 +--R +--R +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 296 + +--S 297 of 1393 +r0:=-1/12*a*(a+b*x^2)^6/b^2+1/14*(a+b*x^2)^7/b^2 +--R +--R +--R (2) +--R 1 7 14 5 6 12 2 5 10 5 3 4 8 5 4 3 6 1 5 2 4 1 7 +--R -- b x + -- a b x + a b x + - a b x + - a b x + - a b x - -- a +--R 14 12 4 6 4 84 +--R ------------------------------------------------------------------------ +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 297 + +--S 298 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 14 5 4 12 2 3 10 5 3 2 8 5 4 6 1 5 4 +--R (3) -- b x + -- a b x + a b x + - a b x + - a b x + - a x +--R 14 12 4 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 298 + +--S 299 of 1393 +m0:=a0-r0 +--R +--R +--R 1 7 +--R -- a +--R 84 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 299 + +--S 300 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 300 + +)clear all + +--S 301 of 1393 +t0:=x*(a+b*x^2)^5 +--R +--R +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 301 + +--S 302 of 1393 +r0:=1/12*(a+b*x^2)^6/b +--R +--R +--R (2) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R -- b x + - a b x + - a b x + - a b x + - a b x + - a b x + -- a +--R 12 2 4 3 4 2 12 +--R ------------------------------------------------------------------------ +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 302 + +--S 303 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 12 1 4 10 5 2 3 8 5 3 2 6 5 4 4 1 5 2 +--R (3) -- b x + - a b x + - a b x + - a b x + - a b x + - a x +--R 12 2 4 3 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 303 + +--S 304 of 1393 +m0:=a0-r0 +--R +--R +--R 1 6 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 304 + +--S 305 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 305 + +)clear all + +--S 306 of 1393 +t0:=(a+b*x^2)^5/x +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1393 +r0:=5/2*a^4*b*x^2+5/2*a^3*b^2*x^4+5/3*a^2*b^3*x^6+5/8*a*b^4*x^8+_ + 1/10*b^5*x^10+a^5*log(x) +--R +--R +--R 5 5 10 4 8 2 3 6 3 2 4 4 2 +--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (2) -------------------------------------------------------------------- +--R 120 +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 5 10 4 8 2 3 6 3 2 4 4 2 +--R 120a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (3) -------------------------------------------------------------------- +--R 120 +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1393 +t0:=(a+b*x^2)^5/x^3 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1393 +r0:=-1/2*a^5/x^2+5*a^3*b^2*x^2+5/2*a^2*b^3*x^4+5/6*a*b^4*x^6+_ + 1/8*b^5*x^8+5*a^4*b*log(x) +--R +--R +--R 4 2 5 10 4 8 2 3 6 3 2 4 5 +--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (2) ----------------------------------------------------------------- +--R 2 +--R 24x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 2 5 10 4 8 2 3 6 3 2 4 5 +--R 120a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (3) ----------------------------------------------------------------- +--R 2 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1393 +t0:=(a+b*x^2)^5/x^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1393 +r0:=-1/4*a^5/x^4-5/2*a^4*b/x^2+5*a^2*b^3*x^2+5/4*a*b^4*x^4+_ + 1/6*b^5*x^6+10*a^3*b^2*log(x) +--R +--R +--R 3 2 4 5 10 4 8 2 3 6 4 2 5 +--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (2) --------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 2 4 5 10 4 8 2 3 6 4 2 5 +--R 120a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (3) --------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1393 +t0:=(a+b*x^2)^5/x^7 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1393 +r0:=-1/6*a^5/x^6-5/4*a^4*b/x^4-5*a^3*b^2/x^2+5/2*a*b^4*x^2+_ + 1/4*b^5*x^4+10*a^2*b^3*log(x) +--R +--R +--R 2 3 6 5 10 4 8 3 2 4 4 2 5 +--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (2) --------------------------------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 3 6 5 10 4 8 3 2 4 4 2 5 +--R 120a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (3) --------------------------------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1393 +t0:=(a+b*x^2)^5/x^9 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1393 +r0:=-1/8*a^5/x^8-5/6*a^4*b/x^6-5/2*a^3*b^2/x^4-5*a^2*b^3/x^2+_ + 1/2*b^5*x^2+5*a*b^4*log(x) +--R +--R +--R 4 8 5 10 2 3 6 3 2 4 4 2 5 +--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (2) ----------------------------------------------------------------- +--R 8 +--R 24x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 8 5 10 2 3 6 3 2 4 4 2 5 +--R 120a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (3) ----------------------------------------------------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1393 +t0:=(a+b*x^2)^5/x^11 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1393 +r0:=-1/10*a^5/x^10-5/8*a^4*b/x^8-5/3*a^3*b^2/x^6-5/2*a^2*b^3/x^4-_ + 5/2*a*b^4/x^2+b^5*log(x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (2) -------------------------------------------------------------------- +--R 10 +--R 120x +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 120b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (3) -------------------------------------------------------------------- +--R 10 +--R 120x +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1393 +t0:=(a+b*x^2)^5/x^13 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1393 +r0:=-1/12*(a+b*x^2)^6/(a*x^12) +--R +--R +--R (2) +--R 1 6 12 1 5 10 5 2 4 8 5 3 3 6 5 4 2 4 1 5 2 1 6 +--R - -- b x - - a b x - - a b x - - a b x - - a b x - - a b x - -- a +--R 12 2 4 3 4 2 12 +--R -------------------------------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 337 + +--S 338 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (3) -------------------------------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1393 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) --- +--R 12a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1393 +t0:=(a+b*x^2)^5/x^15 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1393 +r0:=-1/14*(a+b*x^2)^6/(a*x^14)+1/84*b*(a+b*x^2)^6/(a^2*x^12) +--R +--R +--R (2) +--R 1 7 14 1 2 5 10 5 3 4 8 5 4 3 6 5 2 4 5 6 2 1 7 +--R -- b x - - a b x - - a b x - - a b x - a b x - -- a b x - -- a +--R 84 4 6 4 12 14 +--R ----------------------------------------------------------------------- +--R 2 14 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 342 + +--S 343 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (3) ------------------------------------------------------------ +--R 14 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1393 +m0:=a0-r0 +--R +--R +--R 7 +--R b +--R (4) - ---- +--R 2 +--R 84a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1393 +t0:=(a+b*x^2)^5/x^17 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 346 + +--S 347 of 1393 +r0:=-1/16*a^5/x^16-5/14*a^4*b/x^14-5/6*a^3*b^2/x^12-a^2*b^3/x^10-_ + 5/8*a*b^4/x^8-1/6*b^5/x^6 +--R +--R +--R 1 5 10 5 4 8 2 3 6 5 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - a b x - - a b x - -- a b x - -- a +--R 6 8 6 14 16 +--R (2) ------------------------------------------------------------ +--R 16 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 347 + +--S 348 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a +--R (3) ---------------------------------------------------------------- +--R 16 +--R 336x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1393 +t0:=(a+b*x^2)^5/x^19 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 351 + +--S 352 of 1393 +r0:=-1/18*a^5/x^18-5/16*a^4*b/x^16-5/7*a^3*b^2/x^14-5/6*a^2*b^3/x^12-_ + 1/2*a*b^4/x^10-1/8*b^5/x^8 +--R +--R +--R 1 5 10 1 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - - a b x - - a b x - -- a b x - -- a +--R 8 2 6 7 16 18 +--R (2) -------------------------------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 352 + +--S 353 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) ----------------------------------------------------------------- +--R 18 +--R 1008x +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1393 +t0:=(a+b*x^2)^5/x^21 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 356 + +--S 357 of 1393 +r0:=-1/20*a^5/x^20-5/18*a^4*b/x^18-5/8*a^3*b^2/x^16-5/7*a^2*b^3/x^14-_ + 5/12*a*b^4/x^12-1/10*b^5/x^10 +--R +--R +--R 1 5 10 5 4 8 5 2 3 6 5 3 2 4 5 4 2 1 5 +--R - -- b x - -- a b x - - a b x - - a b x - -- a b x - -- a +--R 10 12 7 8 18 20 +--R (2) ---------------------------------------------------------------- +--R 20 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 357 + +--S 358 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a +--R (3) --------------------------------------------------------------------- +--R 20 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1393 +t0:=x^8*(a+b*x^2)^5 +--R +--R +--R 5 18 4 16 2 3 14 3 2 12 4 10 5 8 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 361 + +--S 362 of 1393 +r0:=1/9*a^5*x^9+5/11*a^4*b*x^11+10/13*a^3*b^2*x^13+2/3*a^2*b^3*x^15+_ + 5/17*a*b^4*x^17+1/19*b^5*x^19 +--R +--R +--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9 +--R (2) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x +--R 19 17 3 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 362 + +--S 363 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 19 5 4 17 2 2 3 15 10 3 2 13 5 4 11 1 5 9 +--R (3) -- b x + -- a b x + - a b x + -- a b x + -- a b x + - a x +--R 19 17 3 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 363 + +--S 364 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 364 + +--S 365 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 365 + +)clear all + +--S 366 of 1393 +t0:=x^6*(a+b*x^2)^5 +--R +--R +--R 5 16 4 14 2 3 12 3 2 10 4 8 5 6 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 366 + +--S 367 of 1393 +r0:=1/7*a^5*x^7+5/9*a^4*b*x^9+10/11*a^3*b^2*x^11+10/13*a^2*b^3*x^13+_ + 1/3*a*b^4*x^15+1/17*b^5*x^17 +--R +--R +--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7 +--R (2) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x +--R 17 3 13 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 367 + +--S 368 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 17 1 4 15 10 2 3 13 10 3 2 11 5 4 9 1 5 7 +--R (3) -- b x + - a b x + -- a b x + -- a b x + - a b x + - a x +--R 17 3 13 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 368 + +--S 369 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 369 + +--S 370 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 370 + +)clear all + +--S 371 of 1393 +t0:=x^4*(a+b*x^2)^5 +--R +--R +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 371 + +--S 372 of 1393 +r0:=1/5*a^5*x^5+5/7*a^4*b*x^7+10/9*a^3*b^2*x^9+10/11*a^2*b^3*x^11+_ + 5/13*a*b^4*x^13+1/15*b^5*x^15 +--R +--R +--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5 +--R (2) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x +--R 15 13 11 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 372 + +--S 373 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 15 5 4 13 10 2 3 11 10 3 2 9 5 4 7 1 5 5 +--R (3) -- b x + -- a b x + -- a b x + -- a b x + - a b x + - a x +--R 15 13 11 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 373 + +--S 374 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 374 + +--S 375 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 375 + +)clear all + +--S 376 of 1393 +t0:=x^2*(a+b*x^2)^5 +--R +--R +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 376 + +--S 377 of 1393 +r0:=1/3*a^5*x^3+a^4*b*x^5+10/7*a^3*b^2*x^7+10/9*a^2*b^3*x^9+_ + 5/11*a*b^4*x^11+1/13*b^5*x^13 +--R +--R +--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3 +--R (2) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x +--R 13 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 377 + +--S 378 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 13 5 4 11 10 2 3 9 10 3 2 7 4 5 1 5 3 +--R (3) -- b x + -- a b x + -- a b x + -- a b x + a b x + - a x +--R 13 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 378 + +--S 379 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 379 + +--S 380 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 380 + +)clear all + +--S 381 of 1393 +t0:=(a+b*x^2)^5 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 381 + +--S 382 of 1393 +r0:=a^5*x+5/3*a^4*b*x^3+2*a^3*b^2*x^5+10/7*a^2*b^3*x^7+5/9*a*b^4*x^9+_ + 1/11*b^5*x^11 +--R +--R +--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5 +--R (2) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x +--R 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 382 + +--S 383 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 5 11 5 4 9 10 2 3 7 3 2 5 5 4 3 5 +--R (3) -- b x + - a b x + -- a b x + 2a b x + - a b x + a x +--R 11 9 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 383 + +--S 384 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 384 + +--S 385 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 385 + +)clear all + +--S 386 of 1393 +t0:=(a+b*x^2)^5/x^2 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 386 + +--S 387 of 1393 +r0:=-a^5/x+5*a^4*b*x+10/3*a^3*b^2*x^3+2*a^2*b^3*x^5+5/7*a*b^4*x^7+1/9*b^5*x^9 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a +--R (2) ------------------------------------------------------------ +--R 63x +--R Type: Fraction(Polynomial(Integer)) +--E 387 + +--S 388 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 45a b x + 126a b x + 210a b x + 315a b x - 63a +--R (3) ------------------------------------------------------------ +--R 63x +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1393 +t0:=(a+b*x^2)^5/x^4 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 391 + +--S 392 of 1393 +r0:=-1/3*a^5/x^3-5*a^4*b/x+10*a^3*b^2*x+10/3*a^2*b^3*x^3+a*b^4*x^5+1/7*b^5*x^7 +--R +--R +--R 1 5 10 4 8 10 2 3 6 3 2 4 4 2 1 5 +--R - b x + a b x + -- a b x + 10a b x - 5a b x - - a +--R 7 3 3 +--R (2) -------------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 392 + +--S 393 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 21a b x + 70a b x + 210a b x - 105a b x - 7a +--R (3) ---------------------------------------------------------- +--R 3 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1393 +t0:=(a+b*x^2)^5/x^6 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 396 + +--S 397 of 1393 +r0:=-1/5*a^5/x^5-5/3*a^4*b/x^3-10*a^3*b^2/x+10*a^2*b^3*x+_ + 5/3*a*b^4*x^3+1/5*b^5*x^5 +--R +--R +--R 1 5 10 5 4 8 2 3 6 3 2 4 5 4 2 1 5 +--R - b x + - a b x + 10a b x - 10a b x - - a b x - - a +--R 5 3 3 5 +--R (2) ---------------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 397 + +--S 398 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x + 150a b x - 150a b x - 25a b x - 3a +--R (3) ---------------------------------------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1393 +t0:=(a+b*x^2)^5/x^8 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 401 + +--S 402 of 1393 +r0:=-1/7*a^5/x^7-a^4*b/x^5-10/3*a^3*b^2/x^3-10*a^2*b^3/x+5*a*b^4*x+1/3*b^5*x^3 +--R +--R +--R 1 5 10 4 8 2 3 6 10 3 2 4 4 2 1 5 +--R - b x + 5a b x - 10a b x - -- a b x - a b x - - a +--R 3 3 7 +--R (2) -------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 402 + +--S 403 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 7b x + 105a b x - 210a b x - 70a b x - 21a b x - 3a +--R (3) ---------------------------------------------------------- +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1393 +t0:=(a+b*x^2)^5/x^10 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 406 + +--S 407 of 1393 +r0:=-1/9*a^5/x^9-5/7*a^4*b/x^7-2*a^3*b^2/x^5-10/3*a^2*b^3/x^3-5*a*b^4/x+b^5*x +--R +--R +--R 5 10 4 8 10 2 3 6 3 2 4 5 4 2 1 5 +--R b x - 5a b x - -- a b x - 2a b x - - a b x - - a +--R 3 7 9 +--R (2) ------------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 407 + +--S 408 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 63b x - 315a b x - 210a b x - 126a b x - 45a b x - 7a +--R (3) ------------------------------------------------------------ +--R 9 +--R 63x +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1393 +t0:=(a+b*x^2)^5/x^12 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 411 + +--S 412 of 1393 +r0:=-1/11*a^5/x^11-5/9*a^4*b/x^9-10/7*a^3*b^2/x^7-2*a^2*b^3/x^5-_ + 5/3*a*b^4/x^3-b^5/x +--R +--R +--R 5 10 5 4 8 2 3 6 10 3 2 4 5 4 2 1 5 +--R - b x - - a b x - 2a b x - -- a b x - - a b x - -- a +--R 3 7 9 11 +--R (2) ----------------------------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 412 + +--S 413 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 693b x - 1155a b x - 1386a b x - 990a b x - 385a b x - 63a +--R (3) ------------------------------------------------------------------- +--R 11 +--R 693x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1393 +t0:=(a+b*x^2)^5/x^14 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 416 + +--S 417 of 1393 +r0:=-1/13*a^5/x^13-5/11*a^4*b/x^11-10/9*a^3*b^2/x^9-10/7*a^2*b^3/x^7-_ + a*b^4/x^5-1/3*b^5/x^3 +--R +--R +--R 1 5 10 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5 +--R - - b x - a b x - -- a b x - -- a b x - -- a b x - -- a +--R 3 7 9 11 13 +--R (2) -------------------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 417 + +--S 418 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 3003b x - 9009a b x - 12870a b x - 10010a b x - 4095a b x - 693a +--R ------------------------------------------------------------------------- +--R 13 +--R 9009x +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1393 +t0:=(a+b*x^2)^5/x^16 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 421 + +--S 422 of 1393 +r0:=-1/15*a^5/x^15-5/13*a^4*b/x^13-10/11*a^3*b^2/x^11-10/9*a^2*b^3/x^9-_ + 5/7*a*b^4/x^7-1/5*b^5/x^5 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 5 4 2 1 5 +--R - - b x - - a b x - -- a b x - -- a b x - -- a b x - -- a +--R 5 7 9 11 13 15 +--R (2) ---------------------------------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 422 + +--S 423 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 9009b x - 32175a b x - 50050a b x - 40950a b x - 17325a b x - 3003a +--R ---------------------------------------------------------------------------- +--R 15 +--R 45045x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1393 +t0:=(a+b*x^2)^5/x^18 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 426 + +--S 427 of 1393 +r0:=-1/17*a^5/x^17-1/3*a^4*b/x^15-10/13*a^3*b^2/x^13-_ + 10/11*a^2*b^3/x^11-5/9*a*b^4/x^9-1/7*b^5/x^7 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 10 3 2 4 1 4 2 1 5 +--R - - b x - - a b x - -- a b x - -- a b x - - a b x - -- a +--R 7 9 11 13 3 17 +--R (2) --------------------------------------------------------------- +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 427 + +--S 428 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 21879b x - 85085a b x - 139230a b x - 117810a b x - 51051a b x +--R + +--R 5 +--R - 9009a +--R / +--R 17 +--R 153153x +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1393 +t0:=(a+b*x^2)^5/x^20 +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ---------------------------------------------------- +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 431 + +--S 432 of 1393 +r0:=-1/19*a^5/x^19-5/17*a^4*b/x^17-2/3*a^3*b^2/x^15-10/13*a^2*b^3/x^13-_ + 5/11*a*b^4/x^11-1/9*b^5/x^9 +--R +--R +--R 1 5 10 5 4 8 10 2 3 6 2 3 2 4 5 4 2 1 5 +--R - - b x - -- a b x - -- a b x - - a b x - -- a b x - -- a +--R 9 11 13 3 17 19 +--R (2) ---------------------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 432 + +--S 433 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 46189b x - 188955a b x - 319770a b x - 277134a b x - 122265a b x +--R + +--R 5 +--R - 21879a +--R / +--R 19 +--R 415701x +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1393 +t0:=x^m*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1393 +r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(3+m)/(3+m)+28*a^6*b^2*x^(5+m)/(5+m)+_ + 56*a^5*b^3*x^(7+m)/(7+m)+70*a^4*b^4*x^(9+m)/(9+m)+_ + 56*a^3*b^5*x^(11+m)/(11+m)+28*a^2*b^6*x^(13+m)/(13+m)+_ + 8*a*b^7*x^(15+m)/(15+m)+b^8*x^(17+m)/(17+m) +--R +--R +--R (2) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R m + 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R m + 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b +--R * +--R m + 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m + 15772064a b m +--R + +--R 3 5 3 3 5 2 3 5 3 5 +--R 82703600a b m + 242205264a b m + 349055280a b m + 175429800a b +--R * +--R m + 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m + 22248660a b m +--R + +--R 4 4 3 4 4 2 4 4 4 4 +--R 120007440a b m + 359864120a b m + 527864400a b m + 268017750a b +--R * +--R m + 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m + 20318144a b m +--R + +--R 5 3 3 5 3 2 5 3 5 3 +--R 113969296a b m + 354159792a b m + 534194640a b m + 275675400a b +--R * +--R m + 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m + 11730712a b m +--R + +--R 6 2 3 6 2 2 6 2 6 2 +--R 69444592a b m + 228749472a b m + 362909232a b m + 192972780a b +--R * +--R m + 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R m + 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m + 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 36270416a b m + 104457024a b m + 148715280a b m + 74220300a b +--R * +--R 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 3 5 +--R 15772064a b m + 82703600a b m + 242205264a b m + 349055280a b m +--R + +--R 3 5 +--R 175429800a b +--R * +--R 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 +--R 22248660a b m + 120007440a b m + 359864120a b m + 527864400a b m +--R + +--R 4 4 +--R 268017750a b +--R * +--R 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 5 3 +--R 20318144a b m + 113969296a b m + 354159792a b m + 534194640a b m +--R + +--R 5 3 +--R 275675400a b +--R * +--R 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 6 2 +--R 11730712a b m + 69444592a b m + 228749472a b m + 362909232a b m +--R + +--R 6 2 +--R 192972780a b +--R * +--R 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1393 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 64b m + 1708b m + 24640b m + 208054b m + 1038016b m +--R + +--R 8 2 8 8 +--R 2924172b m + 4098240b m + 2027025b +--R * +--R 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 528a b m + 14448a b m + 212688a b m + 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R 9222192a b m + 26230672a b m + 37013232a b m + 18378360a b +--R * +--R 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 1904a b m + 53536a b m + 806960a b m +--R + +--R 2 6 4 2 6 3 2 6 2 2 6 +--R 7063672a b m + 36270416a b m + 104457024a b m + 148715280a b m +--R + +--R 2 6 +--R 74220300a b +--R * +--R 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 3920a b m + 113456a b m + 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R 15772064a b m + 82703600a b m + 242205264a b m +--R + +--R 3 5 3 5 +--R 349055280a b m + 175429800a b +--R * +--R 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 5040a b m + 150360a b m + 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R 22248660a b m + 120007440a b m + 359864120a b m +--R + +--R 4 4 4 4 +--R 527864400a b m + 268017750a b +--R * +--R 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 4144a b m + 127568a b m + 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R 20318144a b m + 113969296a b m + 354159792a b m +--R + +--R 5 3 5 3 +--R 534194640a b m + 275675400a b +--R * +--R 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 2128a b m + 67648a b m + 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R 11730712a b m + 69444592a b m + 228749472a b m +--R + +--R 6 2 6 2 +--R 362909232a b m + 192972780a b +--R * +--R 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 624a b m + 20496a b m + 367920a b m + 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R 24864336a b m + 89970544a b m + 160561680a b m + 91891800a b +--R * +--R 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 80a m + 2716a m + 50960a m + 575974a m + 3998960a m +--R + +--R 8 2 8 8 +--R 16571484a m + 37237680a m + 34459425a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - b m - 64b m - 1708b m - 24640b m - 208054b m - 1038016b m +--R + +--R 8 2 8 8 +--R - 2924172b m - 4098240b m - 2027025b +--R * +--R m + 17 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 528a b m - 14448a b m - 212688a b m - 1825152a b m +--R + +--R 7 3 7 2 7 7 +--R - 9222192a b m - 26230672a b m - 37013232a b m - 18378360a b +--R * +--R m + 15 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R - 28a b m - 1904a b m - 53536a b m - 806960a b m - 7063672a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R - 36270416a b m - 104457024a b m - 148715280a b m - 74220300a b +--R * +--R m + 13 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R - 56a b m - 3920a b m - 113456a b m - 1757840a b m +--R + +--R 3 5 4 3 5 3 3 5 2 3 5 +--R - 15772064a b m - 82703600a b m - 242205264a b m - 349055280a b m +--R + +--R 3 5 +--R - 175429800a b +--R * +--R m + 11 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R - 70a b m - 5040a b m - 150360a b m - 2404080a b m +--R + +--R 4 4 4 4 4 3 4 4 2 4 4 +--R - 22248660a b m - 120007440a b m - 359864120a b m - 527864400a b m +--R + +--R 4 4 +--R - 268017750a b +--R * +--R m + 9 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R - 56a b m - 4144a b m - 127568a b m - 2112880a b m +--R + +--R 5 3 4 5 3 3 5 3 2 5 3 +--R - 20318144a b m - 113969296a b m - 354159792a b m - 534194640a b m +--R + +--R 5 3 +--R - 275675400a b +--R * +--R m + 7 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R - 28a b m - 2128a b m - 67648a b m - 1164688a b m +--R + +--R 6 2 4 6 2 3 6 2 2 6 2 +--R - 11730712a b m - 69444592a b m - 228749472a b m - 362909232a b m +--R + +--R 6 2 +--R - 192972780a b +--R * +--R m + 5 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 624a b m - 20496a b m - 367920a b m - 3911712a b m +--R + +--R 7 3 7 2 7 7 +--R - 24864336a b m - 89970544a b m - 160561680a b m - 91891800a b +--R * +--R m + 3 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - a m - 80a m - 2716a m - 50960a m - 575974a m - 3998960a m +--R + +--R 8 2 8 8 +--R - 16571484a m - 37237680a m - 34459425a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 81m + 2796m + 53676m + 626934m + 4574934m + 20570444m +--R + +--R 2 +--R 53809164m + 71697105m + 34459425 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1393 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1393 +t0:=x^13*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 29 7 27 2 6 25 3 5 23 4 4 21 5 3 19 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 17 7 15 8 13 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 441 + +--S 442 of 1393 +r0:=1/14*a^8*x^14+1/2*a^7*b*x^16+14/9*a^6*b^2*x^18+14/5*a^5*b^3*x^20+_ + 35/11*a^4*b^4*x^22+7/3*a^3*b^5*x^24+14/13*a^2*b^6*x^26+_ + 2/7*a*b^7*x^28+1/30*b^8*x^30 +--R +--R +--R (2) +--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 30 7 13 3 11 5 +--R + +--R 14 6 2 18 1 7 16 1 8 14 +--R -- a b x + - a b x + -- a x +--R 9 2 14 +--R Type: Polynomial(Fraction(Integer)) +--E 442 + +--S 443 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 30 2 7 28 14 2 6 26 7 3 5 24 35 4 4 22 14 5 3 20 +--R -- b x + - a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 30 7 13 3 11 5 +--R + +--R 14 6 2 18 1 7 16 1 8 14 +--R -- a b x + - a b x + -- a x +--R 9 2 14 +--R Type: Polynomial(Fraction(Integer)) +--E 443 + +--S 444 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 444 + +--S 445 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 445 + +)clear all + +--S 446 of 1393 +t0:=x^11*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 27 7 25 2 6 23 3 5 21 4 4 19 5 3 17 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 15 7 13 8 11 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 446 + +--S 447 of 1393 +r0:=-1/18*a^5*(a+b*x^2)^9/b^6+1/4*a^4*(a+b*x^2)^10/b^6-_ + 5/11*a^3*(a+b*x^2)^11/b^6+5/12*a^2*(a+b*x^2)^12/b^6-_ + 5/26*a*(a+b*x^2)^13/b^6+1/28*(a+b*x^2)^14/b^6 +--R +--R +--R (2) +--R 1 14 28 4 13 26 7 2 12 24 28 3 11 22 7 4 10 20 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x +--R 28 13 6 11 2 +--R + +--R 28 5 9 18 7 6 8 16 4 7 7 14 1 8 6 12 1 14 +--R -- a b x + - a b x + - a b x + -- a b x - ----- a +--R 9 4 7 12 36036 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 447 + +--S 448 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 28 4 7 26 7 2 6 24 28 3 5 22 7 4 4 20 28 5 3 18 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x +--R 28 13 6 11 2 9 +--R + +--R 7 6 2 16 4 7 14 1 8 12 +--R - a b x + - a b x + -- a x +--R 4 7 12 +--R Type: Polynomial(Fraction(Integer)) +--E 448 + +--S 449 of 1393 +m0:=a0-r0 +--R +--R +--R 1 14 +--R ----- a +--R 36036 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 449 + +--S 450 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 450 + +)clear all + +--S 451 of 1393 +t0:=x^9*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 25 7 23 2 6 21 3 5 19 4 4 17 5 3 15 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 13 7 11 8 9 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 451 + +--S 452 of 1393 +r0:=1/18*a^4*(a+b*x^2)^9/b^5-1/5*a^3*(a+b*x^2)^10/b^5+_ + 3/11*a^2*(a+b*x^2)^11/b^5-1/6*a*(a+b*x^2)^12/b^5+1/26*(a+b*x^2)^13/b^5 +--R +--R +--R (2) +--R 1 13 26 1 12 24 14 2 11 22 14 3 10 20 35 4 9 18 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x +--R 26 3 11 5 9 +--R + +--R 7 5 8 16 6 7 14 2 7 6 12 1 8 5 10 1 13 +--R - a b x + 2a b x + - a b x + -- a b x + ----- a +--R 2 3 10 12870 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 452 + +--S 453 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 26 1 7 24 14 2 6 22 14 3 5 20 35 4 4 18 7 5 3 16 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 26 3 11 5 9 2 +--R + +--R 6 2 14 2 7 12 1 8 10 +--R 2a b x + - a b x + -- a x +--R 3 10 +--R Type: Polynomial(Fraction(Integer)) +--E 453 + +--S 454 of 1393 +m0:=a0-r0 +--R +--R +--R 1 13 +--R ----- a +--R 12870 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 454 + +--S 455 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 455 + +)clear all + +--S 456 of 1393 +t0:=x^7*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 23 7 21 2 6 19 3 5 17 4 4 15 5 3 13 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 11 7 9 8 7 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 456 + +--S 457 of 1393 +r0:=-1/18*a^3*(a+b*x^2)^9/b^4+3/20*a^2*(a+b*x^2)^10/b^4-_ + 3/22*a*(a+b*x^2)^11/b^4+1/24*(a+b*x^2)^12/b^4 +--R +--R +--R (2) +--R 1 12 24 4 11 22 7 2 10 20 28 3 9 18 35 4 8 16 5 7 14 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x +--R 24 11 5 9 8 +--R + +--R 7 6 6 12 4 7 5 10 1 8 4 8 1 12 +--R - a b x + - a b x + - a b x - ---- a +--R 3 5 8 3960 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 457 + +--S 458 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 24 4 7 22 7 2 6 20 28 3 5 18 35 4 4 16 5 3 14 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + 4a b x +--R 24 11 5 9 8 +--R + +--R 7 6 2 12 4 7 10 1 8 8 +--R - a b x + - a b x + - a x +--R 3 5 8 +--R Type: Polynomial(Fraction(Integer)) +--E 458 + +--S 459 of 1393 +m0:=a0-r0 +--R +--R +--R 1 12 +--R ---- a +--R 3960 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 459 + +--S 460 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 460 + +)clear all + +--S 461 of 1393 +t0:=x^5*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 21 7 19 2 6 17 3 5 15 4 4 13 5 3 11 6 2 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 7 8 5 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 461 + +--S 462 of 1393 +r0:=1/18*a^2*(a+b*x^2)^9/b^3-1/10*a*(a+b*x^2)^10/b^3+1/22*(a+b*x^2)^11/b^3 +--R +--R +--R (2) +--R 1 11 22 2 10 20 14 2 9 18 7 3 8 16 4 7 14 14 5 6 12 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x +--R 22 5 9 2 3 +--R + +--R 14 6 5 10 7 4 8 1 8 3 6 1 11 +--R -- a b x + a b x + - a b x + --- a +--R 5 6 990 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 462 + +--S 463 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 22 2 7 20 14 2 6 18 7 3 5 16 4 4 14 14 5 3 12 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x + -- a b x +--R 22 5 9 2 3 +--R + +--R 14 6 2 10 7 8 1 8 6 +--R -- a b x + a b x + - a x +--R 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 463 + +--S 464 of 1393 +m0:=a0-r0 +--R +--R +--R 1 11 +--R --- a +--R 990 +--R (4) - ------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 464 + +--S 465 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 465 + +)clear all + +--S 466 of 1393 +t0:=x^3*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 19 7 17 2 6 15 3 5 13 4 4 11 5 3 9 6 2 7 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 5 8 3 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 466 + +--S 467 of 1393 +r0:=-1/18*a*(a+b*x^2)^9/b^2+1/20*(a+b*x^2)^10/b^2 +--R +--R +--R (2) +--R 1 10 20 4 9 18 7 2 8 16 3 7 14 35 4 6 12 28 5 5 10 +--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x +--R 20 9 4 6 5 +--R + +--R 7 6 4 8 4 7 3 6 1 8 2 4 1 10 +--R - a b x + - a b x + - a b x - --- a +--R 2 3 4 180 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 467 + +--S 468 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 20 4 7 18 7 2 6 16 3 5 14 35 4 4 12 28 5 3 10 +--R -- b x + - a b x + - a b x + 4a b x + -- a b x + -- a b x +--R 20 9 4 6 5 +--R + +--R 7 6 2 8 4 7 6 1 8 4 +--R - a b x + - a b x + - a x +--R 2 3 4 +--R Type: Polynomial(Fraction(Integer)) +--E 468 + +--S 469 of 1393 +m0:=a0-r0 +--R +--R +--R 1 10 +--R --- a +--R 180 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 469 + +--S 470 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 470 + +)clear all + +--S 471 of 1393 +t0:=x*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 5 3 7 6 2 5 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 3 8 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 471 + +--S 472 of 1393 +r0:=1/18*(a+b*x^2)^9/b +--R +--R +--R (2) +--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8 +--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x +--R 18 2 3 +--R + +--R 14 6 3 6 7 2 4 1 8 2 1 9 +--R -- a b x + 2a b x + - a b x + -- a +--R 3 2 18 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 472 + +--S 473 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 18 1 7 16 2 6 14 14 3 5 12 4 4 10 5 3 8 +--R -- b x + - a b x + 2a b x + -- a b x + 7a b x + 7a b x +--R 18 2 3 +--R + +--R 14 6 2 6 7 4 1 8 2 +--R -- a b x + 2a b x + - a x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 473 + +--S 474 of 1393 +m0:=a0-r0 +--R +--R +--R 1 9 +--R -- a +--R 18 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 474 + +--S 475 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 475 + +)clear all + +--S 476 of 1393 +t0:=(a+b*x^2)^8/x +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 476 + +--S 477 of 1393 +r0:=4*a^7*b*x^2+7*a^6*b^2*x^4+28/3*a^5*b^3*x^6+35/4*a^4*b^4*x^8+_ + 28/5*a^3*b^5*x^10+7/3*a^2*b^6*x^12+4/7*a*b^7*x^14+_ + 1/16*b^8*x^16+a^8*log(x) +--R +--R +--R (2) +--R 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 1680 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 1680 +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1393 +t0:=(a+b*x^2)^8/x^3 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 481 + +--S 482 of 1393 +r0:=-1/2*a^8/x^2+14*a^6*b^2*x^2+14*a^5*b^3*x^4+35/3*a^4*b^4*x^6+_ + 7*a^3*b^5*x^8+14/5*a^2*b^6*x^10+2/3*a*b^7*x^12+_ + 1/14*b^8*x^14+8*a^7*b*log(x) +--R +--R +--R (2) +--R 7 2 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 8 5 3 6 6 2 4 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 2 +--R 210x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 2 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 8 5 3 6 6 2 4 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 2 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1393 +t0:=(a+b*x^2)^8/x^5 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 486 + +--S 487 of 1393 +r0:=-1/4*a^8/x^4-4*a^7*b/x^2+28*a^5*b^3*x^2+35/2*a^4*b^4*x^4+_ + 28/3*a^3*b^5*x^6+7/2*a^2*b^6*x^8+4/5*a*b^7*x^10+_ + 1/12*b^8*x^12+28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 6 2 4 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 8 5 3 6 7 2 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 4 +--R 60x +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 4 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 8 5 3 6 7 2 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 4 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 488 + +--S 489 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +)clear all + +--S 491 of 1393 +t0:=(a+b*x^2)^8/x^7 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1393 +r0:=-1/6*a^8/x^6-2*a^7*b/x^4-14*a^6*b^2/x^2+35*a^4*b^4*x^2+_ + 14*a^3*b^5*x^4+14/3*a^2*b^6*x^6+a*b^7*x^8+1/10*b^8*x^10+_ + 56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 5 3 6 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 8 6 2 4 7 2 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 6 +--R 30x +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 6 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 8 6 2 4 7 2 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 6 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 493 + +--S 494 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1393 +t0:=(a+b*x^2)^8/x^9 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 496 + +--S 497 of 1393 +r0:=-1/8*a^8/x^8-4/3*a^7*b/x^6-7*a^6*b^2/x^4-28*a^5*b^3/x^2+_ + 28*a^3*b^5*x^2+7*a^2*b^6*x^4+4/3*a*b^7*x^6+1/8*b^8*x^8+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 4 4 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 8 +--R 24x +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 8 8 16 7 14 2 6 12 3 5 10 +--R 1680a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 498 + +--S 499 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +)clear all + +--S 501 of 1393 +t0:=(a+b*x^2)^8/x^11 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 501 + +--S 502 of 1393 +r0:=-1/10*a^8/x^10-a^7*b/x^8-14/3*a^6*b^2/x^6-14*a^5*b^3/x^4-_ + 35*a^4*b^4/x^2+14*a^2*b^6*x^2+2*a*b^7*x^4+1/6*b^8*x^6+56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 3 5 10 8 16 7 14 2 6 12 4 4 8 +--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 10 +--R 30x +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 10 8 16 7 14 2 6 12 4 4 8 +--R 1680a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 10 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 503 + +--S 504 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 505 + +)clear all + +--S 506 of 1393 +t0:=(a+b*x^2)^8/x^13 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 506 + +--S 507 of 1393 +r0:=-1/12*a^8/x^12-4/5*a^7*b/x^10-7/2*a^6*b^2/x^8-28/3*a^5*b^3/x^6-_ + 35/2*a^4*b^4/x^4-28*a^3*b^5/x^2+4*a*b^7*x^2+1/4*b^8*x^4+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 2 6 12 8 16 7 14 3 5 10 4 4 8 +--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 12 +--R 60x +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 12 8 16 7 14 3 5 10 4 4 8 +--R 1680a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 12 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 508 + +--S 509 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 510 + +)clear all + +--S 511 of 1393 +t0:=(a+b*x^2)^8/x^15 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1393 +r0:=-1/14*a^8/x^14-2/3*a^7*b/x^12-14/5*a^6*b^2/x^10-7*a^5*b^3/x^8-_ + 35/3*a^4*b^4/x^6-14*a^3*b^5/x^4-14*a^2*b^6/x^2+1/2*b^8*x^2+8*a*b^7*log(x) +--R +--R +--R (2) +--R 7 14 8 16 2 6 12 3 5 10 4 4 8 +--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 14 +--R 210x +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 8 16 2 6 12 3 5 10 4 4 8 +--R 1680a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 14 +--R 210x +--R Type: Union(Expression(Integer),...) +--E 513 + +--S 514 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 515 + +)clear all + +--S 516 of 1393 +t0:=(a+b*x^2)^8/x^17 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 516 + +--S 517 of 1393 +r0:=-1/16*a^8/x^16-4/7*a^7*b/x^14-7/3*a^6*b^2/x^12-28/5*a^5*b^3/x^10-_ + 35/4*a^4*b^4/x^8-28/3*a^3*b^5/x^6-7*a^2*b^6/x^4-4*a*b^7/x^2+b^8*log(x) +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 16 +--R 1680x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 1680b x log(x) - 6720a b x - 11760a b x - 15680a b x - 14700a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 16 +--R 1680x +--R Type: Union(Expression(Integer),...) +--E 518 + +--S 519 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 520 + +)clear all + +--S 521 of 1393 +t0:=(a+b*x^2)^8/x^19 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 521 + +--S 522 of 1393 +r0:=-1/18*(a+b*x^2)^9/(a*x^18) +--R +--R +--R (2) +--R 1 9 18 1 8 16 2 7 14 14 3 6 12 4 5 10 5 4 8 +--R - -- b x - - a b x - 2a b x - -- a b x - 7a b x - 7a b x +--R 18 2 3 +--R + +--R 14 6 3 6 7 2 4 1 8 2 1 9 +--R - -- a b x - 2a b x - - a b x - -- a +--R 3 2 18 +--R / +--R 18 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 522 + +--S 523 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 4 7 2 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 523 + +--S 524 of 1393 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 18a +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1393 +t0:=(a+b*x^2)^8/x^21 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 21 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1393 +r0:=-1/20*(a+b*x^2)^9/(a*x^20)+1/180*b*(a+b*x^2)^9/(a^2*x^18) +--R +--R +--R (2) +--R 1 10 20 1 2 8 16 4 3 7 14 7 4 6 12 28 5 5 10 35 6 4 8 +--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 180 4 3 2 5 6 +--R + +--R 7 3 6 7 8 2 4 4 9 2 1 10 +--R - 4a b x - - a b x - - a b x - -- a +--R 4 9 20 +--R / +--R 2 20 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 527 + +--S 528 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 720a b x - 315a b x - 80a b x - 9a +--R / +--R 20 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1393 +m0:=a0-r0 +--R +--R +--R 10 +--R b +--R (4) - ----- +--R 2 +--R 180a +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1393 +t0:=(a+b*x^2)^8/x^23 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 23 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1393 +r0:=-1/22*(a+b*x^2)^9/(a*x^22)+1/110*b*(a+b*x^2)^9/(a^2*x^20)-_ + 1/990*b^2*(a+b*x^2)^9/(a^3*x^18) +--R +--R +--R (2) +--R 1 11 22 1 3 8 16 4 7 14 14 5 6 12 14 6 5 10 7 4 8 +--R - --- b x - - a b x - a b x - -- a b x - -- a b x - 5a b x +--R 990 6 5 3 +--R + +--R 7 8 3 6 14 9 2 4 2 10 2 1 11 +--R - - a b x - -- a b x - - a b x - -- a +--R 2 9 5 22 +--R / +--R 3 22 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 532 + +--S 533 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 3465a b x - 1540a b x - 396a b x - 45a +--R / +--R 22 +--R 990x +--R Type: Union(Expression(Integer),...) +--E 533 + +--S 534 of 1393 +m0:=a0-r0 +--R +--R +--R 11 +--R b +--R (4) ----- +--R 3 +--R 990a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +)clear all + +--S 536 of 1393 +t0:=(a+b*x^2)^8/x^25 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 536 + +--S 537 of 1393 +r0:=-1/24*(a+b*x^2)^9/(a*x^24)+1/88*b*(a+b*x^2)^9/(a^2*x^22)-_ + 1/440*b^2*(a+b*x^2)^9/(a^3*x^20)+1/3960*b^3*(a+b*x^2)^9/(a^4*x^18) +--R +--R +--R (2) +--R 1 12 24 1 4 8 16 4 5 7 14 7 6 6 12 7 5 10 35 8 4 8 +--R ---- b x - - a b x - - a b x - - a b x - 4a b x - -- a b x +--R 3960 8 5 3 8 +--R + +--R 28 9 3 6 7 10 2 4 4 11 2 1 12 +--R - -- a b x - - a b x - -- a b x - -- a +--R 9 5 11 24 +--R / +--R 4 24 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 537 + +--S 538 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 12320a b x - 5544a b x - 1440a b x - 165a +--R / +--R 24 +--R 3960x +--R Type: Union(Expression(Integer),...) +--E 538 + +--S 539 of 1393 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ------ +--R 4 +--R 3960a +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 540 + +)clear all + +--S 541 of 1393 +t0:=(a+b*x^2)^8/x^27 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 27 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 541 + +--S 542 of 1393 +r0:=-1/26*a^8/x^26-1/3*a^7*b/x^24-14/11*a^6*b^2/x^22-14/5*a^5*b^3/x^20-_ + 35/9*a^4*b^4/x^18-7/2*a^3*b^5/x^16-2*a^2*b^6/x^14-_ + 2/3*a*b^7/x^12-1/10*b^8/x^10 +--R +--R +--R (2) +--R 1 8 16 2 7 14 2 6 12 7 3 5 10 35 4 4 8 14 5 3 6 +--R - -- b x - - a b x - 2a b x - - a b x - -- a b x - -- a b x +--R 10 3 2 9 5 +--R + +--R 14 6 2 4 1 7 2 1 8 +--R - -- a b x - - a b x - -- a +--R 11 3 26 +--R / +--R 26 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 542 + +--S 543 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 36036a b x - 16380a b x - 4290a b x - 495a +--R / +--R 26 +--R 12870x +--R Type: Union(Expression(Integer),...) +--E 543 + +--S 544 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 545 + +)clear all + +--S 546 of 1393 +t0:=(a+b*x^2)^8/x^29 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 29 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 546 + +--S 547 of 1393 +r0:=-1/28*a^8/x^28-4/13*a^7*b/x^26-7/6*a^6*b^2/x^24-28/11*a^5*b^3/x^22-_ + 7/2*a^4*b^4/x^20-28/9*a^3*b^5/x^18-7/4*a^2*b^6/x^16-_ + 4/7*a*b^7/x^14-1/12*b^8/x^12 +--R +--R +--R (2) +--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 7 4 4 8 28 5 3 6 +--R - -- b x - - a b x - - a b x - -- a b x - - a b x - -- a b x +--R 12 7 4 9 2 11 +--R + +--R 7 6 2 4 4 7 2 1 8 +--R - - a b x - -- a b x - -- a +--R 6 13 28 +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 547 + +--S 548 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 91728a b x - 42042a b x - 11088a b x - 1287a +--R / +--R 28 +--R 36036x +--R Type: Union(Expression(Integer),...) +--E 548 + +--S 549 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 550 + +)clear all + +--S 551 of 1393 +t0:=(a+b*x^2)^8/x^31 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1393 +r0:=-1/30*a^8/x^30-2/7*a^7*b/x^28-14/13*a^6*b^2/x^26-7/3*a^5*b^3/x^24-_ + 35/11*a^4*b^4/x^22-14/5*a^3*b^5/x^20-14/9*a^2*b^6/x^18-_ + 1/2*a*b^7/x^16-1/14*b^8/x^14 +--R +--R +--R (2) +--R 1 8 16 1 7 14 14 2 6 12 14 3 5 10 35 4 4 8 7 5 3 6 +--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - - a b x +--R 14 2 9 5 11 3 +--R + +--R 14 6 2 4 2 7 2 1 8 +--R - -- a b x - - a b x - -- a +--R 13 7 30 +--R / +--R 30 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 552 + +--S 553 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 6435b x - 45045a b x - 140140a b x - 252252a b x - 286650a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 210210a b x - 97020a b x - 25740a b x - 3003a +--R / +--R 30 +--R 90090x +--R Type: Union(Expression(Integer),...) +--E 553 + +--S 554 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 555 + +)clear all + +--S 556 of 1393 +t0:=(a+b*x^2)^8/x^33 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 33 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 556 + +--S 557 of 1393 +r0:=-1/32*a^8/x^32-4/15*a^7*b/x^30-a^6*b^2/x^28-28/13*a^5*b^3/x^26-_ + 35/12*a^4*b^4/x^24-28/11*a^3*b^5/x^22-7/5*a^2*b^6/x^20-_ + 4/9*a*b^7/x^18-1/16*b^8/x^16 +--R +--R +--R (2) +--R 1 8 16 4 7 14 7 2 6 12 28 3 5 10 35 4 4 8 28 5 3 6 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 16 9 5 11 12 13 +--R + +--R 6 2 4 4 7 2 1 8 +--R - a b x - -- a b x - -- a +--R 15 32 +--R / +--R 32 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 557 + +--S 558 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 12870b x - 91520a b x - 288288a b x - 524160a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 600600a b x - 443520a b x - 205920a b x - 54912a b x - 6435a +--R / +--R 32 +--R 205920x +--R Type: Union(Expression(Integer),...) +--E 558 + +--S 559 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 560 + +)clear all + +--S 561 of 1393 +t0:=x^8*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 24 7 22 2 6 20 3 5 18 4 4 16 5 3 14 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 12 7 10 8 8 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 561 + +--S 562 of 1393 +r0:=1/9*a^8*x^9+8/11*a^7*b*x^11+28/13*a^6*b^2*x^13+56/15*a^5*b^3*x^15+_ + 70/17*a^4*b^4*x^17+56/19*a^3*b^5*x^19+4/3*a^2*b^6*x^21+_ + 8/23*a*b^7*x^23+1/25*b^8*x^25 +--R +--R +--R (2) +--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 25 23 3 19 17 15 +--R + +--R 28 6 2 13 8 7 11 1 8 9 +--R -- a b x + -- a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 562 + +--S 563 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 25 8 7 23 4 2 6 21 56 3 5 19 70 4 4 17 56 5 3 15 +--R -- b x + -- a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 25 23 3 19 17 15 +--R + +--R 28 6 2 13 8 7 11 1 8 9 +--R -- a b x + -- a b x + - a x +--R 13 11 9 +--R Type: Polynomial(Fraction(Integer)) +--E 563 + +--S 564 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 564 + +--S 565 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 565 + +)clear all + +--S 566 of 1393 +t0:=x^6*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 22 7 20 2 6 18 3 5 16 4 4 14 5 3 12 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 10 7 8 8 6 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 566 + +--S 567 of 1393 +r0:=1/7*a^8*x^7+8/9*a^7*b*x^9+28/11*a^6*b^2*x^11+56/13*a^5*b^3*x^13+_ + 14/3*a^4*b^4*x^15+56/17*a^3*b^5*x^17+28/19*a^2*b^6*x^19+_ + 8/21*a*b^7*x^21+1/23*b^8*x^23 +--R +--R +--R (2) +--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 23 21 19 17 3 13 +--R + +--R 28 6 2 11 8 7 9 1 8 7 +--R -- a b x + - a b x + - a x +--R 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 567 + +--S 568 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 23 8 7 21 28 2 6 19 56 3 5 17 14 4 4 15 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 23 21 19 17 3 13 +--R + +--R 28 6 2 11 8 7 9 1 8 7 +--R -- a b x + - a b x + - a x +--R 11 9 7 +--R Type: Polynomial(Fraction(Integer)) +--E 568 + +--S 569 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 569 + +--S 570 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 570 + +)clear all + +--S 571 of 1393 +t0:=x^4*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 20 7 18 2 6 16 3 5 14 4 4 12 5 3 10 6 2 8 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 6 8 4 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 571 + +--S 572 of 1393 +r0:=1/5*a^8*x^5+8/7*a^7*b*x^7+28/9*a^6*b^2*x^9+56/11*a^5*b^3*x^11+_ + 70/13*a^4*b^4*x^13+56/15*a^3*b^5*x^15+28/17*a^2*b^6*x^17+_ + 8/19*a*b^7*x^19+1/21*b^8*x^21 +--R +--R +--R (2) +--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 21 19 17 15 13 11 +--R + +--R 28 6 2 9 8 7 7 1 8 5 +--R -- a b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 572 + +--S 573 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 21 8 7 19 28 2 6 17 56 3 5 15 70 4 4 13 56 5 3 11 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 21 19 17 15 13 11 +--R + +--R 28 6 2 9 8 7 7 1 8 5 +--R -- a b x + - a b x + - a x +--R 9 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 573 + +--S 574 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 574 + +--S 575 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 575 + +)clear all + +--S 576 of 1393 +t0:=x^2*(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 18 7 16 2 6 14 3 5 12 4 4 10 5 3 8 6 2 6 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 4 8 2 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 576 + +--S 577 of 1393 +r0:=1/3*a^8*x^3+8/5*a^7*b*x^5+4*a^6*b^2*x^7+56/9*a^5*b^3*x^9+_ + 70/11*a^4*b^4*x^11+56/13*a^3*b^5*x^13+28/15*a^2*b^6*x^15+_ + 8/17*a*b^7*x^17+1/19*b^8*x^19 +--R +--R +--R (2) +--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 19 17 15 13 11 9 +--R + +--R 6 2 7 8 7 5 1 8 3 +--R 4a b x + - a b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 577 + +--S 578 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 19 8 7 17 28 2 6 15 56 3 5 13 70 4 4 11 56 5 3 9 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 19 17 15 13 11 9 +--R + +--R 6 2 7 8 7 5 1 8 3 +--R 4a b x + - a b x + - a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 578 + +--S 579 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 579 + +--S 580 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 580 + +)clear all + +--S 581 of 1393 +t0:=(a+b*x^2)^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R Type: Polynomial(Integer) +--E 581 + +--S 582 of 1393 +r0:=a^8*x+8/3*a^7*b*x^3+28/5*a^6*b^2*x^5+8*a^5*b^3*x^7+_ + 70/9*a^4*b^4*x^9+56/11*a^3*b^5*x^11+28/13*a^2*b^6*x^13+_ + 8/15*a*b^7*x^15+1/17*b^8*x^17 +--R +--R +--R (2) +--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x +--R 17 15 13 11 9 +--R + +--R 28 6 2 5 8 7 3 8 +--R -- a b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 582 + +--S 583 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 17 8 7 15 28 2 6 13 56 3 5 11 70 4 4 9 5 3 7 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 8a b x +--R 17 15 13 11 9 +--R + +--R 28 6 2 5 8 7 3 8 +--R -- a b x + - a b x + a x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 583 + +--S 584 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 584 + +--S 585 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 585 + +)clear all + +--S 586 of 1393 +t0:=(a+b*x^2)^8/x^2 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1393 +r0:=-a^8/x+8*a^7*b*x+28/3*a^6*b^2*x^3+56/5*a^5*b^3*x^5+10*a^4*b^4*x^7+_ + 56/9*a^3*b^5*x^9+28/11*a^2*b^6*x^11+8/13*a*b^7*x^13+1/15*b^8*x^15 +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 72072a b x + 60060a b x + 51480a b x - 6435a +--R / +--R 6435x +--R Type: Fraction(Polynomial(Integer)) +--E 587 + +--S 588 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 3960a b x + 16380a b x + 40040a b x + 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 72072a b x + 60060a b x + 51480a b x - 6435a +--R / +--R 6435x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1393 +t0:=(a+b*x^2)^8/x^4 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1393 +r0:=-1/3*a^8/x^3-8*a^7*b/x+28*a^6*b^2*x+56/3*a^5*b^3*x^3+14*a^4*b^4*x^5+_ + 8*a^3*b^5*x^7+28/9*a^2*b^6*x^9+8/11*a*b^7*x^11+1/13*b^8*x^13 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6 +--R -- b x + -- a b x + -- a b x + 8a b x + 14a b x + -- a b x +--R 13 11 9 3 +--R + +--R 6 2 4 7 2 1 8 +--R 28a b x - 8a b x - - a +--R 3 +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 592 + +--S 593 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 99b x + 936a b x + 4004a b x + 10296a b x + 18018a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 24024a b x + 36036a b x - 10296a b x - 429a +--R / +--R 3 +--R 1287x +--R Type: Union(Expression(Integer),...) +--E 593 + +--S 594 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +)clear all + +--S 596 of 1393 +t0:=(a+b*x^2)^8/x^6 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 596 + +--S 597 of 1393 +r0:=-1/5*a^8/x^5-8/3*a^7*b/x^3-28*a^6*b^2/x+56*a^5*b^3*x+70/3*a^4*b^4*x^3+_ + 56/5*a^3*b^5*x^5+4*a^2*b^6*x^7+8/9*a*b^7*x^9+1/11*b^8*x^11 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 5 3 6 +--R -- b x + - a b x + 4a b x + -- a b x + -- a b x + 56a b x +--R 11 9 5 3 +--R + +--R 6 2 4 8 7 2 1 8 +--R - 28a b x - - a b x - - a +--R 3 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 597 + +--S 598 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 45b x + 440a b x + 1980a b x + 5544a b x + 11550a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 27720a b x - 13860a b x - 1320a b x - 99a +--R / +--R 5 +--R 495x +--R Type: Union(Expression(Integer),...) +--E 598 + +--S 599 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 600 + +)clear all + +--S 601 of 1393 +t0:=(a+b*x^2)^8/x^8 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 601 + +--S 602 of 1393 +r0:=-1/7*a^8/x^7-8/5*a^7*b/x^5-28/3*a^6*b^2/x^3-56*a^5*b^3/x+70*a^4*b^4*x+_ + 56/3*a^3*b^5*x^3+28/5*a^2*b^6*x^5+8/7*a*b^7*x^7+1/9*b^8*x^9 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 56 3 5 10 4 4 8 5 3 6 +--R - b x + - a b x + -- a b x + -- a b x + 70a b x - 56a b x +--R 9 7 5 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - - a b x - - a +--R 3 5 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 602 + +--S 603 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 35b x + 360a b x + 1764a b x + 5880a b x + 22050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 17640a b x - 2940a b x - 504a b x - 45a +--R / +--R 7 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 603 + +--S 604 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 605 + +)clear all + +--S 606 of 1393 +t0:=(a+b*x^2)^8/x^10 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 606 + +--S 607 of 1393 +r0:=-1/9*a^8/x^9-8/7*a^7*b/x^7-28/5*a^6*b^2/x^5-56/3*a^5*b^3/x^3-_ + 70*a^4*b^4/x+56*a^3*b^5*x+28/3*a^2*b^6*x^3+8/5*a*b^7*x^5+1/7*b^8*x^7 +--R +--R +--R (2) +--R 1 8 16 8 7 14 28 2 6 12 3 5 10 4 4 8 56 5 3 6 +--R - b x + - a b x + -- a b x + 56a b x - 70a b x - -- a b x +--R 7 5 3 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - - a b x - - a +--R 5 7 9 +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 607 + +--S 608 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 45b x + 504a b x + 2940a b x + 17640a b x - 22050a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 5880a b x - 1764a b x - 360a b x - 35a +--R / +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 608 + +--S 609 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 610 + +)clear all + +--S 611 of 1393 +t0:=(a+b*x^2)^8/x^12 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 611 + +--S 612 of 1393 +r0:=-1/11*a^8/x^11-8/9*a^7*b/x^9-4*a^6*b^2/x^7-56/5*a^5*b^3/x^5-_ + 70/3*a^4*b^4/x^3-56*a^3*b^5/x+28*a^2*b^6*x+8/3*a*b^7*x^3+1/5*b^8*x^5 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 3 5 10 70 4 4 8 56 5 3 6 +--R - b x + - a b x + 28a b x - 56a b x - -- a b x - -- a b x +--R 5 3 3 5 +--R + +--R 6 2 4 8 7 2 1 8 +--R - 4a b x - - a b x - -- a +--R 9 11 +--R / +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 612 + +--S 613 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 99b x + 1320a b x + 13860a b x - 27720a b x - 11550a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 5544a b x - 1980a b x - 440a b x - 45a +--R / +--R 11 +--R 495x +--R Type: Union(Expression(Integer),...) +--E 613 + +--S 614 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 615 + +)clear all + +--S 616 of 1393 +t0:=(a+b*x^2)^8/x^14 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 14 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 616 + +--S 617 of 1393 +r0:=-1/13*a^8/x^13-8/11*a^7*b/x^11-28/9*a^6*b^2/x^9-8*a^5*b^3/x^7-_ + 14*a^4*b^4/x^5-56/3*a^3*b^5/x^3-28*a^2*b^6/x+8*a*b^7*x+1/3*b^8*x^3 +--R +--R +--R (2) +--R 1 8 16 7 14 2 6 12 56 3 5 10 4 4 8 5 3 6 +--R - b x + 8a b x - 28a b x - -- a b x - 14a b x - 8a b x +--R 3 3 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 9 11 13 +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 617 + +--S 618 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 429b x + 10296a b x - 36036a b x - 24024a b x - 18018a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 10296a b x - 4004a b x - 936a b x - 99a +--R / +--R 13 +--R 1287x +--R Type: Union(Expression(Integer),...) +--E 618 + +--S 619 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 620 + +)clear all + +--S 621 of 1393 +t0:=(a+b*x^2)^8/x^16 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 621 + +--S 622 of 1393 +r0:=-1/15*a^8/x^15-8/13*a^7*b/x^13-28/11*a^6*b^2/x^11-56/9*a^5*b^3/x^9-_ + 10*a^4*b^4/x^7-56/5*a^3*b^5/x^5-28/3*a^2*b^6/x^3-8*a*b^7/x+b^8*x +--R +--R +--R (2) +--R 8 16 7 14 28 2 6 12 56 3 5 10 4 4 8 56 5 3 6 +--R b x - 8a b x - -- a b x - -- a b x - 10a b x - -- a b x +--R 3 5 9 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 11 13 15 +--R / +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 622 + +--S 623 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 6435b x - 51480a b x - 60060a b x - 72072a b x - 64350a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 40040a b x - 16380a b x - 3960a b x - 429a +--R / +--R 15 +--R 6435x +--R Type: Union(Expression(Integer),...) +--E 623 + +--S 624 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 625 + +)clear all + +--S 626 of 1393 +t0:=(a+b*x^2)^8/x^18 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 18 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 626 + +--S 627 of 1393 +r0:=-1/17*a^8/x^17-8/15*a^7*b/x^15-28/13*a^6*b^2/x^13-56/11*a^5*b^3/x^11-_ + 70/9*a^4*b^4/x^9-8*a^3*b^5/x^7-28/5*a^2*b^6/x^5-8/3*a*b^7/x^3-b^8/x +--R +--R +--R (2) +--R 8 16 8 7 14 28 2 6 12 3 5 10 70 4 4 8 56 5 3 6 +--R - b x - - a b x - -- a b x - 8a b x - -- a b x - -- a b x +--R 3 5 9 11 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 13 15 17 +--R / +--R 17 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 627 + +--S 628 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 109395b x - 291720a b x - 612612a b x - 875160a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 850850a b x - 556920a b x - 235620a b x - 58344a b x - 6435a +--R / +--R 17 +--R 109395x +--R Type: Union(Expression(Integer),...) +--E 628 + +--S 629 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 630 + +)clear all + +--S 631 of 1393 +t0:=(a+b*x^2)^8/x^20 +--R +--R +--R (1) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 2 8 +--R 8a b x + a +--R / +--R 20 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 631 + +--S 632 of 1393 +r0:=-1/19*a^8/x^19-8/17*a^7*b/x^17-28/15*a^6*b^2/x^15-56/13*a^5*b^3/x^13-_ + 70/11*a^4*b^4/x^11-56/9*a^3*b^5/x^9-4*a^2*b^6/x^7-_ + 8/5*a*b^7/x^5-1/3*b^8/x^3 +--R +--R +--R (2) +--R 1 8 16 8 7 14 2 6 12 56 3 5 10 70 4 4 8 56 5 3 6 +--R - - b x - - a b x - 4a b x - -- a b x - -- a b x - -- a b x +--R 3 5 9 11 13 +--R + +--R 28 6 2 4 8 7 2 1 8 +--R - -- a b x - -- a b x - -- a +--R 15 17 19 +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 632 + +--S 633 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 +--R - 692835b x - 3325608a b x - 8314020a b x - 12932920a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 13226850a b x - 8953560a b x - 3879876a b x - 978120a b x - 109395a +--R / +--R 19 +--R 2078505x +--R Type: Union(Expression(Integer),...) +--E 633 + +--S 634 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1393 +t0:=x^m/(a+b*x^2) +--R +--R +--R m +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1393 +--r0:=x^(1+m)*hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a*(1+m)) +--E 637 + +--S 638 of 1393 +--a0:=integrate(t0,x) +--E 638 + +--S 639 of 1393 +--m0:=a0-r0 +--E 639 + +--S 640 of 1393 +--d0:=D(m0,x) +--E 640 + +)clear all + +--S 641 of 1393 +t0:=x^11/(a+b*x^2) +--R +--R +--R 11 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 1393 +r0:=1/2*a^4*x^2/b^5-1/4*a^3*x^4/b^4+1/6*a^2*x^6/b^3-1/8*a*x^8/b^2+_ + 1/10*x^10/b-1/2*a^5*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R ------------------------------------------------------------------------- +--R 6 +--R 120b +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 60a log(b x + a) + 12b x - 15a b x + 20a b x - 30a b x + 60a b x +--R ------------------------------------------------------------------------- +--R 6 +--R 120b +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1393 +t0:=x^10/(a+b*x^2) +--R +--R +--R 10 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 646 + +--S 647 of 1393 +r0:=a^4*x/b^5-1/3*a^3*x^3/b^4+1/5*a^2*x^5/b^3-1/7*a*x^7/b^2+_ + 1/9*x^9/b-a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 +-+ x\|b +--R - 315a \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (35b x - 45a b x + 63a b x - 105a b x + 315a x)\|b +--R / +--R 5 +-+ +--R 315b \|b +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 | a \| b 4 9 3 7 2 2 5 +--R 315a |- - log(-----------------------) + 70b x - 90a b x + 126a b x +--R \| b 2 +--R b x + a +--R + +--R 3 3 4 +--R - 210a b x + 630a x +--R / +--R 5 +--R 630b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 4 |a \|b 4 9 3 7 2 2 5 3 3 4 +--R 315a |- atan(----) + 35b x - 45a b x + 63a b x - 105a b x + 315a x +--R \|b x +--R -----------------------------------------------------------------------] +--R 5 +--R 315b +--R Type: Union(List(Expression(Integer)),...) +--E 648 + +--S 649 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R a \|a atan(-----) + a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 5 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1393 +t0:=x^9/(a+b*x^2) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 653 + +--S 654 of 1393 +r0:=-1/2*a^3*x^2/b^4+1/4*a^2*x^4/b^3-1/6*a*x^6/b^2+1/8*x^8/b+_ + 1/2*a^4*log(a+b*x^2)/b^5 +--R +--R +--R 4 2 4 8 3 6 2 2 4 3 2 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) -------------------------------------------------------- +--R 5 +--R 24b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 4 2 4 8 3 6 2 2 4 3 2 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) -------------------------------------------------------- +--R 5 +--R 24b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1393 +t0:=x^8/(a+b*x^2) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 of 1393 +r0:=-a^3*x/b^4+1/3*a^2*x^3/b^3-1/5*a*x^5/b^2+1/7*x^7/b+_ + a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 3 7 2 5 2 3 3 +-+ +--R 105a \|a atan(-----) + (15b x - 21a b x + 35a b x - 105a x)\|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 4 +-+ +--R 105b \|b +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 | a \| b 3 7 2 5 2 3 +--R 105a |- - log(---------------------) + 30b x - 42a b x + 70a b x +--R \| b 2 +--R b x + a +--R + +--R 3 +--R - 210a x +--R / +--R 4 +--R 210b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 3 |a \|b 3 7 2 5 2 3 3 +--R - 105a |- atan(----) + 15b x - 21a b x + 35a b x - 105a x +--R \|b x +--R -------------------------------------------------------------] +--R 4 +--R 105b +--R Type: Union(List(Expression(Integer)),...) +--E 660 + +--S 661 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R a |- - \|b log(---------------------) - 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - a \|a atan(-----) - a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1393 +t0:=x^7/(a+b*x^2) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1393 +r0:=1/2*a^2*x^2/b^3-1/4*a*x^4/b^2+1/6*x^6/b-1/2*a^3*log(a+b*x^2)/b^4 +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ---------------------------------------------- +--R 4 +--R 12b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) ---------------------------------------------- +--R 4 +--R 12b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1393 +t0:=x^6/(a+b*x^2) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1393 +r0:=a^2*x/b^3-1/3*a*x^3/b^2+1/5*x^5/b-a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2) +--R +--R +--R +-+ +--R 2 +-+ x\|b 2 5 3 2 +-+ +--R - 15a \|a atan(-----) + (3b x - 5a b x + 15a x)\|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 3 +-+ +--R 15b \|b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 | a \| b 2 5 3 2 +--R 15a |- - log(-----------------------) + 6b x - 10a b x + 30a x +--R \| b 2 +--R b x + a +--R [-----------------------------------------------------------------, +--R 3 +--R 30b +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 2 5 3 2 +--R 15a |- atan(----) + 3b x - 5a b x + 15a x +--R \|b x +--R --------------------------------------------] +--R 3 +--R 15b +--R Type: Union(List(Expression(Integer)),...) +--E 672 + +--S 673 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R a \|a atan(-----) + a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1393 +t0:=x^5/(a+b*x^2) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 677 + +--S 678 of 1393 +r0:=-1/2*a*x^2/b^2+1/4*x^4/b+1/2*a^2*log(a+b*x^2)/b^3 +--R +--R +--R 2 2 2 4 2 +--R 2a log(b x + a) + b x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 4b +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 4 2 +--R 2a log(b x + a) + b x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1393 +t0:=x^4/(a+b*x^2) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 682 + +--S 683 of 1393 +r0:=-a*x/b^2+1/3*x^3/b+a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(5/2) +--R +--R +--R +-+ +--R +-+ x\|b 3 +-+ +--R 3a\|a atan(-----) + (b x - 3a x)\|b +--R +-+ +--R \|a +--R (2) ------------------------------------- +--R 2 +-+ +--R 3b \|b +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R | a \| b 3 +--R 3a |- - log(---------------------) + 2b x - 6a x +--R \| b 2 +--R b x + a +--R [-------------------------------------------------, +--R 2 +--R 6b +--R +-+ +--R |a +--R +-+ |- +--R |a \|b 3 +--R - 3a |- atan(----) + b x - 3a x +--R \|b x +--R --------------------------------] +--R 2 +--R 3b +--R Type: Union(List(Expression(Integer)),...) +--E 684 + +--S 685 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R a |- - \|b log(---------------------) - 2a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - a\|a atan(-----) - a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1393 +t0:=x^3/(a+b*x^2) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1393 +r0:=1/2*x^2/b-1/2*a*log(a+b*x^2)/b^2 +--R +--R +--R 2 2 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1393 +t0:=x^2/(a+b*x^2) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1393 +r0:=x/b-atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R - \|a atan(-----) + x\|b +--R +-+ +--R \|a +--R (2) ------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | a 2 +-+ +--R +---+ - 2b x |- - + b x - a |a +--R | a \| b +-+ |- +--R |- - log(-----------------------) + 2x |a \|b +--R \| b 2 |- atan(----) + x +--R b x + a \|b x +--R (3) [---------------------------------------,------------------] +--R 2b b +--R Type: Union(List(Expression(Integer)),...) +--E 696 + +--S 697 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R |- - \|b log(-----------------------) + 2\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R \|a atan(-----) + |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1393 +t0:=x/(a+b*x^2) +--R +--R +--R x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 1393 +r0:=1/2*log(a+b*x^2)/b +--R +--R +--R 2 +--R log(b x + a) +--R (2) ------------- +--R 2b +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x + a) +--R (3) ------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1393 +t0:=1/(a+b*x^2) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 of 1393 +r0:=atan(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R (2) ----------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +---+ +--R log(---------------------------) x\|a b +--R 2 atan(-------) +--R b x + a a +--R (3) [--------------------------------,-------------] +--R +-----+ +---+ +--R 2\|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 708 + +--S 709 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a b \|a \|b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1393 +t0:=1/(x*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------- +--R 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 713 + +--S 714 of 1393 +r0:=log(x)/a-1/2*log(a+b*x^2)/a +--R +--R +--R 2 +--R - log(b x + a) + 2log(x) +--R (2) ------------------------- +--R 2a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x + a) + 2log(x) +--R (3) ------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1393 +t0:=1/(x^2*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 4 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 of 1393 +r0:=(-1)/(a*x)-atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R - x\|b atan(-----) - \|a +--R +-+ +--R \|a +--R (2) ------------------------- +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | b 2 +-+ +--R +---+ - 2a x |- - + b x - a |b +--R | b \| a +-+ a |- +--R x |- - log(-----------------------) - 2 |b \|a +--R \| a 2 x |- atan(-----) - 1 +--R b x + a \|a b x +--R (3) [---------------------------------------,--------------------] +--R 2a x a x +--R Type: Union(List(Expression(Integer)),...) +--E 720 + +--S 721 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R |- - \|a log(-----------------------) + 2\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R \|b atan(-----) + \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1393 +t0:=1/(x^3*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 725 + +--S 726 of 1393 +r0:=(-1/2)/(a*x^2)-b*log(x)/a^2+1/2*b*log(a+b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R b x log(b x + a) - 2b x log(x) - a +--R (2) ----------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x + a) - 2b x log(x) - a +--R (3) ----------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1393 +t0:=1/(x^4*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1393 +r0:=(-1/3)/(a*x^3)+b/(a^2*x)+b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R 3b x \|b atan(-----) + (3b x - a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 | b \| a 2 +--R 3b x |- - log(---------------------) + 6b x - 2a +--R \| a 2 +--R b x + a +--R [--------------------------------------------------, +--R 2 3 +--R 6a x +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 +--R - 3b x |- atan(-----) + 3b x - a +--R \|a b x +--R ----------------------------------] +--R 2 3 +--R 3a x +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R b |- - \|a log(---------------------) - 2b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - b\|b atan(-----) - b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1393 +t0:=1/(x^5*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 737 + +--S 738 of 1393 +r0:=(-1/4)/(a*x^4)+1/2*b/(a^2*x^2)+b^2*log(x)/a^3-1/2*b^2*log(a+b*x^2)/a^3 +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a +--R (2) ------------------------------------------------- +--R 3 4 +--R 4a x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2b x log(b x + a) + 4b x log(x) + 2a b x - a +--R (3) ------------------------------------------------- +--R 3 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 739 + +--S 740 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1393 +t0:=1/(x^6*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 1393 +r0:=(-1/5)/(a*x^5)+1/3*b/(a^2*x^3)-b^2/(a^3*x)-_ + b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2) +--R +--R +--R +-+ +--R 2 5 +-+ x\|b 2 4 2 2 +-+ +--R - 15b x \|b atan(-----) + (- 15b x + 5a b x - 3a )\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------- +--R 3 5 +-+ +--R 15a x \|a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 2 5 | b \| a 2 4 2 2 +--R 15b x |- - log(-----------------------) - 30b x + 10a b x - 6a +--R \| a 2 +--R b x + a +--R [------------------------------------------------------------------, +--R 3 5 +--R 30a x +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 |b \|a 2 4 2 2 +--R 15b x |- atan(-----) - 15b x + 5a b x - 3a +--R \|a b x +--R ----------------------------------------------] +--R 3 5 +--R 15a x +--R Type: Union(List(Expression(Integer)),...) +--E 744 + +--S 745 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R b |- - \|a log(-----------------------) + 2b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R b \|b atan(-----) + b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1393 +t0:=1/(x^7*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 749 + +--S 750 of 1393 +r0:=(-1/6)/(a*x^6)+1/4*b/(a^2*x^4)-1/2*b^2/(a^3*x^2)-b^3*log(x)/a^4+_ + 1/2*b^3*log(a+b*x^2)/a^4 +--R +--R +--R 3 6 2 3 6 2 4 2 2 3 +--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a +--R (2) ----------------------------------------------------------- +--R 4 6 +--R 12a x +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 3 6 2 4 2 2 3 +--R 6b x log(b x + a) - 12b x log(x) - 6a b x + 3a b x - 2a +--R (3) ----------------------------------------------------------- +--R 4 6 +--R 12a x +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1393 +t0:=1/(x^8*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 8 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1393 +r0:=(-1/7)/(a*x^7)+1/5*b/(a^2*x^5)-1/3*b^2/(a^3*x^3)+_ + b^3/(a^4*x)+b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R +-+ +--R 3 7 +-+ x\|b 3 6 2 4 2 2 3 +-+ +--R 105b x \|b atan(-----) + (105b x - 35a b x + 21a b x - 15a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 7 +-+ +--R 105a x \|a +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 7 | b \| a 3 6 2 4 2 2 +--R 105b x |- - log(---------------------) + 210b x - 70a b x + 42a b x +--R \| a 2 +--R b x + a +--R + +--R 3 +--R - 30a +--R / +--R 4 7 +--R 210a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 |b \|a 3 6 2 4 2 2 3 +--R - 105b x |- atan(-----) + 105b x - 35a b x + 21a b x - 15a +--R \|a b x +--R ---------------------------------------------------------------] +--R 4 7 +--R 105a x +--R Type: Union(List(Expression(Integer)),...) +--E 756 + +--S 757 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R b |- - \|a log(---------------------) - 2b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - b \|b atan(-----) - b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 760 + +)clear all + +--S 761 of 1393 +t0:=1/(x^9*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 1393 +r0:=(-1/8)/(a*x^8)+1/6*b/(a^2*x^6)-1/4*b^2/(a^3*x^4)+1/2*b^3/(a^4*x^2)+_ + b^4*log(x)/a^5-1/2*b^4*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 2 4 8 3 6 2 2 4 3 2 4 +--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ------------------------------------------------------------------------- +--R 5 8 +--R 24a x +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 2 4 8 3 6 2 2 4 3 2 4 +--R - 12b x log(b x + a) + 24b x log(x) + 12a b x - 6a b x + 4a b x - 3a +--R ------------------------------------------------------------------------- +--R 5 8 +--R 24a x +--R Type: Union(Expression(Integer),...) +--E 763 + +--S 764 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1393 +t0:=x^m/(a+b*x^2)^2 +--R +--R +--R m +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1393 +--r0:=1/2*x^(1+m)/(a*(a+b*x^2))+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-b*x^2/a)/(a^2*(1+m)) +--E 767 + +--S 768 of 1393 +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1393 +--m0:=a0-r0 +--E 769 + +--S 770 of 1393 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1393 +t0:=x^13/(a+b*x^2)^2 +--R +--R +--R 13 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 771 + +--S 772 of 1393 +r0:=5/2*a^4*x^2/b^6-a^3*x^4/b^5+1/2*a^2*x^6/b^4-1/4*a*x^8/b^3+_ + 1/10*x^10/b^2-1/2*a^6/(b^7*(a+b*x^2))-3*a^5*log(a+b*x^2)/b^7 +--R +--R +--R (2) +--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 4 5 2 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 2 7 +--R 20b x + 20a b +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 2 6 12 5 10 2 4 8 3 3 6 +--R (- 60a b x - 60a )log(b x + a) + 2b x - 3a b x + 5a b x - 10a b x +--R + +--R 4 2 4 5 2 6 +--R 30a b x + 50a b x - 10a +--R / +--R 8 2 7 +--R 20b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1393 +t0:=x^12/(a+b*x^2)^2 +--R +--R +--R 12 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 776 + +--S 777 of 1393 +r0:=11/2*a^4*x/b^6-11/6*a^3*x^3/b^5+11/10*a^2*x^5/b^4-11/14*a*x^7/b^3+_ + 11/18*x^9/b^2-1/2*x^11/(b*(a+b*x^2))-_ + 11/2*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2) +--R +--R +--R (2) +--R +-+ +--R 4 2 5 +-+ x\|b +--R (- 3465a b x - 3465a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (70b x - 110a b x + 198a b x - 462a b x + 2310a b x + 3465a x)\|b +--R / +--R 7 2 6 +-+ +--R (630b x + 630a b )\|b +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 2 5 | a \| b 5 11 +--R (3465a b x + 3465a ) |- - log(-----------------------) + 140b x +--R \| b 2 +--R b x + a +--R + +--R 4 9 2 3 7 3 2 5 4 3 5 +--R - 220a b x + 396a b x - 924a b x + 4620a b x + 6930a x +--R / +--R 7 2 6 +--R 1260b x + 1260a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 4 2 5 |a \|b 5 11 4 9 2 3 7 +--R (3465a b x + 3465a ) |- atan(----) + 70b x - 110a b x + 198a b x +--R \|b x +--R + +--R 3 2 5 4 3 5 +--R - 462a b x + 2310a b x + 3465a x +--R / +--R 7 2 6 +--R 630b x + 630a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 778 + +--S 779 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R 11a |- - \|b log(-----------------------) + 22a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 6 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R 11a \|a atan(-----) + 11a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 6 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1393 +t0:=x^11/(a+b*x^2)^2 +--R +--R +--R 11 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1393 +r0:=-2*a^3*x^2/b^5+3/4*a^2*x^4/b^4-1/3*a*x^6/b^3+1/8*x^8/b^2+_ + 1/2*a^5/(b^6*(a+b*x^2))+5/2*a^4*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 2 5 +--R - 48a b x + 12a +--R / +--R 7 2 6 +--R 24b x + 24a b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 2 5 10 4 8 2 3 6 3 2 4 +--R (60a b x + 60a )log(b x + a) + 3b x - 5a b x + 10a b x - 30a b x +--R + +--R 4 2 5 +--R - 48a b x + 12a +--R / +--R 7 2 6 +--R 24b x + 24a b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1393 +t0:=x^10/(a+b*x^2)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 788 + +--S 789 of 1393 +r0:=-9/2*a^3*x/b^5+3/2*a^2*x^3/b^4-9/10*a*x^5/b^3+9/14*x^7/b^2-_ + 1/2*x^9/(b*(a+b*x^2))+9/2*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 +-+ x\|b +--R (315a b x + 315a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (10b x - 18a b x + 42a b x - 210a b x - 315a x)\|b +--R / +--R 6 2 5 +-+ +--R (70b x + 70a b )\|b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 2 4 | a \| b 4 9 3 7 +--R (315a b x + 315a ) |- - log(---------------------) + 20b x - 36a b x +--R \| b 2 +--R b x + a +--R + +--R 2 2 5 3 3 4 +--R 84a b x - 420a b x - 630a x +--R / +--R 6 2 5 +--R 140b x + 140a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 3 2 4 |a \|b 4 9 3 7 2 2 5 +--R (- 315a b x - 315a ) |- atan(----) + 10b x - 18a b x + 42a b x +--R \|b x +--R + +--R 3 3 4 +--R - 210a b x - 315a x +--R / +--R 6 2 5 +--R 70b x + 70a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 790 + +--S 791 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R 9a |- - \|b log(---------------------) - 18a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - 9a \|a atan(-----) - 9a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1393 +t0:=x^9/(a+b*x^2)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1393 +r0:=3/2*a^2*x^2/b^4-1/2*a*x^4/b^3+1/6*x^6/b^2-1/2*a^4/(b^5*(a+b*x^2))-_ + 2*a^3*log(a+b*x^2)/b^5 +--R +--R +--R (2) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6b x + 6a b +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x - 3a +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 797 + +--S 798 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1393 +t0:=x^8/(a+b*x^2)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 800 + +--S 801 of 1393 +r0:=7/2*a^2*x/b^4-7/6*a*x^3/b^3+7/10*x^5/b^2-1/2*x^7/(b*(a+b*x^2))-_ + 7/2*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 3 +-+ x\|b +--R (- 105a b x - 105a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6b x - 14a b x + 70a b x + 105a x)\|b +--R / +--R 5 2 4 +-+ +--R (30b x + 30a b )\|b +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 2 3 | a \| b 3 7 +--R (105a b x + 105a ) |- - log(-----------------------) + 12b x +--R \| b 2 +--R b x + a +--R + +--R 2 5 2 3 3 +--R - 28a b x + 140a b x + 210a x +--R / +--R 5 2 4 +--R 60b x + 60a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 2 3 |a \|b 3 7 2 5 2 3 3 +--R (105a b x + 105a ) |- atan(----) + 6b x - 14a b x + 70a b x + 105a x +--R \|b x +--R ------------------------------------------------------------------------] +--R 5 2 4 +--R 30b x + 30a b +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 7a |- - \|b log(-----------------------) + 14a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 7a \|a atan(-----) + 7a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1393 +t0:=x^7/(a+b*x^2)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 807 + +--S 808 of 1393 +r0:=-a*x^2/b^3+1/4*x^4/b^2+1/2*a^3/(b^4*(a+b*x^2))+3/2*a^2*log(a+b*x^2)/b^4 +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) ------------------------------------------------------------- +--R 5 2 4 +--R 4b x + 4a b +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) ------------------------------------------------------------- +--R 5 2 4 +--R 4b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 809 + +--S 810 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +)clear all + +--S 812 of 1393 +t0:=x^6/(a+b*x^2)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 812 + +--S 813 of 1393 +r0:=-5/2*a*x/b^3+5/6*x^3/b^2-1/2*x^5/(b*(a+b*x^2))+_ + 5/2*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(7/2) +--R +--R +--R +-+ +--R 2 2 +-+ x\|b 2 5 3 2 +-+ +--R (15a b x + 15a )\|a atan(-----) + (2b x - 10a b x - 15a x)\|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R 4 2 3 +-+ +--R (6b x + 6a b )\|b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 2 | a \| b 2 5 3 2 +--R (15a b x + 15a ) |- - log(---------------------) + 4b x - 20a b x - 30a x +--R \| b 2 +--R b x + a +--R [---------------------------------------------------------------------------- +--R 4 2 3 +--R 12b x + 12a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 2 |a \|b 2 5 3 2 +--R (- 15a b x - 15a ) |- atan(----) + 2b x - 10a b x - 15a x +--R \|b x +--R ------------------------------------------------------------] +--R 4 2 3 +--R 6b x + 6a b +--R Type: Union(List(Expression(Integer)),...) +--E 814 + +--S 815 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 5a\|a atan(-----) - 5a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------ +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1393 +t0:=x^5/(a+b*x^2)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 819 + +--S 820 of 1393 +r0:=1/2*x^2/b^2-1/2*a^2/(b^3*(a+b*x^2))-a*log(a+b*x^2)/b^3 +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) --------------------------------------------------- +--R 4 2 3 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) --------------------------------------------------- +--R 4 2 3 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1393 +t0:=x^4/(a+b*x^2)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 824 + +--S 825 of 1393 +r0:=3/2*x/b^2-1/2*x^3/(b*(a+b*x^2))-3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(5/2) +--R +--R +--R +-+ +--R 2 +-+ x\|b 3 +-+ +--R (- 3b x - 3a)\|a atan(-----) + (2b x + 3a x)\|b +--R +-+ +--R \|a +--R (2) -------------------------------------------------- +--R 3 2 2 +-+ +--R (2b x + 2a b )\|b +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 | a \| b 3 +--R (3b x + 3a) |- - log(-----------------------) + 4b x + 6a x +--R \| b 2 +--R b x + a +--R [-------------------------------------------------------------, +--R 3 2 2 +--R 4b x + 4a b +--R +-+ +--R |a +--R +-+ |- +--R 2 |a \|b 3 +--R (3b x + 3a) |- atan(----) + 2b x + 3a x +--R \|b x +--R -----------------------------------------] +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(List(Expression(Integer)),...) +--E 826 + +--S 827 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 3 |- - \|b log(----------------------- + 6\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 3\|a atan(-----) + 3 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1393 +t0:=x^3/(a+b*x^2)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 831 + +--S 832 of 1393 +r0:=1/2*a/(b^2*(a+b*x^2))+1/2*log(a+b*x^2)/b^2 +--R +--R +--R 2 2 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 2 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 833 + +--S 834 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1393 +t0:=x^2/(a+b*x^2)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 836 + +--S 837 of 1393 +r0:=-1/2*x/(b*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x + a)atan(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2b x + 2a b)\|a \|b +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (b x - a)\|- a b + 2a b x +-----+ +--R (b x + a)log(---------------------------) - 2x\|- a b +--R 2 +--R b x + a +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4b x + 4a b)\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (b x + a)atan(-------) - x\|a b +--R a +--R ---------------------------------] +--R 2 2 +---+ +--R (2b x + 2a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 838 + +--S 839 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1393 +t0:=x/(a+b*x^2)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1393 +r0:=(-1/2)/(b*(a+b*x^2)) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ---------- +--R 2 2 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 844 + +--S 845 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1393 +t0:=1/(a+b*x^2)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1393 +r0:=1/2*x/(a*(a+b*x^2))+1/2*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x + a)atan(-----) + x\|a \|b +--R +-+ +--R \|a +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x + 2a )\|a \|b +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (b x - a)\|- a b + 2a b x +-----+ +--R (b x + a)log(---------------------------) + 2x\|- a b +--R 2 +--R b x + a +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a b x + 4a )\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (b x + a)atan(-------) + x\|a b +--R a +--R ---------------------------------] +--R 2 2 +---+ +--R (2a b x + 2a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 850 + +--S 851 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +--S 853 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1393 +t0:=1/(x*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 855 + +--S 856 of 1393 +r0:=1/2/(a*(a+b*x^2))+log(x)/a^2-1/2*log(a+b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2a +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x - a)log(b x + a) + (2b x + 2a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1393 +t0:=1/(x^2*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 860 + +--S 861 of 1393 +r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a+b*x^2))-_ + 3/2*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (- 3b x - 3a x)\|b atan(-----) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x + 2a x)\|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 | b \| a 2 +--R (3b x + 3a x) |- - log(-----------------------) - 6b x - 4a +--R \| a 2 +--R b x + a +--R [-------------------------------------------------------------, +--R 2 3 3 +--R 4a b x + 4a x +--R +-+ +--R |b +--R +-+ a |- +--R 3 |b \|a 2 +--R (3b x + 3a x) |- atan(-----) - 3b x - 2a +--R \|a b x +--R ------------------------------------------] +--R 2 3 3 +--R 2a b x + 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 862 + +--S 863 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 3 |- - \|a log(----------------------- + 6\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 3\|b atan(-----) + 3\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 866 + +)clear all + +--S 867 of 1393 +t0:=1/(x^3*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 867 + +--S 868 of 1393 +r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a+b*x^2))-2*b*log(x)/a^3+b*log(a+b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2a x +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (2b x + 2a b x )log(b x + a) + (- 4b x - 4a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 869 + +--S 870 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1393 +t0:=1/(x^4*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 6 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 872 + +--S 873 of 1393 +r0:=(-5/6)/(a^2*x^3)+5/2*b/(a^3*x)+1/2/(a*x^3*(a+b*x^2))+_ + 5/2*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(7/2) +--R +--R +--R +-+ +--R 2 5 3 +-+ x\|b 2 4 2 2 +-+ +--R (15b x + 15a b x )\|b atan(-----) + (15b x + 10a b x - 2a )\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 5 4 3 +-+ +--R (6a b x + 6a x )\|a +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 2 5 3 | b \| a 2 4 2 +--R (15b x + 15a b x ) |- - log(---------------------) + 30b x + 20a b x +--R \| a 2 +--R b x + a +--R + +--R 2 +--R - 4a +--R / +--R 3 5 4 3 +--R 12a b x + 12a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 3 |b \|a 2 4 2 2 +--R (- 15b x - 15a b x ) |- atan(-----) + 15b x + 10a b x - 2a +--R \|a b x +--R --------------------------------------------------------------] +--R 3 5 4 3 +--R 6a b x + 6a x +--R Type: Union(List(Expression(Integer)),...) +--E 874 + +--S 875 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 5b\|b atan(-----) - 5b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 878 + +)clear all + +--S 879 of 1393 +t0:=1/(x^5*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 7 2 5 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 879 + +--S 880 of 1393 +r0:=(-3/4)/(a^2*x^4)+3/2*b/(a^3*x^2)+1/2/(a*x^4*(a+b*x^2))+_ + 3*b^2*log(x)/a^4-3/2*b^2*log(a+b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - a +--R / +--R 4 6 5 4 +--R 4a b x + 4a x +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6b x - 6a b x )log(b x + a) + (12b x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - a +--R / +--R 4 6 5 4 +--R 4a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 881 + +--S 882 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 883 + +)clear all + +--S 884 of 1393 +t0:=1/(x^6*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 8 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 884 + +--S 885 of 1393 +r0:=(-7/10)/(a^2*x^5)+7/6*b/(a^3*x^3)-7/2*b^2/(a^4*x)+_ + 1/2/(a*x^5*(a+b*x^2))-7/2*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 +-+ x\|b +--R (- 105b x - 105a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 105b x - 70a b x + 14a b x - 6a )\|a +--R / +--R 4 7 5 5 +-+ +--R (30a b x + 30a x )\|a +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 3 7 2 5 | b \| a 3 6 +--R (105b x + 105a b x ) |- - log(-----------------------) - 210b x +--R \| a 2 +--R b x + a +--R + +--R 2 4 2 2 3 +--R - 140a b x + 28a b x - 12a +--R / +--R 4 7 5 5 +--R 60a b x + 60a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 2 5 |b \|a 3 6 2 4 2 2 3 +--R (105b x + 105a b x ) |- atan(-----) - 105b x - 70a b x + 14a b x - 6a +--R \|a b x +--R --------------------------------------------------------------------------] +--R 4 7 5 5 +--R 30a b x + 30a x +--R Type: Union(List(Expression(Integer)),...) +--E 886 + +--S 887 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 7b \|b atan(-----) + 7b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1393 +t0:=1/(x^7*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 11 9 2 7 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 891 + +--S 892 of 1393 +r0:=(-2/3)/(a^2*x^6)+b/(a^3*x^4)-2*b^2/(a^4*x^2)+1/2/(a*x^6*(a+b*x^2))-_ + 4*b^3*log(x)/a^5+2*b^3*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 4 8 3 6 3 6 +--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 8 6 6 +--R 6a b x + 6a x +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 4 8 3 6 3 6 +--R (12b x + 12a b x )log(b x + a) + (- 24b x - 24a b x )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R - 6a b x + 2a b x - a +--R / +--R 5 8 6 6 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 893 + +--S 894 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 895 + +)clear all + +--S 896 of 1393 +t0:=1/(x^8*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 12 10 2 8 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 896 + +--S 897 of 1393 +r0:=(-9/14)/(a^2*x^7)+9/10*b/(a^3*x^5)-3/2*b^2/(a^4*x^3)+9/2*b^3/(a^5*x)+_ + 1/2/(a*x^7*(a+b*x^2))+9/2*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 +-+ x\|b +--R (315b x + 315a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 210a b x - 42a b x + 18a b x - 10a )\|a +--R / +--R 5 9 6 7 +-+ +--R (70a b x + 70a x )\|a +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 4 9 3 7 | b \| a 4 8 +--R (315b x + 315a b x ) |- - log(---------------------) + 630b x +--R \| a 2 +--R b x + a +--R + +--R 3 6 2 2 4 3 2 4 +--R 420a b x - 84a b x + 36a b x - 20a +--R / +--R 5 9 6 7 +--R 140a b x + 140a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 4 9 3 7 |b \|a 4 8 3 6 2 2 4 +--R (- 315b x - 315a b x ) |- atan(-----) + 315b x + 210a b x - 42a b x +--R \|a b x +--R + +--R 3 2 4 +--R 18a b x - 10a +--R / +--R 5 9 6 7 +--R 70a b x + 70a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 898 + +--S 899 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - 9b \|b atan(-----) - 9b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1393 +t0:=1/(x^9*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 13 11 2 9 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 903 + +--S 904 of 1393 +r0:=(-5/8)/(a^2*x^8)+5/6*b/(a^3*x^6)-5/4*b^2/(a^4*x^4)+5/2*b^3/(a^5*x^2)+_ + 1/2/(a*x^8*(a+b*x^2))+5*b^4*log(x)/a^6-5/2*b^4*log(a+b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 5 10 4 8 +--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 60a b x + 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 10 7 8 +--R 24a b x + 24a x +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 5 10 4 8 +--R (- 60b x - 60a b x )log(b x + a) + (120b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 60a b x + 30a b x - 10a b x + 5a b x - 3a +--R / +--R 6 10 7 8 +--R 24a b x + 24a x +--R Type: Union(Expression(Integer),...) +--E 905 + +--S 906 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1393 +t0:=x^m/(a+b*x^2)^3 +--R +--R +--R m +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1393 +--r0:=1/4*x^(1+m)/(a*(a+b*x^2)^2)+1/8*(3-m)*x^(1+m)/(a^2*(a+b*x^2))+_ +-- 1/8*(1-m)*(3-m)*x^(1+m)*hypergeometric(1,1/2*(1+m),_ +-- 1/2*(3+m),-b*x^2/a)/(a^3*(1+m)) +--E 909 + +--S 910 of 1393 +--a0:=integrate(t0,x) +--E 910 + +--S 911 of 1393 +--m0:=a0-r0 +--E 911 + +--S 912 of 1393 +--d0:=D(m0,x) +--E 912 + +)clear all + +--S 913 of 1393 +t0:=x^15/(a+b*x^2)^3 +--R +--R +--R 15 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1393 +r0:=15/2*a^4*x^2/b^7-5/2*a^3*x^4/b^6+a^2*x^6/b^5-3/8*a*x^8/b^4+_ + 1/10*x^10/b^3+1/4*a^7/(b^8*(a+b*x^2)^2)-7/2*a^6/(b^8*(a+b*x^2))-_ + 21/2*a^5*log(a+b*x^2)/b^8 +--R +--R +--R (2) +--R 5 2 4 6 2 7 2 7 14 6 12 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x +--R + +--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7 +--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 4 9 2 2 8 +--R 40b x + 80a b x + 40a b +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 4 6 2 7 2 7 14 6 12 +--R (- 420a b x - 840a b x - 420a )log(b x + a) + 4b x - 7a b x +--R + +--R 2 5 10 3 4 8 4 3 6 5 2 4 6 2 7 +--R 14a b x - 35a b x + 140a b x + 500a b x + 160a b x - 130a +--R / +--R 10 4 9 2 2 8 +--R 40b x + 80a b x + 40a b +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1393 +t0:=x^14/(a+b*x^2)^3 +--R +--R +--R 14 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1393 +r0:=143/8*a^4*x/b^7-143/24*a^3*x^3/b^6+143/40*a^2*x^5/b^5-_ + 143/56*a*x^7/b^4+143/72*x^9/b^3-1/4*x^13/(b*(a+b*x^2)^2)-_ + 13/8*x^11/(b^2*(a+b*x^2))-143/8*a^(9/2)*atan(x*sqrt(b)/sqrt(a))/b^(15/2) +--R +--R +--R (2) +--R +-+ +--R 4 2 4 5 2 6 +-+ x\|b +--R (- 45045a b x - 90090a b x - 45045a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 280b x - 520a b x + 1144a b x - 3432a b x + 24024a b x +--R + +--R 5 3 6 +--R 75075a b x + 45045a x +--R * +--R +-+ +--R \|b +--R / +--R 9 4 8 2 2 7 +-+ +--R (2520b x + 5040a b x + 2520a b )\|b +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 4 2 4 5 2 6 | a \| b +--R (45045a b x + 90090a b x + 45045a ) |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 560b x - 1040a b x + 2288a b x - 6864a b x + 48048a b x +--R + +--R 5 3 6 +--R 150150a b x + 90090a x +--R / +--R 9 4 8 2 2 7 +--R 5040b x + 10080a b x + 5040a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 4 2 4 5 2 6 |a \|b 6 13 +--R (45045a b x + 90090a b x + 45045a ) |- atan(----) + 280b x +--R \|b x +--R + +--R 5 11 2 4 9 3 3 7 4 2 5 5 3 +--R - 520a b x + 1144a b x - 3432a b x + 24024a b x + 75075a b x +--R + +--R 6 +--R 45045a x +--R / +--R 9 4 8 2 2 7 +--R 2520b x + 5040a b x + 2520a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 920 + +--S 921 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 4 | a +-+ \| b 4 +-+ x\|b +--R 143a |- - \|b log(-----------------------) + 286a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 7 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 4 +-+ x\|b 4 |a +-+ \|b +--R 143a \|a atan(-----) + 143a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------------- +--R 7 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1393 +t0:=x^13/(a+b*x^2)^3 +--R +--R +--R 13 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 925 + +--S 926 of 1393 +r0:=-5*a^3*x^2/b^6+3/2*a^2*x^4/b^5-1/2*a*x^6/b^4+1/8*x^8/b^3-_ + 1/4*a^6/(b^7*(a+b*x^2)^2)+3*a^5/(b^7*(a+b*x^2))+15/2*a^4*log(a+b*x^2)/b^7 +--R +--R +--R (2) +--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 4 8 2 2 7 +--R 8b x + 16a b x + 8a b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 4 5 2 6 2 6 12 5 10 2 4 8 +--R (60a b x + 120a b x + 60a )log(b x + a) + b x - 2a b x + 5a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R - 20a b x - 68a b x - 16a b x + 22a +--R / +--R 9 4 8 2 2 7 +--R 8b x + 16a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 927 + +--S 928 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1393 +t0:=x^12/(a+b*x^2)^3 +--R +--R +--R 12 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 930 + +--S 931 of 1393 +r0:=-99/8*a^3*x/b^6+33/8*a^2*x^3/b^5-99/40*a*x^5/b^4+99/56*x^7/b^3-_ + 1/4*x^11/(b*(a+b*x^2)^2)-11/8*x^9/(b^2*(a+b*x^2))+_ + 99/8*a^(7/2)*atan(x*sqrt(b)/sqrt(a))/b^(13/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 4 2 5 +-+ x\|b +--R (3465a b x + 6930a b x + 3465a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (40b x - 88a b x + 264a b x - 1848a b x - 5775a b x - 3465a x)\|b +--R / +--R 8 4 7 2 2 6 +-+ +--R (280b x + 560a b x + 280a b )\|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 3 2 4 4 2 5 | a \| b +--R (3465a b x + 6930a b x + 3465a ) |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R 80b x - 176a b x + 528a b x - 3696a b x - 11550a b x - 6930a x +--R / +--R 8 4 7 2 2 6 +--R 560b x + 1120a b x + 560a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 3 2 4 4 2 5 |a \|b 5 11 4 9 +--R (- 3465a b x - 6930a b x - 3465a ) |- atan(----) + 40b x - 88a b x +--R \|b x +--R + +--R 2 3 7 3 2 5 4 3 5 +--R 264a b x - 1848a b x - 5775a b x - 3465a x +--R / +--R 8 4 7 2 2 6 +--R 280b x + 560a b x + 280a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 932 + +--S 933 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R 3 | a +-+ \| b 3 +-+ x\|b +--R 99a |- - \|b log(---------------------) - 198a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 6 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 3 +-+ x\|b 3 |a +-+ \|b +--R - 99a \|a atan(-----) - 99a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------------- +--R 6 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 936 + +)clear all + +--S 937 of 1393 +t0:=x^11/(a+b*x^2)^3 +--R +--R +--R 11 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 937 + +--S 938 of 1393 +r0:=3*a^2*x^2/b^5-3/4*a*x^4/b^4+1/6*x^6/b^3+1/4*a^5/(b^6*(a+b*x^2)^2)-_ + 5/2*a^4/(b^6*(a+b*x^2))-5*a^3*log(a+b*x^2)/b^6 +--R +--R +--R (2) +--R 3 2 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x +--R + +--R 2 3 6 3 2 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27a +--R / +--R 8 4 7 2 2 6 +--R 12b x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60a )log(b x + a) + 2b x - 5a b x +--R + +--R 2 3 6 3 2 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27a +--R / +--R 8 4 7 2 2 6 +--R 12b x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 939 + +--S 940 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 941 + +)clear all + +--S 942 of 1393 +t0:=x^10/(a+b*x^2)^3 +--R +--R +--R 10 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 942 + +--S 943 of 1393 +r0:=63/8*a^2*x/b^5-21/8*a*x^3/b^4+63/40*x^5/b^3-1/4*x^9/(b*(a+b*x^2)^2)-_ + 9/8*x^7/(b^2*(a+b*x^2))-63/8*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(11/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 4 3 2 4 +-+ x\|b +--R (- 315a b x - 630a b x - 315a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (8b x - 24a b x + 168a b x + 525a b x + 315a x)\|b +--R / +--R 7 4 6 2 2 5 +-+ +--R (40b x + 80a b x + 40a b )\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 2 4 3 2 4 | a \| b +--R (315a b x + 630a b x + 315a ) |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +--R 16b x - 48a b x + 336a b x + 1050a b x + 630a x +--R / +--R 7 4 6 2 2 5 +--R 80b x + 160a b x + 80a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 2 4 3 2 4 |a \|b 4 9 3 7 +--R (315a b x + 630a b x + 315a ) |- atan(----) + 8b x - 24a b x +--R \|b x +--R + +--R 2 2 5 3 3 4 +--R 168a b x + 525a b x + 315a x +--R / +--R 7 4 6 2 2 5 +--R 40b x + 80a b x + 40a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 944 + +--S 945 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 63a |- - \|b log(-----------------------) + 126a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 63a \|a atan(-----) + 63a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1393 +t0:=x^9/(a+b*x^2)^3 +--R +--R +--R 9 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 949 + +--S 950 of 1393 +r0:=-3/2*a*x^2/b^4+1/4*x^4/b^3-1/4*a^4/(b^5*(a+b*x^2)^2)+_ + 2*a^3/(b^5*(a+b*x^2))+3*a^2*log(a+b*x^2)/b^5 +--R +--R +--R (2) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7a +--R / +--R 7 4 6 2 2 5 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12a )log(b x + a) + b x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7a +--R / +--R 7 4 6 2 2 5 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1393 +t0:=x^8/(a+b*x^2)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 954 + +--S 955 of 1393 +r0:=-35/8*a*x/b^4+35/24*x^3/b^3-1/4*x^7/(b*(a+b*x^2)^2)-_ + 7/8*x^5/(b^2*(a+b*x^2))+35/8*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 3 +-+ x\|b +--R (105a b x + 210a b x + 105a )\|a atan(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (8b x - 56a b x - 175a b x - 105a x)\|b +--R / +--R 6 4 5 2 2 4 +-+ +--R (24b x + 48a b x + 24a b )\|b +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R 2 4 2 2 3 | a \| b +--R (105a b x + 210a b x + 105a ) |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 3 7 2 5 2 3 3 +--R 16b x - 112a b x - 350a b x - 210a x +--R / +--R 6 4 5 2 2 4 +--R 48b x + 96a b x + 48a b +--R , +--R +--R +-+ +--R |a +--R +-+ |- +--R 2 4 2 2 3 |a \|b 3 7 2 5 +--R (- 105a b x - 210a b x - 105a ) |- atan(----) + 8b x - 56a b x +--R \|b x +--R + +--R 2 3 3 +--R - 175a b x - 105a x +--R / +--R 6 4 5 2 2 4 +--R 24b x + 48a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 956 + +--S 957 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 35a\|a atan(-----) - 35a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) -------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1393 +t0:=x^7/(a+b*x^2)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1393 +r0:=1/2*x^2/b^3+1/4*a^3/(b^4*(a+b*x^2)^2)-3/2*a^2/(b^4*(a+b*x^2))-_ + 3/2*a*log(a+b*x^2)/b^4 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R --------------------------------------------------------------------------- +--R 6 4 5 2 2 4 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6a )log(b x + a) + 2b x + 4a b x - 4a b x - 5a +--R --------------------------------------------------------------------------- +--R 6 4 5 2 2 4 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1393 +t0:=x^6/(a+b*x^2)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 1393 +r0:=15/8*x/b^3-1/4*x^5/(b*(a+b*x^2)^2)-5/8*x^3/(b^2*(a+b*x^2))-_ + 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 +-+ x\|b 2 5 3 2 +-+ +--R (- 15b x - 30a b x - 15a )\|a atan(-----) + (8b x + 25a b x + 15a x)\|b +--R +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R 5 4 4 2 2 3 +-+ +--R (8b x + 16a b x + 8a b )\|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R 2 4 2 2 | a \| b 2 5 +--R (15b x + 30a b x + 15a ) |- - log(-----------------------) + 16b x +--R \| b 2 +--R b x + a +--R + +--R 3 2 +--R 50a b x + 30a x +--R / +--R 5 4 4 2 2 3 +--R 16b x + 32a b x + 16a b +--R , +--R +-+ +--R |a +--R +-+ |- +--R 2 4 2 2 |a \|b 2 5 3 2 +--R (15b x + 30a b x + 15a ) |- atan(----) + 8b x + 25a b x + 15a x +--R \|b x +--R -------------------------------------------------------------------] +--R 5 4 4 2 2 3 +--R 8b x + 16a b x + 8a b +--R Type: Union(List(Expression(Integer)),...) +--E 968 + +--S 969 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 15 |- - \|b log(----------------------- + 30\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 15\|a atan(-----) + 15 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ---------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1393 +t0:=x^5/(a+b*x^2)^3 +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1393 +r0:=-1/4*a^2/(b^3*(a+b*x^2)^2)+a/(b^3*(a+b*x^2))+1/2*log(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ---------------------------------------------------- +--R 5 4 4 2 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 2 2 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ---------------------------------------------------- +--R 5 4 4 2 2 3 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1393 +t0:=x^4/(a+b*x^2)^3 +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 978 + +--S 979 of 1393 +r0:=-1/4*x^3/(b*(a+b*x^2)^2)-3/8*x/(b^2*(a+b*x^2))+_ + 3/8*atan(x*sqrt(b)/sqrt(a))/(b^(5/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x + 6a b x + 3a )atan(-----) + (- 5b x - 3a x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 4 4 3 2 2 2 +-+ +-+ +--R (8b x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (3b x + 6a b x + 3a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (- 10b x - 6a x)\|- a b +--R / +--R 4 4 3 2 2 2 +-----+ +--R (16b x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3b x + 6a b x + 3a )atan(-------) + (- 5b x - 3a x)\|a b +--R a +--R -------------------------------------------------------------] +--R 4 4 3 2 2 2 +---+ +--R (8b x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 980 + +--S 981 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1393 +t0:=x^3/(a+b*x^2)^3 +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 985 + +--S 986 of 1393 +r0:=1/4*x^4/(a*(a+b*x^2)^2) +--R +--R +--R 1 4 +--R - x +--R 4 +--R (2) --------------------- +--R 2 4 2 2 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 986 + +--S 987 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2b x - a +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 987 + +--S 988 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +)clear all + +--S 990 of 1393 +t0:=x^2/(a+b*x^2)^3 +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 990 + +--S 991 of 1393 +r0:=-1/4*x/(b*(a+b*x^2)^2)+1/8*x/(a*b*(a+b*x^2))+_ + 1/8*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (b x + 2a b x + a )atan(-----) + (b x - a x)\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x + 16a b x + 8a b)\|a \|b +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (b x + 2a b x + a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (2b x - 2a x)\|- a b +--R / +--R 3 4 2 2 2 3 +-----+ +--R (16a b x + 32a b x + 16a b)\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (b x + 2a b x + a )atan(-------) + (b x - a x)\|a b +--R a +--R -------------------------------------------------------] +--R 3 4 2 2 2 3 +---+ +--R (8a b x + 16a b x + 8a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 992 + +--S 993 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R \|a \|b atan(-------) - \|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 996 + +)clear all + +--S 997 of 1393 +t0:=x/(a+b*x^2)^3 +--R +--R +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 997 + +--S 998 of 1393 +r0:=(-1/4)/(b*(a+b*x^2)^2) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - -------------------- +--R 3 4 2 2 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 998 + +--S 999 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 3 4 2 2 2 +--R 4b x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 999 + +--S 1000 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1001 + +)clear all + +--S 1002 of 1393 +t0:=1/(a+b*x^2)^3 +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1002 + +--S 1003 of 1393 +r0:=1/4*x/(a*(a+b*x^2)^2)+3/8*x/(a^2*(a+b*x^2))+_ + 3/8*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x + 6a b x + 3a )atan(-----) + (3b x + 5a x)\|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x + 16a b x + 8a )\|a \|b +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (b x - a)\|- a b + 2a b x +--R (3b x + 6a b x + 3a )log(---------------------------) +--R 2 +--R b x + a +--R + +--R 3 +-----+ +--R (6b x + 10a x)\|- a b +--R / +--R 2 2 4 3 2 4 +-----+ +--R (16a b x + 32a b x + 16a )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3b x + 6a b x + 3a )atan(-------) + (3b x + 5a x)\|a b +--R a +--R -----------------------------------------------------------] +--R 2 2 4 3 2 4 +---+ +--R (8a b x + 16a b x + 8a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1004 + +--S 1005 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1393 +t0:=1/(x*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 7 2 5 2 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1009 + +--S 1010 of 1393 +r0:=1/4/(a*(a+b*x^2)^2)+1/2/(a^2*(a+b*x^2))+log(x)/a^3-1/2*log(a+b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x) +--R + +--R 2 2 +--R 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x + 8a b x + 4a +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (4b x + 8a b x + 4a )log(x) +--R + +--R 2 2 +--R 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x + 8a b x + 4a +--R Type: Union(Expression(Integer),...) +--E 1011 + +--S 1012 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1013 + +)clear all + +--S 1014 of 1393 +t0:=1/(x^2*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1014 + +--S 1015 of 1393 +r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a+b*x^2)^2)+5/8/(a^2*x*(a+b*x^2))-_ + 15/8*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|b +--R (- 15b x - 30a b x - 15a x)\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +--R (- 15b x - 25a b x - 8a )\|a +--R / +--R 3 2 5 4 3 5 +-+ +--R (8a b x + 16a b x + 8a x)\|a +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 2 5 3 2 | b \| a 2 4 +--R (15b x + 30a b x + 15a x) |- - log(-----------------------) - 30b x +--R \| a 2 +--R b x + a +--R + +--R 2 2 +--R - 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x + 32a b x + 16a x +--R , +--R +-+ +--R |b +--R +-+ a |- +--R 2 5 3 2 |b \|a 2 4 2 2 +--R (15b x + 30a b x + 15a x) |- atan(-----) - 15b x - 25a b x - 8a +--R \|a b x +--R --------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x + 16a b x + 8a x +--R Type: Union(List(Expression(Integer)),...) +--E 1016 + +--S 1017 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 15 |- - \|a log(----------------------- + 30\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 15\|b atan(-----) + 15\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1393 +t0:=1/(x^3*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 1393 +r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a+b*x^2)^2)+3/4/(a^2*x^2*(a+b*x^2))-_ + 3*b*log(x)/a^4+3/2*b*log(a+b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 2 +--R (6b x + 12a b x + 6a b x )log(b x + a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (6b x + 12a b x + 6a b x )log(b x + a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12b x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1393 +t0:=1/(x^4*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 10 2 8 2 6 3 4 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 1393 +r0:=(-35/24)/(a^3*x^3)+35/8*b/(a^4*x)+1/4/(a*x^3*(a+b*x^2)^2)+_ + 7/8/(a^2*x^3*(a+b*x^2))+35/8*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 2 3 +-+ x\|b +--R (105b x + 210a b x + 105a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105b x + 175a b x + 56a b x - 8a )\|a +--R / +--R 4 2 7 5 5 6 3 +-+ +--R (24a b x + 48a b x + 24a x )\|a +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 3 7 2 5 2 3 | b \| a +--R (105b x + 210a b x + 105a b x ) |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 3 6 2 4 2 2 3 +--R 210b x + 350a b x + 112a b x - 16a +--R / +--R 4 2 7 5 5 6 3 +--R 48a b x + 96a b x + 48a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 3 7 2 5 2 3 |b \|a 3 6 +--R (- 105b x - 210a b x - 105a b x ) |- atan(-----) + 105b x +--R \|a b x +--R + +--R 2 4 2 2 3 +--R 175a b x + 56a b x - 8a +--R / +--R 4 2 7 5 5 6 3 +--R 24a b x + 48a b x + 24a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1028 + +--S 1029 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 35b\|b atan(-----) - 35b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1032 + +)clear all + +--S 1033 of 1393 +t0:=1/(x^5*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 11 2 9 2 7 3 5 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1033 + +--S 1034 of 1393 +r0:=(-3/2)/(a^3*x^4)+3*b/(a^4*x^2)+1/4/(a*x^4*(a+b*x^2)^2)+_ + 1/(a^2*x^4*(a+b*x^2))+6*b^2*log(x)/a^5-3*b^2*log(a+b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 8 6 6 7 4 +--R 4a b x + 8a b x + 4a x +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 2 +--R (- 12b x - 24a b x - 12a b x )log(b x + a) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24b x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - a +--R / +--R 5 2 8 6 6 7 4 +--R 4a b x + 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1035 + +--S 1036 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1393 +t0:=1/(x^6*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 12 2 10 2 8 3 6 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1038 + +--S 1039 of 1393 +r0:=(-63/40)/(a^3*x^5)+21/8*b/(a^4*x^3)-63/8*b^2/(a^5*x)+_ + 1/4/(a*x^5*(a+b*x^2)^2)+9/8/(a^2*x^5*(a+b*x^2))-_ + 63/8*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 2 2 5 +-+ x\|b +--R (- 315b x - 630a b x - 315a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x - 525a b x - 168a b x + 24a b x - 8a )\|a +--R / +--R 5 2 9 6 7 7 5 +-+ +--R (40a b x + 80a b x + 40a x )\|a +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R 4 9 3 7 2 2 5 | b \| a +--R (315b x + 630a b x + 315a b x ) |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x - 1050a b x - 336a b x + 48a b x - 16a +--R / +--R 5 2 9 6 7 7 5 +--R 80a b x + 160a b x + 80a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 4 9 3 7 2 2 5 |b \|a 4 8 3 6 +--R (315b x + 630a b x + 315a b x ) |- atan(-----) - 315b x - 525a b x +--R \|a b x +--R + +--R 2 2 4 3 2 4 +--R - 168a b x + 24a b x - 8a +--R / +--R 5 2 9 6 7 7 5 +--R 40a b x + 80a b x + 40a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 63b \|b atan(-----) + 63b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1393 +t0:=1/(x^7*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 13 2 11 2 9 3 7 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1045 + +--S 1046 of 1393 +r0:=(-5/3)/(a^3*x^6)+5/2*b/(a^4*x^4)-5*b^2/(a^5*x^2)+_ + 1/4/(a*x^6*(a+b*x^2)^2)+5/4/(a^2*x^6*(a+b*x^2))-_ + 10*b^3*log(x)/a^6+5*b^3*log(a+b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 3 6 2 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 10 4 8 2 3 6 4 8 2 3 6 +--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x +--R + +--R 3 2 4 4 2 5 +--R - 20a b x + 5a b x - 2a +--R / +--R 6 2 10 7 8 8 6 +--R 12a b x + 24a b x + 12a x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 2 +--R (60b x + 120a b x + 60a b x )log(b x + a) +--R + +--R 5 10 4 8 2 3 6 4 8 2 3 6 +--R (- 120b x - 240a b x - 120a b x )log(x) - 60a b x - 90a b x +--R + +--R 3 2 4 4 2 5 +--R - 20a b x + 5a b x - 2a +--R / +--R 6 2 10 7 8 8 6 +--R 12a b x + 24a b x + 12a x +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1393 +t0:=1/(x^8*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 14 2 12 2 10 3 8 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1050 + +--S 1051 of 1393 +r0:=(-99/56)/(a^3*x^7)+99/40*b/(a^4*x^5)-33/8*b^2/(a^5*x^3)+_ + 99/8*b^3/(a^6*x)+1/4/(a*x^7*(a+b*x^2)^2)+11/8/(a^2*x^7*(a+b*x^2))+_ + 99/8*b^(7/2)*atan(x*sqrt(b)/sqrt(a))/a^(13/2) +--R +--R +--R (2) +--R +-+ +--R 5 11 4 9 2 3 7 +-+ x\|b +--R (3465b x + 6930a b x + 3465a b x )\|b atan(-----) +--R +-+ +--R \|a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (3465b x + 5775a b x + 1848a b x - 264a b x + 88a b x - 40a )\|a +--R / +--R 6 2 11 7 9 8 7 +-+ +--R (280a b x + 560a b x + 280a x )\|a +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R 5 11 4 9 2 3 7 | b \| a +--R (3465b x + 6930a b x + 3465a b x ) |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 6930b x + 11550a b x + 3696a b x - 528a b x + 176a b x - 80a +--R / +--R 6 2 11 7 9 8 7 +--R 560a b x + 1120a b x + 560a x +--R , +--R +--R +-+ +--R |b +--R +-+ a |- +--R 5 11 4 9 2 3 7 |b \|a 5 10 +--R (- 3465b x - 6930a b x - 3465a b x ) |- atan(-----) + 3465b x +--R \|a b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 5775a b x + 1848a b x - 264a b x + 88a b x - 40a +--R / +--R 6 2 11 7 9 8 7 +--R 280a b x + 560a b x + 280a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1052 + +--S 1053 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R 3 | b +-+ \| a 3 +-+ x\|b +--R 99b |- - \|a log(---------------------) - 198b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------- +--R 6 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 3 +-+ x\|b 3 +-+ |b \|a +--R - 99b \|b atan(-----) - 99b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ----------------------------------------------- +--R 6 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1056 + +)clear all + +--S 1057 of 1393 +t0:=1/(x^9*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 15 2 13 2 11 3 9 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1057 + +--S 1058 of 1393 +r0:=(-15/8)/(a^3*x^8)+5/2*b/(a^4*x^6)-15/4*b^2/(a^5*x^4)+_ + 15/2*b^3/(a^6*x^2)+1/4/(a*x^8*(a+b*x^2)^2)+3/2/(a^2*x^8*(a+b*x^2))+_ + 15*b^4*log(x)/a^7-15/2*b^4*log(a+b*x^2)/a^7 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 2 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 12 5 10 2 4 8 5 10 2 4 8 +--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R 20a b x - 5a b x + 2a b x - a +--R / +--R 7 2 12 8 10 9 8 +--R 8a b x + 16a b x + 8a x +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 2 +--R (- 60b x - 120a b x - 60a b x )log(b x + a) +--R + +--R 6 12 5 10 2 4 8 5 10 2 4 8 +--R (120b x + 240a b x + 120a b x )log(x) + 60a b x + 90a b x +--R + +--R 3 3 6 4 2 4 5 2 6 +--R 20a b x - 5a b x + 2a b x - a +--R / +--R 7 2 12 8 10 9 8 +--R 8a b x + 16a b x + 8a x +--R Type: Union(Expression(Integer),...) +--E 1059 + +--S 1060 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1061 + +)clear all + +--S 1062 of 1393 +t0:=x^25/(a+b*x^2)^10 +--R +--R +--R (1) +--R 25 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1062 + +--S 1063 of 1393 +r0:=55/2*a^2*x^2/b^12-5/2*a*x^4/b^11+1/6*x^6/b^10-_ + 1/18*a^12/(b^13*(a+b*x^2)^9)+3/4*a^11/(b^13*(a+b*x^2)^8)-_ + 33/7*a^10/(b^13*(a+b*x^2)^7)+55/3*a^9/(b^13*(a+b*x^2)^6)-_ + 99/2*a^8/(b^13*(a+b*x^2)^5)+99*a^7/(b^13*(a+b*x^2)^4)-_ + 154*a^6/(b^13*(a+b*x^2)^3)+198*a^5/(b^13*(a+b*x^2)^2)-_ + 495/2*a^4/(b^13*(a+b*x^2))-110*a^3*log(a+b*x^2)/b^13 +--R +--R +--R (2) +--R 3 9 18 4 8 16 5 7 14 6 6 12 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 10 8 4 8 9 3 6 10 2 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 2 12 +--R - 249480a b x - 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 4 8 16 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 18 21 16 2 20 14 3 19 12 4 18 10 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 18 4 8 16 5 7 14 6 6 12 +--R - 27720a b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 7 5 10 8 4 8 9 3 6 10 2 4 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 11 2 12 +--R - 249480a b x - 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 4 8 16 +--R 42b x - 252a b x + 2772a b x + 43218a b x + 139482a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R 58968a b x - 638568a b x - 1831032a b x - 2529576a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 2074464a b x - 1031616a b x - 289089a b x - 35201a +--R / +--R 22 18 21 16 2 20 14 3 19 12 4 18 10 +--R 252b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 5 17 8 6 16 6 7 15 4 8 14 2 9 13 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a b +--R Type: Union(Expression(Integer),...) +--E 1064 + +--S 1065 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1066 + +)clear all + +--S 1067 of 1393 +t0:=x^23/(a+b*x^2)^10 +--R +--R +--R (1) +--R 23 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1067 + +--S 1068 of 1393 +r0:=-5*a*x^2/b^11+1/4*x^4/b^10+1/18*a^11/(b^12*(a+b*x^2)^9)-_ + 11/16*a^10/(b^12*(a+b*x^2)^8)+55/14*a^9/(b^12*(a+b*x^2)^7)-_ + 55/4*a^8/(b^12*(a+b*x^2)^6)+33*a^7/(b^12*(a+b*x^2)^5)-_ + 231/4*a^6/(b^12*(a+b*x^2)^4)+77*a^5/(b^12*(a+b*x^2)^3)-_ + 165/2*a^4/(b^12*(a+b*x^2)^2)+165/2*a^3/(b^12*(a+b*x^2))+_ + 55/2*a^2*log(a+b*x^2)/b^12 +--R +--R +--R (2) +--R 2 9 18 3 8 16 4 7 14 5 6 12 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 2 11 +--R 249480a b x + 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 4 10 2 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 18 20 16 2 19 14 3 18 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 17 10 5 16 8 6 15 6 7 14 4 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 8 13 2 9 12 +--R 9072a b x + 1008a b +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 18 3 8 16 4 7 14 5 6 12 +--R 27720a b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 10 2 11 +--R 249480a b x + 27720a +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 252b x - 2772a b x - 36288a b x - 77112a b x + 190512a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 1220688a b x + 2704212a b x + 3402756a b x + 2656584a b x +--R + +--R 9 2 4 10 2 11 +--R 1281096a b x + 351459a b x + 42131a +--R / +--R 21 18 20 16 2 19 14 3 18 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 17 10 5 16 8 6 15 6 7 14 4 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 8 13 2 9 12 +--R 9072a b x + 1008a b +--R Type: Union(Expression(Integer),...) +--E 1069 + +--S 1070 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1393 +t0:=x^21/(a+b*x^2)^10 +--R +--R +--R (1) +--R 21 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1072 + +--S 1073 of 1393 +r0:=1/2*x^2/b^10-1/18*a^10/(b^11*(a+b*x^2)^9)+5/8*a^9/(b^11*(a+b*x^2)^8)-_ + 45/14*a^8/(b^11*(a+b*x^2)^7)+10*a^7/(b^11*(a+b*x^2)^6)-_ + 21*a^6/(b^11*(a+b*x^2)^5)+63/2*a^5/(b^11*(a+b*x^2)^4)-_ + 35*a^4/(b^11*(a+b*x^2)^3)+30*a^3/(b^11*(a+b*x^2)^2)-_ + 45/2*a^2/(b^11*(a+b*x^2))-5*a*log(a+b*x^2)/b^11 +--R +--R +--R (2) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 2 10 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x +--R + +--R 9 2 10 +--R - 41229a b x - 4861a +--R / +--R 20 18 19 16 2 18 14 3 17 12 4 16 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 9 2 10 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 252b x + 2268a b x - 2268a b x - 54432a b x - 197568a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 375732a b x - 439236a b x - 328104a b x - 153576a b x +--R + +--R 9 2 10 +--R - 41229a b x - 4861a +--R / +--R 20 18 19 16 2 18 14 3 17 12 4 16 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 15 8 6 14 6 7 13 4 8 12 2 9 11 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1074 + +--S 1075 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1393 +t0:=x^19/(a+b*x^2)^10 +--R +--R +--R (1) +--R 19 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1393 +r0:=1/18*a^9/(b^10*(a+b*x^2)^9)-9/16*a^8/(b^10*(a+b*x^2)^8)+_ + 18/7*a^7/(b^10*(a+b*x^2)^7)-7*a^6/(b^10*(a+b*x^2)^6)+_ + 63/5*a^5/(b^10*(a+b*x^2)^5)-63/4*a^4/(b^10*(a+b*x^2)^4)+_ + 14*a^3/(b^10*(a+b*x^2)^3)-9*a^2/(b^10*(a+b*x^2)^2)+_ + 9/2*a/(b^10*(a+b*x^2))+1/2*log(a+b*x^2)/b^10 +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 9 +--R 22680a b x + 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 18 18 16 2 17 14 3 16 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 15 10 5 14 8 6 13 6 7 12 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 11 2 9 10 +--R 45360a b x + 5040a b +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 9 +--R 22680a b x + 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 22680a b x + 136080a b x + 388080a b x + 661500a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 725004a b x + 518616a b x + 235224a b x + 61641a b x + 7129a +--R / +--R 19 18 18 16 2 17 14 3 16 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 15 10 5 14 8 6 13 6 7 12 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 11 2 9 10 +--R 45360a b x + 5040a b +--R Type: Union(Expression(Integer),...) +--E 1079 + +--S 1080 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +)clear all + +--S 1082 of 1393 +t0:=x^17/(a+b*x^2)^10 +--R +--R +--R (1) +--R 17 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1082 + +--S 1083 of 1393 +r0:=1/18*x^18/(a*(a+b*x^2)^9) +--R +--R +--R (2) +--R 1 18 +--R -- x +--R 18 +--R / +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 6 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 4 7 2 8 +--R - 36a b x - 9a b x - a +--R / +--R 18 18 17 16 2 16 14 3 15 12 4 14 10 +--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x +--R + +--R 5 13 8 6 12 6 7 11 4 8 10 2 9 9 +--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b +--R Type: Union(Expression(Integer),...) +--E 1084 + +--S 1085 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------ +--R 9 +--R 18a b +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1086 + +)clear all + +--S 1087 of 1393 +t0:=x^15/(a+b*x^2)^10 +--R +--R +--R (1) +--R 15 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1087 + +--S 1088 of 1393 +r0:=1/18*x^16/(a*(a+b*x^2)^9)+1/144*x^16/(a^2*(a+b*x^2)^8) +--R +--R +--R (2) +--R 1 18 1 16 +--R --- b x + -- a x +--R 144 16 +--R / +--R 2 9 18 3 8 16 4 7 14 5 6 12 6 5 10 7 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 8 3 6 9 2 4 10 2 11 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 36b x - 84a b x - 126a b x - 126a b x - 84a b x - 36a b x +--R + +--R 6 2 7 +--R - 9a b x - a +--R / +--R 17 18 16 16 2 15 14 3 14 12 4 13 10 +--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x +--R + +--R 5 12 8 6 11 6 7 10 4 8 9 2 9 8 +--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b +--R Type: Union(Expression(Integer),...) +--E 1089 + +--S 1090 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------- +--R 2 8 +--R 144a b +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1091 + +)clear all + +--S 1092 of 1393 +t0:=x^13/(a+b*x^2)^10 +--R +--R +--R (1) +--R 13 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1092 + +--S 1093 of 1393 +r0:=1/18*x^14/(a*(a+b*x^2)^9)+1/72*x^14/(a^2*(a+b*x^2)^8)+_ + 1/504*x^14/(a^3*(a+b*x^2)^7) +--R +--R +--R (2) +--R 1 2 18 1 16 1 2 14 +--R --- b x + -- a b x + -- a x +--R 504 56 14 +--R / +--R 3 9 18 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R - 84b x - 126a b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 16 18 15 16 2 14 14 3 13 12 4 12 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 11 8 6 10 6 7 9 4 8 8 2 9 7 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1094 + +--S 1095 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ------- +--R 3 7 +--R 504a b +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1096 + +)clear all + +--S 1097 of 1393 +t0:=x^11/(a+b*x^2)^10 +--R +--R +--R (1) +--R 11 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1097 + +--S 1098 of 1393 +r0:=1/18*x^12/(a*(a+b*x^2)^9)+1/48*x^12/(a^2*(a+b*x^2)^8)+_ + 1/168*x^12/(a^3*(a+b*x^2)^7)+1/1008*x^12/(a^4*(a+b*x^2)^6) +--R +--R +--R (2) +--R 1 3 18 1 2 16 1 2 14 1 3 12 +--R ---- b x + --- a b x + -- a b x + -- a x +--R 1008 112 28 12 +--R / +--R 4 9 18 5 8 16 6 7 14 7 6 12 8 5 10 9 4 8 +--R a b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 10 3 6 11 2 4 12 2 13 +--R 84a b x + 36a b x + 9a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1098 + +--S 1099 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 126b x - 126a b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 15 18 14 16 2 13 14 3 12 12 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 4 11 10 5 10 8 6 9 6 7 8 4 8 7 2 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x + 9072a b x +--R + +--R 9 6 +--R 1008a b +--R Type: Union(Expression(Integer),...) +--E 1099 + +--S 1100 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - -------- +--R 4 6 +--R 1008a b +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1101 + +)clear all + +--S 1102 of 1393 +t0:=x^9/(a+b*x^2)^10 +--R +--R +--R (1) +--R 9 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1102 + +--S 1103 of 1393 +r0:=-1/18*a^4/(b^5*(a+b*x^2)^9)+1/4*a^3/(b^5*(a+b*x^2)^8)-_ + 3/7*a^2/(b^5*(a+b*x^2)^7)+1/3*a/(b^5*(a+b*x^2)^6)+_ + (-1/10)/(b^5*(a+b*x^2)^5) +--R +--R +--R (2) +--R 1 4 8 1 3 6 1 2 2 4 1 3 2 1 4 +--R - -- b x - -- a b x - -- a b x - --- a b x - ---- a +--R 10 15 35 140 1260 +--R / +--R 14 18 13 16 2 12 14 3 11 12 4 10 10 5 9 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 8 6 7 7 4 8 6 2 9 5 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 3 2 4 +--R - 126b x - 84a b x - 36a b x - 9a b x - a +--R / +--R 14 18 13 16 2 12 14 3 11 12 +--R 1260b x + 11340a b x + 45360a b x + 105840a b x +--R + +--R 4 10 10 5 9 8 6 8 6 7 7 4 8 6 2 +--R 158760a b x + 158760a b x + 105840a b x + 45360a b x + 11340a b x +--R + +--R 9 5 +--R 1260a b +--R Type: Union(Expression(Integer),...) +--E 1104 + +--S 1105 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1106 + +)clear all + +--S 1107 of 1393 +t0:=x^7/(a+b*x^2)^10 +--R +--R +--R (1) +--R 7 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1107 + +--S 1108 of 1393 +r0:=1/18*a^3/(b^4*(a+b*x^2)^9)-3/16*a^2/(b^4*(a+b*x^2)^8)+_ + 3/14*a/(b^4*(a+b*x^2)^7)+(-1/12)/(b^4*(a+b*x^2)^6) +--R +--R +--R (2) +--R 1 3 6 1 2 4 1 2 2 1 3 +--R - -- b x - -- a b x - --- a b x - ---- a +--R 12 28 112 1008 +--R / +--R 13 18 12 16 2 11 14 3 10 12 4 9 10 5 8 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 7 6 7 6 4 8 5 2 9 4 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1108 + +--S 1109 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 3 +--R - 84b x - 36a b x - 9a b x - a +--R / +--R 13 18 12 16 2 11 14 3 10 12 4 9 10 +--R 1008b x + 9072a b x + 36288a b x + 84672a b x + 127008a b x +--R + +--R 5 8 8 6 7 6 7 6 4 8 5 2 9 4 +--R 127008a b x + 84672a b x + 36288a b x + 9072a b x + 1008a b +--R Type: Union(Expression(Integer),...) +--E 1109 + +--S 1110 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1111 + +)clear all + +--S 1112 of 1393 +t0:=x^5/(a+b*x^2)^10 +--R +--R +--R (1) +--R 5 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1112 + +--S 1113 of 1393 +r0:=-1/18*a^2/(b^3*(a+b*x^2)^9)+1/8*a/(b^3*(a+b*x^2)^8)+_ + (-1/14)/(b^3*(a+b*x^2)^7) +--R +--R +--R (2) +--R 1 2 4 1 2 1 2 +--R - -- b x - -- a b x - --- a +--R 14 56 504 +--R / +--R 12 18 11 16 2 10 14 3 9 12 4 8 10 5 7 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 6 6 7 5 4 8 4 2 9 3 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1113 + +--S 1114 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 +--R - 36b x - 9a b x - a +--R / +--R 12 18 11 16 2 10 14 3 9 12 4 8 10 +--R 504b x + 4536a b x + 18144a b x + 42336a b x + 63504a b x +--R + +--R 5 7 8 6 6 6 7 5 4 8 4 2 9 3 +--R 63504a b x + 42336a b x + 18144a b x + 4536a b x + 504a b +--R Type: Union(Expression(Integer),...) +--E 1114 + +--S 1115 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1116 + +)clear all + +--S 1117 of 1393 +t0:=x^3/(a+b*x^2)^10 +--R +--R +--R (1) +--R 3 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1117 + +--S 1118 of 1393 +r0:=1/18*a/(b^2*(a+b*x^2)^9)+(-1/16)/(b^2*(a+b*x^2)^8) +--R +--R +--R (2) +--R 1 2 1 +--R - -- b x - --- a +--R 16 144 +--R / +--R 11 18 10 16 2 9 14 3 8 12 4 7 10 5 6 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 5 6 7 4 4 8 3 2 9 2 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1118 + +--S 1119 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +--R - 9b x - a +--R / +--R 11 18 10 16 2 9 14 3 8 12 4 7 10 +--R 144b x + 1296a b x + 5184a b x + 12096a b x + 18144a b x +--R + +--R 5 6 8 6 5 6 7 4 4 8 3 2 9 2 +--R 18144a b x + 12096a b x + 5184a b x + 1296a b x + 144a b +--R Type: Union(Expression(Integer),...) +--E 1119 + +--S 1120 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1121 + +)clear all + +--S 1122 of 1393 +t0:=x/(a+b*x^2)^10 +--R +--R +--R (1) +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1122 + +--S 1123 of 1393 +r0:=(-1/18)/(b*(a+b*x^2)^9) +--R +--R +--R (2) +--R - +--R 1 +--R -- +--R 18 +--R / +--R 10 18 9 16 2 8 14 3 7 12 4 6 10 5 5 8 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x +--R + +--R 6 4 6 7 3 4 8 2 2 9 +--R 84a b x + 36a b x + 9a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1123 + +--S 1124 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 10 18 9 16 2 8 14 3 7 12 4 6 10 +--R 18b x + 162a b x + 648a b x + 1512a b x + 2268a b x +--R + +--R 5 5 8 6 4 6 7 3 4 8 2 2 9 +--R 2268a b x + 1512a b x + 648a b x + 162a b x + 18a b +--R Type: Union(Expression(Integer),...) +--E 1124 + +--S 1125 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1126 + +)clear all + +--S 1127 of 1393 +t0:=1/(x*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 21 9 19 2 8 17 3 7 15 4 6 13 5 5 11 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1127 + +--S 1128 of 1393 +r0:=1/18/(a*(a+b*x^2)^9)+1/16/(a^2*(a+b*x^2)^8)+1/14/(a^3*(a+b*x^2)^7)+_ + 1/12/(a^4*(a+b*x^2)^6)+1/10/(a^5*(a+b*x^2)^5)+_ + 1/8/(a^6*(a+b*x^2)^4)+1/6/(a^7*(a+b*x^2)^3)+_ + 1/4/(a^8*(a+b*x^2)^2)+1/2/(a^9*(a+b*x^2))+log(x)/a^10-_ + 1/2*log(a+b*x^2)/a^10 +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 9 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 2 9 +--R 45360a b x + 5040a +--R * +--R log(x) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 18 11 8 16 12 7 14 13 6 12 +--R 5040a b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 14 5 10 15 4 8 16 3 6 17 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 18 2 19 +--R 45360a b x + 5040a +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2520b x - 22680a b x - 90720a b x - 211680a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 317520a b x - 317520a b x - 211680a b x - 90720a b x +--R + +--R 8 2 9 +--R - 22680a b x - 2520a +--R * +--R 2 +--R log(b x + a) +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 5040b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 8 2 9 +--R 45360a b x + 5040a +--R * +--R log(x) +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2520a b x + 21420a b x + 80220a b x + 173250a b x + 236754a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 210756a b x + 120564a b x + 41481a b x + 7129a +--R / +--R 10 9 18 11 8 16 12 7 14 13 6 12 +--R 5040a b x + 45360a b x + 181440a b x + 423360a b x +--R + +--R 14 5 10 15 4 8 16 3 6 17 2 4 +--R 635040a b x + 635040a b x + 423360a b x + 181440a b x +--R + +--R 18 2 19 +--R 45360a b x + 5040a +--R Type: Union(Expression(Integer),...) +--E 1129 + +--S 1130 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1131 + +)clear all + +--S 1132 of 1393 +t0:=1/(x^3*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 23 9 21 2 8 19 3 7 17 4 6 15 5 5 13 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 11 7 3 9 8 2 7 9 5 10 3 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1132 + +--S 1133 of 1393 +r0:=(-5)/(a^10*x^2)+1/18/(a*x^2*(a+b*x^2)^9)+5/72/(a^2*x^2*(a+b*x^2)^8)+_ + 5/56/(a^3*x^2*(a+b*x^2)^7)+5/42/(a^4*x^2*(a+b*x^2)^6)+_ + 1/6/(a^5*x^2*(a+b*x^2)^5)+1/4/(a^6*x^2*(a+b*x^2)^4)+_ + 5/12/(a^7*x^2*(a+b*x^2)^3)+5/6/(a^8*x^2*(a+b*x^2)^2)+_ + 5/2/(a^9*x^2*(a+b*x^2))-10*b*log(x)/a^11+5*b*log(a+b*x^2)/a^11 +--R +--R +--R (2) +--R 10 20 9 18 2 8 16 3 7 14 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 4 9 2 +--R 22680a b x + 2520a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 5040b x - 45360a b x - 181440a b x - 423360a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x +--R + +--R 8 2 4 9 2 +--R - 45360a b x - 5040a b x +--R * +--R log(x) +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x +--R + +--R 10 +--R - 252a +--R / +--R 11 9 20 12 8 18 13 7 16 14 6 14 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x +--R + +--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4 +--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x +--R + +--R 20 2 +--R 504a x +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 +--R 2520b x + 22680a b x + 90720a b x + 211680a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R 317520a b x + 317520a b x + 211680a b x + 90720a b x +--R + +--R 8 2 4 9 2 +--R 22680a b x + 2520a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 5040b x - 45360a b x - 181440a b x - 423360a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 635040a b x - 635040a b x - 423360a b x - 181440a b x +--R + +--R 8 2 4 9 2 +--R - 45360a b x - 5040a b x +--R * +--R log(x) +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 2520a b x - 21420a b x - 80220a b x - 173250a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 236754a b x - 210756a b x - 120564a b x - 41481a b x - 7129a b x +--R + +--R 10 +--R - 252a +--R / +--R 11 9 20 12 8 18 13 7 16 14 6 14 +--R 504a b x + 4536a b x + 18144a b x + 42336a b x +--R + +--R 15 5 12 16 4 10 17 3 8 18 2 6 19 4 +--R 63504a b x + 63504a b x + 42336a b x + 18144a b x + 4536a b x +--R + +--R 20 2 +--R 504a x +--R Type: Union(Expression(Integer),...) +--E 1134 + +--S 1135 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1136 + +)clear all + +--S 1137 of 1393 +t0:=1/(x^5*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 25 9 23 2 8 21 3 7 19 4 6 17 5 5 15 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 13 7 3 11 8 2 9 9 7 10 5 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1137 + +--S 1138 of 1393 +r0:=(-55/4)/(a^10*x^4)+55/2*b/(a^11*x^2)+1/18/(a*x^4*(a+b*x^2)^9)+_ + 11/144/(a^2*x^4*(a+b*x^2)^8)+55/504/(a^3*x^4*(a+b*x^2)^7)+_ + 55/336/(a^4*x^4*(a+b*x^2)^6)+11/42/(a^5*x^4*(a+b*x^2)^5)+_ + 11/24/(a^6*x^4*(a+b*x^2)^4)+11/12/(a^7*x^4*(a+b*x^2)^3)+_ + 55/24/(a^8*x^4*(a+b*x^2)^2)+55/6/(a^9*x^4*(a+b*x^2))+_ + 55*b^2*log(x)/a^12-55/2*b^2*log(a+b*x^2)/a^12 +--R +--R +--R (2) +--R 11 22 10 20 2 9 18 3 8 16 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 6 9 2 4 +--R - 249480a b x - 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 +--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x +--R + +--R 8 3 6 9 2 4 +--R 498960a b x + 55440a b x +--R * +--R log(x) +--R + +--R 10 20 2 9 18 3 8 16 4 7 14 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 4 10 2 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 22 13 8 20 14 7 18 15 6 16 +--R 1008a b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 16 5 14 17 4 12 18 3 10 19 2 8 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 20 6 21 4 +--R 9072a b x + 1008a x +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 22 10 20 2 9 18 3 8 16 +--R - 27720b x - 249480a b x - 997920a b x - 2328480a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R - 3492720a b x - 3492720a b x - 2328480a b x - 997920a b x +--R + +--R 8 3 6 9 2 4 +--R - 249480a b x - 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 11 22 10 20 2 9 18 3 8 16 +--R 55440b x + 498960a b x + 1995840a b x + 4656960a b x +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 +--R 6985440a b x + 6985440a b x + 4656960a b x + 1995840a b x +--R + +--R 8 3 6 9 2 4 +--R 498960a b x + 55440a b x +--R * +--R log(x) +--R + +--R 10 20 2 9 18 3 8 16 4 7 14 +--R 27720a b x + 235620a b x + 882420a b x + 1905750a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R 2604294a b x + 2318316a b x + 1326204a b x + 456291a b x +--R + +--R 9 2 4 10 2 11 +--R 78419a b x + 2772a b x - 252a +--R / +--R 12 9 22 13 8 20 14 7 18 15 6 16 +--R 1008a b x + 9072a b x + 36288a b x + 84672a b x +--R + +--R 16 5 14 17 4 12 18 3 10 19 2 8 +--R 127008a b x + 127008a b x + 84672a b x + 36288a b x +--R + +--R 20 6 21 4 +--R 9072a b x + 1008a x +--R Type: Union(Expression(Integer),...) +--E 1139 + +--S 1140 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1393 +t0:=1/(x^7*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 27 9 25 2 8 23 3 7 21 4 6 19 5 5 17 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 15 7 3 13 8 2 11 9 9 10 7 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1393 +r0:=(-110/3)/(a^10*x^6)+55*b/(a^11*x^4)-110*b^2/(a^12*x^2)+_ + 1/18/(a*x^6*(a+b*x^2)^9)+1/12/(a^2*x^6*(a+b*x^2)^8)+_ + 11/84/(a^3*x^6*(a+b*x^2)^7)+55/252/(a^4*x^6*(a+b*x^2)^6)+_ + 11/28/(a^5*x^6*(a+b*x^2)^5)+11/14/(a^6*x^6*(a+b*x^2)^4)+_ + 11/6/(a^7*x^6*(a+b*x^2)^3)+11/2/(a^8*x^6*(a+b*x^2)^2)+_ + 55/2/(a^9*x^6*(a+b*x^2))-220*b^3*log(x)/a^13+110*b^3*log(a+b*x^2)/a^13 +--R +--R +--R (2) +--R 12 24 11 22 2 10 20 3 9 18 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 8 9 3 6 +--R 249480a b x + 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x +--R + +--R 8 4 8 9 3 6 +--R - 498960a b x - 55440a b x +--R * +--R log(x) +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 18 4 14 19 3 12 20 2 10 21 8 22 6 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 24 11 22 2 10 20 3 9 18 +--R 27720b x + 249480a b x + 997920a b x + 2328480a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R 3492720a b x + 3492720a b x + 2328480a b x + 997920a b x +--R + +--R 8 4 8 9 3 6 +--R 249480a b x + 27720a b x +--R * +--R 2 +--R log(b x + a) +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R - 55440b x - 498960a b x - 1995840a b x - 4656960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 6985440a b x - 6985440a b x - 4656960a b x - 1995840a b x +--R + +--R 8 4 8 9 3 6 +--R - 498960a b x - 55440a b x +--R * +--R log(x) +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 27720a b x - 235620a b x - 882420a b x - 1905750a b x +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 +--R - 2604294a b x - 2318316a b x - 1326204a b x - 456291a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R - 78419a b x - 2772a b x + 252a b x - 42a +--R / +--R 13 9 24 14 8 22 15 7 20 16 6 18 17 5 16 +--R 252a b x + 2268a b x + 9072a b x + 21168a b x + 31752a b x +--R + +--R 18 4 14 19 3 12 20 2 10 21 8 22 6 +--R 31752a b x + 21168a b x + 9072a b x + 2268a b x + 252a x +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1393 +t0:=x^24/(a+b*x^2)^10 +--R +--R +--R (1) +--R 24 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1393 +r0:=7436429/65536*a^2*x/b^12-7436429/196608*a*x^3/b^11+_ + 7436429/327680*x^5/b^10-1/18*x^23/(b*(a+b*x^2)^9)-_ + 23/288*x^21/(b^2*(a+b*x^2)^8)-23/192*x^19/(b^3*(a+b*x^2)^7)-_ + 437/2304*x^17/(b^4*(a+b*x^2)^6)-7429/23040*x^15/(b^5*(a+b*x^2)^5)-_ + 7429/12288*x^13/(b^6*(a+b*x^2)^4)-96577/73728*x^11/(b^7*(a+b*x^2)^3)-_ + 1062347/294912*x^9/(b^8*(a+b*x^2)^2)-_ + 1062347/65536*x^7/(b^9*(a+b*x^2))-_ + 7436429/65536*a^(5/2)*atan(x*sqrt(b)/sqrt(a))/b^(25/2) +--R +--R +--R (2) +--R 2 9 18 3 8 16 4 7 14 +--R - 334639305a b x - 3011753745a b x - 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R - 28109701620a b x - 42164552430a b x - 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R - 28109701620a b x - 12047014980a b x - 3011753745a b x +--R + +--R 11 +--R - 334639305a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 7323998514a b x + 19562592546a b x + 32314857354a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 34810986496a b x + 24648575094a b x + 11110024926a b x +--R + +--R 10 3 11 +--R 2900207310a b x + 334639305a x +--R * +--R +-+ +--R \|b +--R / +--R 21 18 20 16 2 19 14 +--R 2949120b x + 26542080a b x + 106168320a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 9 18 3 8 16 4 7 14 +--R 334639305a b x + 3011753745a b x + 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 11 +--R 334639305a +--R * +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b +--R |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 1179648b x - 9043968a b x + 189923328a b x + 2939264622a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 14647997028a b x + 39125185092a b x + 64629714708a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 69621972992a b x + 49297150188a b x + 22220049852a b x +--R + +--R 10 3 11 +--R 5800414620a b x + 669278610a x +--R / +--R 21 18 20 16 2 19 14 +--R 5898240b x + 53084160a b x + 212336640a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 495452160a b x + 743178240a b x + 743178240a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a b +--R , +--R +--R 2 9 18 3 8 16 4 7 14 +--R 334639305a b x + 3011753745a b x + 12047014980a b x +--R + +--R 5 6 12 6 5 10 7 4 8 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 8 3 6 9 2 4 10 2 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 11 +--R 334639305a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 589824b x - 4521984a b x + 94961664a b x + 1469632311a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 7323998514a b x + 19562592546a b x + 32314857354a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 34810986496a b x + 24648575094a b x + 11110024926a b x +--R + +--R 10 3 11 +--R 2900207310a b x + 334639305a x +--R / +--R 21 18 20 16 2 19 14 +--R 2949120b x + 26542080a b x + 106168320a b x +--R + +--R 3 18 12 4 17 10 5 16 8 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 6 15 6 7 14 4 8 13 2 9 12 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1149 + +--S 1150 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R 2 | a +-+ \| b 2 +-+ x\|b +--R 7436429a |- - \|b log(-----------------------) + 14872858a \|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R --------------------------------------------------------------------------- +--R 12 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R 2 +-+ x\|b 2 |a +-+ \|b +--R 7436429a \|a atan(-----) + 7436429a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------------ +--R 12 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1153 + +)clear all + +--S 1154 of 1393 +t0:=x^22/(a+b*x^2)^10 +--R +--R +--R (1) +--R 22 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1154 + +--S 1155 of 1393 +r0:=-1616615/65536*a*x/b^11+1616615/196608*x^3/b^10-_ + 1/18*x^21/(b*(a+b*x^2)^9)-7/96*x^19/(b^2*(a+b*x^2)^8)-_ + 19/192*x^17/(b^3*(a+b*x^2)^7)-323/2304*x^15/(b^4*(a+b*x^2)^6)-_ + 323/1536*x^13/(b^5*(a+b*x^2)^5)-4199/12288*x^11/(b^6*(a+b*x^2)^4)-_ + 46189/73728*x^9/(b^7*(a+b*x^2)^3)-46189/32768*x^7/(b^8*(a+b*x^2)^2)-_ + 323323/65536*x^5/(b^9*(a+b*x^2))+_ + 1616615/65536*a^(3/2)*atan(x*sqrt(b)/sqrt(a))/b^(23/2) +--R +--R +--R (2) +--R 9 18 2 8 16 3 7 14 +--R 14549535a b x + 130945815a b x + 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 850547502a b x - 1404993798a b x - 1513521152a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x +--R * +--R +-+ +--R \|b +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 4 16 10 5 15 8 6 14 6 7 13 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 8 12 2 9 11 +--R 5308416a b x + 589824a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 2 8 16 3 7 14 +--R 14549535a b x + 130945815a b x + 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +--R | a \| b +--R |- - log(---------------------) +--R \| b 2 +--R b x + a +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 393216b x - 8257536a b x - 127794114a b x - 636869436a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 1701095004a b x - 2809987596a b x - 3027042304a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 2143354356a b x - 966089124a b x - 252191940a b x - 29099070a x +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 1179648b x + 10616832a b x + 42467328a b x + 99090432a b x +--R + +--R 4 16 10 5 15 8 6 14 6 +--R 148635648a b x + 148635648a b x + 99090432a b x +--R + +--R 7 13 4 8 12 2 9 11 +--R 42467328a b x + 10616832a b x + 1179648a b +--R , +--R +--R 9 18 2 8 16 3 7 14 +--R - 14549535a b x - 130945815a b x - 523783260a b x +--R + +--R 4 6 12 5 5 10 6 4 8 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 7 3 6 8 2 4 9 2 10 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 10 21 9 19 2 8 17 3 7 15 +--R 196608b x - 4128768a b x - 63897057a b x - 318434718a b x +--R + +--R 4 6 13 5 5 11 6 4 9 +--R - 850547502a b x - 1404993798a b x - 1513521152a b x +--R + +--R 7 3 7 8 2 5 9 3 10 +--R - 1071677178a b x - 483044562a b x - 126095970a b x - 14549535a x +--R / +--R 20 18 19 16 2 18 14 3 17 12 +--R 589824b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 4 16 10 5 15 8 6 14 6 7 13 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 8 12 2 9 11 +--R 5308416a b x + 589824a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1156 + +--S 1157 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 1616615a |- - \|b log(---------------------) - 3233230a\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------------- +--R 11 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R - 1616615a\|a atan(-----) - 1616615a |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------------ +--R 11 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1393 +t0:=x^20/(a+b*x^2)^10 +--R +--R +--R (1) +--R 20 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 1393 +r0:=230945/65536*x/b^10-1/18*x^19/(b*(a+b*x^2)^9)-_ + 19/288*x^17/(b^2*(a+b*x^2)^8)-323/4032*x^15/(b^3*(a+b*x^2)^7)-_ + 1615/16128*x^13/(b^4*(a+b*x^2)^6)-4199/32256*x^11/(b^5*(a+b*x^2)^5)-_ + 46189/258048*x^9/(b^6*(a+b*x^2)^4)-_ + 46189/172032*x^7/(b^7*(a+b*x^2)^3)-46189/98304*x^5/(b^8*(a+b*x^2)^2)-_ + 230945/196608*x^3/(b^9*(a+b*x^2))-_ + 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(21/2) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a +--R * +--R +-+ +--R +-+ x\|b +--R \|a atan(-----) +--R +-+ +--R \|a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 1404993798a b x + 1513521152a b x + 1071677178a b x +--R + +--R 7 2 5 8 3 9 +--R 483044562a b x + 126095970a b x + 14549535a x +--R * +--R +-+ +--R \|b +--R / +--R 19 18 18 16 2 17 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +--R | a \| b +--R |- - log(-----------------------) +--R \| b 2 +--R b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 8257536b x + 127794114a b x + 636869436a b x + 1701095004a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 2809987596a b x + 3027042304a b x + 2143354356a b x +--R + +--R 7 2 5 8 3 9 +--R 966089124a b x + 252191940a b x + 29099070a x +--R / +--R 19 18 18 16 2 17 14 +--R 8257536b x + 74317824a b x + 297271296a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R , +--R +--R 9 18 8 16 2 7 14 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a +--R * +--R +-+ +--R |a +--R +-+ |- +--R |a \|b +--R |- atan(----) +--R \|b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 4128768b x + 63897057a b x + 318434718a b x + 850547502a b x +--R + +--R 4 5 11 5 4 9 6 3 7 +--R 1404993798a b x + 1513521152a b x + 1071677178a b x +--R + +--R 7 2 5 8 3 9 +--R 483044562a b x + 126095970a b x + 14549535a x +--R / +--R 19 18 18 16 2 17 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 16 12 4 15 10 5 14 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 13 6 7 12 4 8 11 2 9 10 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1163 + +--S 1164 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + b x - a +-+ +--R | a +-+ \| b +-+ x\|b +--R 230945 |- - \|b log(----------------------- + 461890\|a atan(-----) +--R \| b 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 10 +-+ +--R 131072b \|b +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ +-+ |- +--R +-+ x\|b |a +-+ \|b +--R 230945\|a atan(-----) + 230945 |- \|b atan(----) +--R +-+ \|b x +--R \|a +--R (6) ------------------------------------------------ +--R 10 +-+ +--R 65536b \|b +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1167 + +)clear all + +--S 1168 of 1393 +t0:=x^18/(a+b*x^2)^10 +--R +--R +--R (1) +--R 18 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1168 + +--S 1169 of 1393 +r0:=-1/18*x^17/(b*(a+b*x^2)^9)-17/288*x^15/(b^2*(a+b*x^2)^8)-_ + 85/1344*x^13/(b^3*(a+b*x^2)^7)-1105/16128*x^11/(b^4*(a+b*x^2)^6)-_ + 2431/32256*x^9/(b^5*(a+b*x^2)^5)-2431/28672*x^7/(b^6*(a+b*x^2)^4)-_ + 2431/24576*x^5/(b^7*(a+b*x^2)^3)-12155/98304*x^3/(b^8*(a+b*x^2)^2)-_ + 12155/65536*x/(b^9*(a+b*x^2))+_ + 12155/65536*atan(x*sqrt(b)/sqrt(a))/(b^(19/2)*sqrt(a)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 3363003b x - 16759722a b x - 44765658a b x - 73947042a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 79659008a b x - 56404062a b x - 25423398a b x - 6636630a b x +--R + +--R 8 +--R - 765765a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 18 18 17 16 2 16 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 +--R - 6726006b x - 33519444a b x - 89531316a b x +--R + +--R 3 5 11 4 4 9 5 3 7 +--R - 147894084a b x - 159318016a b x - 112808124a b x +--R + +--R 6 2 5 7 3 8 +--R - 50846796a b x - 13273260a b x - 1531530a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 18 18 17 16 2 16 14 +--R 8257536b x + 74317824a b x + 297271296a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 +--R - 3363003b x - 16759722a b x - 44765658a b x +--R + +--R 3 5 11 4 4 9 5 3 7 +--R - 73947042a b x - 79659008a b x - 56404062a b x +--R + +--R 6 2 5 7 3 8 +--R - 25423398a b x - 6636630a b x - 765765a x +--R * +--R +---+ +--R \|a b +--R / +--R 18 18 17 16 2 16 14 +--R 4128768b x + 37158912a b x + 148635648a b x +--R + +--R 3 15 12 4 14 10 5 13 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 6 12 6 7 11 4 8 10 2 9 9 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1170 + +--S 1171 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R ------------------------------------------------------------------------ +--R 9 +-----+ +-+ +-+ +--R 131072b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------------- +--R 9 +-+ +-+ +---+ +--R 65536b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1393 +t0:=x^16/(a+b*x^2)^10 +--R +--R +--R (1) +--R 16 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1175 + +--S 1176 of 1393 +r0:=-1/18*x^15/(b*(a+b*x^2)^9)-5/96*x^13/(b^2*(a+b*x^2)^8)-_ + 65/1344*x^11/(b^3*(a+b*x^2)^7)-715/16128*x^9/(b^4*(a+b*x^2)^6)-_ + 143/3584*x^7/(b^5*(a+b*x^2)^5)-143/4096*x^5/(b^6*(a+b*x^2)^4)-_ + 715/24576*x^3/(b^7*(a+b*x^2)^3)-715/32768*x/(b^8*(a+b*x^2)^2)+_ + 715/65536*x/(a*b^8*(a+b*x^2))+_ + 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(17/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 17 18 2 16 16 3 15 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x - 1971732a b x - 5266548a b x - 8699652a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 17 18 2 16 16 3 15 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x - 985866a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 17 18 2 16 16 3 15 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 4 14 12 5 13 10 6 12 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 7 11 6 8 10 4 9 9 2 10 8 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1177 + +--S 1178 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------------- +--R 8 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 715\|a \|b atan(-------) - 715\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 8 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1181 + +)clear all + +--S 1182 of 1393 +t0:=x^14/(a+b*x^2)^10 +--R +--R +--R (1) +--R 14 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1182 + +--S 1183 of 1393 +r0:=-1/18*x^13/(b*(a+b*x^2)^9)-13/288*x^11/(b^2*(a+b*x^2)^8)-_ + 143/4032*x^9/(b^3*(a+b*x^2)^7)-143/5376*x^7/(b^4*(a+b*x^2)^6)-_ + 143/7680*x^5/(b^5*(a+b*x^2)^5)-143/12288*x^3/(b^6*(a+b*x^2)^4)-_ + 143/24576*x/(b^7*(a+b*x^2)^3)+143/98304*x/(a*b^7*(a+b*x^2)^2)+_ + 143/65536*x/(a^2*b^7*(a+b*x^2))+_ + 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(5/2)*b^(15/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x - 5266548a b x - 8699652a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 9371648a b x - 6635772a b x - 2990988a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 41287680a b x + 371589120a b x + 1486356480a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 3468165120a b x + 5202247680a b x + 5202247680a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 3468165120a b x + 1486356480a b x + 371589120a b x + 41287680a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x - 2633274a b x - 4349826a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 4685824a b x - 3317886a b x - 1495494a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 2 16 18 3 15 16 4 14 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 5 13 12 6 12 10 7 11 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 8 10 6 9 9 4 10 8 2 11 7 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1184 + +--S 1185 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 2 7 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 143\|a \|b atan(-------) - 143\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 2 7 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1188 + +)clear all + +--S 1189 of 1393 +t0:=x^12/(a+b*x^2)^10 +--R +--R +--R (1) +--R 12 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1189 + +--S 1190 of 1393 +r0:=-1/18*x^11/(b*(a+b*x^2)^9)-11/288*x^9/(b^2*(a+b*x^2)^8)-_ + 11/448*x^7/(b^3*(a+b*x^2)^7)-11/768*x^5/(b^4*(a+b*x^2)^6)-_ + 11/1536*x^3/(b^5*(a+b*x^2)^5)-11/4096*x/(b^6*(a+b*x^2)^4)+_ + 11/24576*x/(a*b^6*(a+b*x^2)^3)+55/98304*x/(a^2*b^6*(a+b*x^2)^2)+_ + 55/65536*x/(a^3*b^6*(a+b*x^2))+_ + 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(13/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x - 334602a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 6930b x + 60060a b x + 230076a b x - 669204a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 720896a b x - 510444a b x - 230076a b x - 60060a b x - 6930a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x - 334602a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R - 360448a b x - 255222a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +---+ +--R \|a b +--R / +--R 3 15 18 4 14 16 5 13 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 6 12 12 7 11 10 8 10 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 9 9 6 10 8 4 11 7 2 12 6 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1191 + +--S 1192 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------- +--R 3 6 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 55\|a \|b atan(-------) - 55\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 3 6 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1393 +t0:=x^10/(a+b*x^2)^10 +--R +--R +--R (1) +--R 10 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 1393 +r0:=-1/18*x^9/(b*(a+b*x^2)^9)-1/32*x^7/(b^2*(a+b*x^2)^8)-_ + 1/64*x^5/(b^3*(a+b*x^2)^7)-5/768*x^3/(b^4*(a+b*x^2)^6)-_ + 1/512*x/(b^5*(a+b*x^2)^5)+1/4096*x/(a*b^5*(a+b*x^2)^4)+_ + 7/24576*x/(a^2*b^5*(a+b*x^2)^3)+35/98304*x/(a^3*b^5*(a+b*x^2)^2)+_ + 35/65536*x/(a^4*b^5*(a+b*x^2))+_ + 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(9/2)*b^(11/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 4 14 18 5 13 16 6 12 14 7 11 12 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 8 10 10 9 9 8 10 8 6 11 7 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 12 6 2 13 5 +--R 5308416a b x + 589824a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 630b x + 5460a b x + 20916a b x + 46404a b x - 65536a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 46404a b x - 20916a b x - 5460a b x - 630a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 4 14 18 5 13 16 6 12 14 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 7 11 12 8 10 10 9 9 8 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 10 8 6 11 7 4 12 6 2 13 5 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x - 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +---+ +--R \|a b +--R / +--R 4 14 18 5 13 16 6 12 14 +--R 589824a b x + 5308416a b x + 21233664a b x +--R + +--R 7 11 12 8 10 10 9 9 8 +--R 49545216a b x + 74317824a b x + 74317824a b x +--R + +--R 10 8 6 11 7 4 12 6 2 13 5 +--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1198 + +--S 1199 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 4 5 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 35\|a \|b atan(-------) - 35\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 4 5 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1202 + +)clear all + +--S 1203 of 1393 +t0:=x^8/(a+b*x^2)^10 +--R +--R +--R (1) +--R 8 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1203 + +--S 1204 of 1393 +r0:=-1/18*x^7/(b*(a+b*x^2)^9)-7/288*x^5/(b^2*(a+b*x^2)^8)-_ + 5/576*x^3/(b^3*(a+b*x^2)^7)-5/2304*x/(b^4*(a+b*x^2)^6)+_ + 1/4608*x/(a*b^4*(a+b*x^2)^5)+1/4096*x/(a^2*b^4*(a+b*x^2)^4)+_ + 7/24576*x/(a^3*b^4*(a+b*x^2)^3)+35/98304*x/(a^4*b^4*(a+b*x^2)^2)+_ + 35/65536*x/(a^5*b^4*(a+b*x^2))+_ + 35/65536*atan(x*sqrt(b)/sqrt(a))/(a^(11/2)*b^(9/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 5 13 18 6 12 16 7 11 14 8 10 12 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 9 9 10 10 8 8 11 7 6 12 6 4 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 13 5 2 14 4 +--R 5308416a b x + 589824a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 630b x + 5460a b x + 20916a b x + 46404a b x + 65536a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 46404a b x - 20916a b x - 5460a b x - 630a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 5 13 18 6 12 16 7 11 14 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 8 10 12 9 9 10 10 8 8 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 11 7 6 12 6 4 13 5 2 14 4 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 315b x + 2835a b x + 11340a b x + 26460a b x + 39690a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 39690a b x + 26460a b x + 11340a b x + 2835a b x + 315a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 4 4 9 +--R 315b x + 2730a b x + 10458a b x + 23202a b x + 32768a b x +--R + +--R 5 3 7 6 2 5 7 3 8 +--R - 23202a b x - 10458a b x - 2730a b x - 315a x +--R * +--R +---+ +--R \|a b +--R / +--R 5 13 18 6 12 16 7 11 14 +--R 589824a b x + 5308416a b x + 21233664a b x +--R + +--R 8 10 12 9 9 10 10 8 8 +--R 49545216a b x + 74317824a b x + 74317824a b x +--R + +--R 11 7 6 12 6 4 13 5 2 14 4 +--R 49545216a b x + 21233664a b x + 5308416a b x + 589824a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1205 + +--S 1206 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 35\|a \|b log(---------------------------) - 70\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------ +--R 5 4 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 35\|a \|b atan(-------) - 35\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 5 4 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1393 +t0:=x^6/(a+b*x^2)^10 +--R +--R +--R (1) +--R 6 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1393 +r0:=-1/18*x^5/(b*(a+b*x^2)^9)-5/288*x^3/(b^2*(a+b*x^2)^8)-_ + 5/1344*x/(b^3*(a+b*x^2)^7)+5/16128*x/(a*b^3*(a+b*x^2)^6)+_ + 11/32256*x/(a^2*b^3*(a+b*x^2)^5)+11/28672*x/(a^3*b^3*(a+b*x^2)^4)+_ + 11/24576*x/(a^4*b^3*(a+b*x^2)^3)+55/98304*x/(a^5*b^3*(a+b*x^2)^2)+_ + 55/65536*x/(a^6*b^3*(a+b*x^2))+_ + 55/65536*atan(x*sqrt(b)/sqrt(a))/(a^(13/2)*b^(7/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x + 255222a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 6930b x + 60060a b x + 230076a b x + 510444a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 720896a b x + 669204a b x - 230076a b x - 60060a b x - 6930a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 3465b x + 31185a b x + 124740a b x + 291060a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 436590a b x + 436590a b x + 291060a b x + 124740a b x +--R + +--R 8 2 9 +--R 31185a b x + 3465a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 3465b x + 30030a b x + 115038a b x + 255222a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 360448a b x + 334602a b x - 115038a b x - 30030a b x - 3465a x +--R * +--R +---+ +--R \|a b +--R / +--R 6 12 18 7 11 16 8 10 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 9 9 12 10 8 10 11 7 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 12 6 6 13 5 4 14 4 2 15 3 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1212 + +--S 1213 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 55\|a \|b log(---------------------------) - 110\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) ------------------------------------------------------------------- +--R 6 3 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 55\|a \|b atan(-------) - 55\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 6 3 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1216 + +)clear all + +--S 1217 of 1393 +t0:=x^4/(a+b*x^2)^10 +--R +--R +--R (1) +--R 4 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1393 +r0:=-1/18*x^3/(b*(a+b*x^2)^9)-1/96*x/(b^2*(a+b*x^2)^8)+_ + 1/1344*x/(a*b^2*(a+b*x^2)^7)+13/16128*x/(a^2*b^2*(a+b*x^2)^6)+_ + 143/161280*x/(a^3*b^2*(a+b*x^2)^5)+143/143360*x/(a^4*b^2*(a+b*x^2)^4)+_ + 143/122880*x/(a^5*b^2*(a+b*x^2)^3)+143/98304*x/(a^6*b^2*(a+b*x^2)^2)+_ + 143/65536*x/(a^7*b^2*(a+b*x^2))+_ + 143/65536*atan(x*sqrt(b)/sqrt(a))/(a^(15/2)*b^(5/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 13 5 6 14 4 4 15 3 2 16 2 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 9371648a b x + 8699652a b x + 5266548a b x - 780780a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 41287680a b x + 371589120a b x + 1486356480a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 3468165120a b x + 5202247680a b x + 5202247680a b x +--R + +--R 13 5 6 14 4 4 15 3 2 +--R 3468165120a b x + 1486356480a b x + 371589120a b x +--R + +--R 16 2 +--R 41287680a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 4685824a b x + 4349826a b x + 2633274a b x - 390390a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 7 11 18 8 10 16 9 9 14 +--R 20643840a b x + 185794560a b x + 743178240a b x +--R + +--R 10 8 12 11 7 10 12 6 8 +--R 1734082560a b x + 2601123840a b x + 2601123840a b x +--R + +--R 13 5 6 14 4 4 15 3 2 16 2 +--R 1734082560a b x + 743178240a b x + 185794560a b x + 20643840a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1219 + +--S 1220 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 143\|a \|b log(---------------------------) - 286\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 7 2 +-----+ +-+ +-+ +--R 131072a b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 143\|a \|b atan(-------) - 143\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 7 2 +-+ +-+ +---+ +--R 65536a b \|a \|b \|a b +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1223 + +)clear all + +--S 1224 of 1393 +t0:=x^2/(a+b*x^2)^10 +--R +--R +--R (1) +--R 2 +--R x +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1224 + +--S 1225 of 1393 +r0:=-1/18*x/(b*(a+b*x^2)^9)+1/288*x/(a*b*(a+b*x^2)^8)+_ + 5/1344*x/(a^2*b*(a+b*x^2)^7)+65/16128*x/(a^3*b*(a+b*x^2)^6)+_ + 143/32256*x/(a^4*b*(a+b*x^2)^5)+143/28672*x/(a^5*b*(a+b*x^2)^4)+_ + 143/24576*x/(a^6*b*(a+b*x^2)^3)+715/98304*x/(a^7*b*(a+b*x^2)^2)+_ + 715/65536*x/(a^8*b*(a+b*x^2))+_ + 715/65536*atan(x*sqrt(b)/sqrt(a))/(a^(17/2)*b^(3/2)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x - 45045a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 90090b x + 780780a b x + 2990988a b x + 6635772a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 9371648a b x + 8699652a b x + 5266548a b x + 1971732a b x +--R + +--R 8 +--R - 90090a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a b +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 45045b x + 405405a b x + 1621620a b x + 3783780a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 5675670a b x + 5675670a b x + 3783780a b x + 1621620a b x +--R + +--R 8 2 9 +--R 405405a b x + 45045a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 45045b x + 390390a b x + 1495494a b x + 3317886a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 4685824a b x + 4349826a b x + 2633274a b x + 985866a b x +--R + +--R 8 +--R - 45045a x +--R * +--R +---+ +--R \|a b +--R / +--R 8 10 18 9 9 16 10 8 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 11 7 12 12 6 10 13 5 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 14 4 6 15 3 4 16 2 2 17 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a b +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1226 + +--S 1227 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 715\|a \|b log(---------------------------) - 1430\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R (4) --------------------------------------------------------------------- +--R 8 +-----+ +-+ +-+ +--R 131072a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 715\|a \|b atan(-------) - 715\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) ----------------------------------------------- +--R 8 +-+ +-+ +---+ +--R 65536a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1393 +t0:=1/(a+b*x^2)^10 +--R +--R +--R (1) +--R 1 +--R / +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 210a b x + 120a b x + 45a b x + 10a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 1393 +r0:=1/18*x/(a*(a+b*x^2)^9)+17/288*x/(a^2*(a+b*x^2)^8)+_ + 85/1344*x/(a^3*(a+b*x^2)^7)+1105/16128*x/(a^4*(a+b*x^2)^6)+_ + 2431/32256*x/(a^5*(a+b*x^2)^5)+2431/28672*x/(a^6*(a+b*x^2)^4)+_ + 2431/24576*x/(a^7*(a+b*x^2)^3)+12155/98304*x/(a^8*(a+b*x^2)^2)+_ + 12155/65536*x/(a^9*(a+b*x^2))+_ + 12155/65536*atan(x*sqrt(b)/sqrt(a))/(a^(19/2)*sqrt(b)) +--R +--R +--R (2) +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +-+ +--R x\|b +--R atan(-----) +--R +-+ +--R \|a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x +--R + +--R 8 +--R 3363003a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a +--R * +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R 2 +-----+ +--R (b x - a)\|- a b + 2a b x +--R log(---------------------------) +--R 2 +--R b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 1531530b x + 13273260a b x + 50846796a b x + 112808124a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 159318016a b x + 147894084a b x + 89531316a b x + 33519444a b x +--R + +--R 8 +--R 6726006a x +--R * +--R +-----+ +--R \|- a b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a +--R * +--R +-----+ +--R \|- a b +--R , +--R +--R 9 18 8 16 2 7 14 3 6 12 +--R 765765b x + 6891885a b x + 27567540a b x + 64324260a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 96486390a b x + 96486390a b x + 64324260a b x + 27567540a b x +--R + +--R 8 2 9 +--R 6891885a b x + 765765a +--R * +--R +---+ +--R x\|a b +--R atan(-------) +--R a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 765765b x + 6636630a b x + 25423398a b x + 56404062a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 79659008a b x + 73947042a b x + 44765658a b x + 16759722a b x +--R + +--R 8 +--R 3363003a x +--R * +--R +---+ +--R \|a b +--R / +--R 9 9 18 10 8 16 11 7 14 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 12 6 12 13 5 10 14 4 8 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 15 3 6 16 2 4 17 2 18 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a +--R * +--R +---+ +--R \|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1233 + +--S 1234 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x\|b +--R 12155\|a \|b log(---------------------------) - 24310\|- a b atan(-----) +--R 2 +-+ +--R b x + a \|a +--R ------------------------------------------------------------------------ +--R 9 +-----+ +-+ +-+ +--R 131072a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|b +--R 12155\|a \|b atan(-------) - 12155\|a b atan(-----) +--R a +-+ +--R \|a +--R (6) --------------------------------------------------- +--R 9 +-+ +-+ +---+ +--R 65536a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1393 +t0:=1/(x^2*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 22 9 20 2 8 18 3 7 16 4 6 14 5 5 12 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1238 + +--S 1239 of 1393 +r0:=(-230945/65536)/(a^10*x)+1/18/(a*x*(a+b*x^2)^9)+_ + 19/288/(a^2*x*(a+b*x^2)^8)+323/4032/(a^3*x*(a+b*x^2)^7)+_ + 1615/16128/(a^4*x*(a+b*x^2)^6)+4199/32256/(a^5*x*(a+b*x^2)^5)+_ + 46189/258048/(a^6*x*(a+b*x^2)^4)+46189/172032/(a^7*x*(a+b*x^2)^3)+_ + 46189/98304/(a^8*x*(a+b*x^2)^2)+230945/196608/(a^9*x*(a+b*x^2))-_ + 230945/65536*atan(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(21/2) +--R +--R +--R (2) +--R 9 19 8 17 2 7 15 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R - 1222160940a b x - 523783260a b x - 130945815a b x - 14549535a x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 126095970a b x - 483044562a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1071677178a b x - 1513521152a b x - 1404993798a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a +--R * +--R +-+ +--R \|a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 9 19 8 17 2 7 15 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x +--R * +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R | b \| a +--R |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 9 18 8 16 2 7 14 +--R - 29099070b x - 252191940a b x - 966089124a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 2143354356a b x - 3027042304a b x - 2809987596a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 1701095004a b x - 636869436a b x - 127794114a b x - 8257536a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 8257536a b x + 74317824a b x + 297271296a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 693633024a b x + 1040449536a b x + 1040449536a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 693633024a b x + 297271296a b x + 74317824a b x + 8257536a x +--R , +--R +--R 9 19 8 17 2 7 15 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 6 13 4 5 11 5 4 9 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 3 7 7 2 5 8 3 9 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 9 18 8 16 2 7 14 +--R - 14549535b x - 126095970a b x - 483044562a b x +--R + +--R 3 6 12 4 5 10 5 4 8 +--R - 1071677178a b x - 1513521152a b x - 1404993798a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 850547502a b x - 318434718a b x - 63897057a b x - 4128768a +--R / +--R 10 9 19 11 8 17 12 7 15 +--R 4128768a b x + 37158912a b x + 148635648a b x +--R + +--R 13 6 13 14 5 11 15 4 9 +--R 346816512a b x + 520224768a b x + 520224768a b x +--R + +--R 16 3 7 17 2 5 18 3 19 +--R 346816512a b x + 148635648a b x + 37158912a b x + 4128768a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1240 + +--S 1241 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 230945 |- - \|a log(----------------------- + 461890\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) -------------------------------------------------------------------- +--R 10 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R 230945\|b atan(-----) + 230945\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------- +--R 10 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1393 +t0:=1/(x^4*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 24 9 22 2 8 20 3 7 18 4 6 16 5 5 14 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 12 7 3 10 8 2 8 9 6 10 4 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1393 +r0:=(-1616615/196608)/(a^10*x^3)+1616615/65536*b/(a^11*x)+_ + 1/18/(a*x^3*(a+b*x^2)^9)+7/96/(a^2*x^3*(a+b*x^2)^8)+_ + 19/192/(a^3*x^3*(a+b*x^2)^7)+323/2304/(a^4*x^3*(a+b*x^2)^6)+_ + 323/1536/(a^5*x^3*(a+b*x^2)^5)+4199/12288/(a^6*x^3*(a+b*x^2)^4)+_ + 46189/73728/(a^7*x^3*(a+b*x^2)^3)+46189/32768/(a^8*x^3*(a+b*x^2)^2)+_ + 323323/65536/(a^9*x^3*(a+b*x^2))+_ + 1616615/65536*b^(3/2)*atan(x*sqrt(b)/sqrt(a))/a^(23/2) +--R +--R +--R (2) +--R 10 21 9 19 2 8 17 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 10 20 9 18 2 8 16 +--R 14549535b x + 126095970a b x + 483044562a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 1071677178a b x + 1513521152a b x + 1404993798a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x +--R + +--R 10 +--R - 196608a +--R * +--R +-+ +--R \|a +--R / +--R 11 9 21 12 8 19 13 7 17 14 6 15 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 15 5 13 16 4 11 17 3 9 18 2 7 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 19 5 20 3 +--R 5308416a b x + 589824a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 10 21 9 19 2 8 17 +--R 14549535b x + 130945815a b x + 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R 1222160940a b x + 1833241410a b x + 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 9 3 +--R 1222160940a b x + 523783260a b x + 130945815a b x + 14549535a b x +--R * +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +--R | b \| a +--R |- - log(---------------------) +--R \| a 2 +--R b x + a +--R + +--R 10 20 9 18 2 8 16 +--R 29099070b x + 252191940a b x + 966089124a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 2143354356a b x + 3027042304a b x + 2809987596a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 1701095004a b x + 636869436a b x + 127794114a b x + 8257536a b x +--R + +--R 10 +--R - 393216a +--R / +--R 11 9 21 12 8 19 13 7 17 +--R 1179648a b x + 10616832a b x + 42467328a b x +--R + +--R 14 6 15 15 5 13 16 4 11 +--R 99090432a b x + 148635648a b x + 148635648a b x +--R + +--R 17 3 9 18 2 7 19 5 20 3 +--R 99090432a b x + 42467328a b x + 10616832a b x + 1179648a x +--R , +--R +--R 10 21 9 19 2 8 17 +--R - 14549535b x - 130945815a b x - 523783260a b x +--R + +--R 3 7 15 4 6 13 5 5 11 +--R - 1222160940a b x - 1833241410a b x - 1833241410a b x +--R + +--R 6 4 9 7 3 7 8 2 5 +--R - 1222160940a b x - 523783260a b x - 130945815a b x +--R + +--R 9 3 +--R - 14549535a b x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 10 20 9 18 2 8 16 +--R 14549535b x + 126095970a b x + 483044562a b x +--R + +--R 3 7 14 4 6 12 5 5 10 +--R 1071677178a b x + 1513521152a b x + 1404993798a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 +--R 850547502a b x + 318434718a b x + 63897057a b x + 4128768a b x +--R + +--R 10 +--R - 196608a +--R / +--R 11 9 21 12 8 19 13 7 17 14 6 15 +--R 589824a b x + 5308416a b x + 21233664a b x + 49545216a b x +--R + +--R 15 5 13 16 4 11 17 3 9 18 2 7 +--R 74317824a b x + 74317824a b x + 49545216a b x + 21233664a b x +--R + +--R 19 5 20 3 +--R 5308416a b x + 589824a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1247 + +--S 1248 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + b x - a +-+ +--R | b +-+ \| a +-+ x\|b +--R 1616615b |- - \|a log(---------------------) - 3233230b\|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R (4) ---------------------------------------------------------------------- +--R 11 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R +-+ x\|b +-+ |b \|a +--R - 1616615b\|b atan(-----) - 1616615b\|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------------- +--R 11 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1251 + +)clear all + +--S 1252 of 1393 +t0:=1/(x^6*(a+b*x^2)^10) +--R +--R +--R (1) +--R 1 +--R / +--R 10 26 9 24 2 8 22 3 7 20 4 6 18 5 5 16 +--R b x + 10a b x + 45a b x + 120a b x + 210a b x + 252a b x +--R + +--R 6 4 14 7 3 12 8 2 10 9 8 10 6 +--R 210a b x + 120a b x + 45a b x + 10a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1252 + +--S 1253 of 1393 +r0:=(-7436429/327680)/(a^10*x^5)+7436429/196608*b/(a^11*x^3)-_ + 7436429/65536*b^2/(a^12*x)+1/18/(a*x^5*(a+b*x^2)^9)+_ + 23/288/(a^2*x^5*(a+b*x^2)^8)+23/192/(a^3*x^5*(a+b*x^2)^7)+_ + 437/2304/(a^4*x^5*(a+b*x^2)^6)+7429/23040/(a^5*x^5*(a+b*x^2)^5)+_ + 7429/12288/(a^6*x^5*(a+b*x^2)^4)+96577/73728/(a^7*x^5*(a+b*x^2)^3)+_ + 1062347/294912/(a^8*x^5*(a+b*x^2)^2)+_ + 1062347/65536/(a^9*x^5*(a+b*x^2))-_ + 7436429/65536*b^(5/2)*atan(x*sqrt(b)/sqrt(a))/a^(25/2) +--R +--R +--R (2) +--R 11 23 10 21 2 9 19 +--R - 334639305b x - 3011753745a b x - 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R - 28109701620a b x - 42164552430a b x - 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R - 28109701620a b x - 12047014980a b x - 3011753745a b x +--R + +--R 9 2 5 +--R - 334639305a b x +--R * +--R +-+ +--R +-+ x\|b +--R \|b atan(-----) +--R +-+ +--R \|a +--R + +--R 11 22 10 20 2 9 18 +--R - 334639305b x - 2900207310a b x - 11110024926a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 24648575094a b x - 34810986496a b x - 32314857354a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 19562592546a b x - 7323998514a b x - 1469632311a b x +--R + +--R 9 2 4 10 2 11 +--R - 94961664a b x + 4521984a b x - 589824a +--R * +--R +-+ +--R \|a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 2949120a b x + 26542080a b x + 106168320a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x +--R * +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 11 23 10 21 2 9 19 +--R 334639305b x + 3011753745a b x + 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 9 2 5 +--R 334639305a b x +--R * +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +--R | b \| a +--R |- - log(-----------------------) +--R \| a 2 +--R b x + a +--R + +--R 11 22 10 20 2 9 18 +--R - 669278610b x - 5800414620a b x - 22220049852a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 49297150188a b x - 69621972992a b x - 64629714708a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 39125185092a b x - 14647997028a b x - 2939264622a b x +--R + +--R 9 2 4 10 2 11 +--R - 189923328a b x + 9043968a b x - 1179648a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 5898240a b x + 53084160a b x + 212336640a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 495452160a b x + 743178240a b x + 743178240a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 495452160a b x + 212336640a b x + 53084160a b x + 5898240a x +--R , +--R +--R 11 23 10 21 2 9 19 +--R 334639305b x + 3011753745a b x + 12047014980a b x +--R + +--R 3 8 17 4 7 15 5 6 13 +--R 28109701620a b x + 42164552430a b x + 42164552430a b x +--R + +--R 6 5 11 7 4 9 8 3 7 +--R 28109701620a b x + 12047014980a b x + 3011753745a b x +--R + +--R 9 2 5 +--R 334639305a b x +--R * +--R +-+ +--R |b +--R +-+ a |- +--R |b \|a +--R |- atan(-----) +--R \|a b x +--R + +--R 11 22 10 20 2 9 18 +--R - 334639305b x - 2900207310a b x - 11110024926a b x +--R + +--R 3 8 16 4 7 14 5 6 12 +--R - 24648575094a b x - 34810986496a b x - 32314857354a b x +--R + +--R 6 5 10 7 4 8 8 3 6 +--R - 19562592546a b x - 7323998514a b x - 1469632311a b x +--R + +--R 9 2 4 10 2 11 +--R - 94961664a b x + 4521984a b x - 589824a +--R / +--R 12 9 23 13 8 21 14 7 19 +--R 2949120a b x + 26542080a b x + 106168320a b x +--R + +--R 15 6 17 16 5 15 17 4 13 +--R 247726080a b x + 371589120a b x + 371589120a b x +--R + +--R 18 3 11 19 2 9 20 7 21 5 +--R 247726080a b x + 106168320a b x + 26542080a b x + 2949120a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1254 + +--S 1255 of 1393 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + b x - a +-+ +--R 2 | b +-+ \| a 2 +-+ x\|b +--R 7436429b |- - \|a log(-----------------------) + 14872858b \|b atan(-----) +--R \| a 2 +-+ +--R b x + a \|a +--R --------------------------------------------------------------------------- +--R 12 +-+ +--R 131072a \|a +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ +-+ a |- +--R 2 +-+ x\|b 2 +-+ |b \|a +--R 7436429b \|b atan(-----) + 7436429b \|a |- atan(-----) +--R +-+ \|a b x +--R \|a +--R (6) ------------------------------------------------------- +--R 12 +-+ +--R 65536a \|a +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1258 + +)clear all + +--S 1259 of 1393 +t0:=x^3/(a-b*x^2) +--R +--R +--R 3 +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1259 + +--S 1260 of 1393 +r0:=-1/2*x^2/b-1/2*a*log(a-b*x^2)/b^2 +--R +--R +--R 2 2 +--R - a log(- b x + a) - b x +--R (2) -------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - a log(b x - a) - b x +--R (3) ------------------------ +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1261 + +--S 1262 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - a log(b x - a) + a log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1263 + +)clear all + +--S 1264 of 1393 +t0:=x^2/(a-b*x^2) +--R +--R +--R 2 +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1264 + +--S 1265 of 1393 +r0:=-x/b+atanh(x*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R \|a atanh(-----) - x\|b +--R +-+ +--R \|a +--R (2) ------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R |a 2 +---+ +--R +-+ 2b x |- + b x + a | a +--R |a \|b +---+ |- - +--R |- log(-------------------) - 2x | a \| b +--R \|b 2 - |- - atan(------) - x +--R b x - a \| b x +--R (3) [---------------------------------,------------------------] +--R 2b b +--R Type: Union(List(Expression(Integer)),...) +--E 1266 + +--S 1267 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |a 2 +--R +-+ 2b x |- + b x + a +-+ +--R |a +-+ \|b +-+ x\|b +--R |- \|b log(-------------------) - 2\|a atanh(-----) +--R \|b 2 +-+ +--R b x - a \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | a +--R +-+ +---+ |- - +--R +-+ x\|b | a +-+ \| b +--R - \|a atanh(-----) - |- - \|b atan(------) +--R +-+ \| b x +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 1393 +t0:=x/(a-b*x^2) +--R +--R +--R x +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1271 + +--S 1272 of 1393 +r0:=-1/2*log(a-b*x^2)/b +--R +--R +--R 2 +--R log(- b x + a) +--R (2) - --------------- +--R 2b +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x - a) +--R (3) - ------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 1393 +t0:=1/(a-b*x^2) +--R +--R +--R 1 +--R (1) - -------- +--R 2 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1276 + +--S 1277 of 1393 +r0:=atanh(x*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +---+ +--R (b x + a)\|a b + 2a b x +-----+ +--R log(-------------------------) x\|- a b +--R 2 atan(---------) +--R b x - a a +--R (3) [------------------------------,---------------] +--R +---+ +-----+ +--R 2\|a b \|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1278 + +--S 1279 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) - 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2\|a \|b \|a b +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - \|- a b atanh(-----) + \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1282 + +)clear all + +--S 1283 of 1393 +t0:=1/(x*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ---------- +--R 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1283 + +--S 1284 of 1393 +r0:=log(x)/a-1/2*log(a-b*x^2)/a +--R +--R +--R 2 +--R 2log(x) - log(- b x + a) +--R (2) ------------------------- +--R 2a +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x - a) + 2log(x) +--R (3) ------------------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 1285 + +--S 1286 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2a +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1287 + +)clear all + +--S 1288 of 1393 +t0:=1/(x^2*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ----------- +--R 4 2 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1288 + +--S 1289 of 1393 +r0:=(-1)/(a*x)+atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|b +-+ +--R x\|b atanh(-----) - \|a +--R +-+ +--R \|a +--R (2) ------------------------ +--R +-+ +--R a x\|a +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1393 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R |b 2 +---+ +--R +-+ 2a x |- + b x + a | b +--R |b \|a +---+ a |- - +--R x |- log(-------------------) - 2 | b \| a +--R \|a 2 - x |- - atan(-------) - 1 +--R b x - a \| a b x +--R (3) [---------------------------------,--------------------------] +--R 2a x a x +--R Type: Union(List(Expression(Integer)),...) +--E 1290 + +--S 1291 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R \|a |- log(-------------------) - 2\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - \|b atanh(-----) - |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) -------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1393 +t0:=1/(x^3*(a-b*x^2)) +--R +--R +--R 1 +--R (1) - ----------- +--R 5 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1393 +r0:=(-1/2)/(a*x^2)+b*log(x)/a^2-1/2*b*log(a-b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R 2b x log(x) - b x log(- b x + a) - a +--R (2) ------------------------------------- +--R 2 2 +--R 2a x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - b x log(b x - a) + 2b x log(x) - a +--R (3) ------------------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1393 +t0:=x^3/(a-b*x^2)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1393 +r0:=1/2*a/(b^2*(a-b*x^2))+1/2*log(a-b*x^2)/b^2 +--R +--R +--R 2 2 +--R (b x - a)log(- b x + a) - a +--R (2) ----------------------------- +--R 3 2 2 +--R 2b x - 2a b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (b x - a)log(b x - a) - a +--R (3) --------------------------- +--R 3 2 2 +--R 2b x - 2a b +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R log(b x - a) - log(- b x + a) +--R (4) ------------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1393 +t0:=x^2/(a-b*x^2)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1393 +r0:=1/2*x/(b*(a-b*x^2))-1/2*atanh(x*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (- b x + a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------ +--R 2 2 +-+ +-+ +--R (2b x - 2a b)\|a \|b +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 (b x + a)\|a b - 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4b x - 4a b)\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (- b x + a)atan(---------) - x\|- a b +--R a +--R ---------------------------------------] +--R 2 2 +-----+ +--R (2b x - 2a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1307 + +--S 1308 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1311 + +)clear all + +--S 1312 of 1393 +t0:=x/(a-b*x^2)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1312 + +--S 1313 of 1393 +r0:=1/2/(b*(a-b*x^2)) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ---------- +--R 2 2 +--R b x - a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1313 + +--S 1314 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2b x - 2a b +--R Type: Union(Expression(Integer),...) +--E 1314 + +--S 1315 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1316 + +)clear all + +--S 1317 of 1393 +t0:=1/(a-b*x^2)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R b x - 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1317 + +--S 1318 of 1393 +r0:=1/2*x/(a*(a-b*x^2))+1/2*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|b +-+ +-+ +--R (b x - a)atanh(-----) - x\|a \|b +--R +-+ +--R \|a +--R (2) ---------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x - 2a )\|a \|b +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 (b x + a)\|a b + 2a b x +---+ +--R (b x - a)log(-------------------------) - 2x\|a b +--R 2 +--R b x - a +--R [---------------------------------------------------, +--R 2 2 +---+ +--R (4a b x - 4a )\|a b +--R +-----+ +--R 2 x\|- a b +-----+ +--R (b x - a)atan(---------) - x\|- a b +--R a +--R -------------------------------------] +--R 2 2 +-----+ +--R (2a b x - 2a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1319 + +--S 1320 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) - 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 4a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - \|- a b atanh(-----) + \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1323 + +)clear all + +--S 1324 of 1393 +t0:=1/(x*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1324 + +--S 1325 of 1393 +r0:=1/2/(a*(a-b*x^2))+log(x)/a^2-1/2*log(a-b*x^2)/a^2 +--R +--R +--R 2 2 2 +--R (2b x - 2a)log(x) + (- b x + a)log(- b x + a) - a +--R (2) ---------------------------------------------------- +--R 2 2 3 +--R 2a b x - 2a +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x + a)log(b x - a) + (2b x - 2a)log(x) - a +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 1326 + +--S 1327 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 1327 + +--S 1328 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1328 + +)clear all + +--S 1329 of 1393 +t0:=1/(x^2*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1329 + +--S 1330 of 1393 +r0:=(-3/2)/(a^2*x)+1/2/(a*x*(a-b*x^2))+_ + 3/2*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|b 2 +-+ +--R (3b x - 3a x)\|b atanh(-----) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x - 2a x)\|a +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 3 |b \|a 2 +--R (3b x - 3a x) |- log(-------------------) - 6b x + 4a +--R \|a 2 +--R b x - a +--R [-------------------------------------------------------, +--R 2 3 3 +--R 4a b x - 4a x +--R +---+ +--R | b +--R +---+ a |- - +--R 3 | b \| a 2 +--R (- 3b x + 3a x) |- - atan(-------) - 3b x + 2a +--R \| a b x +--R ------------------------------------------------] +--R 2 3 3 +--R 2a b x - 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 1331 + +--S 1332 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 3\|a |- log(-------------------) - 6\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ----------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 3\|b atanh(-----) - 3 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) ---------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1335 + +)clear all + +--S 1336 of 1393 +t0:=1/(x^3*(a-b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R b x - 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1336 + +--S 1337 of 1393 +r0:=(-1)/(a^2*x^2)+1/2/(a*x^2*(a-b*x^2))+2*b*log(x)/a^3-b*log(a-b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 4 2 2 2 2 +--R (4b x - 4a b x )log(x) + (- 2b x + 2a b x )log(- b x + a) - 2a b x + a +--R --------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x - 2a x +--R Type: Expression(Integer) +--E 1337 + +--S 1338 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (- 2b x + 2a b x )log(b x - a) + (4b x - 4a b x )log(x) - 2a b x + a +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x - 2a x +--R Type: Union(Expression(Integer),...) +--E 1338 + +--S 1339 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1340 + +)clear all + +--S 1341 of 1393 +t0:=x^3/(a-b*x^2)^3 +--R +--R +--R 3 +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1341 + +--S 1342 of 1393 +r0:=1/4*x^4/(a*(a-b*x^2)^2) +--R +--R +--R 1 4 +--R - x +--R 4 +--R (2) --------------------- +--R 2 4 2 2 3 +--R a b x - 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1342 + +--S 1343 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x - a +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4b x - 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 1343 + +--S 1344 of 1393 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1345 + +)clear all + +--S 1346 of 1393 +t0:=x^2/(a-b*x^2)^3 +--R +--R +--R 2 +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1346 + +--S 1347 of 1393 +r0:=1/4*x/(b*(a-b*x^2)^2)-1/8*x/(a*b*(a-b*x^2))-_ + 1/8*atanh(x*sqrt(b)/sqrt(a))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (- b x + 2a b x - a )atanh(-----) + (b x + a x)\|a \|b +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x - 16a b x + 8a b)\|a \|b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b - 2a b x 3 +---+ +--R (b x - 2a b x + a )log(-------------------------) + (2b x + 2a x)\|a b +--R 2 +--R b x - a +--R [--------------------------------------------------------------------------, +--R 3 4 2 2 2 3 +---+ +--R (16a b x - 32a b x + 16a b)\|a b +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (- b x + 2a b x - a )atan(---------) + (b x + a x)\|- a b +--R a +--R -------------------------------------------------------------] +--R 3 4 2 2 2 3 +-----+ +--R (8a b x - 16a b x + 8a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1348 + +--S 1349 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R \|a \|b log(-------------------------) + 2\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 16a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R \|- a b atanh(-----) - \|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1352 + +)clear all + +--S 1353 of 1393 +t0:=x/(a-b*x^2)^3 +--R +--R +--R x +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1353 + +--S 1354 of 1393 +r0:=1/4/(b*(a-b*x^2)^2) +--R +--R +--R 1 +--R - +--R 4 +--R (2) -------------------- +--R 3 4 2 2 2 +--R b x - 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1354 + +--S 1355 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) ---------------------- +--R 3 4 2 2 2 +--R 4b x - 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 1355 + +--S 1356 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1357 + +)clear all + +--S 1358 of 1393 +t0:=1/(a-b*x^2)^3 +--R +--R +--R 1 +--R (1) - ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1358 + +--S 1359 of 1393 +r0:=1/4*x/(a*(a-b*x^2)^2)+3/8*x/(a^2*(a-b*x^2))+_ + 3/8*atanh(x*sqrt(b)/sqrt(a))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|b 3 +-+ +-+ +--R (3b x - 6a b x + 3a )atanh(-----) + (- 3b x + 5a x)\|a \|b +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x - 16a b x + 8a )\|a \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +---+ +--R 2 4 2 2 (b x + a)\|a b + 2a b x +--R (3b x - 6a b x + 3a )log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 +---+ +--R (- 6b x + 10a x)\|a b +--R / +--R 2 2 4 3 2 4 +---+ +--R (16a b x - 32a b x + 16a )\|a b +--R , +--R +-----+ +--R 2 4 2 2 x\|- a b 3 +-----+ +--R (3b x - 6a b x + 3a )atan(---------) + (- 3b x + 5a x)\|- a b +--R a +--R -----------------------------------------------------------------] +--R 2 2 4 3 2 4 +-----+ +--R (8a b x - 16a b x + 8a )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 1360 + +--S 1361 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R 3\|a \|b log(-------------------------) - 6\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16a \|a \|b \|a b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1362 + +--S 1363 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - 3\|- a b atanh(-----) + 3\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1393 +t0:=1/(x*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------ +--R 3 7 2 5 2 3 3 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1365 + +--S 1366 of 1393 +r0:=1/4/(a*(a-b*x^2)^2)+1/2/(a^2*(a-b*x^2))+log(x)/a^3-1/2*log(a-b*x^2)/a^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (4b x - 8a b x + 4a )log(x) + (- 2b x + 4a b x - 2a )log(- b x + a) +--R + +--R 2 2 +--R - 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x - 8a b x + 4a +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2b x + 4a b x - 2a )log(b x - a) + (4b x - 8a b x + 4a )log(x) +--R + +--R 2 2 +--R - 2a b x + 3a +--R / +--R 3 2 4 4 2 5 +--R 4a b x - 8a b x + 4a +--R Type: Union(Expression(Integer),...) +--E 1367 + +--S 1368 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1369 + +)clear all + +--S 1370 of 1393 +t0:=1/(x^2*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1370 + +--S 1371 of 1393 +r0:=(-15/8)/(a^3*x)+1/4/(a*x*(a-b*x^2)^2)+5/8/(a^2*x*(a-b*x^2))+_ + 15/8*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|b 2 4 2 2 +-+ +--R (15b x - 30a b x + 15a x)\|b atanh(-----) + (- 15b x + 25a b x - 8a )\|a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 2 5 4 3 5 +-+ +--R (8a b x - 16a b x + 8a x)\|a +--R Type: Expression(Integer) +--E 1371 + +--S 1372 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +--R 2 5 3 2 |b \|a 2 4 +--R (15b x - 30a b x + 15a x) |- log(-------------------) - 30b x +--R \|a 2 +--R b x - a +--R + +--R 2 2 +--R 50a b x - 16a +--R / +--R 3 2 5 4 3 5 +--R 16a b x - 32a b x + 16a x +--R , +--R +---+ +--R | b +--R +---+ a |- - +--R 2 5 3 2 | b \| a 2 4 2 2 +--R (- 15b x + 30a b x - 15a x) |- - atan(-------) - 15b x + 25a b x - 8a +--R \| a b x +--R --------------------------------------------------------------------------] +--R 3 2 5 4 3 5 +--R 8a b x - 16a b x + 8a x +--R Type: Union(List(Expression(Integer)),...) +--E 1372 + +--S 1373 of 1393 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 15\|a |- log(-------------------) - 30\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) ------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1373 + +--S 1374 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1374 + +--S 1375 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 15\|b atanh(-----) - 15 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) ------------------------------------------------ +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1376 + +)clear all + +--S 1377 of 1393 +t0:=1/(x^3*(a-b*x^2)^3) +--R +--R +--R 1 +--R (1) - ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R b x - 3a b x + 3a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 1377 + +--S 1378 of 1393 +r0:=(-3/2)/(a^3*x^2)+1/4/(a*x^2*(a-b*x^2)^2)+_ + 3/4/(a^2*x^2*(a-b*x^2))+3*b*log(x)/a^4-3/2*b*log(a-b*x^2)/a^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 +--R (12b x - 24a b x + 12a b x )log(x) +--R + +--R 3 6 2 4 2 2 2 2 4 2 2 3 +--R (- 6b x + 12a b x - 6a b x )log(- b x + a) - 6a b x + 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x - 8a b x + 4a x +--R Type: Expression(Integer) +--E 1378 + +--S 1379 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (- 6b x + 12a b x - 6a b x )log(b x - a) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (12b x - 24a b x + 12a b x )log(x) - 6a b x + 9a b x - 2a +--R / +--R 4 2 6 5 4 6 2 +--R 4a b x - 8a b x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1379 + +--S 1380 of 1393 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 3b log(b x - a) + 3b log(- b x + a) +--R (4) --------------------------------------- +--R 4 +--R 2a +--R Type: Expression(Integer) +--E 1380 + +--S 1381 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1381 + +)clear all + +--S 1382 of 1393 +t0:=x^3/(a-b*x^2)^5 +--R +--R +--R 3 +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1382 + +--S 1383 of 1393 +r0:=1/8*a/(b^2*(a-b*x^2)^4)+(-1/6)/(b^2*(a-b*x^2)^3) +--R +--R +--R 1 2 1 +--R - b x - -- a +--R 6 24 +--R (2) ----------------------------------------- +--R 6 8 5 6 2 4 4 3 3 2 4 2 +--R b x - 4a b x + 6a b x - 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1383 + +--S 1384 of 1393 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 4b x - a +--R (3) ------------------------------------------------- +--R 6 8 5 6 2 4 4 3 3 2 4 2 +--R 24b x - 96a b x + 144a b x - 96a b x + 24a b +--R Type: Union(Expression(Integer),...) +--E 1384 + +--S 1385 of 1393 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1385 + +--S 1386 of 1393 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1386 + +)clear all + +--S 1387 of 1393 +t0:=x^2/(a-b*x^2)^5 +--R +--R +--R 2 +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1387 + +--S 1388 of 1393 +r0:=1/8*x/(b*(a-b*x^2)^4)-1/48*x/(a*b*(a-b*x^2)^3)-_ + 5/192*x/(a^2*b*(a-b*x^2)^2)-5/128*x/(a^3*b*(a-b*x^2))-_ + 5/128*atanh(x*sqrt(b)/sqrt(a))/(a^(7/2)*b^(3/2)) +--R +--R +--R (2) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (15b x - 55a b x + 73a b x + 15a x)\|a \|b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|a \|b +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1393 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (15b x - 60a b x + 90a b x - 60a b x + 15a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b - 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (30b x - 110a b x + 146a b x + 30a x)\|a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a b)\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (- 15b x + 60a b x - 90a b x + 60a b x - 15a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (15b x - 55a b x + 73a b x + 15a x)\|- a b +--R / +--R 3 5 8 4 4 6 5 3 4 6 2 2 7 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a b)\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1389 + +--S 1390 of 1393 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b - 2a b x +---+ x\|b +--R 5\|a \|b log(-------------------------) + 10\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +-+ +---+ +--R 256a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1390 + +--S 1391 of 1393 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1391 + +--S 1392 of 1393 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R 5\|- a b atanh(-----) - 5\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------ +--R 3 +-----+ +-+ +-+ +--R 128a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1392 + +--S 1393 of 1393 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1393 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4b.input.pamphlet b/src/input/rich4b.input.pamphlet new file mode 100644 index 0000000..bb0584e --- /dev/null +++ b/src/input/rich4b.input.pamphlet @@ -0,0 +1,25024 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4b.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 287 matching answers. +\item 6 cases where Axiom answer differs from Rubi +\item 47 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 9 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4b.output +)spool rich4b.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1369 +t0:=x/(a-b*x^2)^5 +--R +--R +--R x +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 1369 +r0:=1/8/(b*(a-b*x^2)^4) +--R +--R +--R 1 +--R - +--R 8 +--R (2) ---------------------------------------- +--R 5 8 4 6 2 3 4 3 2 2 4 +--R b x - 4a b x + 6a b x - 4a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 2 + +--S 3 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) --------------------------------------------- +--R 5 8 4 6 2 3 4 3 2 2 4 +--R 8b x - 32a b x + 48a b x - 32a b x + 8a b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1369 +t0:=1/(a-b*x^2)^5 +--R +--R +--R 1 +--R (1) - ---------------------------------------------------- +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 1369 +r0:=1/8*x/(a*(a-b*x^2)^4)+7/48*x/(a^2*(a-b*x^2)^3)+_ + 35/192*x/(a^3*(a-b*x^2)^2)+35/128*x/(a^4*(a-b*x^2))+_ + 35/128*atanh(x*sqrt(b)/sqrt(a))/(a^(9/2)*sqrt(b)) +--R +--R +--R (2) +--R +-+ +--R 4 8 3 6 2 2 4 3 2 4 x\|b +--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atanh(-----) +--R +-+ +--R \|a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (- 105b x + 385a b x - 511a b x + 279a x)\|a \|b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +-+ +-+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|a \|b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 8 3 6 2 2 4 3 2 4 +--R (105b x - 420a b x + 630a b x - 420a b x + 105a ) +--R * +--R 2 +---+ +--R (b x + a)\|a b + 2a b x +--R log(-------------------------) +--R 2 +--R b x - a +--R + +--R 3 7 2 5 2 3 3 +---+ +--R (- 210b x + 770a b x - 1022a b x + 558a x)\|a b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +---+ +--R (768a b x - 3072a b x + 4608a b x - 3072a b x + 768a )\|a b +--R , +--R +--R +-----+ +--R 4 8 3 6 2 2 4 3 2 4 x\|- a b +--R (105b x - 420a b x + 630a b x - 420a b x + 105a )atan(---------) +--R a +--R + +--R 3 7 2 5 2 3 3 +-----+ +--R (- 105b x + 385a b x - 511a b x + 279a x)\|- a b +--R / +--R 4 4 8 5 3 6 6 2 4 7 2 8 +-----+ +--R (384a b x - 1536a b x + 2304a b x - 1536a b x + 384a )\|- a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 8 + +--S 9 of 1369 +m0a:=a0.1-r0 +--R +--R +--R 2 +---+ +-+ +--R +-+ +-+ (b x + a)\|a b + 2a b x +---+ x\|b +--R 35\|a \|b log(-------------------------) - 70\|a b atanh(-----) +--R 2 +-+ +--R b x - a \|a +--R (4) --------------------------------------------------------------- +--R 4 +-+ +-+ +---+ +--R 256a \|a \|b \|a b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-----+ +--R +-----+ x\|b +-+ +-+ x\|- a b +--R - 35\|- a b atanh(-----) + 35\|a \|b atan(---------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------- +--R 4 +-----+ +-+ +-+ +--R 128a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1369 +t0:=1/(x*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ----------------------------------------------------- +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 13 + +--S 14 of 1369 +r0:=1/8/(a*(a-b*x^2)^4)+1/6/(a^2*(a-b*x^2)^3)+1/4/(a^3*(a-b*x^2)^2)+_ + 1/2/(a^4*(a-b*x^2))+log(x)/a^5-1/2*log(a-b*x^2)/a^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 3 2 4 +--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x) +--R + +--R 4 8 3 6 2 2 4 3 2 4 2 +--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(- b x + a) +--R + +--R 3 6 2 2 4 3 2 4 +--R - 12a b x + 42a b x - 52a b x + 25a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 3 2 4 2 +--R (- 12b x + 48a b x - 72a b x + 48a b x - 12a )log(b x - a) +--R + +--R 4 8 3 6 2 2 4 3 2 4 3 6 +--R (24b x - 96a b x + 144a b x - 96a b x + 24a )log(x) - 12a b x +--R + +--R 2 2 4 3 2 4 +--R 42a b x - 52a b x + 25a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a +--R Type: Union(Expression(Integer),...) +--E 15 + +--S 16 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 5 +--R 2a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 17 + +)clear all + +--S 18 of 1369 +t0:=1/(x^2*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 12 4 10 2 3 8 3 2 6 4 4 5 2 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 18 + +--S 19 of 1369 +r0:=(-315/128)/(a^5*x)+1/8/(a*x*(a-b*x^2)^4)+3/16/(a^2*x*(a-b*x^2)^3)+_ + 21/64/(a^3*x*(a-b*x^2)^2)+105/128/(a^4*x*(a-b*x^2))+_ + 315/128*atanh(x*sqrt(b)/sqrt(a))*sqrt(b)/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ x\|b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x)\|b atanh(-----) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x + 1155a b x - 1533a b x + 837a b x - 128a )\|a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +-+ +--R (128a b x - 512a b x + 768a b x - 512a b x + 128a x)\|a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +--R 4 9 3 7 2 2 5 3 3 4 |b +--R (315b x - 1260a b x + 1890a b x - 1260a b x + 315a x) |- +--R \|a +--R * +--R +-+ +--R |b 2 +--R 2a x |- + b x + a +--R \|a +--R log(-------------------) +--R 2 +--R b x - a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 630b x + 2310a b x - 3066a b x + 1674a b x - 256a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 256a b x - 1024a b x + 1536a b x - 1024a b x + 256a x +--R , +--R +--R +---+ +--R 4 9 3 7 2 2 5 3 3 4 | b +--R (- 315b x + 1260a b x - 1890a b x + 1260a b x - 315a x) |- - +--R \| a +--R * +--R +---+ +--R | b +--R a |- - +--R \| a +--R atan(-------) +--R b x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +--R - 315b x + 1155a b x - 1533a b x + 837a b x - 128a +--R / +--R 5 4 9 6 3 7 7 2 5 8 3 9 +--R 128a b x - 512a b x + 768a b x - 512a b x + 128a x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 20 + +--S 21 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +--R |b 2 +--R +-+ 2a x |- + b x + a +-+ +--R +-+ |b \|a +-+ x\|b +--R 315\|a |- log(-------------------) - 630\|b atanh(-----) +--R \|a 2 +-+ +--R b x - a \|a +--R (4) --------------------------------------------------------- +--R 5 +-+ +--R 256a \|a +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +--R | b +--R +-+ +---+ a |- - +--R +-+ x\|b | b +-+ \| a +--R - 315\|b atanh(-----) - 315 |- - \|a atan(-------) +--R +-+ \| a b x +--R \|a +--R (6) -------------------------------------------------- +--R 5 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 24 + +)clear all + +--S 25 of 1369 +t0:=1/(x^3*(a-b*x^2)^5) +--R +--R +--R 1 +--R (1) - ------------------------------------------------------- +--R 5 13 4 11 2 3 9 3 2 7 4 5 5 3 +--R b x - 5a b x + 10a b x - 10a b x + 5a b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 25 + +--S 26 of 1369 +r0:=(-5/2)/(a^5*x^2)+1/8/(a*x^2*(a-b*x^2)^4)+5/24/(a^2*x^2*(a-b*x^2)^3)+_ + 5/12/(a^3*x^2*(a-b*x^2)^2)+5/4/(a^4*x^2*(a-b*x^2))+_ + 5*b*log(x)/a^6-5/2*b*log(a-b*x^2)/a^6 +--R +--R +--R (2) +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x) +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 2 +--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(- b x + a) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a +--R / +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 2 +--R (- 60b x + 240a b x - 360a b x + 240a b x - 60a b x )log(b x - a) +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R (120b x - 480a b x + 720a b x - 480a b x + 120a b x )log(x) +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 60a b x + 210a b x - 260a b x + 125a b x - 12a +--R / +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R 24a b x - 96a b x + 144a b x - 96a b x + 24a x +--R Type: Union(Expression(Integer),...) +--E 27 + +--S 28 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 5b log(b x - a) + 5b log(- b x + a) +--R (4) --------------------------------------- +--R 6 +--R 2a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 29 + +)clear all + +--S 30 of 1369 +t0:=1/(x*(1+b*x^2)) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 30 + +--S 31 of 1369 +r0:=-atanh(1+2*b*x^2) +--R +--R +--R 2 +--R (2) - atanh(2b x + 1) +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(b x + 1) + 2log(x) +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 32 + +--S 33 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 34 + +)clear all + +--S 35 of 1369 +t0:=1/(x*(-1+b*x^2)) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 35 + +--S 36 of 1369 +r0:=atanh(1-2*b*x^2) +--R +--R +--R 2 +--R (2) - atanh(2b x - 1) +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(b x - 1) - 2log(x) +--R (3) ----------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 37 + +--S 38 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R log(b x - 1) - 2log(x) + 2atanh(2b x - 1) +--R (4) ------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 38 + +--S 39 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 39 + +)clear all + +--S 40 of 1369 +t0:=1/(x^3*(1+b*x^2)) +--R +--R +--R 1 +--R (1) --------- +--R 5 3 +--R b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 40 + +--S 41 of 1369 +r0:=(-1/2)/x^2+b*atanh(1+2*b*x^2) +--R +--R +--R 2 2 +--R 2b x atanh(2b x + 1) - 1 +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x + 1) - 2b x log(x) - 1 +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 42 + +--S 43 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R b log(b x + 1) - 2b log(x) - 2b atanh(2b x + 1) +--R (4) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 44 + +)clear all + +--S 45 of 1369 +t0:=1/(x^3*(-1+b*x^2)) +--R +--R +--R 1 +--R (1) --------- +--R 5 3 +--R b x - x +--R Type: Fraction(Polynomial(Integer)) +--E 45 + +--S 46 of 1369 +r0:=1/2/x^2+b*atanh(1-2*b*x^2) +--R +--R +--R 2 2 +--R - 2b x atanh(2b x - 1) + 1 +--R (2) --------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R b x log(b x - 1) - 2b x log(x) + 1 +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 47 + +--S 48 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R b log(b x - 1) - 2b log(x) + 2b atanh(2b x - 1) +--R (4) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 49 + +)clear all + +--S 50 of 1369 +t0:=1/(-1+a+a*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +--R a x + a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 50 + +--S 51 of 1369 +r0:=-atanh(x*sqrt(a)/sqrt(1-a))/sqrt((1-a)*a) +--R +--R +--R +-+ +--R x\|a +--R atanh(----------) +--R +-------+ +--R \|- a + 1 +--R (2) - ----------------- +--R +--------+ +--R | 2 +--R \|- a + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 | 2 2 +------+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x | 2 +--R log(---------------------------------------) x\|a - a +--R 2 atan(----------) +--R a x + a - 1 a - 1 +--R (3) [--------------------------------------------,----------------] +--R +--------+ +------+ +--R | 2 | 2 +--R 2\|- a + a \|a - a +--R Type: Union(List(Expression(Integer)),...) +--E 52 + +--S 53 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R 2 | 2 2 +-+ +--R (a x - a + 1)\|- a + a + (2a - 2a)x x\|a +--R log(---------------------------------------) + 2atanh(----------) +--R 2 +-------+ +--R a x + a - 1 \|- a + 1 +--R (4) ----------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2\|- a + a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1369 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-+ 2 | 2 +--R (2x\|- a + a - a x + a - 1)\|- a + 1 \|a + (a x - a + 1)\|- a + a +--R + +--R 2 +--R (2a - 2a)x +--R / +--R +--------+ +--R 2 4 2 | 2 3 2 3 3 2 +--R (a x - a + 2a - 1)\|- a + a + (2a - 2a )x + (2a - 4a + 2a)x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------+ +--R +------+ +-+ +--------+ | 2 +--R | 2 x\|a | 2 x\|a - a +--R \|a - a atanh(----------) + \|- a + a atan(----------) +--R +-------+ a - 1 +--R \|- a + 1 +--R (6) -------------------------------------------------------- +--R +--------+ +------+ +--R | 2 | 2 +--R \|- a + a \|a - a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1369 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +--------+ +--R | 2 +-------+ +-+ 2 +--R \|- a + a \|- a + 1 \|a + a - a +--R (7) ---------------------------------- +--R 3 2 2 3 2 +--R (a - a )x + a - 2a + a +--R Type: Expression(Integer) +--E 56 + +)clear all + +--S 57 of 1369 +t0:=1/(-c-d+(c-d)*x^2) +--R +--R +--R 1 +--R (1) - ----------------- +--R 2 +--R (d - c)x + d + c +--R Type: Fraction(Polynomial(Integer)) +--E 57 + +--S 58 of 1369 +r0:=-atanh(x*sqrt(c-d)/sqrt(c+d))/(sqrt(c-d)*sqrt(c+d)) +--R +--R +--R +-------+ +--R x\|- d + c +--R atanh(-----------) +--R +-----+ +--R \|d + c +--R (2) - ------------------ +--R +-------+ +-----+ +--R \|- d + c \|d + c +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 2 2 2 +-------+ +--R ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x | 2 2 +--R log(------------------------------------------------) x\|d - c +--R 2 atan(-----------) +--R (d - c)x + d + c d + c +--R [-----------------------------------------------------,- -----------------] +--R +---------+ +-------+ +--R | 2 2 | 2 2 +--R 2\|- d + c \|d - c +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 2 2 2 +--R +-------+ +-----+ ((d - c)x - d - c)\|- d + c + (- 2d + 2c )x +--R \|- d + c \|d + c log(------------------------------------------------) +--R 2 +--R (d - c)x + d + c +--R + +--R +---------+ +-------+ +--R | 2 2 x\|- d + c +--R 2\|- d + c atanh(-----------) +--R +-----+ +--R \|d + c +--R / +--R +---------+ +--R | 2 2 +-------+ +-----+ +--R 2\|- d + c \|- d + c \|d + c +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +--R +-------+ +-------+ | 2 2 +--R | 2 2 x\|- d + c +-------+ +-----+ x\|d - c +--R \|d - c atanh(-----------) - \|- d + c \|d + c atan(-----------) +--R +-----+ d + c +--R \|d + c +--R (6) ------------------------------------------------------------------ +--R +-------+ +--R +-------+ +-----+ | 2 2 +--R \|- d + c \|d + c \|d - c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1369 +t0:=1/(x*(1+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 5 3 +--R b x + 2b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 64 + +--S 65 of 1369 +r0:=1/2/(1+b*x^2)-atanh(1+2*b*x^2) +--R +--R +--R 2 2 +--R (- 2b x - 2)atanh(2b x + 1) + 1 +--R (2) --------------------------------- +--R 2 +--R 2b x + 2 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x - 1)log(b x + 1) + (2b x + 2)log(x) + 1 +--R (3) ------------------------------------------------- +--R 2 +--R 2b x + 2 +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x + 1) + 2log(x) + 2atanh(2b x + 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1369 +t0:=1/(x*(-1+b*x^2)^2) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 5 3 +--R b x - 2b x + x +--R Type: Fraction(Polynomial(Integer)) +--E 69 + +--S 70 of 1369 +r0:=1/2/(1-b*x^2)-atanh(1-2*b*x^2) +--R +--R +--R 2 2 +--R (2b x - 2)atanh(2b x - 1) - 1 +--R (2) ------------------------------- +--R 2 +--R 2b x - 2 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- b x + 1)log(b x - 1) + (2b x - 2)log(x) - 1 +--R (3) ------------------------------------------------- +--R 2 +--R 2b x - 2 +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(b x - 1) + 2log(x) - 2atanh(2b x - 1) +--R (4) --------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1369 +t0:=x^m/(1+a*x^2/b)^2 +--R +--R +--R 2 m +--R b x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1369 +--r0:=1/2*b*x^(1+m)/(b+a*x^2)+1/2*(1-m)*x^(1+m)*_ +-- hypergeometric(1,1/2*(1+m),1/2*(3+m),-a*x^2/b)/(1+m) +--E 75 + +--S 76 of 1369 +--a0:=integrate(t0,x) +--E 76 + +--S 77 of 1369 +--m0:=a0-r0 +--E 77 + +--S 78 of 1369 +--d0:=D(m0,x) +--E 78 + +)clear all + +--S 79 of 1369 +t0:=x^m*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1369 +--r0:=x^(1+m)*sqrt(a+b*x^2)/(2+m)+a*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((2+3*m+m^2)*sqrt(a+b*x^2)) +--E 80 + +--S 81 of 1369 +--a0:=integrate(t0,x) +--E 81 + +--S 82 of 1369 +--m0:=a0-r0 +--E 82 + +--S 83 of 1369 +--d0:=D(m0,x) +--E 83 + +)clear all + +--S 84 of 1369 +t0:=x^7*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 7 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1369 +r0:=-1/3*a^3*(a+b*x^2)^(3/2)/b^4+3/5*a^2*(a+b*x^2)^(5/2)/b^4-_ + 3/7*a*(a+b*x^2)^(7/2)/b^4+1/9*(a+b*x^2)^(9/2)/b^4 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a +--R (2) -------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 16 2 3 14 3 2 12 4 10 5 8 +--R (- 315a b x - 4245a b x - 15666a b x - 21672a b x - 10080a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 18 4 16 2 3 14 3 2 12 4 10 +--R 35b x + 1440a b x + 9999a b x + 25242a b x + 26712a b x +--R + +--R 5 8 +--R 10080a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 86 + +--S 87 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (- 16a b x - 640a b x - 3840a b x - 7168a b x - 4096a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (144a b x + 1920a b x + 6912a b x + 9216a b x + 4096a )\|a +--R / +--R 8 8 7 6 2 6 4 3 5 2 4 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 88 + +)clear all + +--S 89 of 1369 +t0:=x^5*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 5 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1369 +r0:=1/3*a^2*(a+b*x^2)^(3/2)/b^3-2/5*a*(a+b*x^2)^(5/2)/b^3+_ + 1/7*(a+b*x^2)^(7/2)/b^3 +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (15b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) --------------------------------------------- +--R 3 +--R 105b +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 12 2 2 10 3 8 4 6 | 2 +--R (- 105a b x - 861a b x - 1820a b x - 1120a x )\|b x + a +--R + +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (15b x + 378a b x + 1631a b x + 2380a b x + 1120a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x +--R + +--R 2 2 4 3 2 4 +--R - 5880a b x - 11760a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 91 + +--S 92 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (8a b x + 192a b x + 640a b x + 512a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (- 56a b x - 448a b x - 896a b x - 512a )\|a +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +-+ | 2 6 6 +--R (105b x + 2520a b x + 8400a b x + 6720a b )\|a \|b x + a - 735a b x +--R + +--R 2 5 4 3 4 2 4 3 +--R - 5880a b x - 11760a b x - 6720a b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 93 + +)clear all + +--S 94 of 1369 +t0:=x^3*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 3 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1369 +r0:=-1/3*a*(a+b*x^2)^(3/2)/b^2+1/5*(a+b*x^2)^(5/2)/b^2 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (3b x + a b x - 2a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 2 6 3 4 | 2 +--R (- 15a b x - 65a b x - 60a x )\|b x + a +--R + +--R 3 10 2 8 2 6 3 4 +-+ +--R (3b x + 40a b x + 95a b x + 60a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 96 + +--S 97 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+ +--R (- 2a b x - 24a b x - 32a )\|b x + a + (10a b x + 40a b x + 32a )\|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ | 2 4 4 2 3 2 +--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x +--R + +--R 3 2 +--R - 240a b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 98 + +)clear all + +--S 99 of 1369 +t0:=x*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)/b +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (2) --------------------- +--R 3b +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a +--R (3) ------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 101 + +--S 102 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (a b x + 4a )\|b x + a + (- 3a b x - 4a )\|a +--R (4) ------------------------------------------------- +--R +--------+ +--R 2 2 +-+ | 2 2 2 2 +--R (3b x + 12a b)\|a \|b x + a - 9a b x - 12a b +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 103 + +)clear all + +--S 104 of 1369 +t0:=sqrt(a+b*x^2)/x +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R +-+ \|b x + a | 2 +--R (2) - \|a atanh(-----------) + \|b x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a - a\|a )log(------------------) + b x \|a +--R x +--R (3) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (a\|b x + a - a\|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|b x + a | 2 +-+ +--R (a\|b x + a - a\|a )atanh(-----------) + a\|b x + a - a\|a +--R +-+ +--R \|a +--R / +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1369 +t0:=sqrt(a+b*x^2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1369 +r0:=-1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-1/2*sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 \|b x + a +-+ | 2 +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 2 +-+ +--R 2x \|a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|b x + a - \|a +--R (2a b x \|b x + a + (- b x - 2a b x )\|a )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4a x \|a \|b x + a - 2a b x - 4a x +--R Type: Union(Expression(Integer),...) +--E 111 + +--S 112 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R b log(------------------) + b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 113 + +)clear all + +--S 114 of 1369 +t0:=sqrt(a+b*x^2)/x^5 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1369 +r0:=1/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/4*sqrt(a+b*x^2)/x^4-_ + 1/8*b*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 4 +-+ +--R 8a x \|a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+ +--R ((- 4a b x - 8a b x )\|b x + a + (b x + 8a b x + 8a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (a b x + 10a b x + 24a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 4a b x - 20a b x - 32a b x - 16a )\|a +--R / +--R +--------+ +--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 116 + +--S 117 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1369 +t0:=sqrt(a+b*x^2)/x^7 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1369 +r0:=-1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-1/6*sqrt(a+b*x^2)/x^6-_ + 1/24*b*sqrt(a+b*x^2)/(a*x^4)+1/16*b^2*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R - 3b x atanh(-----------) + (3b x - 2a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------ +--R 2 6 +-+ +--R 48a x \|a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (18a b x + 96a b x + 96a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (- 3b x - 54a b x - 144a b x - 96a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (- 3a b x - 52a b x - 100a b x + 144a b x + 448a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+ +--R (18a b x + 102a b x + 68a b x - 336a b x - 576a b x - 256a )\|a +--R / +--R +--------+ +--R 3 2 10 4 8 5 6 +-+ | 2 3 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 4 2 10 5 8 6 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 121 + +--S 122 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R b log(------------------) + b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------ +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1369 +t0:=x^4*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 4 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1369 +r0:=1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 1/16*a^2*x*sqrt(a+b*x^2)/b^2+1/24*a*x^3*sqrt(a+b*x^2)/b+_ + 1/6*x^5*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R 3a atanh(-----------) + (8b x + 2a b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------------------- +--R 2 +-+ +--R 48b \|b +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x +--R + +--R 5 2 6 +--R - 144a b x - 96a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x)\|b +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +-+ +-+ +--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b )\|a \|b \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (36a b x + 192a b x + 192a )\|a \|b x + a - 6a b x - 108a b x +--R + +--R 5 2 6 +--R - 288a b x - 192a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 146a b x - 417a b x - 298a b x + 80a b x + 96a x) +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 316a b x + 570a b x + 270a b x - 128a b x - 96a x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b )\|- b \|a \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 126 + +--S 127 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R - a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R - a \|- b atanh(-----------) + 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R -------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 16b \|- b \|b +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1369 +t0:=x^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1369 +r0:=-1/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 1/8*a*x*sqrt(a+b*x^2)/b+1/4*x^3*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R - a atanh(-----------) + (2b x + a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 8b\|b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8a )\|a \|b x + a - a b x - 8a b x - 8a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 17a b x - 24a b x - 8a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 28a b x + 28a b x + 8a x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32b x + 64a b)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b)\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16a )\|a \|b x + a + 2a b x + 16a b x + 16a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 17a b x - 24a b x - 8a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 28a b x + 28a b x + 8a x)\|- b \|a +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32b x + 64a b)\|- b \|a \|b x + a +--R + +--R 3 4 2 2 2 +---+ +--R (- 8b x - 64a b x - 64a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 133 + +--S 134 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 8b\|b +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R a \|- b atanh(-----------) - 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 8b\|- b \|b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 1369 +t0:=sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1369 +r0:=1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+1/2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R x\|b +-+ | 2 +--R a atanh(-----------) + x\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2a\|a \|b x + a - a b x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|b x + a + (- 2b x - 4a)\|b +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- b \|b x + a - \|- b \|a +--R (4a\|a \|b x + a - 2a b x - 4a )atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- b \|a \|b x + a + (- 2b x - 4a)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 140 + +--S 141 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - a\|- b atanh(-----------) + 2a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1369 +t0:=sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)-sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R +-+ x\|b | 2 +--R x\|b atanh(-----------) - \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------- +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|b \|b x + a - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R / +--R +--------+ +--R | 2 +-+ +--R x\|b x + a - x\|a +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|b x + a - \|a +--R (2x\|- b \|b x + a - 2x\|- b \|a )atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R / +--R +--------+ +--R | 2 +-+ +--R x\|b x + a - x\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 147 + +--S 148 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R (6) - \|b atanh(-----------) + 2\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 151 + +)clear all + +--S 152 of 1369 +t0:=sqrt(a+b*x^2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1369 +r0:=-1/3*(a+b*x^2)^(3/2)/(a*x^3) +--R +--R +--R +--------+ +--R 2 | 2 +--R (- b x - a)\|b x + a +--R (2) ----------------------- +--R 3 +--R 3a x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (3b x + 7a b x + 4a )\|a \|b x + a - b x - 6a b x - 9a b x - 4a +--R ----------------------------------------------------------------------- +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a +--R Type: Union(Expression(Integer),...) +--E 154 + +--S 155 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1369 +t0:=sqrt(a+b*x^2)/x^6 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1369 +r0:=-1/5*(a+b*x^2)^(3/2)/(a*x^5)+2/15*b*(a+b*x^2)^(3/2)/(a^2*x^3) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (2b x - a b x - 3a )\|b x + a +--R (2) --------------------------------- +--R 2 5 +--R 15a x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (- 10b x - 35a b x + 3a b x + 76a b x + 48a )\|a \|b x + a + 2b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 25a b x + 40a b x - 35a b x - 100a b x - 48a +--R / +--R +--------+ +--R 2 2 9 3 7 4 5 | 2 +--R (15a b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 2 9 3 7 4 5 +-+ +--R (- 75a b x - 300a b x - 240a x )\|a +--R Type: Union(Expression(Integer),...) +--E 159 + +--S 160 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 161 + +)clear all + +--S 162 of 1369 +t0:=sqrt(a+b*x^2)/x^8 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1369 +r0:=-1/7*(a+b*x^2)^(3/2)/(a*x^7)+4/35*b*(a+b*x^2)^(3/2)/(a^2*x^5)-_ + 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^3) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (- 8b x + 4a b x - 3a b x - 15a )\|b x + a +--R (2) ----------------------------------------------- +--R 3 7 +--R 105a x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 56b x + 420a b x + 693a b x + 337a b x + 920a b x + 1872a b x +--R + +--R 6 +--R 960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 8b x - 196a b x - 735a b x - 826a b x - 623a b x - 1736a b x +--R + +--R 6 2 7 +--R - 2352a b x - 960a +--R / +--R +--------+ +--R 3 3 13 4 2 11 5 9 6 7 | 2 +--R (105a b x + 2520a b x + 8400a b x + 6720a x )\|b x + a +--R + +--R 3 3 13 4 2 11 5 9 6 7 +-+ +--R (- 735a b x - 5880a b x - 11760a b x - 6720a x )\|a +--R Type: Union(Expression(Integer),...) +--E 164 + +--S 165 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 166 + +)clear all + +--S 167 of 1369 +t0:=sqrt(a+b*x^2)/x^10 +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1369 +r0:=-1/9*(a+b*x^2)^(3/2)/(a*x^9)+2/21*b*(a+b*x^2)^(3/2)/(a^2*x^7)-_ + 8/105*b^2*(a+b*x^2)^(3/2)/(a^3*x^5)+16/315*b^3*(a+b*x^2)^(3/2)/(a^4*x^3) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x - 8a b x + 6a b x - 5a b x - 35a )\|b x + a +--R (2) -------------------------------------------------------- +--R 4 9 +--R 315a x +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 144b x - 1848a b x - 6006a b x - 6435a b x - 1165a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 4952a b x + 16464a b x + 21440a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 648a b x + 4158a b x + 9009a b x + 7200a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 243a b x - 11064a b x - 26064a b x - 25920a b x - 8960a +--R / +--R 4 4 17 5 3 15 6 2 13 7 11 8 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 4 17 5 3 15 6 2 13 7 11 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 169 + +--S 170 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 171 + +)clear all + +--S 172 of 1369 +t0:=x^m*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 m | 2 +--R (1) (b x + a)x \|b x + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1369 +--r0:=x^(1+m)*(a+b*x^2)^(3/2)/(4+m)+3*a*x^(1+m)*sqrt(a+b*x^2)/(8+6*m+m^2)+_ +-- 3*a^2*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 173 + +--S 174 of 1369 +--a0:=integrate(t0,x) +--E 174 + +--S 175 of 1369 +--m0:=a0-r0 +--E 175 + +--S 176 of 1369 +--d0:=D(m0,x) +--E 176 + +)clear all + +--S 177 of 1369 +t0:=x^7*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 9 7 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1369 +r0:=-1/5*a^3*(a+b*x^2)^(5/2)/b^4+3/7*a^2*(a+b*x^2)^(7/2)/b^4-_ + 1/3*a*(a+b*x^2)^(9/2)/b^4+1/11*(a+b*x^2)^(11/2)/b^4 +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (105b x + 140a b x + 5a b x - 6a b x + 8a b x - 16a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 +--R 1155b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 20 2 5 18 3 4 16 4 3 14 +--R - 1155a b x - 24640a b x - 160215a b x - 469194a b x +--R + +--R 5 2 12 6 10 7 8 +--R - 694848a b x - 510048a b x - 147840a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 22 6 20 2 5 18 3 4 16 4 3 14 +--R 105b x + 6545a b x + 73645a b x + 334059a b x + 762102a b x +--R + +--R 5 2 12 6 10 7 8 +--R 931392a b x + 583968a b x + 147840a x +--R * +--R +-+ +--R \|a +--R / +--R 5 10 4 8 2 3 6 3 2 4 +--R 1155b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 4 2 5 +--R 2661120a b x + 1182720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 5 2 6 +--R - 3252480a b x - 1182720a +--R Type: Union(Expression(Integer),...) +--E 179 + +--S 180 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R - 16a b x - 960a b x - 8960a b x - 28672a b x - 36864a b x +--R + +--R 11 +--R - 16384a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R 176a b x + 3520a b x + 19712a b x + 45056a b x + 45056a b x +--R + +--R 11 +--R 16384a +--R * +--R +-+ +--R \|a +--R / +--R 9 10 8 8 2 7 6 3 6 4 +--R 1155b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 4 5 2 5 4 +--R 2661120a b x + 1182720a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 10 2 8 8 3 7 6 4 6 4 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 5 5 2 6 4 +--R - 3252480a b x - 1182720a b +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 181 + +)clear all + +--S 182 of 1369 +t0:=x^5*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 7 5 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1369 +r0:=1/5*a^2*(a+b*x^2)^(5/2)/b^3-2/7*a*(a+b*x^2)^(7/2)/b^3+_ + 1/9*(a+b*x^2)^(9/2)/b^3 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 50a b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) -------------------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 16 2 4 14 3 3 12 4 2 10 +--R - 315a b x - 4650a b x - 21147a b x - 42084a b x +--R + +--R 5 8 6 6 +--R - 38640a b x - 13440a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 18 5 16 2 4 14 3 3 12 4 2 10 +--R 35b x + 1485a b x + 11853a b x + 38199a b x + 59724a b x +--R + +--R 5 8 6 6 +--R 45360a b x + 13440a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 184 + +--S 185 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (8a b x + 320a b x + 1920a b x + 3584a b x + 2048a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (- 72a b x - 960a b x - 3456a b x - 4608a b x - 2048a )\|a +--R / +--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 8 2 6 6 3 5 4 4 4 2 5 3 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a b +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 186 + +)clear all + +--S 187 of 1369 +t0:=x^3*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 5 3 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1369 +r0:=-1/5*a*(a+b*x^2)^(5/2)/b^2+1/7*(a+b*x^2)^(7/2)/b^2 +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (5b x + 8a b x + a b x - 2a )\|b x + a +--R (2) ------------------------------------------- +--R 2 +--R 35b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2 +--R (- 35a b x - 336a b x - 1015a b x - 1260a b x - 560a x )\|b x + a +--R + +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+ +--R (5b x + 133a b x + 721a b x + 1575a b x + 1540a b x + 560a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (35b x + 840a b x + 2800a b x + 2240a )\|a \|b x + a - 245a b x +--R + +--R 2 2 4 3 2 4 +--R - 1960a b x - 3920a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 189 + +--S 190 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (- 2a b x - 48a b x - 160a b x - 128a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (14a b x + 112a b x + 224a b x + 128a )\|a +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +-+ | 2 5 6 +--R (35b x + 840a b x + 2800a b x + 2240a b )\|a \|b x + a - 245a b x +--R + +--R 2 4 4 3 3 2 4 2 +--R - 1960a b x - 3920a b x - 2240a b +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 191 + +)clear all + +--S 192 of 1369 +t0:=x*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 3 | 2 +--R (1) (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1369 +r0:=1/5*(a+b*x^2)^(5/2)/b +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (2) -------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 8 2 2 6 3 4 4 2 | 2 +--R (- 5a b x - 30a b x - 60a b x - 40a x )\|b x + a +--R + +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ +--R (b x + 15a b x + 55a b x + 80a b x + 40a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (5b x + 60a b x + 80a )\|a \|b x + a - 25a b x - 100a b x - 80a +--R Type: Union(Expression(Integer),...) +--E 194 + +--S 195 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 3 2 4 4 2 5 +-+ +--R (a b x + 12a b x + 16a )\|b x + a + (- 5a b x - 20a b x - 16a )\|a +--R ------------------------------------------------------------------------- +--R +--------+ +--R 3 4 2 2 2 +-+ | 2 3 4 2 2 2 3 +--R (5b x + 60a b x + 80a b)\|a \|b x + a - 25a b x - 100a b x - 80a b +--R Type: Expression(Integer) +--E 195 + +--S 196 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 196 + +)clear all + +--S 197 of 1369 +t0:=(a+b*x^2)^(3/2)/x +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)-a^(3/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R +-+ \|b x + a 2 | 2 +--R - 3a\|a atanh(-----------) + (b x + 4a)\|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (- 3a b x - 12a b x )\|b x + a + (b x + 9a b x + 12a b x )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 199 + +--S 200 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 2 3 | 2 2 2 3 +-+ \|b x + a +--R ((3a b x + 12a )\|b x + a + (- 9a b x - 12a )\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (4a b x + 16a )\|b x + a + (- 12a b x - 16a )\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 201 + +)clear all + +--S 202 of 1369 +t0:=(a+b*x^2)^(3/2)/x^3 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1369 +r0:=-1/2*(a+b*x^2)^(3/2)/x^2-3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))*_ + sqrt(a)+3/2*b*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 | 2 +--R - 3b x \|a atanh(-----------) + (2b x - a)\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|b x + a + (- 9a b x - 12a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 4a b x + 3a b x + 4a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2b x + 3a b x - 5a b x - 4a )\|a +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2b x + 8a x )\|a \|b x + a - 6a b x - 8a x +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R ((3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 2 | 2 2 2 2 +-+ +--R (2a b x + 8a b)\|b x + a + (- 6a b x - 8a b)\|a +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (2b x + 8a)\|a \|b x + a - 6a b x - 8a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 206 + +)clear all + +--S 207 of 1369 +t0:=(a+b*x^2)^(3/2)/x^5 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1369 +r0:=-1/4*(a+b*x^2)^(3/2)/x^4-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_ + 3/8*b*sqrt(a+b*x^2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R - 3b x atanh(-----------) + (- 5b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 4 +-+ +--R 8x \|a +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|b x + a +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3b x - 24a b x - 24a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (5a b x + 42a b x + 56a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 20a b x - 68a b x - 64a b x - 16a )\|a +--R / +--R +--------+ +--R 6 2 4 +-+ | 2 2 8 2 6 3 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 211 + +)clear all + +--S 212 of 1369 +t0:=(a+b*x^2)^(3/2)/x^7 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1369 +r0:=-1/6*(a+b*x^2)^(3/2)/x^6+1/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 1/8*b*sqrt(a+b*x^2)/x^4-1/16*b^2*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R 3b x atanh(-----------) + (- 3b x - 14a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 6 +-+ +--R 48a x \|a +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (- 18a b x - 96a b x - 96a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (3b x + 54a b x + 144a b x + 96a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +-+ +--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256a )\|a +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 +-+ | 2 2 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 3 2 10 4 8 5 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1369 +t0:=(a+b*x^2)^(3/2)/x^9 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1369 +r0:=-1/8*(a+b*x^2)^(3/2)/x^8-3/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/16*b*sqrt(a+b*x^2)/x^6-1/64*b^2*sqrt(a+b*x^2)/(a*x^4)+_ + 3/128*b^3*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 \|b x + a +--R - 3b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 +--R (3b x - 2a b x - 24a b x - 16a )\|a \|b x + a +--R / +--R 2 8 +-+ +--R 128a x \|a +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 2 6 12 3 5 10 4 4 8 | 2 +--R (24a b x + 240a b x + 576a b x + 384a b x )\|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+ +--R (- 3b x - 96a b x - 480a b x - 768a b x - 384a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 3a b x - 94a b x - 392a b x + 336a b x + 4480a b x +--R + +--R 6 2 4 7 2 8 +--R 8960a b x + 7168a b x + 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 24a b x + 248a b x + 448a b x - 1824a b x - 8192a b x +--R + +--R 6 2 4 7 2 8 +--R - 12288a b x - 8192a b x - 2048a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 3 14 4 2 12 5 10 6 8 +-+ | 2 +--R (1024a b x + 10240a b x + 24576a b x + 16384a x )\|a \|b x + a +--R + +--R 3 4 16 4 3 14 5 2 12 6 10 7 8 +--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a x +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 4 \|b x + a - \|a 4 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 221 + +)clear all + +--S 222 of 1369 +t0:=x^4*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 6 4 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1369 +r0:=1/8*x^5*(a+b*x^2)^(3/2)+3/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/128*a^3*x*sqrt(a+b*x^2)/b^2+1/64*a^2*x^3*sqrt(a+b*x^2)/b+_ + 1/16*a*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--------+ +--R 4 x\|b 3 7 2 5 2 3 3 +-+ | 2 +--R 3a atanh(-----------) + (16b x + 24a b x + 2a b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 4 4 8 +--R (24a b x + 240a b x + 576a b x + 384a )\|a \|b x + a - 3a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 96a b x - 480a b x - 768a b x - 384a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x +--R + +--R 5 2 5 6 3 7 +--R - 3104a b x + 512a b x + 384a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x +--R + +--R 5 2 5 6 3 7 +--R 2896a b x - 704a b x - 384a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +-+ +-+ | 2 +--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|a \|b \|b x + a +--R + +--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+ +--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|b +--R , +--R +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (48a b x + 480a b x + 1152a b x + 768a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 6a b x - 192a b x - 960a b x - 1536a b x - 768a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 16b x - 536a b x - 3330a b x - 7997a b x - 8416a b x +--R + +--R 5 2 5 6 3 7 +--R - 3104a b x + 512a b x + 384a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 128b x + 1600a b x + 6480a b x + 11800a b x + 10008a b x +--R + +--R 5 2 5 6 3 7 +--R 2896a b x - 704a b x - 384a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 +---+ +-+ | 2 +--R (1024b x + 10240a b x + 24576a b x + 16384a b )\|- b \|a \|b x + a +--R + +--R 6 8 5 6 2 4 4 3 3 2 4 2 +---+ +--R (- 128b x - 4096a b x - 20480a b x - 32768a b x - 16384a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 224 + +--S 225 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 4 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 128b \|b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 128b \|- b \|b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 228 + +)clear all + +--S 229 of 1369 +t0:=x^2*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 4 2 | 2 +--R (1) (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1369 +r0:=1/6*x^3*(a+b*x^2)^(3/2)-1/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 1/16*a^2*x*sqrt(a+b*x^2)/b+1/8*a*x^3*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R - 3a atanh(-----------) + (8b x + 14a b x + 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 48b\|b +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (18a b x + 96a b x + 96a )\|a \|b x + a - 3a b x - 54a b x +--R + +--R 5 2 6 +--R - 144a b x - 96a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a x) +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 3 4 2 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b)\|a \|b \|b x + a +--R + +--R 4 6 3 4 2 2 2 3 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (- 36a b x - 192a b x - 192a )\|a \|b x + a + 6a b x +--R + +--R 4 2 4 5 2 6 +--R 108a b x + 288a b x + 192a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (- 8b x - 158a b x - 639a b x - 982a b x - 592a b x - 96a x) +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 5 +--R (48b x + 388a b x + 1062a b x + 1266a b x + 640a b x + 96a x) +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 3 4 2 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a b)\|- b \|a \|b x + a +--R + +--R 4 6 3 4 2 2 2 3 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 231 + +--S 232 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 16b\|b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R a \|- b atanh(-----------) - 2a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 16b\|- b \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1369 +t0:=(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1369 +r0:=1/4*x*(a+b*x^2)^(3/2)+3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_ + 3/8*a*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R 3a atanh(-----------) + (2b x + 5a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +-+ +--R 8\|b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 21a b x - 56a b x - 40a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 44a b x + 76a b x + 40a x)\|a \|b +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32b x + 64a)\|a \|b \|b x + a + (- 8b x - 64a b x - 64a )\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 21a b x - 56a b x - 40a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 44a b x + 76a b x + 40a x)\|- b \|a +--R / +--R +--------+ +--R 2 +---+ +-+ | 2 2 4 2 2 +---+ +--R (32b x + 64a)\|- b \|a \|b x + a + (- 8b x - 64a b x - 64a )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 238 + +--S 239 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 8\|b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 8\|- b \|b +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1369 +t0:=(a+b*x^2)^(3/2)/x^2 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1369 +r0:=-(a+b*x^2)^(3/2)/x+3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_ + 3/2*b*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R +-+ x\|b 2 | 2 +--R 3a x\|b atanh(-----------) + (b x - 2a)\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12a x)\|b \|b x + a + (- 9a b x - 12a x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a +--R , +--R +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24a x)\|- b \|b x + a + (- 18a b x - 24a x)\|- b \|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3b x + 2a b x + 8a )\|a \|b x + a + b x + 3a b x - 6a b x - 8a +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2b x + 8a x)\|b x + a + (- 6b x - 8a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 245 + +--S 246 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 3a\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - 3a\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R - 3a\|b atanh(-----------) + 6a\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1369 +t0:=(a+b*x^2)^(3/2)/x^4 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1369 +r0:=-1/3*(a+b*x^2)^(3/2)/x^3+b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-_ + b*sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R 3 +-+ x\|b 2 | 2 +--R 3b x \|b atanh(-----------) + (- 4b x - a)\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------ +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3b x + 12a b x )\|b \|b x + a + (- 9b x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a +--R , +--R +--R +--------+ +--R 2 5 3 +---+ | 2 +--R (6b x + 24a b x )\|- b \|b x + a +--R + +--R 2 5 3 +---+ +-+ +--R (- 18b x - 24a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12b x + 19a b x + 4a )\|a \|b x + a - 4b x - 21a b x - 21a b x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3b x + 12a x )\|b x + a + (- 9b x - 12a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 252 + +--S 253 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R (6) - b\|b atanh(-----------) + 2b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 256 + +)clear all + +--S 257 of 1369 +t0:=(a+b*x^2)^(3/2)/x^6 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1369 +r0:=-1/5*(a+b*x^2)^(5/2)/(a*x^5) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (- b x - 2a b x - a )\|b x + a +--R (2) ---------------------------------- +--R 5 +--R 5a x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (5b x + 30a b x + 61a b x + 52a b x + 16a )\|a \|b x + a - b x +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16a +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80a x )\|b x + a +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80a x )\|a +--R Type: Union(Expression(Integer),...) +--E 259 + +--S 260 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 261 + +)clear all + +--S 262 of 1369 +t0:=(a+b*x^2)^(3/2)/x^8 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1369 +r0:=-1/7*(a+b*x^2)^(5/2)/(a*x^7)+2/35*b*(a+b*x^2)^(5/2)/(a^2*x^5) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (2b x - a b x - 8a b x - 5a )\|b x + a +--R (2) ------------------------------------------- +--R 2 7 +--R 35a x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R - 14b x - 105a b x - 112a b x + 467a b x + 1240a b x +--R + +--R 5 2 6 +--R 1072a b x + 320a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 2b x + 49a b x + 175a b x - 21a b x - 973a b x - 1736a b x +--R + +--R 6 2 7 +--R - 1232a b x - 320a +--R / +--R +--------+ +--R 2 3 13 3 2 11 4 9 5 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a x )\|b x + a +--R + +--R 2 3 13 3 2 11 4 9 5 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a x )\|a +--R Type: Union(Expression(Integer),...) +--E 264 + +--S 265 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 266 + +)clear all + +--S 267 of 1369 +t0:=(a+b*x^2)^(3/2)/x^10 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1369 +r0:=-1/9*(a+b*x^2)^(5/2)/(a*x^9)+4/63*b*(a+b*x^2)^(5/2)/(a^2*x^7)-_ + 8/315*b^2*(a+b*x^2)^(5/2)/(a^3*x^5) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (- 8b x + 4a b x - 3a b x - 50a b x - 35a )\|b x + a +--R (2) ---------------------------------------------------------- +--R 3 9 +--R 315a x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R 72b x + 924a b x + 3003a b x + 3690a b x + 7355a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 26504a b x + 44688a b x + 32960a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R - 8b x - 324a b x - 2079a b x - 4557a b x - 5805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 16731a b x - 45288a b x - 60048a b x - 37440a b x - 8960a +--R / +--R 3 4 17 4 3 15 5 2 13 6 11 7 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 4 17 4 3 15 5 2 13 6 11 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 269 + +--S 270 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 271 + +)clear all + +--S 272 of 1369 +t0:=(a+b*x^2)^(3/2)/x^12 +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1369 +r0:=-1/11*(a+b*x^2)^(5/2)/(a*x^11)+2/33*b*(a+b*x^2)^(5/2)/(a^2*x^9)-_ + 8/231*b^2*(a+b*x^2)^(5/2)/(a^3*x^7)+16/1155*b^3*(a+b*x^2)^(5/2)/(a^4*x^5) +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (16b x - 8a b x + 6a b x - 5a b x - 140a b x - 105a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 4 11 +--R 1155a x +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 +--R - 176b x - 3432a b x - 18018a b x - 36465a b x +--R + +--R 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 27280a b x + 27363a b x + 200956a b x + 531536a b x +--R + +--R 8 2 4 9 2 10 +--R 695040a b x + 439040a b x + 107520a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R 16b x + 968a b x + 9438a b x + 33033a b x + 49995a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4 +--R 22847a b x - 90629a b x - 403084a b x - 830896a b x - 901120a b x +--R + +--R 10 2 11 +--R - 492800a b x - 107520a +--R / +--R 4 5 21 5 4 19 6 3 17 7 2 15 +--R 1155a b x + 69300a b x + 646800a b x + 2069760a b x +--R + +--R 8 13 9 11 +--R 2661120a b x + 1182720a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 21 5 4 19 6 3 17 7 2 15 +--R - 12705a b x - 254100a b x - 1422960a b x - 3252480a b x +--R + +--R 8 13 9 11 +--R - 3252480a b x - 1182720a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 274 + +--S 275 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 276 + +)clear all + +--S 277 of 1369 +t0:=x^m*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 m | 2 +--R (1) (b x + 2a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1369 +--r0:=5*a*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m))+x^(1+m)*(a+b*x^2)^(5/2)/_ +-- (6+m)+15*a^2*x^(1+m)*sqrt(a+b*x^2)/((6+m)*(8+6*m+m^2))+15*_ +-- a^3*x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((6+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 278 + +--S 279 of 1369 +--a0:=integrate(t0,x) +--E 279 + +--S 280 of 1369 +--m0:=a0-r0 +--E 280 + +--S 281 of 1369 +--d0:=D(m0,x) +--E 281 + +)clear all + +--S 282 of 1369 +t0:=x^7*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 11 9 2 7 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1369 +r0:=-1/7*a^3*(a+b*x^2)^(7/2)/b^4+1/3*a^2*(a+b*x^2)^(9/2)/b^4-_ + 3/11*a*(a+b*x^2)^(11/2)/b^4+1/13*(a+b*x^2)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (231b x + 567a b x + 371a b x + 5a b x - 6a b x + 8a b x - 16a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 +--R 3003b +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 2 7 22 3 6 20 4 5 18 +--R - 3003a b x - 91455a b x - 883883a b x - 4092517a b x +--R + +--R 5 4 16 6 3 14 7 2 12 +--R - 10586862a b x - 16226496a b x - 14702688a b x +--R + +--R 8 10 9 8 +--R - 7303296a b x - 1537536a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 26 8 24 2 7 22 3 6 20 +--R 231b x + 20202a b x + 326690a b x + 2214784a b x +--R + +--R 4 5 18 5 4 16 6 3 14 7 2 12 +--R 8033311a b x + 17258670a b x + 22761024a b x + 18162144a b x +--R + +--R 8 10 9 8 +--R 8072064a b x + 1537536a x +--R * +--R +-+ +--R \|a +--R / +--R 6 12 5 10 2 4 8 3 3 6 +--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 4 2 4 5 2 6 +--R 34594560a b x + 33825792a b x + 12300288a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 5 2 4 6 2 7 +--R - 49969920a b x - 39975936a b x - 12300288a +--R Type: Union(Expression(Integer),...) +--E 284 + +--S 285 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R - 16a b x - 1344a b x - 17920a b x - 86016a b x +--R + +--R 11 2 4 12 2 13 +--R - 184320a b x - 180224a b x - 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 208a b x + 5824a b x + 46592a b x + 159744a b x +--R + +--R 11 2 4 12 2 13 +--R 266240a b x + 212992a b x + 65536a +--R * +--R +-+ +--R \|a +--R / +--R 10 12 9 10 2 8 8 3 7 6 +--R 3003b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 4 6 4 5 5 2 6 4 +--R 34594560a b x + 33825792a b x + 12300288a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 10 12 2 9 10 3 8 8 4 7 6 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 5 6 4 6 5 2 7 4 +--R - 49969920a b x - 39975936a b x - 12300288a b +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 286 + +)clear all + +--S 287 of 1369 +t0:=x^5*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1369 +r0:=1/7*a^2*(a+b*x^2)^(7/2)/b^3-2/9*a*(a+b*x^2)^(9/2)/b^3+_ + 1/11*(a+b*x^2)^(11/2)/b^3 +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (63b x + 161a b x + 113a b x + 3a b x - 4a b x + 8a )\|b x + a +--R (2) ---------------------------------------------------------------------- +--R 3 +--R 693b +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 20 2 6 18 3 5 16 4 4 14 +--R - 693a b x - 15631a b x - 114279a b x - 400653a b x +--R + +--R 5 3 12 6 2 10 7 8 8 6 +--R - 770616a b x - 838992a b x - 487872a b x - 118272a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 22 7 20 2 6 18 3 5 16 4 4 14 +--R 63b x + 4004a b x + 48994a b x + 254892a b x + 706959a b x +--R + +--R 5 3 12 6 2 10 7 8 8 6 +--R 1136520a b x + 1068144a b x + 547008a b x + 118272a x +--R * +--R +-+ +--R \|a +--R / +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x +--R + +--R 5 +--R 709632a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 5 2 6 +--R - 1951488a b x - 709632a +--R Type: Union(Expression(Integer),...) +--E 289 + +--S 290 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R 8a b x + 480a b x + 4480a b x + 14336a b x + 18432a b x +--R + +--R 11 +--R 8192a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 5 10 7 4 8 8 3 6 9 2 4 10 2 +--R - 88a b x - 1760a b x - 9856a b x - 22528a b x - 22528a b x +--R + +--R 11 +--R - 8192a +--R * +--R +-+ +--R \|a +--R / +--R 8 10 7 8 2 6 6 3 5 4 4 4 2 +--R 693b x + 41580a b x + 388080a b x + 1241856a b x + 1596672a b x +--R + +--R 5 3 +--R 709632a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 10 2 7 8 3 6 6 4 5 4 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 5 4 2 6 3 +--R - 1951488a b x - 709632a b +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 291 + +)clear all + +--S 292 of 1369 +t0:=x^3*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1369 +r0:=-1/7*a*(a+b*x^2)^(7/2)/b^2+1/9*(a+b*x^2)^(9/2)/b^2 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (7b x + 19a b x + 15a b x + a b x - 2a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 +--R 63b +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 16 2 5 14 3 4 12 4 3 10 5 2 8 +--R - 63a b x - 1011a b x - 5439a b x - 14049a b x - 19320a b x +--R + +--R 6 6 7 4 +--R - 13776a b x - 4032a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 18 6 16 2 5 14 3 4 12 4 3 10 +--R 7b x + 306a b x + 2754a b x + 10752a b x + 22239a b x +--R + +--R 5 2 8 6 6 7 4 +--R 25704a b x + 15792a b x + 4032a x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a +--R Type: Union(Expression(Integer),...) +--E 294 + +--S 295 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 4 8 6 3 6 7 2 4 8 2 9 | 2 +--R (- 2a b x - 80a b x - 480a b x - 896a b x - 512a )\|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (18a b x + 240a b x + 864a b x + 1152a b x + 512a )\|a +--R / +--R 6 8 5 6 2 4 4 3 3 2 4 2 +-+ +--R (63b x + 2520a b x + 15120a b x + 28224a b x + 16128a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 2 5 6 3 4 4 4 3 2 5 2 +--R - 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a b +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 296 + +)clear all + +--S 297 of 1369 +t0:=x*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 5 3 2 | 2 +--R (1) (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1369 +r0:=1/7*(a+b*x^2)^(7/2)/b +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (b x + 3a b x + 3a b x + a )\|b x + a +--R (2) ------------------------------------------ +--R 7b +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2 +--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4 +--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x +--R + +--R 6 2 +--R 224a x +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (7b x + 168a b x + 560a b x + 448a )\|a \|b x + a - 49a b x +--R + +--R 2 2 4 3 2 4 +--R - 392a b x - 784a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 299 + +--S 300 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (a b x + 24a b x + 80a b x + 64a )\|b x + a +--R + +--R 4 3 6 5 2 4 6 2 7 +-+ +--R (- 7a b x - 56a b x - 112a b x - 64a )\|a +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +-+ | 2 4 6 +--R (7b x + 168a b x + 560a b x + 448a b)\|a \|b x + a - 49a b x +--R + +--R 2 3 4 3 2 2 4 +--R - 392a b x - 784a b x - 448a b +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 301 + +)clear all + +--S 302 of 1369 +t0:=(a+b*x^2)^(5/2)/x +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1369 +r0:=1/3*a*(a+b*x^2)^(3/2)+1/5*(a+b*x^2)^(5/2)-_ + a^(5/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+a^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15a \|a atanh(-----------) + (3b x + 11a b x + 23a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 | 2 +--R (- 15a b x - 115a b x - 360a b x - 360a b x )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+ +--R (3b x + 50a b x + 250a b x + 540a b x + 360a b x )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 304 + +--S 305 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (15a b x + 180a b x + 240a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 75a b x - 300a b x - 240a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (23a b x + 276a b x + 368a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 115a b x - 460a b x - 368a )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 306 + +)clear all + +--S 307 of 1369 +t0:=(a+b*x^2)^(5/2)/x^3 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1369 +r0:=5/6*b*(a+b*x^2)^(3/2)-1/2*(a+b*x^2)^(5/2)/x^2-_ + 5/2*a^(3/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+5/2*a*b*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15a b x \|a atanh(-----------) + (2b x + 14a b x - 3a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 3 6 3 2 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|b x + a +--R + +--R 2 3 6 3 2 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (2b x + 40a b x + 165a b x + 105a b x - 84a b x - 48a )\|a +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6b x + 72a b x + 96a x )\|a \|b x + a - 30a b x - 120a b x - 96a x +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (15a b x + 180a b x + 240a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (15a b x + 180a b x + 240a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 3 4 3 2 2 4 | 2 +--R (14a b x + 168a b x + 224a b)\|b x + a +--R + +--R 2 3 4 3 2 2 4 +-+ +--R (- 70a b x - 280a b x - 224a b)\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (6b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 311 + +)clear all + +--S 312 of 1369 +t0:=(a+b*x^2)^(5/2)/x^5 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1369 +r0:=-5/8*b*(a+b*x^2)^(3/2)/x^2-1/4*(a+b*x^2)^(5/2)/x^4-_ + 15/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+15/8*b^2*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 +-+ \|b x + a 2 4 2 2 | 2 +--R - 15b x \|a atanh(-----------) + (8b x - 9a b x - 2a )\|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------------- +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 2 3 6 3 2 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|b x + a +--R + +--R 4 8 2 3 6 3 2 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (8b x + 55a b x - 55a b x - 278a b x - 200a b x - 32a )\|a +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8b x + 96a b x + 128a x )\|a \|b x + a - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128a x +--R Type: Union(Expression(Integer),...) +--E 314 + +--S 315 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (15a b x + 180a b x + 240a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 75a b x - 300a b x - 240a b )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (15a b x + 180a b x + 240a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 75a b x - 300a b x - 240a b )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 4 2 3 2 3 2 | 2 +--R (8a b x + 96a b x + 128a b )\|b x + a +--R + +--R 4 4 2 3 2 3 2 +-+ +--R (- 40a b x - 160a b x - 128a b )\|a +--R / +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (8b x + 96a b x + 128a )\|a \|b x + a - 40a b x - 160a b x - 128a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1369 +t0:=(a+b*x^2)^(5/2)/x^7 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1369 +r0:=-5/24*b*(a+b*x^2)^(3/2)/x^4-1/6*(a+b*x^2)^(5/2)/x^6-_ + 5/16*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-5/16*b^2*sqrt(a+b*x^2)/x^2 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--------+ +--R 3 6 \|b x + a 2 4 2 2 +-+ | 2 +--R - 15b x atanh(-----------) + (- 33b x - 26a b x - 8a )\|a \|b x + a +--R +-+ +--R \|a +--R ----------------------------------------------------------------------- +--R 6 +-+ +--R 48x \|a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 2 4 8 3 3 6 | 2 +--R (90a b x + 480a b x + 480a b x )\|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 +-+ +--R (- 15b x - 270a b x - 720a b x - 480a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (33a b x + 620a b x + 2060a b x + 2448a b x + 1216a b x + 256a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x +--R + +--R 6 +--R - 256a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 2 10 2 8 3 6 +-+ | 2 3 12 +--R (288a b x + 1536a b x + 1536a x )\|a \|b x + a - 48a b x +--R + +--R 2 2 10 3 8 4 6 +--R - 864a b x - 2304a b x - 1536a x +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 3 \|b x + a - \|a 3 \|b x + a +--R 5b log(------------------) + 5b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1369 +t0:=(a+b*x^2)^(5/2)/x^9 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1369 +r0:=-5/48*b*(a+b*x^2)^(3/2)/x^6-1/8*(a+b*x^2)^(5/2)/x^8+_ + 5/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 5/64*b^2*sqrt(a+b*x^2)/x^4-5/128*b^3*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 \|b x + a +--R 15b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 +--R (- 15b x - 118a b x - 136a b x - 48a )\|a \|b x + a +--R / +--R 8 +-+ +--R 384a x \|a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 2 6 12 3 5 10 4 4 8 | 2 +--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +-+ +--R (15b x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 6 2 4 7 2 8 +--R 57600a b x + 29696a b x + 6144a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 6 2 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144a +--R * +--R +-+ +--R \|a +--R / +--R +--------+ +--R 2 3 14 3 2 12 4 10 5 8 +-+ | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152a x )\|a \|b x + a +--R + +--R 2 4 16 3 3 14 4 2 12 5 10 6 8 +--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152a x +--R Type: Union(Expression(Integer),...) +--E 324 + +--S 325 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 4 \|b x + a - \|a 4 \|b x + a +--R - 5b log(------------------) - 5b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +)clear all + +--S 327 of 1369 +t0:=(a+b*x^2)^(5/2)/x^11 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1369 +r0:=-1/16*b*(a+b*x^2)^(3/2)/x^8-1/10*(a+b*x^2)^(5/2)/x^10-_ + 3/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/32*b^2*sqrt(a+b*x^2)/x^6-1/128*b^3*sqrt(a+b*x^2)/(a*x^4)+_ + 3/256*b^4*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 5 10 \|b x + a +--R - 15b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (15b x - 10a b x - 248a b x - 336a b x - 128a )\|a \|b x + a +--R / +--R 2 10 +-+ +--R 1280a x \|a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 150a b x + 2400a b x + 10080a b x + 15360a b x +--R + +--R 5 5 10 +--R 7680a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 15b x - 750a b x - 6000a b x - 16800a b x +--R + +--R 4 6 12 5 5 10 +--R - 19200a b x - 7680a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R - 15a b x - 740a b x - 5252a b x - 64a b x + 108128a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R 423680a b x + 750080a b x + 700416a b x + 335872a b x + 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 5 5 10 +--R 150a b x + 2450a b x + 8300a b x - 28400a b x - 258656a b x +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R - 729600a b x - 1062400a b x - 860160a b x - 368640a b x - 65536a +--R * +--R +-+ +--R \|a +--R / +--R 3 4 18 4 3 16 5 2 14 6 12 +--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 7 10 +--R 655360a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 5 20 4 4 18 5 3 16 6 2 14 +--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 7 12 8 10 +--R - 1638400a b x - 655360a x +--R Type: Union(Expression(Integer),...) +--E 329 + +--S 330 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 5 \|b x + a - \|a 5 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 256a \|a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 331 + +)clear all + +--S 332 of 1369 +t0:=x^4*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 8 6 2 4 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1369 +r0:=1/16*a*x^5*(a+b*x^2)^(3/2)+1/10*x^5*(a+b*x^2)^(5/2)+_ + 3/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/256*a^4*x*sqrt(a+b*x^2)/b^2+1/128*a^3*x^3*sqrt(a+b*x^2)/b+_ + 1/32*a^2*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 5 x\|b +--R 15a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (128b x + 336a b x + 248a b x + 10a b x - 15a x)\|b \|b x + a +--R / +--R 2 +-+ +--R 1280b \|b +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (150a b x + 2400a b x + 10080a b x + 15360a b x + 7680a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 15a b x - 750a b x - 6000a b x - 16800a b x - 19200a b x +--R + +--R 10 +--R - 7680a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 6736a b x - 68248a b x - 290170a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x +--R + +--R 8 3 9 +--R 14080a b x + 7680a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 25120a b x + 166096a b x + 538900a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x +--R + +--R 8 3 9 +--R - 17920a b x - 7680a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 8 5 6 2 4 4 3 3 2 +--R 12800b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 4 2 +--R 655360a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 7 10 6 8 2 5 6 3 4 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 3 2 5 2 +--R - 1638400a b x - 655360a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (300a b x + 4800a b x + 20160a b x + 30720a b x + 15360a ) +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 9 2 +--R - 30a b x - 1500a b x - 12000a b x - 33600a b x - 38400a b x +--R + +--R 10 +--R - 15360a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 6736a b x - 68248a b x - 290170a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 639845a b x - 776626a b x - 494672a b x - 122976a b x +--R + +--R 8 3 9 +--R 14080a b x + 7680a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 25120a b x + 166096a b x + 538900a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 974350a b x + 1008010a b x + 557440a b x + 116896a b x +--R + +--R 8 3 9 +--R - 17920a b x - 7680a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 6 8 5 6 2 4 4 3 3 2 +--R 12800b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 4 2 +--R 655360a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 7 10 6 8 2 5 6 3 4 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 3 2 5 2 +--R - 1638400a b x - 655360a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 334 + +--S 335 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 5 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 5 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 256b \|b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 5 +---+ x\|b 5 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 256b \|- b \|b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1369 +t0:=x^2*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 6 4 2 2 | 2 +--R (1) (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1369 +r0:=5/48*a*x^3*(a+b*x^2)^(3/2)+1/8*x^3*(a+b*x^2)^(5/2)-_ + 5/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 5/128*a^3*x*sqrt(a+b*x^2)/b+5/64*a^2*x^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 4 x\|b +--R - 15a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (48b x + 136a b x + 118a b x + 15a x)\|b \|b x + a +--R / +--R +-+ +--R 384b\|b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (120a b x + 1200a b x + 2880a b x + 1920a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 15a b x - 480a b x - 2400a b x - 3840a b x - 1920a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x +--R + +--R 5 2 5 6 3 7 +--R - 50016a b x - 18944a b x - 1920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x +--R + +--R 5 2 5 6 3 7 +--R 59248a b x + 19904a b x + 1920a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +-+ +-+ | 2 +--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|a \|b \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|b +--R , +--R +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (- 240a b x - 2400a b x - 5760a b x - 3840a )\|a \|b x + a +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 30a b x + 960a b x + 4800a b x + 7680a b x + 3840a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R - 48b x - 1672a b x - 12150a b x - 37839a b x - 60320a b x +--R + +--R 5 2 5 6 3 7 +--R - 50016a b x - 18944a b x - 1920a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 384b x + 5312a b x + 25968a b x + 62856a b x + 83080a b x +--R + +--R 5 2 5 6 3 7 +--R 59248a b x + 19904a b x + 1920a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 4 6 3 4 2 2 2 3 +---+ +-+ | 2 +--R (3072b x + 30720a b x + 73728a b x + 49152a b)\|- b \|a \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +---+ +--R (- 384b x - 12288a b x - 61440a b x - 98304a b x - 49152a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 341 + +--S 342 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 4 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 x\|b +--R 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 128b\|b +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 4 +---+ x\|b 4 +-+ \|- b \|b x + a - \|- b \|a +--R 5a \|- b atanh(-----------) - 10a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R -------------------------------------------------------------------------- +--R +---+ +-+ +--R 128b\|- b \|b +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1369 +t0:=(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (1) (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1369 +r0:=5/24*a*x*(a+b*x^2)^(3/2)+1/6*x*(a+b*x^2)^(5/2)+_ + 5/16*a^3*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+5/16*a^2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 x\|b 2 5 3 2 +-+ | 2 +--R 15a atanh(-----------) + (8b x + 26a b x + 33a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------------------------------------ +--R +-+ +--R 48\|b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (90a b x + 480a b x + 480a )\|a \|b x + a - 15a b x +--R + +--R 4 2 4 5 2 6 +--R - 270a b x - 720a b x - 480a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x +--R + +--R 5 +--R - 1056a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x +--R + +--R 5 +--R 1056a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R +--------+ +--R 2 4 2 2 +-+ +-+ | 2 +--R (288b x + 1536a b x + 1536a )\|a \|b \|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 48b x - 864a b x - 2304a b x - 1536a )\|b +--R , +--R +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 +--R (180a b x + 960a b x + 960a )\|a \|b x + a - 30a b x +--R + +--R 4 2 4 5 2 6 +--R - 540a b x - 1440a b x - 960a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R - 8b x - 170a b x - 885a b x - 2098a b x - 2416a b x +--R + +--R 5 +--R - 1056a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 48b x + 460a b x + 1698a b x + 3174a b x + 2944a b x +--R + +--R 5 +--R 1056a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R +--------+ +--R 2 4 2 2 +---+ +-+ | 2 +--R (288b x + 1536a b x + 1536a )\|- b \|a \|b x + a +--R + +--R 3 6 2 4 2 2 3 +---+ +--R (- 48b x - 864a b x - 2304a b x - 1536a )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 348 + +--S 349 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 3 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 x\|b +--R - 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 16\|b +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 3 +---+ x\|b 3 +-+ \|- b \|b x + a - \|- b \|a +--R - 5a \|- b atanh(-----------) + 10a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ---------------------------------------------------------------------------- +--R +---+ +-+ +--R 16\|- b \|b +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1369 +t0:=(a+b*x^2)^(5/2)/x^2 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1369 +r0:=5/4*b*x*(a+b*x^2)^(3/2)-(a+b*x^2)^(5/2)/x+_ + 15/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+15/8*a*b*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 2 +-+ x\|b 2 4 2 2 | 2 +--R 15a x\|b atanh(-----------) + (2b x + 9a b x - 8a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ---------------------------------------------------------------- +--R 8x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240a x)\|b \|b x + a +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240a x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8b x + 96a b x + 128a x)\|b x + a +--R + +--R 2 5 3 2 +-+ +--R (- 40b x - 160a b x - 128a x)\|a +--R , +--R +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480a x)\|- b \|b x + a +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480a x)\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10b x - 85a b x - 172a b x + 16a b x + 128a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 2b x + 35a b x + 165a b x + 180a b x - 80a b x - 128a +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8b x + 96a b x + 128a x)\|b x + a +--R + +--R 2 5 3 2 +-+ +--R (- 40b x - 160a b x - 128a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 355 + +--S 356 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 15a \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 +-+ x\|b +--R - 15a \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a +--R - 15a \|b atanh(-----------) + 30a \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ----------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 359 + +)clear all + +--S 360 of 1369 +t0:=(a+b*x^2)^(5/2)/x^4 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1369 +r0:=-5/3*b*(a+b*x^2)^(3/2)/x-1/3*(a+b*x^2)^(5/2)/x^3+_ + 5/2*a*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+5/2*b^2*x*sqrt(a+b*x^2) +--R +--R +--R +-+ +--------+ +--R 3 +-+ x\|b 2 4 2 2 | 2 +--R 15a b x \|b atanh(-----------) + (3b x - 14a b x - 2a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) -------------------------------------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|b \|b x + a +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6b x + 72a b x + 96a x )\|b x + a +--R + +--R 2 7 5 2 3 +-+ +--R (- 30b x - 120a b x - 96a x )\|a +--R , +--R +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- b \|b x + a +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15b x + 10a b x + 242a b x + 264a b x + 32a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 3b x + 25a b x - 100a b x - 370a b x - 280a b x - 32a +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6b x + 72a b x + 96a x )\|b x + a +--R + +--R 2 7 5 2 3 +-+ +--R (- 30b x - 120a b x - 96a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 362 + +--S 363 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 5a b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R +-+ x\|b +--R - 5a b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R +-+ x\|b +---+ \|b x + a - \|a +--R - 5a b\|b atanh(-----------) + 10a b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 366 + +)clear all + +--S 367 of 1369 +t0:=(a+b*x^2)^(5/2)/x^6 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1369 +r0:=-1/3*b*(a+b*x^2)^(3/2)/x^3-1/5*(a+b*x^2)^(5/2)/x^5+_ + b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^2*sqrt(a+b*x^2)/x +--R +--R +--R +-+ +--------+ +--R 2 5 +-+ x\|b 2 4 2 2 | 2 +--R 15b x \|b atanh(-----------) + (- 23b x - 11a b x - 3a )\|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) --------------------------------------------------------------------- +--R 5 +--R 15x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15b x + 180a b x + 240a b x )\|b \|b x + a +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 9 7 2 5 +-+ +--R (- 75b x - 300a b x - 240a x )\|a +--R , +--R +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30b x + 360a b x + 480a b x )\|- b \|b x + a +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150b x - 600a b x - 480a b x )\|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115b x + 515a b x + 603a b x + 236a b x + 48a )\|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R - 23b x - 310a b x - 790a b x - 715a b x - 260a b x - 48a +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15b x + 180a b x + 240a x )\|b x + a +--R + +--R 2 9 7 2 5 +-+ +--R (- 75b x - 300a b x - 240a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 369 + +--S 370 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 +-+ x\|b +--R - b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 +-+ x\|b 2 +---+ \|b x + a - \|a +--R (6) - b \|b atanh(-----------) + 2b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1369 +t0:=(a+b*x^2)^(5/2)/x^8 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1369 +r0:=-1/7*(a+b*x^2)^(7/2)/(a*x^7) +--R +--R +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (- b x - 3a b x - 3a b x - a )\|b x + a +--R (2) -------------------------------------------- +--R 7 +--R 7a x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 7b x + 77a b x + 301a b x + 575a b x + 584a b x + 304a b x +--R + +--R 6 +--R 64a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - b x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64a +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448a x )\|b x + a +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448a x )\|a +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1369 +t0:=(a+b*x^2)^(5/2)/x^10 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1369 +r0:=-1/9*(a+b*x^2)^(7/2)/(a*x^9)+2/63*b*(a+b*x^2)^(7/2)/(a^2*x^7) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (2b x - a b x - 15a b x - 19a b x - 7a )\|b x + a +--R (2) ------------------------------------------------------- +--R 2 9 +--R 63a x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 18b x - 231a b x - 609a b x + 1251a b x + 8887a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 17944a b x + 17808a b x + 8896a b x + 1792a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R 2b x + 81a b x + 504a b x + 462a b x - 4266a b x - 16119a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 25848a b x - 22032a b x - 9792a b x - 1792a +--R / +--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +--R (63a b x + 2520a b x + 15120a b x + 28224a b x + 16128a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 4 17 3 3 15 4 2 13 5 11 6 9 +-+ +--R (- 567a b x - 7560a b x - 27216a b x - 36288a b x - 16128a x )\|a +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1369 +t0:=(a+b*x^2)^(5/2)/x^12 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1369 +r0:=-1/11*(a+b*x^2)^(7/2)/(a*x^11)+4/99*b*(a+b*x^2)^(7/2)/(a^2*x^9)-_ + 8/693*b^2*(a+b*x^2)^(7/2)/(a^3*x^7) +--R +--R +--R (2) +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 8b x + 4a b x - 3a b x - 113a b x - 161a b x - 63a )\|b x + a +--R ------------------------------------------------------------------------ +--R 3 11 +--R 693a x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 88b x + 1716a b x + 9009a b x + 19503a b x + 41591a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 180705a b x + 534772a b x + 852272a b x + 746496a b x +--R + +--R 9 2 10 +--R 342272a b x + 64512a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R - 8b x - 484a b x - 4719a b x - 16632a b x - 32274a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 97240a b x - 376607a b x - 886468a b x - 1186768a b x +--R + +--R 9 2 4 10 2 11 +--R - 909568a b x - 374528a b x - 64512a +--R / +--R 3 5 21 4 4 19 5 3 17 6 2 15 +--R 693a b x + 41580a b x + 388080a b x + 1241856a b x +--R + +--R 7 13 8 11 +--R 1596672a b x + 709632a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 5 21 4 4 19 5 3 17 6 2 15 +--R - 7623a b x - 152460a b x - 853776a b x - 1951488a b x +--R + +--R 7 13 8 11 +--R - 1951488a b x - 709632a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1369 +t0:=(a+b*x^2)^(5/2)/x^14 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 14 +--R x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1369 +r0:=-1/13*(a+b*x^2)^(7/2)/(a*x^13)+6/143*b*(a+b*x^2)^(7/2)/(a^2*x^11)-_ + 8/429*b^2*(a+b*x^2)^(7/2)/(a^3*x^9)+16/3003*b^3*(a+b*x^2)^(7/2)/(a^4*x^7) +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (16b x - 8a b x + 6a b x - 5a b x - 371a b x - 567a b x - 231a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 13 +--R 3003a x +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 24 11 22 2 10 20 3 9 18 +--R - 208b x - 5720a b x - 43758a b x - 138567a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 +--R - 197197a b x + 17199a b x + 1280783a b x + 5475348a b x +--R + +--R 8 4 8 9 3 6 10 2 4 11 2 +--R 12549024a b x + 16700416a b x + 12911360a b x + 5397504a b x +--R + +--R 12 +--R 946176a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 13 26 12 24 2 11 22 3 10 20 4 9 18 +--R 16b x + 1352a b x + 18590a b x + 94809a b x + 224796a b x +--R + +--R 5 8 16 6 7 14 7 6 12 8 5 10 +--R 230230a b x - 362726a b x - 3117439a b x - 10284300a b x +--R + +--R 9 4 8 10 3 6 11 2 4 12 2 +--R - 19585696a b x - 22540544a b x - 15491840a b x - 5870592a b x +--R + +--R 13 +--R - 946176a +--R / +--R 4 6 25 5 5 23 6 4 21 7 3 19 +--R 3003a b x + 252252a b x + 3363360a b x + 16144128a b x +--R + +--R 8 2 17 9 15 10 13 +--R 34594560a b x + 33825792a b x + 12300288a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 6 25 5 5 23 6 4 21 7 3 19 +--R - 39039a b x - 1093092a b x - 8744736a b x - 29981952a b x +--R + +--R 8 2 17 9 15 10 13 +--R - 49969920a b x - 39975936a b x - 12300288a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1369 +t0:=(a+b*x^2)^(5/2)/x^16 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 16 +--R x +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1369 +r0:=-1/15*(a+b*x^2)^(7/2)/(a*x^15)+8/195*b*(a+b*x^2)^(7/2)/(a^2*x^13)-_ + 16/715*b^2*(a+b*x^2)^(7/2)/(a^3*x^11)+_ + 64/6435*b^3*(a+b*x^2)^(7/2)/(a^4*x^9)-_ + 128/45045*b^4*(a+b*x^2)^(7/2)/(a^5*x^7) +--R +--R +--R (2) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R - 128b x + 64a b x - 48a b x + 40a b x - 35a b x - 4473a b x +--R + +--R 6 2 7 +--R - 7161a b x - 3003a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 5 15 +--R 45045a x +--R Type: Expression(Integer) +--E 395 + +--S 396 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 28 13 26 2 12 24 3 11 22 +--R 1920b x + 70720a b x + 739024a b x + 3325608a b x +--R + +--R 4 10 20 5 9 18 6 8 16 7 7 14 +--R 7436429a b x + 8518055a b x + 7017255a b x + 31888581a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R 174491952a b x + 540852576a b x + 1004347520a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R 1146763520a b x + 790013952a b x + 301830144a b x + 49201152a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 15 30 14 28 2 13 26 3 12 24 +--R - 128b x - 14400a b x - 265200a b x - 1847560a b x +--R + +--R 4 11 22 5 10 20 6 9 18 7 8 16 +--R - 6235515a b x - 11159148a b x - 11079250a b x - 15095700a b x +--R + +--R 8 7 14 9 6 12 10 5 10 +--R - 85709115a b x - 367431760a b x - 938611872a b x +--R + +--R 11 4 8 12 3 6 13 2 4 +--R - 1495920000a b x - 1507116800a b x - 934778880a b x +--R + +--R 14 2 15 +--R - 326430720a b x - 49201152a +--R / +--R 5 7 29 6 6 27 7 5 25 8 4 23 +--R 45045a b x + 5045040a b x + 90810720a b x + 605404800a b x +--R + +--R 9 3 21 10 2 19 11 17 +--R 1902700800a b x + 3044321280a b x + 2398556160a b x +--R + +--R 12 15 +--R 738017280a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 7 29 6 6 27 7 5 25 +--R - 675675a b x - 25225200a b x - 272432160a b x +--R + +--R 8 4 23 9 3 21 10 2 19 +--R - 1297296000a b x - 3171168000a b x - 4151347200a b x +--R + +--R 11 17 12 15 +--R - 2767564800a b x - 738017280a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1369 +t0:=(a+b*x^2)^(5/2)/x^18 +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 18 +--R x +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1369 +r0:=-1/17*(a+b*x^2)^(7/2)/(a*x^17)+2/51*b*(a+b*x^2)^(7/2)/(a^2*x^15)-_ + 16/663*b^2*(a+b*x^2)^(7/2)/(a^3*x^13)+_ + 32/2431*b^3*(a+b*x^2)^(7/2)/(a^4*x^11)-_ + 128/21879*b^4*(a+b*x^2)^(7/2)/(a^5*x^9)+_ + 256/153153*b^5*(a+b*x^2)^(7/2)/(a^6*x^7) +--R +--R +--R (2) +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R 256b x - 128a b x + 96a b x - 80a b x + 70a b x - 63a b x +--R + +--R 6 2 4 7 2 8 +--R - 12705a b x - 21021a b x - 9009a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 6 17 +--R 153153a x +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 32 15 30 2 14 28 3 13 26 +--R - 4352b x - 206720a b x - 2821728a b x - 16997552a b x +--R + +--R 4 12 24 5 11 22 6 10 20 +--R - 53117350a b x - 91265265a b x - 84612927a b x +--R + +--R 7 9 18 8 8 16 9 7 14 +--R - 26796675a b x + 158507217a b x + 1163856848a b x +--R + +--R 10 6 12 11 5 10 12 4 8 +--R 4663848992a b x + 11445343104a b x + 17876348672a b x +--R + +--R 13 3 6 14 2 4 15 2 +--R 17866512384a b x + 11078774784a b x + 3886891008a b x +--R + +--R 16 +--R 590413824a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 17 34 16 32 2 15 30 3 14 28 +--R 256b x + 36992a b x + 878560a b x + 7994896a b x +--R + +--R 4 13 26 5 12 24 6 11 22 +--R 36119798a b x + 90299495a b x + 129279696a b x +--R + +--R 7 10 20 8 9 18 9 8 16 +--R 101136162a b x - 7854510a b x - 490730449a b x +--R + +--R 10 7 14 11 6 12 12 5 10 +--R - 2717211728a b x - 8930043424a b x - 18706939264a b x +--R + +--R 13 4 8 14 3 6 15 2 4 +--R - 25644625664a b x - 22956939264a b x - 12948418560a b x +--R + +--R 16 2 17 +--R - 4182097920a b x - 590413824a +--R / +--R 6 8 33 7 7 31 8 6 29 +--R 153153a b x + 22054032a b x + 514594080a b x +--R + +--R 9 5 27 10 4 25 11 3 23 +--R 4528427904a b x + 19407548160a b x + 44853000192a b x +--R + +--R 12 2 21 13 19 14 17 +--R 57085636608a b x + 37638881280a b x + 10037035008a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 33 7 7 31 8 6 29 +--R - 2603601a b x - 124972848a b x - 1749619872a b x +--R + +--R 9 5 27 10 4 25 11 3 23 +--R - 10997610624a b x - 36658702080a b x - 69318273024a b x +--R + +--R 12 2 21 13 19 14 17 +--R - 74650447872a b x - 42657398784a b x - 10037035008a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1369 +t0:=x^m*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 m | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )x \|b x + a +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1369 +--r0:=315*a^3*x^(1+m)*(a+b*x^2)^(3/2)/((4+m)*(6+m)*(8+m)*(10+m))+_ +-- 63*a^2*x^(1+m)*(a+b*x^2)^(5/2)/((6+m)*(8+m)*(10+m))+_ +-- 9*a*x^(1+m)*(a+b*x^2)^(7/2)/(80+18*m+m^2)+x^(1+m)*_ +-- (a+b*x^2)^(9/2)/(10+m)+945*a^4*x^(1+m)*sqrt(a+b*x^2)/_ +-- ((6+m)*(8+m)*(10+m)*(8+6*m+m^2))+945*a^5*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((6+m)*(8+m)*(10+m)*(8+14*m+7*m^2+m^3)*sqrt(a+b*x^2)) +--E 405 + +--S 406 of 1369 +--a0:=integrate(t0,x) +--E 406 + +--S 407 of 1369 +--m0:=a0-r0 +--E 407 + +--S 408 of 1369 +--d0:=D(m0,x) +--E 408 + +)clear all + +--S 409 of 1369 +t0:=x^15*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 23 3 21 2 2 19 3 17 4 15 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1369 +r0:=-1/11*a^7*(a+b*x^2)^(11/2)/b^8+7/13*a^6*(a+b*x^2)^(13/2)/b^8-_ + 7/5*a^5*(a+b*x^2)^(15/2)/b^8+35/17*a^4*(a+b*x^2)^(17/2)/b^8-_ + 35/19*a^3*(a+b*x^2)^(19/2)/b^8+a^2*(a+b*x^2)^(21/2)/b^8-_ + 7/23*a*(a+b*x^2)^(23/2)/b^8+1/25*(a+b*x^2)^(25/2)/b^8 +--R +--R +--R (2) +--R 12 24 11 22 2 10 20 3 9 18 +--R 1062347b x + 4665089a b x + 7759752a b x + 5810090a b x +--R + +--R 4 8 16 5 7 14 6 6 12 7 5 10 8 4 8 +--R 1659515a b x + 429a b x - 462a b x + 504a b x - 560a b x +--R + +--R 9 3 6 10 2 4 11 2 12 +--R 640a b x - 768a b x + 1024a b x - 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R 26558675b +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 48 2 15 46 3 14 44 +--R - 26558675a b x - 2878729425a b x - 97395972960a b x +--R + +--R 4 13 42 5 12 40 +--R - 1609225902570a b x - 15696010222035a b x +--R + +--R 6 11 38 7 10 36 +--R - 100124312670525a b x - 444286575778650a b x +--R + +--R 8 9 34 9 8 32 +--R - 1425766406694360a b x - 3390169039300720a b x +--R + +--R 10 7 30 11 6 28 +--R - 6054288088284160a b x - 8157338113996800a b x +--R + +--R 12 5 26 13 4 24 +--R - 8256379402444800a b x - 6184960931901440a b x +--R + +--R 14 3 22 15 2 20 +--R - 3328737290977280a b x - 1218036417495040a b x +--R + +--R 16 18 17 16 +--R - 271525694668800a b x - 27848789196800a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 17 50 16 48 2 15 46 +--R 1062347b x + 337179700a b x + 18813934425a b x +--R + +--R 3 14 44 4 13 42 5 12 40 +--R 435911726250a b x + 5537985721125a b x + 44226266816160a b x +--R + +--R 6 11 38 7 10 36 +--R 240242576724975a b x + 932460385321650a b x +--R + +--R 8 9 34 9 8 32 +--R 2668614201361000a b x + 5742120965670000a b x +--R + +--R 10 7 30 11 6 28 +--R 9385626998420480a b x + 11679727644825600a b x +--R + +--R 12 5 26 13 4 24 +--R 10999050000998400a b x + 7712957537792000a b x +--R + +--R 14 3 22 15 2 20 +--R 3905555337216000a b x + 1350318166179840a b x +--R + +--R 16 18 17 16 +--R 285450089267200a b x + 27848789196800a x +--R * +--R +-+ +--R \|a +--R / +--R 12 24 11 22 2 10 20 +--R 26558675b x + 8286306600a b x + 425363738800a b x +--R + +--R 3 9 18 4 8 16 5 7 14 +--R 8507274776000a b x + 87503397696000a b x + 528909426073600a b x +--R + +--R 6 6 12 7 5 10 +--R 2019472354099200a b x + 5059776887193600a b x +--R + +--R 8 4 8 9 3 6 +--R 8432961478656000a b x + 9259722407936000a b x +--R + +--R 10 2 4 11 2 12 +--R 6433070304460800a b x + 2562088606105600a 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+-+ | 2 +--R \|a \|b x + a +--R + +--R 10 14 2 9 12 3 8 10 4 7 8 +--R - 32175a b x - 1201200a b x - 12972960a b x - 61776000a b x +--R + +--R 5 6 6 6 5 4 7 4 2 8 3 +--R - 151008000a b x - 197683200a b x - 131788800a b x - 35143680a b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1369 +t0:=x^3*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 11 3 9 2 2 7 3 5 4 3 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1369 +r0:=-1/11*a*(a+b*x^2)^(11/2)/b^2+1/13*(a+b*x^2)^(13/2)/b^2 +--R +--R +--R (2) +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 6 +--R (11b x + 53a b x + 100a b x + 90a b x + 35a b x + a b x - 2a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R 143b +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 24 2 9 22 3 8 20 4 7 18 +--R - 143a b x - 4693a b x - 52624a b x - 301730a b x +--R + +--R 5 6 16 6 5 14 7 4 12 8 3 10 +--R - 1036607a b x - 2301585a b x - 3415412a b x - 3397680a b x +--R + +--R 9 2 8 10 6 11 4 +--R - 2196480a b x - 841984a b x - 146432a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 11 26 10 24 2 9 22 3 8 20 4 7 18 +--R 11b x + 988a b x + 17849a b x + 143858a b x + 658229a b x +--R + +--R 5 6 16 6 5 14 7 4 12 8 3 10 +--R 1907048a b x + 3692975a b x + 4886596a b x + 4399824a b x +--R + +--R 9 2 8 10 6 11 4 +--R 2599168a b x + 915200a b x + 146432a x +--R * +--R +-+ +--R \|a +--R / +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x +--R + +--R 5 2 6 +--R 1610752a b x + 585728a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 +--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x +--R + +--R 5 2 4 6 2 7 +--R - 2379520a b x - 1903616a b x - 585728a +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4 +--R - 2a b x - 168a b x - 2240a b x - 10752a b x - 23040a b x +--R + +--R 12 2 13 +--R - 22528a b x - 8192a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 6 12 8 5 10 9 4 8 10 3 6 11 2 4 +--R 26a b x + 728a b x + 5824a b x + 19968a b x + 33280a b x +--R + +--R 12 2 13 +--R 26624a b x + 8192a +--R * +--R +-+ +--R \|a +--R / +--R 8 12 7 10 2 6 8 3 5 6 4 4 4 +--R 143b x + 12012a b x + 160160a b x + 768768a b x + 1647360a b x +--R + +--R 5 3 2 6 2 +--R 1610752a b x + 585728a b +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 12 2 7 10 3 6 8 4 5 6 +--R - 1859a b x - 52052a b x - 416416a b x - 1427712a b x +--R + +--R 5 4 4 6 3 2 7 2 +--R - 2379520a b x - 1903616a b x - 585728a b +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1369 +t0:=x*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1369 +r0:=1/11*(a+b*x^2)^(11/2)/b +--R +--R +--R +--------+ +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )\|b x + a +--R (2) ----------------------------------------------------------------- +--R 11b +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 20 2 8 18 3 7 16 4 6 14 5 5 12 +--R - 11a b x - 275a b x - 2442a b x - 11286a b x - 31471a b x +--R + +--R 6 4 10 7 3 8 8 2 6 9 4 10 2 +--R - 56694a b x - 67760a b x - 53152a b x - 25344a b x - 5632a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 22 9 20 2 8 18 3 7 16 4 6 14 +--R b x + 66a b x + 935a b x + 6072a b x + 22671a b x +--R + +--R 5 5 12 6 4 10 7 3 8 8 2 6 9 4 +--R 53834a b x + 85294a b x + 91520a b x + 65120a b x + 28160a b x +--R + +--R 10 2 +--R 5632a x 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13552a b x - 30976a b x - 30976a b x +--R + +--R 6 +--R - 11264a b +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1369 +t0:=(a+b*x^2)^(9/2)/x +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1369 +r0:=1/3*a^3*(a+b*x^2)^(3/2)+1/5*a^2*(a+b*x^2)^(5/2)+1/7*a*(a+b*x^2)^(7/2)+_ + 1/9*(a+b*x^2)^(9/2)-a^(9/2)*atanh(sqrt(a+b*x^2)/sqrt(a))+_ + a^4*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 +-+ \|b x + a +--R - 315a \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x + 185a b x + 408a b x + 506a b x + 563a )\|b x + a +--R / +--R 315 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 315a b x - 5865a b x - 40992a b x - 153594a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 357000a b x - 546000a b x - 504000a b x - 201600a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1620a b x + 17793a b x + 93114a b x + 287469a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 579600a b x + 772800a b x + 604800a b x + 201600a b x +--R * +--R +-+ +--R \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 9 +--R - 80640a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R (563a b x + 22520a b x + 135120a b x + 252224a b x + 144128a ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (- 5067a b x - 67560a b x - 243216a b x - 324288a b x - 144128a )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x - 80640a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1369 +t0:=(a+b*x^2)^(9/2)/x^3 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1369 +r0:=3/2*a^2*b*(a+b*x^2)^(3/2)+9/10*a*b*(a+b*x^2)^(5/2)+_ + 9/14*b*(a+b*x^2)^(7/2)-1/2*(a+b*x^2)^(9/2)/x^2-_ + 9/2*a^(7/2)*b*atanh(sqrt(a+b*x^2)/sqrt(a))+9/2*a^3*b*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 3 2 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (10b x + 58a b x + 156a b x + 388a b x - 35a )\|b x + a +--R / +--R 2 +--R 70x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 8 2 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 2 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 90a b x - 1722a b x - 12684a b x - 52640a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 134085a b x - 175000a b x - 74480a b x + 20160a b x + 8960a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 468a b x + 5334a b x + 29904a b x + 103005a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 211365a b x + 214200a b x + 65520a b x - 24640a b x - 8960a +--R * +--R +-+ +--R \|a +--R / +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 10 2 3 8 3 2 6 4 4 5 2 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a x +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +--R (388a b x + 15520a b x + 93120a b x + 173824a b x + 99328a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 5 8 5 4 6 6 3 4 7 2 2 8 +-+ +--R (- 3492a b x - 46560a b x - 167616a b x - 223488a b x - 99328a b)\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1369 +t0:=(a+b*x^2)^(9/2)/x^5 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1369 +r0:=21/8*a*b^2*(a+b*x^2)^(3/2)+63/40*b^2*(a+b*x^2)^(5/2)-_ + 9/8*b*(a+b*x^2)^(7/2)/x^2-1/4*(a+b*x^2)^(9/2)/x^4-_ + 63/8*a^(5/2)*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))+63/8*a^2*b^2*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 2 2 4 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (8b x + 56a b x + 288a b x - 85a b x - 10a )\|b x + a +--R / +--R 4 +--R 40x +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 12 4 5 10 5 4 8 6 3 6 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 7 2 4 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 4 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 5 4 8 +--R - 72a b x - 1464a b x - 12480a b x - 51075a b x - 79310a b x +--R + +--R 6 3 6 7 2 4 8 2 9 +--R - 13280a b x + 53280a b x + 27520a b x + 2560a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 384a b x + 4824a b x + 30315a b x + 86745a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 90990a b x - 10080a b x - 66720a b x - 28800a b x - 2560a +--R * +--R +-+ +--R \|a +--R / +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 12 2 3 10 3 2 8 4 6 5 4 +--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a x +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 2 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +--R (288a b x + 11520a b x + 69120a b x + 129024a b x + 73728a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 6 8 4 5 6 5 4 4 6 3 2 7 2 +-+ +--R (- 2592a b x - 34560a b x - 124416a b x - 165888a b x - 73728a b )\|a +--R / +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 360a b x - 4800a b x - 17280a b x - 23040a b x - 10240a +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1369 +t0:=(a+b*x^2)^(9/2)/x^7 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1369 +r0:=35/16*b^3*(a+b*x^2)^(3/2)-21/16*b^2*(a+b*x^2)^(5/2)/x^2-_ + 3/8*b*(a+b*x^2)^(7/2)/x^4-1/6*(a+b*x^2)^(9/2)/x^6-_ + 105/16*a^(3/2)*b^3*atanh(sqrt(a+b*x^2)/sqrt(a))+_ + 105/16*a*b^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 3 6 +-+ \|b x + a +--R - 315a b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x + 208a b x - 165a b x - 50a b x - 8a )\|b x + a +--R / +--R 6 +--R 48x +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 14 3 6 12 4 5 10 5 4 8 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 6 3 6 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 6 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 144a b x - 3584a b x - 22067a b x - 28902a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 46632a b x + 117600a b x + 74496a b x + 17408a b x + 2048a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 864a b x + 10971a b x + 37473a b x + 16254a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 97128a b x - 152800a b x - 82944a b x - 18432a b x - 2048a +--R * +--R +-+ +--R \|a +--R / +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 14 2 3 12 3 2 10 4 8 5 6 +--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a x +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 3 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +--R (208a b x + 8320a b x + 49920a b x + 93184a b x + 53248a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 7 8 3 6 6 4 5 4 5 4 2 6 3 +-+ +--R (- 1872a b x - 24960a b x - 89856a b x - 119808a b x - 53248a b )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 432a b x - 5760a b x - 20736a b x - 27648a b x - 12288a +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1369 +t0:=(a+b*x^2)^(9/2)/x^9 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1369 +r0:=-105/128*b^3*(a+b*x^2)^(3/2)/x^2-21/64*b^2*(a+b*x^2)^(5/2)/x^4-_ + 3/16*b*(a+b*x^2)^(7/2)/x^6-1/8*(a+b*x^2)^(9/2)/x^8-_ + 315/128*b^4*atanh(sqrt(a+b*x^2)/sqrt(a))*sqrt(a)+_ + 315/128*b^4*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 4 8 +-+ \|b x + a +--R - 315b x \|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (128b x - 325a b x - 210a b x - 88a b x - 16a )\|b x + a +--R / +--R 8 +--R 128x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 5 4 8 +--R 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 8 +--R - 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 1024a b x - 7315a b x + 16314a b x + 150008a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 288624a b x + 244096a b x + 111360a b x + 31744a b x + 4096a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 128b x + 3771a b x + 6945a b x - 66930a b x - 269640a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 398576a b x - 296064a b x - 126720a b x - 33792a b x - 4096a +--R * +--R +-+ +--R \|a +--R / +--R 4 16 3 14 2 2 12 3 10 4 8 +-+ +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 16 2 3 14 3 2 12 4 10 5 8 +--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a x +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 4 +--R - 80640a b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +--R (128a b x + 5120a b x + 30720a b x + 57344a b x + 32768a b ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 8 8 2 7 6 3 6 4 4 5 2 5 4 +-+ +--R (- 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a b )\|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 1152a b x - 15360a b x - 55296a b x - 73728a b x - 32768a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1369 +t0:=(a+b*x^2)^(9/2)/x^11 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1369 +r0:=-21/128*b^3*(a+b*x^2)^(3/2)/x^4-21/160*b^2*(a+b*x^2)^(5/2)/x^6-_ + 9/80*b*(a+b*x^2)^(7/2)/x^8-1/10*(a+b*x^2)^(9/2)/x^10-_ + 63/256*b^5*atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a)-_ + 63/256*b^4*sqrt(a+b*x^2)/x^2 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 5 10 \|b x + a +--R - 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 965b x - 1490a b x - 1368a b x - 656a b x - 128a )\|a \|b x + a +--R / +--R 10 +-+ +--R 1280x \|a +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 3150a b x + 50400a b x + 211680a b x + 322560a b x +--R + +--R 5 5 10 +--R 161280a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 +--R - 315b x - 15750a b x - 126000a b x - 352800a b x +--R + +--R 4 6 12 5 5 10 +--R - 403200a b x - 161280a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R 965a b x + 49740a b x + 461868a b x + 1745856a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 3484128a b x + 4202240a b x + 3299840a b x + 1683456a b x +--R + +--R 9 2 10 +--R 499712a b x + 65536a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 2 8 16 3 7 14 4 6 12 +--R - 9650a b x - 178950a b x - 1069860a b x - 3115440a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 5260256a b x - 5670400a b x - 4083200a b x - 1925120a b x +--R + +--R 9 2 10 +--R - 532480a b x - 65536a +--R * +--R +-+ +--R \|a +--R / +--R 4 18 2 3 16 3 2 14 4 12 +--R 12800a b x + 204800a b x + 860160a b x + 1310720a b x +--R + +--R 5 10 +--R 655360a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 20 2 4 18 3 3 16 4 2 14 +--R - 1280a b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 5 12 6 10 +--R - 1638400a b x - 655360a x +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 5 \|b x + a - \|a 5 \|b x + a +--R 63b log(------------------) + 63b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ---------------------------------------------------- +--R +-+ +--R 256\|a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1369 +t0:=(a+b*x^2)^(9/2)/x^13 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1369 +r0:=-7/128*b^3*(a+b*x^2)^(3/2)/x^6-21/320*b^2*(a+b*x^2)^(5/2)/x^8-_ + 3/40*b*(a+b*x^2)^(7/2)/x^10-1/12*(a+b*x^2)^(9/2)/x^12+_ + 21/1024*b^6*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-_ + 21/512*b^4*sqrt(a+b*x^2)/x^4-21/1024*b^5*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 6 12 \|b x + a +--R 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +--R - 315b x - 4910a b x - 11432a b x - 12144a b x - 6272a b x +--R + +--R 5 +--R - 1280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R / +--R 12 +-+ +--R 15360a x \|a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 3780a b x - 88200a b x - 564480a b x - 1451520a b x +--R + +--R 5 7 14 6 6 12 +--R - 1612800a b x - 645120a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 12 24 11 22 2 10 20 3 9 18 +--R 315b x + 22680a b x + 264600a b x + 1128960a b x +--R + +--R 4 8 16 5 7 14 6 6 12 +--R 2177280a b x + 1935360a b x + 645120a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R 315a b x + 27590a b x + 629552a b x + 6088608a b x +--R + +--R 5 7 14 6 6 12 7 5 10 +--R 30258240a b x + 87499392a b x + 158714880a b x +--R + +--R 8 4 8 9 3 6 10 2 4 11 2 +--R 187787264a b x + 145965056a b x + 72253440a b x + 20709376a b x +--R + +--R 12 +--R 2621440a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 11 22 2 10 20 3 9 18 4 8 16 +--R - 3780a b x - 150900a b x - 2223584a b x - 15673392a b x +--R + +--R 5 7 14 6 6 12 7 5 10 +--R - 61796736a b x - 150196352a b x - 238141440a b x +--R + +--R 8 4 8 9 3 6 10 2 4 +--R - 252930048a b x - 179666944a b x - 82280448a b x +--R + +--R 11 2 12 +--R - 22020096a b x - 2621440a +--R * +--R +-+ +--R \|a +--R / +--R 2 5 22 3 4 20 4 3 18 5 2 16 +--R 184320a b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 6 14 7 12 +--R 78643200a b x + 31457280a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 6 24 3 5 22 4 4 20 5 3 18 +--R - 15360a b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 6 2 16 7 14 8 12 +--R - 106168320a b x - 94371840a b x - 31457280a x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 6 \|b x + a - \|a 6 \|b x + a +--R - 21b log(------------------) - 21b atanh(-----------) +--R x +-+ +--R \|a +--R (4) ------------------------------------------------------ +--R +-+ +--R 1024a\|a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1369 +t0:=(a+b*x^2)^(9/2)/x^15 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 15 +--R x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1369 +r0:=-3/128*b^3*(a+b*x^2)^(3/2)/x^8-3/80*b^2*(a+b*x^2)^(5/2)/x^10-_ + 3/56*b*(a+b*x^2)^(7/2)/x^12-1/14*(a+b*x^2)^(9/2)/x^14-_ + 9/2048*b^7*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 3/256*b^4*sqrt(a+b*x^2)/x^6-3/1024*b^5*sqrt(a+b*x^2)/(a*x^4)+_ + 9/2048*b^6*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R 7 14 \|b x + a +--R - 315b x atanh(-----------) +--R +-+ +--R \|a +--R + +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 +--R 315b x - 210a b x - 14168a b x - 39056a b x - 44928a b x +--R + +--R 5 2 6 +--R - 24320a b x - 5120a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R / +--R 2 14 +-+ +--R 71680a x \|a +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 26 2 12 24 3 11 22 4 10 20 +--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R 8870400a b x + 7741440a b x + 2580480a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 14 28 13 26 2 12 24 3 11 22 +--R - 315b x - 30870a b x - 493920a b x - 2963520a b x +--R + +--R 4 10 20 5 9 18 6 8 16 +--R - 8467200a b x - 12418560a b x - 9031680a b x +--R + +--R 7 7 14 +--R - 2580480a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 13 26 2 12 24 3 11 22 4 10 20 +--R - 315a b x - 30660a b x - 459172a b x - 1206720a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R 19596320a b x + 192185856a b x + 820357632a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R 2073143296a b x + 3392184320a b x + 3709009920a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R 2704539648a b x + 1267204096a b x + 346030080a b x + 41943040a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 13 26 2 12 24 3 11 22 4 10 20 +--R 4410a b x + 142590a b x + 1115828a b x - 1924720a b x +--R + +--R 5 9 18 6 8 16 7 7 14 +--R - 72509024a b x - 463341312a b x - 1587302912a b x +--R + +--R 8 6 12 9 5 10 10 4 8 +--R - 3433744384a b x - 4975452160a b x - 4922867712a b x +--R + +--R 11 3 6 12 2 4 13 2 +--R - 3297509376a b x - 1434976256a b x - 367001600a b x +--R + +--R 14 +--R - 41943040a +--R * +--R +-+ +--R \|a +--R / +--R 3 6 26 4 5 24 5 4 22 +--R 1003520a b x + 32112640a b x + 289013760a b x +--R + +--R 6 3 20 7 2 18 8 16 +--R 1101004800a b x + 2018508800a b x + 1761607680a b x +--R + +--R 9 14 +--R 587202560a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 28 4 6 26 5 5 24 6 4 22 +--R - 71680a b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 7 3 20 8 2 18 9 16 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 10 14 +--R - 587202560a x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 7 \|b x + a - \|a 7 \|b x + a +--R 9b log(------------------) + 9b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 2048a \|a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1369 +t0:=x^6*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 14 3 12 2 2 10 3 8 4 6 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1369 +r0:=3/256*a^3*x^7*(a+b*x^2)^(3/2)+3/128*a^2*x^7*(a+b*x^2)^(5/2)+_ + 9/224*a*x^7*(a+b*x^2)^(7/2)+1/16*x^7*(a+b*x^2)^(9/2)-_ + 45/32768*a^8*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(7/2)+_ + 45/32768*a^7*x*sqrt(a+b*x^2)/b^3-15/16384*a^6*x^3*_ + sqrt(a+b*x^2)/b^2+3/4096*a^5*x^5*sqrt(a+b*x^2)/b+_ + 9/2048*a^4*x^7*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 8 x\|b +--R - 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 15 6 13 2 5 11 3 4 9 4 3 7 +--R 14336b x + 66560a b x + 119040a b x + 98432a b x + 32624a b x +--R + +--R 5 2 5 6 3 7 +--R 168a b x - 210a b x + 315a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R / +--R 3 +-+ +--R 229376b \|b +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 7 14 9 6 12 10 5 10 11 4 8 +--R 5040a b x + 211680a b x + 2540160a b x + 13305600a b x +--R + +--R 12 3 6 13 2 4 14 2 15 +--R 35481600a b x + 50319360a b x + 36126720a b x + 10321920a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 8 16 9 7 14 10 6 12 11 5 10 +--R - 315a b x - 40320a b x - 846720a b x - 6773760a b x +--R + +--R 12 4 8 13 3 6 14 2 4 +--R - 26611200a b x - 56770560a b x - 67092480a b x +--R + +--R 15 2 16 +--R - 41287680a b x - 10321920a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 15 31 14 29 2 13 27 +--R - 14336b x - 1901568a b x - 47173888a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R - 502530176a b x - 2975022960a b x - 11035277480a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R - 27310058286a b x - 46527167547a b x - 55047454848a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R - 44639228800a b x - 23770343424a b x - 7526059520a b x +--R + +--R 12 3 7 13 2 5 14 3 +--R - 1103085568a b x - 45072384a b x - 34406400a b x +--R + +--R 15 +--R - 10321920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 15 31 14 29 2 13 27 +--R 229376b x + 10928128a b x + 172937216a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R 1386100736a b x + 6676770560a b x + 21084247936a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R 45737690208a b x + 69692308560a b x + 74823758928a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R 55651554400a b x + 27397242752a b x + 8073715456a b x +--R + +--R 12 3 7 13 2 5 14 3 15 +--R 1121966080a b x + 60985344a b x + 39567360a b x + 10321920a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 10 14 9 12 2 8 10 +--R 3670016b x + 154140672a b x + 1849688064a b x +--R + +--R 3 7 8 4 6 6 5 5 4 +--R 9688842240a b x + 25836912640a b x + 36641439744a b x +--R + +--R 6 4 2 7 3 +--R 26306674688a b x + 7516192768a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 11 16 10 14 2 9 12 +--R - 229376b x - 29360128a b x - 616562688a b x +--R + +--R 3 8 10 4 7 8 5 6 6 +--R - 4932501504a b x - 19377684480a b x - 41339060224a b x +--R + +--R 6 5 4 7 4 2 8 3 +--R - 48855252992a b x - 30064771072a b x - 7516192768a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 8 7 14 9 6 12 10 5 10 +--R - 10080a b x - 423360a b x - 5080320a b x +--R + +--R 11 4 8 12 3 6 13 2 4 +--R - 26611200a b x - 70963200a b x - 100638720a b x +--R + +--R 14 2 15 +--R - 72253440a b x - 20643840a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 8 16 9 7 14 10 6 12 11 5 10 +--R 630a b x + 80640a b x + 1693440a b x + 13547520a b x +--R + +--R 12 4 8 13 3 6 14 2 4 +--R 53222400a b x + 113541120a b x + 134184960a b x +--R + +--R 15 2 16 +--R 82575360a b x + 20643840a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 15 31 14 29 2 13 27 +--R - 14336b x - 1901568a b x - 47173888a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R - 502530176a b x - 2975022960a b x - 11035277480a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R - 27310058286a b x - 46527167547a b x - 55047454848a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R - 44639228800a b x - 23770343424a b x - 7526059520a b x +--R + +--R 12 3 7 13 2 5 14 3 +--R - 1103085568a b x - 45072384a b x - 34406400a b x +--R + +--R 15 +--R - 10321920a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 15 31 14 29 2 13 27 +--R 229376b x + 10928128a b x + 172937216a b x +--R + +--R 3 12 25 4 11 23 5 10 21 +--R 1386100736a b x + 6676770560a b x + 21084247936a b x +--R + +--R 6 9 19 7 8 17 8 7 15 +--R 45737690208a b x + 69692308560a b x + 74823758928a b x +--R + +--R 9 6 13 10 5 11 11 4 9 +--R 55651554400a b x + 27397242752a b x + 8073715456a b x +--R + +--R 12 3 7 13 2 5 14 3 15 +--R 1121966080a b x + 60985344a b x + 39567360a b x + 10321920a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 10 14 9 12 2 8 10 +--R 3670016b x + 154140672a b x + 1849688064a b x +--R + +--R 3 7 8 4 6 6 5 5 4 +--R 9688842240a b x + 25836912640a b x + 36641439744a b x +--R + +--R 6 4 2 7 3 +--R 26306674688a b x + 7516192768a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 11 16 10 14 2 9 12 +--R - 229376b x - 29360128a b x - 616562688a b x +--R + +--R 3 8 10 4 7 8 5 6 6 +--R - 4932501504a b x - 19377684480a b x - 41339060224a b x +--R + +--R 6 5 4 7 4 2 8 3 +--R - 48855252992a b x - 30064771072a b x - 7516192768a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 491 + +--S 492 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 8 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 45a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 8 x\|b +--R 45a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 3 +-+ +--R 32768b \|b +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 8 +---+ x\|b 8 +-+ \|- b \|b x + a - \|- b \|a +--R 45a \|- b atanh(-----------) - 90a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 3 +---+ +-+ +--R 32768b \|- b \|b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 495 + +)clear all + +--S 496 of 1369 +t0:=x^4*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 12 3 10 2 2 8 3 6 4 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1369 +r0:=3/128*a^3*x^5*(a+b*x^2)^(3/2)+3/80*a^2*x^5*(a+b*x^2)^(5/2)+_ + 3/56*a*x^5*(a+b*x^2)^(7/2)+1/14*x^5*(a+b*x^2)^(9/2)+_ + 9/2048*a^7*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 9/2048*a^6*x*sqrt(a+b*x^2)/b^2+3/1024*a^5*x^3*sqrt(a+b*x^2)/b+_ + 3/256*a^4*x^5*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 7 x\|b +--R 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 5120b x + 24320a b x + 44928a b x + 39056a b x + 14168a b x +--R + +--R 5 3 6 +--R 210a b x - 315a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R / +--R 2 +-+ +--R 71680b \|b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 4410a b x + 141120a b x + 1270080a b x + 4838400a b x +--R + +--R 11 2 4 12 2 13 +--R 8870400a b x + 7741440a b x + 2580480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 7 14 8 6 12 9 5 10 10 4 8 +--R - 315a b x - 30870a b x - 493920a b x - 2963520a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R - 8467200a b x - 12418560a b x - 9031680a b x - 2580480a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 13 27 12 25 2 11 23 3 10 21 +--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x +--R + +--R 4 9 19 5 8 17 6 7 15 +--R - 440716920a b x - 1340883586a b x - 2702931497a b x +--R + +--R 7 6 13 8 5 11 9 4 9 +--R - 3693903786a b x - 3409466400a b x - 2049104320a b x +--R + +--R 10 3 7 11 2 5 12 3 13 +--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 13 27 12 25 2 11 23 +--R 71680b x + 2705920a b x + 34802432a b x +--R + +--R 3 10 21 4 9 19 5 8 17 +--R 229544160a b x + 913955504a b x + 2381177932a b x +--R + +--R 6 7 15 7 6 13 8 5 11 +--R 4226517442a b x + 5183442054a b x + 4350339840a b x +--R + +--R 9 4 9 10 3 7 11 2 5 +--R 2398031552a b x + 781569536a b x + 106333696a b x +--R + +--R 12 3 13 +--R - 8601600a b x - 2580480a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 12 7 10 2 6 8 3 5 6 +--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x +--R + +--R 4 4 4 5 3 2 6 2 +--R 2018508800a b x + 1761607680a b x + 587202560a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 9 14 8 12 2 7 10 3 6 8 +--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 4 5 6 5 4 4 6 3 2 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 7 2 +--R - 587202560a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 7 6 12 8 5 10 9 4 8 10 3 6 +--R 8820a b x + 282240a b x + 2540160a b x + 9676800a b x +--R + +--R 11 2 4 12 2 13 +--R 17740800a b x + 15482880a b x + 5160960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 7 14 8 6 12 9 5 10 10 4 8 +--R - 630a b x - 61740a b x - 987840a b x - 5927040a b x +--R + +--R 11 3 6 12 2 4 13 2 14 +--R - 16934400a b x - 24837120a b x - 18063360a b x - 5160960a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 13 27 12 25 2 11 23 3 10 21 +--R - 5120b x - 526080a b x - 10456448a b x - 90744720a b x +--R + +--R 4 9 19 5 8 17 6 7 15 +--R - 440716920a b x - 1340883586a b x - 2702931497a b x +--R + +--R 7 6 13 8 5 11 9 4 9 +--R - 3693903786a b x - 3409466400a b x - 2049104320a b x +--R + +--R 10 3 7 11 2 5 12 3 13 +--R - 725983488a b x - 109666816a b x + 7311360a b x + 2580480a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 13 27 12 25 2 11 23 +--R 71680b x + 2705920a b x + 34802432a b x +--R + +--R 3 10 21 4 9 19 5 8 17 +--R 229544160a b x + 913955504a b x + 2381177932a b x +--R + +--R 6 7 15 7 6 13 8 5 11 +--R 4226517442a b x + 5183442054a b x + 4350339840a b x +--R + +--R 9 4 9 10 3 7 11 2 5 +--R 2398031552a b x + 781569536a b x + 106333696a b x +--R + +--R 12 3 13 +--R - 8601600a b x - 2580480a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 8 12 7 10 2 6 8 3 5 6 +--R 1003520b x + 32112640a b x + 289013760a b x + 1101004800a b x +--R + +--R 4 4 4 5 3 2 6 2 +--R 2018508800a b x + 1761607680a b x + 587202560a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 9 14 8 12 2 7 10 3 6 8 +--R - 71680b x - 7024640a b x - 112394240a b x - 674365440a b x +--R + +--R 4 5 6 5 4 4 6 3 2 +--R - 1926758400a b x - 2825912320a b x - 2055208960a b x +--R + +--R 7 2 +--R - 587202560a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 498 + +--S 499 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 7 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 9a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 7 x\|b +--R - 9a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 2048b \|b +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 7 +---+ x\|b 7 +-+ \|- b \|b x + a - \|- b \|a +--R - 9a \|- b atanh(-----------) + 18a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ---------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2048b \|- b \|b +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1369 +t0:=x^2*(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 10 3 8 2 2 6 3 4 4 2 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1369 +r0:=7/128*a^3*x^3*(a+b*x^2)^(3/2)+21/320*a^2*x^3*(a+b*x^2)^(5/2)+_ + 3/40*a*x^3*(a+b*x^2)^(7/2)+1/12*x^3*(a+b*x^2)^(9/2)-_ + 21/1024*a^6*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+_ + 21/1024*a^5*x*sqrt(a+b*x^2)/b+21/512*a^4*x^3*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 6 x\|b +--R - 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 11 4 9 2 3 7 3 2 5 4 3 +--R 1280b x + 6272a b x + 12144a b x + 11432a b x + 4910a b x +--R + +--R 5 +--R 315a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R / +--R +-+ +--R 15360b\|b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R 3780a b x + 88200a b x + 564480a b x + 1451520a b x +--R + +--R 10 2 11 +--R 1612800a b x + 645120a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 6 12 7 5 10 8 4 8 9 3 6 +--R - 315a b x - 22680a b x - 264600a b x - 1128960a b x +--R + +--R 10 2 4 11 2 12 +--R - 2177280a b x - 1935360a b x - 645120a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R - 42355182a b x - 104697195a b x - 170215304a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R - 184337816a b x - 130176000a b x - 55757056a b x +--R + +--R 10 3 11 +--R - 11991040a b x - 645120a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 81152072a b x + 173035260a b x + 249146268a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 243180424a b x + 156595968a b x + 61671936a b x +--R + +--R 10 3 11 +--R 12313600a b x + 645120a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 6 10 5 8 2 4 6 3 3 4 +--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 4 2 2 5 +--R 78643200a b x + 31457280a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 7 12 6 10 2 5 8 3 4 6 +--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 4 3 4 5 2 2 6 +--R - 106168320a b x - 94371840a b x - 31457280a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 6 5 10 7 4 8 8 3 6 9 2 4 +--R - 7560a b x - 176400a b x - 1128960a b x - 2903040a b x +--R + +--R 10 2 11 +--R - 3225600a b x - 1290240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 6 12 7 5 10 8 4 8 9 3 6 +--R 630a b x + 45360a b x + 529200a b x + 2257920a b x +--R + +--R 10 2 4 11 2 12 +--R 4354560a b x + 3870720a b x + 1290240a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R - 1280b x - 98432a b x - 1538928a b x - 10741800a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R - 42355182a b x - 104697195a b x - 170215304a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R - 184337816a b x - 130176000a b x - 55757056a b x +--R + +--R 10 3 11 +--R - 11991040a b x - 645120a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 11 23 10 21 2 9 19 3 8 17 +--R 15360b x + 449024a b x + 4629312a b x + 24870816a b x +--R + +--R 4 7 15 5 6 13 6 5 11 +--R 81152072a b x + 173035260a b x + 249146268a b x +--R + +--R 7 4 9 8 3 7 9 2 5 +--R 243180424a b x + 156595968a b x + 61671936a b x +--R + +--R 10 3 11 +--R 12313600a b x + 645120a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 6 10 5 8 2 4 6 3 3 4 +--R 184320b x + 4300800a b x + 27525120a b x + 70778880a b x +--R + +--R 4 2 2 5 +--R 78643200a b x + 31457280a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 7 12 6 10 2 5 8 3 4 6 +--R - 15360b x - 1105920a b x - 12902400a b x - 55050240a b x +--R + +--R 4 3 4 5 2 2 6 +--R - 106168320a b x - 94371840a b x - 31457280a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 505 + +--S 506 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 6 (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 21a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 6 x\|b +--R 21a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 1024b\|b +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 6 +---+ x\|b 6 +-+ \|- b \|b x + a - \|- b \|a +--R 21a \|- b atanh(-----------) - 42a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 1024b\|- b \|b +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 509 + +)clear all + +--S 510 of 1369 +t0:=(a+b*x^2)^(9/2) +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (1) (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1369 +r0:=21/128*a^3*x*(a+b*x^2)^(3/2)+21/160*a^2*x*(a+b*x^2)^(5/2)+_ + 9/80*a*x*(a+b*x^2)^(7/2)+1/10*x*(a+b*x^2)^(9/2)+_ + 63/256*a^5*atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b)+_ + 63/256*a^4*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 5 x\|b +--R 315a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (128b x + 656a b x + 1368a b x + 1490a b x + 965a x)\|b \|b x + a +--R / +--R +-+ +--R 1280\|b +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 3150a b x + 50400a b x + 211680a b x + 322560a b x +--R + +--R 9 +--R 161280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 315a b x - 15750a b x - 126000a b x - 352800a b x +--R + +--R 9 2 10 +--R - 403200a b x - 161280a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 7056a b x - 85368a b x - 475650a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x +--R + +--R 8 3 9 +--R - 1998080a b x - 494080a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 28320a b x + 231696a b x + 1010340a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x +--R + +--R 8 3 9 +--R 2245120a b x + 494080a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 4 8 3 6 2 2 4 3 2 4 +--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 2 5 +--R - 1638400a b x - 655360a +--R * +--R +-+ +--R \|b +--R , +--R +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 6300a b x + 100800a b x + 423360a b x + 645120a b x +--R + +--R 9 +--R 322560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R - 630a b x - 31500a b x - 252000a b x - 705600a b x +--R + +--R 9 2 10 +--R - 806400a b x - 322560a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R - 128b x - 7056a b x - 85368a b x - 475650a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R - 1521225a b x - 3081626a b x - 4141712a b x - 3688416a b x +--R + +--R 8 3 9 +--R - 1998080a b x - 494080a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 9 19 8 17 2 7 15 3 6 13 +--R 1280b x + 28320a b x + 231696a b x + 1010340a b x +--R + +--R 4 5 11 5 4 9 6 3 7 7 2 5 +--R 2710310a b x + 4797010a b x + 5767040a b x + 4625696a b x +--R + +--R 8 3 9 +--R 2245120a b x + 494080a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 4 8 3 6 2 2 4 3 2 4 +--R (12800b x + 204800a b x + 860160a b x + 1310720a b x + 655360a ) +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 +--R - 1280b x - 64000a b x - 512000a b x - 1433600a b x +--R + +--R 4 2 5 +--R - 1638400a b x - 655360a +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 512 + +--S 513 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 5 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 63a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 5 x\|b +--R - 63a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 256\|b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +-+ +--R 5 +---+ x\|b +--R - 63a \|- b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R 5 +-+ \|- b \|b x + a - \|- b \|a +--R 126a \|b atan(------------------------------) +--R b x +--R / +--R +---+ +-+ +--R 256\|- b \|b +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 516 + +)clear all + +--S 517 of 1369 +t0:=(a+b*x^2)^(9/2)/x^2 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1369 +r0:=105/64*a^2*b*x*(a+b*x^2)^(3/2)+21/16*a*b*x*(a+b*x^2)^(5/2)+_ + 9/8*b*x*(a+b*x^2)^(7/2)-(a+b*x^2)^(9/2)/x+_ + 315/128*a^4*atanh(x*sqrt(b)/sqrt(a+b*x^2))*sqrt(b)+_ + 315/128*a^3*b*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 4 +-+ x\|b +--R 315a x\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (16b x + 88a b x + 210a b x + 325a b x - 128a )\|b x + a +--R / +--R 128x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 4 9 5 3 7 6 2 5 7 3 8 +--R (315a b x + 12600a b x + 75600a b x + 141120a b x + 80640a x) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 144b x - 2712a b x - 19362a b x - 75357a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a +--R / +--R 4 9 3 7 2 2 5 3 3 4 +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a +--R , +--R +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 8 +--R 161280a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 8 +--R - 161280a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 144b x - 2712a b x - 19362a b x - 75357a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R - 183352a b x - 268528a b x - 185664a b x - 9472a b x + 32768a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 16b x + 744a b x + 8298a b x + 44583a b x + 143805a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 296280a b x + 358128a b x + 194496a b x - 6912a b x - 32768a +--R / +--R 4 9 3 7 2 2 5 3 3 4 +--R (128b x + 5120a b x + 30720a b x + 57344a b x + 32768a x) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- 1152b x - 15360a b x - 55296a b x - 73728a b x - 32768a x)\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 519 + +--S 520 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 4 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 315a \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 4 +-+ x\|b +--R - 315a \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 128 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 4 +-+ x\|b 4 +---+ \|b x + a - \|a +--R - 315a \|b atanh(-----------) + 630a \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ------------------------------------------------------------------- +--R 128 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1369 +t0:=(a+b*x^2)^(9/2)/x^4 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1369 +r0:=35/8*a*b^2*x*(a+b*x^2)^(3/2)+7/2*b^2*x*(a+b*x^2)^(5/2)-_ + 3*b*(a+b*x^2)^(7/2)/x-1/3*(a+b*x^2)^(9/2)/x^3+_ + 105/16*a^3*b^(3/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_ + 105/16*a^2*b^2*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 3 3 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (8b x + 50a b x + 165a b x - 208a b x - 16a )\|b x + a +--R / +--R 3 +--R 48x +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 7 3 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 7 3 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 16064a b x + 84480a b x + 62464a b x + 4096a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a +--R / +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a +--R , +--R +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 7 3 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 3 5 11 4 4 9 5 3 7 6 2 5 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 7 3 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 72b x - 1410a b x - 10941a b x - 44136a b x - 77024a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 16064a b x + 84480a b x + 62464a b x + 4096a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 8b x + 378a b x + 4455a b x + 26061a b x + 77688a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R 91872a b x - 18624a b x - 115200a b x - 64512a b x - 4096a +--R / +--R 4 11 3 9 2 2 7 3 5 4 3 +--R (48b x + 1920a b x + 11520a b x + 21504a b x + 12288a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (- 432b x - 5760a b x - 20736a b x - 27648a b x - 12288a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 526 + +--S 527 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 105a b\|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 +-+ x\|b +--R - 105a b\|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 16 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a +--R - 105a b\|b atanh(-----------) + 210a b\|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) --------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1369 +t0:=(a+b*x^2)^(9/2)/x^6 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1369 +r0:=21/4*b^3*x*(a+b*x^2)^(3/2)-21/5*b^2*(a+b*x^2)^(5/2)/x-_ + 3/5*b*(a+b*x^2)^(7/2)/x^3-1/5*(a+b*x^2)^(9/2)/x^5+_ + 63/8*a^2*b^(5/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+_ + 63/8*a*b^3*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 2 2 5 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (10b x + 85a b x - 288a b x - 56a b x - 8a )\|b x + a +--R / +--R 5 +--R 40x +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 6 2 5 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 6 2 5 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 169280a b x + 109440a b x + 18944a b x + 2048a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a +--R / +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a +--R , +--R +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 6 2 5 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 2 6 13 3 5 11 4 4 9 5 3 7 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 6 2 5 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 90b x - 1965a b x - 11928a b x - 7416a b x + 79688a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 169280a b x + 109440a b x + 18944a b x + 2048a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 10b x + 495a b x + 5997a b x + 18816a b x - 17424a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 151752a b x - 221760a b x - 118656a b x - 19968a b x - 2048a +--R / +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (40b x + 1600a b x + 9600a b x + 17920a b x + 10240a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (- 360b x - 4800a b x - 17280a b x - 23040a b x - 10240a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 533 + +--S 534 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 2 2 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 63a b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 2 +-+ x\|b +--R - 63a b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 8 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 2 2 +-+ x\|b 2 2 +---+ \|b x + a - \|a +--R - 63a b \|b atanh(-----------) + 126a b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1369 +t0:=(a+b*x^2)^(9/2)/x^8 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1369 +r0:=-3*b^3*(a+b*x^2)^(3/2)/x-3/5*b^2*(a+b*x^2)^(5/2)/x^3-_ + 9/35*b*(a+b*x^2)^(7/2)/x^5-1/7*(a+b*x^2)^(9/2)/x^7+_ + 9/2*a*b^(7/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))+9/2*b^4*x*sqrt(a+b*x^2) +--R +--R +--R (2) +--R +-+ +--R 3 7 +-+ x\|b +--R 315a b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (35b x - 388a b x - 156a b x - 58a b x - 10a )\|b x + a +--R / +--R 7 +--R 70x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 15 2 6 13 3 5 11 4 4 9 +--R 315a b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 5 3 7 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 7 15 2 6 13 3 5 11 4 4 9 +--R - 2835a b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 5 3 7 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 315b x - 708a b x + 32844a b x + 166698a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a +--R / +--R 4 15 3 13 2 2 11 3 9 4 7 +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 15 3 13 2 2 11 3 9 4 7 +-+ +--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a +--R , +--R +--R 7 15 2 6 13 3 5 11 4 4 9 +--R 630a b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 5 3 7 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 7 15 2 6 13 3 5 11 4 4 9 +--R - 5670a b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 5 3 7 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R - 315b x - 708a b x + 32844a b x + 166698a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 288970a b x + 215440a b x + 77664a b x + 20608a b x + 2560a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 4 5 10 +--R 35b x + 1047a b x - 6264a b x - 91014a b x - 288372a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 388170a b x - 251856a b x - 87648a b x - 21888a b x - 2560a +--R / +--R 4 15 3 13 2 2 11 3 9 4 7 +--R (70b x + 2800a b x + 16800a b x + 31360a b x + 17920a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 15 3 13 2 2 11 3 9 4 7 +-+ +--R (- 630b x - 8400a b x - 30240a b x - 40320a b x - 17920a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 540 + +--S 541 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R 3 +-+ (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R 9a b \|b log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 3 +-+ x\|b +--R - 9a b \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +-+ +--R 3 +-+ x\|b 3 +---+ \|b x + a - \|a +--R - 9a b \|b atanh(-----------) + 18a b \|- b atan(------------------) +--R +--------+ +---+ +--R | 2 x\|- b +--R \|b x + a +--R (6) -------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1369 +t0:=(a+b*x^2)^(9/2)/x^10 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1369 +r0:=-1/3*b^3*(a+b*x^2)^(3/2)/x^3-1/5*b^2*(a+b*x^2)^(5/2)/x^5-_ + 1/7*b*(a+b*x^2)^(7/2)/x^7-1/9*(a+b*x^2)^(9/2)/x^9+_ + b^(9/2)*atanh(x*sqrt(b)/sqrt(a+b*x^2))-b^4*sqrt(a+b*x^2)/x +--R +--R +--R (2) +--R +-+ +--R 4 9 +-+ x\|b +--R 315b x \|b atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (- 563b x - 506a b x - 408a b x - 185a b x - 35a )\|b x + a +--R / +--R 9 +--R 315x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 12600a b x + 75600a b x + 141120a b x +--R + +--R 4 4 9 +--R 80640a b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 2835b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 4 4 9 +--R - 80640a b x +--R * +--R +-+ +-+ +--R \|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (- x\|b + \|a )\|b x + a + x\|a \|b - b x - a +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 16 7 14 2 6 12 3 5 10 +--R 5067b x + 72114a b x + 307608a b x + 593505a b x +--R + +--R 4 4 8 5 3 6 6 2 4 7 2 8 +--R 634355a b x + 448664a b x + 226128a b x + 67520a b x + 8960a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R - 563b x - 23589a b x - 178794a b x - 545937a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 866340a b x - 834291a b x - 553848a b x - 258768a b x +--R + +--R 8 2 9 +--R - 72000a b x - 8960a +--R / +--R 4 17 3 15 2 2 13 3 11 4 9 +--R (315b x + 12600a b x + 75600a b x + 141120a b x + 80640a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 17 3 15 2 2 13 3 11 +--R - 2835b x - 37800a b x - 136080a b x - 181440a b x +--R + +--R 4 9 +--R - 80640a x +--R * +--R +-+ +--R \|a +--R , +--R +--R 8 17 7 15 2 6 13 3 5 11 +--R 630b x + 25200a b x + 151200a b x + 282240a b x +--R + +--R 4 4 9 +--R 161280a b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 5670b x - 75600a b x - 272160a b x - 362880a b x +--R + +--R 4 4 9 +--R - 161280a b x +--R * +--R +---+ +-+ +--R \|- b \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R atan(------------------) +--R +---+ +--R x\|- b +--R + +--R 8 16 7 14 2 6 12 3 5 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+ +)clear all + +--S 582 of 1369 +t0:=(a+b*x^2)^(9/2)/x^24 +--R +--R +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R (1) ---------------------------------------------------- +--R 24 +--R x +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1369 +r0:=-1/23*(a+b*x^2)^(11/2)/(a*x^23)+4/161*b*(a+b*x^2)^(11/2)/(a^2*x^21)-_ + 40/3059*b^2*(a+b*x^2)^(11/2)/(a^3*x^19)+_ + 320/52003*b^3*(a+b*x^2)^(11/2)/(a^4*x^17)-_ + 128/52003*b^4*(a+b*x^2)^(11/2)/(a^5*x^15)+_ + 512/676039*b^5*(a+b*x^2)^(11/2)/(a^6*x^13)-_ + 1024/7436429*b^6*(a+b*x^2)^(11/2)/(a^7*x^11) +--R +--R +--R (2) +--R 11 22 10 20 2 9 18 3 8 16 4 7 14 +--R - 1024b x + 512a b x - 384a b x + 320a b x - 280a b x +--R + +--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4 +--R 252a b x - 231a b x - 530959a b x - 1826110a b x - 2406690a b x +--R + +--R 10 2 11 +--R - 1431859a b x - 323323a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 7 23 +--R 7436429a x +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 22 44 21 42 2 20 40 3 19 38 +--R 23552b x + 2060800a b x + 52859520a b x + 620470080a b x +--R + +--R 4 18 36 5 17 34 6 16 32 +--R 4007202600a b x + 15628090140a b x + 38569325025a b x +--R + +--R 7 15 30 8 14 28 9 13 26 +--R 61172146673a b x + 62501873434a b x + 68498444014a b x +--R + +--R 10 12 24 11 11 22 +--R 447722087813a b x + 3519807368805a b x +--R + +--R 12 10 20 13 9 18 +--R 18390187227048a b x + 66180088214128a b x +--R + +--R 14 8 16 15 7 14 +--R 170212073470272a b x + 319842513071872a b x +--R + +--R 16 6 12 17 5 10 +--R 443676599296000a b x + 454256483090432a b x +--R + +--R 18 4 8 19 3 6 +--R 339251670810624a b x + 179812413800448a b x +--R + +--R 20 2 4 21 2 22 +--R 64121040535552a b x + 13803312906240a b x + 1356114952192a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 23 46 22 44 2 21 42 3 20 40 +--R - 1024b x - 270848a b x - 11849600a b x - 202628160a b x +--R + +--R 4 19 38 5 18 36 6 17 34 +--R - 1783851480a b x - 9216565980a b x - 29953839435a b x +--R + +--R 7 16 32 8 15 30 9 14 28 +--R - 63364422286a b x - 88059985805a b x - 85139238184a b x +--R + +--R 10 13 26 11 12 24 12 11 22 +--R - 172487832517a b x - 1389299606422a b x - 9097536087003a b x +--R + +--R 13 10 20 14 9 18 +--R - 40522439458872a b x - 127747340088848a b x +--R + +--R 15 8 16 16 7 14 +--R - 293619192660032a b x - 500570144755968a b x +--R + +--R 17 6 12 18 5 10 +--R - 637481553092608a b x - 604911221161984a b x +--R + +--R 19 4 8 20 3 6 21 2 4 +--R - 421952481460224a b x - 210232277139456a b x - 70853182619648a b x +--R + +--R 22 2 23 +--R - 14481370382336a b x - 1356114952192a +--R / +--R 7 11 45 8 10 43 9 9 41 +--R 7436429a b x + 1963217256a b x + 85072747760a b x +--R + +--R 10 8 39 11 7 37 +--R 1429222162368a b x + 12250475677440a b x +--R + +--R 12 6 35 13 5 33 +--R 60980145594368a b x + 188484086382592a b x +--R + +--R 14 4 31 15 3 29 +--R 372825665372160a b x + 472245842804736a b x +--R + +--R 16 2 27 17 25 +--R 370388896317440a b x + 163750880477184a b x +--R + +--R 18 23 +--R 31190643900416a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 11 45 8 10 43 9 9 41 +--R - 171037867a b x - 15051332296a b x - 391334639696a b x +--R + +--R 10 8 39 11 7 37 +--R - 4696015676352a b x - 31306771175680a b x +--R + +--R 12 6 35 13 5 33 +--R - 127503940788224a b x - 333471845138432a b x +--R + +--R 14 4 31 15 3 29 +--R - 571666020237312a b x - 638920846147584a b x +--R + +--R 16 2 27 17 25 +--R - 448365506068480a b x - 179346202427392a b x +--R + +--R 18 23 +--R - 31190643900416a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 584 + +--S 585 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 586 + +)clear all + +--S 587 of 1369 +t0:=x^5*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 5 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1369 +r0:=27/64*(9+4*x^2)^(3/2)-9/160*(9+4*x^2)^(5/2)+1/448*(9+4*x^2)^(7/2) +--R +--R +--R +-------+ +--R 6 4 2 | 2 +--R (40x + 18x - 54x + 243)\|4x + 9 +--R (2) ------------------------------------ +--R 280 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 11 9 7 5 +--R - 327680x - 1437696x - 1589760x - 1310256x - 6062364x +--R + +--R 3 +--R - 8266860x - 2480058x +--R * +--R +-------+ +--R | 2 +--R \|4x + 9 +--R + +--R 14 12 10 8 6 4 +--R 655360x + 3612672x + 5999616x + 4844448x + 14451696x + 28934010x +--R + +--R 2 +--R 17360406x + 1594323 +--R / +--R +-------+ +--R 6 4 2 | 2 7 +--R (1146880x + 3225600x + 2177280x + 204120)\|4x + 9 - 2293760x +--R + +--R 5 3 +--R - 9031680x - 10160640x - 2857680x +--R Type: Union(Expression(Integer),...) +--E 589 + +--S 590 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 591 + +)clear all + +--S 592 of 1369 +t0:=x^4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 4 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1369 +r0:=729/512*asinh(2/3*x)-81/256*x*sqrt(9+4*x^2)+_ + 3/32*x^3*sqrt(9+4*x^2)+1/6*x^5*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 5 3 | 2 2x +--R (256x + 144x - 486x)\|4x + 9 + 2187asinh(--) +--R 3 +--R (2) ------------------------------------------------ +--R 1536 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 3 | 2 6 +--R (- 2239488x - 5038848x - 2125764x)\|4x + 9 + 4478976x +--R + +--R 4 2 +--R 15116544x + 12754584x + 1594323 +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R 11 9 7 5 3 +--R (- 524288x - 2064384x - 1492992x + 2332800x + 2729376x + 354294x) +--R * +--R +-------+ +--R | 2 +--R \|4x + 9 +--R + +--R 12 10 8 6 4 2 +--R 1048576x + 5308416x + 6967296x - 3172608x - 10707552x - 4251528x +--R / +--R +-------+ +--R 5 3 | 2 6 4 +--R (1572864x + 3538944x + 1492992x)\|4x + 9 - 3145728x - 10616832x +--R + +--R 2 +--R - 8957952x - 1119744 +--R Type: Union(Expression(Integer),...) +--E 594 + +--S 595 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 729log(\|4x + 9 - 2x) - 729asinh(--) +--R 3 +--R (4) ---------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 596 + +)clear all + +--S 597 of 1369 +t0:=x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1369 +r0:=-3/16*(9+4*x^2)^(3/2)+1/80*(9+4*x^2)^(5/2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (8x + 6x - 27)\|4x + 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 4096x - 14592x - 1296x + 34020x + 21870x)\|4x + 9 + 8192x +--R + +--R 8 6 4 2 +--R 38400x + 30240x - 77760x - 109350x - 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 599 + +--S 600 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 601 + +)clear all + +--S 602 of 1369 +t0:=x^2*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) x \|4x + 9 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1369 +r0:=-81/64*asinh(2/3*x)+9/32*x*sqrt(9+4*x^2)+1/4*x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 2x +--R (16x + 18x)\|4x + 9 - 81asinh(--) +--R 3 +--R (2) ------------------------------------ +--R 64 +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((5184x + 5832x)\|4x + 9 - 10368x - 23328x - 6561) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 6 +--R (- 2048x - 6912x - 6480x - 1458x)\|4x + 9 + 4096x + 18432x +--R + +--R 4 2 +--R 25920x + 11664x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (4096x + 4608x)\|4x + 9 - 8192x - 18432x - 5184 +--R Type: Union(Expression(Integer),...) +--E 604 + +--S 605 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 81log(\|4x + 9 - 2x) + 81asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 64 +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 606 + +)clear all + +--S 607 of 1369 +t0:=x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) x\|4x + 9 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1369 +r0:=1/12*(9+4*x^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x + 9)\|4x + 9 +--R (2) ------------------- +--R 12 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 128x - 504x - 486x)\|4x + 9 + 256x + 1296x + 1944x + 729 +--R (3) ------------------------------------------------------------------ +--R +-------+ +--R 2 | 2 3 +--R (192x + 108)\|4x + 9 - 384x - 648x +--R Type: Union(Expression(Integer),...) +--E 609 + +--S 610 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 611 + +)clear all + +--S 612 of 1369 +t0:=sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) \|4x + 9 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1369 +r0:=9/4*asinh(2/3*x)+1/2*x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 2x +--R 2x\|4x + 9 + 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 4 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 36x\|4x + 9 + 72x + 81)log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x - 18x)\|4x + 9 + 32x + 72x +--R / +--R +-------+ +--R | 2 2 +--R 16x\|4x + 9 - 32x - 36 +--R Type: Union(Expression(Integer),...) +--E 614 + +--S 615 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 9log(\|4x + 9 - 2x) - 9asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 616 + +)clear all + +--S 617 of 1369 +t0:=sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1369 +r0:=-3*atanh(1/3*sqrt(9+4*x^2))+sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +-------+ +--R \|4x + 9 | 2 +--R (2) - 3atanh(----------) + \|4x + 9 +--R 3 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 | 2 +--R (- 3\|4x + 9 + 6x)log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +-------+ +--R | 2 | 2 | 2 2 +--R (3\|4x + 9 - 6x)log(\|4x + 9 - 2x - 3) - 2x\|4x + 9 + 4x + 9 +--R / +--R +-------+ +--R | 2 +--R \|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 619 + +--S 620 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 3log(\|4x + 9 - 2x + 3) + 3log(\|4x + 9 - 2x - 3) + 3atanh(----------) +--R 3 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1369 +t0:=sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1369 +r0:=2*asinh(2/3*x)-sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 2x +--R - \|4x + 9 + 2x asinh(--) +--R 3 +--R (2) --------------------------- +--R x +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 2x\|4x + 9 + 4x )log(\|4x + 9 - 2x) - 9 +--R (3) ---------------------------------------------- +--R +-------+ +--R | 2 2 +--R x\|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 624 + +--S 625 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R (4) - 2log(\|4x + 9 - 2x) - 2asinh(--) - 2 +--R 3 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +)clear all + +--S 627 of 1369 +t0:=sqrt(9+4*x^2)/x^3 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1369 +r0:=-2/3*atanh(1/3*sqrt(9+4*x^2))-1/2*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x + 9 | 2 +--R - 4x atanh(----------) - 3\|4x + 9 +--R 3 +--R (2) ------------------------------------ +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x + 27)\|4x + 9 - 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 24x \|4x + 9 - 48x - 54x +--R Type: Union(Expression(Integer),...) +--E 629 + +--S 630 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------) +--R 3 +--R ---------------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 631 + +)clear all + +--S 632 of 1369 +t0:=sqrt(9+4*x^2)/x^4 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1369 +r0:=-1/27*(9+4*x^2)^(3/2)/x^3 +--R +--R +--R +-------+ +--R 2 | 2 +--R (- 4x - 9)\|4x + 9 +--R (2) --------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 | 2 4 2 +--R (16x + 18x)\|4x + 9 - 32x - 72x - 27 +--R (3) ----------------------------------------- +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x + 9x )\|4x + 9 - 32x - 54x +--R Type: Union(Expression(Integer),...) +--E 634 + +--S 635 of 1369 +m0:=a0-r0 +--R +--R +--R 8 +--R (4) - -- +--R 27 +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 636 + +)clear all + +--S 637 of 1369 +t0:=sqrt(9+4*x^2)/x^5 +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1369 +r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/4*sqrt(9+4*x^2)/x^4-1/18*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x + 9 2 | 2 +--R 8x atanh(----------) + (- 6x - 27)\|4x + 9 +--R 3 +--R (2) --------------------------------------------- +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (768x + 5184x + 8262x + 2187)\|4x + 9 - 1536x - 12096x - 27216x +--R + +--R - 17496x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (6912x + 7776x )\|4x + 9 - 13824x - 31104x - 8748x +--R Type: Union(Expression(Integer),...) +--E 639 + +--S 640 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------) +--R 3 +--R -------------------------------------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 641 + +)clear all + +--S 642 of 1369 +t0:=x^5*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 5 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1369 +r0:=-27/64*(9-4*x^2)^(3/2)+9/160*(9-4*x^2)^(5/2)-1/448*(9-4*x^2)^(7/2) +--R +--R +--R +---------+ +--R 6 4 2 | 2 +--R (40x - 18x - 54x - 243)\|- 4x + 9 +--R (2) -------------------------------------- +--R 280 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 12 10 8 6 | 2 14 12 +--R (- 420x + 7749x - 36855x + 51030x )\|- 4x + 9 - 80x + 4536x +--R + +--R 10 8 6 +--R - 44037x + 144585x - 153090x +--R / +--R +---------+ +--R 6 4 2 | 2 6 4 +--R (140x - 7560x + 56700x - 102060)\|- 4x + 9 - 2940x + 52920x +--R + +--R 2 +--R - 238140x + 306180 +--R Type: Union(Expression(Integer),...) +--E 644 + +--S 645 of 1369 +m0:=a0-r0 +--R +--R +--R 729 +--R (4) - --- +--R 280 +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 646 + +)clear all + +--S 647 of 1369 +t0:=x^4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 4 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1369 +r0:=729/512*asin(2/3*x)-81/256*x*sqrt(9-4*x^2)-_ + 3/32*x^3*sqrt(9-4*x^2)+1/6*x^5*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 5 3 | 2 2x +--R (256x - 144x - 486x)\|- 4x + 9 + 2187asin(--) +--R 3 +--R (2) ------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 4 2 | 2 6 4 +--R (- 19683x + 236196x - 531441)\|- 4x + 9 - 4374x + 177147x +--R + +--R 2 +--R - 1062882x + 1594323 +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 11 9 7 5 3 | 2 +--R (256x - 10512x + 67554x - 108621x - 65610x + 177147x)\|- 4x + 9 +--R + +--R 11 9 7 5 3 +--R - 4608x + 68256x - 277020x + 295245x + 314928x - 531441x +--R / +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (6912x - 82944x + 186624)\|- 4x + 9 + 1536x - 62208x + 373248x +--R + +--R - 559872 +--R Type: Union(Expression(Integer),...) +--E 649 + +--S 650 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 1458atan(----------------) - 729asin(--) +--R 2x 3 +--R (4) ------------------------------------------ +--R 512 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 651 + +)clear all + +--S 652 of 1369 +t0:=x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1369 +r0:=-3/16*(9-4*x^2)^(3/2)+1/80*(9-4*x^2)^(5/2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (8x - 6x - 27)\|- 4x + 9 +--R (2) ---------------------------- +--R 40 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 8 6 4 | 2 10 8 6 4 +--R (- 60x + 585x - 1215x )\|- 4x + 9 - 16x + 480x - 2565x + 3645x +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 | 2 4 2 +--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860 +--R Type: Union(Expression(Integer),...) +--E 654 + +--S 655 of 1369 +m0:=a0-r0 +--R +--R +--R 81 +--R (4) - -- +--R 40 +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 656 + +)clear all + +--S 657 of 1369 +t0:=x^2*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (1) x \|- 4x + 9 +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1369 +r0:=81/64*asin(2/3*x)-9/32*x*sqrt(9-4*x^2)+1/4*x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 2x +--R (16x - 18x)\|- 4x + 9 + 81asin(--) +--R 3 +--R (2) ------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +--R ((- 486x + 2187)\|- 4x + 9 - 162x + 2916x - 6561) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 7 5 3 | 2 7 5 3 +--R (16x - 306x + 972x - 729x)\|- 4x + 9 - 192x + 1512x - 3402x + 2187x +--R / +--R +---------+ +--R 2 | 2 4 2 +--R (192x - 864)\|- 4x + 9 + 64x - 1152x + 2592 +--R Type: Union(Expression(Integer),...) +--E 659 + +--S 660 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 162atan(----------------) - 81asin(--) +--R 2x 3 +--R (4) ---------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 661 + +)clear all + +--S 662 of 1369 +t0:=x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) x\|- 4x + 9 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1369 +r0:=-1/12*(9-4*x^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x - 9)\|- 4x + 9 +--R (2) --------------------- +--R 12 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (- 18x + 81x )\|- 4x + 9 - 8x + 108x - 243x +--R (3) ------------------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (6x - 54)\|- 4x + 9 - 54x + 162 +--R Type: Union(Expression(Integer),...) +--E 664 + +--S 665 of 1369 +m0:=a0-r0 +--R +--R +--R 9 +--R (4) - - +--R 4 +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 666 + +)clear all + +--S 667 of 1369 +t0:=sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) \|- 4x + 9 +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1369 +r0:=9/4*asin(2/3*x)+1/2*x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 2x +--R 2x\|- 4x + 9 + 9asin(--) +--R 3 +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R | 2 2 \|- 4x + 9 - 3 +--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +--R (2x - 9x)\|- 4x + 9 - 12x + 27x +--R / +--R +---------+ +--R | 2 2 +--R 6\|- 4x + 9 + 4x - 18 +--R Type: Union(Expression(Integer),...) +--E 669 + +--S 670 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 18atan(----------------) - 9asin(--) +--R 2x 3 +--R (4) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 671 + +)clear all + +--S 672 of 1369 +t0:=sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1369 +r0:=-3*atanh(1/3*sqrt(9-4*x^2))+sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +---------+ +--R \|- 4x + 9 | 2 +--R (2) - 3atanh(------------) + \|- 4x + 9 +--R 3 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +--R | 2 \|- 4x + 9 - 3 2 +--R (3\|- 4x + 9 - 9)log(----------------) - 4x +--R x +--R (3) ---------------------------------------------- +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R Type: Union(Expression(Integer),...) +--E 674 + +--S 675 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R (4) 3log(----------------) + 3atanh(------------) + 3 +--R x 3 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1369 +t0:=sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 677 + +--S 678 of 1369 +r0:=-2*asin(2/3*x)-sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 2x +--R - \|- 4x + 9 - 2x asin(--) +--R 3 +--R (2) ---------------------------- +--R x +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +---------+ +--R | 2 \|- 4x + 9 - 3 | 2 2 +--R (4x\|- 4x + 9 - 12x)atan(----------------) + 3\|- 4x + 9 + 4x - 9 +--R 2x +--R (3) ---------------------------------------------------------------------- +--R +---------+ +--R | 2 +--R x\|- 4x + 9 - 3x +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R (4) 4atan(----------------) + 2asin(--) +--R 2x 3 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1369 +t0:=sqrt(9-4*x^2)/x^3 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1369 +r0:=2/3*atanh(1/3*sqrt(9-4*x^2))-1/2*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x + 9 | 2 +--R 4x atanh(------------) - 3\|- 4x + 9 +--R 3 +--R (2) -------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 4 2 \|- 4x + 9 - 3 +--R (- 12x \|- 4x + 9 - 8x + 36x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 6x + 27)\|- 4x + 9 + 36x - 81 +--R / +--R +---------+ +--R 2 | 2 4 2 +--R 18x \|- 4x + 9 + 12x - 54x +--R Type: Union(Expression(Integer),...) +--E 684 + +--S 685 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R - 2log(----------------) - 2atanh(------------) +--R x 3 +--R (4) ----------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +)clear all + +--S 687 of 1369 +t0:=sqrt(9-4*x^2)/x^4 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1369 +r0:=-1/27*(9-4*x^2)^(3/2)/x^3 +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x - 9)\|- 4x + 9 +--R (2) --------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (- 36x + 189x - 243)\|- 4x + 9 - 16x + 216x - 729x + 729 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +--R (27x - 243x )\|- 4x + 9 - 243x + 729x +--R Type: Union(Expression(Integer),...) +--E 689 + +--S 690 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 691 + +)clear all + +--S 692 of 1369 +t0:=sqrt(9-4*x^2)/x^5 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (1) ------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1369 +r0:=2/27*atanh(1/3*sqrt(9-4*x^2))-1/4*sqrt(9-4*x^2)/x^4+1/18*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x + 9 2 | 2 +--R 8x atanh(------------) + (6x - 27)\|- 4x + 9 +--R 3 +--R (2) ----------------------------------------------- +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +--R ((- 48x + 216x )\|- 4x + 9 - 16x + 288x - 648x ) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R log(----------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 2 +--R (12x - 270x + 1458x - 2187)\|- 4x + 9 - 144x + 1620x - 5832x + 6561 +--R / +--R +---------+ +--R 6 4 | 2 8 6 4 +--R (648x - 2916x )\|- 4x + 9 + 216x - 3888x + 8748x +--R Type: Union(Expression(Integer),...) +--E 694 + +--S 695 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R - 2log(----------------) - 2atanh(------------) +--R x 3 +--R (4) ----------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 696 + +)clear all + +--S 697 of 1369 +t0:=x^5*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 5 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1369 +r0:=27/64*(-9+4*x^2)^(3/2)+9/160*(-9+4*x^2)^(5/2)+1/448*(-9+4*x^2)^(7/2) +--R +--R +--R +-------+ +--R 6 4 2 | 2 +--R (40x - 18x - 54x - 243)\|4x - 9 +--R (2) ------------------------------------ +--R 280 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 13 11 9 7 5 +--R - 327680x + 1437696x - 1589760x + 1310256x - 6062364x +--R + +--R 3 +--R 8266860x - 2480058x +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 +--R + +--R 14 12 10 8 6 4 +--R 655360x - 3612672x + 5999616x - 4844448x + 14451696x - 28934010x +--R + +--R 2 +--R 17360406x - 1594323 +--R / +--R +-------+ +--R 6 4 2 | 2 7 +--R (1146880x - 3225600x + 2177280x - 204120)\|4x - 9 - 2293760x +--R + +--R 5 3 +--R 9031680x - 10160640x + 2857680x +--R Type: Union(Expression(Integer),...) +--E 699 + +--S 700 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 701 + +)clear all + +--S 702 of 1369 +t0:=x^4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 4 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1369 +r0:=-729/512*atanh(2*x/sqrt(-9+4*x^2))-81/256*x*sqrt(-9+4*x^2)-_ + 3/32*x^3*sqrt(-9+4*x^2)+1/6*x^5*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 5 3 | 2 +--R - 2187atanh(----------) + (256x - 144x - 486x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 3 | 2 6 4 +--R (2239488x - 5038848x + 2125764x)\|4x - 9 - 4478976x + 15116544x +--R + +--R 2 +--R - 12754584x + 1594323 +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R 11 9 7 5 3 +--R (- 524288x + 2064384x - 1492992x - 2332800x + 2729376x - 354294x) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 +--R + +--R 12 10 8 6 4 2 +--R 1048576x - 5308416x + 6967296x + 3172608x - 10707552x + 4251528x +--R / +--R +-------+ +--R 5 3 | 2 6 4 +--R (1572864x - 3538944x + 1492992x)\|4x - 9 - 3145728x + 10616832x +--R + +--R 2 +--R - 8957952x + 1119744 +--R Type: Union(Expression(Integer),...) +--E 704 + +--S 705 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 729log(\|4x - 9 - 2x) + 729atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ---------------------------------------------- +--R 512 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 706 + +)clear all + +--S 707 of 1369 +t0:=x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1369 +r0:=3/16*(-9+4*x^2)^(3/2)+1/80*(-9+4*x^2)^(5/2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (8x - 6x - 27)\|4x - 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 4096x + 14592x - 1296x - 34020x + 21870x)\|4x - 9 + 8192x +--R + +--R 8 6 4 2 +--R - 38400x + 30240x + 77760x - 109350x + 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 709 + +--S 710 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 711 + +)clear all + +--S 712 of 1369 +t0:=x^2*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (1) x \|4x - 9 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1369 +r0:=-81/64*atanh(2*x/sqrt(-9+4*x^2))-9/32*x*sqrt(-9+4*x^2)+_ + 1/4*x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 3 | 2 +--R - 81atanh(----------) + (16x - 18x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((5184x - 5832x)\|4x - 9 - 10368x + 23328x - 6561) +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 6 +--R (- 2048x + 6912x - 6480x + 1458x)\|4x - 9 + 4096x - 18432x +--R + +--R 4 2 +--R 25920x - 11664x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (4096x - 4608x)\|4x - 9 - 8192x + 18432x - 5184 +--R Type: Union(Expression(Integer),...) +--E 714 + +--S 715 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 81log(\|4x - 9 - 2x) + 81atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) -------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 716 + +)clear all + +--S 717 of 1369 +t0:=x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) x\|4x - 9 +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1369 +r0:=1/12*(-9+4*x^2)^(3/2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x - 9)\|4x - 9 +--R (2) ------------------- +--R 12 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 128x + 504x - 486x)\|4x - 9 + 256x - 1296x + 1944x - 729 +--R (3) ------------------------------------------------------------------ +--R +-------+ +--R 2 | 2 3 +--R (192x - 108)\|4x - 9 - 384x + 648x +--R Type: Union(Expression(Integer),...) +--E 719 + +--S 720 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 721 + +)clear all + +--S 722 of 1369 +t0:=sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R (1) \|4x - 9 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1369 +r0:=-9/4*atanh(2*x/sqrt(-9+4*x^2))+1/2*x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x | 2 +--R - 9atanh(----------) + 2x\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ----------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (36x\|4x - 9 - 72x + 81)log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x + 18x)\|4x - 9 + 32x - 72x +--R / +--R +-------+ +--R | 2 2 +--R 16x\|4x - 9 - 32x + 36 +--R Type: Union(Expression(Integer),...) +--E 724 + +--S 725 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 9log(\|4x - 9 - 2x) + 9atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 726 + +)clear all + +--S 727 of 1369 +t0:=sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1369 +r0:=-3*atan(1/3*sqrt(-9+4*x^2))+sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +-------+ +--R \|4x - 9 | 2 +--R (2) - 3atan(----------) + \|4x - 9 +--R 3 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R +-------+ | 2 +-------+ +--R | 2 \|4x - 9 - 2x | 2 2 +--R (- 6\|4x - 9 + 12x)atan(---------------) - 2x\|4x - 9 + 4x - 9 +--R 3 +--R (3) ------------------------------------------------------------------- +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 729 + +--S 730 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R (4) 3atan(----------) - 6atan(---------------) +--R 3 3 +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 731 + +)clear all + +--S 732 of 1369 +t0:=sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1369 +r0:=2*atanh(2*x/sqrt(-9+4*x^2))-sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R 2x | 2 +--R 2x atanh(----------) - \|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 2x\|4x - 9 + 4x )log(\|4x - 9 - 2x) + 9 +--R (3) ---------------------------------------------- +--R +-------+ +--R | 2 2 +--R x\|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 734 + +--S 735 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R (4) - 2log(\|4x - 9 - 2x) - 2atanh(----------) - 2 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1369 +t0:=sqrt(-9+4*x^2)/x^3 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1369 +r0:=2/3*atan(1/3*sqrt(-9+4*x^2))-1/2*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x - 9 | 2 +--R 4x atan(----------) - 3\|4x - 9 +--R 3 +--R (2) --------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-------+ | 2 +--R 3 | 2 4 2 \|4x - 9 - 2x +--R (32x \|4x - 9 - 64x + 72x )atan(---------------) +--R 3 +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x - 27)\|4x - 9 - 48x + 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 24x \|4x - 9 - 48x + 54x +--R Type: Union(Expression(Integer),...) +--E 739 + +--S 740 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1369 +t0:=sqrt(-9+4*x^2)/x^4 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1369 +r0:=1/27*(-9+4*x^2)^(3/2)/x^3 +--R +--R +--R +-------+ +--R 2 | 2 +--R (4x - 9)\|4x - 9 +--R (2) ------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 | 2 4 2 +--R (16x - 18x)\|4x - 9 - 32x + 72x - 27 +--R (3) ----------------------------------------- +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x - 9x )\|4x - 9 - 32x + 54x +--R Type: Union(Expression(Integer),...) +--E 744 + +--S 745 of 1369 +m0:=a0-r0 +--R +--R +--R 8 +--R (4) -- +--R 27 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 1369 +t0:=sqrt(-9+4*x^2)/x^5 +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1369 +r0:=2/27*atan(1/3*sqrt(-9+4*x^2))-1/4*sqrt(-9+4*x^2)/x^4+_ + 1/18*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x - 9 2 | 2 +--R 8x atan(----------) + (6x - 27)\|4x - 9 +--R 3 +--R (2) ------------------------------------------ +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x ) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R atan(---------------) +--R 3 +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x + 5184x - 8262x + 2187)\|4x - 9 + 1536x - 12096x + 27216x +--R + +--R - 17496x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (6912x - 7776x )\|4x - 9 - 13824x + 31104x - 8748x +--R Type: Union(Expression(Integer),...) +--E 749 + +--S 750 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 751 + +)clear all + +--S 752 of 1369 +t0:=x^5*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 5 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1369 +r0:=-27/64*(-9-4*x^2)^(3/2)-9/160*(-9-4*x^2)^(5/2)-1/448*(-9-4*x^2)^(7/2) +--R +--R +--R +---------+ +--R 6 4 2 | 2 +--R (40x + 18x - 54x + 243)\|- 4x - 9 +--R (2) -------------------------------------- +--R 280 +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 12 10 8 6 | 2 +--R (420x + 7749x + 36855x + 51030x )\|- 4x - 9 +--R + +--R 14 12 10 8 6 +---+ +--R (- 80x - 4536x - 44037x - 144585x - 153090x )\|- 1 +--R / +--R +---------+ +--R 6 4 2 +---+ | 2 6 4 +--R (140x + 7560x + 56700x + 102060)\|- 1 \|- 4x - 9 + 2940x + 52920x +--R + +--R 2 +--R 238140x + 306180 +--R Type: Union(Expression(Integer),...) +--E 754 + +--S 755 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 6 4 2 | 2 +--R (- 729x - 39366x - 295245x - 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (15309x + 275562x + 1240029x + 1594323)\|- 1 +--R / +--R +---------+ +--R 6 4 2 +---+ | 2 6 +--R (280x + 15120x + 113400x + 204120)\|- 1 \|- 4x - 9 + 5880x +--R + +--R 4 2 +--R 105840x + 476280x + 612360 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 756 + +)clear all + +--S 757 of 1369 +t0:=x^4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 4 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1369 +r0:=-729/512*atan(2*x/sqrt(-9-4*x^2))-81/256*x*sqrt(-9-4*x^2)+_ + 3/32*x^3*sqrt(-9-4*x^2)+1/6*x^5*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 5 3 | 2 +--R - 2187atan(------------) + (256x + 144x - 486x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------------------------------------------------------- +--R 1536 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 4 2 | 2 +--R (- 19683x - 236196x - 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (4374x + 177147x + 1062882x + 1594323)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 4 2 | 2 +--R (19683x + 236196x + 531441)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (- 4374x - 177147x - 1062882x - 1594323)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 11 9 7 5 3 | 2 +--R (512x + 21024x + 135108x + 217242x - 131220x - 354294x)\|- 4x - 9 +--R + +--R 11 9 7 5 3 +---+ +--R (- 9216x - 136512x - 554040x - 590490x + 629856x + 1062882x)\|- 1 +--R / +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (13824x + 165888x + 373248)\|- 1 \|- 4x - 9 + 3072x + 124416x +--R + +--R 2 +--R 746496x + 1119744 +--R Type: Union(Expression(Integer),...) +--E 759 + +--S 760 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 +--R (- 6561x - 78732x - 177147)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (1458x + 59049x + 354294x + 531441)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 4 2 | 2 +--R (6561x + 78732x + 177147)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (- 1458x - 59049x - 354294x - 531441)\|- 1 +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (6561x + 78732x + 177147)\|- 1 \|- 4x - 9 + 1458x + 59049x +--R + +--R 2 +--R 354294x + 531441 +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 4 2 +---+ | 2 6 4 +--R (4608x + 55296x + 124416)\|- 1 \|- 4x - 9 + 1024x + 41472x +--R + +--R 2 +--R 248832x + 373248 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 761 + +)clear all + +--S 762 of 1369 +t0:=x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1369 +r0:=3/16*(-9-4*x^2)^(3/2)+1/80*(-9-4*x^2)^(5/2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (8x + 6x - 27)\|- 4x - 9 +--R (2) ---------------------------- +--R 40 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 8 6 4 | 2 +--R (60x + 585x + 1215x )\|- 4x - 9 +--R + +--R 10 8 6 4 +---+ +--R (- 16x - 480x - 2565x - 3645x )\|- 1 +--R / +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860 +--R Type: Union(Expression(Integer),...) +--E 764 + +--S 765 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 4 2 +---+ +--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1 +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720 +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 766 + +)clear all + +--S 767 of 1369 +t0:=x^2*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (1) x \|- 4x - 9 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1369 +r0:=81/64*atan(2*x/sqrt(-9-4*x^2))+9/32*x*sqrt(-9-4*x^2)+1/4*x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 3 | 2 +--R 81atan(------------) + (16x + 18x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ----------------------------------------------- +--R 64 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 7 5 3 | 2 +--R (32x + 612x + 1944x + 1458x)\|- 4x - 9 +--R + +--R 7 5 3 +---+ +--R (- 384x - 3024x - 6804x - 4374x)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184 +--R Type: Union(Expression(Integer),...) +--E 769 + +--S 770 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((486x + 2187)\|- 4x - 9 + (- 162x - 2916x - 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 486x - 2187)\|- 4x - 9 + (162x + 2916x + 6561)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 +---+ | 2 4 2 +--R ((- 486x - 2187)\|- 1 \|- 4x - 9 - 162x - 2916x - 6561) +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (384x + 1728)\|- 1 \|- 4x - 9 + 128x + 2304x + 5184 +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 771 + +)clear all + +--S 772 of 1369 +t0:=x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) x\|- 4x - 9 +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1369 +r0:=-1/12*(-9-4*x^2)^(3/2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (4x + 9)\|- 4x - 9 +--R (2) --------------------- +--R 12 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +---+ +--R (18x + 81x )\|- 4x - 9 + (- 8x - 108x - 243x )\|- 1 +--R (3) --------------------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (6x + 54)\|- 1 \|- 4x - 9 + 54x + 162 +--R Type: Union(Expression(Integer),...) +--E 774 + +--S 775 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1 +--R (4) --------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (4x + 36)\|- 1 \|- 4x - 9 + 36x + 108 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 776 + +)clear all + +--S 777 of 1369 +t0:=sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R (1) \|- 4x - 9 +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1369 +r0:=-9/4*atan(2*x/sqrt(-9-4*x^2))+1/2*x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x | 2 +--R - 9atan(------------) + 2x\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (4x + 18x)\|- 4x - 9 + (- 24x - 54x)\|- 1 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 12\|- 1 \|- 4x - 9 + 8x + 36 +--R Type: Union(Expression(Integer),...) +--E 779 + +--S 780 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 2x +--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 12\|- 1 \|- 4x - 9 + 8x + 36 +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 781 + +)clear all + +--S 782 of 1369 +t0:=sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1369 +r0:=-3*atan(1/3*sqrt(-9-4*x^2))+sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +---------+ +--R \|- 4x - 9 | 2 +--R (2) - 3atan(------------) + \|- 4x - 9 +--R 3 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 +---+ \|- 4x - 9 - 3\|- 1 2 +---+ +--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------) - 4x \|- 1 +--R x +--R (3) ------------------------------------------------------------------ +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Union(Expression(Integer),...) +--E 784 + +--S 785 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 3\|- 4x - 9 + 9\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---------+ +--R +---+ | 2 \|- 4x - 9 | 2 +---+ +--R (3\|- 1 \|- 4x - 9 + 9)atan(------------) - 3\|- 4x - 9 + 9\|- 1 +--R 3 +--R / +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 786 + +)clear all + +--S 787 of 1369 +t0:=sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1369 +r0:=-2*atan(2*x/sqrt(-9-4*x^2))-sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R 2x | 2 +--R - 2x atan(------------) - \|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R x +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1 +--R (2x\|- 1 \|- 4x - 9 + 6x)log(-----------------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1 +--R (- 2x\|- 1 \|- 4x - 9 - 6x)log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 +--R 3\|- 1 \|- 4x - 9 + 4x + 9 +--R / +--R +---------+ +--R | 2 +---+ +--R x\|- 4x - 9 - 3x\|- 1 +--R Type: Union(Expression(Integer),...) +--E 789 + +--S 790 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (2x - 3)\|- 1 +--R (2\|- 1 \|- 4x - 9 + 6)log(-----------------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +---+ +--R +---+ | 2 \|- 4x - 9 + (- 2x - 3)\|- 1 +--R (- 2\|- 1 \|- 4x - 9 - 6)log(-------------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ 2x +--R (2\|- 4x - 9 - 6\|- 1 )atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 791 + +)clear all + +--S 792 of 1369 +t0:=sqrt(-9-4*x^2)/x^3 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1369 +r0:=-2/3*atan(1/3*sqrt(-9-4*x^2))-1/2*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x - 9 | 2 +--R - 4x atan(------------) - 3\|- 4x - 9 +--R 3 +--R (2) --------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 6x - 27)\|- 4x - 9 + (36x + 81)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R 18x \|- 1 \|- 4x - 9 + 12x + 54x +--R Type: Union(Expression(Integer),...) +--E 794 + +--S 795 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R +---+ | 2 2 \|- 4x - 9 +--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------) +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 9\|- 1 \|- 4x - 9 + 6x + 27 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 796 + +)clear all + +--S 797 of 1369 +t0:=sqrt(-9-4*x^2)/x^4 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1369 +r0:=1/27*(-9-4*x^2)^(3/2)/x^3 +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 4x - 9)\|- 4x - 9 +--R (2) ----------------------- +--R 3 +--R 27x +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 +---+ | 2 6 4 2 +--R (36x + 189x + 243)\|- 1 \|- 4x - 9 + 16x + 216x + 729x + 729 +--R (3) ------------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +---+ +--R (27x + 243x )\|- 4x - 9 + (- 243x - 729x )\|- 1 +--R Type: Union(Expression(Integer),...) +--E 799 + +--S 800 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 801 + +)clear all + +--S 802 of 1369 +t0:=sqrt(-9-4*x^2)/x^5 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (1) ------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1369 +r0:=2/27*atan(1/3*sqrt(-9-4*x^2))-1/4*sqrt(-9-4*x^2)/x^4-_ + 1/18*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x - 9 2 | 2 +--R 8x atan(------------) + (- 6x - 27)\|- 4x - 9 +--R 3 +--R (2) ------------------------------------------------ +--R 4 +--R 108x +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +---+ +--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 +--R (- 12x - 270x - 1458x - 2187)\|- 4x - 9 +--R + +--R 6 4 2 +---+ +--R (144x + 1620x + 5832x + 6561)\|- 1 +--R / +--R +---------+ +--R 6 4 +---+ | 2 8 6 4 +--R (648x + 2916x )\|- 1 \|- 4x - 9 + 216x + 3888x + 8748x +--R Type: Union(Expression(Integer),...) +--E 804 + +--S 805 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 +---+ | 2 4 2 \|- 4x - 9 +--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------) +--R 3 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (162x + 729)\|- 1 \|- 4x - 9 + 54x + 972x + 2187 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1369 +t0:=x^m/(a+b*x^2)^(1/2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1369 +--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2)) +--E 808 + +--S 809 of 1369 +--a0:=integrate(t0,x) +--E 809 + +--S 810 of 1369 +--m0:=a0-r0 +--E 810 + +--S 811 of 1369 +--d0:=D(m0,x) +--E 811 + +)clear all + +--S 812 of 1369 +t0:=x^5/sqrt(a+b*x^2) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1369 +r0:=8/15*a^2*sqrt(a+b*x^2)/b^3-4/15*a*x^2*sqrt(a+b*x^2)/b^2+_ + 1/5*x^4*sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (3b x - 4a b x + 8a )\|b x + a +--R (2) ---------------------------------- +--R 3 +--R 15b +--R Type: Expression(Integer) +--E 813 + +--S 814 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 8 2 6 | 2 2 10 8 2 6 +-+ +--R (- 15a b x - 40a x )\|b x + a + (3b x + 35a b x + 40a x )\|a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15b x + 180a b x + 240a )\|a \|b x + a - 75a b x - 300a b x - 240a +--R Type: Union(Expression(Integer),...) +--E 814 + +--S 815 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 4 4 2 5 | 2 +--R (8a b x + 96a b x + 128a )\|b x + a +--R + +--R 3 2 4 4 2 5 +-+ +--R (- 40a b x - 160a b x - 128a )\|a +--R / +--R +--------+ +--R 5 4 4 2 2 3 +-+ | 2 5 4 2 4 2 +--R (15b x + 180a b x + 240a b )\|a \|b x + a - 75a b x - 300a b x +--R + +--R 3 3 +--R - 240a b +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 816 + +)clear all + +--S 817 of 1369 +t0:=x^4/sqrt(a+b*x^2) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1369 +r0:=3/8*a^2*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + 3/8*a*x*sqrt(a+b*x^2)/b^2+1/4*x^3*sqrt(a+b*x^2)/b +--R +--R +--R +-+ +--------+ +--R 2 x\|b 3 +-+ | 2 +--R 3a atanh(-----------) + (2b x - 3a x)\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24a )\|a \|b x + a - 3a b x - 24a b x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2b x - 13a b x + 8a b x + 24a x)\|b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8b x + 12a b x - 20a b x - 24a x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32b x + 64a b )\|a \|b \|b x + a + (- 8b x - 64a b x - 64a b )\|b +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48a )\|a \|b x + a - 6a b x - 48a b x - 48a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2b x - 13a b x + 8a b x + 24a x)\|- b \|b x + a +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8b x + 12a b x - 20a b x - 24a x)\|- b \|a +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32b x + 64a b )\|- b \|a \|b x + a +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8b x - 64a b x - 64a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 819 + +--S 820 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R 2 (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R 2 x\|b +--R - 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R 2 +---+ x\|b 2 +-+ \|- b \|b x + a - \|- b \|a +--R - 3a \|- b atanh(-----------) + 6a \|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R --------------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 8b \|- b \|b +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1369 +t0:=x^3/sqrt(a+b*x^2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1369 +r0:=-2/3*a*sqrt(a+b*x^2)/b^2+1/3*x^2*sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x - 2a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3a x \|b x + a + (b x + 3a x )\|a +--R (3) --------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3b x + 12a)\|a \|b x + a - 9a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 826 + +--S 827 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R (- 2a b x - 8a )\|b x + a + (6a b x + 8a )\|a +--R (4) -------------------------------------------------- +--R +--------+ +--R 3 2 2 +-+ | 2 3 2 2 2 +--R (3b x + 12a b )\|a \|b x + a - 9a b x - 12a b +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 828 + +)clear all + +--S 829 of 1369 +t0:=x^2/sqrt(a+b*x^2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1369 +r0:=-1/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)+1/2*x*sqrt(a+b*x^2)/b +--R +--R +--R +-+ +--------+ +--R x\|b +-+ | 2 +--R - a atanh(-----------) + x\|b \|b x + a +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2a\|a \|b x + a - a b x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- b x - 2a x)\|b \|b x + a + (2b x + 2a x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4b\|a \|b \|b x + a + (- 2b x - 4a b)\|b +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4a\|a \|b x + a + 2a b x + 4a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- b x - 2a x)\|- b \|b x + a + (2b x + 2a x)\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4b\|- b \|a \|b x + a + (- 2b x - 4a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 831 + +--S 832 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R a\|- b atanh(-----------) - 2a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2b\|- b \|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 835 + +)clear all + +--S 836 of 1369 +t0:=x/sqrt(a+b*x^2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1369 +r0:=sqrt(a+b*x^2)/b +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|a +--R (3) ------------------- +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R Type: Union(Expression(Integer),...) +--E 838 + +--S 839 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 2 +-+ +--R a\|b x + a - a\|a +--R (4) ---------------------- +--R +--------+ +--R +-+ | 2 +--R b\|a \|b x + a - a b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 840 + +)clear all + +--S 841 of 1369 +t0:=1/sqrt(a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R [-------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R 2atan(------------------------------) +--R b x +--R -------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 843 + +--S 844 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1369 +t0:=1/(x*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 2 +--R x\|b x + a +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|b x + a - \|a +--R \|a log(------------------) +--R x +--R (3) --------------------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R log(------------------) + atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1369 +t0:=1/(x^2*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1369 +r0:=-sqrt(a+b*x^2)/(a*x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) - ----------- +--R a x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R (3) -------------------------- +--R +--------+ +--R | 2 +-+ +--R a x\|b x + a - a x\|a +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1369 +t0:=1/(x^3*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1369 +r0:=1/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)-1/2*sqrt(a+b*x^2)/(a*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 \|b x + a +-+ | 2 +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 2 +-+ +--R 2a x \|a +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|b x + a - \|a +--R (- 2a b x \|b x + a + (b x + 2a b x )\|a )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2a )\|b x + a + (- 2a b x - 2a )\|a +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 4 3 2 +--R 4a x \|a \|b x + a - 2a b x - 4a x +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R \|b x + a - \|a \|b x + a +--R - b log(------------------) - b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1369 +t0:=1/(x^4*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1369 +r0:=-1/3*sqrt(a+b*x^2)/(a*x^3)+2/3*b*sqrt(a+b*x^2)/(a^2*x) +--R +--R +--R +--------+ +--R 2 | 2 +--R (2b x - a)\|b x + a +--R (2) ---------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 6b x - 5a b x + 4a )\|a \|b x + a + 2b x + 9a b x + 3a b x - 4a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12a x )\|b x + a + (- 9a b x - 12a x )\|a +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1369 +t0:=1/(x^5*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 | 2 +--R x \|b x + a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1369 +r0:=-3/8*b^2*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)-_ + 1/4*sqrt(a+b*x^2)/(a*x^4)+3/8*b*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R | 2 +--------+ +--R 2 4 \|b x + a 2 +-+ | 2 +--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 4 +-+ +--R 8a x \|a +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|b x + a +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3b x - 24a b x - 24a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (- 3a b x - 22a b x - 8a b x + 16a )\|b x + a +--R + +--R 3 6 2 2 4 4 +-+ +--R (12a b x + 28a b x - 16a )\|a +--R / +--R +--------+ +--R 3 6 4 4 +-+ | 2 3 2 8 4 6 5 4 +--R (32a b x + 64a x )\|a \|b x + a - 8a b x - 64a b x - 64a x +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +-+ | 2 +--R 2 \|b x + a - \|a 2 \|b x + a +--R 3b log(------------------) + 3b atanh(-----------) +--R x +-+ +--R \|a +--R (4) -------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1369 +t0:=x^m/(a+b*x^2)^(3/2) +--R +--R +--R m +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1369 +--r0:=x^(1+m)/(a*sqrt(a+b*x^2))-m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a*(1+m)*sqrt(a+b*x^2)) +--E 874 + +--S 875 of 1369 +--a0:=integrate(t0,x) +--E 875 + +--S 876 of 1369 +--m0:=a0-r0 +--E 876 + +--S 877 of 1369 +--d0:=D(m0,x) +--E 877 + +)clear all + +--S 878 of 1369 +t0:=x^5/(a+b*x^2)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1369 +r0:=1/3*(a+b*x^2)^(3/2)/b^3-a^2/(b^3*sqrt(a+b*x^2))-2*a*sqrt(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R b x - 4a b x - 8a +--R (2) -------------------- +--R +--------+ +--R 3 | 2 +--R 3b \|b x + a +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4a x \|b x + a + (b x + 4a x )\|a +--R (3) --------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (3b x + 24a b x + 24a )\|a \|b x + a - 12a b x - 36a b x - 24a +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R (- 32a b x - 64a )\|a \|b x + a + 8a b x + 64a b x + 64a +--R (4) ------------------------------------------------------------------ +--R +--------+ +--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+ +--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1369 +t0:=x^4/(a+b*x^2)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1369 +r0:=-3/2*a*atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + x^3/(b*sqrt(a+b*x^2))+3/2*x*sqrt(a+b*x^2)/b^2 +--R +--R +--R +--------+ +-+ +--R | 2 x\|b 3 +-+ +--R - 3a\|b x + a atanh(-----------) + (b x + 3a x)\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ----------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 +--R 2b \|b \|b x + a +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((9a b x + 12a )\|a \|b x + a - 3a b x - 15a b x - 12a ) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (- b x - 7a b x - 12a x)\|b \|b x + a +--R + +--R 2 5 3 2 +-+ +-+ +--R (3b x + 13a b x + 12a x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (6b x + 8a b )\|a \|b \|b x + a + (- 2b x - 10a b x - 8a b )\|b +--R , +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((- 18a b x - 24a )\|a \|b x + a + 6a b x + 30a b x + 24a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (- b x - 7a b x - 12a x)\|- b \|b x + a +--R + +--R 2 5 3 2 +---+ +-+ +--R (3b x + 13a b x + 12a x)\|- b \|a +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+ +--R (6b x + 8a b )\|- b \|a \|b x + a + (- 2b x - 10a b x - 8a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 885 + +--S 886 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 3a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 3a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 3a\|- b atanh(-----------) - 6a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 889 + +)clear all + +--S 890 of 1369 +t0:=x^3/(a+b*x^2)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1369 +r0:=a/(b^2*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^2 +--R +--R +--R 2 +--R b x + 2a +--R (2) ------------- +--R +--------+ +--R 2 | 2 +--R b \|b x + a +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R x \|a +--R (3) ------------------------------------------ +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (b x + 2a)\|a \|b x + a - 2a b x - 2a +--R Type: Union(Expression(Integer),...) +--E 892 + +--S 893 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +-+ | 2 2 2 +--R 4a\|a \|b x + a - 2a b x - 4a +--R (4) --------------------------------------- +--R +--------+ +--R 2 | 2 3 2 2 +-+ +--R 2a b \|b x + a + (- b x - 2a b )\|a +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1369 +t0:=x^2/(a+b*x^2)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(3/2)-x/(b*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +-+ +--R | 2 x\|b +-+ +--R \|b x + a atanh(-----------) - x\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------------------------- +--R +--------+ +--R +-+ | 2 +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|a \|b x + a - b x - a) +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R x\|b \|b x + a - x\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R b\|a \|b \|b x + a + (- b x - a b)\|b +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 \|- b \|b x + a - \|- b \|a +--R (2\|a \|b x + a - 2b x - 2a)atan(------------------------------) +--R b x +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R x\|- b \|b x + a - x\|- b \|a +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R b\|- b \|a \|b x + a + (- b x - a b)\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 897 + +--S 898 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R b\|- b \|b +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 901 + +)clear all + +--S 902 of 1369 +t0:=x/(a+b*x^2)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1369 +r0:=(-1)/(b*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (2) - ------------ +--R +--------+ +--R | 2 +--R b\|b x + a +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|a +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R a\|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 904 + +--S 905 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +-+ | 2 +--R - \|a \|b x + a + a +--R (4) ------------------------ +--R +--------+ +--R | 2 +-+ +--R a b\|b x + a - a b\|a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 906 + +)clear all + +--S 907 of 1369 +t0:=1/(a+b*x^2)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1369 +r0:=x/(a*sqrt(a+b*x^2)) +--R +--R +--R x +--R (2) ------------ +--R +--------+ +--R | 2 +--R a\|b x + a +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R - x\|b x + a + x\|a +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R a\|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 909 + +--S 910 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 911 + +)clear all + +--S 912 of 1369 +t0:=1/(x*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R 3 | 2 +--R (b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1369 +r0:=-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(3/2)+1/(a*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 \|b x + a +-+ +--R - \|b x + a atanh(-----------) + \|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 2 +--R a\|a \|b x + a +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 2 +-+ \|b x + a - \|a 2 +-+ +--R (a\|b x + a + (- b x - a)\|a )log(------------------) - b x \|a +--R x +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 3 +--R a \|a \|b x + a - a b x - a +--R Type: Union(Expression(Integer),...) +--E 914 + +--S 915 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|b x + a - \|a +--R (\|b x + a - \|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--------+ +--R | 2 +-+ \|b x + a | 2 +-+ +--R (\|b x + a - \|a )atanh(-----------) + \|b x + a - \|a +--R +-+ +--R \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R a\|a \|b x + a - a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 916 + +)clear all + +--S 917 of 1369 +t0:=1/(x^2*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 4 2 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1369 +r0:=1/(a*x*sqrt(a+b*x^2))-2*sqrt(a+b*x^2)/(a^2*x) +--R +--R +--R 2 +--R - 2b x - a +--R (2) -------------- +--R +--------+ +--R 2 | 2 +--R a x\|b x + a +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 4 2 2 +--R (4b x + 2a)\|a \|b x + a - 2b x - 5a b x - 2a +--R (3) --------------------------------------------------- +--R +--------+ +--R 2 3 3 | 2 2 3 3 +-+ +--R (a b x + 2a x)\|b x + a + (- 2a b x - 2a x)\|a +--R Type: Union(Expression(Integer),...) +--E 919 + +--S 920 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 921 + +)clear all + +--S 922 of 1369 +t0:=1/(x^3*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 5 3 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1369 +r0:=3/2*b*atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_ + 1/(a*x^2*sqrt(a+b*x^2))-3/2*sqrt(a+b*x^2)/(a^2*x^2) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 \|b x + a 2 +-+ +--R 3b x \|b x + a atanh(-----------) + (- 3b x - a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 2 +-+ | 2 +--R 2a x \|a \|b x + a +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R ((- 9a b x - 12a b x )\|b x + a + (3b x + 15a b x + 12a b x )\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 3a b x + 5a b x + 4a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2b x + a b x - 7a b x - 4a )\|a +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 3 2 6 4 4 5 2 +--R (6a b x + 8a x )\|a \|b x + a - 2a b x - 10a b x - 8a x +--R Type: Union(Expression(Integer),...) +--E 924 + +--S 925 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 2 | 2 2 2 +-+ \|b x + a +--R ((- 3b x - 12a b)\|b x + a + (9b x + 12a b)\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (- 2b x - 8a b)\|b x + a + (6b x + 8a b)\|a +--R / +--R +--------+ +--R 2 2 3 +-+ | 2 3 2 4 +--R (2a b x + 8a )\|a \|b x + a - 6a b x - 8a +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 926 + +)clear all + +--S 927 of 1369 +t0:=1/(x^4*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 6 4 | 2 +--R (b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1369 +r0:=1/(a*x^3*sqrt(a+b*x^2))-4/3*sqrt(a+b*x^2)/(a^2*x^3)+_ + 8/3*b*sqrt(a+b*x^2)/(a^3*x) +--R +--R +--R 2 4 2 2 +--R 8b x + 4a b x - a +--R (2) -------------------- +--R +--------+ +--R 3 3 | 2 +--R 3a x \|b x + a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (- 32b x - 80a b x - 28a b x + 8a )\|a \|b x + a + 8b x + 68a b x +--R + +--R 2 2 4 3 2 4 +--R 95a b x + 24a b x - 8a +--R / +--R +--------+ +--R 3 2 7 4 5 5 3 | 2 +--R (3a b x + 24a b x + 24a x )\|b x + a +--R + +--R 3 2 7 4 5 5 3 +-+ +--R (- 12a b x - 36a b x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 929 + +--S 930 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 931 + +)clear all + +--S 932 of 1369 +t0:=x^m/(a+b*x^2)^(5/2) +--R +--R +--R m +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1369 +--r0:=1/3*x^(1+m)/(a*(a+b*x^2)^(3/2))+1/3*(2-m)*x^(1+m)/_ +-- (a^2*sqrt(a+b*x^2))-1/3*(2-m)*m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a^2*(1+m)*sqrt(a+b*x^2)) +--E 933 + +--S 934 of 1369 +--a0:=integrate(t0,x) +--E 934 + +--S 935 of 1369 +--m0:=a0-r0 +--E 935 + +--S 936 of 1369 +--d0:=D(m0,x) +--E 936 + +)clear all + +--S 937 of 1369 +t0:=x^6/(a+b*x^2)^(5/2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1369 +r0:=-1/3*x^5/(b*(a+b*x^2)^(3/2))-5/2*a*atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(7/2)-5/3*x^3/(b^2*sqrt(a+b*x^2))+_ + 5/2*x*sqrt(a+b*x^2)/b^3 +--R +--R +--R (2) +--R +--------+ +-+ +--R 2 2 | 2 x\|b +--R (- 15a b x - 15a )\|b x + a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 2 5 3 2 +-+ +--R (3b x + 20a b x + 15a x)\|b +--R / +--R +--------+ +--R 4 2 3 +-+ | 2 +--R (6b x + 6a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|b \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|a \|b +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +-+ +-+ | 2 +--R (30b x + 150a b x + 216a b x + 96a b )\|a \|b \|b x + a +--R + +--R 7 8 6 6 2 5 4 3 4 2 4 3 +-+ +--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|b +--R , +--R +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 150a b x - 750a b x - 1080a b x - 480a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 3b x - 56a b x - 303a b x - 500a b x - 240a x)\|- b \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15b x + 160a b x + 523a b x + 620a b x + 240a x)\|- b \|a +--R / +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 +---+ +-+ | 2 +--R (30b x + 150a b x + 216a b x + 96a b )\|- b \|a \|b x + a +--R + +--R 7 8 6 6 2 5 4 3 4 2 4 3 +---+ +--R (- 6b x - 84a b x - 246a b x - 264a b x - 96a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 939 + +--S 940 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 5a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 5a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 5a\|- b atanh(-----------) - 10a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R 3 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 943 + +)clear all + +--S 944 of 1369 +t0:=x^5/(a+b*x^2)^(5/2) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1369 +r0:=-1/3*a^2/(b^3*(a+b*x^2)^(3/2))+2*a/(b^3*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R 3b x + 12a b x + 8a +--R (2) -------------------------- +--R +--------+ +--R 4 2 3 | 2 +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4a x \|b x + a + (3b x + 4a x )\|a +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (3b x + 27a b x + 48a b x + 24a )\|a \|b x + a - 12a b x - 48a b x +--R + +--R 3 2 4 +--R - 60a b x - 24a +--R Type: Union(Expression(Integer),...) +--E 946 + +--S 947 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R (32a b x + 64a )\|a \|b x + a - 8a b x - 64a b x - 64a +--R (4) ------------------------------------------------------------------ +--R +--------+ +--R 4 2 2 3 | 2 5 4 4 2 2 3 +-+ +--R (12a b x + 24a b )\|b x + a + (- 3b x - 24a b x - 24a b )\|a +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1369 +t0:=x^4/(a+b*x^2)^(5/2) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1369 +r0:=-1/3*x^3/(b*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/sqrt(a+b*x^2))/b^(5/2)-_ + x/(b^2*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +-+ +--R 2 | 2 x\|b 3 +-+ +--R (3b x + 3a)\|b x + a atanh(-----------) + (- 4b x - 3a x)\|b +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R 3 2 2 +-+ | 2 +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (9b x + 21a b x + 12a )\|a \|b x + a - 3b x - 18a b x +--R + +--R 2 2 3 +--R - 27a b x - 12a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (4b x + 19a b x + 12a x)\|b \|b x + a +--R + +--R 2 5 3 2 +-+ +-+ +--R (- 12b x - 25a b x - 12a x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (9b x + 21a b x + 12a b )\|a \|b \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +-+ +--R (- 3b x - 18a b x - 27a b x - 12a b )\|b +--R , +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (18b x + 42a b x + 24a )\|a \|b x + a - 6b x - 36a b x +--R + +--R 2 2 3 +--R - 54a b x - 24a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (4b x + 19a b x + 12a x)\|- b \|b x + a +--R + +--R 2 5 3 2 +---+ +-+ +--R (- 12b x - 25a b x - 12a x)\|- b \|a +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (9b x + 21a b x + 12a b )\|- b \|a \|b x + a +--R + +--R 5 6 4 4 2 3 2 3 2 +---+ +--R (- 3b x - 18a b x - 27a b x - 12a b )\|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 951 + +--S 952 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 2 +---+ +-+ +--R b \|- b \|b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 1369 +t0:=x^3/(a+b*x^2)^(5/2) +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1369 +r0:=1/3*a/(b^2*(a+b*x^2)^(3/2))+(-1)/(b^2*sqrt(a+b*x^2)) +--R +--R +--R 2 +--R - 3b x - 2a +--R (2) -------------------------- +--R +--------+ +--R 3 2 2 | 2 +--R (3b x + 3a b )\|b x + a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3a x \|b x + a + (2b x + 3a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (- 2b x - 8a)\|a \|b x + a + 6a b x + 8a +--R (4) -------------------------------------------------------- +--R +--------+ +--R 3 2 2 2 | 2 3 2 2 2 +-+ +--R (3a b x + 12a b )\|b x + a + (- 9a b x - 12a b )\|a +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1369 +t0:=x^2/(a+b*x^2)^(5/2) +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1369 +r0:=1/3*x^3/(a*(a+b*x^2)^(3/2)) +--R +--R +--R 3 +--R x +--R (2) -------------------------- +--R +--------+ +--R 2 2 | 2 +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (- b x - 4a x )\|b x + a + (3b x + 4a x )\|a +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1369 +t0:=x/(a+b*x^2)^(5/2) +--R +--R +--R x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1369 +r0:=(-1/3)/(b*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (2) - ------------------------- +--R +--------+ +--R 2 2 | 2 +--R (3b x + 3a b)\|b x + a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6a x )\|b x + a + (b x + 6a b x + 6a x )\|a +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (- b x - 4a)\|a \|b x + a + 3a b x + 4a +--R (4) ------------------------------------------------------ +--R +--------+ +--R 2 2 2 3 | 2 2 2 2 3 +-+ +--R (3a b x + 12a b)\|b x + a + (- 9a b x - 12a b)\|a +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1369 +t0:=1/(a+b*x^2)^(5/2) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1369 +r0:=1/3*x/(a*(a+b*x^2)^(3/2))+2/3*x/(a^2*sqrt(a+b*x^2)) +--R +--R +--R 3 +--R 2b x + 3a x +--R (2) -------------------------- +--R +--------+ +--R 2 2 3 | 2 +--R (3a b x + 3a )\|b x + a +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 5 3 2 | 2 2 5 3 2 +-+ +--R (- 2b x - 11a b x - 12a x)\|b x + a + (6b x + 17a b x + 12a x)\|a +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 2 3 6 3 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1369 +t0:=1/(x*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +--------+ +--R 2 5 3 2 | 2 +--R (b x + 2a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1369 +r0:=1/3/(a*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/a^(5/2)+_ + 1/(a^2*sqrt(a+b*x^2)) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 \|b x + a 2 +-+ +--R (- 3b x - 3a)\|b x + a atanh(-----------) + (3b x + 4a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 2 2 3 +-+ | 2 +--R (3a b x + 3a )\|a \|b x + a +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (9a b x + 21a b x + 12a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3b x - 18a b x - 27a b x - 12a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (9a b x + 12a b x )\|b x + a + (- 4b x - 15a b x - 12a b x )\|a +--R / +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 3 3 6 4 2 4 +--R (9a b x + 21a b x + 12a )\|a \|b x + a - 3a b x - 18a b x +--R + +--R 5 2 6 +--R - 27a b x - 12a +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 +-+ \|b x + a - \|a +--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ | 2 +--R 2 | 2 2 +-+ \|b x + a +--R ((3b x + 12a)\|b x + a + (- 9b x - 12a)\|a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 | 2 2 +-+ +--R (4b x + 16a)\|b x + a + (- 12b x - 16a)\|a +--R / +--R +--------+ +--R 2 2 3 +-+ | 2 3 2 4 +--R (3a b x + 12a )\|a \|b x + a - 9a b x - 12a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1369 +t0:=1/(x^2*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 6 4 2 2 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1369 +r0:=1/3/(a*x*(a+b*x^2)^(3/2))+4/3/(a^2*x*sqrt(a+b*x^2))-_ + 8/3*sqrt(a+b*x^2)/(a^3*x) +--R +--R +--R 2 4 2 2 +--R - 8b x - 12a b x - 3a +--R (2) --------------------------- +--R +--------+ +--R 3 3 4 | 2 +--R (3a b x + 3a x)\|b x + a +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (32b x + 112a b x + 108a b x + 24a )\|a \|b x + a - 8b x - 76a b x +--R + +--R 2 2 4 3 2 4 +--R - 163a b x - 120a b x - 24a +--R / +--R +--------+ +--R 3 3 7 4 2 5 5 3 6 | 2 +--R (3a b x + 27a b x + 48a b x + 24a x)\|b x + a +--R + +--R 3 3 7 4 2 5 5 3 6 +-+ +--R (- 12a b x - 48a b x - 60a b x - 24a x)\|a +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1369 +t0:=1/(x^3*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1369 +r0:=1/3/(a*x^2*(a+b*x^2)^(3/2))+5/2*b*atanh(sqrt(a+b*x^2)/_ + sqrt(a))/a^(7/2)+5/3/(a^2*x^2*sqrt(a+b*x^2))-_ + 5/2*sqrt(a+b*x^2)/(a^3*x^2) +--R +--R +--R (2) +--R +--------+ +--R +--------+ | 2 +--R 2 4 2 | 2 \|b x + a +--R (15b x + 15a b x )\|b x + a atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +--R (- 15b x - 20a b x - 3a )\|a +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 +--R (6a b x + 6a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 | 2 +--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 +-+ +--R (15b x + 210a b x + 615a b x + 660a b x + 240a b x )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 2 3 6 3 2 4 4 2 5 | 2 +--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48a )\|b x + a +--R + +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (14b x + 121a b x + 174a b x - 39a b x - 156a b x - 48a )\|a +--R / +--R +--------+ +--R 4 3 8 5 2 6 6 4 7 2 +-+ | 2 4 4 10 +--R (30a b x + 150a b x + 216a b x + 96a x )\|a \|b x + a - 6a b x +--R + +--R 5 3 8 6 2 6 7 4 8 2 +--R - 84a b x - 246a b x - 264a b x - 96a x +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 15b x - 180a b x - 240a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (75b x + 300a b x + 240a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 15b x - 180a b x - 240a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (75b x + 300a b x + 240a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 4 2 2 2 | 2 +--R (- 14b x - 168a b x - 224a b)\|b x + a +--R + +--R 3 4 2 2 2 +-+ +--R (70b x + 280a b x + 224a b)\|a +--R / +--R +--------+ +--R 3 2 4 4 2 5 +-+ | 2 4 2 4 5 2 6 +--R (6a b x + 72a b x + 96a )\|a \|b x + a - 30a b x - 120a b x - 96a +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1369 +t0:=1/(x^4*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R 2 8 6 2 4 | 2 +--R (b x + 2a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1369 +r0:=1/3/(a*x^3*(a+b*x^2)^(3/2))+2/(a^2*x^3*sqrt(a+b*x^2))-_ + 8/3*sqrt(a+b*x^2)/(a^3*x^3)+16/3*b*sqrt(a+b*x^2)/(a^4*x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 16b x + 24a b x + 6a b x - a +--R (2) -------------------------------- +--R +--------+ +--R 4 5 5 3 | 2 +--R (3a b x + 3a x )\|b x + a +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +-+ +--R (- 96b x - 656a b x - 1316a b x - 954a b x - 160a b x + 32a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 12 5 10 2 4 8 3 3 6 4 2 4 5 2 +--R 16b x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x +--R + +--R 6 +--R - 32a +--R / +--R +--------+ +--R 4 4 11 5 3 9 6 2 7 7 5 8 3 | 2 +--R (3a b x + 57a b x + 198a b x + 240a b x + 96a x )\|b x + a +--R + +--R 4 4 11 5 3 9 6 2 7 7 5 8 3 +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a x )\|a +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1369 +t0:=x^m/(a+b*x^2)^(9/2) +--R +--R +--R m +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1369 +--r0:=1/7*x^(1+m)/(a*(a+b*x^2)^(7/2))+1/35*(6-m)*x^(1+m)/_ +-- (a^2*(a+b*x^2)^(5/2))+1/105*(4-m)*(6-m)*x^(1+m)/_ +-- (a^3*(a+b*x^2)^(3/2))+1/105*(2-m)*(4-m)*(6-m)*x^(1+m)/_ +-- (a^4*sqrt(a+b*x^2))-1/105*(2-m)*(4-m)*(6-m)*m*x^(1+m)*_ +-- hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +-- sqrt((a+b*x^2)/a)/(a^4*(1+m)*sqrt(a+b*x^2)) +--E 997 + +--S 998 of 1369 +--a0:=integrate(t0,x) +--E 998 + +--S 999 of 1369 +--m0:=a0-r0 +--E 999 + +--S 1000 of 1369 +--d0:=D(m0,x) +--E 1000 + +)clear all + +--S 1001 of 1369 +t0:=x^10/(a+b*x^2)^(9/2) +--R +--R +--R 10 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1369 +r0:=-1/7*x^9/(b*(a+b*x^2)^(7/2))-9/35*x^7/(b^2*(a+b*x^2)^(5/2))-_ + 3/5*x^5/(b^3*(a+b*x^2)^(3/2))-9/2*a*atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(11/2)-3*x^3/(b^4*sqrt(a+b*x^2))+_ + 9/2*x*sqrt(a+b*x^2)/b^5 +--R +--R +--R (2) +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (- 315a b x - 945a b x - 945a b x - 315a )\|b x + a +--R * +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (35b x + 528a b x + 1218a b x + 1050a b x + 315a x)\|b +--R / +--R +--------+ +--R 8 6 7 4 2 6 2 3 5 +-+ | 2 +--R (70b x + 210a b x + 210a b x + 70a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 7 14 2 6 12 3 5 10 4 4 8 +--R 2835a b x + 46305a b x + 257985a b x + 705915a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R 1071000a b x + 922320a b x + 423360a b x + 80640a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 315a b x - 13860a b x - 127890a b x - 520380a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 1149435a b x - 1484280a b x - 1123920a b x - 463680a b x +--R + +--R 9 +--R - 80640a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 35b x - 1928a b x - 30738a b x - 192170a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 8952a b x + 89442a b x + 403866a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x +--R + +--R 8 +--R 80640a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 12 14 11 12 2 10 10 3 9 8 +--R 630b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 4 8 6 5 7 4 6 6 2 7 5 +--R 238000a b x + 204960a b x + 94080a b x + 17920a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 13 16 12 14 2 11 12 3 10 10 +--R - 70b x - 3080a b x - 28420a b x - 115640a b x +--R + +--R 4 9 8 5 8 6 6 7 4 7 6 2 +--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x +--R + +--R 8 5 +--R - 17920a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 7 14 2 6 12 3 5 10 4 4 8 +--R - 5670a b x - 92610a b x - 515970a b x - 1411830a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 2142000a b x - 1844640a b x - 846720a b x - 161280a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R 630a b x + 27720a b x + 255780a b x + 1040760a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R 2298870a b x + 2968560a b x + 2247840a b x + 927360a b x +--R + +--R 9 +--R 161280a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R - 35b x - 1928a b x - 30738a b x - 192170a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R - 580139a b x - 945432a b x - 857808a b x - 409920a b x +--R + +--R 8 +--R - 80640a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 8 17 7 15 2 6 13 3 5 11 +--R 315b x + 8952a b x + 89442a b x + 403866a b x +--R + +--R 4 4 9 5 3 7 6 2 5 7 3 +--R 968099a b x + 1328136a b x + 1052688a b x + 450240a b x +--R + +--R 8 +--R 80640a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 12 14 11 12 2 10 10 3 9 8 +--R 630b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 4 8 6 5 7 4 6 6 2 7 5 +--R 238000a b x + 204960a b x + 94080a b x + 17920a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 13 16 12 14 2 11 12 3 10 10 +--R - 70b x - 3080a b x - 28420a b x - 115640a b x +--R + +--R 4 9 8 5 8 6 6 7 4 7 6 2 +--R - 255430a b x - 329840a b x - 249760a b x - 103040a b x +--R + +--R 8 5 +--R - 17920a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1003 + +--S 1004 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b + b x)\|b x + a + (- b x - a)\|b - b x\|a +--R 9a log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R 9a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 5 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1369 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R 9a\|- b atanh(-----------) - 18a\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R ------------------------------------------------------------------------ +--R 5 +---+ +-+ +--R 2b \|- b \|b +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1007 + +)clear all + +--S 1008 of 1369 +t0:=x^9/(a+b*x^2)^(9/2) +--R +--R +--R 9 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1369 +r0:=-1/7*a^4/(b^5*(a+b*x^2)^(7/2))+4/5*a^3/(b^5*(a+b*x^2)^(5/2))-_ + 2*a^2/(b^5*(a+b*x^2)^(3/2))+4*a/(b^5*sqrt(a+b*x^2))+sqrt(a+b*x^2)/b^5 +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R 35b x + 280a b x + 560a b x + 448a b x + 128a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 8 6 7 4 2 6 2 3 5 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 14 2 12 3 10 | 2 +--R (- 152a b x - 560a b x - 448a x )\|b x + a +--R + +--R 3 16 2 14 2 12 3 10 +-+ +--R (35b x + 376a b x + 784a b x + 448a x )\|a +--R / +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R 35b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x +--R + +--R 5 2 4 6 2 7 +--R 45920a b x + 22400a b x + 4480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x +--R + +--R 6 2 4 7 2 8 +--R - 56560a b x - 24640a b x - 4480a +--R Type: Union(Expression(Integer),...) +--E 1010 + +--S 1011 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (1024a b x + 10240a b x + 24576a b x + 16384a )\|a \|b x + a +--R + +--R 4 8 2 3 6 3 2 4 4 2 5 +--R - 128a b x - 4096a b x - 20480a b x - 32768a b x - 16384a +--R / +--R +--------+ +--R 8 6 2 7 4 3 6 2 4 5 | 2 +--R (280a b x + 2800a b x + 6720a b x + 4480a b )\|b x + a +--R + +--R 9 8 8 6 2 7 4 3 6 2 4 5 +-+ +--R (- 35b x - 1120a b x - 5600a b x - 8960a b x - 4480a b )\|a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1369 +t0:=x^8/(a+b*x^2)^(9/2) +--R +--R +--R 8 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1369 +r0:=-1/7*x^7/(b*(a+b*x^2)^(7/2))-1/5*x^5/(b^2*(a+b*x^2)^(5/2))-_ + 1/3*x^3/(b^3*(a+b*x^2)^(3/2))+atanh(x*sqrt(b)/_ + sqrt(a+b*x^2))/b^(9/2)-x/(b^4*sqrt(a+b*x^2)) +--R +--R +--R (2) +--R +--------+ +-+ +--R 3 6 2 4 2 2 3 | 2 x\|b +--R (105b x + 315a b x + 315a b x + 105a )\|b x + a atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 176b x - 406a b x - 350a b x - 105a x)\|b +--R / +--R +--------+ +--R 7 6 6 4 2 5 2 3 4 +-+ | 2 +--R (105b x + 315a b x + 315a b x + 105a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 6 12 5 10 2 4 8 3 3 6 +--R 735b x + 8085a b x + 31605a b x + 60375a b x +--R + +--R 4 2 4 5 2 6 +--R 61320a b x + 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 5 2 4 6 2 7 +--R - 76440a b x - 35280a b x - 6720a +--R * +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x +--R + +--R 5 3 6 +--R 30800a b x + 6720a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 +--R - 1232b x - 12698a b x - 44898a b x - 77071a b x +--R + +--R 4 2 5 5 3 6 +--R - 71064a b x - 34160a b x - 6720a x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 10 12 9 10 2 8 8 3 7 6 4 6 4 +--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 5 5 2 6 4 +--R 31920a b x + 6720a b +--R * +--R +--------+ +--R +-+ +-+ | 2 +--R \|a \|b \|b x + a +--R + +--R 11 14 10 12 2 9 10 3 8 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 7 6 5 6 4 6 5 2 7 4 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a b +--R * +--R +-+ +--R \|b +--R , +--R +--R 6 12 5 10 2 4 8 3 3 6 +--R 1470b x + 16170a b x + 63210a b x + 120750a b x +--R + +--R 4 2 4 5 2 6 +--R 122640a b x + 63840a b x + 13440a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 +--R - 210b x - 5880a b x - 38220a b x - 111720a b x +--R + +--R 4 3 6 5 2 4 6 2 7 +--R - 174930a b x - 152880a b x - 70560a b x - 13440a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R atan(------------------------------) +--R b x +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 176b x + 4630a b x + 24174a b x + 52249a b x + 56504a b x +--R + +--R 5 3 6 +--R 30800a b x + 6720a x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- b \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 +--R - 1232b x - 12698a b x - 44898a b x - 77071a b x +--R + +--R 4 2 5 5 3 6 +--R - 71064a b x - 34160a b x - 6720a x +--R * +--R +---+ +-+ +--R \|- b \|a +--R / +--R 10 12 9 10 2 8 8 3 7 6 4 6 4 +--R 735b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 5 5 2 6 4 +--R 31920a b x + 6720a b +--R * +--R +--------+ +--R +---+ +-+ | 2 +--R \|- b \|a \|b x + a +--R + +--R 11 14 10 12 2 9 10 3 8 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 7 6 5 6 4 6 5 2 7 4 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a b +--R * +--R +---+ +--R \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R 4 +---+ +-+ +--R b \|- b \|b +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1369 +t0:=x^7/(a+b*x^2)^(9/2) +--R +--R +--R 7 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1369 +r0:=1/7*a^3/(b^4*(a+b*x^2)^(7/2))-3/5*a^2/(b^4*(a+b*x^2)^(5/2))+_ + a/(b^4*(a+b*x^2)^(3/2))+(-1)/(b^4*sqrt(a+b*x^2)) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35b x - 70a b x - 56a b x - 16a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 7 6 6 4 2 5 2 3 4 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 12 2 10 3 8 | 2 +--R (- 77a b x - 322a b x - 280a x )\|b x + a +--R + +--R 3 14 2 12 2 10 3 8 +-+ +--R (16b x + 203a b x + 462a b x + 280a x )\|a +--R / +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 6 2 7 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 6 2 4 7 2 8 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1022 + +--S 1023 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 16b x - 384a b x - 1280a b x - 1024a )\|a \|b x + a + 112a b x +--R + +--R 2 2 4 3 2 4 +--R 896a b x + 1792a b x + 1024a +--R / +--R +--------+ +--R 7 6 2 6 4 3 5 2 4 4 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a +--R + +--R 7 6 2 6 4 3 5 2 4 4 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +)clear all + +--S 1025 of 1369 +t0:=x^6/(a+b*x^2)^(9/2) +--R +--R +--R 6 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1369 +r0:=1/7*x^7/(a*(a+b*x^2)^(7/2)) +--R +--R +--R 7 +--R x +--R (2) ------------------------------------------------ +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (7a b x + 21a b x + 21a b x + 7a )\|b x + a +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 13 2 11 2 9 3 7 | 2 +--R (- b x - 24a b x - 80a b x - 64a x )\|b x + a +--R + +--R 3 13 2 11 2 9 3 7 +-+ +--R (7b x + 56a b x + 112a b x + 64a x )\|a +--R / +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x +--R + +--R 6 2 7 +--R 2128a b x + 448a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 7 14 2 6 12 3 5 10 4 4 8 5 3 6 +--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x +--R + +--R 6 2 4 7 2 8 +--R - 5096a b x - 2352a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 1027 + +--S 1028 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +)clear all + +--S 1030 of 1369 +t0:=x^5/(a+b*x^2)^(9/2) +--R +--R +--R 5 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1369 +r0:=-1/7*a^2/(b^3*(a+b*x^2)^(7/2))+2/5*a/(b^3*(a+b*x^2)^(5/2))+_ + (-1/3)/(b^3*(a+b*x^2)^(3/2)) +--R +--R +--R 2 4 2 2 +--R - 35b x - 28a b x - 8a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 6 6 5 4 2 4 2 3 3 | 2 +--R (105b x + 315a b x + 315a b x + 105a b )\|b x + a +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 12 2 2 10 3 8 4 6 | 2 +--R (- 56a b x - 581a b x - 1540a b x - 1120a x )\|b x + a +--R + +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (8b x + 224a b x + 1211a b x + 2100a b x + 1120a x )\|a +--R / +--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 7 2 8 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 7 2 4 8 2 9 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 8b x - 192a b x - 640a b x - 512a )\|a \|b x + a + 56a b x +--R + +--R 2 2 4 3 2 4 +--R 448a b x + 896a b x + 512a +--R / +--R +--------+ +--R 2 6 6 3 5 4 4 4 2 5 3 | 2 +--R (105a b x + 2520a b x + 8400a b x + 6720a b )\|b x + a +--R + +--R 2 6 6 3 5 4 4 4 2 5 3 +-+ +--R (- 735a b x - 5880a b x - 11760a b x - 6720a b )\|a +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1369 +t0:=x^4/(a+b*x^2)^(9/2) +--R +--R +--R 4 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1369 +r0:=1/7*x^5/(a*(a+b*x^2)^(7/2))+2/35*x^5/(a^2*(a+b*x^2)^(5/2)) +--R +--R +--R 7 5 +--R 2b x + 7a x +--R (2) ---------------------------------------------------- +--R +--------+ +--R 2 3 6 3 2 4 4 2 5 | 2 +--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 13 3 11 2 2 9 3 7 4 5 | 2 +--R (- 2b x - 55a b x - 328a b x - 688a b x - 448a x )\|b x + a +--R + +--R 4 13 3 11 2 2 9 3 7 4 5 +-+ +--R (14b x + 161a b x + 616a b x + 912a b x + 448a x )\|a +--R / +--R 2 6 12 3 5 10 4 4 8 5 3 6 6 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 7 2 8 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 2 7 14 3 6 12 4 5 10 5 4 8 6 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 7 2 4 8 2 9 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1369 +t0:=x^3/(a+b*x^2)^(9/2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1369 +r0:=1/7*a/(b^2*(a+b*x^2)^(7/2))+(-1/5)/(b^2*(a+b*x^2)^(5/2)) +--R +--R +--R 2 +--R - 7b x - 2a +--R (2) ---------------------------------------------------- +--R +--------+ +--R 5 6 4 4 2 3 2 3 2 | 2 +--R (35b x + 105a b x + 105a b x + 35a b )\|b x + a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 12 2 3 10 3 2 8 4 6 5 4 | 2 +--R (- 14a b x - 154a b x - 595a b x - 980a b x - 560a x )\|b x + a +--R + +--R 5 14 4 12 2 3 10 3 2 8 4 6 5 4 +-+ +--R (2b x + 56a b x + 364a b x + 1015a b x + 1260a b x + 560a x )\|a +--R / +--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 8 2 9 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 8 2 4 9 2 10 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 +--R (- 2b x - 48a b x - 160a b x - 128a )\|a \|b x + a + 14a b x +--R + +--R 2 2 4 3 2 4 +--R 112a b x + 224a b x + 128a +--R / +--R +--------+ +--R 3 5 6 4 4 4 5 3 2 6 2 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240a b )\|b x + a +--R + +--R 3 5 6 4 4 4 5 3 2 6 2 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240a b )\|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1369 +t0:=x^2/(a+b*x^2)^(9/2) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1369 +r0:=1/7*x^3/(a*(a+b*x^2)^(7/2))+4/35*x^3/(a^2*(a+b*x^2)^(5/2))+_ + 8/105*x^3/(a^3*(a+b*x^2)^(3/2)) +--R +--R +--R 2 7 5 2 3 +--R 8b x + 28a b x + 35a x +--R (2) ------------------------------------------------------ +--R +--------+ +--R 3 3 6 4 2 4 5 2 6 | 2 +--R (105a b x + 315a b x + 315a b x + 105a )\|b x + a +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 13 4 11 2 3 9 3 2 7 4 5 +--R - 8b x - 220a b x - 1347a b x - 3592a b x - 4592a b x +--R + +--R 5 3 +--R - 2240a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 13 4 11 2 3 9 3 2 7 4 5 +--R 56b x + 644a b x + 2709a b x + 5608a b x + 5712a b x +--R + +--R 5 3 +--R 2240a x +--R * +--R +-+ +--R \|a +--R / +--R 3 6 12 4 5 10 5 4 8 6 3 6 7 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 8 2 9 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 3 7 14 4 6 12 5 5 10 6 4 8 7 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 8 2 4 9 2 10 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1369 +t0:=x/(a+b*x^2)^(9/2) +--R +--R +--R x +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1369 +r0:=(-1/7)/(b*(a+b*x^2)^(7/2)) +--R +--R +--R 1 +--R (2) - ----------------------------------------------- +--R +--------+ +--R 4 6 3 4 2 2 2 3 | 2 +--R (7b x + 21a b x + 21a b x + 7a b)\|b x + a +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 12 2 4 10 3 3 8 4 2 6 5 4 6 2 +--R (- 7a b x - 77a b x - 301a b x - 574a b x - 560a b x - 224a x ) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 14 5 12 2 4 10 3 3 8 4 2 6 5 4 +--R b x + 28a b x + 182a b x + 532a b x + 826a b x + 672a b x +--R + +--R 6 2 +--R 224a x +--R * +--R +-+ +--R \|a +--R / +--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4 +--R 49a b x + 539a b x + 2107a b x + 4025a b x + 4088a b x +--R + +--R 9 2 10 +--R 2128a b x + 448a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 7a b x - 196a b x - 1274a b x - 3724a b x - 5831a b x +--R + +--R 9 2 4 10 2 11 +--R - 5096a b x - 2352a b x - 448a +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (- b x - 24a b x - 80a b x - 64a )\|a \|b x + a + 7a b x + 56a b x +--R + +--R 3 2 4 +--R 112a b x + 64a +--R / +--R +--------+ +--R 4 4 6 5 3 4 6 2 2 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448a b)\|b x + a +--R + +--R 4 4 6 5 3 4 6 2 2 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448a b)\|a +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1369 +t0:=1/(a+b*x^2)^(9/2) +--R +--R +--R 1 +--R (1) ---------------------------------------------------- +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1369 +r0:=1/7*x/(a*(a+b*x^2)^(7/2))+6/35*x/(a^2*(a+b*x^2)^(5/2))+_ + 8/35*x/(a^3*(a+b*x^2)^(3/2))+16/35*x/(a^4*sqrt(a+b*x^2)) +--R +--R +--R 3 7 2 5 2 3 3 +--R 16b x + 56a b x + 70a b x + 35a x +--R (2) ---------------------------------------------------- +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 | 2 +--R (35a b x + 105a b x + 105a b x + 35a )\|b x + a +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R - 16b x - 440a b x - 2694a b x - 7219a b x - 10024a b x +--R + +--R 5 3 6 +--R - 7280a b x - 2240a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 13 5 11 2 4 9 3 3 7 4 2 5 +--R 112b x + 1288a b x + 5418a b x + 11461a b x + 13384a b x +--R + +--R 5 3 6 +--R 8400a b x + 2240a x +--R * +--R +-+ +--R \|a +--R / +--R 4 6 12 5 5 10 6 4 8 7 3 6 8 2 4 +--R 245a b x + 2695a b x + 10535a b x + 20125a b x + 20440a b x +--R + +--R 9 2 10 +--R 10640a b x + 2240a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 4 7 14 5 6 12 6 5 10 7 4 8 8 3 6 +--R - 35a b x - 980a b x - 6370a b x - 18620a b x - 29155a b x +--R + +--R 9 2 4 10 2 11 +--R - 25480a b x - 11760a b x - 2240a +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1369 +t0:=1/(x*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------------------- +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1369 +r0:=1/7/(a*(a+b*x^2)^(7/2))+1/5/(a^2*(a+b*x^2)^(5/2))+_ + 1/3/(a^3*(a+b*x^2)^(3/2))-atanh(sqrt(a+b*x^2)/sqrt(a))/_ + a^(9/2)+1/(a^4*sqrt(a+b*x^2)) +--R +--R +--R (2) +--R +--------+ +--R +--------+ | 2 +--R 3 6 2 4 2 2 3 | 2 \|b x + a +--R (- 105b x - 315a b x - 315a b x - 105a )\|b x + a atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105b x + 350a b x + 406a b x + 176a )\|a +--R / +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 +--R (105a b x + 315a b x + 315a b x + 105a )\|a \|b x + a +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 2 5 10 3 4 8 4 3 6 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x +--R + +--R 5 2 4 6 2 7 +--R 61320a b x + 31920a b x + 6720a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 +--R - 105b x - 2940a b x - 19110a b x - 55860a b x +--R + +--R 4 3 6 5 2 4 6 2 7 +--R - 87465a b x - 76440a b x - 35280a b x - 6720a +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 6 12 2 5 10 3 4 8 4 3 6 5 2 4 +--R 1127a b x + 10682a b x + 35770a b x + 56560a b x + 43680a b x +--R + +--R 6 2 +--R 13440a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R - 176b x - 4193a b x - 23702a b x - 59430a b x - 76720a b x +--R + +--R 5 2 4 6 2 +--R - 50400a b x - 13440a b x +--R * +--R +-+ +--R \|a +--R / +--R 5 6 12 6 5 10 7 4 8 8 3 6 9 2 4 +--R 735a b x + 8085a b x + 31605a b x + 60375a b x + 61320a b x +--R + +--R 10 2 11 +--R 31920a b x + 6720a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 5 7 14 6 6 12 7 5 10 8 4 8 9 3 6 +--R - 105a b x - 2940a b x - 19110a b x - 55860a b x - 87465a b x +--R + +--R 10 2 4 11 2 12 +--R - 76440a b x - 35280a b x - 6720a +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (105b x + 2520a b x + 8400a b x + 6720a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 735b x - 5880a b x - 11760a b x - 6720a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 6 2 4 2 2 3 | 2 +--R (176b x + 4224a b x + 14080a b x + 11264a )\|b x + a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 1232b x - 9856a b x - 19712a b x - 11264a )\|a +--R / +--R +--------+ +--R 4 3 6 5 2 4 6 2 7 +-+ | 2 5 3 6 +--R (105a b x + 2520a b x + 8400a b x + 6720a )\|a \|b x + a - 735a b x +--R + +--R 6 2 4 7 2 8 +--R - 5880a b x - 11760a b x - 6720a +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1369 +t0:=1/(x^2*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R +--------+ +--R 4 10 3 8 2 2 6 3 4 4 2 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1369 +r0:=1/7/(a*x*(a+b*x^2)^(7/2))+8/35/(a^2*x*(a+b*x^2)^(5/2))+_ + 16/35/(a^3*x*(a+b*x^2)^(3/2))+64/35/(a^4*x*sqrt(a+b*x^2))-_ + 128/35*sqrt(a+b*x^2)/(a^5*x) +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - 128b x - 448a b x - 560a b x - 280a b x - 35a +--R (2) ----------------------------------------------------- +--R +--------+ +--R 5 3 7 6 2 5 7 3 8 | 2 +--R (35a b x + 105a b x + 105a b x + 35a x)\|b x + a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 14 6 12 2 5 10 3 4 8 4 3 6 +--R 1024b x + 13824a b x + 64896a b x + 149440a b x + 187544a b x +--R + +--R 5 2 4 6 2 7 +--R 128240a b x + 42560a b x + 4480a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 8 16 7 14 2 6 12 3 5 10 4 4 8 +--R - 128b x - 4544a b x - 35376a b x - 122648a b x - 229667a b x +--R + +--R 5 3 6 6 2 4 7 2 8 +--R - 246624a b x - 148960a b x - 44800a b x - 4480a +--R / +--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7 +--R 35a b x + 1225a b x + 9065a b x + 29155a b x + 49280a b x +--R + +--R 10 2 5 11 3 12 +--R 45920a b x + 22400a b x + 4480a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 7 15 6 6 13 7 5 11 8 4 9 9 3 7 +--R - 280a b x - 3920a b x - 19600a b x - 49280a b x - 69720a b x +--R + +--R 10 2 5 11 3 12 +--R - 56560a b x - 24640a b x - 4480a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1369 +t0:=1/(x^3*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------- +--R +--------+ +--R 4 11 3 9 2 2 7 3 5 4 3 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1369 +r0:=1/7/(a*x^2*(a+b*x^2)^(7/2))+9/35/(a^2*x^2*(a+b*x^2)^(5/2))+_ + 3/5/(a^3*x^2*(a+b*x^2)^(3/2))+9/2*b*atanh(sqrt(a+b*x^2)/_ + sqrt(a))/a^(11/2)+3/(a^4*x^2*sqrt(a+b*x^2))-9/2*sqrt(a+b*x^2)/(a^5*x^2) +--R +--R +--R (2) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 | 2 +--R (315b x + 945a b x + 945a b x + 315a b x )\|b x + a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 315b x - 1050a b x - 1218a b x - 528a b x - 35a )\|a +--R / +--R +--------+ +--R 5 3 8 6 2 6 7 4 8 2 +-+ | 2 +--R (70a b x + 210a b x + 210a b x + 70a x )\|a \|b x + a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 2835a b x - 46305a b x - 257985a b x - 705915a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 +--R - 1071000a b x - 922320a b x - 423360a b x - 80640a b x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 315b x + 13860a b x + 127890a b x + 520380a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 1149435a b x + 1484280a b x + 1123920a b x + 463680a b x +--R + +--R 8 2 +--R 80640a b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 8 16 2 7 14 3 6 12 4 5 10 +--R - 3177a b x - 43386a b x - 198954a b x - 427140a b x +--R + +--R 5 4 8 6 3 6 7 2 4 8 2 9 +--R - 454685a b x - 193480a b x + 35280a b x + 51520a b x + 8960a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 9 18 8 16 2 7 14 3 6 12 +--R 388b x + 14237a b x + 110278a b x + 367934a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R 629860a b x + 552965a b x + 181720a b x - 59920a b x +--R + +--R 8 2 9 +--R - 56000a b x - 8960a +--R * +--R +-+ +--R \|a +--R / +--R 6 7 16 7 6 14 8 5 12 9 4 10 +--R 630a b x + 10290a b x + 57330a b x + 156870a b x +--R + +--R 10 3 8 11 2 6 12 4 13 2 +--R 238000a b x + 204960a b x + 94080a b x + 17920a x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 6 8 18 7 7 16 8 6 14 9 5 12 10 4 10 +--R - 70a b x - 3080a b x - 28420a b x - 115640a b x - 255430a b x +--R + +--R 11 3 8 12 2 6 13 4 14 2 +--R - 329840a b x - 249760a b x - 103040a b x - 17920a x +--R Type: Union(Expression(Integer),...) +--E 1072 + +--S 1073 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a +--R * +--R +--------+ +--R | 2 +-+ +--R \|b x + a - \|a +--R log(------------------) +--R x +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 315b x - 12600a b x - 75600a b x - 141120a b x - 80640a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (2835b x + 37800a b x + 136080a b x + 181440a b x + 80640a b)\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +--R (- 388b x - 15520a b x - 93120a b x - 173824a b x - 99328a b) +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 5 8 4 6 2 3 4 3 2 2 4 +-+ +--R (3492b x + 46560a b x + 167616a b x + 223488a b x + 99328a b)\|a +--R / +--R 5 4 8 6 3 6 7 2 4 8 2 9 +-+ +--R (70a b x + 2800a b x + 16800a b x + 31360a b x + 17920a )\|a +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 4 8 7 3 6 8 2 4 9 2 10 +--R - 630a b x - 8400a b x - 30240a b x - 40320a b x - 17920a +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1074 + +)clear all + +--S 1075 of 1369 +t0:=1/(x^4*(a+b*x^2)^(9/2)) +--R +--R +--R 1 +--R (1) -------------------------------------------------------- +--R +--------+ +--R 4 12 3 10 2 2 8 3 6 4 4 | 2 +--R (b x + 4a b x + 6a b x + 4a b x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1369 +r0:=1/7/(a*x^3*(a+b*x^2)^(7/2))+2/7/(a^2*x^3*(a+b*x^2)^(5/2))+_ + 16/21/(a^3*x^3*(a+b*x^2)^(3/2))+32/7/(a^4*x^3*sqrt(a+b*x^2))-_ + 128/21*sqrt(a+b*x^2)/(a^5*x^3)+256/21*b*sqrt(a+b*x^2)/(a^6*x) +--R +--R +--R 5 10 4 8 2 3 6 3 2 4 4 2 5 +--R 256b x + 896a b x + 1120a b x + 560a b x + 70a b x - 7a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 6 3 9 7 2 7 8 5 9 3 | 2 +--R (21a b x + 63a b x + 63a b x + 21a x )\|b x + a +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 18 8 16 2 7 14 3 6 12 +--R - 2560b x - 49920a b x - 326592a b x - 1049056a b x +--R + +--R 4 5 10 5 4 8 6 3 6 7 2 4 +--R - 1891516a b x - 1993082a b x - 1192800a b x - 353696a b x +--R + +--R 8 2 9 +--R - 28672a b x + 3584a +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a +--R + +--R 10 20 9 18 2 8 16 3 7 14 4 6 12 +--R 256b x + 13696a b x + 148320a b x + 701680a b x + 1807270a b x +--R + +--R 5 5 10 6 4 8 7 3 6 8 2 4 +--R 2759845a b x + 2547202a b x + 1365840a b x + 368480a b x +--R + +--R 9 2 10 +--R 26880a b x - 3584a +--R / +--R 6 8 19 7 7 17 8 6 15 9 5 13 +--R 21a b x + 1113a b x + 11613a b x + 51891a b x +--R + +--R 10 4 11 11 3 9 12 2 7 13 5 +--R 123690a b x + 170352a b x + 136416a b x + 59136a b x +--R + +--R 14 3 +--R 10752a x +--R * +--R +--------+ +--R | 2 +--R \|b x + a +--R + +--R 6 8 19 7 7 17 8 6 15 9 5 13 +--R - 210a b x - 4200a b x - 28812a b x - 98952a b x +--R + +--R 10 4 11 11 3 9 12 2 7 13 5 +--R - 195090a b x - 231840a b x - 164640a b x - 64512a b x +--R + +--R 14 3 +--R - 10752a x +--R * +--R +-+ +--R \|a +--R Type: Union(Expression(Integer),...) +--E 1077 + +--S 1078 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1079 + +)clear all + +--S 1080 of 1369 +t0:=x^5/sqrt(9+4*x^2) +--R +--R +--R 5 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1369 +r0:=27/40*sqrt(9+4*x^2)-3/20*x^2*sqrt(9+4*x^2)+1/20*x^4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (2x - 6x + 27)\|4x + 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 1024x + 192x - 6804x - 34020x - 21870x)\|4x + 9 + 2048x +--R + +--R 8 6 4 2 +--R 1920x + 11880x + 85050x + 109350x + 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x + 17280x + 3240)\|4x + 9 - 20480x - 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 1082 + +--S 1083 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1084 + +)clear all + +--S 1085 of 1369 +t0:=x^4/sqrt(9+4*x^2) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1369 +r0:=243/256*asinh(2/3*x)-27/128*x*sqrt(9+4*x^2)+1/16*x^3*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 3 | 2 2x +--R (16x - 54x)\|4x + 9 + 243asinh(--) +--R 3 +--R (2) ------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((- 15552x - 17496x)\|4x + 9 + 31104x + 69984x + 19683) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 4 +--R (- 2048x + 2304x + 14256x + 4374x)\|4x + 9 + 4096x - 36288x +--R + +--R 2 +--R - 34992x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (16384x + 18432x)\|4x + 9 - 32768x - 73728x - 20736 +--R Type: Union(Expression(Integer),...) +--E 1087 + +--S 1088 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 243log(\|4x + 9 - 2x) - 243asinh(--) +--R 3 +--R (4) ---------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1089 + +)clear all + +--S 1090 of 1369 +t0:=x^3/sqrt(9+4*x^2) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1369 +r0:=-3/8*sqrt(9+4*x^2)+1/12*x^2*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2x - 9)\|4x + 9 +--R (2) ------------------- +--R 24 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 64x + 180x + 486x)\|4x + 9 + 128x - 216x - 1458x - 729 +--R (3) ---------------------------------------------------------------- +--R +-------+ +--R 2 | 2 3 +--R (384x + 216)\|4x + 9 - 768x - 1296x +--R Type: Union(Expression(Integer),...) +--E 1092 + +--S 1093 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1094 + +)clear all + +--S 1095 of 1369 +t0:=x^2/sqrt(9+4*x^2) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1369 +r0:=-9/16*asinh(2/3*x)+1/8*x*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 2x +--R 2x\|4x + 9 - 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (36x\|4x + 9 - 72x - 81)log(\|4x + 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x - 18x)\|4x + 9 + 32x + 72x +--R / +--R +-------+ +--R | 2 2 +--R 64x\|4x + 9 - 128x - 144 +--R Type: Union(Expression(Integer),...) +--E 1097 + +--S 1098 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R 9log(\|4x + 9 - 2x) + 9asinh(--) +--R 3 +--R (4) ---------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1099 + +)clear all + +--S 1100 of 1369 +t0:=x/sqrt(9+4*x^2) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1369 +r0:=1/4*sqrt(9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (2) ---------- +--R 4 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R - 2x\|4x + 9 + 4x + 9 +--R (3) ------------------------ +--R +-------+ +--R | 2 +--R 4\|4x + 9 - 8x +--R Type: Union(Expression(Integer),...) +--E 1102 + +--S 1103 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1104 + +)clear all + +--S 1105 of 1369 +t0:=1/sqrt(9+4*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x + 9 +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1369 +r0:=1/2*asinh(2/3*x) +--R +--R +--R 2x +--R asinh(--) +--R 3 +--R (2) --------- +--R 2 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x) +--R (3) - -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - log(\|4x + 9 - 2x) - asinh(--) +--R 3 +--R (4) ---------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1369 +t0:=1/(x*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 2 +--R x\|4x + 9 +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1369 +r0:=-1/3*atanh(1/3*sqrt(9+4*x^2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R atanh(----------) +--R 3 +--R (2) - ----------------- +--R 3 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3) +--R (3) ----------------------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - log(\|4x + 9 - 2x + 3) + log(\|4x + 9 - 2x - 3) + atanh(----------) +--R 3 +--R ------------------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1369 +t0:=1/(x^2*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1369 +r0:=-1/9*sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x + 9 +--R (2) - ---------- +--R 9x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------- +--R +-------+ +--R | 2 2 +--R x\|4x + 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1369 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - - +--R 9 +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1369 +t0:=1/(x^3*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1369 +r0:=2/27*atanh(1/3*sqrt(9+4*x^2))-1/18*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x + 9 | 2 +--R 4x atanh(----------) - 3\|4x + 9 +--R 3 +--R (2) ---------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (16x \|4x + 9 - 32x - 36x )log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +-------+ +--R 3 | 2 4 2 | 2 +--R (- 16x \|4x + 9 + 32x + 36x )log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 2 | 2 3 +--R (24x + 27)\|4x + 9 - 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 216x \|4x + 9 - 432x - 486x +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R 2log(\|4x + 9 - 2x + 3) - 2log(\|4x + 9 - 2x - 3) - 2atanh(----------) +--R 3 +--R -------------------------------------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1369 +t0:=1/(x^4*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1369 +r0:=-1/27*sqrt(9+4*x^2)/x^3+8/243*sqrt(9+4*x^2)/x +--R +--R +--R +-------+ +--R 2 | 2 +--R (8x - 9)\|4x + 9 +--R (2) ------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R 2x\|4x + 9 - 4x - 3 +--R (3) ------------------------------------ +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x + 9x )\|4x + 9 - 32x - 54x +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1369 +m0:=a0-r0 +--R +--R +--R 16 +--R (4) --- +--R 243 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1369 +t0:=1/(x^5*sqrt(9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 | 2 +--R x \|4x + 9 +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1369 +r0:=-2/81*atanh(1/3*sqrt(9+4*x^2))-1/36*sqrt(9+4*x^2)/x^4+_ + 1/54*sqrt(9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x + 9 2 | 2 +--R - 8x atanh(----------) + (6x - 9)\|4x + 9 +--R 3 +--R (2) -------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((- 512x - 576x )\|4x + 9 + 1024x + 2304x + 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x + 3) +--R + +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((512x + 576x )\|4x + 9 - 1024x - 2304x - 648x ) +--R * +--R +-------+ +--R | 2 +--R log(\|4x + 9 - 2x - 3) +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x - 576x + 2106x + 729)\|4x + 9 + 1536x + 2880x - 3888x +--R + +--R - 5832x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (20736x + 23328x )\|4x + 9 - 41472x - 93312x - 26244x +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-------+ +-------+ | 2 +--R | 2 | 2 \|4x + 9 +--R - 2log(\|4x + 9 - 2x + 3) + 2log(\|4x + 9 - 2x - 3) + 2atanh(----------) +--R 3 +--R ---------------------------------------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1369 +t0:=x^5/sqrt(9-4*x^2) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1369 +r0:=-27/40*sqrt(9-4*x^2)-3/20*x^2*sqrt(9-4*x^2)-1/20*x^4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (- 2x - 6x - 27)\|- 4x + 9 +--R (2) ------------------------------ +--R 40 +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 8 6 | 2 10 8 6 +--R (15x - 90x )\|- 4x + 9 + 4x - 105x + 270x +--R (3) --------------------------------------------------------- +--R +---------+ +--R 4 2 | 2 4 2 +--R (20x - 540x + 1620)\|- 4x + 9 - 300x + 2700x - 4860 +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1369 +m0:=a0-r0 +--R +--R +--R 81 +--R (4) - -- +--R 40 +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1369 +t0:=x^4/sqrt(9-4*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1369 +r0:=243/256*asin(2/3*x)-27/128*x*sqrt(9-4*x^2)-1/16*x^3*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 3 | 2 2x +--R (- 16x - 54x)\|- 4x + 9 + 243asin(--) +--R 3 +--R (2) ---------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +--R ((- 1458x + 6561)\|- 4x + 9 - 486x + 8748x - 19683) +--R * +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R atan(----------------) +--R 2x +--R + +--R +---------+ +--R 7 5 3 | 2 7 5 3 +--R (- 16x + 234x + 324x - 2187x)\|- 4x + 9 + 192x - 648x - 2430x +--R + +--R 6561x +--R / +--R +---------+ +--R 2 | 2 4 2 +--R (768x - 3456)\|- 4x + 9 + 256x - 4608x + 10368 +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 486atan(----------------) - 243asin(--) +--R 2x 3 +--R (4) ----------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1369 +t0:=x^3/sqrt(9-4*x^2) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1369 +r0:=-3/8*sqrt(9-4*x^2)-1/12*x^2*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2x - 9)\|- 4x + 9 +--R (2) ----------------------- +--R 24 +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 2 6 4 +--R 9x \|- 4x + 9 + 4x - 27x +--R (3) -------------------------------------- +--R +---------+ +--R 2 | 2 2 +--R (12x - 108)\|- 4x + 9 - 108x + 324 +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1369 +m0:=a0-r0 +--R +--R +--R 9 +--R (4) - - +--R 8 +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1369 +t0:=x^2/sqrt(9-4*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1369 +r0:=9/16*asin(2/3*x)-1/8*x*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 2x +--R - 2x\|- 4x + 9 + 9asin(--) +--R 3 +--R (2) ---------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R | 2 2 \|- 4x + 9 - 3 +--R (- 27\|- 4x + 9 - 18x + 81)atan(----------------) +--R 2x +--R + +--R +---------+ +--R 3 | 2 3 +--R (- 2x + 9x)\|- 4x + 9 + 12x - 27x +--R / +--R +---------+ +--R | 2 2 +--R 24\|- 4x + 9 + 16x - 72 +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 18atan(----------------) - 9asin(--) +--R 2x 3 +--R (4) -------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1369 +t0:=x/sqrt(9-4*x^2) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1369 +r0:=-1/4*sqrt(9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (2) - ------------ +--R 4 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R x +--R (3) ---------------- +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R (4) - - +--R 4 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1369 +t0:=1/sqrt(9-4*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1369 +r0:=1/2*asin(2/3*x) +--R +--R +--R 2x +--R asin(--) +--R 3 +--R (2) -------- +--R 2 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R (3) - atan(----------------) +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 2x +--R - 2atan(----------------) - asin(--) +--R 2x 3 +--R (4) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1369 +t0:=1/(x*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 2 +--R x\|- 4x + 9 +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1369 +r0:=-1/3*atanh(1/3*sqrt(9-4*x^2)) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R atanh(------------) +--R 3 +--R (2) - ------------------- +--R 3 +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 - 3 +--R log(----------------) +--R x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R log(----------------) + atanh(------------) +--R x 3 +--R (4) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1369 +t0:=1/(x^2*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1369 +r0:=-1/9*sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x + 9 +--R (2) - ------------ +--R 9x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 2 +--R 3\|- 4x + 9 + 4x - 9 +--R (3) ----------------------- +--R +---------+ +--R | 2 +--R 9x\|- 4x + 9 - 27x +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1369 +t0:=1/(x^3*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1369 +r0:=-2/27*atanh(1/3*sqrt(9-4*x^2))-1/18*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x + 9 | 2 +--R - 4x atanh(------------) - 3\|- 4x + 9 +--R 3 +--R (2) ---------------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 2 | 2 4 2 \|- 4x + 9 - 3 +--R (12x \|- 4x + 9 + 8x - 36x )log(----------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +--R (- 6x + 27)\|- 4x + 9 + 36x - 81 +--R / +--R +---------+ +--R 2 | 2 4 2 +--R 162x \|- 4x + 9 + 108x - 486x +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R 2log(----------------) + 2atanh(------------) +--R x 3 +--R (4) --------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1369 +t0:=1/(x^4*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1369 +r0:=-1/27*sqrt(9-4*x^2)/x^3-8/243*sqrt(9-4*x^2)/x +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 8x - 9)\|- 4x + 9 +--R (2) ----------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 | 2 6 4 2 +--R (72x - 135x - 243)\|- 4x + 9 + 32x - 324x + 243x + 729 +--R (3) ------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +--R (243x - 2187x )\|- 4x + 9 - 2187x + 6561x +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1369 +t0:=1/(x^5*sqrt(9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 5 | 2 +--R x \|- 4x + 9 +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1369 +r0:=-2/81*atanh(1/3*sqrt(9-4*x^2))-1/36*sqrt(9-4*x^2)/x^4-_ + 1/54*sqrt(9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x + 9 2 | 2 +--R - 8x atanh(------------) + (- 6x - 9)\|- 4x + 9 +--R 3 +--R (2) -------------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +--R 6 4 | 2 8 6 4 \|- 4x + 9 - 3 +--R ((48x - 216x )\|- 4x + 9 + 16x - 288x + 648x )log(----------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 +--R (- 12x + 198x - 162x - 729)\|- 4x + 9 + 144x - 756x + 2187 +--R / +--R +---------+ +--R 6 4 | 2 8 6 4 +--R (1944x - 8748x )\|- 4x + 9 + 648x - 11664x + 26244x +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 9 - 3 \|- 4x + 9 +--R 2log(----------------) + 2atanh(------------) +--R x 3 +--R (4) --------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1369 +t0:=x^5/sqrt(-9+4*x^2) +--R +--R +--R 5 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1369 +r0:=27/40*sqrt(-9+4*x^2)+3/20*x^2*sqrt(-9+4*x^2)+1/20*x^4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 4 2 | 2 +--R (2x + 6x + 27)\|4x - 9 +--R (2) -------------------------- +--R 40 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 9 7 5 3 | 2 10 +--R (- 1024x - 192x - 6804x + 34020x - 21870x)\|4x - 9 + 2048x +--R + +--R 8 6 4 2 +--R - 1920x + 11880x - 85050x + 109350x - 19683 +--R / +--R +-------+ +--R 4 2 | 2 5 3 +--R (10240x - 17280x + 3240)\|4x - 9 - 20480x + 57600x - 32400x +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1369 +t0:=x^4/sqrt(-9+4*x^2) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1369 +r0:=243/256*atanh(2*x/sqrt(-9+4*x^2))+27/128*x*sqrt(-9+4*x^2)+_ + 1/16*x^3*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x 3 | 2 +--R 243atanh(----------) + (16x + 54x)\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 3 | 2 4 2 +--R ((- 15552x + 17496x)\|4x - 9 + 31104x - 69984x + 19683) +--R * +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 7 5 3 | 2 8 4 +--R (- 2048x - 2304x + 14256x - 4374x)\|4x - 9 + 4096x - 36288x +--R + +--R 2 +--R 34992x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (16384x - 18432x)\|4x - 9 - 32768x + 73728x - 20736 +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 243log(\|4x - 9 - 2x) - 243atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------------ +--R 256 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1369 +t0:=x^3/sqrt(-9+4*x^2) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1369 +r0:=3/8*sqrt(-9+4*x^2)+1/12*x^2*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2 | 2 +--R (2x + 9)\|4x - 9 +--R (2) ------------------- +--R 24 +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 3 | 2 6 4 2 +--R (- 64x - 180x + 486x)\|4x - 9 + 128x + 216x - 1458x + 729 +--R (3) ---------------------------------------------------------------- +--R +-------+ +--R 2 | 2 3 +--R (384x - 216)\|4x - 9 - 768x + 1296x +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1369 +t0:=x^2/sqrt(-9+4*x^2) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1369 +r0:=9/16*atanh(2*x/sqrt(-9+4*x^2))+1/8*x*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R 2x | 2 +--R 9atanh(----------) + 2x\|4x - 9 +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) --------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 2 2 | 2 +--R (- 36x\|4x - 9 + 72x - 81)log(\|4x - 9 - 2x) +--R + +--R +-------+ +--R 3 | 2 4 2 +--R (- 16x + 18x)\|4x - 9 + 32x - 72x +--R / +--R +-------+ +--R | 2 2 +--R 64x\|4x - 9 - 128x + 144 +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - 9log(\|4x - 9 - 2x) - 9atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) -------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1369 +t0:=x/sqrt(-9+4*x^2) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1369 +r0:=1/4*sqrt(-9+4*x^2) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------- +--R 4 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R - 2x\|4x - 9 + 4x - 9 +--R (3) ------------------------ +--R +-------+ +--R | 2 +--R 4\|4x - 9 - 8x +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1369 +t0:=1/sqrt(-9+4*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | 2 +--R \|4x - 9 +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1369 +r0:=1/2*atanh(2*x/sqrt(-9+4*x^2)) +--R +--R +--R 2x +--R atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ----------------- +--R 2 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R log(\|4x - 9 - 2x) +--R (3) - -------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 2x +--R - log(\|4x - 9 - 2x) - atanh(----------) +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (4) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1369 +t0:=1/(x*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 2 +--R x\|4x - 9 +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1369 +r0:=1/3*atan(1/3*sqrt(-9+4*x^2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R atan(----------) +--R 3 +--R (2) ---------------- +--R 3 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R 2atan(---------------) +--R 3 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - atan(----------) + 2atan(---------------) +--R 3 3 +--R (4) ------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1369 +t0:=1/(x^2*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1369 +r0:=1/9*sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 9 +--R (2) ---------- +--R 9x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------- +--R +-------+ +--R | 2 2 +--R x\|4x - 9 - 2x +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1369 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - +--R 9 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1369 +t0:=1/(x^3*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1369 +r0:=2/27*atan(1/3*sqrt(-9+4*x^2))+1/18*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 2 \|4x - 9 | 2 +--R 4x atan(----------) + 3\|4x - 9 +--R 3 +--R (2) --------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-------+ | 2 +--R 3 | 2 4 2 \|4x - 9 - 2x +--R (32x \|4x - 9 - 64x + 72x )atan(---------------) +--R 3 +--R + +--R +-------+ +--R 2 | 2 3 +--R (- 24x + 27)\|4x - 9 + 48x - 108x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R 216x \|4x - 9 - 432x + 486x +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 27 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1369 +t0:=1/(x^4*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1369 +r0:=1/27*sqrt(-9+4*x^2)/x^3+8/243*sqrt(-9+4*x^2)/x +--R +--R +--R +-------+ +--R 2 | 2 +--R (8x + 9)\|4x - 9 +--R (2) ------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 2 +--R 2x\|4x - 9 - 4x + 3 +--R (3) ------------------------------------ +--R +-------+ +--R 5 3 | 2 6 4 +--R (16x - 9x )\|4x - 9 - 32x + 54x +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1369 +m0:=a0-r0 +--R +--R +--R 16 +--R (4) --- +--R 243 +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1369 +t0:=1/(x^5*sqrt(-9+4*x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 | 2 +--R x \|4x - 9 +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1369 +r0:=2/81*atan(1/3*sqrt(-9+4*x^2))+1/36*sqrt(-9+4*x^2)/x^4+_ + 1/54*sqrt(-9+4*x^2)/x^2 +--R +--R +--R +-------+ +--R | 2 +-------+ +--R 4 \|4x - 9 2 | 2 +--R 8x atan(----------) + (6x + 9)\|4x - 9 +--R 3 +--R (2) ----------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 7 5 | 2 8 6 4 +--R ((1024x - 1152x )\|4x - 9 - 2048x + 4608x - 1296x ) +--R * +--R +-------+ +--R | 2 +--R \|4x - 9 - 2x +--R atan(---------------) +--R 3 +--R + +--R +-------+ +--R 6 4 2 | 2 7 5 3 +--R (- 768x + 576x + 2106x - 729)\|4x - 9 + 1536x - 2880x - 3888x +--R + +--R 5832x +--R / +--R +-------+ +--R 7 5 | 2 8 6 4 +--R (20736x - 23328x )\|4x - 9 - 41472x + 93312x - 26244x +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ +-------+ +--R | 2 | 2 +--R \|4x - 9 \|4x - 9 - 2x +--R - 2atan(----------) + 4atan(---------------) +--R 3 3 +--R (4) -------------------------------------------- +--R 81 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1369 +t0:=x^5/sqrt(-9-4*x^2) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1369 +r0:=-27/40*sqrt(-9-4*x^2)+3/20*x^2*sqrt(-9-4*x^2)-1/20*x^4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 4 2 | 2 +--R (- 2x + 6x - 27)\|- 4x - 9 +--R (2) ------------------------------ +--R 40 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 8 6 | 2 10 8 6 +---+ +--R (- 15x - 90x )\|- 4x - 9 + (4x + 105x + 270x )\|- 1 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (20x + 540x + 1620)\|- 1 \|- 4x - 9 + 300x + 2700x + 4860 +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 4 2 | 2 4 2 +---+ +--R (81x + 2187x + 6561)\|- 4x - 9 + (- 1215x - 10935x - 19683)\|- 1 +--R ----------------------------------------------------------------------- +--R +---------+ +--R 4 2 +---+ | 2 4 2 +--R (40x + 1080x + 3240)\|- 1 \|- 4x - 9 + 600x + 5400x + 9720 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1369 +t0:=x^4/sqrt(-9-4*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1369 +r0:=243/256*atan(2*x/sqrt(-9-4*x^2))+27/128*x*sqrt(-9-4*x^2)-_ + 1/16*x^3*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x 3 | 2 +--R 243atan(------------) + (- 16x + 54x)\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------------------- +--R 256 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 7 5 3 | 2 +--R (- 32x - 468x + 648x + 4374x)\|- 4x - 9 +--R + +--R 7 5 3 +---+ +--R (384x + 1296x - 4860x - 13122x)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((1458x + 6561)\|- 4x - 9 + (- 486x - 8748x - 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (2x - 3)\|- 1 +--R log(-----------------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((- 1458x - 6561)\|- 4x - 9 + (486x + 8748x + 19683)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 2 +---+ | 2 4 2 +--R ((- 1458x - 6561)\|- 1 \|- 4x - 9 - 486x - 8748x - 19683) +--R * +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (1536x + 6912)\|- 1 \|- 4x - 9 + 512x + 9216x + 20736 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1369 +t0:=x^3/sqrt(-9-4*x^2) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1369 +r0:=3/8*sqrt(-9-4*x^2)-1/12*x^2*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 2x + 9)\|- 4x - 9 +--R (2) ----------------------- +--R 24 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 2 6 4 +---+ +--R - 9x \|- 4x - 9 + (4x + 27x )\|- 1 +--R (3) -------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (12x + 108)\|- 1 \|- 4x - 9 + 108x + 324 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R 2 | 2 2 +---+ +--R (- 9x - 81)\|- 4x - 9 + (81x + 243)\|- 1 +--R (4) --------------------------------------------- +--R +---------+ +--R 2 +---+ | 2 2 +--R (8x + 72)\|- 1 \|- 4x - 9 + 72x + 216 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1369 +t0:=x^2/sqrt(-9-4*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1369 +r0:=-9/16*atan(2*x/sqrt(-9-4*x^2))-1/8*x*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R 2x | 2 +--R - 9atan(------------) - 2x\|- 4x - 9 +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) -------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R 3 | 2 3 +---+ +--R (- 4x - 18x)\|- 4x - 9 + (24x + 54x)\|- 1 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 48\|- 1 \|- 4x - 9 + 32x + 144 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R (- 27\|- 4x - 9 + (18x + 81)\|- 1 )log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 2 +---+ +--R (27\|- 4x - 9 + (- 18x - 81)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 + (- 2x - 3)\|- 1 +--R log(-------------------------------) +--R x +--R + +--R +---------+ +--R +---+ | 2 2 2x +--R (27\|- 1 \|- 4x - 9 + 18x + 81)atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 48\|- 1 \|- 4x - 9 + 32x + 144 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1369 +t0:=x/sqrt(-9-4*x^2) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1369 +r0:=-1/4*sqrt(-9-4*x^2) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) - ------------ +--R 4 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +---+ +--R x \|- 1 +--R (3) ---------------------- +--R +---------+ +--R +---+ | 2 +--R \|- 1 \|- 4x - 9 + 3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 +---+ +--R 3\|- 4x - 9 - 9\|- 1 +--R (4) ------------------------ +--R +---------+ +--R +---+ | 2 +--R 4\|- 1 \|- 4x - 9 + 12 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1369 +t0:=1/sqrt(-9-4*x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1369 +r0:=1/2*atan(2*x/sqrt(-9-4*x^2)) +--R +--R +--R 2x +--R atan(------------) +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------------ +--R 2 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R - \|- 1 log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1 +--R \|- 1 log(-------------------------------) +--R x +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (2x - 3)\|- 1 +--R - \|- 1 log(-----------------------------) +--R x +--R + +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 + (- 2x - 3)\|- 1 2x +--R \|- 1 log(-------------------------------) - atan(------------) +--R x +---------+ +--R | 2 +--R \|- 4x - 9 +--R / +--R 2 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1369 +t0:=1/(x*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 2 +--R x\|- 4x - 9 +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1369 +r0:=1/3*atan(1/3*sqrt(-9-4*x^2)) +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R atan(------------) +--R 3 +--R (2) ------------------ +--R 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 +---+ +--R +---+ \|- 4x - 9 - 3\|- 1 +--R \|- 1 log(----------------------) +--R x +--R (3) - --------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +---------+ +--R | 2 +---+ | 2 +--R +---+ \|- 4x - 9 - 3\|- 1 \|- 4x - 9 +--R - \|- 1 log(----------------------) - atan(------------) +--R x 3 +--R (4) -------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1369 +t0:=1/(x^2*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1369 +r0:=1/9*sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R | 2 +--R \|- 4x - 9 +--R (2) ------------ +--R 9x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +---+ | 2 2 +--R - 3\|- 1 \|- 4x - 9 - 4x - 9 +--R (3) ------------------------------- +--R +---------+ +--R | 2 +---+ +--R 9x\|- 4x - 9 - 27x\|- 1 +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1369 +t0:=1/(x^3*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1369 +r0:=-2/27*atan(1/3*sqrt(-9-4*x^2))+1/18*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 2 \|- 4x - 9 | 2 +--R - 4x atan(------------) + 3\|- 4x - 9 +--R 3 +--R (2) --------------------------------------- +--R 2 +--R 54x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 2 +---+ +--R 2 | 2 4 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 12x \|- 4x - 9 + (8x + 36x )\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R 2 | 2 2 +---+ +--R (6x + 27)\|- 4x - 9 + (- 36x - 81)\|- 1 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R 162x \|- 1 \|- 4x - 9 + 108x + 486x +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R +---------+ | 2 +---+ +--R | 2 2 +---+ \|- 4x - 9 - 3\|- 1 +--R (- 6\|- 4x - 9 + (4x + 18)\|- 1 )log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R +---+ | 2 2 \|- 4x - 9 +--R (6\|- 1 \|- 4x - 9 + 4x + 18)atan(------------) +--R 3 +--R / +--R +---------+ +--R +---+ | 2 2 +--R 81\|- 1 \|- 4x - 9 + 54x + 243 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1369 +t0:=1/(x^4*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1369 +r0:=1/27*sqrt(-9-4*x^2)/x^3-8/243*sqrt(-9-4*x^2)/x +--R +--R +--R +---------+ +--R 2 | 2 +--R (- 8x + 9)\|- 4x - 9 +--R (2) ----------------------- +--R 3 +--R 243x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 2 +---+ | 2 6 4 2 +--R (72x + 135x - 243)\|- 1 \|- 4x - 9 + 32x + 324x + 243x - 729 +--R (3) ------------------------------------------------------------------- +--R +---------+ +--R 5 3 | 2 5 3 +---+ +--R (243x + 2187x )\|- 4x - 9 + (- 2187x - 6561x )\|- 1 +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1369 +t0:=1/(x^5*sqrt(-9-4*x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 5 | 2 +--R x \|- 4x - 9 +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1369 +r0:=2/81*atan(1/3*sqrt(-9-4*x^2))+1/36*sqrt(-9-4*x^2)/x^4-_ + 1/54*sqrt(-9-4*x^2)/x^2 +--R +--R +--R +---------+ +--R | 2 +---------+ +--R 4 \|- 4x - 9 2 | 2 +--R 8x atan(------------) + (- 6x + 9)\|- 4x - 9 +--R 3 +--R (2) ----------------------------------------------- +--R 4 +--R 324x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R 6 4 | 2 8 6 4 +---+ +--R ((48x + 216x )\|- 4x - 9 + (- 16x - 288x - 648x )\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R 6 4 2 | 2 6 4 +---+ +--R (- 12x - 198x - 162x + 729)\|- 4x - 9 + (144x + 756x - 2187)\|- 1 +--R / +--R +---------+ +--R 6 4 +---+ | 2 8 6 4 +--R (1944x + 8748x )\|- 1 \|- 4x - 9 + 648x + 11664x + 26244x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------+ +--R 2 | 2 4 2 +---+ +--R ((12x + 54)\|- 4x - 9 + (- 4x - 72x - 162)\|- 1 ) +--R * +--R +---------+ +--R | 2 +---+ +--R \|- 4x - 9 - 3\|- 1 +--R log(----------------------) +--R x +--R + +--R +---------+ +--R +---------+ | 2 +--R 2 +---+ | 2 4 2 \|- 4x - 9 +--R ((- 12x - 54)\|- 1 \|- 4x - 9 - 4x - 72x - 162)atan(------------) +--R 3 +--R / +--R +---------+ +--R 2 +---+ | 2 4 2 +--R (486x + 2187)\|- 1 \|- 4x - 9 + 162x + 2916x + 6561 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1369 +t0:=1/sqrt(9+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + 9 +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1369 +r0:=asinh(1/3*x*sqrt(b))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asinh(-----) +--R 3 +--R (2) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 2 2 +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x +--R log(--------------------------------------------------) +--R +--------+ +--R | 2 +--R \|b x + 9 - 3 +--R [-------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +--R \|- b \|b x + 9 - 3\|- b +--R 2atan(---------------------------) +--R b x +--R ----------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1302 + +--S 1303 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R +-+ | 2 2 +-+ +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b +--R log(--------------------------------------------------) - asinh(-----) +--R +--------+ 3 +--R | 2 +--R \|b x + 9 - 3 +--R (4) ---------------------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b +--R 2\|b atan(---------------------------) - \|- b asinh(-----) +--R b x 3 +--R (6) ----------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1306 + +)clear all + +--S 1307 of 1369 +t0:=1/sqrt(9-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x + 9 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1369 +r0:=asin(1/3*x*sqrt(b))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asin(-----) +--R 3 +--R (2) ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R [----------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R | 2 +-+ +--R (\|- b x + 9 - 3)\|b +--R 2atan(-----------------------) +--R b x +--R - ------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1309 + +--S 1310 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R \|b log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(-----) +--R 3 +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R (\|- b x + 9 - 3)\|b x\|b +--R - 2atan(-----------------------) - asin(-----) +--R b x 3 +--R (6) ---------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1313 + +)clear all + +--S 1314 of 1369 +t0:=1/sqrt(-9+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x - 9 +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(-9+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - 9 +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +---+ | 2 +--R +--------+ \|- b \|b x - 9 +--R +-+ | 2 2 atan(-----------------) +--R log(2x\|b \|b x - 9 + 2b x - 9) b x +--R (3) [----------------------------------,-----------------------] +--R +-+ +---+ +--R 2\|b \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1316 + +--S 1317 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +-+ +--R +-+ | 2 2 x\|b +--R log(2x\|b \|b x - 9 + 2b x - 9) - 2atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - 9 +--R (4) -------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +--R +---+ x\|b +-+ \|- b \|b x - 9 +--R - \|- b atanh(-----------) + \|b atan(-----------------) +--R +--------+ b x +--R | 2 +--R \|b x - 9 +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1369 +t0:=1/sqrt(-9-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1369 +r0:=atan(x*sqrt(b)/sqrt(-9-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R | 2 +-+ +--R +----------+ \|- b x - 9 \|b +--R | 2 +---+ 2 atan(-----------------) +--R log(2x\|- b x - 9 \|- b - 2b x - 9) b x +--R (3) [--------------------------------------,- -----------------------] +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +-+ +--R +-+ | 2 +---+ 2 +---+ x\|b +--R \|b log(2x\|- b x - 9 \|- b - 2b x - 9) - 2\|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - 9 +--R ----------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R \|- b x - 9 \|b x\|b +--R - atan(-----------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x - 9 +--R (6) ----------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 1369 +t0:=1/sqrt(%pi+b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|b x + %pi +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1369 +r0:=asinh(x*sqrt(b)/sqrt(%pi))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asinh(------) +--R +---+ +--R \|%pi +--R (2) ------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R [---------------------------------------------------------------------, +--R +-+ +--R \|b +--R +----------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x + %pi - \|- b \|%pi +--R 2atan(----------------------------------) +--R b x +--R -----------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R + +--R +-+ +--R x\|b +--R - asinh(------) +--R +---+ +--R \|%pi +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1369 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) +--R +----------+ +--R | 2 +--R 2 2 +-+ +---+ 2 3 2 |b x + %pi +--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |---------- +--R \| %pi +--R + +--R 2 4 2 2 +-+ +---+ 2 3 2 +--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R \|b x + %pi +--R + +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R + +--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+ +--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b +--R / +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R |---------- \|b x + %pi +--R \| %pi +--R + +--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3 +--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x +--R + +--R 3 +--R - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +---+ | 2 +---+ +---+ +-+ +--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b +--R 2\|b atan(----------------------------------) - \|- b asinh(------) +--R b x +---+ +--R \|%pi +--R (6) ------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1369 +d0b:=normalize(D(m0b,x)) +--R +--R +--R +----------+ +--R +----------+ | 2 +--R +---+ | 2 |b x + %pi +--R - \|%pi \|b x + %pi + %pi |---------- +--R \| %pi +--R (7) ---------------------------------------- +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R %pi |---------- \|b x + %pi +--R \| %pi +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1369 +t0:=1/sqrt(%pi-b*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|- b x + %pi +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1369 +r0:=asin(x*sqrt(b)/sqrt(%pi))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R asin(------) +--R +---+ +--R \|%pi +--R (2) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R / +--R +---+ +--R \|- b +--R , +--R +------------+ +--R +-+ +---+ | 2 +-+ +--R \|b \|%pi - \|- b x + %pi \|b +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(------) +--R +---+ +--R \|%pi +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +------------+ +--R +------------+ | 2 +--R 2 2 | 2 |- b x + %pi +--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 4 2 2 | 2 +--R (b x - 5b %pi x + 4%pi )\|- b x + %pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R | 2 +--R 2 3 2 |- b x + %pi 3 5 2 3 2 +--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi 2 4 +--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x +--R \| %pi +--R + +--R 2 2 3 +--R 7b %pi x - 4%pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 3 2 | 2 +--R (- 3b %pi x + 4b %pi x)\|- b x + %pi +--R / +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi +---+ +--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 4 2 2 3 | 2 |- b x + %pi +---+ +--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R | 2 +--R 3 5 2 2 3 3 |- b x + %pi +--R (b %pi x - 5b %pi x + 4b %pi x) |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------------+ +--R +-+ +---+ | 2 +-+ +-+ +--R \|b \|%pi - \|- b x + %pi \|b x\|b +--R 2atan(--------------------------------) - asin(------) +--R b x +---+ +--R \|%pi +--R (6) ------------------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1369 +d0b:=D(m0b,x) +--R +--R +--R +------------+ +--R +------------+ | 2 +--R | 2 +---+ |- b x + %pi +--R - \|- b x + %pi \|%pi + %pi |------------ +--R \| %pi +--R (7) -------------------------------------------- +--R +------------+ +--R +------------+ | 2 +--R | 2 |- b x + %pi +--R %pi\|- b x + %pi |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 1369 +t0:=1/sqrt(-%pi+b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|b x - %pi +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(-%pi+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-------------) +--R +----------+ +--R | 2 +--R \|b x - %pi +--R (2) -------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R +---+ | 2 +--R +----------+ \|- b \|b x - %pi +--R +-+ | 2 2 atan(-------------------) +--R log(2x\|b \|b x - %pi + 2b x - %pi) b x +--R (3) [--------------------------------------,-------------------------] +--R +-+ +---+ +--R 2\|b \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +----------+ +-+ +--R +-+ | 2 2 x\|b +--R log(2x\|b \|b x - %pi + 2b x - %pi) - 2atanh(-------------) +--R +----------+ +--R | 2 +--R \|b x - %pi +--R (4) -------------------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ +---+ | 2 +--R +---+ x\|b +-+ \|- b \|b x - %pi +--R - \|- b atanh(-------------) + \|b atan(-------------------) +--R +----------+ b x +--R | 2 +--R \|b x - %pi +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 1369 +t0:=1/sqrt(-%pi-b*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1369 +r0:=atan(x*sqrt(b)/sqrt(-%pi-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(---------------) +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R (2) --------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------+ +--R | 2 +-+ +--R +------------+ \|- b x - %pi \|b +--R | 2 +---+ 2 atan(-------------------) +--R log(2x\|- b x - %pi \|- b - 2b x - %pi) b x +--R [------------------------------------------,- -------------------------] +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1351 + +--S 1352 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +------------+ +-+ +--R +-+ | 2 +---+ 2 +---+ x\|b +--R \|b log(2x\|- b x - %pi \|- b - 2b x - %pi) - 2\|- b atan(---------------) +--R +------------+ +--R | 2 +--R \|- b x - %pi +--R ----------------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +------------+ +--R | 2 +-+ +-+ +--R \|- b x - %pi \|b x\|b +--R - atan(-------------------) - atan(---------------) +--R b x +------------+ +--R | 2 +--R \|- b x - %pi +--R (6) --------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1355 + +)clear all + +--S 1356 of 1369 +t0:=1/sqrt(a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1369 +r0:=atanh(x*sqrt(b)/sqrt(a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R [-------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- b \|b x + a - \|- b \|a +--R 2atan(------------------------------) +--R b x +--R -------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 1358 + +--S 1359 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +-+ +--R (\|a \|b - b x)\|b x + a + (- b x - a)\|b + b x\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|a \|b x + a - a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x + a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 2 +---+ +-+ +--R +---+ x\|b +-+ \|- b \|b x + a - \|- b \|a +--R - \|- b atanh(-----------) + 2\|b atan(------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1362 + +)clear all + +--S 1363 of 1369 +t0:=1/sqrt(a-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x + a +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1369 +r0:=atan(x*sqrt(b)/sqrt(a-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x + a +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b + b x\|- b x + a +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- b x + a \|a - a +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R +-+ | 2 +-+ +--R (\|a - \|- b x + a )\|b +--R 2atan(--------------------------) +--R b x +--R ---------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 1365 + +--S 1366 of 1369 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- b x + a \|- b - b x)\|a + (b x - a)\|- b +--R + +--R +----------+ +--R | 2 +--R b x\|- b x + a +--R / +--R +----------+ +--R | 2 +-+ +--R \|- b x + a \|a - a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x + a +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +-+ | 2 +-+ +-+ +--R (\|a - \|- b x + a )\|b x\|b +--R 2atan(--------------------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x + a +--R (6) ------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1369 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4c.input.pamphlet b/src/input/rich4c.input.pamphlet new file mode 100644 index 0000000..ea77292 --- /dev/null +++ b/src/input/rich4c.input.pamphlet @@ -0,0 +1,16055 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4c.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 257 supplied "optimal results". +\item 187 matching answers. +\item 2 cases where Axiom supplied 2 results. +\item 0 cases that Axiom failed to integrate. +\item 70 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4c.output +)spool rich4c.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1285 +t0:=1/sqrt(-a+b*x^2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x - a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1285 +r0:=atanh(x*sqrt(b)/sqrt(-a+b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - a +--R (2) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +---+ +-+ | 2 2 +-+ +---+ +--R (\|- a \|b - b x)\|b x - a + (- b x + a)\|b + b x\|- a +--R log(------------------------------------------------------------) +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R [-----------------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x - a - \|- b \|- a +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1285 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +---+ +-+ | 2 2 +-+ +---+ +--R (\|- a \|b - b x)\|b x - a + (- b x + a)\|b + b x\|- a +--R log(------------------------------------------------------------) +--R +--------+ +--R +---+ | 2 +--R \|- a \|b x - a + a +--R + +--R +-+ +--R x\|b +--R - atanh(-----------) +--R +--------+ +--R | 2 +--R \|b x - a +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1285 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1285 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 2 +---+ +---+ +--R +---+ x\|b +-+ \|- b \|b x - a - \|- b \|- a +--R - \|- b atanh(-----------) + 2\|b atan(--------------------------------) +--R +--------+ b x +--R | 2 +--R \|b x - a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1285 +t0:=1/sqrt(-a-b*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +----------+ +--R | 2 +--R \|- b x - a +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1285 +r0:=atan(x*sqrt(b)/sqrt(-a-b*x^2))/sqrt(b) +--R +--R +--R +-+ +--R x\|b +--R atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - a +--R (2) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +---+ 2 +---+ | 2 +--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b + b x\|- b x - a +--R log(-----------------------------------------------------------------------) +--R +----------+ +--R | 2 +---+ +--R \|- b x - a \|- a + a +--R [---------------------------------------------------------------------------- +--R +---+ +--R \|- b +--R , +--R +----------+ +--R +---+ | 2 +-+ +--R (\|- a - \|- b x - a )\|b +--R 2atan(----------------------------) +--R b x +--R -----------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1285 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|b +--R * +--R log +--R +----------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x - a \|- b - b x)\|- a + (b x + a)\|- b +--R + +--R +----------+ +--R | 2 +--R b x\|- b x - a +--R / +--R +----------+ +--R | 2 +---+ +--R \|- b x - a \|- a + a +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b atan(-------------) +--R +----------+ +--R | 2 +--R \|- b x - a +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1285 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1285 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R +---+ | 2 +-+ +-+ +--R (\|- a - \|- b x - a )\|b x\|b +--R 2atan(----------------------------) - atan(-------------) +--R b x +----------+ +--R | 2 +--R \|- b x - a +--R (6) --------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1285 +t0:=1/sqrt(a^2-x^2) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1285 +r0:=atan(x/sqrt(a^2-x^2)) +--R +--R +--R x +--R (2) atan(------------) +--R +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a +--R (3) - 2atan(----------------) +--R x +--R Type: Union(Expression(Integer),...) +--E 17 + +--S 18 of 1285 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 2 2 +--R \|- x + a - a x +--R (4) - 2atan(----------------) - atan(------------) +--R x +---------+ +--R | 2 2 +--R \|- x + a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 19 + +)clear all + +--S 20 of 1285 +t0:=x^(3+m)/sqrt(a+b*x^2) +--R +--R +--R m + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1285 +--r0:=x^(2+m)*sqrt(a+b*x^2)/(b*(3+m))-a*x^(2+m)*_ +--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*sqrt((a+b*x^2)/a)/_ +--(b*(3+m)*sqrt(a+b*x^2)) +--E 21 + +--S 22 of 1285 +--a0:=integrate(t0,x) +--E 22 + +--S 23 of 1285 +--m0:=a0-r0 +--E 23 + +--S 24 of 1285 +--d0:=D(m0,x) +--E 24 + +)clear all + +--S 25 of 1285 +t0:=x^(2+m)/sqrt(a+b*x^2) +--R +--R +--R m + 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1285 +--r0:=x^(1+m)*sqrt(a+b*x^2)/(b*(2+m))-a*x^(1+m)*_ +--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(b*(2+m)*sqrt(a+b*x^2)) +--E 26 + +--S 27 of 1285 +--a0:=integrate(t0,x) +--E 27 + +--S 28 of 1285 +--m0:=a0-r0 +--E 28 + +--S 29 of 1285 +--d0:=D(m0,x) +--E 29 + +)clear all + +--S 30 of 1285 +t0:=x^(1+m)/sqrt(a+b*x^2) +--R +--R +--R m + 1 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1285 +--r0:=x^(2+m)*hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/((2+m)*sqrt(a+b*x^2)) +--E 31 + +--S 32 of 1285 +--a0:=integrate(t0,x) +--E 32 + +--S 33 of 1285 +--m0:=a0-r0 +--E 33 + +--S 34 of 1285 +--d0:=D(m0,x) +--E 34 + +)clear all + +--S 35 of 1285 +t0:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1285 +--r0:=x^(1+m)*hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/((1+m)*sqrt(a+b*x^2)) +--E 36 + +--S 37 of 1285 +--a0:=integrate(t0,x) +--E 37 + +--S 38 of 1285 +--m0:=a0-r0 +--E 38 + +--S 39 of 1285 +--d0:=D(m0,x) +--E 39 + +)clear all + +--S 40 of 1285 +t0:=x^(-1+m)/sqrt(a+b*x^2) +--R +--R +--R m - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1285 +--r0:=x^m*sqrt(a+b*x^2)/(a*m)-b*(1+m)*x^(2+m)*_ +--hypergeometric(1/2,1/2*(2+m),1/2*(4+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(a*m*(2+m)*sqrt(a+b*x^2)) +--E 41 + +--S 42 of 1285 +--a0:=integrate(t0,x) +--E 42 + +--S 43 of 1285 +--m0:=a0-r0 +--E 43 + +--S 44 of 1285 +--d0:=D(m0,x) +--E 44 + +)clear all + +--S 45 of 1285 +t0:=x^(-2+m)/sqrt(a+b*x^2) +--R +--R +--R m - 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 45 + +--S 46 of 1285 +--r0:=-x^(-1+m)*sqrt(a+b*x^2)/(a*(1-m))+b*m*x^(1+m)*_ +--hypergeometric(1/2,1/2*(1+m),1/2*(3+m),-b*x^2/a)*_ +--sqrt((a+b*x^2)/a)/(a*(1-m^2)*sqrt(a+b*x^2)) +--E 46 + +--S 47 of 1285 +--a0:=integrate(t0,x) +--E 47 + +--S 48 of 1285 +--m0:=a0-r0 +--E 48 + +--S 49 of 1285 +--d0:=D(m0,x) +--E 49 + +)clear all + +--S 50 of 1285 +t0:=x^(1+m)*(a*(2+m)+b*(3+m)*x^2)/sqrt(a+b*x^2) +--R +--R +--R 2 m + 1 +--R ((b m + 3b)x + a m + 2a)x +--R (1) ------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1285 +r0:=x^(2+m)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (2) x \|b x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 52 + +--S 53 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 54 + +)clear all + +--S 55 of 1285 +t0:=a*(2+m)*x^(1+m)/sqrt(a+b*x^2)+b*(3+m)*x^(3+m)/sqrt(a+b*x^2) +--R +--R +--R m + 3 m + 1 +--R (b m + 3b)x + (a m + 2a)x +--R (1) ----------------------------------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1285 +r0:=x^(2+m)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R m + 2 | 2 +--R (2) x \|b x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R (3) ---------------------------------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Union(Expression(Integer),...) +--E 57 + +--S 58 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 | 2 3 +-+ (m + 1)log(x) +--R ((- b x - 2a x)\|b x + a + (2b x + 2a x)\|a )%e +--R + +--R +--------+ +--R 2 m + 2 | 2 2 m + 2 +-+ +--R (b x + 2a)x \|b x + a + (- 2b x - 2a)x \|a +--R / +--R +--------+ +--R +-+ | 2 2 +--R 2\|a \|b x + a - b x - 2a +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 59 + +)clear all + +--S 60 of 1285 +t0:=x^(-1+m)*(a*m+b*(-1+m)*x^2)/(a+b*x^2)^(3/2) +--R +--R +--R 2 m - 1 +--R ((b m - b)x + a m)x +--R (1) ------------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1285 +r0:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ (m - 1)log(x) +--R (- x\|b x + a + x\|a )%e +--R (3) --------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R Type: Union(Expression(Integer),...) +--E 62 + +--S 63 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2 +--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a +--R + +--R 2 m +--R (- b x - a)x +--R / +--R +--------+ +--R 2 | 2 2 +-+ +--R (b x + a)\|b x + a + (- b x - a)\|a +--R Type: Expression(Integer) +--E 63 + +--S 64 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 64 + +)clear all + +--S 65 of 1285 +t0:=-b*x^(1+m)/(a+b*x^2)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^2) +--R +--R +--R m + 1 2 m - 1 +--R - b x + (b m x + a m)x +--R (1) --------------------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1285 +r0a:=x^m/sqrt(a+b*x^2) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1285 +r0b:=-b*x^(2+m)/(a*sqrt(a+b*x^2))+x^m*sqrt(a+b*x^2)/a +--R +--R +--R m + 2 2 m +--R - b x + (b x + a)x +--R (3) ------------------------- +--R +--------+ +--R | 2 +--R a\|b x + a +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ (m - 1)log(x) +--R (- x\|b x + a + x\|a )%e +--R (4) --------------------------------------- +--R +--------+ +--R +-+ | 2 2 +--R \|a \|b x + a - b x - a +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1285 +m0a:=a0-r0a +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 2 3 (m - 1)log(x) m +-+ | 2 +--R (- x\|a \|b x + a + b x + a x)%e + x \|a \|b x + a +--R + +--R 2 m +--R (- b x - a)x +--R / +--R +--------+ +--R 2 | 2 2 +-+ +--R (b x + a)\|b x + a + (- b x - a)\|a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1285 +--d0:=normalize m0a +--E 70 + +--S 71 of 1285 +m0b:=a0-r0b +--R +--R +--R (6) +--R +--------+ +--R +-+ | 2 3 2 (m - 1)log(x) +--R (- a x\|a \|b x + a + a b x + a x)%e +--R + +--R +--------+ +--R m + 2 2 m +-+ | 2 2 2 m + 2 +--R (- b x + (b x + a)x )\|a \|b x + a + (b x + a b)x +--R + +--R 2 4 2 2 m +--R (- b x - 2a b x - a )x +--R / +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + a )\|b x + a + (- a b x - a )\|a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1285 +--d0:=normalize m0b +--E 72 + +)clear all + +--S 73 of 1285 +t0:=x*(-1+x^2)^(7/3) +--R +--R +--R +------+ +--R 5 3 3| 2 +--R (1) (x - 2x + x)\|x - 1 +--R Type: Expression(Integer) +--E 73 + +--S 74 of 1285 +r0:=3/20*(-1+x^2)^(10/3) +--R +--R +--R +------+ +--R 6 4 2 3| 2 +--R (3x - 9x + 9x - 3)\|x - 1 +--R (2) ------------------------------ +--R 20 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 6 4 2 3| 2 +--R (3x - 9x + 9x - 3)\|x - 1 +--R (3) ------------------------------ +--R 20 +--R Type: Union(Expression(Integer),...) +--E 75 + +--S 76 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 77 + +)clear all + +--S 78 of 1285 +t0:=x*(1+x^2)^(1/3) +--R +--R +--R +------+ +--R 3| 2 +--R (1) x\|x + 1 +--R Type: Expression(Integer) +--E 78 + +--S 79 of 1285 +r0:=3/8*(1+x^2)^(4/3) +--R +--R +--R +------+ +--R 2 3| 2 +--R (3x + 3)\|x + 1 +--R (2) ------------------ +--R 8 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 2 3| 2 +--R (3x + 3)\|x + 1 +--R (3) ------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 80 + +--S 81 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 82 + +)clear all + +--S 83 of 1285 +t0:=x*(1-x^2)^(1/3) +--R +--R +--R +--------+ +--R 3| 2 +--R (1) x\|- x + 1 +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1285 +r0:=-3/8*(1-x^2)^(4/3) +--R +--R +--R +--------+ +--R 2 3| 2 +--R (3x - 3)\|- x + 1 +--R (2) -------------------- +--R 8 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 3| 2 +--R (3x - 3)\|- x + 1 +--R (3) -------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 85 + +--S 86 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 87 + +)clear all + +--S 88 of 1285 +t0:=x^3*(1+x^2)^(1/3) +--R +--R +--R +------+ +--R 3 3| 2 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 1285 +r0:=-3/8*(1+x^2)^(4/3)+3/14*(1+x^2)^(7/3) +--R +--R +--R +------+ +--R 4 2 3| 2 +--R (12x + 3x - 9)\|x + 1 +--R (2) ------------------------- +--R 56 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 4 2 3| 2 +--R (12x + 3x - 9)\|x + 1 +--R (3) ------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 90 + +--S 91 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 92 + +)clear all + +--S 93 of 1285 +t0:=x/(3+2*x^2)^(1/3) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R 3| 2 +--R \|2x + 3 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1285 +r0:=3/8*(3+2*x^2)^(2/3) +--R +--R +--R +-------+2 +--R 3| 2 +--R 3\|2x + 3 +--R (2) ------------ +--R 8 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +-------+2 +--R 3| 2 +--R 3\|2x + 3 +--R (3) ------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 97 + +)clear all + +--S 98 of 1285 +t0:=x^3/(4+x^2)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 2 +--R \|x + 4 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1285 +r0:=-9/5*(4+x^2)^(2/3)+3/10*x^2*(4+x^2)^(2/3) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (3x - 18)\|x + 4 +--R (2) -------------------- +--R 10 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (3x - 18)\|x + 4 +--R (3) -------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 100 + +--S 101 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 102 + +)clear all + +--S 103 of 1285 +t0:=x^3/(1+x^2)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1285 +r0:=-9/20*(1+x^2)^(2/3)+3/10*x^2*(1+x^2)^(2/3) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (6x - 9)\|x + 1 +--R (2) ------------------- +--R 20 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1285 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 2 3| 2 +--R (6x - 9)\|x + 1 +--R (3) ------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 105 + +--S 106 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 107 + +)clear all + +--S 108 of 1285 +t0:=x^3/(-1+x^2)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ----------------- +--R +------+ +--R 2 3| 2 +--R (x - 1)\|x - 1 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1285 +r0:=(-3/2)/(-1+x^2)^(1/3)+3/4*(-1+x^2)^(2/3) +--R +--R +--R 2 +--R 3x - 9 +--R (2) ---------- +--R +------+ +--R 3| 2 +--R 4\|x - 1 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 3x - 9 +--R (3) ---------- +--R +------+ +--R 3| 2 +--R 4\|x - 1 +--R Type: Union(Expression(Integer),...) +--E 110 + +--S 111 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 112 + +)clear all + +--S 113 of 1285 +t0:=x^(7/2)*(a+b*x^2) +--R +--R +--R 5 3 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1285 +r0:=2/9*a*x^(9/2)+2/13*b*x^(13/2) +--R +--R +--R 6 4 +-+ +--R (18b x + 26a x )\|x +--R (2) --------------------- +--R 117 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 6 4 +-+ +--R (18b x + 26a x )\|x +--R (3) --------------------- +--R 117 +--R Type: Union(Expression(Integer),...) +--E 115 + +--S 116 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 117 + +)clear all + +--S 118 of 1285 +t0:=x^(5/2)*(a+b*x^2) +--R +--R +--R 4 2 +-+ +--R (1) (b x + a x )\|x +--R Type: Expression(Integer) +--E 118 + +--S 119 of 1285 +r0:=2/7*a*x^(7/2)+2/11*b*x^(11/2) +--R +--R +--R 5 3 +-+ +--R (14b x + 22a x )\|x +--R (2) --------------------- +--R 77 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 3 +-+ +--R (14b x + 22a x )\|x +--R (3) --------------------- +--R 77 +--R Type: Union(Expression(Integer),...) +--E 120 + +--S 121 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 122 + +)clear all + +--S 123 of 1285 +t0:=x^(3/2)*(a+b*x^2) +--R +--R +--R 3 +-+ +--R (1) (b x + a x)\|x +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1285 +r0:=2/5*a*x^(5/2)+2/9*b*x^(9/2) +--R +--R +--R 4 2 +-+ +--R (10b x + 18a x )\|x +--R (2) --------------------- +--R 45 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +-+ +--R (10b x + 18a x )\|x +--R (3) --------------------- +--R 45 +--R Type: Union(Expression(Integer),...) +--E 125 + +--S 126 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 127 + +)clear all + +--S 128 of 1285 +t0:=(a+b*x^2)*sqrt(x) +--R +--R +--R 2 +-+ +--R (1) (b x + a)\|x +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1285 +r0:=2/3*a*x^(3/2)+2/7*b*x^(7/2) +--R +--R +--R 3 +-+ +--R (6b x + 14a x)\|x +--R (2) ------------------- +--R 21 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ +--R (6b x + 14a x)\|x +--R (3) ------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 130 + +--S 131 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1285 +t0:=(a+b*x^2)/sqrt(x) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1285 +r0:=2/5*b*x^(5/2)+2*a*sqrt(x) +--R +--R +--R 2 +-+ +--R (2b x + 10a)\|x +--R (2) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (2b x + 10a)\|x +--R (3) ----------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 135 + +--S 136 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 137 + +)clear all + +--S 138 of 1285 +t0:=(a+b*x^2)/x^(3/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1285 +r0:=2/3*b*x^(3/2)-2*a/sqrt(x) +--R +--R +--R 2 +--R 2b x - 6a +--R (2) ---------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b x - 6a +--R (3) ---------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 140 + +--S 141 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 142 + +)clear all + +--S 143 of 1285 +t0:=(a+b*x^2)/x^(5/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1285 +r0:=-2/3*a/x^(3/2)+2*b*sqrt(x) +--R +--R +--R 2 +--R 6b x - 2a +--R (2) ---------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 6b x - 2a +--R (3) ---------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 145 + +--S 146 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 147 + +)clear all + +--S 148 of 1285 +t0:=(a+b*x^2)/x^(7/2) +--R +--R +--R 2 +--R b x + a +--R (1) -------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1285 +r0:=-2/5*a/x^(5/2)-2*b/sqrt(x) +--R +--R +--R 2 +--R - 10b x - 2a +--R (2) ------------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 10b x - 2a +--R (3) ------------- +--R 2 +-+ +--R 5x \|x +--R Type: Union(Expression(Integer),...) +--E 150 + +--S 151 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 152 + +)clear all + +--S 153 of 1285 +t0:=x^(7/2)*(a+b*x^2)^2 +--R +--R +--R 2 7 5 2 3 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1285 +r0:=2/9*a^2*x^(9/2)+4/13*a*b*x^(13/2)+2/17*b^2*x^(17/2) +--R +--R +--R 2 8 6 2 4 +-+ +--R (234b x + 612a b x + 442a x )\|x +--R (2) ----------------------------------- +--R 1989 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 8 6 2 4 +-+ +--R (234b x + 612a b x + 442a x )\|x +--R (3) ----------------------------------- +--R 1989 +--R Type: Union(Expression(Integer),...) +--E 155 + +--S 156 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 1285 +t0:=x^(5/2)*(a+b*x^2)^2 +--R +--R +--R 2 6 4 2 2 +-+ +--R (1) (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1285 +r0:=2/7*a^2*x^(7/2)+4/11*a*b*x^(11/2)+2/15*b^2*x^(15/2) +--R +--R +--R 2 7 5 2 3 +-+ +--R (154b x + 420a b x + 330a x )\|x +--R (2) ----------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 7 5 2 3 +-+ +--R (154b x + 420a b x + 330a x )\|x +--R (3) ----------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 160 + +--S 161 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 162 + +)clear all + +--S 163 of 1285 +t0:=x^(3/2)*(a+b*x^2)^2 +--R +--R +--R 2 5 3 2 +-+ +--R (1) (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1285 +r0:=2/5*a^2*x^(5/2)+4/9*a*b*x^(9/2)+2/13*b^2*x^(13/2) +--R +--R +--R 2 6 4 2 2 +-+ +--R (90b x + 260a b x + 234a x )\|x +--R (2) ---------------------------------- +--R 585 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 4 2 2 +-+ +--R (90b x + 260a b x + 234a x )\|x +--R (3) ---------------------------------- +--R 585 +--R Type: Union(Expression(Integer),...) +--E 165 + +--S 166 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 167 + +)clear all + +--S 168 of 1285 +t0:=(a+b*x^2)^2*sqrt(x) +--R +--R +--R 2 4 2 2 +-+ +--R (1) (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1285 +r0:=2/3*a^2*x^(3/2)+4/7*a*b*x^(7/2)+2/11*b^2*x^(11/2) +--R +--R +--R 2 5 3 2 +-+ +--R (42b x + 132a b x + 154a x)\|x +--R (2) --------------------------------- +--R 231 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 2 +-+ +--R (42b x + 132a b x + 154a x)\|x +--R (3) --------------------------------- +--R 231 +--R Type: Union(Expression(Integer),...) +--E 170 + +--S 171 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 172 + +)clear all + +--S 173 of 1285 +t0:=(a+b*x^2)^2/sqrt(x) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1285 +r0:=4/5*a*b*x^(5/2)+2/9*b^2*x^(9/2)+2*a^2*sqrt(x) +--R +--R +--R 2 4 2 2 +-+ +--R (10b x + 36a b x + 90a )\|x +--R (2) ------------------------------ +--R 45 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +-+ +--R (10b x + 36a b x + 90a )\|x +--R (3) ------------------------------ +--R 45 +--R Type: Union(Expression(Integer),...) +--E 175 + +--S 176 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 177 + +)clear all + +--S 178 of 1285 +t0:=(a+b*x^2)^2/x^(3/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1285 +r0:=4/3*a*b*x^(3/2)+2/7*b^2*x^(7/2)-2*a^2/sqrt(x) +--R +--R +--R 2 4 2 2 +--R 6b x + 28a b x - 42a +--R (2) ----------------------- +--R +-+ +--R 21\|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 6b x + 28a b x - 42a +--R (3) ----------------------- +--R +-+ +--R 21\|x +--R Type: Union(Expression(Integer),...) +--E 180 + +--S 181 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 182 + +)clear all + +--S 183 of 1285 +t0:=(a+b*x^2)^2/x^(5/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1285 +r0:=-2/3*a^2/x^(3/2)+2/5*b^2*x^(5/2)+4*a*b*sqrt(x) +--R +--R +--R 2 4 2 2 +--R 6b x + 60a b x - 10a +--R (2) ----------------------- +--R +-+ +--R 15x\|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 6b x + 60a b x - 10a +--R (3) ----------------------- +--R +-+ +--R 15x\|x +--R Type: Union(Expression(Integer),...) +--E 185 + +--S 186 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 187 + +)clear all + +--S 188 of 1285 +t0:=(a+b*x^2)^2/x^(7/2) +--R +--R +--R 2 4 2 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1285 +r0:=-2/5*a^2/x^(5/2)+2/3*b^2*x^(3/2)-4*a*b/sqrt(x) +--R +--R +--R 2 4 2 2 +--R 10b x - 60a b x - 6a +--R (2) ----------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 10b x - 60a b x - 6a +--R (3) ----------------------- +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 190 + +--S 191 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 192 + +)clear all + +--S 193 of 1285 +t0:=x^(7/2)*(a+b*x^2)^3 +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1285 +r0:=2/9*a^3*x^(9/2)+6/13*a^2*b*x^(13/2)+6/17*a*b^2*x^(17/2)+2/21*b^3*x^(21/2) +--R +--R +--R 3 10 2 8 2 6 3 4 +-+ +--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x +--R (2) ---------------------------------------------------- +--R 13923 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 10 2 8 2 6 3 4 +-+ +--R (1326b x + 4914a b x + 6426a b x + 3094a x )\|x +--R (3) ---------------------------------------------------- +--R 13923 +--R Type: Union(Expression(Integer),...) +--E 195 + +--S 196 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 197 + +)clear all + +--S 198 of 1285 +t0:=x^(5/2)*(a+b*x^2)^3 +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (1) (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1285 +r0:=2/7*a^3*x^(7/2)+6/11*a^2*b*x^(11/2)+2/5*a*b^2*x^(15/2)+2/19*b^3*x^(19/2) +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x +--R (2) -------------------------------------------------- +--R 7315 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 7 2 5 3 3 +-+ +--R (770b x + 2926a b x + 3990a b x + 2090a x )\|x +--R (3) -------------------------------------------------- +--R 7315 +--R Type: Union(Expression(Integer),...) +--E 200 + +--S 201 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 202 + +)clear all + +--S 203 of 1285 +t0:=x^(3/2)*(a+b*x^2)^3 +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1285 +r0:=2/5*a^3*x^(5/2)+2/3*a^2*b*x^(9/2)+6/13*a*b^2*x^(13/2)+2/17*b^3*x^(17/2) +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x +--R (2) -------------------------------------------------- +--R 3315 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 8 2 6 2 4 3 2 +-+ +--R (390b x + 1530a b x + 2210a b x + 1326a x )\|x +--R (3) -------------------------------------------------- +--R 3315 +--R Type: Union(Expression(Integer),...) +--E 205 + +--S 206 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 207 + +)clear all + +--S 208 of 1285 +t0:=(a+b*x^2)^3*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (1) (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1285 +r0:=2/3*a^3*x^(3/2)+6/7*a^2*b*x^(7/2)+6/11*a*b^2*x^(11/2)+2/15*b^3*x^(15/2) +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (154b x + 630a b x + 990a b x + 770a x)\|x +--R (2) ---------------------------------------------- +--R 1155 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 5 2 3 3 +-+ +--R (154b x + 630a b x + 990a b x + 770a x)\|x +--R (3) ---------------------------------------------- +--R 1155 +--R Type: Union(Expression(Integer),...) +--E 210 + +--S 211 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 212 + +)clear all + +--S 213 of 1285 +t0:=(a+b*x^2)^3/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1285 +r0:=6/5*a^2*b*x^(5/2)+2/3*a*b^2*x^(9/2)+2/13*b^3*x^(13/2)+2*a^3*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (30b x + 130a b x + 234a b x + 390a )\|x +--R (2) -------------------------------------------- +--R 195 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +-+ +--R (30b x + 130a b x + 234a b x + 390a )\|x +--R (3) -------------------------------------------- +--R 195 +--R Type: Union(Expression(Integer),...) +--E 215 + +--S 216 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1285 +t0:=(a+b*x^2)^3/x^(3/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1285 +r0:=2*a^2*b*x^(3/2)+6/7*a*b^2*x^(7/2)+2/11*b^3*x^(11/2)-2*a^3/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 14b x + 66a b x + 154a b x - 154a +--R (2) ------------------------------------- +--R +-+ +--R 77\|x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 14b x + 66a b x + 154a b x - 154a +--R (3) ------------------------------------- +--R +-+ +--R 77\|x +--R Type: Union(Expression(Integer),...) +--E 220 + +--S 221 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 222 + +)clear all + +--S 223 of 1285 +t0:=(a+b*x^2)^3/x^(5/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1285 +r0:=-2/3*a^3/x^(3/2)+6/5*a*b^2*x^(5/2)+2/9*b^3*x^(9/2)+6*a^2*b*sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 54a b x + 270a b x - 30a +--R (2) ------------------------------------ +--R +-+ +--R 45x\|x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 54a b x + 270a b x - 30a +--R (3) ------------------------------------ +--R +-+ +--R 45x\|x +--R Type: Union(Expression(Integer),...) +--E 225 + +--S 226 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 227 + +)clear all + +--S 228 of 1285 +t0:=(a+b*x^2)^3/x^(7/2) +--R +--R +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1285 +r0:=-2/5*a^3/x^(5/2)+2*a*b^2*x^(3/2)+2/7*b^3*x^(7/2)-6*a^2*b/sqrt(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 70a b x - 210a b x - 14a +--R (2) ------------------------------------ +--R 2 +-+ +--R 35x \|x +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 10b x + 70a b x - 210a b x - 14a +--R (3) ------------------------------------ +--R 2 +-+ +--R 35x \|x +--R Type: Union(Expression(Integer),...) +--E 230 + +--S 231 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 232 + +)clear all + +--S 233 of 1285 +t0:=x^(7/2)/(a+b*x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1285 +r0:=2/5*x^(5/2)/b-a^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_ + sqrt(2))+a^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*_ + sqrt(2))-1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(b^(9/4)*sqrt(2))+1/2*a^(5/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-2*a*sqrt(x)/b^2 +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5a\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5a\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10a\|a atan(-------------------) + 10a\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 2 +-+4+-+ +-+ +--R (4b x - 20a)\|2 \|b \|x +--R / +--R 2 +-+4+-+ +--R 10b \|2 \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +--R | 5 | 5 +--R 2 | a +-+ 2 | a +--R 5b |- ---- log(a\|x + 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R +------+ +--R | 5 +--R 2 | a +--R +------+ +------+ +------+ 2b |- ---- +--R | 5 | 5 | 5 4| 9 +--R 2 | a +-+ 2 | a 2 | a \| 16b +--R - 5b |- ---- log(a\|x - 2b |- ---- - 10b |- ---- atan(------------) +--R 4| 9 4| 9 4| 9 +-+ +--R \| 16b \| 16b \| 16b a\|x +--R + +--R 2 +-+ +--R (2b x - 10a)\|x +--R / +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 235 + +--S 236 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - a\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R | 5 | 5 +--R 2 +-+ | a 4+-+ +-+ 2 | a +--R 2b \|2 |- ---- \|b log(a\|x + 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R +------+ +------+ +--R | 5 | 5 +--R 2 +-+ | a 4+-+ +-+ 2 | a +--R - 2b \|2 |- ---- \|b log(a\|x - 2b |- ----) +--R 4| 9 4| 9 +--R \| 16b \| 16b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R a\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2a\|a atan(-------------------) - 2a\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | 5 +--R 2 | a +--R +------+ 2b |- ---- +--R | 5 4| 9 +--R 2 +-+ | a 4+-+ \| 16b +--R - 4b \|2 |- ---- \|b atan(------------) +--R 4| 9 +-+ +--R \| 16b a\|x +--R / +--R 2 +-+4+-+ +--R 2b \|2 \|b +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 237 + +)clear all + +--S 238 of 1285 +t0:=x^(5/2)/(a+b*x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1285 +r0:=2/3*x^(3/2)/b+a^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_ + sqrt(2))-a^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(7/4)*_ + sqrt(2))-1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(b^(7/4)*sqrt(2))+1/2*a^(3/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 3\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R - 6\|a atan(-------------------) - 6\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +-+ +--R 4x\|2 \|b \|x +--R / +--R +-+4+-+3 +--R 6b\|2 \|b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | 3 | 3 +--R | a 2 +-+ 5 | a +--R - 3b |- ---- log(a \|x + 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R +------+3 +--R | 3 +--R 5 | a +--R +------+ +------+3 +------+ 8b |- ---- +--R | 3 | 3 | 3 4| 7 +--R | a 2 +-+ 5 | a | a \| 16b +--R 3b |- ---- log(a \|x - 8b |- ---- - 6b |- ---- atan(-------------) +--R 4| 7 4| 7 4| 7 2 +-+ +--R \| 16b \| 16b \| 16b a \|x +--R + +--R +-+ +--R 2x\|x +--R / +--R 3b +--R Type: Union(Expression(Integer),...) +--E 240 + +--S 241 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R | 3 | 3 +--R +-+ | a 4+-+3 2 +-+ 5 | a +--R - 2b\|2 |- ---- \|b log(a \|x + 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R +------+ +------+3 +--R | 3 | 3 +--R +-+ | a 4+-+3 2 +-+ 5 | a +--R 2b\|2 |- ---- \|b log(a \|x - 8b |- ---- ) +--R 4| 7 4| 7 +--R \| 16b \| 16b +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 2\|a atan(-------------------) + 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R | 3 +--R 5 | a +--R +------+ 8b |- ---- +--R | 3 4| 7 +--R +-+ | a 4+-+3 \| 16b +--R - 4b\|2 |- ---- \|b atan(-------------) +--R 4| 7 2 +-+ +--R \| 16b a \|x +--R / +--R +-+4+-+3 +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 242 + +)clear all + +--S 243 of 1285 +t0:=x^(3/2)/(a+b*x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1285 +r0:=a^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))-_ + a^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(b^(5/4)*sqrt(2))+_ + 1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (b^(5/4)*sqrt(2))-1/2*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(b^(5/4)*sqrt(2))+2*sqrt(x)/b +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2\|a atan(-------------------) - 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +-+ +--R 4\|2 \|b \|x +--R / +--R +-+4+-+ +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +------+ +--R | a +-+ | a | a +-+ | a +--R - b |- ---- log(\|x + 2b |- ---- + b |- ---- log(\|x - 2b |- ----) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 16b \| 16b \| 16b \| 16b +--R + +--R +------+ +--R | a +--R 2b |- ---- +--R +------+ 4| 5 +--R | a \| 16b +-+ +--R 2b |- ---- atan(----------- + 2\|x +--R 4| 5 +-+ +--R \| 16b \|x +--R / +--R b +--R Type: Union(Expression(Integer),...) +--E 245 + +--S 246 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R +-+ | a 4+-+ +-+ | a +--R - 2b\|2 |- ---- \|b log(\|x + 2b |- ----) +--R 4| 5 4| 5 +--R \| 16b \| 16b +--R + +--R +------+ +------+ +--R +-+ | a 4+-+ +-+ | a +--R 2b\|2 |- ---- \|b log(\|x - 2b |- ----) +--R 4| 5 4| 5 +--R \| 16b \| 16b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 2\|a atan(-------------------) + 2\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | a +--R 2b |- ---- +--R +------+ 4| 5 +--R +-+ | a 4+-+ \| 16b +--R 4b\|2 |- ---- \|b atan(-----------) +--R 4| 5 +-+ +--R \| 16b \|x +--R / +--R +-+4+-+ +--R 2b\|2 \|b +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 247 + +)clear all + +--S 248 of 1285 +t0:=sqrt(x)/(a+b*x^2) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1285 +r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*_ + b^(3/4)*sqrt(2))-1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(1/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R 2atan(-------------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R | 1 +-+ 2 | 1 +--R |- ------ log(\|x + 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+ +--------+3 +--R | 1 +-+ 2 | 1 +--R - |- ------ log(\|x - 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+3 +--R 2 | 1 +--R 8a b |- ------ +--R +--------+ 4| 3 +--R | 1 \| 16a b +--R 2 |- ------ atan(-----------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R Type: Union(Expression(Integer),...) +--E 250 + +--S 251 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1 +--R 2\|2 |- ------ \|a \|b log(\|x + 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +--------+ +--------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 2 | 1 +--R - 2\|2 |- ------ \|a \|b log(\|x - 8a b |- ------ ) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------+3 +--R 2 | 1 +--R 8a b |- ------ +--R +--------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 16a b +--R 4\|2 |- ------ \|a \|b atan(-----------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R / +--R +-+4+-+4+-+3 +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 252 + +)clear all + +--S 253 of 1285 +t0:=1/((a+b*x^2)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R 2 +-+ +--R (b x + a)\|x +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1285 +r0:=-atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_ + atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_ + 1/2*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*_ + b^(1/4)*sqrt(2))+1/2*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(3/4)*b^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) + 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R 2atan(-------------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 4+-+ +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | 1 +-+ | 1 | 1 +-+ | 1 +--R |- ----- log(\|x + 2a |- -----) - |- ----- log(\|x - 2a |- -----) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 16a b \| 16a b \| 16a b \| 16a b +--R + +--R +-------+ +--R | 1 +--R 2a |- ----- +--R +-------+ 4| 3 +--R | 1 \| 16a b +--R - 2 |- ----- atan(------------) +--R 4| 3 +-+ +--R \| 16a b \|x +--R Type: Union(Expression(Integer),...) +--E 255 + +--S 256 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R 2\|2 |- ----- \|a \|b log(\|x + 2a |- -----) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-------+ +-------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R - 2\|2 |- ----- \|a \|b log(\|x - 2a |- -----) +--R 4| 3 4| 3 +--R \| 16a b \| 16a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-------+ +--R | 1 +--R 2a |- ----- +--R +-+4+-+ +-+ 4+-+ +-------+ 4| 3 +--R \|2 \|b \|x - \|a +-+ | 1 4+-+3 4+-+ \| 16a b +--R - 2atan(-------------------) - 4\|2 |- ----- \|a \|b atan(------------) +--R 4+-+ 4| 3 +-+ +--R \|a \| 16a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 2\|2 \|a \|b +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 257 + +)clear all + +--S 258 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------------- +--R 3 +-+ +--R (b x + a x)\|x +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1285 +r0:=b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_ + b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*sqrt(2))-_ + 1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(5/4)*sqrt(2))+1/2*b^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(5/4)*sqrt(2))+(-2)/(a*sqrt(x)) +--R +--R +--R (2) +--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ +-+ \|2 \|b \|x + \|a 4+-+ +-+ \|2 \|b \|x - \|a +--R - 2\|b \|x atan(-------------------) - 2\|b \|x atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R +-+4+-+ +-+ +--R 2a\|2 \|a \|x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | b +-+ +-+ 4 | b +--R - a |- ---- \|x log(b\|x + 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | b +-+ +-+ 4 | b +--R a |- ---- \|x log(b\|x - 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+3 +--R 4 | b +--R 8a |- ---- +--R +------+ 4| 5 +--R | b +-+ \| 16a +--R - 2a |- ---- \|x atan(------------- - 2 +--R 4| 5 +-+ +--R \| 16a b\|x +--R / +--R +-+ +--R a\|x +--R Type: Union(Expression(Integer),...) +--E 260 + +--S 261 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R +-+ | b 4+-+ +-+ 4 | b +--R - 2a\|2 |- ---- \|a log(b\|x + 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R +-+ | b 4+-+ +-+ 4 | b +--R 2a\|2 |- ---- \|a log(b\|x - 8a |- ---- ) +--R 4| 5 4| 5 +--R \| 16a \| 16a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 2\|b atan(-------------------) + 2\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R 4 | b +--R 8a |- ---- +--R +------+ 4| 5 +--R +-+ | b 4+-+ \| 16a +--R - 4a\|2 |- ---- \|a atan(-------------) +--R 4| 5 +-+ +--R \| 16a b\|x +--R / +--R +-+4+-+ +--R 2a\|2 \|a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 2 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1285 +r0:=(-2/3)/(a*x^(3/2))+b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(7/4)*sqrt(2))-b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(7/4)*sqrt(2))+1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2))-1/2*b^(3/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 3x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 4+-+3 +-+ \|2 \|b \|x + \|a +--R - 6x \|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 4+-+3 +-+ \|2 \|b \|x - \|a +-+4+-+3 +--R - 6x \|b \|x atan(-------------------) - 4\|2 \|a +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 +-+ +--R 6a x\|2 \|a \|x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +--R | 3 | 3 +--R | b +-+ +-+ 2 | b +--R - 3a x |- ---- \|x log(b\|x + 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +------+ +--R | 3 | 3 +--R | b +-+ +-+ 2 | b +--R 3a x |- ---- \|x log(b\|x - 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +--R | 3 +--R 2 | b +--R +------+ 2a |- ---- +--R | 3 4| 7 +--R | b +-+ \| 16a +--R 6a x |- ---- \|x atan(------------ - 2 +--R 4| 7 +-+ +--R \| 16a b\|x +--R / +--R +-+ +--R 3a x\|x +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R \|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 +-+ 2 | b +--R - 2a\|2 |- ---- \|a log(b\|x + 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R +------+ +------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 +-+ 2 | b +--R 2a\|2 |- ---- \|a log(b\|x - 2a |- ----) +--R 4| 7 4| 7 +--R \| 16a \| 16a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - \|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 2\|b atan(-------------------) + 2\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+ +--R | 3 +--R 2 | b +--R +------+ 2a |- ---- +--R | 3 4| 7 +--R +-+ | b 4+-+3 \| 16a +--R 4a\|2 |- ---- \|a atan(------------) +--R 4| 7 +-+ +--R \| 16a b\|x +--R / +--R +-+4+-+3 +--R 2a\|2 \|a +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 5 3 +-+ +--R (b x + a x )\|x +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1285 +r0:=(-2/5)/(a*x^(5/2))-b^(5/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(9/4)*sqrt(2))+b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(9/4)*sqrt(2))+1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))-1/2*b^(5/4)*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+2*b/(a^2*sqrt(x)) +--R +--R +--R (2) +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5b x \|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5b x \|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x + \|a +--R 10b x \|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x - \|a 2 +-+4+-+ +--R 10b x \|b \|x atan(------------------- + (20b x - 4a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+ +-+ +--R 10a x \|2 \|a \|x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+3 +--R | 5 | 5 +--R 2 2 | b +-+ 4 +-+ 7 | b +--R 5a x |- ---- \|x log(b \|x + 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 2 | b +-+ 4 +-+ 7 | b +--R - 5a x |- ---- \|x log(b \|x - 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+3 +--R | 5 +--R 7 | b +--R +------+ 8a |- ---- +--R | 5 4| 9 +--R 2 2 | b +-+ \| 16a 2 +--R 10a x |- ---- \|x atan(------------- + 10b x - 2a +--R 4| 9 4 +-+ +--R \| 16a b \|x +--R / +--R 2 2 +-+ +--R 5a x \|x +--R Type: Union(Expression(Integer),...) +--E 270 + +--S 271 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 +-+ | b 4+-+ 4 +-+ 7 | b +--R 2a \|2 |- ---- \|a log(b \|x + 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R +------+ +------+3 +--R | 5 | 5 +--R 2 +-+ | b 4+-+ 4 +-+ 7 | b +--R - 2a \|2 |- ---- \|a log(b \|x - 8a |- ---- ) +--R 4| 9 4| 9 +--R \| 16a \| 16a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 2b\|b atan(-------------------) - 2b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +------+3 +--R | 5 +--R 7 | b +--R +------+ 8a |- ---- +--R | 5 4| 9 +--R 2 +-+ | b 4+-+ \| 16a +--R 4a \|2 |- ---- \|a atan(-------------) +--R 4| 9 4 +-+ +--R \| 16a b \|x +--R / +--R 2 +-+4+-+ +--R 2a \|2 \|a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +)clear all + +--S 273 of 1285 +t0:=x^(7/2)/(a+b*x^2)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1285 +r0:=-1/2*x^(5/2)/(b*(a+b*x^2))+5/4*a^(1/4)*atan(1-b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))-5/4*a^(1/4)*atan(1+b^(1/4)*_ + sqrt(2)*sqrt(x)/a^(1/4))/(b^(9/4)*sqrt(2))+5/8*a^(1/4)*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(b^(9/4)*sqrt(2))-_ + 5/8*a^(1/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (b^(9/4)*sqrt(2))+5/2*sqrt(x)/b^2 +--R +--R +--R (2) +--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 5a)\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 5a)\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ \|2 \|b \|x + \|a +--R (- 10b x - 10a)\|a atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ \|2 \|b \|x - \|a 2 +-+4+-+ +-+ +--R (- 10b x - 10a)\|a atan(-------------------) + (16b x + 20a)\|2 \|b \|x +--R 4+-+ +--R \|a +--R / +--R 3 2 2 +-+4+-+ +--R (8b x + 8a b )\|2 \|b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R 3 2 2 | 625a +-+ 2 | 625a +--R (- 2b x - 2a b ) |- ------ log(5\|x + 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R 3 2 2 | 625a +-+ 2 | 625a +--R (2b x + 2a b ) |- ------ log(5\|x - 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--R 2 | 625a +--R 8b |- ------ +--R +--------+ 4| 9 +--R 3 2 2 | 625a \| 4096b 2 +-+ +--R (4b x + 4a b ) |- ------ atan(-------------- + (4b x + 5a)\|x +--R 4| 9 +-+ +--R \| 4096b 5\|x +--R / +--R 3 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 275 + +--S 276 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5\|a log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+ +--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a +--R - 8b \|2 |- ------ \|b log(5\|x + 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R 2 +-+ | 625a 4+-+ +-+ 2 | 625a +--R 8b \|2 |- ------ \|b log(5\|x - 8b |- ------) +--R 4| 9 4| 9 +--R \| 4096b \| 4096b +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5\|a log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10\|a atan(-------------------) + 10\|a atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R 2 | 625a +--R 8b |- ------ +--R +--------+ 4| 9 +--R 2 +-+ | 625a 4+-+ \| 4096b +--R 16b \|2 |- ------ \|b atan(--------------) +--R 4| 9 +-+ +--R \| 4096b 5\|x +--R / +--R 2 +-+4+-+ +--R 8b \|2 \|b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1285 +t0:=x^(5/2)/(a+b*x^2)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1285 +r0:=-1/2*x^(3/2)/(b*(a+b*x^2))-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/4*atan(1+b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(1/4)*b^(7/4)*sqrt(2))+3/8*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(1/4)*b^(7/4)*_ + sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(1/4)*b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 3a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 3a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (6b x + 6a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+ +--R (6b x + 6a)atan(-------------------) - 4x\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+4+-+3 +--R (8b x + 8a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 5 | 1 +--R (6b x + 6a b) |- -------- log(\|x + 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 5 | 1 +--R (- 6b x - 6a b) |- -------- log(\|x - 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 5 | 1 +--R 512a b |- -------- +--R +----------+ 4| 7 +--R 2 2 | 1 \| 4096a b +-+ +--R (12b x + 12a b) |- -------- atan(--------------------- - x\|x +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 280 + +--S 281 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1 +--R 24b\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 5 | 1 +--R - 24b\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- ) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 5 | 1 +--R 512a b |- -------- +--R +----------+ 4| 7 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 48b\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+4+-+3 +--R 8b\|2 \|a \|b +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 282 + +)clear all + +--S 283 of 1285 +t0:=x^(3/2)/(a+b*x^2)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1285 +r0:=-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*b^(5/4)*_ + sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(3/4)*_ + b^(5/4)*sqrt(2))-1/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*sqrt(2))+1/8*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(5/4)*_ + sqrt(2))-1/2*sqrt(x)/(b*(a+b*x^2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (b x + a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- b x - a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (2b x + 2a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+ +--R (2b x + 2a)atan(-------------------) - 4\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+3 4+-+ +--R (8b x + 8a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R 2 2 | 1 +-+ | 1 +--R (2b x + 2a b) |- -------- log(\|x + 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+ +--R 2 2 | 1 +-+ | 1 +--R (- 2b x - 2a b) |- -------- log(\|x - 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +--R | 1 +--R 8a b |- -------- +--R +----------+ 4| 3 5 +--R 2 2 | 1 \| 4096a b +-+ +--R (- 4b x - 4a b) |- -------- atan(----------------- - \|x +--R 4| 3 5 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 285 + +--S 286 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R 8b\|2 |- -------- \|a \|b log(\|x + 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ +-+ | 1 +--R - 8b\|2 |- -------- \|a \|b log(\|x - 8a b |- --------) +--R 4| 3 5 4| 3 5 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+ +--R | 1 +--R 8a b |- -------- +--R +----------+ 4| 3 5 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 16b\|2 |- -------- \|a \|b atan(-----------------) +--R 4| 3 5 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 8b\|2 \|a \|b +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 287 + +)clear all + +--S 288 of 1285 +t0:=sqrt(x)/(a+b*x^2)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R 2 4 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1285 +r0:=1/2*x^(3/2)/(a*(a+b*x^2))-1/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(5/4)*b^(3/4)*sqrt(2))+1/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(5/4)*b^(3/4)*sqrt(2))+1/8*log(sqrt(a)+x*sqrt(b)-_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(3/4)*sqrt(2))-_ + 1/8*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(5/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- b x - a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (b x + a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (2b x + 2a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+4+-+3 +-+ +--R (2b x + 2a)atan(-------------------) + 4x\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+4+-+3 +--R (8a b x + 8a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 4 2 | 1 +--R (2a b x + 2a ) |- -------- log(\|x + 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R 2 2 | 1 +-+ 4 2 | 1 +--R (- 2a b x - 2a ) |- -------- log(\|x - 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 4 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 5 3 +--R 2 2 | 1 \| 4096a b +-+ +--R (4a b x + 4a ) |- -------- atan(--------------------- + x\|x +--R 4| 5 3 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 290 + +--S 291 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1 +--R 8a\|2 |- -------- \|a \|b log(\|x + 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 +-+ 4 2 | 1 +--R - 8a\|2 |- -------- \|a \|b log(\|x - 512a b |- -------- ) +--R 4| 5 3 4| 5 3 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - log(- \|2 \|a \|b \|x + x\|b + \|a ) - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 2atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 4 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 5 3 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 16a\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 5 3 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+4+-+3 +--R 8a\|2 \|a \|b +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 292 + +)clear all + +--S 293 of 1285 +t0:=1/((a+b*x^2)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 4 2 2 +-+ +--R (b x + 2a b x + a )\|x +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1285 +r0:=-3/4*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*sqrt(2))+_ + 3/4*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(1/4)*_ + sqrt(2))-3/8*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+3/8*log(sqrt(a)+x*sqrt(b)+_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(1/4)*sqrt(2))+_ + 1/2*sqrt(x)/(a*(a+b*x^2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 3a)log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 3a)log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x + \|a +--R (6b x + 6a)atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 \|2 \|b \|x - \|a +-+4+-+3 4+-+ +-+ +--R (6b x + 6a)atan(-------------------) + 4\|2 \|a \|b \|x +--R 4+-+ +--R \|a +--R / +--R 2 2 +-+4+-+3 4+-+ +--R (8a b x + 8a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R 2 2 | 1 +-+ 2 | 1 +--R (6a b x + 6a ) |- ------- log(\|x + 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R 2 2 | 1 +-+ 2 | 1 +--R (- 6a b x - 6a ) |- ------- log(\|x - 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +--R 2 | 1 +--R 8a |- ------- +--R +---------+ 4| 7 +--R 2 2 | 1 \| 4096a b +-+ +--R (- 12a b x - 12a ) |- ------- atan(--------------- + \|x +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R 2 2 +--R 2a b x + 2a +--R Type: Union(Expression(Integer),...) +--E 295 + +--S 296 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 24a\|2 |- ------- \|a \|b log(\|x + 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 24a\|2 |- ------- \|a \|b log(\|x - 8a |- -------) +--R 4| 7 4| 7 +--R \| 4096a b \| 4096a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +---------+ +--R 2 | 1 +--R 8a |- ------- +--R +---------+ 4| 7 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 48a\|2 |- ------- \|a \|b atan(---------------) +--R 4| 7 +-+ +--R \| 4096a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 8a\|2 \|a \|b +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 297 + +)clear all + +--S 298 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 5 3 2 +-+ +--R (b x + 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1285 +r0:=5/4*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*sqrt(2))-_ + 5/4*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_ + sqrt(2))-5/8*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+5/8*b^(1/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*sqrt(2))+_ + (-5/2)/(a^2*sqrt(x))+1/2/(a*(a+b*x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 5a)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 5a)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (- 10b x - 10a)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (- 10b x - 10a)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ +--R (- 20b x - 16a)\|2 \|a +--R / +--R 2 2 3 +-+4+-+ +-+ +--R (8a b x + 8a )\|2 \|a \|x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R 2 2 3 | 625b +-+ +-+ 7 | 625b +--R (- 2a b x - 2a ) |- ------ \|x log(125b\|x + 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 2 3 | 625b +-+ +-+ 7 | 625b +--R (2a b x + 2a ) |- ------ \|x log(125b\|x - 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+3 +--R 7 | 625b +--R 512a |- ------ +--R +--------+ 4| 9 +--R 2 2 3 | 625b +-+ \| 4096a 2 +--R (- 4a b x - 4a ) |- ------ \|x atan(----------------- - 5b x - 4a +--R 4| 9 +-+ +--R \| 4096a 125b\|x +--R / +--R 2 2 3 +-+ +--R (2a b x + 2a )\|x +--R Type: Union(Expression(Integer),...) +--E 300 + +--S 301 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------+ +--------+3 +--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b +--R - 8a \|2 |- ------ \|a log(125b\|x + 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 +-+ | 625b 4+-+ +-+ 7 | 625b +--R 8a \|2 |- ------ \|a log(125b\|x - 512a |- ------ ) +--R 4| 9 4| 9 +--R \| 4096a \| 4096a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 5\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 10\|b atan(-------------------) + 10\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+3 +--R 7 | 625b +--R 512a |- ------ +--R +--------+ 4| 9 +--R 2 +-+ | 625b 4+-+ \| 4096a +--R - 16a \|2 |- ------ \|a atan(-----------------) +--R 4| 9 +-+ +--R \| 4096a 125b\|x +--R / +--R 2 +-+4+-+ +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 302 + +)clear all + +--S 303 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 6 4 2 2 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1285 +r0:=(-7/6)/(a^2*x^(3/2))+1/2/(a*x^(3/2)*(a+b*x^2))+7/4*b^(3/4)*_ + atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*sqrt(2))-_ + 7/4*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_ + sqrt(2))+7/8*b^(3/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2))-7/8*b^(3/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 21b x - 21a x)\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 3 4+-+3 +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (21b x + 21a x)\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 4+-+3 +-+ \|2 \|b \|x + \|a +--R (- 42b x - 42a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 4+-+3 +-+ \|2 \|b \|x - \|a +--R (- 42b x - 42a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 +--R (- 28b x - 16a)\|2 \|a +--R / +--R 2 3 3 +-+4+-+3 +-+ +--R (24a b x + 24a x)\|2 \|a \|x +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b +--R (- 6a b x - 6a x) |- ------- \|x log(7b\|x + 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 3 3 | 2401b +-+ +-+ 3 | 2401b +--R (6a b x + 6a x) |- ------- \|x log(7b\|x - 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +--R | 3 +--R 3 | 2401b +--R +---------+ 8a |- ------- +--R | 3 4| 11 +--R 2 3 3 | 2401b +-+ \| 4096a 2 +--R (12a b x + 12a x) |- ------- \|x atan(--------------- - 7b x - 4a +--R 4| 11 +-+ +--R \| 4096a 7b\|x +--R / +--R 2 3 3 +-+ +--R (6a b x + 6a x)\|x +--R Type: Union(Expression(Integer),...) +--E 305 + +--S 306 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 7\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b +--R - 8a \|2 |- ------- \|a log(7b\|x + 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+ +--R | 3 | 3 +--R 2 +-+ | 2401b 4+-+3 +-+ 3 | 2401b +--R 8a \|2 |- ------- \|a log(7b\|x - 8a |- -------) +--R 4| 11 4| 11 +--R \| 4096a \| 4096a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 7\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 14\|b atan(-------------------) + 14\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +---------+ +--R | 3 +--R 3 | 2401b +--R +---------+ 8a |- ------- +--R | 3 4| 11 +--R 2 +-+ | 2401b 4+-+3 \| 4096a +--R 16a \|2 |- ------- \|a atan(---------------) +--R 4| 11 +-+ +--R \| 4096a 7b\|x +--R / +--R 2 +-+4+-+3 +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 307 + +)clear all + +--S 308 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 7 5 2 3 +-+ +--R (b x + 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1285 +r0:=(-9/10)/(a^2*x^(5/2))+1/2/(a*x^(5/2)*(a+b*x^2))-9/4*b^(5/4)*_ + atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*sqrt(2))+_ + 9/4*b^(5/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_ + sqrt(2))+9/8*b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))-9/8*b^(5/4)*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+_ + 9/2*b/(a^3*sqrt(x)) +--R +--R +--R (2) +--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 45b x - 45a b x )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (45b x + 45a b x )\|b \|x log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (90b x + 90a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (90b x + 90a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+ +--R (180b x + 144a b x - 16a )\|2 \|a +--R / +--R 3 4 4 2 +-+4+-+ +-+ +--R (40a b x + 40a x )\|2 \|a \|x +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b +--R (10a b x + 10a x ) |- ------- \|x log(729b \|x + 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 4 4 2 | 6561b +-+ 4 +-+ 10 | 6561b +--R (- 10a b x - 10a x ) |- ------- \|x log(729b \|x - 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+3 +--R | 5 +--R 10 | 6561b +--R +---------+ 512a |- ------- +--R | 5 4| 13 +--R 3 4 4 2 | 6561b +-+ \| 4096a 2 4 +--R (20a b x + 20a x ) |- ------- \|x atan(------------------- + 45b x +--R 4| 13 4 +-+ +--R \| 4096a 729b \|x +--R + +--R 2 2 +--R 36a b x - 4a +--R / +--R 3 4 4 2 +-+ +--R (10a b x + 10a x )\|x +--R Type: Union(Expression(Integer),...) +--E 310 + +--S 311 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 9b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b +--R 8a \|2 |- ------- \|a log(729b \|x + 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R +---------+ +---------+3 +--R | 5 | 5 +--R 3 +-+ | 6561b 4+-+ 4 +-+ 10 | 6561b +--R - 8a \|2 |- ------- \|a log(729b \|x - 512a |- ------- ) +--R 4| 13 4| 13 +--R \| 4096a \| 4096a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 9b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 18b\|b atan(-------------------) - 18b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +---------+3 +--R | 5 +--R 10 | 6561b +--R +---------+ 512a |- ------- +--R | 5 4| 13 +--R 3 +-+ | 6561b 4+-+ \| 4096a +--R 16a \|2 |- ------- \|a atan(-------------------) +--R 4| 13 4 +-+ +--R \| 4096a 729b \|x +--R / +--R 3 +-+4+-+ +--R 8a \|2 \|a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 312 + +)clear all + +--S 313 of 1285 +t0:=x^(7/2)/(a+b*x^2)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1285 +r0:=-1/4*x^(5/2)/(b*(a+b*x^2)^2)-5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(3/4)*b^(9/4)*sqrt(2))-5/64*log(sqrt(a)+_ + x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(3/4)*b^(9/4)*_ + sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*_ + sqrt(x))/(a^(3/4)*b^(9/4)*sqrt(2))-5/16*sqrt(x)/(b^2*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 10a b x + 5a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 10a b x - 5a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (- 36b x - 20a)\|2 \|a \|b \|x +--R / +--R 4 4 3 2 2 2 +-+4+-+3 4+-+ +--R (64b x + 128a b x + 64a b )\|2 \|a \|b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (80b x + 160a b x + 80a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x + 64a b |- ------------) +--R 4| 3 9 +--R \| 16777216a b +--R + +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (- 80b x - 160a b x - 80a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x - 64a b |- ------------) +--R 4| 3 9 +--R \| 16777216a b +--R + +--R +--------------+ +--R 4 4 3 2 2 2 | 1 +--R (- 160b x - 320a b x - 160a b ) |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R * +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R 4| 3 9 +--R \| 16777216a b +--R atan(-----------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (- 9b x - 5a)\|x +--R / +--R 4 4 3 2 2 2 +--R 16b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 315 + +--S 316 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 5log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 320b \|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------) +--R 4| 3 9 4| 3 9 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 320b \|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------) +--R 4| 3 9 4| 3 9 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R +--------------+ 4| 3 9 +--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 640b \|2 |- ------------ \|a \|b atan(-----------------------) +--R 4| 3 9 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+3 4+-+ +--R 64b \|2 \|a \|b +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 317 + +)clear all + +--S 318 of 1285 +t0:=x^(5/2)/(a+b*x^2)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1285 +r0:=-1/4*x^(3/2)/(b*(a+b*x^2)^2)+3/16*x^(3/2)/(a*b*(a+b*x^2))-_ + 3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*b^(7/4)*_ + sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(5/4)*_ + b^(7/4)*sqrt(2))+3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2))-3/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(5/4)*b^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 6a b x - 3a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 +-+4+-+4+-+3 +-+ +--R (12b x - 4a x)\|2 \|a \|b \|x +--R / +--R 3 4 2 2 2 3 +-+4+-+4+-+3 +--R (64a b x + 128a b x + 64a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (48a b x + 96a b x + 48a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 48a b x - 96a b x - 48a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (96a b x + 192a b x + 96a b) |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R 4 5 | 1 +--R 262144a b |- ------------ +--R 4| 5 7 +--R \| 16777216a b +--R atan(----------------------------) +--R +-+ +--R \|x +--R + +--R 3 +-+ +--R (3b x - a x)\|x +--R / +--R 3 4 2 2 2 3 +--R 16a b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 320 + +--S 321 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--R +-+ | 1 4+-+4+-+3 +--R 192a b\|2 |- ------------ \|a \|b +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R +-+ | 1 4+-+4+-+3 +--R 192a b\|2 |- ------------ \|a \|b +--R 4| 5 7 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 4 5 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 5 7 +--R \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 4 5 | 1 +--R 262144a b |- ------------ +--R +--------------+ 4| 5 7 +--R +-+ | 1 4+-+4+-+3 \| 16777216a b +--R 384a b\|2 |- ------------ \|a \|b atan(----------------------------) +--R 4| 5 7 +-+ +--R \| 16777216a b \|x +--R / +--R +-+4+-+4+-+3 +--R 64a b\|2 \|a \|b +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 322 + +)clear all + +--S 323 of 1285 +t0:=x^(3/2)/(a+b*x^2)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1285 +r0:=-3/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*b^(5/4)*_ + sqrt(2))+3/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(7/4)*_ + b^(5/4)*sqrt(2))-3/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*sqrt(2))+3/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(7/4)*b^(5/4)*_ + sqrt(2))-1/4*sqrt(x)/(b*(a+b*x^2)^2)+1/16*sqrt(x)/(a*b*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (3b x + 6a b x + 3a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 3b x - 6a b x - 3a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (6b x + 12a b x + 6a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (4b x - 12a)\|2 \|a \|b \|x +--R / +--R 3 4 2 2 2 3 +-+4+-+3 4+-+ +--R (64a b x + 128a b x + 64a b)\|2 \|a \|b +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (48a b x + 96a b x + 48a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x + 64a b |- ------------) +--R 4| 7 5 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 48a b x - 96a b x - 48a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 2 | 1 +--R log(\|x - 64a b |- ------------) +--R 4| 7 5 +--R \| 16777216a b +--R + +--R +--------------+ +--R 3 4 2 2 2 3 | 1 +--R (- 96a b x - 192a b x - 96a b) |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R * +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R 4| 7 5 +--R \| 16777216a b +--R atan(----------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (b x - 3a)\|x +--R / +--R 3 4 2 2 2 3 +--R 16a b x + 32a b x + 16a b +--R Type: Union(Expression(Integer),...) +--E 325 + +--S 326 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 3log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R 192a b\|2 |- ------------ \|a \|b log(\|x + 64a b |- ------------) +--R 4| 7 5 4| 7 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R +-+ | 1 4+-+3 4+-+ +-+ 2 | 1 +--R - 192a b\|2 |- ------------ \|a \|b log(\|x - 64a b |- ------------) +--R 4| 7 5 4| 7 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 3log(- \|2 \|a \|b \|x + x\|b + \|a ) - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 6atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 2 | 1 +--R 64a b |- ------------ +--R +--------------+ 4| 7 5 +--R +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 384a b\|2 |- ------------ \|a \|b atan(----------------------) +--R 4| 7 5 +-+ +--R \| 16777216a b \|x +--R / +--R +-+4+-+3 4+-+ +--R 64a b\|2 \|a \|b +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 327 + +)clear all + +--S 328 of 1285 +t0:=sqrt(x)/(a+b*x^2)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1285 +r0:=1/4*x^(3/2)/(a*(a+b*x^2)^2)+5/16*x^(3/2)/(a^2*(a+b*x^2))-_ + 5/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*b^(3/4)*_ + sqrt(2))+5/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(9/4)*_ + b^(3/4)*sqrt(2))+5/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2))-5/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(9/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 5b x - 10a b x - 5a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (5b x + 10a b x + 5a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (10b x + 20a b x + 10a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 +-+4+-+4+-+3 +-+ +--R (20b x + 36a x)\|2 \|a \|b \|x +--R / +--R 2 2 4 3 2 4 +-+4+-+4+-+3 +--R (64a b x + 128a b x + 64a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (80a b x + 160a b x + 80a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 80a b x - 160a b x - 80a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (160a b x + 320a b x + 160a ) |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R 7 2 | 1 +--R 262144a b |- ------------ +--R 4| 9 3 +--R \| 16777216a b +--R atan(----------------------------) +--R +-+ +--R \|x +--R + +--R 3 +-+ +--R (5b x + 9a x)\|x +--R / +--R 2 2 4 3 2 4 +--R 16a b x + 32a b x + 16a +--R Type: Union(Expression(Integer),...) +--E 330 + +--S 331 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R 5log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 320a \|2 |- ------------ \|a \|b +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x + 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 320a \|2 |- ------------ \|a \|b +--R 4| 9 3 +--R \| 16777216a b +--R * +--R +--------------+3 +--R +-+ 7 2 | 1 +--R log(\|x - 262144a b |- ------------ ) +--R 4| 9 3 +--R \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R - 5log(- \|2 \|a \|b \|x + x\|b + \|a ) - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 10atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 7 2 | 1 +--R 262144a b |- ------------ +--R +--------------+ 4| 9 3 +--R 2 +-+ | 1 4+-+4+-+3 \| 16777216a b +--R 640a \|2 |- ------------ \|a \|b atan(----------------------------) +--R 4| 9 3 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+4+-+3 +--R 64a \|2 \|a \|b +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 332 + +)clear all + +--S 333 of 1285 +t0:=1/((a+b*x^2)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 6 2 4 2 2 3 +-+ +--R (b x + 3a b x + 3a b x + a )\|x +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1285 +r0:=-21/32*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*b^(1/4)*_ + sqrt(2))+21/32*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(11/4)*_ + b^(1/4)*sqrt(2))-21/64*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*_ + sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*sqrt(2))+21/64*log(sqrt(a)+_ + x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(11/4)*b^(1/4)*_ + sqrt(2))+1/4*sqrt(x)/(a*(a+b*x^2)^2)+7/16*sqrt(x)/(a^2*(a+b*x^2)) +--R +--R +--R (2) +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (21b x + 42a b x + 21a )log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 +-+4+-+4+-+ +-+ +-+ +-+ +--R (- 21b x - 42a b x - 21a )log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x + \|a +--R (42b x + 84a b x + 42a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 \|2 \|b \|x - \|a +--R (42b x + 84a b x + 42a )atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+3 4+-+ +-+ +--R (28b x + 44a)\|2 \|a \|b \|x +--R / +--R 2 2 4 3 2 4 +-+4+-+3 4+-+ +--R (64a b x + 128a b x + 64a )\|2 \|a \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (336a b x + 672a b x + 336a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 3 | 1 +--R log(\|x + 64a |- ------------) +--R 4| 11 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 336a b x - 672a b x - 336a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R +-+ 3 | 1 +--R log(\|x - 64a |- ------------) +--R 4| 11 +--R \| 16777216a b +--R + +--R +--------------+ +--R 2 2 4 3 2 4 | 1 +--R (- 672a b x - 1344a b x - 672a ) |- ------------ +--R 4| 11 +--R \| 16777216a b +--R * +--R +--------------+ +--R 3 | 1 +--R 64a |- ------------ +--R 4| 11 +--R \| 16777216a b +--R atan(---------------------) +--R +-+ +--R \|x +--R + +--R 2 +-+ +--R (7b x + 11a)\|x +--R / +--R 2 2 4 3 2 4 +--R 16a b x + 32a b x + 16a +--R Type: Union(Expression(Integer),...) +--E 335 + +--S 336 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R - 21log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1 +--R 1344a \|2 |- ------------ \|a \|b log(\|x + 64a |- ------------) +--R 4| 11 4| 11 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +-+ 3 | 1 +--R - 1344a \|2 |- ------------ \|a \|b log(\|x - 64a |- ------------) +--R 4| 11 4| 11 +--R \| 16777216a b \| 16777216a b +--R + +--R +-+4+-+ +-+ 4+-+ +--R +-+4+-+4+-+ +-+ +-+ +-+ \|2 \|b \|x + \|a +--R 21log(- \|2 \|a \|b \|x + x\|b + \|a ) - 42atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R \|2 \|b \|x - \|a +--R - 42atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+ +--R 3 | 1 +--R 64a |- ------------ +--R +--------------+ 4| 11 +--R 2 +-+ | 1 4+-+3 4+-+ \| 16777216a b +--R - 2688a \|2 |- ------------ \|a \|b atan(---------------------) +--R 4| 11 +-+ +--R \| 16777216a b \|x +--R / +--R 2 +-+4+-+3 4+-+ +--R 64a \|2 \|a \|b +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 337 + +)clear all + +--S 338 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 7 2 5 2 3 3 +-+ +--R (b x + 3a b x + 3a b x + a x)\|x +--R Type: Expression(Integer) +--E 338 + +--S 339 of 1285 +r0:=45/32*b^(1/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(13/4)*_ + sqrt(2))-45/32*b^(1/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(13/4)*sqrt(2))-45/64*b^(1/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*sqrt(2))+45/64*b^(1/4)*_ + log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(13/4)*_ + sqrt(2))+(-45/16)/(a^3*sqrt(x))+1/4/(a*(a+b*x^2)^2*sqrt(x))+_ + 9/16/(a^2*(a+b*x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 4 2 2 4+-+ +-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R (45b x + 90a b x + 45a )\|b \|x log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 4 2 2 4+-+ +-+ +--R (- 45b x - 90a b x - 45a )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (- 90b x - 180a b x - 90a )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+ +--R (- 180b x - 324a b x - 128a )\|2 \|a +--R / +--R 3 2 4 4 2 5 +-+4+-+ +-+ +--R (64a b x + 128a b x + 64a )\|2 \|a \|x +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (- 16a b x - 32a b x - 16a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x + 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (16a b x + 32a b x + 16a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x - 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +--R 3 2 4 4 2 5 | 4100625b +-+ +--R (- 32a b x - 64a b x - 32a ) |- ----------- \|x +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R 10 | 4100625b +--R 262144a |- ----------- +--R 4| 13 +--R \| 16777216a +--R atan(--------------------------) +--R +-+ +--R 91125b\|x +--R + +--R 2 4 2 2 +--R - 45b x - 81a b x - 32a +--R / +--R 3 2 4 4 2 5 +-+ +--R (16a b x + 32a b x + 16a )\|x +--R Type: Union(Expression(Integer),...) +--E 340 + +--S 341 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 45\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R - +--R +-------------+ +--R 3 +-+ | 4100625b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 13 +--R \| 16777216a +--R * +--R +-------------+3 +--R +-+ 10 | 4100625b +--R log(91125b\|x + 262144a |- ----------- ) +--R 4| 13 +--R \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R 3 +-+ | 4100625b 4+-+ +-+ 10 | 4100625b +--R 64a \|2 |- ----------- \|a log(91125b\|x - 262144a |- ----------- ) +--R 4| 13 4| 13 +--R \| 16777216a \| 16777216a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 45\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R 90\|b atan(-------------------) + 90\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+3 +--R 10 | 4100625b +--R 262144a |- ----------- +--R +-------------+ 4| 13 +--R 3 +-+ | 4100625b 4+-+ \| 16777216a +--R - 128a \|2 |- ----------- \|a atan(--------------------------) +--R 4| 13 +-+ +--R \| 16777216a 91125b\|x +--R / +--R 3 +-+4+-+ +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 342 + +)clear all + +--S 343 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 8 2 6 2 4 3 2 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1285 +r0:=(-77/48)/(a^3*x^(3/2))+1/4/(a*x^(3/2)*(a+b*x^2)^2)+11/16/(a^2*x^(3/2)*_ + (a+b*x^2))+77/32*b^(3/4)*atan(1-b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/_ + (a^(15/4)*sqrt(2))-77/32*b^(3/4)*atan(1+b^(1/4)*sqrt(2)*sqrt(x)/_ + a^(1/4))/(a^(15/4)*sqrt(2))+77/64*b^(3/4)*log(sqrt(a)+x*sqrt(b)-_ + a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2))-77/64*b^(3/4)*_ + log(sqrt(a)+x*sqrt(b)+a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/(a^(15/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 5 3 2 4+-+3 +-+ +--R (- 231b x - 462a b x - 231a x)\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 2 5 3 2 4+-+3 +-+ +--R (231b x + 462a b x + 231a x)\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x + \|a +--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 2 5 3 2 4+-+3 +-+ \|2 \|b \|x - \|a +--R (- 462b x - 924a b x - 462a x)\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 2 4 2 2 +-+4+-+3 +--R (- 308b x - 484a b x - 128a )\|2 \|a +--R / +--R 3 2 5 4 3 5 +-+4+-+3 +-+ +--R (192a b x + 384a b x + 192a x)\|2 \|a \|x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (- 48a b x - 96a b x - 48a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R +-+ 4 | 35153041b +--R log(77b\|x + 64a |- -----------) +--R 4| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (48a b x + 96a b x + 48a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R +-+ 4 | 35153041b +--R log(77b\|x - 64a |- -----------) +--R 4| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 2 5 4 3 5 | 35153041b +-+ +--R (96a b x + 192a b x + 96a x) |- ----------- \|x +--R 4| 15 +--R \| 16777216a +--R * +--R +-------------+ +--R | 3 +--R 4 | 35153041b +--R 64a |- ----------- +--R 4| 15 +--R \| 16777216a +--R atan(--------------------) +--R +-+ +--R 77b\|x +--R + +--R 2 4 2 2 +--R - 77b x - 121a b x - 32a +--R / +--R 3 2 5 4 3 5 +-+ +--R (48a b x + 96a b x + 48a x)\|x +--R Type: Union(Expression(Integer),...) +--E 345 + +--S 346 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R 77\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------------+ +-------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b +--R - 64a \|2 |- ----------- \|a log(77b\|x + 64a |- -----------) +--R 4| 15 4| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041b 4+-+3 +-+ 4 | 35153041b +--R 64a \|2 |- ----------- \|a log(77b\|x - 64a |- -----------) +--R 4| 15 4| 15 +--R \| 16777216a \| 16777216a +--R + +--R 4+-+3 +-+4+-+4+-+ +-+ +-+ +-+ +--R - 77\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+3 \|2 \|b \|x + \|a 4+-+3 \|2 \|b \|x - \|a +--R 154\|b atan(-------------------) + 154\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+ +--R | 3 +--R 4 | 35153041b +--R +-------------+ 64a |- ----------- +--R | 3 4| 15 +--R 3 +-+ | 35153041b 4+-+3 \| 16777216a +--R 128a \|2 |- ----------- \|a atan(--------------------) +--R 4| 15 +-+ +--R \| 16777216a 77b\|x +--R / +--R 3 +-+4+-+3 +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 9 2 7 2 5 3 3 +-+ +--R (b x + 3a b x + 3a b x + a x )\|x +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1285 +r0:=(-117/80)/(a^3*x^(5/2))+1/4/(a*x^(5/2)*(a+b*x^2)^2)+13/16/(a^2*_ + x^(5/2)*(a+b*x^2))-117/32*b^(5/4)*atan(1-b^(1/4)*sqrt(2)*_ + sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/32*b^(5/4)*atan(1+_ + b^(1/4)*sqrt(2)*sqrt(x)/a^(1/4))/(a^(17/4)*sqrt(2))+117/64*_ + b^(5/4)*log(sqrt(a)+x*sqrt(b)-a^(1/4)*b^(1/4)*sqrt(2)*sqrt(x))/_ + (a^(17/4)*sqrt(2))-117/64*b^(5/4)*log(sqrt(a)+x*sqrt(b)+a^(1/4)*_ + b^(1/4)*sqrt(2)*sqrt(x))/(a^(17/4)*sqrt(2))+117/16*b/(a^4*sqrt(x)) +--R +--R +--R (2) +--R 3 6 2 4 2 2 4+-+ +-+ +--R (- 585b x - 1170a b x - 585a b x )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R 3 6 2 4 2 2 4+-+ +-+ +--R (585b x + 1170a b x + 585a b x )\|b \|x +--R * +--R +-+4+-+4+-+ +-+ +-+ +-+ +--R log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x + \|a +--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ +-+ 4+-+ +--R 3 6 2 4 2 2 4+-+ +-+ \|2 \|b \|x - \|a +--R (1170b x + 2340a b x + 1170a b x )\|b \|x atan(-------------------) +--R 4+-+ +--R \|a +--R + +--R 3 6 2 4 2 2 3 +-+4+-+ +--R (2340b x + 4212a b x + 1664a b x - 128a )\|2 \|a +--R / +--R 4 2 6 5 4 6 2 +-+4+-+ +-+ +--R (320a b x + 640a b x + 320a x )\|2 \|a \|x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (80a b x + 160a b x + 80a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x + 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (- 80a b x - 160a b x - 80a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x - 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 4 2 6 5 4 6 2 | 187388721b +-+ +--R (160a b x + 320a b x + 160a x ) |- ----------- \|x +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 13 | 187388721b +--R 262144a |- ----------- +--R 4| 17 +--R \| 16777216a +--R atan(--------------------------) +--R 4 +-+ +--R 1601613b \|x +--R + +--R 3 6 2 4 2 2 3 +--R 585b x + 1053a b x + 416a b x - 32a +--R / +--R 4 2 6 5 4 6 2 +-+ +--R (80a b x + 160a b x + 80a x )\|x +--R Type: Union(Expression(Integer),...) +--E 350 + +--S 351 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R 117b\|b log(\|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-------------+ +--R | 5 +--R 4 +-+ | 187388721b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x + 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R - +--R +-------------+ +--R | 5 +--R 4 +-+ | 187388721b 4+-+ +--R 64a \|2 |- ----------- \|a +--R 4| 17 +--R \| 16777216a +--R * +--R +-------------+3 +--R | 5 +--R 4 +-+ 13 | 187388721b +--R log(1601613b \|x - 262144a |- ----------- ) +--R 4| 17 +--R \| 16777216a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ +-+ +-+ +--R - 117b\|b log(- \|2 \|a \|b \|x + x\|b + \|a ) +--R + +--R +-+4+-+ +-+ 4+-+ +-+4+-+ +-+ 4+-+ +--R 4+-+ \|2 \|b \|x + \|a 4+-+ \|2 \|b \|x - \|a +--R - 234b\|b atan(-------------------) - 234b\|b atan(-------------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------------+3 +--R | 5 +--R 13 | 187388721b +--R +-------------+ 262144a |- ----------- +--R | 5 4| 17 +--R 4 +-+ | 187388721b 4+-+ \| 16777216a +--R 128a \|2 |- ----------- \|a atan(--------------------------) +--R 4| 17 4 +-+ +--R \| 16777216a 1601613b \|x +--R / +--R 4 +-+4+-+ +--R 64a \|2 \|a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1285 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 352 + +)clear all + +--S 353 of 1285 +t0:=x^(7/2)/(1+x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1285 +r0:=2/5*x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-2*sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 5log(\|2 \|x + x + 1) - 5log(- \|2 \|x + x + 1) + 10atan(\|2 \|x + 1) +--R + +--R +-+ +-+ 2 +-+ +-+ +--R 10atan(\|2 \|x - 1) + (4x - 20)\|2 \|x +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 5\|2 log(\|2 \|x + x + 1) - 5\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 2 +-+ +--R - 10\|2 atan(------------) - 10\|2 atan(------------) + (8x - 40)\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1285 +t0:=x^(5/2)/(1+x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1285 +r0:=2/3*x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 3log(\|2 \|x + x + 1) - 3log(- \|2 \|x + x + 1) - 6atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ +--R - 6atan(\|2 \|x - 1) + 4x\|2 \|x +--R / +--R +-+ +--R 6\|2 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R 3\|2 log(\|2 \|x + x + 1) - 3\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 6\|2 atan(------------) + 6\|2 atan(------------) + 8x\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 360 + +--S 361 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 362 + +)clear all + +--S 363 of 1285 +t0:=x^(3/2)/(1+x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1285 +r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_ + 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/_ + sqrt(2)+2*sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) - 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ +--R - 2atan(\|2 \|x - 1) + 4\|2 \|x +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 2\|2 atan(------------) + 2\|2 atan(------------) + 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 365 + +--S 366 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1285 +t0:=sqrt(x)/(1+x^2) +--R +--R +--R +-+ +--R \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1285 +r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)+_ + 1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - log(\|2 \|x + x + 1) + log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +--R 2atan(\|2 \|x - 1) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - \|2 log(\|2 \|x + x + 1) + \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(------------) - 2\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 370 + +--S 371 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +)clear all + +--S 373 of 1285 +t0:=1/((1+x^2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------ +--R 2 +-+ +--R (x + 1)\|x +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1285 +r0:=-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R log(\|2 \|x + x + 1) - log(- \|2 \|x + x + 1) + 2atan(\|2 \|x + 1) +--R + +--R +-+ +-+ +--R 2atan(\|2 \|x - 1) +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R \|2 log(\|2 \|x + x + 1) - \|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(------------) - 2\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 375 + +--S 376 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 377 + +)clear all + +--S 378 of 1285 +t0:=1/(x^(3/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +-+ +--R (x + x)\|x +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1285 +r0:=atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/2*log(1+x+sqrt(2)*sqrt(x))/_ + sqrt(2)+(-2)/sqrt(x) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R \|x log(\|2 \|x + x + 1) - \|x log(- \|2 \|x + x + 1) +--R + +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 2\|x atan(\|2 \|x + 1) - 2\|x atan(\|2 \|x - 1) - 4\|2 +--R / +--R +-+ +-+ +--R 2\|2 \|x +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R x\|2 log(\|2 \|x + x + 1) - x\|2 log(- \|2 \|x + x + 1) +--R + +--R +-+ 1 +-+ 1 +-+ +--R 2x\|2 atan(------------) + 2x\|2 atan(------------) - 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 4x +--R Type: Union(Expression(Integer),...) +--E 380 + +--S 381 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 382 + +)clear all + +--S 383 of 1285 +t0:=1/(x^(5/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R 4 2 +-+ +--R (x + x )\|x +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1285 +r0:=(-2/3)/x^(3/2)+atan(1-sqrt(2)*sqrt(x))/sqrt(2)-atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R +-+ +-+ +-+ +-+ +-+ +-+ +--R - 3x\|x log(\|2 \|x + x + 1) + 3x\|x log(- \|2 \|x + x + 1) +--R + +--R +-+ +-+ +-+ +-+ +-+ +-+ +-+ +--R - 6x\|x atan(\|2 \|x + 1) - 6x\|x atan(\|2 \|x - 1) - 4\|2 +--R / +--R +-+ +-+ +--R 6x\|2 \|x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R - 3x \|2 log(\|2 \|x + x + 1) + 3x \|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +-+ +--R 6x \|2 atan(------------) + 6x \|2 atan(------------) - 8\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 2 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 385 + +--S 386 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R atan(\|2 \|x + 1) + atan(\|2 \|x - 1) + atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 387 + +)clear all + +--S 388 of 1285 +t0:=1/(x^(7/2)*(1+x^2)) +--R +--R +--R 1 +--R (1) ------------- +--R 5 3 +-+ +--R (x + x )\|x +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1285 +r0:=(-2/5)/x^(5/2)-atan(1-sqrt(2)*sqrt(x))/sqrt(2)+atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-1/2*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+2/sqrt(x) +--R +--R +--R (2) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R - 5x \|x log(\|2 \|x + x + 1) + 5x \|x log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ 2 +-+ +--R 10x \|x atan(\|2 \|x + 1) + 10x \|x atan(\|2 \|x - 1) + (20x - 4)\|2 +--R / +--R 2 +-+ +-+ +--R 10x \|2 \|x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ +-+ +-+ 3 +-+ +-+ +-+ +--R - 5x \|2 log(\|2 \|x + x + 1) + 5x \|2 log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ 1 3 +-+ 1 2 +-+ +--R - 10x \|2 atan(------------) - 10x \|2 atan(------------) + (40x - 8)\|x +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 3 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1285 +t0:=x^(7/2)/(1+x^2)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1285 +r0:=-1/2*x^(5/2)/(1+x^2)+5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)-5/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+5/2*sqrt(x) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 5x - 5)log(\|2 \|x + x + 1) + (5x + 5)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 10x - 10)atan(\|2 \|x + 1) + (- 10x - 10)atan(\|2 \|x - 1) +--R + +--R 2 +-+ +-+ +--R (16x + 20)\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (- 5x - 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ 1 +--R (5x + 5)\|2 log(- \|2 \|x + x + 1) + (10x + 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 2 +-+ 1 2 +-+ +--R (10x + 10)\|2 atan(------------) + (32x + 40)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 395 + +--S 396 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 397 + +)clear all + +--S 398 of 1285 +t0:=x^(5/2)/(1+x^2)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1285 +r0:=-1/2*x^(3/2)/(1+x^2)-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+_ + 3/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-3/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- 3x - 3)log(\|2 \|x + x + 1) + (3x + 3)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) - 4x\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (- 3x - 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ 1 +--R (3x + 3)\|2 log(- \|2 \|x + x + 1) + (- 6x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 2 +-+ 1 +-+ +--R (- 6x - 6)\|2 atan(------------) - 8x\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1285 +t0:=x^(3/2)/(1+x^2)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1285 +r0:=-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-1/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-1/2*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (x + 1)log(\|2 \|x + x + 1) + (- x - 1)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) - 4\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (x + 1)\|2 log(\|2 \|x + x + 1) + (- x - 1)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R - 8\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 405 + +--S 406 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 407 + +)clear all + +--S 408 of 1285 +t0:=sqrt(x)/(1+x^2)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------ +--R 4 2 +--R x + 2x + 1 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1285 +r0:=1/2*x^(3/2)/(1+x^2)-1/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+1/4*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)+1/8*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)-1/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (- x - 1)log(\|2 \|x + x + 1) + (x + 1)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (2x + 2)atan(\|2 \|x + 1) + (2x + 2)atan(\|2 \|x - 1) + 4x\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (- x - 1)\|2 log(\|2 \|x + x + 1) + (x + 1)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 2x - 2)\|2 atan(------------) + (- 2x - 2)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R 8x\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - atan(\|2 \|x + 1) - atan(\|2 \|x - 1) - atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1285 +t0:=1/((1+x^2)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------ +--R 4 2 +-+ +--R (x + 2x + 1)\|x +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1285 +r0:=-3/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-3/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)+1/2*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 2 +-+ +-+ 2 +-+ +-+ +--R (3x + 3)log(\|2 \|x + x + 1) + (- 3x - 3)log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ +-+ +-+ +--R (6x + 6)atan(\|2 \|x + 1) + (6x + 6)atan(\|2 \|x - 1) + 4\|2 \|x +--R / +--R 2 +-+ +--R (8x + 8)\|2 +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +-+ +-+ +--R (3x + 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ +--R (- 3x - 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R (- 6x - 6)\|2 atan(------------) + (- 6x - 6)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R +-+ +--R 8\|x +--R / +--R 2 +--R 16x + 16 +--R Type: Union(Expression(Integer),...) +--E 415 + +--S 416 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 417 + +)clear all + +--S 418 of 1285 +t0:=1/(x^(3/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 5 3 +-+ +--R (x + 2x + x)\|x +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1285 +r0:=5/4*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-5/4*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-5/8*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+5/8*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)+(-5/2)/sqrt(x)+1/2/((1+x^2)*sqrt(x)) +--R +--R +--R (2) +--R 2 +-+ +-+ +-+ +--R (5x + 5)\|x log(\|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ +--R (- 5x - 5)\|x log(- \|2 \|x + x + 1) +--R + +--R 2 +-+ +-+ +-+ 2 +-+ +-+ +-+ +--R (- 10x - 10)\|x atan(\|2 \|x + 1) + (- 10x - 10)\|x atan(\|2 \|x - 1) +--R + +--R 2 +-+ +--R (- 20x - 16)\|2 +--R / +--R 2 +-+ +-+ +--R (8x + 8)\|2 \|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ +-+ +-+ +--R (5x + 5x)\|2 log(\|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (- 5x - 5x)\|2 log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ 1 3 +-+ 1 +--R (10x + 10x)\|2 atan(------------) + (10x + 10x)\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R 2 +-+ +--R (- 40x - 32)\|x +--R / +--R 3 +--R 16x + 16x +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 5atan(\|2 \|x + 1) + 5atan(\|2 \|x - 1) + 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1285 +t0:=1/(x^(5/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------- +--R 6 4 2 +-+ +--R (x + 2x + x )\|x +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1285 +r0:=(-7/6)/x^(3/2)+1/2/(x^(3/2)*(1+x^2))+7/4*atan(1-sqrt(2)*sqrt(x))/_ + sqrt(2)-7/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+7/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-7/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 3 +-+ +-+ +-+ +--R (- 21x - 21x)\|x log(\|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (21x + 21x)\|x log(- \|2 \|x + x + 1) +--R + +--R 3 +-+ +-+ +-+ +--R (- 42x - 42x)\|x atan(\|2 \|x + 1) +--R + +--R 3 +-+ +-+ +-+ 2 +-+ +--R (- 42x - 42x)\|x atan(\|2 \|x - 1) + (- 28x - 16)\|2 +--R / +--R 3 +-+ +-+ +--R (24x + 24x)\|2 \|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 21x - 21x )\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (21x + 21x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 4 2 +-+ 1 +--R (42x + 42x )\|2 atan(------------) + (42x + 42x )\|2 atan(------------) +--R +-+ +-+ +-+ +-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R + +--R 2 +-+ +--R (- 56x - 32)\|x +--R / +--R 4 2 +--R 48x + 48x +--R Type: Union(Expression(Integer),...) +--E 425 + +--S 426 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 7atan(\|2 \|x + 1) + 7atan(\|2 \|x - 1) + 7atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 7atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 427 + +)clear all + +--S 428 of 1285 +t0:=1/(x^(7/2)*(1+x^2)^2) +--R +--R +--R 1 +--R (1) ------------------- +--R 7 5 3 +-+ +--R (x + 2x + x )\|x +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1285 +r0:=(-9/10)/x^(5/2)+1/2/(x^(5/2)*(1+x^2))-9/4*atan(1-sqrt(2)*sqrt(x))/_ + sqrt(2)+9/4*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+9/8*log(1+x-sqrt(2)*_ + sqrt(x))/sqrt(2)-9/8*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+9/2/sqrt(x) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +-+ +--R (- 45x - 45x )\|x log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (45x + 45x )\|x log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ 4 2 +-+ +-+ +-+ +--R (90x + 90x )\|x atan(\|2 \|x + 1) + (90x + 90x )\|x atan(\|2 \|x - 1) +--R + +--R 4 2 +-+ +--R (180x + 144x - 16)\|2 +--R / +--R 4 2 +-+ +-+ +--R (40x + 40x )\|2 \|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 +-+ +-+ +-+ +--R (- 45x - 45x )\|2 log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (45x + 45x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ 1 +--R (- 90x - 90x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 5 3 +-+ 1 4 2 +-+ +--R (- 90x - 90x )\|2 atan(------------) + (360x + 288x - 32)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 5 3 +--R 80x + 80x +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 9atan(\|2 \|x + 1) - 9atan(\|2 \|x - 1) - 9atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 9atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1285 +t0:=x^(7/2)/(1+x^2)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1285 +r0:=-1/4*x^(5/2)/(1+x^2)^2-5/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+5/32*_ + atan(1+sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x-sqrt(2)*sqrt(x))/_ + sqrt(2)+5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2)-5/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (5x + 10x + 5)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 5x - 10x - 5)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x - 1) + (- 36x - 20)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (5x + 10x + 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 5x - 10x - 5)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 10x - 20x - 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 10x - 20x - 10)\|2 atan(------------) + (- 72x - 40)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 435 + +--S 436 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 437 + +)clear all + +--S 438 of 1285 +t0:=x^(5/2)/(1+x^2)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1285 +r0:=-1/4*x^(3/2)/(1+x^2)^2+3/16*x^(3/2)/(1+x^2)-3/32*atan(1-sqrt(2)*_ + sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+3/64*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-3/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (- 3x - 6x - 3)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (3x + 6x + 3)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ 4 2 +-+ +-+ +--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1) +--R + +--R 3 +-+ +-+ +--R (12x - 4x)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 3x - 6x - 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (3x + 6x + 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 6x - 12x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 3 +-+ +--R (- 6x - 12x - 6)\|2 atan(------------) + (24x - 8x)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1285 +t0:=x^(3/2)/(1+x^2)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1285 +r0:=-3/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+3/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-3/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+3/64*log(1+x+sqrt(2)*_ + sqrt(x))/sqrt(2)-1/4*sqrt(x)/(1+x^2)^2+1/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (3x + 6x + 3)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 3x - 6x - 3)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ 4 2 +-+ +-+ +--R (6x + 12x + 6)atan(\|2 \|x + 1) + (6x + 12x + 6)atan(\|2 \|x - 1) +--R + +--R 2 +-+ +-+ +--R (4x - 12)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (3x + 6x + 3)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 3x - 6x - 3)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 6x - 12x - 6)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 6x - 12x - 6)\|2 atan(------------) + (8x - 24)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 445 + +--S 446 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 3atan(\|2 \|x + 1) - 3atan(\|2 \|x - 1) - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 3atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1285 +t0:=sqrt(x)/(1+x^2)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------ +--R 6 4 2 +--R x + 3x + 3x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1285 +r0:=1/4*x^(3/2)/(1+x^2)^2+5/16*x^(3/2)/(1+x^2)-5/32*atan(1-sqrt(2)*_ + sqrt(x))/sqrt(2)+5/32*atan(1+sqrt(2)*sqrt(x))/sqrt(2)+5/64*_ + log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-5/64*log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (- 5x - 10x - 5)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (5x + 10x + 5)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 3 +-+ +-+ +--R (10x + 20x + 10)atan(\|2 \|x - 1) + (20x + 36x)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (- 5x - 10x - 5)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (5x + 10x + 5)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 10x - 20x - 10)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 3 +-+ +--R (- 10x - 20x - 10)\|2 atan(------------) + (40x + 72x)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 5atan(\|2 \|x + 1) - 5atan(\|2 \|x - 1) - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 5atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1285 +t0:=1/((1+x^2)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 6 4 2 +-+ +--R (x + 3x + 3x + 1)\|x +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1285 +r0:=-21/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+21/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-21/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+21/64*log(1+x+_ + sqrt(2)*sqrt(x))/sqrt(2)+1/4*sqrt(x)/(1+x^2)^2+7/16*sqrt(x)/(1+x^2) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +--R (21x + 42x + 21)log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (- 21x - 42x - 21)log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +--R (42x + 84x + 42)atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ 2 +-+ +-+ +--R (42x + 84x + 42)atan(\|2 \|x - 1) + (28x + 44)\|2 \|x +--R / +--R 4 2 +-+ +--R (64x + 128x + 64)\|2 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ +-+ +-+ +--R (21x + 42x + 21)\|2 log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 21x - 42x - 21)\|2 log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ 1 +--R (- 42x - 84x - 42)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 4 2 +-+ 1 2 +-+ +--R (- 42x - 84x - 42)\|2 atan(------------) + (56x + 88)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 4 2 +--R 128x + 256x + 128 +--R Type: Union(Expression(Integer),...) +--E 455 + +--S 456 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 21atan(\|2 \|x + 1) - 21atan(\|2 \|x - 1) - 21atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 21atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 457 + +)clear all + +--S 458 of 1285 +t0:=1/(x^(3/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------ +--R 7 5 3 +-+ +--R (x + 3x + 3x + x)\|x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1285 +r0:=45/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-45/32*atan(1+sqrt(2)*sqrt(x))/_ + sqrt(2)-45/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)+45/64*log(1+x+_ + sqrt(2)*sqrt(x))/sqrt(2)+(-45/16)/sqrt(x)+1/4/((1+x^2)^2*sqrt(x))+_ + 9/16/((1+x^2)*sqrt(x)) +--R +--R +--R (2) +--R 4 2 +-+ +-+ +-+ +--R (45x + 90x + 45)\|x log(\|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 45x - 90x - 45)\|x log(- \|2 \|x + x + 1) +--R + +--R 4 2 +-+ +-+ +-+ +--R (- 90x - 180x - 90)\|x atan(\|2 \|x + 1) +--R + +--R 4 2 +-+ +-+ +-+ 4 2 +-+ +--R (- 90x - 180x - 90)\|x atan(\|2 \|x - 1) + (- 180x - 324x - 128)\|2 +--R / +--R 4 2 +-+ +-+ +--R (64x + 128x + 64)\|2 \|x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 +-+ +-+ +-+ +--R (45x + 90x + 45x)\|2 log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 45x - 90x - 45x)\|2 log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ 1 +--R (90x + 180x + 90x)\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 5 3 +-+ 1 4 2 +-+ +--R (90x + 180x + 90x)\|2 atan(------------) + (- 360x - 648x - 256)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 5 3 +--R 128x + 256x + 128x +--R Type: Union(Expression(Integer),...) +--E 460 + +--S 461 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 45atan(\|2 \|x + 1) + 45atan(\|2 \|x - 1) + 45atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 45atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 462 + +)clear all + +--S 463 of 1285 +t0:=1/(x^(5/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------- +--R 8 6 4 2 +-+ +--R (x + 3x + 3x + x )\|x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1285 +r0:=(-77/48)/x^(3/2)+1/4/(x^(3/2)*(1+x^2)^2)+11/16/(x^(3/2)*(1+x^2))+_ + 77/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)-77/32*atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+77/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-77/64*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2) +--R +--R +--R (2) +--R 5 3 +-+ +-+ +-+ +--R (- 231x - 462x - 231x)\|x log(\|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (231x + 462x + 231x)\|x log(- \|2 \|x + x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 462x - 924x - 462x)\|x atan(\|2 \|x + 1) +--R + +--R 5 3 +-+ +-+ +-+ +--R (- 462x - 924x - 462x)\|x atan(\|2 \|x - 1) +--R + +--R 4 2 +-+ +--R (- 308x - 484x - 128)\|2 +--R / +--R 5 3 +-+ +-+ +--R (192x + 384x + 192x)\|2 \|x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 4 2 +-+ +-+ +-+ +--R (- 231x - 462x - 231x )\|2 log(\|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (231x + 462x + 231x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ 1 +--R (462x + 924x + 462x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 6 4 2 +-+ 1 4 2 +-+ +--R (462x + 924x + 462x )\|2 atan(------------) + (- 616x - 968x - 256)\|x +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R 6 4 2 +--R 384x + 768x + 384x +--R Type: Union(Expression(Integer),...) +--E 465 + +--S 466 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R 77atan(\|2 \|x + 1) + 77atan(\|2 \|x - 1) + 77atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R 77atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 467 + +)clear all + +--S 468 of 1285 +t0:=1/(x^(7/2)*(1+x^2)^3) +--R +--R +--R 1 +--R (1) ------------------------- +--R 9 7 5 3 +-+ +--R (x + 3x + 3x + x )\|x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1285 +r0:=(-117/80)/x^(5/2)+1/4/(x^(5/2)*(1+x^2)^2)+13/16/(x^(5/2)*(1+x^2))-_ + 117/32*atan(1-sqrt(2)*sqrt(x))/sqrt(2)+117/32*atan(1+sqrt(2)*_ + sqrt(x))/sqrt(2)+117/64*log(1+x-sqrt(2)*sqrt(x))/sqrt(2)-117/64*_ + log(1+x+sqrt(2)*sqrt(x))/sqrt(2)+117/16/sqrt(x) +--R +--R +--R (2) +--R 6 4 2 +-+ +-+ +-+ +--R (- 585x - 1170x - 585x )\|x log(\|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (585x + 1170x + 585x )\|x log(- \|2 \|x + x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x + 1) +--R + +--R 6 4 2 +-+ +-+ +-+ +--R (1170x + 2340x + 1170x )\|x atan(\|2 \|x - 1) +--R + +--R 6 4 2 +-+ +--R (2340x + 4212x + 1664x - 128)\|2 +--R / +--R 6 4 2 +-+ +-+ +--R (320x + 640x + 320x )\|2 \|x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 5 3 +-+ +-+ +-+ +--R (- 585x - 1170x - 585x )\|2 log(\|2 \|x + x + 1) +--R + +--R 7 5 3 +-+ +-+ +-+ +--R (585x + 1170x + 585x )\|2 log(- \|2 \|x + x + 1) +--R + +--R 7 5 3 +-+ 1 +--R (- 1170x - 2340x - 1170x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 7 5 3 +-+ 1 +--R (- 1170x - 2340x - 1170x )\|2 atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R + +--R 6 4 2 +-+ +--R (4680x + 8424x + 3328x - 256)\|x +--R / +--R 7 5 3 +--R 640x + 1280x + 640x +--R Type: Union(Expression(Integer),...) +--E 470 + +--S 471 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ 1 +--R - 117atan(\|2 \|x + 1) - 117atan(\|2 \|x - 1) - 117atan(------------) +--R +-+ +-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 117atan(------------) +--R +-+ +-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 32\|2 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 472 + +)clear all + +--S 473 of 1285 +t0:=x^(2/3)/(1+x^2) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------ +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1285 +r0a:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))-_ + 1/2*atanh(x^(1/3)*sqrt(3)/(1+x^(2/3)))*sqrt(3) +--R +--R +--R (2) +--R +-+3+-+ +--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+ +--R - \|3 atanh(---------) + atan(2\|x + \|3 ) + atan(2\|x - \|3 ) +--R 3+-+2 +--R \|x + 1 +--R + +--R 3+-+ +--R 2atan(\|x ) +--R / +--R 2 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1285 +r0b:=atan(x^(1/3))-1/2*atan(-2*x^(1/3)+sqrt(3))+1/2*atan(2*x^(1/3)+sqrt(3))+_ + 1/4*log(1+x^(2/3)-x^(1/3)*sqrt(3))*sqrt(3)-1/4*log(1+x^(2/3)+_ + x^(1/3)*sqrt(3))*sqrt(3) +--R +--R +--R (3) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R 3+-+ +-+ 3+-+ +-+ 3+-+ +--R 2atan(2\|x + \|3 ) + 2atan(2\|x - \|3 ) + 4atan(\|x ) +--R / +--R 4 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R 3+-+ +--R 2\|x 1 1 +--R - 2atan(---------) - 2atan(------------) - 2atan(------------) +--R 3+-+2 3+-+ +-+ 3+-+ +-+ +--R \|x - 1 2\|x - \|3 2\|x + \|3 +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1285 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 3+-+2 +-+3+-+ +-+ 3+-+2 +-+3+-+ +--R - \|3 log(\|x + \|3 \|x + 1) + \|3 log(\|x - \|3 \|x + 1) +--R + +--R +-+3+-+ +--R +-+ \|3 \|x 3+-+ +-+ 3+-+ +-+ +--R 2\|3 atanh(---------) - 2atan(2\|x + \|3 ) - 2atan(2\|x - \|3 ) +--R 3+-+2 +--R \|x + 1 +--R + +--R 3+-+ +--R 3+-+ 2\|x 1 +--R - 4atan(\|x ) - 2atan(---------) - 2atan(------------) +--R 3+-+2 3+-+ +-+ +--R \|x - 1 2\|x - \|3 +--R + +--R 1 +--R - 2atan(------------) +--R 3+-+ +-+ +--R 2\|x + \|3 +--R / +--R 4 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1285 +d0:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1285 +m0b:=a0-r0b +--R +--R +--R (7) +--R 3+-+ +--R 3+-+ +-+ 3+-+ +-+ 3+-+ 2\|x +--R - atan(2\|x + \|3 ) - atan(2\|x - \|3 ) - 2atan(\|x ) - atan(---------) +--R 3+-+2 +--R \|x - 1 +--R + +--R 1 1 +--R - atan(------------) - atan(------------) +--R 3+-+ +-+ 3+-+ +-+ +--R 2\|x - \|3 2\|x + \|3 +--R / +--R 2 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1285 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1285 +t0:=x^(7/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 3 +-+ | 2 +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1285 +--r0:=4/77*a*x^(5/2)*sqrt(a+b*x^2)/b+2/11*x^(9/2)*sqrt(a+b*x^2)-_ +-- 20/231*a^2*sqrt(x)*sqrt(a+b*x^2)/b^2+20/231*a^(13/4)*_ +-- elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +-- ((-b)^(9/4)*sqrt(a+b*x^2)) +--E 482 + +--S 483 of 1285 +--a0:=integrate(t0,x) +--E 483 + +--S 484 of 1285 +--m0:=a0-r0 +--E 484 + +--S 485 of 1285 +--d0:=D(m0,x) +--E 485 + +)clear all + +--S 486 of 1285 +t0:=x^(5/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R 2 +-+ | 2 +--R (1) x \|x \|b x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1285 +--r0:=4/45*a*x^(3/2)*sqrt(a+b*x^2)/b+2/9*x^(7/2)*sqrt(a+b*x^2)+4/15*_ +--a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+_ +--b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-4/15*a^(11/4)*elliptic_f(_ +--asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2)) +--E 487 + +--S 488 of 1285 +--a0:=integrate(t0,x) +--E 488 + +--S 489 of 1285 +--m0:=a0-r0 +--E 489 + +--S 490 of 1285 +--d0:=D(m0,x) +--E 490 + +)clear all + +--S 491 of 1285 +t0:=x^(3/2)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R (1) x\|x \|b x + a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1285 +--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)+4/21*a*sqrt(x)*sqrt(a+b*x^2)/b+4/21*_ +--a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 492 + +--S 493 of 1285 +--a0:=integrate(t0,x) +--E 493 + +--S 494 of 1285 +--m0:=a0-r0 +--E 494 + +--S 495 of 1285 +--d0:=D(m0,x) +--E 495 + +)clear all + +--S 496 of 1285 +t0:=sqrt(x)*sqrt(a+b*x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R (1) \|x \|b x + a +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1285 +--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)+4/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-_ +--4/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2)) +--E 497 + +--S 498 of 1285 +--a0:=integrate(t0,x) +--E 498 + +--S 499 of 1285 +--m0:=a0-r0 +--E 499 + +--S 500 of 1285 +--d0:=D(m0,x) +--E 500 + +)clear all + +--S 501 of 1285 +t0:=sqrt(a+b*x^2)/sqrt(x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1285 +--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)+4/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 502 + +--S 503 of 1285 +--a0:=integrate(t0,x) +--E 503 + +--S 504 of 1285 +--m0:=a0-r0 +--E 504 + +--S 505 of 1285 +--d0:=D(m0,x) +--E 505 + +)clear all + +--S 506 of 1285 +t0:=sqrt(a+b*x^2)/x^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1285 +--r0:=-2*sqrt(a+b*x^2)/sqrt(x)-4*a^(3/4)*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)+4*a^(3/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 507 + +--S 508 of 1285 +--a0:=integrate(t0,x) +--E 508 + +--S 509 of 1285 +--m0:=a0-r0 +--E 509 + +--S 510 of 1285 +--d0:=D(m0,x) +--E 510 + +)clear all + +--S 511 of 1285 +t0:=sqrt(a+b*x^2)/x^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1285 +--r0:=-2/3*sqrt(a+b*x^2)/x^(3/2)-4/3*a^(1/4)*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 512 + +--S 513 of 1285 +--a0:=integrate(t0,x) +--E 513 + +--S 514 of 1285 +--m0:=a0-r0 +--E 514 + +--S 515 of 1285 +--d0:=D(m0,x) +--E 515 + +)clear all + +--S 516 of 1285 +t0:=sqrt(a+b*x^2)/x^(7/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (1) ----------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1285 +--r0:=-2/5*sqrt(a+b*x^2)/x^(5/2)-4/5*b*sqrt(a+b*x^2)/(a*sqrt(x))+4/5*_ +--(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2))-4/5*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*sqrt(a+b*x^2)) +--E 517 + +--S 518 of 1285 +--a0:=integrate(t0,x) +--E 518 + +--S 519 of 1285 +--m0:=a0-r0 +--E 519 + +--S 520 of 1285 +--d0:=D(m0,x) +--E 520 + +)clear all + +--S 521 of 1285 +t0:=x^(7/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 5 3 +-+ | 2 +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1285 +--r0:=2/15*x^(9/2)*(a+b*x^2)^(3/2)+8/385*a^2*x^(5/2)*sqrt(a+b*x^2)/b+_ +--4/55*a*x^(9/2)*sqrt(a+b*x^2)-8/231*a^3*sqrt(x)*sqrt(a+b*x^2)/b^2+_ +--8/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 522 + +--S 523 of 1285 +--a0:=integrate(t0,x) +--E 523 + +--S 524 of 1285 +--m0:=a0-r0 +--E 524 + +--S 525 of 1285 +--d0:=D(m0,x) +--E 525 + +)clear all + +--S 526 of 1285 +t0:=x^(5/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 4 2 +-+ | 2 +--R (1) (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1285 +--r0:=2/13*x^(7/2)*(a+b*x^2)^(3/2)+8/195*a^2*x^(3/2)*sqrt(a+b*x^2)/b+_ +--4/39*a*x^(7/2)*sqrt(a+b*x^2)+8/65*a^(15/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-_ +--8/65*a^(15/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 527 + +--S 528 of 1285 +--a0:=integrate(t0,x) +--E 528 + +--S 529 of 1285 +--m0:=a0-r0 +--E 529 + +--S 530 of 1285 +--d0:=D(m0,x) +--E 530 + +)clear all + +--S 531 of 1285 +t0:=x^(3/2)*(a+b*x^2)^(3/2) +--R +--R +--R +--------+ +--R 3 +-+ | 2 +--R (1) (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1285 +--r0:=2/11*x^(5/2)*(a+b*x^2)^(3/2)+12/77*a*x^(5/2)*sqrt(a+b*x^2)+_ +--8/77*a^2*sqrt(x)*sqrt(a+b*x^2)/b+8/77*a^(13/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(5/4)*sqrt(a+b*x^2)) +--E 532 + +--S 533 of 1285 +--a0:=integrate(t0,x) +--E 533 + +--S 534 of 1285 +--m0:=a0-r0 +--E 534 + +--S 535 of 1285 +--d0:=D(m0,x) +--E 535 + +)clear all + +--S 536 of 1285 +t0:=(a+b*x^2)^(3/2)*sqrt(x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 +--R (1) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1285 +--r0:=2/9*x^(3/2)*(a+b*x^2)^(3/2)+4/15*a*x^(3/2)*sqrt(a+b*x^2)+_ +--8/15*a^(11/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-8/15*a^(11/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 537 + +--S 538 of 1285 +--a0:=integrate(t0,x) +--E 538 + +--S 539 of 1285 +--m0:=a0-r0 +--E 539 + +--S 540 of 1285 +--d0:=D(m0,x) +--E 540 + +)clear all + +--S 541 of 1285 +t0:=(a+b*x^2)^(3/2)/sqrt(x) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1285 +--r0:=2/7*(a+b*x^2)^(3/2)*sqrt(x)+4/7*a*sqrt(x)*sqrt(a+b*x^2)+_ +--8/7*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 542 + +--S 543 of 1285 +--a0:=integrate(t0,x) +--E 543 + +--S 544 of 1285 +--m0:=a0-r0 +--E 544 + +--S 545 of 1285 +--d0:=D(m0,x) +--E 545 + +)clear all + +--S 546 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1285 +--r0:=-2*(a+b*x^2)^(3/2)/sqrt(x)+12/5*b*x^(3/2)*sqrt(a+b*x^2)-_ +--24/5*a^(7/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)+24/5*a^(7/4)*(-b)^(1/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 547 + +--S 548 of 1285 +--a0:=integrate(t0,x) +--E 548 + +--S 549 of 1285 +--m0:=a0-r0 +--E 549 + +--S 550 of 1285 +--d0:=D(m0,x) +--E 550 + +)clear all + +--S 551 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(5/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1285 +--r0:=-2/3*(a+b*x^2)^(3/2)/x^(3/2)+4/3*b*sqrt(x)*sqrt(a+b*x^2)-_ +--8/3*a^(5/4)*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 552 + +--S 553 of 1285 +--a0:=integrate(t0,x) +--E 553 + +--S 554 of 1285 +--m0:=a0-r0 +--E 554 + +--S 555 of 1285 +--d0:=D(m0,x) +--E 555 + +)clear all + +--S 556 of 1285 +t0:=(a+b*x^2)^(3/2)/x^(7/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1285 +--r0:=-2/5*(a+b*x^2)^(3/2)/x^(5/2)-12/5*b*sqrt(a+b*x^2)/sqrt(x)+_ +--24/5*a^(3/4)*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/sqrt(a+b*x^2)-24/5*a^(3/4)*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 557 + +--S 558 of 1285 +--a0:=integrate(t0,x) +--E 558 + +--S 559 of 1285 +--m0:=a0-r0 +--E 559 + +--S 560 of 1285 +--d0:=D(m0,x) +--E 560 + +)clear all + +--S 561 of 1285 +t0:=x^(7/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 7 5 2 3 +-+ | 2 +--R (1) (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1285 +--r0:=4/57*a*x^(9/2)*(a+b*x^2)^(3/2)+2/19*x^(9/2)*(a+b*x^2)^(5/2)+_ +--16/1463*a^3*x^(5/2)*sqrt(a+b*x^2)/b+8/209*a^2*x^(9/2)*sqrt(a+b*x^2)-_ +--80/4389*a^4*sqrt(x)*sqrt(a+b*x^2)/b^2+80/4389*a^(21/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(9/4)*sqrt(a+b*x^2)) +--E 562 + +--S 563 of 1285 +--a0:=integrate(t0,x) +--E 563 + +--S 564 of 1285 +--m0:=a0-r0 +--E 564 + +--S 565 of 1285 +--d0:=D(m0,x) +--E 565 + +)clear all + +--S 566 of 1285 +t0:=x^(5/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 +--R (1) (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1285 +--r0:=20/221*a*x^(7/2)*(a+b*x^2)^(3/2)+2/17*x^(7/2)*(a+b*x^2)^(5/2)+_ +--16/663*a^3*x^(3/2)*sqrt(a+b*x^2)/b+40/663*a^2*x^(7/2)*sqrt(a+b*x^2)+_ +--16/221*a^(19/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))-16/221*a^(19/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2)) +--E 567 + +--S 568 of 1285 +--a0:=integrate(t0,x) +--E 568 + +--S 569 of 1285 +--m0:=a0-r0 +--E 569 + +--S 570 of 1285 +--d0:=D(m0,x) +--E 570 + +)clear all + +--S 571 of 1285 +t0:=x^(3/2)*(a+b*x^2)^(5/2) +--R +--R +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (1) (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1285 +--r0:=4/33*a*x^(5/2)*(a+b*x^2)^(3/2)+2/15*x^(5/2)*(a+b*x^2)^(5/2)+_ +--8/77*a^2*x^(5/2)*sqrt(a+b*x^2)+16/231*a^3*sqrt(x)*sqrt(a+b*x^2)/_ +--b+16/231*a^(17/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 572 + +--S 573 of 1285 +--a0:=integrate(t0,x) +--E 573 + +--S 574 of 1285 +--m0:=a0-r0 +--E 574 + +--S 575 of 1285 +--d0:=D(m0,x) +--E 575 + +)clear all + +--S 576 of 1285 +t0:=(a+b*x^2)^(5/2)*sqrt(x) +--R +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 +--R (1) (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1285 +--r0:=20/117*a*x^(3/2)*(a+b*x^2)^(3/2)+2/13*x^(3/2)*(a+b*x^2)^(5/2)+_ +--8/39*a^2*x^(3/2)*sqrt(a+b*x^2)+16/39*a^(15/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2))-16/39*a^(15/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 577 + +--S 578 of 1285 +--a0:=integrate(t0,x) +--E 578 + +--S 579 of 1285 +--m0:=a0-r0 +--E 579 + +--S 580 of 1285 +--d0:=D(m0,x) +--E 580 + +)clear all + +--S 581 of 1285 +t0:=(a+b*x^2)^(5/2)/sqrt(x) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1285 +--r0:=20/77*a*(a+b*x^2)^(3/2)*sqrt(x)+2/11*(a+b*x^2)^(5/2)*sqrt(x)+_ +--40/77*a^2*sqrt(x)*sqrt(a+b*x^2)+80/77*a^(13/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(1/4)*sqrt(a+b*x^2)) +--E 582 + +--S 583 of 1285 +--a0:=integrate(t0,x) +--E 583 + +--S 584 of 1285 +--m0:=a0-r0 +--E 584 + +--S 585 of 1285 +--d0:=D(m0,x) +--E 585 + +)clear all + +--S 586 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(3/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1285 +--r0:=20/9*b*x^(3/2)*(a+b*x^2)^(3/2)-2*(a+b*x^2)^(5/2)/sqrt(x)+_ +--8/3*a*b*x^(3/2)*sqrt(a+b*x^2)-16/3*a^(11/4)*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)+16/3*a^(11/4)*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 587 + +--S 588 of 1285 +--a0:=integrate(t0,x) +--E 588 + +--S 589 of 1285 +--m0:=a0-r0 +--E 589 + +--S 590 of 1285 +--d0:=D(m0,x) +--E 590 + +)clear all + +--S 591 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(5/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1285 +--r0:=-2/3*(a+b*x^2)^(5/2)/x^(3/2)+20/21*b*(a+b*x^2)^(3/2)*sqrt(x)+_ +--40/21*a*b*sqrt(x)*sqrt(a+b*x^2)-80/21*a^(9/4)*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2) +--E 592 + +--S 593 of 1285 +--a0:=integrate(t0,x) +--E 593 + +--S 594 of 1285 +--m0:=a0-r0 +--E 594 + +--S 595 of 1285 +--d0:=D(m0,x) +--E 595 + +)clear all + +--S 596 of 1285 +t0:=(a+b*x^2)^(5/2)/x^(7/2) +--R +--R +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R (1) -------------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1285 +--r0:=-2/5*(a+b*x^2)^(5/2)/x^(5/2)-4*b*(a+b*x^2)^(3/2)/sqrt(x)+_ +--24/5*b^2*x^(3/2)*sqrt(a+b*x^2)+48/5*a^(7/4)*(-b)^(5/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--sqrt(a+b*x^2)-48/5*a^(7/4)*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/sqrt(a+b*x^2) +--E 597 + +--S 598 of 1285 +--a0:=integrate(t0,x) +--E 598 + +--S 599 of 1285 +--m0:=a0-r0 +--E 599 + +--S 600 of 1285 +--d0:=D(m0,x) +--E 600 + +)clear all + +--S 601 of 1285 +t0:=x^(7/2)/sqrt(a+b*x^2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1285 +--r0:=2/7*x^(5/2)*sqrt(a+b*x^2)/b-10/21*a*sqrt(x)*sqrt(a+b*x^2)/b^2+_ +--10/21*a^(9/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 602 + +--S 603 of 1285 +--a0:=integrate(t0,x) +--E 603 + +--S 604 of 1285 +--m0:=a0-r0 +--E 604 + +--S 605 of 1285 +--d0:=D(m0,x) +--E 605 + +)clear all + +--S 606 of 1285 +t0:=x^(5/2)/sqrt(a+b*x^2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1285 +--r0:=2/5*x^(3/2)*sqrt(a+b*x^2)/b+6/5*a^(7/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(7/4)*sqrt(a+b*x^2))-6/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 607 + +--S 608 of 1285 +--a0:=integrate(t0,x) +--E 608 + +--S 609 of 1285 +--m0:=a0-r0 +--E 609 + +--S 610 of 1285 +--d0:=D(m0,x) +--E 610 + +)clear all + +--S 611 of 1285 +t0:=x^(3/2)/sqrt(a+b*x^2) +--R +--R +--R +-+ +--R x\|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1285 +--r0:=2/3*sqrt(x)*sqrt(a+b*x^2)/b+2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 612 + +--S 613 of 1285 +--a0:=integrate(t0,x) +--E 613 + +--S 614 of 1285 +--m0:=a0-r0 +--E 614 + +--S 615 of 1285 +--d0:=D(m0,x) +--E 615 + +)clear all + +--S 616 of 1285 +t0:=sqrt(x)/sqrt(a+b*x^2) +--R +--R +--R +-+ +--R \|x +--R (1) ----------- +--R +--------+ +--R | 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1285 +--r0:=2*a^(3/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(3/4)*sqrt(a+b*x^2))-2*a^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--((-b)^(3/4)*sqrt(a+b*x^2)) +--E 617 + +--S 618 of 1285 +--a0:=integrate(t0,x) +--E 618 + +--S 619 of 1285 +--m0:=a0-r0 +--E 619 + +--S 620 of 1285 +--d0:=D(m0,x) +--E 620 + +)clear all + +--S 621 of 1285 +t0:=1/(sqrt(x)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) --------------- +--R +--------+ +--R +-+ | 2 +--R \|x \|b x + a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1285 +--r0:=2*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(1/4)*sqrt(a+b*x^2)) +--E 622 + +--S 623 of 1285 +--a0:=integrate(t0,x) +--E 623 + +--S 624 of 1285 +--m0:=a0-r0 +--E 624 + +--S 625 of 1285 +--d0:=D(m0,x) +--E 625 + +)clear all + +--S 626 of 1285 +t0:=1/(x^(3/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +--------+ +--R +-+ | 2 +--R x\|x \|b x + a +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1285 +--r0:=-2*sqrt(a+b*x^2)/(a*sqrt(x))-2*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*sqrt(a+b*x^2))+2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*sqrt(a+b*x^2)) +--E 627 + +--S 628 of 1285 +--a0:=integrate(t0,x) +--E 628 + +--S 629 of 1285 +--m0:=a0-r0 +--E 629 + +--S 630 of 1285 +--d0:=D(m0,x) +--E 630 + +)clear all + +--S 631 of 1285 +t0:=1/(x^(5/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 2 +-+ | 2 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1285 +--r0:=-2/3*sqrt(a+b*x^2)/(a*x^(3/2))+2/3*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(3/4)*sqrt(a+b*x^2)) +--E 632 + +--S 633 of 1285 +--a0:=integrate(t0,x) +--E 633 + +--S 634 of 1285 +--m0:=a0-r0 +--E 634 + +--S 635 of 1285 +--d0:=D(m0,x) +--E 635 + +)clear all + +--S 636 of 1285 +t0:=1/(x^(7/2)*sqrt(a+b*x^2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 3 +-+ | 2 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1285 +--r0:=-2/5*sqrt(a+b*x^2)/(a*x^(5/2))+6/5*b*sqrt(a+b*x^2)/(a^2*sqrt(x))-_ +--6/5*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+6/5*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*sqrt(a+b*x^2)) +--E 637 + +--S 638 of 1285 +--a0:=integrate(t0,x) +--E 638 + +--S 639 of 1285 +--m0:=a0-r0 +--E 639 + +--S 640 of 1285 +--d0:=D(m0,x) +--E 640 + +)clear all + +--S 641 of 1285 +t0:=x^(7/2)/(a+b*x^2)^(3/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1285 +--r0:=-x^(5/2)/(b*sqrt(a+b*x^2))+5/3*sqrt(x)*sqrt(a+b*x^2)/b^2-_ +--5/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 642 + +--S 643 of 1285 +--a0:=integrate(t0,x) +--E 643 + +--S 644 of 1285 +--m0:=a0-r0 +--E 644 + +--S 645 of 1285 +--d0:=D(m0,x) +--E 645 + +)clear all + +--S 646 of 1285 +t0:=x^(5/2)/(a+b*x^2)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1285 +--r0:=-x^(3/2)/(b*sqrt(a+b*x^2))-3*a^(3/4)*elliptic_e(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2))+_ +--3*a^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(7/4)*sqrt(a+b*x^2)) +--E 647 + +--S 648 of 1285 +--a0:=integrate(t0,x) +--E 648 + +--S 649 of 1285 +--m0:=a0-r0 +--E 649 + +--S 650 of 1285 +--d0:=D(m0,x) +--E 650 + +)clear all + +--S 651 of 1285 +t0:=x^(3/2)/(a+b*x^2)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1285 +--r0:=-sqrt(x)/(b*sqrt(a+b*x^2))-a^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/((-b)^(5/4)*sqrt(a+b*x^2)) +--E 652 + +--S 653 of 1285 +--a0:=integrate(t0,x) +--E 653 + +--S 654 of 1285 +--m0:=a0-r0 +--E 654 + +--S 655 of 1285 +--d0:=D(m0,x) +--E 655 + +)clear all + +--S 656 of 1285 +t0:=sqrt(x)/(a+b*x^2)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (1) --------------------- +--R +--------+ +--R 2 | 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1285 +--r0:=x^(3/2)/(a*sqrt(a+b*x^2))-elliptic_e(asin((-b)^(1/4)*sqrt(x)/_ +--a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2))+_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*(-b)^(3/4)*sqrt(a+b*x^2)) +--E 657 + +--S 658 of 1285 +--a0:=integrate(t0,x) +--E 658 + +--S 659 of 1285 +--m0:=a0-r0 +--E 659 + +--S 660 of 1285 +--d0:=D(m0,x) +--E 660 + +)clear all + +--S 661 of 1285 +t0:=1/((a+b*x^2)^(3/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R 2 +-+ | 2 +--R (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1285 +--r0:=sqrt(x)/(a*sqrt(a+b*x^2))+elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b*x^2)) +--E 662 + +--S 663 of 1285 +--a0:=integrate(t0,x) +--E 663 + +--S 664 of 1285 +--m0:=a0-r0 +--E 664 + +--S 665 of 1285 +--d0:=D(m0,x) +--E 665 + +)clear all + +--S 666 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +--------+ +--R 3 +-+ | 2 +--R (b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1285 +--r0:=1/(a*sqrt(x)*sqrt(a+b*x^2))-3*sqrt(a+b*x^2)/(a^2*sqrt(x))-3*_ +--(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(5/4)*sqrt(a+b*x^2))+3*(-b)^(1/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*sqrt(a+b*x^2)) +--E 667 + +--S 668 of 1285 +--a0:=integrate(t0,x) +--E 668 + +--S 669 of 1285 +--m0:=a0-r0 +--E 669 + +--S 670 of 1285 +--d0:=D(m0,x) +--E 670 + +)clear all + +--S 671 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +--R 4 2 +-+ | 2 +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1285 +--r0:=1/(a*x^(3/2)*sqrt(a+b*x^2))-5/3*sqrt(a+b*x^2)/(a^2*x^(3/2))+_ +--5/3*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(7/4)*sqrt(a+b*x^2)) +--E 672 + +--S 673 of 1285 +--a0:=integrate(t0,x) +--E 673 + +--S 674 of 1285 +--m0:=a0-r0 +--E 674 + +--S 675 of 1285 +--d0:=D(m0,x) +--E 675 + +)clear all + +--S 676 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^(3/2)) +--R +--R +--R 1 +--R (1) ---------------------------- +--R +--------+ +--R 5 3 +-+ | 2 +--R (b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1285 +--r0:=1/(a*x^(5/2)*sqrt(a+b*x^2))-7/5*sqrt(a+b*x^2)/(a^2*x^(5/2))+_ +--21/5*b*sqrt(a+b*x^2)/(a^3*sqrt(x))-21/5*(-b)^(5/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(9/4)*sqrt(a+b*x^2))+21/5*(-b)^(5/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2)) +--E 677 + +--S 678 of 1285 +--a0:=integrate(t0,x) +--E 678 + +--S 679 of 1285 +--m0:=a0-r0 +--E 679 + +--S 680 of 1285 +--d0:=D(m0,x) +--E 680 + +)clear all + +--S 681 of 1285 +t0:=x^(7/2)/(a+b*x^2)^(5/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1285 +--r0:=-1/3*x^(5/2)/(b*(a+b*x^2)^(3/2))-5/6*sqrt(x)/(b^2*sqrt(a+b*x^2))+_ +--5/6*a^(1/4)*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/((-b)^(9/4)*sqrt(a+b*x^2)) +--E 682 + +--S 683 of 1285 +--a0:=integrate(t0,x) +--E 683 + +--S 684 of 1285 +--m0:=a0-r0 +--E 684 + +--S 685 of 1285 +--d0:=D(m0,x) +--E 685 + +)clear all + +--S 686 of 1285 +t0:=x^(5/2)/(a+b*x^2)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1285 +--r0:=-1/3*x^(3/2)/(b*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a*b*sqrt(a+b*x^2))+_ +--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2))-1/2*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(1/4)*(-b)^(7/4)*sqrt(a+b*x^2)) +--E 687 + +--S 688 of 1285 +--a0:=integrate(t0,x) +--E 688 + +--S 689 of 1285 +--m0:=a0-r0 +--E 689 + +--S 690 of 1285 +--d0:=D(m0,x) +--E 690 + +)clear all + +--S 691 of 1285 +t0:=x^(3/2)/(a+b*x^2)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1285 +--r0:=-1/3*sqrt(x)/(b*(a+b*x^2)^(3/2))+1/6*sqrt(x)/(a*b*sqrt(a+b*x^2))-_ +--1/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(3/4)*(-b)^(5/4)*sqrt(a+b*x^2)) +--E 692 + +--S 693 of 1285 +--a0:=integrate(t0,x) +--E 693 + +--S 694 of 1285 +--m0:=a0-r0 +--E 694 + +--S 695 of 1285 +--d0:=D(m0,x) +--E 695 + +)clear all + +--S 696 of 1285 +t0:=sqrt(x)/(a+b*x^2)^(5/2) +--R +--R +--R +-+ +--R \|x +--R (1) -------------------------------- +--R +--------+ +--R 2 4 2 2 | 2 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1285 +--r0:=1/3*x^(3/2)/(a*(a+b*x^2)^(3/2))+1/2*x^(3/2)/(a^2*sqrt(a+b*x^2))-_ +--1/2*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2))+1/2*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b*x^2)) +--E 697 + +--S 698 of 1285 +--a0:=integrate(t0,x) +--E 698 + +--S 699 of 1285 +--m0:=a0-r0 +--E 699 + +--S 700 of 1285 +--d0:=D(m0,x) +--E 700 + +)clear all + +--S 701 of 1285 +t0:=1/((a+b*x^2)^(5/2)*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R +--------+ +--R 2 4 2 2 +-+ | 2 +--R (b x + 2a b x + a )\|x \|b x + a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1285 +--r0:=1/3*sqrt(x)/(a*(a+b*x^2)^(3/2))+5/6*sqrt(x)/(a^2*sqrt(a+b*x^2))+_ +--5/6*elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^2)) +--E 702 + +--S 703 of 1285 +--a0:=integrate(t0,x) +--E 703 + +--S 704 of 1285 +--m0:=a0-r0 +--E 704 + +--S 705 of 1285 +--d0:=D(m0,x) +--E 705 + +)clear all + +--S 706 of 1285 +t0:=1/(x^(3/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (b x + 2a b x + a x)\|x \|b x + a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1285 +--r0:=1/3/(a*(a+b*x^2)^(3/2)*sqrt(x))+7/6/(a^2*sqrt(x)*sqrt(a+b*x^2))-_ +--7/2*sqrt(a+b*x^2)/(a^3*sqrt(x))-7/2*(-b)^(1/4)*_ +--elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(9/4)*sqrt(a+b*x^2))+7/2*(-b)^(1/4)*elliptic_f(asin((-b)^(1/4)*_ +--sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/(a^(9/4)*sqrt(a+b*x^2)) +--E 707 + +--S 708 of 1285 +--a0:=integrate(t0,x) +--E 708 + +--S 709 of 1285 +--m0:=a0-r0 +--E 709 + +--S 710 of 1285 +--d0:=D(m0,x) +--E 710 + +)clear all + +--S 711 of 1285 +t0:=1/(x^(5/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 +--R (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1285 +--r0:=1/3/(a*x^(3/2)*(a+b*x^2)^(3/2))+3/2/(a^2*x^(3/2)*sqrt(a+b*x^2))-_ +--5/2*sqrt(a+b*x^2)/(a^3*x^(3/2))+5/2*(-b)^(3/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(11/4)*sqrt(a+b*x^2)) +--E 712 + +--S 713 of 1285 +--a0:=integrate(t0,x) +--E 713 + +--S 714 of 1285 +--m0:=a0-r0 +--E 714 + +--S 715 of 1285 +--d0:=D(m0,x) +--E 715 + +)clear all + +--S 716 of 1285 +t0:=1/(x^(7/2)*(a+b*x^2)^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +--------+ +--R 2 7 5 2 3 +-+ | 2 +--R (b x + 2a b x + a x )\|x \|b x + a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1285 +--r0:=1/3/(a*x^(5/2)*(a+b*x^2)^(3/2))+11/6/(a^2*x^(5/2)*sqrt(a+b*x^2))-_ +--77/30*sqrt(a+b*x^2)/(a^3*x^(5/2))+77/10*b*sqrt(a+b*x^2)/(a^4*sqrt(x))-_ +--77/10*(-b)^(5/4)*elliptic_e(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*_ +--sqrt((a+b*x^2)/a)/(a^(13/4)*sqrt(a+b*x^2))+77/10*(-b)^(5/4)*_ +--elliptic_f(asin((-b)^(1/4)*sqrt(x)/a^(1/4)),-1)*sqrt((a+b*x^2)/a)/_ +--(a^(13/4)*sqrt(a+b*x^2)) +--E 717 + +--S 718 of 1285 +--a0:=integrate(t0,x) +--E 718 + +--S 719 of 1285 +--m0:=a0-r0 +--E 719 + +--S 720 of 1285 +--d0:=D(m0,x) +--E 720 + +)clear all + +--S 721 of 1285 +t0:=x^m*(a+b*x^2)^p +--R +--R +--R m 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1285 +--r0:=x^(1+m)*(a+b*x^2)^p*hypergeometric(1/2*(1+m),-p,1/2*(3+m),-b*x^2/a)/_ +--((1+m)*((a+b*x^2)/a)^p) +--E 722 + +--S 723 of 1285 +--a0:=integrate(t0,x) +--E 723 + +--S 724 of 1285 +--m0:=a0-r0 +--E 724 + +--S 725 of 1285 +--d0:=D(m0,x) +--E 725 + +)clear all + +--S 726 of 1285 +t0:=x^7*(a+b*x^2)^p +--R +--R +--R 7 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1285 +r0:=-1/2*a^3*(a+b*x^2)^(1+p)/(b^4*(1+p))+3/2*a^2*(a+b*x^2)^(2+p)/_ + (b^4*(2+p))-3/2*a*(a+b*x^2)^(3+p)/(b^4*(3+p))+1/2*(a+b*x^2)^(4+p)/_ + (b^4*(4+p)) +--R +--R +--R (2) +--R 3 2 2 p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 2 p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 2 p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 2 p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 8 3 3 3 2 3 6 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 4 3 2 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 2 +--R p log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Union(Expression(Integer),...) +--E 728 + +--S 729 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 8 3 3 3 2 3 6 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 4 3 2 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 2 +--R p log(b x + a) +--R %e +--R + +--R 3 2 2 p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 2 p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 2 p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 2 p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 2b p + 20b p + 70b p + 100b p + 48b +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 730 + +)clear all + +--S 731 of 1285 +t0:=x^5*(a+b*x^2)^p +--R +--R +--R 5 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1285 +r0:=1/2*a^2*(a+b*x^2)^(1+p)/(b^3*(1+p))-a*(a+b*x^2)^(2+p)/(b^3*(2+p))+_ + 1/2*(a+b*x^2)^(3+p)/(b^3*(3+p)) +--R +--R +--R (2) +--R 2 2 p + 3 2 2 p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 2 p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 6 2 2 2 4 2 2 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 2 +--R p log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Union(Expression(Integer),...) +--E 733 + +--S 734 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 6 2 2 2 4 2 2 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 2 +--R p log(b x + a) +--R %e +--R + +--R 2 2 p + 3 2 2 p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 2 p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 2b p + 12b p + 22b p + 12b +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 735 + +)clear all + +--S 736 of 1285 +t0:=x^4*(a+b*x^2)^p +--R +--R +--R 4 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1285 +--r0:=-3*a*x*(a+b*x^2)^(1+p)/(b^2*(3+2*p)*(5+2*p))+x^3*(a+b*x^2)^(1+p)/_ +-- (b*(5+2*p))+3*a^2*x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,_ +-- -b*x^2/a)/(b^2*(3+2*p)*(5+2*p)*((a+b*x^2)/a)^p) +--E 737 + +--S 738 of 1285 +--a0:=integrate(t0,x) +--E 738 + +--S 739 of 1285 +--m0:=a0-r0 +--E 739 + +--S 740 of 1285 +--d0:=normalize m0 +--E 740 + +)clear all + +--S 741 of 1285 +t0:=x^3*(a+b*x^2)^p +--R +--R +--R 3 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1285 +r0:=-1/2*a*(a+b*x^2)^(1+p)/(b^2*(1+p))+1/2*(a+b*x^2)^(2+p)/(b^2*(2+p)) +--R +--R +--R 2 p + 2 2 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2 2 4 2 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Union(Expression(Integer),...) +--E 743 + +--S 744 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +--R 2 2 4 2 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 2 p + 2 2 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 2b p + 6b p + 4b +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 745 + +)clear all + +--S 746 of 1285 +t0:=x^2*(a+b*x^2)^p +--R +--R +--R 2 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1285 +--r0:=x*(a+b*x^2)^(1+p)/(b*(3+2*p))-a*x*(a+b*x^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(b*(3+2*p)*((a+b*x^2)/a)^p) +--E 747 + +--S 748 of 1285 +--a0:=integrate(t0,x) +--E 748 + +--S 749 of 1285 +--m0:=a0-r0 +--E 749 + +--S 750 of 1285 +--d0:=D(m0,x) +--E 750 + +)clear all + +--S 751 of 1285 +t0:=x*(a+b*x^2)^p +--R +--R +--R 2 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1285 +r0:=1/2*(a+b*x^2)^(1+p)/(b*(1+p)) +--R +--R +--R 2 p + 1 +--R (b x + a) +--R (2) --------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 2b p + 2b +--R Type: Union(Expression(Integer),...) +--E 753 + +--S 754 of 1285 +m0:=a0-r0 +--R +--R +--R 2 +--R 2 p log(b x + a) 2 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 2b p + 2b +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 755 + +)clear all + +--S 756 of 1285 +t0:=(a+b*x^2)^p +--R +--R +--R 2 p +--R (1) (b x + a) +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1285 +--r0:=x*(a+b*x^2)^p*hypergeometric(1/2,-p,3/2,-b*x^2/a)/((a+b*x^2)/a)^p +--E 757 + +--S 758 of 1285 +--a0:=integrate(t0,x) +--E 758 + +--S 759 of 1285 +--m0:=a0-r0 +--E 759 + +--S 760 of 1285 +--d0:=D(m0,x) +--E 760 + +)clear all + +--S 761 of 1285 +t0:=(a+b*x^2)^p/x +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1285 +--r0:=1/2*(a+b*x^2)^p*_ +-- hypergeometric(-p,-p,1-p,-a/(b*x^2))/(p*((a+b*x^2)/(b*x^2))^p) +--E 762 + +--S 763 of 1285 +--a0:=integrate(t0,x) +--E 763 + +--S 764 of 1285 +--m0:=a0-r0 +--E 764 + +--S 765 of 1285 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1285 +t0:=(a+b*x^2)^p/x^2 +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1285 +--r0:=-(a+b*x^2)^(1+p)/(a*x)+b*(1+2*p)*x*(a+b*x^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*x^2/a)/(a*((a+b*x^2)/a)^p) +--E 767 + +--S 768 of 1285 +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1285 +--m0:=a0-r0 +--E 769 + +--S 770 of 1285 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1285 +t0:=(a+b*x^2)^p/x^3 +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1285 +--r0:=-1/2*(a+b*x^2)^(1+p)/(a*x^2)-1/2*b*p*(a+b*x^2)^(1+p)*_ +-- hypergeometric(1,1+p,2+p,(a+b*x^2)/a)/(a^2*(1+p)) +--E 772 + +--S 773 of 1285 +--a0:=integrate(t0,x) +--E 773 + +--S 774 of 1285 +--m0:=a0-r0 +--E 774 + +--S 775 of 1285 +--d0:=D(m0,x) +--E 775 + +)clear all + +--S 776 of 1285 +t0:=x^(9/2)*(a+b*x^2)^p +--R +--R +--R 4 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1285 +--r0:=-14*a*x^(3/2)*(a+b*x^2)^(1+p)/(b^2*(7+4*p)*(11+4*p))+2*x^(7/2)*_ +-- (a+b*x^2)^(1+p)/(b*(11+4*p))+14*a^2*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b^2*(7+4*p)*(11+4*p)*_ +-- ((a+b*x^2)/a)^p) +--E 777 + +--S 778 of 1285 +--a0:=integrate(t0,x) +--E 778 + +--S 779 of 1285 +--m0:=a0-r0 +--E 779 + +--S 780 of 1285 +--d0:=D(m0,x) +--E 780 + +)clear all + +--S 781 of 1285 +t0:=x^(7/2)*(a+b*x^2)^p +--R +--R +--R 3 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1285 +--r0:=2*x^(5/2)*(a+b*x^2)^(1+p)/(b*(9+4*p))-2*a*x^(5/2)*(a+b*x^2)^p*_ +-- hypergeometric(5/4,-p,9/4,-b*x^2/a)/(b*(9+4*p)*((a+b*x^2)/a)^p) +--E 782 + +--S 783 of 1285 +--a0:=integrate(t0,x) +--E 783 + +--S 784 of 1285 +--m0:=a0-r0 +--E 784 + +--S 785 of 1285 +--d0:=D(m0,x) +--E 785 + +)clear all + +--S 786 of 1285 +t0:=x^(5/2)*(a+b*x^2)^p +--R +--R +--R 2 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1285 +--r0:=2*x^(3/2)*(a+b*x^2)^(1+p)/(b*(7+4*p))-2*a*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(b*(7+4*p)*((a+b*x^2)/a)^p) +--E 787 + +--S 788 of 1285 +--a0:=integrate(t0,x) +--E 788 + +--S 789 of 1285 +--m0:=a0-r0 +--E 789 + +--S 790 of 1285 +--d0:=D(m0,x) +--E 790 + +)clear all + +--S 791 of 1285 +t0:=x^(3/2)*(a+b*x^2)^p +--R +--R +--R 2 p +-+ +--R (1) x (b x + a) \|x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1285 +--r0:=2/5*x^(5/2)*(a+b*x^2)^p*hypergeometric(5/4,-p,9/4,-b*x^2/a)/_ +-- ((a+b*x^2)/a)^p +--E 792 + +--S 793 of 1285 +--a0:=integrate(t0,x) +--E 793 + +--S 794 of 1285 +--m0:=a0-r0 +--E 794 + +--S 795 of 1285 +--d0:=D(m0,x) +--E 795 + +)clear all + +--S 796 of 1285 +t0:=x^(1/2)*(a+b*x^2)^p +--R +--R +--R 2 p +-+ +--R (1) (b x + a) \|x +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1285 +--r0:=2/3*x^(3/2)*(a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/_ +-- ((a+b*x^2)/a)^p +--E 797 + +--S 798 of 1285 +--a0:=integrate(t0,x) +--E 798 + +--S 799 of 1285 +--m0:=a0-r0 +--E 799 + +--S 800 of 1285 +--d0:=D(m0,x) +--E 800 + +)clear all + +--S 801 of 1285 +t0:=(a+b*x^2)^p/x^(1/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1285 +--r0:=2*(a+b*x^2)^p*hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/((a+b*x^2)/a)^p +--E 802 + +--S 803 of 1285 +--a0:=integrate(t0,x) +--E 803 + +--S 804 of 1285 +--m0:=a0-r0 +--E 804 + +--S 805 of 1285 +--d0:=D(m0,x) +--E 805 + +)clear all + +--S 806 of 1285 +t0:=(a+b*x^2)^p/x^(3/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1285 +--r0:=2/3*b*(3+4*p)*x^(3/2)*(a+b*x^2)^p*_ +-- hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a*((a+b*x^2)/a)^p)-_ +-- 2*(a+b*x^2)^(1+p)/(a*sqrt(x)) +--E 807 + +--S 808 of 1285 +--a0:=integrate(t0,x) +--E 808 + +--S 809 of 1285 +--m0:=a0-r0 +--E 809 + +--S 810 of 1285 +--d0:=D(m0,x) +--E 810 + +)clear all + +--S 811 of 1285 +t0:=(a+b*x^2)^p/x^(5/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1285 +--r0:=-2/3*(a+b*x^2)^(1+p)/(a*x^(3/2))+2/3*b*(1+4*p)*(a+b*x^2)^p*_ +-- hypergeometric(1/4,-p,5/4,-b*x^2/a)*sqrt(x)/(a*((a+b*x^2)/a)^p) +--E 812 + +--S 813 of 1285 +--a0:=integrate(t0,x) +--E 813 + +--S 814 of 1285 +--m0:=a0-r0 +--E 814 + +--S 815 of 1285 +--d0:=D(m0,x) +--E 815 + +)clear all + +--S 816 of 1285 +t0:=(a+b*x^2)^p/x^(7/2) +--R +--R +--R 2 p +--R (b x + a) +--R (1) ----------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1285 +--r0:=-2/5*(a+b*x^2)^(1+p)/(a*x^(5/2))-2/15*b^2*(1-4*p)*(3+4*p)*x^(3/2)*_ +-- (a+b*x^2)^p*hypergeometric(3/4,-p,7/4,-b*x^2/a)/(a^2*((a+b*x^2)/a)^p)+_ +-- 2/5*b*(1-4*p)*(a+b*x^2)^(1+p)/(a^2*sqrt(x)) +--E 817 + +--S 818 of 1285 +--a0:=integrate(t0,x) +--E 818 + +--S 819 of 1285 +--m0:=a0-r0 +--E 819 + +--S 820 of 1285 +--d0:=D(m0,x) +--E 820 + +)clear all + +--S 821 of 1285 +t0:=x^m*(a+b*x^3) +--R +--R +--R 3 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1285 +r0:=a*x^(1+m)/(1+m)+b*x^(4+m)/(4+m) +--R +--R +--R m + 4 m + 1 +--R (b m + b)x + (a m + 4a)x +--R (2) ---------------------------------- +--R 2 +--R m + 5m + 4 +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 m log(x) +--R ((b m + b)x + (a m + 4a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 5m + 4 +--R Type: Union(Expression(Integer),...) +--E 823 + +--S 824 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 m log(x) m + 4 +--R ((b m + b)x + (a m + 4a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 4a)x +--R / +--R 2 +--R m + 5m + 4 +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1285 +t0:=x^3*(a+b*x^3) +--R +--R +--R 6 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 826 + +--S 827 of 1285 +r0:=1/4*a*x^4+1/7*b*x^7 +--R +--R +--R 1 7 1 4 +--R (2) - b x + - a x +--R 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 827 + +--S 828 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 4 +--R (3) - b x + - a x +--R 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 828 + +--S 829 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 829 + +--S 830 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 830 + +)clear all + +--S 831 of 1285 +t0:=x^2*(a+b*x^3) +--R +--R +--R 5 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 831 + +--S 832 of 1285 +r0:=1/3*a*x^3+1/6*b*x^6 +--R +--R +--R 1 6 1 3 +--R (2) - b x + - a x +--R 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 832 + +--S 833 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 3 +--R (3) - b x + - a x +--R 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 833 + +--S 834 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 834 + +--S 835 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 835 + +)clear all + +--S 836 of 1285 +t0:=x*(a+b*x^3) +--R +--R +--R 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 836 + +--S 837 of 1285 +r0:=1/2*a*x^2+1/5*b*x^5 +--R +--R +--R 1 5 1 2 +--R (2) - b x + - a x +--R 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 837 + +--S 838 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 1 2 +--R (3) - b x + - a x +--R 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 838 + +--S 839 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 839 + +--S 840 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 840 + +)clear all + +--S 841 of 1285 +t0:=a+b*x^3 +--R +--R +--R 3 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 841 + +--S 842 of 1285 +r0:=a*x+1/4*b*x^4 +--R +--R +--R 1 4 +--R (2) - b x + a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 842 + +--S 843 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 4 +--R (3) - b x + a x +--R 4 +--R Type: Polynomial(Fraction(Integer)) +--E 843 + +--S 844 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 844 + +--S 845 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 845 + +)clear all + +--S 846 of 1285 +t0:=(a+b*x^3)/x +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 846 + +--S 847 of 1285 +r0:=1/3*b*x^3+a*log(x) +--R +--R +--R 3 +--R 3a log(x) + b x +--R (2) ---------------- +--R 3 +--R Type: Expression(Integer) +--E 847 + +--S 848 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3a log(x) + b x +--R (3) ---------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 848 + +--S 849 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 850 + +)clear all + +--S 851 of 1285 +t0:=(a+b*x^3)/x^2 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 851 + +--S 852 of 1285 +r0:=-a/x+1/2*b*x^2 +--R +--R +--R 3 +--R b x - 2a +--R (2) --------- +--R 2x +--R Type: Fraction(Polynomial(Integer)) +--E 852 + +--S 853 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R b x - 2a +--R (3) --------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 853 + +--S 854 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 855 + +)clear all + +--S 856 of 1285 +t0:=(a+b*x^3)/x^3 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 856 + +--S 857 of 1285 +r0:=-1/2*a/x^2+b*x +--R +--R +--R 3 1 +--R b x - - a +--R 2 +--R (2) ---------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 857 + +--S 858 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2b x - a +--R (3) --------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 858 + +--S 859 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 860 + +)clear all + +--S 861 of 1285 +t0:=(a+b*x^3)/x^4 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 861 + +--S 862 of 1285 +r0:=-1/3*a/x^3+b*log(x) +--R +--R +--R 3 +--R 3b x log(x) - a +--R (2) --------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 862 + +--S 863 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3b x log(x) - a +--R (3) --------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 863 + +--S 864 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 865 + +)clear all + +--S 866 of 1285 +t0:=(a+b*x^3)/x^5 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 866 + +--S 867 of 1285 +r0:=-1/4*a/x^4-b/x +--R +--R +--R 3 1 +--R - b x - - a +--R 4 +--R (2) ------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 867 + +--S 868 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 4b x - a +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 868 + +--S 869 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 870 + +)clear all + +--S 871 of 1285 +t0:=(a+b*x^3)/x^6 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 871 + +--S 872 of 1285 +r0:=-1/5*a/x^5-1/2*b/x^2 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 2 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 872 + +--S 873 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 5b x - 2a +--R (3) ------------ +--R 5 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 873 + +--S 874 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 875 + +)clear all + +--S 876 of 1285 +t0:=(a+b*x^3)/x^7 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 876 + +--S 877 of 1285 +r0:=-1/6*a/x^6-1/3*b/x^3 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 3 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 877 + +--S 878 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 2b x - a +--R (3) ----------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 878 + +--S 879 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1285 +t0:=(a+b*x^3)/x^8 +--R +--R +--R 3 +--R b x + a +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 881 + +--S 882 of 1285 +r0:=-1/7*a/x^7-1/4*b/x^4 +--R +--R +--R 1 3 1 +--R - - b x - - a +--R 4 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 882 + +--S 883 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 7b x - 4a +--R (3) ------------ +--R 7 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 883 + +--S 884 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +)clear all + +--S 886 of 1285 +t0:=x^m*(a+b*x^3)^2 +--R +--R +--R 2 6 3 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1285 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(4+m)/(4+m)+b^2*x^(7+m)/(7+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 7 2 m + 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 11a m + 28a )x +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 7 2 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 +--R (a m + 11a m + 28a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Union(Expression(Integer),...) +--E 888 + +--S 889 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 7 2 4 +--R (b m + 5b m + 4b )x + (2a b m + 16a b m + 14a b)x +--R + +--R 2 2 2 2 +--R (a m + 11a m + 28a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 7 2 m + 4 +--R (- b m - 5b m - 4b )x + (- 2a b m - 16a b m - 14a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 11a m - 28a )x +--R / +--R 3 2 +--R m + 12m + 39m + 28 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 890 + +)clear all + +--S 891 of 1285 +t0:=x^4*(a+b*x^3)^2 +--R +--R +--R 2 10 7 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 891 + +--S 892 of 1285 +r0:=1/5*a^2*x^5+1/4*a*b*x^8+1/11*b^2*x^11 +--R +--R +--R 1 2 11 1 8 1 2 5 +--R (2) -- b x + - a b x + - a x +--R 11 4 5 +--R Type: Polynomial(Fraction(Integer)) +--E 892 + +--S 893 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 11 1 8 1 2 5 +--R (3) -- b x + - a b x + - a x +--R 11 4 5 +--R Type: Polynomial(Fraction(Integer)) +--E 893 + +--S 894 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 894 + +--S 895 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 895 + +)clear all + +--S 896 of 1285 +t0:=x^3*(a+b*x^3)^2 +--R +--R +--R 2 9 6 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 896 + +--S 897 of 1285 +r0:=1/4*a^2*x^4+2/7*a*b*x^7+1/10*b^2*x^10 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R (2) -- b x + - a b x + - a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 897 + +--S 898 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 2 7 1 2 4 +--R (3) -- b x + - a b x + - a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 898 + +--S 899 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 899 + +--S 900 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 900 + +)clear all + +--S 901 of 1285 +t0:=x^2*(a+b*x^3)^2 +--R +--R +--R 2 8 5 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 901 + +--S 902 of 1285 +r0:=1/9*(a+b*x^3)^3/b +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - b x + - a b x + - a b x + - a +--R 9 3 3 9 +--R (2) ----------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 902 + +--S 903 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 1 6 1 2 3 +--R (3) - b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 903 + +--S 904 of 1285 +m0:=a0-r0 +--R +--R +--R 1 3 +--R - a +--R 9 +--R (4) - ---- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 904 + +--S 905 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 905 + +)clear all + +--S 906 of 1285 +t0:=x*(a+b*x^3)^2 +--R +--R +--R 2 7 4 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 906 + +--S 907 of 1285 +r0:=1/2*a^2*x^2+2/5*a*b*x^5+1/8*b^2*x^8 +--R +--R +--R 1 2 8 2 5 1 2 2 +--R (2) - b x + - a b x + - a x +--R 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 907 + +--S 908 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 8 2 5 1 2 2 +--R (3) - b x + - a b x + - a x +--R 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 908 + +--S 909 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 909 + +--S 910 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 910 + +)clear all + +--S 911 of 1285 +t0:=(a+b*x^3)^2 +--R +--R +--R 2 6 3 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 911 + +--S 912 of 1285 +r0:=a^2*x+1/2*a*b*x^4+1/7*b^2*x^7 +--R +--R +--R 1 2 7 1 4 2 +--R (2) - b x + - a b x + a x +--R 7 2 +--R Type: Polynomial(Fraction(Integer)) +--E 912 + +--S 913 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 2 7 1 4 2 +--R (3) - b x + - a b x + a x +--R 7 2 +--R Type: Polynomial(Fraction(Integer)) +--E 913 + +--S 914 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 914 + +--S 915 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 915 + +)clear all + +--S 916 of 1285 +t0:=(a+b*x^3)^2/x +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 916 + +--S 917 of 1285 +r0:=2/3*a*b*x^3+1/6*b^2*x^6+a^2*log(x) +--R +--R +--R 2 2 6 3 +--R 6a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 2 6 3 +--R 6a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 918 + +--S 919 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 920 + +)clear all + +--S 921 of 1285 +t0:=(a+b*x^3)^2/x^2 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 921 + +--S 922 of 1285 +r0:=-a^2/x+a*b*x^2+1/5*b^2*x^5 +--R +--R +--R 2 6 3 2 +--R b x + 5a b x - 5a +--R (2) -------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 922 + +--S 923 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R b x + 5a b x - 5a +--R (3) -------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 923 + +--S 924 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 925 + +)clear all + +--S 926 of 1285 +t0:=(a+b*x^3)^2/x^3 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 926 + +--S 927 of 1285 +r0:=-1/2*a^2/x^2+2*a*b*x+1/4*b^2*x^4 +--R +--R +--R 1 2 6 3 1 2 +--R - b x + 2a b x - - a +--R 4 2 +--R (2) ----------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 927 + +--S 928 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R b x + 8a b x - 2a +--R (3) -------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 928 + +--S 929 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 930 + +)clear all + +--S 931 of 1285 +t0:=(a+b*x^3)^2/x^4 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 931 + +--S 932 of 1285 +r0:=-1/3*a^2/x^3+1/3*b^2*x^3+2*a*b*log(x) +--R +--R +--R 3 2 6 2 +--R 6a b x log(x) + b x - a +--R (2) ------------------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 2 6 2 +--R 6a b x log(x) + b x - a +--R (3) ------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 933 + +--S 934 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1285 +t0:=(a+b*x^3)^2/x^5 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 936 + +--S 937 of 1285 +r0:=-1/4*a^2/x^4-2*a*b/x+1/2*b^2*x^2 +--R +--R +--R 1 2 6 3 1 2 +--R - b x - 2a b x - - a +--R 2 4 +--R (2) ----------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 937 + +--S 938 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 2b x - 8a b x - a +--R (3) -------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 940 + +)clear all + +--S 941 of 1285 +t0:=(a+b*x^3)^2/x^6 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 941 + +--S 942 of 1285 +r0:=-1/5*a^2/x^5-a*b/x^2+b^2*x +--R +--R +--R 2 6 3 1 2 +--R b x - a b x - - a +--R 5 +--R (2) -------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 942 + +--S 943 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 5b x - 5a b x - a +--R (3) -------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 943 + +--S 944 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1285 +t0:=(a+b*x^3)^2/x^7 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 946 + +--S 947 of 1285 +r0:=-1/6*a^2/x^6-2/3*a*b/x^3+b^2*log(x) +--R +--R +--R 2 6 3 2 +--R 6b x log(x) - 4a b x - a +--R (2) -------------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R 6b x log(x) - 4a b x - a +--R (3) -------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 948 + +--S 949 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +)clear all + +--S 951 of 1285 +t0:=(a+b*x^3)^2/x^8 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 951 + +--S 952 of 1285 +r0:=-1/7*a^2/x^7-1/2*a*b/x^4-b^2/x +--R +--R +--R 2 6 1 3 1 2 +--R - b x - - a b x - - a +--R 2 7 +--R (2) ------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 952 + +--S 953 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 14b x - 7a b x - 2a +--R (3) ------------------------ +--R 7 +--R 14x +--R Type: Union(Expression(Integer),...) +--E 953 + +--S 954 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 955 + +)clear all + +--S 956 of 1285 +t0:=(a+b*x^3)^2/x^9 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 956 + +--S 957 of 1285 +r0:=-1/8*a^2/x^8-2/5*a*b/x^5-1/2*b^2/x^2 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - - a +--R 2 5 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +--S 958 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 20b x - 16a b x - 5a +--R (3) ------------------------- +--R 8 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 958 + +--S 959 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 960 + +)clear all + +--S 961 of 1285 +t0:=(a+b*x^3)^2/x^10 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 961 + +--S 962 of 1285 +r0:=-1/9*(a+b*x^3)^3/(a*x^9) +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - - a +--R 9 3 3 9 +--R (2) ------------------------------------- +--R 9 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 962 + +--S 963 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 3b x - 3a b x - a +--R (3) ---------------------- +--R 9 +--R 9x +--R Type: Union(Expression(Integer),...) +--E 963 + +--S 964 of 1285 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R 9a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1285 +t0:=(a+b*x^3)^2/x^11 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 966 + +--S 967 of 1285 +r0:=-1/10*a^2/x^10-2/7*a*b/x^7-1/4*b^2/x^4 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - -- a +--R 4 7 10 +--R (2) --------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 967 + +--S 968 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 35b x - 40a b x - 14a +--R (3) -------------------------- +--R 10 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1285 +t0:=(a+b*x^3)^2/x^12 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 971 + +--S 972 of 1285 +r0:=-1/11*a^2/x^11-1/4*a*b/x^8-1/5*b^2/x^5 +--R +--R +--R 1 2 6 1 3 1 2 +--R - - b x - - a b x - -- a +--R 5 4 11 +--R (2) --------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 972 + +--S 973 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 44b x - 55a b x - 20a +--R (3) -------------------------- +--R 11 +--R 220x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1285 +t0:=(a+b*x^3)^2/x^13 +--R +--R +--R 2 6 3 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 976 + +--S 977 of 1285 +r0:=-1/12*a^2/x^12-2/9*a*b/x^9-1/6*b^2/x^6 +--R +--R +--R 1 2 6 2 3 1 2 +--R - - b x - - a b x - -- a +--R 6 9 12 +--R (2) --------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 977 + +--S 978 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 +--R - 6b x - 8a b x - 3a +--R (3) ----------------------- +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1285 +t0:=x^m*(a+b*x^3)^3 +--R +--R +--R 3 9 2 6 2 3 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1285 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(4+m)/(4+m)+3*a*b^2*x^(7+m)/(7+m)+_ + b^3*x^(10+m)/(10+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 m + 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 m + 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 21a m + 138a m + 280a )x +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 21a m + 138a m + 280a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 10 +--R (b m + 12b m + 39b m + 28b )x +--R + +--R 2 3 2 2 2 2 7 +--R (3a b m + 45a b m + 162a b m + 120a b )x +--R + +--R 2 3 2 2 2 2 4 +--R (3a b m + 54a b m + 261a b m + 210a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 21a m + 138a m + 280a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 10 +--R (- b m - 12b m - 39b m - 28b )x +--R + +--R 2 3 2 2 2 2 m + 7 +--R (- 3a b m - 45a b m - 162a b m - 120a b )x +--R + +--R 2 3 2 2 2 2 m + 4 +--R (- 3a b m - 54a b m - 261a b m - 210a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 21a m - 138a m - 280a )x +--R / +--R 4 3 2 +--R m + 22m + 159m + 418m + 280 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1285 +t0:=x^14*(a+b*x^3)^3 +--R +--R +--R 3 23 2 20 2 17 3 14 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 986 + +--S 987 of 1285 +r0:=1/15*a^3*x^15+1/6*a^2*b*x^18+1/7*a*b^2*x^21+1/24*b^3*x^24 +--R +--R +--R 1 3 24 1 2 21 1 2 18 1 3 15 +--R (2) -- b x + - a b x + - a b x + -- a x +--R 24 7 6 15 +--R Type: Polynomial(Fraction(Integer)) +--E 987 + +--S 988 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 24 1 2 21 1 2 18 1 3 15 +--R (3) -- b x + - a b x + - a b x + -- a x +--R 24 7 6 15 +--R Type: Polynomial(Fraction(Integer)) +--E 988 + +--S 989 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 989 + +--S 990 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 990 + +)clear all + +--S 991 of 1285 +t0:=x^11*(a+b*x^3)^3 +--R +--R +--R 3 20 2 17 2 14 3 11 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 991 + +--S 992 of 1285 +r0:=1/12*a^3*x^12+1/5*a^2*b*x^15+1/6*a*b^2*x^18+1/21*b^3*x^21 +--R +--R +--R 1 3 21 1 2 18 1 2 15 1 3 12 +--R (2) -- b x + - a b x + - a b x + -- a x +--R 21 6 5 12 +--R Type: Polynomial(Fraction(Integer)) +--E 992 + +--S 993 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 21 1 2 18 1 2 15 1 3 12 +--R (3) -- b x + - a b x + - a b x + -- a x +--R 21 6 5 12 +--R Type: Polynomial(Fraction(Integer)) +--E 993 + +--S 994 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 994 + +--S 995 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 995 + +)clear all + +--S 996 of 1285 +t0:=x^8*(a+b*x^3)^3 +--R +--R +--R 3 17 2 14 2 11 3 8 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 996 + +--S 997 of 1285 +r0:=1/9*a^3*x^9+1/4*a^2*b*x^12+1/5*a*b^2*x^15+1/18*b^3*x^18 +--R +--R +--R 1 3 18 1 2 15 1 2 12 1 3 9 +--R (2) -- b x + - a b x + - a b x + - a x +--R 18 5 4 9 +--R Type: Polynomial(Fraction(Integer)) +--E 997 + +--S 998 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 18 1 2 15 1 2 12 1 3 9 +--R (3) -- b x + - a b x + - a b x + - a x +--R 18 5 4 9 +--R Type: Polynomial(Fraction(Integer)) +--E 998 + +--S 999 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 999 + +--S 1000 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1000 + +)clear all + +--S 1001 of 1285 +t0:=x^5*(a+b*x^3)^3 +--R +--R +--R 3 14 2 11 2 8 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1001 + +--S 1002 of 1285 +r0:=-1/12*a*(a+b*x^3)^4/b^2+1/15*(a+b*x^3)^5/b^2 +--R +--R +--R 1 5 15 1 4 12 1 2 3 9 1 3 2 6 1 5 +--R -- b x + - a b x + - a b x + - a b x - -- a +--R 15 4 3 6 60 +--R (2) -------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1002 + +--S 1003 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 15 1 2 12 1 2 9 1 3 6 +--R (3) -- b x + - a b x + - a b x + - a x +--R 15 4 3 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1003 + +--S 1004 of 1285 +m0:=a0-r0 +--R +--R +--R 1 5 +--R -- a +--R 60 +--R (4) ----- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1004 + +--S 1005 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1005 + +)clear all + +--S 1006 of 1285 +t0:=x^2*(a+b*x^3)^3 +--R +--R +--R 3 11 2 8 2 5 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1006 + +--S 1007 of 1285 +r0:=1/12*(a+b*x^3)^4/b +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 12 3 2 3 12 +--R (2) ------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1007 + +--S 1008 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 12 1 2 9 1 2 6 1 3 3 +--R (3) -- b x + - a b x + - a b x + - a x +--R 12 3 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1008 + +--S 1009 of 1285 +m0:=a0-r0 +--R +--R +--R 1 4 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1009 + +--S 1010 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1010 + +)clear all + +--S 1011 of 1285 +t0:=(a+b*x^3)^3/x +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1011 + +--S 1012 of 1285 +r0:=a^2*b*x^3+1/2*a*b^2*x^6+1/9*b^3*x^9+a^3*log(x) +--R +--R +--R 3 3 9 2 6 2 3 +--R 18a log(x) + 2b x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 18 +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 3 9 2 6 2 3 +--R 18a log(x) + 2b x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 18 +--R Type: Union(Expression(Integer),...) +--E 1013 + +--S 1014 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1015 + +)clear all + +--S 1016 of 1285 +t0:=(a+b*x^3)^3/x^4 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1016 + +--S 1017 of 1285 +r0:=-1/3*a^3/x^3+a*b^2*x^3+1/6*b^3*x^6+3*a^2*b*log(x) +--R +--R +--R 2 3 3 9 2 6 3 +--R 18a b x log(x) + b x + 6a b x - 2a +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 9 2 6 3 +--R 18a b x log(x) + b x + 6a b x - 2a +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1018 + +--S 1019 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1020 + +)clear all + +--S 1021 of 1285 +t0:=(a+b*x^3)^3/x^7 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1021 + +--S 1022 of 1285 +r0:=-1/6*a^3/x^6-a^2*b/x^3+1/3*b^3*x^3+3*a*b^2*log(x) +--R +--R +--R 2 6 3 9 2 3 3 +--R 18a b x log(x) + 2b x - 6a b x - a +--R (2) ------------------------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 9 2 3 3 +--R 18a b x log(x) + 2b x - 6a b x - a +--R (3) ------------------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1023 + +--S 1024 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1025 + +)clear all + +--S 1026 of 1285 +t0:=(a+b*x^3)^3/x^10 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1026 + +--S 1027 of 1285 +r0:=-1/9*a^3/x^9-1/2*a^2*b/x^6-a*b^2/x^3+b^3*log(x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 18b x log(x) - 18a b x - 9a b x - 2a +--R (2) --------------------------------------- +--R 9 +--R 18x +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 18b x log(x) - 18a b x - 9a b x - 2a +--R (3) --------------------------------------- +--R 9 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1028 + +--S 1029 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1030 + +)clear all + +--S 1031 of 1285 +t0:=(a+b*x^3)^3/x^13 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1031 + +--S 1032 of 1285 +r0:=-1/12*(a+b*x^3)^4/(a*x^12) +--R +--R +--R 1 4 12 1 3 9 1 2 2 6 1 3 3 1 4 +--R - -- b x - - a b x - - a b x - - a b x - -- a +--R 12 3 2 3 12 +--R (2) --------------------------------------------------- +--R 12 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1032 + +--S 1033 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 4b x - 6a b x - 4a b x - a +--R (3) -------------------------------- +--R 12 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 1033 + +--S 1034 of 1285 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) --- +--R 12a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1285 +t0:=(a+b*x^3)^3/x^16 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1036 + +--S 1037 of 1285 +r0:=-1/15*a^3/x^15-1/4*a^2*b/x^12-1/3*a*b^2/x^9-1/6*b^3/x^6 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 6 3 4 15 +--R (2) -------------------------------------- +--R 15 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1037 + +--S 1038 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 10b x - 20a b x - 15a b x - 4a +--R (3) ------------------------------------ +--R 15 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 1038 + +--S 1039 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +)clear all + +--S 1041 of 1285 +t0:=(a+b*x^3)^3/x^19 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1041 + +--S 1042 of 1285 +r0:=-1/18*a^3/x^18-1/5*a^2*b/x^15-1/4*a*b^2/x^12-1/9*b^3/x^9 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - - b x - - a b x - - a b x - -- a +--R 9 4 5 18 +--R (2) -------------------------------------- +--R 18 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1042 + +--S 1043 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 20b x - 45a b x - 36a b x - 10a +--R (3) ------------------------------------- +--R 18 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 1043 + +--S 1044 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1045 + +)clear all + +--S 1046 of 1285 +t0:=(a+b*x^3)^3/x^22 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1046 + +--S 1047 of 1285 +r0:=-1/21*a^3/x^21-1/6*a^2*b/x^18-1/5*a*b^2/x^15-1/12*b^3/x^12 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - -- b x - - a b x - - a b x - -- a +--R 12 5 6 21 +--R (2) --------------------------------------- +--R 21 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1047 + +--S 1048 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 35b x - 84a b x - 70a b x - 20a +--R (3) ------------------------------------- +--R 21 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 1048 + +--S 1049 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1050 + +)clear all + +--S 1051 of 1285 +t0:=(a+b*x^3)^3/x^25 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1051 + +--S 1052 of 1285 +r0:=-1/24*a^3/x^24-1/7*a^2*b/x^21-1/6*a*b^2/x^18-1/15*b^3/x^15 +--R +--R +--R 1 3 9 1 2 6 1 2 3 1 3 +--R - -- b x - - a b x - - a b x - -- a +--R 15 6 7 24 +--R (2) --------------------------------------- +--R 24 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1052 + +--S 1053 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R - 56b x - 140a b x - 120a b x - 35a +--R (3) --------------------------------------- +--R 24 +--R 840x +--R Type: Union(Expression(Integer),...) +--E 1053 + +--S 1054 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1055 + +)clear all + +--S 1056 of 1285 +t0:=x^4*(a+b*x^3)^3 +--R +--R +--R 3 13 2 10 2 7 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1056 + +--S 1057 of 1285 +r0:=1/5*a^3*x^5+3/8*a^2*b*x^8+3/11*a*b^2*x^11+1/14*b^3*x^14 +--R +--R +--R 1 3 14 3 2 11 3 2 8 1 3 5 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 14 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1057 + +--S 1058 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 3 2 11 3 2 8 1 3 5 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 14 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1058 + +--S 1059 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1059 + +--S 1060 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1060 + +)clear all + +--S 1061 of 1285 +t0:=x^3*(a+b*x^3)^3 +--R +--R +--R 3 12 2 9 2 6 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1061 + +--S 1062 of 1285 +r0:=1/4*a^3*x^4+3/7*a^2*b*x^7+3/10*a*b^2*x^10+1/13*b^3*x^13 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 13 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1062 + +--S 1063 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 13 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1063 + +--S 1064 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1064 + +--S 1065 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1065 + +)clear all + +--S 1066 of 1285 +t0:=x*(a+b*x^3)^3 +--R +--R +--R 3 10 2 7 2 4 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 1066 + +--S 1067 of 1285 +r0:=1/2*a^3*x^2+3/5*a^2*b*x^5+3/8*a*b^2*x^8+1/11*b^3*x^11 +--R +--R +--R 1 3 11 3 2 8 3 2 5 1 3 2 +--R (2) -- b x + - a b x + - a b x + - a x +--R 11 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1067 + +--S 1068 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 11 3 2 8 3 2 5 1 3 2 +--R (3) -- b x + - a b x + - a b x + - a x +--R 11 8 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1068 + +--S 1069 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1069 + +--S 1070 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1070 + +)clear all + +--S 1071 of 1285 +t0:=(a+b*x^3)^3 +--R +--R +--R 3 9 2 6 2 3 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 1071 + +--S 1072 of 1285 +r0:=a^3*x+3/4*a^2*b*x^4+3/7*a*b^2*x^7+1/10*b^3*x^10 +--R +--R +--R 1 3 10 3 2 7 3 2 4 3 +--R (2) -- b x + - a b x + - a b x + a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1072 + +--S 1073 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 3 10 3 2 7 3 2 4 3 +--R (3) -- b x + - a b x + - a b x + a x +--R 10 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1073 + +--S 1074 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1074 + +--S 1075 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1075 + +)clear all + +--S 1076 of 1285 +t0:=(a+b*x^3)^3/x^2 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 1285 +r0:=-a^3/x+3/2*a^2*b*x^2+3/5*a*b^2*x^5+1/8*b^3*x^8 +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 24a b x + 60a b x - 40a +--R (2) ---------------------------------- +--R 40x +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 24a b x + 60a b x - 40a +--R (3) ---------------------------------- +--R 40x +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1285 +t0:=(a+b*x^3)^3/x^3 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 1285 +r0:=-1/2*a^3/x^2+3*a^2*b*x+3/4*a*b^2*x^4+1/7*b^3*x^7 +--R +--R +--R 1 3 9 3 2 6 2 3 1 3 +--R - b x + - a b x + 3a b x - - a +--R 7 4 2 +--R (2) ---------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1082 + +--S 1083 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 4b x + 21a b x + 84a b x - 14a +--R (3) ---------------------------------- +--R 2 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1285 +t0:=(a+b*x^3)^3/x^5 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 1285 +r0:=-1/4*a^3/x^4-3*a^2*b/x+3/2*a*b^2*x^2+1/5*b^3*x^5 +--R +--R +--R 1 3 9 3 2 6 2 3 1 3 +--R - b x + - a b x - 3a b x - - a +--R 5 2 4 +--R (2) ---------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1087 + +--S 1088 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 4b x + 30a b x - 60a b x - 5a +--R (3) --------------------------------- +--R 4 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1285 +t0:=(a+b*x^3)^3/x^6 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 1285 +r0:=-1/5*a^3/x^5-3/2*a^2*b/x^2+3*a*b^2*x+1/4*b^3*x^4 +--R +--R +--R 1 3 9 2 6 3 2 3 1 3 +--R - b x + 3a b x - - a b x - - a +--R 4 2 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1092 + +--S 1093 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 5b x + 60a b x - 30a b x - 4a +--R (3) --------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1285 +t0:=(a+b*x^3)^3/x^8 +--R +--R +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1096 + +--S 1097 of 1285 +r0:=-1/7*a^3/x^7-3/4*a^2*b/x^4-3*a*b^2/x+1/2*b^3*x^2 +--R +--R +--R 1 3 9 2 6 3 2 3 1 3 +--R - b x - 3a b x - - a b x - - a +--R 2 4 7 +--R (2) ---------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1097 + +--S 1098 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 9 2 6 2 3 3 +--R 14b x - 84a b x - 21a b x - 4a +--R (3) ---------------------------------- +--R 7 +--R 28x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1285 +t0:=x^m*(a+b*x^3)^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 m +--R (1) (b x + 5a b x + 10a b x + 10a b x + 5a b x + a )x +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1285 +r0:=a^5*x^(1+m)/(1+m)+5*a^4*b*x^(4+m)/(4+m)+10*a^3*b^2*x^(7+m)/(7+m)+_ + 10*a^2*b^3*x^(10+m)/(10+m)+5*a*b^4*x^(13+m)/(13+m)+b^5*x^(16+m)/(16+m) +--R +--R +--R (2) +--R 5 5 5 4 5 3 5 2 5 5 m + 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R m + 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R m + 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R m + 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R m + 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R * +--R m log(x) +--R %e +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 5 4 5 3 5 2 5 5 16 +--R (b m + 35b m + 445b m + 2485b m + 5714b m + 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 190a b m + 2555a b m + 14810a b m + 34840a b m +--R + +--R 4 +--R 22400a b +--R * +--R 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 10a b m + 410a b m + 5950a b m + 36550a b m + 89240a b m +--R + +--R 2 3 +--R 58240a b +--R * +--R 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R 10a b m + 440a b m + 6970a b m + 47260a b m + 123920a b m +--R + +--R 3 2 +--R 83200a b +--R * +--R 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 5a b m + 235a b m + 4085a b m + 31685a b m + 100630a b m +--R + +--R 4 +--R 72800a b +--R * +--R 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 +--R (a m + 50a m + 955a m + 8650a m + 36824a m + 58240a )x +--R * +--R m log(x) +--R %e +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 16 +--R (- b m - 35b m - 445b m - 2485b m - 5714b m - 3640b )x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 190a b m - 2555a b m - 14810a b m - 34840a b m +--R + +--R 4 +--R - 22400a b +--R * +--R m + 13 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R - 10a b m - 410a b m - 5950a b m - 36550a b m - 89240a b m +--R + +--R 2 3 +--R - 58240a b +--R * +--R m + 10 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 +--R - 10a b m - 440a b m - 6970a b m - 47260a b m - 123920a b m +--R + +--R 3 2 +--R - 83200a b +--R * +--R m + 7 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R - 5a b m - 235a b m - 4085a b m - 31685a b m - 100630a b m +--R + +--R 4 +--R - 72800a b +--R * +--R m + 4 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (- a m - 50a m - 955a m - 8650a m - 36824a m - 58240a )x +--R / +--R 6 5 4 3 2 +--R m + 51m + 1005m + 9605m + 45474m + 95064m + 58240 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1285 +t0:=x^17*(a+b*x^3)^5 +--R +--R +--R 5 32 4 29 2 3 26 3 2 23 4 20 5 17 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1106 + +--S 1107 of 1285 +r0:=1/18*a^5*x^18+5/21*a^4*b*x^21+5/12*a^3*b^2*x^24+10/27*a^2*b^3*x^27+_ + 1/6*a*b^4*x^30+1/33*b^5*x^33 +--R +--R +--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18 +--R (2) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 33 6 27 12 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1107 + +--S 1108 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 33 1 4 30 10 2 3 27 5 3 2 24 5 4 21 1 5 18 +--R (3) -- b x + - a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 33 6 27 12 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1108 + +--S 1109 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1109 + +--S 1110 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1110 + +)clear all + +--S 1111 of 1285 +t0:=x^14*(a+b*x^3)^5 +--R +--R +--R 5 29 4 26 2 3 23 3 2 20 4 17 5 14 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1111 + +--S 1112 of 1285 +r0:=1/15*a^5*x^15+5/18*a^4*b*x^18+10/21*a^3*b^2*x^21+5/12*a^2*b^3*x^24+_ + 5/27*a*b^4*x^27+1/30*b^5*x^30 +--R +--R +--R (2) +--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 30 27 12 21 18 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1112 + +--S 1113 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 30 5 4 27 5 2 3 24 10 3 2 21 5 4 18 1 5 15 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a x +--R 30 27 12 21 18 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1113 + +--S 1114 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1114 + +--S 1115 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1115 + +)clear all + +--S 1116 of 1285 +t0:=x^11*(a+b*x^3)^5 +--R +--R +--R 5 26 4 23 2 3 20 3 2 17 4 14 5 11 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1116 + +--S 1117 of 1285 +r0:=1/12*a^5*x^12+1/3*a^4*b*x^15+5/9*a^3*b^2*x^18+10/21*a^2*b^3*x^21+_ + 5/24*a*b^4*x^24+1/27*b^5*x^27 +--R +--R +--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12 +--R (2) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x +--R 27 24 21 9 3 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1117 + +--S 1118 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 27 5 4 24 10 2 3 21 5 3 2 18 1 4 15 1 5 12 +--R (3) -- b x + -- a b x + -- a b x + - a b x + - a b x + -- a x +--R 27 24 21 9 3 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1118 + +--S 1119 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1119 + +--S 1120 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1120 + +)clear all + +--S 1121 of 1285 +t0:=x^8*(a+b*x^3)^5 +--R +--R +--R 5 23 4 20 2 3 17 3 2 14 4 11 5 8 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1121 + +--S 1122 of 1285 +r0:=1/18*a^2*(a+b*x^3)^6/b^3-2/21*a*(a+b*x^3)^7/b^3+1/24*(a+b*x^3)^8/b^3 +--R +--R +--R (2) +--R 1 8 24 5 7 21 5 2 6 18 2 3 5 15 5 4 4 12 1 5 3 9 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + - a b x +--R 24 21 9 3 12 9 +--R + +--R 1 8 +--R --- a +--R 504 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1122 + +--S 1123 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 24 5 4 21 5 2 3 18 2 3 2 15 5 4 12 1 5 9 +--R (3) -- b x + -- a b x + - a b x + - a b x + -- a b x + - a x +--R 24 21 9 3 12 9 +--R Type: Polynomial(Fraction(Integer)) +--E 1123 + +--S 1124 of 1285 +m0:=a0-r0 +--R +--R +--R 1 8 +--R --- a +--R 504 +--R (4) - ------ +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1124 + +--S 1125 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1125 + +)clear all + +--S 1126 of 1285 +t0:=x^5*(a+b*x^3)^5 +--R +--R +--R 5 20 4 17 2 3 14 3 2 11 4 8 5 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1126 + +--S 1127 of 1285 +r0:=-1/18*a*(a+b*x^3)^6/b^2+1/21*(a+b*x^3)^7/b^2 +--R +--R +--R (2) +--R 1 7 21 5 6 18 2 2 5 15 5 3 4 12 5 4 3 9 1 5 2 6 1 7 +--R -- b x + -- a b x + - a b x + - a b x + - a b x + - a b x - --- a +--R 21 18 3 6 9 6 126 +--R ---------------------------------------------------------------------------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1127 + +--S 1128 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 21 5 4 18 2 2 3 15 5 3 2 12 5 4 9 1 5 6 +--R (3) -- b x + -- a b x + - a b x + - a b x + - a b x + - a x +--R 21 18 3 6 9 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1128 + +--S 1129 of 1285 +m0:=a0-r0 +--R +--R +--R 1 7 +--R --- a +--R 126 +--R (4) ------ +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1129 + +--S 1130 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1130 + +)clear all + +--S 1131 of 1285 +t0:=x^2*(a+b*x^3)^5 +--R +--R +--R 5 17 4 14 2 3 11 3 2 8 4 5 5 2 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1131 + +--S 1132 of 1285 +r0:=1/18*(a+b*x^3)^6/b +--R +--R +--R (2) +--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6 +--R -- b x + - a b x + - a b x + -- a b x + - a b x + - a b x + -- a +--R 18 3 6 9 6 3 18 +--R -------------------------------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1132 + +--S 1133 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 18 1 4 15 5 2 3 12 10 3 2 9 5 4 6 1 5 3 +--R (3) -- b x + - a b x + - a b x + -- a b x + - a b x + - a x +--R 18 3 6 9 6 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1133 + +--S 1134 of 1285 +m0:=a0-r0 +--R +--R +--R 1 6 +--R -- a +--R 18 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1134 + +--S 1135 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1135 + +)clear all + +--S 1136 of 1285 +t0:=(a+b*x^3)^5/x +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 1285 +r0:=5/3*a^4*b*x^3+5/3*a^3*b^2*x^6+10/9*a^2*b^3*x^9+5/12*a*b^4*x^12+_ + 1/15*b^5*x^15+a^5*log(x) +--R +--R +--R 5 5 15 4 12 2 3 9 3 2 6 4 3 +--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (2) --------------------------------------------------------------------- +--R 180 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 5 15 4 12 2 3 9 3 2 6 4 3 +--R 180a log(x) + 12b x + 75a b x + 200a b x + 300a b x + 300a b x +--R (3) --------------------------------------------------------------------- +--R 180 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1285 +t0:=(a+b*x^3)^5/x^4 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 1285 +r0:=-1/3*a^5/x^3+10/3*a^3*b^2*x^3+5/3*a^2*b^3*x^6+5/9*a*b^4*x^9+_ + 1/12*b^5*x^12+5*a^4*b*log(x) +--R +--R +--R 4 3 5 15 4 12 2 3 9 3 2 6 5 +--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (2) ------------------------------------------------------------------ +--R 3 +--R 36x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 3 5 15 4 12 2 3 9 3 2 6 5 +--R 180a b x log(x) + 3b x + 20a b x + 60a b x + 120a b x - 12a +--R (3) ------------------------------------------------------------------ +--R 3 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1285 +t0:=(a+b*x^3)^5/x^7 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1146 + +--S 1147 of 1285 +r0:=-1/6*a^5/x^6-5/3*a^4*b/x^3+10/3*a^2*b^3*x^3+5/6*a*b^4*x^6+_ + 1/9*b^5*x^9+10*a^3*b^2*log(x) +--R +--R +--R 3 2 6 5 15 4 12 2 3 9 4 3 5 +--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (2) ---------------------------------------------------------------- +--R 6 +--R 18x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 3 2 6 5 15 4 12 2 3 9 4 3 5 +--R 180a b x log(x) + 2b x + 15a b x + 60a b x - 30a b x - 3a +--R (3) ---------------------------------------------------------------- +--R 6 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1285 +t0:=(a+b*x^3)^5/x^10 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1151 + +--S 1152 of 1285 +r0:=-1/9*a^5/x^9-5/6*a^4*b/x^6-10/3*a^3*b^2/x^3+5/3*a*b^4*x^3+_ + 1/6*b^5*x^6+10*a^2*b^3*log(x) +--R +--R +--R 2 3 9 5 15 4 12 3 2 6 4 3 5 +--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (2) ---------------------------------------------------------------- +--R 9 +--R 18x +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 2 3 9 5 15 4 12 3 2 6 4 3 5 +--R 180a b x log(x) + 3b x + 30a b x - 60a b x - 15a b x - 2a +--R (3) ---------------------------------------------------------------- +--R 9 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1285 +t0:=(a+b*x^3)^5/x^13 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1156 + +--S 1157 of 1285 +r0:=-1/12*a^5/x^12-5/9*a^4*b/x^9-5/3*a^3*b^2/x^6-10/3*a^2*b^3/x^3+_ + 1/3*b^5*x^3+5*a*b^4*log(x) +--R +--R +--R 4 12 5 15 2 3 9 3 2 6 4 3 5 +--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (2) ------------------------------------------------------------------ +--R 12 +--R 36x +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 4 12 5 15 2 3 9 3 2 6 4 3 5 +--R 180a b x log(x) + 12b x - 120a b x - 60a b x - 20a b x - 3a +--R (3) ------------------------------------------------------------------ +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1285 +t0:=(a+b*x^3)^5/x^16 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1161 + +--S 1162 of 1285 +r0:=-1/15*a^5/x^15-5/12*a^4*b/x^12-10/9*a^3*b^2/x^9-5/3*a^2*b^3/x^6-_ + 5/3*a*b^4/x^3+b^5*log(x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (2) --------------------------------------------------------------------- +--R 15 +--R 180x +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 180b x log(x) - 300a b x - 300a b x - 200a b x - 75a b x - 12a +--R (3) --------------------------------------------------------------------- +--R 15 +--R 180x +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1285 +t0:=(a+b*x^3)^5/x^19 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 1285 +r0:=-1/18*(a+b*x^3)^6/(a*x^18) +--R +--R +--R (2) +--R 1 6 18 1 5 15 5 2 4 12 10 3 3 9 5 4 2 6 1 5 3 1 6 +--R - -- b x - - a b x - - a b x - -- a b x - - a b x - - a b x - -- a +--R 18 3 6 9 6 3 18 +--R ---------------------------------------------------------------------------- +--R 18 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1167 + +--S 1168 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 6b x - 15a b x - 20a b x - 15a b x - 6a b x - a +--R (3) --------------------------------------------------------- +--R 18 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1285 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) --- +--R 18a +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1285 +t0:=(a+b*x^3)^5/x^22 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 1285 +r0:=-1/21*(a+b*x^3)^6/(a*x^21)+1/126*b*(a+b*x^3)^6/(a^2*x^18) +--R +--R +--R (2) +--R 1 7 21 1 2 5 15 5 3 4 12 5 4 3 9 2 5 2 6 5 6 3 1 7 +--R --- b x - - a b x - - a b x - - a b x - - a b x - -- a b x - -- a +--R 126 6 9 6 3 18 21 +--R --------------------------------------------------------------------------- +--R 2 21 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1172 + +--S 1173 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 21b x - 70a b x - 105a b x - 84a b x - 35a b x - 6a +--R (3) ------------------------------------------------------------- +--R 21 +--R 126x +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1285 +m0:=a0-r0 +--R +--R +--R 7 +--R b +--R (4) - ----- +--R 2 +--R 126a +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1285 +t0:=(a+b*x^3)^5/x^25 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1176 + +--S 1177 of 1285 +r0:=-1/24*a^5/x^24-5/21*a^4*b/x^21-5/9*a^3*b^2/x^18-2/3*a^2*b^3/x^15-_ + 5/12*a*b^4/x^12-1/9*b^5/x^9 +--R +--R +--R 1 5 15 5 4 12 2 2 3 9 5 3 2 6 5 4 3 1 5 +--R - - b x - -- a b x - - a b x - - a b x - -- a b x - -- a +--R 9 12 3 9 21 24 +--R (2) ---------------------------------------------------------------- +--R 24 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1177 + +--S 1178 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 56b x - 210a b x - 336a b x - 280a b x - 120a b x - 21a +--R (3) ----------------------------------------------------------------- +--R 24 +--R 504x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1285 +t0:=(a+b*x^3)^5/x^28 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1181 + +--S 1182 of 1285 +r0:=-1/27*a^5/x^27-5/24*a^4*b/x^24-10/21*a^3*b^2/x^21-5/9*a^2*b^3/x^18-_ + 1/3*a*b^4/x^15-1/12*b^5/x^12 +--R +--R +--R 1 5 15 1 4 12 5 2 3 9 10 3 2 6 5 4 3 1 5 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a +--R 12 3 9 21 24 27 +--R (2) ----------------------------------------------------------------- +--R 27 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1182 + +--S 1183 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 126b x - 504a b x - 840a b x - 720a b x - 315a b x - 56a +--R (3) ------------------------------------------------------------------ +--R 27 +--R 1512x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1285 +t0:=(a+b*x^3)^5/x^31 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 1285 +r0:=-1/30*a^5/x^30-5/27*a^4*b/x^27-5/12*a^3*b^2/x^24-10/21*a^2*b^3/x^21-_ + 5/18*a*b^4/x^18-1/15*b^5/x^15 +--R +--R +--R 1 5 15 5 4 12 10 2 3 9 5 3 2 6 5 4 3 1 5 +--R - -- b x - -- a b x - -- a b x - -- a b x - -- a b x - -- a +--R 15 18 21 12 27 30 +--R (2) ------------------------------------------------------------------- +--R 30 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1187 + +--S 1188 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 252b x - 1050a b x - 1800a b x - 1575a b x - 700a b x - 126a +--R (3) ---------------------------------------------------------------------- +--R 30 +--R 3780x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1285 +t0:=(a+b*x^3)^5/x^34 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 34 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 1285 +r0:=-1/33*a^5/x^33-1/6*a^4*b/x^30-10/27*a^3*b^2/x^27-5/12*a^2*b^3/x^24-_ + 5/21*a*b^4/x^21-1/18*b^5/x^18 +--R +--R +--R 1 5 15 5 4 12 5 2 3 9 10 3 2 6 1 4 3 1 5 +--R - -- b x - -- a b x - -- a b x - -- a b x - - a b x - -- a +--R 18 21 12 27 6 33 +--R (2) ------------------------------------------------------------------ +--R 33 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1192 + +--S 1193 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R - 462b x - 1980a b x - 3465a b x - 3080a b x - 1386a b x - 252a +--R ----------------------------------------------------------------------- +--R 33 +--R 8316x +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1285 +t0:=x^4*(a+b*x^3)^5 +--R +--R +--R 5 19 4 16 2 3 13 3 2 10 4 7 5 4 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1196 + +--S 1197 of 1285 +r0:=1/5*a^5*x^5+5/8*a^4*b*x^8+10/11*a^3*b^2*x^11+5/7*a^2*b^3*x^14+_ + 5/17*a*b^4*x^17+1/20*b^5*x^20 +--R +--R +--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5 +--R (2) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x +--R 20 17 7 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1197 + +--S 1198 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 20 5 4 17 5 2 3 14 10 3 2 11 5 4 8 1 5 5 +--R (3) -- b x + -- a b x + - a b x + -- a b x + - a b x + - a x +--R 20 17 7 11 8 5 +--R Type: Polynomial(Fraction(Integer)) +--E 1198 + +--S 1199 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1199 + +--S 1200 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1200 + +)clear all + +--S 1201 of 1285 +t0:=x^3*(a+b*x^3)^5 +--R +--R +--R 5 18 4 15 2 3 12 3 2 9 4 6 5 3 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1201 + +--S 1202 of 1285 +r0:=1/4*a^5*x^4+5/7*a^4*b*x^7+a^3*b^2*x^10+10/13*a^2*b^3*x^13+_ + 5/16*a*b^4*x^16+1/19*b^5*x^19 +--R +--R +--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4 +--R (2) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x +--R 19 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1202 + +--S 1203 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 19 5 4 16 10 2 3 13 3 2 10 5 4 7 1 5 4 +--R (3) -- b x + -- a b x + -- a b x + a b x + - a b x + - a x +--R 19 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1203 + +--S 1204 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1204 + +--S 1205 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1205 + +)clear all + +--S 1206 of 1285 +t0:=x*(a+b*x^3)^5 +--R +--R +--R 5 16 4 13 2 3 10 3 2 7 4 4 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a x +--R Type: Polynomial(Integer) +--E 1206 + +--S 1207 of 1285 +r0:=1/2*a^5*x^2+a^4*b*x^5+5/4*a^3*b^2*x^8+10/11*a^2*b^3*x^11+_ + 5/14*a*b^4*x^14+1/17*b^5*x^17 +--R +--R +--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2 +--R (2) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x +--R 17 14 11 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1207 + +--S 1208 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 17 5 4 14 10 2 3 11 5 3 2 8 4 5 1 5 2 +--R (3) -- b x + -- a b x + -- a b x + - a b x + a b x + - a x +--R 17 14 11 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1208 + +--S 1209 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1209 + +--S 1210 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1210 + +)clear all + +--S 1211 of 1285 +t0:=(a+b*x^3)^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R (1) b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Polynomial(Integer) +--E 1211 + +--S 1212 of 1285 +r0:=a^5*x+5/4*a^4*b*x^4+10/7*a^3*b^2*x^7+a^2*b^3*x^10+5/13*a*b^4*x^13+_ + 1/16*b^5*x^16 +--R +--R +--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5 +--R (2) -- b x + -- a b x + a b x + -- a b x + - a b x + a x +--R 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1212 + +--S 1213 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 1 5 16 5 4 13 2 3 10 10 3 2 7 5 4 4 5 +--R (3) -- b x + -- a b x + a b x + -- a b x + - a b x + a x +--R 16 13 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 1213 + +--S 1214 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1214 + +--S 1215 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1215 + +)clear all + +--S 1216 of 1285 +t0:=(a+b*x^3)^5/x^2 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1216 + +--S 1217 of 1285 +r0:=-a^5/x+5/2*a^4*b*x^2+2*a^3*b^2*x^5+5/4*a^2*b^3*x^8+5/11*a*b^4*x^11+_ + 1/14*b^5*x^14 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a +--R (2) ---------------------------------------------------------------- +--R 308x +--R Type: Fraction(Polynomial(Integer)) +--E 1217 + +--S 1218 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 22b x + 140a b x + 385a b x + 616a b x + 770a b x - 308a +--R (3) ---------------------------------------------------------------- +--R 308x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1285 +t0:=(a+b*x^3)^5/x^3 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1221 + +--S 1222 of 1285 +r0:=-1/2*a^5/x^2+5*a^4*b*x+5/2*a^3*b^2*x^4+10/7*a^2*b^3*x^7+_ + 1/2*a*b^4*x^10+1/13*b^5*x^13 +--R +--R +--R 1 5 15 1 4 12 10 2 3 9 5 3 2 6 4 3 1 5 +--R -- b x + - a b x + -- a b x + - a b x + 5a b x - - a +--R 13 2 7 2 2 +--R (2) ------------------------------------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1222 + +--S 1223 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 14b x + 91a b x + 260a b x + 455a b x + 910a b x - 91a +--R (3) -------------------------------------------------------------- +--R 2 +--R 182x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1285 +t0:=(a+b*x^3)^5/x^5 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1226 + +--S 1227 of 1285 +r0:=-1/4*a^5/x^4-5*a^4*b/x+5*a^3*b^2*x^2+2*a^2*b^3*x^5+5/8*a*b^4*x^8+_ + 1/11*b^5*x^11 +--R +--R +--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5 +--R -- b x + - a b x + 2a b x + 5a b x - 5a b x - - a +--R 11 8 4 +--R (2) --------------------------------------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1227 + +--S 1228 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 8b x + 55a b x + 176a b x + 440a b x - 440a b x - 22a +--R (3) ------------------------------------------------------------- +--R 4 +--R 88x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1285 +t0:=(a+b*x^3)^5/x^6 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1231 + +--S 1232 of 1285 +r0:=-1/5*a^5/x^5-5/2*a^4*b/x^2+10*a^3*b^2*x+5/2*a^2*b^3*x^4+5/7*a*b^4*x^7+_ + 1/10*b^5*x^10 +--R +--R +--R 1 5 15 5 4 12 5 2 3 9 3 2 6 5 4 3 1 5 +--R -- b x + - a b x + - a b x + 10a b x - - a b x - - a +--R 10 7 2 2 5 +--R (2) ------------------------------------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1232 + +--S 1233 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 7b x + 50a b x + 175a b x + 700a b x - 175a b x - 14a +--R (3) ------------------------------------------------------------- +--R 5 +--R 70x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1285 +t0:=(a+b*x^3)^5/x^8 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1236 + +--S 1237 of 1285 +r0:=-1/7*a^5/x^7-5/4*a^4*b/x^4-10*a^3*b^2/x+5*a^2*b^3*x^2+a*b^4*x^5+1/8*b^5*x^8 +--R +--R +--R 1 5 15 4 12 2 3 9 3 2 6 5 4 3 1 5 +--R - b x + a b x + 5a b x - 10a b x - - a b x - - a +--R 8 4 7 +--R (2) -------------------------------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1237 + +--S 1238 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 7b x + 56a b x + 280a b x - 560a b x - 70a b x - 8a +--R (3) ----------------------------------------------------------- +--R 7 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1285 +t0:=(a+b*x^3)^5/x^9 +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (1) ----------------------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1241 + +--S 1242 of 1285 +r0:=-1/8*a^5/x^8-a^4*b/x^5-5*a^3*b^2/x^2+10*a^2*b^3*x+5/4*a*b^4*x^4+1/7*b^5*x^7 +--R +--R +--R 1 5 15 5 4 12 2 3 9 3 2 6 4 3 1 5 +--R - b x + - a b x + 10a b x - 5a b x - a b x - - a +--R 7 4 8 +--R (2) -------------------------------------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1242 + +--S 1243 of 1285 +a0:=integrate(t0,x) +--R +--R +--R 5 15 4 12 2 3 9 3 2 6 4 3 5 +--R 8b x + 70a b x + 560a b x - 280a b x - 56a b x - 7a +--R (3) ----------------------------------------------------------- +--R 8 +--R 56x +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1285 +t0:=x^m*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R * +--R m +--R x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1285 +r0:=a^8*x^(1+m)/(1+m)+8*a^7*b*x^(4+m)/(4+m)+28*a^6*b^2*x^(7+m)/(7+m)+_ + 56*a^5*b^3*x^(10+m)/(10+m)+70*a^4*b^4*x^(13+m)/(13+m)+_ + 56*a^3*b^5*x^(16+m)/(16+m)+28*a^2*b^6*x^(19+m)/(19+m)+_ + 8*a*b^7*x^(22+m)/(22+m)+b^8*x^(25+m)/(25+m) +--R +--R +--R (2) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R m + 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R m + 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 2 6 4 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m + 29390452a b m +--R + +--R 2 6 3 2 6 2 2 6 2 6 +--R 210422576a b m + 827034544a b m + 1540629440a b m + 896896000a b +--R * +--R m + 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 3 5 4 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m + 65946104a b m +--R + +--R 3 5 3 3 5 2 3 5 3 5 +--R 482544664a b m + 1929412352a b m + 3637973920a b m + 2130128000a b +--R * +--R m + 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 4 4 4 +--R 70a b m + 7280a b m + 312340a b m + 7138040a b m + 93585310a b m +--R + +--R 4 4 3 4 4 2 4 4 4 4 +--R 705493880a b m + 2891238280a b m + 5549616800a b m + 3277120000a b +--R * +--R m + 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 5 3 4 +--R 56a b m + 5992a b m + 265664a b m + 6302128a b m + 86082584a b m +--R + +--R 5 3 3 5 3 2 5 3 5 3 +--R 676856488a b m + 2881562096a b m + 5692950592a b m + 3408204800a b +--R * +--R m + 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 6 2 4 +--R 28a b m + 3080a b m + 141232a b m + 3490760a b m + 50116612a b m +--R + +--R 6 2 3 6 2 2 6 2 6 2 +--R 418024880a b m + 1898889328a b m + 3962060480a b m + 2434432000a b +--R * +--R m + 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 904a b m + 42896a b m + 1108240a b m + 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b +--R * +--R m + 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m +--R + +--R 8 2 8 8 +--R 147373372a m + 468851120a m + 608608000a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R 29390452a b m + 210422576a b m + 827034544a b m +--R + +--R 2 6 2 6 +--R 1540629440a b m + 896896000a b +--R * +--R 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m 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b m + 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R 152198536a b m + 769795424a b m + 1850614240a b m + 1217216000a b +--R * +--R 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m + 24950324a m +--R + +--R 8 2 8 8 +--R 147373372a m + 468851120a m + 608608000a +--R * +--R x +--R * +--R m log(x) +--R %e +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1285 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R b m + 92b m + 3514b m + 72128b m + 859369b m + 5974388b m +--R + +--R 8 2 8 8 +--R 22963996b m + 42124592b m + 24344320b +--R * +--R 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R 8a b m + 760a b m + 29792a b m + 624400a b m + 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R 53266360a b m + 206729648a b m + 381743680a b m + 221312000a b +--R * +--R 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R 28a b m + 2744a b m + 110656a b m + 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R 29390452a b m + 210422576a b m + 827034544a b m +--R + +--R 2 6 2 6 +--R 1540629440a b m + 896896000a b +--R * +--R 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R 56a b m + 5656a b m + 235088a b m + 5197360a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R 65946104a b m + 482544664a b m + 1929412352a b m +--R + +--R 3 5 3 5 +--R 3637973920a b m + 2130128000a b +--R * +--R 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R 70a b m + 7280a b m + 312340a b m + 7138040a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R 93585310a b m + 705493880a b m + 2891238280a b m +--R + +--R 4 4 4 4 +--R 5549616800a b m + 3277120000a b +--R * +--R 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R 56a b m + 5992a b m + 265664a b m + 6302128a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R 86082584a b m + 676856488a b m + 2881562096a b m +--R + +--R 5 3 5 3 +--R 5692950592a b m + 3408204800a b +--R * +--R 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R 28a b m + 3080a b m + 141232a b m + 3490760a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R 50116612a b m + 418024880a b m + 1898889328a b m +--R + +--R 6 2 6 2 +--R 3962060480a b m + 2434432000a b +--R * +--R 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 +--R 8a b m + 904a b m + 42896a b m + 1108240a b m +--R + +--R 7 4 7 3 7 2 +--R 16867592a b m + 152198536a b m + 769795424a b m +--R + +--R 7 7 +--R 1850614240a b m + 1217216000a b +--R * +--R 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 +--R a m + 116a m + 5698a m + 154280a m + 2508289a m +--R + +--R 8 3 8 2 8 8 +--R 24950324a m + 147373372a m + 468851120a m + 608608000a +--R * +--R x +--R * +--R m log(x) +--R %e +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - b m - 92b m - 3514b m - 72128b m - 859369b m - 5974388b m +--R + +--R 8 2 8 8 +--R - 22963996b m - 42124592b m - 24344320b +--R * +--R m + 25 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 760a b m - 29792a b m - 624400a b m - 7563752a b m +--R + +--R 7 3 7 2 7 7 +--R - 53266360a b m - 206729648a b m - 381743680a b m - 221312000a b +--R * +--R m + 22 +--R x +--R + +--R 2 6 8 2 6 7 2 6 6 2 6 5 +--R - 28a b m - 2744a b m - 110656a b m - 2376920a b m +--R + +--R 2 6 4 2 6 3 2 6 2 +--R - 29390452a b m - 210422576a b m - 827034544a b m +--R + +--R 2 6 2 6 +--R - 1540629440a b m - 896896000a b +--R * +--R m + 19 +--R x +--R + +--R 3 5 8 3 5 7 3 5 6 3 5 5 +--R - 56a b m - 5656a b m - 235088a b m - 5197360a b m +--R + +--R 3 5 4 3 5 3 3 5 2 +--R - 65946104a b m - 482544664a b m - 1929412352a b m +--R + +--R 3 5 3 5 +--R - 3637973920a b m - 2130128000a b +--R * +--R m + 16 +--R x +--R + +--R 4 4 8 4 4 7 4 4 6 4 4 5 +--R - 70a b m - 7280a b m - 312340a b m - 7138040a b m +--R + +--R 4 4 4 4 4 3 4 4 2 +--R - 93585310a b m - 705493880a b m - 2891238280a b m +--R + +--R 4 4 4 4 +--R - 5549616800a b m - 3277120000a b +--R * +--R m + 13 +--R x +--R + +--R 5 3 8 5 3 7 5 3 6 5 3 5 +--R - 56a b m - 5992a b m - 265664a b m - 6302128a b m +--R + +--R 5 3 4 5 3 3 5 3 2 +--R - 86082584a b m - 676856488a b m - 2881562096a b m +--R + +--R 5 3 5 3 +--R - 5692950592a b m - 3408204800a b +--R * +--R m + 10 +--R x +--R + +--R 6 2 8 6 2 7 6 2 6 6 2 5 +--R - 28a b m - 3080a b m - 141232a b m - 3490760a b m +--R + +--R 6 2 4 6 2 3 6 2 2 +--R - 50116612a b m - 418024880a b m - 1898889328a b m +--R + +--R 6 2 6 2 +--R - 3962060480a b m - 2434432000a b +--R * +--R m + 7 +--R x +--R + +--R 7 8 7 7 7 6 7 5 7 4 +--R - 8a b m - 904a b m - 42896a b m - 1108240a b m - 16867592a b m +--R + +--R 7 3 7 2 7 7 +--R - 152198536a b m - 769795424a b m - 1850614240a b m - 1217216000a b +--R * +--R m + 4 +--R x +--R + +--R 8 8 8 7 8 6 8 5 8 4 8 3 +--R - a m - 116a m - 5698a m - 154280a m - 2508289a m - 24950324a m +--R + +--R 8 2 8 8 +--R - 147373372a m - 468851120a m - 608608000a +--R * +--R m + 1 +--R x +--R / +--R 9 8 7 6 5 4 3 +--R m + 117m + 5814m + 159978m + 2662569m + 27458613m + 172323696m +--R + +--R 2 +--R 616224492m + 1077459120m + 608608000 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1285 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1285 +t0:=x^20*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 44 7 41 2 6 38 3 5 35 4 4 32 5 3 29 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 26 7 23 8 20 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1251 + +--S 1252 of 1285 +r0:=1/21*a^8*x^21+1/3*a^7*b*x^24+28/27*a^6*b^2*x^27+28/15*a^5*b^3*x^30+_ + 70/33*a^4*b^4*x^33+14/9*a^3*b^5*x^36+28/39*a^2*b^6*x^39+_ + 4/21*a*b^7*x^42+1/45*b^8*x^45 +--R +--R +--R (2) +--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 45 21 39 9 33 15 +--R + +--R 28 6 2 27 1 7 24 1 8 21 +--R -- a b x + - a b x + -- a x +--R 27 3 21 +--R Type: Polynomial(Fraction(Integer)) +--E 1252 + +--S 1253 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 45 4 7 42 28 2 6 39 14 3 5 36 70 4 4 33 28 5 3 30 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 45 21 39 9 33 15 +--R + +--R 28 6 2 27 1 7 24 1 8 21 +--R -- a b x + - a b x + -- a x +--R 27 3 21 +--R Type: Polynomial(Fraction(Integer)) +--E 1253 + +--S 1254 of 1285 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1254 + +--S 1255 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 1255 + +)clear all + +--S 1256 of 1285 +t0:=x^17*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 41 7 38 2 6 35 3 5 32 4 4 29 5 3 26 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 23 7 20 8 17 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1256 + +--S 1257 of 1285 +r0:=-1/27*a^5*(a+b*x^3)^9/b^6+1/6*a^4*(a+b*x^3)^10/b^6-_ + 10/33*a^3*(a+b*x^3)^11/b^6+5/18*a^2*(a+b*x^3)^12/b^6-_ + 5/39*a*(a+b*x^3)^13/b^6+1/42*(a+b*x^3)^14/b^6 +--R +--R +--R (2) +--R 1 14 42 8 13 39 7 2 12 36 56 3 11 33 7 4 10 30 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x +--R 42 39 9 33 3 +--R + +--R 56 5 9 27 7 6 8 24 8 7 7 21 1 8 6 18 1 14 +--R -- a b x + - a b x + -- a b x + -- a b x - ----- a +--R 27 6 21 18 54054 +--R / +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1257 + +--S 1258 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 42 8 7 39 7 2 6 36 56 3 5 33 7 4 4 30 56 5 3 27 +--R -- b x + -- a b x + - a b x + -- a b x + - a b x + -- a b x +--R 42 39 9 33 3 27 +--R + +--R 7 6 2 24 8 7 21 1 8 18 +--R - a b x + -- a b x + -- a x +--R 6 21 18 +--R Type: Polynomial(Fraction(Integer)) +--E 1258 + +--S 1259 of 1285 +m0:=a0-r0 +--R +--R +--R 1 14 +--R ----- a +--R 54054 +--R (4) --------- +--R 6 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1259 + +--S 1260 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1260 + +)clear all + +--S 1261 of 1285 +t0:=x^14*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 38 7 35 2 6 32 3 5 29 4 4 26 5 3 23 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 20 7 17 8 14 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1261 + +--S 1262 of 1285 +r0:=1/27*a^4*(a+b*x^3)^9/b^5-2/15*a^3*(a+b*x^3)^10/b^5+_ + 2/11*a^2*(a+b*x^3)^11/b^5-1/9*a*(a+b*x^3)^12/b^5+_ + 1/39*(a+b*x^3)^13/b^5 +--R +--R +--R (2) +--R 1 13 39 2 12 36 28 2 11 33 28 3 10 30 70 4 9 27 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x +--R 39 9 33 15 27 +--R + +--R 7 5 8 24 4 6 7 21 4 7 6 18 1 8 5 15 1 13 +--R - a b x + - a b x + - a b x + -- a b x + ----- a +--R 3 3 9 15 19305 +--R / +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1262 + +--S 1263 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 39 2 7 36 28 2 6 33 28 3 5 30 70 4 4 27 7 5 3 24 +--R -- b x + - a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 39 9 33 15 27 3 +--R + +--R 4 6 2 21 4 7 18 1 8 15 +--R - a b x + - a b x + -- a x +--R 3 9 15 +--R Type: Polynomial(Fraction(Integer)) +--E 1263 + +--S 1264 of 1285 +m0:=a0-r0 +--R +--R +--R 1 13 +--R ----- a +--R 19305 +--R (4) - --------- +--R 5 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1264 + +--S 1265 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1265 + +)clear all + +--S 1266 of 1285 +t0:=x^11*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 35 7 32 2 6 29 3 5 26 4 4 23 5 3 20 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 17 7 14 8 11 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1266 + +--S 1267 of 1285 +r0:=-1/27*a^3*(a+b*x^3)^9/b^4+1/10*a^2*(a+b*x^3)^10/b^4-_ + 1/11*a*(a+b*x^3)^11/b^4+1/36*(a+b*x^3)^12/b^4 +--R +--R +--R (2) +--R 1 12 36 8 11 33 14 2 10 30 56 3 9 27 35 4 8 24 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 36 33 15 27 12 +--R + +--R 8 5 7 21 14 6 6 18 8 7 5 15 1 8 4 12 1 12 +--R - a b x + -- a b x + -- a b x + -- a b x - ---- a +--R 3 9 15 12 5940 +--R / +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1267 + +--S 1268 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 36 8 7 33 14 2 6 30 56 3 5 27 35 4 4 24 8 5 3 21 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + - a b x +--R 36 33 15 27 12 3 +--R + +--R 14 6 2 18 8 7 15 1 8 12 +--R -- a b x + -- a b x + -- a x +--R 9 15 12 +--R Type: Polynomial(Fraction(Integer)) +--E 1268 + +--S 1269 of 1285 +m0:=a0-r0 +--R +--R +--R 1 12 +--R ---- a +--R 5940 +--R (4) -------- +--R 4 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1269 + +--S 1270 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1270 + +)clear all + +--S 1271 of 1285 +t0:=x^8*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 32 7 29 2 6 26 3 5 23 4 4 20 5 3 17 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 14 7 11 8 8 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1271 + +--S 1272 of 1285 +r0:=1/27*a^2*(a+b*x^3)^9/b^3-1/15*a*(a+b*x^3)^10/b^3+1/33*(a+b*x^3)^11/b^3 +--R +--R +--R (2) +--R 1 11 33 4 10 30 28 2 9 27 7 3 8 24 10 4 7 21 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x +--R 33 15 27 3 3 +--R + +--R 28 5 6 18 28 6 5 15 2 7 4 12 1 8 3 9 1 11 +--R -- a b x + -- a b x + - a b x + - a b x + ---- a +--R 9 15 3 9 1485 +--R / +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1272 + +--S 1273 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 33 4 7 30 28 2 6 27 7 3 5 24 10 4 4 21 28 5 3 18 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 33 15 27 3 3 9 +--R + +--R 28 6 2 15 2 7 12 1 8 9 +--R -- a b x + - a b x + - a x +--R 15 3 9 +--R Type: Polynomial(Fraction(Integer)) +--E 1273 + +--S 1274 of 1285 +m0:=a0-r0 +--R +--R +--R 1 11 +--R ---- a +--R 1485 +--R (4) - -------- +--R 3 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1274 + +--S 1275 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1275 + +)clear all + +--S 1276 of 1285 +t0:=x^5*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 29 7 26 2 6 23 3 5 20 4 4 17 5 3 14 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 11 7 8 8 5 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 1276 + +--S 1277 of 1285 +r0:=-1/27*a*(a+b*x^3)^9/b^2+1/30*(a+b*x^3)^10/b^2 +--R +--R +--R (2) +--R 1 10 30 8 9 27 7 2 8 24 8 3 7 21 35 4 6 18 56 5 5 15 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x +--R 30 27 6 3 9 15 +--R + +--R 7 6 4 12 8 7 3 9 1 8 2 6 1 10 +--R - a b x + - a b x + - a b x - --- a +--R 3 9 6 270 +--R / +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1277 + +--S 1278 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 30 8 7 27 7 2 6 24 8 3 5 21 35 4 4 18 56 5 3 15 +--R -- b x + -- a b x + - a b x + - a b x + -- a b x + -- a b x +--R 30 27 6 3 9 15 +--R + +--R 7 6 2 12 8 7 9 1 8 6 +--R - a b x + - a b x + - a x +--R 3 9 6 +--R Type: Polynomial(Fraction(Integer)) +--E 1278 + +--S 1279 of 1285 +m0:=a0-r0 +--R +--R +--R 1 10 +--R --- a +--R 270 +--R (4) ------- +--R 2 +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1279 + +--S 1280 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1280 + +)clear all + +--S 1281 of 1285 +t0:=x^2*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 26 7 23 2 6 20 3 5 17 4 4 14 5 3 11 6 2 8 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 5 8 2 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 1281 + +--S 1282 of 1285 +r0:=1/27*(a+b*x^3)^9/b +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R -- a b x + - a b x + - a b x + -- a +--R 9 3 3 27 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1282 + +--S 1283 of 1285 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 27 1 7 24 4 2 6 21 28 3 5 18 14 4 4 15 14 5 3 12 +--R -- b x + - a b x + - a b x + -- a b x + -- a b x + -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 2 9 4 7 6 1 8 3 +--R -- a b x + - a b x + - a x +--R 9 3 3 +--R Type: Polynomial(Fraction(Integer)) +--E 1283 + +--S 1284 of 1285 +m0:=a0-r0 +--R +--R +--R 1 9 +--R -- a +--R 27 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1284 + +--S 1285 of 1285 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1285 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4d.input.pamphlet b/src/input/rich4d.input.pamphlet new file mode 100644 index 0000000..895334e --- /dev/null +++ b/src/input/rich4d.input.pamphlet @@ -0,0 +1,19462 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4d.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 232 matching answers. +\item 10 cases where Axiom's result differs from Rubi +\item 17 cases where Axiom supplied 2 results. +\item 2 cases that Axiom failed to integrate. +\item 28 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4d.output +)spool rich4d.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1309 +t0:=(a+b*x^3)^8/x +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 1 + +--S 2 of 1309 +r0:=8/3*a^7*b*x^3+14/3*a^6*b^2*x^6+56/9*a^5*b^3*x^9+35/6*a^4*b^4*x^12+_ + 56/15*a^3*b^5*x^15+14/9*a^2*b^6*x^18+8/21*a*b^7*x^21+_ + 1/24*b^8*x^24+a^8*log(x) +--R +--R +--R (2) +--R 8 8 24 7 21 2 6 18 3 5 15 +--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 2520 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 24 7 21 2 6 18 3 5 15 +--R 2520a log(x) + 105b x + 960a b x + 3920a b x + 9408a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 +--R 14700a b x + 15680a b x + 11760a b x + 6720a b x +--R / +--R 2520 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1309 +t0:=(a+b*x^3)^8/x^4 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 6 + +--S 7 of 1309 +r0:=-1/3*a^8/x^3+28/3*a^6*b^2*x^3+28/3*a^5*b^3*x^6+70/9*a^4*b^4*x^9+_ + 14/3*a^3*b^5*x^12+28/15*a^2*b^6*x^15+4/9*a*b^7*x^18+1/21*b^8*x^21+_ + 8*a^7*b*log(x) +--R +--R +--R (2) +--R 7 3 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 12 5 3 9 6 2 6 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 3 +--R 315x +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 15b x + 140a b x + 588a b x + 1470a b x +--R + +--R 4 4 12 5 3 9 6 2 6 8 +--R 2450a b x + 2940a b x + 2940a b x - 105a +--R / +--R 3 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1309 +t0:=(a+b*x^3)^8/x^7 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 11 + +--S 12 of 1309 +r0:=-1/6*a^8/x^6-8/3*a^7*b/x^3+56/3*a^5*b^3*x^3+35/3*a^4*b^4*x^6+_ + 56/9*a^3*b^5*x^9+7/3*a^2*b^6*x^12+8/15*a*b^7*x^15+_ + 1/18*b^8*x^18+28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 6 2 6 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 12 5 3 9 7 3 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 6 +--R 90x +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 6 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 5b x + 48a b x + 210a b x + 560a b x +--R + +--R 4 4 12 5 3 9 7 3 8 +--R 1050a b x + 1680a b x - 240a b x - 15a +--R / +--R 6 +--R 90x +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1309 +t0:=(a+b*x^3)^8/x^10 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 16 + +--S 17 of 1309 +r0:=-1/9*a^8/x^9-4/3*a^7*b/x^6-28/3*a^6*b^2/x^3+70/3*a^4*b^4*x^3+_ + 28/3*a^3*b^5*x^6+28/9*a^2*b^6*x^9+2/3*a*b^7*x^12+_ + 1/15*b^8*x^15+56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 5 3 9 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 12 6 2 6 7 3 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 9 +--R 45x +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 9 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 30a b x + 140a b x + 420a b x +--R + +--R 4 4 12 6 2 6 7 3 8 +--R 1050a b x - 420a b x - 60a b x - 5a +--R / +--R 9 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1309 +t0:=(a+b*x^3)^8/x^13 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 13 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 21 + +--S 22 of 1309 +r0:=-1/12*a^8/x^12-8/9*a^7*b/x^9-14/3*a^6*b^2/x^6-56/3*a^5*b^3/x^3+_ + 56/3*a^3*b^5*x^3+14/3*a^2*b^6*x^6+8/9*a*b^7*x^9+_ + 1/12*b^8*x^12+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 4 4 12 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 12 +--R 36x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 12 8 24 7 21 2 6 18 3 5 15 +--R 2520a b x log(x) + 3b x + 32a b x + 168a b x + 672a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 672a b x - 168a b x - 32a b x - 3a +--R / +--R 12 +--R 36x +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1309 +t0:=(a+b*x^3)^8/x^16 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 16 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 26 + +--S 27 of 1309 +r0:=-1/15*a^8/x^15-2/3*a^7*b/x^12-28/9*a^6*b^2/x^9-28/3*a^5*b^3/x^6-_ + 70/3*a^4*b^4/x^3+28/3*a^2*b^6*x^3+4/3*a*b^7*x^6+1/9*b^8*x^9+_ + 56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 3 5 15 8 24 7 21 2 6 18 4 4 12 +--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 15 +--R 45x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 15 8 24 7 21 2 6 18 4 4 12 +--R 2520a b x log(x) + 5b x + 60a b x + 420a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 420a b x - 140a b x - 30a b x - 3a +--R / +--R 15 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1309 +t0:=(a+b*x^3)^8/x^19 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 19 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 31 + +--S 32 of 1309 +r0:=-1/18*a^8/x^18-8/15*a^7*b/x^15-7/3*a^6*b^2/x^12-56/9*a^5*b^3/x^9-_ + 35/3*a^4*b^4/x^6-56/3*a^3*b^5/x^3+8/3*a*b^7*x^3+_ + 1/6*b^8*x^6+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 2 6 18 8 24 7 21 3 5 15 4 4 12 +--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 18 +--R 90x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 18 8 24 7 21 3 5 15 4 4 12 +--R 2520a b x log(x) + 15b x + 240a b x - 1680a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 560a b x - 210a b x - 48a b x - 5a +--R / +--R 18 +--R 90x +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1309 +t0:=(a+b*x^3)^8/x^22 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 22 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1309 +r0:=-1/21*a^8/x^21-4/9*a^7*b/x^18-28/15*a^6*b^2/x^15-14/3*a^5*b^3/x^12-_ + 70/9*a^4*b^4/x^9-28/3*a^3*b^5/x^6-28/3*a^2*b^6/x^3+_ + 1/3*b^8*x^3+8*a*b^7*log(x) +--R +--R +--R (2) +--R 7 21 8 24 2 6 18 3 5 15 4 4 12 +--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 21 +--R 315x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 21 8 24 2 6 18 3 5 15 4 4 12 +--R 2520a b x log(x) + 105b x - 2940a b x - 2940a b x - 2450a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 1470a b x - 588a b x - 140a b x - 15a +--R / +--R 21 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1309 +t0:=(a+b*x^3)^8/x^25 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 25 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1309 +r0:=-1/24*a^8/x^24-8/21*a^7*b/x^21-14/9*a^6*b^2/x^18-_ + 56/15*a^5*b^3/x^15-35/6*a^4*b^4/x^12-56/9*a^3*b^5/x^9-_ + 14/3*a^2*b^6/x^6-8/3*a*b^7/x^3+b^8*log(x) +--R +--R +--R (2) +--R 8 24 7 21 2 6 18 3 5 15 +--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 24 +--R 2520x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 +--R 2520b x log(x) - 6720a b x - 11760a b x - 15680a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 14700a b x - 9408a b x - 3920a b x - 960a b x - 105a +--R / +--R 24 +--R 2520x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1309 +t0:=(a+b*x^3)^8/x^28 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1309 +r0:=-1/27*(a+b*x^3)^9/(a*x^27) +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R - -- a b x - - a b x - - a b x - -- a +--R 9 3 3 27 +--R / +--R 27 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 47 + +--S 48 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 6 7 3 8 +--R - 36a b x - 9a b x - a +--R / +--R 27 +--R 27x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1309 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 27a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1309 +t0:=(a+b*x^3)^8/x^31 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 31 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1309 +r0:=-1/30*(a+b*x^3)^9/(a*x^30)+1/270*b*(a+b*x^3)^9/(a^2*x^27) +--R +--R +--R (2) +--R 1 10 30 1 2 8 24 8 3 7 21 7 4 6 18 56 5 5 15 35 6 4 12 +--R --- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 270 6 9 3 15 9 +--R + +--R 8 7 3 9 7 8 2 6 8 9 3 1 10 +--R - - a b x - - a b x - -- a b x - -- a +--R 3 6 27 30 +--R / +--R 2 30 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 52 + +--S 53 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 45b x - 240a b x - 630a b x - 1008a b x - 1050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 720a b x - 315a b x - 80a b x - 9a +--R / +--R 30 +--R 270x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1309 +m0:=a0-r0 +--R +--R +--R 10 +--R b +--R (4) - ----- +--R 2 +--R 270a +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1309 +t0:=(a+b*x^3)^8/x^34 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 34 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 56 + +--S 57 of 1309 +r0:=-1/33*(a+b*x^3)^9/(a*x^33)+1/165*b*(a+b*x^3)^9/(a^2*x^30)-_ + 1/1485*b^2*(a+b*x^3)^9/(a^3*x^27) +--R +--R +--R (2) +--R 1 11 33 1 3 8 24 2 4 7 21 28 5 6 18 28 6 5 15 +--R - ---- b x - - a b x - - a b x - -- a b x - -- a b x +--R 1485 9 3 15 9 +--R + +--R 10 7 4 12 7 8 3 9 28 9 2 6 4 10 3 1 11 +--R - -- a b x - - a b x - -- a b x - -- a b x - -- a +--R 3 3 27 15 33 +--R / +--R 3 33 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 57 + +--S 58 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 165b x - 990a b x - 2772a b x - 4620a b x - 4950a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 3465a b x - 1540a b x - 396a b x - 45a +--R / +--R 33 +--R 1485x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1309 +m0:=a0-r0 +--R +--R +--R 11 +--R b +--R (4) ------ +--R 3 +--R 1485a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1309 +t0:=(a+b*x^3)^8/x^37 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 37 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 61 + +--S 62 of 1309 +r0:=-1/36*(a+b*x^3)^9/(a*x^36)+1/132*b*(a+b*x^3)^9/(a^2*x^33)-_ + 1/660*b^2*(a+b*x^3)^9/(a^3*x^30)+1/5940*b^3*(a+b*x^3)^9/(a^4*x^27) +--R +--R +--R (2) +--R 1 12 36 1 4 8 24 8 5 7 21 14 6 6 18 8 7 5 15 +--R ---- b x - -- a b x - -- a b x - -- a b x - - a b x +--R 5940 12 15 9 3 +--R + +--R 35 8 4 12 56 9 3 9 14 10 2 6 8 11 3 1 12 +--R - -- a b x - -- a b x - -- a b x - -- a b x - -- a +--R 12 27 15 33 36 +--R / +--R 4 36 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 62 + +--S 63 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 495b x - 3168a b x - 9240a b x - 15840a b x - 17325a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 12320a b x - 5544a b x - 1440a b x - 165a +--R / +--R 36 +--R 5940x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1309 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ------ +--R 4 +--R 5940a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1309 +t0:=(a+b*x^3)^8/x^40 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 40 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 66 + +--S 67 of 1309 +r0:=-1/39*a^8/x^39-2/9*a^7*b/x^36-28/33*a^6*b^2/x^33-28/15*a^5*b^3/x^30-_ + 70/27*a^4*b^4/x^27-7/3*a^3*b^5/x^24-4/3*a^2*b^6/x^21-_ + 4/9*a*b^7/x^18-1/15*b^8/x^15 +--R +--R +--R (2) +--R 1 8 24 4 7 21 4 2 6 18 7 3 5 15 70 4 4 12 28 5 3 9 +--R - -- b x - - a b x - - a b x - - a b x - -- a b x - -- a b x +--R 15 9 3 3 27 15 +--R + +--R 28 6 2 6 2 7 3 1 8 +--R - -- a b x - - a b x - -- a +--R 33 9 39 +--R / +--R 39 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 67 + +--S 68 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 1287b x - 8580a b x - 25740a b x - 45045a b x - 50050a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 36036a b x - 16380a b x - 4290a b x - 495a +--R / +--R 39 +--R 19305x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1309 +t0:=(a+b*x^3)^8/x^43 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 43 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 71 + +--S 72 of 1309 +r0:=-1/42*a^8/x^42-8/39*a^7*b/x^39-7/9*a^6*b^2/x^36-56/33*a^5*b^3/x^33-_ + 7/3*a^4*b^4/x^30-56/27*a^3*b^5/x^27-7/6*a^2*b^6/x^24-_ + 8/21*a*b^7/x^21-1/18*b^8/x^18 +--R +--R +--R (2) +--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 7 4 4 12 56 5 3 9 +--R - -- b x - -- a b x - - a b x - -- a b x - - a b x - -- a b x +--R 18 21 6 27 3 33 +--R + +--R 7 6 2 6 8 7 3 1 8 +--R - - a b x - -- a b x - -- a +--R 9 39 42 +--R / +--R 42 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 72 + +--S 73 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R - 3003b x - 20592a b x - 63063a b x - 112112a b x - 126126a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R - 91728a b x - 42042a b x - 11088a b x - 1287a +--R / +--R 42 +--R 54054x +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1309 +t0:=(a+b*x^3)^8/x^46 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 46 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 76 + +--S 77 of 1309 +r0:=-1/45*a^8/x^45-4/21*a^7*b/x^42-28/39*a^6*b^2/x^39-_ + 14/9*a^5*b^3/x^36-70/33*a^4*b^4/x^33-28/15*a^3*b^5/x^30-_ + 28/27*a^2*b^6/x^27-1/3*a*b^7/x^24-1/21*b^8/x^21 +--R +--R +--R (2) +--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 70 4 4 12 14 5 3 9 +--R - -- b x - - a b x - -- a b x - -- a b x - -- a b x - -- a b x +--R 21 3 27 15 33 9 +--R + +--R 28 6 2 6 4 7 3 1 8 +--R - -- a b x - -- a b x - -- a +--R 39 21 45 +--R / +--R 45 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 77 + +--S 78 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 +--R - 6435b x - 45045a b x - 140140a b x - 252252a b x +--R + +--R 4 4 12 5 3 9 6 2 6 7 3 8 +--R - 286650a b x - 210210a b x - 97020a b x - 25740a b x - 3003a +--R / +--R 45 +--R 135135x +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1309 +t0:=x^4*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 28 7 25 2 6 22 3 5 19 4 4 16 5 3 13 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 10 7 7 8 4 +--R 28a b x + 8a b x + a x +--R Type: Polynomial(Integer) +--E 81 + +--S 82 of 1309 +r0:=1/5*a^8*x^5+a^7*b*x^8+28/11*a^6*b^2*x^11+4*a^5*b^3*x^14+_ + 70/17*a^4*b^4*x^17+14/5*a^3*b^5*x^20+28/23*a^2*b^6*x^23+_ + 4/13*a*b^7*x^26+1/29*b^8*x^29 +--R +--R +--R (2) +--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x +--R 29 13 23 5 17 +--R + +--R 28 6 2 11 7 8 1 8 5 +--R -- a b x + a b x + - a x +--R 11 5 +--R Type: Polynomial(Fraction(Integer)) +--E 82 + +--S 83 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 29 4 7 26 28 2 6 23 14 3 5 20 70 4 4 17 5 3 14 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + 4a b x +--R 29 13 23 5 17 +--R + +--R 28 6 2 11 7 8 1 8 5 +--R -- a b x + a b x + - a x +--R 11 5 +--R Type: Polynomial(Fraction(Integer)) +--E 83 + +--S 84 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 84 + +--S 85 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 85 + +)clear all + +--S 86 of 1309 +t0:=x^3*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 27 7 24 2 6 21 3 5 18 4 4 15 5 3 12 6 2 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 6 8 3 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 86 + +--S 87 of 1309 +r0:=1/4*a^8*x^4+8/7*a^7*b*x^7+14/5*a^6*b^2*x^10+56/13*a^5*b^3*x^13+_ + 35/8*a^4*b^4*x^16+56/19*a^3*b^5*x^19+14/11*a^2*b^6*x^22+_ + 8/25*a*b^7*x^25+1/28*b^8*x^28 +--R +--R +--R (2) +--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 28 25 11 19 8 13 +--R + +--R 14 6 2 10 8 7 7 1 8 4 +--R -- a b x + - a b x + - a x +--R 5 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 87 + +--S 88 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 28 8 7 25 14 2 6 22 56 3 5 19 35 4 4 16 56 5 3 13 +--R -- b x + -- a b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 28 25 11 19 8 13 +--R + +--R 14 6 2 10 8 7 7 1 8 4 +--R -- a b x + - a b x + - a x +--R 5 7 4 +--R Type: Polynomial(Fraction(Integer)) +--E 88 + +--S 89 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 89 + +--S 90 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 90 + +)clear all + +--S 91 of 1309 +t0:=x*(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 25 7 22 2 6 19 3 5 16 4 4 13 5 3 10 6 2 7 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 4 8 +--R 8a b x + a x +--R Type: Polynomial(Integer) +--E 91 + +--S 92 of 1309 +r0:=1/2*a^8*x^2+8/5*a^7*b*x^5+7/2*a^6*b^2*x^8+56/11*a^5*b^3*x^11+_ + 5*a^4*b^4*x^14+56/17*a^3*b^5*x^17+7/5*a^2*b^6*x^20+_ + 8/23*a*b^7*x^23+1/26*b^8*x^26 +--R +--R +--R (2) +--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x +--R 26 23 5 17 11 +--R + +--R 7 6 2 8 8 7 5 1 8 2 +--R - a b x + - a b x + - a x +--R 2 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 92 + +--S 93 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 26 8 7 23 7 2 6 20 56 3 5 17 4 4 14 56 5 3 11 +--R -- b x + -- a b x + - a b x + -- a b x + 5a b x + -- a b x +--R 26 23 5 17 11 +--R + +--R 7 6 2 8 8 7 5 1 8 2 +--R - a b x + - a b x + - a x +--R 2 5 2 +--R Type: Polynomial(Fraction(Integer)) +--E 93 + +--S 94 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 94 + +--S 95 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 95 + +)clear all + +--S 96 of 1309 +t0:=(a+b*x^3)^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 6 2 6 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x + 28a b x +--R + +--R 7 3 8 +--R 8a b x + a +--R Type: Polynomial(Integer) +--E 96 + +--S 97 of 1309 +r0:=a^8*x+2*a^7*b*x^4+4*a^6*b^2*x^7+28/5*a^5*b^3*x^10+_ + 70/13*a^4*b^4*x^13+7/2*a^3*b^5*x^16+28/19*a^2*b^6*x^19+_ + 4/11*a*b^7*x^22+1/25*b^8*x^25 +--R +--R +--R (2) +--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 25 11 19 2 13 5 +--R + +--R 6 2 7 7 4 8 +--R 4a b x + 2a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 97 + +--S 98 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 8 25 4 7 22 28 2 6 19 7 3 5 16 70 4 4 13 28 5 3 10 +--R -- b x + -- a b x + -- a b x + - a b x + -- a b x + -- a b x +--R 25 11 19 2 13 5 +--R + +--R 6 2 7 7 4 8 +--R 4a b x + 2a b x + a x +--R Type: Polynomial(Fraction(Integer)) +--E 98 + +--S 99 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 99 + +--S 100 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 100 + +)clear all + +--S 101 of 1309 +t0:=(a+b*x^3)^8/x^2 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 101 + +--S 102 of 1309 +r0:=-a^8/x+4*a^7*b*x^2+28/5*a^6*b^2*x^5+7*a^5*b^3*x^8+_ + 70/11*a^4*b^4*x^11+4*a^3*b^5*x^14+28/17*a^2*b^6*x^17+_ + 2/5*a*b^7*x^20+1/23*b^8*x^23 +--R +--R +--R (2) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 150535a b x + 120428a b x + 86020a b x - 21505a +--R / +--R 21505x +--R Type: Fraction(Polynomial(Integer)) +--E 102 + +--S 103 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 935b x + 8602a b x + 35420a b x + 86020a b x + 136850a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 150535a b x + 120428a b x + 86020a b x - 21505a +--R / +--R 21505x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1309 +t0:=(a+b*x^3)^8/x^3 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 106 + +--S 107 of 1309 +r0:=-1/2*a^8/x^2+8*a^7*b*x+7*a^6*b^2*x^4+8*a^5*b^3*x^7+7*a^4*b^4*x^10+_ + 56/13*a^3*b^5*x^13+7/4*a^2*b^6*x^16+8/19*a*b^7*x^19+1/22*b^8*x^22 +--R +--R +--R (2) +--R 1 8 24 8 7 21 7 2 6 18 56 3 5 15 4 4 12 5 3 9 +--R -- b x + -- a b x + - a b x + -- a b x + 7a b x + 8a b x +--R 22 19 4 13 +--R + +--R 6 2 6 7 3 1 8 +--R 7a b x + 8a b x - - a +--R 2 +--R / +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 107 + +--S 108 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 494b x + 4576a b x + 19019a b x + 46816a b x + 76076a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 86944a b x + 76076a b x + 86944a b x - 5434a +--R / +--R 2 +--R 10868x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1309 +t0:=(a+b*x^3)^8/x^5 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 111 + +--S 112 of 1309 +r0:=-1/4*a^8/x^4-8*a^7*b/x+14*a^6*b^2*x^2+56/5*a^5*b^3*x^5+_ + 35/4*a^4*b^4*x^8+56/11*a^3*b^5*x^11+2*a^2*b^6*x^14+_ + 8/17*a*b^7*x^17+1/20*b^8*x^20 +--R +--R +--R (2) +--R 1 8 24 8 7 21 2 6 18 56 3 5 15 35 4 4 12 56 5 3 9 +--R -- b x + -- a b x + 2a b x + -- a b x + -- a b x + -- a b x +--R 20 17 11 4 5 +--R + +--R 6 2 6 7 3 1 8 +--R 14a b x - 8a b x - - a +--R 4 +--R / +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 112 + +--S 113 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 187b x + 1760a b x + 7480a b x + 19040a b x + 32725a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 41888a b x + 52360a b x - 29920a b x - 935a +--R / +--R 4 +--R 3740x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1309 +t0:=(a+b*x^3)^8/x^6 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 116 + +--S 117 of 1309 +r0:=-1/5*a^8/x^5-4*a^7*b/x^2+28*a^6*b^2*x+14*a^5*b^3*x^4+10*a^4*b^4*x^7+_ + 28/5*a^3*b^5*x^10+28/13*a^2*b^6*x^13+1/2*a*b^7*x^16+1/19*b^8*x^19 +--R +--R +--R (2) +--R 1 8 24 1 7 21 28 2 6 18 28 3 5 15 4 4 12 5 3 9 +--R -- b x + - a b x + -- a b x + -- a b x + 10a b x + 14a b x +--R 19 2 13 5 +--R + +--R 6 2 6 7 3 1 8 +--R 28a b x - 4a b x - - a +--R 5 +--R / +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 117 + +--S 118 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 130b x + 1235a b x + 5320a b x + 13832a b x + 24700a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 34580a b x + 69160a b x - 9880a b x - 494a +--R / +--R 5 +--R 2470x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1309 +t0:=(a+b*x^3)^8/x^8 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 121 + +--S 122 of 1309 +r0:=-1/7*a^8/x^7-2*a^7*b/x^4-28*a^6*b^2/x+28*a^5*b^3*x^2+_ + 14*a^4*b^4*x^5+7*a^3*b^5*x^8+28/11*a^2*b^6*x^11+4/7*a*b^7*x^14+_ + 1/17*b^8*x^17 +--R +--R +--R (2) +--R 1 8 24 4 7 21 28 2 6 18 3 5 15 4 4 12 5 3 9 +--R -- b x + - a b x + -- a b x + 7a b x + 14a b x + 28a b x +--R 17 7 11 +--R + +--R 6 2 6 7 3 1 8 +--R - 28a b x - 2a b x - - a +--R 7 +--R / +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 122 + +--S 123 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 77b x + 748a b x + 3332a b x + 9163a b x + 18326a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 36652a b x - 36652a b x - 2618a b x - 187a +--R / +--R 7 +--R 1309x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1309 +t0:=(a+b*x^3)^8/x^9 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 126 + +--S 127 of 1309 +r0:=-1/8*a^8/x^8-8/5*a^7*b/x^5-14*a^6*b^2/x^2+56*a^5*b^3*x+_ + 35/2*a^4*b^4*x^4+8*a^3*b^5*x^7+14/5*a^2*b^6*x^10+_ + 8/13*a*b^7*x^13+1/16*b^8*x^16 +--R +--R +--R (2) +--R 1 8 24 8 7 21 14 2 6 18 3 5 15 35 4 4 12 5 3 9 +--R -- b x + -- a b x + -- a b x + 8a b x + -- a b x + 56a b x +--R 16 13 5 2 +--R + +--R 6 2 6 8 7 3 1 8 +--R - 14a b x - - a b x - - a +--R 5 8 +--R / +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 127 + +--S 128 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 +--R 65b x + 640a b x + 2912a b x + 8320a b x + 18200a b x +--R + +--R 5 3 9 6 2 6 7 3 8 +--R 58240a b x - 14560a b x - 1664a b x - 130a +--R / +--R 8 +--R 1040x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1309 +t0:=x^5/(a+b*x^3) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 131 + +--S 132 of 1309 +r0:=1/3*x^3/b-1/3*a*log(a+b*x^3)/b^2 +--R +--R +--R 3 3 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1309 +t0:=x^4/(a+b*x^3) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 136 + +--S 137 of 1309 +r0:=1/2*x^2/b+1/3*a^(2/3)*log(a^(1/3)+b^(1/3)*x)/b^(5/3)-_ + 1/6*a^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)+_ + a^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 2x\|b - \|a 2 +-+3+-+2 +--R - 6\|a atan(-------------) + 3x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 +--R - \|3 |-- log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- - 2a x\|3 +--R | 2 3| 2 +--R |a \|b 2 +-+ +--R 6 |-- atan(---------------------- + 3x \|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a x) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a 3+-+2 |a |a 2 +--R - \|3 |-- \|b log(- b x |-- + a |-- + a x ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- - 2a x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b - \|a |a 3+-+2 \|b +--R 6\|a atan(-------------) + 6 |-- \|b atan(----------------------) +--R +-+3+-+ 3| 2 +--+2 +--R \|3 \|a \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1309 +t0:=x^3/(a+b*x^3) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 141 + +--S 142 of 1309 +r0:=x/b-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*x)/b^(4/3)+1/6*a^(1/3)*_ + log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+a^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b - \|a +-+3+-+ +--R - 6\|a atan(-------------) + 6x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a | a 2 +-+ | a | a +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(------------------- + 6x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x\|a \|b + \|a ) + 2\|3 \|a log(x\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 +--R - \|3 3|- - \|b log(3|- - + x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ 3+-+ 3+-+ +--R +-+ | a 3+-+ | a 3+-+ 2x\|b - \|a +--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(-------------) +--R \| b \| b +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(-------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1309 +t0:=x^2/(a+b*x^3) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1309 +r0:=1/3*log(a+b*x^3)/b +--R +--R +--R 3 +--R log(b x + a) +--R (2) ------------- +--R 3b +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(b x + a) +--R (3) ------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1309 +t0:=x/(a+b*x^3) +--R +--R +--R x +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 151 + +--S 152 of 1309 +r0:=-1/3*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((a^(1/3)-_ + 2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b - x\|a \|b + \|a ) - 2\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b - \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R +-+ 3| 2 2 3| 2 +--R - \|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +------+2 +-+3| 2 +-+ +--R +-+ 3| 2 2x\|3 \|- a b - a b\|3 +--R 2\|3 log(x \|- a b + a b) - 6atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1309 +t0:=1/(a+b*x^3) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 156 + +--S 157 of 1309 +r0:=1/3*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(1/3))-1/6*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))-_ + atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R - \|3 log(x \|b - x\|a \|b + \|a ) + 2\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b - \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +---+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|a b - a x\|a b + a ) + 2\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2x\|3 \|a b - a\|3 +--R 6atan(--------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 6\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 6\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1309 +t0:=1/(x*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 161 + +--S 162 of 1309 +r0:=log(x)/a-1/3*log(a+b*x^3)/a +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1309 +t0:=1/(x^2*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 5 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 166 + +--S 167 of 1309 +r0:=(-1)/(a*x)+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*x)/a^(4/3)-_ + 1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)+_ + b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - x\|3 \|b log(x \|b - x\|a \|b + \|a ) + 2x\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b - \|a +-+3+-+ +--R - 6x\|b atan(-------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+2 +-+ +--R +-+ |b |b +-+ |b |b |b 2 +--R 2x\|3 3|- log(a 3|- + b x - x\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R |b \|a +-+ +--R 6x 3|- atan(--------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+ +--R 6a x\|3 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|b log(x\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 3+-+ 3+-+ +--R +-+3+-+ |b |b |b 2 3+-+ 2x\|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(-------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(---------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1309 +t0:=1/(x^3*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 171 + +--S 172 of 1309 +r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*x)/a^(5/3)+_ + 1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b - \|a +-+3+-+2 +--R - 2x \|3 \|b log(x\|b + \|a ) - 6x \|b atan(------------- - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+2 +--R 6a x \|3 \|a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | b 2 | b | b 2 2 +--R - x \|3 |- -- log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | b | b +--R 2x \|3 |- -- log(- a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R 2 | b \| a +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 6a x \|3 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|b log(x \|b - x\|a \|b + \|a ) + 2\|3 \|b log(x\|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - \|3 |- -- \|a log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 3+-+ 3+-+ +--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a +--R 2\|3 |- -- \|a log(- a |- -- + b x + 6\|b atan(-------------) +--R 3| 2 3| 2 +-+3+-+ +--R \| a \| a \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1309 +t0:=1/(x^4*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 176 + +--S 177 of 1309 +r0:=(-1/3)/(a*x^3)-b*log(x)/a^2+1/3*b*log(a+b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R b x log(b x + a) - 3b x log(x) - a +--R (2) ----------------------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R b x log(b x + a) - 3b x log(x) - a +--R (3) ----------------------------------- +--R 2 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1309 +t0:=x^4/(a-b*x^3) +--R +--R +--R 4 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 181 + +--S 182 of 1309 +r0:=-1/2*x^2/b-1/3*a^(2/3)*log(a^(1/3)-b^(1/3)*x)/b^(5/3)+_ + 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(5/3)-_ + a^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 2x\|b + \|a 2 +-+3+-+2 +--R - 6\|a atan(-------------) - 3x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a | a | a 2 +--R - \|3 |- -- log(b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | a | a +--R 2\|3 |- -- log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 +--R | a \| b 2 +-+ +--R 6 |- -- atan(------------------------ - 3x \|3 +--R 3| 2 +----+2 +--R \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log(x \|b + x\|a \|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a 3+-+2 | a | a 2 +--R - \|3 |- -- \|b log(b x |- -- - a |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | a 3+-+2 | a +-+3+-+2 3+-+ 3+-+ +--R 2\|3 |- -- \|b log(- b |- -- + a x + 2\|3 \|a log(- x\|b + \|a ) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+2 +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b + \|a | a 3+-+2 \| b +--R 6\|a atan(-------------) + 6 |- -- \|b atan(------------------------) +--R +-+3+-+ 3| 2 +----+2 +--R \|3 \|a \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1309 +t0:=x^3/(a-b*x^3) +--R +--R +--R 3 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 186 + +--S 187 of 1309 +r0:=-x/b-1/3*a^(1/3)*log(a^(1/3)-b^(1/3)*x)/b^(4/3)+_ + 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/b^(4/3)+_ + a^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(x \|b + x\|a \|b + \|a ) - 2\|3 \|a log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b + \|a +-+3+-+ +--R 6\|a atan(-------------) - 6x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a | a 2 +-+ | a | a +--R - \|3 3|- - log(3|- - - x 3|- - + x + 2\|3 3|- - log(3|- - + x) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - - 2x\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(------------------- - 6x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b\|3 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log(x \|b + x\|a \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 +--R - \|3 3|- - \|b log(3|- - - x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +-+3+-+ 3+-+ 3+-+ +--R 2\|3 3|- - \|b log(3|- - + x + 2\|3 \|a log(- x\|b + \|a ) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R 3+-+ 3+-+ +---+ \|3 3|- - - 2x\|3 +--R 3+-+ 2x\|b + \|a | a 3+-+ \| b +--R - 6\|a atan(-------------) - 6 3|- - \|b atan(-------------------) +--R +-+3+-+ \| b +---+ +--R \|3 \|a | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1309 +t0:=x^2/(a-b*x^3) +--R +--R +--R 2 +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 191 + +--S 192 of 1309 +r0:=-1/3*log(a-b*x^3)/b +--R +--R +--R 3 +--R log(- b x + a) +--R (2) - --------------- +--R 3b +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(b x - a) +--R (3) - ------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1309 +t0:=x/(a-b*x^3) +--R +--R +--R x +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 196 + +--S 197 of 1309 +r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(1/3)*b^(2/3))+1/6*log(a^(2/3)+_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(2/3))-_ + atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b + \|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log(x \|- a b - a b) +--R + +--R +------+2 +------+ +--R +-+ 3| 2 2 3| 2 +--R - \|3 log(- x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b + a b\|3 +--R 6atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a ) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x \|- a b - a b) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(- x \|- a b + b x \|- a b - a b) +--R + +--R +------+ +------+ 3+-+ 3+-+ +--R +-+3| 2 3+-+ 3+-+ 3| 2 2x\|b + \|a +--R 2\|3 \|- a b log(- x\|b + \|a ) + 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b + a b\|3 +--R 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1309 +t0:=1/(a-b*x^3) +--R +--R +--R 1 +--R (1) - -------- +--R 3 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 201 + +--S 202 of 1309 +r0:=-1/3*log(a^(1/3)-b^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(a^(2/3)+_ + a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(1/3))+_ + atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(x \|b + x\|a \|b + \|a ) - 2\|3 log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2x\|b + \|a +--R 6atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +-----+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|- a b - a x\|- a b + a ) + 2\|3 log(x\|- a b + a) +--R + +--R +-----+ +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b - a\|3 +--R 6atan(----------------------) +--R 3a +--R / +--R +-----+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b + x\|a \|b + \|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|- a b - a x\|- a b + a ) +--R + +--R +-----+ +-----+ +--R +-+3+-+2 3+-+ 3| 2 +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|a \|b log(x\|- a b + a + 2\|3 \|- a b log(- x\|b + \|a ) +--R + +--R +-----+ +--R +-----+ 3+-+ 3+-+ +-+3| 2 +-+ +--R 3| 2 2x\|b + \|a 3+-+2 3+-+ 2x\|3 \|- a b - a\|3 +--R - 6\|- a b atan(-------------) + 6\|a \|b atan(----------------------) +--R +-+3+-+ 3a +--R \|3 \|a +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1309 +t0:=1/(x*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ---------- +--R 4 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 206 + +--S 207 of 1309 +r0:=log(x)/a-1/3*log(a-b*x^3)/a +--R +--R +--R 3 +--R 3log(x) - log(- b x + a) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x - a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - log(b x - a) + log(- b x + a) +--R (4) --------------------------------- +--R 3a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1309 +t0:=1/(x^2*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 5 2 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 211 + +--S 212 of 1309 +r0:=(-1)/(a*x)-1/3*b^(1/3)*log(a^(1/3)-b^(1/3)*x)/a^(4/3)+_ + 1/6*b^(1/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(4/3)-_ + b^(1/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R x\|3 \|b log(x \|b + x\|a \|b + \|a ) - 2x\|3 \|b log(- x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ 2x\|b + \|a +-+3+-+ +--R - 6x\|b atan(-------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6a x\|3 \|a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R +-+ | b | b | b 2 +--R - x\|3 3|- - log(a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+ +---+2 +--R +-+ | b | b +--R 2x\|3 3|- - log(- a 3|- - + b x) +--R \| a \| a +--R + +--R +---+2 +--R +-+ | b +-+ +--R +---+ a\|3 3|- - + 2b x\|3 +--R | b \| a +-+ +--R 6x 3|- - atan(----------------------- - 6\|3 +--R \| a +---+2 +--R | b +--R 3a 3|- - +--R \| a +--R / +--R +-+ +--R 6a x\|3 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - \|3 3|- - \|a log(a x 3|- - - a 3|- - + b x ) +--R \| a \| a \| a +--R + +--R +---+ +---+2 +--R +-+ | b 3+-+ | b +-+3+-+ 3+-+ 3+-+ +--R 2\|3 3|- - \|a log(- a 3|- - + b x + 2\|3 \|b log(- x\|b + \|a ) +--R \| a \| a +--R + +--R +---+2 +--R +-+ | b +-+ +--R 3+-+ 3+-+ +---+ a\|3 3|- - + 2b x\|3 +--R 3+-+ 2x\|b + \|a | b 3+-+ \| a +--R 6\|b atan(-------------) + 6 3|- - \|a atan(-----------------------) +--R +-+3+-+ \| a +---+2 +--R \|3 \|a | b +--R 3a 3|- - +--R \| a +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1309 +t0:=1/(x^3*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 6 3 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 216 + +--S 217 of 1309 +r0:=(-1/2)/(a*x^2)-1/3*b^(2/3)*log(a^(1/3)-b^(1/3)*x)/a^(5/3)+_ + 1/6*b^(2/3)*log(a^(2/3)+a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((a^(1/3)+2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R x \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 2x\|b + \|a +--R - 2x \|3 \|b log(- x\|b + \|a ) + 6x \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 +--R - 3\|3 \|a +--R / +--R 2 +-+3+-+2 +--R 6a x \|3 \|a +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | b 2 | b | b 2 2 +--R - x \|3 |- -- log(a |- -- - a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | b | b +--R 2x \|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R 2 | b \| a +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 6a x \|3 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log(x \|b + x\|a \|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - \|3 |- -- \|a log(a |- -- - a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +-+3+-+2 3+-+ 3+-+ +--R 2\|3 |- -- \|a log(a |- -- + b x + 2\|3 \|b log(- x\|b + \|a ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R 3+-+ 3+-+ | 2 3| 2 +--R 3+-+2 2x\|b + \|a | b 3+-+2 \| a +--R - 6\|b atan(-------------) - 6 |- -- \|a atan(-----------------------) +--R +-+3+-+ 3| 2 +----+ +--R \|3 \|a \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1309 +t0:=1/(x^4*(a-b*x^3)) +--R +--R +--R 1 +--R (1) - ----------- +--R 7 4 +--R b x - a x +--R Type: Fraction(Polynomial(Integer)) +--E 221 + +--S 222 of 1309 +r0:=(-1/3)/(a*x^3)+b*log(x)/a^2-1/3*b*log(a-b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R 3b x log(x) - b x log(- b x + a) - a +--R (2) ------------------------------------- +--R 2 3 +--R 3a x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R - b x log(b x - a) + 3b x log(x) - a +--R (3) ------------------------------------- +--R 2 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1309 +m0:=a0-r0 +--R +--R +--R 3 3 +--R - b log(b x - a) + b log(- b x + a) +--R (4) ------------------------------------- +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1309 +t0:=1/(1+a+b*x^3) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +--R b x + a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 226 + +--S 227 of 1309 +r0:=1/3*log((1+a)^(1/3)+b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))-_ + 1/6*log((1+a)^(2/3)-(1+a)^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))-atan(((1+a)^(1/3)-_ + 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R - \|3 log(x \|b - x\|a + 1 \|b + \|a + 1 ) +--R + +--R 3+-+ 3+-----+ +--R +-+ 3+-+ 3+-----+ 2x\|b - \|a + 1 +--R 2\|3 log(x\|b + \|a + 1 ) + 6atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +-+3+-----+2 3+-+ +--R 6\|3 \|a + 1 \|b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1) +--R + +--R +--------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(a + 2a + 1)b + a + 1) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3 +--R 6atan(---------------------------------------) +--R 3a + 3 +--R / +--R +--------------+ +--R +-+3| 2 +--R 6\|3 \|(a + 2a + 1)b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-----+2 3+-+ +--R \|3 \|a + 1 \|b +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a + 2a + 1)b + (- a - 1)x\|(a + 2a + 1)b + a + 2a + 1) +--R + +--R +--------------+ +--R +-+3+-----+2 3+-+ 3| 2 +--R 2\|3 \|a + 1 \|b log(x\|(a + 2a + 1)b + a + 1) +--R + +--R +--------------+ +--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R \|3 \|(a + 2a + 1)b log(x \|b - x\|a + 1 \|b + \|a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 3+-+ 3+-----+ +--R - 2\|3 \|(a + 2a + 1)b log(x\|b + \|a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 3+-----+2 3+-+ 2x\|3 \|(a + 2a + 1)b + (- a - 1)\|3 +--R 6\|a + 1 \|b atan(---------------------------------------) +--R 3a + 3 +--R + +--R +--------------+ 3+-+ 3+-----+ +--R 3| 2 2x\|b - \|a + 1 +--R - 6\|(a + 2a + 1)b atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +--------------+ +--R +-+3+-----+2 3+-+3| 2 +--R 6\|3 \|a + 1 \|b \|(a + 2a + 1)b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1309 +t0:=1/(1+a-b*x^3) +--R +--R +--R 1 +--R (1) - ------------ +--R 3 +--R b x - a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 231 + +--S 232 of 1309 +r0:=-1/3*log((1+a)^(1/3)-b^(1/3)*x)/((1+a)^(2/3)*b^(1/3))+_ + 1/6*log((1+a)^(2/3)+(1+a)^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/((1+a)^(2/3)*b^(1/3))+atan(((1+a)^(1/3)+_ + 2*b^(1/3)*x)/((1+a)^(1/3)*sqrt(3)))/((1+a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R \|3 log(x \|b + x\|a + 1 \|b + \|a + 1 ) +--R + +--R 3+-+ 3+-----+ +--R +-+ 3+-+ 3+-----+ 2x\|b + \|a + 1 +--R - 2\|3 log(- x\|b + \|a + 1 ) + 6atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R / +--R +-+3+-----+2 3+-+ +--R 6\|3 \|a + 1 \|b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a +--R + +--R 2a + 1 +--R + +--R +----------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(- a - 2a - 1)b + a + 1) +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3 +--R 6atan(-----------------------------------------) +--R 3a + 3 +--R / +--R +----------------+ +--R +-+3| 2 +--R 6\|3 \|(- a - 2a - 1)b +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+3| 2 2 3+-+2 3+-----+3+-+ 3+-----+2 +--R - \|3 \|(- a - 2a - 1)b log(x \|b + x\|a + 1 \|b + \|a + 1 ) +--R + +--R - +--R +-+3+-----+2 3+-+ +--R \|3 \|a + 1 \|b +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a - 2a - 1)b + (- a - 1)x\|(- a - 2a - 1)b + a +--R + +--R 2a + 1 +--R + +--R +----------------+ +--R +-+3+-----+2 3+-+ 3| 2 +--R 2\|3 \|a + 1 \|b log(x\|(- a - 2a - 1)b + a + 1) +--R + +--R +----------------+ +--R +-+3| 2 3+-+ 3+-----+ +--R 2\|3 \|(- a - 2a - 1)b log(- x\|b + \|a + 1 ) +--R + +--R +----------------+ 3+-+ 3+-----+ +--R 3| 2 2x\|b + \|a + 1 +--R - 6\|(- a - 2a - 1)b atan(-----------------) +--R +-+3+-----+ +--R \|3 \|a + 1 +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 3+-----+2 3+-+ 2x\|3 \|(- a - 2a - 1)b + (- a - 1)\|3 +--R 6\|a + 1 \|b atan(-----------------------------------------) +--R 3a + 3 +--R / +--R +----------------+ +--R +-+3| 2 3+-----+2 3+-+ +--R 6\|3 \|(- a - 2a - 1)b \|a + 1 \|b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1309 +t0:=1/(-1+a+b*x^3) +--R +--R +--R 1 +--R (1) ------------ +--R 3 +--R b x + a - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 236 + +--S 237 of 1309 +r0:=1/3*log((1-a)^(1/3)-b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))-_ + 1/6*log((1-a)^(2/3)+(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_ + b^(1/3))-atan(((1-a)^(1/3)+2*b^(1/3)*x)/((1-a)^(1/3)*_ + sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R - \|3 log(x \|b + x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R 3+-+ 3+-------+ +--R +-+ 3+-+ 3+-------+ 2x\|b + \|- a + 1 +--R 2\|3 log(- x\|b + \|- a + 1 ) - 6atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +-+3+-------+2 3+-+ +--R 6\|3 \|- a + 1 \|b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1) +--R + +--R +--------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(a - 2a + 1)b + a - 1) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3 +--R 6atan(---------------------------------------) +--R 3a - 3 +--R / +--R +--------------+ +--R +-+3| 2 +--R 6\|3 \|(a - 2a + 1)b +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-------+2 3+-+ +--R \|3 \|- a + 1 \|b +--R * +--R +--------------+2 +--------------+ +--R 2 3| 2 3| 2 2 +--R log(x \|(a - 2a + 1)b + (- a + 1)x\|(a - 2a + 1)b + a - 2a + 1) +--R + +--R +--------------+ +--R +-+3+-------+2 3+-+ 3| 2 +--R 2\|3 \|- a + 1 \|b log(x\|(a - 2a + 1)b + a - 1) +--R + +--R +--------------+ +--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R \|3 \|(a - 2a + 1)b log(x \|b + x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 3+-+ 3+-------+ +--R - 2\|3 \|(a - 2a + 1)b log(- x\|b + \|- a + 1 ) +--R + +--R +--------------+ +--R +-+3| 2 +-+ +--R 3+-------+2 3+-+ 2x\|3 \|(a - 2a + 1)b + (- a + 1)\|3 +--R 6\|- a + 1 \|b atan(---------------------------------------) +--R 3a - 3 +--R + +--R +--------------+ 3+-+ 3+-------+ +--R 3| 2 2x\|b + \|- a + 1 +--R 6\|(a - 2a + 1)b atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +--------------+ +--R +-+3+-------+2 3+-+3| 2 +--R 6\|3 \|- a + 1 \|b \|(a - 2a + 1)b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1309 +t0:=1/(-1+a-b*x^3) +--R +--R +--R 1 +--R (1) - ------------ +--R 3 +--R b x - a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 241 + +--S 242 of 1309 +r0:=-1/3*log((1-a)^(1/3)+b^(1/3)*x)/((1-a)^(2/3)*b^(1/3))+_ + 1/6*log((1-a)^(2/3)-(1-a)^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/((1-a)^(2/3)*_ + b^(1/3))+atan(((1-a)^(1/3)-2*b^(1/3)*x)/((1-a)^(1/3)*_ + sqrt(3)))/((1-a)^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R \|3 log(x \|b - x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R 3+-+ 3+-------+ +--R +-+ 3+-+ 3+-------+ 2x\|b - \|- a + 1 +--R - 2\|3 log(x\|b + \|- a + 1 ) - 6atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R / +--R +-+3+-------+2 3+-+ +--R 6\|3 \|- a + 1 \|b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a +--R + +--R - 2a + 1 +--R + +--R +----------------+ +--R +-+ 3| 2 +--R 2\|3 log(x\|(- a + 2a - 1)b + a - 1) +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3 +--R 6atan(-----------------------------------------) +--R 3a - 3 +--R / +--R +----------------+ +--R +-+3| 2 +--R 6\|3 \|(- a + 2a - 1)b +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+3| 2 2 3+-+2 3+-------+3+-+ 3+-------+2 +--R - \|3 \|(- a + 2a - 1)b log(x \|b - x\|- a + 1 \|b + \|- a + 1 ) +--R + +--R +----------------+ +--R +-+3| 2 3+-+ 3+-------+ +--R 2\|3 \|(- a + 2a - 1)b log(x\|b + \|- a + 1 ) +--R + +--R - +--R +-+3+-------+2 3+-+ +--R \|3 \|- a + 1 \|b +--R * +--R log +--R +----------------+2 +----------------+ +--R 2 3| 2 3| 2 2 +--R x \|(- a + 2a - 1)b + (- a + 1)x\|(- a + 2a - 1)b + a +--R + +--R - 2a + 1 +--R + +--R +----------------+ +--R +-+3+-------+2 3+-+ 3| 2 +--R 2\|3 \|- a + 1 \|b log(x\|(- a + 2a - 1)b + a - 1) +--R + +--R +----------------+ 3+-+ 3+-------+ +--R 3| 2 2x\|b - \|- a + 1 +--R 6\|(- a + 2a - 1)b atan(-------------------) +--R +-+3+-------+ +--R \|3 \|- a + 1 +--R + +--R +----------------+ +--R +-+3| 2 +-+ +--R 3+-------+2 3+-+ 2x\|3 \|(- a + 2a - 1)b + (- a + 1)\|3 +--R 6\|- a + 1 \|b atan(-----------------------------------------) +--R 3a - 3 +--R / +--R +----------------+ +--R +-+3| 2 3+-------+2 3+-+ +--R 6\|3 \|(- a + 2a - 1)b \|- a + 1 \|b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1309 +t0:=x^5/(a+b*x^3)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 246 + +--S 247 of 1309 +r0:=1/3*a/(b^2*(a+b*x^3))+1/3*log(a+b*x^3)/b^2 +--R +--R +--R 3 3 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 3 2 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 3 2 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1309 +t0:=x^4/(a+b*x^3)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 251 + +--S 252 of 1309 +r0:=-1/3*x^2/(b*(a+b*x^3))-2/9*log(a^(1/3)+b^(1/3)*x)/(a^(1/3)*b^(5/3))+_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+3+-+2 +--R - 3x \|3 \|a \|b +--R / +--R 2 3 +-+3+-+3+-+2 +--R (9b x + 9a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 3 +-+ 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +------+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6b x - 6a)atan(--------------------------) - 3x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 2 3 +-+3| 2 +--R (9b x + 9a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1309 +t0:=x^3/(a+b*x^3)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 256 + +--S 257 of 1309 +r0:=-1/3*x/(b*(a+b*x^3))+1/9*log(a^(1/3)+b^(1/3)*x)/(a^(2/3)*b^(4/3))-_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R - 6x\|3 \|a \|b +--R / +--R 2 3 +-+3+-+2 3+-+ +--R (18b x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3 +--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R - 6x\|3 \|a b +--R / +--R +---+ +--R 2 3 +-+3| 2 +--R (18b x + 18a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1309 +t0:=x^2/(a+b*x^3)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 261 + +--S 262 of 1309 +r0:=(-1/3)/(b*(a+b*x^3)) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - ---------- +--R 2 3 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 262 + +--S 263 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 3 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1309 +t0:=x/(a+b*x^3)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 266 + +--S 267 of 1309 +r0:=1/3*x^2/(a*(a+b*x^3))-1/9*log(a^(1/3)+b^(1/3)*x)/(a^(4/3)*b^(2/3))+_ + 1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (- 2b x - 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+3+-+2 +--R 6x \|3 \|a \|b +--R / +--R 3 2 +-+3+-+3+-+2 +--R (18a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 3 +-+ 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +------+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6b x - 6a)atan(--------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 3 2 +-+3| 2 +--R (18a b x + 18a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1309 +t0:=1/(a+b*x^3)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 6 3 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 271 + +--S 272 of 1309 +r0:=1/3*x/(a*(a+b*x^3))+2/9*log(a^(1/3)+b^(1/3)*x)/(a^(5/3)*b^(1/3))-_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*x+b^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*x)/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 2x\|b - \|a +--R (2b x + 2a)\|3 log(x\|b + \|a ) + (6b x + 6a)atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R 3x\|3 \|a \|b +--R / +--R 3 2 +-+3+-+2 3+-+ +--R (9a b x + 9a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R 3 +-+ 3| 2 3 2x\|3 \|a b - a\|3 +--R (2b x + 2a)\|3 log(x\|a b + a) + (6b x + 6a)atan(--------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R 3x\|3 \|a b +--R / +--R +---+ +--R 3 2 +-+3| 2 +--R (9a b x + 9a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1309 +t0:=1/(x*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 7 4 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 276 + +--S 277 of 1309 +r0:=1/3/(a*(a+b*x^3))+log(x)/a^2-1/3*log(a+b*x^3)/a^2 +--R +--R +--R 3 3 3 +--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3a +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R (- b x - a)log(b x + a) + (3b x + 3a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3a +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1309 +t0:=1/(x^2*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 5 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 281 + +--S 282 of 1309 +r0:=(-4/3)/(a^2*x)+1/3/(a*x*(a+b*x^3))+4/9*b^(1/3)*log(a^(1/3)+_ + b^(1/3)*x)/a^(7/3)-2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 4 +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 2b x - 2a x)\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 4 +-+3+-+ 3+-+ 3+-+ +--R (4b x + 4a x)\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 4 3+-+ 2x\|b - \|a 3 +-+3+-+ +--R (- 12b x - 12a x)\|b atan(-------------) + (- 12b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 4 3 +-+3+-+ +--R (9a b x + 9a x)\|3 \|a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 4 +-+ |b |b +--R (4b x + 4a x)\|3 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 4 +-+ |b |b |b 2 +--R (- 2b x - 2a x)\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- - 2b x\|3 +--R 4 |b \|a 3 +-+ +--R (12b x + 12a x) 3|- atan(--------------------- + (- 12b x - 9a)\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 4 3 +-+ +--R (9a b x + 9a x)\|3 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 3+-+2 3+-+3+-+ 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R 2\|3 \|b log(x \|b - x\|a \|b + \|a ) - 4\|3 \|b log(x\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b x) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R +-+3+-+ |b |b |b 2 +--R - 2\|3 \|a 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R 3+-+ 3+-+ +-+ a\|3 3|- - 2b x\|3 +--R 3+-+ 2x\|b - \|a 3+-+ |b \|a +--R 12\|b atan(-------------) + 12\|a 3|- atan(---------------------) +--R +-+3+-+ \|a +-+2 +--R \|3 \|a |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1309 +t0:=1/(x^3*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 6 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 286 + +--S 287 of 1309 +r0:=(-5/6)/(a^2*x^2)+1/3/(a*x^2*(a+b*x^3))-5/9*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*x)/a^(8/3)+5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 5 2 +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R (5b x + 5a x )\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R 5 2 +-+3+-+2 3+-+ 3+-+ +--R (- 10b x - 10a x )\|3 \|b log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 5 2 3+-+2 2x\|b - \|a 3 +-+3+-+2 +--R (- 30b x - 30a x )\|b atan(-------------) + (- 15b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 5 3 2 +-+3+-+2 +--R (18a b x + 18a x )\|3 \|a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 5 2 +-+ | b 2 | b | b 2 2 +--R (- 5b x - 5a x )\|3 |- -- log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 5 2 +-+ | b | b +--R (10b x + 10a x )\|3 |- -- log(- a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R 5 2 | b \| a +--R (- 30b x - 30a x ) |- -- atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 +-+ +--R (- 15b x - 9a)\|3 +--R / +--R 2 5 3 2 +-+ +--R (18a b x + 18a x )\|3 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log(x \|b - x\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log(x\|b + \|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 2 | b | b 2 2 +--R - 5\|3 |- -- \|a log(a |- -- + a b x |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 3+-+ 3+-+ +--R +-+ | b 3+-+2 | b 3+-+2 2x\|b - \|a +--R 10\|3 |- -- \|a log(- a |- -- + b x + 30\|b atan(-------------) +--R 3| 2 3| 2 +-+3+-+ +--R \| a \| a \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(-----------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1309 +t0:=1/(x^4*(a+b*x^3)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 7 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 291 + +--S 292 of 1309 +r0:=(-2/3)/(a^2*x^3)+1/3/(a*x^3*(a+b*x^3))-2*b*log(x)/a^3+_ + 2/3*b*log(a+b*x^3)/a^3 +--R +--R +--R (2) +--R 2 6 3 3 2 6 3 3 2 +--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 6 4 3 +--R 3a b x + 3a x +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 3 2 6 3 3 2 +--R (2b x + 2a b x )log(b x + a) + (- 6b x - 6a b x )log(x) - 2a b x - a +--R ------------------------------------------------------------------------- +--R 3 6 4 3 +--R 3a b x + 3a x +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1309 +t0:=x^8/(a+b*x^3)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 296 + +--S 297 of 1309 +r0:=-1/6*a^2/(b^3*(a+b*x^3)^2)+2/3*a/(b^3*(a+b*x^3))+1/3*log(a+b*x^3)/b^3 +--R +--R +--R 2 6 3 2 3 3 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ---------------------------------------------------- +--R 5 6 4 3 2 3 +--R 6b x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 6 3 2 3 3 2 +--R (2b x + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (3) ---------------------------------------------------- +--R 5 6 4 3 2 3 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1309 +t0:=x^7/(a+b*x^3)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 301 + +--S 302 of 1309 +r0:=-1/6*x^5/(b*(a+b*x^3)^2)-5/18*x^2/(b^2*(a+b*x^3))-5/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(1/3)*b^(8/3))+5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(1/3)*b^(8/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (5b x + 10a b x + 5a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 10b x - 20a b x - 10a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (30b x + 60a b x + 30a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 2 +-+3+-+3+-+2 +--R (- 24b x - 15a x )\|3 \|a \|b +--R / +--R 4 6 3 3 2 2 +-+3+-+3+-+2 +--R (54b x + 108a b x + 54a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (10b x + 20a b x + 10a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 30b x - 60a b x - 30a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (- 24b x - 15a x )\|3 \|- a b +--R / +--R +------+ +--R 4 6 3 3 2 2 +-+3| 2 +--R (54b x + 108a b x + 54a b )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 10\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - 5\|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 10\|3 \|a \|b log(x \|- a b + a b) - 30\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 30\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 54b \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1309 +t0:=x^6/(a+b*x^3)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 306 + +--S 307 of 1309 +r0:=-1/6*x^4/(b*(a+b*x^3)^2)-2/9*x/(b^2*(a+b*x^3))+2/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(2/3)*b^(7/3))-1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(2/3)*b^(7/3))-2/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(2/3)*b^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (4b x + 8a b x + 4a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (12b x + 24a b x + 12a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+2 3+-+ +--R (- 21b x - 12a x)\|3 \|a \|b +--R / +--R 4 6 3 3 2 2 +-+3+-+2 3+-+ +--R (54b x + 108a b x + 54a b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (4b x + 8a b x + 4a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (12b x + 24a b x + 12a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (- 21b x - 12a x)\|3 \|a b +--R / +--R +---+ +--R 4 6 3 3 2 2 +-+3| 2 +--R (54b x + 108a b x + 54a b )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 27b \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1309 +t0:=x^5/(a+b*x^3)^3 +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 311 + +--S 312 of 1309 +r0:=1/6*x^6/(a*(a+b*x^3)^2) +--R +--R +--R 1 6 +--R - x +--R 6 +--R (2) --------------------- +--R 2 6 2 3 3 +--R a b x + 2a b x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 312 + +--S 313 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - 2b x - a +--R (3) ------------------------ +--R 4 6 3 3 2 2 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1309 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 6a b +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1309 +t0:=x^4/(a+b*x^3)^3 +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 316 + +--S 317 of 1309 +r0:=-1/6*x^2/(b*(a+b*x^3)^2)+1/9*x^2/(a*b*(a+b*x^3))-1/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(4/3)*b^(5/3))+1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(4/3)*b^(5/3))-1/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(4/3)*b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (b x + 2a b x + a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 2b x - 4a b x - 2a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a 5 2 +-+3+-+3+-+2 +--R (6b x + 12a b x + 6a )atan(-------------) + (6b x - 3a x )\|3 \|a \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 6 2 2 3 3 +-+3+-+3+-+2 +--R (54a b x + 108a b x + 54a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- b x - 2a b x - a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (2b x + 4a b x + 2a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 6b x - 12a b x - 6a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (6b x - 3a x )\|3 \|- a b +--R / +--R +------+ +--R 3 6 2 2 3 3 +-+3| 2 +--R (54a b x + 108a b x + 54a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1309 +t0:=x^3/(a+b*x^3)^3 +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 321 + +--S 322 of 1309 +r0:=-1/6*x/(b*(a+b*x^3)^2)+1/18*x/(a*b*(a+b*x^3))+1/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(5/3)*b^(4/3))-1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(5/3)*b^(4/3))-1/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- b x - 2a b x - a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (2b x + 4a b x + 2a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a 4 +-+3+-+2 3+-+ +--R (6b x + 12a b x + 6a )atan(-------------) + (3b x - 6a x)\|3 \|a \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 6 2 2 3 3 +-+3+-+2 3+-+ +--R (54a b x + 108a b x + 54a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- b x - 2a b x - a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (2b x + 4a b x + 2a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (6b x + 12a b x + 6a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (3b x - 6a x)\|3 \|a b +--R / +--R +---+ +--R 3 6 2 2 3 3 +-+3| 2 +--R (54a b x + 108a b x + 54a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +-+3| 2 3+-+ 3+-+ +--R \|3 \|a b log(x \|b - x\|a \|b + \|a ) - 2\|3 \|a b log(x\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +---+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|a b - a\|3 3| 2 2x\|b - \|a +--R 6\|a \|b atan(-------------------- - 6\|a b atan(-------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1309 +t0:=x^2/(a+b*x^3)^3 +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 326 + +--S 327 of 1309 +r0:=(-1/6)/(b*(a+b*x^3)^2) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - -------------------- +--R 3 6 2 3 2 +--R b x + 2a b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 327 + +--S 328 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 6 2 3 2 +--R 6b x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1309 +t0:=x/(a+b*x^3)^3 +--R +--R +--R x +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 331 + +--S 332 of 1309 +r0:=1/6*x^2/(a*(a+b*x^3)^2)+2/9*x^2/(a^2*(a+b*x^3))-2/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(7/3)*b^(2/3))+1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(7/3)*b^(2/3))-2/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (2b x + 4a b x + 2a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (- 4b x - 8a b x - 4a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (12b x + 24a b x + 12a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 2 +-+3+-+3+-+2 +--R (12b x + 21a x )\|3 \|a \|b +--R / +--R 2 2 6 3 3 4 +-+3+-+3+-+2 +--R (54a b x + 108a b x + 54a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 2 6 3 2 +-+ 3| 2 2 3| 2 +--R (- 2b x - 4a b x - 2a )\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 2 6 3 2 +-+ 3| 2 +--R (4b x + 8a b x + 4a )\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|- a b - a b\|3 +--R (- 12b x - 24a b x - 12a )atan(--------------------------) +--R 3a b +--R + +--R +------+ +--R 5 2 +-+3| 2 +--R (12b x + 21a x )\|3 \|- a b +--R / +--R +------+ +--R 2 2 6 3 3 4 +-+3| 2 +--R (54a b x + 108a b x + 54a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x\|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 3+-+ 3+-+ +--R +-+3+-+3+-+2 3| 2 3| 2 2x\|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 2x\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(--------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a \|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1309 +t0:=1/(a+b*x^3)^3 +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 9 2 6 2 3 3 +--R b x + 3a b x + 3a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 336 + +--S 337 of 1309 +r0:=1/6*x/(a*(a+b*x^3)^2)+5/18*x/(a^2*(a+b*x^3))+5/27*log(a^(1/3)+_ + b^(1/3)*x)/(a^(8/3)*b^(1/3))-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*x+_ + b^(2/3)*x^2)/(a^(8/3)*b^(1/3))-5/9*atan((a^(1/3)-2*b^(1/3)*x)/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 2 +-+ 2 3+-+2 3+-+3+-+ 3+-+2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|b - x\|a \|b + \|a ) +--R + +--R 2 6 3 2 +-+ 3+-+ 3+-+ +--R (10b x + 20a b x + 10a )\|3 log(x\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 6 3 2 2x\|b - \|a +--R (30b x + 60a b x + 30a )atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+2 3+-+ +--R (15b x + 24a x)\|3 \|a \|b +--R / +--R 2 2 6 3 3 4 +-+3+-+2 3+-+ +--R (54a b x + 108a b x + 54a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 2 6 3 2 +-+ 2 3| 2 3| 2 2 +--R (- 5b x - 10a b x - 5a )\|3 log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R 2 6 3 2 +-+ 3| 2 +--R (10b x + 20a b x + 10a )\|3 log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 2 6 3 2 2x\|3 \|a b - a\|3 +--R (30b x + 60a b x + 30a )atan(--------------------) +--R 3a +--R + +--R +---+ +--R 4 +-+3| 2 +--R (15b x + 24a x)\|3 \|a b +--R / +--R +---+ +--R 2 2 6 3 3 4 +-+3| 2 +--R (54a b x + 108a b x + 54a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 2 3| 2 3| 2 2 +--R - 5\|3 \|a \|b log(x \|a b - a x\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log(x \|b - x\|a \|b + \|a ) +--R + +--R +---+ +--R +---+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+2 3+-+ 2x\|3 \|a b - a\|3 +--R - 10\|3 \|a b log(x\|b + \|a ) + 30\|a \|b atan(--------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 2x\|b - \|a +--R - 30\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a \|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1309 +t0:=1/(x*(a+b*x^3)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 10 2 7 2 4 3 +--R b x + 3a b x + 3a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 341 + +--S 342 of 1309 +r0:=1/6/(a*(a+b*x^3)^2)+1/3/(a^2*(a+b*x^3))+log(x)/a^3-1/3*log(a+b*x^3)/a^3 +--R +--R +--R (2) +--R 2 6 3 2 3 2 6 3 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x) +--R + +--R 3 2 +--R 2a b x + 3a +--R / +--R 3 2 6 4 3 5 +--R 6a b x + 12a b x + 6a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 2 3 2 6 3 2 +--R (- 2b x - 4a b x - 2a )log(b x + a) + (6b x + 12a b x + 6a )log(x) +--R + +--R 3 2 +--R 2a b x + 3a +--R / +--R 3 2 6 4 3 5 +--R 6a b x + 12a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1309 +t0:=x^8*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 8 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1309 +r0:=2/9*a^2*(a+b*x^3)^(3/2)/b^3-4/15*a*(a+b*x^3)^(5/2)/b^3+_ + 2/21*(a+b*x^3)^(7/2)/b^3 +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 | 3 +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (2) ---------------------------------------------- +--R 3 +--R 315b +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 | 3 +--R (30b x + 6a b x - 8a b x + 16a )\|b x + a +--R (3) ---------------------------------------------- +--R 3 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1309 +t0:=x^5*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 5 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1309 +r0:=-2/9*a*(a+b*x^3)^(3/2)/b^2+2/15*(a+b*x^3)^(5/2)/b^2 +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x + 2a b x - 4a )\|b x + a +--R (2) ---------------------------------- +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x + 2a b x - 4a )\|b x + a +--R (3) ---------------------------------- +--R 2 +--R 45b +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1309 +t0:=x^2*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R 2 | 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1309 +r0:=2/9*(a+b*x^3)^(3/2)/b +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x + 2a)\|b x + a +--R (2) ----------------------- +--R 9b +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x + 2a)\|b x + a +--R (3) ----------------------- +--R 9b +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1309 +t0:=sqrt(a+b*x^3)/x +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1309 +r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))*sqrt(a)+2/3*sqrt(a+b*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R +-+ \|b x + a | 3 +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 3 3 +--------+ +--R +-+ - 2\|a \|b x + a + b x + 2a | 3 +--R \|a log(------------------------------) + 2\|b x + a +--R 3 +--R x +--R [------------------------------------------------------, +--R 3 +--R +--------+ +--R | 3 +--------+ +--R +---+ \|b x + a | 3 +--R - 2\|- a atan(-----------) + 2\|b x + a +--R +---+ +--R \|- a +--R -----------------------------------------] +--R 3 +--R Type: Union(List(Expression(Integer)),...) +--E 363 + +--S 364 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 3 3 | 3 +--R +-+ - 2\|a \|b x + a + b x + 2a +-+ \|b x + a +--R \|a log(------------------------------) + 2\|a atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ \|b x + a +---+ \|b x + a +--R 2\|a atanh(-----------) - 2\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 367 + +)clear all + +--S 368 of 1309 +t0:=sqrt(a+b*x^3)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1309 +r0:=-1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a)-1/3*sqrt(a+b*x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 3 \|b x + a +-+ | 3 +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 3 +-+ +--R 3x \|a +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 3 - 2a\|b x + a + (b x + 2a)\|a +-+ | 3 +--R b x log(---------------------------------) - 2\|a \|b x + a +--R 3 +--R x +--R [-------------------------------------------------------------, +--R 3 +-+ +--R 6x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 3 \|- a \|b x + a +---+ | 3 +--R - b x atan(-----------------) - \|- a \|b x + a +--R a +--R -------------------------------------------------] +--R 3 +---+ +--R 3x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 370 + +--S 371 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(---------------------------------) + 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 6\|a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R b\|- a atanh(-----------) - b\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 3\|- a \|a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 374 + +)clear all + +--S 375 of 1309 +t0:=sqrt(a+b*x^3)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1309 +r0:=1/12*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/6*sqrt(a+b*x^3)/x^6-_ + 1/12*b*sqrt(a+b*x^3)/(a*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 2 6 \|b x + a 3 +-+ | 3 +--R b x atanh(-----------) + (- b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 6 +-+ +--R 12a x \|a +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 2 6 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3 +--R b x log(-------------------------------) + (- 2b x - 4a)\|a \|b x + a +--R 3 +--R x +--R [------------------------------------------------------------------------, +--R 6 +-+ +--R 24a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 2 6 \|- a \|b x + a 3 +---+ | 3 +--R b x atan(-----------------) + (- b x - 2a)\|- a \|b x + a +--R a +--R ------------------------------------------------------------] +--R 6 +---+ +--R 12a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 377 + +--S 378 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(-------------------------------) - 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 24a\|a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R - b \|- a atanh(-----------) + b \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 12a\|- a \|a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 381 + +)clear all + +--S 382 of 1309 +t0:=x^3*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R 3 | 3 +--R (1) x \|27x + 8 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1309 +--r0:=16/495*x*sqrt(8+27*x^3)+2/11*x^4*sqrt(8+27*x^3)-256/1485*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 383 + +--S 384 of 1309 +--a0:=integrate(t0,x) +--E 384 + +--S 385 of 1309 +--m0:=a0-r0 +--E 385 + +--S 386 of 1309 +--d0:=D(m0,x) +--E 386 + +)clear all + +--S 387 of 1309 +t0:=sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R | 3 +--R (1) \|27x + 8 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1309 +--r0:=2/5*x*sqrt(8+27*x^3)+16/5*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 388 + +--S 389 of 1309 +--a0:=integrate(t0,x) +--E 389 + +--S 390 of 1309 +--m0:=a0-r0 +--E 390 + +--S 391 of 1309 +--d0:=D(m0,x) +--E 391 + +)clear all + +--S 392 of 1309 +t0:=sqrt(8+27*x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--R \|27x + 8 +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1309 +--r0:=-1/2*sqrt(8+27*x^3)/x^2+27/2*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 393 + +--S 394 of 1309 +--a0:=integrate(t0,x) +--E 394 + +--S 395 of 1309 +--m0:=a0-r0 +--E 395 + +--S 396 of 1309 +--d0:=D(m0,x) +--E 396 + +)clear all + +--S 397 of 1309 +t0:=x^4*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R 4 | 3 +--R (1) x \|27x + 8 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1309 +--r0:=16/819*x^2*sqrt(8+27*x^3)+2/13*x^5*sqrt(8+27*x^3)-_ +-- 512/7371*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))+1024/7371*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 398 + +--S 399 of 1309 +--a0:=integrate(t0,x) +--E 399 + +--S 400 of 1309 +--m0:=a0-r0 +--E 400 + +--S 401 of 1309 +--d0:=D(m0,x) +--E 401 + +)clear all + +--S 402 of 1309 +t0:=x*sqrt(8+27*x^3) +--R +--R +--R +--------+ +--R | 3 +--R (1) x\|27x + 8 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1309 +--r0:=2/7*x^2*sqrt(8+27*x^3)+16/21*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-32/21*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 403 + +--S 404 of 1309 +--a0:=integrate(t0,x) +--E 404 + +--S 405 of 1309 +--m0:=a0-r0 +--E 405 + +--S 406 of 1309 +--d0:=D(m0,x) +--E 406 + +)clear all + +--R +--S 407 of 1309 +t0:=sqrt(8+27*x^3)/x^2 +--R +--R +--R +--------+ +--R | 3 +--R \|27x + 8 +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1309 +--r0:=-sqrt(8+27*x^3)/x+9*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-18*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 408 + +--S 409 of 1309 +--a0:=integrate(t0,x) +--E 409 + +--S 410 of 1309 +--m0:=a0-r0 +--E 410 + +--S 411 of 1309 +--d0:=D(m0,x) +--E 411 + +)clear all + +--S 412 of 1309 +t0:=x^8/sqrt(a+b*x^3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1309 +r0:=16/45*a^2*sqrt(a+b*x^3)/b^3-8/45*a*x^3*sqrt(a+b*x^3)/b^2+_ + 2/15*x^6*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x - 8a b x + 16a )\|b x + a +--R (2) ----------------------------------- +--R 3 +--R 45b +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 | 3 +--R (6b x - 8a b x + 16a )\|b x + a +--R (3) ----------------------------------- +--R 3 +--R 45b +--R Type: Union(Expression(Integer),...) +--E 414 + +--S 415 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 416 + +)clear all + +--S 417 of 1309 +t0:=x^5/sqrt(a+b*x^3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1309 +r0:=-4/9*a*sqrt(a+b*x^3)/b^2+2/9*x^3*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x - 4a)\|b x + a +--R (2) ----------------------- +--R 2 +--R 9b +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 | 3 +--R (2b x - 4a)\|b x + a +--R (3) ----------------------- +--R 2 +--R 9b +--R Type: Union(Expression(Integer),...) +--E 419 + +--S 420 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 421 + +)clear all + +--S 422 of 1309 +t0:=x^2/sqrt(a+b*x^3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1309 +r0:=2/3*sqrt(a+b*x^3)/b +--R +--R +--R +--------+ +--R | 3 +--R 2\|b x + a +--R (2) ------------ +--R 3b +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2\|b x + a +--R (3) ------------ +--R 3b +--R Type: Union(Expression(Integer),...) +--E 424 + +--S 425 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 426 + +)clear all + +--S 427 of 1309 +t0:=1/(x*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 3 +--R x\|b x + a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1309 +r0:=-2/3*atanh(sqrt(a+b*x^3)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 3 +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 3 +-+ +--------+ +--R - 2a\|b x + a + (b x + 2a)\|a +---+ | 3 +--R log(---------------------------------) \|- a \|b x + a +--R 3 2atan(-----------------) +--R x a +--R (3) [--------------------------------------,- ------------------------] +--R +-+ +---+ +--R 3\|a 3\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 429 + +--S 430 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R - 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R 2\|- a atanh(-----------) - 2\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 3\|- a \|a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1309 +t0:=1/(x^4*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1309 +r0:=1/3*b*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(3/2)-1/3*sqrt(a+b*x^3)/(a*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 3 \|b x + a +-+ | 3 +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 3 2a\|b x + a + (b x + 2a)\|a +-+ | 3 +--R b x log(-------------------------------) - 2\|a \|b x + a +--R 3 +--R x +--R [-----------------------------------------------------------, +--R 3 +-+ +--R 6a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 3 \|- a \|b x + a +---+ | 3 +--R b x atan(-----------------) - \|- a \|b x + a +--R a +--R -----------------------------------------------] +--R 3 +---+ +--R 3a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 436 + +--S 437 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2a\|b x + a + (b x + 2a)\|a \|b x + a +--R b log(-------------------------------) - 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R +---+ \|b x + a +-+ \|- a \|b x + a +--R - b\|- a atanh(-----------) + b\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 3a\|- a \|a +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1309 +t0:=1/(x^7*sqrt(a+b*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 7 | 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1309 +r0:=-1/4*b^2*atanh(sqrt(a+b*x^3)/sqrt(a))/a^(5/2)-_ + 1/6*sqrt(a+b*x^3)/(a*x^6)+1/4*b*sqrt(a+b*x^3)/(a^2*x^3) +--R +--R +--R +--------+ +--R | 3 +--------+ +--R 2 6 \|b x + a 3 +-+ | 3 +--R - 3b x atanh(-----------) + (3b x - 2a)\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------- +--R 2 6 +-+ +--R 12a x \|a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 3 3 +-+ +--------+ +--R 2 6 - 2a\|b x + a + (b x + 2a)\|a 3 +-+ | 3 +--R 3b x log(---------------------------------) + (6b x - 4a)\|a \|b x + a +--R 3 +--R x +--R [-------------------------------------------------------------------------, +--R 2 6 +-+ +--R 24a x \|a +--R +--------+ +--R +---+ | 3 +--------+ +--R 2 6 \|- a \|b x + a 3 +---+ | 3 +--R - 3b x atan(-----------------) + (3b x - 2a)\|- a \|b x + a +--R a +--R --------------------------------------------------------------] +--R 2 6 +---+ +--R 12a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 443 + +--S 444 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 3 +-+ | 3 +--R 2 - 2a\|b x + a + (b x + 2a)\|a 2 \|b x + a +--R b log(---------------------------------) + 2b atanh(-----------) +--R 3 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 +---+ | 3 +--R 2 +---+ \|b x + a 2 +-+ \|- a \|b x + a +--R b \|- a atanh(-----------) - b \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 447 + +)clear all + +--S 448 of 1309 +t0:=x^3/sqrt(8+27*x^3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1309 +--r0:=2/135*x*sqrt(8+27*x^3)-32/405*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 449 + +--S 450 of 1309 +--a0:=integrate(t0,x) +--E 450 + +--S 451 of 1309 +--m0:=a0-r0 +--E 451 + +--S 452 of 1309 +--d0:=D(m0,x) +--E 452 + +)clear all + +--S 453 of 1309 +t0:=1/sqrt(8+27*x^3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1309 +--r0:=2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1-3*x-%i*sqrt(3)))*sqrt((2+3*x)/(3+%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 454 + +--S 455 of 1309 +--a0:=integrate(t0,x) +--E 455 + +--S 456 of 1309 +--m0:=a0-r0 +--E 456 + +--S 457 of 1309 +--d0:=D(m0,x) +--E 457 + +)clear all + +--S 458 of 1309 +t0:=1/(x^3*sqrt(8+27*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 3 +--R x \|27x + 8 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1309 +--r0:=-1/16*sqrt(8+27*x^3)/x^2-9/16*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 459 + +--S 460 of 1309 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 1309 +--m0:=a0-r0 +--E 461 + +--S 462 of 1309 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 1309 +t0:=x^4/sqrt(8+27*x^3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1309 +--r0:=2/189*x^2*sqrt(8+27*x^3)-64/1701*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))+128/1701*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 464 + +--S 465 of 1309 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 1309 +--m0:=a0-r0 +--E 466 + +--S 467 of 1309 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 1309 +t0:=x/sqrt(8+27*x^3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R \|27x + 8 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1309 +--r0:=2/9*(-1)^(1/4)*(2+3*x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1-3*x+%i*sqrt(3))/3^(1/4)), +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-4/9*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 469 + +--S 470 of 1309 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 1309 +--m0:=a0-r0 +--E 471 + +--S 472 of 1309 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 1309 +t0:=1/(x^2*sqrt(8+27*x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 3 +--R x \|27x + 8 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1309 +--r0:=-1/8*sqrt(8+27*x^3)/x+3/8*(-1)^(1/4)*(2+3*x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt(1-3*x+%i*sqrt(3))/(sqrt(8+27*x^3)*sqrt((2+3*x)/_ +-- (3+%i*sqrt(3))))-3/4*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1-3*x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1-3*x-%i*sqrt(3)))*_ +-- sqrt((2+3*x)/(3+%i*sqrt(3)))*sqrt(1-3*x+%i*sqrt(3))/sqrt(8+27*x^3) +--E 474 + +--S 475 of 1309 +--a0:=integrate(t0,x) +--E 475 + +--S 476 of 1309 +--m0:=a0-r0 +--E 476 + +--S 477 of 1309 +--d0:=D(m0,x) +--E 477 + +)clear all + +--S 478 of 1309 +t0:=x^5/(1+x^3)^(3/2) +--R +--R +--R 5 +--R x +--R (1) ----------------- +--R +------+ +--R 3 | 3 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1309 +r0:=2/3/sqrt(1+x^3)+2/3*sqrt(1+x^3) +--R +--R +--R 3 +--R 2x + 4 +--R (2) ---------- +--R +------+ +--R | 3 +--R 3\|x + 1 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2x + 4 +--R (3) ---------- +--R +------+ +--R | 3 +--R 3\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1309 +t0:=x^8*(1-x^3)^(1/3) +--R +--R +--R +--------+ +--R 8 3| 3 +--R (1) x \|- x + 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1309 +r0:=-1/4*(1-x^3)^(4/3)+2/7*(1-x^3)^(7/3)-1/10*(1-x^3)^(10/3) +--R +--R +--R +--------+ +--R 9 6 3 3| 3 +--R (14x - 2x - 3x - 9)\|- x + 1 +--R (2) --------------------------------- +--R 140 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 9 6 3 3| 3 +--R (14x - 2x - 3x - 9)\|- x + 1 +--R (3) --------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1309 +t0:=x^5*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 5 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1309 +r0:=-1/4*a*(a+b*x^3)^(4/3)/b^2+1/7*(a+b*x^3)^(7/3)/b^2 +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (4b x + a b x - 3a )\|b x + a +--R (2) --------------------------------- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (4b x + a b x - 3a )\|b x + a +--R (3) --------------------------------- +--R 2 +--R 28b +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1309 +t0:=x^4*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 4 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1309 +r0:=1/18*a*x^2*(a+b*x^3)^(1/3)/b+1/6*x^5*(a+b*x^3)^(1/3)+_ + 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(5/3)-_ + 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(5/3)+1/9*a^2*_ + atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b +--R 2a \|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 5 2 +-+3+-+2 3| 3 +--R (9b x + 3a x )\|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R 2 +-+ \|b \|b x + a + b x\|b \|b x + a + b x +--R - a \|3 log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a atan(-------------------------------) +--R 3b x +--R + +--R +--+ +--------+ +--R 5 2 +-+3| 2 3| 3 +--R (9b x + 3a x )\|3 \|b \|b x + a +--R / +--R +--+ +--R +-+3| 2 +--R 54b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R 2 +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x +--R - a \|3 \|b log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R 2 +-+3+-+2 \|b \|b x + a - b x +--R 2a \|3 \|b log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +--+ 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R a \|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 2 +-+3| 2 \|b x + a - x\|b +--R - 2a \|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2 3+-+2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a \|b atan(-------------------------------) +--R 3b x +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 2 3| 2 \|b x + a + 2x\|b +--R - 6a \|b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 54b\|3 \|b \|b +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1309 +t0:=x^3*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1309 +--r0:=1/10*a*x*(a+b*x^3)^(1/3)/b+1/5*x^4*(a+b*x^3)^(1/3)-_ +-- 1/10*a^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3)) +--E 499 + +--S 500 of 1309 +--a0:=integrate(t0,x) +--E 500 + +--S 501 of 1309 +--m0:=a0-r0 +--E 501 + +--S 502 of 1309 +--d0:=D(m0,x) +--E 502 + +)clear all + +--S 503 of 1309 +t0:=x^2*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 2 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1309 +r0:=1/4*(a+b*x^3)^(4/3)/b +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (2) --------------------- +--R 4b +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (3) --------------------- +--R 4b +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1309 +t0:=x*(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1309 +r0:=1/3*x^2*(a+b*x^3)^(1/3)-1/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(2/3)+1/18*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)-_ + 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2a\|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 2 +-+3+-+2 3| 3 +--R 6x \|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 18\|3 \|b +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - a\|3 log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|- b \|b x + a + b x +--R 2a\|3 log(------------------------) +--R x +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +----+ +--------+ +--R 2\|3 \|- b \|b x + a - b x\|3 2 +-+3| 2 3| 3 +--R 6a atan(---------------------------------) + 6x \|3 \|- b \|b x + a +--R 3b x +--R / +--R +----+ +--R +-+3| 2 +--R 18\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - a\|3 \|b log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|- b \|b x + a + b x +--R 2a\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +----+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R 2a\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3 +--R 6a \|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R 6a\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 18\|3 \|- b \|b +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1309 +t0:=(a+b*x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1309 +--r0:=1/2*x*(a+b*x^3)^(1/3)+1/2*a*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 514 + +--S 515 of 1309 +--a0:=integrate(t0,x) +--E 515 + +--S 516 of 1309 +--m0:=a0-r0 +--E 516 + +--S 517 of 1309 +--d0:=D(m0,x) +--E 517 + +)clear all + +--S 518 of 1309 +t0:=(a+b*x^3)^(1/3)/x +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1309 +r0:=(a+b*x^3)^(1/3)+1/3*a^(1/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_ + 1/6*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|b x + a + \|a +--R 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3| 3 +--R 6\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R +-+3+-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ +-+3| 3 +-+3+-+ +--R +-+3+-+ 3| 3 3+-+ 3+-+ 2\|3 \|b x + a + \|3 \|a +--R 2\|3 \|a log(\|b x + a - \|a ) - 6\|a atan(---------------------------) +--R 3+-+ +--R 3\|a +--R + +--R +--------+ +--R +-+3| 3 +--R 6\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+3+-+ 3| 3 3+-+ +-+3+-+ 3| 3 3+-+ +--R \|3 \|a log(\|b x + a - \|a ) - \|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+3+-+ 3| 3 3+-+ +--R 3+-+ 2\|3 \|b x + a + \|3 \|a 3+-+ 2\|b x + a + \|a +--R - 3\|a atan(---------------------------) + 3\|a atan(-------------------) +--R 3+-+ +-+3+-+ +--R 3\|a \|3 \|a +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1309 +t0:=(a+b*x^3)^(1/3)/x^2 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1309 +r0:=-(a+b*x^3)^(1/3)/x-1/3*b^(1/3)*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))+_ + 1/6*b^(1/3)*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_ + b^(1/3)*x/(a+b*x^3)^(1/3))-b^(1/3)*_ + atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+-+ \|b x + a + x\|b \|b x + a + x \|b +--R x\|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+3+-+ \|b x + a - x\|b 3+-+ \|b x + a + 2x\|b +--R - 2x\|3 \|b log(-------------------) - 6x\|b atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R +-+3| 3 +--R - 6\|3 \|b x + a +--R / +--R +-+ +--R 6x\|3 +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1309 +--a0:=integrate(t0,x) +--E 525 + +--S 526 of 1309 +--m0:=a0-r0 +--E 526 + +--S 527 of 1309 +--d0:=D(m0,x) +--E 527 + +)clear all + +--S 528 of 1309 +t0:=(a+b*x^3)^(1/3)/x^3 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1309 +--r0:=-1/2*(a+b*x^3)^(1/3)/x^2+1/2*b*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 529 + +--S 530 of 1309 +--a0:=integrate(t0,x) +--E 530 + +--S 531 of 1309 +--m0:=a0-r0 +--E 531 + +--S 532 of 1309 +--d0:=D(m0,x) +--E 532 + +)clear all + +--S 533 of 1309 +t0:=(a+b*x^3)^(1/3)/x^4 +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1309 +r0:=-1/3*(a+b*x^3)^(1/3)/x^3+1/9*b*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-_ + 1/18*b*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_ + (a+b*x^3)^(2/3))/a^(2/3)-1/3*b*atan((a^(1/3)+_ + 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +--R - 6\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+2 +--R 18x \|3 \|a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - b x \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+ +--R 3 +-+ 3| 2 3| 3 +--R 2b x \|3 log(\|a \|b x + a - a) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--+ +--------+ +--R 3 2\|3 \|a \|b x + a + a\|3 +-+3| 2 3| 3 +--R - 6b x atan(-----------------------------) - 6\|3 \|a \|b x + a +--R 3a +--R / +--R +--+ +--R 3 +-+3| 2 +--R 18x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - b\|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R b\|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +--R 2b\|3 \|a log(\|a \|b x + a - a) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 3+-+ +--R - 2b\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6b \|a atan(-----------------------------) +--R 3a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6b\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 18\|3 \|a \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1309 +t0:=x^5*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 5 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1309 +r0:=-1/5*a*(a+b*x^3)^(5/3)/b^2+1/8*(a+b*x^3)^(8/3)/b^2 +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x + 2a b x - 3a )\|b x + a +--R (2) ----------------------------------- +--R 2 +--R 40b +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x + 2a b x - 3a )\|b x + a +--R (3) ----------------------------------- +--R 2 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1309 +t0:=x^4*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 4 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1309 +--r0:=1/14*a*x^2*(a+b*x^3)^(2/3)/b+1/7*x^5*(a+b*x^3)^(2/3)-_ +-- 1/14*a^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3)) +--E 544 + +--S 545 of 1309 +--a0:=integrate(t0,x) +--E 545 + +--S 546 of 1309 +--m0:=a0-r0 +--E 546 + +--S 547 of 1309 +--d0:=D(m0,x) +--E 547 + +)clear all + +--S 548 of 1309 +t0:=x^3*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1309 +r0:=1/9*a*x*(a+b*x^3)^(2/3)/b+1/6*x^4*(a+b*x^3)^(2/3)+_ + 1/27*a^2*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/54*a^2*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+_ + b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/9*a^2*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b 2 \|b x + a + 2x\|b +--R 2a \|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R 4 +-+3+-+3| 3 +--R (9b x + 6a x)\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a \|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 +--R 6a atan(-------------------------------) +--R 3b x +--R + +--R +--------+2 +--R 4 +-+3+-+3| 3 +--R (9b x + 6a x)\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R 2 +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a \|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R 2 +-+ \|b \|b x + a - b x +--R 2a \|3 log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 2 +-+ \|b x + a - x\|b +--R - 2a \|3 log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2 2\|3 \|b \|b x + a + b x\|3 2 \|b x + a + 2x\|b +--R 6a atan(-------------------------------) + 6a atan(--------------------) +--R 3b x +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+-+ +--R 54b\|3 \|b +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1309 +t0:=x^2*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 2 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1309 +r0:=1/5*(a+b*x^3)^(5/3)/b +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (2) ---------------------- +--R 5b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (b x + a)\|b x + a +--R (3) ---------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1309 +t0:=x*(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3| 3 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1309 +--r0:=1/4*x^2*(a+b*x^3)^(2/3)+1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 559 + +--S 560 of 1309 +--a0:=integrate(t0,x) +--E 560 + +--S 561 of 1309 +--m0:=a0-r0 +--E 561 + +--S 562 of 1309 +--d0:=D(m0,x) +--E 562 + +)clear all + +--S 563 of 1309 +t0:=(a+b*x^3)^(2/3) +--R +--R +--R +--------+2 +--R 3| 3 +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1309 +r0:=1/3*x*(a+b*x^3)^(2/3)-2/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(1/3)+1/9*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_ + 2/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2a\|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R 3x\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 9\|3 \|b +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - a\|3 log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+ \|- b \|b x + a - b x +--R 2a\|3 log(------------------------) +--R x +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--------+2 +--R 2\|3 \|- b \|b x + a + b x\|3 +-+3+---+3| 3 +--R 6a atan(---------------------------------) + 3x\|3 \|- b \|b x + a +--R 3b x +--R / +--R +-+3+---+ +--R 9\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - a\|3 \|b log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+3+-+ \|- b \|b x + a - b x +--R 2a\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+3+---+ \|b x + a - x\|b +--R 2a\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3 +--R 6a\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ \|b x + a + 2x\|b +--R - 6a\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+---+3+-+ +--R 9\|3 \|- b \|b +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1309 +t0:=(a+b*x^3)^(2/3)/x +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1309 +r0:=1/2*(a+b*x^3)^(2/3)+1/3*a^(2/3)*log(a^(1/3)-(a+b*x^3)^(1/3))-_ + 1/6*a^(2/3)*log(a^(2/3)+a^(1/3)*(a+b*x^3)^(1/3)+_ + (a+b*x^3)^(2/3))+a^(2/3)*atan((a^(1/3)+_ + 2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2 +--R - \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a +--R 2\|3 \|a log(- \|b x + a + \|a ) + 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3| 3 +--R 3\|3 \|b x + a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--------+2 +--+2 +--------+ +--+ +--R +-+3| 2 3| 3 3| 2 3| 3 3| 2 +--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--+ +--------+ +--+2 +--R +-+3| 2 3| 3 3| 2 +--R 2\|3 \|a log(a\|b x + a - \|a ) +--R + +--R +--------+ +--+2 +--R +--+ +-+3| 3 +-+3| 2 +--------+2 +--R 3| 2 2a\|3 \|b x + a + \|3 \|a +-+3| 3 +--R 6\|a atan(------------------------------) + 3\|3 \|b x + a +--R +--+2 +--R 3| 2 +--R 3\|a +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--------+2 +--+2 +--------+ +--+ +--R +-+3| 2 3| 3 3| 2 3| 3 3| 2 +--R - \|3 \|a log(a \|b x + a + \|a \|b x + a + a\|a ) +--R + +--R +--------+2 +--------+ +--R +-+3+-+2 3| 3 3+-+3| 3 3+-+2 +--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--+2 +--R +-+3| 2 3| 3 3| 2 +--R 2\|3 \|a log(a\|b x + a - \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+3+-+2 3| 3 3+-+ 3+-+2 2\|b x + a + \|a +--R - 2\|3 \|a log(- \|b x + a + \|a ) - 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--+2 +--R +--+ +-+3| 3 +-+3| 2 +--R 3| 2 2a\|3 \|b x + a + \|3 \|a +--R 6\|a atan(------------------------------) +--R +--+2 +--R 3| 2 +--R 3\|a +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1309 +t0:=(a+b*x^3)^(2/3)/x^2 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1309 +--r0:=-(a+b*x^3)^(2/3)/x+b*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 574 + +--S 575 of 1309 +--a0:=integrate(t0,x) +--E 575 + +--S 576 of 1309 +--m0:=a0-r0 +--E 576 + +--S 577 of 1309 +--d0:=D(m0,x) +--E 577 + +)clear all + +--S 578 of 1309 +t0:=(a+b*x^3)^(2/3)/x^3 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1309 +r0:=-1/2*(a+b*x^3)^(2/3)/x^2-1/3*b^(2/3)*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))+1/6*b^(2/3)*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))+_ + b^(2/3)*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R 2 +-+3+-+2 \|b x + a + x\|b \|b x + a + x \|b +--R x \|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 2 +-+3+-+2 \|b x + a - x\|b +--R - 2x \|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--------+2 +--R 2 3+-+2 \|b x + a + 2x\|b +-+3| 3 +--R 6x \|b atan(-------------------- - 3\|3 \|b x + a +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R 2 +-+ +--R 6x \|3 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1309 +--a0:=integrate(t0,x) +--E 580 + +--S 581 of 1309 +--m0:=a0-r0 +--E 581 + +--S 582 of 1309 +--d0:=D(m0,x) +--E 582 + +)clear all + +--S 583 of 1309 +t0:=(a+b*x^3)^(2/3)/x^4 +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (1) ------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1309 +r0:=-1/3*(a+b*x^3)^(2/3)/x^3+2/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(1/3)-1/9*b*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_ + 2/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R - b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R - 3\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+ +--R 9x \|3 \|a +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3 +-+ 3+-+3| 3 3+-+2 3| 3 +--R - b x \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+ +--R 3 +-+ 3+-+2 3| 3 +--R 2b x \|3 log(\|a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--------+2 +--R 3 2\|3 \|a \|b x + a + a\|3 +-+3+-+3| 3 +--R 6b x atan(-----------------------------) - 3\|3 \|a \|b x + a +--R 3a +--R / +--R 3 +-+3+-+ +--R 9x \|3 \|a +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - b\|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R b\|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2b\|3 log(\|a \|b x + a - a) - 2b\|3 log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6b atan(-----------------------------) - 6b atan(-------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 9\|3 \|a +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1309 +t0:=x^8*(1-x^3)^(6/5) +--R +--R +--R +--------+ +--R 11 8 5| 3 +--R (1) (- x + x )\|- x + 1 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1309 +r0:=-5/33*(1-x^3)^(11/5)+5/24*(1-x^3)^(16/5)-5/63*(1-x^3)^(21/5) +--R +--R +--R +--------+ +--R 12 9 6 3 5| 3 +--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1 +--R (2) ------------------------------------------------- +--R 5544 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 12 9 6 3 5| 3 +--R (- 440x + 605x - 15x - 25x - 125)\|- x + 1 +--R (3) ------------------------------------------------- +--R 5544 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1309 +t0:=x^11/(a+b*x^3)^(1/3) +--R +--R +--R 11 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1309 +r0:=-81/440*a^3*(a+b*x^3)^(2/3)/b^4+27/220*a^2*x^3*_ + (a+b*x^3)^(2/3)/b^3-9/88*a*x^6*(a+b*x^3)^(2/3)/b^2+_ + 1/11*x^9*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (40b x - 45a b x + 54a b x - 81a )\|b x + a +--R (2) ------------------------------------------------- +--R 4 +--R 440b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (40b x - 45a b x + 54a b x - 81a )\|b x + a +--R (3) ------------------------------------------------- +--R 4 +--R 440b +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1309 +t0:=x^8/(a+b*x^3)^(1/3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1309 +r0:=9/40*a^2*(a+b*x^3)^(2/3)/b^3-3/20*a*x^3*(a+b*x^3)^(2/3)/b^2+_ + 1/8*x^6*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x - 6a b x + 9a )\|b x + a +--R (2) ----------------------------------- +--R 3 +--R 40b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (5b x - 6a b x + 9a )\|b x + a +--R (3) ----------------------------------- +--R 3 +--R 40b +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1309 +t0:=x^5/(a+b*x^3)^(1/3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1309 +r0:=-3/10*a*(a+b*x^3)^(2/3)/b^2+1/5*x^3*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (2b x - 3a)\|b x + a +--R (2) ------------------------ +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (2b x - 3a)\|b x + a +--R (3) ------------------------ +--R 2 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1309 +t0:=x^2/(a+b*x^3)^(1/3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1309 +r0:=1/2*(a+b*x^3)^(2/3)/b +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (2) ------------ +--R 2b +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (3) ------------ +--R 2b +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1309 +t0:=1/(x*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R 3| 3 +--R x\|b x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1309 +r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(1/3)-1/6*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(1/3)+_ + 1/3*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/a^(1/3) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 3+-+2 +--R - log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3| 3 3+-+ +-+ 2\|b x + a + \|a +--R 2log(- \|b x + a + \|a ) + 2\|3 atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3+-+ +--R 6\|a +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+ +--R +--------+ +-+3+-+2 3| 3 +-+ +--R +-+ 3+-+2 3| 3 2\|3 \|a \|b x + a + a\|3 +--R 2\|3 log(\|a \|b x + a - a) + 6atan(-----------------------------) +--R 3a +--R / +--R +-+3+-+ +--R 6\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 615 + +--S 616 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+ 3+-+3| 3 3+-+2 3| 3 +--R - \|3 log(\|a \|b x + a + \|a \|b x + a + a) +--R + +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ 3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 log(\|a \|b x + a - a) - 2\|3 log(- \|b x + a + \|a ) +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|a \|b x + a + a\|3 2\|b x + a + \|a +--R 6atan(-----------------------------) - 6atan(-------------------) +--R 3a +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6\|3 \|a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +)clear all + +--S 618 of 1309 +t0:=1/(x^4*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1309 +r0:=-1/3*(a+b*x^3)^(2/3)/(a*x^3)-1/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(4/3)+1/18*b*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(4/3)-_ + 1/3*b*atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) - 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R - 6\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+ +--R 18a x \|3 \|a +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3 +-+ 3+---+3| 3 3+---+2 3| 3 +--R - b x \|3 log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +--------+ +--R 3 +-+ 3+---+2 3| 3 +--R 2b x \|3 log(\|- a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--------+2 +--R 3 2\|3 \|- a \|b x + a + a\|3 +-+3+---+3| 3 +--R 6b x atan(-------------------------------) - 6\|3 \|- a \|b x + a +--R 3a +--R / +--R 3 +-+3+---+ +--R 18a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 620 + +--S 621 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R +-+3+-+ 3+---+3| 3 3+---+2 3| 3 +--R - b\|3 \|a log(\|- a \|b x + a - \|- a \|b x + a - a) +--R + +--R +--------+2 +--------+ +--R +-+3+---+ 3| 3 3+-+3| 3 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +-+3+-+ 3+---+2 3| 3 +--R 2b\|3 \|a log(\|- a \|b x + a - a) +--R + +--R +--------+ +--R +-+3+---+ 3| 3 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- a \|b x + a + a\|3 +--R 6b\|a atan(-------------------------------) +--R 3a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ 2\|b x + a + \|a +--R 6b\|- a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+---+3+-+ +--R 18a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1309 +t0:=x^7/(a+b*x^3)^(1/3) +--R +--R +--R 7 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1309 +--r0:=-5/28*a*x^2*(a+b*x^3)^(2/3)/b^2+1/7*x^5*(a+b*x^3)^(2/3)/b+_ +-- 5/28*a^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b^2*(a+b*x^3)^(1/3)) +--E 624 + +--S 625 of 1309 +--a0:=integrate(t0,x) +--E 625 + +--S 626 of 1309 +--m0:=a0-r0 +--E 626 + +--S 627 of 1309 +--d0:=D(m0,x) +--E 627 + +)clear all + +--S 628 of 1309 +t0:=x^4/(a+b*x^3)^(1/3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1309 +--r0:=1/4*x^2*(a+b*x^3)^(2/3)/b-1/4*a*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(b*(a+b*x^3)^(1/3)) +--E 629 + +--S 630 of 1309 +--a0:=integrate(t0,x) +--E 630 + +--S 631 of 1309 +--m0:=a0-r0 +--E 631 + +--S 632 of 1309 +--d0:=D(m0,x) +--E 632 + +)clear all + +--S 633 of 1309 +t0:=x/(a+b*x^3)^(1/3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1309 +--r0:=1/2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a+b*x^3)^(1/3) +--E 634 + +--S 635 of 1309 +--a0:=integrate(t0,x) +--E 635 + +--S 636 of 1309 +--m0:=a0-r0 +--E 636 + +--S 637 of 1309 +--d0:=D(m0,x) +--E 637 + +)clear all + +--S 638 of 1309 +t0:=1/(x^2*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1309 +--r0:=-(a+b*x^3)^(2/3)/(a*x)+1/2*b*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a*(a+b*x^3)^(1/3)) +--E 639 + +--S 640 of 1309 +--a0:=integrate(t0,x) +--E 640 + +--S 641 of 1309 +--m0:=a0-r0 +--E 641 + +--S 642 of 1309 +--d0:=D(m0,x) +--E 642 + +)clear all + +--S 643 of 1309 +t0:=1/(x^5*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1309 +--r0:=-1/4*(a+b*x^3)^(2/3)/(a*x^4)+1/2*b*(a+b*x^3)^(2/3)/(a^2*x)-_ +-- 1/4*b^2*x^2*((a+b*x^3)/a)^(1/3)*_ +-- hypergeometric(1/3,2/3,5/3,-b*x^3/a)/(a^2*(a+b*x^3)^(1/3)) +--E 644 + +--S 645 of 1309 +--a0:=integrate(t0,x) +--E 645 + +--S 646 of 1309 +--m0:=a0-r0 +--E 646 + +--S 647 of 1309 +--d0:=D(m0,x) +--E 647 + +)clear all + +--S 648 of 1309 +t0:=x^3/(a+b*x^3)^(1/3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1309 +r0:=1/3*x*(a+b*x^3)^(2/3)/b+1/9*a*log(1-b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(4/3)-1/18*a*log(1+b^(2/3)*_ + x^2/(a+b*x^3)^(2/3)+b^(1/3)*x/(a+b*x^3)^(1/3))/b^(4/3)-_ + 1/3*a*atan((1+2*b^(1/3)*x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R 2a\|3 log(-------------------) - 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+2 +--R +-+3+-+3| 3 +--R 6x\|3 \|b \|b x + a +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a\|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +-+ +--------+2 +--R 2\|3 \|b \|b x + a + b x\|3 +-+3+-+3| 3 +--R 6a atan(-------------------------------) + 6x\|3 \|b \|b x + a +--R 3b x +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+-+3| 3 3+-+2 3| 3 2 +--R +-+ \|b \|b x + a + x \|b \|b x + a + b x +--R - a\|3 log(--------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+-+2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+ \|b x + a - x\|b +--R - 2a\|3 log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R +-+3+-+2 3| 3 +-+ 3| 3 3+-+ +--R 2\|3 \|b \|b x + a + b x\|3 \|b x + a + 2x\|b +--R 6a atan(-------------------------------) + 6a atan(--------------------) +--R 3b x +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+-+ +--R 18b\|3 \|b +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1309 +t0:=1/(a+b*x^3)^(1/3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1309 +r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(1/3)+_ + 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(1/3)+atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2\|3 log(-------------------) + 6atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R / +--R +-+3+-+ +--R 6\|3 \|b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - \|3 log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+ \|- b \|b x + a - b x +--R 2\|3 log(------------------------) +--R x +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 2\|3 \|- b \|b x + a + b x\|3 +--R 6atan(---------------------------------) +--R 3b x +--R / +--R +-+3+---+ +--R 6\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+2 +--------+ +--R 3+---+3| 3 3+---+2 3| 3 2 +--R +-+3+-+ \|- b \|b x + a - x \|- b \|b x + a - b x +--R - \|3 \|b log(------------------------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R 3+---+2 3| 3 +--R +-+3+-+ \|- b \|b x + a - b x +--R 2\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3+---+ \|b x + a + x\|b \|b x + a + x \|b +--R - \|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R 3| 3 3+-+ +--R +-+3+---+ \|b x + a - x\|b +--R 2\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +-+3+---+2 3| 3 +-+ +--R 3+-+ 2\|3 \|- b \|b x + a + b x\|3 +--R 6\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R 3| 3 3+-+ +--R 3+---+ \|b x + a + 2x\|b +--R - 6\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +-+3+---+3+-+ +--R 6\|3 \|- b \|b +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1309 +t0:=1/(x^3*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1309 +r0:=-1/2*(a+b*x^3)^(2/3)/(a*x^2) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (2) - ------------ +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R (3) - ------------ +--R 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1309 +t0:=1/(x^6*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 6 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1309 +r0:=-1/5*(a+b*x^3)^(2/3)/(a*x^5)+3/10*b*(a+b*x^3)^(2/3)/(a^2*x^2) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (3b x - 2a)\|b x + a +--R (2) ------------------------ +--R 2 5 +--R 10a x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 3| 3 +--R (3b x - 2a)\|b x + a +--R (3) ------------------------ +--R 2 5 +--R 10a x +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1309 +t0:=1/(x^9*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 9 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1309 +r0:=-1/8*(a+b*x^3)^(2/3)/(a*x^8)+3/20*b*(a+b*x^3)^(2/3)/(a^2*x^5)-_ + 9/40*b^2*(a+b*x^3)^(2/3)/(a^3*x^2) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (- 9b x + 6a b x - 5a )\|b x + a +--R (2) ------------------------------------- +--R 3 8 +--R 40a x +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 2 6 3 2 3| 3 +--R (- 9b x + 6a b x - 5a )\|b x + a +--R (3) ------------------------------------- +--R 3 8 +--R 40a x +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1309 +t0:=1/(x^12*(a+b*x^3)^(1/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R 12 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1309 +r0:=-1/11*(a+b*x^3)^(2/3)/(a*x^11)+9/88*b*(a+b*x^3)^(2/3)/(a^2*x^8)-_ + 27/220*b^2*(a+b*x^3)^(2/3)/(a^3*x^5)+81/440*b^3*(a+b*x^3)^(2/3)/(a^4*x^2) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 54a b x + 45a b x - 40a )\|b x + a +--R (2) ------------------------------------------------- +--R 4 11 +--R 440a x +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+2 +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 54a b x + 45a b x - 40a )\|b x + a +--R (3) ------------------------------------------------- +--R 4 11 +--R 440a x +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1309 +t0:=x^11/(a+b*x^3)^(2/3) +--R +--R +--R 11 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1309 +r0:=-81/140*a^3*(a+b*x^3)^(1/3)/b^4+27/140*a^2*x^3*(a+b*x^3)^(1/3)/b^3-_ + 9/70*a*x^6*(a+b*x^3)^(1/3)/b^2+1/10*x^9*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (14b x - 18a b x + 27a b x - 81a )\|b x + a +--R (2) ------------------------------------------------ +--R 4 +--R 140b +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (14b x - 18a b x + 27a b x - 81a )\|b x + a +--R (3) ------------------------------------------------ +--R 4 +--R 140b +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1309 +t0:=x^8/(a+b*x^3)^(2/3) +--R +--R +--R 8 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1309 +r0:=9/14*a^2*(a+b*x^3)^(1/3)/b^3-3/14*a*x^3*(a+b*x^3)^(1/3)/b^2+_ + 1/7*x^6*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (2b x - 3a b x + 9a )\|b x + a +--R (2) ---------------------------------- +--R 3 +--R 14b +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (2b x - 3a b x + 9a )\|b x + a +--R (3) ---------------------------------- +--R 3 +--R 14b +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1309 +t0:=x^5/(a+b*x^3)^(2/3) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1309 +r0:=-3/4*a*(a+b*x^3)^(1/3)/b^2+1/4*x^3*(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x - 3a)\|b x + a +--R (2) ---------------------- +--R 2 +--R 4b +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (b x - 3a)\|b x + a +--R (3) ---------------------- +--R 2 +--R 4b +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1309 +t0:=x^2/(a+b*x^3)^(2/3) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1309 +r0:=(a+b*x^3)^(1/3)/b +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (2) ----------- +--R b +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (3) ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1309 +t0:=1/(x*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1309 +r0:=1/3*log(a^(1/3)-(a+b*x^3)^(1/3))/a^(2/3)-1/6*log(a^(2/3)+_ + a^(1/3)*(a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(2/3)-_ + atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R +-+ 3| 3 3+-+3| 3 3+-+2 +--R - \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R +-+ 3| 3 3+-+ 2\|b x + a + \|a +--R 2\|3 log(- \|b x + a + \|a ) - 6atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 6\|3 \|a +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - \|3 log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+ +--R +--+ +--------+ +-+3| 2 3| 3 +-+ +--R +-+ 3| 2 3| 3 2\|3 \|a \|b x + a + a\|3 +--R 2\|3 log(\|a \|b x + a - a) - 6atan(-----------------------------) +--R 3a +--R / +--R +--+ +--R +-+3| 2 +--R 6\|3 \|a +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - \|3 \|a log(\|a \|b x + a + a\|a \|b x + a + a ) +--R + +--R +--+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R \|3 \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +-+3| 2 3| 3 3+-+ +--R 2\|3 \|a log(\|a \|b x + a - a) - 2\|3 \|a log(- \|b x + a + \|a ) +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|a \|b x + a + a\|3 +--R - 6\|a atan(-----------------------------) +--R 3a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R 6\|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 6\|3 \|a \|a +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1309 +t0:=1/(x^4*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 4 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1309 +r0:=-1/3*(a+b*x^3)^(1/3)/(a*x^3)-2/9*b*log(a^(1/3)-_ + (a+b*x^3)^(1/3))/a^(5/3)+1/9*b*log(a^(2/3)+a^(1/3)*_ + (a+b*x^3)^(1/3)+(a+b*x^3)^(2/3))/a^(5/3)+2/3*b*_ + atan((a^(1/3)+2*(a+b*x^3)^(1/3))/(a^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3 +-+ 3| 3 3+-+3| 3 3+-+2 +--R b x \|3 log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| 3 3+-+ +--R 3 +-+ 3| 3 3+-+ 3 2\|b x + a + \|a +--R - 2b x \|3 log(- \|b x + a + \|a ) + 6b x atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R +-+3+-+2 3| 3 +--R - 3\|3 \|a \|b x + a +--R / +--R 3 +-+3+-+2 +--R 9a x \|3 \|a +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3 +-+ 3| 2 3| 3 3| 2 3| 3 2 +--R - b x \|3 log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--------+ +--R 3 +-+ 3| 2 3| 3 +--R 2b x \|3 log(\|- a \|b x + a + a) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +----+ +--------+ +--R 3 2\|3 \|- a \|b x + a - a\|3 +-+3| 2 3| 3 +--R 6b x atan(-------------------------------) - 3\|3 \|- a \|b x + a +--R 3a +--R / +--R +----+ +--R 3 +-+3| 2 +--R 9a x \|3 \|- a +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R +-+3+-+2 3| 2 3| 3 3| 2 3| 3 2 +--R - b\|3 \|a log(\|- a \|b x + a - a\|- a \|b x + a + a ) +--R + +--R +----+ +--------+2 +--------+ +--R +-+3| 2 3| 3 3+-+3| 3 3+-+2 +--R - b\|3 \|- a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +----+ +--------+ +--R +-+3+-+2 3| 2 3| 3 +--R 2b\|3 \|a log(\|- a \|b x + a + a) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 3+-+ +--R 2b\|3 \|- a log(- \|b x + a + \|a ) +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- a \|b x + a - a\|3 +--R 6b \|a atan(-------------------------------) +--R 3a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 2\|b x + a + \|a +--R - 6b\|- a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 9a\|3 \|- a \|a +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1309 +t0:=x^4/(a+b*x^3)^(2/3) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1309 +r0:=1/3*x^2*(a+b*x^3)^(1/3)/b+2/9*a*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/_ + b^(5/3)-1/9*a*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(5/3)+2/3*a*atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R - a\|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R 2a\|3 log(-------------------) + 6a atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R + +--R +--------+ +--R 2 +-+3+-+2 3| 3 +--R 3x \|3 \|b \|b x + a +--R / +--R +-+3+-+2 +--R 9b\|3 \|b +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|b \|b x + a + b x\|b \|b x + a + b x +--R - a\|3 log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|b \|b x + a - b x +--R 2a\|3 log(----------------------) +--R x +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--+ +--------+ +--R 2\|3 \|b \|b x + a + b x\|3 2 +-+3| 2 3| 3 +--R - 6a atan(-------------------------------) + 3x \|3 \|b \|b x + a +--R 3b x +--R / +--R +--+ +--R +-+3| 2 +--R 9b\|3 \|b +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+2 +--------+2 +--+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|b \|b x + a + b x\|b \|b x + a + b x +--R - a\|3 \|b log(-----------------------------------------------) +--R 2 +--R x +--R + +--R +--+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|b \|b x + a - b x +--R 2a\|3 \|b log(----------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +--+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R a\|3 \|b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R - 2a\|3 \|b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +--+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|b \|b x + a + b x\|3 +--R - 6a \|b atan(-------------------------------) +--R 3b x +--R + +--R +--------+ +--R +--+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R - 6a\|b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +--+ +--R +-+3+-+2 3| 2 +--R 9b\|3 \|b \|b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1309 +t0:=x/(a+b*x^3)^(2/3) +--R +--R +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1309 +r0:=-1/3*log(1-b^(1/3)*x/(a+b*x^3)^(1/3))/b^(2/3)+_ + 1/6*log(1+b^(2/3)*x^2/(a+b*x^3)^(2/3)+b^(1/3)*_ + x/(a+b*x^3)^(1/3))/b^(2/3)-atan((1+2*b^(1/3)*_ + x/(a+b*x^3)^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3| 3 3+-+3| 3 2 3+-+2 +--R +-+ \|b x + a + x\|b \|b x + a + x \|b +--R \|3 log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--------+ +--R 3| 3 3+-+ 3| 3 3+-+ +--R +-+ \|b x + a - x\|b \|b x + a + 2x\|b +--R - 2\|3 log(-------------------) - 6atan(--------------------) +--R +--------+ +--------+ +--R 3| 3 +-+3| 3 +--R \|b x + a \|3 \|b x + a +--R / +--R +-+3+-+2 +--R 6\|3 \|b +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+ \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - \|3 log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+ \|- b \|b x + a + b x +--R 2\|3 log(------------------------) +--R x +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 2\|3 \|- b \|b x + a - b x\|3 +--R 6atan(---------------------------------) +--R 3b x +--R / +--R +----+ +--R +-+3| 2 +--R 6\|3 \|- b +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +--------+2 +----+ +--------+ +--R 3| 2 3| 3 3| 2 3| 3 2 2 +--R +-+3+-+2 \|- b \|b x + a - b x\|- b \|b x + a + b x +--R - \|3 \|b log(---------------------------------------------------) +--R 2 +--R x +--R + +--R +----+ +--------+ +--R 3| 2 3| 3 +--R +-+3+-+2 \|- b \|b x + a + b x +--R 2\|3 \|b log(------------------------) +--R x +--R + +--R +--------+2 +--------+ +--R +----+ 3| 3 3+-+3| 3 2 3+-+2 +--R +-+3| 2 \|b x + a + x\|b \|b x + a + x \|b +--R - \|3 \|- b log(-----------------------------------------) +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R +-+3| 2 \|b x + a - x\|b +--R 2\|3 \|- b log(-------------------) +--R +--------+ +--R 3| 3 +--R \|b x + a +--R + +--R +----+ +--------+ +--R +-+3| 2 3| 3 +-+ +--R 3+-+2 2\|3 \|- b \|b x + a - b x\|3 +--R 6\|b atan(---------------------------------) +--R 3b x +--R + +--R +--------+ +--R +----+ 3| 3 3+-+ +--R 3| 2 \|b x + a + 2x\|b +--R 6\|- b atan(--------------------) +--R +--------+ +--R +-+3| 3 +--R \|3 \|b x + a +--R / +--R +----+ +--R +-+3| 2 3+-+2 +--R 6\|3 \|- b \|b +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1309 +t0:=1/(x^2*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 2 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1309 +r0:=-(a+b*x^3)^(1/3)/(a*x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (2) - ----------- +--R a x +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3| 3 +--R \|b x + a +--R (3) - ----------- +--R a x +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1309 +t0:=1/(x^5*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 5 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1309 +r0:=-1/4*(a+b*x^3)^(1/3)/(a*x^4)+3/4*b*(a+b*x^3)^(1/3)/(a^2*x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (3b x - a)\|b x + a +--R (2) ---------------------- +--R 2 4 +--R 4a x +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 3| 3 +--R (3b x - a)\|b x + a +--R (3) ---------------------- +--R 2 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1309 +t0:=1/(x^8*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 8 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1309 +r0:=-1/7*(a+b*x^3)^(1/3)/(a*x^7)+3/14*b*(a+b*x^3)^(1/3)/(a^2*x^4)-_ + 9/14*b^2*(a+b*x^3)^(1/3)/(a^3*x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (- 9b x + 3a b x - 2a )\|b x + a +--R (2) ------------------------------------ +--R 3 7 +--R 14a x +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 6 3 2 3| 3 +--R (- 9b x + 3a b x - 2a )\|b x + a +--R (3) ------------------------------------ +--R 3 7 +--R 14a x +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1309 +t0:=1/(x^11*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) --------------- +--R +--------+2 +--R 11 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1309 +r0:=-1/10*(a+b*x^3)^(1/3)/(a*x^10)+9/70*b*(a+b*x^3)^(1/3)/(a^2*x^7)-_ + 27/140*b^2*(a+b*x^3)^(1/3)/(a^3*x^4)+81/140*b^3*(a+b*x^3)^(1/3)/(a^4*x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 27a b x + 18a b x - 14a )\|b x + a +--R (2) ------------------------------------------------ +--R 4 10 +--R 140a x +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 9 2 6 2 3 3 3| 3 +--R (81b x - 27a b x + 18a b x - 14a )\|b x + a +--R (3) ------------------------------------------------ +--R 4 10 +--R 140a x +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1309 +t0:=x^6/(a+b*x^3)^(2/3) +--R +--R +--R 6 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1309 +--r0:=-2/5*a*x*(a+b*x^3)^(1/3)/b^2+1/5*x^4*(a+b*x^3)^(1/3)/b+_ +-- 2/5*a^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b^2*(a+b*x^3)^(2/3)) +--E 739 + +--S 740 of 1309 +--a0:=integrate(t0,x) +--E 740 + +--S 741 of 1309 +--m0:=a0-r0 +--E 741 + +--S 742 of 1309 +--d0:=D(m0,x) +--E 742 + +)clear all + +--S 743 of 1309 +t0:=x^3/(a+b*x^3)^(2/3) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1309 +--r0:=1/2*x*(a+b*x^3)^(1/3)/b-1/2*a*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(b*(a+b*x^3)^(2/3)) +--E 744 + +--S 745 of 1309 +--a0:=integrate(t0,x) +--E 745 + +--S 746 of 1309 +--m0:=a0-r0 +--E 746 + +--S 747 of 1309 +--d0:=D(m0,x) +--E 747 + +)clear all + +--S 748 of 1309 +t0:=1/(a+b*x^3)^(2/3) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+2 +--R 3| 3 +--R \|b x + a +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1309 +--r0:=x*((a+b*x^3)/a)^(2/3)*_ +--hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a+b*x^3)^(2/3) +--E 749 + +--S 750 of 1309 +--a0:=integrate(t0,x) +--E 750 + +--S 751 of 1309 +--m0:=a0-r0 +--E 751 + +--S 752 of 1309 +--d0:=D(m0,x) +--E 752 + +)clear all + +--S 753 of 1309 +t0:=1/(x^3*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 3 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1309 +--r0:=-1/2*(a+b*x^3)^(1/3)/(a*x^2)-1/2*b*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a*(a+b*x^3)^(2/3)) +--E 754 + +--S 755 of 1309 +--a0:=integrate(t0,x) +--E 755 + +--S 756 of 1309 +--m0:=a0-r0 +--E 756 + +--S 757 of 1309 +--d0:=D(m0,x) +--E 757 + +)clear all + +--S 758 of 1309 +t0:=1/(x^6*(a+b*x^3)^(2/3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+2 +--R 6 3| 3 +--R x \|b x + a +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1309 +--r0:=-1/5*(a+b*x^3)^(1/3)/(a*x^5)+2/5*b*(a+b*x^3)^(1/3)/(a^2*x^2)+_ +-- 2/5*b^2*x*((a+b*x^3)/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^3/a)/(a^2*(a+b*x^3)^(2/3)) +--E 759 + +--S 760 of 1309 +--a0:=integrate(t0,x) +--E 760 + +--S 761 of 1309 +--m0:=a0-r0 +--E 761 + +--S 762 of 1309 +--d0:=D(m0,x) +--E 762 + +)clear all + +--S 763 of 1309 +t0:=x^2/(2+x^3)^(1/4) +--R +--R +--R 2 +--R x +--R (1) --------- +--R +------+ +--R 4| 3 +--R \|x + 2 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1309 +r0:=4/9*(2+x^3)^(3/4) +--R +--R +--R +------+3 +--R 4| 3 +--R 4\|x + 2 +--R (2) ----------- +--R 9 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +------+3 +--R 4| 3 +--R 4\|x + 2 +--R (3) ----------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1309 +t0:=sqrt(x)/(1+x^3) +--R +--R +--R +-+ +--R \|x +--R (1) ------ +--R 3 +--R x + 1 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1309 +r0:=2/3*atan(x^(3/2)) +--R +--R +--R +-+ +--R 2atan(x\|x ) +--R (2) ------------ +--R 3 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2atan(x\|x ) +--R (3) ------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1309 +t0:=x^2*(a+b*x^3)^p +--R +--R +--R 2 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1309 +r0:=1/3*(a+b*x^3)^(1+p)/(b*(1+p)) +--R +--R +--R 3 p + 1 +--R (b x + a) +--R (2) --------------- +--R 3b p + 3b +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 3 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 3b p + 3b +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1309 +m0:=a0-r0 +--R +--R +--R 3 +--R 3 p log(b x + a) 3 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 3b p + 3b +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1309 +t0:=x^5*(a+b*x^3)^p +--R +--R +--R 5 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1309 +r0:=-1/3*a*(a+b*x^3)^(1+p)/(b^2*(1+p))+1/3*(a+b*x^3)^(2+p)/(b^2*(2+p)) +--R +--R +--R 3 p + 2 3 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 2 2 6 3 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R 2 2 6 3 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 3 p + 2 3 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 3b p + 9b p + 6b +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1309 +t0:=x^8*(a+b*x^3)^p +--R +--R +--R 8 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1309 +r0:=1/3*a^2*(a+b*x^3)^(1+p)/(b^3*(1+p))-_ + 2/3*a*(a+b*x^3)^(2+p)/(b^3*(2+p))+1/3*(a+b*x^3)^(3+p)/(b^3*(3+p)) +--R +--R +--R (2) +--R 2 3 p + 3 2 3 p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 3 p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 9 2 2 2 6 2 3 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 3 +--R p log(b x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 9 2 2 2 6 2 3 3 +--R ((b p + 3b p + 2b )x + (a b p + a b p)x - 2a b p x + 2a ) +--R * +--R 3 +--R p log(b x + a) +--R %e +--R + +--R 2 3 p + 3 2 3 p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 3 p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R 3b p + 18b p + 33b p + 18b +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1309 +t0:=x^11*(a+b*x^3)^p +--R +--R +--R 11 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1309 +r0:=-1/3*a^3*(a+b*x^3)^(1+p)/(b^4*(1+p))+a^2*(a+b*x^3)^(2+p)/(b^4*(2+p))-_ + a*(a+b*x^3)^(3+p)/(b^4*(3+p))+1/3*(a+b*x^3)^(4+p)/(b^4*(4+p)) +--R +--R +--R (2) +--R 3 2 3 p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 3 p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 3 p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 3 p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 12 3 3 3 2 3 9 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 6 3 3 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 3 +--R p log(b x + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 12 3 3 3 2 3 9 +--R (b p + 6b p + 11b p + 6b )x + (a b p + 3a b p + 2a b p)x +--R + +--R 2 2 2 2 2 6 3 3 4 +--R (- 3a b p - 3a b p)x + 6a b p x - 6a +--R * +--R 3 +--R p log(b x + a) +--R %e +--R + +--R 3 2 3 p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 3 p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 3 p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 3 p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R 3b p + 30b p + 105b p + 150b p + 72b +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1309 +t0:=x^m*(a+b*x^4) +--R +--R +--R 4 m +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1309 +r0:=a*x^(1+m)/(1+m)+b*x^(5+m)/(5+m) +--R +--R +--R m + 5 m + 1 +--R (b m + b)x + (a m + 5a)x +--R (2) ---------------------------------- +--R 2 +--R m + 6m + 5 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 5 m log(x) +--R ((b m + b)x + (a m + 5a)x)%e +--R (3) ------------------------------------- +--R 2 +--R m + 6m + 5 +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 m log(x) m + 5 +--R ((b m + b)x + (a m + 5a)x)%e + (- b m - b)x +--R + +--R m + 1 +--R (- a m - 5a)x +--R / +--R 2 +--R m + 6m + 5 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1309 +t0:=x^5*(a+b*x^4) +--R +--R +--R 9 5 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 798 + +--S 799 of 1309 +r0:=1/6*a*x^6+1/10*b*x^10 +--R +--R +--R 1 10 1 6 +--R (2) -- b x + - a x +--R 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 799 + +--S 800 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 10 1 6 +--R (3) -- b x + - a x +--R 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 800 + +--S 801 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 801 + +--S 802 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 802 + +)clear all + +--S 803 of 1309 +t0:=x^4*(a+b*x^4) +--R +--R +--R 8 4 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 803 + +--S 804 of 1309 +r0:=1/5*a*x^5+1/9*b*x^9 +--R +--R +--R 1 9 1 5 +--R (2) - b x + - a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 804 + +--S 805 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 9 1 5 +--R (3) - b x + - a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 805 + +--S 806 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 806 + +--S 807 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 807 + +)clear all + +--S 808 of 1309 +t0:=x^3*(a+b*x^4) +--R +--R +--R 7 3 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 808 + +--S 809 of 1309 +r0:=1/4*a*x^4+1/8*b*x^8 +--R +--R +--R 1 8 1 4 +--R (2) - b x + - a x +--R 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 809 + +--S 810 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 8 1 4 +--R (3) - b x + - a x +--R 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 810 + +--S 811 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 811 + +--S 812 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 812 + +)clear all + +--S 813 of 1309 +t0:=x^2*(a+b*x^4) +--R +--R +--R 6 2 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 813 + +--S 814 of 1309 +r0:=1/3*a*x^3+1/7*b*x^7 +--R +--R +--R 1 7 1 3 +--R (2) - b x + - a x +--R 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 814 + +--S 815 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 7 1 3 +--R (3) - b x + - a x +--R 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 815 + +--S 816 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 816 + +--S 817 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 817 + +)clear all + +--S 818 of 1309 +t0:=x*(a+b*x^4) +--R +--R +--R 5 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 818 + +--S 819 of 1309 +r0:=1/2*a*x^2+1/6*b*x^6 +--R +--R +--R 1 6 1 2 +--R (2) - b x + - a x +--R 6 2 +--R Type: Polynomial(Fraction(Integer)) +--E 819 + +--S 820 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 6 1 2 +--R (3) - b x + - a x +--R 6 2 +--R Type: Polynomial(Fraction(Integer)) +--E 820 + +--S 821 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 821 + +--S 822 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 822 + +)clear all + +--S 823 of 1309 +t0:=a+b*x^4 +--R +--R +--R 4 +--R (1) b x + a +--R Type: Polynomial(Integer) +--E 823 + +--S 824 of 1309 +r0:=a*x+1/5*b*x^5 +--R +--R +--R 1 5 +--R (2) - b x + a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 824 + +--S 825 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 5 +--R (3) - b x + a x +--R 5 +--R Type: Polynomial(Fraction(Integer)) +--E 825 + +--S 826 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 826 + +--S 827 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 827 + +)clear all + +--S 828 of 1309 +t0:=(a+b*x^4)/x +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 828 + +--S 829 of 1309 +r0:=1/4*b*x^4+a*log(x) +--R +--R +--R 4 +--R 4a log(x) + b x +--R (2) ---------------- +--R 4 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4a log(x) + b x +--R (3) ---------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1309 +t0:=(a+b*x^4)/x^2 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 833 + +--S 834 of 1309 +r0:=-a/x+1/3*b*x^3 +--R +--R +--R 4 +--R b x - 3a +--R (2) --------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 834 + +--S 835 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R b x - 3a +--R (3) --------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1309 +t0:=(a+b*x^4)/x^3 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 838 + +--S 839 of 1309 +r0:=-1/2*a/x^2+1/2*b*x^2 +--R +--R +--R 1 4 1 +--R - b x - - a +--R 2 2 +--R (2) ------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 839 + +--S 840 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R b x - a +--R (3) -------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1309 +t0:=(a+b*x^4)/x^4 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1309 +r0:=-1/3*a/x^3+b*x +--R +--R +--R 4 1 +--R b x - - a +--R 3 +--R (2) ---------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 844 + +--S 845 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 3b x - a +--R (3) --------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1309 +t0:=(a+b*x^4)/x^5 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1309 +r0:=-1/4*a/x^4+b*log(x) +--R +--R +--R 4 +--R 4b x log(x) - a +--R (2) --------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4b x log(x) - a +--R (3) --------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1309 +t0:=(a+b*x^4)/x^6 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 853 + +--S 854 of 1309 +r0:=-1/5*a/x^5-b/x +--R +--R +--R 4 1 +--R - b x - - a +--R 5 +--R (2) ------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 854 + +--S 855 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 5b x - a +--R (3) ----------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1309 +t0:=(a+b*x^4)/x^7 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 858 + +--S 859 of 1309 +r0:=-1/6*a/x^6-1/2*b/x^2 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 2 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 859 + +--S 860 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 3b x - a +--R (3) ----------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1309 +t0:=(a+b*x^4)/x^8 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 863 + +--S 864 of 1309 +r0:=-1/7*a/x^7-1/3*b/x^3 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 3 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 864 + +--S 865 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 7b x - 3a +--R (3) ------------ +--R 7 +--R 21x +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1309 +t0:=(a+b*x^4)/x^9 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 868 + +--S 869 of 1309 +r0:=-1/8*a/x^8-1/4*b/x^4 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 4 8 +--R (2) -------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 869 + +--S 870 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 2b x - a +--R (3) ----------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1309 +t0:=(a+b*x^4)/x^10 +--R +--R +--R 4 +--R b x + a +--R (1) -------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 873 + +--S 874 of 1309 +r0:=-1/9*a/x^9-1/5*b/x^5 +--R +--R +--R 1 4 1 +--R - - b x - - a +--R 5 9 +--R (2) -------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 874 + +--S 875 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 9b x - 5a +--R (3) ------------ +--R 9 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1309 +t0:=x^m*(a+b*x^4)^2 +--R +--R +--R 2 8 4 2 m +--R (1) (b x + 2a b x + a )x +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1309 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(5+m)/(5+m)+b^2*x^(9+m)/(9+m) +--R +--R +--R (2) +--R 2 2 2 2 m + 9 2 m + 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 m + 1 +--R (a m + 14a m + 45a )x +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 9 2 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 +--R (a m + 14a m + 45a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 9 2 5 +--R (b m + 6b m + 5b )x + (2a b m + 20a b m + 18a b)x +--R + +--R 2 2 2 2 +--R (a m + 14a m + 45a )x +--R * +--R m log(x) +--R %e +--R + +--R 2 2 2 2 m + 9 2 m + 5 +--R (- b m - 6b m - 5b )x + (- 2a b m - 20a b m - 18a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- a m - 14a m - 45a )x +--R / +--R 3 2 +--R m + 15m + 59m + 45 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1309 +t0:=x^5*(a+b*x^4)^2 +--R +--R +--R 2 13 9 2 5 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 883 + +--S 884 of 1309 +r0:=1/6*a^2*x^6+1/5*a*b*x^10+1/14*b^2*x^14 +--R +--R +--R 1 2 14 1 10 1 2 6 +--R (2) -- b x + - a b x + - a x +--R 14 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 884 + +--S 885 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 14 1 10 1 2 6 +--R (3) -- b x + - a b x + - a x +--R 14 5 6 +--R Type: Polynomial(Fraction(Integer)) +--E 885 + +--S 886 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 886 + +--S 887 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 887 + +)clear all + +--S 888 of 1309 +t0:=x^4*(a+b*x^4)^2 +--R +--R +--R 2 12 8 2 4 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 888 + +--S 889 of 1309 +r0:=1/5*a^2*x^5+2/9*a*b*x^9+1/13*b^2*x^13 +--R +--R +--R 1 2 13 2 9 1 2 5 +--R (2) -- b x + - a b x + - a x +--R 13 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 889 + +--S 890 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 13 2 9 1 2 5 +--R (3) -- b x + - a b x + - a x +--R 13 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 890 + +--S 891 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 891 + +--S 892 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 892 + +)clear all + +--S 893 of 1309 +t0:=x^3*(a+b*x^4)^2 +--R +--R +--R 2 11 7 2 3 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 893 + +--S 894 of 1309 +r0:=1/12*(a+b*x^4)^3/b +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R -- b x + - a b x + - a b x + -- a +--R 12 4 4 12 +--R (2) -------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 894 + +--S 895 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 12 1 8 1 2 4 +--R (3) -- b x + - a b x + - a x +--R 12 4 4 +--R Type: Polynomial(Fraction(Integer)) +--E 895 + +--S 896 of 1309 +m0:=a0-r0 +--R +--R +--R 1 3 +--R -- a +--R 12 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 896 + +--S 897 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 897 + +)clear all + +--S 898 of 1309 +t0:=x^2*(a+b*x^4)^2 +--R +--R +--R 2 10 6 2 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 898 + +--S 899 of 1309 +r0:=1/3*a^2*x^3+2/7*a*b*x^7+1/11*b^2*x^11 +--R +--R +--R 1 2 11 2 7 1 2 3 +--R (2) -- b x + - a b x + - a x +--R 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 899 + +--S 900 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 11 2 7 1 2 3 +--R (3) -- b x + - a b x + - a x +--R 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 900 + +--S 901 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 901 + +--S 902 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 902 + +)clear all + +--S 903 of 1309 +t0:=x*(a+b*x^4)^2 +--R +--R +--R 2 9 5 2 +--R (1) b x + 2a b x + a x +--R Type: Polynomial(Integer) +--E 903 + +--S 904 of 1309 +r0:=1/2*a^2*x^2+1/3*a*b*x^6+1/10*b^2*x^10 +--R +--R +--R 1 2 10 1 6 1 2 2 +--R (2) -- b x + - a b x + - a x +--R 10 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 904 + +--S 905 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 10 1 6 1 2 2 +--R (3) -- b x + - a b x + - a x +--R 10 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 905 + +--S 906 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 906 + +--S 907 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 907 + +)clear all + +--S 908 of 1309 +t0:=(a+b*x^4)^2 +--R +--R +--R 2 8 4 2 +--R (1) b x + 2a b x + a +--R Type: Polynomial(Integer) +--E 908 + +--S 909 of 1309 +r0:=a^2*x+2/5*a*b*x^5+1/9*b^2*x^9 +--R +--R +--R 1 2 9 2 5 2 +--R (2) - b x + - a b x + a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 909 + +--S 910 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 2 9 2 5 2 +--R (3) - b x + - a b x + a x +--R 9 5 +--R Type: Polynomial(Fraction(Integer)) +--E 910 + +--S 911 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 911 + +--S 912 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 912 + +)clear all + +--S 913 of 1309 +t0:=(a+b*x^4)^2/x +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1309 +r0:=1/2*a*b*x^4+1/8*b^2*x^8+a^2*log(x) +--R +--R +--R 2 2 8 4 +--R 8a log(x) + b x + 4a b x +--R (2) -------------------------- +--R 8 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 2 8 4 +--R 8a log(x) + b x + 4a b x +--R (3) -------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1309 +t0:=(a+b*x^4)^2/x^2 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1309 +r0:=-a^2/x+2/3*a*b*x^3+1/7*b^2*x^7 +--R +--R +--R 2 8 4 2 +--R 3b x + 14a b x - 21a +--R (2) ----------------------- +--R 21x +--R Type: Fraction(Polynomial(Integer)) +--E 919 + +--S 920 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3b x + 14a b x - 21a +--R (3) ----------------------- +--R 21x +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1309 +t0:=(a+b*x^4)^2/x^3 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 923 + +--S 924 of 1309 +r0:=-1/2*a^2/x^2+a*b*x^2+1/6*b^2*x^6 +--R +--R +--R 1 2 8 4 1 2 +--R - b x + a b x - - a +--R 6 2 +--R (2) ---------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 924 + +--S 925 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R b x + 6a b x - 3a +--R (3) -------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 925 + +--S 926 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1309 +t0:=(a+b*x^4)^2/x^4 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1309 +r0:=-1/3*a^2/x^3+2*a*b*x+1/5*b^2*x^5 +--R +--R +--R 1 2 8 4 1 2 +--R - b x + 2a b x - - a +--R 5 3 +--R (2) ----------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 929 + +--S 930 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3b x + 30a b x - 5a +--R (3) ---------------------- +--R 3 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 930 + +--S 931 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1309 +t0:=(a+b*x^4)^2/x^5 +--R +--R +--R 2 8 4 2 +--R b x + 2a b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 933 + +--S 934 of 1309 +r0:=-1/4*a^2/x^4+1/4*b^2*x^4+2*a*b*log(x) +--R +--R +--R 4 2 8 2 +--R 8a b x log(x) + b x - a +--R (2) ------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 2 8 2 +--R 8a b x log(x) + b x - a +--R (3) ------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 935 + +--S 936 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 937 + +)clear all + +--S 938 of 1309 +t0:=x^m*(a+b*x^4)^3 +--R +--R +--R 3 12 2 8 2 4 3 m +--R (1) (b x + 3a b x + 3a b x + a )x +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1309 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(5+m)/(5+m)+3*a*b^2*x^(9+m)/(9+m)+_ + b^3*x^(13+m)/(13+m) +--R +--R +--R (2) +--R 3 3 3 2 3 3 m + 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 m + 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (a m + 27a m + 227a m + 585a )x +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 27a m + 227a m + 585a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Union(Expression(Integer),...) +--E 940 + +--S 941 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 13 +--R (b m + 15b m + 59b m + 45b )x +--R + +--R 2 3 2 2 2 2 9 +--R (3a b m + 57a b m + 249a b m + 195a b )x +--R + +--R 2 3 2 2 2 2 5 +--R (3a b m + 69a b m + 417a b m + 351a b)x +--R + +--R 3 3 3 2 3 3 +--R (a m + 27a m + 227a m + 585a )x +--R * +--R m log(x) +--R %e +--R + +--R 3 3 3 2 3 3 m + 13 +--R (- b m - 15b m - 59b m - 45b )x +--R + +--R 2 3 2 2 2 2 m + 9 +--R (- 3a b m - 57a b m - 249a b m - 195a b )x +--R + +--R 2 3 2 2 2 2 m + 5 +--R (- 3a b m - 69a b m - 417a b m - 351a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- a m - 27a m - 227a m - 585a )x +--R / +--R 4 3 2 +--R m + 28m + 254m + 812m + 585 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1309 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1309 +t0:=x^5*(a+b*x^4)^3 +--R +--R +--R 3 17 2 13 2 9 3 5 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 943 + +--S 944 of 1309 +r0:=1/6*a^3*x^6+3/10*a^2*b*x^10+3/14*a*b^2*x^14+1/18*b^3*x^18 +--R +--R +--R 1 3 18 3 2 14 3 2 10 1 3 6 +--R (2) -- b x + -- a b x + -- a b x + - a x +--R 18 14 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 944 + +--S 945 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 18 3 2 14 3 2 10 1 3 6 +--R (3) -- b x + -- a b x + -- a b x + - a x +--R 18 14 10 6 +--R Type: Polynomial(Fraction(Integer)) +--E 945 + +--S 946 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 946 + +--S 947 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 947 + +)clear all + +--S 948 of 1309 +t0:=x^4*(a+b*x^4)^3 +--R +--R +--R 3 16 2 12 2 8 3 4 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 948 + +--S 949 of 1309 +r0:=1/5*a^3*x^5+1/3*a^2*b*x^9+3/13*a*b^2*x^13+1/17*b^3*x^17 +--R +--R +--R 1 3 17 3 2 13 1 2 9 1 3 5 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 17 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 949 + +--S 950 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 17 3 2 13 1 2 9 1 3 5 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 17 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 950 + +--S 951 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 951 + +--S 952 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 952 + +)clear all + +--S 953 of 1309 +t0:=x^3*(a+b*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 953 + +--S 954 of 1309 +r0:=1/16*(a+b*x^4)^4/b +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R -- b x + - a b x + - a b x + - a b x + -- a +--R 16 4 8 4 16 +--R (2) -------------------------------------------------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 954 + +--S 955 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 16 1 2 12 3 2 8 1 3 4 +--R (3) -- b x + - a b x + - a b x + - a x +--R 16 4 8 4 +--R Type: Polynomial(Fraction(Integer)) +--E 955 + +--S 956 of 1309 +m0:=a0-r0 +--R +--R +--R 1 4 +--R -- a +--R 16 +--R (4) - ----- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 956 + +--S 957 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 957 + +)clear all + +--S 958 of 1309 +t0:=x^2*(a+b*x^4)^3 +--R +--R +--R 3 14 2 10 2 6 3 2 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 958 + +--S 959 of 1309 +r0:=1/3*a^3*x^3+3/7*a^2*b*x^7+3/11*a*b^2*x^11+1/15*b^3*x^15 +--R +--R +--R 1 3 15 3 2 11 3 2 7 1 3 3 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 15 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 959 + +--S 960 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 15 3 2 11 3 2 7 1 3 3 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 15 11 7 3 +--R Type: Polynomial(Fraction(Integer)) +--E 960 + +--S 961 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 961 + +--S 962 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 962 + +)clear all + +--S 963 of 1309 +t0:=x*(a+b*x^4)^3 +--R +--R +--R 3 13 2 9 2 5 3 +--R (1) b x + 3a b x + 3a b x + a x +--R Type: Polynomial(Integer) +--E 963 + +--S 964 of 1309 +r0:=1/2*a^3*x^2+1/2*a^2*b*x^6+3/10*a*b^2*x^10+1/14*b^3*x^14 +--R +--R +--R 1 3 14 3 2 10 1 2 6 1 3 2 +--R (2) -- b x + -- a b x + - a b x + - a x +--R 14 10 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 964 + +--S 965 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 14 3 2 10 1 2 6 1 3 2 +--R (3) -- b x + -- a b x + - a b x + - a x +--R 14 10 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 965 + +--S 966 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 966 + +--S 967 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 967 + +)clear all + +--S 968 of 1309 +t0:=(a+b*x^4)^3 +--R +--R +--R 3 12 2 8 2 4 3 +--R (1) b x + 3a b x + 3a b x + a +--R Type: Polynomial(Integer) +--E 968 + +--S 969 of 1309 +r0:=a^3*x+3/5*a^2*b*x^5+1/3*a*b^2*x^9+1/13*b^3*x^13 +--R +--R +--R 1 3 13 1 2 9 3 2 5 3 +--R (2) -- b x + - a b x + - a b x + a x +--R 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 969 + +--S 970 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 3 13 1 2 9 3 2 5 3 +--R (3) -- b x + - a b x + - a b x + a x +--R 13 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 970 + +--S 971 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 971 + +--S 972 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 972 + +)clear all + +--S 973 of 1309 +t0:=(a+b*x^4)^3/x +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 973 + +--S 974 of 1309 +r0:=3/4*a^2*b*x^4+3/8*a*b^2*x^8+1/12*b^3*x^12+a^3*log(x) +--R +--R +--R 3 3 12 2 8 2 4 +--R 24a log(x) + 2b x + 9a b x + 18a b x +--R (2) ---------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 3 12 2 8 2 4 +--R 24a log(x) + 2b x + 9a b x + 18a b x +--R (3) ---------------------------------------- +--R 24 +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1309 +t0:=(a+b*x^4)^3/x^2 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 978 + +--S 979 of 1309 +r0:=-a^3/x+a^2*b*x^3+3/7*a*b^2*x^7+1/11*b^3*x^11 +--R +--R +--R 3 12 2 8 2 4 3 +--R 7b x + 33a b x + 77a b x - 77a +--R (2) ----------------------------------- +--R 77x +--R Type: Fraction(Polynomial(Integer)) +--E 979 + +--S 980 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 7b x + 33a b x + 77a b x - 77a +--R (3) ----------------------------------- +--R 77x +--R Type: Union(Expression(Integer),...) +--E 980 + +--S 981 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 982 + +)clear all + +--S 983 of 1309 +t0:=(a+b*x^4)^3/x^3 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 983 + +--S 984 of 1309 +r0:=-1/2*a^3/x^2+3/2*a^2*b*x^2+1/2*a*b^2*x^6+1/10*b^3*x^10 +--R +--R +--R 1 3 12 1 2 8 3 2 4 1 3 +--R -- b x + - a b x + - a b x - - a +--R 10 2 2 2 +--R (2) ------------------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 984 + +--S 985 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 5a b x + 15a b x - 5a +--R (3) -------------------------------- +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 985 + +--S 986 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 987 + +)clear all + +--S 988 of 1309 +t0:=(a+b*x^4)^3/x^4 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 988 + +--S 989 of 1309 +r0:=-1/3*a^3/x^3+3*a^2*b*x+3/5*a*b^2*x^5+1/9*b^3*x^9 +--R +--R +--R 1 3 12 3 2 8 2 4 1 3 +--R - b x + - a b x + 3a b x - - a +--R 9 5 3 +--R (2) ----------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 989 + +--S 990 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 5b x + 27a b x + 135a b x - 15a +--R (3) ------------------------------------ +--R 3 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 990 + +--S 991 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 992 + +)clear all + +--S 993 of 1309 +t0:=(a+b*x^4)^3/x^5 +--R +--R +--R 3 12 2 8 2 4 3 +--R b x + 3a b x + 3a b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 993 + +--S 994 of 1309 +r0:=-1/4*a^3/x^4+3/4*a*b^2*x^4+1/8*b^3*x^8+3*a^2*b*log(x) +--R +--R +--R 2 4 3 12 2 8 3 +--R 24a b x log(x) + b x + 6a b x - 2a +--R (2) -------------------------------------- +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 12 2 8 3 +--R 24a b x log(x) + b x + 6a b x - 2a +--R (3) -------------------------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 995 + +--S 996 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 997 + +)clear all + +--S 998 of 1309 +t0:=x^5/(a+c*x^4) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 998 + +--S 999 of 1309 +r0:=1/2*x^2/c-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(a)/c^(3/2) +--R +--R +--R 2 +-+ +--R +-+ x \|c 2 +-+ +--R - \|a atan(------) + x \|c +--R +-+ +--R \|a +--R (2) --------------------------- +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 2 | a 4 |a +--R +---+ - 2c x |- - + c x - a +-+ |- +--R | a \| c 2 |a \|c 2 +--R |- - log(------------------------) + 2x |- atan(----) + x +--R \| c 4 \|c 2 +--R c x + a x +--R (3) [-----------------------------------------,-------------------] +--R 4c 2c +--R Type: Union(List(Expression(Integer)),...) +--E 1000 + +--S 1001 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | a 4 +--R +---+ - 2c x |- - + c x - a 2 +-+ +--R | a +-+ \| c +-+ x \|c +--R |- - \|c log(------------------------) + 2\|a atan(------) +--R \| c 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R 2 +-+ +-+ |- +--R +-+ x \|c |a +-+ \|c +--R \|a atan(------) + |- \|c atan(----) +--R +-+ \|c 2 +--R \|a x +--R (6) ------------------------------------- +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1004 + +)clear all + +--S 1005 of 1309 +t0:=x^4/(a+c*x^4) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1005 + +--S 1006 of 1309 +r0:=x/c+1/2*a^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))-_ + 1/2*a^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(c^(5/4)*sqrt(2))+_ + 1/4*a^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(c^(5/4)*sqrt(2))-1/4*a^(1/4)*log(a^(1/4)*c^(1/4)*_ + x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - \|a log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R \|a log(- x\|2 \|a \|c + x \|c + \|a ) - 2\|a atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +-+4+-+ +--R - 2\|a atan(----------------) + 4x\|2 \|c +--R 4+-+ +--R \|a +--R / +--R +-+4+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | a | a | a | a +--R - c |- ----- log(4c |- ----- + x + c |- ----- log(- 4c |- ----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 256c \| 256c \| 256c \| 256c +--R + +--R +-------+ +--R | a +--R 4c |- ----- +--R +-------+ 4| 5 +--R | a \| 256c +--R 2c |- ----- atan(------------ + x +--R 4| 5 x +--R \| 256c +--R / +--R c +--R Type: Union(Expression(Integer),...) +--E 1007 + +--S 1008 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R \|a log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | a 4+-+ | a +--R - 4c\|2 |- ----- \|c log(4c |- ----- + x) +--R 4| 5 4| 5 +--R \| 256c \| 256c +--R + +--R +-------+ +-------+ +--R +-+ | a 4+-+ | a +--R 4c\|2 |- ----- \|c log(- 4c |- ----- + x) +--R 4| 5 4| 5 +--R \| 256c \| 256c +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R - \|a log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|a atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-------+ +--R | a +--R 4c |- ----- +--R +-+4+-+ 4+-+ +-------+ 4| 5 +--R 4+-+ x\|2 \|c - \|a +-+ | a 4+-+ \| 256c +--R 2\|a atan(----------------) + 8c\|2 |- ----- \|c atan(------------) +--R 4+-+ 4| 5 x +--R \|a \| 256c +--R / +--R +-+4+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1009 + +)clear all + +--S 1010 of 1309 +t0:=x^3/(a+c*x^4) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1010 + +--S 1011 of 1309 +r0:=1/4*log(a+c*x^4)/c +--R +--R +--R 4 +--R log(c x + a) +--R (2) ------------- +--R 4c +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R log(c x + a) +--R (3) ------------- +--R 4c +--R Type: Union(Expression(Integer),...) +--E 1012 + +--S 1013 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1309 +t0:=x^2/(a+c*x^4) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1015 + +--S 1016 of 1309 +r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_ + 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(3/4)*sqrt(2))+_ + 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2))-_ + 1/4*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) + 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R 2atan(----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R | 1 2 | 1 +--R |- ------- log(64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+ +---------+3 +--R | 1 2 | 1 +--R - |- ------- log(- 64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+3 +--R 2 | 1 +--R 64a c |- ------- +--R +---------+ 4| 3 +--R | 1 \| 256a c +--R 2 |- ------- atan(-------------------) +--R 4| 3 x +--R \| 256a c +--R Type: Union(Expression(Integer),...) +--E 1017 + +--S 1018 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------+ +---------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 +--R 4\|2 |- ------- \|a \|c log(64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +---------+ +---------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 +--R - 4\|2 |- ------- \|a \|c log(- 64a c |- ------- + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+3 +--R 2 | 1 +--R 64a c |- ------- +--R +---------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 256a c +--R 8\|2 |- ------- \|a \|c atan(-------------------) +--R 4| 3 x +--R \| 256a c +--R / +--R +-+4+-+4+-+3 +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1309 +t0:=x/(a+c*x^4) +--R +--R +--R x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1020 + +--S 1021 of 1309 +r0:=1/2*atan(x^2*sqrt(c)/sqrt(a))/(sqrt(a)*sqrt(c)) +--R +--R +--R 2 +-+ +--R x \|c +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 2\|a \|c +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +-----+ 2 +--R (c x - a)\|- a c + 2a c x 2 +---+ +--R log(----------------------------) x \|a c +--R 4 atan(--------) +--R c x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 4\|- a c 2\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1022 + +--S 1023 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 2\|a \|c \|a c +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1026 + +)clear all + +--S 1027 of 1309 +t0:=1/(a+c*x^4) +--R +--R +--R 1 +--R (1) -------- +--R 4 +--R c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1027 + +--S 1028 of 1309 +r0:=-1/2*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))+_ + 1/2*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(1/4)*sqrt(2))-_ + 1/4*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2))+1/4*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R +-+4+-+4+-+ 2 +-+ +-+ +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) - log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R x\|2 \|c + \|a x\|2 \|c - \|a +--R 2atan(----------------) + 2atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R +-+4+-+3 4+-+ +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--------+ +--------+ +--R | 1 | 1 | 1 | 1 +--R |- ------ log(4a |- ------ + x) - |- ------ log(- 4a |- ------ + x) +--R 4| 3 4| 3 4| 3 4| 3 +--R \| 256a c \| 256a c \| 256a c \| 256a c +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +--------+ 4| 3 +--R | 1 \| 256a c +--R - 2 |- ------ atan(-------------) +--R 4| 3 x +--R \| 256a c +--R Type: Union(Expression(Integer),...) +--E 1029 + +--S 1030 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R 4\|2 |- ------ \|a \|c log(4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +--------+ +--------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R - 4\|2 |- ------ \|a \|c log(- 4a |- ------ + x) +--R 4| 3 4| 3 +--R \| 256a c \| 256a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +--------+ +--R | 1 +--R 4a |- ------ +--R +-+4+-+ 4+-+ +--------+ 4| 3 +--R x\|2 \|c - \|a +-+ | 1 4+-+3 4+-+ \| 256a c +--R - 2atan(----------------) - 8\|2 |- ------ \|a \|c atan(-------------) +--R 4+-+ 4| 3 x +--R \|a \| 256a c +--R / +--R +-+4+-+3 4+-+ +--R 4\|2 \|a \|c +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1309 +t0:=1/(x*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ---------- +--R 5 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1032 + +--S 1033 of 1309 +r0:=log(x)/a-1/4*log(a+c*x^4)/a +--R +--R +--R 4 +--R - log(c x + a) + 4log(x) +--R (2) ------------------------- +--R 4a +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - log(c x + a) + 4log(x) +--R (3) ------------------------- +--R 4a +--R Type: Union(Expression(Integer),...) +--E 1034 + +--S 1035 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1036 + +)clear all + +--S 1037 of 1309 +t0:=1/(x^2*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 2 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1037 + +--S 1038 of 1309 +r0:=(-1)/(a*x)+1/2*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_ + sqrt(2))-1/2*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*_ + sqrt(2))-1/4*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2))+1/4*c^(1/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R x\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - x\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c + \|a 4+-+ x\|2 \|c - \|a +-+4+-+ +--R - 2x\|c atan(----------------) - 2x\|c atan(----------------) - 4\|2 \|a +--R 4+-+ 4+-+ +--R \|a \|a +--R / +--R +-+4+-+ +--R 4a x\|2 \|a +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+3 +--R | c 4 | c +--R - a x |- ----- log(64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+3 +--R | c 4 | c +--R a x |- ----- log(- 64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+3 +--R 4 | c +--R 64a |- ----- +--R +-------+ 4| 5 +--R | c \| 256a +--R - 2a x |- ----- atan(--------------- - 1 +--R 4| 5 c x +--R \| 256a +--R / +--R a x +--R Type: Union(Expression(Integer),...) +--E 1039 + +--S 1040 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+3 +--R +-+ | c 4+-+ 4 | c +--R - 4a\|2 |- ----- \|a log(64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+3 +--R +-+ | c 4+-+ 4 | c +--R 4a\|2 |- ----- \|a log(- 64a |- ----- + c x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R \|c log(- x\|2 \|a \|c + x \|c + \|a ) + 2\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-------+3 +--R 4 | c +--R 64a |- ----- +--R +-+4+-+ 4+-+ +-------+ 4| 5 +--R 4+-+ x\|2 \|c - \|a +-+ | c 4+-+ \| 256a +--R 2\|c atan(----------------) - 8a\|2 |- ----- \|a atan(---------------) +--R 4+-+ 4| 5 c x +--R \|a \| 256a +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1041 + +)clear all + +--S 1042 of 1309 +t0:=1/(x^3*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 7 3 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1042 + +--S 1043 of 1309 +r0:=(-1/2)/(a*x^2)-1/2*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(3/2) +--R +--R +--R 2 +-+ +--R 2 +-+ x \|c +-+ +--R - x \|c atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 2 +-+ +--R 2a x \|a +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 2 | c 4 |c +--R +---+ - 2a x |- - + c x - a +-+ a |- +--R 2 | c \| a 2 |c \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 4 \|a 2 +--R c x + a c x +--R (3) [-----------------------------------------,---------------------] +--R 2 2 +--R 4a x 2a x +--R Type: Union(List(Expression(Integer)),...) +--E 1044 + +--S 1045 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R |- - \|a log(------------------------) + 2\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R \|c atan(------) + \|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) -------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1048 + +)clear all + +--S 1049 of 1309 +t0:=1/(x^4*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 4 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1049 + +--S 1050 of 1309 +r0:=(-1/3)/(a*x^3)+1/2*c^(3/4)*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))-1/2*c^(3/4)*atan(1+c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*sqrt(2))+1/4*c^(3/4)*_ + log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*_ + sqrt(c))/(a^(7/4)*sqrt(2))-1/4*c^(3/4)*log(a^(1/4)*c^(1/4)*x*_ + sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 3x \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 3x \|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 3 4+-+3 x\|2 \|c + \|a 3 4+-+3 x\|2 \|c - \|a +--R - 6x \|c atan(---------------- - 6x \|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 3 +-+4+-+3 +--R 12a x \|2 \|a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R | 3 | 3 +--R 3 | c 2 | c +--R - 3a x |- ----- log(4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R 3 | c 2 | c +--R 3a x |- ----- log(- 4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +--R | 3 +--R 2 | c +--R +-------+ 4a |- ----- +--R | 3 4| 7 +--R 3 | c \| 256a +--R 6a x |- ----- atan(------------- - 1 +--R 4| 7 c x +--R \| 256a +--R / +--R 3 +--R 3a x +--R Type: Union(Expression(Integer),...) +--E 1051 + +--S 1052 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R \|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R +-+ | c 4+-+3 2 | c +--R - 4a\|2 |- ----- \|a log(4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R | 3 | 3 +--R +-+ | c 4+-+3 2 | c +--R 4a\|2 |- ----- \|a log(- 4a |- ----- + c x) +--R 4| 7 4| 7 +--R \| 256a \| 256a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - \|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 2\|c atan(----------------) + 2\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-------+ +--R | 3 +--R 2 | c +--R +-------+ 4a |- ----- +--R | 3 4| 7 +--R +-+ | c 4+-+3 \| 256a +--R 8a\|2 |- ----- \|a atan(-------------) +--R 4| 7 c x +--R \| 256a +--R / +--R +-+4+-+3 +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1053 + +)clear all + +--S 1054 of 1309 +t0:=1/(x^5*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 5 +--R c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1054 + +--S 1055 of 1309 +r0:=(-1/4)/(a*x^4)-c*log(x)/a^2+1/4*c*log(a+c*x^4)/a^2 +--R +--R +--R 4 4 4 +--R c x log(c x + a) - 4c x log(x) - a +--R (2) ----------------------------------- +--R 2 4 +--R 4a x +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R c x log(c x + a) - 4c x log(x) - a +--R (3) ----------------------------------- +--R 2 4 +--R 4a x +--R Type: Union(Expression(Integer),...) +--E 1056 + +--S 1057 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1309 +t0:=x^7/(a+c*x^4)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1059 + +--S 1060 of 1309 +r0:=1/4*a/(c^2*(a+c*x^4))+1/4*log(a+c*x^4)/c^2 +--R +--R +--R 4 4 +--R (c x + a)log(c x + a) + a +--R (2) --------------------------- +--R 3 4 2 +--R 4c x + 4a c +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R (c x + a)log(c x + a) + a +--R (3) --------------------------- +--R 3 4 2 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1061 + +--S 1062 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1309 +t0:=x^6/(a+c*x^4)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1064 + +--S 1065 of 1309 +r0:=-1/4*x^3/(c*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_ + 3/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(7/4)*sqrt(2))+_ + 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2))-_ + 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 3a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 3a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 3 +-+4+-+4+-+3 +--R - 4x \|2 \|a \|c +--R / +--R 2 4 +-+4+-+4+-+3 +--R (16c x + 16a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+3 +--R 2 4 | 1 5 | 1 +--R (12c x + 12a c) |- --------- log(4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R 2 4 | 1 5 | 1 +--R (- 12c x - 12a c) |- --------- log(- 4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 5 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 7 +--R 2 4 | 1 \| 65536a c 3 +--R (24c x + 24a c) |- --------- atan(----------------------- - x +--R 4| 7 x +--R \| 65536a c +--R / +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1066 + +--S 1067 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 5 | 1 +--R 48c\|2 |- --------- \|a \|c log(4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 5 | 1 +--R - 48c\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+3 +--R 5 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 7 +--R +-+ | 1 4+-+4+-+3 \| 65536a c +--R 96c\|2 |- --------- \|a \|c atan(-----------------------) +--R 4| 7 x +--R \| 65536a c +--R / +--R +-+4+-+4+-+3 +--R 16c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1309 +t0:=x^5/(a+c*x^4)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1069 + +--S 1070 of 1309 +r0:=-1/4*x^2/(c*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(c^(3/2)*sqrt(a)) +--R +--R +--R 2 +-+ +--R 4 x \|c 2 +-+ +-+ +--R (c x + a)atan(------) - x \|a \|c +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 2 4 +-+ +-+ +--R (4c x + 4a c)\|a \|c +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-----+ 2 +--R 4 (c x - a)\|- a c + 2a c x 2 +-----+ +--R (c x + a)log(----------------------------) - 2x \|- a c +--R 4 +--R c x + a +--R [---------------------------------------------------------, +--R 2 4 +-----+ +--R (8c x + 8a c)\|- a c +--R 2 +---+ +--R 4 x \|a c 2 +---+ +--R (c x + a)atan(--------) - x \|a c +--R a +--R -----------------------------------] +--R 2 4 +---+ +--R (4c x + 4a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1071 + +--S 1072 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1075 + +)clear all + +--S 1076 of 1309 +t0:=x^4/(a+c*x^4)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1076 + +--S 1077 of 1309 +r0:=-1/4*x/(c*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(3/4)*c^(5/4)*sqrt(2))+_ + 1/8*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*_ + c^(5/4)*sqrt(2))-1/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2))+_ + 1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (c x + a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- c x - a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 4+-+ +--R - 4x\|2 \|a \|c +--R / +--R 2 4 +-+4+-+3 4+-+ +--R (16c x + 16a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+ +--R 2 4 | 1 | 1 +--R (4c x + 4a c) |- --------- log(16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+ +--R 2 4 | 1 | 1 +--R (- 4c x - 4a c) |- --------- log(- 16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +--R | 1 +--R 16a c |- --------- +--R +-----------+ 4| 3 5 +--R 2 4 | 1 \| 65536a c +--R (- 8c x - 8a c) |- --------- atan(------------------- - x +--R 4| 3 5 x +--R \| 65536a c +--R / +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1078 + +--S 1079 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R 16c\|2 |- --------- \|a \|c log(16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 4+-+3 4+-+ | 1 +--R - 16c\|2 |- --------- \|a \|c log(- 16a c |- --------- + x) +--R 4| 3 5 4| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+ +--R | 1 +--R 16a c |- --------- +--R +-----------+ 4| 3 5 +--R +-+ | 1 4+-+3 4+-+ \| 65536a c +--R - 32c\|2 |- --------- \|a \|c atan(-------------------) +--R 4| 3 5 x +--R \| 65536a c +--R / +--R +-+4+-+3 4+-+ +--R 16c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1080 + +)clear all + +--S 1081 of 1309 +t0:=x^3/(a+c*x^4)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1081 + +--S 1082 of 1309 +r0:=(-1/4)/(c*(a+c*x^4)) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - ---------- +--R 2 4 +--R c x + a c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1082 + +--S 1083 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 4 +--R 4c x + 4a c +--R Type: Union(Expression(Integer),...) +--E 1083 + +--S 1084 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1309 +t0:=x^2/(a+c*x^4)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1086 + +--S 1087 of 1309 +r0:=1/4*x^3/(a*(a+c*x^4))-1/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_ + (a^(5/4)*c^(3/4)*sqrt(2))+1/8*atan(1+c^(1/4)*x*sqrt(2)/_ + a^(1/4))/(a^(5/4)*c^(3/4)*sqrt(2))+1/16*log(-a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(3/4)*_ + sqrt(2))-1/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(5/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- c x - a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (c x + a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (2c x + 2a)atan(----------------) + (2c x + 2a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R 3 +-+4+-+4+-+3 +--R 4x \|2 \|a \|c +--R / +--R 4 2 +-+4+-+4+-+3 +--R (16a c x + 16a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+3 +--R 4 2 | 1 4 2 | 1 +--R (4a c x + 4a ) |- --------- log(4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R 4 2 | 1 4 2 | 1 +--R (- 4a c x - 4a ) |- --------- log(- 4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 4 2 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 5 3 +--R 4 2 | 1 \| 65536a c 3 +--R (8a c x + 8a ) |- --------- atan(----------------------- + x +--R 4| 5 3 x +--R \| 65536a c +--R / +--R 4 2 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 4 2 | 1 +--R 16a\|2 |- --------- \|a \|c log(4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 4+-+4+-+3 4 2 | 1 +--R - 16a\|2 |- --------- \|a \|c log(- 4096a c |- --------- + x) +--R 4| 5 3 4| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - log(- x\|2 \|a \|c + x \|c + \|a ) - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 2atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-----------+3 +--R 4 2 | 1 +--R 4096a c |- --------- +--R +-----------+ 4| 5 3 +--R +-+ | 1 4+-+4+-+3 \| 65536a c +--R 32a\|2 |- --------- \|a \|c atan(-----------------------) +--R 4| 5 3 x +--R \| 65536a c +--R / +--R +-+4+-+4+-+3 +--R 16a\|2 \|a \|c +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1309 +t0:=x/(a+c*x^4)^2 +--R +--R +--R x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1091 + +--S 1092 of 1309 +r0:=1/4*x^2/(a*(a+c*x^4))+1/4*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*sqrt(c)) +--R +--R +--R 2 +-+ +--R 4 x \|c 2 +-+ +-+ +--R (c x + a)atan(------) + x \|a \|c +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 4 2 +-+ +-+ +--R (4a c x + 4a )\|a \|c +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-----+ 2 +--R 4 (c x - a)\|- a c + 2a c x 2 +-----+ +--R (c x + a)log(----------------------------) + 2x \|- a c +--R 4 +--R c x + a +--R [---------------------------------------------------------, +--R 4 2 +-----+ +--R (8a c x + 8a )\|- a c +--R 2 +---+ +--R 4 x \|a c 2 +---+ +--R (c x + a)atan(--------) + x \|a c +--R a +--R -----------------------------------] +--R 4 2 +---+ +--R (4a c x + 4a )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1093 + +--S 1094 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4a\|a \|c \|a c +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1097 + +)clear all + +--S 1098 of 1309 +t0:=1/(a+c*x^4)^2 +--R +--R +--R 1 +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1098 + +--S 1099 of 1309 +r0:=1/4*x/(a*(a+c*x^4))-3/8*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/_ + (a^(7/4)*c^(1/4)*sqrt(2))+3/8*atan(1+c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(7/4)*c^(1/4)*sqrt(2))-_ + 3/16*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(7/4)*c^(1/4)*sqrt(2))+_ + 3/16*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/_ + (a^(7/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 3a)log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 4 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 3a)log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4 x\|2 \|c + \|a 4 x\|2 \|c - \|a +--R (6c x + 6a)atan(----------------) + (6c x + 6a)atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 4+-+ +--R 4x\|2 \|a \|c +--R / +--R 4 2 +-+4+-+3 4+-+ +--R (16a c x + 16a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R 4 2 | 1 2 | 1 +--R (12a c x + 12a ) |- -------- log(16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R 4 2 | 1 2 | 1 +--R (- 12a c x - 12a ) |- -------- log(- 16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +--R 2 | 1 +--R 16a |- -------- +--R +----------+ 4| 7 +--R 4 2 | 1 \| 65536a c +--R (- 24a c x - 24a ) |- -------- atan(----------------- + x +--R 4| 7 x +--R \| 65536a c +--R / +--R 4 2 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1100 + +--S 1101 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 48a\|2 |- -------- \|a \|c log(16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R - 48a\|2 |- -------- \|a \|c log(- 16a |- -------- + x) +--R 4| 7 4| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +----------+ +--R 2 | 1 +--R 16a |- -------- +--R +----------+ 4| 7 +--R +-+ | 1 4+-+3 4+-+ \| 65536a c +--R - 96a\|2 |- -------- \|a \|c atan(-----------------) +--R 4| 7 x +--R \| 65536a c +--R / +--R +-+4+-+3 4+-+ +--R 16a\|2 \|a \|c +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1102 + +)clear all + +--S 1103 of 1309 +t0:=1/(x*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 9 5 2 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1103 + +--S 1104 of 1309 +r0:=1/4/(a*(a+c*x^4))+log(x)/a^2-1/4*log(a+c*x^4)/a^2 +--R +--R +--R 4 4 4 +--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 4 3 +--R 4a c x + 4a +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R (- c x - a)log(c x + a) + (4c x + 4a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 4 3 +--R 4a c x + 4a +--R Type: Union(Expression(Integer),...) +--E 1105 + +--S 1106 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1107 + +)clear all + +--S 1108 of 1309 +t0:=1/(x^2*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 10 6 2 2 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1108 + +--S 1109 of 1309 +r0:=(-5/4)/(a^2*x)+1/4/(a*x*(a+c*x^4))+5/8*c^(1/4)*atan(1-c^(1/4)*x*_ + sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-5/8*c^(1/4)*_ + atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*sqrt(2))-_ + 5/16*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2))+5/16*c^(1/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*sqrt(2)) +--R +--R +--R (2) +--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 5a x)\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 5 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 5a x)\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 5 4+-+ x\|2 \|c + \|a +--R (- 10c x - 10a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 5 4+-+ x\|2 \|c - \|a 4 +-+4+-+ +--R (- 10c x - 10a x)\|c atan(----------------) + (- 20c x - 16a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 5 3 +-+4+-+ +--R (16a c x + 16a x)\|2 \|a +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+3 +--R 2 5 3 | 625c 7 | 625c +--R (- 4a c x - 4a x) |- ------- log(4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+3 +--R 2 5 3 | 625c 7 | 625c +--R (4a c x + 4a x) |- ------- log(- 4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+3 +--R 7 | 625c +--R 4096a |- ------- +--R +---------+ 4| 9 +--R 2 5 3 | 625c \| 65536a 4 +--R (- 8a c x - 8a x) |- ------- atan(------------------- - 5c x - 4a +--R 4| 9 125c x +--R \| 65536a +--R / +--R 2 5 3 +--R 4a c x + 4a x +--R Type: Union(Expression(Integer),...) +--E 1110 + +--S 1111 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - 5\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------+ +---------+3 +--R 2 +-+ | 625c 4+-+ 7 | 625c +--R - 16a \|2 |- ------- \|a log(4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+3 +--R 2 +-+ | 625c 4+-+ 7 | 625c +--R 16a \|2 |- ------- \|a log(- 4096a |- ------- + 125c x) +--R 4| 9 4| 9 +--R \| 65536a \| 65536a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R 5\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 10\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +--R 10\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+3 +--R 7 | 625c +--R 4096a |- ------- +--R +---------+ 4| 9 +--R 2 +-+ | 625c 4+-+ \| 65536a +--R - 32a \|2 |- ------- \|a atan(-------------------) +--R 4| 9 125c x +--R \| 65536a +--R / +--R 2 +-+4+-+ +--R 16a \|2 \|a +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1112 + +)clear all + +--S 1113 of 1309 +t0:=1/(x^3*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 11 7 2 3 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1113 + +--S 1114 of 1309 +r0:=(-3/4)/(a^2*x^2)+1/4/(a*x^2*(a+c*x^4))-_ + 3/4*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(5/2) +--R +--R +--R 2 +-+ +--R 6 2 +-+ x \|c 4 +-+ +--R (- 3c x - 3a x )\|c atan(------) + (- 3c x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 6 3 2 +-+ +--R (4a c x + 4a x )\|a +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a +--R 6 2 | c \| a 4 +--R (3c x + 3a x ) |- - log(------------------------) - 6c x - 4a +--R \| a 4 +--R c x + a +--R [---------------------------------------------------------------, +--R 2 6 3 2 +--R 8a c x + 8a x +--R +-+ +--R |c +--R +-+ a |- +--R 6 2 |c \|a 4 +--R (3c x + 3a x ) |- atan(-----) - 3c x - 2a +--R \|a 2 +--R c x +--R -------------------------------------------] +--R 2 6 3 2 +--R 4a c x + 4a x +--R Type: Union(List(Expression(Integer)),...) +--E 1115 + +--S 1116 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R 3 |- - \|a log(------------------------ + 6\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R 3\|c atan(------) + 3\|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) ---------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1309 +t0:=1/(x^4*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 12 8 2 4 +--R c x + 2a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1120 + +--S 1121 of 1309 +r0:=(-7/12)/(a^2*x^3)+1/4/(a*x^3*(a+c*x^4))+7/8*c^(3/4)*_ + atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*sqrt(2))-_ + 7/8*c^(3/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*_ + sqrt(2))+7/16*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2))-7/16*c^(3/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 21a x )\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 7 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 21a x )\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 7 3 4+-+3 x\|2 \|c + \|a +--R (- 42c x - 42a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 7 3 4+-+3 x\|2 \|c - \|a 4 +-+4+-+3 +--R (- 42c x - 42a x )\|c atan(----------------) + (- 28c x - 16a)\|2 \|a +--R 4+-+ +--R \|a +--R / +--R 2 7 3 3 +-+4+-+3 +--R (48a c x + 48a x )\|2 \|a +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 7 3 3 | 2401c 3 | 2401c +--R (- 12a c x - 12a x ) |- -------- log(16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 7 3 3 | 2401c 3 | 2401c +--R (12a c x + 12a x ) |- -------- log(- 16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R 3 | 2401c +--R +----------+ 16a |- -------- +--R | 3 4| 11 +--R 2 7 3 3 | 2401c \| 65536a 4 +--R (24a c x + 24a x ) |- -------- atan(----------------- - 7c x - 4a +--R 4| 11 7c x +--R \| 65536a +--R / +--R 2 7 3 3 +--R 12a c x + 12a x +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 7\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 +-+ | 2401c 4+-+3 3 | 2401c +--R - 16a \|2 |- -------- \|a log(16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+ +--R | 3 | 3 +--R 2 +-+ | 2401c 4+-+3 3 | 2401c +--R 16a \|2 |- -------- \|a log(- 16a |- -------- + 7c x) +--R 4| 11 4| 11 +--R \| 65536a \| 65536a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 7\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 14\|c atan(----------------) + 14\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +----------+ +--R | 3 +--R 3 | 2401c +--R +----------+ 16a |- -------- +--R | 3 4| 11 +--R 2 +-+ | 2401c 4+-+3 \| 65536a +--R 32a \|2 |- -------- \|a atan(-----------------) +--R 4| 11 7c x +--R \| 65536a +--R / +--R 2 +-+4+-+3 +--R 16a \|2 \|a +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1309 +t0:=x^11/(a+c*x^4)^3 +--R +--R +--R 11 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1125 + +--S 1126 of 1309 +r0:=-1/8*a^2/(c^3*(a+c*x^4)^2)+1/2*a/(c^3*(a+c*x^4))+1/4*log(a+c*x^4)/c^3 +--R +--R +--R 2 8 4 2 4 4 2 +--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a +--R (2) ---------------------------------------------------- +--R 5 8 4 4 2 3 +--R 8c x + 16a c x + 8a c +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 4 4 2 +--R (2c x + 4a c x + 2a )log(c x + a) + 4a c x + 3a +--R (3) ---------------------------------------------------- +--R 5 8 4 4 2 3 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1309 +t0:=x^10/(a+c*x^4)^3 +--R +--R +--R 10 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1130 + +--S 1131 of 1309 +r0:=-1/8*x^7/(c*(a+c*x^4)^2)-7/32*x^3/(c^2*(a+c*x^4))-_ + 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*c^(11/4)*_ + sqrt(2))+21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(1/4)*_ + c^(11/4)*sqrt(2))+21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+_ + sqrt(a)+x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2))-21/128*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(1/4)*c^(11/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 42a c x - 21a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 42a c x + 21a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (- 44c x - 28a x )\|2 \|a \|c +--R / +--R 4 8 3 4 2 2 +-+4+-+4+-+3 +--R (128c x + 256a c x + 128a c )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (672c x + 1344a c x + 672a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 672c x - 1344a c x - 672a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(- 2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +----------------+ +--R 4 8 3 4 2 2 | 1 +--R (1344c x + 2688a c x + 1344a c ) |- -------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R 2097152a c |- -------------- +--R 4| 11 +--R \| 268435456a c +--R atan(-------------------------------) +--R x +--R + +--R 7 3 +--R - 11c x - 7a x +--R / +--R 4 8 3 4 2 2 +--R 32c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 21log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +----------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 2688c \|2 |- -------------- \|a \|c +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R - +--R +----------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 2688c \|2 |- -------------- \|a \|c +--R 4| 11 +--R \| 268435456a c +--R * +--R +----------------+3 +--R 8 | 1 +--R log(- 2097152a c |- -------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +----------------+3 +--R 8 | 1 +--R 2097152a c |- -------------- +--R +----------------+ 4| 11 +--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 5376c \|2 |- -------------- \|a \|c atan(-------------------------------) +--R 4| 11 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+4+-+3 +--R 128c \|2 \|a \|c +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1309 +t0:=x^9/(a+c*x^4)^3 +--R +--R +--R 9 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1135 + +--S 1136 of 1309 +r0:=-1/8*x^6/(c*(a+c*x^4)^2)-3/16*x^2/(c^2*(a+c*x^4))+_ + 3/16*atan(x^2*sqrt(c)/sqrt(a))/(c^(5/2)*sqrt(a)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (3c x + 6a c x + 3a )atan(------) + (- 5c x - 3a x )\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------- +--R 4 8 3 4 2 2 +-+ +-+ +--R (16c x + 32a c x + 16a c )\|a \|c +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (3c x + 6a c x + 3a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (- 10c x - 6a x )\|- a c +--R / +--R 4 8 3 4 2 2 +-----+ +--R (32c x + 64a c x + 32a c )\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (3c x + 6a c x + 3a )atan(--------) + (- 5c x - 3a x )\|a c +--R a +--R ---------------------------------------------------------------] +--R 4 8 3 4 2 2 +---+ +--R (16c x + 32a c x + 16a c )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1137 + +--S 1138 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 32c \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R 3\|a \|c atan(--------) - 3\|a c atan(------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16c \|a \|c \|a c +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1141 + +)clear all + +--S 1142 of 1309 +t0:=x^8/(a+c*x^4)^3 +--R +--R +--R 8 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1142 + +--S 1143 of 1309 +r0:=-1/8*x^5/(c*(a+c*x^4)^2)-5/32*x/(c^2*(a+c*x^4))-_ + 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))+_ + 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(3/4)*c^(9/4)*sqrt(2))-_ + 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2))+_ + 5/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(3/4)*c^(9/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 10a c x + 5a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 10a c x - 5a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (- 36c x - 20a x)\|2 \|a \|c +--R / +--R 4 8 3 4 2 2 +-+4+-+3 4+-+ +--R (128c x + 256a c x + 128a c )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (160c x + 320a c x + 160a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 160c x - 320a c x - 160a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +---------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 320c x - 640a c x - 320a c ) |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R 4| 3 9 +--R \| 268435456a c +--R atan(-------------------------) +--R x +--R + +--R 5 +--R - 9c x - 5a x +--R / +--R 4 8 3 4 2 2 +--R 32c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1144 + +--S 1145 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 5log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 640c \|2 |- ------------- \|a \|c log(128a c |- ------------- + x) +--R 4| 3 9 4| 3 9 +--R \| 268435456a c \| 268435456a c +--R + +--R - +--R +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ +--R 640c \|2 |- ------------- \|a \|c +--R 4| 3 9 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 3 9 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R +---------------+ 4| 3 9 +--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 1280c \|2 |- ------------- \|a \|c atan(-------------------------) +--R 4| 3 9 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+3 4+-+ +--R 128c \|2 \|a \|c +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1146 + +)clear all + +--S 1147 of 1309 +t0:=x^7/(a+c*x^4)^3 +--R +--R +--R 7 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1147 + +--S 1148 of 1309 +r0:=1/8*x^8/(a*(a+c*x^4)^2) +--R +--R +--R 1 8 +--R - x +--R 8 +--R (2) --------------------- +--R 2 8 2 4 3 +--R a c x + 2a c x + a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1148 + +--S 1149 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 2c x - a +--R (3) ------------------------ +--R 4 8 3 4 2 2 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1149 + +--S 1150 of 1309 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ----- +--R 2 +--R 8a c +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1151 + +)clear all + +--S 1152 of 1309 +t0:=x^6/(a+c*x^4)^3 +--R +--R +--R 6 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1152 + +--S 1153 of 1309 +r0:=-1/8*x^3/(c*(a+c*x^4)^2)+3/32*x^3/(a*c*(a+c*x^4))-_ + 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_ + 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(5/4)*c^(7/4)*sqrt(2))+_ + 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2))-3/128*log(a^(1/4)*c^(1/4)*_ + x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(5/4)*c^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 6a c x - 3a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 6a c x + 3a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (12c x - 4a x )\|2 \|a \|c +--R / +--R 3 8 2 2 4 3 +-+4+-+4+-+3 +--R (128a c x + 256a c x + 128a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (96a c x + 192a c x + 96a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 96a c x - 192a c x - 96a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (192a c x + 384a c x + 192a c) |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R 2097152a c |- ------------- +--R 4| 5 7 +--R \| 268435456a c +--R atan(------------------------------) +--R x +--R + +--R 7 3 +--R 3c x - a x +--R / +--R 3 8 2 2 4 3 +--R 32a c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1154 + +--S 1155 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +--R +-+ | 1 4+-+4+-+3 +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R - +--R +---------------+ +--R +-+ | 1 4+-+4+-+3 +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 5 7 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 4 5 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 5 7 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+3 +--R 4 5 | 1 +--R 2097152a c |- ------------- +--R +---------------+ 4| 5 7 +--R +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 768a c\|2 |- ------------- \|a \|c atan(------------------------------) +--R 4| 5 7 x +--R \| 268435456a c +--R / +--R +-+4+-+4+-+3 +--R 128a c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1156 + +)clear all + +--S 1157 of 1309 +t0:=x^5/(a+c*x^4)^3 +--R +--R +--R 5 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1157 + +--S 1158 of 1309 +r0:=-1/8*x^2/(c*(a+c*x^4)^2)+1/16*x^2/(a*c*(a+c*x^4))+_ + 1/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(3/2)*c^(3/2)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (c x + 2a c x + a )atan(------) + (c x - a x )\|a \|c +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 3 8 2 2 4 3 +-+ +-+ +--R (16a c x + 32a c x + 16a c)\|a \|c +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (c x + 2a c x + a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (2c x - 2a x )\|- a c +--R / +--R 3 8 2 2 4 3 +-----+ +--R (32a c x + 64a c x + 32a c)\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (c x + 2a c x + a )atan(--------) + (c x - a x )\|a c +--R a +--R ---------------------------------------------------------] +--R 3 8 2 2 4 3 +---+ +--R (16a c x + 32a c x + 16a c)\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1159 + +--S 1160 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R \|a \|c log(----------------------------) - 2\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 32a c\|- a c \|a \|c +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R \|a \|c atan(--------) - \|a c atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 16a c\|a \|c \|a c +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1163 + +)clear all + +--S 1164 of 1309 +t0:=x^4/(a+c*x^4)^3 +--R +--R +--R 4 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1164 + +--S 1165 of 1309 +r0:=-1/8*x/(c*(a+c*x^4)^2)+1/32*x/(a*c*(a+c*x^4))-_ + 3/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))+_ + 3/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(7/4)*c^(5/4)*sqrt(2))-_ + 3/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2))+3/128*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(7/4)*c^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (3c x + 6a c x + 3a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 3c x - 6a c x - 3a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (6c x + 12a c x + 6a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (4c x - 12a x)\|2 \|a \|c +--R / +--R 3 8 2 2 4 3 +-+4+-+3 4+-+ +--R (128a c x + 256a c x + 128a c)\|2 \|a \|c +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (96a c x + 192a c x + 96a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 96a c x - 192a c x - 96a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +---------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 192a c x - 384a c x - 192a c) |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R 4| 7 5 +--R \| 268435456a c +--R atan(------------------------) +--R x +--R + +--R 5 +--R c x - 3a x +--R / +--R 3 8 2 2 4 3 +--R 32a c x + 64a c x + 32a c +--R Type: Union(Expression(Integer),...) +--E 1166 + +--S 1167 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 3log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R +-+ | 1 4+-+3 4+-+ 2 | 1 +--R 384a c\|2 |- ------------- \|a \|c log(128a c |- ------------- + x) +--R 4| 7 5 4| 7 5 +--R \| 268435456a c \| 268435456a c +--R + +--R - +--R +---------------+ +--R +-+ | 1 4+-+3 4+-+ +--R 384a c\|2 |- ------------- \|a \|c +--R 4| 7 5 +--R \| 268435456a c +--R * +--R +---------------+ +--R 2 | 1 +--R log(- 128a c |- ------------- + x) +--R 4| 7 5 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 3log(- x\|2 \|a \|c + x \|c + \|a ) - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 6atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 2 | 1 +--R 128a c |- ------------- +--R +---------------+ 4| 7 5 +--R +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 768a c\|2 |- ------------- \|a \|c atan(------------------------) +--R 4| 7 5 x +--R \| 268435456a c +--R / +--R +-+4+-+3 4+-+ +--R 128a c\|2 \|a \|c +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1168 + +)clear all + +--S 1169 of 1309 +t0:=x^3/(a+c*x^4)^3 +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1169 + +--S 1170 of 1309 +r0:=(-1/8)/(c*(a+c*x^4)^2) +--R +--R +--R 1 +--R - +--R 8 +--R (2) - -------------------- +--R 3 8 2 4 2 +--R c x + 2a c x + a c +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1170 + +--S 1171 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 8 2 4 2 +--R 8c x + 16a c x + 8a c +--R Type: Union(Expression(Integer),...) +--E 1171 + +--S 1172 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1173 + +)clear all + +--S 1174 of 1309 +t0:=x^2/(a+c*x^4)^3 +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1174 + +--S 1175 of 1309 +r0:=1/8*x^3/(a*(a+c*x^4)^2)+5/32*x^3/(a^2*(a+c*x^4))-_ + 5/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_ + 5/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(9/4)*c^(3/4)*sqrt(2))+_ + 5/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2))-5/128*log(a^(1/4)*_ + c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(9/4)*c^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 5c x - 10a c x - 5a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (5c x + 10a c x + 5a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (10c x + 20a c x + 10a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 7 3 +-+4+-+4+-+3 +--R (20c x + 36a x )\|2 \|a \|c +--R / +--R 2 2 8 3 4 4 +-+4+-+4+-+3 +--R (128a c x + 256a c x + 128a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (160a c x + 320a c x + 160a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 160a c x - 320a c x - 160a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (320a c x + 640a c x + 320a ) |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R 2097152a c |- ------------- +--R 4| 9 3 +--R \| 268435456a c +--R atan(------------------------------) +--R x +--R + +--R 7 3 +--R 5c x + 9a x +--R / +--R 2 2 8 3 4 4 +--R 32a c x + 64a c x + 32a +--R Type: Union(Expression(Integer),...) +--E 1176 + +--S 1177 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R 5log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 640a \|2 |- ------------- \|a \|c +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R - +--R +---------------+ +--R 2 +-+ | 1 4+-+4+-+3 +--R 640a \|2 |- ------------- \|a \|c +--R 4| 9 3 +--R \| 268435456a c +--R * +--R +---------------+3 +--R 7 2 | 1 +--R log(- 2097152a c |- ------------- + x) +--R 4| 9 3 +--R \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R - 5log(- x\|2 \|a \|c + x \|c + \|a ) - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 10atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+3 +--R 7 2 | 1 +--R 2097152a c |- ------------- +--R +---------------+ 4| 9 3 +--R 2 +-+ | 1 4+-+4+-+3 \| 268435456a c +--R 1280a \|2 |- ------------- \|a \|c atan(------------------------------) +--R 4| 9 3 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+4+-+3 +--R 128a \|2 \|a \|c +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1178 + +)clear all + +--S 1179 of 1309 +t0:=x/(a+c*x^4)^3 +--R +--R +--R x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1179 + +--S 1180 of 1309 +r0:=1/8*x^2/(a*(a+c*x^4)^2)+3/16*x^2/(a^2*(a+c*x^4))+_ + 3/16*atan(x^2*sqrt(c)/sqrt(a))/(a^(5/2)*sqrt(c)) +--R +--R +--R 2 +-+ +--R 2 8 4 2 x \|c 6 2 +-+ +-+ +--R (3c x + 6a c x + 3a )atan(------) + (3c x + 5a x )\|a \|c +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R 2 2 8 3 4 4 +-+ +-+ +--R (16a c x + 32a c x + 16a )\|a \|c +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 +-----+ 2 +--R 2 8 4 2 (c x - a)\|- a c + 2a c x +--R (3c x + 6a c x + 3a )log(----------------------------) +--R 4 +--R c x + a +--R + +--R 6 2 +-----+ +--R (6c x + 10a x )\|- a c +--R / +--R 2 2 8 3 4 4 +-----+ +--R (32a c x + 64a c x + 32a )\|- a c +--R , +--R 2 +---+ +--R 2 8 4 2 x \|a c 6 2 +---+ +--R (3c x + 6a c x + 3a )atan(--------) + (3c x + 5a x )\|a c +--R a +--R -------------------------------------------------------------] +--R 2 2 8 3 4 4 +---+ +--R (16a c x + 32a c x + 16a )\|a c +--R Type: Union(List(Expression(Integer)),...) +--E 1181 + +--S 1182 of 1309 +m0a:=a0.1-r0 +--R +--R +--R 4 +-----+ 2 2 +-+ +--R +-+ +-+ (c x - a)\|- a c + 2a c x +-----+ x \|c +--R 3\|a \|c log(----------------------------) - 6\|- a c atan(------) +--R 4 +-+ +--R c x + a \|a +--R (4) ------------------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 32a \|- a c \|a \|c +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1309 +m0b:=a0.2-r0 +--R +--R +--R 2 +---+ 2 +-+ +--R +-+ +-+ x \|a c +---+ x \|c +--R 3\|a \|c atan(--------) - 3\|a c atan(------) +--R a +-+ +--R \|a +--R (6) --------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 16a \|a \|c \|a c +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1309 +t0:=1/(a+c*x^4)^3 +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1186 + +--S 1187 of 1309 +r0:=1/8*x/(a*(a+c*x^4)^2)+7/32*x/(a^2*(a+c*x^4))-_ + 21/64*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))+_ + 21/64*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(11/4)*c^(1/4)*sqrt(2))-_ + 21/128*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2))+_ + 21/128*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(11/4)*c^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (21c x + 42a c x + 21a )log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 8 4 2 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 21c x - 42a c x - 21a )log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c + \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 8 4 2 x\|2 \|c - \|a +--R (42c x + 84a c x + 42a )atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 5 +-+4+-+3 4+-+ +--R (28c x + 44a x)\|2 \|a \|c +--R / +--R 2 2 8 3 4 4 +-+4+-+3 4+-+ +--R (128a c x + 256a c x + 128a )\|2 \|a \|c +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (672a c x + 1344a c x + 672a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R log(128a |- ------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 672a c x - 1344a c x - 672a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R log(- 128a |- ------------- + x) +--R 4| 11 +--R \| 268435456a c +--R + +--R +---------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 1344a c x - 2688a c x - 1344a ) |- ------------- +--R 4| 11 +--R \| 268435456a c +--R * +--R +---------------+ +--R 3 | 1 +--R 128a |- ------------- +--R 4| 11 +--R \| 268435456a c +--R atan(-----------------------) +--R x +--R + +--R 5 +--R 7c x + 11a x +--R / +--R 2 2 8 3 4 4 +--R 32a c x + 64a c x + 32a +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+-+ 2 +-+ +-+ +--R - 21log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1 +--R 2688a \|2 |- ------------- \|a \|c log(128a |- ------------- + x) +--R 4| 11 4| 11 +--R \| 268435456a c \| 268435456a c +--R + +--R +---------------+ +---------------+ +--R 2 +-+ | 1 4+-+3 4+-+ 3 | 1 +--R - 2688a \|2 |- ------------- \|a \|c log(- 128a |- ------------- + x) +--R 4| 11 4| 11 +--R \| 268435456a c \| 268435456a c +--R + +--R +-+4+-+ 4+-+ +--R +-+4+-+4+-+ 2 +-+ +-+ x\|2 \|c + \|a +--R 21log(- x\|2 \|a \|c + x \|c + \|a ) - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R x\|2 \|c - \|a +--R - 42atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +---------------+ +--R 3 | 1 +--R 128a |- ------------- +--R +---------------+ 4| 11 +--R 2 +-+ | 1 4+-+3 4+-+ \| 268435456a c +--R - 5376a \|2 |- ------------- \|a \|c atan(-----------------------) +--R 4| 11 x +--R \| 268435456a c +--R / +--R 2 +-+4+-+3 4+-+ +--R 128a \|2 \|a \|c +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1309 +t0:=1/(x*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 13 2 9 2 5 3 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1191 + +--S 1192 of 1309 +r0:=1/8/(a*(a+c*x^4)^2)+1/4/(a^2*(a+c*x^4))+log(x)/a^3-1/4*log(a+c*x^4)/a^3 +--R +--R +--R (2) +--R 2 8 4 2 4 2 8 4 2 +--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x) +--R + +--R 4 2 +--R 2a c x + 3a +--R / +--R 3 2 8 4 4 5 +--R 8a c x + 16a c x + 8a +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 4 2 4 2 8 4 2 +--R (- 2c x - 4a c x - 2a )log(c x + a) + (8c x + 16a c x + 8a )log(x) +--R + +--R 4 2 +--R 2a c x + 3a +--R / +--R 3 2 8 4 4 5 +--R 8a c x + 16a c x + 8a +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1309 +t0:=1/(x^2*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 14 2 10 2 6 3 2 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1196 + +--S 1197 of 1309 +r0:=(-45/32)/(a^3*x)+1/8/(a*x*(a+c*x^4)^2)+9/32/(a^2*x*(a+c*x^4))+_ + 45/64*c^(1/4)*atan(1-c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_ + 45/64*c^(1/4)*atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(13/4)*sqrt(2))-_ + 45/128*c^(1/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(13/4)*sqrt(2))+_ + 45/128*c^(1/4)*log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(13/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (45c x + 90a c x + 45a x)\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 9 5 2 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R (- 45c x - 90a c x - 45a x)\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 9 5 2 4+-+ x\|2 \|c + \|a +--R (- 90c x - 180a c x - 90a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 9 5 2 4+-+ x\|2 \|c - \|a +--R (- 90c x - 180a c x - 90a x)\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 8 4 2 +-+4+-+ +--R (- 180c x - 324a c x - 128a )\|2 \|a +--R / +--R 3 2 9 4 5 5 +-+4+-+ +--R (128a c x + 256a c x + 128a x)\|2 \|a +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (- 32a c x - 64a c x - 32a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (32a c x + 64a c x + 32a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(- 2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 2 9 4 5 5 | 4100625c +--R (- 64a c x - 128a c x - 64a x) |- ------------ +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R 2097152a |- ------------ +--R 4| 13 +--R \| 268435456a +--R atan(----------------------------) +--R 91125c x +--R + +--R 2 8 4 2 +--R - 45c x - 81a c x - 32a +--R / +--R 3 2 9 4 5 5 +--R 32a c x + 64a c x + 32a x +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ +--R - 45\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R - +--R +--------------+ +--R 3 +-+ | 4100625c 4+-+ +--R 128a \|2 |- ------------ \|a +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +--------------+ +--R 3 +-+ | 4100625c 4+-+ +--R 128a \|2 |- ------------ \|a +--R 4| 13 +--R \| 268435456a +--R * +--R +--------------+3 +--R 10 | 4100625c +--R log(- 2097152a |- ------------ + 91125c x) +--R 4| 13 +--R \| 268435456a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ +-+4+-+4+-+ 2 +-+ +-+ 4+-+ x\|2 \|c + \|a +--R 45\|c log(- x\|2 \|a \|c + x \|c + \|a ) + 90\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 4+-+ x\|2 \|c - \|a +--R 90\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +--------------+3 +--R 10 | 4100625c +--R 2097152a |- ------------ +--R +--------------+ 4| 13 +--R 3 +-+ | 4100625c 4+-+ \| 268435456a +--R - 256a \|2 |- ------------ \|a atan(----------------------------) +--R 4| 13 91125c x +--R \| 268435456a +--R / +--R 3 +-+4+-+ +--R 128a \|2 \|a +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1309 +t0:=1/(x^3*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 15 2 11 2 7 3 3 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1201 + +--S 1202 of 1309 +r0:=(-15/16)/(a^3*x^2)+1/8/(a*x^2*(a+c*x^4)^2)+_ + 5/16/(a^2*x^2*(a+c*x^4))-15/16*atan(x^2*sqrt(c)/sqrt(a))*sqrt(c)/a^(7/2) +--R +--R +--R (2) +--R 2 +-+ +--R 2 10 6 2 2 +-+ x \|c +--R (- 15c x - 30a c x - 15a x )\|c atan(------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (- 15c x - 25a c x - 8a )\|a +--R / +--R 3 2 10 4 6 5 2 +-+ +--R (16a c x + 32a c x + 16a x )\|a +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a +--R 2 10 6 2 2 | c \| a +--R (15c x + 30a c x + 15a x ) |- - log(------------------------) +--R \| a 4 +--R c x + a +--R + +--R 2 8 4 2 +--R - 30c x - 50a c x - 16a +--R / +--R 3 2 10 4 6 5 2 +--R 32a c x + 64a c x + 32a x +--R , +--R +-+ +--R |c +--R +-+ a |- +--R 2 10 6 2 2 |c \|a 2 8 4 2 +--R (15c x + 30a c x + 15a x ) |- atan(-----) - 15c x - 25a c x - 8a +--R \|a 2 +--R c x +--R ----------------------------------------------------------------------] +--R 3 2 10 4 6 5 2 +--R 16a c x + 32a c x + 16a x +--R Type: Union(List(Expression(Integer)),...) +--E 1203 + +--S 1204 of 1309 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 2 | c 4 +--R +---+ - 2a x |- - + c x - a 2 +-+ +--R | c +-+ \| a +-+ x \|c +--R 15 |- - \|a log(------------------------ + 30\|c atan(------) +--R \| a 4 +-+ +--R c x + a \|a +--R (4) -------------------------------------------------------------- +--R 3 +-+ +--R 32a \|a +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1309 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |c +--R 2 +-+ +-+ a |- +--R +-+ x \|c +-+ |c \|a +--R 15\|c atan(------) + 15\|a |- atan(-----) +--R +-+ \|a 2 +--R \|a c x +--R (6) ------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1207 + +)clear all + +--S 1208 of 1309 +t0:=1/(x^4*(a+c*x^4)^3) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 3 16 2 12 2 8 3 4 +--R c x + 3a c x + 3a c x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1208 + +--S 1209 of 1309 +r0:=(-77/96)/(a^3*x^3)+1/8/(a*x^3*(a+c*x^4)^2)+_ + 11/32/(a^2*x^3*(a+c*x^4))+77/64*c^(3/4)*atan(1-c^(1/4)*_ + x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))-77/64*c^(3/4)*_ + atan(1+c^(1/4)*x*sqrt(2)/a^(1/4))/(a^(15/4)*sqrt(2))+_ + 77/128*c^(3/4)*log(-a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+_ + x^2*sqrt(c))/(a^(15/4)*sqrt(2))-77/128*c^(3/4)*_ + log(a^(1/4)*c^(1/4)*x*sqrt(2)+sqrt(a)+x^2*sqrt(c))/(a^(15/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (- 231c x - 462a c x - 231a x )\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R 2 11 7 2 3 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R (231c x + 462a c x + 231a x )\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +--R 2 11 7 2 3 4+-+3 x\|2 \|c + \|a +--R (- 462c x - 924a c x - 462a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R +-+4+-+ 4+-+ +--R 2 11 7 2 3 4+-+3 x\|2 \|c - \|a +--R (- 462c x - 924a c x - 462a x )\|c atan(----------------) +--R 4+-+ +--R \|a +--R + +--R 2 8 4 2 +-+4+-+3 +--R (- 308c x - 484a c x - 128a )\|2 \|a +--R / +--R 3 2 11 4 7 5 3 +-+4+-+3 +--R (384a c x + 768a c x + 384a x )\|2 \|a +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (- 96a c x - 192a c x - 96a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R log(128a |- ------------ + 77c x) +--R 4| 15 +--R \| 268435456a +--R + +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (96a c x + 192a c x + 96a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R log(- 128a |- ------------ + 77c x) +--R 4| 15 +--R \| 268435456a +--R + +--R +--------------+ +--R | 3 +--R 3 2 11 4 7 5 3 | 35153041c +--R (192a c x + 384a c x + 192a x ) |- ------------ +--R 4| 15 +--R \| 268435456a +--R * +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R 128a |- ------------ +--R 4| 15 +--R \| 268435456a +--R atan(----------------------) +--R 77c x +--R + +--R 2 8 4 2 +--R - 77c x - 121a c x - 32a +--R / +--R 3 2 11 4 7 5 3 +--R 96a c x + 192a c x + 96a x +--R Type: Union(Expression(Integer),...) +--E 1210 + +--S 1211 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R 77\|c log(x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +--------------+ +--------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c +--R - 128a \|2 |- ------------ \|a log(128a |- ------------ + 77c x) +--R 4| 15 4| 15 +--R \| 268435456a \| 268435456a +--R + +--R +--------------+ +--------------+ +--R | 3 | 3 +--R 3 +-+ | 35153041c 4+-+3 4 | 35153041c +--R 128a \|2 |- ------------ \|a log(- 128a |- ------------ + 77c x) +--R 4| 15 4| 15 +--R \| 268435456a \| 268435456a +--R + +--R 4+-+3 +-+4+-+4+-+ 2 +-+ +-+ +--R - 77\|c log(- x\|2 \|a \|c + x \|c + \|a ) +--R + +--R +-+4+-+ 4+-+ +-+4+-+ 4+-+ +--R 4+-+3 x\|2 \|c + \|a 4+-+3 x\|2 \|c - \|a +--R 154\|c atan(----------------) + 154\|c atan(----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------------+ +--R | 3 +--R 4 | 35153041c +--R +--------------+ 128a |- ------------ +--R | 3 4| 15 +--R 3 +-+ | 35153041c 4+-+3 \| 268435456a +--R 256a \|2 |- ------------ \|a atan(----------------------) +--R 4| 15 77c x +--R \| 268435456a +--R / +--R 3 +-+4+-+3 +--R 128a \|2 \|a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1212 + +)clear all + +--S 1213 of 1309 +t0:=x^4/(2+3*x^4) +--R +--R +--R 4 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1213 + +--S 1214 of 1309 +r0:=1/3*x+1/6*atan(1-6^(1/4)*x)/6^(1/4)-1/6*atan(1+6^(1/4)*x)/6^(1/4)+_ + 1/12*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)-_ + 1/12*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ +--R - 2atan(x\|6 + 1) - 2atan(x\|6 - 1) + 4x\|6 +--R / +--R 4+-+ +--R 12\|6 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 4+--+2 +-+4+--+ +--R - \|2 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+ 2 4+--+2 +-+4+--+ +-+ 2 +--R \|2 log(x \|24 - 2x\|2 \|24 + 4) + 2\|2 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+ 2 4+--+ +--R 2\|2 atan(--------------) + 4x\|24 +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+--+ +--R 12\|24 +--R Type: Union(Expression(Integer),...) +--E 1215 + +--S 1216 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R - \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R \|24 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+ +--R - \|24 log(- x \|2 \|3 + x \|3 + \|2 ) + 2\|24 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+ 2 +--R 2\|24 atan(x\|6 - 1) + 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+4+-+ 2 +--R 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+-+4+--+ +--R 12\|6 \|24 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2 +--R (- 4x \|2 \|3 + 4x \|2 \|3 + 6x + 4)\|6 +--R + +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2 +--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6 + 12x \|2 \|3 +--R + +--R 4 +-+ +-+ 6 2 +--R - 12x \|2 \|3 - 18x - 12x +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2 +--R ((36x + 24x )\|2 \|3 + (- 36x - 24x )\|2 \|3 - 54x - 72x - 24)\|6 +--R Type: Expression(Integer) +--E 1217 + +)clear all + +--S 1218 of 1309 +t0:=x^3/(2+3*x^4) +--R +--R +--R 3 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1218 + +--S 1219 of 1309 +r0:=1/12*log(2+3*x^4) +--R +--R +--R 4 +--R log(3x + 2) +--R (2) ------------ +--R 12 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R log(3x + 2) +--R (3) ------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 1220 + +--S 1221 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1222 + +)clear all + +--S 1223 of 1309 +t0:=x^2/(2+3*x^4) +--R +--R +--R 2 +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1223 + +--S 1224 of 1309 +r0:=-1/2*atan(1-6^(1/4)*x)/6^(3/4)+1/2*atan(1+6^(1/4)*x)/6^(3/4)+_ + 1/4*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_ + 1/4*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - log(x \|2 \|3 + x \|3 + \|2 ) + log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ +--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1) +--R / +--R 4+-+3 +--R 4\|6 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+4+--+3 2 4+--+2 +--R - \|2 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R +-+ +-+4+--+3 2 4+--+2 +-+ 18 +--R \|2 log(- x\|2 \|54 + 3x \|54 + 18) - 2\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+ 18 +--R - 2\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+--+ +--R 8\|54 +--R Type: Union(Expression(Integer),...) +--E 1225 + +--S 1226 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+3 +-+4+--+3 2 4+--+2 +--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+ +--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+3 18 +--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+4+-+3 18 +--R - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+-+3 4+--+ +--R 8\|6 \|54 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1309 +d0:=D(normalize(m0),x) +--R +--R +--R 2 4+-+3 4+-+3 4+-+4+-+ 4+-+3 2 4+-+2 +--R (- x \|2 \|3 + 2\|2 \|3 )\|6 + 6x \|6 - 12 +--R (5) ------------------------------------------------- +--R 4 4+-+2 +--R (36x + 24)\|6 +--R Type: Expression(Integer) +--E 1227 + +)clear all + +--S 1228 of 1309 +t0:=x/(2+3*x^4) +--R +--R +--R x +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1228 + +--S 1229 of 1309 +r0:=1/2*atan(x^2*sqrt(3/2))/sqrt(6) +--R +--R +--R 2 +-+ +--R x \|3 +--R atan(------) +--R +-+ +--R \|2 +--R (2) ------------ +--R +-+ +--R 2\|6 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|6 +--R atan(------) +--R 2 +--R (3) ------------ +--R +-+ +--R 2\|6 +--R Type: Union(Expression(Integer),...) +--E 1230 + +--S 1231 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +-+ +--R x \|6 x \|3 +--R atan(------) - atan(------) +--R 2 +-+ +--R \|2 +--R (4) --------------------------- +--R +-+ +--R 2\|6 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1309 +d0:=D(m0,x) +--R +--R +--R +-+ +-+ +-+ +--R - x\|2 \|3 \|6 + 6x +--R (5) -------------------- +--R 4 +--R 18x + 12 +--R Type: Expression(Integer) +--E 1232 + +)clear all + +--S 1233 of 1309 +t0:=1/(2+3*x^4) +--R +--R +--R 1 +--R (1) ------- +--R 4 +--R 3x + 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1233 + +--S 1234 of 1309 +r0:=-1/4*atan(1-6^(1/4)*x)/6^(1/4)+1/4*atan(1+6^(1/4)*x)/6^(1/4)-_ + 1/8*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4)+_ + 1/8*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(1/4) +--R +--R +--R (2) +--R 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 2 +-+ +-+ +--R log(x \|2 \|3 + x \|3 + \|2 ) - log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+ +--R 2atan(x\|6 + 1) + 2atan(x\|6 - 1) +--R / +--R 4+-+ +--R 8\|6 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 4+--+2 +-+4+--+ +-+ 2 4+--+2 +-+4+--+ +--R \|2 log(x \|24 + 2x\|2 \|24 + 4) - \|2 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R +-+ 2 +-+ 2 +--R - 2\|2 atan(--------------) - 2\|2 atan(--------------) +--R +-+4+--+ +-+4+--+ +--R x\|2 \|24 - 2 x\|2 \|24 + 2 +--R / +--R 4+--+ +--R 8\|24 +--R Type: Union(Expression(Integer),...) +--E 1235 + +--S 1236 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R \|2 \|6 log(x \|24 + 2x\|2 \|24 + 4) +--R + +--R +-+4+-+ 2 4+--+2 +-+4+--+ +--R - \|2 \|6 log(x \|24 - 2x\|2 \|24 + 4) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - \|24 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ 4+--+ 4+-+ +--R \|24 log(- x \|2 \|3 + x \|3 + \|2 ) - 2\|24 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+ 2 +--R - 2\|24 atan(x\|6 - 1) - 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 - 2 +--R + +--R +-+4+-+ 2 +--R - 2\|2 \|6 atan(--------------) +--R +-+4+--+ +--R x\|2 \|24 + 2 +--R / +--R 4+-+4+--+ +--R 8\|6 \|24 +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4+-+2 4+-+2 2 +-+ +-+ 4 4+-+2 +--R (4x \|2 \|3 - 4x \|2 \|3 - 6x - 4)\|6 +--R + +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+ 4 4+-+2 4+-+2 +--R ((- 3x - 2x )\|2 \|3 + (3x + 2)\|2 \|2 )\|3 \|6 - 12x \|2 \|3 +--R + +--R 4 +-+ +-+ 6 2 +--R 12x \|2 \|3 + 18x + 12x +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 4+-+2 +--R ((24x + 16x )\|2 \|3 + (- 24x - 16x )\|2 \|3 - 36x - 48x - 16)\|6 +--R Type: Expression(Integer) +--E 1237 + +)clear all + +--S 1238 of 1309 +t0:=1/(x*(2+3*x^4)) +--R +--R +--R 1 +--R (1) -------- +--R 5 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1238 + +--S 1239 of 1309 +r0:=-1/4*atanh(1+3*x^4) +--R +--R +--R 4 +--R atanh(3x + 1) +--R (2) - -------------- +--R 4 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - log(3x + 2) + 4log(x) +--R (3) ------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 1240 + +--S 1241 of 1309 +m0:=a0-r0 +--R +--R +--R 4 4 +--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1) +--R (4) ------------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1242 + +)clear all + +--S 1243 of 1309 +t0:=1/(x^2*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 6 2 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1243 + +--S 1244 of 1309 +r0:=(-1/2)/x+1/4*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_ + 1/4*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-1/8*3^(1/4)*_ + log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_ + 1/8*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4) +--R +--R +--R (2) +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R x\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+ 4+-+ +--R - x\|3 log(- x \|2 \|3 + x \|3 + \|2 ) - 2x\|3 atan(x\|6 + 1) +--R + +--R 4+-+ 4+-+ 4+-+3 +--R - 2x\|3 atan(x\|6 - 1) - 4\|2 +--R / +--R 4+-+3 +--R 8x \|2 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R x\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - x\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+3 +--R +-+4+-+ 2\|3 +--R - 2x\|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+ 2\|3 4+-+ +--R 2x\|2 \|3 atan(--------------------) - 8\|2 +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+ +--R 16x\|2 +--R Type: Union(Expression(Integer),...) +--E 1245 + +--S 1246 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R \|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - \|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ 4+-+ +--R 4\|3 atan(x\|6 + 1) + 4\|3 atan(x\|6 - 1) +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R - 2\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R 2\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+3 +--R 16\|2 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3 +--R (4x \|2 \|3 + (- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 )\|6 +--R + +--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+ +--R (8x \|2 \|3 + (- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 )\|6 +--R + +--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2 +--R ((- 6x - 4x )\|2 \|3 + (6x + 4)\|2 \|2 - 48x )\|3 +--R + +--R 4 +-+4+-+2 +-+ 6 2 4+-+2 +--R 24x \|2 \|2 \|3 + (36x + 24x )\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 72x - 96x - 32)\|2 +--R Type: Expression(Integer) +--E 1247 + +)clear all + +--S 1248 of 1309 +t0:=1/(x^3*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 7 3 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1248 + +--S 1249 of 1309 +r0:=(-1/4)/x^2-1/4*atan(x^2*sqrt(3/2))*sqrt(3/2) +--R +--R +--R 2 +-+ +--R 2 +-+ x \|3 +-+ +--R - x \|3 atan(------) - \|2 +--R +-+ +--R \|2 +--R (2) --------------------------- +--R 2 +-+ +--R 4x \|2 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2 +-+ 2\|3 +-+ +--R x \|3 atan(-------) - \|2 +--R 2 +-+ +--R 3x \|2 +--R (3) -------------------------- +--R 2 +-+ +--R 4x \|2 +--R Type: Union(Expression(Integer),...) +--E 1250 + +--S 1251 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ +-+ +--R +-+ x \|3 +-+ 2\|3 +--R \|3 atan(------) + \|3 atan(-------) +--R +-+ 2 +-+ +--R \|2 3x \|2 +--R (4) ------------------------------------ +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1252 + +)clear all + +--S 1253 of 1309 +t0:=1/(x^4*(2+3*x^4)) +--R +--R +--R 1 +--R (1) --------- +--R 8 4 +--R 3x + 2x +--R Type: Fraction(Polynomial(Integer)) +--E 1253 + +--S 1254 of 1309 +r0:=(-1/6)/x^3+1/8*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)-_ + 1/8*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)+1/16*3^(3/4)*_ + log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)-_ + 1/16*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4) +--R +--R +--R (2) +--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R - 3x \|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 3 4+-+3 4+-+3 4+-+ 2 +-+ +-+ 3 4+-+3 4+-+ +--R 3x \|3 log(- x \|2 \|3 + x \|3 + \|2 - 6x \|3 atan(x\|6 + 1) +--R + +--R 3 4+-+3 4+-+ 4+-+ +--R - 6x \|3 atan(x\|6 - 1 - 8\|2 +--R / +--R 3 4+-+ +--R 48x \|2 +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - 3x \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 3 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R 3x \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+--+ +--R 3 +-+4+--+ 2\|27 +--R - 6x \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R 3 +-+4+--+ 2\|27 4+-+ +--R 6x \|2 \|27 atan(-------------------) - 8\|8 +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 3 4+-+ +--R 48x \|8 +--R Type: Union(Expression(Integer),...) +--E 1255 + +--S 1256 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+ +--R - \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 + 2\|3 \|8 atan(x\|6 + 1) +--R + +--R 4+--+ +--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27 +--R 2\|3 \|8 atan(x\|6 - 1 - 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R +-+4+-+4+--+ 2\|27 +--R 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4+-+4+-+ +--R 16\|2 \|8 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 +-+4+-+ +-+ 6 2 4+-+ 4+-+3 4 4+-+3 4+-4+-+3 +--R ((- 2x \|2 \|2 \|3 + (- 3x - 2x )\|2 )\|3 + 6x \|2 \|)\|6 +--R + +--R 2 +-+4+-+ +-+ 4 4+-+ 4+-+3 2 4+-+3 4+-4+-+ +--R ((- 4x \|2 \|2 \|3 + (- 6x - 4)\|2 )\|3 + 12x \|2 \|)\|6 +--R + +--R 2 4+-+2 2 +-+4+-+2 6 2 +-+ 4 4+-+2 +--R - 48x \|3 + (24x \|2 \|2 + 18x + 12x )\|3 + (36x + 24)\|2 +--R + +--R 4 +-+ +--R (- 18x - 12)\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (96x + 64x )\|3 + (- 48x - 32x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 72x - 96x - 32)\|2 +--R Type: Expression(Integer) +--E 1257 + +)clear all + +--S 1258 of 1309 +t0:=x^3/(2+3*x^4)^2 +--R +--R +--R 3 +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1258 + +--S 1259 of 1309 +r0:=(-1/12)/(2+3*x^4) +--R +--R +--R 1 +--R -- +--R 36 +--R (2) - ------ +--R 4 2 +--R x + - +--R 3 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1259 + +--S 1260 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 4 +--R 36x + 24 +--R Type: Union(Expression(Integer),...) +--E 1260 + +--S 1261 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1262 + +)clear all + +--S 1263 of 1309 +t0:=x^2/(2+3*x^4)^2 +--R +--R +--R 2 +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1263 + +--S 1264 of 1309 +r0:=1/8*x^3/(2+3*x^4)-1/16*atan(1-6^(1/4)*x)/6^(3/4)+_ + 1/16*atan(1+6^(1/4)*x)/6^(3/4)+_ + 1/32*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4)-_ + 1/32*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/6^(3/4) +--R +--R +--R (2) +--R 4 4+-+3 4+-+ 2 +-+ +-+ +--R (- 3x - 2)log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+ 2 +-+ +-+ 4 4+-+ +--R (3x + 2)log(- x \|2 \|3 + x \|3 + \|2 ) + (6x + 4)atan(x\|6 + 1) +--R + +--R 4 4+-+ 3 4+-+3 +--R (6x + 4)atan(x\|6 - 1) + 4x \|6 +--R / +--R 4 4+-+3 +--R (96x + 64)\|6 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ +-+4+--+3 2 4+--+2 +--R (- 3x - 2)\|2 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4 +-+ +-+4+--+3 2 4+--+2 +--R (3x + 2)\|2 log(- x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4 +-+ 18 +--R (- 6x - 4)\|2 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R 4 +-+ 18 3 4+--+ +--R (- 6x - 4)\|2 atan(----------------) + 8x \|54 +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4 4+--+ +--R (192x + 128)\|54 +--R Type: Union(Expression(Integer),...) +--E 1265 + +--S 1266 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+3 +-+4+--+3 2 4+--+2 +--R - \|2 \|6 log(x\|2 \|54 + 3x \|54 + 18) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R 2\|54 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+--+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 2\|54 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+3 +-+4+--+3 2 4+--+2 4+--+ 4+-+ +--R \|2 \|6 log(- x\|2 \|54 + 3x \|54 + 18) - 4\|54 atan(x\|6 + 1) +--R + +--R 4+--+ 4+-+ +-+4+-+3 18 +--R - 4\|54 atan(x\|6 - 1) - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 - 18 +--R + +--R +-+4+-+3 18 +--R - 2\|2 \|6 atan(----------------) +--R +-+4+--+3 +--R x\|2 \|54 + 18 +--R / +--R 4+-+3 4+--+ +--R 64\|6 \|54 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 2 4+-+3 +-+ 4 +-+4+-+3 4+-+4+-+3 +--R ((3x + 2x )\|2 \|3 + (- 3x - 2)\|2 \|2 )\|3 \|6 +--R + +--R 4 4+-+2 4+-+2 4 +-+ +-+ 6 2 4+-+2 2 4+-+2 4+-+2 +--R (12x \|2 \|3 - 12x \|2 \|3 - 18x - 12x )\|6 - 24x \|2 \|3 +--R + +--R 2 +-+ +-+ 4 +--R 24x \|2 \|3 + 36x + 24 +--R / +--R 6 2 4+-+2 4+-+2 6 2 +-+ +-+ 8 4 +--R (576x + 384x )\|2 \|3 + (- 576x - 384x )\|2 \|3 - 864x - 1152x +--R + +--R - 384 +--R * +--R 4+-+2 +--R \|6 +--R Type: Expression(Integer) +--E 1267 + +)clear all + +--S 1268 of 1309 +t0:=x/(2+3*x^4)^2 +--R +--R +--R x +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1268 + +--S 1269 of 1309 +r0:=1/8*x^2/(2+3*x^4)+1/8*atan(x^2*sqrt(3/2))/sqrt(6) +--R +--R +--R 2 +-+ +--R 4 x \|3 2 +-+ +--R (3x + 2)atan(------) + x \|6 +--R +-+ +--R \|2 +--R (2) ------------------------------ +--R 4 +-+ +--R (24x + 16)\|6 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R 4 x \|6 2 +-+ +--R (3x + 2)atan(------) + x \|6 +--R 2 +--R (3) ------------------------------ +--R 4 +-+ +--R (24x + 16)\|6 +--R Type: Union(Expression(Integer),...) +--E 1270 + +--S 1271 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +-+ +--R x \|6 x \|3 +--R atan(------) - atan(------) +--R 2 +-+ +--R \|2 +--R (4) --------------------------- +--R +-+ +--R 8\|6 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1309 +d0:=D(m0,x) +--R +--R +--R +-+ +-+ +-+ +--R - x\|2 \|3 \|6 + 6x +--R (5) -------------------- +--R 4 +--R 72x + 48 +--R Type: Expression(Integer) +--E 1272 + +)clear all + +--S 1273 of 1309 +t0:=1/(2+3*x^4)^2 +--R +--R +--R 1 +--R (1) -------------- +--R 8 4 +--R 9x + 12x + 4 +--R Type: Fraction(Polynomial(Integer)) +--E 1273 + +--S 1274 of 1309 +r0:=1/8*x/(2+3*x^4)-1/32*3^(3/4)*atan(1-6^(1/4)*x)/2^(1/4)+_ + 1/32*3^(3/4)*atan(1+6^(1/4)*x)/2^(1/4)-_ + 1/64*3^(3/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4)+_ + 1/64*3^(3/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(1/4) +--R +--R +--R (2) +--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R (3x + 2)\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+3 4+-+ 2 +-+ +-+ +--R (- 3x - 2)\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4 4+-+3 4+-+ 4 4+-+3 4+-+ 4+-+ +--R (6x + 4)\|3 atan(x\|6 + 1) + (6x + 4)\|3 atan(x\|6 - 1) + 8x\|2 +--R / +--R 4 4+-+ +--R (192x + 128)\|2 +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R (3x + 2)\|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4 +-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R (- 3x - 2)\|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+--+ +--R 4 +-+4+--+ 2\|27 +--R (6x + 4)\|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R 4 +-+4+--+ 2\|27 4+-+ +--R (- 6x - 4)\|2 \|27 atan(-------------------) + 8x\|8 +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4 4+-+ +--R (192x + 128)\|8 +--R Type: Union(Expression(Integer),...) +--E 1275 + +--S 1276 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R \|2 \|2 \|27 log(4\|27 + 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R +-+4+-+4+--+ 4+--+2 +-+4+-+4+--+ 2 4+-+2 +--R - \|2 \|2 \|27 log(4\|27 - 6x\|2 \|8 \|27 + 9x \|8 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - \|3 \|8 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+3 4+-+ 4+-+3 4+-+ 2 +-+ +-+ 4+-+3 4+-+ 4+-+ +--R \|3 \|8 log(- x \|2 \|3 + x \|3 + \|2 - 2\|3 \|8 atan(x\|6 + 1) +--R + +--R 4+--+ +--R 4+-+3 4+-+ 4+-+ +-+4+-+4+--+ 2\|27 +--R - 2\|3 \|8 atan(x\|6 - 1 + 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 - 3x\|2 \|8 +--R + +--R 4+--+ +--R +-+4+-+4+--+ 2\|27 +--R - 2\|2 \|2 \|27 atan(-------------------) +--R 4+--+ +-+4+-+ +--R 2\|27 + 3x\|2 \|8 +--R / +--R 4+-+4+-+ +--R 64\|2 \|8 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1309 +d0:=normalize(D(m0,x)) +--R +--R +--R 2 4+-+4+-+3 4+-+3 4+-+4+-+3 4+-+ 2 4+-+2 4+-+2 +--R - x \|2 \|3 \|6 - 2\|2 \|3 \|6 + 6x \|3 + 6\|2 +--R (5) ------------------------------------------------------- +--R 4 4+-+2 +--R (96x + 64)\|2 +--R Type: Expression(Integer) +--E 1277 + +)clear all + +--S 1278 of 1309 +t0:=1/(x*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) --------------- +--R 9 5 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1278 + +--S 1279 of 1309 +r0:=1/8/(2+3*x^4)-1/8*atanh(1+3*x^4) +--R +--R +--R 4 4 +--R (- 3x - 2)atanh(3x + 1) + 1 +--R (2) ----------------------------- +--R 4 +--R 24x + 16 +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1309 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 +--R (- 3x - 2)log(3x + 2) + (12x + 8)log(x) + 2 +--R (3) ---------------------------------------------- +--R 4 +--R 48x + 32 +--R Type: Union(Expression(Integer),...) +--E 1280 + +--S 1281 of 1309 +m0:=a0-r0 +--R +--R +--R 4 4 +--R - log(3x + 2) + 4log(x) + 2atanh(3x + 1) +--R (4) ------------------------------------------ +--R 16 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1282 + +)clear all + +--S 1283 of 1309 +t0:=1/(x^2*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 10 6 2 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1283 + +--S 1284 of 1309 +r0:=(-5/16)/x+1/8/(x*(2+3*x^4))+5/32*3^(1/4)*atan(1-6^(1/4)*x)/2^(3/4)-_ + 5/32*3^(1/4)*atan(1+6^(1/4)*x)/2^(3/4)-_ + 5/64*3^(1/4)*log(-2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4)+_ + 5/64*3^(1/4)*log(2^(3/4)*3^(1/4)*x+sqrt(2)+x^2*sqrt(3))/2^(3/4) +--R +--R +--R (2) +--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R (15x + 10x)\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 5 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R (- 15x - 10x)\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 5 4+-+ 4+-+ 5 4+-+ 4+-+ +--R (- 30x - 20x)\|3 atan(x\|6 + 1) + (- 30x - 20x)\|3 atan(x\|6 - 1) +--R + +--R 4 4+-+3 +--R (- 60x - 32)\|2 +--R / +--R 5 4+-+3 +--R (192x + 128x)\|2 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R (15x + 10x)\|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 5 +-+4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R (- 15x - 10x)\|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+3 +--R 5 +-+4+-+ 2\|3 +--R (- 30x - 20x)\|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R 5 +-+4+-+ 2\|3 4 4+-+ +--R (30x + 20x)\|2 \|3 atan(--------------------) + (- 120x - 64)\|2 +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 5 4+-+ +--R (384x + 256x)\|2 +--R Type: Union(Expression(Integer),...) +--E 1285 + +--S 1286 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R 5\|2 \|2 \|3 log(x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R - 10\|3 log(x \|2 \|3 + x \|3 + \|2 ) +--R + +--R 4+-+ 4+-+3 4+-+ 2 +-+ +-+ +--R 10\|3 log(- x \|2 \|3 + x \|3 + \|2 ) +--R + +--R +-+4+-+2 4+-+ +-+4+-+3 4+-+3 4+-+2 2 4+-+2 +--R - 5\|2 \|2 \|3 log(- x\|2 \|2 \|3 + 2\|3 + 3x \|2 ) +--R + +--R 4+-+ 4+-+ 4+-+ 4+-+ +--R 20\|3 atan(x\|6 + 1) + 20\|3 atan(x\|6 - 1) +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R - 10\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 - 3x\|2 \|2 +--R + +--R 4+-+3 +--R +-+4+-+2 4+-+ 2\|3 +--R 10\|2 \|2 \|3 atan(--------------------) +--R 4+-+3 +-+4+-+3 +--R 2\|3 + 3x\|2 \|2 +--R / +--R 4+-+3 +--R 128\|2 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 4+-+4+-+3 4 +-+4+-+3 +-+ 6 2 4+-+3 4+-+ 4+-+3 +--R (20x \|2 \|3 + (- 10x \|2 \|2 \|3 + (- 15x - 10x )\|2 )\|3 )\|6 +--R + +--R 2 4+-+4+-+3 2 +-+4+-+3 +-+ 4 4+-+3 4+-+ 4+-+ +--R (40x \|2 \|3 + (- 20x \|2 \|2 \|3 + (- 30x - 20)\|2 )\|3 )\|6 +--R + +--R 6 2 4+-+2 +-+ 4 +-+4+-+2 4 4+-+2 +--R ((- 30x - 20x )\|2 \|3 + (30x + 20)\|2 \|2 - 240x )\|3 +--R + +--R 4 +-+4+-+2 +-+ 6 2 4+-+2 +--R 120x \|2 \|2 \|3 + (180x + 120x )\|2 +--R / +--R 6 2 4+-+2 6 2 +-+4+-+2 +-+ +--R (768x + 512x )\|3 + (- 384x - 256x )\|2 \|2 \|3 +--R + +--R 8 4 4+-+2 +--R (- 576x - 768x - 256)\|2 +--R Type: Expression(Integer) +--E 1287 + +)clear all + +--S 1288 of 1309 +t0:=1/(x^3*(2+3*x^4)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R 11 7 3 +--R 9x + 12x + 4x +--R Type: Fraction(Polynomial(Integer)) +--E 1288 + +--S 1289 of 1309 +r0:=(-3/16)/x^2+1/8/(x^2*(2+3*x^4))-3/16*atan(x^2*sqrt(3/2))*sqrt(3/2) +--R +--R +--R 2 +-+ +--R 6 2 +-+ x \|3 4 +-+ +--R (- 9x - 6x )\|3 atan(------) + (- 9x - 4)\|2 +--R +-+ +--R \|2 +--R (2) ----------------------------------------------- +--R 6 2 +-+ +--R (48x + 32x )\|2 +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 6 2 +-+ 2\|3 4 +-+ +--R (9x + 6x )\|3 atan(-------) + (- 9x - 4)\|2 +--R 2 +-+ +--R 3x \|2 +--R (3) ---------------------------------------------- +--R 6 2 +-+ +--R (48x + 32x )\|2 +--R Type: Union(Expression(Integer),...) +--E 1290 + +--S 1291 of 1309 +m0:=a0-r0 +--R +--R +--R 2 +-+ +-+ +--R +-+ x \|3 +-+ 2\|3 +--R 3\|3 atan(------) + 3\|3 atan(-------) +--R +-+ 2 +-+ +--R \|2 3x \|2 +--R (4) -------------------------------------- +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1292 + +)clear all + +--S 1293 of 1309 +t0:=1/(1+a+(-1+a)*x^4) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 +--R (a - 1)x + a + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1293 + +--S 1294 of 1309 +r0:=-1/2*atan((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4))-_ + 1/2*atanh((-1+a)^(1/4)*x/(-1-a)^(1/4))/((-1-a)^(3/4)*(-1+a)^(1/4)) +--R +--R +--R 4+-----+ 4+-----+ +--R x\|a - 1 x\|a - 1 +--R - atanh(----------) - atan(----------) +--R 4+-------+ 4+-------+ +--R \|- a - 1 \|- a - 1 +--R (2) -------------------------------------- +--R 4+-------+3 4+-----+ +--R 2\|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((4a + 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((- 4a - 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R | 1 +--R 2 |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R (4a + 4) |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R atan(---------------------------------------) +--R x +--R Type: Union(Expression(Integer),...) +--E 1295 + +--S 1296 of 1309 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 2\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((4a + 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R - +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 2\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R log((- 4a - 4) |- -------------------------- + x) +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R + +--R 4+-----+ 4+-----+ +--R x\|a - 1 x\|a - 1 +--R atanh(----------) + atan(----------) +--R 4+-------+ 4+-------+ +--R \|- a - 1 \|- a - 1 +--R + +--R - +--R +----------------------------+ +--R 4+-------+3 | 1 4+-----+ +--R 4\|- a - 1 |- -------------------------- \|a - 1 +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R * +--R +----------------------------+ +--R | 1 +--R (4a + 4) |- -------------------------- +--R 4| 4 3 +--R \| 256a + 512a - 512a - 256 +--R atan(---------------------------------------) +--R x +--R / +--R 4+-------+3 4+-----+ +--R 2\|- a - 1 \|a - 1 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1297 + +)clear all + +--S 1298 of 1309 +t0:=x^7*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 7 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1309 +r0:=-1/6*a*(a+c*x^4)^(3/2)/c^2+1/10*(a+c*x^4)^(5/2)/c^2 +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (3c x + a c x - 2a )\|c x + a +--R (2) --------------------------------- +--R 2 +--R 30c +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1309 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (3c x + a c x - 2a )\|c x + a +--R (3) --------------------------------- +--R 2 +--R 30c +--R Type: Union(Expression(Integer),...) +--E 1300 + +--S 1301 of 1309 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1309 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1302 + +)clear all + +--S 1303 of 1309 +t0:=x^5*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 5 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1309 +r0:=-1/16*a^2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+_ + 1/16*a*x^2*sqrt(a+c*x^4)/c+1/8*x^6*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 x \|c 6 2 +-+ | 4 +--R - a atanh(-----------) + (2c x + a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R 16c\|c +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1309 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((4a c x + 8a )\|a \|c x + a - a c x - 8a c x - 8a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +-+ | 4 +--R (- 2c x - 17a c x - 24a c x - 8a x )\|c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +-+ +-+ +--R (8c x + 28a c x + 28a c x + 8a x )\|a \|c +--R / +--R +--------+ +--R 2 4 +-+ +-+ | 4 +--R (64c x + 128a c)\|a \|c \|c x + a +--R + +--R 3 8 2 4 2 +-+ +--R (- 16c x - 128a c x - 128a c)\|c +--R , +--R +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((- 8a c x - 16a )\|a \|c x + a + 2a c x + 16a c x + 16a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +---+ | 4 +--R (- 2c x - 17a c x - 24a c x - 8a x )\|- c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +---+ +-+ +--R (8c x + 28a c x + 28a c x + 8a x )\|- c \|a +--R / +--R +--------+ +--R 2 4 +---+ +-+ | 4 +--R (64c x + 128a c)\|- c \|a \|c x + a +--R + +--R 3 8 2 4 2 +---+ +--R (- 16c x - 128a c x - 128a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1305 + +--S 1306 of 1309 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 2 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 2 x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 16c\|c +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1309 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1309 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a +--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 16c\|- c \|c +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1309 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1309 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4e.input.pamphlet b/src/input/rich4e.input.pamphlet new file mode 100644 index 0000000..3df315e --- /dev/null +++ b/src/input/rich4e.input.pamphlet @@ -0,0 +1,28917 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4e.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 261 supplied "optimal results". +\item 193 matching answers. +\item 39 cases where Axiom differs from Rubi +\item 27 cases where Axiom supplied 2 results. +\item 3 cases that Axiom failed to integrate. +\item 40 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4e.output +)spool rich4e.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1347 +t0:=x^3*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 3 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1347 +r0:=1/6*(a+c*x^4)^(3/2)/c +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (2) --------------------- +--R 6c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (3) --------------------- +--R 6c +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1347 +t0:=x*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--R (1) x\|c x + a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1347 +r0:=1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c)+1/4*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R x \|c 2 +-+ | 4 +--R a atanh(-----------) + x \|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ---------------------------------------- +--R +-+ +--R 4\|c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2a\|a \|c x + a - a c x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|c \|c x + a + (- 4c x - 8a)\|c +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 2 \|- c \|c x + a - \|- c \|a +--R (4a\|a \|c x + a - 2a c x - 4a )atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 4 +---+ +--R 8\|- c \|a \|c x + a + (- 4c x - 8a)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 8 + +--S 9 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 4\|c +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - a\|- c atanh(-----------) + 2a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 4\|- c \|c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 12 + +)clear all + +--S 13 of 1347 +t0:=sqrt(a+c*x^4)/x +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))*sqrt(a)+1/2*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R +-+ \|c x + a | 4 +--R - \|a atanh(-----------) + \|c x + a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|a \|c x + a + c x + 2a | 4 +--R \|a log(------------------------------) + 2\|c x + a +--R 4 +--R x +--R [------------------------------------------------------, +--R 4 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|c x + a | 4 +--R - \|- a atan(-----------) + \|c x + a +--R +---+ +--R \|- a +--R ---------------------------------------] +--R 2 +--R Type: Union(List(Expression(Integer)),...) +--E 15 + +--S 16 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R \|a log(------------------------------) + 2\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R \|a atanh(-----------) - \|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 19 + +)clear all + +--S 20 of 1347 +t0:=sqrt(a+c*x^4)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*sqrt(c)-1/2*sqrt(a+c*x^4)/x^2 +--R +--R +--R 2 +-+ +--------+ +--R 2 +-+ x \|c | 4 +--R x \|c atanh(-----------) - \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|c \|c x + a - x \|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|c x + a - 2x \|a +--R , +--R +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|c x + a - \|a +--R (2x \|- c \|c x + a - 2x \|- c \|a )atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|c x + a - 2x \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 22 + +--S 23 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R \|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - \|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - \|c atanh(-----------) + 2\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 26 + +)clear all + +--S 27 of 1347 +t0:=sqrt(a+c*x^4)/x^5 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1347 +r0:=-1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a)-1/4*sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 \|c x + a +-+ | 4 +--R - c x atanh(-----------) - \|a \|c x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R 4 +-+ +--R 4x \|a +--R Type: Expression(Integer) +--E 28 + +--S 29 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 - 2a\|c x + a + (c x + 2a)\|a +-+ | 4 +--R c x log(---------------------------------) - 2\|a \|c x + a +--R 4 +--R x +--R [-------------------------------------------------------------, +--R 4 +-+ +--R 8x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- a \|c x + a +---+ | 4 +--R - c x atan(-----------------) - \|- a \|c x + a +--R a +--R -------------------------------------------------] +--R 4 +---+ +--R 4x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 29 + +--S 30 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R c log(---------------------------------) + 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R c\|- a atanh(-----------) - c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 33 + +)clear all + +--S 34 of 1347 +t0:=sqrt(a+c*x^4)/x^7 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1347 +r0:=-1/6*(a+c*x^4)^(3/2)/(a*x^6) +--R +--R +--R +--------+ +--R 4 | 4 +--R (- c x - a)\|c x + a +--R (2) ----------------------- +--R 6 +--R 6a x +--R Type: Expression(Integer) +--E 35 + +--S 36 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3 +--R (3c x + 7a c x + 4a )\|a \|c x + a - c x - 6a c x - 9a c x - 4a +--R ------------------------------------------------------------------------ +--R +--------+ +--R 10 2 6 | 4 10 2 6 +-+ +--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 36 + +--S 37 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 38 + +)clear all + +--S 39 of 1347 +t0:=sqrt(a+c*x^4)/x^9 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1347 +r0:=1/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-_ + 1/8*sqrt(a+c*x^4)/x^8-1/16*c*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 8 \|c x + a 4 +-+ | 4 +--R c x atanh(-----------) + (- c x - 2a)\|a \|c x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------- +--R 8 +-+ +--R 16a x \|a +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4 +--R c x log(-------------------------------) + (- 2c x - 4a)\|a \|c x + a +--R 4 +--R x +--R [------------------------------------------------------------------------, +--R 8 +-+ +--R 32a x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- a \|c x + a 4 +---+ | 4 +--R c x atan(-----------------) + (- c x - 2a)\|- a \|c x + a +--R a +--R ------------------------------------------------------------] +--R 8 +---+ +--R 16a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 41 + +--S 42 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 32a\|a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a +--R - c \|- a atanh(-----------) + c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 16a\|- a \|a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1347 +t0:=sqrt(a+c*x^4)/x^11 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1347 +r0:=-1/10*(a+c*x^4)^(3/2)/(a*x^10)+1/15*c*(a+c*x^4)^(3/2)/(a^2*x^6) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (2c x - a c x - 3a )\|c x + a +--R (2) --------------------------------- +--R 2 10 +--R 30a x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 10c x - 35a c x + 3a c x + 76a c x + 48a )\|a \|c x + a +--R + +--R 5 20 4 16 2 3 12 3 2 8 4 4 5 +--R 2c x + 25a c x + 40a c x - 35a c x - 100a c x - 48a +--R / +--R +--------+ +--R 2 2 18 3 14 4 10 | 4 +--R (30a c x + 360a c x + 480a x )\|c x + a +--R + +--R 2 2 18 3 14 4 10 +-+ +--R (- 150a c x - 600a c x - 480a x )\|a +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1347 +t0:=x^4*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1347 +--r0:=2/21*a*x*sqrt(a+c*x^4)/c+1/7*x^5*sqrt(a+c*x^4)+2/21*a^(9/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 52 + +--S 53 of 1347 +--a0:=integrate(t0,x) +--E 53 + +--S 54 of 1347 +--m0:=a0-r0 +--E 54 + +--S 55 of 1347 +--d0:=D(m0,x) +--E 55 + +)clear all + +--S 56 of 1347 +t0:=x^2*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R 2 | 4 +--R (1) x \|c x + a +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1347 +--r0:=1/5*x^3*sqrt(a+c*x^4)+2/5*a^(7/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(3/4)*sqrt(a+c*x^4))-2/5*a^(7/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 57 + +--S 58 of 1347 +--a0:=integrate(t0,x) +--E 58 + +--S 59 of 1347 +--m0:=a0-r0 +--E 59 + +--S 60 of 1347 +--d0:=D(m0,x) +--E 60 + +)clear all + +--S 61 of 1347 +t0:=sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--R (1) \|c x + a +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1347 +--r0:=1/3*x*sqrt(a+c*x^4)+2/3*a^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 62 + +--S 63 of 1347 +--a0:=integrate(t0,x) +--E 63 + +--S 64 of 1347 +--m0:=a0-r0 +--E 64 + +--S 65 of 1347 +--d0:=D(m0,x) +--E 65 + +)clear all + +--S 66 of 1347 +t0:=sqrt(a+c*x^4)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1347 +--r0:=-sqrt(a+c*x^4)/x-2*a^(3/4)*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)+2*a^(3/4)*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 67 + +--S 68 of 1347 +--a0:=integrate(t0,x) +--E 68 + +--S 69 of 1347 +--m0:=a0-r0 +--E 69 + +--S 70 of 1347 +--d0:=D(m0,x) +--E 70 + +)clear all + +--S 71 of 1347 +t0:=sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1347 +--r0:=-1/3*sqrt(a+c*x^4)/x^3-2/3*a^(1/4)*(-c)^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 72 + +--S 73 of 1347 +--a0:=integrate(t0,x) +--E 73 + +--S 74 of 1347 +--m0:=a0-r0 +--E 74 + +--S 75 of 1347 +--d0:=D(m0,x) +--E 75 + +)clear all + +--S 76 of 1347 +t0:=sqrt(a+c*x^4)/x^6 +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1347 +--r0:=-1/5*sqrt(a+c*x^4)/x^5-2/5*c*sqrt(a+c*x^4)/(a*x)+_ +-- 2/5*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4))-2/5*(-c)^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4)) +--E 77 + +--S 78 of 1347 +--a0:=integrate(t0,x) +--E 78 + +--S 79 of 1347 +--m0:=a0-r0 +--E 79 + +--S 80 of 1347 +--d0:=D(m0,x) +--E 80 + +)clear all + +--S 81 of 1347 +t0:=x^7*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 11 7 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1347 +r0:=-1/10*a*(a+c*x^4)^(5/2)/c^2+1/14*(a+c*x^4)^(7/2)/c^2 +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (5c x + 8a c x + a c x - 2a )\|c x + a +--R (2) -------------------------------------------- +--R 2 +--R 70c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (5c x + 8a c x + a c x - 2a )\|c x + a +--R (3) -------------------------------------------- +--R 2 +--R 70c +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1347 +t0:=x^5*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 9 5 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1347 +r0:=1/12*x^6*(a+c*x^4)^(3/2)-1/32*a^3*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))/c^(3/2)+1/32*a^2*x^2*sqrt(a+c*x^4)/c+_ + 1/16*a*x^6*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 3 x \|c 2 10 6 2 2 +-+ | 4 +--R - 3a atanh(-----------) + (8c x + 14a c x + 3a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------------------------------------- +--R +-+ +--R 96c\|c +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 8 4 4 5 +-+ | 4 3 3 12 4 2 8 +--R (18a c x + 96a c x + 96a )\|a \|c x + a - 3a c x - 54a c x +--R + +--R 5 4 6 +--R - 144a c x - 96a +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x +--R + +--R 5 2 +--R - 96a x +--R * +--R +--------+ +--R +-+ | 4 +--R \|c \|c x + a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x +--R + +--R 5 2 +--R 96a x +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R +--------+ +--R 3 8 2 4 2 +-+ +-+ | 4 +--R (576c x + 3072a c x + 3072a c)\|a \|c \|c x + a +--R + +--R 4 12 3 8 2 2 4 3 +-+ +--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|c +--R , +--R +--R +--------+ +--R 3 2 8 4 4 5 +-+ | 4 3 3 12 +--R (- 36a c x - 192a c x - 192a )\|a \|c x + a + 6a c x +--R + +--R 4 2 8 5 4 6 +--R 108a c x + 288a c x + 192a +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R - 8c x - 158a c x - 639a c x - 982a c x - 592a c x +--R + +--R 5 2 +--R - 96a x +--R * +--R +--------+ +--R +---+ | 4 +--R \|- c \|c x + a +--R + +--R 5 22 4 18 2 3 14 3 2 10 4 6 +--R 48c x + 388a c x + 1062a c x + 1266a c x + 640a c x +--R + +--R 5 2 +--R 96a x +--R * +--R +---+ +-+ +--R \|- c \|a +--R / +--R +--------+ +--R 3 8 2 4 2 +---+ +-+ | 4 +--R (576c x + 3072a c x + 3072a c)\|- c \|a \|c x + a +--R + +--R 4 12 3 8 2 2 4 3 +---+ +--R (- 96c x - 1728a c x - 4608a c x - 3072a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 88 + +--S 89 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 3 (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 3 x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 32c\|c +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 3 +---+ x \|c 3 +-+ \|- c \|c x + a - \|- c \|a +--R a \|- c atanh(-----------) - 2a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ------------------------------------------------------------------------ +--R +---+ +-+ +--R 32c\|- c \|c +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 92 + +)clear all + +--S 93 of 1347 +t0:=x^3*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 7 3 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1347 +r0:=1/10*(a+c*x^4)^(5/2)/c +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (c x + 2a c x + a )\|c x + a +--R (2) -------------------------------- +--R 10c +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (c x + 2a c x + a )\|c x + a +--R (3) -------------------------------- +--R 10c +--R Type: Union(Expression(Integer),...) +--E 95 + +--S 96 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 97 + +)clear all + +--S 98 of 1347 +t0:=x*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 5 | 4 +--R (1) (c x + a x)\|c x + a +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1347 +r0:=1/8*x^2*(a+c*x^4)^(3/2)+3/16*a^2*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))/sqrt(c)+3/16*a*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 x \|c 6 2 +-+ | 4 +--R 3a atanh(-----------) + (2c x + 5a x )\|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R 16\|c +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((12a c x + 24a )\|a \|c x + a - 3a c x - 24a c x - 24a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +-+ | 4 +--R (- 2c x - 21a c x - 56a c x - 40a x )\|c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +-+ +-+ +--R (8c x + 44a c x + 76a c x + 40a x )\|a \|c +--R / +--R +--------+ +--R 4 +-+ +-+ | 4 2 8 4 2 +-+ +--R (64c x + 128a)\|a \|c \|c x + a + (- 16c x - 128a c x - 128a )\|c +--R , +--R +--R +--------+ +--R 2 4 3 +-+ | 4 2 2 8 3 4 4 +--R ((24a c x + 48a )\|a \|c x + a - 6a c x - 48a c x - 48a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 3 14 2 10 2 6 3 2 +---+ | 4 +--R (- 2c x - 21a c x - 56a c x - 40a x )\|- c \|c x + a +--R + +--R 3 14 2 10 2 6 3 2 +---+ +-+ +--R (8c x + 44a c x + 76a c x + 40a x )\|- c \|a +--R / +--R +--------+ +--R 4 +---+ +-+ | 4 +--R (64c x + 128a)\|- c \|a \|c x + a +--R + +--R 2 8 4 2 +---+ +--R (- 16c x - 128a c x - 128a )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 100 + +--S 101 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R 2 (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R 3a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R 2 x \|c +--R - 3a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 16\|c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R 2 +---+ x \|c 2 +-+ \|- c \|c x + a - \|- c \|a +--R - 3a \|- c atanh(-----------) + 6a \|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R --------------------------------------------------------------------------- +--R +---+ +-+ +--R 16\|- c \|c +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 104 + +)clear all + +--S 105 of 1347 +t0:=(a+c*x^4)^(3/2)/x +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1347 +r0:=1/6*(a+c*x^4)^(3/2)-1/2*a^(3/2)*atanh(sqrt(a+c*x^4)/sqrt(a))+_ + 1/2*a*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R +-+ \|c x + a 4 | 4 +--R - 3a\|a atanh(-----------) + (c x + 4a)\|c x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|a \|c x + a + c x + 2a 4 | 4 +--R 3a\|a log(------------------------------) + (2c x + 8a)\|c x + a +--R 4 +--R x +--R [-------------------------------------------------------------------, +--R 12 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|c x + a 4 | 4 +--R - 3a\|- a atan(-----------) + (c x + 4a)\|c x + a +--R +---+ +--R \|- a +--R ----------------------------------------------------] +--R 6 +--R Type: Union(List(Expression(Integer)),...) +--E 107 + +--S 108 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R a\|a log(------------------------------) + 2a\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R a\|a atanh(-----------) - a\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 111 + +)clear all + +--S 112 of 1347 +t0:=(a+c*x^4)^(3/2)/x^3 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1347 +r0:=-1/2*(a+c*x^4)^(3/2)/x^2+3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))*_ + sqrt(c)+3/4*c*x^2*sqrt(a+c*x^4) +--R +--R +--R 2 +-+ +--------+ +--R 2 +-+ x \|c 4 | 4 +--R 3a x \|c atanh(-----------) + (c x - 2a)\|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ---------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a c x + 12a x )\|c \|c x + a + (- 9a c x - 12a x )\|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x +--R + +--R 3 +--R - 8a +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a +--R , +--R +--R +--------+ +--R 6 2 2 +---+ | 4 +--R (6a c x + 24a x )\|- c \|c x + a +--R + +--R 6 2 2 +---+ +-+ +--R (- 18a c x - 24a x )\|- c \|a +--R * +--R +--------+ +--R | 4 +-+ +--R \|c x + a - \|a +--R atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3c x + 2a c x + 8a )\|a \|c x + a + c x + 3a c x - 6a c x +--R + +--R 3 +--R - 8a +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4c x + 16a x )\|c x + a + (- 12c x - 16a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 114 + +--S 115 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R 3a\|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - 3a\|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 4 +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - 3a\|c atanh(-----------) + 6a\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1347 +t0:=(a+c*x^4)^(3/2)/x^5 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1347 +r0:=-1/4*(a+c*x^4)^(3/2)/x^4-3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))*_ + sqrt(a)+3/4*c*sqrt(a+c*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ \|c x + a 4 | 4 +--R - 3c x \|a atanh(-----------) + (2c x - a)\|c x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R 4 +-+ - 2\|a \|c x + a + c x + 2a 4 | 4 +--R 3c x \|a log(------------------------------) + (4c x - 2a)\|c x + a +--R 4 +--R x +--R [----------------------------------------------------------------------, +--R 4 +--R 8x +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ \|c x + a 4 | 4 +--R - 3c x \|- a atan(-----------) + (2c x - a)\|c x + a +--R +---+ +--R \|- a +--R -------------------------------------------------------] +--R 4 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 121 + +--S 122 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R +-+ | 4 4 | 4 +--R +-+ - 2\|a \|c x + a + c x + 2a +-+ \|c x + a +--R 3c\|a log(------------------------------) + 6c\|a atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 | 4 +--R +-+ \|c x + a +---+ \|c x + a +--R 3c\|a atanh(-----------) - 3c\|- a atan(-----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) ---------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1347 +t0:=(a+c*x^4)^(3/2)/x^7 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1347 +r0:=-1/6*(a+c*x^4)^(3/2)/x^6+1/2*c^(3/2)*atanh(x^2*sqrt(c)/_ + sqrt(a+c*x^4))-1/2*c*sqrt(a+c*x^4)/x^2 +--R +--R +--R 2 +-+ +--------+ +--R 6 +-+ x \|c 4 | 4 +--R 3c x \|c atanh(-----------) + (- 4c x - a)\|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3c x + 12a c x )\|c \|c x + a + (- 9c x - 12a c x )\|a \|c ) +--R * +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a +--R , +--R +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6c x + 24a c x )\|- c \|c x + a +--R + +--R 2 10 6 +---+ +-+ +--R (- 18c x - 24a c x )\|- c \|a +--R * +--R +--------+ +--R | 4 +-+ +--R \|c x + a - \|a +--R atan(------------------) +--R 2 +---+ +--R x \|- c +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12c x + 19a c x + 4a )\|a \|c x + a - 4c x - 21a c x - 21a c x +--R + +--R 3 +--R - 4a +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6c x + 24a x )\|c x + a + (- 18c x - 24a x )\|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 128 + +--S 129 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ +-+ | 4 2 +-+ +-+ 4 +--R +-+ (- x \|c + \|a )\|c x + a + x \|a \|c - c x - a +--R c\|c log(----------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R +-+ x \|c +--R - c\|c atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ | 4 +-+ +--R +-+ x \|c +---+ \|c x + a - \|a +--R - c\|c atanh(-----------) + 2c\|- c atan(------------------) +--R +--------+ 2 +---+ +--R | 4 x \|- c +--R \|c x + a +--R (6) ------------------------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 132 + +)clear all + +--S 133 of 1347 +t0:=(a+c*x^4)^(3/2)/x^9 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1347 +r0:=-1/8*(a+c*x^4)^(3/2)/x^8-3/16*c^2*atanh(sqrt(a+c*x^4)/sqrt(a))/_ + sqrt(a)-3/16*c*sqrt(a+c*x^4)/x^4 +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 8 \|c x + a 4 +-+ | 4 +--R - 3c x atanh(-----------) + (- 5c x - 2a)\|a \|c x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------- +--R 8 +-+ +--R 16x \|a +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 - 2a\|c x + a + (c x + 2a)\|a 4 +-+ | 4 +--R 3c x log(---------------------------------) + (- 10c x - 4a)\|a \|c x + a +--R 4 +--R x +--R [---------------------------------------------------------------------------- +--R 8 +-+ +--R 32x \|a +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- a \|c x + a 4 +---+ | 4 +--R - 3c x atan(-----------------) + (- 5c x - 2a)\|- a \|c x + a +--R a +--R ----------------------------------------------------------------] +--R 8 +---+ +--R 16x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 135 + +--S 136 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2 - 2a\|c x + a + (c x + 2a)\|a 2 \|c x + a +--R 3c log(---------------------------------) + 6c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 32\|a +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 2 +---+ \|c x + a 2 +-+ \|- a \|c x + a +--R 3c \|- a atanh(-----------) - 3c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 16\|- a \|a +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 139 + +)clear all + +--S 140 of 1347 +t0:=(a+c*x^4)^(3/2)/x^11 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1347 +r0:=-1/10*(a+c*x^4)^(5/2)/(a*x^10) +--R +--R +--R +--------+ +--R 2 8 4 2 | 4 +--R (- c x - 2a c x - a )\|c x + a +--R (2) ---------------------------------- +--R 10 +--R 10a x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 5 20 +--R (5c x + 30a c x + 61a c x + 52a c x + 16a )\|a \|c x + a - c x +--R + +--R 4 16 2 3 12 3 2 8 4 4 5 +--R - 15a c x - 55a c x - 85a c x - 60a c x - 16a +--R / +--R +--------+ +--R 2 18 2 14 3 10 | 4 +--R (10a c x + 120a c x + 160a x )\|c x + a +--R + +--R 2 18 2 14 3 10 +-+ +--R (- 50a c x - 200a c x - 160a x )\|a +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1347 +t0:=(a+c*x^4)^(3/2)/x^13 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1347 +r0:=-1/12*(a+c*x^4)^(3/2)/x^12+1/32*c^3*atanh(sqrt(a+c*x^4)/sqrt(a))/_ + a^(3/2)-1/16*c*sqrt(a+c*x^4)/x^8-1/32*c^2*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 3 12 \|c x + a 2 8 4 2 +-+ | 4 +--R 3c x atanh(-----------) + (- 3c x - 14a c x - 8a )\|a \|c x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------------- +--R 12 +-+ +--R 96a x \|a +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R | 4 4 +-+ +--R 3 12 2a\|c x + a + (c x + 2a)\|a +--R 3c x log(-------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 +--R (- 6c x - 28a c x - 16a )\|a \|c x + a +--R / +--R 12 +-+ +--R 192a x \|a +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 3 12 \|- a \|c x + a 2 8 4 2 +---+ | 4 +--R 3c x atan(-----------------) + (- 3c x - 14a c x - 8a )\|- a \|c x + a +--R a +--R ---------------------------------------------------------------------------] +--R 12 +---+ +--R 96a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 147 + +--S 148 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 3 2a\|c x + a + (c x + 2a)\|a 3 \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 64a\|a +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R 3 +---+ \|c x + a 3 +-+ \|- a \|c x + a +--R - c \|- a atanh(-----------) + c \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 32a\|- a \|a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 151 + +)clear all + +--S 152 of 1347 +t0:=(a+c*x^4)^(3/2)/x^15 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 15 +--R x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1347 +r0:=-1/14*(a+c*x^4)^(5/2)/(a*x^14)+1/35*c*(a+c*x^4)^(5/2)/(a^2*x^10) +--R +--R +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (2c x - a c x - 8a c x - 5a )\|c x + a +--R (2) -------------------------------------------- +--R 2 14 +--R 70a x +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 24 5 20 2 4 16 3 3 12 4 2 8 +--R - 14c x - 105a c x - 112a c x + 467a c x + 1240a c x +--R + +--R 5 4 6 +--R 1072a c x + 320a +--R * +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a +--R + +--R 7 28 6 24 2 5 20 3 4 16 4 3 12 5 2 8 +--R 2c x + 49a c x + 175a c x - 21a c x - 973a c x - 1736a c x +--R + +--R 6 4 7 +--R - 1232a c x - 320a +--R / +--R +--------+ +--R 2 3 26 3 2 22 4 18 5 14 | 4 +--R (70a c x + 1680a c x + 5600a c x + 4480a x )\|c x + a +--R + +--R 2 3 26 3 2 22 4 18 5 14 +-+ +--R (- 490a c x - 3920a c x - 7840a c x - 4480a x )\|a +--R Type: Union(Expression(Integer),...) +--E 154 + +--S 155 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 156 + +)clear all + +--S 157 of 1347 +t0:=x^4*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 8 4 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1347 +--r0:=1/11*x^5*(a+c*x^4)^(3/2)+4/77*a^2*x*sqrt(a+c*x^4)/c+_ +-- 6/77*a*x^5*sqrt(a+c*x^4)+4/77*a^(13/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 158 + +--S 159 of 1347 +--a0:=integrate(t0,x) +--E 159 + +--S 160 of 1347 +--m0:=a0-r0 +--E 160 + +--S 161 of 1347 +--d0:=D(m0,x) +--E 161 + +)clear all + +--S 162 of 1347 +t0:=x^2*(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 6 2 | 4 +--R (1) (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1347 +--r0:=1/9*x^3*(a+c*x^4)^(3/2)+2/15*a*x^3*sqrt(a+c*x^4)+_ +-- 4/15*a^(11/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-4/15*a^(11/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 163 + +--S 164 of 1347 +--a0:=integrate(t0,x) +--E 164 + +--S 165 of 1347 +--m0:=a0-r0 +--E 165 + +--S 166 of 1347 +--d0:=D(m0,x) +--E 166 + +)clear all + +--S 167 of 1347 +t0:=(a+c*x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1347 +--r0:=1/7*x*(a+c*x^4)^(3/2)+2/7*a*x*sqrt(a+c*x^4)+4/7*a^(9/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 168 + +--S 169 of 1347 +--a0:=integrate(t0,x) +--E 169 + +--S 170 of 1347 +--m0:=a0-r0 +--E 170 + +--S 171 of 1347 +--d0:=D(m0,x) +--E 171 + +)clear all + +--S 172 of 1347 +t0:=(a+c*x^4)^(3/2)/x^2 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1347 +--r0:=-(a+c*x^4)^(3/2)/x+6/5*c*x^3*sqrt(a+c*x^4)-12/5*a^(7/4)*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- sqrt(a+c*x^4)+12/5*a^(7/4)*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 173 + +--S 174 of 1347 +--a0:=integrate(t0,x) +--E 174 + +--S 175 of 1347 +--m0:=a0-r0 +--E 175 + +--S 176 of 1347 +--d0:=D(m0,x) +--E 176 + +)clear all + +--S 177 of 1347 +t0:=(a+c*x^4)^(3/2)/x^4 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1347 +--r0:=-1/3*(a+c*x^4)^(3/2)/x^3+2/3*c*x*sqrt(a+c*x^4)-_ +-- 4/3*a^(5/4)*(-c)^(3/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 178 + +--S 179 of 1347 +--a0:=integrate(t0,x) +--E 179 + +--S 180 of 1347 +--m0:=a0-r0 +--E 180 + +--S 181 of 1347 +--d0:=D(m0,x) +--E 181 + +)clear all + +--S 182 of 1347 +t0:=(a+c*x^4)^(3/2)/x^6 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1347 +--r0:=-1/5*(a+c*x^4)^(3/2)/x^5-6/5*c*sqrt(a+c*x^4)/x+_ +-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_e(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4)-_ +-- 12/5*a^(3/4)*(-c)^(5/4)*elliptic_f(asin((-c)^(1/4)*x/_ +-- a^(1/4)),-1)*sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 183 + +--S 184 of 1347 +--a0:=integrate(t0,x) +--E 184 + +--S 185 of 1347 +--m0:=a0-r0 +--E 185 + +--S 186 of 1347 +--d0:=D(m0,x) +--E 186 + +)clear all + +--S 187 of 1347 +t0:=(a+c*x^4)^(3/2)/x^8 +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1347 +--r0:=-1/7*(a+c*x^4)^(3/2)/x^7-2/7*c*sqrt(a+c*x^4)/x^3+_ +-- 4/7*a^(1/4)*(-c)^(7/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/sqrt(a+c*x^4) +--E 188 + +--S 189 of 1347 +--a0:=integrate(t0,x) +--E 189 + +--S 190 of 1347 +--m0:=a0-r0 +--E 190 + +--S 191 of 1347 +--d0:=D(m0,x) +--E 191 + +)clear all + +--S 192 of 1347 +t0:=(1+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (1) (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1347 +--r0:=1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+_ +-- 2/7*x*sqrt(1+x^4) +--E 193 + +--S 194 of 1347 +--a0:=integrate(t0,x) +--E 194 + +--S 195 of 1347 +--m0:=a0-r0 +--E 195 + +--S 196 of 1347 +--d0:=D(m0,x) +--E 196 + +)clear all + +--S 197 of 1347 +t0:=(1-x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (1) (- x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1347 +--r0:=1/7*x*(1-x^4)^(3/2)+4/7*elliptic_f(asin(x),-1)+2/7*x*sqrt(1-x^4) +--E 198 + +--S 199 of 1347 +--a0:=integrate(t0,x) +--E 199 + +--S 200 of 1347 +--m0:=a0-r0 +--E 200 + +--S 201 of 1347 +--d0:=D(m0,x) +--E 201 + +)clear all + +--S 202 of 1347 +t0:=x^7*sqrt(5+3*x^4) +--R +--R +--R +-------+ +--R 7 | 4 +--R (1) x \|3x + 5 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1347 +r0:=-5/54*(5+3*x^4)^(3/2)+1/90*(5+3*x^4)^(5/2) +--R +--R +--R +-------+ +--R 8 4 | 4 +--R (27x + 15x - 50)\|3x + 5 +--R (2) ---------------------------- +--R 270 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 8 4 | 4 +--R (27x + 15x - 50)\|3x + 5 +--R (3) ---------------------------- +--R 270 +--R Type: Union(Expression(Integer),...) +--E 204 + +--S 205 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 206 + +)clear all + +--S 207 of 1347 +t0:=x^3*sqrt(5+x^4) +--R +--R +--R +------+ +--R 3 | 4 +--R (1) x \|x + 5 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1347 +r0:=1/6*(5+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (x + 5)\|x + 5 +--R (2) ----------------- +--R 6 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 4 | 4 +--R (x + 5)\|x + 5 +--R (3) ----------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 209 + +--S 210 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 211 + +)clear all + +--S 212 of 1347 +t0:=x*sqrt(3+2*x^4) +--R +--R +--R +-------+ +--R | 4 +--R (1) x\|2x + 3 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1347 +r0:=3/4*asinh(x^2*sqrt(2/3))/sqrt(2)+1/4*x^2*sqrt(3+2*x^4) +--R +--R +--R +-------+ 2 +-+ +--R 2 +-+ | 4 x \|2 +--R x \|2 \|2x + 3 + 3asinh(------) +--R +-+ +--R \|3 +--R (2) --------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R +-+ | 4 4 +--R (3\|3 \|2x + 3 - 3x - 9) +--R * +--R +-------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2 +--R log(------------------------------------------------------) +--R +-------+ +--R +-+ | 4 +--R \|3 \|2x + 3 - 3 +--R + +--R +-------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- x - 3x )\|2 \|2x + 3 + (2x + 3x )\|2 \|3 +--R / +--R +-------+ +--R +-+ +-+ | 4 4 +-+ +--R 4\|2 \|3 \|2x + 3 + (- 4x - 12)\|2 +--R Type: Union(Expression(Integer),...) +--E 214 + +--S 215 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ 2 +-+ +--R (\|2 \|3 - 2x )\|2x + 3 + 2x \|3 + (- 2x - 3)\|2 x \|2 +--R 3log(------------------------------------------------------) - 3asinh(------) +--R +-------+ +-+ +--R +-+ | 4 \|3 +--R \|3 \|2x + 3 - 3 +--R ----------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 216 + +)clear all + +--S 217 of 1347 +t0:=x*sqrt(-2+x^4) +--R +--R +--R +------+ +--R | 4 +--R (1) x\|x - 2 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1347 +r0:=-1/2*atanh(x^2/sqrt(-2+x^4))+1/4*x^2*sqrt(-2+x^4) +--R +--R +--R 2 +------+ +--R x 2 | 4 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 4 +--R \|x - 2 +--R (2) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 2 | 4 4 | 4 2 6 2 | 4 8 4 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x - 2x +--R ----------------------------------------------------------------------------- +--R +------+ +--R 2 | 4 4 +--R 4x \|x - 2 - 4x + 4 +--R Type: Union(Expression(Integer),...) +--E 219 + +--S 220 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 4 +--R \|x - 2 +--R (4) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 221 + +)clear all + +--S 222 of 1347 +t0:=(1+x^4)^(1/2) +--R +--R +--R +------+ +--R | 4 +--R (1) \|x + 1 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1347 +--r0:=-2/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/3*x*sqrt(1+x^4) +--E 223 + +--S 224 of 1347 +--a0:=integrate(t0,x) +--E 224 + +--S 225 of 1347 +--m0:=a0-r0 +--E 225 + +--S 226 of 1347 +--d0:=D(m0,x) +--E 226 + +)clear all + +--S 227 of 1347 +t0:=(1-x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (1) \|- x + 1 +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1347 +--r0:=2/3*elliptic_f(asin(x),-1)+1/3*x*sqrt(1-x^4) +--E 228 + +--S 229 of 1347 +--a0:=integrate(t0,x) +--E 229 + +--S 230 of 1347 +--m0:=a0-r0 +--E 230 + +--S 231 of 1347 +--d0:=D(m0,x) +--E 231 + +)clear all + +--S 232 of 1347 +t0:=x^7/sqrt(a+c*x^4) +--R +--R +--R 7 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1347 +r0:=-1/3*a*sqrt(a+c*x^4)/c^2+1/6*x^4*sqrt(a+c*x^4)/c +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x - 2a)\|c x + a +--R (2) ---------------------- +--R 2 +--R 6c +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 4 +--R (c x - 2a)\|c x + a +--R (3) ---------------------- +--R 2 +--R 6c +--R Type: Union(Expression(Integer),...) +--E 234 + +--S 235 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 236 + +)clear all + +--S 237 of 1347 +t0:=x^5/sqrt(a+c*x^4) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1347 +r0:=-1/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)+1/4*x^2*sqrt(a+c*x^4)/c +--R +--R +--R 2 +-+ +--------+ +--R x \|c 2 +-+ | 4 +--R - a atanh(-----------) + x \|c \|c x + a +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------ +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2a\|a \|c x + a - a c x - 2a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- c x - 2a x )\|c \|c x + a + (2c x + 2a x )\|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8c\|a \|c \|c x + a + (- 4c x - 8a c)\|c +--R , +--R +--R +--------+ +--R +-+ | 4 4 2 +--R (- 4a\|a \|c x + a + 2a c x + 4a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- c x - 2a x )\|- c \|c x + a + (2c x + 2a x )\|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 8c\|- c \|a \|c x + a + (- 4c x - 8a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 239 + +--S 240 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 4c\|c +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R a\|- c atanh(-----------) - 2a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 4c\|- c \|c +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1347 +t0:=x^3/sqrt(a+c*x^4) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1347 +r0:=1/2*sqrt(a+c*x^4)/c +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ----------- +--R 2c +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (3) ----------- +--R 2c +--R Type: Union(Expression(Integer),...) +--E 246 + +--S 247 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 248 + +)clear all + +--S 249 of 1347 +t0:=x/sqrt(a+c*x^4) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/sqrt(c) +--R +--R +--R 2 +-+ +--R x \|c +--R atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------ +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|c +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R ------------------------------------] +--R +---+ +--R \|- c +--R Type: Union(List(Expression(Integer)),...) +--E 251 + +--S 252 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 2\|c +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - \|- c atanh(-----------) + 2\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- c \|c +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1347 +t0:=1/(x*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 4 +--R x\|c x + a +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2a\|c x + a + (c x + 2a)\|a +---+ | 4 +--R log(---------------------------------) \|- a \|c x + a +--R 4 atan(-----------------) +--R x a +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|a 2\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 258 + +--S 259 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R \|- a atanh(-----------) - \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 262 + +)clear all + +--S 263 of 1347 +t0:=1/(x^3*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1347 +r0:=-1/2*sqrt(a+c*x^4)/(a*x^2) +--R +--R +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) - ----------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 4 4 +--R \|a \|c x + a - c x - a +--R (3) ---------------------------- +--R +--------+ +--R 2 | 4 2 +-+ +--R 2a x \|c x + a - 2a x \|a +--R Type: Union(Expression(Integer),...) +--E 265 + +--S 266 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 267 + +)clear all + +--S 268 of 1347 +t0:=1/(x^5*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 5 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1347 +r0:=1/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)-1/4*sqrt(a+c*x^4)/(a*x^4) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 4 \|c x + a +-+ | 4 +--R c x atanh(-----------) - \|a \|c x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R 4 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 2a\|c x + a + (c x + 2a)\|a +-+ | 4 +--R c x log(-------------------------------) - 2\|a \|c x + a +--R 4 +--R x +--R [-----------------------------------------------------------, +--R 4 +-+ +--R 8a x \|a +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- a \|c x + a +---+ | 4 +--R c x atan(-----------------) - \|- a \|c x + a +--R a +--R -----------------------------------------------] +--R 4 +---+ +--R 4a x \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 270 + +--S 271 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R c log(-------------------------------) - 2c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R - c\|- a atanh(-----------) + c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 1347 +t0:=1/(x^7*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 7 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1347 +r0:=-1/6*sqrt(a+c*x^4)/(a*x^6)+1/3*c*sqrt(a+c*x^4)/(a^2*x^2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (2c x - a)\|c x + a +--R (2) ---------------------- +--R 2 6 +--R 6a x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 3 +--R (- 6c x - 5a c x + 4a )\|a \|c x + a + 2c x + 9a c x + 3a c x - 4a +--R --------------------------------------------------------------------------- +--R +--------+ +--R 2 10 3 6 | 4 2 10 3 6 +-+ +--R (6a c x + 24a x )\|c x + a + (- 18a c x - 24a x )\|a +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1347 +t0:=x^6/sqrt(a+b*x^4) +--R +--R +--R 6 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|b x + a +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1347 +--r0:=1/5*x^3*sqrt(a+b*x^4)/b+3/5*a^(7/4)*_ +-- elliptic_e(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4))-_ +-- 3/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/((-b)^(7/4)*sqrt(a+b*x^4)) +--E 281 + +--S 282 of 1347 +--a0:=integrate(t0,x) +--E 282 + +--S 283 of 1347 +--m0:=a0-r0 +--E 283 + +--S 284 of 1347 +--d0:=D(m0,x) +--E 284 + +)clear all + +--S 285 of 1347 +t0:=x^4/sqrt(a+c*x^4) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1347 +--r0:=1/3*x*sqrt(a+c*x^4)/c+1/3*a^(5/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 286 + +--S 287 of 1347 +--a0:=integrate(t0,x) +--E 287 + +--S 288 of 1347 +--m0:=a0-r0 +--E 288 + +--S 289 of 1347 +--d0:=D(m0,x) +--E 289 + +)clear all + +--S 290 of 1347 +t0:=x^2/sqrt(a+c*x^4) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1347 +--r0:=a^(3/4)*elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4))-a^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(3/4)*sqrt(a+c*x^4)) +--E 291 + +--S 292 of 1347 +--a0:=integrate(t0,x) +--E 292 + +--S 293 of 1347 +--m0:=a0-r0 +--E 293 + +--S 294 of 1347 +--d0:=D(m0,x) +--E 294 + +)clear all + +--S 295 of 1347 +t0:=1/sqrt(a+c*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 4 +--R \|c x + a +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1347 +--r0:=a^(1/4)*elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/((-c)^(1/4)*sqrt(a+c*x^4)) +--E 296 + +--S 297 of 1347 +--a0:=integrate(t0,x) +--E 297 + +--S 298 of 1347 +--m0:=a0-r0 +--E 298 + +--S 299 of 1347 +--d0:=D(m0,x) +--E 299 + +)clear all + +--S 300 of 1347 +t0:=1/(x^2*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1347 +--r0:=-sqrt(a+c*x^4)/(a*x)-(-c)^(1/4)*elliptic_e(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*_ +-- sqrt(a+c*x^4))+(-c)^(1/4)*elliptic_f(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/(a^(1/4)*sqrt(a+c*x^4)) +--E 301 + +--S 302 of 1347 +--a0:=integrate(t0,x) +--E 302 + +--S 303 of 1347 +--m0:=a0-r0 +--E 303 + +--S 304 of 1347 +--d0:=D(m0,x) +--E 304 + +)clear all + +--S 305 of 1347 +t0:=1/(x^4*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 4 | 4 +--R x \|c x + a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1347 +--r0:=-1/3*sqrt(a+c*x^4)/(a*x^3)+1/3*(-c)^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(3/4)*sqrt(a+c*x^4)) +--E 306 + +--S 307 of 1347 +--a0:=integrate(t0,x) +--E 307 + +--S 308 of 1347 +--m0:=a0-r0 +--E 308 + +--S 309 of 1347 +--d0:=D(m0,x) +--E 309 + +)clear all + +--S 310 of 1347 +t0:=x^9/(a+c*x^4)^(3/2) +--R +--R +--R 9 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1347 +r0:=-3/4*a*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(5/2)-_ + 1/2*x^6/(c*sqrt(a+c*x^4))+3/4*x^2*sqrt(a+c*x^4)/c^2 +--R +--R +--R +--------+ 2 +-+ +--R | 4 x \|c 6 2 +-+ +--R - 3a\|c x + a atanh(-----------) + (c x + 3a x )\|c +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 +-+ | 4 +--R 4c \|c \|c x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((9a c x + 12a )\|a \|c x + a - 3a c x - 15a c x - 12a ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (- c x - 7a c x - 12a x )\|c \|c x + a +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (3c x + 13a c x + 12a x )\|a \|c +--R / +--R +--------+ +--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+ +--R (12c x + 16a c )\|a \|c \|c x + a + (- 4c x - 20a c x - 16a c )\|c +--R , +--R +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((- 18a c x - 24a )\|a \|c x + a + 6a c x + 30a c x + 24a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- c \|c x + a - \|- c \|a +--R atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (- c x - 7a c x - 12a x )\|- c \|c x + a +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (3c x + 13a c x + 12a x )\|- c \|a +--R / +--R +--------+ +--R 3 4 2 +---+ +-+ | 4 +--R (12c x + 16a c )\|- c \|a \|c x + a +--R + +--R 4 8 3 4 2 2 +---+ +--R (- 4c x - 20a c x - 16a c )\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 312 + +--S 313 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c + c x )\|c x + a + (- c x - a)\|c - c x \|a +--R 3a log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R 3a atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R 2 +-+ +--R 4c \|c +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1347 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R 3a\|- c atanh(-----------) - 6a\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R ----------------------------------------------------------------------- +--R 2 +---+ +-+ +--R 4c \|- c \|c +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 316 + +)clear all + +--S 317 of 1347 +t0:=x^7/(a+c*x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1347 +r0:=1/2*a/(c^2*sqrt(a+c*x^4))+1/2*sqrt(a+c*x^4)/c^2 +--R +--R +--R 4 +--R c x + 2a +--R (2) -------------- +--R +--------+ +--R 2 | 4 +--R 2c \|c x + a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R c x + 2a +--R (3) -------------- +--R +--------+ +--R 2 | 4 +--R 2c \|c x + a +--R Type: Union(Expression(Integer),...) +--E 319 + +--S 320 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 321 + +)clear all + +--S 322 of 1347 +t0:=x^5/(a+c*x^4)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1347 +r0:=1/2*atanh(x^2*sqrt(c)/sqrt(a+c*x^4))/c^(3/2)-1/2*x^2/(c*sqrt(a+c*x^4)) +--R +--R +--R +--------+ 2 +-+ +--R | 4 x \|c 2 +-+ +--R \|c x + a atanh(-----------) - x \|c +--R +--------+ +--R | 4 +--R \|c x + a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 4 +--R 2c\|c \|c x + a +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R (\|a \|c x + a - c x - a) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R x \|c \|c x + a - x \|a \|c +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 2c\|a \|c \|c x + a + (- 2c x - 2a c)\|c +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 \|- c \|c x + a - \|- c \|a +--R (2\|a \|c x + a - 2c x - 2a)atan(------------------------------) +--R 2 +--R c x +--R + +--R +--------+ +--R 2 +---+ | 4 2 +---+ +-+ +--R x \|- c \|c x + a - x \|- c \|a +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 2c\|- c \|a \|c x + a + (- 2c x - 2a c)\|- c +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 324 + +--S 325 of 1347 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 4 +-+ 2 +-+ +--R (\|a \|c - c x )\|c x + a + (- c x - a)\|c + c x \|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|a \|c x + a - a +--R + +--R 2 +-+ +--R x \|c +--R - atanh(-----------) +--R +--------+ +--R | 4 +--R \|c x + a +--R / +--R +-+ +--R 2c\|c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R 2 +-+ +---+ | 4 +---+ +-+ +--R +---+ x \|c +-+ \|- c \|c x + a - \|- c \|a +--R - \|- c atanh(-----------) + 2\|c atan(------------------------------) +--R +--------+ 2 +--R | 4 c x +--R \|c x + a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2c\|- c \|c +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 1347 +t0:=x^3/(a+c*x^4)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1347 +r0:=(-1/2)/(c*sqrt(a+c*x^4)) +--R +--R +--R 1 +--R (2) - ------------- +--R +--------+ +--R | 4 +--R 2c\|c x + a +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +--------+ +--R | 4 +--R 2c\|c x + a +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1347 +t0:=x/(a+c*x^4)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1347 +r0:=1/2*x^2/(a*sqrt(a+c*x^4)) +--R +--R +--R 2 +--R x +--R (2) ------------- +--R +--------+ +--R | 4 +--R 2a\|c x + a +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 | 4 2 +-+ +--R - x \|c x + a + x \|a +--R (3) --------------------------------- +--R +--------+ +--R +-+ | 4 4 2 +--R 2a\|a \|c x + a - 2a c x - 2a +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1347 +t0:=1/(x*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R 5 | 4 +--R (c x + a x)\|c x + a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1347 +r0:=-1/2*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(3/2)+1/2/(a*sqrt(a+c*x^4)) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 \|c x + a +-+ +--R - \|c x + a atanh(-----------) + \|a +--R +-+ +--R \|a +--R (2) -------------------------------------- +--R +--------+ +--R +-+ | 4 +--R 2a\|a \|c x + a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 4 4 +-+ +--R | 4 - 2a\|c x + a + (c x + 2a)\|a +-+ +--R \|c x + a log(---------------------------------) + 2\|a +--R 4 +--R x +--R [---------------------------------------------------------, +--R +--------+ +--R +-+ | 4 +--R 4a\|a \|c x + a +--R +--------+ +--R +--------+ +---+ | 4 +--R | 4 \|- a \|c x + a +---+ +--R - \|c x + a atan(-----------------) + \|- a +--R a +--R ---------------------------------------------] +--R +--------+ +--R +---+ | 4 +--R 2a\|- a \|c x + a +--R Type: Union(List(Expression(Integer)),...) +--E 341 + +--S 342 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R - 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R log(---------------------------------) + 2atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) ------------------------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R \|- a atanh(-----------) - \|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1347 +t0:=1/(x^3*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 7 3 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1347 +r0:=1/2/(a*x^2*sqrt(a+c*x^4))-sqrt(a+c*x^4)/(a^2*x^2) +--R +--R +--R 4 +--R - 2c x - a +--R (2) ---------------- +--R +--------+ +--R 2 2 | 4 +--R 2a x \|c x + a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 +-+ | 4 2 8 4 2 +--R (4c x + 2a)\|a \|c x + a - 2c x - 5a c x - 2a +--R (3) ------------------------------------------------------ +--R +--------+ +--R 2 6 3 2 | 4 2 6 3 2 +-+ +--R (2a c x + 4a x )\|c x + a + (- 4a c x - 4a x )\|a +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1347 +t0:=1/(x^5*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 9 5 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1347 +r0:=3/4*c*atanh(sqrt(a+c*x^4)/sqrt(a))/a^(5/2)+1/2/(a*x^4*sqrt(a+c*x^4))-_ + 3/4*sqrt(a+c*x^4)/(a^2*x^4) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 \|c x + a 4 +-+ +--R 3c x \|c x + a atanh(-----------) + (- 3c x - a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R +--------+ +--R 2 4 +-+ | 4 +--R 4a x \|a \|c x + a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 4 4 +-+ +--R 4 | 4 2a\|c x + a + (c x + 2a)\|a 4 +-+ +--R 3c x \|c x + a log(-------------------------------) + (- 6c x - 2a)\|a +--R 4 +--R x +--R [-------------------------------------------------------------------------, +--R +--------+ +--R 2 4 +-+ | 4 +--R 8a x \|a \|c x + a +--R +--------+ +--R +--------+ +---+ | 4 +--R 4 | 4 \|- a \|c x + a 4 +---+ +--R 3c x \|c x + a atan(-----------------) + (- 3c x - a)\|- a +--R a +--R -------------------------------------------------------------] +--R +--------+ +--R 2 4 +---+ | 4 +--R 4a x \|- a \|c x + a +--R Type: Union(List(Expression(Integer)),...) +--E 353 + +--S 354 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 4 +-+ | 4 +--R 2a\|c x + a + (c x + 2a)\|a \|c x + a +--R 3c log(-------------------------------) - 6c atanh(-----------) +--R 4 +-+ +--R x \|a +--R (4) --------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--------+ +--R | 4 +---+ | 4 +--R +---+ \|c x + a +-+ \|- a \|c x + a +--R - 3c\|- a atanh(-----------) + 3c\|a atan(-----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1347 +t0:=x^6/(a+c*x^4)^(3/2) +--R +--R +--R 6 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1347 +--r0:=-1/2*x^3/(c*sqrt(a+c*x^4))-3/2*a^(3/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(7/4)*sqrt(a+c*x^4))+3/2*a^(3/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- ((-c)^(7/4)*sqrt(a+c*x^4)) +--E 359 + +--S 360 of 1347 +--a0:=integrate(t0,x) +--E 360 + +--S 361 of 1347 +--m0:=a0-r0 +--E 361 + +--S 362 of 1347 +--d0:=D(m0,x) +--E 362 + +)clear all + +--S 363 of 1347 +t0:=x^4/(a+c*x^4)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1347 +--r0:=-1/2*x/(c*sqrt(a+c*x^4))-1/2*a^(1/4)*elliptic_f(asin((-c)^(1/4)*_ +-- x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/((-c)^(5/4)*sqrt(a+c*x^4)) +--E 364 + +--S 365 of 1347 +--a0:=integrate(t0,x) +--E 365 + +--S 366 of 1347 +--m0:=a0-r0 +--E 366 + +--S 367 of 1347 +--d0:=D(m0,x) +--E 367 + +)clear all + +--S 368 of 1347 +t0:=x^2/(a+c*x^4)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1347 +--r0:=1/2*x^3/(a*sqrt(a+c*x^4))-1/2*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- (a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4))+1/2*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(1/4)*(-c)^(3/4)*sqrt(a+c*x^4)) +--E 369 + +--S 370 of 1347 +--a0:=integrate(t0,x) +--E 370 + +--S 371 of 1347 +--m0:=a0-r0 +--E 371 + +--S 372 of 1347 +--d0:=D(m0,x) +--E 372 + +)clear all + +--S 373 of 1347 +t0:=1/(a+c*x^4)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R 4 | 4 +--R (c x + a)\|c x + a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 1347 +--r0:=1/2*x/(a*sqrt(a+c*x^4))+1/2*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(3/4)*(-c)^(1/4)*sqrt(a+c*x^4)) +--E 374 + +--S 375 of 1347 +--a0:=integrate(t0,x) +--E 375 + +--S 376 of 1347 +--m0:=a0-r0 +--E 376 + +--S 377 of 1347 +--d0:=D(m0,x) +--E 377 + +)clear all + +--S 378 of 1347 +t0:=1/(x^2*(a+c*x^4)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R 6 2 | 4 +--R (c x + a x )\|c x + a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1347 +--r0:=1/2/(a*x*sqrt(a+c*x^4))-3/2*sqrt(a+c*x^4)/(a^2*x)-3/2*(-c)^(1/4)*_ +-- elliptic_e(asin((-c)^(1/4)*x/a^(1/4)),-1)*sqrt((a+c*x^4)/a)/_ +-- (a^(5/4)*sqrt(a+c*x^4))+3/2*(-c)^(1/4)*_ +-- elliptic_f(asin((-c)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+c*x^4)/a)/(a^(5/4)*sqrt(a+c*x^4)) +--E 379 + +--S 380 of 1347 +--a0:=integrate(t0,x) +--E 380 + +--S 381 of 1347 +--m0:=a0-r0 +--E 381 + +--S 382 of 1347 +--d0:=D(m0,x) +--E 382 + +)clear all + +--S 383 of 1347 +t0:=1/(a+b*x^4)^(5/2) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R 2 8 4 2 | 4 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1347 +--r0:=1/6*x/(a*(a+b*x^4)^(3/2))+5/12*x/(a^2*sqrt(a+b*x^4))+_ +-- 5/12*elliptic_f(asin((-b)^(1/4)*x/a^(1/4)),-1)*_ +-- sqrt((a+b*x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b*x^4)) +--E 384 + +--S 385 of 1347 +--a0:=integrate(t0,x) +--E 385 + +--S 386 of 1347 +--m0:=a0-r0 +--E 386 + +--S 387 of 1347 +--d0:=D(m0,x) +--E 387 + +)clear all + +--S 388 of 1347 +t0:=x^7/sqrt(16-x^4) +--R +--R +--R 7 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1347 +r0:=-16/3*sqrt(16-x^4)-1/6*x^4*sqrt(16-x^4) +--R +--R +--R +---------+ +--R 4 | 4 +--R (- x - 32)\|- x + 16 +--R (2) ----------------------- +--R 6 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 4 | 4 +--R (- x - 32)\|- x + 16 +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 390 + +--S 391 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 392 + +)clear all + +--S 393 of 1347 +t0:=x^6/sqrt(16-x^4) +--R +--R +--R 6 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1347 +--r0:=96/5*elliptic_e(asin(1/2*x),-1)-96/5*elliptic_f(asin(1/2*x),-1)-_ +-- 1/5*x^3*sqrt(16-x^4) +--E 394 + +--S 395 of 1347 +--a0:=integrate(t0,x) +--E 395 + +--S 396 of 1347 +--m0:=a0-r0 +--E 396 + +--S 397 of 1347 +--d0:=D(m0,x) +--E 397 + +)clear all + +--S 398 of 1347 +t0:=x^5/sqrt(16-x^4) +--R +--R +--R 5 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1347 +r0:=4*asin(1/4*x^2)-1/4*x^2*sqrt(16-x^4) +--R +--R +--R +---------+ 2 +--R 2 | 4 x +--R - x \|- x + 16 + 16asin(--) +--R 4 +--R (2) ----------------------------- +--R 4 +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +---------+ | 4 +--R | 4 4 \|- x + 16 - 4 +--R (- 256\|- x + 16 - 32x + 1024)atan(----------------) +--R 2 +--R x +--R + +--R +---------+ +--R 6 2 | 4 6 2 +--R (- x + 32x )\|- x + 16 + 8x - 128x +--R / +--R +---------+ +--R | 4 4 +--R 32\|- x + 16 + 4x - 128 +--R Type: Union(Expression(Integer),...) +--E 400 + +--S 401 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 4 2 +--R \|- x + 16 - 4 x +--R (4) - 8atan(----------------) - 4asin(--) +--R 2 4 +--R x +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 402 + +)clear all + +--S 403 of 1347 +t0:=x^4/sqrt(16-x^4) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1347 +--r0:=8/3*elliptic_f(asin(1/2*x),-1)-1/3*x*sqrt(16-x^4) +--E 404 + +--S 405 of 1347 +--a0:=integrate(t0,x) +--E 405 + +--S 406 of 1347 +--m0:=a0-r0 +--E 406 + +--S 407 of 1347 +--d0:=D(m0,x) +--E 407 + +)clear all + +--S 408 of 1347 +t0:=x^3/sqrt(16-x^4) +--R +--R +--R 3 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1347 +r0:=-1/2*sqrt(16-x^4) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (2) - ------------ +--R 2 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (3) - ------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 410 + +--S 411 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 412 + +)clear all + +--S 413 of 1347 +t0:=x^2/sqrt(16-x^4) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1347 +--r0:=2*elliptic_e(asin(1/2*x),-1)-2*elliptic_f(asin(1/2*x),-1) +--E 414 + +--S 415 of 1347 +--a0:=integrate(t0,x) +--E 415 + +--S 416 of 1347 +--m0:=a0-r0 +--E 416 + +--S 417 of 1347 +--d0:=D(m0,x) +--E 417 + +)clear all + +--S 418 of 1347 +t0:=x/sqrt(16-x^4) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1347 +r0:=1/2*asin(1/4*x^2) +--R +--R +--R 2 +--R x +--R asin(--) +--R 4 +--R (2) -------- +--R 2 +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 - 4 +--R (3) - atan(----------------) +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 420 + +--S 421 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 4 2 +--R \|- x + 16 - 4 x +--R - 2atan(----------------) - asin(--) +--R 2 4 +--R x +--R (4) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 422 + +)clear all + +--S 423 of 1347 +t0:=1/sqrt(16-x^4) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | 4 +--R \|- x + 16 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1347 +--r0:=1/2*elliptic_f(asin(1/2*x),-1) +--E 424 + +--S 425 of 1347 +--a0:=integrate(t0,x) +--E 425 + +--S 426 of 1347 +--m0:=a0-r0 +--E 426 + +--S 427 of 1347 +--d0:=D(m0,x) +--E 427 + +)clear all + +--S 428 of 1347 +t0:=1/(x*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | 4 +--R x\|- x + 16 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1347 +r0:=-1/8*atanh(1/4*sqrt(16-x^4)) +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R atanh(------------) +--R 4 +--R (2) - ------------------- +--R 8 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +---------+ +--R | 4 | 4 +--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4) +--R (3) ----------------------------------------------- +--R 16 +--R Type: Union(Expression(Integer),...) +--E 430 + +--S 431 of 1347 +m0:=a0-r0 +--R +--R +--R +---------+ +--R +---------+ +---------+ | 4 +--R | 4 | 4 \|- x + 16 +--R - log(\|- x + 16 + 4) + log(\|- x + 16 - 4) + 2atanh(------------) +--R 4 +--R (4) ---------------------------------------------------------------------- +--R 16 +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 432 + +)clear all + +--S 433 of 1347 +t0:=1/(x^2*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1347 +--r0:=-1/8*elliptic_e(asin(1/2*x),-1)+1/8*elliptic_f(asin(1/2*x),-1)-_ +-- 1/16*sqrt(16-x^4)/x +--E 434 + +--S 435 of 1347 +--a0:=integrate(t0,x) +--E 435 + +--S 436 of 1347 +--m0:=a0-r0 +--E 436 + +--S 437 of 1347 +--d0:=D(m0,x) +--E 437 + +)clear all + +--S 438 of 1347 +t0:=1/(x^3*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1347 +r0:=-1/32*sqrt(16-x^4)/x^2 +--R +--R +--R +---------+ +--R | 4 +--R \|- x + 16 +--R (2) - ------------ +--R 2 +--R 32x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 4 4 +--R 4\|- x + 16 + x - 16 +--R (3) ------------------------ +--R +---------+ +--R 2 | 4 2 +--R 32x \|- x + 16 - 128x +--R Type: Union(Expression(Integer),...) +--E 440 + +--S 441 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 442 + +)clear all + +--S 443 of 1347 +t0:=1/(x^4*sqrt(16-x^4)) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 4 | 4 +--R x \|- x + 16 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1347 +--r0:=1/96*elliptic_f(asin(1/2*x),-1)-1/48*sqrt(16-x^4)/x^3 +--E 444 + +--S 445 of 1347 +--a0:=integrate(t0,x) +--E 445 + +--S 446 of 1347 +--m0:=a0-r0 +--E 446 + +--S 447 of 1347 +--d0:=D(m0,x) +--E 447 + +)clear all + +--S 448 of 1347 +t0:=x^7/(1+x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1347 +r0:=1/2/sqrt(1+x^4)+1/2*sqrt(1+x^4) +--R +--R +--R 4 +--R x + 2 +--R (2) ---------- +--R +------+ +--R | 4 +--R 2\|x + 1 +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R x + 2 +--R (3) ---------- +--R +------+ +--R | 4 +--R 2\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 450 + +--S 451 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 452 + +)clear all + +--S 453 of 1347 +t0:=1/(1+x^4)^(3/2) +--R +--R +--R 1 +--R (1) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1347 +--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x),-1)+1/2*x/sqrt(1+x^4) +--E 454 + +--S 455 of 1347 +--a0:=integrate(t0,x) +--E 455 + +--S 456 of 1347 +--m0:=a0-r0 +--E 456 + +--S 457 of 1347 +--d0:=D(m0,x) +--E 457 + +)clear all + +--S 458 of 1347 +t0:=1/(1+x^4)^(5/2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +------+ +--R 8 4 | 4 +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1347 +--r0:=1/6*x/(1+x^4)^(3/2)-5/12*(-1)^(3/4)*_ +-- elliptic_f(asin((-1)^(1/4)*x),-1)+5/12*x/sqrt(1+x^4) +--E 459 + +--S 460 of 1347 +--a0:=integrate(t0,x) +--E 460 + +--S 461 of 1347 +--m0:=a0-r0 +--E 461 + +--S 462 of 1347 +--d0:=D(m0,x) +--E 462 + +)clear all + +--S 463 of 1347 +t0:=1/(1-x^4)^(3/2) +--R +--R +--R 1 +--R (1) - ------------------- +--R +--------+ +--R 4 | 4 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1347 +--r0:=1/2*elliptic_f(asin(x),-1)+1/2*x/sqrt(1-x^4) +--E 464 + +--S 465 of 1347 +--a0:=integrate(t0,x) +--E 465 + +--S 466 of 1347 +--m0:=a0-r0 +--E 466 + +--S 467 of 1347 +--d0:=D(m0,x) +--E 467 + +)clear all + +--S 468 of 1347 +t0:=1/(1-x^4)^(5/2) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R 8 4 | 4 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1347 +--r0:=1/6*x/(1-x^4)^(3/2)+5/12*elliptic_f(asin(x),-1)+5/12*x/sqrt(1-x^4) +--E 469 + +--S 470 of 1347 +--a0:=integrate(t0,x) +--E 470 + +--S 471 of 1347 +--m0:=a0-r0 +--E 471 + +--S 472 of 1347 +--d0:=D(m0,x) +--E 472 + +)clear all + +--S 473 of 1347 +t0:=x/sqrt(-4+x^4) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 4 +--R \|x - 4 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1347 +r0:=1/2*atanh(x^2/sqrt(-4+x^4)) +--R +--R +--R 2 +--R x +--R atanh(---------) +--R +------+ +--R | 4 +--R \|x - 4 +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 2 +--R log(\|x - 4 - x ) +--R (3) - ------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 475 + +--S 476 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R - log(\|x - 4 - x ) - atanh(---------) +--R +------+ +--R | 4 +--R \|x - 4 +--R (4) ---------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 477 + +)clear all + +--S 478 of 1347 +t0:=x/sqrt(4+x^4) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 4 +--R \|x + 4 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1347 +r0:=1/2*asinh(1/2*x^2) +--R +--R +--R 2 +--R x +--R asinh(--) +--R 2 +--R (2) --------- +--R 2 +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 2 +--R log(\|x + 4 - x ) +--R (3) - ------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 480 + +--S 481 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ 2 +--R | 4 2 x +--R - log(\|x + 4 - x ) - asinh(--) +--R 2 +--R (4) --------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 482 + +)clear all + +--S 483 of 1347 +t0:=1/(x*sqrt(-1+x^4)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 4 +--R x\|x - 1 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1347 +r0:=1/2*atan(sqrt(-1+x^4)) +--R +--R +--R +------+ +--R | 4 +--R atan(\|x - 1 ) +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 4 +--R atan(\|x - 1 ) +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 485 + +--S 486 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 487 + +)clear all + +--S 488 of 1347 +t0:=x^(7/2)*(a+c*x^4) +--R +--R +--R 7 3 +-+ +--R (1) (c x + a x )\|x +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1347 +r0:=2/9*a*x^(9/2)+2/17*c*x^(17/2) +--R +--R +--R 8 4 +-+ +--R (18c x + 34a x )\|x +--R (2) --------------------- +--R 153 +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 8 4 +-+ +--R (18c x + 34a x )\|x +--R (3) --------------------- +--R 153 +--R Type: Union(Expression(Integer),...) +--E 490 + +--S 491 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1347 +t0:=x^(5/2)*(a+c*x^4) +--R +--R +--R 6 2 +-+ +--R (1) (c x + a x )\|x +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1347 +r0:=2/7*a*x^(7/2)+2/15*c*x^(15/2) +--R +--R +--R 7 3 +-+ +--R (14c x + 30a x )\|x +--R (2) --------------------- +--R 105 +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 7 3 +-+ +--R (14c x + 30a x )\|x +--R (3) --------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 495 + +--S 496 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 497 + +)clear all + +--S 498 of 1347 +t0:=x^(3/2)*(a+c*x^4) +--R +--R +--R 5 +-+ +--R (1) (c x + a x)\|x +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1347 +r0:=2/5*a*x^(5/2)+2/13*c*x^(13/2) +--R +--R +--R 6 2 +-+ +--R (10c x + 26a x )\|x +--R (2) --------------------- +--R 65 +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 2 +-+ +--R (10c x + 26a x )\|x +--R (3) --------------------- +--R 65 +--R Type: Union(Expression(Integer),...) +--E 500 + +--S 501 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 502 + +)clear all + +--S 503 of 1347 +t0:=(a+c*x^4)*sqrt(x) +--R +--R +--R 4 +-+ +--R (1) (c x + a)\|x +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1347 +r0:=2/3*a*x^(3/2)+2/11*c*x^(11/2) +--R +--R +--R 5 +-+ +--R (6c x + 22a x)\|x +--R (2) ------------------- +--R 33 +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ +--R (6c x + 22a x)\|x +--R (3) ------------------- +--R 33 +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1347 +t0:=(a+c*x^4)/sqrt(x) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1347 +r0:=2/9*c*x^(9/2)+2*a*sqrt(x) +--R +--R +--R 4 +-+ +--R (2c x + 18a)\|x +--R (2) ----------------- +--R 9 +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R (2c x + 18a)\|x +--R (3) ----------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 510 + +--S 511 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +)clear all + +--S 513 of 1347 +t0:=(a+c*x^4)/x^(3/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1347 +r0:=2/7*c*x^(7/2)-2*a/sqrt(x) +--R +--R +--R 4 +--R 2c x - 14a +--R (2) ----------- +--R +-+ +--R 7\|x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 2c x - 14a +--R (3) ----------- +--R +-+ +--R 7\|x +--R Type: Union(Expression(Integer),...) +--E 515 + +--S 516 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 517 + +)clear all + +--S 518 of 1347 +t0:=(a+c*x^4)/x^(5/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1347 +r0:=-2/3*a/x^(3/2)+2/5*c*x^(5/2) +--R +--R +--R 4 +--R 6c x - 10a +--R (2) ----------- +--R +-+ +--R 15x\|x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 6c x - 10a +--R (3) ----------- +--R +-+ +--R 15x\|x +--R Type: Union(Expression(Integer),...) +--E 520 + +--S 521 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 522 + +)clear all + +--S 523 of 1347 +t0:=(a+c*x^4)/x^(7/2) +--R +--R +--R 4 +--R c x + a +--R (1) -------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1347 +r0:=-2/5*a/x^(5/2)+2/3*c*x^(3/2) +--R +--R +--R 4 +--R 10c x - 6a +--R (2) ----------- +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 10c x - 6a +--R (3) ----------- +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 525 + +--S 526 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 526 + +--S 527 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 527 + +)clear all + +--S 528 of 1347 +t0:=x^(7/2)*(a+c*x^4)^2 +--R +--R +--R 2 11 7 2 3 +-+ +--R (1) (c x + 2a c x + a x )\|x +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1347 +r0:=2/9*a^2*x^(9/2)+4/17*a*c*x^(17/2)+2/25*c^2*x^(25/2) +--R +--R +--R 2 12 8 2 4 +-+ +--R (306c x + 900a c x + 850a x )\|x +--R (2) ------------------------------------ +--R 3825 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 12 8 2 4 +-+ +--R (306c x + 900a c x + 850a x )\|x +--R (3) ------------------------------------ +--R 3825 +--R Type: Union(Expression(Integer),...) +--E 530 + +--S 531 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 532 + +)clear all + +--S 533 of 1347 +t0:=x^(5/2)*(a+c*x^4)^2 +--R +--R +--R 2 10 6 2 2 +-+ +--R (1) (c x + 2a c x + a x )\|x +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1347 +r0:=2/7*a^2*x^(7/2)+4/15*a*c*x^(15/2)+2/23*c^2*x^(23/2) +--R +--R +--R 2 11 7 2 3 +-+ +--R (210c x + 644a c x + 690a x )\|x +--R (2) ------------------------------------ +--R 2415 +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 11 7 2 3 +-+ +--R (210c x + 644a c x + 690a x )\|x +--R (3) ------------------------------------ +--R 2415 +--R Type: Union(Expression(Integer),...) +--E 535 + +--S 536 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1347 +t0:=x^(3/2)*(a+c*x^4)^2 +--R +--R +--R 2 9 5 2 +-+ +--R (1) (c x + 2a c x + a x)\|x +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1347 +r0:=2/5*a^2*x^(5/2)+4/13*a*c*x^(13/2)+2/21*c^2*x^(21/2) +--R +--R +--R 2 10 6 2 2 +-+ +--R (130c x + 420a c x + 546a x )\|x +--R (2) ------------------------------------ +--R 1365 +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 10 6 2 2 +-+ +--R (130c x + 420a c x + 546a x )\|x +--R (3) ------------------------------------ +--R 1365 +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1347 +t0:=(a+c*x^4)^2*sqrt(x) +--R +--R +--R 2 8 4 2 +-+ +--R (1) (c x + 2a c x + a )\|x +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1347 +r0:=2/3*a^2*x^(3/2)+4/11*a*c*x^(11/2)+2/19*c^2*x^(19/2) +--R +--R +--R 2 9 5 2 +-+ +--R (66c x + 228a c x + 418a x)\|x +--R (2) --------------------------------- +--R 627 +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 9 5 2 +-+ +--R (66c x + 228a c x + 418a x)\|x +--R (3) --------------------------------- +--R 627 +--R Type: Union(Expression(Integer),...) +--E 545 + +--S 546 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 547 + +)clear all + +--S 548 of 1347 +t0:=(a+c*x^4)^2/sqrt(x) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1347 +r0:=4/9*a*c*x^(9/2)+2/17*c^2*x^(17/2)+2*a^2*sqrt(x) +--R +--R +--R 2 8 4 2 +-+ +--R (18c x + 68a c x + 306a )\|x +--R (2) ------------------------------- +--R 153 +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +-+ +--R (18c x + 68a c x + 306a )\|x +--R (3) ------------------------------- +--R 153 +--R Type: Union(Expression(Integer),...) +--E 550 + +--S 551 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 552 + +)clear all + +--S 553 of 1347 +t0:=(a+c*x^4)^2/x^(3/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1347 +r0:=4/7*a*c*x^(7/2)+2/15*c^2*x^(15/2)-2*a^2/sqrt(x) +--R +--R +--R 2 8 4 2 +--R 14c x + 60a c x - 210a +--R (2) ------------------------- +--R +-+ +--R 105\|x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 14c x + 60a c x - 210a +--R (3) ------------------------- +--R +-+ +--R 105\|x +--R Type: Union(Expression(Integer),...) +--E 555 + +--S 556 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 557 + +)clear all + +--S 558 of 1347 +t0:=(a+c*x^4)^2/x^(5/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1347 +r0:=-2/3*a^2/x^(3/2)+4/5*a*c*x^(5/2)+2/13*c^2*x^(13/2) +--R +--R +--R 2 8 4 2 +--R 30c x + 156a c x - 130a +--R (2) -------------------------- +--R +-+ +--R 195x\|x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 30c x + 156a c x - 130a +--R (3) -------------------------- +--R +-+ +--R 195x\|x +--R Type: Union(Expression(Integer),...) +--E 560 + +--S 561 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 562 + +)clear all + +--S 563 of 1347 +t0:=(a+c*x^4)^2/x^(7/2) +--R +--R +--R 2 8 4 2 +--R c x + 2a c x + a +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1347 +r0:=-2/5*a^2/x^(5/2)+4/3*a*c*x^(3/2)+2/11*c^2*x^(11/2) +--R +--R +--R 2 8 4 2 +--R 30c x + 220a c x - 66a +--R (2) ------------------------- +--R 2 +-+ +--R 165x \|x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 30c x + 220a c x - 66a +--R (3) ------------------------- +--R 2 +-+ +--R 165x \|x +--R Type: Union(Expression(Integer),...) +--E 565 + +--S 566 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 567 + +)clear all + +--S 568 of 1347 +t0:=x^(7/2)*(a+c*x^4)^3 +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a x )\|x +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1347 +r0:=2/9*a^3*x^(9/2)+6/17*a^2*c*x^(17/2)+6/25*a*c^2*x^(25/2)+2/33*c^3*x^(33/2) +--R +--R +--R 3 16 2 12 2 8 3 4 +-+ +--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x +--R (2) ------------------------------------------------------- +--R 42075 +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 16 2 12 2 8 3 4 +-+ +--R (2550c x + 10098a c x + 14850a c x + 9350a x )\|x +--R (3) ------------------------------------------------------- +--R 42075 +--R Type: Union(Expression(Integer),...) +--E 570 + +--S 571 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 572 + +)clear all + +--S 573 of 1347 +t0:=x^(5/2)*(a+c*x^4)^3 +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (1) (c x + 3a c x + 3a c x + a x )\|x +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1347 +r0:=2/7*a^3*x^(7/2)+2/5*a^2*c*x^(15/2)+6/23*a*c^2*x^(23/2)+2/31*c^3*x^(31/2) +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x +--R (2) ----------------------------------------------------- +--R 24955 +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 15 2 11 2 7 3 3 +-+ +--R (1610c x + 6510a c x + 9982a c x + 7130a x )\|x +--R (3) ----------------------------------------------------- +--R 24955 +--R Type: Union(Expression(Integer),...) +--E 575 + +--S 576 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 576 + +--S 577 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 577 + +)clear all + +--S 578 of 1347 +t0:=x^(3/2)*(a+c*x^4)^3 +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a x)\|x +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1347 +r0:=2/5*a^3*x^(5/2)+6/13*a^2*c*x^(13/2)+2/7*a*c^2*x^(21/2)+2/29*c^3*x^(29/2) +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x +--R (2) ---------------------------------------------------- +--R 13195 +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 14 2 10 2 6 3 2 +-+ +--R (910c x + 3770a c x + 6090a c x + 5278a x )\|x +--R (3) ---------------------------------------------------- +--R 13195 +--R Type: Union(Expression(Integer),...) +--E 580 + +--S 581 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 582 + +)clear all + +--S 583 of 1347 +t0:=(a+c*x^4)^3*sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (1) (c x + 3a c x + 3a c x + a )\|x +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1347 +r0:=2/3*a^3*x^(3/2)+6/11*a^2*c*x^(11/2)+6/19*a*c^2*x^(19/2)+2/27*c^3*x^(27/2) +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x +--R (2) -------------------------------------------------- +--R 5643 +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 13 2 9 2 5 3 +-+ +--R (418c x + 1782a c x + 3078a c x + 3762a x)\|x +--R (3) -------------------------------------------------- +--R 5643 +--R Type: Union(Expression(Integer),...) +--E 585 + +--S 586 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1347 +t0:=(a+c*x^4)^3/sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1347 +r0:=2/3*a^2*c*x^(9/2)+6/17*a*c^2*x^(17/2)+2/25*c^3*x^(25/2)+2*a^3*sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (102c x + 450a c x + 850a c x + 2550a )\|x +--R (2) ----------------------------------------------- +--R 1275 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +-+ +--R (102c x + 450a c x + 850a c x + 2550a )\|x +--R (3) ----------------------------------------------- +--R 1275 +--R Type: Union(Expression(Integer),...) +--E 590 + +--S 591 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +)clear all + +--S 593 of 1347 +t0:=(a+c*x^4)^3/x^(3/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1347 +r0:=6/7*a^2*c*x^(7/2)+2/5*a*c^2*x^(15/2)+2/23*c^3*x^(23/2)-2*a^3/sqrt(x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 70c x + 322a c x + 690a c x - 1610a +--R (2) ---------------------------------------- +--R +-+ +--R 805\|x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 70c x + 322a c x + 690a c x - 1610a +--R (3) ---------------------------------------- +--R +-+ +--R 805\|x +--R Type: Union(Expression(Integer),...) +--E 595 + +--S 596 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1347 +t0:=(a+c*x^4)^3/x^(5/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1347 +r0:=-2/3*a^3/x^(3/2)+6/5*a^2*c*x^(5/2)+6/13*a*c^2*x^(13/2)+2/21*c^3*x^(21/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R 130c x + 630a c x + 1638a c x - 910a +--R (2) ----------------------------------------- +--R +-+ +--R 1365x\|x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 130c x + 630a c x + 1638a c x - 910a +--R (3) ----------------------------------------- +--R +-+ +--R 1365x\|x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1347 +t0:=(a+c*x^4)^3/x^(7/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R (1) ------------------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1347 +r0:=-2/5*a^3/x^(5/2)+2*a^2*c*x^(3/2)+6/11*a*c^2*x^(11/2)+2/19*c^3*x^(19/2) +--R +--R +--R 3 12 2 8 2 4 3 +--R 110c x + 570a c x + 2090a c x - 418a +--R (2) ----------------------------------------- +--R 2 +-+ +--R 1045x \|x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 12 2 8 2 4 3 +--R 110c x + 570a c x + 2090a c x - 418a +--R (3) ----------------------------------------- +--R 2 +-+ +--R 1045x \|x +--R Type: Union(Expression(Integer),...) +--E 605 + +--S 606 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +)clear all + +--S 608 of 1347 +t0:=x^(9/2)/(a+c*x^4) +--R +--R +--R 4 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1347 +r0:=2/3*x^(3/2)/c+1/2*(-a)^(3/8)*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/c^(11/8)-1/2*(-a)^(3/8)*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/c^(11/8)+1/2*(-a)^(3/8)*_ + atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/(c^(11/8)*_ + sqrt(2))-1/2*(-a)^(3/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/(c^(11/8)*sqrt(2))-1/4*(-a)^(3/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(11/8)*sqrt(2))+1/4*(-a)^(3/8)*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 3\|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3\|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a +--R - 6\|2 \|- a atanh(--------) - 6\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x +--R - 6\|- a atan(---------------------) + 6\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+3 +-+ +--R 8x\|2 \|c \|x +--R / +--R +-+8+-+3 +--R 12c\|2 \|c +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 3 +--R | a +--R 3c |- -------- +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a +-+ 4 | a +--R 3c\|2 |- -------- log(a\|x + 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a +-+ 4 | a +--R - 3c\|2 |- -------- log(a\|x - 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +--R | 3 +--R | a +--R 3c |- -------- +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R +-+ | a \| 65536c +--R 6c\|2 |- -------- atan(------------------) +--R 8| 11 +-+ +--R \| 65536c a\|x +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a \| 65536c +--R - 6c |- -------- atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x - 64c |- -------- +--R 8| 11 +--R \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a \| 65536c +-+ +-+ +--R - 6c |- -------- atan(------------------------------ + 2x\|2 \|x +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x + 64c |- -------- +--R 8| 11 +--R \| 65536c +--R / +--R +-+ +--R 3c\|2 +--R Type: Union(Expression(Integer),...) +--E 610 + +--S 611 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 3 +--R | a 8+-+3 +--R 4c |- -------- \|c +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a 8+-+3 +-+ 4 | a +--R 4c\|2 |- -------- \|c log(a\|x + 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +----------+3 +--R | 3 | 3 +--R +-+ | a 8+-+3 +-+ 4 | a +--R - 4c\|2 |- -------- \|c log(a\|x - 64c |- -------- ) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R +----------+ +--R | 3 +--R | a 8+-+3 +--R 4c |- -------- \|c +--R 8| 11 +--R \| 65536c +--R * +--R +----------+3 +----------+6 +--R | 3 | 3 +--R 4 +-+ | a +-+ 8 | a 2 +--R log(- 64a c \|2 |- -------- \|x + 4096c |- -------- + a x) +--R 8| 11 8| 11 +--R \| 65536c \| 65536c +--R + +--R 8+---+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+3 \|c \|x 8+---+3 \|2 \|c \|x + \|- a +--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+3 \|2 \|c \|x - \|- a +-+8+---+3 \|c \|x +--R 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R +-+ | a 8+-+3 \| 65536c +--R 8c\|2 |- -------- \|c atan(------------------) +--R 8| 11 +-+ +--R \| 65536c a\|x +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a 8+-+3 \| 65536c +--R - 8c |- -------- \|c atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x - 64c |- -------- +--R 8| 11 +--R \| 65536c +--R + +--R +----------+3 +--R | 3 +--R 4 | a +--R +----------+ 64c |- -------- +--R | 3 8| 11 +--R | a 8+-+3 \| 65536c +--R - 8c |- -------- \|c atan(------------------------------) +--R 8| 11 +----------+3 +--R \| 65536c | 3 +--R +-+ +-+ 4 | a +--R a\|2 \|x + 64c |- -------- +--R 8| 11 +--R \| 65536c +--R / +--R +-+8+-+3 +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 612 + +)clear all + +--S 613 of 1347 +t0:=x^(7/2)/(a+c*x^4) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1347 +r0:=-1/2*(-a)^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)-_ + 1/2*(-a)^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/c^(9/8)+_ + 1/2*(-a)^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + (c^(9/8)*sqrt(2))-1/2*(-a)^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/(c^(9/8)*sqrt(2))+1/4*(-a)^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/(c^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/(c^(9/8)*_ + sqrt(2))+2*sqrt(x)/c +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a +--R - 2\|2 \|- a atanh(--------) - 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x +--R - 2\|- a atan(---------------------) - 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ +--R 8\|2 \|c \|x +--R / +--R +-+8+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +---------+2 +--R | a +-+ | a +-+ 2 | a +--R - c |- ------- log(4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a +-+ | a +--R - c\|2 |- ------- log(\|x + 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a +-+ | a +--R c\|2 |- ------- log(\|x - 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +---------+2 +--R | a +-+ | a +-+ 2 | a +--R c |- ------- log(- 4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R +-+ | a \| 65536c +--R 2c\|2 |- ------- atan(--------------) +--R 8| 9 +-+ +--R \| 65536c \|x +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a \| 65536c +--R 2c |- ------- atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x - 4c |- ------- +--R 8| 9 +--R \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a \| 65536c +-+ +-+ +--R 2c |- ------- atan(------------------------- + 2\|2 \|x +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x + 4c |- ------- +--R 8| 9 +--R \| 65536c +--R / +--R +-+ +--R c\|2 +--R Type: Union(Expression(Integer),...) +--E 615 + +--S 616 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|- a log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +---------+ +---------+ +---------+2 +--R | a 8+-+ +-+ | a +-+ 2 | a +--R - 4c |- ------- \|c log(4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a 8+-+ +-+ | a +--R - 4c\|2 |- ------- \|c log(\|x + 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +--R +-+ | a 8+-+ +-+ | a +--R 4c\|2 |- ------- \|c log(\|x - 4c |- -------) +--R 8| 9 8| 9 +--R \| 65536c \| 65536c +--R + +--R +---------+ +---------+ +---------+2 +--R | a 8+-+ +-+ | a +-+ 2 | a +--R 4c |- ------- \|c log(- 4c\|2 |- ------- \|x + 16c |- ------- + x) +--R 8| 9 8| 9 8| 9 +--R \| 65536c \| 65536c \| 65536c +--R + +--R 8+---+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|- a log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+---+ \|c \|x 8+---+ \|2 \|c \|x + \|- a +--R 2\|2 \|- a atanh(--------) + 2\|- a atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+---+ \|2 \|c \|x - \|- a +-+8+---+ \|c \|x +--R 2\|- a atan(---------------------) + 2\|2 \|- a atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R +-+ | a 8+-+ \| 65536c +--R 8c\|2 |- ------- \|c atan(--------------) +--R 8| 9 +-+ +--R \| 65536c \|x +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a 8+-+ \| 65536c +--R 8c |- ------- \|c atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x - 4c |- ------- +--R 8| 9 +--R \| 65536c +--R + +--R +---------+ +--R | a +--R 4c |- ------- +--R +---------+ 8| 9 +--R | a 8+-+ \| 65536c +--R 8c |- ------- \|c atan(-------------------------) +--R 8| 9 +---------+ +--R \| 65536c +-+ +-+ | a +--R \|2 \|x + 4c |- ------- +--R 8| 9 +--R \| 65536c +--R / +--R +-+8+-+ +--R 4c\|2 \|c +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 617 + +)clear all + +--S 618 of 1347 +t0:=x^(5/2)/(a+c*x^4) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1347 +r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(7/8))-_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*_ + c^(7/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(1/8)*c^(7/8)*sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*_ + sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+8+-+7 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+ | 1 +-+ 6 | 1 +--R \|2 |- --------- log(\|x + 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+ | 1 +-+ 6 | 1 +--R - \|2 |- --------- log(\|x - 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R | 1 \| 65536a c +--R 2 |- --------- atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x - 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R | 1 \| 65536a c +--R 2 |- --------- atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x + 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 620 + +--S 621 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+ | 1 8+-+7 +--R 4\|- a |- --------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x + 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+7 +--R +-+8+---+ | 1 8+-+7 +-+ 6 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x - 16384a c |- --------- ) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+ | 1 8+-+7 +--R 4\|- a |- --------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +-----------+7 +-----------+6 +--R 6 +-+ | 1 +-+ 5 | 1 +--R log(- 16384a c \|2 |- --------- \|x - 4096a c |- --------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 65536a c +--R 8\|- a |- --------- \|c atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x - 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+7 +--R 6 | 1 +--R 16384a c |- --------- +--R +-----------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 65536a c +--R 8\|- a |- --------- \|c atan(-----------------------------------) +--R 8| 7 +-----------+7 +--R \| 65536a c +-+ +-+ 6 | 1 +--R \|2 \|x + 16384a c |- --------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+8+---+8+-+7 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 7 9 2 6 5 3 5 | 1 +--R (- 12288a c x + 55296a c x - 6144a c x) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+4 +--R 5 8 2 4 4 3 3 | 1 +--R (1600a c x - 2944a c x + 64a c ) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 7 2 2 3 | 1 2 10 6 2 2 +--R (- 168a c x + 120a c x ) |- --------- - c x + 13a c x - 4a x +--R 8| 7 +--R \| 65536a c +--R / +--R +-----------+6 +--R 8 10 2 7 6 3 6 2 | 1 +--R (32768a c x - 8192a c x - 40960a c x ) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+4 +--R 6 9 2 5 5 3 4 | 1 +--R (- 3328a c x - 2048a c x + 1280a c x) |- --------- +--R 8| 7 +--R \| 65536a c +--R + +--R +-----------+2 +--R 4 8 2 3 4 3 2 | 1 3 11 2 7 +--R (272a c x + 256a c x - 16a c ) |- --------- + 4c x - 10a c x +--R 8| 7 +--R \| 65536a c +--R + +--R 2 3 +--R - 14a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 622 + +)clear all + +--S 623 of 1347 +t0:=x^(3/2)/(a+c*x^4) +--R +--R +--R +-+ +--R x\|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1347 +r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*c^(5/8))-_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_ + c^(5/8)*sqrt(2))+1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(5/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*_ + sqrt(2))+1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+3 8+-+5 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+ | 1 +-+ 2 3 | 1 +--R - \|2 |- --------- log(\|x + 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+ | 1 +-+ 2 3 | 1 +--R \|2 |- --------- log(\|x - 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R | 1 \| 65536a c +--R - 2 |- --------- atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x - 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R | 1 \| 65536a c +--R - 2 |- --------- atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x + 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 625 + +--S 626 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+3 | 1 8+-+5 +--R 4\|- a |- --------- \|c +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x + 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+5 +--R +-+8+---+3 | 1 8+-+5 +-+ 2 3 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x - 1024a c |- --------- ) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+3 | 1 8+-+5 +--R 4\|- a |- --------- \|c +--R 8| 3 5 +--R \| 65536a c +--R * +--R +-----------+5 +-----------+2 +--R 2 3 +-+ | 1 +-+ | 1 +--R log(- 1024a c \|2 |- --------- \|x - 16a c |- --------- + x) +--R 8| 3 5 8| 3 5 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 65536a c +--R - 8\|- a |- --------- \|c atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x - 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+5 +--R 2 3 | 1 +--R 1024a c |- --------- +--R +-----------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 65536a c +--R - 8\|- a |- --------- \|c atan(----------------------------------) +--R 8| 3 5 +-----------+5 +--R \| 65536a c +-+ +-+ 2 3 | 1 +--R \|2 \|x + 1024a c |- --------- +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-+8+---+3 8+-+5 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 2 6 10 3 5 6 4 4 2 | 1 +--R (8192a c x - 106496a c x + 32768a c x ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 4 7 3 3 3 | 1 +--R (- 5376a c x + 3840a c x ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 8 2 2 4 3 | 1 2 9 5 2 +--R (- 200a c x + 368a c x - 8a c) |- --------- - 6c x + 27a c x - 3a x +--R 8| 3 5 +--R \| 65536a c +--R / +--R +-----------+6 +--R 3 6 8 4 5 4 5 4 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 5 9 3 4 5 4 3 | 1 +--R (6656a c x + 4096a c x - 2560a c x) |- --------- +--R 8| 3 5 +--R \| 65536a c +--R + +--R +-----------+2 +--R 4 10 2 3 6 3 2 2 | 1 3 11 2 7 +--R (256a c x - 64a c x - 320a c x ) |- --------- + 8c x - 20a c x +--R 8| 3 5 +--R \| 65536a c +--R + +--R 2 3 +--R - 28a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 627 + +)clear all + +--S 628 of 1347 +t0:=sqrt(x)/(a+c*x^4) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R 4 +--R c x + a +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1347 +r0:=1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8))+_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(3/8)*_ + sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_ + c^(3/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(3/8)*sqrt(2))+1/4*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(5/8)*c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+5 8+-+3 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 +-+ 2 | 1 +--R - \|2 |- --------- log(\|x + 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+ | 1 +-+ 2 | 1 +--R \|2 |- --------- log(\|x - 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R | 1 \| 65536a c +--R 2 |- --------- atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x - 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R | 1 \| 65536a c +--R 2 |- --------- atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x + 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 630 + +--S 631 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------+ +--R 8+---+5 | 1 8+-+3 +--R 4\|- a |- --------- \|c +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1 +--R - 4\|2 \|- a |- --------- \|c log(\|x + 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R +-----------+ +-----------+3 +--R +-+8+---+5 | 1 8+-+3 +-+ 2 | 1 +--R 4\|2 \|- a |- --------- \|c log(\|x - 64a c |- --------- ) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +-----------+ +--R 8+---+5 | 1 8+-+3 +--R 4\|- a |- --------- \|c +--R 8| 5 3 +--R \| 65536a c +--R * +--R +-----------+3 +-----------+6 +--R 2 +-+ | 1 +-+ 4 2 | 1 +--R log(- 64a c\|2 |- --------- \|x + 4096a c |- --------- + x) +--R 8| 5 3 8| 5 3 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 65536a c +--R 8\|- a |- --------- \|c atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x - 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+3 +--R 2 | 1 +--R 64a c |- --------- +--R +-----------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 65536a c +--R 8\|- a |- --------- \|c atan(--------------------------------) +--R 8| 5 3 +-----------+3 +--R \| 65536a c +-+ +-+ 2 | 1 +--R \|2 \|x + 64a c |- --------- +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-+8+---+5 8+-+3 +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +-----------+6 +--R 4 4 7 5 3 3 | 1 +--R (- 172032a c x + 122880a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+4 +--R 2 4 10 3 3 6 4 2 2 | 1 +--R (1024a c x - 13312a c x + 4096a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+2 +--R 3 9 2 2 5 3 | 1 2 8 4 2 +--R (192a c x - 864a c x + 96a c x) |- --------- + 25c x - 46a c x + a +--R 8| 5 3 +--R \| 65536a c +--R / +--R +-----------+6 +--R 4 5 10 5 4 6 6 3 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+4 +--R 3 4 9 4 3 5 5 2 | 1 +--R (13312a c x + 8192a c x - 5120a c x) |- --------- +--R 8| 5 3 +--R \| 65536a c +--R + +--R +-----------+2 +--R 2 3 8 3 2 4 4 | 1 3 11 2 7 +--R (1088a c x + 1024a c x - 64a c) |- --------- - 16c x + 40a c x +--R 8| 5 3 +--R \| 65536a c +--R + +--R 2 3 +--R 56a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 632 + +)clear all + +--S 633 of 1347 +t0:=1/((a+c*x^4)*sqrt(x)) +--R +--R +--R 1 +--R (1) -------------- +--R 4 +-+ +--R (c x + a)\|x +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1347 +r0:=-1/2*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))-_ + 1/2*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(1/8))+_ + 1/2*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(1/8)*sqrt(2))-1/2*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(7/8)*c^(1/8)*sqrt(2))+1/4*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*_ + c^(1/8)*sqrt(2))-1/4*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+7 8+-+ +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +----------+2 +--R | 1 +-+ | 1 +-+ 2 | 1 +--R |- -------- log(4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 8| 7 +--R \| 65536a c \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 +-+ | 1 +--R \|2 |- -------- log(\|x + 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+ | 1 +-+ | 1 +--R - \|2 |- -------- log(\|x - 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +----------+2 +--R | 1 +-+ | 1 +-+ 2 | 1 +--R - |- -------- log(- 4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 8| 7 +--R \| 65536a c \| 65536a c \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R | 1 \| 65536a c +--R - 2 |- -------- atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x - 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R | 1 \| 65536a c +--R - 2 |- -------- atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x + 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 635 + +--S 636 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +----------+ +--R 8+---+7 | 1 8+-+ +--R 4\|- a |- -------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +----------+ +----------+2 +--R +-+ | 1 +-+ 2 | 1 +--R log(4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+8+---+7 | 1 8+-+ +-+ | 1 +--R 4\|2 \|- a |- -------- \|c log(\|x + 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R +----------+ +----------+ +--R +-+8+---+7 | 1 8+-+ +-+ | 1 +--R - 4\|2 \|- a |- -------- \|c log(\|x - 4a |- --------) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R - +--R +----------+ +--R 8+---+7 | 1 8+-+ +--R 4\|- a |- -------- \|c +--R 8| 7 +--R \| 65536a c +--R * +--R +----------+ +----------+2 +--R +-+ | 1 +-+ 2 | 1 +--R log(- 4a\|2 |- -------- \|x + 16a |- -------- + x) +--R 8| 7 8| 7 +--R \| 65536a c \| 65536a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 65536a c +--R - 8\|- a |- -------- \|c atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x - 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+ +--R | 1 +--R 4a |- -------- +--R +----------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 65536a c +--R - 8\|- a |- -------- \|c atan(--------------------------) +--R 8| 7 +----------+ +--R \| 65536a c +-+ +-+ | 1 +--R \|2 \|x + 4a |- -------- +--R 8| 7 +--R \| 65536a c +--R / +--R +-+8+---+7 8+-+ +--R 4\|2 \|- a \|c +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1347 sometimes Axiom computes a zero +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+6 +--R 6 8 7 4 8+---+2 | 1 +--R (- 34816a c x + 2048a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 9 5 5 8+---+2 | 1 +--R (1664a c x - 640a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 10 3 6 8+---+2 | 1 +--R (- 64a c x + 80a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 11 7 8+---+2 +--R (2c x - 7a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 7 7 3 4+---+8+---+2 | 1 +--R (- 69632a c x + 4096a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 8 5 4 4+---+8+---+2 | 1 +--R (3328a c x - 1280a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 9 3 5 4+---+8+---+2 | 1 +--R (- 128a c x + 160a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 10 6 4+---+8+---+2 +--R (4c x - 14a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 6 7 2 8+---+6 +--R (69632a c x - 4096a x )\|- a +--R + +--R 6 6 7 2 4+---+2 8+---+2 +--R (- 34816a c x + 2048a x )\|- a \|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 7 5 3 8+---+6 +--R (- 3328a c x + 1280a x )\|- a +--R + +--R 4 7 5 3 4+---+2 8+---+2 +--R (1664a c x - 640a x )\|- a \|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 8 3 4 8+---+6 +--R (128a c x - 160a x )\|- a +--R + +--R 2 8 3 4 4+---+2 8+---+2 +--R (- 64a c x + 80a x )\|- a \|- a +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 8+---+6 9 5 4+---+2 8+---+2 +--R (- 4c x + 14a x )\|- a + (2c x - 7a x )\|- a \|- a +--R * +--R 8+-+6 +--R \|c +--R + +--R +----------+6 +--R 6 7 7 3 8+---+4 | 1 +--R (- 34816a c x + 2048a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 8 5 4 8+---+4 | 1 +--R (1664a c x - 640a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 9 3 5 8+---+4 | 1 +--R (- 64a c x + 80a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 10 6 8+---+4 +--R (2c x - 7a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 6 7 2 4+---+8+---+4 | 1 +--R (- 69632a c x + 4096a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 7 5 3 4+---+8+---+4 | 1 +--R (3328a c x - 1280a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 8 3 4 4+---+8+---+4 | 1 +--R (- 128a c x + 160a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 4+---+8+---+4 +--R (4c x - 14a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 5 7 4+---+2 8+---+4 6 2 9 +--R (- 34816a c x + 2048a x)\|- a \|- a + 102400a c x +--R + +--R 7 5 +--R - 118784a c x +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 6 5 2 4+---+2 8+---+4 4 2 10 5 6 +--R (1664a c x - 640a x )\|- a \|- a - 3072a c x + 10496a c x +--R + +--R 6 2 +--R - 256a x +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 7 3 3 4+---+2 8+---+4 2 2 11 3 7 +--R (- 64a c x + 80a x )\|- a \|- a + 64a c x - 704a c x +--R + +--R 4 3 +--R 96a x +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 8 4 4+---+2 8+---+4 8 2 4 +--R (2c x - 7a x )\|- a \|- a + 38a c x - 16a x +--R * +--R 8+-+4 +--R \|c +--R + +--R +----------+6 +--R 5 2 10 6 6 8+---+6 | 1 +--R (51200a c x - 59392a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 3 2 11 4 7 5 3 8+---+6 | 1 +--R (- 1536a c x + 5248a c x - 128a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 12 2 8 3 4 8+---+6 | 1 +--R (32a c x - 352a c x + 48a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 9 5 8+---+6 +--R (19c x - 8a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R 5 2 9 6 5 4+---+8+---+6 6 2 9 +--R (102400a c x - 118784a c x )\|- a \|- a - 34816a c x +--R + +--R 7 5 8 +--R - 32768a c x + 2048a x +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 3 2 10 4 6 5 2 4+---+8+---+6 +--R (- 3072a c x + 10496a c x - 256a x )\|- a \|- a +--R + +--R 4 2 10 5 6 6 2 +--R 1664a c x + 1024a c x - 640a x +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 2 7 3 3 4+---+8+---+6 2 2 11 +--R (64a c x - 704a c x + 96a x )\|- a \|- a - 64a c x +--R + +--R 3 7 4 3 +--R 16a c x + 80a x +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 8 4 4+---+8+---+6 2 12 8 2 4 +--R (38c x - 16a x )\|- a \|- a + 2c x - 5a c x - 7a x +--R * +--R 4+-+ +--R \|c +--R + +--R 5 2 8 6 4 4+---+2 8+---+6 +--R (51200a c x - 59392a c x )\|- a \|- a +--R + +--R 6 2 8 7 4 8+---+2 +--R (- 69632a c x + 4096a c x )\|- a +--R + +--R 6 2 8 7 4 8 4+---+ +--R (34816a c x + 32768a c x - 2048a )\|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 3 2 9 4 5 5 4+---+2 8+---+6 +--R (- 1536a c x + 5248a c x - 128a x)\|- a \|- a +--R + +--R 4 2 9 5 5 8+---+2 +--R (3328a c x - 1280a c x )\|- a +--R + +--R 4 2 9 5 5 6 4+---+ +--R (- 1664a c x - 1024a c x + 640a x)\|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 10 2 6 3 2 4+---+2 8+---+6 +--R (32a c x - 352a c x + 48a x )\|- a \|- a +--R + +--R 2 2 10 3 6 8+---+2 +--R (- 128a c x + 160a c x )\|- a +--R + +--R 2 2 10 3 6 4 2 4+---+ +--R (64a c x - 16a c x - 80a x )\|- a +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 7 3 4+---+2 8+---+6 2 11 7 8+---+2 +--R (19c x - 8a x )\|- a \|- a + (4c x - 14a c x )\|- a +--R + +--R 2 11 7 2 3 4+---+ +--R (- 2c x + 5a c x + 7a x )\|- a +--R * +--R 8+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 2 9 7 5 | 1 +--R (34816a c x - 2048a c x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 10 5 6 | 1 +--R (- 1664a c x + 640a c x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 11 3 7 | 1 2 12 8 +--R (64a c x - 80a c x ) |- -------- - 2c x + 7a c x +--R 8| 7 +--R \| 65536a c +--R * +--R 4+-+2 +--R \|c +--R + +--R +----------+6 +--R 6 2 8 7 4 4+---+ | 1 +--R (69632a c x - 4096a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 9 5 5 4+---+ | 1 +--R (- 3328a c x + 1280a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 10 3 6 4+---+ | 1 +--R (128a c x - 160a c x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 7 4+---+ +--R (- 4c x + 14a c x )\|- a +--R * +--R 4+-+ +--R \|c +--R + +--R 6 2 7 7 3 8+---+4 6 2 7 7 3 4+---+2 +--R ((69632a c x - 4096a c x )\|- a + (34816a c x - 2048a c x )\|- a ) +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 2 8 5 4 8+---+4 +--R (- 3328a c x + 1280a c x )\|- a +--R + +--R 4 2 8 5 4 4+---+2 +--R (- 1664a c x + 640a c x )\|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 2 9 3 5 8+---+4 2 2 9 3 5 4+---+2 +--R ((128a c x - 160a c x )\|- a + (64a c x - 80a c x )\|- a ) +--R * +--R +----------+2 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 10 6 8+---+4 2 10 6 4+---+2 +--R (- 4c x + 14a c x )\|- a + (- 2c x + 7a c x )\|- a +--R / +--R +----------+6 +--R 7 2 9 8 5 9 | 1 +--R (278528a c x + 262144a c x - 16384a x) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 5 2 10 6 6 7 2 | 1 +--R (- 13312a c x - 8192a c x + 5120a x ) |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 3 2 11 4 7 5 3 | 1 2 12 +--R (512a c x - 128a c x - 640a x ) |- -------- - 16a c x +--R 8| 7 +--R \| 65536a c +--R + +--R 2 8 3 4 +--R 40a c x + 56a x +--R * +--R 8+-+4 +--R \|c +--R + +--R +----------+6 +--R 6 2 10 7 6 8 2 8+---+6 | 1 +--R (139264a c x + 131072a c x - 8192a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 11 5 7 6 3 8+---+6 | 1 +--R (- 6656a c x - 4096a c x + 2560a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 12 3 8 4 4 8+---+6 | 1 +--R (256a c x - 64a c x - 320a x )\|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 13 9 2 5 8+---+6 +--R (- 8c x + 20a c x + 28a x )\|- a +--R * +--R 4+-+2 +--R \|c +--R + +--R 6 2 9 7 5 8 4+---+8+---+6 +--R (278528a c x + 262144a c x - 16384a x)\|- a \|- a +--R * +--R +----------+6 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 4 2 10 5 6 6 2 4+---+8+---+6 +--R (- 13312a c x - 8192a c x + 5120a x )\|- a \|- a +--R * +--R +----------+4 +--R | 1 +--R |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 11 3 7 4 3 4+---+8+---+6 | 1 +--R (512a c x - 128a c x - 640a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 12 8 2 4 4+---+8+---+6 +--R (- 16c x + 40a c x + 56a x )\|- a \|- a +--R * +--R 4+-+ +--R \|c +--R + +--R +----------+6 +--R 6 2 8 7 4 8 4+---+2 8+---+6 | 1 +--R (139264a c x + 131072a c x - 8192a )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+4 +--R 4 2 9 5 5 6 4+---+2 8+---+6 | 1 +--R (- 6656a c x - 4096a c x + 2560a x)\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R +----------+2 +--R 2 2 10 3 6 4 2 4+---+2 8+---+6 | 1 +--R (256a c x - 64a c x - 320a x )\|- a \|- a |- -------- +--R 8| 7 +--R \| 65536a c +--R + +--R 2 11 7 2 3 4+---+2 8+---+6 +--R (- 8c x + 20a c x + 28a x )\|- a \|- a +--R * +--R 8+-+2 +--R \|c +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 637 + +)clear all + +--S 638 of 1347 +t0:=1/(x^(3/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ---------------- +--R 5 +-+ +--R (c x + a x)\|x +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1347 +r0:=1/2*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_ + 1/2*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(9/8)-_ + 1/2*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*sqrt(2))+1/2*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+1/4*c^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(9/8)*sqrt(2))-1/4*c^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_ + sqrt(2))+(-2)/(a*sqrt(x)) +--R +--R +--R (2) +--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+ +-+ \|c \|x 8+-+ +-+ \|2 \|c \|x + \|- a +--R 2\|2 \|c \|x atanh(--------) - 2\|c \|x atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+ +-+ \|2 \|c \|x - \|- a +-+8+-+ +-+ \|c \|x +--R - 2\|c \|x atan(---------------------) - 2\|2 \|c \|x atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+ +--R - 8\|2 \|- a +--R / +--R +-+8+---+ +-+ +--R 4a\|2 \|- a \|x +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +---------+ +--R | c +-+ +--R a |- ------- \|x +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c +-+ +-+ 8 | c +--R - a\|2 |- ------- \|x log(c\|x + 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c +-+ +-+ 8 | c +--R a\|2 |- ------- \|x log(c\|x - 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +--R | c +-+ +--R a |- ------- \|x +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c +-+ \| 65536a +--R - 2a |- ------- \|x atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x - 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c +-+ \| 65536a +-+ +--R - 2a |- ------- \|x atan(-------------------------------- - 2\|2 +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x + 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R / +--R +-+ +-+ +--R a\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 640 + +--S 641 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +---------+ +--R | c 8+---+ +--R 4a |- ------- \|- a +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c 8+---+ +-+ 8 | c +--R - 4a\|2 |- ------- \|- a log(c\|x + 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +---------+7 +--R +-+ | c 8+---+ +-+ 8 | c +--R 4a\|2 |- ------- \|- a log(c\|x - 16384a |- ------- ) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R +---------+ +--R | c 8+---+ +--R 4a |- ------- \|- a +--R 8| 9 +--R \| 65536a +--R * +--R +---------+7 +---------+6 +--R 8 +-+ | c +-+ 7 | c +--R log(- 16384a \|2 |- ------- \|x - 4096a |- ------- + c x) +--R 8| 9 8| 9 +--R \| 65536a \| 65536a +--R + +--R 8+-+ +-+ +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+8+-+ \|c \|x +--R \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) - 2\|2 \|c atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R 8+-+ \|2 \|c \|x + \|- a 8+-+ \|2 \|c \|x - \|- a +--R 2\|c atan(---------------------) + 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+8+-+ \|c \|x +--R 2\|2 \|c atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c 8+---+ \| 65536a +--R - 8a |- ------- \|- a atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x - 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+7 +--R 8 | c +--R 16384a |- ------- +--R +---------+ 8| 9 +--R | c 8+---+ \| 65536a +--R - 8a |- ------- \|- a atan(--------------------------------) +--R 8| 9 +---------+7 +--R \| 65536a +-+ +-+ 8 | c +--R c\|2 \|x + 16384a |- ------- +--R 8| 9 +--R \| 65536a +--R / +--R +-+8+---+ +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +---------+6 +--R 7 2 9 8 5 9 | c +--R (12288a c x - 55296a c x + 6144a x) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+4 +--R 5 2 8 6 4 7 | c +--R (- 1600a c x + 2944a c x - 64a ) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+2 +--R 3 2 7 4 3 | c 3 10 2 6 2 2 +--R (168a c x - 120a c x ) |- ------- + c x - 13a c x + 4a c x +--R 8| 9 +--R \| 65536a +--R / +--R +---------+6 +--R 8 2 10 9 6 10 2 | c +--R (32768a c x - 8192a c x - 40960a x ) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+4 +--R 6 2 9 7 5 8 | c +--R (- 3328a c x - 2048a c x + 1280a x) |- ------- +--R 8| 9 +--R \| 65536a +--R + +--R +---------+2 +--R 4 2 8 5 4 6 | c 3 11 2 2 7 +--R (272a c x + 256a c x - 16a ) |- ------- + 4a c x - 10a c x +--R 8| 9 +--R \| 65536a +--R + +--R 3 3 +--R - 14a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1347 +t0:=1/(x^(5/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------------- +--R 6 2 +-+ +--R (c x + a x )\|x +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1347 +r0:=(-2/3)/(a*x^(3/2))-1/2*c^(3/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(11/8)-1/2*c^(3/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(11/8)-1/2*c^(3/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*sqrt(2))+1/2*c^(3/8)*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(11/8)*sqrt(2))-1/4*c^(3/8)*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_ + sqrt(2))+1/4*c^(3/8)*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+3 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 3x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+3 +-+ \|c \|x 8+-+3 +-+ \|2 \|c \|x + \|- a +--R 6x\|2 \|c \|x atanh(--------) - 6x \|c \|x atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+3 +-+ \|2 \|c \|x - \|- a +-+8+-+3 +-+ \|c \|x +--R - 6x \|c \|x atan(---------------------) + 6x\|2 \|c \|x atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+3 +--R - 8\|2 \|- a +--R / +--R +-+8+---+3 +-+ +--R 12a x\|2 \|- a \|x +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 3 +--R | c +-+ +--R 3a x |- -------- \|x +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c +-+ 2 +-+ 7 | c +--R 3a x\|2 |- -------- \|x log(c \|x + 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c +-+ 2 +-+ 7 | c +--R - 3a x\|2 |- -------- \|x log(c \|x - 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R | c +-+ +--R 3a x |- -------- \|x +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c +-+ \| 65536a +--R 6a x |- -------- \|x atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x - 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c +-+ \| 65536a +-+ +--R 6a x |- -------- \|x atan(--------------------------------- - 2\|2 +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x + 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R / +--R +-+ +-+ +--R 3a x\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 645 + +--S 646 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 3 +--R | c 8+---+3 +--R 4a |- -------- \|- a +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c 8+---+3 2 +-+ 7 | c +--R 4a\|2 |- -------- \|- a log(c \|x + 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+5 +--R | 3 | 3 +--R +-+ | c 8+---+3 2 +-+ 7 | c +--R - 4a\|2 |- -------- \|- a log(c \|x - 1024a |- -------- ) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 3 +--R | c 8+---+3 +--R 4a |- -------- \|- a +--R 8| 11 +--R \| 65536a +--R * +--R +----------+5 +----------+2 +--R | 3 | 3 +--R 7 +-+ | c +-+ 3 | c 2 +--R log(- 1024a \|2 |- -------- \|x - 16a c |- -------- + c x) +--R 8| 11 8| 11 +--R \| 65536a \| 65536a +--R + +--R 8+-+3 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+3 \|c \|x 8+-+3 \|2 \|c \|x + \|- a +--R - 2\|2 \|c atanh(--------) + 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+3 \|2 \|c \|x - \|- a +-+8+-+3 \|c \|x +--R 2\|c atan(---------------------) - 2\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c 8+---+3 \| 65536a +--R 8a |- -------- \|- a atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x - 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+5 +--R | 3 +--R 7 | c +--R +----------+ 1024a |- -------- +--R | 3 8| 11 +--R | c 8+---+3 \| 65536a +--R 8a |- -------- \|- a atan(---------------------------------) +--R 8| 11 +----------+5 +--R \| 65536a | 3 +--R 2 +-+ +-+ 7 | c +--R c \|2 \|x + 1024a |- -------- +--R 8| 11 +--R \| 65536a +--R / +--R +-+8+---+3 +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +----------+6 +--R | 3 +--R 8 3 10 9 2 6 10 2 | c +--R (- 8192a c x + 106496a c x - 32768a c x ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+4 +--R | 3 +--R 6 3 7 7 2 3 | c +--R (5376a c x - 3840a c x ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+2 +--R | 3 +--R 3 4 8 4 3 4 5 2 | c 5 9 4 5 2 3 +--R (200a c x - 368a c x + 8a c ) |- -------- + 6c x - 27a c x + 3a c x +--R 8| 11 +--R \| 65536a +--R / +--R +----------+6 +--R | 3 +--R 10 2 8 11 4 12 | c +--R (139264a c x + 131072a c x - 8192a ) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+4 +--R | 3 +--R 7 3 9 8 2 5 9 | c +--R (6656a c x + 4096a c x - 2560a c x) |- -------- +--R 8| 11 +--R \| 65536a +--R + +--R +----------+2 +--R | 3 +--R 4 4 10 5 3 6 6 2 2 | c 5 11 2 4 7 +--R (256a c x - 64a c x - 320a c x ) |- -------- + 8a c x - 20a c x +--R 8| 11 +--R \| 65536a +--R + +--R 3 3 3 +--R - 28a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 647 + +)clear all + +--S 648 of 1347 +t0:=1/(x^(7/2)*(a+c*x^4)) +--R +--R +--R 1 +--R (1) ----------------- +--R 7 3 +-+ +--R (c x + a x )\|x +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1347 +r0:=(-2/5)/(a*x^(5/2))+1/2*c^(5/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(13/8)-1/2*c^(5/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + (-a)^(13/8)+1/2*c^(5/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*sqrt(2))-1/2*c^(5/8)*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_ + 1/4*c^(5/8)*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2))+1/4*c^(5/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5x \|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8+-+5 +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 5x \|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 +-+8+-+5 +-+ \|c \|x +--R 10x \|2 \|c \|x atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8+-+5 +-+ \|2 \|c \|x + \|- a +--R 10x \|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8+-+5 +-+ \|2 \|c \|x - \|- a +--R 10x \|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 +-+8+-+5 +-+ \|c \|x +-+8+---+5 +--R - 10x \|2 \|c \|x atan(--------) - 8\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R 2 +-+8+---+5 +-+ +--R 20a x \|2 \|- a \|x +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +----------+ +--R | 5 +--R 2 | c +-+ +--R 5a x |- -------- \|x +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R 2 +-+ | c +-+ 2 +-+ 5 | c +--R 5a x \|2 |- -------- \|x log(c \|x + 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R 2 +-+ | c +-+ 2 +-+ 5 | c +--R - 5a x \|2 |- -------- \|x log(c \|x - 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 5 +--R 2 | c +-+ +--R 5a x |- -------- \|x +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R 2 | c +-+ \| 65536a +--R - 10a x |- -------- \|x atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x - 64a |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R 2 | c +-+ \| 65536a +-+ +--R - 10a x |- -------- \|x atan(------------------------------- - 2\|2 +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x + 64a |- -------- +--R 8| 13 +--R \| 65536a +--R / +--R 2 +-+ +-+ +--R 5a x \|2 \|x +--R Type: Union(Expression(Integer),...) +--E 650 + +--S 651 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R \|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +----------+ +--R | 5 +--R | c 8+---+5 +--R 4a |- -------- \|- a +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R +-+ | c 8+---+5 2 +-+ 5 | c +--R 4a\|2 |- -------- \|- a log(c \|x + 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +----------+3 +--R | 5 | 5 +--R +-+ | c 8+---+5 2 +-+ 5 | c +--R - 4a\|2 |- -------- \|- a log(c \|x - 64a |- -------- ) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R +----------+ +--R | 5 +--R | c 8+---+5 +--R 4a |- -------- \|- a +--R 8| 13 +--R \| 65536a +--R * +--R +----------+3 +----------+6 +--R | 5 | 5 +--R 5 2 +-+ | c +-+ 10 | c 4 +--R log(- 64a c \|2 |- -------- \|x + 4096a |- -------- + c x) +--R 8| 13 8| 13 +--R \| 65536a \| 65536a +--R + +--R 8+-+5 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - \|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+5 \|c \|x 8+-+5 \|2 \|c \|x + \|- a +--R - 2\|2 \|c atanh(--------) - 2\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+5 \|2 \|c \|x - \|- a +-+8+-+5 \|c \|x +--R - 2\|c atan(---------------------) + 2\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R | c 8+---+5 \| 65536a +--R - 8a |- -------- \|- a atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x - 64a |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+3 +--R | 5 +--R 5 | c +--R +----------+ 64a |- -------- +--R | 5 8| 13 +--R | c 8+---+5 \| 65536a +--R - 8a |- -------- \|- a atan(-------------------------------) +--R 8| 13 +----------+3 +--R \| 65536a | 5 +--R 2 +-+ +-+ 5 | c +--R c \|2 \|x + 64a |- -------- +--R 8| 13 +--R \| 65536a +--R / +--R +-+8+---+5 +--R 4a\|2 \|- a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +----------+6 +--R | 5 +--R 10 2 7 11 3 | c +--R (172032a c x - 122880a c x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+4 +--R | 5 +--R 6 4 10 7 3 6 8 2 2 | c +--R (- 1024a c x + 13312a c x - 4096a c x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+2 +--R | 5 +--R 3 5 9 4 4 5 5 3 | c 6 8 5 4 +--R (- 192a c x + 864a c x - 96a c x) |- -------- - 25c x + 46a c x +--R 8| 13 +--R \| 65536a +--R + +--R 2 4 +--R - a c +--R / +--R +----------+6 +--R | 5 +--R 11 2 10 12 6 13 2 | c +--R (131072a c x - 32768a c x - 163840a x ) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+4 +--R | 5 +--R 8 3 9 9 2 5 10 | c +--R (13312a c x + 8192a c x - 5120a c x) |- -------- +--R 8| 13 +--R \| 65536a +--R + +--R +----------+2 +--R | 5 +--R 5 4 8 6 3 4 7 2 | c 6 11 2 5 7 +--R (1088a c x + 1024a c x - 64a c ) |- -------- - 16a c x + 40a c x +--R 8| 13 +--R \| 65536a +--R + +--R 3 4 3 +--R 56a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1347 +t0:=x^(13/2)/(a+c*x^4)^2 +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1347 +r0:=-1/4*x^(7/2)/(c*(a+c*x^4))+7/16*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8))-7/16*atan(1-c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(1/8)*c^(15/8)*sqrt(2))+_ + 7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(1/8)*c^(15/8)*sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*_ + c^(15/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(1/8)*c^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 14c x - 14a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (14c x + 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (14c x + 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 3 +-+8+---+8+-+7 +-+ +--R (14c x + 14a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+8+-+7 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (28c x + 28a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (28c x + 28a c)\|2 |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x + 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 28c x - 28a c)\|2 |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x - 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 28c x - 28a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (56c x + 56a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x - 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (56c x + 56a c) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x + 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 3 +-+ +-+ +--R - x \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 224c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 224c\|2 \|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x + 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 224c\|2 \|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R +-+ 13 | 1 +--R log(\|x - 34359738368a c |- ------------------ ) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 224c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+7 +--R 13 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ------------------ \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 11 | 1 +--R - 1073741824a c |- ------------------ + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 14atan(---------------------) - 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 448c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x - 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+ | 1 8+-+7 +--R 448c\|- a |- ------------------ \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +--------------------+7 +--R 13 | 1 +--R 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R atan(---------------------------------------------------) +--R +--------------------+7 +--R +-+ +-+ 13 | 1 +--R \|2 \|x + 34359738368a c |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R / +--R +-+8+---+8+-+7 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 9 2 12 5 3 11 +--R (- 22548578304a c x + 101468602368a c x - 11274289152a c x) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 9 8 2 8 4 3 7 | 1 +--R (45875200a c x - 84410368a c x + 1835008a c ) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 7 2 4 3 | 1 2 10 6 +--R (- 75264a c x + 53760a c x ) |- ------------------ - 7c x + 91a c x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 2 2 +--R - 28a x +--R / +--R 15 10 2 14 6 3 13 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 11 9 2 10 5 3 9 +--R (- 109051904a c x - 67108864a c x + 41943040a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 7 8 2 6 4 3 5 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- ------------------ +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R 32c x - 80a c x - 112a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1347 +t0:=x^(11/2)/(a+c*x^4)^2 +--R +--R +--R 5 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1347 +r0:=-1/4*x^(5/2)/(c*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(13/8))-5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(3/8)*c^(13/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(3/8)*c^(13/8)*sqrt(2))+5/16*_ + atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(3/8)*_ + c^(13/8)*sqrt(2))-5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2))+_ + 5/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(3/8)*c^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 10c x - 10a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (10c x + 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (10c x + 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+ +--R (- 10c x - 10a)\|2 atan(--------) - 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+3 8+-+5 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (20c x + 20a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 20c x - 20a c)\|2 |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (20c x + 20a c)\|2 |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 20c x - 20a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 40c x - 40a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 40c x - 40a c) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 +-+ +-+ +--R - x \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 660 + +--S 661 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 160c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 160c\|2 \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 160c\|2 \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 2 8 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 160c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 2 8 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 10atan(---------------------) - 10atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 10\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 320c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 320c \|- a |- ------------------ \|c +--R 8| 3 13 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 2 8 | 1 +--R 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 2 8 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R / +--R +-+8+---+3 8+-+5 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 2 12 10 3 11 6 4 10 2 +--R (10737418240a c x - 139586437120a c x + 42949672960a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 2 8 7 3 7 3 | 1 +--R (- 110100480a c x + 78643200a c x ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 8 2 4 4 3 3 | 1 +--R (- 64000a c x + 117760a c x - 2560a c ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 9 5 2 +--R - 30c x + 135a c x - 15a x +--R / +--R 3 13 8 4 12 4 5 11 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 2 10 9 3 9 5 4 8 +--R (218103808a c x + 134217728a c x - 83886080a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 7 10 2 6 6 3 5 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------ +--R 8| 3 13 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R 64c x - 160a c x - 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 662 + +)clear all + +--S 663 of 1347 +t0:=x^(9/2)/(a+c*x^4)^2 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1347 +r0:=-1/4*x^(3/2)/(c*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(5/8)*c^(11/8))-3/16*atanh(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8))+3/16*atan(1-c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*c^(11/8)*sqrt(2))-3/16*_ + atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(5/8)*_ + c^(11/8)*sqrt(2))-3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2))+_ + 3/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(5/8)*c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 6c x - 6a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 6c x - 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 6c x - 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+ +--R (6c x + 6a)\|2 atan(--------) - 8x\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+5 8+-+3 +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 2 4 | 1 +--R (12c x + 12a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (- 12c x - 12a c)\|2 |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 +-+ | 1 +--R (12c x + 12a c)\|2 |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (- 12c x - 12a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R - 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (24c x + 24a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 2 4 | 1 +--R (24c x + 24a c) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R - x\|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 665 + +--S 666 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 96c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 96c\|2 \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 96c\|2 \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 2 4 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 96c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 2 4 +-+ | 1 +-+ +--R - 32768a c \|2 |- ------------------ \|x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 4 8 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 6atan(---------------------) + 6atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 6\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 192c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 192c \|- a |- ------------------ \|c +--R 8| 5 11 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 2 4 | 1 +--R 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 2 4 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R / +--R +-+8+---+5 8+-+3 +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--------------------+6 +--R 4 10 7 5 9 3 | 1 +--R (- 135291469824a c x + 96636764160a c x ) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 2 8 10 3 7 6 4 6 2 +--R (12582912a c x - 163577856a c x + 50331648a c x ) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 9 2 4 5 3 3 | 1 +--R (36864a c x - 165888a c x + 18432a c x) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 2 8 4 2 +--R 75c x - 138a c x + 3a +--R / +--R 4 12 10 5 11 6 6 10 2 +--R (274877906944a c x - 68719476736a c x - 343597383680a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 3 9 9 4 8 5 5 7 +--R (436207616a c x + 268435456a c x - 167772160a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 2 6 8 3 5 4 4 4 | 1 +--R (557056a c x + 524288a c x - 32768a c ) |- ------------------ +--R 8| 5 11 +--R \| 1099511627776a c +--R + +--R 4 11 3 7 2 2 3 +--R - 128c x + 320a c x + 448a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 667 + +)clear all + +--S 668 of 1347 +t0:=x^(7/2)/(a+c*x^4)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1347 +r0:=-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))-_ + 1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8))+_ + 1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(9/8)*_ + sqrt(2))-1/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(9/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*sqrt(2))-1/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(9/8)*_ + sqrt(2))-1/4*sqrt(x)/(c*(a+c*x^4)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 2c x - 2a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 2c x - 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 2c x - 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+ +--R (- 2c x - 2a)\|2 atan(--------) - 8\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 2 4 +-+8+---+7 8+-+ +--R (32c x + 32a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 2 4 | 1 +--R (4c x + 4a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 +-+ | 1 +--R (4c x + 4a c)\|2 |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x + 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 +-+ | 1 +--R (- 4c x - 4a c)\|2 |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x - 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 4c x - 4a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R - 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 8c x - 8a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x - 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 2 4 | 1 +--R (- 8c x - 8a c) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x + 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R - \|2 \|x +--R / +--R 2 4 +-+ +--R (4c x + 4a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 670 + +--S 671 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 32c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 32c\|2 \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x + 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 32c\|2 \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ | 1 +--R log(\|x - 32a c |- -----------------) +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 32c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R +-+ | 1 +-+ +--R - 32a c\|2 |- ----------------- \|x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 2 | 1 +--R 1024a c |- ----------------- + x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 2atan(---------------------) + 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 64c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x - 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 64c \|- a |- ----------------- \|c +--R 8| 7 9 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R | 1 +--R 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R atan(--------------------------------------) +--R +-------------------+ +--R +-+ +-+ | 1 +--R \|2 \|x + 32a c |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R / +--R +-+8+---+7 8+-+ +--R 32c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 8 8 6 7 4 7 6 +--R (13421772800a c x - 24696061952a c x + 536870912a c ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 3 6 9 4 5 5 5 4 | 1 +--R (- 6291456a c x + 28311552a c x - 3145728a c x) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 10 2 3 6 3 2 2 | 1 7 +--R (2048a c x - 26624a c x + 8192a c x ) |- ----------------- + 21c x +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 3 +--R - 15a x +--R / +--R 6 9 8 7 8 4 8 7 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 4 7 9 5 6 5 6 5 +--R (- 218103808a c x - 134217728a c x + 83886080a c x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 2 5 10 3 4 6 4 3 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ----------------- +--R 8| 7 9 +--R \| 1099511627776a c +--R + +--R 3 11 2 7 2 3 +--R - 64c x + 160a c x + 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 672 + +)clear all + +--S 673 of 1347 +t0:=x^(5/2)/(a+c*x^4)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1347 +r0:=1/4*x^(7/2)/(a*(a+c*x^4))-1/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*c^(7/8))+1/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(9/8)*c^(7/8))+1/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-1/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(7/8)*sqrt(2))-_ + 1/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(9/8)*c^(7/8)*sqrt(2))+1/32*log((-a)^(1/4)+c^(1/4)*x+_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- c x - a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (c x + a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 2c x - 2a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (2c x + 2a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 4 \|2 \|c \|x - \|- a 4 +-+ \|c \|x +--R (2c x + 2a)atan(---------------------) + (2c x + 2a)\|2 atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 3 +-+8+---+8+-+7 +-+ +--R 8x \|2 \|- a \|c \|x +--R / +--R 4 2 +-+8+---+8+-+7 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 4 2 | 1 +--R (4a c x + 4a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (4a c x + 4a )\|2 |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x + 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (- 4a c x - 4a )\|2 |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x - 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 4a c x - 4a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (8a c x + 8a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x - 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (8a c x + 8a ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x + 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 3 +-+ +-+ +--R x \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 675 + +--S 676 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 32a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 32a\|2 \|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x + 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 32a\|2 \|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R +-+ 8 6 | 1 +--R log(\|x - 34359738368a c |- ----------------- ) +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 32a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+7 +--R 8 6 +-+ | 1 +-+ +--R - 34359738368a c \|2 |- ----------------- \|x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+6 +--R 7 5 | 1 +--R - 1073741824a c |- ----------------- + x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 2\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 2atan(---------------------) - 2atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 2\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 64a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x - 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 8+---+ | 1 8+-+7 +--R 64a\|- a |- ----------------- \|c +--R 8| 9 7 +--R \| 1099511627776a c +--R * +--R +-------------------+7 +--R 8 6 | 1 +--R 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R atan(-------------------------------------------------) +--R +-------------------+7 +--R +-+ +-+ 8 6 | 1 +--R \|2 \|x + 34359738368a c |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R / +--R +-+8+---+8+-+7 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 7 7 9 8 6 5 9 5 +--R (- 3221225472a c x + 14495514624a c x - 1610612736a c x) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 5 5 8 6 4 4 7 3 | 1 +--R (6553600a c x - 12058624a c x + 262144a c ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 3 3 7 4 2 3 | 1 2 10 6 +--R (- 10752a c x + 7680a c x ) |- ----------------- - c x + 13a c x +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 2 2 +--R - 4a x +--R / +--R 8 8 10 9 7 6 10 6 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a c x ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 6 6 9 7 5 5 8 4 +--R (- 109051904a c x - 67108864a c x + 41943040a c x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 4 8 5 3 4 6 2 | 1 +--R (139264a c x + 131072a c x - 8192a c ) |- ----------------- +--R 8| 9 7 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R 32a c x - 80a c x - 112a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 677 + +)clear all + +--S 678 of 1347 +t0:=x^(3/2)/(a+c*x^4)^2 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1347 +r0:=1/4*x^(5/2)/(a*(a+c*x^4))+3/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(5/8))+3/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(5/8))+3/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(5/8)*sqrt(2))+_ + 3/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(11/8)*c^(5/8)*sqrt(2))-3/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(11/8)*_ + c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (3c x + 3a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 3c x - 3a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 6c x - 6a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (6c x + 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (6c x + 6a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x 2 +-+8+---+3 8+-+5 +-+ +--R (- 6c x - 6a)\|2 atan(--------) + 8x \|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+3 8+-+5 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 4 2 | 1 +--R (12a c x + 12a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (- 12a c x - 12a )\|2 |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (12a c x + 12a )\|2 |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 12a c x - 12a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 24a c x - 24a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 24a c x - 24a ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 2 +-+ +-+ +--R x \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 680 + +--S 681 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 3log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 96a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 96a\|2 \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x + 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 96a\|2 \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R +-+ 7 3 | 1 +--R log(\|x - 33554432a c |- ------------------ ) +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 96a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+5 +--R 7 3 +-+ | 1 +-+ +--R - 33554432a c \|2 |- ------------------ \|x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 | 1 +--R - 1024a c |- ------------------ + x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 3log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 6\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 6atan(---------------------) - 6atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 6\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 192a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x - 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+3 | 1 8+-+5 +--R 192a \|- a |- ------------------ \|c +--R 8| 11 5 +--R \| 1099511627776a c +--R * +--R +--------------------+5 +--R 7 3 | 1 +--R 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R atan(-----------------------------------------------) +--R +--------------------+5 +--R +-+ +-+ 7 3 | 1 +--R \|2 \|x + 33554432a c |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R / +--R +-+8+---+3 8+-+5 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 8 6 10 9 5 6 10 4 2 +--R (6442450944a c x - 83751862272a c x + 25769803776a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+4 +--R 6 4 7 7 3 3 | 1 +--R (- 66060288a c x + 47185920a c x ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 3 8 4 2 4 5 | 1 2 9 +--R (- 38400a c x + 70656a c x - 1536a c) |- ------------------ - 18c x +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 5 2 +--R 81a c x - 9a x +--R / +--R 10 6 8 11 5 4 12 4 +--R (292057776128a c x + 274877906944a c x - 17179869184a c ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 7 5 9 8 4 5 9 3 +--R (218103808a c x + 134217728a c x - 83886080a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 4 4 10 5 3 6 6 2 2 | 1 +--R (131072a c x - 32768a c x - 163840a c x ) |- ------------------ +--R 8| 11 5 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R 64a c x - 160a c x - 224a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 682 + +)clear all + +--S 683 of 1347 +t0:=sqrt(x)/(a+c*x^4)^2 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------- +--R 2 8 4 2 +--R c x + 2a c x + a +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1347 +r0:=1/4*x^(3/2)/(a*(a+c*x^4))-5/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(13/8)*c^(3/8))+5/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(13/8)*c^(3/8))-5/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+5/16*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(3/8)*sqrt(2))+_ + 5/32*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(3/8)*sqrt(2))-5/32*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(13/8)*_ + c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (5c x + 5a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 5c x - 5a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 10c x - 10a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 10c x - 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 10c x - 10a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+5 8+-+3 +-+ +--R (10c x + 10a)\|2 atan(--------) + 8x\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+5 8+-+3 +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------+ +--R 4 2 | 1 +--R (20a c x + 20a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (- 20a c x - 20a )\|2 |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 +-+ | 1 +--R (20a c x + 20a )\|2 |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (- 20a c x - 20a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R - 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (40a c x + 40a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 4 2 | 1 +--R (40a c x + 40a ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R x\|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 685 + +--S 686 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 5log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 160a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 160a\|2 \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x + 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 160a\|2 \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R +-+ 5 | 1 +--R log(\|x - 32768a c |- ------------------ ) +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R - +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 160a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R log +--R +--------------------+3 +--R 5 +-+ | 1 +-+ +--R - 32768a c\|2 |- ------------------ \|x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+6 +--R 10 2 | 1 +--R 1073741824a c |- ------------------ + x +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 5log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 10\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 10atan(---------------------) + 10atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 10\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 320a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x - 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+ +--R 8+---+5 | 1 8+-+3 +--R 320a \|- a |- ------------------ \|c +--R 8| 13 3 +--R \| 1099511627776a c +--R * +--R +--------------------+3 +--R 5 | 1 +--R 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R atan(--------------------------------------------) +--R +--------------------+3 +--R +-+ +-+ 5 | 1 +--R \|2 \|x + 32768a c |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R / +--R +-+8+---+5 8+-+3 +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R +--------------------+6 +--R 10 4 7 11 3 3 | 1 +--R (- 225485783040a c x + 161061273600a c x ) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 6 4 10 7 3 6 8 2 2 +--R (20971520a c x - 272629760a c x + 83886080a c x ) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 3 3 9 4 2 5 5 | 1 +--R (61440a c x - 276480a c x + 30720a c x) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 2 8 4 2 +--R 125c x - 230a c x + 5a +--R / +--R 11 5 10 12 4 6 13 3 2 +--R (274877906944a c x - 68719476736a c x - 343597383680a c x ) +--R * +--R +--------------------+6 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 8 4 9 9 3 5 10 2 +--R (436207616a c x + 268435456a c x - 167772160a c x) +--R * +--R +--------------------+4 +--R | 1 +--R |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R +--------------------+2 +--R 5 3 8 6 2 4 7 | 1 +--R (557056a c x + 524288a c x - 32768a c) |- ------------------ +--R 8| 13 3 +--R \| 1099511627776a c +--R + +--R 3 11 2 2 7 3 3 +--R - 128a c x + 320a c x + 448a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 687 + +)clear all + +--S 688 of 1347 +t0:=1/((a+c*x^4)^2*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 8 4 2 +-+ +--R (c x + 2a c x + a )\|x +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1347 +r0:=7/16*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))+_ + 7/16*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(1/8))-_ + 7/16*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_ + c^(1/8)*sqrt(2))+7/16*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(15/8)*c^(1/8)*sqrt(2))-7/32*log((-a)^(1/4)+c^(1/4)*x-_ + (-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*_ + sqrt(2))+7/32*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(15/8)*c^(1/8)*sqrt(2))+1/4*_ + sqrt(x)/(a*(a+c*x^4)) +--R +--R +--R (2) +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 7a)log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 7a)log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +--R (- 14c x - 14a)\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x + \|- a +--R (- 14c x - 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 \|2 \|c \|x - \|- a +--R (- 14c x - 14a)atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+ \|c \|x +-+8+---+7 8+-+ +-+ +--R (- 14c x - 14a)\|2 atan(--------) + 8\|2 \|- a \|c \|x +--R 8+---+ +--R \|- a +--R / +--R 4 2 +-+8+---+7 8+-+ +--R (32a c x + 32a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------------+ +--R 4 2 | 1 +--R (28a c x + 28a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +-------------------+2 +--R 2 +-+ | 1 +-+ 4 | 1 +--R 32a \|2 |- ----------------- \|x + 1024a |- ----------------- +--R 8| 15 8| 15 +--R \| 1099511627776a c \| 1099511627776a c +--R + +--R x +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (28a c x + 28a )\|2 |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x + 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 +-+ | 1 +--R (- 28a c x - 28a )\|2 |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x - 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 28a c x - 28a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 1 +-+ +--R - 32a \|2 |- ----------------- \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 | 1 +--R 1024a |- ----------------- + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 56a c x - 56a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+ +--R 4 2 | 1 +--R (- 56a c x - 56a ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-+ +-+ +--R \|2 \|x +--R / +--R 4 2 +-+ +--R (4a c x + 4a )\|2 +--R Type: Union(Expression(Integer),...) +--E 690 + +--S 691 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 224a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +-------------------+2 +--R 2 +-+ | 1 +-+ 4 | 1 +--R 32a \|2 |- ----------------- \|x + 1024a |- ----------------- +--R 8| 15 8| 15 +--R \| 1099511627776a c \| 1099511627776a c +--R + +--R x +--R + +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 224a\|2 \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x + 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 224a\|2 \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R +-+ 2 | 1 +--R log(\|x - 32a |- -----------------) +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 224a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R log +--R +-------------------+ +--R 2 +-+ | 1 +-+ +--R - 32a \|2 |- ----------------- \|x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 4 | 1 +--R 1024a |- ----------------- + x +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 14atan(---------------------) + 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 448a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R - +--R +-------------------+ +--R 8+---+7 | 1 8+-+ +--R 448a \|- a |- ----------------- \|c +--R 8| 15 +--R \| 1099511627776a c +--R * +--R +-------------------+ +--R 2 | 1 +--R 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R atan(-------------------------------------) +--R +-------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 32a |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R / +--R +-+8+---+7 8+-+ +--R 32a\|2 \|- a \|c +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 11 2 8 12 4 13 +--R (93952409600a c x - 172872433664a c x + 3758096384a ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+4 +--R 7 2 9 8 5 9 | 1 +--R (- 44040192a c x + 198180864a c x - 22020096a x) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 3 2 10 4 6 5 2 | 1 +--R (14336a c x - 186368a c x + 57344a x ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 7 3 +--R 147c x - 105a x +--R / +--R 13 2 8 14 4 15 +--R (292057776128a c x + 274877906944a c x - 17179869184a ) +--R * +--R +-------------------+6 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 9 2 9 10 5 11 +--R (- 218103808a c x - 134217728a c x + 83886080a x) +--R * +--R +-------------------+4 +--R | 1 +--R |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R +-------------------+2 +--R 5 2 10 6 6 7 2 | 1 +--R (131072a c x - 32768a c x - 163840a x ) |- ----------------- +--R 8| 15 +--R \| 1099511627776a c +--R + +--R 2 11 2 7 3 3 +--R - 64a c x + 160a c x + 224a x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 692 + +)clear all + +--S 693 of 1347 +t0:=1/(x^(3/2)*(a+c*x^4)^2) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 9 5 2 +-+ +--R (c x + 2a c x + a x)\|x +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1347 +r0:=-9/16*c^(1/8)*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_ + 9/16*c^(1/8)*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/(-a)^(17/8)+_ + 9/16*c^(1/8)*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(17/8)*sqrt(2))-9/16*c^(1/8)*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*sqrt(2))-9/32*c^(1/8)*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(17/8)*sqrt(2))+9/32*c^(1/8)*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(17/8)*_ + sqrt(2))+(-9/4)/(a^2*sqrt(x))+1/4/(a*(a+c*x^4)*sqrt(x)) +--R +--R +--R (2) +--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 9a)\|c \|x log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 4 8+-+ +-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 9a)\|c \|x log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 4 +-+8+-+ +-+ \|c \|x +--R (18c x + 18a)\|2 \|c \|x atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 8+-+ +-+ \|2 \|c \|x + \|- a +--R (- 18c x - 18a)\|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 4 8+-+ +-+ \|2 \|c \|x - \|- a +--R (- 18c x - 18a)\|c \|x atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 4 +-+8+-+ +-+ \|c \|x 4 +-+8+---+ +--R (- 18c x - 18a)\|2 \|c \|x atan(--------) + (- 72c x - 64a)\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R 2 4 3 +-+8+---+ +-+ +--R (32a c x + 32a )\|2 \|- a \|x +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 4a c x - 4a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 +-+ | 43046721c +-+ +--R (- 4a c x - 4a )\|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x + 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 +-+ | 43046721c +-+ +--R (4a c x + 4a )\|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x - 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (4a c x + 4a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R - 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 8a c x - 8a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x - 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 4 3 | 43046721c +-+ +--R (- 8a c x - 8a ) |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x + 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 4 +-+ +--R (- 9c x - 8a)\|2 +--R / +--R 2 4 3 +-+ +-+ +--R (4a c x + 4a )\|2 \|x +--R Type: Union(Expression(Integer),...) +--E 695 + +--S 696 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 9\|c log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 32a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R - +--R +------------------+ +--R 2 +-+ | 43046721c 8+---+ +--R 32a \|2 |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x + 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 +-+ | 43046721c 8+---+ +--R 32a \|2 |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R +-+ 15 | 43046721c +--R log(4782969c\|x - 34359738368a |- ---------------- ) +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 32a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R log +--R +------------------+7 +--R 15 +-+ | 43046721c +-+ +--R - 34359738368a \|2 |- ---------------- \|x +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+6 +--R 13 | 43046721c +--R - 9663676416a |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R 8+-+ +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9\|c log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +-+8+-+ +-+ 8+---+ +--R +-+8+-+ \|c \|x 8+-+ \|2 \|c \|x + \|- a +--R - 18\|2 \|c atanh(--------) + 18\|c atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ +-+ 8+---+ 8+-+ +-+ +--R 8+-+ \|2 \|c \|x - \|- a +-+8+-+ \|c \|x +--R 18\|c atan(---------------------) + 18\|2 \|c atan(--------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 64a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x - 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R - +--R +------------------+ +--R 2 | 43046721c 8+---+ +--R 64a |- ---------------- \|- a +--R 8| 17 +--R \| 1099511627776a +--R * +--R +------------------+7 +--R 15 | 43046721c +--R 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R atan(-------------------------------------------------------) +--R +------------------+7 +--R +-+ +-+ 15 | 43046721c +--R 4782969c\|2 \|x + 34359738368a |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R / +--R 2 +-+8+---+ +--R 32a \|2 \|- a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 2 9 14 5 15 +--R (28991029248a c x - 130459631616a c x + 14495514624a x) +--R * +--R +------------------+6 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 9 2 8 10 4 11 +--R (- 4777574400a c x + 8790736896a c x - 191102976a ) +--R * +--R +------------------+4 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+2 +--R 5 2 7 6 3 | 43046721c 3 10 +--R (634894848a c x - 453496320a c x ) |- ---------------- + 4782969c x +--R 8| 17 +--R \| 1099511627776a +--R + +--R 2 6 2 2 +--R - 62178597a c x + 19131876a c x +--R / +--R 15 2 10 16 6 17 2 +--R (68719476736a c x - 17179869184a c x - 85899345920a x ) +--R * +--R +------------------+6 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 11 2 9 12 5 13 +--R (- 8833204224a c x - 5435817984a c x + 3397386240a x) +--R * +--R +------------------+4 +--R | 43046721c +--R |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R +------------------+2 +--R 7 2 8 8 4 9 | 43046721c +--R (913711104a c x + 859963392a c x - 53747712a ) |- ---------------- +--R 8| 17 +--R \| 1099511627776a +--R + +--R 2 3 11 3 2 7 4 3 +--R 17006112a c x - 42515280a c x - 59521392a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 697 + +)clear all + +--S 698 of 1347 +t0:=x^(15/2)/(a+c*x^4)^3 +--R +--R +--R 7 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1347 +r0:=-1/8*x^(9/2)/(c*(a+c*x^4)^2)-9/256*atan(c^(1/8)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))-9/256*_ + atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8))+_ + 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*_ + c^(17/8)*sqrt(2))-9/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(7/8)*c^(17/8)*sqrt(2))+_ + 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_ + 9/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(7/8)*c^(17/8)*sqrt(2))-_ + 9/64*sqrt(x)/(c^2*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 18c x - 36a c x - 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 18c x - 36a c x - 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (- 136c x - 72a)\|2 \|- a \|c \|x +--R / +--R 4 8 3 4 2 2 +-+8+---+7 8+-+ +--R (512c x + 1024a c x + 512a c )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (576c x + 1152a c x + 576a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 +-+ | 1 +--R (576c x + 1152a c x + 576a c )\|2 |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 +-+ | 1 +--R (- 576c x - 1152a c x - 576a c )\|2 |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 576c x - 1152a c x - 576a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 1152c x - 2304a c x - 1152a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 4 8 3 4 2 2 | 1 +--R (- 1152c x - 2304a c x - 1152a c ) |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (- 17c x - 9a)\|2 \|x +--R / +--R 4 8 3 4 2 2 +-+ +--R (64c x + 128a c x + 64a c )\|2 +--R Type: Union(Expression(Integer),...) +--E 700 + +--S 701 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 4608c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 4608c \|2 \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 4608c \|2 \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 4608c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c \|2 |- --------------------------- \|x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 2 4 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 18atan(---------------------) + 18atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 18\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 9216c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 9216c \|- a |- --------------------------- \|c +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R atan(--------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+7 8+-+ +--R 512c \|2 \|- a \|c +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 5 14 8 6 13 4 +--R 2026619832316723200a c x - 3728980491462770688a c x +--R + +--R 7 12 +--R 81064793292668928a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 3 10 9 4 9 5 5 8 +--R (- 3710851743744a c x + 16698832846848a c x - 1855425871872a c x) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 6 10 2 5 6 3 4 2 +--R (4718592a c x - 61341696a c x + 18874368a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 189c x - 135a x +--R / +--R 6 16 8 7 15 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 8 14 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 12 9 5 11 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 6 10 +--R 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 2 8 10 3 7 6 4 6 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 7 17 +--R \| 4722366482869645213696a c +--R + +--R 4 11 3 7 2 2 3 +--R - 1024c x + 2560a c x + 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 702 + +)clear all + +--S 703 of 1347 +t0:=x^(13/2)/(a+c*x^4)^3 +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1347 +r0:=-1/8*x^(7/2)/(c*(a+c*x^4)^2)+7/64*x^(7/2)/(a*c*(a+c*x^4))-_ + 7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_ + 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8))+_ + 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*_ + c^(15/8)*sqrt(2))-7/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(9/8)*c^(15/8)*sqrt(2))-_ + 7/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(9/8)*c^(15/8)*sqrt(2))+7/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(9/8)*_ + c^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (14c x + 28a c x + 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (14c x + 28a c x + 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (14c x + 28a c x + 14a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 7 3 +-+8+---+8+-+7 +-+ +--R (56c x - 8a x )\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+8+-+7 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (448a c x + 896a c x + 448a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (448a c x + 896a c x + 448a c)\|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (- 448a c x - 896a c x - 448a c)\|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 448a c x - 896a c x - 448a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +--R 9223372036854775808a c \|2 |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-+ +--R \|x +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (896a c x + 1792a c x + 896a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (896a c x + 1792a c x + 896a c) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +-+ +-+ +--R (7c x - a x )\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 705 + +--S 706 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 3584a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 8 13 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R +-+8+---+ | 1 8+-+7 +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 8 13 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 3584a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R 8 13 +-+ +--R 9223372036854775808a c \|2 +--R * +--R +-----------------------------+7 +--R | 1 +-+ +--R |- --------------------------- \|x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 7 11 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 14atan(---------------------) - 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 7168a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 8+---+ | 1 8+-+7 +--R 7168a c\|- a |- --------------------------- \|c +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 8 13 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 8 13 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+8+-+7 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 7 13 9 8 12 5 +--R - 378302368699121664a c x + 1702360659146047488a c x +--R + +--R 9 11 +--R - 189151184349560832a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 5 9 8 6 8 4 7 7 +--R (3006477107200a c x - 5531917877248a c x + 120259084288a c ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 3 5 7 4 4 3 | 1 +--R (- 19267584a c x + 13762560a c x ) |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 2 10 6 2 2 +--R - 7c x + 91a c x - 28a x +--R / +--R 8 15 10 9 14 6 +--R 18446744073709551616a c x - 4611686018427387904a c x +--R + +--R 10 13 2 +--R - 23058430092136939520a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 6 11 9 7 10 5 +--R - 114349209288704a c x - 70368744177664a c x +--R + +--R 8 9 +--R 43980465111040a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 4 7 8 5 6 4 6 5 +--R (570425344a c x + 536870912a c x - 33554432a c ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 9 15 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R 512a c x - 1280a c x - 1792a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 707 + +)clear all + +--S 708 of 1347 +t0:=x^(11/2)/(a+c*x^4)^3 +--R +--R +--R 5 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1347 +r0:=-1/8*x^(5/2)/(c*(a+c*x^4)^2)+5/64*x^(5/2)/(a*c*(a+c*x^4))+_ + 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8))+_ + 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*_ + c^(13/8))+15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(11/8)*c^(13/8)*sqrt(2))-15/256*atan(1+c^(1/8)*_ + sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(11/8)*c^(13/8)*sqrt(2))+_ + 15/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2))-_ + 15/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(11/8)*c^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (30c x + 60a c x + 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (30c x + 60a c x + 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 6 2 +-+8+---+3 8+-+5 +-+ +--R (40c x - 24a x )\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+3 8+-+5 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (960a c x + 1920a c x + 960a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 3 8 2 2 4 3 +-+ +--R (- 960a c x - 1920a c x - 960a c)\|2 +--R * +--R +------------------------------+ +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x + 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (960a c x + 1920a c x + 960a c)\|2 |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x - 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 960a c x - 1920a c x - 960a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 1920a c x - 3840a c x - 1920a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x - 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 1920a c x - 3840a c x - 1920a c) |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x + 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 6 2 +-+ +-+ +--R (5c x - 3a x )\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 710 + +--S 711 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x + 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R +-+8+---+3 | 1 8+-+5 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R +-+ 7 8 | 1 +--R log(\|x - 35184372088832a c |- ---------------------------- ) +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+5 +--R 7 8 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- ---------------------------- \|x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+2 +--R 3 3 | 1 +--R - 262144a c |- ---------------------------- + x +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 30atan(---------------------) - 30atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 30\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x - 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+3 | 1 8+-+5 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+5 +--R 7 8 | 1 +--R 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +------------------------------+5 +--R +-+ +-+ 7 8 | 1 +--R \|2 \|x + 35184372088832a c |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+3 8+-+5 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 8 12 10 9 11 6 +--R 540431955284459520a c x - 7025615418697973760a c x +--R + +--R 10 10 2 +--R 2161727821137838080a c x +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 6 8 7 7 7 3 +--R (- 21646635171840a c x + 15461882265600a c x ) +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 3 5 8 4 4 4 5 3 +--R (- 49152000a c x + 90439680a c x - 1966080a c ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 2 9 5 2 +--R - 90c x + 405a c x - 45a x +--R / +--R 10 13 8 11 12 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 12 11 +--R - 4611686018427387904a c +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 7 10 9 8 9 5 +--R 228698418577408a c x + 140737488355328a c x +--R + +--R 9 8 +--R - 87960930222080a c x +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 4 7 10 5 6 6 6 5 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 11 13 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R 1024a c x - 2560a c x - 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 712 + +)clear all + +--S 713 of 1347 +t0:=x^(9/2)/(a+c*x^4)^3 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1347 +r0:=-1/8*x^(3/2)/(c*(a+c*x^4)^2)+3/64*x^(3/2)/(a*c*(a+c*x^4))-_ + 15/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))+_ + 15/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*c^(11/8))-_ + 15/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(13/8)*_ + c^(11/8)*sqrt(2))+15/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(13/8)*c^(11/8)*sqrt(2))+15/512*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2))-15/512*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(13/8)*c^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (15c x + 30a c x + 15a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 15c x - 30a c x - 15a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 30c x - 60a c x - 30a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 30c x - 60a c x - 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 30c x - 60a c x - 30a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (30c x + 60a c x + 30a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 5 +-+8+---+5 8+-+3 +-+ +--R (24c x - 40a x)\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+5 8+-+3 +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (960a c x + 1920a c x + 960a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 3 8 2 2 4 3 +-+ +--R (- 960a c x - 1920a c x - 960a c)\|2 +--R * +--R +------------------------------+ +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x + 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (960a c x + 1920a c x + 960a c)\|2 |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x - 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 960a c x - 1920a c x - 960a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R - 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (1920a c x + 3840a c x + 1920a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x - 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (1920a c x + 3840a c x + 1920a c) |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x + 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 5 +-+ +-+ +--R (3c x - 5a x)\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 715 + +--S 716 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 15log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x + 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R +-+8+---+5 | 1 8+-+3 +--R 7680a c\|2 \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R +-+ 5 4 | 1 +--R log(\|x - 134217728a c |- ---------------------------- ) +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R - +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 7680a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R log +--R +------------------------------+3 +--R 5 4 +-+ | 1 +-+ +--R - 134217728a c \|2 |- ---------------------------- \|x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+6 +--R 10 8 | 1 +--R 18014398509481984a c |- ---------------------------- + x +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 15log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 30\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 30atan(---------------------) + 30atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 30\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x - 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R +------------------------------+ +--R 8+---+5 | 1 8+-+3 +--R 15360a c \|- a |- ---------------------------- \|c +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R * +--R +------------------------------+3 +--R 5 4 | 1 +--R 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R atan(----------------------------------------------------------) +--R +------------------------------+3 +--R +-+ +-+ 5 4 | 1 +--R \|2 \|x + 134217728a c |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+5 8+-+3 +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 10 10 7 11 9 3 +--R (- 11349071060973649920a c x + 8106479329266892800a c x ) +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 6 8 10 7 7 6 8 6 2 +--R (4123168604160a c x - 53601191854080a c x + 16492674416640a c x ) +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 3 5 9 4 4 5 5 3 +--R (47185920a c x - 212336640a c x + 23592960a c x) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 2 8 4 2 +--R 375c x - 690a c x + 15a +--R / +--R 11 12 10 12 11 6 +--R 73786976294838206464a c x - 18446744073709551616a c x +--R + +--R 13 10 2 +--R - 92233720368547758080a c x +--R * +--R +------------------------------+6 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 8 9 9 9 8 5 +--R 457396837154816a c x + 281474976710656a c x +--R + +--R 10 7 +--R - 175921860444160a c x +--R * +--R +------------------------------+4 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 5 6 8 6 5 4 7 4 +--R (2281701376a c x + 2147483648a c x - 134217728a c ) +--R * +--R +------------------------------+2 +--R | 1 +--R |- ---------------------------- +--R 8| 13 11 +--R \| 4722366482869645213696a c +--R + +--R 4 11 2 3 7 3 2 3 +--R - 2048a c x + 5120a c x + 7168a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1347 +t0:=x^(7/2)/(a+c*x^4)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1347 +r0:=7/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))+_ + 7/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*c^(9/8))-_ + 7/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(15/8)*_ + c^(9/8)*sqrt(2))+7/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(15/8)*c^(9/8)*sqrt(2))-7/512*_ + log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(15/8)*c^(9/8)*sqrt(2))+7/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(15/8)*_ + c^(9/8)*sqrt(2))-1/8*sqrt(x)/(c*(a+c*x^4)^2)+1/64*_ + sqrt(x)/(a*c*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 7c x - 14a c x - 7a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (7c x + 14a c x + 7a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 14c x - 28a c x - 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 14c x - 28a c x - 14a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 14c x - 28a c x - 14a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (8c x - 56a)\|2 \|- a \|c \|x +--R / +--R 3 8 2 2 4 3 +-+8+---+7 8+-+ +--R (512a c x + 1024a c x + 512a c)\|2 \|- a \|c +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (448a c x + 896a c x + 448a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (448a c x + 896a c x + 448a c)\|2 |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 +-+ | 1 +--R (- 448a c x - 896a c x - 448a c)\|2 |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 448a c x - 896a c x - 448a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 896a c x - 1792a c x - 896a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 3 8 2 2 4 3 | 1 +--R (- 896a c x - 1792a c x - 896a c) |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (c x - 7a)\|2 \|x +--R / +--R 3 8 2 2 4 3 +-+ +--R (64a c x + 128a c x + 64a c)\|2 +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 7log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 3584a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x + 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R +-+8+---+7 | 1 8+-+ +--R 3584a c\|2 \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R +-+ 2 | 1 +--R log(\|x - 512a c |- ---------------------------) +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 3584a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+ +--R 2 +-+ | 1 +-+ +--R - 512a c\|2 |- --------------------------- \|x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 4 2 | 1 +--R 262144a c |- --------------------------- + x +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 7log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 14\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 14atan(---------------------) + 14atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 14\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 7168a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x - 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 8+---+7 | 1 8+-+ +--R 7168a c \|- a |- --------------------------- \|c +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+ +--R 2 | 1 +--R 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R atan(-------------------------------------------------) +--R +-----------------------------+ +--R +-+ +-+ 2 | 1 +--R \|2 \|x + 512a c |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R / +--R +-+8+---+7 8+-+ +--R 512a c\|2 \|- a \|c +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 11 8 8 12 7 4 +--R 1576259869579673600a c x - 2900318160026599424a c x +--R + +--R 13 6 +--R 63050394783186944a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 7 6 9 8 5 5 9 4 +--R (- 2886218022912a c x + 12987981103104a c x - 1443109011456a c x) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 3 4 10 4 3 6 5 2 2 +--R (3670016a c x - 47710208a c x + 14680064a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 147c x - 105a x +--R / +--R 13 9 8 14 8 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 15 7 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 9 7 9 10 6 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 11 5 +--R 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 5 5 10 6 4 6 7 3 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 15 9 +--R \| 4722366482869645213696a c +--R + +--R 3 11 2 2 7 3 3 +--R - 1024a c x + 2560a c x + 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1347 +t0:=x^(5/2)/(a+c*x^4)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1347 +r0:=1/8*x^(7/2)/(a*(a+c*x^4)^2)+9/64*x^(7/2)/(a^2*(a+c*x^4))+_ + 9/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_ + 9/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8))-_ + 9/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/_ + ((-a)^(17/8)*c^(7/8)*sqrt(2))+9/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(17/8)*c^(7/8)*sqrt(2))+_ + 9/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(17/8)*c^(7/8)*sqrt(2))-9/512*log((-a)^(1/4)+_ + c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/_ + ((-a)^(17/8)*c^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 9c x - 18a c x - 9a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (9c x + 18a c x + 9a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 18c x - 36a c x - 18a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (18c x + 36a c x + 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (18c x + 36a c x + 18a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (18c x + 36a c x + 18a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 7 3 +-+8+---+8+-+7 +-+ +--R (72c x + 136a x )\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+8+-+7 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (576a c x + 1152a c x + 576a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (576a c x + 1152a c x + 576a )\|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (- 576a c x - 1152a c x - 576a )\|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 576a c x - 1152a c x - 576a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +--R 9223372036854775808a c \|2 |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-+ +--R \|x +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (1152a c x + 2304a c x + 1152a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (1152a c x + 2304a c x + 1152a ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +-+ +-+ +--R (9c x + 17a x )\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 725 + +--S 726 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 9log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 4608a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+7 +--R 15 6 +-+ | 1 +-+ +--R 9223372036854775808a c \|2 |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+ | 1 8+-+7 +--R 4608a \|2 \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x + 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+ | 1 8+-+7 +--R 4608a \|2 \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+7 +--R +-+ 15 6 | 1 +--R log(\|x - 9223372036854775808a c |- --------------------------- ) +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 4608a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R log +--R - +--R 15 6 +-+ +--R 9223372036854775808a c \|2 +--R * +--R +-----------------------------+7 +--R | 1 +-+ +--R |- --------------------------- \|x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 13 5 | 1 +--R - 18014398509481984a c |- --------------------------- + x +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 9log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 18\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 18atan(---------------------) - 18atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 18\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 9216a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x - 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 8+---+ | 1 8+-+7 +--R 9216a \|- a |- --------------------------- \|c +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R * +--R atan +--R +-----------------------------+7 +--R 15 6 | 1 +--R 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R -------------------------------------------------------------------- +--R +-----------------------------+7 +--R +-+ +-+ 15 6 | 1 +--R \|2 \|x + 9223372036854775808a c |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+8+-+7 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 13 7 9 14 6 5 +--R - 486388759756013568a c x + 2188749418902061056a c x +--R + +--R 15 5 +--R - 243194379878006784a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 9 5 8 10 4 4 11 3 +--R (3865470566400a c x - 7112465842176a c x + 154618822656a c ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 3 7 6 2 3 | 1 +--R (- 24772608a c x + 17694720a c x ) |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 2 10 6 2 2 +--R - 9c x + 117a c x - 36a x +--R / +--R 15 8 10 16 7 6 +--R 18446744073709551616a c x - 4611686018427387904a c x +--R + +--R 17 6 2 +--R - 23058430092136939520a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 11 6 9 12 5 5 +--R - 114349209288704a c x - 70368744177664a c x +--R + +--R 13 4 +--R 43980465111040a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 7 4 8 8 3 4 9 2 +--R (570425344a c x + 536870912a c x - 33554432a c ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 17 7 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R 512a c x - 1280a c x - 1792a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 727 + +)clear all + +--S 728 of 1347 +t0:=x^(3/2)/(a+c*x^4)^3 +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1347 +r0:=1/8*x^(5/2)/(a*(a+c*x^4)^2)+11/64*x^(5/2)/(a^2*(a+c*x^4))-_ + 33/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_ + 33/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8))-_ + 33/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*_ + c^(5/8)*sqrt(2))+33/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(19/8)*c^(5/8)*sqrt(2))-_ + 33/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2))+_ + 33/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(19/8)*c^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (33c x + 66a c x + 33a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 33c x - 66a c x - 33a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 66c x - 132a c x - 66a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (66c x + 132a c x + 66a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (66c x + 132a c x + 66a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 66c x - 132a c x - 66a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 6 2 +-+8+---+3 8+-+5 +-+ +--R (88c x + 152a x )\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+3 8+-+5 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (2112a c x + 4224a c x + 2112a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 2112a c x - 4224a c x - 2112a )\|2 +--R * +--R +-----------------------------+ +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x + 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (2112a c x + 4224a c x + 2112a )\|2 |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x - 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 2112a c x - 4224a c x - 2112a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4224a c x - 8448a c x - 4224a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x - 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4224a c x - 8448a c x - 4224a ) |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x + 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 6 2 +-+ +-+ +--R (11c x + 19a x )\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 730 + +--S 731 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 33log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 16896a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+3 | 1 8+-+5 +--R 16896a \|2 \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x + 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+3 | 1 8+-+5 +--R 16896a \|2 \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R +-+ 12 3 | 1 +--R log(\|x - 35184372088832a c |- --------------------------- ) +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 16896a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+5 +--R 12 3 +-+ | 1 +-+ +--R - 35184372088832a c \|2 |- --------------------------- \|x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+2 +--R 5 | 1 +--R - 262144a c |- --------------------------- + x +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 33log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 66\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R - 66atan(---------------------) - 66atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 66\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 33792a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x - 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+3 | 1 8+-+5 +--R 33792a \|- a |- --------------------------- \|c +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+5 +--R 12 3 | 1 +--R 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------------) +--R +-----------------------------+5 +--R +-+ +-+ 12 3 | 1 +--R \|2 \|x + 35184372088832a c |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+3 8+-+5 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 14 6 10 15 5 6 +--R 1188950301625810944a c x - 15456353921135542272a c x +--R + +--R 16 4 2 +--R 4755801206503243776a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 10 4 7 11 3 3 +--R (- 47622597378048a c x + 34016140984320a c x ) +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 5 3 8 6 2 4 7 +--R (- 108134400a c x + 198967296a c x - 4325376a c) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 9 5 2 +--R - 198c x + 891a c x - 99a x +--R / +--R 17 6 8 18 5 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 19 4 +--R - 4611686018427387904a c +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 12 5 9 13 4 5 +--R 228698418577408a c x + 140737488355328a c x +--R + +--R 14 3 +--R - 87960930222080a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 7 4 10 8 3 6 9 2 2 +--R (536870912a c x - 134217728a c x - 671088640a c x ) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 19 5 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R 1024a c x - 2560a c x - 3584a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 732 + +)clear all + +--S 733 of 1347 +t0:=sqrt(x)/(a+c*x^4)^3 +--R +--R +--R +-+ +--R \|x +--R (1) ------------------------------ +--R 3 12 2 8 2 4 3 +--R c x + 3a c x + 3a c x + a +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1347 +r0:=1/8*x^(3/2)/(a*(a+c*x^4)^2)+13/64*x^(3/2)/(a^2*(a+c*x^4))+_ + 65/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))-_ + 65/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8))+_ + 65/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*_ + c^(3/8)*sqrt(2))-65/256*atan(1+c^(1/8)*sqrt(2)*_ + sqrt(x)/(-a)^(1/8))/((-a)^(21/8)*c^(3/8)*sqrt(2))-_ + 65/512*log((-a)^(1/4)+c^(1/4)*x-(-a)^(1/8)*c^(1/8)*_ + sqrt(2)*sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2))+65/512*_ + log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*c^(1/8)*sqrt(2)*_ + sqrt(x))/((-a)^(21/8)*c^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (65c x + 130a c x + 65a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 65c x - 130a c x - 65a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 130c x - 260a c x - 130a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 130c x - 260a c x - 130a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 130c x - 260a c x - 130a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (130c x + 260a c x + 130a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 5 +-+8+---+5 8+-+3 +-+ +--R (104c x + 168a x)\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+5 8+-+3 +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (4160a c x + 8320a c x + 4160a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 4160a c x - 8320a c x - 4160a )\|2 +--R * +--R +-----------------------------+ +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x + 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (4160a c x + 8320a c x + 4160a )\|2 |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x - 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 4160a c x - 8320a c x - 4160a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R - 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (8320a c x + 16640a c x + 8320a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x - 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (8320a c x + 16640a c x + 8320a ) |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x + 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 5 +-+ +-+ +--R (13c x + 21a x)\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 735 + +--S 736 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R - 65log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 33280a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 +-+8+---+5 | 1 8+-+3 +--R 33280a \|2 \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x + 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 +-+8+---+5 | 1 8+-+3 +--R 33280a \|2 \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R +-+ 8 | 1 +--R log(\|x - 134217728a c |- --------------------------- ) +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R - +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 33280a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R log +--R +-----------------------------+3 +--R 8 +-+ | 1 +-+ +--R - 134217728a c\|2 |- --------------------------- \|x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+6 +--R 16 2 | 1 +--R 18014398509481984a c |- --------------------------- + x +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R 65log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 130\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 130atan(---------------------) + 130atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R - 130\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 66560a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x - 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R +-----------------------------+ +--R 2 8+---+5 | 1 8+-+3 +--R 66560a \|- a |- --------------------------- \|c +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R * +--R +-----------------------------+3 +--R 8 | 1 +--R 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R atan(---------------------------------------------------------) +--R +-----------------------------+3 +--R +-+ +-+ 8 | 1 +--R \|2 \|x + 134217728a c |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+5 8+-+3 +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 16 4 7 17 3 3 +--R (- 49179307930885816320a c x + 35128077093489868800a c x ) +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 10 4 10 11 3 6 +--R 17867063951360a c x - 232271831367680a c x +--R + +--R 12 2 2 +--R 71468255805440a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 5 3 9 6 2 5 7 +--R (204472320a c x - 920125440a c x + 102236160a c x) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 8 4 2 +--R 1625c x - 2990a c x + 65a +--R / +--R 18 5 10 19 4 6 +--R 73786976294838206464a c x - 18446744073709551616a c x +--R + +--R 20 3 2 +--R - 92233720368547758080a c x +--R * +--R +-----------------------------+6 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 13 4 9 14 3 5 +--R 457396837154816a c x + 281474976710656a c x +--R + +--R 15 2 +--R - 175921860444160a c x +--R * +--R +-----------------------------+4 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 8 3 8 9 2 4 10 +--R (2281701376a c x + 2147483648a c x - 134217728a c) +--R * +--R +-----------------------------+2 +--R | 1 +--R |- --------------------------- +--R 8| 21 3 +--R \| 4722366482869645213696a c +--R + +--R 2 3 11 3 2 7 4 3 +--R - 2048a c x + 5120a c x + 7168a c x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 737 + +)clear all + +--S 738 of 1347 +t0:=1/((a+c*x^4)^3*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 12 2 8 2 4 3 +-+ +--R (c x + 3a c x + 3a c x + a )\|x +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1347 +r0:=-105/256*atan(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))-_ + 105/256*atanh(c^(1/8)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*c^(1/8))+_ + 105/256*atan(1-c^(1/8)*sqrt(2)*sqrt(x)/(-a)^(1/8))/((-a)^(23/8)*_ + c^(1/8)*sqrt(2))-105/256*atan(1+c^(1/8)*sqrt(2)*sqrt(x)/_ + (-a)^(1/8))/((-a)^(23/8)*c^(1/8)*sqrt(2))+105/512*log((-a)^(1/4)+_ + c^(1/4)*x-(-a)^(1/8)*c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*_ + c^(1/8)*sqrt(2))-105/512*log((-a)^(1/4)+c^(1/4)*x+(-a)^(1/8)*_ + c^(1/8)*sqrt(2)*sqrt(x))/((-a)^(23/8)*c^(1/8)*sqrt(2))+_ + 1/8*sqrt(x)/(a*(a+c*x^4)^2)+15/64*sqrt(x)/(a^2*(a+c*x^4)) +--R +--R +--R (2) +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (- 105c x - 210a c x - 105a )log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 2 8 4 2 +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R (105c x + 210a c x + 105a )log(- \|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 210c x - 420a c x - 210a )\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x + \|- a +--R (- 210c x - 420a c x - 210a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +--R 2 8 4 2 \|2 \|c \|x - \|- a +--R (- 210c x - 420a c x - 210a )atan(---------------------) +--R 8+---+ +--R \|- a +--R + +--R 8+-+ +-+ +--R 2 8 4 2 +-+ \|c \|x +--R (- 210c x - 420a c x - 210a )\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R 4 +-+8+---+7 8+-+ +-+ +--R (120c x + 184a)\|2 \|- a \|c \|x +--R / +--R 2 2 8 3 4 4 +-+8+---+7 8+-+ +--R (512a c x + 1024a c x + 512a )\|2 \|- a \|c +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (6720a c x + 13440a c x + 6720a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 +-+ | 1 +--R (6720a c x + 13440a c x + 6720a )\|2 |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x + 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 2 2 8 3 4 4 +-+ +--R (- 6720a c x - 13440a c x - 6720a )\|2 +--R * +--R +----------------------------+ +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x - 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 6720a c x - 13440a c x - 6720a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R - 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 13440a c x - 26880a c x - 13440a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x - 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 2 8 3 4 4 | 1 +--R (- 13440a c x - 26880a c x - 13440a ) |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x + 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 4 +-+ +-+ +--R (15c x + 23a)\|2 \|x +--R / +--R 2 2 8 3 4 4 +-+ +--R (64a c x + 128a c x + 64a )\|2 +--R Type: Union(Expression(Integer),...) +--E 740 + +--S 741 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +--R 105log(\|2 \|- a \|c \|x + x\|c + \|- a ) +--R + +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 53760a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 53760a \|2 \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x + 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 +-+8+---+7 | 1 8+-+ +--R 53760a \|2 \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R +-+ 3 | 1 +--R log(\|x - 512a |- --------------------------) +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 53760a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R log +--R +----------------------------+ +--R 3 +-+ | 1 +-+ +--R - 512a \|2 |- -------------------------- \|x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R +----------------------------+2 +--R 6 | 1 +--R 262144a |- -------------------------- + x +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 8+-+ +-+ +--R +-+8+---+8+-+ +-+ 4+-+ 4+---+ +-+ \|c \|x +--R - 105log(- \|2 \|- a \|c \|x + x\|c + \|- a ) + 210\|2 atanh(--------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ +-+ 8+---+ +-+8+-+ +-+ 8+---+ +--R \|2 \|c \|x + \|- a \|2 \|c \|x - \|- a +--R 210atan(---------------------) + 210atan(---------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +-+ +--R +-+ \|c \|x +--R 210\|2 atan(--------) +--R 8+---+ +--R \|- a +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 107520a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x - 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R - +--R +----------------------------+ +--R 2 8+---+7 | 1 8+-+ +--R 107520a \|- a |- -------------------------- \|c +--R 8| 23 +--R \| 4722366482869645213696a c +--R * +--R +----------------------------+ +--R 3 | 1 +--R 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R atan(-----------------------------------------------) +--R +----------------------------+ +--R +-+ +-+ 3 | 1 +--R \|2 \|x + 512a |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R / +--R 2 +-+8+---+7 8+-+ +--R 512a \|2 \|- a \|c +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1347 sometimes Axiom computes a zero +d0:=normalize(D(m0,x)) +--R +--R +--R (5) +--R 17 2 8 18 4 +--R 23643898043695104000a c x - 43504772400398991360a c x +--R + +--R 19 +--R 945755921747804160a +--R * +--R +----------------------------+6 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 11 2 9 12 5 13 +--R (- 43293270343680a c x + 194819716546560a c x - 21646635171840a x) +--R * +--R +----------------------------+4 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 5 2 10 6 6 7 2 +--R (55050240a c x - 715653120a c x + 220200960a x ) +--R * +--R +----------------------------+2 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 7 3 +--R 2205c x - 1575a x +--R / +--R 20 2 8 21 4 +--R 78398662313265594368a c x + 73786976294838206464a c x +--R + +--R 22 +--R - 4611686018427387904a +--R * +--R +----------------------------+6 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 14 2 9 15 5 +--R - 228698418577408a c x - 140737488355328a c x +--R + +--R 16 +--R 87960930222080a x +--R * +--R +----------------------------+4 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 8 2 10 9 6 10 2 +--R (536870912a c x - 134217728a c x - 671088640a x ) +--R * +--R +----------------------------+2 +--R | 1 +--R |- -------------------------- +--R 8| 23 +--R \| 4722366482869645213696a c +--R + +--R 2 2 11 3 7 4 3 +--R - 1024a c x + 2560a c x + 3584a x +--R * +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 742 + +)clear all + +--S 743 of 1347 +t0:=x^7*(a+b*x^4)^p +--R +--R +--R 7 4 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1347 +r0:=-1/4*a*(a+b*x^4)^(1+p)/(b^2*(1+p))+1/4*(a+b*x^4)^(2+p)/(b^2*(2+p)) +--R +--R +--R 4 p + 2 4 p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 2 2 8 4 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R (3) ----------------------------------------------- +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Union(Expression(Integer),...) +--E 745 + +--S 746 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 +--R 2 2 8 4 2 p log(b x + a) +--R ((b p + b )x + a b p x - a )%e +--R + +--R 4 p + 2 4 p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R 4b p + 12b p + 8b +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 747 + +)clear all + +--S 748 of 1347 +t0:=x^3*(a+b*x^4)^p +--R +--R +--R 3 4 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1347 +r0:=1/4*(a+b*x^4)^(1+p)/(b*(1+p)) +--R +--R +--R 4 p + 1 +--R (b x + a) +--R (2) --------------- +--R 4b p + 4b +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R 4 p log(b x + a) +--R (b x + a)%e +--R (3) --------------------------- +--R 4b p + 4b +--R Type: Union(Expression(Integer),...) +--E 750 + +--S 751 of 1347 +m0:=a0-r0 +--R +--R +--R 4 +--R 4 p log(b x + a) 4 p + 1 +--R (b x + a)%e - (b x + a) +--R (4) --------------------------------------------- +--R 4b p + 4b +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 752 + +)clear all + +--S 753 of 1347 +t0:=(a+b*x^4)^p/x +--R +--R +--R 4 p +--R (b x + a) +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1347 +--r0:=1/4*(a+b*x^4)^p*hypergeometric(-p,-p,1-p,-a/(b*x^4))/_ +-- (p*((a+b*x^4)/(b*x^4))^p) +--E 754 + +--S 755 of 1347 +--a0:=integrate(t0,x) +--E 755 + +--S 756 of 1347 +--m0:=a0-r0 +--E 756 + +--S 757 of 1347 +--d0:=D(m0,x) +--E 757 + +)clear all + +--S 758 of 1347 +t0:=x^7*(1+x^4)^(1/3) +--R +--R +--R +------+ +--R 7 3| 4 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1347 +r0:=-3/16*(1+x^4)^(4/3)+3/28*(1+x^4)^(7/3) +--R +--R +--R +------+ +--R 8 4 3| 4 +--R (12x + 3x - 9)\|x + 1 +--R (2) ------------------------- +--R 112 +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 8 4 3| 4 +--R (12x + 3x - 9)\|x + 1 +--R (3) ------------------------- +--R 112 +--R Type: Union(Expression(Integer),...) +--E 760 + +--S 761 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 762 + +)clear all + +--S 763 of 1347 +t0:=x^3/(1+x^4)^(4/3) +--R +--R +--R 3 +--R x +--R (1) ----------------- +--R +------+ +--R 4 3| 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1347 +r0:=(-3/4)/(1+x^4)^(1/3) +--R +--R +--R 3 +--R (2) - ---------- +--R +------+ +--R 3| 4 +--R 4\|x + 1 +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R (3) - ---------- +--R +------+ +--R 3| 4 +--R 4\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 765 + +--S 766 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 767 + +)clear all + +--S 768 of 1347 +t0:=x^3/(1+x^4)^(1/3) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 3| 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1347 +r0:=3/8*(1+x^4)^(2/3) +--R +--R +--R +------+2 +--R 3| 4 +--R 3\|x + 1 +--R (2) ----------- +--R 8 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R 3| 4 +--R 3\|x + 1 +--R (3) ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 770 + +--S 771 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 772 + +)clear all + +--S 773 of 1347 +t0:=x^3/(1+x^4)^(1/4) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R 4| 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1347 +r0:=1/3*(1+x^4)^(3/4) +--R +--R +--R +------+3 +--R 4| 4 +--R \|x + 1 +--R (2) ---------- +--R 3 +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+3 +--R 4| 4 +--R \|x + 1 +--R (3) ---------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 775 + +--S 776 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1347 +t0:=x^24/(a+b*x^5) +--R +--R +--R 24 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 778 + +--S 779 of 1347 +r0:=-1/5*a^3*x^5/b^4+1/10*a^2*x^10/b^3-1/15*a*x^15/b^2+1/20*x^20/b+_ + 1/5*a^4*log(a+b*x^5)/b^5 +--R +--R +--R 4 5 4 20 3 15 2 2 10 3 5 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (2) ----------------------------------------------------------- +--R 5 +--R 60b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 4 5 4 20 3 15 2 2 10 3 5 +--R 12a log(b x + a) + 3b x - 4a b x + 6a b x - 12a b x +--R (3) ----------------------------------------------------------- +--R 5 +--R 60b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1347 +t0:=x^19/(a+b*x^5) +--R +--R +--R 19 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1347 +r0:=1/5*a^2*x^5/b^3-1/10*a*x^10/b^2+1/15*x^15/b-1/5*a^3*log(a+b*x^5)/b^4 +--R +--R +--R 3 5 3 15 2 10 2 5 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 30b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 5 3 15 2 10 2 5 +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (3) ------------------------------------------------ +--R 4 +--R 30b +--R Type: Union(Expression(Integer),...) +--E 785 + +--S 786 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +)clear all + +--S 788 of 1347 +t0:=x^14/(a+b*x^5) +--R +--R +--R 14 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 788 + +--S 789 of 1347 +r0:=-1/5*a*x^5/b^2+1/10*x^10/b+1/5*a^2*log(a+b*x^5)/b^3 +--R +--R +--R 2 5 2 10 5 +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 10b +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 5 2 10 5 +--R 2a log(b x + a) + b x - 2a b x +--R (3) ---------------------------------- +--R 3 +--R 10b +--R Type: Union(Expression(Integer),...) +--E 790 + +--S 791 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 792 + +)clear all + +--S 793 of 1347 +t0:=x^9/(a+b*x^5) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 793 + +--S 794 of 1347 +r0:=1/5*x^5/b-1/5*a*log(a+b*x^5)/b^2 +--R +--R +--R 5 5 +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R 5b +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - a log(b x + a) + b x +--R (3) ------------------------ +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 795 + +--S 796 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 797 + +)clear all + +--S 798 of 1347 +t0:=x^4/(a+b*x^5) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 798 + +--S 799 of 1347 +r0:=1/5*log(a+b*x^5)/b +--R +--R +--R 5 +--R log(b x + a) +--R (2) ------------- +--R 5b +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(b x + a) +--R (3) ------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 800 + +--S 801 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 802 + +)clear all + +--S 803 of 1347 +t0:=1/(x*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ---------- +--R 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 803 + +--S 804 of 1347 +r0:=log(x)/a-1/5*log(a+b*x^5)/a +--R +--R +--R 5 +--R - log(b x + a) + 5log(x) +--R (2) ------------------------- +--R 5a +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(b x + a) + 5log(x) +--R (3) ------------------------- +--R 5a +--R Type: Union(Expression(Integer),...) +--E 805 + +--S 806 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 807 + +)clear all + +--S 808 of 1347 +t0:=1/(x^6*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 808 + +--S 809 of 1347 +r0:=(-1/5)/(a*x^5)-b*log(x)/a^2+1/5*b*log(a+b*x^5)/a^2 +--R +--R +--R 5 5 5 +--R b x log(b x + a) - 5b x log(x) - a +--R (2) ----------------------------------- +--R 2 5 +--R 5a x +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R b x log(b x + a) - 5b x log(x) - a +--R (3) ----------------------------------- +--R 2 5 +--R 5a x +--R Type: Union(Expression(Integer),...) +--E 810 + +--S 811 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 812 + +)clear all + +--S 813 of 1347 +t0:=1/(x^11*(a+b*x^5)) +--R +--R +--R 1 +--R (1) ------------- +--R 16 11 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 813 + +--S 814 of 1347 +r0:=(-1/10)/(a*x^10)+1/5*b/(a^2*x^5)+b^2*log(x)/a^3-1/5*b^2*log(a+b*x^5)/a^3 +--R +--R +--R 2 10 5 2 10 5 2 +--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a +--R (2) ---------------------------------------------------- +--R 3 10 +--R 10a x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 10 5 2 10 5 2 +--R - 2b x log(b x + a) + 10b x log(x) + 2a b x - a +--R (3) ---------------------------------------------------- +--R 3 10 +--R 10a x +--R Type: Union(Expression(Integer),...) +--E 815 + +--S 816 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 816 + +--S 817 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 817 + +)clear all + +--S 818 of 1347 +t0:=x^24/(a+b*x^5)^2 +--R +--R +--R 24 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 818 + +--S 819 of 1347 +r0:=3/5*a^2*x^5/b^4-1/5*a*x^10/b^3+1/15*x^15/b^2-_ + 1/5*a^4/(b^5*(a+b*x^5))-4/5*a^3*log(a+b*x^5)/b^5 +--R +--R +--R (2) +--R 3 5 4 5 4 20 3 15 2 2 10 3 5 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x +--R + +--R 4 +--R - 3a +--R / +--R 6 5 5 +--R 15b x + 15a b +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 5 4 5 4 20 3 15 2 2 10 3 5 +--R (- 12a b x - 12a )log(b x + a) + b x - 2a b x + 6a b x + 9a b x +--R + +--R 4 +--R - 3a +--R / +--R 6 5 5 +--R 15b x + 15a b +--R Type: Union(Expression(Integer),...) +--E 820 + +--S 821 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 822 + +)clear all + +--S 823 of 1347 +t0:=x^19/(a+b*x^5)^2 +--R +--R +--R 19 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 823 + +--S 824 of 1347 +r0:=-2/5*a*x^5/b^3+1/10*x^10/b^2+1/5*a^3/(b^4*(a+b*x^5))+_ + 3/5*a^2*log(a+b*x^5)/b^4 +--R +--R +--R 2 5 3 5 3 15 2 10 2 5 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (2) --------------------------------------------------------------- +--R 5 5 4 +--R 10b x + 10a b +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 5 3 15 2 10 2 5 3 +--R (6a b x + 6a )log(b x + a) + b x - 3a b x - 4a b x + 2a +--R (3) --------------------------------------------------------------- +--R 5 5 4 +--R 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 825 + +--S 826 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1347 +t0:=x^14/(a+b*x^5)^2 +--R +--R +--R 14 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 828 + +--S 829 of 1347 +r0:=1/5*x^5/b^2-1/5*a^2/(b^3*(a+b*x^5))-2/5*a*log(a+b*x^5)/b^3 +--R +--R +--R 5 2 5 2 10 5 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (2) ---------------------------------------------------- +--R 4 5 3 +--R 5b x + 5a b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 2 5 2 10 5 2 +--R (- 2a b x - 2a )log(b x + a) + b x + a b x - a +--R (3) ---------------------------------------------------- +--R 4 5 3 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 830 + +--S 831 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +)clear all + +--S 833 of 1347 +t0:=x^9/(a+b*x^5)^2 +--R +--R +--R 9 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 833 + +--S 834 of 1347 +r0:=1/5*a/(b^2*(a+b*x^5))+1/5*log(a+b*x^5)/b^2 +--R +--R +--R 5 5 +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 5 2 +--R 5b x + 5a b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R (b x + a)log(b x + a) + a +--R (3) --------------------------- +--R 3 5 2 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 835 + +--S 836 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1347 +t0:=x^4/(a+b*x^5)^2 +--R +--R +--R 4 +--R x +--R (1) -------------------- +--R 2 10 5 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 838 + +--S 839 of 1347 +r0:=(-1/5)/(b*(a+b*x^5)) +--R +--R +--R 1 +--R - +--R 5 +--R (2) - ---------- +--R 2 5 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 839 + +--S 840 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 5 +--R 5b x + 5a b +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1347 +t0:=1/(x*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 11 6 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 843 + +--S 844 of 1347 +r0:=1/5/(a*(a+b*x^5))+log(x)/a^2-1/5*log(a+b*x^5)/a^2 +--R +--R +--R 5 5 5 +--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 5 3 +--R 5a b x + 5a +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R (- b x - a)log(b x + a) + (5b x + 5a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 5 3 +--R 5a b x + 5a +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1347 +t0:=1/(x^6*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 16 11 2 6 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 848 + +--S 849 of 1347 +r0:=(-2/5)/(a^2*x^5)+1/5/(a*x^5*(a+b*x^5))-_ + 2*b*log(x)/a^3+2/5*b*log(a+b*x^5)/a^3 +--R +--R +--R (2) +--R 2 10 5 5 2 10 5 5 2 +--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a +--R ----------------------------------------------------------------------------- +--R 3 10 4 5 +--R 5a b x + 5a x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 10 5 5 2 10 5 5 2 +--R (2b x + 2a b x )log(b x + a) + (- 10b x - 10a b x )log(x) - 2a b x - a +--R ----------------------------------------------------------------------------- +--R 3 10 4 5 +--R 5a b x + 5a x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1347 +t0:=1/(x^11*(a+b*x^5)^2) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 21 16 2 11 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 853 + +--S 854 of 1347 +r0:=(-3/10)/(a^2*x^10)+3/5*b/(a^3*x^5)+1/5/(a*x^10*(a+b*x^5))+_ + 3*b^2*log(x)/a^4-3/5*b^2*log(a+b*x^5)/a^4 +--R +--R +--R (2) +--R 3 15 2 10 5 3 15 2 10 +--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x) +--R + +--R 2 10 2 5 3 +--R 6a b x + 3a b x - a +--R / +--R 4 15 5 10 +--R 10a b x + 10a x +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 15 2 10 5 3 15 2 10 +--R (- 6b x - 6a b x )log(b x + a) + (30b x + 30a b x )log(x) +--R + +--R 2 10 2 5 3 +--R 6a b x + 3a b x - a +--R / +--R 4 15 5 10 +--R 10a b x + 10a x +--R Type: Union(Expression(Integer),...) +--E 855 + +--S 856 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 857 + +)clear all + +--S 858 of 1347 +t0:=x^9/(2*b+b*x^5) +--R +--R +--R 9 +--R x +--R (1) --------- +--R 5 +--R b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 858 + +--S 859 of 1347 +r0:=1/5*x^5/b-2/5*log(2+x^5)/b +--R +--R +--R 5 5 +--R - 2log(x + 2) + x +--R (2) ------------------- +--R 5b +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - 2log(x + 2) + x +--R (3) ------------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 860 + +--S 861 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 862 + +)clear all + +--S 863 of 1347 +t0:=x^4/(2*b+b*x^5) +--R +--R +--R 4 +--R x +--R (1) --------- +--R 5 +--R b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 863 + +--S 864 of 1347 +r0:=1/5*log(2+x^5)/b +--R +--R +--R 5 +--R log(x + 2) +--R (2) ----------- +--R 5b +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(x + 2) +--R (3) ----------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 865 + +--S 866 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 867 + +)clear all + +--S 868 of 1347 +t0:=1/(x*(2*b+b*x^5)) +--R +--R +--R 1 +--R (1) ----------- +--R 6 +--R b x + 2b x +--R Type: Fraction(Polynomial(Integer)) +--E 868 + +--S 869 of 1347 +r0:=-1/5*atanh(1+x^5)/b +--R +--R +--R 5 +--R atanh(x + 1) +--R (2) - ------------- +--R 5b +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(x + 2) + 5log(x) +--R (3) ----------------------- +--R 10b +--R Type: Union(Expression(Integer),...) +--E 870 + +--S 871 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R - log(x + 2) + 5log(x) + 2atanh(x + 1) +--R (4) ---------------------------------------- +--R 10b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 872 + +)clear all + +--S 873 of 1347 +t0:=1/(x^6*(2*b+b*x^5)) +--R +--R +--R 1 +--R (1) ------------- +--R 11 6 +--R b x + 2b x +--R Type: Fraction(Polynomial(Integer)) +--E 873 + +--S 874 of 1347 +r0:=(-1/10)/(b*x^5)+1/10*atanh(1+x^5)/b +--R +--R +--R 5 5 +--R x atanh(x + 1) - 1 +--R (2) ------------------- +--R 5 +--R 10b x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R x log(x + 2) - 5x log(x) - 2 +--R (3) ----------------------------- +--R 5 +--R 20b x +--R Type: Union(Expression(Integer),...) +--E 875 + +--S 876 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R log(x + 2) - 5log(x) - 2atanh(x + 1) +--R (4) -------------------------------------- +--R 20b +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 877 + +)clear all + +--S 878 of 1347 +t0:=x^9/(3+b*x^5) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 5 +--R b x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 878 + +--S 879 of 1347 +r0:=1/5*x^5/b-3/5*log(3+b*x^5)/b^2 +--R +--R +--R 5 5 +--R - 3log(b x + 3) + b x +--R (2) ----------------------- +--R 2 +--R 5b +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 +--R - 3log(b x + 3) + b x +--R (3) ----------------------- +--R 2 +--R 5b +--R Type: Union(Expression(Integer),...) +--E 880 + +--S 881 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 882 + +)clear all + +--S 883 of 1347 +t0:=x^4/(3+b*x^5) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 5 +--R b x + 3 +--R Type: Fraction(Polynomial(Integer)) +--E 883 + +--S 884 of 1347 +r0:=1/5*log(3+b*x^5)/b +--R +--R +--R 5 +--R log(b x + 3) +--R (2) ------------- +--R 5b +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(b x + 3) +--R (3) ------------- +--R 5b +--R Type: Union(Expression(Integer),...) +--E 885 + +--S 886 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1347 +t0:=1/(x*(3+b*x^5)) +--R +--R +--R 1 +--R (1) --------- +--R 6 +--R b x + 3x +--R Type: Fraction(Polynomial(Integer)) +--E 888 + +--S 889 of 1347 +r0:=-2/15*atanh(1+2/3*b*x^5) +--R +--R +--R 5 +--R 2b x + 3 +--R 2atanh(---------) +--R 3 +--R (2) - ----------------- +--R 15 +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(b x + 3) + 5log(x) +--R (3) ------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 890 + +--S 891 of 1347 +m0:=a0-r0 +--R +--R +--R 5 +--R 5 2b x + 3 +--R - log(b x + 3) + 5log(x) + 2atanh(---------) +--R 3 +--R (4) --------------------------------------------- +--R 15 +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +)clear all + +--S 893 of 1347 +t0:=1/(x^6*(3+b*x^5)) +--R +--R +--R 1 +--R (1) ----------- +--R 11 6 +--R b x + 3x +--R Type: Fraction(Polynomial(Integer)) +--E 893 + +--S 894 of 1347 +r0:=(-1/15)/x^5+2/45*b*atanh(1+2/3*b*x^5) +--R +--R +--R 5 +--R 5 2b x + 3 +--R 2b x atanh(---------) - 3 +--R 3 +--R (2) ------------------------- +--R 5 +--R 45x +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 +--R b x log(b x + 3) - 5b x log(x) - 3 +--R (3) ----------------------------------- +--R 5 +--R 45x +--R Type: Union(Expression(Integer),...) +--E 895 + +--S 896 of 1347 +m0:=a0-r0 +--R +--R +--R 5 +--R 5 2b x + 3 +--R b log(b x + 3) - 5b log(x) - 2b atanh(---------) +--R 3 +--R (4) ------------------------------------------------- +--R 45 +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 897 + +)clear all + +--S 898 of 1347 +t0:=x^5/(1+x^5) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 898 + +--S 899 of 1347 +r0:=x-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*_ + (1-sqrt(5))+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) + 20x\|2 +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I - 5%%ID1 - 5%%ID0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I - 5%%ID1 - 5%%ID0 + 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--I 10%%ID1 log(- 5%%ID1 + x) + 10%%ID0 log(- 5%%ID0 + x) - 2log(x + 1) + 10x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 900 + +--S 901 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%ID1 - 10\|2 %%ID0 + 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%ID1 + (- 50%%ID0 + 10)%%ID1 - 75%%ID0 + 10%%ID0 - 3 +--R + +--I 5%%ID1 + 5%%ID0 + 2x - 1 +--R + +--R +-+ +-+ +--I 20\|2 %%ID1 log(- 5%%ID1 + x) + 20\|2 %%ID0 log(- 5%%ID0 + x) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R - 200x + 200x - 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 902 + +)clear all + +--S 903 of 1347 +t0:=x^4/(1+x^5) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 903 + +--S 904 of 1347 +r0:=1/5*log(1+x^5) +--R +--R +--R 5 +--R log(x + 1) +--R (2) ----------- +--R 5 +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R log(x + 1) +--R (3) ----------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 905 + +--S 906 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 907 + +)clear all + +--S 908 of 1347 +t0:=x^3/(1+x^5) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 908 + +--S 909 of 1347 +r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))+_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/sqrt(2*_ + (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--I - 5%%IE1 - 5%%IE0 + 1 +--R * +--R log +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--I - 5%%IE1 - 5%%IE0 + 1 +--R * +--R log +--R - +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--I 10%%IE1 +--R * +--R log +--R 2 2 3 +--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0 +--R + +--R 2 +--I 25%%IE0 - 5%%IE0 + x +--R + +--R 3 2 +--I 10%%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1) - 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 910 + +--S 911 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2 +--R * +--R log +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IE1 - 10\|2 %%IE0 + 2\|2 +--R * +--R log +--R - +--I 25%%IE0 %%IE1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IE1 + (- 50%%IE0 + 10)%%IE1 - 75%%IE0 + 10%%IE0 - 3 +--R + +--R 2 2 +--I 125%%IE0 %%IE1 + (125%%IE0 - 25%%IE0)%%IE1 + 2x +--R + +--R +-+ +--I 20\|2 %%IE1 +--R * +--R log +--R 2 2 3 +--I - 125%%IE0 %%IE1 + (- 125%%IE0 + 25%%IE0)%%IE1 - 125%%IE0 +--R + +--R 2 +--I 25%%IE0 - 5%%IE0 + x +--R + +--R +-+ 3 2 +--I 20\|2 %%IE0 log(125%%IE0 - 25%%IE0 + 5%%IE0 + x - 1) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R 200x - 200x + 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 912 + +)clear all + +--S 913 of 1347 +t0:=x^2/(1+x^5) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 913 + +--S 914 of 1347 +r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--I - 5%%IF1 - 5%%IF0 - 1 +--R * +--R log +--I (5%%IF1 + 5%%IF0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--I - 5%%IF1 - 5%%IF0 - 1 +--R * +--R log +--I (- 5%%IF1 - 5%%IF0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R 2 2 +--I 10%%IF1 log(25%%IF1 + x) + 10%%IF0 log(25%%IF0 + x) + 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 915 + +--S 916 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2 +--R * +--R log +--I (5%%IF1 + 5%%IF0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IF1 - 10\|2 %%IF0 - 2\|2 +--R * +--R log +--I (- 5%%IF1 - 5%%IF0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IF1 + (- 50%%IF0 - 10)%%IF1 - 75%%IF0 - 10%%IF0 - 3 +--R + +--R 2 2 +--I - 25%%IF1 - 25%%IF0 + 2x - 1 +--R + +--R +-+ 2 +-+ 2 +--I 20\|2 %%IF1 log(25%%IF1 + x) + 20\|2 %%IF0 log(25%%IF0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1347 +t0:=x/(1+x^5) +--R +--R +--R x +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 918 + +--S 919 of 1347 +r0:=-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1-sqrt(5))+_ + 1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))+atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) - 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--I - 5%%IG1 - 5%%IG0 + 1 +--R * +--R log +--I ((25%%IG0 - 5)%%IG1 - 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--I - 5%%IG1 - 5%%IG0 + 1 +--R * +--R log +--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--I 10%%IG1 +--R * +--R log +--R 2 2 3 +--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0 +--R + +--R 2 +--I - 25%%IG0 + 5%%IG0 + x - 1 +--R + +--R 3 +--I 10%%IG0 log(- 125%%IG0 + x) - 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2 +--R * +--R log +--I ((25%%IG0 - 5)%%IG1 - 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IG1 - 10\|2 %%IG0 + 2\|2 +--R * +--R log +--I ((- 25%%IG0 + 5)%%IG1 + 5%%IG0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IG1 + (- 50%%IG0 + 10)%%IG1 - 75%%IG0 + 10%%IG0 - 3 +--R + +--R 2 2 +--I (- 125%%IG0 + 25)%%IG1 + (- 125%%IG0 + 25%%IG0 - 5)%%IG1 +--R + +--R 2 +--I 25%%IG0 - 5%%IG0 + 2x +--R + +--R +-+ +--I 20\|2 %%IG1 +--R * +--R log +--R 2 2 3 +--I (125%%IG0 - 25)%%IG1 + (125%%IG0 - 25%%IG0 + 5)%%IG1 + 125%%IG0 +--R + +--R 2 +--I - 25%%IG0 + 5%%IG0 + x - 1 +--R + +--R +-+ 3 +--I 20\|2 %%IG0 log(- 125%%IG0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- x\|2 \|5 + (2x - x + 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (- 2x\|2 \|5 + (- 4x + 2x - 4)\|2 )\|10 + 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1347 +t0:=1/(1+x^5) +--R +--R +--R 1 +--R (1) ------ +--R 5 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 923 + +--S 924 of 1347 +r0:=1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))-_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (\|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) + 4\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 - 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 - 1 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--I 10%%IH1 log(5%%IH1 + x) + 10%%IH0 log(5%%IH0 + x) + 2log(x + 1) +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 925 + +--S 926 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IH1 - 10\|2 %%IH0 - 2\|2 +--R * +--R log +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - \|- 75%%IH1 + (- 50%%IH0 - 10)%%IH1 - 75%%IH0 - 10%%IH0 - 3 +--R + +--I - 5%%IH1 - 5%%IH0 + 2x - 1 +--R + +--R +-+ +-+ +--I 20\|2 %%IH1 log(5%%IH1 + x) + 20\|2 %%IH0 log(5%%IH0 + x) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (5x\|2 \|5 + (- 10x + 5x - 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((x - 3x + 1)\|2 \|5 + (- 5x + 5x - 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R 200x - 200x + 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 927 + +)clear all + +--S 928 of 1347 +t0:=1/(x*(1+x^5)) +--R +--R +--R 1 +--R (1) ------ +--R 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 928 + +--S 929 of 1347 +r0:=-2/5*atanh(1+2*x^5) +--R +--R +--R 5 +--R 2atanh(2x + 1) +--R (2) - --------------- +--R 5 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 5 +--R - log(x + 1) + 5log(x) +--R (3) ----------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 930 + +--S 931 of 1347 +m0:=a0-r0 +--R +--R +--R 5 5 +--R - log(x + 1) + 5log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 932 + +)clear all + +--S 933 of 1347 +t0:=1/(x^2*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 7 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 933 + +--S 934 of 1347 +r0:=(-1)/x+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1-sqrt(5))-_ + 1/20*log(2+2*x^2-x*(1+sqrt(5)))*(1+sqrt(5))+_ + 1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))+1/5*atan((1-4*x-sqrt(5))/_ + sqrt(2*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4x\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4x\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (x\|2 \|5 - x\|2 )log(x\|5 + 2x - x + 2) + 4x\|2 log(x + 1) +--R + +--R +-+ +-+ +-+ +-+ 2 +-+ +--R (- x\|2 \|5 - x\|2 )log(- x\|5 + 2x - x + 2) - 20\|2 +--R / +--R +-+ +--R 20x\|2 +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R | 2 2 +--I - x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--I - 5x %%II1 - 5x %%II0 - x +--R * +--R log +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R | 2 2 +--I x\|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--I - 5x %%II1 - 5x %%II0 - x +--R * +--R log +--R - +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--I 10x %%II1 +--R * +--R log +--R 2 2 3 +--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0 +--R + +--R 2 +--I 25%%II0 + 5%%II0 + x +--R + +--R 3 2 +--I 10x %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1) + 2x log(x + 1) - 10 +--R / +--R 10x +--R Type: Union(Expression(Integer),...) +--E 935 + +--S 936 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2 +--R * +--R log +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%II1 - 10\|2 %%II0 - 2\|2 +--R * +--R log +--R - +--I 25%%II0 %%II1 +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%II1 + (- 50%%II0 - 10)%%II1 - 75%%II0 - 10%%II0 - 3 +--R + +--R 2 2 +--I - 125%%II0 %%II1 + (- 125%%II0 - 25%%II0)%%II1 + 2x +--R + +--R +-+ +--I 20\|2 %%II1 +--R * +--R log +--R 2 2 3 +--I 125%%II0 %%II1 + (125%%II0 + 25%%II0)%%II1 + 125%%II0 +--R + +--R 2 +--I 25%%II0 + 5%%II0 + x +--R + +--R +-+ 3 2 +--I 20\|2 %%II0 log(- 125%%II0 - 25%%II0 - 5%%II0 + x - 1) +--R + +--R +----------+ +--R +--------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4\|\|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +----------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|- \|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (- 5x\|2 \|5 + (10x - 5x + 10)\|2 )\|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ +--+ | +-+ +--R ((- x + 3x - 1)\|2 \|5 + (5x - 5x + 5)\|2 )\|10 \|- \|5 + 5 +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R 2 +--R - 200x + 200x - 200 +--R / +--R 4 3 2 +--R 400x - 400x + 400x - 400x + 400 +--R Type: Expression(Integer) +--E 937 + +)clear all + +--S 938 of 1347 +t0:=1/(x^3*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 8 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 938 + +--S 939 of 1347 +r0:=(-1/2)/x^2-1/5*log(1+x)+1/20*log(2+2*x^2-x*(1+sqrt(5)))*_ + (1-sqrt(5))+1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_ + (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*sqrt(1/10*_ + (5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R 2 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 4x \|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R 2 | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 4x \|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R 2 +-+ +-+ 2 +-+ +-+ 2 2 +-+ +--R (x \|2 \|5 + x \|2 )log(x\|5 + 2x - x + 2) - 4x \|2 log(x + 1) +--R + +--R 2 +-+ +-+ 2 +-+ +-+ 2 +-+ +--R (- x \|2 \|5 + x \|2 )log(- x\|5 + 2x - x + 2) - 10\|2 +--R / +--R 2 +-+ +--R 20x \|2 +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R 2 | 2 2 +--I - x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 2 +--I - 5x %%IJ1 - 5x %%IJ0 + x +--R * +--R log +--I (5%%IJ1 + 5%%IJ0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R 2 | 2 2 +--I x \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 2 +--I - 5x %%IJ1 - 5x %%IJ0 + x +--R * +--R log +--I (- 5%%IJ1 - 5%%IJ0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R 2 2 2 2 2 +--I 10x %%IJ1 log(25%%IJ1 + x) + 10x %%IJ0 log(25%%IJ0 + x) - 2x log(x + 1) +--R + +--R - 5 +--R / +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 940 + +--S 941 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2 +--R * +--R log +--I (5%%IJ1 + 5%%IJ0 - 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IJ1 - 10\|2 %%IJ0 + 2\|2 +--R * +--R log +--I (- 5%%IJ1 - 5%%IJ0 + 1) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IJ1 + (- 50%%IJ0 + 10)%%IJ1 - 75%%IJ0 + 10%%IJ0 - 3 +--R + +--R 2 2 +--I - 25%%IJ1 - 25%%IJ0 + 2x - 1 +--R + +--R +-+ 2 +-+ 2 +--I 20\|2 %%IJ1 log(25%%IJ1 + x) + 20\|2 %%IJ0 log(25%%IJ0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 - \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 - \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1347 +t0:=1/(x^4*(1+x^5)) +--R +--R +--R 1 +--R (1) ------- +--R 9 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 943 + +--S 944 of 1347 +r0:=(-1/3)/x^3+1/5*log(1+x)-1/20*log(2+2*x^2-x*(1+sqrt(5)))*_ + (1-sqrt(5))-1/20*log(2+2*x^2-x*(1-sqrt(5)))*(1+sqrt(5))-_ + atan((1-4*x-sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/_ + (5+sqrt(5)))+1/5*atan(1/2*(1-4*x+sqrt(5))*_ + sqrt(1/10*(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R +----------+ +--R +----------+ +-+ | +-+ +--R 3 | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R - 12x \|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R 3 | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R 12x \|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R 3 +-+ +-+ 3 +-+ +-+ 2 3 +-+ +--R (- 3x \|2 \|5 - 3x \|2 )log(x\|5 + 2x - x + 2) + 12x \|2 log(x + 1) +--R + +--R 3 +-+ +-+ 3 +-+ +-+ 2 +-+ +--R (3x \|2 \|5 - 3x \|2 )log(- x\|5 + 2x - x + 2) - 20\|2 +--R / +--R 3 +-+ +--R 60x \|2 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------------------------------------------------------+ +--R 3 | 2 2 +--I 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 3 3 3 +--I - 15x %%IK1 - 15x %%IK0 - 3x +--R * +--R log +--I ((25%%IK0 + 5)%%IK1 + 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R 3 | 2 2 +--I - 3x \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 3 3 3 +--I - 15x %%IK1 - 15x %%IK0 - 3x +--R * +--R log +--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R 3 +--I 30x %%IK1 +--R * +--R log +--R 2 2 +--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1 +--R + +--R 3 2 +--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1 +--R + +--R 3 3 3 +--I 30x %%IK0 log(125%%IK0 + x) + 6x log(x + 1) - 10 +--R / +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 945 + +--S 946 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2 +--R * +--R log +--I ((25%%IK0 + 5)%%IK1 + 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-----------------------------------------------------------+ +--R +-+ | 2 2 +--I - 2\|2 \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R +-+ +-+ +-+ +--I - 10\|2 %%IK1 - 10\|2 %%IK0 - 2\|2 +--R * +--R log +--I ((- 25%%IK0 - 5)%%IK1 - 5%%IK0) +--R * +--R +-----------------------------------------------------------+ +--R | 2 2 +--I \|- 75%%IK1 + (- 50%%IK0 - 10)%%IK1 - 75%%IK0 - 10%%IK0 - 3 +--R + +--R 2 2 2 +--I (125%%IK0 + 25)%%IK1 + (125%%IK0 + 25%%IK0 + 5)%%IK1 + 25%%IK0 +--R + +--I 5%%IK0 + 2x +--R + +--R +-+ +--I 20\|2 %%IK1 +--R * +--R log +--R 2 2 +--I (- 125%%IK0 - 25)%%IK1 + (- 125%%IK0 - 25%%IK0 - 5)%%IK1 +--R + +--R 3 2 +--I - 125%%IK0 - 25%%IK0 - 5%%IK0 + x - 1 +--R + +--R +-+ 3 +--I 20\|2 %%IK0 log(125%%IK0 + x) +--R + +--R +----------+ +--R +----------+ +-+ | +-+ +--R | +-+ ((2x - 3)\|5 - 10x + 5)\|2\|5 + 10 +--R 4\|- \|5 + 5 atan(-------------------------------------) +--R 20 +--R + +--R +--------+ +--R +--------+ +-+ | +-+ +--R | +-+ (\|5 - 4x + 1)\|\|5 + 5 +--R - 4\|\|5 + 5 atan(--------------------------) +--R +--+ +--R 2\|10 +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (\|2 \|5 + \|2 )log(x\|5 + 2x - x + 2) +--R + +--R +-+ +-+ +-+ +-+ 2 +--R (- \|2 \|5 + \|2 )log(- x\|5 + 2x - x + 2) +--R / +--R +-+ +--R 20\|2 +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R +-+ +-+ 2 +-+ | +-+ | +-+ +--R (x\|2 \|5 + (- 2x + x - 2)\|2 )\|- \|5 + 5 \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ +--+ +--R (2x\|2 \|5 + (4x - 2x + 4)\|2 )\|10 - 40x +--R / +--R 4 3 2 +--R 80x - 80x + 80x - 80x + 80 +--R Type: Expression(Integer) +--E 947 + +)clear all + +--S 948 of 1347 +t0:=1/(a+b*x^5) +--R +--R +--R 1 +--R (1) -------- +--R 5 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 948 + +--S 949 of 1347 +r0a:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_ + 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_ + (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_ + b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5-sqrt(5)))))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5)) +--R +--R +--R (2) +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +----------+ 5+-+ +-+ 5+-+ +--R +-+ 5+-+ 5+-+ | +-+ 4x\|b + (- \|5 - 1)\|a +--R 4\|2 log(x\|b + \|a ) + 4\|- \|5 + 5 atan(-------------------------) +--R +------------+ +--R | +-+ 5+-+ +--R \|- 2\|5 + 10 \|a +--R + +--R +--------+ 5+-+ +-+ 5+-+ +--R | +-+ 4x\|b + (\|5 - 1)\|a +--R 4\|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +-+5+-+4 5+-+ +--R 20\|2 \|a \|b +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1347 +r0b:=1/5*log(a^(1/5)+b^(1/5)*x)/(a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+_ + 2*b^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*(1-sqrt(5))/_ + (a^(4/5)*b^(1/5))-1/20*log(2*a^(2/5)+2*b^(2/5)*x^2-a^(1/5)*_ + b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/(a^(4/5)*b^(1/5))-_ + 1/5*atan(1/2*(-4*b^(1/5)*x+a^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_ + (a^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/(a^(4/5)*b^(1/5))-_ + 1/5*atan((-4*b^(1/5)*x+a^(1/5)*(1-sqrt(5)))/(a^(1/5)*_ + sqrt(2*(5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/(a^(4/5)*b^(1/5)) +--R +--R +--R (3) +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 - \|2 )log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ +-+ +-+ 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 - \|2 )log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +-+ 5+-+ 5+-+ +--R 4\|2 log(x\|b + \|a ) +--R + +--R +--------+ +--R +----------+ 5+-+ +-+ 5+-+ | +-+ +--R | +-+ (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5 +--R 4\|- \|5 + 5 atan(--------------------------------------) +--R +--+5+-+ +--R 2\|10 \|a +--R + +--R +--------+ 5+-+ +-+ 5+-+ +--R | +-+ 4x\|b + (\|5 - 1)\|a +--R 4\|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +-+5+-+4 5+-+ +--R 20\|2 \|a \|b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1 +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R 5| 4 +--R 5\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I - 5\|a b %%IM1 - 5\|a b %%IM0 - 1 +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +---+ +--R 5| 4 5| 4 +--I 10\|a b %%IM1 log(5a %%IM1 + x) + 10\|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R 5| 4 +--R 2log(x\|a b + a) +--R / +--R +---+ +--R 5| 4 +--R 10\|a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+ 5| 4 +--R 4\|2 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+5| 4 5+-+ 5+-+ +--R - 4\|2 \|a b log(x\|b + \|a ) +--R + +--R +----------+ +---+ 5+-+ +-+ 5+-+ +--R | +-+ 5| 4 4x\|b + (- \|5 - 1)\|a +--R - 4\|- \|5 + 5 \|a b atan(-------------------------) +--R +------------+ +--R | +-+ 5+-+ +--R \|- 2\|5 + 10 \|a +--R + +--R +---+ +--------+ 5+-+ +-+ 5+-+ +--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a +--R - 4\|a b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 20\|2 \|a \|b \|a b +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R +--------+ +--R 2 +-+5+-+2 +-+ +-+ +-+ 5+-+5+-+ +-+5+-+2 | +-+ +--R (- 2x \|2 \|b + (x\|2 \|5 + x\|2 )\|a \|b - 2\|2 \|a )\|\|5 + 5 +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +------------+ +----------+ +--R 2 +-+ | +-+ | +-+ 2 5+-+2 +--R (- 2x \|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40x )\|b +--R + +--R +------------+ +----------+ +--R +-+ +-+ +-+ | +-+ | +-+ 5+-+5+-+ +--R ((- x\|2 \|5 + x\|2 )\|- 2\|5 + 10 \|- \|5 + 5 - 40x)\|a \|b +--R + +--R +------------+ +----------+ +--R +-+ | +-+ | +-+ 5+-+2 +--R (- 2\|2 \|- 2\|5 + 10 \|- \|5 + 5 + 40)\|a +--R / +--R 4 5+-+3 5+-+4 3 5+-+4 5+-+3 2 5+-+2 5+-+5+-+ 5+-+2 +--R 80x \|a \|b - 80x \|a \|b + 80a x \|b - 80a x\|a \|b + 80a \|a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1347 +m0a:=a0-r0b +--R +--R +--R (7) +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R - +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 10\|2 \|a \|b \|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +--R +-+5+-+4 5+-+5| 4 +-+5+-+4 5+-+5| 4 +--I - 10\|2 \|a \|b \|a b %%IM - 10\|2 \|a \|b \|a b %%IM0 +--R + +--R +-+5+-+4 5+-+ +--R - 2\|2 \|a \|b +--R * +--R log +--R - +--R +---+ +--R 5| 4 +--R 5a\|a b +--R * +--R ROOT +--R +---+2 +---+2 +---+ +--R 5| 4 2 5| 4 5| 4 +--I - 75\|a b %%IM1 + (- 50\|a b %%IM0 - 10\|a b )%%IM1 +--R + +--R +---+2 +---+ +--R 5| 4 2 5| 4 +--I - 75\|a b %%IM0 - 10\|a b %%IM0 - 3 +--R / +--R +---+2 +--R 5| 4 +--R 25\|a b +--R + +--R +---+ +---+ +---+ +--R 5| 4 5| 4 5| 4 +--I - 5a\|a b %%IM1 - 5a\|a b %%IM0 + 2x\|a b - a +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM1 log(5a %%IM1 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--I 20\|2 \|a \|b \|a b %%IM0 log(5a %%IM0 + x) +--R + +--R +---+ +--R +-+5+-+4 5+-+ 5| 4 +--R 4\|2 \|a \|b log(x\|a b + a) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (- \|2 \|5 + \|2 )\|a b log(2x \|b + (x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+ +-+ +-+ 5| 4 2 5+-+2 +-+ 5+-+5+-+ 5+-+2 +--R (\|2 \|5 + \|2 )\|a b log(2x \|b + (- x\|5 - x)\|a \|b + 2\|a ) +--R + +--R +---+ +--R +-+5| 4 5+-+ 5+-+ +--R - 4\|2 \|a b log(x\|b + \|a ) +--R + +--R +--------+ +--R +----------+ +---+ 5+-+ +-+ 5+-+ | +-+ +--R | +-+ 5| 4 (4x\|b + (- \|5 - 1)\|a )\|\|5 + 5 +--R - 4\|- \|5 + 5 \|a b atan(--------------------------------------) +--R +--+5+-+ +--R 2\|10 \|a +--R + +--R +---+ +--------+ 5+-+ +-+ 5+-+ +--R 5| 4 | +-+ 4x\|b + (\|5 - 1)\|a +--R - 4\|a b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|a \|2\|5 + 10 +--R / +--R +---+ +--R +-+5+-+4 5+-+5| 4 +--R 20\|2 \|a \|b \|a b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Polynomial(Integer) +--E 955 + +)clear all + +--S 956 of 1347 +t0:=x^(23/2)/sqrt(a+b*x^5) +--R +--R +--R 11 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1347 +r0:=3/20*a^2*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(5/2)-_ + 3/20*a*x^(5/2)*sqrt(a+b*x^5)/b^2+1/10*x^(15/2)*sqrt(a+b*x^5)/b +--R +--R +--R 2 +-+ +-+ +--------+ +--R 2 x \|b \|x 7 2 +-+ +-+ | 5 +--R 3a atanh(-----------) + (2b x - 3a x )\|b \|x \|b x + a +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ---------------------------------------------------------- +--R 2 +-+ +--R 20b \|b +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1347 +--a0:=integrate(t0,x) +--E 958 + +--S 959 of 1347 +--m0:=a0-r0 +--E 959 + +--S 960 of 1347 +--d0:=D(m0,x) +--E 960 + +)clear all + +--S 961 of 1347 +t0:=x^(13/2)/sqrt(a+b*x^5) +--R +--R +--R 6 +-+ +--R x \|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1347 +r0:=-1/5*a*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/b^(3/2)+_ + 1/5*x^(5/2)*sqrt(a+b*x^5)/b +--R +--R +--R 2 +-+ +-+ +--------+ +--R x \|b \|x 2 +-+ +-+ | 5 +--R - a atanh(-----------) + x \|b \|x \|b x + a +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ---------------------------------------------- +--R +-+ +--R 5b\|b +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1347 +--a0:=integrate(t0,x) +--E 963 + +--S 964 of 1347 +--m0:=a0-r0 +--E 964 + +--S 965 of 1347 +--d0:=D(m0,x) +--E 965 + +)clear all + +--S 966 of 1347 +t0:=x^(3/2)/sqrt(a+b*x^5) +--R +--R +--R +-+ +--R x\|x +--R (1) ----------- +--R +--------+ +--R | 5 +--R \|b x + a +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1347 +r0:=2/5*atanh(x^(5/2)*sqrt(b)/sqrt(a+b*x^5))/sqrt(b) +--R +--R +--R 2 +-+ +-+ +--R x \|b \|x +--R 2atanh(-----------) +--R +--------+ +--R | 5 +--R \|b x + a +--R (2) ------------------- +--R +-+ +--R 5\|b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1347 +--a0:=integrate(t0,x) +--E 968 + +--S 969 of 1347 +--m0:=a0-r0 +--E 969 + +--S 970 of 1347 +--d0:=D(m0,x) +--E 970 + +)clear all + +--S 971 of 1347 +t0:=1/(x^(7/2)*sqrt(a+b*x^5)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 3 +-+ | 5 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1347 +r0:=-2/5*sqrt(a+b*x^5)/(a*x^(5/2)) +--R +--R +--R +--------+ +--R | 5 +--R 2\|b x + a +--R (2) - ------------ +--R 2 +-+ +--R 5a x \|x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 5 3 +--R - 2\|x \|b x + a + (- b - a - 1)x +--R (3) ------------------------------------ +--R 3 +--R 5a x +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R - b - a - 1 +--R (4) ----------- +--R 5a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1347 +t0:=1/(x^(17/2)*sqrt(a+b*x^5)) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------+ +--R 8 +-+ | 5 +--R x \|x \|b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1347 +r0:=-2/15*sqrt(a+b*x^5)/(a*x^(15/2))+4/15*b*sqrt(a+b*x^5)/(a^2*x^(5/2)) +--R +--R +--R +--------+ +--R 5 | 5 +--R (4b x - 2a)\|b x + a +--R (2) ----------------------- +--R 2 7 +-+ +--R 15a x \|x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 5 +-+ | 5 2 2 8 +--R (12b x - 6a)\|x \|b x + a + (- 2b + (- a - 18)b + a + 9a)x +--R (3) ---------------------------------------------------------------- +--R 2 8 +--R 45a x +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 2 2 +--R - 2b + (- a - 18)b + a + 9a +--R (4) ----------------------------- +--R 2 +--R 45a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1347 +t0:=x^(23/2)/sqrt(1+x^5) +--R +--R +--R 11 +-+ +--R x \|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1347 +r0:=3/20*asinh(x^(5/2))-3/20*x^(5/2)*sqrt(1+x^5)+1/10*x^(15/2)*sqrt(1+x^5) +--R +--R +--R +------+ +--R 2 +-+ 7 2 +-+ | 5 +--R 3asinh(x \|x ) + (2x - 3x )\|x \|x + 1 +--R (2) ----------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R 2 +-+ | 5 5 7 2 +-+ | 5 +--R - 3log(- 2x \|x \|x + 1 + 2x + 1) + (4x - 6x )\|x \|x + 1 +--R (3) --------------------------------------------------------------- +--R 40 +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ +--R 2 +-+ | 5 5 2 +-+ +--R - 3log(- 2x \|x \|x + 1 + 2x + 1) - 6asinh(x \|x ) +--R (4) ----------------------------------------------------- +--R 40 +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1347 +t0:=x^(13/2)/sqrt(1+x^5) +--R +--R +--R 6 +-+ +--R x \|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1347 +r0:=-1/5*asinh(x^(5/2))+1/5*x^(5/2)*sqrt(1+x^5) +--R +--R +--R +------+ +--R 2 +-+ 2 +-+ | 5 +--R - asinh(x \|x ) + x \|x \|x + 1 +--R (2) --------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 987 + +-- (1 . failed) cannot be coerced to mode +-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3)))) +--S 988 of 1347 +--a0:=integrate(t0,x) +--E 988 + +--S 989 of 1347 +--m0:=a0-r0 +--E 989 + +--S 990 of 1347 +--d0:=normalize(D(m0,x)) +--E 990 + +)clear all + +--S 991 of 1347 +t0:=x^(3/2)/sqrt(1+x^5) +--R +--R +--R +-+ +--R x\|x +--R (1) --------- +--R +------+ +--R | 5 +--R \|x + 1 +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1347 +r0:=2/5*asinh(x^(5/2)) +--R +--R +--R 2 +-+ +--R 2asinh(x \|x ) +--R (2) -------------- +--R 5 +--R Type: Expression(Integer) +--E 992 + +-- (1 . failed) cannot be coerced to mode +-- (Matrix (Fraction (SparseUnivariatePolynomial (InnerPrimeField 3)))) +--S 993 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 2 +-+ | 5 5 +--R log(- 2x \|x \|x + 1 + 2x + 1) +--R (3) - --------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1347 +m0:=a0-r0 +--R +--R +--R +------+ +--R 2 +-+ | 5 5 2 +-+ +--R - log(- 2x \|x \|x + 1 + 2x + 1) - 2asinh(x \|x ) +--R (4) ---------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1347 +t0:=1/(x^(7/2)*sqrt(1+x^5)) +--R +--R +--R 1 +--R (1) --------------- +--R +------+ +--R 3 +-+ | 5 +--R x \|x \|x + 1 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1347 +r0:=-2/5*sqrt(1+x^5)/x^(5/2) +--R +--R +--R +------+ +--R | 5 +--R 2\|x + 1 +--R (2) - ---------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R +-+ | 5 3 +--R - 2\|x \|x + 1 + 3x +--R (3) ---------------------- +--R 3 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 3 +--R (4) - +--R 5 +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1347 +t0:=1/(x^(17/2)*sqrt(1+x^5)) +--R +--R +--R 1 +--R (1) --------------- +--R +------+ +--R 8 +-+ | 5 +--R x \|x \|x + 1 +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1347 +r0:=-2/15*sqrt(1+x^5)/x^(15/2)+4/15*sqrt(1+x^5)/x^(5/2) +--R +--R +--R +------+ +--R 5 | 5 +--R (4x - 2)\|x + 1 +--R (2) ------------------ +--R 7 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1347 ok to fail, differs by a constant +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R 5 +-+ | 5 8 +--R (8x - 4)\|x \|x + 1 + 9x +--R (3) ---------------------------- +--R 8 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1347 ok to fail, differs by a constant +m0:=a0-r0 +--R +--R +--R 3 +--R (4) -- +--R 10 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1347 +t0:=x^8/(a+b*x^6) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1006 + +--S 1007 of 1347 +r0:=1/3*x^3/b-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(a)/b^(3/2) +--R +--R +--R 3 +-+ +--R +-+ x \|b 3 +-+ +--R - \|a atan(------) + x \|b +--R +-+ +--R \|a +--R (2) --------------------------- +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 3 | a 6 |a +--R +---+ - 2b x |- - + b x - a +-+ |- +--R | a \| b 3 |a \|b 3 +--R |- - log(------------------------) + 2x |- atan(----) + x +--R \| b 6 \|b 3 +--R b x + a x +--R (3) [-----------------------------------------,-------------------] +--R 6b 3b +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | a 6 +--R +---+ - 2b x |- - + b x - a 3 +-+ +--R | a +-+ \| b +-+ x \|b +--R |- - \|b log(------------------------) + 2\|a atan(------) +--R \| b 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 6b\|b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R 3 +-+ +-+ |- +--R +-+ x \|b |a +-+ \|b +--R \|a atan(------) + |- \|b atan(----) +--R +-+ \|b 3 +--R \|a x +--R (6) ------------------------------------- +--R +-+ +--R 3b\|b +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1347 +t0:=x^7/(a+b*x^6) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1013 + +--S 1014 of 1347 +r0:=1/2*x^2/b-1/6*a^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/b^(4/3)+_ + 1/12*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/b^(4/3)+_ + 1/2*a^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_ + sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|a log(x \|b - x \|a \|b + \|a ) - 2\|3 \|a log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 3+-+ 2x \|b - \|a 2 +-+3+-+ +--R - 6\|a atan(--------------) + 6x \|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 12b\|3 \|b +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | a | a 2 | a 4 +-+ | a | a 2 +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x ) +--R \| b \| b \| b \| b \| b +--R + +--R +---+ +--R +-+ | a 2 +-+ +--R +---+ \|3 3|- - + 2x \|3 +--R | a \| b 2 +-+ +--R - 6 3|- - atan(-------------------- + 6x \|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 12b\|3 +--R Type: Union(Expression(Integer),...) +--E 1015 + +--S 1016 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R - \|3 \|a log(x \|b - x \|a \|b + \|a ) + 2\|3 \|a log(x \|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a 2 | a 4 +--R - \|3 3|- - \|b log(3|- - + x 3|- - + x ) +--R \| b \| b \| b +--R + +--R +---+ +---+ 2 3+-+ 3+-+ +--R +-+ | a 3+-+ | a 2 3+-+ 2x \|b - \|a +--R 2\|3 3|- - \|b log(- 3|- - + x + 6\|a atan(--------------) +--R \| b \| b +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a 2 +-+ +--R +---+ \|3 3|- - + 2x \|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(--------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 12b\|3 \|b +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1347 +t0:=x^6/(a+b*x^6) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1018 + +--S 1019 of 1347 +r0:=x/b-1/3*a^(1/6)*atan(b^(1/6)*x/a^(1/6))/b^(7/6)-_ + 1/3*a^(1/6)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2))-1/3*a^(1/6)*_ + atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(b^(4/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|a \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+6+-+3+-+ x\|b +-+3+-+6+-+ +--R - \|2 \|a \|b atan(-----) + 3x\|2 \|b \|b +--R 6+-+ +--R \|a +--R / +--R +-+3+-+6+-+ +--R 3b\|2 \|b \|b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+2 +---------+ +--R | a 2 | a | a 2 +--R - b |- ------- log(36b |- ------- + 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+2 +---------+ +--R | a 2 | a | a 2 +--R b |- ------- log(36b |- ------- - 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R | a | a +--R - 2b |- ------- log(6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R | a | a +--R 2b |- ------- log(- 6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | a \| 46656b +--R - 2b\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- - x +--R 6| 7 +--R \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | a \| 46656b +--R 2b\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- + x +--R 6| 7 +--R \| 46656b +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1020 + +--S 1021 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|a \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|a \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------+ +--R +-+ | a 3+-+6+-+ +--R 3b\|2 |- ------- \|b \|b +--R 6| 7 +--R \| 46656b +--R * +--R +---------+2 +---------+ +--R 2 | a | a 2 +--R log(36b |- ------- + 6b x |- ------- + x ) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | a 3+-+6+-+ 2 | a | a 2 +--R 3b\|2 |- ------- \|b \|b log(36b |- ------- - 6b x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656b \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R +-+ | a 3+-+6+-+ | a +--R - 6b\|2 |- ------- \|b \|b log(6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R +---------+ +---------+ +--R +-+ | a 3+-+6+-+ | a +--R 6b\|2 |- ------- \|b \|b log(- 6b |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656b \| 46656b +--R + +--R 6+-+ +--R +-+6+-+3+-+ x\|b +--R 2\|2 \|a \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | a 3+-+6+-+ \| 46656b +--R - 6b\|2 \|3 |- ------- \|b \|b atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- - x +--R 6| 7 +--R \| 46656b +--R + +--R +---------+ +--R +-+ | a +--R 3b\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | a 3+-+6+-+ \| 46656b +--R 6b\|2 \|3 |- ------- \|b \|b atan(------------------) +--R 6| 7 +---------+ +--R \| 46656b | a +--R 3b |- ------- + x +--R 6| 7 +--R \| 46656b +--R / +--R +-+3+-+6+-+ +--R 6b\|2 \|b \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1022 + +)clear all + +--S 1023 of 1347 +t0:=x^5/(a+b*x^6) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1023 + +--S 1024 of 1347 +r0:=1/6*log(a+b*x^6)/b +--R +--R +--R 6 +--R log(b x + a) +--R (2) ------------- +--R 6b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(b x + a) +--R (3) ------------- +--R 6b +--R Type: Union(Expression(Integer),...) +--E 1025 + +--S 1026 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1027 + +)clear all + +--S 1028 of 1347 +t0:=x^4/(a+b*x^6) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1028 + +--S 1029 of 1347 +r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(1/6)*b^(5/6))+_ + 1/3*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3))))-1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(1/6)*b^(2/3)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +---------------------+ +---------------------+ +--R 6+-+ | +-------+ | +-------+ +--R 3+-+2 x\|b | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|b atan(-----)\|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R 6+-+ +--R \|a +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 3\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +--R | 1 +--R |- --------- +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 4 | 1 +--R 2 |- --------- log(7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 4 | 1 +--R - 2 |- --------- log(- 7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +-----------+ +--R | 1 +--R |- --------- +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(- 7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- --------- atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- --------- atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1030 + +--S 1031 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +-----------+ +--R | 1 6+-+3+-+2 6+-+5 +--R 3 |- --------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 6+-+3+-+2 6+-+5 4 | 1 +--R 6 |- --------- \|a \|b \|b log(7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +-----------+ +-----------+5 +--R | 1 6+-+3+-+2 6+-+5 4 | 1 +--R - 6 |- --------- \|a \|b \|b log(- 7776a b |- --------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +-----------+ +--R | 1 6+-+3+-+2 6+-+5 +--R 3 |- --------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +-----------+5 +-----------+4 +--R 4 | 1 3 | 1 2 +--R log(- 7776a b x |- --------- - 1296a b |- --------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R 6+-+ +--R 3+-+2 x\|b +--R - 2\|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b +--R - 6\|3 |- --------- \|a \|b \|b atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +-----------+5 +--R 4 +-+ | 1 +--R 3888a b \|3 |- --------- +--R +-----------+ 6| 5 +--R +-+ | 1 6+-+3+-+2 6+-+5 \| 46656a b +--R 6\|3 |- --------- \|a \|b \|b atan(---------------------------) +--R 6| 5 +-----------+5 +--R \| 46656a b 4 | 1 +--R 3888a b |- --------- + x +--R 6| 5 +--R \| 46656a b +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 6\|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1032 + +)clear all + +--S 1033 of 1347 +t0:=x^3/(a+b*x^6) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1033 + +--S 1034 of 1347 +r0:=-1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(1/3)*b^(2/3))+1/12*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(1/3)*b^(2/3))-_ + 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+ +--R \|3 log(x \|b - x \|a \|b + \|a ) - 2\|3 log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2x \|b - \|a +--R 6atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 12\|3 \|a \|b +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R +-+ 2 3| 2 4 3| 2 +--R - \|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R +------+2 2 +-+3| 2 +-+ +--R +-+ 2 3| 2 2x \|3 \|- a b - a b\|3 +--R 2\|3 log(x \|- a b + a b) - 6atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 12\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1035 + +--S 1036 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x \|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 4 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 2 3+-+ 3+-+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 12\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1037 + +)clear all + +--S 1038 of 1347 +t0:=x^2/(a+b*x^6) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1038 + +--S 1039 of 1347 +r0:=1/3*atan(x^3*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R 3 +-+ +--R x \|b +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 3\|a \|b +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +-----+ 3 +--R (b x - a)\|- a b + 2a b x 3 +---+ +--R log(----------------------------) x \|a b +--R 6 atan(--------) +--R b x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 6\|- a b 3\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1040 + +--S 1041 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 6\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 3\|a \|b \|a b +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1347 +t0:=x/(a+b*x^6) +--R +--R +--R x +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1045 + +--S 1046 of 1347 +r0:=1/6*log(a^(1/3)+b^(1/3)*x^2)/(a^(2/3)*b^(1/3))-1/12*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/(a^(2/3)*b^(1/3))-_ + 1/2*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+ 2 3+-+ 3+-+ +--R - \|3 log(x \|b - x \|a \|b + \|a ) + 2\|3 log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2x \|b - \|a +--R 6atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 3+-+ +--R 12\|3 \|a \|b +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +---+ +--R +-+ 4 3| 2 2 3| 2 2 +-+ 2 3| 2 +--R - \|3 log(x \|a b - a x \|a b + a ) + 2\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +--R 2x \|3 \|a b - a\|3 +--R 6atan(---------------------) +--R 3a +--R / +--R +---+ +--R +-+3| 2 +--R 12\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 12\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1347 +t0:=1/(a+b*x^6) +--R +--R +--R 1 +--R (1) -------- +--R 6 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1050 + +--S 1051 of 1347 +r0:=1/3*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*b^(1/6))+1/3*atan(b^(1/3)*_ + x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*_ + sqrt(2))+1/3*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))/(a^(5/6)*b^(1/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R / +--R +-+6+-+5 3+-+6+-+ +--R 3\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R |- -------- log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+2 +----------+ +--R | 1 2 | 1 | 1 2 +--R - |- -------- log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 6| 5 +--R \| 46656a b \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R 2 |- -------- log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R | 1 | 1 +--R - 2 |- -------- log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ | 1 \| 46656a b +--R - 2\|3 |- -------- atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 3\|2 |- -------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +----------+2 +----------+ +--R 2 | 1 | 1 2 +--R log(36a |- -------- + 6a x |- -------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R - +--R +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 3\|2 |- -------- \|a \|b \|b +--R 6| 5 +--R \| 46656a b +--R * +--R +----------+2 +----------+ +--R 2 | 1 | 1 2 +--R log(36a |- -------- - 6a x |- -------- + x ) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R 6\|2 |- -------- \|a \|b \|b log(6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R +----------+ +----------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R - 6\|2 |- -------- \|a \|b \|b log(- 6a |- -------- + x) +--R 6| 5 6| 5 +--R \| 46656a b \| 46656a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - 2\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b +--R 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- - x +--R 6| 5 +--R \| 46656a b +--R + +--R +----------+ +--R +-+ | 1 +--R 3a\|3 |- -------- +--R +----------+ 6| 5 +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ \| 46656a b +--R - 6\|2 \|3 |- -------- \|a \|b \|b atan(-------------------) +--R 6| 5 +----------+ +--R \| 46656a b | 1 +--R 3a |- -------- + x +--R 6| 5 +--R \| 46656a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 6\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1347 +t0:=1/(x*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ---------- +--R 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1055 + +--S 1056 of 1347 +r0:=log(x)/a-1/6*log(a+b*x^6)/a +--R +--R +--R 6 +--R - log(b x + a) + 6log(x) +--R (2) ------------------------- +--R 6a +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(b x + a) + 6log(x) +--R (3) ------------------------- +--R 6a +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1347 +t0:=1/(x^2*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R 8 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1060 + +--S 1061 of 1347 +r0:=(-1)/(a*x)-1/3*b^(1/6)*atan(b^(1/6)*x/a^(1/6))/a^(7/6)-_ + 1/3*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(2)/(a^(7/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3))))+1/3*b^(1/3)*atanh(b^(1/3)*x*_ + sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(2)/(a^(7/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R x\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - x\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +---------------------+ +--R 6+-+ | +-------+ +--R 6+-+ x\|b 6+-+ | +-+ | 3+-+2 3+-+ +--R (- x\|b atan(-----) - 3\|a )\|\|3 \|- \|b - \|b +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 3a x\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R - a x |- ------- log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R - 2a x |- ------- log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6 | b +--R 2a x |- ------- log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +---------+4 +--R | b 6 | b 5 | b 2 +--R a x |- ------- log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a x\|3 |- ------- atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a x\|3 |- ------- atan(------------------------- - 2 +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R / +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|2 \|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R +-+3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|2 \|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------+ +--R | b 6+-+ +--R 3a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R - 6a |- ------- \|a log(7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+5 +--R | b 6+-+ 6 | b +--R 6a |- ------- \|a log(- 7776a |- ------- + b x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R | b 6+-+ +--R 3a |- ------- \|a +--R 6| 7 +--R \| 46656a +--R * +--R +---------+5 +---------+4 +--R 6 | b 5 | b 2 +--R log(- 7776a x |- ------- - 1296a |- ------- + b x ) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R 6+-+ +--R 6+-+ x\|b +--R 2\|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R 6a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- - b x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+5 +--R 6 +-+ | b +--R 3888a \|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b 6+-+ \| 46656a +--R - 6a\|3 |- ------- \|a atan(-------------------------) +--R 6| 7 +---------+5 +--R \| 46656a 6 | b +--R 3888a |- ------- + b x +--R 6| 7 +--R \| 46656a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 6a\|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1347 +t0:=1/(x^3*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R 9 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1065 + +--S 1066 of 1347 +r0:=(-1/2)/(a*x^2)+1/6*b^(1/3)*log(a^(1/3)+b^(1/3)*x^2)/a^(4/3)-_ + 1/12*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(4/3)+_ + 1/2*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*_ + sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - x \|3 \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 2 +-+3+-+ 2 3+-+ 3+-+ 2 3+-+ 2x \|b - \|a +-+3+-+ +--R 2x \|3 \|b log(x \|b + \|a ) - 6x \|b atan(-------------- - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R 12a x \|3 \|a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 2 +-+ |b |b 2 +--R 2x \|3 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 2 +-+ |b 2 |b |b 4 +--R - x \|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 2 |b \|a +-+ +--R 6x 3|- atan(---------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R 12a x \|3 +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b 2 +--R 2\|3 \|a 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 2 3+-+ 3+-+ +--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 12a\|3 \|a +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1347 +t0:=1/(x^4*(a+b*x^6)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1070 + +--S 1071 of 1347 +r0:=(-1/3)/(a*x^3)-1/3*atan(x^3*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R 3 +-+ +--R 3 +-+ x \|b +-+ +--R - x \|b atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 3 +-+ +--R 3a x \|a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 3 | b 6 |b +--R +---+ - 2a x |- - + b x - a +-+ a |- +--R 3 | b \| a 3 |b \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 6 \|a 3 +--R b x + a b x +--R (3) [-----------------------------------------,---------------------] +--R 3 3 +--R 6a x 3a x +--R Type: Union(List(Expression(Integer)),...) +--E 1072 + +--S 1073 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a 3 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 3 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 3 +--R \|a b x +--R (6) -------------------------------------- +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1076 + +)clear all + +--S 1077 of 1347 +t0:=x^8/(a+b*x^6)^2 +--R +--R +--R 8 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1077 + +--S 1078 of 1347 +r0:=-1/6*x^3/(b*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(b^(3/2)*sqrt(a)) +--R +--R +--R 3 +-+ +--R 6 x \|b 3 +-+ +-+ +--R (b x + a)atan(------) - x \|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 2 6 +-+ +-+ +--R (6b x + 6a b)\|a \|b +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-----+ 3 +--R 6 (b x - a)\|- a b + 2a b x 3 +-----+ +--R (b x + a)log(----------------------------) - 2x \|- a b +--R 6 +--R b x + a +--R [---------------------------------------------------------, +--R 2 6 +-----+ +--R (12b x + 12a b)\|- a b +--R 3 +---+ +--R 6 x \|a b 3 +---+ +--R (b x + a)atan(--------) - x \|a b +--R a +--R -----------------------------------] +--R 2 6 +---+ +--R (6b x + 6a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1079 + +--S 1080 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 12b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 6b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1083 + +)clear all + +--S 1084 of 1347 +t0:=x^7/(a+b*x^6)^2 +--R +--R +--R 7 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1084 + +--S 1085 of 1347 +r0:=-1/6*x^2/(b*(a+b*x^6))+1/18*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(2/3)*b^(4/3))-1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_ + b^(2/3)*x^4)/(a^(2/3)*b^(4/3))-1/6*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(2/3)*b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+2 3+-+ +--R - 6x \|3 \|a \|b +--R / +--R 2 6 +-+3+-+2 3+-+ +--R (36b x + 36a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 6 +-+ 4 3| 2 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +---+ +--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2 +--R (6b x + 6a)atan(---------------------) - 6x \|3 \|a b +--R 3a +--R / +--R +---+ +--R 2 6 +-+3| 2 +--R (36b x + 36a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 36b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1088 + +)clear all + +--S 1089 of 1347 +t0:=x^6/(a+b*x^6)^2 +--R +--R +--R 6 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1089 + +--S 1090 of 1347 +r0:=-1/6*x/(b*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/(a^(5/6)*_ + b^(7/6))+1/18*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/_ + (a^(5/6)*b^(4/3)*sqrt(2))+1/18*atanh(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(5/6)*b^(4/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R (b x + a)\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R (b x + a)\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+ +--R (b x + a)\|2 \|b atan(-----) - 3x\|2 \|a \|b \|b +--R 6+-+ +--R \|a +--R / +--R 2 6 +-+6+-+5 3+-+6+-+ +--R (18b x + 18a b)\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 2 6 | 1 +--R (3b x + 3a b) |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- + 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 2 6 | 1 +--R (- 3b x - 3a b) |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- - 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 2 6 | 1 | 1 +--R (6b x + 6a b) |- -------------- log(36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 2 6 | 1 | 1 +--R (- 6b x - 6a b) |- -------------- log(- 36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R +----------------+ 6| 5 7 +--R 2 6 +-+ | 1 \| 2176782336a b +--R (6b x + 6a b)\|3 |- -------------- atan(----------------------------) +--R 6| 5 7 +----------------+ +--R \| 2176782336a b | 1 +--R 18a b |- -------------- - x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R +----------------+ 6| 5 7 +--R 2 6 +-+ | 1 \| 2176782336a b +--R (- 6b x - 6a b)\|3 |- -------------- atan(----------------------------) +--R 6| 5 7 +----------------+ +--R \| 2176782336a b | 1 +--R 18a b |- -------------- + x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R - x +--R / +--R 2 6 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1091 + +--S 1092 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - \|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 9b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- + 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 9b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 2 2 | 1 | 1 2 +--R log(1296a b |- -------------- - 36a b x |- -------------- + x ) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ | 1 +--R 18b\|2 |- -------------- \|a \|b \|b log(36a b |- -------------- + x) +--R 6| 5 7 6| 5 7 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R | 1 +--R log(- 36a b |- -------------- + x) +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R atan(----------------------------) +--R +----------------+ +--R | 1 +--R 18a b |- -------------- - x +--R 6| 5 7 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 18b\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 5 7 +--R \| 2176782336a b +--R * +--R +----------------+ +--R +-+ | 1 +--R 18a b\|3 |- -------------- +--R 6| 5 7 +--R \| 2176782336a b +--R atan(----------------------------) +--R +----------------+ +--R | 1 +--R 18a b |- -------------- + x +--R 6| 5 7 +--R \| 2176782336a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 18b\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1093 + +)clear all + +--S 1094 of 1347 +t0:=x^5/(a+b*x^6)^2 +--R +--R +--R 5 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1094 + +--S 1095 of 1347 +r0:=(-1/6)/(b*(a+b*x^6)) +--R +--R +--R 1 +--R - +--R 6 +--R (2) - ---------- +--R 2 6 +--R b x + a b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1095 + +--S 1096 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 6 +--R 6b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1096 + +--S 1097 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1098 + +)clear all + +--S 1099 of 1347 +t0:=x^4/(a+b*x^6)^2 +--R +--R +--R 4 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1099 + +--S 1100 of 1347 +r0:=1/6*x^5/(a*(a+b*x^6))+1/18*atan(b^(1/6)*x/a^(1/6))/_ + (a^(7/6)*b^(5/6))+1/9*atan(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*_ + sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))-1/9*_ + atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+sqrt(3)*_ + sqrt(-b^(2/3)))))/(a^(7/6)*b^(2/3)*sqrt(2)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 6 6+-+5 | +-+ | 3+-+2 3+-+ +--R (- 2b x - 2a)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 6 6+-+5 | +-+ | 3+-+2 3+-+ +--R (2b x + 2a)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+2 x\|b 5 +-+6+-+3+-+2 6+-+5 +--R ((b x + a)\|2 \|b atan(-----) + 3x \|2 \|a \|b \|b ) +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +--R | +-------+ +--R 6 2 +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ +--R (18a b x + 18a )\|2 \|a \|b \|b \|\|3 \|- \|b - \|b +--R * +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 6 2 | 1 +--R (3a b x + 3a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (6a b x + 6a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 6a b x - 6a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(- 60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 3a b x - 3a ) |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R - 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (- 6a b x - 6a )\|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- - x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (6a b x + 6a )\|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R 5 +--R x +--R / +--R 6 2 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1101 + +--S 1102 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 2\|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+5 | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 2\|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 9a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 | 1 +--R log(- 60466176a b |- -------------- + x) +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+3+-+2 6+-+5 +--R 9a\|2 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R log +--R +----------------+5 +--R 6 4 | 1 +--R - 60466176a b x |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+4 +--R 5 3 | 1 2 +--R - 1679616a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+2 x\|b +--R - \|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- - x +--R 6| 7 5 +--R \| 2176782336a b +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+3+-+2 6+-+5 +--R 18a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +----------------+5 +--R 6 4 +-+ | 1 +--R 30233088a b \|3 |- -------------- +--R 6| 7 5 +--R \| 2176782336a b +--R atan(------------------------------------) +--R +----------------+5 +--R 6 4 | 1 +--R 30233088a b |- -------------- + x +--R 6| 7 5 +--R \| 2176782336a b +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R +-+6+-+3+-+2 6+-+5 | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 18a\|2 \|a \|b \|b \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1103 + +)clear all + +--S 1104 of 1347 +t0:=x^3/(a+b*x^6)^2 +--R +--R +--R 3 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1104 + +--S 1105 of 1347 +r0:=1/6*x^4/(a*(a+b*x^6))-1/18*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(4/3)*b^(2/3))+1/36*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + x^2+b^(2/3)*x^4)/(a^(4/3)*b^(2/3))-1/6*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(4/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (b x + a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (- 2b x - 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 +-+3+-+3+-+2 +--R 6x \|3 \|a \|b +--R / +--R 6 2 +-+3+-+3+-+2 +--R (36a b x + 36a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1105 + +--S 1106 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+2 +------+ +--R 6 +-+ 2 3| 2 4 3| 2 +--R (- b x - a)\|3 log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|- a b + a b) +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +------+ +--R 6 2x \|3 \|- a b - a b\|3 4 +-+3| 2 +--R (- 6b x - 6a)atan(---------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +------+ +--R 6 2 +-+3| 2 +--R (36a b x + 36a )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1106 + +--S 1107 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +------+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R - \|3 \|- a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(x \|b + \|a ) +--R + +--R +------+2 +------+ +--R +-+3+-+3+-+2 2 3| 2 4 3| 2 +--R - \|3 \|a \|b log(x \|- a b + b x \|- a b - a b) +--R + +--R +------+2 +------+ 2 3+-+ 3+-+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2x \|b - \|a +--R 2\|3 \|a \|b log(x \|- a b + a b) - 6\|- a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R 2 +-+3| 2 +-+ +--R 3+-+3+-+2 2x \|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(---------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 36a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1108 + +)clear all + +--S 1109 of 1347 +t0:=x^2/(a+b*x^6)^2 +--R +--R +--R 2 +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1109 + +--S 1110 of 1347 +r0:=1/6*x^3/(a*(a+b*x^6))+1/6*atan(x^3*sqrt(b)/sqrt(a))/(a^(3/2)*sqrt(b)) +--R +--R +--R 3 +-+ +--R 6 x \|b 3 +-+ +-+ +--R (b x + a)atan(------) + x \|a \|b +--R +-+ +--R \|a +--R (2) ----------------------------------- +--R 6 2 +-+ +-+ +--R (6a b x + 6a )\|a \|b +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-----+ 3 +--R 6 (b x - a)\|- a b + 2a b x 3 +-----+ +--R (b x + a)log(----------------------------) + 2x \|- a b +--R 6 +--R b x + a +--R [---------------------------------------------------------, +--R 6 2 +-----+ +--R (12a b x + 12a )\|- a b +--R 3 +---+ +--R 6 x \|a b 3 +---+ +--R (b x + a)atan(--------) + x \|a b +--R a +--R -----------------------------------] +--R 6 2 +---+ +--R (6a b x + 6a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1111 + +--S 1112 of 1347 +m0a:=a0.1-r0 +--R +--R +--R 6 +-----+ 3 3 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 12a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1347 +m0b:=a0.2-r0 +--R +--R +--R 3 +---+ 3 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 6a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1347 +t0:=x/(a+b*x^6)^2 +--R +--R +--R x +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1116 + +--S 1117 of 1347 +r0:=1/6*x^2/(a*(a+b*x^6))+1/9*log(a^(1/3)+b^(1/3)*x^2)/_ + (a^(5/3)*b^(1/3))-1/18*log(a^(2/3)-a^(1/3)*b^(1/3)*x^2+_ + b^(2/3)*x^4)/(a^(5/3)*b^(1/3))-1/3*atan((a^(1/3)-_ + 2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 6 +-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- b x - a)\|3 log(x \|b - x \|a \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 6 +-+ 2 3+-+ 3+-+ 6 2x \|b - \|a +--R (2b x + 2a)\|3 log(x \|b + \|a ) + (6b x + 6a)atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 +-+3+-+2 3+-+ +--R 3x \|3 \|a \|b +--R / +--R 6 2 +-+3+-+2 3+-+ +--R (18a b x + 18a )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+2 +---+ +--R 6 +-+ 4 3| 2 2 3| 2 2 +--R (- b x - a)\|3 log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R 6 +-+ 2 3| 2 +--R (2b x + 2a)\|3 log(x \|a b + a) +--R + +--R +---+ +--R 2 +-+3| 2 +-+ +---+ +--R 6 2x \|3 \|a b - a\|3 2 +-+3| 2 +--R (6b x + 6a)atan(---------------------) + 3x \|3 \|a b +--R 3a +--R / +--R +---+ +--R 6 2 +-+3| 2 +--R (18a b x + 18a )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+2 +---+ +--R +-+3+-+2 3+-+ 4 3| 2 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - a x \|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 2 3| 2 +--R 2\|3 \|a \|b log(x \|a b + a) +--R + +--R +---+ +--R +-+3| 2 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log(x \|b - x \|a \|b + \|a ) +--R + +--R +---+ +--R +---+ 2 +-+3| 2 +-+ +--R +-+3| 2 2 3+-+ 3+-+ 3+-+2 3+-+ 2x \|3 \|a b - a\|3 +--R - 2\|3 \|a b log(x \|b + \|a ) + 6\|a \|b atan(---------------------) +--R 3a +--R + +--R +---+ 2 3+-+ 3+-+ +--R 3| 2 2x \|b - \|a +--R - 6\|a b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1347 +t0:=1/(a+b*x^6)^2 +--R +--R +--R 1 +--R (1) -------------------- +--R 2 12 6 2 +--R b x + 2a b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 1121 + +--S 1122 of 1347 +r0:=1/6*x/(a*(a+b*x^6))+5/18*atan(b^(1/6)*x/a^(1/6))/_ + (a^(11/6)*b^(1/6))+5/18*atan(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*_ + sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*_ + b^(1/3)*sqrt(2))+5/18*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*_ + sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(11/6)*b^(1/3)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ +--R (5b x + 5a)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 6 6+-+ | +-+ | 3+-+2 3+-+ +--R (5b x + 5a)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 6 +-+3+-+ x\|b +-+6+-+5 3+-+6+-+ +--R (5b x + 5a)\|2 \|b atan(-----) + 3x\|2 \|a \|b \|b +--R 6+-+ +--R \|a +--R / +--R 6 2 +-+6+-+5 3+-+6+-+ +--R (18a b x + 18a )\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R 6 2 | 1 +--R (15a b x + 15a ) |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- + 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 | 1 +--R (- 15a b x - 15a ) |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- - 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 6 2 | 1 2 | 1 +--R (30a b x + 30a ) |- -------------- log(36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R 6 2 | 1 2 | 1 +--R (- 30a b x - 30a ) |- -------------- log(- 36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R +----------------+ 6| 11 +--R 6 2 +-+ | 1 \| 2176782336a b +--R (30a b x + 30a )\|3 |- -------------- atan(---------------------------) +--R 6| 11 +----------------+ +--R \| 2176782336a b 2 | 1 +--R 18a |- -------------- - x +--R 6| 11 +--R \| 2176782336a b +--R + +--R +----------------+ +--R 6 2 +-+ | 1 +--R (- 30a b x - 30a )\|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- + x +--R 6| 11 +--R \| 2176782336a b +--R + +--R x +--R / +--R 6 2 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 5\|b \|\|3 \|- \|b + \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 6+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 5\|b \|\|3 \|- \|b - \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 45a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- + 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 45a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+2 +----------------+ +--R 4 | 1 2 | 1 2 +--R log(1296a |- -------------- - 36a x |- -------------- + x ) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R +----------------+ +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ 2 | 1 +--R 90a\|2 |- -------------- \|a \|b \|b log(36a |- -------------- + x) +--R 6| 11 6| 11 +--R \| 2176782336a b \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 | 1 +--R log(- 36a |- -------------- + x) +--R 6| 11 +--R \| 2176782336a b +--R + +--R 6+-+ +--R +-+3+-+ x\|b +--R - 5\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- - x +--R 6| 11 +--R \| 2176782336a b +--R + +--R - +--R +----------------+ +--R +-+ +-+ | 1 6+-+5 3+-+6+-+ +--R 90a\|2 \|3 |- -------------- \|a \|b \|b +--R 6| 11 +--R \| 2176782336a b +--R * +--R +----------------+ +--R 2 +-+ | 1 +--R 18a \|3 |- -------------- +--R 6| 11 +--R \| 2176782336a b +--R atan(---------------------------) +--R +----------------+ +--R 2 | 1 +--R 18a |- -------------- + x +--R 6| 11 +--R \| 2176782336a b +--R / +--R +-+6+-+5 3+-+6+-+ +--R 18a\|2 \|a \|b \|b +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1347 +t0:=1/(x*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 13 7 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1126 + +--S 1127 of 1347 +r0:=1/6/(a*(a+b*x^6))+log(x)/a^2-1/6*log(a+b*x^6)/a^2 +--R +--R +--R 6 6 6 +--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a +--R (2) -------------------------------------------------- +--R 2 6 3 +--R 6a b x + 6a +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R (- b x - a)log(b x + a) + (6b x + 6a)log(x) + a +--R (3) -------------------------------------------------- +--R 2 6 3 +--R 6a b x + 6a +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1347 +t0:=1/(x^2*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 14 8 2 2 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1131 + +--S 1132 of 1347 +r0:=(-7/6)/(a^2*x)+1/6/(a*x*(a+b*x^6))-7/18*b^(1/6)*atan(b^(1/6)*_ + x/a^(1/6))/a^(13/6)-7/9*b^(1/3)*atan(b^(1/3)*x*sqrt(2)/_ + (a^(1/6)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*_ + sqrt(2)*sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))+7/9*_ + b^(1/3)*atanh(b^(1/3)*x*sqrt(2)/(a^(1/6)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))))/(a^(13/6)*sqrt(2)*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +--R 7 3+-+ | +-+ | 3+-+2 3+-+ +--R (14b x + 14a x)\|b \|\|3 \|- \|b - \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +--R 7 3+-+ | +-+ | 3+-+2 3+-+ +--R (- 14b x - 14a x)\|b \|\|3 \|- \|b + \|b +--R * +--R +-+3+-+ +--R x\|2 \|b +--R atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R 7 +-+6+-+ x\|b 6 +-+6+-+ +--R ((- 7b x - 7a x)\|2 \|b atan(-----) + (- 21b x - 18a)\|2 \|a ) +--R 6+-+ +--R \|a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 2 7 3 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R (18a b x + 18a x)\|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------+ +--R 2 7 3 | 117649b +--R (- 3a b x - 3a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +---------------+4 +--R 11 | 117649b 9 | 117649b +--R 60466176a x |- ------------- - 11757312a |- ------------- +--R 6| 13 6| 13 +--R \| 2176782336a \| 2176782336a +--R + +--R 2 +--R 16807b x +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (- 6a b x - 6a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (6a b x + 6a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(- 60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 | 117649b +--R (3a b x + 3a x) |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +---------------+4 +--R 11 | 117649b 9 | 117649b +--R - 60466176a x |- ------------- - 11757312a |- ------------- +--R 6| 13 6| 13 +--R \| 2176782336a \| 2176782336a +--R + +--R 2 +--R 16807b x +--R + +--R +---------------+ +--R 2 7 3 +-+ | 117649b +--R (6a b x + 6a x)\|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- - 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 7 3 +-+ | 117649b +--R (- 6a b x - 6a x)\|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R 6 +--R - 7b x - 6a +--R / +--R 2 7 3 +--R 6a b x + 6a x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R - 14\|b \|\|3 \|- \|b - \|b atanh(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+3+-+ +--R 3+-+ | +-+ | 3+-+2 3+-+ x\|2 \|b +--R 14\|b \|\|3 \|- \|b + \|b atan(----------------------------) +--R +---------------------+ +--R | +-------+ +--R 6+-+ | +-+ | 3+-+2 3+-+ +--R \|a \|\|3 \|- \|b - \|b +--R + +--R - +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 9a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +--R 11 | 117649b +--R 60466176a x |- ------------- +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+4 +--R 9 | 117649b 2 +--R - 11757312a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R - +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 18a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 18a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 | 117649b +--R log(- 60466176a |- ------------- + 16807b x) +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+ +--R 2 +-+ | 117649b 6+-+ +--R 9a \|2 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R log +--R +---------------+5 +--R 11 | 117649b +--R - 60466176a x |- ------------- +--R 6| 13 +--R \| 2176782336a +--R + +--R +---------------+4 +--R 9 | 117649b 2 +--R - 11757312a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R 6+-+ +--R +-+6+-+ x\|b +--R 7\|2 \|b atan(-----) +--R 6+-+ +--R \|a +--R + +--R +---------------+ +--R 2 +-+ +-+ | 117649b 6+-+ +--R 18a \|2 \|3 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- - 16807b x +--R 6| 13 +--R \| 2176782336a +--R + +--R - +--R +---------------+ +--R 2 +-+ +-+ | 117649b 6+-+ +--R 18a \|2 \|3 |- ------------- \|a +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------+5 +--R 11 +-+ | 117649b +--R 30233088a \|3 |- ------------- +--R 6| 13 +--R \| 2176782336a +--R atan(-----------------------------------------) +--R +---------------+5 +--R 11 | 117649b +--R 30233088a |- ------------- + 16807b x +--R 6| 13 +--R \| 2176782336a +--R * +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R / +--R +---------------------+ +---------------------+ +--R | +-------+ | +-------+ +--R 2 +-+6+-+ | +-+ | 3+-+2 3+-+ | +-+ | 3+-+2 3+-+ +--R 18a \|2 \|a \|\|3 \|- \|b - \|b \|\|3 \|- \|b + \|b +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1347 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1347 +t0:=1/(x^3*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 15 9 2 3 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1136 + +--S 1137 of 1347 +r0:=(-2/3)/(a^2*x^2)+1/6/(a*x^2*(a+b*x^6))+2/9*b^(1/3)*_ + log(a^(1/3)+b^(1/3)*x^2)/a^(7/3)-1/9*b^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^2+b^(2/3)*x^4)/a^(7/3)+2/3*b^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*x^2)/(a^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 8 2 +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +--R (- 2b x - 2a x )\|3 \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R 8 2 +-+3+-+ 2 3+-+ 3+-+ +--R (4b x + 4a x )\|3 \|b log(x \|b + \|a ) +--R + +--R 2 3+-+ 3+-+ +--R 8 2 3+-+ 2x \|b - \|a 6 +-+3+-+ +--R (- 12b x - 12a x )\|b atan(--------------) + (- 12b x - 9a)\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 8 3 2 +-+3+-+ +--R (18a b x + 18a x )\|3 \|a +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R 8 2 +-+ |b |b 2 +--R (4b x + 4a x )\|3 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ +--R 8 2 +-+ |b 2 |b |b 4 +--R (- 2b x - 2a x )\|3 3|- log(- a x 3|- + a 3|- + b x ) +--R \|a \|a \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 8 2 |b \|a 6 +-+ +--R (12b x + 12a x ) 3|- atan(---------------------- + (- 12b x - 9a)\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 8 3 2 +-+ +--R (18a b x + 18a x )\|3 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 4 3+-+2 2 3+-+3+-+ 3+-+2 +-+3+-+ 2 3+-+ 3+-+ +--R \|3 \|b log(x \|b - x \|a \|b + \|a ) - 2\|3 \|b log(x \|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b 2 +--R 2\|3 \|a 3|- log(a 3|- + b x ) +--R \|a \|a +--R + +--R +-+ +-+2 +-+ 2 3+-+ 3+-+ +--R +-+3+-+ |b 2 |b |b 4 3+-+ 2x \|b - \|a +--R - \|3 \|a 3|- log(- a x 3|- + a 3|- + b x + 6\|b atan(--------------) +--R \|a \|a \|a +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b 2 +-+ +--R +-+ a\|3 3|- - 2b x \|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1347 +t0:=1/(x^4*(a+b*x^6)^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 16 10 2 4 +--R b x + 2a b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 1141 + +--S 1142 of 1347 +r0:=(-1/2)/(a^2*x^3)+1/6/(a*x^3*(a+b*x^6))-1/2*atan(x^3*_ + sqrt(b)/sqrt(a))*sqrt(b)/a^(5/2) +--R +--R +--R 3 +-+ +--R 9 3 +-+ x \|b 6 +-+ +--R (- 3b x - 3a x )\|b atan(------) + (- 3b x - 2a)\|a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------ +--R 2 9 3 3 +-+ +--R (6a b x + 6a x )\|a +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a +--R 9 3 | b \| a 6 +--R (3b x + 3a x ) |- - log(------------------------) - 6b x - 4a +--R \| a 6 +--R b x + a +--R [---------------------------------------------------------------, +--R 2 9 3 3 +--R 12a b x + 12a x +--R +-+ +--R |b +--R +-+ a |- +--R 9 3 |b \|a 6 +--R (3b x + 3a x ) |- atan(-----) - 3b x - 2a +--R \|a 3 +--R b x +--R -------------------------------------------] +--R 2 9 3 3 +--R 6a b x + 6a x +--R Type: Union(List(Expression(Integer)),...) +--E 1143 + +--S 1144 of 1347 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 3 | b 6 +--R +---+ - 2a x |- - + b x - a 3 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 6 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1347 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 3 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 3 +--R \|a b x +--R (6) -------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1147 + +)clear all + +--S 1148 of 1347 +t0:=x^8/(1-x^6) +--R +--R +--R 8 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1148 + +--S 1149 of 1347 +r0:=-1/3*x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R atanh(x ) - x +--R (2) -------------- +--R 3 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2x +--R (3) ------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1150 + +--S 1151 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1152 + +)clear all + +--S 1153 of 1347 +t0:=x^7/(1-x^6) +--R +--R +--R 7 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1153 + +--S 1154 of 1347 +r0:=-1/2*x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/_ + sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R -------------------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 2 +-+ +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) - 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1155 + +--S 1156 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1157 + +)clear all + +--S 1158 of 1347 +t0:=x^6/(1-x^6) +--R +--R +--R 6 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1158 + +--S 1159 of 1347 +r0a:=-x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +-+ +--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------) - 6x\|3 +--R 2 2 +--R x + 1 x - 1 +--R (2) ---------------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1347 +r0b:=-x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +-+ +--R 6atan(------------) + 6atan(------------) - 12x\|3 +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------) - 12x\|3 +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1161 + +--S 1162 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R 6atan(------------) + 6atan(------------) + 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1347 +t0:=x^5/(1-x^6) +--R +--R +--R 5 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1166 + +--S 1167 of 1347 +r0:=-1/6*log(1-x^6) +--R +--R +--R 6 +--R log(- x + 1) +--R (2) - ------------- +--R 6 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(x - 1) +--R (3) - ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1347 +t0:=x^4/(1-x^6) +--R +--R +--R 4 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1171 + +--S 1172 of 1347 +r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +--R 2\|3 atanh(x) + \|3 atanh(------) + 3atan(------) +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1347 +r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)+_ + 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +--R - 6atan(------------) - 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +--R - 2\|3 log(x - 1) - 6atan(------------) - 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R - 6atan(------------) - 6atan(------------) - 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1178 + +)clear all + +--S 1179 of 1347 +t0:=x^3/(1-x^6) +--R +--R +--R 3 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1179 + +--S 1180 of 1347 +r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) - 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1180 + +--S 1181 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) - 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1181 + +--S 1182 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1183 + +)clear all + +--S 1184 of 1347 +t0:=x^2/(1-x^6) +--R +--R +--R 2 +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1184 + +--S 1185 of 1347 +r0:=1/3*atanh(x^3) +--R +--R +--R 3 +--R atanh(x ) +--R (2) --------- +--R 3 +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R log(x + 1) - log(x - 1) +--R (3) ------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1186 + +--S 1187 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1188 + +)clear all + +--S 1189 of 1347 +t0:=x/(1-x^6) +--R +--R +--R x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1189 + +--S 1190 of 1347 +r0:=-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(- x + 1) + 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x + 1)\|3 +--R \|3 log(x + x + 1) - 2\|3 log(x - 1) + 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1191 + +--S 1192 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1193 + +)clear all + +--S 1194 of 1347 +t0:=1/(1-x^6) +--R +--R +--R 1 +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1194 + +--S 1195 of 1347 +r0a:=1/3*atanh(x)+1/6*atanh(x/(1+x^2))+1/2*atan(x*sqrt(3)/(1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +--R 2\|3 atanh(x) + \|3 atanh(------) - 3atan(------) +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1347 +r0b:=1/3*atanh(x)-1/12*log(1-x+x^2)+1/12*log(1+x+x^2)-_ + 1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 4\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +--R 6atan(------------) + 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +--R - 2\|3 log(x - 1) + 6atan(------------) + 6atan(------------) +--R 3 3 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R 6atan(------------) + 6atan(------------) + 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1201 + +)clear all + +--S 1202 of 1347 +t0:=1/(x*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------ +--R 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1202 + +--S 1203 of 1347 +r0:=-1/3*atanh(1-2*x^6) +--R +--R +--R 6 +--R atanh(2x - 1) +--R (2) -------------- +--R 3 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(x - 1) + 6log(x) +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1204 + +--S 1205 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + 6log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1206 + +)clear all + +--S 1207 of 1347 +t0:=1/(x^2*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------- +--R 8 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1207 + +--S 1208 of 1347 +r0a:=(-1)/x+1/3*atanh(x)+1/6*atanh(x/(1+x^2))-1/2*atan(x*sqrt(3)/_ + (1-x^2))/sqrt(3) +--R +--R +--R +-+ +--R +-+ +-+ x x\|3 +-+ +--R 2x\|3 atanh(x) + x\|3 atanh(------) + 3x atan(------) - 6\|3 +--R 2 2 +--R x + 1 x - 1 +--R (2) ------------------------------------------------------------- +--R +-+ +--R 6x\|3 +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1347 +r0b:=(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (3) +--R +-+ 2 +-+ 2 +-+ +--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 4x\|3 atanh(x) +--R + +--R +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 6x atan(------------) - 6x atan(------------) - 12\|3 +--R 3 3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-+ 2 +-+ 2 +-+ +--R x\|3 log(x + x + 1) - x\|3 log(x - x + 1) + 2x\|3 log(x + 1) +--R + +--R +-+ +-+ +--R +-+ (2x + 1)\|3 (2x - 1)\|3 +-+ +--R - 2x\|3 log(x - 1) - 6x atan(------------) - 6x atan(------------) - 12\|3 +--R 3 3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Union(Expression(Integer),...) +--E 1210 + +--S 1211 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-+ 2 +-+ 2 +-+ +--R \|3 log(x + x + 1) - \|3 log(x - x + 1) + 2\|3 log(x + 1) +--R + +--R +-+ +-+ +-+ x +--R - 2\|3 log(x - 1) - 4\|3 atanh(x) - 2\|3 atanh(------) +--R 2 +--R x + 1 +--R + +--R +-+ +-+ +-+ +--R (2x + 1)\|3 (2x - 1)\|3 x\|3 +--R - 6atan(------------) - 6atan(------------) - 6atan(------) +--R 3 3 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1347 +m0b:=a0-r0b +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (7) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1347 +t0:=1/(x^3*(1-x^6)) +--R +--R +--R 1 +--R (1) - ------- +--R 9 3 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1347 +r0:=(-1/2)/x^2-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)-_ + 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) - 6x atan(-------------) - 6\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1347 +t0:=1/(x^4*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 10 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1347 +r0:=(-1/3)/x^3+1/3*atanh(x^3) +--R +--R +--R 3 3 +--R x atanh(x ) - 1 +--R (2) --------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 3 +--R x log(x + 1) - x log(x - 1) - 2 +--R (3) --------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1347 +m0:=a0-r0 +--R +--R +--R 3 3 3 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1347 +t0:=1/(x^5*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 11 5 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1347 +r0:=(-1/4)/x^4-1/6*log(1-x^2)+1/12*log(1+x^2+x^4)+_ + 1/2*atan((1+2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +--R x \|3 log(x + x + 1) - 2x \|3 log(- x + 1) + 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 3\|3 +--R / +--R 4 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x + 1)\|3 +-+ +--R x \|3 log(x + x + 1) - 2x \|3 log(x - 1) + 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1347 +m0:=a0-r0 +--R +--R +--R 2 2 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1347 +t0:=1/(x^6*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 12 6 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1347 +r0:=(-1/5)/x^5+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)-1/2*atan((1-2*x)/sqrt(3))/sqrt(3)+_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 20x \|3 atanh(x) +--R + +--R +-+ +-+ +--R 5 (2x + 1)\|3 5 (2x - 1)\|3 +-+ +--R 30x atan(------------) + 30x atan(------------) - 12\|3 +--R 3 3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R 5x \|3 log(x + x + 1) - 5x \|3 log(x - x + 1) + 10x \|3 log(x + 1) +--R + +--R +-+ +-+ +--R 5 +-+ 5 (2x + 1)\|3 5 (2x - 1)\|3 +--R - 10x \|3 log(x - 1) + 30x atan(------------) + 30x atan(------------) +--R 3 3 +--R + +--R +-+ +--R - 12\|3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1347 +m0:=a0-r0 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (4) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1347 +t0:=1/(x^7*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 13 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1347 +r0:=(-1/6)/x^6-1/3*atanh(1-2*x^6) +--R +--R +--R 6 6 +--R 2x atanh(2x - 1) - 1 +--R (2) --------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R - x log(x - 1) + 6x log(x) - 1 +--R (3) ------------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x - 1) + 6log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1347 +t0:=1/(x^8*(1-x^6)) +--R +--R +--R 1 +--R (1) - -------- +--R 14 8 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1347 +r0:=(-1/7)/x^7+(-1)/x+1/3*atanh(x)-1/12*log(1-x+x^2)+_ + 1/12*log(1+x+x^2)+1/2*atan((1-2*x)/sqrt(3))/sqrt(3)-_ + 1/2*atan((1+2*x)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 28x \|3 atanh(x) +--R + +--R +-+ +-+ +--R 7 (2x + 1)\|3 7 (2x - 1)\|3 6 +-+ +--R - 42x atan(------------) - 42x atan(------------) + (- 84x - 12)\|3 +--R 3 3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x \|3 log(x + x + 1) - 7x \|3 log(x - x + 1) + 14x \|3 log(x + 1) +--R + +--R +-+ +-+ +--R 7 +-+ 7 (2x + 1)\|3 7 (2x - 1)\|3 +--R - 14x \|3 log(x - 1) - 42x atan(------------) - 42x atan(------------) +--R 3 3 +--R + +--R 6 +-+ +--R (- 84x - 12)\|3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1347 +m0:=a0-r0 +--R +--R +--R log(x + 1) - log(x - 1) - 2atanh(x) +--R (4) ----------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1347 +t0:=x^8/(1+x^6) +--R +--R +--R 8 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1347 +r0:=1/3*x^3-1/3*atan(x^3) +--R +--R +--R 3 3 +--R - atan(x ) + x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - atan(x ) + x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1347 +t0:=x^7/(1+x^6) +--R +--R +--R 7 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1347 +r0:=1/2*x^2-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_ + 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+ +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 2 +-+ +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) - 6atan(-------------) + 6x \|3 +--R 3 +--R ------------------------------------------------------------------------ +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1347 +t0:=x^6/(1+x^6) +--R +--R +--R 6 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1347 +r0:=x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) + 12x\|3 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R - 2sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 2x +--R 2sin(----------)atan(-------------------) + atan(------) + 6x +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R - 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- 2x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1347 +t0:=x^5/(1+x^6) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1347 +r0:=1/6*log(1+x^6) +--R +--R +--R 6 +--R log(x + 1) +--R (2) ----------- +--R 6 +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R log(x + 1) +--R (3) ----------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1347 +t0:=x^4/(1+x^6) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1347 +r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))+_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R - 2sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R 2sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 2x +--R - atan(------) +--R 2 +--R x - 1 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (4x + 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x +--R 2 2 +--R + +--R 4 +--R 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (2x + 6x - 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x +--R 2 2 +--R + +--R 8 +--R x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1347 +t0:=x^3/(1+x^6) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1347 +r0:=-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (2) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R \|3 log(x - x + 1) - 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (3) -------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1347 +t0:=x^2/(1+x^6) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1347 +r0:=1/3*atan(x^3) +--R +--R +--R 3 +--R atan(x ) +--R (2) -------- +--R 3 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R atan(x ) +--R (3) -------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1347 +t0:=x/(1+x^6) +--R +--R +--R x +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1347 +r0:=1/6*log(1+x^2)-1/12*log(1-x^2+x^4)-1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R +-+ 4 2 +-+ 2 (2x - 1)\|3 +--R - \|3 log(x - x + 1) + 2\|3 log(x + 1) + 6atan(-------------) +--R 3 +--R (3) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1347 +t0:=1/(1+x^6) +--R +--R +--R 1 +--R (1) ------ +--R 6 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1347 +r0:=1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+1/6*atan(2*x+sqrt(3))-_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 +--R 2sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R \|3 2 2x +--R - 2sin(----------)atan(-------------------) - atan(------) +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R - 4\|3 sin(----------)atan(-------------------) - 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) + 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (2x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((4x - 2x )cos(----------) + 2x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (2x - x )cos(----------) + (- 2x + 2x )cos(----------) + x - 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1347 +t0:=1/(x*(1+x^6)) +--R +--R +--R 1 +--R (1) ------ +--R 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1347 +r0:=-1/3*atanh(1+2*x^6) +--R +--R +--R 6 +--R atanh(2x + 1) +--R (2) - -------------- +--R 3 +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R - log(x + 1) + 6log(x) +--R (3) ----------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R - log(x + 1) + 6log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1347 +t0:=1/(x^2*(1+x^6)) +--R +--R +--R 1 +--R (1) ------- +--R 8 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1347 +r0:=(-1)/x-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-1/6*atan(2*x+sqrt(3))-_ + 1/4*log(1+x^2-x*sqrt(3))/sqrt(3)+1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3x log(x\|3 + x + 1) - 3x log(- x\|3 + x + 1) - 2x\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2x\|3 atan(\|3 - 2x) - 4x\|3 atan(x) - 12\|3 +--R / +--R +-+ +--R 12x\|3 +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R 2x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R \|3 2 2 +--R - 2x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 2x +--R x atan(------) - 6 +--R 2 +--R x - 1 +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R - 3log(x\|3 + x + 1) + 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R - 2\|3 atan(\|3 - 2x) + 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((4x + 4x )cos(----------) - 4x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (- 4x - 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (6x + 6x )cos(----------) + (- 4x + 2x )cos(----------) + 6x +--R 2 2 +--R + +--R 4 +--R - 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((- 8x - 8x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (4x + 4x )cos(----------) + (4x - 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (16x + 12x + 2x )cos(----------) + x - 5x + 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (- 4x - 4x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 2x - 6x + 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (x + x )cos(----------) + (4x - 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (6x - 3x )cos(----------) + (- x + 5x - 3x )cos(----------) + 2x +--R 2 2 +--R + +--R 8 +--R - x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1347 +t0:=1/(x^3*(1+x^6)) +--R +--R +--R 1 +--R (1) ------- +--R 9 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1347 +r0:=(-1/2)/x^2+1/6*log(1+x^2)-1/12*log(1-x^2+x^4)+1/2*_ + atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3 +--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 2 +-+ 4 2 2 +-+ 2 2 (2x - 1)\|3 +--R - x \|3 log(x - x + 1) + 2x \|3 log(x + 1) - 6x atan(-------------) +--R 3 +--R + +--R +-+ +--R - 6\|3 +--R / +--R 2 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1347 +t0:=1/(x^4*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 10 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1347 +r0:=(-1/3)/x^3-1/3*atan(x^3) +--R +--R +--R 3 3 +--R - x atan(x ) - 1 +--R (2) ---------------- +--R 3 +--R 3x +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - x atan(x ) - 1 +--R (3) ---------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1347 +t0:=1/(x^5*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 11 5 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1347 +r0:=(-1/4)/x^4-1/6*log(1+x^2)+1/12*log(1-x^2+x^4)+_ + 1/2*atan((1-2*x^2)/sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+ +--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ +--R 4 +-+ 4 2 4 +-+ 2 4 (2x - 1)\|3 +-+ +--R x \|3 log(x - x + 1) - 2x \|3 log(x + 1) - 6x atan(-------------) - 3\|3 +--R 3 +--R ---------------------------------------------------------------------------- +--R 4 +-+ +--R 12x \|3 +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1347 +t0:=1/(x^6*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 12 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1315 + +--S 1316 of 1347 +r0:=(-1/5)/x^5-1/3*atan(x)+1/6*atan(-2*x+sqrt(3))-_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 +--R - 15x log(x\|3 + x + 1) + 15x log(- x\|3 + x + 1) +--R + +--R 5 +-+ +-+ 5 +-+ +-+ 5 +-+ +--R - 10x \|3 atan(\|3 + 2x) + 10x \|3 atan(\|3 - 2x) - 20x \|3 atan(x) +--R + +--R +-+ +--R - 12\|3 +--R / +--R 5 +-+ +--R 60x \|3 +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R 5 \|3 +--R 5x cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 5 \|3 +--R 5x cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R 5 \|3 2 +--R - 10x sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R 5 \|3 2 5 2x +--R 10x sin(----------)atan(-------------------) + 5x atan(------) - 6 +--R 2 3 2 +--R atan(----) x - 1 +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R / +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) + 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R 3 2 3 2 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 \|3 2 +--R log(sin(----------) + cos(----------) - 2x cos(----------) + x ) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +--R - 4\|3 sin(----------)atan(-------------------) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) - x +--R 2 +--R + +--R 3 +--R atan(----) +--R 3 +-+ +--R atan(----) \|3 +--R +-+ sin(----------) +--R +-+ \|3 2 +-+ 2 +--R 4\|3 sin(----------)atan(-------------------) + 3log(x\|3 + x + 1) +--R 2 3 +--R atan(----) +--R +-+ +--R \|3 +--R cos(----------) + x +--R 2 +--R + +--R +-+ 2 +-+ +-+ +-+ +-+ +--R - 3log(- x\|3 + x + 1) + 2\|3 atan(\|3 + 2x) - 2\|3 atan(\|3 - 2x) +--R + +--R +-+ +-+ 2x +--R 4\|3 atan(x) + 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- 2x + x )sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 +--R ((- 4x + 2x )cos(----------) - 2x + 2x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 2 \|3 6 4 +--R (- 2x + x )cos(----------) + (2x - 2x )cos(----------) - x + 2x +--R 2 2 +--R / +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((6x - 6x + 6)cos(----------) + 6x - 6x + 6x )sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (- 6x + 6x - 6x )cos(----------) +--R 2 2 +--R + +--R 8 6 4 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1347 +t0:=1/(x^7*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 13 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1320 + +--S 1321 of 1347 +r0:=(-1/6)/x^6+1/3*atanh(1+2*x^6) +--R +--R +--R 6 6 +--R 2x atanh(2x + 1) - 1 +--R (2) --------------------- +--R 6 +--R 6x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1347 +a0:=integrate(t0,x) +--R +--R +--R 6 6 6 +--R x log(x + 1) - 6x log(x) - 1 +--R (3) ----------------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1347 +m0:=a0-r0 +--R +--R +--R 6 6 +--R log(x + 1) - 6log(x) - 2atanh(2x + 1) +--R (4) --------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1347 +t0:=1/(x^8*(1+x^6)) +--R +--R +--R 1 +--R (1) -------- +--R 14 8 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 1325 + +--S 1326 of 1347 +r0:=(-1/7)/x^7+1/x+1/3*atan(x)-1/6*atan(-2*x+sqrt(3))+_ + 1/6*atan(2*x+sqrt(3))+1/4*log(1+x^2-x*sqrt(3))/sqrt(3)-_ + 1/4*log(1+x^2+x*sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 +--R - 21x log(x\|3 + x + 1) + 21x log(- x\|3 + x + 1) +--R + +--R 7 +-+ +-+ 7 +-+ +-+ 7 +-+ +--R 14x \|3 atan(\|3 + 2x) - 14x \|3 atan(\|3 - 2x) + 28x \|3 atan(x) +--R + +--R 6 +-+ +--R (84x - 12)\|3 +--R / +--R 7 +-+ +--R 84x \|3 +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 3 +--R atan(----) +--R +-+ +--R 7 \|3 +--R 7x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 7 \|3 +--R 7x cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R 7 \|3 2 2 +--R - 14x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R 7 \|3 2 2 +--R 14x sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R 7 2x 6 +--R - 7x atan(------) + 42x - 6 +--R 2 +--R x - 1 +--R / +--R 7 +--R 42x +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1347 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) + x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R x cos(----------) + x +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 2 +--R * +--R log +--R 3 2 3 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R sin(----------) - x\|3 sin(----------) + cos(----------) +--R 2 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R \|3 2 +--R - x cos(----------) + x +--R 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R - 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) - 2x +--R 2 2 +--R + +--R 3 3 +--R atan(----) atan(----) +--R 3 +-+ +-+ +--R atan(----) \|3 +-+ \|3 +--R +-+ sin(----------) - \|3 cos(----------) +--R +-+ \|3 2 2 +--R 4\|3 sin(----------)atan(------------------------------------------) +--R 2 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R \|3 sin(----------) + cos(----------) + 2x +--R 2 2 +--R + +--R +-+ 2 +-+ 2 +-+ +-+ +--R 3log(x\|3 + x + 1) - 3log(- x\|3 + x + 1) - 2\|3 atan(\|3 + 2x) +--R + +--R +-+ +-+ +-+ +-+ 2x +--R 2\|3 atan(\|3 - 2x) - 4\|3 atan(x) - 2\|3 atan(------) +--R 2 +--R x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (- x - x )sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R ((- 4x - 4x )cos(----------) + 4x - 2x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 \|3 +--R (4x + 4x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 6 +--R (- 6x - 6x )cos(----------) + (4x - 2x )cos(----------) - 6x +--R 2 2 +--R + +--R 4 +--R 3x +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R ((8x + 8x )\|3 cos(----------) + (- 8x + 4x )\|3 cos(----------)) +--R 2 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 3 4 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- 4x - 4x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (- 16x - 12x - 2x )cos(----------) - x + 5x - 3x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 +-+ \|3 6 4 +-+ \|3 +--R (4x + 4x )\|3 cos(----------) + (8x - 4x )\|3 cos(----------) +--R 2 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (2x + 6x - 2x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 4 2 \|3 +--R (- x - x )cos(----------) + (- 4x + 2x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 \|3 10 8 6 \|3 10 +--R (- 6x + 3x )cos(----------) + (x - 5x + 3x )cos(----------) - 2x +--R 2 2 +--R + +--R 8 +--R x +--R / +--R 3 8 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (3x - 3x + 3)sin(----------) +--R 2 +--R + +--R 3 2 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R ((12x - 12x + 12)cos(----------) - 6x + 6x - 6x )sin(----------) +--R 2 2 +--R + +--R 3 3 5 +--R atan(----) atan(----) +--R +-+ +-+ +--R 6 4 2 +-+ \|3 \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------)sin(----------) +--R 2 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (18x - 18x + 18)cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 8 6 4 +--R (- 6x + 6x - 6x )cos(----------) + 9x - 9x + 9x +--R 2 +--R * +--R 3 4 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 24x + 24x - 24x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (12x - 12x + 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 6 +--R atan(----) +--R +-+ +--R 4 2 \|3 +--R (12x - 12x + 12)cos(----------) +--R 2 +--R + +--R 3 4 +--R atan(----) +--R +-+ +--R 6 4 2 \|3 +--R (6x - 6x + 6x )cos(----------) +--R 2 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 8 6 4 \|3 10 8 6 +--R (42x - 42x + 42x )cos(----------) - 6x + 6x - 6x +--R 2 +--R * +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 5 +--R atan(----) +--R +-+ +--R 6 4 2 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 3 +--R atan(----) +--R +-+ +--R 8 6 4 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R + +--R 3 +--R atan(----) +--R +-+ +--R 10 8 6 +-+ \|3 +--R (- 12x + 12x - 12x )\|3 cos(----------) +--R 2 +--R * +--R 3 +--R atan(----) +--R +-+ +--R \|3 +--R sin(----------) +--R 2 +--R + +--R 3 8 3 6 +--R atan(----) atan(----) +--R +-+ +-+ +--R 4 2 \|3 6 4 2 \|3 +--R (3x - 3x + 3)cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R 8 6 4 \|3 10 8 6 \|3 +--R (9x - 9x + 9x )cos(----------) + (6x - 6x + 6x )cos(----------) +--R 2 2 +--R + +--R 12 10 8 +--R 3x - 3x + 3x +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1347 +t0:=1/(2-3*x^6) +--R +--R +--R 1 +--R (1) - ------- +--R 6 +--R 3x - 2 +--R Type: Fraction(Polynomial(Integer)) +--E 1330 + +--S 1331 of 1347 +r0a:=1/2*atan(3*2^(1/6)*3^(1/3)*x/(2^(1/3)*3^(2/3)-3*x^2))/(2^(5/6)*_ + 3^(2/3))+1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))+_ + 1/6*atanh(2^(1/6)*3^(5/6)*x/(2^(1/3)*3^(2/3)+3*x^2))/_ + (2^(5/6)*3^(1/6)) +--R +--R +--R (2) +--R 6+-+6+-+5 6+-+ 6+-+3+-+ +--R 3+-+2 x\|2 \|3 3+-+2 x\|3 6+-+ 3x\|2 \|3 +--R \|3 atanh(---------------) + 2\|3 atanh(-----) + 3\|3 atan(---------------) +--R 3+-+3+-+2 2 6+-+ 3+-+3+-+2 2 +--R \|2 \|3 + 3x \|2 \|2 \|3 - 3x +--R ----------------------------------------------------------------------------- +--R 6+-+5 3+-+2 6+-+ +--R 6\|2 \|3 \|3 +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1347 +r0b:=-1/2*atan(1/3*(2^(1/6)*3^(5/6)-6*x)/_ + (2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+1/2*atan(1/3*_ + (2^(1/6)*3^(5/6)+6*x)/(2^(1/6)*3^(1/3)))/(2^(5/6)*3^(2/3))+_ + 1/3*atanh((3/2)^(1/6)*x)/(2^(5/6)*3^(1/6))-_ + 1/12*log(2^(1/3)-6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6))+_ + 1/12*log(2^(1/3)+6^(1/6)*x+3^(1/3)*x^2)/(2^(5/6)*3^(1/6)) +--R +--R +--R (3) +--R 3+-+2 6+-+ 2 3+-+ 3+-+ 3+-+2 6+-+ 2 3+-+ 3+-+ +--R \|3 log(x\|6 + x \|3 + \|2 ) - \|3 log(- x\|6 + x \|3 + \|2 ) +--R + +--R 6+-+ 3+-+2 6+-+5 6+-+5 3+-+2 +--R 3+-+2 x\|3 6+-+ \|3 \|3 + 3x \|2 \|3 +--R 4\|3 atanh(-----) + 6\|3 atan(--------------------------) +--R 6+-+ 9 +--R \|2 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+ \|3 \|3 - 3x \|2 \|3 +--R - 6\|3 atan(--------------------------) +--R 9 +--R / +--R 6+-+5 3+-+2 6+-+ +--R 12\|2 \|3 \|3 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R 2 6+--+2 6+--+ 2 6+--+2 6+--+ +--R log(x \|96 + 2x\|96 + 4) - log(x \|96 - 2x\|96 + 4) +--R + +--R +-+ +--R 6+--+ 6+--+ +-+ \|3 +--R 2log(x\|96 + 2) - 2log(x\|96 - 2) - 2\|3 atan(----------) +--R 6+--+ +--R x\|96 - 1 +--R + +--R +-+ +--R +-+ \|3 +--R - 2\|3 atan(----------) +--R 6+--+ +--R x\|96 + 1 +--R / +--R 6+--+ +--R 12\|96 +--R Type: Union(Expression(Integer),...) +--E 1333 + +--S 1334 of 1347 +m0a:=a0-r0a +--R +--R +--R (5) +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+ +--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2) +--R + +--R 6+-+6+-+5 6+-+ +--R 3+-+2 6+--+ x\|2 \|3 3+-+2 6+--+ x\|3 +--R - 2\|3 \|96 atanh(--------------- - 4\|3 \|96 atanh(-----) +--R 3+-+3+-+2 2 6+-+ +--R \|2 \|3 + 3x \|2 +--R + +--R 6+-+3+-+ +-+ +--R 6+-+6+--+ 3x\|2 \|3 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 6\|3 \|96 atan(---------------) - 2\|2 \|3 \|3 \|3 atan(----------) +--R 3+-+3+-+2 2 6+--+ +--R \|2 \|3 - 3x x\|96 - 1 +--R + +--R +-+ +--R 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 2\|2 \|3 \|3 \|3 atan(----------) +--R 6+--+ +--R x\|96 + 1 +--R / +--R 6+-+5 3+-+2 6+-+6+--+ +--R 12\|2 \|3 \|3 \|96 +--R Type: Expression(Integer) +--E 1334 + +--S 1335 of 1347 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2 +--R (- 12x \|2 \|2 + (27x + 54x )\|2 )\|3 +--R + +--R 10 6+-+4 10 4 3+-+2 3+-+ 2 3+-+6+-+4 14 +--R (18x \|2 + (27x + 18x )\|2 )\|3 + 12x \|2 \|2 + 27x +--R + +--R 8 2 +--R 108x - 12x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2 +--R ((- 63x - 30x )\|2 \|2 + (3x + 10x )\|2 )\|3 +--R + +--R 8 2 3+-+2 6+-+2 14 8 2 3+-+ +--R ((- 45x - 6x )\|2 \|2 - 27x - 48x - 4x )\|3 +--R + +--R 12 6 6+-+2 12 6 3+-+ +--R (- 135x - 144x + 12)\|2 + (27x + 42x - 16)\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+ +--R (15x + 2x )\|2 \|2 \|3 + (27x + 12x + 4)\|2 \|3 +--R + +--R 10 4 6+-+4 10 4 3+-+6+-+2 +--R (108x + 36x )\|2 + (- 63x - 30x )\|2 \|2 +--R / +--R 12 6 3+-+2 6+-+4 12 6 3+-+ 3+-+2 +--R ((36x - 24x )\|2 \|2 + (- 216x + 144x )\|2 )\|3 +--R + +--R 16 10 6+-+4 10 4 3+-+2 3+-+ +--R ((- 54x + 36x )\|2 + (- 108x + 72x )\|2 )\|3 +--R + +--R 8 2 3+-+6+-+4 14 8 +--R (- 36x + 24x )\|2 \|2 - 324x + 216x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 3+-+6+-+2 10 4 3+-+2 3+-+2 +--R ((216x - 144x )\|2 \|2 + (- 36x + 24x )\|2 )\|3 +--R + +--R 8 2 3+-+2 6+-+2 14 8 3+-+ +--R ((108x - 72x )\|2 \|2 + 216x - 144x )\|3 +--R + +--R 12 6 6+-+2 12 6 3+-+ +--R (648x - 432x )\|2 + (- 216x + 216x - 48)\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+2 3+-+2 12 6 6+-+2 3+-+ +--R (- 36x + 24x )\|2 \|2 \|3 + (- 108x + 72x )\|2 \|3 +--R + +--R 10 4 6+-+4 10 4 3+-+6+-+2 +--R (- 324x + 216x )\|2 + (216x - 144x )\|2 \|2 +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1347 +m0b:=a0-r0b +--R +--R +--R (7) +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R \|2 \|3 \|3 log(x \|96 + 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 2 6+--+2 6+--+ +--R - \|2 \|3 \|3 log(x \|96 - 2x\|96 + 4) +--R + +--R 6+-+5 3+-+2 6+-+ 6+--+ 6+-+5 3+-+2 6+-+ 6+--+ +--R 2\|2 \|3 \|3 log(x\|96 + - 2\|2 \|3 \|3 log(x\|96 - 2) +--R + +--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+ +--R - \|3 \|96 log(x\|6 + x \|3 + \|2 ) +--R + +--R 6+-+ +--R 3+-+2 6+--+ 6+-+ 2 3+-+ 3+-+ 3+-+2 6+--+ x\|3 +--R \|3 \|96 log(- x\|6 + x \|3 + \|2 - 4\|3 \|96 atanh(-----) +--R 6+-+ +--R \|2 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+6+--+ \|3 \|3 + 3x \|2 \|3 +--R - 6\|3 \|96 atan(--------------------------) +--R 9 +--R + +--R 3+-+2 6+-+5 6+-+5 3+-+2 +--R 6+-+6+--+ \|3 \|3 - 3x \|2 \|3 +--R 6\|3 \|96 atan(--------------------------) +--R 9 +--R + +--R +-+ +-+ +--R 6+-+5 +-+3+-+2 6+-+ \|3 6+-+5 +-+3+-+2 6+-+ \|3 +--R - 2\|2 \|3 \|3 \|3 atan(---------- - 2\|2 \|3 \|3 \|3 atan(----------) +--R 6+--+ 6+--+ +--R x\|96 - 1 x\|96 + 1 +--R / +--R 6+-+5 3+-+2 6+-+6+--+ +--R 12\|2 \|3 \|3 \|96 +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1347 +d0b:=D(m0b,x) +--R +--R +--R (8) +--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 8 +--R (- 144x - 192x )\|2 \|3 + (- 108x - 36x )\|2 \|3 - 564x +--R + +--R 2 +--R 16x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 6+-+4 3+-+2 8 3+-+ 12 6 6+-+2 6+-+2 +--R ((252x + 48x )\|2 \|3 + 324x \|3 + (288x + 672x )\|2 )\|3 +--R + +--R 8 2 3+-+2 10 4 6+-+4 +--R (144x + 48x )\|3 + (- 144x - 228x )\|2 +--R * +--R 6+-+2 +--R \|6 +--R + +--R 6 3+-+6+-+3+-+2 10 4 6+-+5 3+-+ +--R (- 12x + 8)\|2 \|2 \|3 + (- 27x + 18x )\|2 \|3 +--R + +--R 8 2 3+-+6+-+5 8 2 6+-+ +--R (27x - 18x )\|2 \|2 + (36x - 24x )\|2 +--R * +--R 6+-+5 +--R \|3 +--R + +--R 10 4 6+-+5 10 4 3+-+6+-+3 3+-+2 +--R ((- 27x + 18x )\|2 + (72x - 48x )\|2 \|2 )\|3 +--R + +--R 8 2 3+-+6+-+5 14 8 2 6+-+ 3+-+ +--R ((27x - 18x )\|2 \|2 + (- 144x + 102x - 4x )\|2 )\|3 +--R + +--R 12 6 6+-+3 12 6 3+-+6+-+ +--R (- 216x + 144x )\|2 + (144x - 102x + 4)\|2 \|2 +--R * +--R 6+-+3 +--R \|3 +--R + +--R 8 2 3+-+6+-+5 8 2 6+-+ 3+-+2 +--R ((- 54x + 36x )\|2 \|2 + (54x - 36x )\|2 )\|3 +--R + +--R 12 6 6+-+3 6 3+-+6+-+ 3+-+ +--R ((216x - 144x )\|2 + (- 54x + 36)\|2 \|2 )\|3 +--R + +--R 10 4 6+-+5 10 4 3+-+6+-+3 +--R (162x - 108x )\|2 + (- 216x + 144x )\|2 \|2 +--R * +--R 6+-+ +--R \|3 +--R * +--R 6+-+ +--R \|6 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (216x + 72x )\|2 \|2 + (144x + 192x )\|2 \|2 + 564x +--R + +--R 4 +--R - 16x +--R * +--R 3+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (108x + 36x )\|2 \|2 + (432x + 576x )\|2 +--R + +--R 8 2 3+-+ +--R (1128x - 32x )\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 6 3+-+2 +--R (324x + 108x )\|2 + (864x + 1152x )\|2 \|2 + (564x - 16)\|2 +--R * +--R 6+-+4 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 8 3+-+ +--R ((- 252x - 48x )\|2 \|2 + (- 288x - 672x )\|2 - 648x \|2) +--R * +--R 3+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (- 756x - 144x )\|2 + (- 576x - 1344x )\|2 \|2 +--R + +--R 6 3+-+2 +--R - 324x \|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (- 1512x - 288x )\|2 \|2 + (- 288x - 672x )\|2 \|2 - 972x +--R * +--R 6+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 6 3+-+2 3+-+2 +--R ((144x + 228x )\|2 + (- 144x - 48)\|2 )\|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+ +--R ((288x + 456x )\|2 \|2 - 432x - 144x )\|3 +--R + +--R 8 2 3+-+2 6+-+4 8 2 3+-+ +--R (144x + 228x )\|2 \|2 + (- 864x - 288x )\|2 +--R / +--R 12 6 6+-+2 3+-+2 10 4 6+-+4 3+-+ 14 +--R (864x - 576x )\|2 \|3 + (324x - 216x )\|2 \|3 + 1728x +--R + +--R 8 2 +--R - 1224x + 48x +--R * +--R 6+-+4 +--R \|3 +--R + +--R 10 4 6+-+4 3+-+2 8 2 3+-+ +--R (- 648x + 432x )\|2 \|3 + (- 648x + 432x )\|3 +--R + +--R 12 6 6+-+2 +--R (- 2592x + 1728x )\|2 +--R * +--R 6+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 10 4 6+-+4 +--R (- 432x + 288x )\|3 + (972x - 648x )\|2 +--R * +--R 6+-+2 +--R \|6 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 +--R (- 648x + 432x )\|2 \|2 + (- 864x + 576x )\|2 \|2 +--R + +--R 16 10 4 +--R - 1728x + 1224x - 48x +--R * +--R 3+-+2 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (- 324x + 216x )\|2 \|2 + (- 2592x + 1728x )\|2 +--R + +--R 14 8 2 3+-+ +--R (- 3456x + 2448x - 96x )\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (- 972x + 648x )\|2 + (- 5184x + 3456x )\|2 \|2 +--R + +--R 12 6 3+-+2 +--R (- 1728x + 1224x - 48)\|2 +--R * +--R 6+-+4 +--R \|3 +--R + +--R 8 2 3+-+2 6+-+4 14 8 6+-+2 +--R (648x - 432x )\|2 \|2 + (2592x - 1728x )\|2 +--R + +--R 8 2 3+-+ +--R (1296x - 864x )\|2 +--R * +--R 3+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 12 6 3+-+6+-+2 +--R (1944x - 1296x )\|2 + (5184x - 3456x )\|2 \|2 +--R + +--R 6 3+-+2 +--R (648x - 432)\|2 +--R * +--R 3+-+ +--R \|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+2 6+-+2 10 +--R (3888x - 2592x )\|2 \|2 + (2592x - 1728x )\|2 \|2 + 1944x +--R + +--R 4 +--R - 1296x +--R * +--R 6+-+2 +--R \|3 +--R + +--R 12 6 6+-+4 6 3+-+2 3+-+2 +--R ((- 972x + 648x )\|2 + (432x - 288)\|2 )\|3 +--R + +--R 10 4 3+-+6+-+4 10 4 3+-+ +--R ((- 1944x + 1296x )\|2 \|2 + 1296x - 864x )\|3 +--R + +--R 8 2 3+-+2 6+-+4 8 2 3+-+ +--R (- 972x + 648x )\|2 \|2 + (2592x - 1728x )\|2 +--R Type: Expression(Integer) +--E 1337 + +)clear all + +--S 1338 of 1347 +t0:=x^8*sqrt(-1+4*x^6) +--R +--R +--R +-------+ +--R 8 | 6 +--R (1) x \|4x - 1 +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1347 +r0:=-1/192*atanh(2*x^3/sqrt(-1+4*x^6))-1/96*x^3*sqrt(-1+4*x^6)+_ + 1/12*x^9*sqrt(-1+4*x^6) +--R +--R +--R 3 +-------+ +--R 2x 9 3 | 6 +--R - atanh(----------) + (16x - 2x )\|4x - 1 +--R +-------+ +--R | 6 +--R \|4x - 1 +--R (2) -------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1347 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 9 3 | 6 12 6 | 6 3 +--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x ) +--R + +--R +-------+ +--R 21 15 9 3 | 6 24 18 12 +--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x +--R + +--R 6 +--R - 16x +--R / +--R +-------+ +--R 9 3 | 6 12 6 +--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192 +--R Type: Union(Expression(Integer),...) +--E 1340 + +--S 1341 of 1347 +m0:=a0-r0 +--R +--R +--R +-------+ 3 +--R | 6 3 2x +--R log(\|4x - 1 - 2x ) + atanh(----------) +--R +-------+ +--R | 6 +--R \|4x - 1 +--R (4) ----------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1342 + +)clear all + +--S 1343 of 1347 +t0:=x^5*sqrt(a^6-x^6) +--R +--R +--R +---------+ +--R 5 | 6 6 +--R (1) x \|- x + a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1347 +r0:=-1/9*(a^6-x^6)^(3/2) +--R +--R +--R +---------+ +--R 6 6 | 6 6 +--R (x - a )\|- x + a +--R (2) --------------------- +--R 9 +--R Type: Expression(Integer) +--E 1344 + +--S 1345 of 1347 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 6 6 | 6 6 +--R (x - a )\|- x + a +--R (3) --------------------- +--R 9 +--R Type: Union(Expression(Integer),...) +--E 1345 + +--S 1346 of 1347 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1347 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1347 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4f.input.pamphlet b/src/input/rich4f.input.pamphlet new file mode 100644 index 0000000..e70485a --- /dev/null +++ b/src/input/rich4f.input.pamphlet @@ -0,0 +1,21558 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4f.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 311 matching answers. +\item 59 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4f.output +)spool rich4f.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1369 +t0:=x^2*sqrt(-2+x^6) +--R +--R +--R +------+ +--R 2 | 6 +--R (1) x \|x - 2 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1369 +r0:=-1/3*atanh(x^3/sqrt(-2+x^6))+1/6*x^3*sqrt(-2+x^6) +--R +--R +--R 3 +------+ +--R x 3 | 6 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 6 +--R \|x - 2 +--R (2) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 3 | 6 6 | 6 3 9 3 | 6 12 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 6 +--R - 2x +--R / +--R +------+ +--R 3 | 6 6 +--R 6x \|x - 2 - 6x + 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ 3 +--R | 6 3 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 6 +--R \|x - 2 +--R (4) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1369 +t0:=x^2/sqrt(1-x^6) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 6 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1369 +r0:=1/3*asin(x^3) +--R +--R +--R 3 +--R asin(x ) +--R (2) -------- +--R 3 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 6 +--R \|- x + 1 - 1 +--R 2atan(---------------) +--R 3 +--R x +--R (3) - ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1369 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 6 +--R \|- x + 1 - 1 3 +--R - 2atan(---------------) - asin(x ) +--R 3 +--R x +--R (4) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1369 +t0:=x^2/sqrt(1+x^6) +--R +--R +--R 2 +--R x +--R (1) --------- +--R +------+ +--R | 6 +--R \|x + 1 +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1369 +r0:=1/3*asinh(x^3) +--R +--R +--R 3 +--R asinh(x ) +--R (2) --------- +--R 3 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 6 3 +--R log(\|x + 1 - x ) +--R (3) - ------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 6 3 3 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1369 +t0:=1/(x*sqrt(1+x^6)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 6 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1369 +r0:=-1/3*atanh(sqrt(1+x^6)) +--R +--R +--R +------+ +--R | 6 +--R atanh(\|x + 1 ) +--R (2) - ---------------- +--R 3 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (3) ----------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 6 | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1369 +t0:=1/(x*sqrt(-25+x^6)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R | 6 +--R x\|x - 25 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1369 +r0:=1/15*atan(1/5*sqrt(-25+x^6)) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (2) ---------------- +--R 15 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (3) ---------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1369 +t0:=x^(1/3)/(1-x^6) +--R +--R +--R 3+-+ +--R \|x +--R (1) - ------ +--R 6 +--R x - 1 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1369 +r0:=-1/6*log(1-x^(2/3))+1/12*log(1+x^(2/3)+x^(4/3))-1/6*cos(2/9*%pi)*_ + log(1+x^(4/3)+2*x^(2/3)*cos(1/9*%pi))+1/6*cos(1/9*%pi)*log(1+_ + x^(4/3)-2*x^(2/3)*sin(1/18*%pi))-1/6*log(1+x^(4/3)-2*x^(2/3)*_ + cos(2/9*%pi))*sin(1/18*%pi)-1/2*atan((1+2*x^(2/3))/sqrt(3))/_ + sqrt(3)-1/3*atan((x^(2/3)+cos(1/9*%pi))/sqrt(1-cos(1/9*%pi)^2))*_ + cos(1/9*%pi)*(1-cos(2/9*%pi))/sqrt(1-cos(1/9*%pi)^2)+1/3*_ + atan((x^(2/3)-cos(2/9*%pi))/sqrt(1-cos(2/9*%pi)^2))*cos(2/9*%pi)*_ + (1-sin(1/18*%pi))/sqrt(1-cos(2/9*%pi)^2)+1/3*atan((x^(2/3)-_ + sin(1/18*%pi))/sqrt(1-sin(1/18*%pi)^2))*(1+cos(1/9*%pi))*_ + sin(1/18*%pi)/sqrt(1-sin(1/18*%pi)^2) +--R +--R +--R (2) +--R +----------------+ +---------------+ +--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2 +--R (4\|3 cos(---) + 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1 +--R 9 18 \| 9 \| 9 +--R * +--R 3+-+2 %pi +--R \|x - sin(---) +--R 18 +--R atan(------------------) +--R +---------------+ +--R | %pi 2 +--R |- sin(---) + 1 +--R \| 18 +--R + +--R +---------------+ +--R +-+ 2%pi %pi +-+ 2%pi | %pi 2 +--R (- 4\|3 cos(----)sin(---) + 4\|3 cos(----)) |- sin(---) + 1 +--R 9 18 9 \| 18 +--R * +--R 3+-+2 2%pi +--R +---------------+ \|x - cos(----) +--R | %pi 2 9 +--R |- cos(---) + 1 atan(-------------------) +--R \| 9 +----------------+ +--R | 2%pi 2 +--R |- cos(----) + 1 +--R \| 9 +--R + +--R +---------------+ +--R +-+ %pi 2%pi +-+ %pi | %pi 2 +--R (4\|3 cos(---)cos(----) - 4\|3 cos(---)) |- sin(---) + 1 +--R 9 9 9 \| 18 +--R * +--R 3+-+2 %pi +--R +----------------+ \|x + cos(---) +--R | 2%pi 2 9 +--R |- cos(----) + 1 atan(------------------) +--R \| 9 +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +--R - 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) +--R 9 9 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(- \|x + 1) +--R + +--R +-+ %pi 2%pi 3+-+2 3+-+ +--R - 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R 3+-+2 +--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1 +--R 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) - 6atan(----------) +--R 9 18 +-+ +--R \|3 +--R * +--R +---------------+ +----------------+ +---------------+ +--R | %pi 2 | 2%pi 2 | %pi 2 +--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R / +--R +---------------+ +----------------+ +---------------+ +--R +-+ | %pi 2 | 2%pi 2 | %pi 2 +--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 +-+ \|3 +--R (- 3sin(----------) - \|3 cos(----------)) +--R 3 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 2\|3 cos(----------) +--R 3 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) + 6cos(----------)) +--R 3 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +--R +-+ \|3 +--R 4\|3 sin(----------) +--R 3 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R +-+ \|3 \|3 +--R (- 2\|3 sin(----------) - 6cos(----------)) +--R 3 3 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +-+ 3+-+2 3+-+ +-+ 3+-+2 +--R \|3 log(\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R / +--R +-+ +--R 12\|3 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R \|3 +-+ \|3 | %pi 2 +--R (3sin(----------) - \|3 cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) + 2\|x )sin(----------) +--R 3 3 3 +--R + +--R 3 4 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 3+-+2 \|3 3+-+ +--R cos(----------) - 2\|x cos(----------) + x\|x +--R 3 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R \|3 +-+ \|3 | %pi 2 +--R (- 3sin(----------) - \|3 cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 +--R atan(----) +--R +-+ +---------------+ +----------------+ +--R +-+ \|3 | %pi 2 | 2%pi 2 +--R 2\|3 cos(----------) |- sin(---) + 1 |- cos(----) + 1 +--R 3 \| 18 \| 9 +--R * +--R +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R * +--R log +--R 3 4 3 2 3 2 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 \|3 3+-+2 \|3 +--R sin(----------) + (2cos(----------) - \|x )sin(----------) +--R 3 3 3 +--R + +--R 3 3 3 4 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+3+-+2 \|3 \|3 \|3 +--R - 2\|3 \|x cos(----------)sin(----------) + cos(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R 3+-+2 \|3 3+-+ +--R \|x cos(----------) + x\|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R +-+ \|3 \|3 | %pi 2 +--R (- 2\|3 sin(----------) + 6cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) + 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) - 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R - +--R 3 +--R atan(----) +--R +-+ +---------------+ +----------------+ +--R +-+ \|3 | %pi 2 | 2%pi 2 +--R 4\|3 sin(----------) |- sin(---) + 1 |- cos(----) + 1 +--R 3 \| 18 \| 9 +--R * +--R +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R * +--R atan +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R \|3 +-+ \|3 \|3 +--R 3sin(----------) - 2\|3 cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R \|3 +--R - 3cos(----------) +--R 3 +--R / +--R 3 2 3 3 +--R atan(----) atan(----) atan(----) +--R +-+ +-+ +-+ +--R +-+ \|3 \|3 \|3 +--R \|3 sin(----------) + 6cos(----------)sin(----------) +--R 3 3 3 +--R + +--R 3 2 +--R atan(----) +--R +-+ +--R +-+ \|3 +-+3+-+2 +--R - \|3 cos(----------) - 2\|3 \|x +--R 3 +--R + +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +---------------+ +--R +-+ \|3 \|3 | %pi 2 +--R (- 2\|3 sin(----------) - 6cos(----------)) |- sin(---) + 1 +--R 3 3 \| 18 +--R * +--R +----------------+ +---------------+ +--R | 2%pi 2 | %pi 2 +--R |- cos(----) + 1 |- cos(---) + 1 +--R \| 9 \| 9 +--R * +--R 3 3 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 +--R 2cos(----------)sin(----------) +--R 3 3 +--R atan(-------------------------------------------) +--R 3 2 3 2 +--R atan(----) atan(----) +--R +-+ +-+ +--R \|3 \|3 3+-+2 +--R sin(----------) - cos(----------) + \|x +--R 3 3 +--R + +--R +----------------+ +---------------+ +--R +-+ %pi +-+ %pi | 2%pi 2 | %pi 2 +--R (- 4\|3 cos(---) - 4\|3 )sin(---) |- cos(----) + 1 |- cos(---) + 1 +--R 9 18 \| 9 \| 9 +--R * +--R 3+-+2 %pi +--R \|x - sin(---) +--R 18 +--R atan(------------------) +--R +---------------+ +--R | %pi 2 +--R |- sin(---) + 1 +--R \| 18 +--R + +--R +---------------+ +--R +-+ 2%pi %pi +-+ 2%pi | %pi 2 +--R (4\|3 cos(----)sin(---) - 4\|3 cos(----)) |- sin(---) + 1 +--R 9 18 9 \| 18 +--R * +--R 3+-+2 2%pi +--R +---------------+ \|x - cos(----) +--R | %pi 2 9 +--R |- cos(---) + 1 atan(-------------------) +--R \| 9 +----------------+ +--R | 2%pi 2 +--R |- cos(----) + 1 +--R \| 9 +--R + +--R +---------------+ +--R +-+ %pi 2%pi +-+ %pi | %pi 2 +--R (- 4\|3 cos(---)cos(----) + 4\|3 cos(---)) |- sin(---) + 1 +--R 9 9 9 \| 18 +--R * +--R 3+-+2 %pi +--R +----------------+ \|x + cos(---) +--R | 2%pi 2 9 +--R |- cos(----) + 1 atan(------------------) +--R \| 9 +---------------+ +--R | %pi 2 +--R |- cos(---) + 1 +--R \| 9 +--R + +--R +-+ 2%pi %pi 3+-+2 3+-+ +-+ 3+-+2 +--R 2\|3 cos(----)log(2cos(---)\|x + x\|x + 1) - 2\|3 log(\|x - 1) +--R 9 9 +--R + +--R +-+ 3+-+2 +--R 2\|3 log(- \|x + 1) +--R + +--R +-+ %pi 2%pi 3+-+2 3+-+ +--R 2\|3 sin(---)log(- 2cos(----)\|x + x\|x + 1) +--R 18 9 +--R + +--R 3+-+2 +--R +-+ %pi %pi 3+-+2 3+-+ 2\|x + 1 +--R - 2\|3 cos(---)log(- 2sin(---)\|x + x\|x + 1) + 6atan(----------) +--R 9 18 +-+ +--R \|3 +--R + +--R +-+3+-+2 +-+ +--R 2\|3 \|x + \|3 +--R 3atan(-------------------) +--R 3+-+2 3+-+ +--R 2\|x + 2x\|x - 1 +--R * +--R +---------------+ +----------------+ +---------------+ +--R | %pi 2 | 2%pi 2 | %pi 2 +--R |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R / +--R +---------------+ +----------------+ +---------------+ +--R +-+ | %pi 2 | 2%pi 2 | %pi 2 +--R 12\|3 |- sin(---) + 1 |- cos(----) + 1 |- cos(---) + 1 +--R \| 18 \| 9 \| 9 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1369 Value stack overflow +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1369 +t0:=x^8*(a+b*x^7) +--R +--R +--R 15 8 +--R (1) b x + a x +--R Type: Polynomial(Integer) +--E 31 + +--S 32 of 1369 +r0:=1/9*a*x^9+1/16*b*x^16 +--R +--R +--R 1 16 1 9 +--R (2) -- b x + - a x +--R 16 9 +--R Type: Polynomial(Fraction(Integer)) +--E 32 + +--S 33 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 16 1 9 +--R (3) -- b x + - a x +--R 16 9 +--R Type: Polynomial(Fraction(Integer)) +--E 33 + +--S 34 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 34 + +--S 35 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Polynomial(Fraction(Integer)) +--E 35 + +)clear all + +--S 36 of 1369 +t0:=x^9/(a+b*x^8) +--R +--R +--R 9 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 36 + +--S 37 of 1369 +r0:=1/2*x^2/b+1/4*a^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_ + sqrt(2))-1/4*a^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(b^(5/4)*_ + sqrt(2))+1/8*a^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+_ + x^4*sqrt(b))/(b^(5/4)*sqrt(2))-1/8*a^(1/4)*log(a^(1/4)*b^(1/4)*_ + x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(b^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|a log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a +--R \|a log(- x \|2 \|a \|b + x \|b + \|a ) - 2\|a atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b - \|a 2 +-+4+-+ +--R - 2\|a atan(-----------------) + 4x \|2 \|b +--R 4+-+ +--R \|a +--R / +--R +-+4+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | a | a 2 +--R - 2b |- ------ log(8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--R | a +--R 8b |- ------ +--R +--------+ +--------+ +--------+ 4| 5 +--R | a | a 2 | a \| 4096b +--R 2b |- ------ log(- 8b |- ------ + x + 4b |- ------ atan(-------------) +--R 4| 5 4| 5 4| 5 2 +--R \| 4096b \| 4096b \| 4096b x +--R + +--R 2 +--R x +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R \|a log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+ +--R +-+ | a 4+-+ | a 2 +--R - 8b\|2 |- ------ \|b log(8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R +--------+ +--------+ +--R +-+ | a 4+-+ | a 2 +--R 8b\|2 |- ------ \|b log(- 8b |- ------ + x ) +--R 4| 5 4| 5 +--R \| 4096b \| 4096b +--R + +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|a log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b + \|a 4+-+ x \|2 \|b - \|a +--R 2\|a atan(-----------------) + 2\|a atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R | a +--R 8b |- ------ +--R +--------+ 4| 5 +--R +-+ | a 4+-+ \| 4096b +--R 16b\|2 |- ------ \|b atan(-------------) +--R 4| 5 2 +--R \| 4096b x +--R / +--R +-+4+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1369 +t0:=x^7/(a+b*x^8) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 41 + +--S 42 of 1369 +r0:=1/8*log(a+b*x^8)/b +--R +--R +--R 8 +--R log(b x + a) +--R (2) ------------- +--R 8b +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(b x + a) +--R (3) ------------- +--R 8b +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1369 +t0:=x^5/(a+b*x^8) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 46 + +--S 47 of 1369 +r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(1/4)*b^(3/4)*sqrt(2))+_ + 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_ + (a^(1/4)*b^(3/4)*sqrt(2))-1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(1/4)*b^(3/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R 2atan(-----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+4+-+3 +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+3 +--R | 1 2 | 1 2 +--R |- -------- log(512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R | 1 2 | 1 2 +--R - |- -------- log(- 512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+3 +--R 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 3 +--R | 1 \| 4096a b +--R 2 |- -------- atan(---------------------) +--R 4| 3 2 +--R \| 4096a b x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 2 +--R 8\|2 |- -------- \|a \|b log(512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +----------+ +----------+3 +--R +-+ | 1 4+-+4+-+3 2 | 1 2 +--R - 8\|2 |- -------- \|a \|b log(- 512a b |- -------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R - log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +----------+3 +--R 2 | 1 +--R 512a b |- -------- +--R +----------+ 4| 3 +--R +-+ | 1 4+-+4+-+3 \| 4096a b +--R 16\|2 |- -------- \|a \|b atan(---------------------) +--R 4| 3 2 +--R \| 4096a b x +--R / +--R +-+4+-+4+-+3 +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1369 +t0:=x^3/(a+b*x^8) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 51 + +--S 52 of 1369 +r0:=1/4*atan(x^4*sqrt(b)/sqrt(a))/(sqrt(a)*sqrt(b)) +--R +--R +--R 4 +-+ +--R x \|b +--R atan(------) +--R +-+ +--R \|a +--R (2) ------------ +--R +-+ +-+ +--R 4\|a \|b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +-----+ 4 +--R (b x - a)\|- a b + 2a b x 4 +---+ +--R log(----------------------------) x \|a b +--R 8 atan(--------) +--R b x + a a +--R (3) [---------------------------------,--------------] +--R +-----+ +---+ +--R 8\|- a b 4\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 53 + +--S 54 of 1369 +m0a:=a0.1-r0 +--R +--R +--R 8 +-----+ 4 4 +-+ +--R +-+ +-+ (b x - a)\|- a b + 2a b x +-----+ x \|b +--R \|a \|b log(----------------------------) - 2\|- a b atan(------) +--R 8 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8\|- a b \|a \|b +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1369 +m0b:=a0.2-r0 +--R +--R +--R 4 +---+ 4 +-+ +--R +-+ +-+ x \|a b +---+ x \|b +--R \|a \|b atan(--------) - \|a b atan(------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------- +--R +-+ +-+ +---+ +--R 4\|a \|b \|a b +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 57 + +)clear all + +--S 58 of 1369 +t0:=x/(a+b*x^8) +--R +--R +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 58 + +--S 59 of 1369 +r0:=-1/4*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))+_ + 1/4*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/(a^(3/4)*b^(1/4)*sqrt(2))-_ + 1/8*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/_ + (a^(3/4)*b^(1/4)*sqrt(2))+1/8*log(a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(3/4)*b^(1/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R - log(- x \|2 \|a \|b + x \|b + \|a ) + 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R 2atan(-----------------) +--R 4+-+ +--R \|a +--R / +--R +-+4+-+3 4+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+ +--R | 1 | 1 2 +--R |- ------- log(8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +--R | 1 +--R 8a |- ------- +--R +---------+ +---------+ +---------+ 4| 3 +--R | 1 | 1 2 | 1 \| 4096a b +--R - |- ------- log(- 8a |- ------- + x ) - 2 |- ------- atan(--------------) +--R 4| 3 4| 3 4| 3 2 +--R \| 4096a b \| 4096a b \| 4096a b x +--R Type: Union(Expression(Integer),...) +--E 60 + +--S 61 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ | 1 2 +--R 8\|2 |- ------- \|a \|b log(8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R +---------+ +---------+ +--R +-+ | 1 4+-+3 4+-+ | 1 2 +--R - 8\|2 |- ------- \|a \|b log(- 8a |- ------- + x ) +--R 4| 3 4| 3 +--R \| 4096a b \| 4096a b +--R + +--R 2 +-+4+-+ 4+-+ +--R 2 +-+4+-+4+-+ 4 +-+ +-+ x \|2 \|b + \|a +--R log(- x \|2 \|a \|b + x \|b + \|a ) - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R x \|2 \|b - \|a +--R - 2atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +---------+ +--R | 1 +--R 8a |- ------- +--R +---------+ 4| 3 +--R +-+ | 1 4+-+3 4+-+ \| 4096a b +--R - 16\|2 |- ------- \|a \|b atan(--------------) +--R 4| 3 2 +--R \| 4096a b x +--R / +--R +-+4+-+3 4+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 62 + +)clear all + +--S 63 of 1369 +t0:=1/(x*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ---------- +--R 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 63 + +--S 64 of 1369 +r0:=log(x)/a-1/8*log(a+b*x^8)/a +--R +--R +--R 8 +--R - log(b x + a) + 8log(x) +--R (2) ------------------------- +--R 8a +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(b x + a) + 8log(x) +--R (3) ------------------------- +--R 8a +--R Type: Union(Expression(Integer),...) +--E 65 + +--S 66 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 67 + +)clear all + +--S 68 of 1369 +t0:=1/(x^3*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 11 3 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 68 + +--S 69 of 1369 +r0:=(-1/2)/(a*x^2)+1/4*b^(1/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(5/4)*sqrt(2))-1/4*b^(1/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(5/4)*sqrt(2))-1/8*b^(1/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2))+1/8*b^(1/4)*log(a^(1/4)*_ + b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R x \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - x \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 2 4+-+ x \|2 \|b + \|a 2 4+-+ x \|2 \|b - \|a +--R - 2x \|b atan(----------------- - 2x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R 2 +-+4+-+ +--R 8a x \|2 \|a +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+3 +--R 2 | b 4 | b 2 +--R - 2a x |- ------ log(512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R 2 | b 4 | b 2 +--R 2a x |- ------ log(- 512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+3 +--R 4 | b +--R 512a |- ------ +--R +--------+ 4| 5 +--R 2 | b \| 4096a +--R - 4a x |- ------ atan(----------------- - 1 +--R 4| 5 2 +--R \| 4096a b x +--R / +--R 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 70 + +--S 71 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+3 +--R +-+ | b 4+-+ 4 | b 2 +--R - 8a\|2 |- ------ \|a log(512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+3 +--R +-+ | b 4+-+ 4 | b 2 +--R 8a\|2 |- ------ \|a log(- 512a |- ------ + b x ) +--R 4| 5 4| 5 +--R \| 4096a \| 4096a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ 2 +-+4+-+4+-+ 4 +-+ +-+ 4+-+ x \|2 \|b + \|a +--R \|b log(- x \|2 \|a \|b + x \|b + \|a ) + 2\|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R 2 +-+4+-+ 4+-+ +--R 4+-+ x \|2 \|b - \|a +--R 2\|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R +--------+3 +--R 4 | b +--R 512a |- ------ +--R +--------+ 4| 5 +--R +-+ | b 4+-+ \| 4096a +--R - 16a\|2 |- ------ \|a atan(-----------------) +--R 4| 5 2 +--R \| 4096a b x +--R / +--R +-+4+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 72 + +)clear all + +--S 73 of 1369 +t0:=1/(x^5*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 13 5 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 73 + +--S 74 of 1369 +r0:=(-1/4)/(a*x^4)-1/4*atan(x^4*sqrt(b)/sqrt(a))*sqrt(b)/a^(3/2) +--R +--R +--R 4 +-+ +--R 4 +-+ x \|b +-+ +--R - x \|b atan(------) - \|a +--R +-+ +--R \|a +--R (2) --------------------------- +--R 4 +-+ +--R 4a x \|a +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---+ +-+ +--R 4 | b 8 |b +--R +---+ - 2a x |- - + b x - a +-+ a |- +--R 4 | b \| a 4 |b \|a +--R x |- - log(------------------------) - 2 x |- atan(-----) - 1 +--R \| a 8 \|a 4 +--R b x + a b x +--R (3) [-----------------------------------------,---------------------] +--R 4 4 +--R 8a x 4a x +--R Type: Union(List(Expression(Integer)),...) +--E 75 + +--S 76 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R 4 | b 8 +--R +---+ - 2a x |- - + b x - a 4 +-+ +--R | b +-+ \| a +-+ x \|b +--R |- - \|a log(------------------------) + 2\|b atan(------) +--R \| a 8 +-+ +--R b x + a \|a +--R (4) ----------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R 4 +-+ +-+ a |- +--R +-+ x \|b +-+ |b \|a +--R \|b atan(------) + \|a |- atan(-----) +--R +-+ \|a 4 +--R \|a b x +--R (6) -------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 78 + +--S 79 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 79 + +)clear all + +--S 80 of 1369 +t0:=1/(x^7*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 15 7 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 80 + +--S 81 of 1369 +r0:=(-1/6)/(a*x^6)+1/4*b^(3/4)*atan(1-b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(7/4)*sqrt(2))-1/4*b^(3/4)*atan(1+b^(1/4)*x^2*sqrt(2)/a^(1/4))/_ + (a^(7/4)*sqrt(2))+1/8*b^(3/4)*log(-a^(1/4)*b^(1/4)*x^2*sqrt(2)+_ + sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2))-1/8*b^(3/4)*log(a^(1/4)*_ + b^(1/4)*x^2*sqrt(2)+sqrt(a)+x^4*sqrt(b))/(a^(7/4)*sqrt(2)) +--R +--R +--R (2) +--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - 3x \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 6 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R 3x \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 6 4+-+3 x \|2 \|b + \|a 6 4+-+3 x \|2 \|b - \|a +--R - 6x \|b atan(----------------- - 6x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 6 +-+4+-+3 +--R 24a x \|2 \|a +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | 3 | 3 +--R 6 | b 2 | b 2 +--R - 6a x |- ------ log(8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 6 | b 2 | b 2 +--R 6a x |- ------ log(- 8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--R | 3 +--R 2 | b +--R +--------+ 8a |- ------ +--R | 3 4| 7 +--R 6 | b \| 4096a +--R 12a x |- ------ atan(-------------- - 1 +--R 4| 7 2 +--R \| 4096a b x +--R / +--R 6 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 82 + +--S 83 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R \|b log(x \|2 \|a \|b + x \|b + \|a ) +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 2 | b 2 +--R - 8a\|2 |- ------ \|a log(8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R +-+ | b 4+-+3 2 | b 2 +--R 8a\|2 |- ------ \|a log(- 8a |- ------ + b x ) +--R 4| 7 4| 7 +--R \| 4096a \| 4096a +--R + +--R 4+-+3 2 +-+4+-+4+-+ 4 +-+ +-+ +--R - \|b log(- x \|2 \|a \|b + x \|b + \|a ) +--R + +--R 2 +-+4+-+ 4+-+ 2 +-+4+-+ 4+-+ +--R 4+-+3 x \|2 \|b + \|a 4+-+3 x \|2 \|b - \|a +--R 2\|b atan(-----------------) + 2\|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R 2 | b +--R +--------+ 8a |- ------ +--R | 3 4| 7 +--R +-+ | b 4+-+3 \| 4096a +--R 16a\|2 |- ------ \|a atan(--------------) +--R 4| 7 2 +--R \| 4096a b x +--R / +--R +-+4+-+3 +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 83 + +--S 84 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 84 + +)clear all + +--S 85 of 1369 +t0:=1/(x^9*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 17 9 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 85 + +--S 86 of 1369 +r0:=(-1/8)/(a*x^8)-b*log(x)/a^2+1/8*b*log(a+b*x^8)/a^2 +--R +--R +--R 8 8 8 +--R b x log(b x + a) - 8b x log(x) - a +--R (2) ----------------------------------- +--R 2 8 +--R 8a x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R b x log(b x + a) - 8b x log(x) - a +--R (3) ----------------------------------- +--R 2 8 +--R 8a x +--R Type: Union(Expression(Integer),...) +--E 87 + +--S 88 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 88 + +--S 89 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 89 + +)clear all + +--S 90 of 1369 +t0:=x^8/(a+b*x^8) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 90 + +--S 91 of 1369 +r0:=x/b-1/4*(-a)^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/b^(9/8)-1/4*(-a)^(1/8)*_ + atanh(b^(1/8)*x/(-a)^(1/8))/b^(9/8)+1/4*(-a)^(1/8)*atan(1-b^(1/8)*_ + x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))-1/4*(-a)^(1/8)*_ + atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/(b^(9/8)*sqrt(2))+1/8*_ + (-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/(b^(9/8)*sqrt(2))-1/8*(-a)^(1/8)*log((-a)^(1/4)+b^(1/4)*_ + x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/(b^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- a log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|b +--R \|- a log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|- a atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+---+ x\|2 \|b + \|- a 8+---+ x\|2 \|b - \|- a +--R - 2\|- a atan(------------------) - 2\|- a atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+---+ x\|b +-+8+-+ +--R - 2\|2 \|- a atan(------) + 8x\|2 \|b +--R 8+---+ +--R \|- a +--R / +--R +-+8+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | a +--R b |- ---------- +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- + 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+2 +------------+ +--R | a 2 | a +-+ | a 2 +--R b |- ---------- log(64b |- ---------- - 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 8| 9 +--R \| 16777216b \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a | a +--R - b\|2 |- ---------- log(8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a | a +--R b\|2 |- ---------- log(- 8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R +-+ | a \| 16777216b +--R 2b\|2 |- ---------- atan(-----------------) +--R 8| 9 x +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a \| 16777216b +--R - 2b |- ---------- atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a \| 16777216b +-+ +--R 2b |- ---------- atan(------------------------- + x\|2 +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216b +--R / +--R +-+ +--R b\|2 +--R Type: Union(Expression(Integer),...) +--E 92 + +--S 93 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|- a log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +------------+ +--R | a 8+-+ +--R 8b |- ---------- \|b +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- + 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +--R | a 8+-+ +--R 8b |- ---------- \|b +--R 8| 9 +--R \| 16777216b +--R * +--R +------------+2 +------------+ +--R 2 | a +-+ | a 2 +--R log(64b |- ---------- - 8b x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a 8+-+ | a +--R - 8b\|2 |- ---------- \|b log(8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R +------------+ +------------+ +--R +-+ | a 8+-+ | a +--R 8b\|2 |- ---------- \|b log(- 8b |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216b \| 16777216b +--R + +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- a log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R +-+8+---+ x\|b 8+---+ x\|2 \|b + \|- a +--R 2\|2 \|- a atanh(------) + 2\|- a atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 8+---+ x\|2 \|b - \|- a +-+8+---+ x\|b +--R 2\|- a atan(------------------) + 2\|2 \|- a atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R +-+ | a 8+-+ \| 16777216b +--R 16b\|2 |- ---------- \|b atan(-----------------) +--R 8| 9 x +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a 8+-+ \| 16777216b +--R - 16b |- ---------- \|b atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216b +--R + +--R +------------+ +--R | a +--R 8b |- ---------- +--R +------------+ 8| 9 +--R | a 8+-+ \| 16777216b +--R 16b |- ---------- \|b atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216b | a +-+ +--R 8b |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216b +--R / +--R +-+8+-+ +--R 8b\|2 \|b +--R Type: Expression(Integer) +--E 93 + +--S 94 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 94 + +)clear all + +--S 95 of 1369 +t0:=x^6/(a+b*x^8) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 95 + +--S 96 of 1369 +r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(1/8)*b^(7/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(1/8)*b^(7/8)*sqrt(2))+1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(1/8)*b^(7/8)*_ + sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(1/8)*b^(7/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+8+-+7 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--------------+6 +--R 6 +-+ | 1 5 | 1 +--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------ +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+7 +--R +-+ | 1 6 | 1 +--R \|2 |- ------------ log(2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+7 +--R +-+ | 1 6 | 1 +--R - \|2 |- ------------ log(- 2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--R 6 +-+ | 1 +--R - 2097152a b x\|2 |- ------------ +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+6 +--R 5 | 1 2 +--R - 262144a b |- ------------ + x +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R +-+ | 1 \| 16777216a b +--R 2\|2 |- ------------ atan(-----------------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 97 + +--S 98 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 8\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--------------+6 +--R 6 +-+ | 1 5 | 1 +--R 2097152a b x\|2 |- ------------ - 262144a b |- ------------ +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+7 +--R +-+8+---+ | 1 8+-+7 6 | 1 +--R 8\|2 \|- a |- ------------ \|b log(2097152a b |- ------------ + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R +-+8+---+ | 1 8+-+7 +--R 8\|2 \|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +--------------+7 +--R 6 | 1 +--R log(- 2097152a b |- ------------ + x) +--R 8| 7 +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 8\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R log +--R +--------------+7 +--R 6 +-+ | 1 +--R - 2097152a b x\|2 |- ------------ +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+6 +--R 5 | 1 2 +--R - 262144a b |- ------------ + x +--R 8| 7 +--R \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +--R - 2atan(------------------) - 2atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+ x\|b +--R - 2\|2 atan(------) +--R 8+---+ +--R \|- a +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R +-+8+---+ | 1 8+-+7 \| 16777216a b +--R 16\|2 \|- a |- ------------ \|b atan(-----------------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+ | 1 8+-+7 +--R 16\|- a |- ------------ \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R 8| 7 +--R \| 16777216a b +--R atan(-------------------------------------) +--R +--------------+7 +--R 6 | 1 +-+ +--R 2097152a b |- ------------ - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +--------------+7 +--R 6 | 1 +--R 2097152a b |- ------------ +--R +--------------+ 8| 7 +--R 8+---+ | 1 8+-+7 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(-------------------------------------) +--R 8| 7 +--------------+7 +--R \| 16777216a b 6 | 1 +-+ +--R 2097152a b |- ------------ + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+8+---+8+-+7 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 98 + +--S 99 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 99 + +)clear all + +--S 100 of 1369 +t0:=x^4/(a+b*x^8) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 100 + +--S 101 of 1369 +r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(3/8)*b^(5/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(3/8)*b^(5/8)*sqrt(2))-1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(3/8)*b^(5/8)*_ + sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/((-a)^(3/8)*b^(5/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+3 8+-+5 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 3 5 +--R \| 16777216a b +--R * +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 2 +--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x ) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+ | 1 2 3 | 1 +--R - \|2 |- ------------ log(32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+ | 1 2 3 | 1 +--R \|2 |- ------------ log(- 32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 3 5 +--R \| 16777216a b +--R * +--R log +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 +--R - 32768a b x\|2 |- ------------ - 64a b |- ------------ +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R +-+ | 1 \| 16777216a b +--R 2\|2 |- ------------ atan(---------------------------) +--R 8| 3 5 x +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ - x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ + x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 102 + +--S 103 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+3 | 1 8+-+5 +--R 8\|- a |- ------------ \|b +--R 8| 3 5 +--R \| 16777216a b +--R * +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 2 +--R log(32768a b x\|2 |- ------------ - 64a b |- ------------ + x ) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+8+---+3 | 1 8+-+5 2 3 | 1 +--R - 8\|2 \|- a |- ------------ \|b log(32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+5 +--R +-+8+---+3 | 1 8+-+5 2 3 | 1 +--R 8\|2 \|- a |- ------------ \|b log(- 32768a b |- ------------ + x) +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+3 | 1 8+-+5 +--R 8\|- a |- ------------ \|b +--R 8| 3 5 +--R \| 16777216a b +--R * +--R log +--R +--------------+5 +--------------+2 +--R 2 3 +-+ | 1 | 1 +--R - 32768a b x\|2 |- ------------ - 64a b |- ------------ +--R 8| 3 5 8| 3 5 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +--R - 2atan(------------------) - 2atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+ x\|b +--R 2\|2 atan(------) +--R 8+---+ +--R \|- a +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R +-+8+---+3 | 1 8+-+5 \| 16777216a b +--R 16\|2 \|- a |- ------------ \|b atan(---------------------------) +--R 8| 3 5 x +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ - x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R + +--R +--------------+5 +--R 2 3 | 1 +--R 32768a b |- ------------ +--R +--------------+ 8| 3 5 +--R 8+---+3 | 1 8+-+5 \| 16777216a b +--R - 16\|- a |- ------------ \|b atan(-----------------------------------) +--R 8| 3 5 +--------------+5 +--R \| 16777216a b 2 3 | 1 +-+ +--R 32768a b |- ------------ + x\|2 +--R 8| 3 5 +--R \| 16777216a b +--R / +--R +-+8+---+3 8+-+5 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 103 + +--S 104 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 104 + +)clear all + +--S 105 of 1369 +t0:=x^2/(a+b*x^8) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 105 + +--S 106 of 1369 +r0:=1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(5/8)*b^(3/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(5/8)*b^(3/8)*sqrt(2))-_ + 1/8*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_ + ((-a)^(5/8)*b^(3/8)*sqrt(2))+1/8*log((-a)^(1/4)+b^(1/4)*x^2+_ + (-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(5/8)*b^(3/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R - 2atan(------------------) - 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+5 8+-+3 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 5 3 +--R \| 16777216a b +--R * +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 2 +--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x ) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R | 1 +--R |- ------------ +--R 8| 5 3 +--R \| 16777216a b +--R * +--R log +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 +--R 262144a b |- ------------ - 512a b x\|2 |- ------------ +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+3 +--R +-+ | 1 2 | 1 +--R - \|2 |- ------------ log(512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+3 +--R +-+ | 1 2 | 1 +--R \|2 |- ------------ log(- 512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R +-+ | 1 \| 16777216a b +--R - 2\|2 |- ------------ atan(-------------------------) +--R 8| 5 3 x +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R | 1 \| 16777216a b +--R - 2 |- ------------ atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ - x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R | 1 \| 16777216a b +--R 2 |- ------------ atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ + x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 107 + +--S 108 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +--------------+ +--R 8+---+5 | 1 8+-+3 +--R 8\|- a |- ------------ \|b +--R 8| 5 3 +--R \| 16777216a b +--R * +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 2 +--R log(262144a b |- ------------ + 512a b x\|2 |- ------------ + x ) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +--------------+ +--R 8+---+5 | 1 8+-+3 +--R 8\|- a |- ------------ \|b +--R 8| 5 3 +--R \| 16777216a b +--R * +--R log +--R +--------------+6 +--------------+3 +--R 4 2 | 1 2 +-+ | 1 +--R 262144a b |- ------------ - 512a b x\|2 |- ------------ +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 2 +--R x +--R + +--R +--------------+ +--------------+3 +--R +-+8+---+5 | 1 8+-+3 2 | 1 +--R - 8\|2 \|- a |- ------------ \|b log(512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R +--------------+ +--------------+3 +--R +-+8+---+5 | 1 8+-+3 2 | 1 +--R 8\|2 \|- a |- ------------ \|b log(- 512a b |- ------------ + x) +--R 8| 5 3 8| 5 3 +--R \| 16777216a b \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R +-+8+---+5 | 1 8+-+3 \| 16777216a b +--R - 16\|2 \|- a |- ------------ \|b atan(-------------------------) +--R 8| 5 3 x +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 16777216a b +--R - 16\|- a |- ------------ \|b atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ - x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R + +--R +--------------+3 +--R 2 | 1 +--R 512a b |- ------------ +--R +--------------+ 8| 5 3 +--R 8+---+5 | 1 8+-+3 \| 16777216a b +--R 16\|- a |- ------------ \|b atan(---------------------------------) +--R 8| 5 3 +--------------+3 +--R \| 16777216a b 2 | 1 +-+ +--R 512a b |- ------------ + x\|2 +--R 8| 5 3 +--R \| 16777216a b +--R / +--R +-+8+---+5 8+-+3 +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 108 + +--S 109 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 109 + +)clear all + +--S 110 of 1369 +t0:=1/(a+b*x^8) +--R +--R +--R 1 +--R (1) -------- +--R 8 +--R b x + a +--R Type: Fraction(Polynomial(Integer)) +--E 110 + +--S 111 of 1369 +r0:=-1/4*atan(b^(1/8)*x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))-1/4*atanh(b^(1/8)*_ + x/(-a)^(1/8))/((-a)^(7/8)*b^(1/8))+1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + (-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))-1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/(-a)^(1/8))/((-a)^(7/8)*b^(1/8)*sqrt(2))+1/8*log((-a)^(1/4)+_ + b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(7/8)*b^(1/8)*_ + sqrt(2))-1/8*log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*_ + sqrt(2))/((-a)^(7/8)*b^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R - 2atan(------------------) - 2atan(------------------) - 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R / +--R +-+8+---+7 8+-+ +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------------+ +--R | 1 +--R |- ----------- +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- + 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +-------------+ +--R | 1 +--R |- ----------- +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- - 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+ | 1 | 1 +--R \|2 |- ----------- log(8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+ | 1 | 1 +--R - \|2 |- ----------- log(- 8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R +-+ | 1 \| 16777216a b +--R - 2\|2 |- ----------- atan(------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R | 1 \| 16777216a b +--R 2 |- ----------- atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R | 1 \| 16777216a b +--R - 2 |- ----------- atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 112 + +--S 113 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +--R log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R +-------------+ +--R 8+---+7 | 1 8+-+ +--R 8\|- a |- ----------- \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- + 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R - +--R +-------------+ +--R 8+---+7 | 1 8+-+ +--R 8\|- a |- ----------- \|b +--R 8| 7 +--R \| 16777216a b +--R * +--R +-------------+2 +-------------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |- ----------- - 8a x\|2 |- ----------- + x ) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+8+---+7 | 1 8+-+ | 1 +--R 8\|2 \|- a |- ----------- \|b log(8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R +-------------+ +-------------+ +--R +-+8+---+7 | 1 8+-+ | 1 +--R - 8\|2 \|- a |- ----------- \|b log(- 8a |- ----------- + x) +--R 8| 7 8| 7 +--R \| 16777216a b \| 16777216a b +--R + +--R 8+-+ +--R +-+8+---+8+-+ 2 4+-+ 4+---+ +-+ x\|b +--R - log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2\|2 atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ 8+-+ +--R x\|2 \|b + \|- a x\|2 \|b - \|- a +-+ x\|b +--R 2atan(------------------) + 2atan(------------------) + 2\|2 atan(------) +--R 8+---+ 8+---+ 8+---+ +--R \|- a \|- a \|- a +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R +-+8+---+7 | 1 8+-+ \| 16777216a b +--R - 16\|2 \|- a |- ----------- \|b atan(------------------) +--R 8| 7 x +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 16777216a b +--R 16\|- a |- ----------- \|b atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- - x\|2 +--R 8| 7 +--R \| 16777216a b +--R + +--R +-------------+ +--R | 1 +--R 8a |- ----------- +--R +-------------+ 8| 7 +--R 8+---+7 | 1 8+-+ \| 16777216a b +--R - 16\|- a |- ----------- \|b atan(--------------------------) +--R 8| 7 +-------------+ +--R \| 16777216a b | 1 +-+ +--R 8a |- ----------- + x\|2 +--R 8| 7 +--R \| 16777216a b +--R / +--R +-+8+---+7 8+-+ +--R 8\|2 \|- a \|b +--R Type: Expression(Integer) +--E 113 + +--S 114 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 114 + +)clear all + +--S 115 of 1369 +t0:=1/(x^2*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 10 2 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 115 + +--S 116 of 1369 +r0:=(-1)/(a*x)+1/4*b^(1/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-_ + 1/4*b^(1/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(9/8)-1/4*b^(1/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*sqrt(2))+_ + 1/4*b^(1/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(9/8)*_ + sqrt(2))+1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(9/8)*sqrt(2))-1/8*b^(1/8)*log((-a)^(1/4)+b^(1/4)*_ + x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R x\|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b +--R - x\|b log(- x\|2 \|- a \|b + x \|b + \|- a ) + 2x\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a +--R - 2x\|b atan(------------------) - 2x\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+ x\|b +-+8+---+ +--R - 2x\|2 \|b atan(------) - 8\|2 \|- a +--R 8+---+ +--R \|- a +--R / +--R +-+8+---+ +--R 8a x\|2 \|- a +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | b +--R a x |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8 | b +--R - a x\|2 |- ---------- log(2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8 | b +--R a x\|2 |- ---------- log(- 2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b +--R a x |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b \| 16777216a +--R - 2a x\|2 |- ---------- atan(-------------------------) +--R 8| 9 b x +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +--R 2a x |- ---------- atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- - b x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +-+ +--R - 2a x |- ---------- atan(----------------------------------- - \|2 +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- + b x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+ +--R a x\|2 +--R Type: Union(Expression(Integer),...) +--E 117 + +--S 118 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +------------+ +--R | b 8+---+ +--R 8a |- ---------- \|- a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8+---+ 8 | b +--R - 8a\|2 |- ---------- \|- a log(2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+7 +--R +-+ | b 8+---+ 8 | b +--R 8a\|2 |- ---------- \|- a log(- 2097152a |- ---------- + b x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b 8+---+ +--R 8a |- ---------- \|- a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+7 +------------+6 +--R 8 +-+ | b 7 | b 2 +--R log(- 2097152a x\|2 |- ---------- - 262144a |- ---------- + b x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+ x\|b +--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+ x\|2 \|b + \|- a 8+-+ x\|2 \|b - \|- a +--R 2\|b atan(------------------) + 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+ x\|b +--R 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b 8+---+ \| 16777216a +--R - 16a\|2 |- ---------- \|- a atan(-------------------------) +--R 8| 9 b x +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b 8+---+ \| 16777216a +--R 16a |- ---------- \|- a atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- - b x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+7 +--R 8 | b +--R 2097152a |- ---------- +--R +------------+ 8| 9 +--R | b 8+---+ \| 16777216a +--R - 16a |- ---------- \|- a atan(-----------------------------------) +--R 8| 9 +------------+7 +--R \| 16777216a 8 | b +-+ +--R 2097152a |- ---------- + b x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+8+---+ +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 119 + +)clear all + +--S 120 of 1369 +t0:=1/(x^4*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 12 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 120 + +--S 121 of 1369 +r0:=(-1/3)/(a*x^3)-1/4*b^(3/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-_ + 1/4*b^(3/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(11/8)-1/4*b^(3/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*sqrt(2))+_ + 1/4*b^(3/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(11/8)*_ + sqrt(2))-1/8*b^(3/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(11/8)*sqrt(2))+1/8*b^(3/8)*log((-a)^(1/4)+_ + b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(11/8)*sqrt(2)) +--R +--R +--R (2) +--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 3x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 3 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 3x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 3 +-+8+-+3 x\|b 3 8+-+3 x\|2 \|b + \|- a +--R 6x \|2 \|b atanh(------) - 6x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 3 8+-+3 x\|2 \|b - \|- a 3 +-+8+-+3 x\|b +--R - 6x \|b atan(------------------ + 6x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+3 +--R - 8\|2 \|- a +--R / +--R 3 +-+8+---+3 +--R 24a x \|2 \|- a +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 3 +--R 3 | b +--R 3a x |- ----------- +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R 3 +-+ | b 7 | b 2 +--R 3a x \|2 |- ----------- log(32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R 3 +-+ | b 7 | b 2 +--R - 3a x \|2 |- ----------- log(- 32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R 3 | b +--R 3a x |- ----------- +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 +-+ | b \| 16777216a +--R - 6a x \|2 |- ----------- atan(------------------------) +--R 8| 11 2 +--R \| 16777216a b x +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 | b \| 16777216a +--R - 6a x |- ----------- atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- - b x\|2 +--R 8| 11 +--R \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R 3 | b \| 16777216a +-+ +--R 6a x |- ----------- atan(---------------------------------- - \|2 +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- + b x\|2 +--R 8| 11 +--R \| 16777216a +--R / +--R 3 +-+ +--R 3a x \|2 +--R Type: Union(Expression(Integer),...) +--E 122 + +--S 123 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 3 +--R | b 8+---+3 +--R 8a |- ----------- \|- a +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R +-+ | b 8+---+3 7 | b 2 +--R 8a\|2 |- ----------- \|- a log(32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+5 +--R | 3 | 3 +--R +-+ | b 8+---+3 7 | b 2 +--R - 8a\|2 |- ----------- \|- a log(- 32768a |- ----------- + b x) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 3 +--R | b 8+---+3 +--R 8a |- ----------- \|- a +--R 8| 11 +--R \| 16777216a +--R * +--R +-------------+5 +-------------+2 +--R | 3 | 3 +--R 7 +-+ | b 3 | b 2 2 +--R log(- 32768a x\|2 |- ----------- - 64a b |- ----------- + b x ) +--R 8| 11 8| 11 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+3 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+3 x\|b +--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+3 x\|2 \|b + \|- a 8+-+3 x\|2 \|b - \|- a +--R 2\|b atan(------------------) + 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+3 x\|b +--R - 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R +-+ | b 8+---+3 \| 16777216a +--R - 16a\|2 |- ----------- \|- a atan(------------------------) +--R 8| 11 2 +--R \| 16777216a b x +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R | b 8+---+3 \| 16777216a +--R - 16a |- ----------- \|- a atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- - b x\|2 +--R 8| 11 +--R \| 16777216a +--R + +--R +-------------+5 +--R | 3 +--R 7 | b +--R +-------------+ 32768a |- ----------- +--R | 3 8| 11 +--R | b 8+---+3 \| 16777216a +--R 16a |- ----------- \|- a atan(----------------------------------) +--R 8| 11 +-------------+5 +--R \| 16777216a | 3 +--R 7 | b 2 +-+ +--R 32768a |- ----------- + b x\|2 +--R 8| 11 +--R \| 16777216a +--R / +--R +-+8+---+3 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 123 + +--S 124 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 124 + +)clear all + +--S 125 of 1369 +t0:=1/(x^6*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 14 6 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 125 + +--S 126 of 1369 +r0:=(-1/5)/(a*x^5)+1/4*b^(5/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)-_ + 1/4*b^(5/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(13/8)+1/4*b^(5/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*sqrt(2))-_ + 1/4*b^(5/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(13/8)*_ + sqrt(2))-1/8*b^(5/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*b^(1/8)*_ + x*sqrt(2))/((-a)^(13/8)*sqrt(2))+1/8*b^(5/8)*log((-a)^(1/4)+_ + b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/((-a)^(13/8)*sqrt(2)) +--R +--R +--R (2) +--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 5x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 5 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 5x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 5 +-+8+-+5 x\|b 5 8+-+5 x\|2 \|b + \|- a +--R 10x \|2 \|b atanh(------) + 10x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 5 8+-+5 x\|2 \|b - \|- a 5 +-+8+-+5 x\|b +--R 10x \|b atan(------------------ - 10x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+5 +--R - 8\|2 \|- a +--R / +--R 5 +-+8+---+5 +--R 40a x \|2 \|- a +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 5 +--R 5 | b +--R 5a x |- ----------- +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R 5 | b +--R 5a x |- ----------- +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R 5 +-+ | b 5 | b 2 +--R 5a x \|2 |- ----------- log(512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R 5 +-+ | b 5 | b 2 +--R - 5a x \|2 |- ----------- log(- 512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 +-+ | b \| 16777216a +--R 10a x \|2 |- ----------- atan(----------------------) +--R 8| 13 2 +--R \| 16777216a b x +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 | b \| 16777216a +--R 10a x |- ----------- atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- - b x\|2 +--R 8| 13 +--R \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R 5 | b \| 16777216a +-+ +--R - 10a x |- ----------- atan(-------------------------------- - \|2 +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- + b x\|2 +--R 8| 13 +--R \| 16777216a +--R / +--R 5 +-+ +--R 5a x \|2 +--R Type: Union(Expression(Integer),...) +--E 127 + +--S 128 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 5 +--R | b 8+---+5 +--R 8a |- ----------- \|- a +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- + 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 5 +--R | b 8+---+5 +--R 8a |- ----------- \|- a +--R 8| 13 +--R \| 16777216a +--R * +--R +-------------+6 +-------------+3 +--R | 5 | 5 +--R 10 | b 5 2 +-+ | b 4 2 +--R log(262144a |- ----------- - 512a b x\|2 |- ----------- + b x ) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R +-+ | b 8+---+5 5 | b 2 +--R 8a\|2 |- ----------- \|- a log(512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+3 +--R | 5 | 5 +--R +-+ | b 8+---+5 5 | b 2 +--R - 8a\|2 |- ----------- \|- a log(- 512a |- ----------- + b x) +--R 8| 13 8| 13 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+5 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+5 x\|b +--R - \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+5 x\|2 \|b + \|- a 8+-+5 x\|2 \|b - \|- a +--R - 2\|b atan(------------------) - 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+5 x\|b +--R 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R +-+ | b 8+---+5 \| 16777216a +--R 16a\|2 |- ----------- \|- a atan(----------------------) +--R 8| 13 2 +--R \| 16777216a b x +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R | b 8+---+5 \| 16777216a +--R 16a |- ----------- \|- a atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- - b x\|2 +--R 8| 13 +--R \| 16777216a +--R + +--R +-------------+3 +--R | 5 +--R 5 | b +--R +-------------+ 512a |- ----------- +--R | 5 8| 13 +--R | b 8+---+5 \| 16777216a +--R - 16a |- ----------- \|- a atan(--------------------------------) +--R 8| 13 +-------------+3 +--R \| 16777216a | 5 +--R 5 | b 2 +-+ +--R 512a |- ----------- + b x\|2 +--R 8| 13 +--R \| 16777216a +--R / +--R +-+8+---+5 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 128 + +--S 129 of 1369 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 129 + +)clear all + +--S 130 of 1369 +t0:=1/(x^8*(a+b*x^8)) +--R +--R +--R 1 +--R (1) ------------ +--R 16 8 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 130 + +--S 131 of 1369 +r0:=(-1/7)/(a*x^7)-1/4*b^(7/8)*atan(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)-_ + 1/4*b^(7/8)*atanh(b^(1/8)*x/(-a)^(1/8))/(-a)^(15/8)+1/4*b^(7/8)*_ + atan(1-b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*sqrt(2))-_ + 1/4*b^(7/8)*atan(1+b^(1/8)*x*sqrt(2)/(-a)^(1/8))/((-a)^(15/8)*_ + sqrt(2))+1/8*b^(7/8)*log((-a)^(1/4)+b^(1/4)*x^2-(-a)^(1/8)*_ + b^(1/8)*x*sqrt(2))/((-a)^(15/8)*sqrt(2))-1/8*b^(7/8)*_ + log((-a)^(1/4)+b^(1/4)*x^2+(-a)^(1/8)*b^(1/8)*x*sqrt(2))/_ + ((-a)^(15/8)*sqrt(2)) +--R +--R +--R (2) +--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R 7x \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 7 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - 7x \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R 7 +-+8+-+7 x\|b 7 8+-+7 x\|2 \|b + \|- a +--R 14x \|2 \|b atanh(------) + 14x \|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 7 8+-+7 x\|2 \|b - \|- a 7 +-+8+-+7 x\|b +--R 14x \|b atan(------------------ + 14x \|2 \|b atan(------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R +-+8+---+7 +--R - 8\|2 \|- a +--R / +--R 7 +-+8+---+7 +--R 56a x \|2 \|- a +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-------------+ +--R | 7 +--R 7 | b +--R 7a x |- ----------- +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 7 | b +--R 7a x |- ----------- +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R 7 +-+ | b 2 | b +--R - 7a x \|2 |- ----------- log(8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R 7 +-+ | b 2 | b +--R 7a x \|2 |- ----------- log(- 8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 +-+ | b \| 16777216a +--R 14a x \|2 |- ----------- atan(-------------------) +--R 8| 15 b x +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 | b \| 16777216a +--R - 14a x |- ----------- atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- - b x\|2 +--R 8| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R 7 | b \| 16777216a +-+ +--R 14a x |- ----------- atan(----------------------------- - \|2 +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- + b x\|2 +--R 8| 15 +--R \| 16777216a +--R / +--R 7 +-+ +--R 7a x \|2 +--R Type: Union(Expression(Integer),...) +--E 132 + +--S 133 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|b log(x\|2 \|- a \|b + x \|b + \|- a ) +--R + +--R - +--R +-------------+ +--R | 7 +--R | b 8+---+7 +--R 8a |- ----------- \|- a +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- + 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R | b 8+---+7 +--R 8a |- ----------- \|- a +--R 8| 15 +--R \| 16777216a +--R * +--R +-------------+2 +-------------+ +--R | 7 | 7 +--R 4 | b 2 +-+ | b 2 2 +--R log(64a |- ----------- - 8a b x\|2 |- ----------- + b x ) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R +-+ | b 8+---+7 2 | b +--R - 8a\|2 |- ----------- \|- a log(8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R +-------------+ +-------------+ +--R | 7 | 7 +--R +-+ | b 8+---+7 2 | b +--R 8a\|2 |- ----------- \|- a log(- 8a |- ----------- + b x) +--R 8| 15 8| 15 +--R \| 16777216a \| 16777216a +--R + +--R 8+-+ +--R 8+-+7 +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+-+7 x\|b +--R \|b log(- x\|2 \|- a \|b + x \|b + \|- a ) - 2\|2 \|b atanh(------) +--R 8+---+ +--R \|- a +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+-+7 x\|2 \|b + \|- a 8+-+7 x\|2 \|b - \|- a +--R - 2\|b atan(------------------) - 2\|b atan(------------------) +--R 8+---+ 8+---+ +--R \|- a \|- a +--R + +--R 8+-+ +--R +-+8+-+7 x\|b +--R - 2\|2 \|b atan(------) +--R 8+---+ +--R \|- a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R +-+ | b 8+---+7 \| 16777216a +--R 16a\|2 |- ----------- \|- a atan(-------------------) +--R 8| 15 b x +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R | b 8+---+7 \| 16777216a +--R - 16a |- ----------- \|- a atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- - b x\|2 +--R 8| 15 +--R \| 16777216a +--R + +--R +-------------+ +--R | 7 +--R 2 | b +--R +-------------+ 8a |- ----------- +--R | 7 8| 15 +--R | b 8+---+7 \| 16777216a +--R 16a |- ----------- \|- a atan(-----------------------------) +--R 8| 15 +-------------+ +--R \| 16777216a | 7 +--R 2 | b +-+ +--R 8a |- ----------- + b x\|2 +--R 8| 15 +--R \| 16777216a +--R / +--R +-+8+---+7 +--R 8a\|2 \|- a +--R Type: Expression(Integer) +--E 133 + +--S 134 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R 10 4+-+2 8 4+---+4+-+ 6 8+---+4 6 4+---+28+-+6 +--R (- b x \|b - 2b x \|- a \|b - 2b x \|- a - b x \|- a )\|b +--R + +--R 8 8+---+2 4+-+2 6 4+---+8+---+2 4+-+ 4 8+---+6 +--R b x \|- a \|b + 2b x \|- a \|- a \| - 2b x \|- a +--R + +--R 4 4+---+2 8+---+2 +--R b x \|- a \|- a +--R * +--R 8+-+4 +--R \|b +--R + +--R 6 8+---+4 4+-+2 4 4+---+8+---+4 4+-+ 2 4+---+2 8+---+4 +--R b x \|- a \|b + 2b x \|- a \|- a \| + b x \|- a \|- a +--R + +--R 2 +--R - 2a b x +--R * +--R 8+-+2 +--R \|b +--R + +--R 4 8+---+6 4+-+2 2 4+---+8+---+6 2 10 2 4+-+ +--R - b x \|- a \|b + (- 2b x \|- a \|- a + b x + a b x )\|b +--R + +--R 4+---+2 8+---+6 2 8 8+---+2 2 8 4+---+ +--R - b \|- a \|- a + 2b x \|- a + (- b x - a b)\|- a +--R / +--R 2 10 3 2 8+-+2 12 2 4 8+---+6 4+-+2 +--R (8a b x + 8a x )\|b + (4a b x + 4a x )\|- a \|b +--R + +--R 10 2 2 4+---+8+---+6 4+-+ 8 2 4+---+2 8+---+6 +--R (8a b x + 8a x )\|- a \|- a \|b + (4a b x + 4a )\|- a \|- a +--R Type: Expression(Integer) +--E 134 + +)clear all + +--S 135 of 1369 +t0:=1/(a-b*x^8) +--R +--R +--R 1 +--R (1) - -------- +--R 8 +--R b x - a +--R Type: Fraction(Polynomial(Integer)) +--E 135 + +--S 136 of 1369 +r0:=1/4*atan(b^(1/8)*x/a^(1/8))/(a^(7/8)*b^(1/8))+1/4*atanh(b^(1/8)*_ + x/a^(1/8))/(a^(7/8)*b^(1/8))-1/4*atan(1-b^(1/8)*x*sqrt(2)/_ + a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))+1/4*atan(1+b^(1/8)*x*_ + sqrt(2)/a^(1/8))/(a^(7/8)*b^(1/8)*sqrt(2))-1/8*log(a^(1/4)+_ + b^(1/4)*x^2-a^(1/8)*b^(1/8)*x*sqrt(2))/(a^(7/8)*b^(1/8)*sqrt(2))+_ + 1/8*log(a^(1/4)+b^(1/4)*x^2+a^(1/8)*b^(1/8)*x*sqrt(2))/_ + (a^(7/8)*b^(1/8)*sqrt(2)) +--R +--R +--R (2) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+8+-+8+-+ 2 4+-+ 4+-+ +--R log(x\|2 \|a \|b + x \|b + \|a ) - log(- x\|2 \|a \|b + x \|b + \|a ) +--R + +--R 8+-+ +-+8+-+ 8+-+ +-+8+-+ 8+-+ +--R +-+ x\|b x\|2 \|b + \|a x\|2 \|b - \|a +--R 2\|2 atanh(-----) + 2atan(----------------) + 2atan(----------------) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R 8+-+ +--R +-+ x\|b +--R 2\|2 atan(-----) +--R 8+-+ +--R \|a +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R |----------- log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+2 +-----------+ +--R | 1 2 | 1 +-+ | 1 2 +--R - |----------- log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 8| 7 +--R \|16777216a b \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R \|2 |----------- log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 | 1 +--R - \|2 |----------- log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 \|16777216a b +--R - 2\|2 |----------- atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 \|16777216a b +--R - 2 |----------- atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+ +--R \|2 +--R Type: Union(Expression(Integer),...) +--E 137 + +--S 138 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +--R - log(x\|2 \|a \|b + x \|b + \|a ) +--R + +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- + 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R - +--R +-----------+ +--R | 1 8+-+7 8+-+ +--R 8 |----------- \|a \|b +--R 8| 7 +--R \|16777216a b +--R * +--R +-----------+2 +-----------+ +--R 2 | 1 +-+ | 1 2 +--R log(64a |----------- - 8a x\|2 |----------- + x ) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R 8\|2 |----------- \|a \|b log(8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R +-----------+ +-----------+ +--R +-+ | 1 8+-+7 8+-+ | 1 +--R - 8\|2 |----------- \|a \|b log(- 8a |----------- + x) +--R 8| 7 8| 7 +--R \|16777216a b \|16777216a b +--R + +--R 8+-+ +--R +-+8+-+8+-+ 2 4+-+ 4+-+ +-+ x\|b +--R log(- x\|2 \|a \|b + x \|b + \|a ) - 2\|2 atanh(-----) +--R 8+-+ +--R \|a +--R + +--R +-+8+-+ 8+-+ +-+8+-+ 8+-+ 8+-+ +--R x\|2 \|b + \|a x\|2 \|b - \|a +-+ x\|b +--R - 2atan(----------------) - 2atan(----------------) - 2\|2 atan(-----) +--R 8+-+ 8+-+ 8+-+ +--R \|a \|a \|a +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R +-+ | 1 8+-+7 8+-+ \|16777216a b +--R - 16\|2 |----------- \|a \|b atan(----------------) +--R 8| 7 x +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- - x\|2 +--R 8| 7 +--R \|16777216a b +--R + +--R +-----------+ +--R | 1 +--R 8a |----------- +--R +-----------+ 8| 7 +--R | 1 8+-+7 8+-+ \|16777216a b +--R - 16 |----------- \|a \|b atan(------------------------) +--R 8| 7 +-----------+ +--R \|16777216a b | 1 +-+ +--R 8a |----------- + x\|2 +--R 8| 7 +--R \|16777216a b +--R / +--R +-+8+-+7 8+-+ +--R 8\|2 \|a \|b +--R Type: Expression(Integer) +--E 138 + +--S 139 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 8+-+2 4+-+2 6 4+-+8+-+2 4+-+ 4 8+-+6 4 4+-+2 8+-+8+-+6 +--R (- x \|a \|b - 2x \|a \|a \| + 2x \|a - x \|a \|a)\|b +--R + +--R 6 8+-+4 4+-+2 4 4+-+8+-+4 4+-+ 2 4+-+2 8+-+4 2 8+-+4 +--R (- x \|a \|b - 2x \|a \|a \| - x \|a \|a - 2a x )\|b +--R + +--R 4 8+-+6 4+-+2 2 4+-+8+-+6 10 2 4+-+ 4+-+2 8+-+6 +--R x \|a \|b + (2x \|a \|a - b x + a x )\|b + \|a \|a +--R + +--R 8 8+-+2 8 4+-+ +--R - 2b x \|a + (b x - a)\|a +--R * +--R 8+-+2 +--R \|b +--R + +--R 10 4+-+2 8 4+-+4+-+ 6 8+-+4 6 4+-+2 +--R b x \|b + 2b x \|a \|b + 2b x \|a + b x \|a +--R / +--R 10 2 2 8+-+4 +--R (8a b x - 8a x )\|b +--R + +--R 12 4 8+-+6 4+-+2 10 2 4+-+8+-+6 4+-+ +--R (- 4b x + 4a x )\|a \|b + (- 8b x + 8a x )\|a \|a \|b +--R + +--R 8 4+-+2 8+-+6 +--R (- 4b x + 4a)\|a \|a +--R * +--R 8+-+2 +--R \|b +--R Type: Expression(Integer) +--E 139 + +)clear all + +--S 140 of 1369 +t0:=x^9/(1-x^8) +--R +--R +--R 9 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 140 + +--S 141 of 1369 +r0:=-1/2*x^2+1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 2 +--R atanh(x ) + atan(x ) - 2x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R log(x + 1) - log(x - 1) + 2atan(x ) - 4x +--R (3) ------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 142 + +--S 143 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 143 + +--S 144 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 144 + +)clear all + +--S 145 of 1369 +t0:=x^7/(1-x^8) +--R +--R +--R 7 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 145 + +--S 146 of 1369 +r0:=-1/8*log(1-x^8) +--R +--R +--R 8 +--R log(- x + 1) +--R (2) - ------------- +--R 8 +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(x - 1) +--R (3) - ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 147 + +--S 148 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + log(- x + 1) +--R (4) ----------------------------- +--R 8 +--R Type: Expression(Integer) +--E 148 + +--S 149 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 149 + +)clear all + +--S 150 of 1369 +t0:=x^5/(1-x^8) +--R +--R +--R 5 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 150 + +--S 151 of 1369 +r0:=-1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 +--R atanh(x ) - atan(x ) +--R (2) -------------------- +--R 4 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atan(x ) +--R (3) ------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 152 + +--S 153 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 153 + +--S 154 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 154 + +)clear all + +--S 155 of 1369 +t0:=x^3/(1-x^8) +--R +--R +--R 3 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 155 + +--S 156 of 1369 +r0:=1/4*atanh(x^4) +--R +--R +--R 4 +--R atanh(x ) +--R (2) --------- +--R 4 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R log(x + 1) - log(x - 1) +--R (3) ------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 157 + +--S 158 of 1369 +m0:=a0-r0 +--R +--R +--R 4 4 4 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 159 + +)clear all + +--S 160 of 1369 +t0:=x/(1-x^8) +--R +--R +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 160 + +--S 161 of 1369 +r0:=1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 +--R atanh(x ) + atan(x ) +--R (2) -------------------- +--R 4 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) + 2atan(x ) +--R (3) ------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 162 + +--S 163 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 164 + +)clear all + +--S 165 of 1369 +t0:=1/(x*(1-x^8)) +--R +--R +--R 1 +--R (1) - ------ +--R 9 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 165 + +--S 166 of 1369 +r0:=-1/4*atanh(1-2*x^8) +--R +--R +--R 8 +--R atanh(2x - 1) +--R (2) -------------- +--R 4 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(x - 1) + 8log(x) +--R (3) ----------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 167 + +--S 168 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + 8log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 169 + +)clear all + +--S 170 of 1369 +t0:=1/(x^3*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 11 3 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 170 + +--S 171 of 1369 +r0:=(-1/2)/x^2-1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 2 2 2 2 +--R x atanh(x ) - x atan(x ) - 2 +--R (2) ---------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 2 +--R x log(x + 1) - x log(x - 1) - 2x atan(x ) - 4 +--R (3) ----------------------------------------------- +--R 2 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 172 + +--S 173 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 173 + +--S 174 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 174 + +)clear all + +--S 175 of 1369 +t0:=1/(x^5*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 13 5 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 175 + +--S 176 of 1369 +r0:=(-1/4)/x^4+1/4*atanh(x^4) +--R +--R +--R 4 4 +--R x atanh(x ) - 1 +--R (2) --------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 4 +--R x log(x + 1) - x log(x - 1) - 2 +--R (3) --------------------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 177 + +--S 178 of 1369 +m0:=a0-r0 +--R +--R +--R 4 4 4 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 179 + +)clear all + +--S 180 of 1369 +t0:=1/(x^7*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 15 7 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 180 + +--S 181 of 1369 +r0:=(-1/6)/x^6+1/4*atan(x^2)+1/4*atanh(x^2) +--R +--R +--R 6 2 6 2 +--R 3x atanh(x ) + 3x atan(x ) - 2 +--R (2) ------------------------------ +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 2 6 2 6 2 +--R 3x log(x + 1) - 3x log(x - 1) + 6x atan(x ) - 4 +--R (3) ------------------------------------------------- +--R 6 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 182 + +--S 183 of 1369 +m0:=a0-r0 +--R +--R +--R 2 2 2 +--R log(x + 1) - log(x - 1) - 2atanh(x ) +--R (4) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 183 + +--S 184 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 184 + +)clear all + +--S 185 of 1369 +t0:=1/(x^9*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 17 9 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 185 + +--S 186 of 1369 +r0:=(-1/8)/x^8-1/4*atanh(1-2*x^8) +--R +--R +--R 8 8 +--R 2x atanh(2x - 1) - 1 +--R (2) --------------------- +--R 8 +--R 8x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R - x log(x - 1) + 8x log(x) - 1 +--R (3) ------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 187 + +--S 188 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x - 1) + 8log(x) - 2atanh(2x - 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 189 + +)clear all + +--S 190 of 1369 +t0:=x^8/(1-x^8) +--R +--R +--R 8 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 190 + +--S 191 of 1369 +r0:=-x+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x) - 8x\|2 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +-+ +--R - 2atan(---------) - 8x\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 192 + +--S 193 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 193 + +--S 194 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 194 + +)clear all + +--S 195 of 1369 +t0:=x^6/(1-x^8) +--R +--R +--R 6 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 195 + +--S 196 of 1369 +r0:=-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) - 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 197 + +--S 198 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 198 + +--S 199 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 199 + +)clear all + +--S 200 of 1369 +t0:=x^4/(1-x^8) +--R +--R +--R 4 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 200 + +--S 201 of 1369 +r0:=1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R - 2atan(x\|2 + 1) - 2atan(x\|2 - 1) + 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R log(- x\|2 + x + 1) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 202 + +--S 203 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 204 + +)clear all + +--S 205 of 1369 +t0:=x^2/(1-x^8) +--R +--R +--R 2 +--R x +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 205 + +--S 206 of 1369 +r0:=-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)-1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R - log(x\|2 + x + 1) + log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) - 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R - log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R log(- x\|2 + x + 1) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 207 + +--S 208 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 208 + +--S 209 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 209 + +)clear all + +--S 210 of 1369 +t0:=1/(1-x^8) +--R +--R +--R 1 +--R (1) - ------ +--R 8 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 210 + +--S 211 of 1369 +r0:=1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R log(x\|2 + x + 1) - log(- x\|2 + x + 1) + 2\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +--R 2atan(x\|2 + 1) + 2atan(x\|2 - 1) + 2\|2 atan(x) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R log(x\|2 + x + 1) + \|2 log(x + 1) - \|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - log(- x\|2 + x + 1) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 212 + +--S 213 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 213 + +--S 214 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 214 + +)clear all + +--S 215 of 1369 +t0:=1/(x^2*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 10 2 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 215 + +--S 216 of 1369 +r0:=(-1)/x-1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+ 2 +-+ 2 +-+ +--R x log(x\|2 + x + 1) - x log(- x\|2 + x + 1) + 2x\|2 atanh(x) +--R + +--R +-+ +-+ +-+ +-+ +--R - 2x atan(x\|2 + 1) - 2x atan(x\|2 - 1) - 2x\|2 atan(x) - 8\|2 +--R / +--R +-+ +--R 8x\|2 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ +-+ +--R x log(x\|2 + x + 1) + x\|2 log(x + 1) - x\|2 log(x - 1) +--R + +--R +-+ 2 +-+ 2x 1 +--R - x log(- x\|2 + x + 1) + x\|2 atan(------) + 2x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +-+ +--R 2x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8x\|2 +--R Type: Union(Expression(Integer),...) +--E 217 + +--S 218 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 219 + +)clear all + +--S 220 of 1369 +t0:=1/(x^4*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 12 4 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 220 + +--S 221 of 1369 +r0:=(-1/3)/x^3+1/4*atan(x)+1/4*atanh(x)+1/4*atan(1-x*sqrt(2))/sqrt(2)-_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 3 +-+ 2 3 +-+ 2 3 +-+ +--R - 3x log(x\|2 + x + 1) + 3x log(- x\|2 + x + 1) + 6x \|2 atanh(x) +--R + +--R 3 +-+ 3 +-+ 3 +-+ +-+ +--R - 6x atan(x\|2 + 1) - 6x atan(x\|2 - 1) + 6x \|2 atan(x) - 8\|2 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 2 3 +-+ 3 +-+ +--R - 3x log(x\|2 + x + 1) + 3x \|2 log(x + 1) - 3x \|2 log(x - 1) +--R + +--R 3 +-+ 2 3 +-+ 2x 3 1 +--R 3x log(- x\|2 + x + 1) - 3x \|2 atan(------) + 6x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 3 1 +-+ +--R 6x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Union(Expression(Integer),...) +--E 222 + +--S 223 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) + 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) + 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 224 + +)clear all + +--S 225 of 1369 +t0:=1/(x^6*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 14 6 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 225 + +--S 226 of 1369 +r0:=(-1/5)/x^5-1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)+1/8*log(1+x^2-x*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 5 +-+ 2 5 +-+ 2 5 +-+ +--R - 5x log(x\|2 + x + 1) + 5x log(- x\|2 + x + 1) + 10x \|2 atanh(x) +--R + +--R 5 +-+ 5 +-+ 5 +-+ +-+ +--R 10x atan(x\|2 + 1) + 10x atan(x\|2 - 1) - 10x \|2 atan(x) - 8\|2 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 2 5 +-+ 5 +-+ +--R - 5x log(x\|2 + x + 1) + 5x \|2 log(x + 1) - 5x \|2 log(x - 1) +--R + +--R 5 +-+ 2 5 +-+ 2x 5 1 +--R 5x log(- x\|2 + x + 1) + 5x \|2 atan(------) - 10x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 5 1 +-+ +--R - 10x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Union(Expression(Integer),...) +--E 227 + +--S 228 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) + 2\|2 atan(x) + \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 229 + +)clear all + +--S 230 of 1369 +t0:=1/(x^8*(1-x^8)) +--R +--R +--R 1 +--R (1) - -------- +--R 16 8 +--R x - x +--R Type: Fraction(Polynomial(Integer)) +--E 230 + +--S 231 of 1369 +r0:=(-1/7)/x^7+1/4*atan(x)+1/4*atanh(x)-1/4*atan(1-x*sqrt(2))/sqrt(2)+_ + 1/4*atan(1+x*sqrt(2))/sqrt(2)-1/8*log(1+x^2-x*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^2+x*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 7 +-+ 2 7 +-+ 2 7 +-+ +--R 7x log(x\|2 + x + 1) - 7x log(- x\|2 + x + 1) + 14x \|2 atanh(x) +--R + +--R 7 +-+ 7 +-+ 7 +-+ +-+ +--R 14x atan(x\|2 + 1) + 14x atan(x\|2 - 1) + 14x \|2 atan(x) - 8\|2 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 +-+ 2 7 +-+ 7 +-+ +--R 7x log(x\|2 + x + 1) + 7x \|2 log(x + 1) - 7x \|2 log(x - 1) +--R + +--R 7 +-+ 2 7 +-+ 2x 7 1 +--R - 7x log(- x\|2 + x + 1) - 7x \|2 atan(------) - 14x atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 7 1 +-+ +--R - 14x atan(---------) - 8\|2 +--R +-+ +--R x\|2 + 1 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Union(Expression(Integer),...) +--E 232 + +--S 233 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+ +-+ +-+ +-+ +--R \|2 log(x + 1) - \|2 log(x - 1) - 2\|2 atanh(x) - 2atan(x\|2 + 1) +--R + +--R +-+ +-+ +-+ 2x 1 +--R - 2atan(x\|2 - 1) - 2\|2 atan(x) - \|2 atan(------) - 2atan(---------) +--R 2 +-+ +--R x - 1 x\|2 - 1 +--R + +--R 1 +--R - 2atan(---------) +--R +-+ +--R x\|2 + 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 233 + +--S 234 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 234 + +)clear all + +--S 235 of 1369 +t0:=x^9/(1+x^8) +--R +--R +--R 9 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 235 + +--S 236 of 1369 +r0:=1/2*x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_ + x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) - 2atan(x \|2 + 1) +--R + +--R 2 +-+ 2 +-+ +--R - 2atan(x \|2 - 1) + 4x \|2 +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 2 +--R 2\|2 atan(----------) + 2\|2 atan(----------) + 8x +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 237 + +--S 238 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 239 + +)clear all + +--S 240 of 1369 +t0:=x^7/(1+x^8) +--R +--R +--R 7 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 240 + +--S 241 of 1369 +r0:=1/8*log(1+x^8) +--R +--R +--R 8 +--R log(x + 1) +--R (2) ----------- +--R 8 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R log(x + 1) +--R (3) ----------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 242 + +--S 243 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 243 + +--S 244 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 244 + +)clear all + +--S 245 of 1369 +t0:=x^5/(1+x^8) +--R +--R +--R 5 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 245 + +--S 246 of 1369 +r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R - log(x \|2 + x + 1) + log(- x \|2 + x + 1) + 2atan(x \|2 + 1) +--R + +--R 2 +-+ +--R 2atan(x \|2 - 1) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R - \|2 log(x \|2 + x + 1) + \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------) - 2\|2 atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 247 + +--S 248 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 249 + +)clear all + +--S 250 of 1369 +t0:=x^3/(1+x^8) +--R +--R +--R 3 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 250 + +--S 251 of 1369 +r0:=1/4*atan(x^4) +--R +--R +--R 4 +--R atan(x ) +--R (2) -------- +--R 4 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R atan(x ) +--R (3) -------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 252 + +--S 253 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 253 + +--S 254 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 254 + +)clear all + +--S 255 of 1369 +t0:=x/(1+x^8) +--R +--R +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 255 + +--S 256 of 1369 +r0:=-1/4*atan(1-x^2*sqrt(2))/sqrt(2)+1/4*atan(1+x^2*sqrt(2))/sqrt(2)-_ + 1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 +-+ 4 2 +-+ 4 2 +-+ +--R log(x \|2 + x + 1) - log(- x \|2 + x + 1) + 2atan(x \|2 + 1) +--R + +--R 2 +-+ +--R 2atan(x \|2 - 1) +--R / +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 +-+ 4 +-+ 2 +-+ 4 +--R \|2 log(x \|2 + x + 1) - \|2 log(- x \|2 + x + 1) +--R + +--R +-+ 1 +-+ 1 +--R - 2\|2 atan(----------) - 2\|2 atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 16 +--R Type: Union(Expression(Integer),...) +--E 257 + +--S 258 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R - atan(x \|2 + 1) - atan(x \|2 - 1) - atan(----------) - atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R --------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 258 + +--S 259 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 259 + +)clear all + +--S 260 of 1369 +t0:=1/(x*(1+x^8)) +--R +--R +--R 1 +--R (1) ------ +--R 9 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 260 + +--S 261 of 1369 +r0:=-1/4*atanh(1+2*x^8) +--R +--R +--R 8 +--R atanh(2x + 1) +--R (2) - -------------- +--R 4 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 +--R - log(x + 1) + 8log(x) +--R (3) ----------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 262 + +--S 263 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R - log(x + 1) + 8log(x) + 2atanh(2x + 1) +--R (4) ----------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 264 + +)clear all + +--S 265 of 1369 +t0:=1/(x^3*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 11 3 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 265 + +--S 266 of 1369 +r0:=(-1/2)/x^2+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*_ + sqrt(2))/sqrt(2)-1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)+_ + 1/8*log(1+x^4+x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 2 2 +-+ 4 2 2 +-+ 4 2 2 +-+ +--R x log(x \|2 + x + 1) - x log(- x \|2 + x + 1) - 2x atan(x \|2 + 1) +--R + +--R 2 2 +-+ +-+ +--R - 2x atan(x \|2 - 1) - 4\|2 +--R / +--R 2 +-+ +--R 8x \|2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 +-+ 4 2 +-+ 2 +-+ 4 +--R x \|2 log(x \|2 + x + 1) - x \|2 log(- x \|2 + x + 1) +--R + +--R 2 +-+ 1 2 +-+ 1 +--R 2x \|2 atan(----------) + 2x \|2 atan(----------) - 8 +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 2 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 267 + +--S 268 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 268 + +--S 269 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 269 + +)clear all + +--S 270 of 1369 +t0:=1/(x^5*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 13 5 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 270 + +--S 271 of 1369 +r0:=(-1/4)/x^4-1/4*atan(x^4) +--R +--R +--R 4 4 +--R - x atan(x ) - 1 +--R (2) ---------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 +--R - x atan(x ) - 1 +--R (3) ---------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 272 + +--S 273 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 273 + +--S 274 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 274 + +)clear all + +--S 275 of 1369 +t0:=1/(x^7*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 15 7 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 275 + +--S 276 of 1369 +r0:=(-1/6)/x^6+1/4*atan(1-x^2*sqrt(2))/sqrt(2)-1/4*atan(1+x^2*sqrt(2))/_ + sqrt(2)+1/8*log(1+x^4-x^2*sqrt(2))/sqrt(2)-1/8*log(1+x^4+_ + x^2*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R 6 2 +-+ 4 6 2 +-+ 4 +--R - 3x log(x \|2 + x + 1) + 3x log(- x \|2 + x + 1) +--R + +--R 6 2 +-+ 6 2 +-+ +-+ +--R - 6x atan(x \|2 + 1) - 6x atan(x \|2 - 1) - 4\|2 +--R / +--R 6 +-+ +--R 24x \|2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 2 +-+ 4 6 +-+ 2 +-+ 4 +--R - 3x \|2 log(x \|2 + x + 1) + 3x \|2 log(- x \|2 + x + 1) +--R + +--R 6 +-+ 1 6 +-+ 1 +--R 6x \|2 atan(----------) + 6x \|2 atan(----------) - 8 +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R / +--R 6 +--R 48x +--R Type: Union(Expression(Integer),...) +--E 277 + +--S 278 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 +-+ 1 1 +--R atan(x \|2 + 1) + atan(x \|2 - 1) + atan(----------) + atan(----------) +--R 2 +-+ 2 +-+ +--R x \|2 - 1 x \|2 + 1 +--R ------------------------------------------------------------------------- +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 279 + +)clear all + +--S 280 of 1369 +t0:=1/(x^9*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 17 9 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 280 + +--S 281 of 1369 +r0:=(-1/8)/x^8+1/4*atanh(1+2*x^8) +--R +--R +--R 8 8 +--R 2x atanh(2x + 1) - 1 +--R (2) --------------------- +--R 8 +--R 8x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 8 8 8 +--R x log(x + 1) - 8x log(x) - 1 +--R (3) ----------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 282 + +--S 283 of 1369 +m0:=a0-r0 +--R +--R +--R 8 8 +--R log(x + 1) - 8log(x) - 2atanh(2x + 1) +--R (4) --------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 284 + +)clear all + +--S 285 of 1369 +t0:=x^8/(1+x^8) +--R +--R +--R 8 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 285 + +--S 286 of 1369 +r0:=x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 16x +--R / +--R 16 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R \|- 1 \|2 log(- \|- 1 + x) + \|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(------) + 2\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +-+ +--R 2\|- 1 atan(--------------) + 8x\|2 +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 287 + +--S 288 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 289 + +)clear all + +--S 290 of 1369 +t0:=x^6/(1+x^8) +--R +--R +--R 6 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 290 + +--S 291 of 1369 +r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R / +--R 16 +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 292 + +--S 293 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R - 2\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R - 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) + 4\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 atan(---------------) + 4\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 293 + +--S 294 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 294 + +)clear all + +--S 295 of 1369 +t0:=x^4/(1+x^8) +--R +--R +--R 4 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 295 + +--S 296 of 1369 +r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+_ + x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/4*atan((-2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+_ + sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R / +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R 8\|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+5 8+---+ 8+---+5 +-+ 8+---+2 2 +--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+5 8+---+5 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------) +--R x +-+ 8+---+5 +--R x\|2 - \|- 1 +--R + +--R 8+---+5 +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 297 + +--S 298 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ 8+---+5 +--R \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+5 +--R \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+5 8+---+5 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 \|2 atan(-------) - 2\|- 1 atan(---------------) +--R x +-+ 8+---+5 +--R x\|2 - \|- 1 +--R + +--R 8+---+5 +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +--R x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 4 +-+ 4 | +-+ | +-+ +--R ((- 3x - 1)\|2 + 4x + 2)\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 4 +-+ 4 | +-+ | +-+ 4 +--R ((- 3x - 1)\|2 - 4x - 2)\|- 2\|2 + 4 \|- \|2 + 2 + 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 299 + +)clear all + +--S 300 of 1369 +t0:=x^2/(1+x^8) +--R +--R +--R 2 +--R x +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 300 + +--S 301 of 1369 +r0:=-1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-_ + 1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+_ + 1/4*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R | +-+ | +-+ 2 +--R \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R | +-+ +--R 2\|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2\|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R / +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R 8\|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3 +--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+3 8+---+ 8+---+3 +-+ 8+---+6 2 +--R \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 302 + +--S 303 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ 8+---+3 +--R \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) - \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+3 +--R \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(-------) + 2\|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 303 + +--S 304 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ +--R ((- x - 3x )\|2 + 2x + 4x )\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ 2 +--R ((- x - 3x )\|2 - 2x - 4x )\|- 2\|2 + 4 \|- \|2 + 2 + 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 304 + +)clear all + +--S 305 of 1369 +t0:=1/(1+x^8) +--R +--R +--R 1 +--R (1) ------ +--R 8 +--R x + 1 +--R Type: Fraction(Polynomial(Integer)) +--E 305 + +--S 306 of 1369 +r0:=-1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/8*atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R | +-+ +--R 2\|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R - 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R / +--R 16 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R \|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + \|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R - \|- 1 \|2 log(- \|- 1 + x) - \|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 \|2 atan(------) - 2\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 2\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 8\|2 +--R Type: Union(Expression(Integer),...) +--E 307 + +--S 308 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R - 2\|- 1 \|2 log(- \|- 1 + x) - 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R - 4\|- 1 \|2 atan(------) - 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R - 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 309 + +)clear all + +--S 310 of 1369 +t0:=1/(x^2*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 10 2 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 310 + +--S 311 of 1369 +r0:=(-1)/x+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R x\|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R x\|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R | +-+ | +-+ 2 +--R - x\|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R | +-+ | +-+ 2 +--R - x\|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R | +-+ +--R 2x\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R | +-+ +--R 2x\|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 2x\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 2x\|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - 16 +--R / +--R 16x +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R - x\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - x\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R x\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R x\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2x\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +-+ +--R - 2x\|- 1 atan(---------------) - 2x\|- 1 atan(---------------) - 8\|2 +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 8x\|2 +--R Type: Union(Expression(Integer),...) +--E 312 + +--S 313 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ 8+---+7 +--R - 2\|- 1 log(x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+7 +--R 2\|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+7 +--R 8+---+ 8+---+7 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R 2\|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 4\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+7 8+---+7 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R - 4\|- 1 atan(---------------) - 4\|- 1 atan(---------------) +--R +-+ 8+---+7 +-+ 8+---+7 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 314 + +)clear all + +--S 315 of 1369 +t0:=1/(x^4*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 12 4 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 315 + +--S 316 of 1369 +r0:=(-1/3)/x^3+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-_ + sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2-x*sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2+x*sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+sqrt(2-sqrt(2)))/_ + sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+1/4*atan((2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))-_ + 1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R 3 | +-+ | +-+ 2 +--R 3x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 3 | +-+ | +-+ 2 +--R - 3x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 3 | +-+ | +-+ 2 +--R 3x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R 3 | +-+ | +-+ 2 +--R - 3x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R 3 | +-+ +--R 6x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R 3 | +-+ +--R 6x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R 3 | +-+ +--R 6x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +-----------+ +-+ | +-+ +-+ | +-+ +--R 3 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 6x \|- 2\|2 + 4 atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R - 8\|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R 3 | +-+ | +-+ +--R 24x \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - 3x \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 3 8+---+ +-+ 8+---+5 3 8+---+ +-+ 8+---+5 +--R 3x \|- 1 \|2 log(\|- 1 + x - 3x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+5 +--R 3 8+---+ 8+---+5 +-+ 8+---+2 2 3 8+---+ +-+ \|- 1 +--R 3x \|- 1 log(- x \|- 1 \|2 - \|- 1 + x - 6x \|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+5 8+---+5 +--R 3 8+---+ \|- 1 3 8+---+ \|- 1 +-+ +--R 6x \|- 1 atan(--------------- + 6x \|- 1 atan(--------------- - 8\|2 +--R +-+ 8+---+5 +-+ 8+---+5 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R 3 +-+ +--R 24x \|2 +--R Type: Union(Expression(Integer),...) +--E 317 + +--S 318 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+5 +-+ 8+---+2 2 +--R - \|- 1 log(x \|- 1 \|2 - \|- 1 + x ) +--R + +--R 8+---+ +-+ 8+---+5 8+---+ +-+ 8+---+5 +--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+5 +--R 8+---+ 8+---+5 +-+ 8+---+2 2 8+---+ +-+ \|- 1 +--R \|- 1 log(- x \|- 1 \|2 - \|- 1 + x ) - 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+5 8+---+5 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R 2\|- 1 atan(---------------) + 2\|- 1 atan(---------------) +--R +-+ 8+---+5 +-+ 8+---+5 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 4 +-+ 4 | +-+ | +-+ +--R ((3x + 1)\|2 - 4x - 2)\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 4 +-+ 4 | +-+ | +-+ 4 +--R ((3x + 1)\|2 + 4x + 2)\|- 2\|2 + 4 \|- \|2 + 2 - 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 319 + +)clear all + +--S 320 of 1369 +t0:=1/(x^6*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 14 6 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 320 + +--S 321 of 1369 +r0:=(-1/5)/x^5+1/4*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))/_ + sqrt(2*(2-sqrt(2)))-1/4*atan((2*x+sqrt(2+sqrt(2)))/_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/8*log(1+x^2-x*_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))+1/8*log(1+x^2+x*_ + sqrt(2-sqrt(2)))/sqrt(2*(2-sqrt(2)))-1/4*atan((-2*x+_ + sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/sqrt(2*(2+sqrt(2)))+_ + 1/4*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2)))+1/8*log(1+x^2-x*sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2)))-1/8*log(1+x^2+x*sqrt(2+sqrt(2)))/_ + sqrt(2*(2+sqrt(2))) +--R +--R +--R (2) +--R +-----------+ +--------+ +--R 5 | +-+ | +-+ 2 +--R - 5x \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 5 | +-+ | +-+ 2 +--R 5x \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R 5 | +-+ | +-+ 2 +--R - 5x \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R 5 | +-+ | +-+ 2 +--R 5x \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +---------+ +--R 5 | +-+ +--R 10x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +---------+ +--R 5 | +-+ +--R 10x \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R 5 | +-+ +--R 10x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +--R 5 | +-+ +--R 10x \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R - 8\|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R 5 | +-+ | +-+ +--R 40x \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - 5x \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 5 8+---+ +-+ 8+---+3 5 8+---+ +-+ 8+---+3 +--R 5x \|- 1 \|2 log(\|- 1 + x - 5x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 5 8+---+ 8+---+3 +-+ 8+---+6 2 +--R 5x \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+3 8+---+3 +--R 5 8+---+ +-+ \|- 1 5 8+---+ \|- 1 +--R 10x \|- 1 \|2 atan(------- - 10x \|- 1 atan(---------------) +--R x +-+ 8+---+3 +--R x\|2 - \|- 1 +--R + +--R 8+---+3 +--R 5 8+---+ \|- 1 +-+ +--R - 10x \|- 1 atan(--------------- - 8\|2 +--R +-+ 8+---+3 +--R x\|2 + \|- 1 +--R / +--R 5 +-+ +--R 40x \|2 +--R Type: Union(Expression(Integer),...) +--E 322 + +--S 323 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- 2\|2 + 4 log(x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|2\|2 + 4 log(x\|- \|2 + 2 + x + 1) +--R + +--R +---------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|2\|2 + 4 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +-----------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- 2\|2 + 4 log(- x\|\|2 + 2 + x + 1) +--R + +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +---------+ +--R +-+ | +-+ +--R 2\|2 \|2\|2 + 4 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R - +--R +-----------+ +--R +-+ | +-+ +--R 2\|2 \|- 2\|2 + 4 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+3 +-+ 8+---+6 2 +--R - \|- 1 log(x \|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ +-+ 8+---+3 8+---+ +-+ 8+---+3 +--R \|- 1 \|2 log(\|- 1 + x) - \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+3 +--R 8+---+ 8+---+3 +-+ 8+---+6 2 8+---+ +-+ \|- 1 +--R \|- 1 log(- x \|- 1 \|2 + \|- 1 + x ) + 2\|- 1 \|2 atan(-------) +--R x +--R + +--R 8+---+3 8+---+3 +--R 8+---+ \|- 1 8+---+ \|- 1 +--R - 2\|- 1 atan(---------------) - 2\|- 1 atan(---------------) +--R +-+ 8+---+3 +-+ 8+---+3 +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R * +--R +-----------+ +---------+ +--R | +-+ | +-+ +--R \|- 2\|2 + 4 \|2\|2 + 4 +--R / +--R +-----------+ +---------+ +--R +-+ | +-+ | +-+ +--R 8\|2 \|- 2\|2 + 4 \|2\|2 + 4 +--R Type: Expression(Integer) +--E 323 + +--S 324 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +---------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ +--R ((x + 3x )\|2 - 2x - 4x )\|\|2 + 2 \|2\|2 + 4 +--R + +--R +-----------+ +----------+ +--R 6 2 +-+ 6 2 | +-+ | +-+ 2 +--R ((x + 3x )\|2 + 2x + 4x )\|- 2\|2 + 4 \|- \|2 + 2 - 8x +--R / +--R 8 +--R 8x + 8 +--R Type: Expression(Integer) +--E 324 + +)clear all + +--S 325 of 1369 +t0:=1/(x^8*(1+x^8)) +--R +--R +--R 1 +--R (1) -------- +--R 16 8 +--R x + x +--R Type: Fraction(Polynomial(Integer)) +--E 325 + +--S 326 of 1369 +r0:=(-1/7)/x^7+1/8*atan((-2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))-1/8*atan((2*x+sqrt(2+sqrt(2)))/sqrt(2-sqrt(2)))*_ + sqrt(2-sqrt(2))+1/16*log(1+x^2-x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2-sqrt(2)))*sqrt(2-sqrt(2))+1/8*_ + atan((-2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/8*atan((2*x+sqrt(2-sqrt(2)))/sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))+_ + 1/16*log(1+x^2-x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2))-_ + 1/16*log(1+x^2+x*sqrt(2+sqrt(2)))*sqrt(2+sqrt(2)) +--R +--R +--R (2) +--R +--------+ +--------+ +--R 7 | +-+ | +-+ 2 +--R - 7x \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R 7 | +-+ | +-+ 2 +--R - 7x \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R 7 | +-+ | +-+ 2 +--R 7x \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R 7 | +-+ | +-+ 2 +--R 7x \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R - +--R +----------+ +--R 7 | +-+ +--R 14x \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--R 7 | +-+ +--R 14x \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R atan(-----------------------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R 14x \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R 7 | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R - 14x \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R - 16 +--R / +--R 7 +--R 112x +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ 8+---+ +--R - 7x \|- 1 log(x\|- 1 \|2 + \|- 1 + x - 7x \|- 1 \|2 log(\|- 1 + x) +--R + +--R 7 8+---+ +-+ 8+---+ +--R 7x \|- 1 \|2 log(- \|- 1 + x) +--R + +--R 8+---+ +--R 7 8+---+ 8+---+ +-+ 8+---+2 2 7 8+---+ +-+ \|- 1 +--R 7x \|- 1 log(- x\|- 1 \|2 + \|- 1 + x + 14x \|- 1 \|2 atan(------) +--R x +--R + +--R 8+---+ 8+---+ +--R 7 8+---+ \|- 1 7 8+---+ \|- 1 +-+ +--R 14x \|- 1 atan(-------------- + 14x \|- 1 atan(-------------- - 8\|2 +--R +-+ 8+---+ +-+ 8+---+ +--R x\|2 - \|- 1 x\|2 + \|- 1 +--R / +--R 7 +-+ +--R 56x \|2 +--R Type: Union(Expression(Integer),...) +--E 327 + +--S 328 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|\|2 + 2 log(x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R \|2 \|- \|2 + 2 log(x\|- \|2 + 2 + x + 1) +--R + +--R +----------+ +----------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|- \|2 + 2 log(- x\|- \|2 + 2 + x + 1) +--R + +--R +--------+ +--------+ +--R +-+ | +-+ | +-+ 2 +--R - \|2 \|\|2 + 2 log(- x\|\|2 + 2 + x + 1) +--R + +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (2x\|2 + 4x)\|- \|2 + 2 +--R atan(---------------------------------------------------------------) +--R 2 +--R + +--R - +--R +----------+ +--R +-+ | +-+ +--R 2\|2 \|- \|2 + 2 +--R * +--R atan +--R +----------+ +--------+ +----------+ +--R +-+ | +-+ | +-+ +-+ | +-+ +--R (\|2 + 2)\|- \|2 + 2 \|\|2 + 2 + (- 2x\|2 - 4x)\|- \|2 + 2 +--R ----------------------------------------------------------------- +--R 2 +--R + +--R - +--R +--------+ +--R +-+ | +-+ +--R 2\|2 \|\|2 + 2 +--R * +--R +----------+ +--------+ +--R +-+ | +-+ +-+ | +-+ +--R ((\|2 - 2)\|- \|2 + 2 + 2x\|2 - 4x)\|\|2 + 2 +--R atan(--------------------------------------------------) +--R 2 +--R + +--R +----------+ +--------+ +--R +--------+ +-+ | +-+ +-+ | +-+ +--R +-+ | +-+ ((\|2 - 2)\|- \|2 + 2 - 2x\|2 + 4x)\|\|2 + 2 +--R 2\|2 \|\|2 + 2 atan(--------------------------------------------------) +--R 2 +--R + +--R 8+---+ 8+---+ +-+ 8+---+2 2 8+---+ +-+ 8+---+ +--R - 2\|- 1 log(x\|- 1 \|2 + \|- 1 + x ) - 2\|- 1 \|2 log(\|- 1 + x) +--R + +--R 8+---+ +-+ 8+---+ 8+---+ 8+---+ +-+ 8+---+2 2 +--R 2\|- 1 \|2 log(- \|- 1 + x) + 2\|- 1 log(- x\|- 1 \|2 + \|- 1 + x ) +--R + +--R 8+---+ 8+---+ +--R 8+---+ +-+ \|- 1 8+---+ \|- 1 +--R 4\|- 1 \|2 atan(------) + 4\|- 1 atan(--------------) +--R x +-+ 8+---+ +--R x\|2 - \|- 1 +--R + +--R 8+---+ +--R 8+---+ \|- 1 +--R 4\|- 1 atan(--------------) +--R +-+ 8+---+ +--R x\|2 + \|- 1 +--R / +--R +-+ +--R 16\|2 +--R Type: Expression(Integer) +--E 328 + +--S 329 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 329 + +)clear all + +--S 330 of 1369 +t0:=x^3*sqrt(1+x^8) +--R +--R +--R +------+ +--R 3 | 8 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1369 +r0:=1/8*asinh(x^4)+1/8*x^4*sqrt(1+x^8) +--R +--R +--R +------+ +--R 4 | 8 4 +--R x \|x + 1 + asinh(x ) +--R (2) ----------------------- +--R 8 +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 +--R (- 2x \|x + 1 + 2x + 1)log(\|x + 1 - x ) + (- 2x - x )\|x + 1 +--R + +--R 16 8 +--R 2x + 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 16x \|x + 1 - 16x - 8 +--R Type: Union(Expression(Integer),...) +--E 332 + +--S 333 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 8 4 4 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 334 + +)clear all + +--S 335 of 1369 +t0:=x*sqrt(1+x^8) +--R +--R +--R +------+ +--R | 8 +--R (1) x\|x + 1 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 1369 +--r0:=-1/3*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)+1/6*x^2*sqrt(1+x^8) +--E 336 + +--S 337 of 1369 +--a0:=integrate(t0,x) +--E 337 + +--S 338 of 1369 +--m0:=a0-r0 +--E 338 + +--S 339 of 1369 +--d0:=D(m0,x) +--E 339 + +)clear all + +--S 340 of 1369 +t0:=sqrt(1+x^8)/x +--R +--R +--R +------+ +--R | 8 +--R \|x + 1 +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 340 + +--S 341 of 1369 +r0:=-1/4*atanh(sqrt(1+x^8))+1/4*sqrt(1+x^8) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - atanh(\|x + 1 ) + \|x + 1 +--R (2) ------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2\|x + 1 +--R (3) ------------------------------------------------------ +--R 8 +--R Type: Union(Expression(Integer),...) +--E 342 + +--S 343 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 343 + +--S 344 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 344 + +)clear all + +--S 345 of 1369 +t0:=sqrt(1+x^8)/x^3 +--R +--R +--R +------+ +--R | 8 +--R \|x + 1 +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1369 +--r0:=-(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+(-1)^(1/4)*_ +-- elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2 +--E 346 + +--S 347 of 1369 +--a0:=integrate(t0,x) +--E 347 + +--S 348 of 1369 +--m0:=a0-r0 +--E 348 + +--S 349 of 1369 +--d0:=D(m0,x) +--E 349 + +)clear all + +--S 350 of 1369 +t0:=x^3*sqrt(-2+x^8) +--R +--R +--R +------+ +--R 3 | 8 +--R (1) x \|x - 2 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1369 +r0:=-1/4*atanh(x^4/sqrt(-2+x^8))+1/8*x^4*sqrt(-2+x^8) +--R +--R +--R 4 +------+ +--R x 4 | 8 +--R - 2atanh(---------) + x \|x - 2 +--R +------+ +--R | 8 +--R \|x - 2 +--R (2) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 16 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 8 +--R - 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 8x \|x - 2 - 8x + 8 +--R Type: Union(Expression(Integer),...) +--E 352 + +--S 353 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ 4 +--R | 8 4 x +--R log(\|x - 2 - x ) + atanh(---------) +--R +------+ +--R | 8 +--R \|x - 2 +--R (4) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 354 + +)clear all + +--S 355 of 1369 +t0:=x^3/sqrt(1+x^8) +--R +--R +--R 3 +--R x +--R (1) --------- +--R +------+ +--R | 8 +--R \|x + 1 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 1369 +r0:=1/4*asinh(x^4) +--R +--R +--R 4 +--R asinh(x ) +--R (2) --------- +--R 4 +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 8 4 +--R log(\|x + 1 - x ) +--R (3) - ------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 357 + +--S 358 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 8 4 4 +--R - log(\|x + 1 - x ) - asinh(x ) +--R (4) --------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 359 + +)clear all + +--S 360 of 1369 +t0:=x/sqrt(1+x^8) +--R +--R +--R x +--R (1) --------- +--R +------+ +--R | 8 +--R \|x + 1 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1369 +--r0:=-1/2*(-1)^(3/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1) +--E 361 + +--S 362 of 1369 +--a0:=integrate(t0,x) +--E 362 + +--S 363 of 1369 +--m0:=a0-r0 +--E 363 + +--S 364 of 1369 +--d0:=D(m0,x) +--E 364 + +)clear all + +--S 365 of 1369 +t0:=1/(x*sqrt(1+x^8)) +--R +--R +--R 1 +--R (1) ---------- +--R +------+ +--R | 8 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 1369 +r0:=-1/4*atanh(sqrt(1+x^8)) +--R +--R +--R +------+ +--R | 8 +--R atanh(\|x + 1 ) +--R (2) - ---------------- +--R 4 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (3) ----------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 367 + +--S 368 of 1369 +m0:=a0-r0 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (4) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1369 +t0:=1/(x^3*sqrt(1+x^8)) +--R +--R +--R 1 +--R (1) ----------- +--R +------+ +--R 3 | 8 +--R x \|x + 1 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1369 +--r0:=-1/2*(-1)^(1/4)*elliptic_e(asin((-1)^(1/4)*x^2),-1)+_ +-- 1/2*(-1)^(1/4)*elliptic_f(asin((-1)^(1/4)*x^2),-1)-1/2*sqrt(1+x^8)/x^2 +--E 371 + +--S 372 of 1369 +--a0:=integrate(t0,x) +--E 372 + +--S 373 of 1369 +--m0:=a0-r0 +--E 373 + +--S 374 of 1369 +--d0:=D(m0,x) +--E 374 + +)clear all + +--S 375 of 1369 +t0:=1/(1-x^10) +--R +--R +--R 1 +--R (1) - ------- +--R 10 +--R x - 1 +--R Type: Fraction(Polynomial(Integer)) +--E 375 + +--S 376 of 1369 +r0:=1/5*atanh(x)+1/20*atanh(1/2*x*(1-sqrt(5))/(1+x^2))*_ + (1-sqrt(5))+1/20*atanh(1/2*x*(1+sqrt(5))/(1+x^2))*_ + (1+sqrt(5))+1/20*atan(1/2*x*sqrt(10-2*sqrt(5))/(1-x^2))*_ + sqrt(10-2*sqrt(5))+1/20*atan(1/2*x*sqrt(10+2*sqrt(5))/_ + (1-x^2))*sqrt(10+2*sqrt(5)),1/5*atanh(x)-1/20*log(1+x^2-_ + x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))+1/20*_ + log(1+x^2+x*sqrt(1/2*(3-sqrt(5))))*sqrt(1/2*(3-sqrt(5)))-_ + 1/10*atan((-2*x+sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*_ + (5+sqrt(5))))*sqrt(1/2*(5-sqrt(5)))+1/10*atan((2*x+_ + sqrt(1/2*(3+sqrt(5))))*sqrt(1/10*(5+sqrt(5))))*_ + sqrt(1/2*(5-sqrt(5)))-1/20*log(1+x^2-x*sqrt(1/2*(3+sqrt(5))))*_ + sqrt(1/2*(3+sqrt(5)))+1/20*log(1+x^2+x*sqrt(1/2*(3+sqrt(5))))*_ + sqrt(1/2*(3+sqrt(5)))-1/10*atan((-2*x+sqrt(1/2*(3-sqrt(5))))*_ + sqrt(2/(5+sqrt(5))))*sqrt(1/2*(5+sqrt(5)))+1/10*_ + atan((2*x+sqrt(1/2*(3-sqrt(5))))*sqrt(2/(5+sqrt(5))))*_ + sqrt(1/2*(5+sqrt(5))) +--R +--R +--R (2) +--R [ +--R +----------+ +--R +----------+ | +-+ +--R | +-+ x\|2\|5 + 10 +--R - \|2\|5 + 10 atan(--------------) +--R 2 +--R 2x - 2 +--R + +--R +------------+ +--R +------------+ | +-+ +-+ +--R | +-+ x\|- 2\|5 + 10 +-+ x\|5 + x +--R - \|- 2\|5 + 10 atan(----------------) + (\|5 + 1)atanh(---------) +--R 2 2 +--R 2x - 2 2x + 2 +--R + +--R +-+ +--R +-+ x\|5 - x +--R (\|5 - 1)atanh(---------) + 4atanh(x) +--R 2 +--R 2x + 2 +--R / +--R 20 +--R , +--R +--R +--------+ +--R +--------+ | +-+ 2 +-+ +--R | +-+ x\|\|5 + 3 + (x + 1)\|2 +--R \|\|5 + 3 log(---------------------------) +--R +-+ +--R \|2 +--R + +--R +----------+ +--R +----------+ | +-+ 2 +-+ +--R | +-+ x\|- \|5 + 3 + (x + 1)\|2 +--R \|- \|5 + 3 log(-----------------------------) +--R +-+ +--R \|2 +--R + +--R +----------+ +--R +----------+ | +-+ 2 +-+ +--R | +-+ - x\|- \|5 + 3 + (x + 1)\|2 +--R - \|- \|5 + 3 log(-------------------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--R +--------+ | +-+ 2 +-+ +--R | +-+ - x\|\|5 + 3 + (x + 1)\|2 +--R - \|\|5 + 3 log(-----------------------------) +--R +-+ +--R \|2 +--R + +--R +--------+ +--------+ +--R +----------+ | +-+ +-+ | +-+ +--R | +-+ (\|\|5 + 3 + 2x\|2 )\|\|5 + 5 +--R 2\|- \|5 + 5 atan(---------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +--------+ +--------+ +--R +----------+ | +-+ +-+ | +-+ +--R | +-+ (\|\|5 + 3 - 2x\|2 )\|\|5 + 5 +--R - 2\|- \|5 + 5 atan(---------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +----------+ +----------+ +--R +--------+ | +-+ +-+ | +-+ +--R | +-+ (\|- \|5 + 3 + 2x\|2 )\|- \|5 + 5 +--R 2\|\|5 + 5 atan(-------------------------------------) +--R +-+ +--+ +--R \|2 \|10 +--R + +--R +----------+ +----------+ +--R +--------+ | +-+ +-+ | +-+ +--R | +-+ (\|- \|5 + 3 - 2x\|2 )\|- \|5 + 5 +-+ +--R - 2\|\|5 + 5 atan(-------------------------------------) + 4\|2 atanh(x) +--R +-+ +--+ +--R \|2 \|10 +--R / +--R +-+ +--R 20\|2 +--R ] +--R Type: Tuple(Expression(Integer)) +--E 376 + +--S 377 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 +--R + +--R - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 +--R + +--R - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x) +--R + +--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x) + 2log(x + 1) +--R + +--R - 2log(x - 1) +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 1369 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R +--------------------------------------------------------------+ +--R | 2 2 +--R \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 - 3 +--R + +--R - 10%%CE1 - 10%%CE0 - 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CE1 + (- 200%%CE0 - 20)%%CE1 - 300%%CE0 - 20%%CE0 +--R + +--R - 3 +--R + +--R - 10%%CE1 - 10%%CE0 + 2x - 1 +--R + +--R +--------------------------------------------------------------+ +--R | 2 2 +--R - \|- 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 1 +--R * +--R log +--R - +--R ROOT +--R 2 2 +--R - 300%%CD1 + (- 200%%CD0 + 20)%%CD1 - 300%%CD0 + 20%%CD0 +--R + +--R - 3 +--R + +--R - 10%%CD1 - 10%%CD0 + 2x + 1 +--R + +--R 20%%CE1 log(10%%CE1 + x) + 20%%CD1 log(10%%CD1 + x) +--R + +--R 20%%CE0 log(10%%CE0 + x) + 20%%CD0 log(10%%CD0 + x) +--R + +--R +----------+ +------------+ +--R +----------+ | +-+ +------------+ | +-+ +--R | +-+ x\|2\|5 + 10 | +-+ x\|- 2\|5 + 10 +--R \|2\|5 + 10 atan(--------------) + \|- 2\|5 + 10 atan(----------------) +--R 2 2 +--R 2x - 2 2x - 2 +--R + +--R +-+ +--R +-+ x\|5 + x +--R 2log(x + 1) - 2log(x - 1) + (- \|5 - 1)atanh(---------) +--R 2 +--R 2x + 2 +--R + +--R +-+ +--R +-+ x\|5 - x +--R (- \|5 + 1)atanh(---------) - 4atanh(x) +--R 2 +--R 2x + 2 +--R / +--R 20 +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1369 +t0:=x^4/sqrt(1-x^10) +--R +--R +--R 4 +--R x +--R (1) ------------ +--R +---------+ +--R | 10 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1369 +r0:=1/5*asin(x^5) +--R +--R +--R 5 +--R asin(x ) +--R (2) -------- +--R 5 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R | 10 +--R \|- x + 1 - 1 +--R 2atan(----------------) +--R 5 +--R x +--R (3) - ----------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 382 + +--S 383 of 1369 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | 10 +--R \|- x + 1 - 1 5 +--R - 2atan(----------------) - asin(x ) +--R 5 +--R x +--R (4) ------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 384 + +)clear all + +--S 385 of 1369 +t0:=x^4/sqrt(-2+x^10) +--R +--R +--R 4 +--R x +--R (1) ---------- +--R +-------+ +--R | 10 +--R \|x - 2 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1369 +r0:=1/5*atanh(x^5/sqrt(-2+x^10)) +--R +--R +--R 5 +--R x +--R atanh(----------) +--R +-------+ +--R | 10 +--R \|x - 2 +--R (2) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 10 5 +--R log(\|x - 2 - x ) +--R (3) - -------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 387 + +--S 388 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ 5 +--R | 10 5 x +--R - log(\|x - 2 - x ) - atanh(----------) +--R +-------+ +--R | 10 +--R \|x - 2 +--R (4) ------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 389 + +)clear all + +--S 390 of 1369 +t0:=x^5/(9+x^12) +--R +--R +--R 5 +--R x +--R (1) ------- +--R 12 +--R x + 9 +--R Type: Fraction(Polynomial(Integer)) +--E 390 + +--S 391 of 1369 +r0:=1/18*atan(1/3*x^6) +--R +--R +--R 6 +--R x +--R atan(--) +--R 3 +--R (2) -------- +--R 18 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 +--R x +--R atan(--) +--R 3 +--R (3) -------- +--R 18 +--R Type: Union(Expression(Integer),...) +--E 392 + +--S 393 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 393 + +--S 394 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 394 + +)clear all + +--S 395 of 1369 +t0:=x^5/(9-x^12) +--R +--R +--R 5 +--R x +--R (1) - ------- +--R 12 +--R x - 9 +--R Type: Fraction(Polynomial(Integer)) +--E 395 + +--S 396 of 1369 +r0:=1/18*atanh(1/3*x^6) +--R +--R +--R 6 +--R x +--R atanh(--) +--R 3 +--R (2) --------- +--R 18 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 6 +--R log(x + 3) - log(x - 3) +--R (3) ------------------------- +--R 36 +--R Type: Union(Expression(Integer),...) +--E 397 + +--S 398 of 1369 +m0:=a0-r0 +--R +--R +--R 6 +--R 6 6 x +--R log(x + 3) - log(x - 3) - 2atanh(--) +--R 3 +--R (4) -------------------------------------- +--R 36 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 399 + +)clear all + +--S 400 of 1369 +t0:=x^5*sqrt(9+x^12) +--R +--R +--R +-------+ +--R 5 | 12 +--R (1) x \|x + 9 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1369 +r0:=3/4*asinh(1/3*x^6)+1/12*x^6*sqrt(9+x^12) +--R +--R +--R +-------+ 6 +--R 6 | 12 x +--R x \|x + 9 + 9asinh(--) +--R 3 +--R (2) ------------------------- +--R 12 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 6 | 12 12 | 12 6 +--R (- 18x \|x + 9 + 18x + 81)log(\|x + 9 - x ) +--R + +--R +-------+ +--R 18 6 | 12 24 12 +--R (- 2x - 9x )\|x + 9 + 2x + 18x +--R / +--R +-------+ +--R 6 | 12 12 +--R 24x \|x + 9 - 24x - 108 +--R Type: Union(Expression(Integer),...) +--E 402 + +--S 403 of 1369 +m0:=a0-r0 +--R +--R +--R +-------+ 6 +--R | 12 6 x +--R - 3log(\|x + 9 - x ) - 3asinh(--) +--R 3 +--R (4) ------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 403 + +--S 404 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 404 + +)clear all + +--S 405 of 1369 +t0:=(a+b/x)*x^6 +--R +--R +--R 6 5 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 405 + +--S 406 of 1369 +r0:=1/6*b*x^6+1/7*a*x^7 +--R +--R +--R 1 7 1 6 +--R (2) - a x + - b x +--R 7 6 +--R Type: Polynomial(Fraction(Integer)) +--E 406 + +--S 407 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 7 6 +--R 6a x + 7b x +--R (3) ------------- +--R 42 +--R Type: Union(Expression(Integer),...) +--E 407 + +--S 408 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 409 + +)clear all + +--S 410 of 1369 +t0:=(a+b/x)*x^5 +--R +--R +--R 5 4 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 410 + +--S 411 of 1369 +r0:=1/5*b*x^5+1/6*a*x^6 +--R +--R +--R 1 6 1 5 +--R (2) - a x + - b x +--R 6 5 +--R Type: Polynomial(Fraction(Integer)) +--E 411 + +--S 412 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 6 5 +--R 5a x + 6b x +--R (3) ------------- +--R 30 +--R Type: Union(Expression(Integer),...) +--E 412 + +--S 413 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 413 + +--S 414 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 414 + +)clear all + +--S 415 of 1369 +t0:=(a+b/x)*x^4 +--R +--R +--R 4 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 415 + +--S 416 of 1369 +r0:=1/4*b*x^4+1/5*a*x^5 +--R +--R +--R 1 5 1 4 +--R (2) - a x + - b x +--R 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 416 + +--S 417 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 4 +--R 4a x + 5b x +--R (3) ------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 417 + +--S 418 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 419 + +)clear all + +--S 420 of 1369 +t0:=(a+b/x)*x^3 +--R +--R +--R 3 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 420 + +--S 421 of 1369 +r0:=1/3*b*x^3+1/4*a*x^4 +--R +--R +--R 1 4 1 3 +--R (2) - a x + - b x +--R 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 421 + +--S 422 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 3 +--R 3a x + 4b x +--R (3) ------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 422 + +--S 423 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 424 + +)clear all + +--S 425 of 1369 +t0:=(a+b/x)*x^2 +--R +--R +--R 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 425 + +--S 426 of 1369 +r0:=1/2*b*x^2+1/3*a*x^3 +--R +--R +--R 1 3 1 2 +--R (2) - a x + - b x +--R 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 426 + +--S 427 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +--R 2a x + 3b x +--R (3) ------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 427 + +--S 428 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 428 + +--S 429 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 429 + +)clear all + +--S 430 of 1369 +t0:=(a+b/x)*x +--R +--R +--R (1) a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 430 + +--S 431 of 1369 +r0:=b*x+1/2*a*x^2 +--R +--R +--R 1 2 +--R (2) - a x + b x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 431 + +--S 432 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R a x + 2b x +--R (3) ----------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 432 + +--S 433 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 433 + +--S 434 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 434 + +)clear all + +--S 435 of 1369 +t0:=a+b/x +--R +--R +--R a x + b +--R (1) ------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 435 + +--S 436 of 1369 +r0:=a*x+b*log(x) +--R +--R +--R (2) b log(x) + a x +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) b log(x) + a x +--R Type: Union(Expression(Integer),...) +--E 437 + +--S 438 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 438 + +--S 439 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 439 + +)clear all + +--S 440 of 1369 +t0:=(a+b/x)/x +--R +--R +--R a x + b +--R (1) ------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 440 + +--S 441 of 1369 +r0:=-b/x+a*log(x) +--R +--R +--R a x log(x) - b +--R (2) -------------- +--R x +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1369 +a0:=integrate(t0,x) +--R +--R +--R a x log(x) - b +--R (3) -------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 442 + +--S 443 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 443 + +--S 444 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 444 + +)clear all + +--S 445 of 1369 +t0:=(a+b/x)/x^2 +--R +--R +--R a x + b +--R (1) ------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 445 + +--S 446 of 1369 +r0:=-1/2*b/x^2-a/x +--R +--R +--R 1 +--R - a x - - b +--R 2 +--R (2) ----------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 446 + +--S 447 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 2a x - b +--R (3) ---------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 447 + +--S 448 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 448 + +--S 449 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 449 + +)clear all + +--S 450 of 1369 +t0:=(a+b/x)/x^3 +--R +--R +--R a x + b +--R (1) ------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 450 + +--S 451 of 1369 +r0:=-1/3*b/x^3-1/2*a/x^2 +--R +--R +--R 1 1 +--R - - a x - - b +--R 2 3 +--R (2) ------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 451 + +--S 452 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 3a x - 2b +--R (3) ----------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 452 + +--S 453 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 453 + +--S 454 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 454 + +)clear all + +--S 455 of 1369 +t0:=(a+b/x)/x^4 +--R +--R +--R a x + b +--R (1) ------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 455 + +--S 456 of 1369 +r0:=-1/4*b/x^4-1/3*a/x^3 +--R +--R +--R 1 1 +--R - - a x - - b +--R 3 4 +--R (2) ------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 456 + +--S 457 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 4a x - 3b +--R (3) ----------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 457 + +--S 458 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 458 + +--S 459 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 459 + +)clear all + +--S 460 of 1369 +t0:=(a+b/x)/x^5 +--R +--R +--R a x + b +--R (1) ------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 460 + +--S 461 of 1369 +r0:=-1/5*b/x^5-1/4*a/x^4 +--R +--R +--R 1 1 +--R - - a x - - b +--R 4 5 +--R (2) ------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 461 + +--S 462 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 5a x - 4b +--R (3) ----------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 462 + +--S 463 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 463 + +--S 464 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 464 + +)clear all + +--S 465 of 1369 +t0:=(a+b/x)/x^6 +--R +--R +--R a x + b +--R (1) ------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 465 + +--S 466 of 1369 +r0:=-1/6*b/x^6-1/5*a/x^5 +--R +--R +--R 1 1 +--R - - a x - - b +--R 5 6 +--R (2) ------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 466 + +--S 467 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 6a x - 5b +--R (3) ----------- +--R 6 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 467 + +--S 468 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 468 + +--S 469 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 469 + +)clear all + +--S 470 of 1369 +t0:=(a+b/x)^2*x^6 +--R +--R +--R 2 6 5 2 4 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 470 + +--S 471 of 1369 +r0:=1/5*b^2*x^5+1/3*a*b*x^6+1/7*a^2*x^7 +--R +--R +--R 1 2 7 1 6 1 2 5 +--R (2) - a x + - a b x + - b x +--R 7 3 5 +--R Type: Polynomial(Fraction(Integer)) +--E 471 + +--S 472 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 7 6 2 5 +--R 15a x + 35a b x + 21b x +--R (3) -------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 472 + +--S 473 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 473 + +--S 474 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 474 + +)clear all + +--S 475 of 1369 +t0:=(a+b/x)^2*x^5 +--R +--R +--R 2 5 4 2 3 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 475 + +--S 476 of 1369 +r0:=1/4*b^2*x^4+2/5*a*b*x^5+1/6*a^2*x^6 +--R +--R +--R 1 2 6 2 5 1 2 4 +--R (2) - a x + - a b x + - b x +--R 6 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 476 + +--S 477 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 6 5 2 4 +--R 10a x + 24a b x + 15b x +--R (3) -------------------------- +--R 60 +--R Type: Union(Expression(Integer),...) +--E 477 + +--S 478 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 479 + +)clear all + +--S 480 of 1369 +t0:=(a+b/x)^2*x^4 +--R +--R +--R 2 4 3 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 480 + +--S 481 of 1369 +r0:=1/3*b^2*x^3+1/2*a*b*x^4+1/5*a^2*x^5 +--R +--R +--R 1 2 5 1 4 1 2 3 +--R (2) - a x + - a b x + - b x +--R 5 2 3 +--R Type: Polynomial(Fraction(Integer)) +--E 481 + +--S 482 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 5 4 2 3 +--R 6a x + 15a b x + 10b x +--R (3) ------------------------- +--R 30 +--R Type: Union(Expression(Integer),...) +--E 482 + +--S 483 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 483 + +--S 484 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 484 + +)clear all + +--S 485 of 1369 +t0:=(a+b/x)^2*x^3 +--R +--R +--R 2 3 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 485 + +--S 486 of 1369 +r0:=1/2*b^2*x^2+2/3*a*b*x^3+1/4*a^2*x^4 +--R +--R +--R 1 2 4 2 3 1 2 2 +--R (2) - a x + - a b x + - b x +--R 4 3 2 +--R Type: Polynomial(Fraction(Integer)) +--E 486 + +--S 487 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 2 2 +--R 3a x + 8a b x + 6b x +--R (3) ----------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 487 + +--S 488 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 488 + +--S 489 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 489 + +)clear all + +--S 490 of 1369 +t0:=(a+b/x)^2*x^2 +--R +--R +--R 2 2 2 +--R (1) a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 490 + +--S 491 of 1369 +r0:=1/3*(a+b/x)^3*x^3/a +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (2) ---------------------------- +--R 3a +--R Type: Fraction(Polynomial(Integer)) +--E 491 + +--S 492 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +--R a x + 3a b x + 3b x +--R (3) --------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 492 + +--S 493 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R 3a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 494 + +)clear all + +--S 495 of 1369 +t0:=(a+b/x)^2*x +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 495 + +--S 496 of 1369 +r0:=2*a*b*x+1/2*a^2*x^2+b^2*log(x) +--R +--R +--R 2 2 2 +--R 2b log(x) + a x + 4a b x +--R (2) ------------------------- +--R 2 +--R Type: Expression(Integer) +--E 496 + +--S 497 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b log(x) + a x + 4a b x +--R (3) ------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 497 + +--S 498 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 499 + +)clear all + +--S 500 of 1369 +t0:=(a+b/x)^2 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 500 + +--S 501 of 1369 +r0:=-b^2/x+a^2*x+2*a*b*log(x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + a x - b +--R (2) ------------------------- +--R x +--R Type: Expression(Integer) +--E 501 + +--S 502 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a b x log(x) + a x - b +--R (3) ------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 502 + +--S 503 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 504 + +)clear all + +--S 505 of 1369 +t0:=(a+b/x)^2/x +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 505 + +--S 506 of 1369 +r0:=-1/2*b^2/x^2-2*a*b/x+a^2*log(x) +--R +--R +--R 2 2 2 +--R 2a x log(x) - 4a b x - b +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a x log(x) - 4a b x - b +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 507 + +--S 508 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 509 + +)clear all + +--S 510 of 1369 +t0:=(a+b/x)^2/x^2 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 510 + +--S 511 of 1369 +r0:=-1/3*(a+b/x)^3/b +--R +--R +--R 3 3 2 2 2 3 +--R - a x - 3a b x - 3a b x - b +--R (2) ------------------------------ +--R 3 +--R 3b x +--R Type: Fraction(Polynomial(Integer)) +--E 511 + +--S 512 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 3a x - 3a b x - b +--R (3) --------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 512 + +--S 513 of 1369 +m0:=a0-r0 +--R +--R +--R 3 +--R a +--R (4) -- +--R 3b +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 514 + +)clear all + +--S 515 of 1369 +t0:=(a+b/x)^2/x^3 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 515 + +--S 516 of 1369 +r0:=-1/4*b^2/x^4-2/3*a*b/x^3-1/2*a^2/x^2 +--R +--R +--R 1 2 2 2 1 2 +--R - - a x - - a b x - - b +--R 2 3 4 +--R (2) ------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 516 + +--S 517 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 6a x - 8a b x - 3b +--R (3) ---------------------- +--R 4 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 517 + +--S 518 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1369 +t0:=(a+b/x)^2/x^4 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 520 + +--S 521 of 1369 +r0:=-1/5*b^2/x^5-1/2*a*b/x^4-1/3*a^2/x^3 +--R +--R +--R 1 2 2 1 1 2 +--R - - a x - - a b x - - b +--R 3 2 5 +--R (2) ------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 521 + +--S 522 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 10a x - 15a b x - 6b +--R (3) ------------------------ +--R 5 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 522 + +--S 523 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1369 +t0:=(a+b/x)^2/x^5 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 525 + +--S 526 of 1369 +r0:=-1/6*b^2/x^6-2/5*a*b/x^5-1/4*a^2/x^4 +--R +--R +--R 1 2 2 2 1 2 +--R - - a x - - a b x - - b +--R 4 5 6 +--R (2) ------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 526 + +--S 527 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 15a x - 24a b x - 10b +--R (3) ------------------------- +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 527 + +--S 528 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 528 + +--S 529 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 529 + +)clear all + +--S 530 of 1369 +t0:=(a+b/x)^2/x^6 +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 530 + +--S 531 of 1369 +r0:=-1/7*b^2/x^7-1/3*a*b/x^6-1/5*a^2/x^5 +--R +--R +--R 1 2 2 1 1 2 +--R - - a x - - a b x - - b +--R 5 3 7 +--R (2) ------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 531 + +--S 532 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 21a x - 35a b x - 15b +--R (3) ------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 532 + +--S 533 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 533 + +--S 534 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 534 + +)clear all + +--S 535 of 1369 +t0:=(a+b/x)^3*x^6 +--R +--R +--R 3 6 2 5 2 4 3 3 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 535 + +--S 536 of 1369 +r0:=1/4*b^3*x^4+3/5*a*b^2*x^5+1/2*a^2*b*x^6+1/7*a^3*x^7 +--R +--R +--R 1 3 7 1 2 6 3 2 5 1 3 4 +--R (2) - a x + - a b x + - a b x + - b x +--R 7 2 5 4 +--R Type: Polynomial(Fraction(Integer)) +--E 536 + +--S 537 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 6 2 5 3 4 +--R 20a x + 70a b x + 84a b x + 35b x +--R (3) ------------------------------------- +--R 140 +--R Type: Union(Expression(Integer),...) +--E 537 + +--S 538 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 538 + +--S 539 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 539 + +)clear all + +--S 540 of 1369 +t0:=(a+b/x)^3*x^5 +--R +--R +--R 3 5 2 4 2 3 3 2 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 540 + +--S 541 of 1369 +r0:=1/3*b^3*x^3+3/4*a*b^2*x^4+3/5*a^2*b*x^5+1/6*a^3*x^6 +--R +--R +--R 1 3 6 3 2 5 3 2 4 1 3 3 +--R (2) - a x + - a b x + - a b x + - b x +--R 6 5 4 3 +--R Type: Polynomial(Fraction(Integer)) +--E 541 + +--S 542 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 5 2 4 3 3 +--R 10a x + 36a b x + 45a b x + 20b x +--R (3) ------------------------------------- +--R 60 +--R Type: Union(Expression(Integer),...) +--E 542 + +--S 543 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1369 +t0:=(a+b/x)^3*x^4 +--R +--R +--R 3 4 2 3 2 2 3 +--R (1) a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 545 + +--S 546 of 1369 +r0:=-1/4*b*(b+a*x)^4/a^2+1/5*(b+a*x)^5/a^2 +--R +--R +--R 1 5 5 3 4 4 3 2 3 1 2 3 2 1 5 +--R - a x + - a b x + a b x + - a b x - -- b +--R 5 4 2 20 +--R (2) --------------------------------------------- +--R 2 +--R a +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 546 + +--S 547 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 5 2 4 2 3 3 2 +--R 4a x + 15a b x + 20a b x + 10b x +--R (3) ------------------------------------ +--R 20 +--R Type: Union(Expression(Integer),...) +--E 547 + +--S 548 of 1369 +m0:=a0-r0 +--R +--R +--R 5 +--R b +--R (4) ---- +--R 2 +--R 20a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1369 +t0:=(a+b/x)^3*x^3 +--R +--R +--R 3 3 2 2 2 3 +--R (1) a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 550 + +--S 551 of 1369 +r0:=1/4*(a+b/x)^4*x^4/a +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R a x + 4a b x + 6a b x + 4a b x + b +--R (2) -------------------------------------- +--R 4a +--R Type: Fraction(Polynomial(Integer)) +--E 551 + +--S 552 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R a x + 4a b x + 6a b x + 4b x +--R (3) ------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1369 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) - -- +--R 4a +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1369 +t0:=(a+b/x)^3*x^2 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 555 + +--S 556 of 1369 +r0:=3*a*b^2*x+3/2*a^2*b*x^2+1/3*a^3*x^3+b^3*log(x) +--R +--R +--R 3 3 3 2 2 2 +--R 6b log(x) + 2a x + 9a b x + 18a b x +--R (2) ------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 2 2 2 +--R 6b log(x) + 2a x + 9a b x + 18a b x +--R (3) ------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 557 + +--S 558 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +)clear all + +--S 560 of 1369 +t0:=(a+b/x)^3*x +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 560 + +--S 561 of 1369 +r0:=-b^3/x+3*a^2*b*x+1/2*a^3*x^2+3*a*b^2*log(x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + a x + 6a b x - 2b +--R (2) ------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 2 2 3 +--R 6a b x log(x) + a x + 6a b x - 2b +--R (3) ------------------------------------ +--R 2x +--R Type: Union(Expression(Integer),...) +--E 562 + +--S 563 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 564 + +)clear all + +--S 565 of 1369 +t0:=(a+b/x)^3 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 565 + +--S 566 of 1369 +r0:=-1/2*b^3/x^2-3*a*b^2/x+a^3*x+3*a^2*b*log(x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2a x - 6a b x - b +--R (2) ----------------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 566 + +--S 567 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 3 2 3 +--R 6a b x log(x) + 2a x - 6a b x - b +--R (3) ----------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 567 + +--S 568 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 569 + +)clear all + +--S 570 of 1369 +t0:=(a+b/x)^3/x +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 570 + +--S 571 of 1369 +r0:=-1/3*b^3/x^3-3/2*a*b^2/x^2-3*a^2*b/x+a^3*log(x) +--R +--R +--R 3 3 2 2 2 3 +--R 6a x log(x) - 18a b x - 9a b x - 2b +--R (2) ------------------------------------- +--R 3 +--R 6x +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 6a x log(x) - 18a b x - 9a b x - 2b +--R (3) ------------------------------------- +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 572 + +--S 573 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 573 + +--S 574 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 574 + +)clear all + +--S 575 of 1369 +t0:=(a+b/x)^3/x^2 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 575 + +--S 576 of 1369 +r0:=-1/4*(a+b/x)^4/b +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (2) ---------------------------------------- +--R 4 +--R 4b x +--R Type: Fraction(Polynomial(Integer)) +--E 576 + +--S 577 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (3) ------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 577 + +--S 578 of 1369 +m0:=a0-r0 +--R +--R +--R 4 +--R a +--R (4) -- +--R 4b +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 579 + +)clear all + +--S 580 of 1369 +t0:=(a+b/x)^3/x^3 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 580 + +--S 581 of 1369 +r0:=-1/5*b^3/x^5-3/4*a*b^2/x^4-a^2*b/x^3-1/2*a^3/x^2 +--R +--R +--R 1 3 3 2 2 3 2 1 3 +--R - - a x - a b x - - a b x - - b +--R 2 4 5 +--R (2) ---------------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 581 + +--S 582 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 10a x - 20a b x - 15a b x - 4b +--R (3) ----------------------------------- +--R 5 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 582 + +--S 583 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 584 + +)clear all + +--S 585 of 1369 +t0:=(a+b/x)^3/x^4 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 585 + +--S 586 of 1369 +r0:=-1/6*b^3/x^6-3/5*a*b^2/x^5-3/4*a^2*b/x^4-1/3*a^3/x^3 +--R +--R +--R 1 3 3 3 2 2 3 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 3 4 5 6 +--R (2) ------------------------------------ +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 586 + +--S 587 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 20a x - 45a b x - 36a b x - 10b +--R (3) ------------------------------------ +--R 6 +--R 60x +--R Type: Union(Expression(Integer),...) +--E 587 + +--S 588 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 589 + +)clear all + +--S 590 of 1369 +t0:=(a+b/x)^3/x^5 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 590 + +--S 591 of 1369 +r0:=-1/7*b^3/x^7-1/2*a*b^2/x^6-3/5*a^2*b/x^5-1/4*a^3/x^4 +--R +--R +--R 1 3 3 3 2 2 1 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 4 5 2 7 +--R (2) ------------------------------------ +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 591 + +--S 592 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 35a x - 84a b x - 70a b x - 20b +--R (3) ------------------------------------ +--R 7 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 592 + +--S 593 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1369 +t0:=(a+b/x)^3/x^6 +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 595 + +--S 596 of 1369 +r0:=-1/8*b^3/x^8-3/7*a*b^2/x^7-1/2*a^2*b/x^6-1/5*a^3/x^5 +--R +--R +--R 1 3 3 1 2 2 3 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 5 2 7 8 +--R (2) ------------------------------------ +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 596 + +--S 597 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 56a x - 140a b x - 120a b x - 35b +--R (3) -------------------------------------- +--R 8 +--R 280x +--R Type: Union(Expression(Integer),...) +--E 597 + +--S 598 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 599 + +)clear all + +--S 600 of 1369 +t0:=x^4/(a+b/x) +--R +--R +--R 5 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 600 + +--S 601 of 1369 +r0:=b^4*x/a^5-1/2*b^3*x^2/a^4+1/3*b^2*x^3/a^3-1/4*b*x^4/a^2+_ + 1/5*x^5/a-b^5*log(b+a*x)/a^6 +--R +--R +--R 5 5 5 4 4 3 2 3 2 3 2 4 +--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x +--R (2) ---------------------------------------------------------------------- +--R 6 +--R 60a +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 5 4 4 3 2 3 2 3 2 4 +--R - 60b log(a x + b) + 12a x - 15a b x + 20a b x - 30a b x + 60a b x +--R (3) ---------------------------------------------------------------------- +--R 6 +--R 60a +--R Type: Union(Expression(Integer),...) +--E 602 + +--S 603 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 604 + +)clear all + +--S 605 of 1369 +t0:=x^3/(a+b/x) +--R +--R +--R 4 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 605 + +--S 606 of 1369 +r0:=-b^3*x/a^4+1/2*b^2*x^2/a^3-1/3*b*x^3/a^2+1/4*x^4/a+b^4*log(b+a*x)/a^5 +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x +--R (2) ------------------------------------------------------ +--R 5 +--R 12a +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 4 3 3 2 2 2 3 +--R 12b log(a x + b) + 3a x - 4a b x + 6a b x - 12a b x +--R (3) ------------------------------------------------------ +--R 5 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 607 + +--S 608 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1369 +t0:=x^2/(a+b/x) +--R +--R +--R 3 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 of 1369 +r0:=b^2*x/a^3-1/2*b*x^2/a^2+1/3*x^3/a-b^3*log(b+a*x)/a^4 +--R +--R +--R 3 3 3 2 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (2) -------------------------------------------- +--R 4 +--R 6a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 2 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (3) -------------------------------------------- +--R 4 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 612 + +--S 613 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1369 +t0:=x/(a+b/x) +--R +--R +--R 2 +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 615 + +--S 616 of 1369 +r0:=-b*x/a^2+1/2*x^2/a+b^2*log(b+a*x)/a^3 +--R +--R +--R 2 2 2 +--R 2b log(a x + b) + a x - 2a b x +--R (2) ------------------------------- +--R 3 +--R 2a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b log(a x + b) + a x - 2a b x +--R (3) ------------------------------- +--R 3 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 617 + +--S 618 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +)clear all + +--S 620 of 1369 +t0:=1/(a+b/x) +--R +--R +--R x +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 620 + +--S 621 of 1369 +r0:=x/a-b*log(b+a*x)/a^2 +--R +--R +--R - b log(a x + b) + a x +--R (2) ---------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 621 + +--S 622 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - b log(a x + b) + a x +--R (3) ---------------------- +--R 2 +--R a +--R Type: Union(Expression(Integer),...) +--E 622 + +--S 623 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 624 + +)clear all + +--S 625 of 1369 +t0:=1/((a+b/x)*x) +--R +--R +--R 1 +--R (1) ------- +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 625 + +--S 626 of 1369 +r0:=log(b+a*x)/a +--R +--R +--R log(a x + b) +--R (2) ------------ +--R a +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1369 +a0:=integrate(t0,x) +--R +--R +--R log(a x + b) +--R (3) ------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 627 + +--S 628 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 628 + +--S 629 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 629 + +)clear all + +--S 630 of 1369 +t0:=1/((a+b/x)*x^2) +--R +--R +--R 1 +--R (1) ---------- +--R 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 630 + +--S 631 of 1369 +r0:=-log(a+b/x)/b +--R +--R +--R a x + b +--R log(-------) +--R x +--R (2) - ------------ +--R b +--R Type: Expression(Integer) +--E 631 + +--S 632 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - log(a x + b) + log(x) +--R (3) ----------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 632 + +--S 633 of 1369 +m0:=a0-r0 +--R +--R +--R a x + b +--R - log(a x + b) + log(x) + log(-------) +--R x +--R (4) -------------------------------------- +--R b +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 634 + +)clear all + +--S 635 of 1369 +t0:=1/((a+b/x)*x^3) +--R +--R +--R 1 +--R (1) ----------- +--R 3 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 635 + +--S 636 of 1369 +r0:=(-1)/(b*x)-a*log(x)/b^2+a*log(b+a*x)/b^2 +--R +--R +--R a x log(a x + b) - a x log(x) - b +--R (2) --------------------------------- +--R 2 +--R b x +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1369 +a0:=integrate(t0,x) +--R +--R +--R a x log(a x + b) - a x log(x) - b +--R (3) --------------------------------- +--R 2 +--R b x +--R Type: Union(Expression(Integer),...) +--E 637 + +--S 638 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 639 + +)clear all + +--S 640 of 1369 +t0:=1/((a+b/x)*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R 4 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 640 + +--S 641 of 1369 +r0:=(-1/2)/(b*x^2)+a/(b^2*x)+a^2*log(x)/b^3-a^2*log(b+a*x)/b^3 +--R +--R +--R 2 2 2 2 2 +--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b +--R (2) ----------------------------------------------- +--R 3 2 +--R 2b x +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R - 2a x log(a x + b) + 2a x log(x) + 2a b x - b +--R (3) ----------------------------------------------- +--R 3 2 +--R 2b x +--R Type: Union(Expression(Integer),...) +--E 642 + +--S 643 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 644 + +)clear all + +--S 645 of 1369 +t0:=1/((a+b/x)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 645 + +--S 646 of 1369 +r0:=(-1/3)/(b*x^3)+1/2*a/(b^2*x^2)-a^2/(b^3*x)-a^3*log(x)/b^4+_ + a^3*log(b+a*x)/b^4 +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b +--R (2) -------------------------------------------------------- +--R 4 3 +--R 6b x +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 3 2 2 2 3 +--R 6a x log(a x + b) - 6a x log(x) - 6a b x + 3a b x - 2b +--R (3) -------------------------------------------------------- +--R 4 3 +--R 6b x +--R Type: Union(Expression(Integer),...) +--E 647 + +--S 648 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 649 + +)clear all + +--S 650 of 1369 +t0:=1/((a+b/x)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 5 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 650 + +--S 651 of 1369 +r0:=(-1/4)/(b*x^4)+1/3*a/(b^2*x^3)-1/2*a^2/(b^3*x^2)+a^3/(b^4*x)+_ + a^4*log(x)/b^5-a^4*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12b x +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 4 4 3 3 2 2 2 3 4 +--R - 12a x log(a x + b) + 12a x log(x) + 12a b x - 6a b x + 4a b x - 3b +--R ----------------------------------------------------------------------- +--R 5 4 +--R 12b x +--R Type: Union(Expression(Integer),...) +--E 652 + +--S 653 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1369 +t0:=1/((a+b/x)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 6 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 655 + +--S 656 of 1369 +r0:=(-1/5)/(b*x^5)+1/4*a/(b^2*x^4)-1/3*a^2/(b^3*x^3)+_ + 1/2*a^3/(b^4*x^2)-a^4/(b^5*x)-a^5*log(x)/b^6+a^5*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 5 5 4 4 3 2 3 2 3 2 +--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x +--R + +--R 4 5 +--R 15a b x - 12b +--R / +--R 6 5 +--R 60b x +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 5 4 4 3 2 3 2 3 2 +--R 60a x log(a x + b) - 60a x log(x) - 60a b x + 30a b x - 20a b x +--R + +--R 4 5 +--R 15a b x - 12b +--R / +--R 6 5 +--R 60b x +--R Type: Union(Expression(Integer),...) +--E 657 + +--S 658 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 659 + +)clear all + +--S 660 of 1369 +t0:=x^5/(a+b/x)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 660 + +--S 661 of 1369 +r0:=-6*b^5*x/a^7+5/2*b^4*x^2/a^6-4/3*b^3*x^3/a^5+3/4*b^2*x^4/a^4-_ + 2/5*b*x^5/a^3+1/6*x^6/a^2+b^7/(a^8*(b+a*x))+7*b^6*log(b+a*x)/a^8 +--R +--R +--R (2) +--R 6 7 7 7 6 6 5 2 5 4 3 4 +--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x +--R + +--R 3 4 3 2 5 2 6 7 +--R 70a b x - 210a b x - 360a b x + 60b +--R / +--R 9 8 +--R 60a x + 60a b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 7 7 7 6 6 5 2 5 4 3 4 +--R (420a b x + 420b )log(a x + b) + 10a x - 14a b x + 21a b x - 35a b x +--R + +--R 3 4 3 2 5 2 6 7 +--R 70a b x - 210a b x - 360a b x + 60b +--R / +--R 9 8 +--R 60a x + 60a b +--R Type: Union(Expression(Integer),...) +--E 662 + +--S 663 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1369 +t0:=x^4/(a+b/x)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1369 +r0:=5*b^4*x/a^6-2*b^3*x^2/a^5+b^2*x^3/a^4-1/2*b*x^4/a^3+1/5*x^5/a^2-_ + b^6/(a^7*(b+a*x))-6*b^5*log(b+a*x)/a^7 +--R +--R +--R (2) +--R 5 6 6 6 5 5 4 2 4 3 3 3 +--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x +--R + +--R 2 4 2 5 6 +--R 30a b x + 50a b x - 10b +--R / +--R 8 7 +--R 10a x + 10a b +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 6 6 5 5 4 2 4 3 3 3 +--R (- 60a b x - 60b )log(a x + b) + 2a x - 3a b x + 5a b x - 10a b x +--R + +--R 2 4 2 5 6 +--R 30a b x + 50a b x - 10b +--R / +--R 8 7 +--R 10a x + 10a b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1369 +t0:=x^3/(a+b/x)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1369 +r0:=-4*b^3*x/a^5+3/2*b^2*x^2/a^4-2/3*b*x^3/a^3+1/4*x^4/a^2+_ + b^5/(a^6*(b+a*x))+5*b^4*log(b+a*x)/a^6 +--R +--R +--R (2) +--R 4 5 5 5 4 4 3 2 3 2 3 2 +--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12b +--R / +--R 7 6 +--R 12a x + 12a b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 5 5 4 4 3 2 3 2 3 2 +--R (60a b x + 60b )log(a x + b) + 3a x - 5a b x + 10a b x - 30a b x +--R + +--R 4 5 +--R - 48a b x + 12b +--R / +--R 7 6 +--R 12a x + 12a b +--R Type: Union(Expression(Integer),...) +--E 672 + +--S 673 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +)clear all + +--S 675 of 1369 +t0:=x^2/(a+b/x)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 675 + +--S 676 of 1369 +r0:=3*b^2*x/a^4-b*x^2/a^3+1/3*x^3/a^2-b^4/(a^5*(b+a*x))-4*b^3*log(b+a*x)/a^5 +--R +--R +--R (2) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 4 4 3 3 2 2 2 3 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R ------------------------------------------------------------------------ +--R 6 5 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 677 + +--S 678 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 679 + +)clear all + +--S 680 of 1369 +t0:=x/(a+b/x)^2 +--R +--R +--R 3 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 680 + +--S 681 of 1369 +r0:=-2*b*x/a^3+1/2*x^2/a^2+b^3/(a^4*(b+a*x))+3*b^2*log(b+a*x)/a^4 +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 3 2 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ---------------------------------------------------------- +--R 5 4 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 682 + +--S 683 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1369 +t0:=1/(a+b/x)^2 +--R +--R +--R 2 +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 685 + +--S 686 of 1369 +r0:=x/a^2-b^2/(a^3*(b+a*x))-2*b*log(b+a*x)/a^3 +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) ------------------------------------------------ +--R 4 3 +--R a x + a b +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) ------------------------------------------------ +--R 4 3 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 687 + +--S 688 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 689 + +)clear all + +--S 690 of 1369 +t0:=1/((a+b/x)^2*x) +--R +--R +--R x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 690 + +--S 691 of 1369 +r0:=b/(a^2*(b+a*x))+log(b+a*x)/a^2 +--R +--R +--R (a x + b)log(a x + b) + b +--R (2) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (a x + b)log(a x + b) + b +--R (3) ------------------------- +--R 3 2 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 692 + +--S 693 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 694 + +)clear all + +--S 695 of 1369 +t0:=1/((a+b/x)^2*x^2) +--R +--R +--R 1 +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 695 + +--S 696 of 1369 +r0:=1/(b*(a+b/x)) +--R +--R +--R x +--R (2) ---------- +--R 2 +--R a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 696 + +--S 697 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------- +--R 2 +--R a x + a b +--R Type: Union(Expression(Integer),...) +--E 697 + +--S 698 of 1369 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - --- +--R a b +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1369 +t0:=1/((a+b/x)^2*x^3) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 3 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 700 + +--S 701 of 1369 +r0:=1/(b*(b+a*x))+log(x)/b^2-log(b+a*x)/b^2 +--R +--R +--R (- a x - b)log(a x + b) + (a x + b)log(x) + b +--R (2) --------------------------------------------- +--R 2 3 +--R a b x + b +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (- a x - b)log(a x + b) + (a x + b)log(x) + b +--R (3) --------------------------------------------- +--R 2 3 +--R a b x + b +--R Type: Union(Expression(Integer),...) +--E 702 + +--S 703 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 704 + +)clear all + +--S 705 of 1369 +t0:=1/((a+b/x)^2*x^4) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 4 3 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 705 + +--S 706 of 1369 +r0:=(-1)/(b^2*x)-a/(b^2*(b+a*x))-2*a*log(x)/b^3+2*a*log(b+a*x)/b^3 +--R +--R +--R 2 2 2 2 2 +--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b +--R (2) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + b x +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 2 +--R (2a x + 2a b x)log(a x + b) + (- 2a x - 2a b x)log(x) - 2a b x - b +--R (3) --------------------------------------------------------------------- +--R 3 2 4 +--R a b x + b x +--R Type: Union(Expression(Integer),...) +--E 707 + +--S 708 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 709 + +)clear all + +--S 710 of 1369 +t0:=1/((a+b/x)^2*x^5) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 5 4 2 3 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 710 + +--S 711 of 1369 +r0:=(-1/2)/(b^2*x^2)+2*a/(b^3*x)+a^2/(b^3*(b+a*x))+3*a^2*log(x)/b^4-_ + 3*a^2*log(b+a*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - b +--R / +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 3 3 2 2 2 2 +--R (- 6a x - 6a b x )log(a x + b) + (6a x + 6a b x )log(x) + 6a b x +--R + +--R 2 3 +--R 3a b x - b +--R / +--R 4 3 5 2 +--R 2a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 712 + +--S 713 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1369 +t0:=1/((a+b/x)^2*x^6) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 5 2 4 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 715 + +--S 716 of 1369 +r0:=(-1/3)/(b^2*x^3)+a/(b^3*x^2)-3*a^2/(b^4*x)-a^3/(b^4*(b+a*x))-_ + 4*a^3*log(x)/b^5+4*a^3*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - b +--R / +--R 5 4 6 3 +--R 3a b x + 3b x +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 4 4 3 3 3 3 +--R (12a x + 12a b x )log(a x + b) + (- 12a x - 12a b x )log(x) - 12a b x +--R + +--R 2 2 2 3 4 +--R - 6a b x + 2a b x - b +--R / +--R 5 4 6 3 +--R 3a b x + 3b x +--R Type: Union(Expression(Integer),...) +--E 717 + +--S 718 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 719 + +)clear all + +--S 720 of 1369 +t0:=1/((a+b/x)^2*x^7) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 6 2 5 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 720 + +--S 721 of 1369 +r0:=(-1/4)/(b^2*x^4)+2/3*a/(b^3*x^3)-3/2*a^2/(b^4*x^2)+4*a^3/(b^5*x)+_ + a^4/(b^5*(b+a*x))+5*a^4*log(x)/b^6-5*a^4*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x +--R + +--R 3 2 3 2 3 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3b +--R / +--R 6 5 7 4 +--R 12a b x + 12b x +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 5 5 4 4 4 4 +--R (- 60a x - 60a b x )log(a x + b) + (60a x + 60a b x )log(x) + 60a b x +--R + +--R 3 2 3 2 3 2 4 5 +--R 30a b x - 10a b x + 5a b x - 3b +--R / +--R 6 5 7 4 +--R 12a b x + 12b x +--R Type: Union(Expression(Integer),...) +--E 722 + +--S 723 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1369 +t0:=1/((a+b/x)^2*x^8) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 7 2 6 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 725 + +--S 726 of 1369 +r0:=(-1/5)/(b^2*x^5)+1/2*a/(b^3*x^4)-a^2/(b^4*x^3)+2*a^3/(b^5*x^2)-_ + 5*a^4/(b^6*x)-a^5/(b^6*(b+a*x))-6*a^5*log(x)/b^7+6*a^5*log(b+a*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 6 6 5 5 5 5 +--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x +--R + +--R 4 2 4 3 3 3 2 4 2 5 6 +--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b +--R / +--R 7 6 8 5 +--R 10a b x + 10b x +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 6 6 5 5 5 5 +--R (60a x + 60a b x )log(a x + b) + (- 60a x - 60a b x )log(x) - 60a b x +--R + +--R 4 2 4 3 3 3 2 4 2 5 6 +--R - 30a b x + 10a b x - 5a b x + 3a b x - 2b +--R / +--R 7 6 8 5 +--R 10a b x + 10b x +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1369 +t0:=x^4/(a+b/x)^3 +--R +--R +--R 7 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1369 +r0:=15*b^4*x/a^7-5*b^3*x^2/a^6+2*b^2*x^3/a^5-3/4*b*x^4/a^4+1/5*x^5/a^3+_ + 1/2*b^7/(a^8*(b+a*x)^2)-7*b^6/(a^8*(b+a*x))-21*b^5*log(b+a*x)/a^8 +--R +--R +--R (2) +--R 2 5 2 6 7 7 7 6 6 5 2 5 +--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b +--R / +--R 10 2 9 8 2 +--R 20a x + 40a b x + 20a b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 2 6 7 7 7 6 6 5 2 5 +--R (- 420a b x - 840a b x - 420b )log(a x + b) + 4a x - 7a b x + 14a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 35a b x + 140a b x + 500a b x + 160a b x - 130b +--R / +--R 10 2 9 8 2 +--R 20a x + 40a b x + 20a b +--R Type: Union(Expression(Integer),...) +--E 732 + +--S 733 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 1369 +t0:=x^3/(a+b/x)^3 +--R +--R +--R 6 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 735 + +--S 736 of 1369 +r0:=-10*b^3*x/a^6+3*b^2*x^2/a^5-b*x^3/a^4+1/4*x^4/a^3-_ + 1/2*b^6/(a^7*(b+a*x)^2)+6*b^5/(a^7*(b+a*x))+15*b^4*log(b+a*x)/a^7 +--R +--R +--R (2) +--R 2 4 2 5 6 6 6 5 5 4 2 4 +--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x +--R + +--R 3 3 3 2 4 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22b +--R / +--R 9 2 8 7 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 5 6 6 6 5 5 4 2 4 +--R (60a b x + 120a b x + 60b )log(a x + b) + a x - 2a b x + 5a b x +--R + +--R 3 3 3 2 4 2 5 6 +--R - 20a b x - 68a b x - 16a b x + 22b +--R / +--R 9 2 8 7 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 737 + +--S 738 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 739 + +)clear all + +--S 740 of 1369 +t0:=x^2/(a+b/x)^3 +--R +--R +--R 5 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 740 + +--S 741 of 1369 +r0:=6*b^2*x/a^5-3/2*b*x^2/a^4+1/3*x^3/a^3+1/2*b^5/(a^6*(b+a*x)^2)-_ + 5*b^4/(a^6*(b+a*x))-10*b^3*log(b+a*x)/a^6 +--R +--R +--R (2) +--R 2 3 2 4 5 5 5 4 4 3 2 3 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x +--R + +--R 2 3 2 4 5 +--R 63a b x + 6a b x - 27b +--R / +--R 8 2 7 6 2 +--R 6a x + 12a b x + 6a b +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 2 4 5 5 5 4 4 3 2 3 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x + 20a b x +--R + +--R 2 3 2 4 5 +--R 63a b x + 6a b x - 27b +--R / +--R 8 2 7 6 2 +--R 6a x + 12a b x + 6a b +--R Type: Union(Expression(Integer),...) +--E 742 + +--S 743 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 744 + +)clear all + +--S 745 of 1369 +t0:=x/(a+b/x)^3 +--R +--R +--R 4 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 745 + +--S 746 of 1369 +r0:=-3*b*x/a^4+1/2*x^2/a^3-1/2*b^4/(a^5*(b+a*x)^2)+4*b^3/(a^5*(b+a*x))+_ + 6*b^2*log(b+a*x)/a^5 +--R +--R +--R (2) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7b +--R / +--R 7 2 6 5 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 746 + +--S 747 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 4 4 4 3 3 2 2 2 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 4 +--R 2a b x + 7b +--R / +--R 7 2 6 5 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 747 + +--S 748 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 749 + +)clear all + +--S 750 of 1369 +t0:=1/(a+b/x)^3 +--R +--R +--R 3 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 750 + +--S 751 of 1369 +r0:=x/a^3+1/2*b^3/(a^4*(b+a*x)^2)-3*b^2/(a^4*(b+a*x))-3*b*log(b+a*x)/a^4 +--R +--R +--R (2) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 3 3 3 2 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R ------------------------------------------------------------------------ +--R 6 2 5 4 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 752 + +--S 753 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 753 + +--S 754 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 754 + +)clear all + +--S 755 of 1369 +t0:=1/((a+b/x)^3*x) +--R +--R +--R 2 +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 755 + +--S 756 of 1369 +r0:=-1/2*b^2/(a^3*(b+a*x)^2)+2*b/(a^3*(b+a*x))+log(b+a*x)/a^3 +--R +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (2) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (3) ------------------------------------------------- +--R 5 2 4 3 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 757 + +--S 758 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 758 + +--S 759 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 759 + +)clear all + +--S 760 of 1369 +t0:=1/((a+b/x)^3*x^2) +--R +--R +--R x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 760 + +--S 761 of 1369 +r0:=1/2/(b*(a+b/x)^2) +--R +--R +--R 2 +--R x +--R (2) ---------------------- +--R 2 2 2 3 +--R 2a b x + 4a b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 761 + +--S 762 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 2a x - b +--R (3) ---------------------- +--R 4 2 3 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 762 + +--S 763 of 1369 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R 2a b +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 764 + +)clear all + +--S 765 of 1369 +t0:=1/((a+b/x)^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 765 + +--S 766 of 1369 +r0:=(-1/2)/(a*(a+b/x)^2*x^2) +--R +--R +--R 1 +--R (2) - ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 3 2 2 2 +--R 2a x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 767 + +--S 768 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 768 + +--S 769 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 769 + +)clear all + +--S 770 of 1369 +t0:=1/((a+b/x)^3*x^4) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 4 2 3 2 2 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 770 + +--S 771 of 1369 +r0:=1/2/(b*(b+a*x)^2)+1/(b^2*(b+a*x))+log(x)/b^3-log(b+a*x)/b^3 +--R +--R +--R (2) +--R 2 2 2 2 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x) +--R + +--R 2 +--R 2a b x + 3b +--R / +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (2a x + 4a b x + 2b )log(x) +--R + +--R 2 +--R 2a b x + 3b +--R / +--R 2 3 2 4 5 +--R 2a b x + 4a b x + 2b +--R Type: Union(Expression(Integer),...) +--E 772 + +--S 773 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 773 + +--S 774 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 774 + +)clear all + +--S 775 of 1369 +t0:=1/((a+b/x)^3*x^5) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 5 2 4 2 3 3 2 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 775 + +--S 776 of 1369 +r0:=(-1)/(b^3*x)-1/2*a/(b^2*(b+a*x)^2)-2*a/(b^3*(b+a*x))-3*a*log(x)/b^4+_ + 3*a*log(b+a*x)/b^4 +--R +--R +--R (2) +--R 3 3 2 2 2 +--R (6a x + 12a b x + 6a b x)log(a x + b) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 +--R (6a x + 12a b x + 6a b x)log(a x + b) +--R + +--R 3 3 2 2 2 2 2 2 3 +--R (- 6a x - 12a b x - 6a b x)log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 3 5 2 6 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 777 + +--S 778 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 778 + +--S 779 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 779 + +)clear all + +--S 780 of 1369 +t0:=1/((a+b/x)^3*x^6) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 6 2 5 2 4 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 780 + +--S 781 of 1369 +r0:=(-1/2)/(b^3*x^2)+3*a/(b^4*x)+1/2*a^2/(b^3*(b+a*x)^2)+_ + 3*a^2/(b^4*(b+a*x))+6*a^2*log(x)/b^5-6*a^2*log(b+a*x)/b^5 +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 4 3 3 2 2 2 3 3 2 2 2 3 4 +--R (12a x + 24a b x + 12a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 4 6 3 7 2 +--R 2a b x + 4a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 782 + +--S 783 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 783 + +--S 784 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 784 + +)clear all + +--S 785 of 1369 +t0:=1/((a+b/x)^3*x^7) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 7 2 6 2 5 3 4 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 785 + +--S 786 of 1369 +r0:=(-1/3)/(b^3*x^3)+3/2*a/(b^4*x^2)-6*a^2/(b^5*x)-_ + 1/2*a^3/(b^4*(b+a*x)^2)-4*a^3/(b^5*(b+a*x))-10*a^3*log(x)/b^6+_ + 10*a^3*log(b+a*x)/b^6 +--R +--R +--R (2) +--R 5 5 4 4 3 2 3 +--R (60a x + 120a b x + 60a b x )log(a x + b) +--R + +--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2 +--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2b +--R / +--R 2 6 5 7 4 8 3 +--R 6a b x + 12a b x + 6b x +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 3 2 3 +--R (60a x + 120a b x + 60a b x )log(a x + b) +--R + +--R 5 5 4 4 3 2 3 4 4 3 2 3 2 3 2 +--R (- 60a x - 120a b x - 60a b x )log(x) - 60a b x - 90a b x - 20a b x +--R + +--R 4 5 +--R 5a b x - 2b +--R / +--R 2 6 5 7 4 8 3 +--R 6a b x + 12a b x + 6b x +--R Type: Union(Expression(Integer),...) +--E 787 + +--S 788 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 789 + +)clear all + +--S 790 of 1369 +t0:=1/((a+b/x)^3*x^8) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 7 2 6 3 5 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 790 + +--S 791 of 1369 +r0:=(-1/4)/(b^3*x^4)+a/(b^4*x^3)-3*a^2/(b^5*x^2)+10*a^3/(b^6*x)+_ + 1/2*a^4/(b^5*(b+a*x)^2)+5*a^4/(b^6*(b+a*x))+15*a^4*log(x)/b^7-_ + 15*a^4*log(b+a*x)/b^7 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 +--R (- 60a x - 120a b x - 60a b x )log(a x + b) +--R + +--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3 +--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 2 4 2 5 6 +--R - 5a b x + 2a b x - b +--R / +--R 2 7 6 8 5 9 4 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 +--R (- 60a x - 120a b x - 60a b x )log(a x + b) +--R + +--R 6 6 5 5 4 2 4 5 5 4 2 4 3 3 3 +--R (60a x + 120a b x + 60a b x )log(x) + 60a b x + 90a b x + 20a b x +--R + +--R 2 4 2 5 6 +--R - 5a b x + 2a b x - b +--R / +--R 2 7 6 8 5 9 4 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 792 + +--S 793 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1369 +t0:=1/((a+b/x)^3*x^9) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 8 2 7 3 6 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1369 +r0:=(-1/5)/(b^3*x^5)+3/4*a/(b^4*x^4)-2*a^2/(b^5*x^3)+5*a^3/(b^6*x^2)-_ + 15*a^4/(b^7*x)-1/2*a^5/(b^6*(b+a*x)^2)-6*a^5/(b^7*(b+a*x))-_ + 21*a^5*log(x)/b^8+21*a^5*log(b+a*x)/b^8 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 +--R (420a x + 840a b x + 420a b x )log(a x + b) +--R + +--R 7 7 6 6 5 2 5 6 6 5 2 5 +--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b +--R / +--R 2 8 7 9 6 10 5 +--R 20a b x + 40a b x + 20b x +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 +--R (420a x + 840a b x + 420a b x )log(a x + b) +--R + +--R 7 7 6 6 5 2 5 6 6 5 2 5 +--R (- 420a x - 840a b x - 420a b x )log(x) - 420a b x - 630a b x +--R + +--R 4 3 4 3 4 3 2 5 2 6 7 +--R - 140a b x + 35a b x - 14a b x + 7a b x - 4b +--R / +--R 2 8 7 9 6 10 5 +--R 20a b x + 40a b x + 20b x +--R Type: Union(Expression(Integer),...) +--E 797 + +--S 798 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +)clear all + +--S 800 of 1369 +t0:=x^3*sqrt(a+b/x) +--R +--R +--R +-------+ +--R 3 |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1369 +r0:=-5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/64*b^3*x*_ + sqrt(a+b/x)/a^3-5/96*b^2*x^2*sqrt(a+b/x)/a^2+1/24*b*x^3*_ + sqrt(a+b/x)/a+1/4*x^4*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 16a b x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 8a b x - 10a b x + 15b x)\|- a |------- +--R \| x +--R / +--R 3 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 802 + +--S 803 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1369 +t0:=x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R 2 |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1369 +r0:=1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-1/8*b^2*x*_ + sqrt(a+b/x)/a^2+1/12*b*x^2*sqrt(a+b/x)/a+1/3*x^3*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------- +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |------- +--R a \| x +--R --------------------------------------------------------------------] +--R 2 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1369 +t0:=x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R (1) x |------- +--R \| x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1369 +r0:=-1/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+1/4*b*x*sqrt(a+b/x)/a+_ + 1/2*x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R - b atanh(----------) + (2a x + b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R - b atan(----------------) + (2a x + b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 816 + +--S 817 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +--S 819 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 820 + +)clear all + +--S 821 of 1369 +t0:=sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R (1) |------- +--R \| x +--R Type: Expression(Integer) +--E 821 + +--S 822 of 1369 +r0:=b*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [---------------------------------------------------------, +--R +-+ +--R 2\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R b atan(----------------) + x\|- a |------- +--R a \| x +--R --------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 823 + +--S 824 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 827 + +)clear all + +--S 828 of 1369 +t0:=sqrt(a+b/x)/x +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R x +--R Type: Expression(Integer) +--E 828 + +--S 829 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (2) 2\|a atanh(----------) - 2 |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------, +--R \| x \| x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 2\|- a atan(----------) - 2 |-------] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 830 + +--S 831 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (4) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 2\|a atanh(----------) + 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 834 + +)clear all + +--S 835 of 1369 +t0:=sqrt(a+b/x)/x^2 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b +--R +--R +--R +-------+ +--R |a x + b +--R (- 2a x - 2b) |------- +--R \| x +--R (2) ----------------------- +--R 3b x +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R (- 2a x - 2b) |------- +--R \| x +--R (3) ----------------------- +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 837 + +--S 838 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 839 + +)clear all + +--S 840 of 1369 +t0:=sqrt(a+b/x)/x^3 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1369 +r0:=2/3*a*(a+b/x)^(3/2)/b^2-2/5*(a+b/x)^(5/2)/b^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x - 2a b x - 6b ) |------- +--R \| x +--R (2) -------------------------------- +--R 2 2 +--R 15b x +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x - 2a b x - 6b ) |------- +--R \| x +--R (3) -------------------------------- +--R 2 2 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 842 + +--S 843 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 844 + +)clear all + +--S 845 of 1369 +t0:=sqrt(a+b/x)/x^4 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1369 +r0:=-2/3*a^2*(a+b/x)^(3/2)/b^3+4/5*a*(a+b/x)^(5/2)/b^3-2/7*(a+b/x)^(7/2)/b^3 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |------- +--R \| x +--R (2) ---------------------------------------------- +--R 3 3 +--R 105b x +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |------- +--R \| x +--R (3) ---------------------------------------------- +--R 3 3 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 847 + +--S 848 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 849 + +)clear all + +--S 850 of 1369 +t0:=sqrt(a+b/x)/x^5 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1369 +r0:=2/3*a^3*(a+b/x)^(3/2)/b^4-6/5*a^2*(a+b/x)^(5/2)/b^4+6/7*_ + a*(a+b/x)^(7/2)/b^4-2/9*(a+b/x)^(9/2)/b^4 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |------- +--R \| x +--R (2) --------------------------------------------------------- +--R 4 4 +--R 315b x +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 70b ) |------- +--R \| x +--R (3) --------------------------------------------------------- +--R 4 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 852 + +--S 853 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1369 +t0:=sqrt(a+b/x)/x^6 +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1369 +r0:=-2/3*a^4*(a+b/x)^(3/2)/b^5+8/5*a^3*(a+b/x)^(5/2)/b^5-_ + 12/7*a^2*(a+b/x)^(7/2)/b^5+8/9*a*(a+b/x)^(9/2)/b^5-2/11*_ + (a+b/x)^(11/2)/b^5 +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |------- +--R \| x +--R ------------------------------------------------------------------------- +--R 5 5 +--R 3465b x +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 630b ) |------- +--R \| x +--R ------------------------------------------------------------------------- +--R 5 5 +--R 3465b x +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1369 +t0:=(a+b/x)^(3/2)*x^3 +--R +--R +--R +-------+ +--R 3 2 |a x + b +--R (1) (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1369 +r0:=1/4*(a+b/x)^(3/2)*x^4+3/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-_ + 3/64*b^3*x*sqrt(a+b/x)/a^2+1/32*b^2*x^2*sqrt(a+b/x)/a+_ + 1/8*b*x^3*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R 3b atanh(----------) + (16a x + 24a b x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R ------------------------------------------------------------------------- +--R 2 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (32a x + 48a b x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 128a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 3b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (16a x + 24a b x + 2a b x - 3b x)\|- a |------- +--R \| x +--R / +--R 2 +---+ +--R 64a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 862 + +--S 863 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 866 + +)clear all + +--S 867 of 1369 +t0:=(a+b/x)^(3/2)*x^2 +--R +--R +--R +-------+ +--R 2 |a x + b +--R (1) (a x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 867 + +--S 868 of 1369 +r0:=1/3*(a+b/x)^(3/2)*x^3-1/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+_ + 1/8*b^2*x*sqrt(a+b/x)/a+1/4*b*x^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 3b atanh(----------) + (8a x + 14a b x + 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 24a\|a +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 28a b x + 6b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 48a\|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 3b atan(----------------) + (8a x + 14a b x + 3b x)\|- a |------- +--R a \| x +--R -----------------------------------------------------------------------] +--R +---+ +--R 24a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 869 + +--S 870 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16a\|a +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 873 + +)clear all + +--S 874 of 1369 +t0:=(a+b/x)^(3/2)*x +--R +--R +--R +-------+ +--R |a x + b +--R (1) (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1369 +r0:=1/2*(a+b/x)^(3/2)*x^2+3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+_ + 3/4*b*x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x + 5b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x + 10b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x + 5b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 876 + +--S 877 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 4\|- a \|a +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 880 + +)clear all + +--S 881 of 1369 +t0:=(a+b/x)^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1369 +r0:=(a+b/x)^(3/2)*x+3*b*atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-3*b*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (2) 3b\|a atanh(----------) + (a x - 2b) |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R 3b\|a log(2x\|a |------- + 2a x + b) + (2a x - 4b) |------- +--R \| x \| x +--R [--------------------------------------------------------------, +--R 2 +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 3b\|- a atan(----------) + (a x - 2b) |------- ] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 883 + +--S 884 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R 3b\|a log(2x\|a |------- + 2a x + b) - 6b\|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 3b\|a atanh(----------) + 3b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 887 + +)clear all + +--S 888 of 1369 +t0:=(a+b/x)^(3/2)/x +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1369 +r0:=-2/3*(a+b/x)^(3/2)+2*a^(3/2)*atanh(sqrt(a+b/x)/sqrt(a))-2*a*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R 6a x\|a atanh(----------) + (- 8a x - 2b) |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R 3a x\|a log(2x\|a |------- + 2a x + b) + (- 8a x - 2b) |------- +--R \| x \| x +--R [------------------------------------------------------------------, +--R 3x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 6a x\|- a atan(----------) + (- 8a x - 2b) |------- +--R +---+ \| x +--R \|- a +--R ----------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 890 + +--S 891 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (4) a\|a log(2x\|a |------- + 2a x + b) - 2a\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 2a\|a atanh(----------) + 2a\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1369 +t0:=(a+b/x)^(3/2)/x^2 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1369 +r0:=-2/5*(a+b/x)^(5/2)/b +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |------- +--R \| x +--R (2) ---------------------------------- +--R 2 +--R 5b x +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |------- +--R \| x +--R (3) ---------------------------------- +--R 2 +--R 5b x +--R Type: Union(Expression(Integer),...) +--E 897 + +--S 898 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1369 +t0:=(a+b/x)^(3/2)/x^3 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1369 +r0:=2/5*a*(a+b/x)^(5/2)/b^2-2/7*(a+b/x)^(7/2)/b^2 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |------- +--R \| x +--R (2) -------------------------------------------- +--R 2 3 +--R 35b x +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |------- +--R \| x +--R (3) -------------------------------------------- +--R 2 3 +--R 35b x +--R Type: Union(Expression(Integer),...) +--E 902 + +--S 903 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1369 +t0:=(a+b/x)^(3/2)/x^4 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1369 +r0:=-2/5*a^2*(a+b/x)^(5/2)/b^3+4/7*a*(a+b/x)^(7/2)/b^3-2/9*(a+b/x)^(9/2)/b^3 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |------- +--R \| x +--R (2) ---------------------------------------------------------- +--R 3 4 +--R 315b x +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |------- +--R \| x +--R (3) ---------------------------------------------------------- +--R 3 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 907 + +--S 908 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1369 +t0:=(a+b/x)^(3/2)/x^5 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1369 +r0:=2/5*a^3*(a+b/x)^(5/2)/b^4-6/7*a^2*(a+b/x)^(7/2)/b^4+2/3*a*_ + (a+b/x)^(9/2)/b^4-2/11*(a+b/x)^(11/2)/b^4 +--R +--R +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |------- +--R \| x +--R (2) ---------------------------------------------------------------------- +--R 4 5 +--R 1155b x +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (32a x - 16a b x + 12a b x - 10a b x - 280a b x - 210b ) |------- +--R \| x +--R (3) ---------------------------------------------------------------------- +--R 4 5 +--R 1155b x +--R Type: Union(Expression(Integer),...) +--E 912 + +--S 913 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1369 +t0:=(a+b/x)^(3/2)/x^6 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1369 +r0:=-2/5*a^4*(a+b/x)^(5/2)/b^5+8/7*a^3*(a+b/x)^(7/2)/b^5-_ + 4/3*a^2*(a+b/x)^(9/2)/b^5+8/11*a*(a+b/x)^(11/2)/b^5-_ + 2/13*(a+b/x)^(13/2)/b^5 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x +--R + +--R 6 +--R - 2310b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 6 +--R 15015b x +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 2940a b x +--R + +--R 6 +--R - 2310b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 6 +--R 15015b x +--R Type: Union(Expression(Integer),...) +--E 917 + +--S 918 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +)clear all + +--S 920 of 1369 +t0:=(a+b/x)^(3/2)/x^7 +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1369 +r0:=2/5*a^5*(a+b/x)^(5/2)/b^6-10/7*a^4*(a+b/x)^(7/2)/b^6+_ + 20/9*a^3*(a+b/x)^(9/2)/b^6-20/11*a^2*(a+b/x)^(11/2)/b^6+_ + 10/13*a*(a+b/x)^(13/2)/b^6-2/15*(a+b/x)^(15/2)/b^6 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x +--R + +--R 6 7 +--R - 7392a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 6 7 +--R 45045b x +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R 512a x - 256a b x + 192a b x - 160a b x + 140a b x - 126a b x +--R + +--R 6 7 +--R - 7392a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 6 7 +--R 45045b x +--R Type: Union(Expression(Integer),...) +--E 922 + +--S 923 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1369 +t0:=(a+b/x)^(5/2)*x^3 +--R +--R +--R +-------+ +--R 2 3 2 2 |a x + b +--R (1) (a x + 2a b x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1369 +r0:=5/24*b*(a+b/x)^(3/2)*x^3+1/4*(a+b/x)^(5/2)*x^4-_ + 5/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+5/64*b^3*x*_ + sqrt(a+b/x)/a+5/32*b^2*x^2*sqrt(a+b/x) +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R - 15b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x + 136a b x + 118a b x + 15b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 192a\|a +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 272a b x + 236a b x + 30b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 384a\|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 136a b x + 118a b x + 15b x)\|- a |------- +--R \| x +--R / +--R +---+ +--R 192a\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 927 + +--S 928 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R +-+ +--R 128a\|a +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R 64a\|- a \|a +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 931 + +)clear all + +--S 932 of 1369 +t0:=(a+b/x)^(5/2)*x^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (1) (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1369 +r0:=5/12*b*(a+b/x)^(3/2)*x^2+1/3*(a+b/x)^(5/2)*x^3+5/8*b^3*_ + atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a)+5/8*b^2*x*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 15b atanh(----------) + (8a x + 26a b x + 33b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R +-+ +--R 24\|a +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 52a b x + 66b x)\|a |------- +--R \| x +--R / +--R +-+ +--R 48\|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 15b atan(----------------) + (8a x + 26a b x + 33b x)\|- a |------- +--R a \| x +--R -----------------------------------------------------------------------] +--R +---+ +--R 24\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 934 + +--S 935 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(2a x |------- + (2a x + b)\|a ) - 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 16\|a +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - 5b \|- a atanh(----------) + 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R +---+ +-+ +--R 8\|- a \|a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 938 + +)clear all + +--S 939 of 1369 +t0:=(a+b/x)^(5/2)*x +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1369 +r0:=5/4*b*(a+b/x)^(3/2)*x+1/2*(a+b/x)^(5/2)*x^2+15/4*b^2*_ + atanh(sqrt(a+b/x)/sqrt(a))*sqrt(a)-15/4*b^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 +-+ \| x 2 2 2 |a x + b +--R 15b \|a atanh(----------) + (2a x + 9a b x - 8b ) |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------ +--R 4 +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 2 +-+ +-+ |a x + b +--R 15b \|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (4a x + 18a b x - 16b ) |------- +--R \| x +--R / +--R 8 +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 +---+ \| x 2 2 2 |a x + b +--R 15b \|- a atan(----------) + (2a x + 9a b x - 8b ) |------- +--R +---+ \| x +--R \|- a +--R -------------------------------------------------------------] +--R 4 +--R Type: Union(List(Expression(Integer)),...) +--E 941 + +--S 942 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 +-+ +-+ |a x + b 2 +-+ \| x +--R 15b \|a log(2x\|a |------- + 2a x + b) - 30b \|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R 2 +-+ \| x 2 +---+ \| x +--R - 15b \|a atanh(----------) + 15b \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R (6) -------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 945 + +)clear all + +--S 946 of 1369 +t0:=(a+b/x)^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1369 +r0:=-5/3*b*(a+b/x)^(3/2)+(a+b/x)^(5/2)*x+5*a^(3/2)*b*_ + atanh(sqrt(a+b/x)/sqrt(a))-5*a*b*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x 2 2 2 |a x + b +--R 15a b x\|a atanh(----------) + (3a x - 14a b x - 2b ) |------- +--R +-+ \| x +--R \|a +--R (2) ---------------------------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R +-+ +-+ |a x + b +--R 15a b x\|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (6a x - 28a b x - 4b ) |------- +--R \| x +--R / +--R 6x +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x 2 2 2 |a x + b +--R 15a b x\|- a atan(----------) + (3a x - 14a b x - 2b ) |------- +--R +---+ \| x +--R \|- a +--R -----------------------------------------------------------------] +--R 3x +--R Type: Union(List(Expression(Integer)),...) +--E 948 + +--S 949 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R 5a b\|a log(2x\|a |------- + 2a x + b) - 10a b\|a atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (6) - 5a b\|a atanh(----------) + 5a b\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 952 + +)clear all + +--S 953 of 1369 +t0:=(a+b/x)^(5/2)/x +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1369 +r0:=-2/3*a*(a+b/x)^(3/2)-2/5*(a+b/x)^(5/2)+2*a^(5/2)*_ + atanh(sqrt(a+b/x)/sqrt(a))-2*a^2*sqrt(a+b/x) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 2 +-+ \| x 2 2 2 |a x + b +--R 30a x \|a atanh(----------) + (- 46a x - 22a b x - 6b ) |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------------ +--R 2 +--R 15x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 2 2 +-+ +-+ |a x + b +--R 15a x \|a log(2x\|a |------- + 2a x + b) +--R \| x +--R + +--R +-------+ +--R 2 2 2 |a x + b +--R (- 46a x - 22a b x - 6b ) |------- +--R \| x +--R / +--R 2 +--R 15x +--R , +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 2 +---+ \| x 2 2 2 |a x + b +--R 30a x \|- a atan(----------) + (- 46a x - 22a b x - 6b ) |------- +--R +---+ \| x +--R \|- a +--R -------------------------------------------------------------------] +--R 2 +--R 15x +--R Type: Union(List(Expression(Integer)),...) +--E 955 + +--S 956 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 +-+ +-+ |a x + b 2 +-+ \| x +--R (4) a \|a log(2x\|a |------- + 2a x + b) - 2a \|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R 2 +-+ \| x 2 +---+ \| x +--R (6) - 2a \|a atanh(----------) + 2a \|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 959 + +)clear all + +--S 960 of 1369 +t0:=(a+b/x)^(5/2)/x^2 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1369 +r0:=-2/7*(a+b/x)^(7/2)/b +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 2a x - 6a b x - 6a b x - 2b ) |------- +--R \| x +--R (2) -------------------------------------------- +--R 3 +--R 7b x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (- 2a x - 6a b x - 6a b x - 2b ) |------- +--R \| x +--R (3) -------------------------------------------- +--R 3 +--R 7b x +--R Type: Union(Expression(Integer),...) +--E 962 + +--S 963 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 964 + +)clear all + +--S 965 of 1369 +t0:=(a+b/x)^(5/2)/x^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1369 +r0:=2/7*a*(a+b/x)^(7/2)/b^2-2/9*(a+b/x)^(9/2)/b^2 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |------- +--R \| x +--R (2) ------------------------------------------------------- +--R 2 4 +--R 63b x +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (4a x - 2a b x - 30a b x - 38a b x - 14b ) |------- +--R \| x +--R (3) ------------------------------------------------------- +--R 2 4 +--R 63b x +--R Type: Union(Expression(Integer),...) +--E 967 + +--S 968 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 969 + +)clear all + +--S 970 of 1369 +t0:=(a+b/x)^(5/2)/x^4 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 6 +--R x +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1369 +r0:=-2/7*a^2*(a+b/x)^(7/2)/b^3+4/9*a*(a+b/x)^(9/2)/b^3-2/11*(a+b/x)^(11/2)/b^3 +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |------- +--R \| x +--R ----------------------------------------------------------------------- +--R 3 5 +--R 693b x +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +--R (- 16a x + 8a b x - 6a b x - 226a b x - 322a b x - 126b ) |------- +--R \| x +--R ----------------------------------------------------------------------- +--R 3 5 +--R 693b x +--R Type: Union(Expression(Integer),...) +--E 972 + +--S 973 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 974 + +)clear all + +--S 975 of 1369 +t0:=(a+b/x)^(5/2)/x^5 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 7 +--R x +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1369 +r0:=2/7*a^3*(a+b/x)^(7/2)/b^4-2/3*a^2*(a+b/x)^(9/2)/b^4+_ + 6/11*a*(a+b/x)^(11/2)/b^4-2/13*(a+b/x)^(13/2)/b^4 +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b ) +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 4 6 +--R 3003b x +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (32a x - 16a b x + 12a b x - 10a b x - 742a b x - 1134a b x - 462b ) +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 4 6 +--R 3003b x +--R Type: Union(Expression(Integer),...) +--E 977 + +--S 978 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 979 + +)clear all + +--S 980 of 1369 +t0:=(a+b/x)^(5/2)/x^6 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 8 +--R x +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1369 +r0:=-2/7*a^4*(a+b/x)^(7/2)/b^5+8/9*a^3*(a+b/x)^(9/2)/b^5-_ + 12/11*a^2*(a+b/x)^(11/2)/b^5+8/13*a*(a+b/x)^(13/2)/b^5-_ + 2/15*(a+b/x)^(15/2)/b^5 +--R +--R +--R (2) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x +--R + +--R 6 7 +--R - 14322a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 7 +--R 45045b x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 +--R - 256a x + 128a b x - 96a b x + 80a b x - 70a b x - 8946a b x +--R + +--R 6 7 +--R - 14322a b x - 6006b +--R * +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R / +--R 5 7 +--R 45045b x +--R Type: Union(Expression(Integer),...) +--E 982 + +--S 983 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 984 + +)clear all + +--S 985 of 1369 +t0:=x^3/sqrt(a+b/x) +--R +--R +--R 3 +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1369 +r0:=35/64*b^4*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-35/64*b^3*x*_ + sqrt(a+b/x)/a^4+35/96*b^2*x^2*sqrt(a+b/x)/a^3-7/24*b*x^3*_ + sqrt(a+b/x)/a^2+1/4*x^4*sqrt(a+b/x)/a +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R 105b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 105b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x - 112a b x + 140a b x - 210b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 105b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|- a |------- +--R \| x +--R / +--R 4 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 987 + +--S 988 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 991 + +)clear all + +--S 992 of 1369 +t0:=x^2/sqrt(a+b/x) +--R +--R +--R 2 +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1369 +r0:=-5/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)+5/8*b^2*x*_ + sqrt(a+b/x)/a^3-5/12*b*x^2*sqrt(a+b/x)/a^2+1/3*x^3*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) ------------------------------------------------------------------ +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |------- +--R a \| x +--R -------------------------------------------------------------------------] +--R 3 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 994 + +--S 995 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1369 +t0:=x/sqrt(a+b/x) +--R +--R +--R x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1369 +r0:=3/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-3/4*b*x*_ + sqrt(a+b/x)/a^2+1/2*x^2*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |------- +--R \| x \| x +--R [----------------------------------------------------------------------, +--R 2 +-+ +--R 8a \|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x - 3b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R 2 +---+ +--R 4a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1001 + +--S 1002 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1369 +t0:=1/sqrt(a+b/x) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1369 +r0:=-b*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+x*sqrt(a+b/x)/a +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R - b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (2) --------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------, +--R +-+ +--R 2a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R - b atan(----------------) + x\|- a |------- +--R a \| x +--R ----------------------------------------------] +--R +---+ +--R a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1008 + +--S 1009 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1012 + +)clear all + +--S 1013 of 1369 +t0:=1/(x*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ----------- +--R +-------+ +--R |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/sqrt(a) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R 2atanh(----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------) +--R \| x a +--R (3) [------------------------------------,-----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1015 + +--S 1016 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1019 + +)clear all + +--S 1020 of 1369 +t0:=1/(x^2*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 2 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1369 +r0:=-2*sqrt(a+b/x)/b +--R +--R +--R +-------+ +--R |a x + b +--R 2 |------- +--R \| x +--R (2) - ----------- +--R b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R 2 |------- +--R \| x +--R (3) - ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1022 + +--S 1023 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1024 + +)clear all + +--S 1025 of 1369 +t0:=1/(x^3*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 3 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b^2+2*a*sqrt(a+b/x)/b^2 +--R +--R +--R +-------+ +--R |a x + b +--R (4a x - 2b) |------- +--R \| x +--R (2) --------------------- +--R 2 +--R 3b x +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +--R (4a x - 2b) |------- +--R \| x +--R (3) --------------------- +--R 2 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 1027 + +--S 1028 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +)clear all + +--S 1030 of 1369 +t0:=1/(x^4*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 4 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1369 +r0:=4/3*a*(a+b/x)^(3/2)/b^3-2/5*(a+b/x)^(5/2)/b^3-2*a^2*sqrt(a+b/x)/b^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |------- +--R \| x +--R (2) ----------------------------------- +--R 3 2 +--R 15b x +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |------- +--R \| x +--R (3) ----------------------------------- +--R 3 2 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1369 +t0:=1/(x^5*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 5 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1369 +r0:=-2*a^2*(a+b/x)^(3/2)/b^4+6/5*a*(a+b/x)^(5/2)/b^4-_ + 2/7*(a+b/x)^(7/2)/b^4+2*a^3*sqrt(a+b/x)/b^4 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |------- +--R \| x +--R (2) ---------------------------------------------- +--R 4 3 +--R 35b x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |------- +--R \| x +--R (3) ---------------------------------------------- +--R 4 3 +--R 35b x +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1369 +t0:=1/(x^6*sqrt(a+b/x)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R 6 |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1369 +r0:=8/3*a^3*(a+b/x)^(3/2)/b^5-12/5*a^2*(a+b/x)^(5/2)/b^5+_ + 8/7*a*(a+b/x)^(7/2)/b^5-2/9*(a+b/x)^(9/2)/b^5-2*a^4*sqrt(a+b/x)/b^5 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |------- +--R \| x +--R (2) ------------------------------------------------------------- +--R 5 4 +--R 315b x +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +--R (- 256a x + 128a b x - 96a b x + 80a b x - 70b ) |------- +--R \| x +--R (3) ------------------------------------------------------------- +--R 5 4 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1369 +t0:=x^2/(a+b/x)^(3/2) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1369 +r0:=-35/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/a^(9/2)-2*x^3/(a*sqrt(a+b/x))+_ + 35/8*b^2*x*sqrt(a+b/x)/a^4-35/12*b*x^2*sqrt(a+b/x)/a^3+_ + 7/3*x^3*sqrt(a+b/x)/a^2 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b \| x 3 3 2 2 2 3 +-+ +--R - 105b |------- atanh(----------) + (8a x - 14a b x + 35a b x + 105b )\|a +--R \| x +-+ +--R \|a +--R ----------------------------------------------------------------------------- +--R +-------+ +--R 4 +-+ |a x + b +--R 24a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 3 |a x + b |a x + b +-+ +--R 105b |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (16a x - 28a b x + 70a b x + 210b )\|a +--R / +--R +-------+ +--R 4 +-+ |a x + b +--R 48a \|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 3 |a x + b \| x +--R - 105b |------- atan(----------------) +--R \| x a +--R + +--R 3 3 2 2 2 3 +---+ +--R (8a x - 14a b x + 35a b x + 105b )\|- a +--R / +--R +-------+ +--R 4 +---+ |a x + b +--R 24a \|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1047 + +--S 1048 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 35b log(- 2a x |------- + (2a x + b)\|a ) + 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ------------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 35b \|- a atanh(----------) - 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) ------------------------------------------------------------ +--R 4 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1051 + +)clear all + +--S 1052 of 1369 +t0:=x/(a+b/x)^(3/2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1369 +r0:=15/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-2*x^2/(a*sqrt(a+b/x))-_ + 15/4*b*x*sqrt(a+b/x)/a^3+5/2*x^2*sqrt(a+b/x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b \| x 2 2 2 +-+ +--R 15b |------- atanh(----------) + (2a x - 5a b x - 15b )\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------------------------------- +--R +-------+ +--R 3 +-+ |a x + b +--R 4a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 |a x + b |a x + b +-+ +--R 15b |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 2 2 2 +-+ +--R (4a x - 10a b x - 30b )\|a +--R / +--R +-------+ +--R 3 +-+ |a x + b +--R 8a \|a |------- +--R \| x +--R , +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 |a x + b \| x 2 2 2 +---+ +--R 15b |------- atan(----------------) + (2a x - 5a b x - 15b )\|- a +--R \| x a +--R --------------------------------------------------------------------] +--R +-------+ +--R 3 +---+ |a x + b +--R 4a \|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1054 + +--S 1055 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 15b log(2a x |------- + (2a x + b)\|a ) - 30b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 15b \|- a atanh(----------) + 15b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 3 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1369 +t0:=1/(a+b/x)^(3/2) +--R +--R +--R x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1369 +r0:=-3*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)-2*x/(a*sqrt(a+b/x))+_ + 3*x*sqrt(a+b/x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R - 3b |------- atanh(----------) + (a x + 3b)\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------------------ +--R +-------+ +--R 2 +-+ |a x + b +--R a \|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +-+ +--R 3b |------- log(- 2a x |------- + (2a x + b)\|a ) + (2a x + 6b)\|a +--R \| x \| x +--R [--------------------------------------------------------------------, +--R +-------+ +--R 2 +-+ |a x + b +--R 2a \|a |------- +--R \| x +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R - 3b |------- atan(----------------) + (a x + 3b)\|- a +--R \| x a +--R -------------------------------------------------------] +--R +-------+ +--R 2 +---+ |a x + b +--R a \|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1061 + +--S 1062 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R 3b log(- 2a x |------- + (2a x + b)\|a ) + 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R 3b\|- a atanh(----------) - 3b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1065 + +)clear all + +--S 1066 of 1369 +t0:=1/((a+b/x)^(3/2)*x) +--R +--R +--R 1 +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1369 +r0:=2*atanh(sqrt(a+b/x)/sqrt(a))/a^(3/2)+(-2)/(a*sqrt(a+b/x)) +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R 2 |------- atanh(---------- - 2\|a +--R \| x +-+ +--R \|a +--R (2) ------------------------------------ +--R +-------+ +--R +-+ |a x + b +--R a\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +-+ +--R |------- log(2a x |------- + (2a x + b)\|a ) - 2\|a +--R \| x \| x +--R [------------------------------------------------------, +--R +-------+ +--R +-+ |a x + b +--R a\|a |------- +--R \| x +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R 2 |------- atan(---------------- - 2\|- a +--R \| x a +--R -------------------------------------------] +--R +-------+ +--R +---+ |a x + b +--R a\|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1068 + +--S 1069 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 1071 + +--S 1072 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1072 + +)clear all + +--S 1073 of 1369 +t0:=1/((a+b/x)^(3/2)*x^2) +--R +--R +--R 1 +--R (1) ---------------------- +--R +-------+ +--R 2 |a x + b +--R (a x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1369 +r0:=2/(b*sqrt(a+b/x)) +--R +--R +--R 2 +--R (2) ----------- +--R +-------+ +--R |a x + b +--R b |------- +--R \| x +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) ----------- +--R +-------+ +--R |a x + b +--R b |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1075 + +--S 1076 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1077 + +)clear all + +--S 1078 of 1369 +t0:=1/((a+b/x)^(3/2)*x^3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 3 2 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1078 + +--S 1079 of 1369 +r0:=-2*a/(b^2*sqrt(a+b/x))-2*sqrt(a+b/x)/b^2 +--R +--R +--R - 4a x - 2b +--R (2) ------------- +--R +-------+ +--R 2 |a x + b +--R b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 4a x - 2b +--R (3) ------------- +--R +-------+ +--R 2 |a x + b +--R b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1080 + +--S 1081 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1081 + +--S 1082 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1082 + +)clear all + +--S 1083 of 1369 +t0:=1/((a+b/x)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 4 3 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1369 +r0:=-2/3*(a+b/x)^(3/2)/b^3+2*a^2/(b^3*sqrt(a+b/x))+4*a*sqrt(a+b/x)/b^3 +--R +--R +--R 2 2 2 +--R 16a x + 8a b x - 2b +--R (2) --------------------- +--R +-------+ +--R 3 2 |a x + b +--R 3b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 16a x + 8a b x - 2b +--R (3) --------------------- +--R +-------+ +--R 3 2 |a x + b +--R 3b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1085 + +--S 1086 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1087 + +)clear all + +--S 1088 of 1369 +t0:=1/((a+b/x)^(3/2)*x^5) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 5 4 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1088 + +--S 1089 of 1369 +r0:=2*a*(a+b/x)^(3/2)/b^4-2/5*(a+b/x)^(5/2)/b^4-2*a^3/(b^4*sqrt(a+b/x))-_ + 6*a^2*sqrt(a+b/x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (2) ---------------------------------- +--R +-------+ +--R 4 3 |a x + b +--R 5b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (3) ---------------------------------- +--R +-------+ +--R 4 3 |a x + b +--R 5b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1090 + +--S 1091 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1092 + +)clear all + +--S 1093 of 1369 +t0:=1/((a+b/x)^(3/2)*x^6) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 6 5 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1369 +r0:=-4*a^2*(a+b/x)^(3/2)/b^5+8/5*a*(a+b/x)^(5/2)/b^5-_ + 2/7*(a+b/x)^(7/2)/b^5+2*a^4/(b^5*sqrt(a+b/x))+8*a^3*sqrt(a+b/x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 256a x + 128a b x - 32a b x + 16a b x - 10b +--R (2) ----------------------------------------------- +--R +-------+ +--R 5 4 |a x + b +--R 35b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 256a x + 128a b x - 32a b x + 16a b x - 10b +--R (3) ----------------------------------------------- +--R +-------+ +--R 5 4 |a x + b +--R 35b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1095 + +--S 1096 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1097 + +)clear all + +--S 1098 of 1369 +t0:=1/((a+b/x)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R 7 6 |a x + b +--R (a x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1098 + +--S 1099 of 1369 +r0:=20/3*a^3*(a+b/x)^(3/2)/b^6-4*a^2*(a+b/x)^(5/2)/b^6+_ + 10/7*a*(a+b/x)^(7/2)/b^6-2/9*(a+b/x)^(9/2)/b^6-_ + 2*a^5/(b^6*sqrt(a+b/x))-10*a^4*sqrt(a+b/x)/b^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b +--R (2) ------------------------------------------------------------ +--R +-------+ +--R 6 5 |a x + b +--R 63b x |------- +--R \| x +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R - 512a x - 256a b x + 64a b x - 32a b x + 20a b x - 14b +--R (3) ------------------------------------------------------------ +--R +-------+ +--R 6 5 |a x + b +--R 63b x |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1100 + +--S 1101 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1102 + +)clear all + +--S 1103 of 1369 +t0:=x^2/(a+b/x)^(5/2) +--R +--R +--R 4 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1369 +r0:=-2/3*x^3/(a*(a+b/x)^(3/2))-105/8*b^3*atanh(sqrt(a+b/x)/sqrt(a))/_ + a^(11/2)-6*x^3/(a^2*sqrt(a+b/x))+105/8*b^2*x*sqrt(a+b/x)/a^5-_ + 35/4*b*x^2*sqrt(a+b/x)/a^4+7*x^3*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 4 |a x + b \| x +--R (- 315a b x - 315b ) |------- atanh(----------) +--R \| x +-+ +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|a +--R / +--R +-------+ +--R 6 5 +-+ |a x + b +--R (24a x + 24a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 3 4 |a x + b |a x + b +-+ +--R (315a b x + 315b ) |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (16a x - 36a b x + 126a b x + 840a b x + 630b )\|a +--R / +--R +-------+ +--R 6 5 +-+ |a x + b +--R (48a x + 48a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 3 4 |a x + b \| x +--R (- 315a b x - 315b ) |------- atan(----------------) +--R \| x a +--R + +--R 4 4 3 3 2 2 2 3 4 +---+ +--R (8a x - 18a b x + 63a b x + 420a b x + 315b )\|- a +--R / +--R +-------+ +--R 6 5 +---+ |a x + b +--R (24a x + 24a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1105 + +--S 1106 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 105b log(- 2a x |------- + (2a x + b)\|a ) + 210b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) -------------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 105b \|- a atanh(----------) - 105b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 5 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1369 +t0:=x/(a+b/x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1369 +r0:=-2/3*x^2/(a*(a+b/x)^(3/2))+35/4*b^2*atanh(sqrt(a+b/x)/sqrt(a))/_ + a^(9/2)-14/3*x^2/(a^2*sqrt(a+b/x))-35/4*b*x*sqrt(a+b/x)/a^4+_ + 35/6*x^2*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 3 |a x + b \| x +--R (105a b x + 105b ) |------- atanh(----------) +--R \| x +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (6a x - 21a b x - 140a b x - 105b )\|a +--R / +--R +-------+ +--R 5 4 +-+ |a x + b +--R (12a x + 12a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 3 |a x + b |a x + b +-+ +--R (105a b x + 105b ) |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (12a x - 42a b x - 280a b x - 210b )\|a +--R / +--R +-------+ +--R 5 4 +-+ |a x + b +--R (24a x + 24a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 3 |a x + b \| x +--R (105a b x + 105b ) |------- atan(----------------) +--R \| x a +--R + +--R 3 3 2 2 2 3 +---+ +--R (6a x - 21a b x - 140a b x - 105b )\|- a +--R / +--R +-------+ +--R 5 4 +---+ |a x + b +--R (12a x + 12a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1112 + +--S 1113 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 1115 + +--S 1116 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1116 + +)clear all + +--S 1117 of 1369 +t0:=1/(a+b/x)^(5/2) +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1369 +r0:=-2/3*x/(a*(a+b/x)^(3/2))-5*b*atanh(sqrt(a+b/x)/sqrt(a))/a^(7/2)-_ + 10/3*x/(a^2*sqrt(a+b/x))+5*x*sqrt(a+b/x)/a^3 +--R +--R +--R (2) +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b \| x 2 2 2 +-+ +--R (- 15a b x - 15b ) |------- atanh(----------) + (3a x + 20a b x + 15b )\|a +--R \| x +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-------+ +--R 4 3 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R 2 |a x + b |a x + b +-+ +--R (15a b x + 15b ) |------- log(- 2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R 2 2 2 +-+ +--R (6a x + 40a b x + 30b )\|a +--R / +--R +-------+ +--R 4 3 +-+ |a x + b +--R (6a x + 6a b)\|a |------- +--R \| x +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R 2 |a x + b \| x +--R (- 15a b x - 15b ) |------- atan(----------------) +--R \| x a +--R + +--R 2 2 2 +---+ +--R (3a x + 20a b x + 15b )\|- a +--R / +--R +-------+ +--R 4 3 +---+ |a x + b +--R (3a x + 3a b)\|- a |------- +--R \| x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1119 + +--S 1120 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R 5b\|- a atanh(----------) - 5b\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 3 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1123 + +)clear all + +--S 1124 of 1369 +t0:=1/((a+b/x)^(5/2)*x) +--R +--R +--R x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1369 +r0:=(-2/3)/(a*(a+b/x)^(3/2))+2*atanh(sqrt(a+b/x)/sqrt(a))/a^(5/2)+_ + (-2)/(a^2*sqrt(a+b/x)) +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b \| x +-+ +--R (6a x + 6b) |------- atanh(----------) + (- 8a x - 6b)\|a +--R \| x +-+ +--R \|a +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 3 2 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-------+ +-------+ +--R |a x + b |a x + b +-+ +--R (3a x + 3b) |------- log(2a x |------- + (2a x + b)\|a ) +--R \| x \| x +--R + +--R +-+ +--R (- 8a x - 6b)\|a +--R / +--R +-------+ +--R 3 2 +-+ |a x + b +--R (3a x + 3a b)\|a |------- +--R \| x +--R , +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b \| x +---+ +--R (6a x + 6b) |------- atan(----------------) + (- 8a x - 6b)\|- a +--R \| x a +--R -----------------------------------------------------------------] +--R +-------+ +--R 3 2 +---+ |a x + b +--R (3a x + 3a b)\|- a |------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 1126 + +--S 1127 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------- +--R 2 +---+ +-+ +--R a \|- a \|a +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1369 +t0:=1/((a+b/x)^(5/2)*x^2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1369 +r0:=2/3/(b*(a+b/x)^(3/2)) +--R +--R +--R 2x +--R (2) ------------------------ +--R +-------+ +--R 2 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2x +--R (3) ------------------------ +--R +-------+ +--R 2 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1369 +t0:=1/((a+b/x)^(5/2)*x^3) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +-------+ +--R 2 3 2 2 |a x + b +--R (a x + 2a b x + b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1369 +r0:=-2/3*a/(b^2*(a+b/x)^(3/2))+2/(b^2*sqrt(a+b/x)) +--R +--R +--R 4a x + 6b +--R (2) ------------------------ +--R +-------+ +--R 2 3 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4a x + 6b +--R (3) ------------------------ +--R +-------+ +--R 2 3 |a x + b +--R (3a b x + 3b ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1369 +t0:=1/((a+b/x)^(5/2)*x^4) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 4 3 2 2 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1369 +r0:=2/3*a^2/(b^3*(a+b/x)^(3/2))-4*a/(b^3*sqrt(a+b/x))-2*sqrt(a+b/x)/b^3 +--R +--R +--R 2 2 2 +--R - 16a x - 24a b x - 6b +--R (2) -------------------------- +--R +-------+ +--R 3 2 4 |a x + b +--R (3a b x + 3b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 16a x - 24a b x - 6b +--R (3) -------------------------- +--R +-------+ +--R 3 2 4 |a x + b +--R (3a b x + 3b x) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1369 +t0:=1/((a+b/x)^(5/2)*x^5) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 5 4 2 3 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1369 +r0:=-2/3*a^3/(b^4*(a+b/x)^(3/2))-2/3*(a+b/x)^(3/2)/b^4+_ + 6*a^2/(b^4*sqrt(a+b/x))+6*a*sqrt(a+b/x)/b^4 +--R +--R +--R 3 3 2 2 2 3 +--R 32a x + 48a b x + 12a b x - 2b +--R (2) --------------------------------- +--R +-------+ +--R 4 3 5 2 |a x + b +--R (3a b x + 3b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 32a x + 48a b x + 12a b x - 2b +--R (3) --------------------------------- +--R +-------+ +--R 4 3 5 2 |a x + b +--R (3a b x + 3b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1148 + +--S 1149 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1149 + +--S 1150 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1150 + +)clear all + +--S 1151 of 1369 +t0:=1/((a+b/x)^(5/2)*x^6) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 6 5 2 4 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1369 +r0:=2/3*a^4/(b^5*(a+b/x)^(3/2))+8/3*a*(a+b/x)^(3/2)/b^5-_ + 2/5*(a+b/x)^(5/2)/b^5-8*a^3/(b^5*sqrt(a+b/x))-12*a^2*sqrt(a+b/x)/b^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 256a x - 384a b x - 96a b x + 16a b x - 6b +--R (2) ------------------------------------------------ +--R +-------+ +--R 5 4 6 3 |a x + b +--R (15a b x + 15b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R - 256a x - 384a b x - 96a b x + 16a b x - 6b +--R (3) ------------------------------------------------ +--R +-------+ +--R 5 4 6 3 |a x + b +--R (15a b x + 15b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1153 + +--S 1154 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1155 + +)clear all + +--S 1156 of 1369 +t0:=1/((a+b/x)^(5/2)*x^7) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +-------+ +--R 2 7 6 2 5 |a x + b +--R (a x + 2a b x + b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1369 +r0:=-2/3*a^5/(b^6*(a+b/x)^(3/2))-20/3*a^2*(a+b/x)^(3/2)/b^6+_ + 2*a*(a+b/x)^(5/2)/b^6-2/7*(a+b/x)^(7/2)/b^6+_ + 10*a^4/(b^6*sqrt(a+b/x))+20*a^3*sqrt(a+b/x)/b^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 6 5 7 4 |a x + b +--R (21a b x + 21b x ) |------- +--R \| x +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +--R 512a x + 768a b x + 192a b x - 32a b x + 12a b x - 6b +--R (3) ---------------------------------------------------------- +--R +-------+ +--R 6 5 7 4 |a x + b +--R (21a b x + 21b x ) |------- +--R \| x +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1369 +t0:=(a+b/x)*x^(5/2) +--R +--R +--R 2 +-+ +--R (1) (a x + b x)\|x +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1369 +r0:=2/5*b*x^(5/2)+2/7*a*x^(7/2) +--R +--R +--R 3 2 +-+ +--R (10a x + 14b x )\|x +--R (2) --------------------- +--R 35 +--R Type: Expression(Integer) +--E 1162 + +--S 1163 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ +--R (10a x + 14b x )\|x +--R (3) --------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 1163 + +--S 1164 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1165 + +)clear all + +--S 1166 of 1369 +t0:=(a+b/x)*x^(3/2) +--R +--R +--R +-+ +--R (1) (a x + b)\|x +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1369 +r0:=2/3*b*x^(3/2)+2/5*a*x^(5/2) +--R +--R +--R 2 +-+ +--R (6a x + 10b x)\|x +--R (2) ------------------- +--R 15 +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (6a x + 10b x)\|x +--R (3) ------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 1168 + +--S 1169 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1169 + +--S 1170 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1170 + +)clear all + +--S 1171 of 1369 +t0:=(a+b/x)*x^(1/2) +--R +--R +--R +-+ +--R (a x + b)\|x +--R (1) ------------- +--R x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1369 +r0:=2/3*a*x^(3/2)+2*b*sqrt(x) +--R +--R +--R +-+ +--R (2a x + 6b)\|x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (2a x + 6b)\|x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1173 + +--S 1174 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1174 + +--S 1175 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1175 + +)clear all + +--S 1176 of 1369 +t0:=(a+b/x)/x^(1/2) +--R +--R +--R a x + b +--R (1) ------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1369 +r0:=-2*b/sqrt(x)+2*a*sqrt(x) +--R +--R +--R 2a x - 2b +--R (2) --------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2a x - 2b +--R (3) --------- +--R +-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 1178 + +--S 1179 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1179 + +--S 1180 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1180 + +)clear all + +--S 1181 of 1369 +t0:=(a+b/x)/x^(3/2) +--R +--R +--R a x + b +--R (1) ------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1369 +r0:=-2/3*b/x^(3/2)-2*a/sqrt(x) +--R +--R +--R - 6a x - 2b +--R (2) ----------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 6a x - 2b +--R (3) ----------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1369 +t0:=(a+b/x)/x^(5/2) +--R +--R +--R a x + b +--R (1) ------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1369 +r0:=-2/5*b/x^(5/2)-2/3*a/x^(3/2) +--R +--R +--R - 10a x - 6b +--R (2) ------------ +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1369 +a0:=integrate(t0,x) +--R +--R +--R - 10a x - 6b +--R (3) ------------ +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 1188 + +--S 1189 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1189 + +--S 1190 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1190 + +)clear all + +--S 1191 of 1369 +t0:=(a+b/x)^2*x^(5/2) +--R +--R +--R 2 2 2 +-+ +--R (1) (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1369 +r0:=2/3*b^2*x^(3/2)+4/5*a*b*x^(5/2)+2/7*a^2*x^(7/2) +--R +--R +--R 2 3 2 2 +-+ +--R (30a x + 84a b x + 70b x)\|x +--R (2) ------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 2 +-+ +--R (30a x + 84a b x + 70b x)\|x +--R (3) ------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1369 +t0:=(a+b/x)^2*x^(3/2) +--R +--R +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R (1) ------------------------ +--R x +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1369 +r0:=4/3*a*b*x^(3/2)+2/5*a^2*x^(5/2)+2*b^2*sqrt(x) +--R +--R +--R 2 2 2 +-+ +--R (6a x + 20a b x + 30b )\|x +--R (2) ---------------------------- +--R 15 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-+ +--R (6a x + 20a b x + 30b )\|x +--R (3) ---------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1369 +t0:=(a+b/x)^2*x^(1/2) +--R +--R +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R (1) ------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1369 +r0:=2/3*a^2*x^(3/2)-2*b^2/sqrt(x)+4*a*b*sqrt(x) +--R +--R +--R 2 2 2 +--R 2a x + 12a b x - 6b +--R (2) --------------------- +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2a x + 12a b x - 6b +--R (3) --------------------- +--R +-+ +--R 3\|x +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1369 +t0:=(a+b/x)^2/x^(1/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1369 +r0:=-2/3*b^2/x^(3/2)-4*a*b/sqrt(x)+2*a^2*sqrt(x) +--R +--R +--R 2 2 2 +--R 6a x - 12a b x - 2b +--R (2) --------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 6a x - 12a b x - 2b +--R (3) --------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1369 +t0:=(a+b/x)^2/x^(3/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1369 +r0:=-2/5*b^2/x^(5/2)-4/3*a*b/x^(3/2)-2*a^2/sqrt(x) +--R +--R +--R 2 2 2 +--R - 30a x - 20a b x - 6b +--R (2) ------------------------ +--R 2 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 30a x - 20a b x - 6b +--R (3) ------------------------ +--R 2 +-+ +--R 15x \|x +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 1369 +t0:=(a+b/x)^2/x^(5/2) +--R +--R +--R 2 2 2 +--R a x + 2a b x + b +--R (1) ------------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1369 +r0:=-2/7*b^2/x^(7/2)-4/5*a*b/x^(5/2)-2/3*a^2/x^(3/2) +--R +--R +--R 2 2 2 +--R - 70a x - 84a b x - 30b +--R (2) ------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R - 70a x - 84a b x - 30b +--R (3) ------------------------- +--R 3 +-+ +--R 105x \|x +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1369 +t0:=(a+b/x)^3*x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1369 +r0:=2*a*b^2*x^(3/2)+6/5*a^2*b*x^(5/2)+2/7*a^3*x^(7/2)+2*b^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10a x + 42a b x + 70a b x + 70b )\|x +--R (2) ---------------------------------------- +--R 35 +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (10a x + 42a b x + 70a b x + 70b )\|x +--R (3) ---------------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1369 +t0:=(a+b/x)^3*x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1369 +r0:=2*a^2*b*x^(3/2)+2/5*a^3*x^(5/2)-2*b^3/sqrt(x)+6*a*b^2*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 10a b x + 30a b x - 10b +--R (2) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 10a b x + 30a b x - 10b +--R (3) --------------------------------- +--R +-+ +--R 5\|x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1369 +t0:=(a+b/x)^3*x^(1/2) +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R (1) ---------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1369 +r0:=-2/3*b^3/x^(3/2)+2/3*a^3*x^(3/2)-6*a*b^2/sqrt(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 18a b x - 18a b x - 2b +--R (2) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2a x + 18a b x - 18a b x - 2b +--R (3) -------------------------------- +--R +-+ +--R 3x\|x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1369 +t0:=(a+b/x)^3/x^(1/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1369 +r0:=-2/5*b^3/x^(5/2)-2*a*b^2/x^(3/2)-6*a^2*b/sqrt(x)+2*a^3*sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R 10a x - 30a b x - 10a b x - 2b +--R (2) --------------------------------- +--R 2 +-+ +--R 5x \|x +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 10a x - 30a b x - 10a b x - 2b +--R (3) --------------------------------- +--R 2 +-+ +--R 5x \|x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1369 +t0:=(a+b/x)^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1369 +r0:=-2/7*b^3/x^(7/2)-6/5*a*b^2/x^(5/2)-2*a^2*b/x^(3/2)-2*a^3/sqrt(x) +--R +--R +--R 3 3 2 2 2 3 +--R - 70a x - 70a b x - 42a b x - 10b +--R (2) ------------------------------------ +--R 3 +-+ +--R 35x \|x +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 70a x - 70a b x - 42a b x - 10b +--R (3) ------------------------------------ +--R 3 +-+ +--R 35x \|x +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1369 +t0:=(a+b/x)^3/x^(5/2) +--R +--R +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ---------------------------- +--R 5 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1369 +r0:=-2/9*b^3/x^(9/2)-6/7*a*b^2/x^(7/2)-6/5*a^2*b/x^(5/2)-2/3*a^3/x^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R - 210a x - 378a b x - 270a b x - 70b +--R (2) --------------------------------------- +--R 4 +-+ +--R 315x \|x +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1369 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - 210a x - 378a b x - 270a b x - 70b +--R (3) --------------------------------------- +--R 4 +-+ +--R 315x \|x +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1369 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1369 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1369 +t0:=x^(5/2)/(a+b/x) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1369 +r0:=2/3*b^2*x^(3/2)/a^3-2/5*b*x^(5/2)/a^2+2/7*x^(7/2)/a+2*b^(7/2)*_ + atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-2*b^3*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 3 +-+ \|a \|x 3 3 2 2 2 3 +-+ +-+ +--R 210b \|b atan(--------) + (30a x - 42a b x + 70a b x - 210b )\|a \|x +--R +-+ +--R \|b +--R ----------------------------------------------------------------------- +--R 4 +-+ +--R 105a \|a +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 3 | b \| a +--R 105b |- - log(----------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (30a x - 42a b x + 70a b x - 210b )\|x +--R / +--R 4 +--R 105a +--R , +--R +-+ +-+ +--R 3 |b \|x 3 3 2 2 2 3 +-+ +--R 210b |- atan(----) + (30a x - 42a b x + 70a b x - 210b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------------------------] +--R 4 +--R 105a +--R Type: Union(List(Expression(Integer)),...) +--E 1253 + +--S 1254 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R 3 | b +-+ \| a 3 +-+ \|a \|x +--R b |- - \|a log(----------------------) - 2b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 3 +-+ |b \|x 3 +-+ \|a \|x +--R 2b \|a |- atan(----) - 2b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1257 + +)clear all + +--S 1258 of 1369 +t0:=x^(3/2)/(a+b/x) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1369 +r0:=-2/3*b*x^(3/2)/a^2+2/5*x^(5/2)/a-2*b^(5/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/a^(7/2)+2*b^2*sqrt(x)/a^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|a \|x 2 2 2 +-+ +-+ +--R - 30b \|b atan(--------) + (6a x - 10a b x + 30b )\|a \|x +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------- +--R 3 +-+ +--R 15a \|a +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 | b \| a 2 2 2 +-+ +--R 15b |- - log(------------------------) + (6a x - 10a b x + 30b )\|x +--R \| a a x + b +--R [----------------------------------------------------------------------, +--R 3 +--R 15a +--R +-+ +-+ +--R 2 |b \|x 2 2 2 +-+ +--R - 30b |- atan(----) + (6a x - 10a b x + 30b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------------] +--R 3 +--R 15a +--R Type: Union(List(Expression(Integer)),...) +--E 1260 + +--S 1261 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R b |- - \|a log(------------------------) + 2b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 2b \|a |- atan(----) + 2b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ----------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1369 +t0:=x^(1/2)/(a+b/x) +--R +--R +--R +-+ +--R x\|x +--R (1) ------- +--R a x + b +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1369 +r0:=2/3*x^(3/2)/a+2*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(5/2)-_ + 2*b*sqrt(x)/a^2 +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R 6b\|b atan(--------) + (2a x - 6b)\|a \|x +--R +-+ +--R \|b +--R (2) ------------------------------------------ +--R 2 +-+ +--R 3a \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R | b \| a +-+ +--R 3b |- - log(----------------------) + (2a x - 6b)\|x +--R \| a a x + b +--R [-----------------------------------------------------, +--R 2 +--R 3a +--R +-+ +-+ +--R |b \|x +-+ +--R 6b |- atan(----) + (2a x - 6b)\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ----------------------------------] +--R 2 +--R 3a +--R Type: Union(List(Expression(Integer)),...) +--E 1267 + +--S 1268 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R b |- - \|a log(----------------------) - 2b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 2b\|a |- atan(----) - 2b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1271 + +)clear all + +--S 1272 of 1369 +t0:=1/((a+b/x)*x^(1/2)) +--R +--R +--R x +--R (1) ------------- +--R +-+ +--R (a x + b)\|x +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1369 +r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(3/2)+2*sqrt(x)/a +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R - 2\|b atan(--------) + 2\|a \|x +--R +-+ +--R \|b +--R (2) --------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |b \|x +-+ +--R | b +-+ - 2 |- atan(---- + 2\|x +--R +---+ - 2a |- - \|x + a x - b \|a +-+ +--R | b \| a +-+ |b +--R |- - log(------------------------) + 2\|x |- +--R \| a a x + b \|a +--R [-------------------------------------------,-------------------------] +--R a a +--R Type: Union(List(Expression(Integer)),...) +--E 1274 + +--S 1275 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R |- - \|a log(------------------------) + 2\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 2\|a |- atan(----) + 2\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1278 + +)clear all + +--S 1279 of 1369 +t0:=1/((a+b/x)*x^(3/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R (a x + b)\|x +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1369 +r0:=2*atan(sqrt(a)*sqrt(x)/sqrt(b))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +-+ +--R \|a \|x +--R 2atan(--------) +--R +-+ +--R \|b +--R (2) --------------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1369 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-----+ +---+ +-+ +--R 2a b\|x + (a x - b)\|- a b \|a b \|x +--R log(----------------------------) 2atan(----------) +--R a x + b b +--R (3) [---------------------------------,-----------------] +--R +-----+ +---+ +--R \|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1281 + +--S 1282 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 2\|a \|b atan(----------) - 2\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 1369 +t0:=1/((a+b/x)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R 2 +-+ +--R (a x + b x)\|x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1369 +r0:=-2*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(3/2)+(-2)/(b*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R - 2\|a \|x atan(--------) - 2\|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R +-+ +-+ +--R b\|b \|x +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+ +--R +---+ |a +-+ a\|x +--R | a +-+ - 2 |- \|x atan(----- - 2 +--R +---+ - 2b |- - \|x + a x - b \|b +-+ +--R | a +-+ \| b |a +--R |- - \|x log(------------------------) - 2 b |- +--R \| b a x + b \|b +--R [-------------------------------------------,--------------------------] +--R +-+ +-+ +--R b\|x b\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1288 + +--S 1289 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R |- - \|b log(------------------------) + 2\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 2 |- \|b atan(----- + 2\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1292 + +)clear all + +--S 1293 of 1369 +t0:=1/((a+b/x)*x^(7/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 3 2 +-+ +--R (a x + b x )\|x +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1369 +r0:=(-2/3)/(b*x^(3/2))+2*a^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(5/2)+_ + 2*a/(b^2*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R 6a x\|a \|x atan(--------) + (6a x - 2b)\|b +--R +-+ +--R \|b +--R (2) -------------------------------------------- +--R 2 +-+ +-+ +--R 3b x\|b \|x +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R | a +-+ \| b +--R 3a x |- - \|x log(----------------------) + 6a x - 2b +--R \| b a x + b +--R [-----------------------------------------------------, +--R 2 +-+ +--R 3b x\|x +--R +-+ +-+ +--R |a +-+ a\|x +--R 6a x |- \|x atan(-----) + 6a x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R -----------------------------------] +--R 2 +-+ +--R 3b x\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1295 + +--S 1296 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R a |- - \|b log(----------------------) - 2a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 2a |- \|b atan(-----) - 2a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1369 +t0:=1/((a+b/x)*x^(9/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R 4 3 +-+ +--R (a x + b x )\|x +--R Type: Expression(Integer) +--E 1300 + +--S 1301 of 1369 +r0:=(-2/5)/(b*x^(5/2))+2/3*a/(b^2*x^(3/2))-2*a^(5/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(7/2)-2*a^2/(b^3*sqrt(x)) +--R +--R +--R +-+ +-+ +--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+ +--R - 30a x \|a \|x atan(--------) + (- 30a x + 10a b x - 6b )\|b +--R +-+ +--R \|b +--R (2) --------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 15b x \|b \|x +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 2 2 | a +-+ \| b 2 2 2 +--R 15a x |- - \|x log(------------------------) - 30a x + 10a b x - 6b +--R \| b a x + b +--R [----------------------------------------------------------------------, +--R 3 2 +-+ +--R 15b x \|x +--R +-+ +-+ +--R 2 2 |a +-+ a\|x 2 2 2 +--R - 30a x |- \|x atan(-----) - 30a x + 10a b x - 6b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R ----------------------------------------------------] +--R 3 2 +-+ +--R 15b x \|x +--R Type: Union(List(Expression(Integer)),...) +--E 1302 + +--S 1303 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R a |- - \|b log(------------------------) + 2a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 2a |- \|b atan(-----) + 2a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1305 + +--S 1306 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1306 + +)clear all + +--S 1307 of 1369 +t0:=x^(5/2)/(a+b/x)^2 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1369 +r0:=3*b^2*x^(3/2)/a^4-9/5*b*x^(5/2)/a^3+9/7*x^(7/2)/a^2-x^(9/2)/_ + (a*(b+a*x))+9*b^(7/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(11/2)-_ + 9*b^3*sqrt(x)/a^5 +--R +--R +--R (2) +--R +-+ +-+ +--R 3 4 +-+ \|a \|x +--R (315a b x + 315b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|a \|x +--R / +--R 6 5 +-+ +--R (35a x + 35a b)\|a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 3 4 | b \| a +--R (315a b x + 315b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (20a x - 36a b x + 84a b x - 420a b x - 630b )\|x +--R / +--R 6 5 +--R 70a x + 70a b +--R , +--R +--R +-+ +-+ +--R 3 4 |b \|x +--R (315a b x + 315b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b )\|x +--R / +--R 6 5 +--R 35a x + 35a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1309 + +--S 1310 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R 3 | b +-+ \| a 3 +-+ \|a \|x +--R 9b |- - \|a log(----------------------) - 18b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 3 +-+ |b \|x 3 +-+ \|a \|x +--R 9b \|a |- atan(----) - 9b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 5 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1313 + +)clear all + +--S 1314 of 1369 +t0:=x^(3/2)/(a+b/x)^2 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1369 +r0:=-7/3*b*x^(3/2)/a^3+7/5*x^(5/2)/a^2-x^(7/2)/(a*(b+a*x))-_ + 7*b^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)+7*b^2*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 3 +-+ \|a \|x +--R (- 105a b x - 105b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (6a x - 14a b x + 70a b x + 105b )\|a \|x +--R / +--R 5 4 +-+ +--R (15a x + 15a b)\|a +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 3 | b \| a +--R (105a b x + 105b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (12a x - 28a b x + 140a b x + 210b )\|x +--R / +--R 5 4 +--R 30a x + 30a b +--R , +--R +--R +-+ +-+ +--R 2 3 |b \|x +--R (- 105a b x - 105b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (6a x - 14a b x + 70a b x + 105b )\|x +--R / +--R 5 4 +--R 15a x + 15a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1316 + +--S 1317 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R 7b |- - \|a log(------------------------) + 14b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 7b \|a |- atan(----) + 7b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ----------------------------------------------- +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1369 +t0:=x^(1/2)/(a+b/x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------ +--R 2 2 2 +--R a x + 2a b x + b +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1369 +r0:=5/3*x^(3/2)/a^2-x^(5/2)/(a*(b+a*x))+5*b^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/a^(7/2)-5*b*sqrt(x)/a^3 +--R +--R +--R +-+ +-+ +--R 2 +-+ \|a \|x 2 2 2 +-+ +-+ +--R (15a b x + 15b )\|b atan(--------) + (2a x - 10a b x - 15b )\|a \|x +--R +-+ +--R \|b +--R (2) --------------------------------------------------------------------- +--R 4 3 +-+ +--R (3a x + 3a b)\|a +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 2 | b \| a +--R (15a b x + 15b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 2 2 2 +-+ +--R (4a x - 20a b x - 30b )\|x +--R / +--R 4 3 +--R 6a x + 6a b +--R , +--R +-+ +-+ +--R 2 |b \|x 2 2 2 +-+ +--R (15a b x + 15b ) |- atan(----) + (2a x - 10a b x - 15b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -------------------------------------------------------------] +--R 4 3 +--R 3a x + 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 1323 + +--S 1324 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 5b |- - \|a log(----------------------) - 10b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 5b\|a |- atan(----) - 5b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1327 + +)clear all + +--S 1328 of 1369 +t0:=1/((a+b/x)^2*x^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1369 +r0:=-x^(3/2)/(a*(b+a*x))-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*_ + sqrt(b)/a^(5/2)+3*sqrt(x)/a^2 +--R +--R +--R +-+ +-+ +--R +-+ \|a \|x +-+ +-+ +--R (- 3a x - 3b)\|b atan(--------) + (2a x + 3b)\|a \|x +--R +-+ +--R \|b +--R (2) ----------------------------------------------------- +--R 3 2 +-+ +--R (a x + a b)\|a +--R Type: Expression(Integer) +--E 1329 + +--S 1330 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R | b \| a +-+ +--R (3a x + 3b) |- - log(------------------------) + (4a x + 6b)\|x +--R \| a a x + b +--R [----------------------------------------------------------------, +--R 3 2 +--R 2a x + 2a b +--R +-+ +-+ +--R |b \|x +-+ +--R (- 3a x - 3b) |- atan(----) + (2a x + 3b)\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ---------------------------------------------] +--R 3 2 +--R a x + a b +--R Type: Union(List(Expression(Integer)),...) +--E 1330 + +--S 1331 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 3 |- - \|a log(------------------------ + 6\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1332 + +--S 1333 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 3\|a |- atan(----) + 3\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1369 +t0:=1/((a+b/x)^2*x^(3/2)) +--R +--R +--R x +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1369 +r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*sqrt(b))-sqrt(x)/(a*(b+a*x)) +--R +--R +--R +-+ +-+ +--R \|a \|x +-+ +-+ +-+ +--R (a x + b)atan(--------) - \|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a x + a b)\|a \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (a x - b)\|- a b +-----+ +-+ +--R (a x + b)log(----------------------------) - 2\|- a b \|x +--R a x + b +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a x + 2a b)\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (a x + b)atan(----------) - \|a b \|x +--R b +--R --------------------------------------] +--R 2 +---+ +--R (a x + a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1337 + +--S 1338 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +--S 1340 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R a\|a \|b \|a b +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1341 + +)clear all + +--S 1342 of 1369 +t0:=1/((a+b/x)^2*x^(5/2)) +--R +--R +--R 1 +--R (1) ------------------------ +--R 2 2 2 +-+ +--R (a x + 2a b x + b )\|x +--R Type: Expression(Integer) +--E 1342 + +--S 1343 of 1369 +r0:=atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(3/2)*sqrt(a))+sqrt(x)/(b*(b+a*x)) +--R +--R +--R +-+ +-+ +--R \|a \|x +-+ +-+ +-+ +--R (a x + b)atan(--------) + \|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 +-+ +-+ +--R (a b x + b )\|a \|b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-----+ +--R 2a b\|x + (a x - b)\|- a b +-----+ +-+ +--R (a x + b)log(----------------------------) + 2\|- a b \|x +--R a x + b +--R [----------------------------------------------------------, +--R 2 +-----+ +--R (2a b x + 2b )\|- a b +--R +---+ +-+ +--R \|a b \|x +---+ +-+ +--R (a x + b)atan(----------) + \|a b \|x +--R b +--R --------------------------------------] +--R 2 +---+ +--R (a b x + b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 1344 + +--S 1345 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R b\|a \|b \|a b +--R Type: Expression(Integer) +--E 1347 + +--S 1348 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1348 + +)clear all + +--S 1349 of 1369 +t0:=1/((a+b/x)^2*x^(7/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R 2 3 2 2 +-+ +--R (a x + 2a b x + b x)\|x +--R Type: Expression(Integer) +--E 1349 + +--S 1350 of 1369 +r0:=-3*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(5/2)+(-3)/_ + (b^2*sqrt(x))+1/(b*(b+a*x)*sqrt(x)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|a \|x +-+ +--R (- 3a x - 3b)\|a \|x atan(--------) + (- 3a x - 2b)\|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------- +--R 2 3 +-+ +-+ +--R (a b x + b )\|b \|x +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R | a +-+ \| b +--R (3a x + 3b) |- - \|x log(------------------------) - 6a x - 4b +--R \| b a x + b +--R [--------------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x + 2b )\|x +--R +-+ +-+ +--R |a +-+ a\|x +--R (- 3a x - 3b) |- \|x atan(-----) - 3a x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R --------------------------------------------] +--R 2 3 +-+ +--R (a b x + b )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1351 + +--S 1352 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 3 |- - \|b log(------------------------ + 6\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1352 + +--S 1353 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 3 |- \|b atan(----- + 3\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1354 + +--S 1355 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1355 + +)clear all + +--S 1356 of 1369 +t0:=1/((a+b/x)^2*x^(9/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 4 3 2 2 +-+ +--R (a x + 2a b x + b x )\|x +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1369 +r0:=(-5/3)/(b^2*x^(3/2))+1/(b*x^(3/2)*(b+a*x))+5*a^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(7/2)+5*a/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|a \|x 2 2 2 +-+ +--R (15a x + 15a b x)\|a \|x atan(--------) + (15a x + 10a b x - 2b )\|b +--R +-+ +--R \|b +--R ----------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x + 3b x)\|b \|x +--R Type: Expression(Integer) +--E 1357 + +--S 1358 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R 2 2 | a +-+ \| b 2 2 +--R (15a x + 15a b x) |- - \|x log(----------------------) + 30a x +--R \| b a x + b +--R + +--R 2 +--R 20a b x - 4b +--R / +--R 3 2 4 +-+ +--R (6a b x + 6b x)\|x +--R , +--R +-+ +-+ +--R 2 2 |a +-+ a\|x 2 2 2 +--R (15a x + 15a b x) |- \|x atan(-----) + 15a x + 10a b x - 2b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R --------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x + 3b x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 1358 + +--S 1359 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 5a |- - \|b log(----------------------) - 10a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1359 + +--S 1360 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 5a |- \|b atan(-----) - 5a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1362 + +)clear all + +--S 1363 of 1369 +t0:=1/((a+b/x)^2*x^(11/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 5 4 2 3 +-+ +--R (a x + 2a b x + b x )\|x +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1369 +r0:=(-7/5)/(b^2*x^(5/2))+7/3*a/(b^3*x^(3/2))+1/(b*x^(5/2)*(b+a*x))-_ + 7*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(9/2)-7*a^2/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 +-+ +-+ \|a \|x +--R (- 105a x - 105a b x )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 105a x - 70a b x + 14a b x - 6b )\|b +--R / +--R 4 3 5 2 +-+ +-+ +--R (15a b x + 15b x )\|b \|x +--R Type: Expression(Integer) +--E 1364 + +--S 1365 of 1369 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 3 3 2 2 | a +-+ \| b 3 3 +--R (105a x + 105a b x ) |- - \|x log(------------------------) - 210a x +--R \| b a x + b +--R + +--R 2 2 2 3 +--R - 140a b x + 28a b x - 12b +--R / +--R 4 3 5 2 +-+ +--R (30a b x + 30b x )\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 |a +-+ a\|x 3 3 2 2 +--R (- 105a x - 105a b x ) |- \|x atan(-----) - 105a x - 70a b x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 2 3 +--R 14a b x - 6b +--R / +--R 4 3 5 2 +-+ +--R (15a b x + 15b x )\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1365 + +--S 1366 of 1369 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R 7a |- - \|b log(------------------------) + 14a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R 4 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1369 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1367 + +--S 1368 of 1369 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 7a |- \|b atan(-----) + 7a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ------------------------------------------------ +--R 4 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1369 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1369 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4g.input.pamphlet b/src/input/rich4g.input.pamphlet new file mode 100644 index 0000000..845cb44 --- /dev/null +++ b/src/input/rich4g.input.pamphlet @@ -0,0 +1,29082 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4g.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 188 matching answers. +\item 98 cases where Axiom differs from Rubi +\item 52 cases where Axiom supplied 2 results. +\item 24 cases that Axiom failed to integrate. +\item 2 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4g.output +)spool rich4g.output +)set message test on +)set message auto off +)clear all + + +--S 1 of 1379 +t0:=x^(3/2)/(a+b/x)^3 +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1379 +r0:=-21/4*b*x^(3/2)/a^4+63/20*x^(5/2)/a^3-1/2*x^(9/2)/(a*(b+a*x)^2)-_ + 9/4*x^(7/2)/(a^2*(b+a*x))-63/4*b^(5/2)*atan(sqrt(a)*sqrt(x)/_ + sqrt(b))/a^(11/2)+63/4*b^2*sqrt(x)/a^5 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 4 +-+ \|a \|x +--R (- 315a b x - 630a b x - 315b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|a \|x +--R / +--R 7 2 6 5 2 +-+ +--R (20a x + 40a b x + 20a b )\|a +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 2 2 3 4 | b \| a +--R (315a b x + 630a b x + 315b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (16a x - 48a b x + 336a b x + 1050a b x + 630b )\|x +--R / +--R 7 2 6 5 2 +--R 40a x + 80a b x + 40a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 4 |b \|x +--R (- 315a b x - 630a b x - 315b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b )\|x +--R / +--R 7 2 6 5 2 +--R 20a x + 40a b x + 20a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 3 + +--S 4 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R 2 | b +-+ \| a 2 +-+ \|a \|x +--R 63b |- - \|a log(------------------------) + 126b \|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 +-+ |b \|x 2 +-+ \|a \|x +--R - 63b \|a |- atan(----) + 63b \|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) ------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 7 + +)clear all + +--S 8 of 1379 +t0:=x^(1/2)/(a+b/x)^3 +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------------------------- +--R 3 3 2 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Expression(Integer) +--E 8 + +--S 9 of 1379 +r0:=35/12*x^(3/2)/a^3-1/2*x^(7/2)/(a*(b+a*x)^2)-7/4*x^(5/2)/(a^2*(b+a*x))+_ + 35/4*b^(3/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/a^(9/2)-35/4*b*sqrt(x)/a^4 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 3 +-+ \|a \|x +--R (105a b x + 210a b x + 105b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +-+ +--R (8a x - 56a b x - 175a b x - 105b )\|a \|x +--R / +--R 6 2 5 4 2 +-+ +--R (12a x + 24a b x + 12a b )\|a +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +--R 2 2 2 3 | b \| a +--R (105a b x + 210a b x + 105b ) |- - log(----------------------) +--R \| a a x + b +--R + +--R 3 3 2 2 2 3 +-+ +--R (16a x - 112a b x - 350a b x - 210b )\|x +--R / +--R 6 2 5 4 2 +--R 24a x + 48a b x + 24a b +--R , +--R +--R +-+ +-+ +--R 2 2 2 3 |b \|x +--R (105a b x + 210a b x + 105b ) |- atan(----) +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (8a x - 56a b x - 175a b x - 105b )\|x +--R / +--R 6 2 5 4 2 +--R 12a x + 24a b x + 12a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 10 + +--S 11 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 35b |- - \|a log(----------------------) - 70b\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R 35b\|a |- atan(----) - 35b\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 13 + +--S 14 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 14 + +)clear all + +--S 15 of 1379 +t0:=1/((a+b/x)^3*x^(1/2)) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 15 + +--S 16 of 1379 +r0:=-1/2*x^(5/2)/(a*(b+a*x)^2)-5/4*x^(3/2)/(a^2*(b+a*x))-_ + 15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(b)/a^(7/2)+15/4*sqrt(x)/a^3 +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ \|a \|x +--R (- 15a x - 30a b x - 15b )\|b atan(--------) +--R +-+ +--R \|b +--R + +--R 2 2 2 +-+ +-+ +--R (8a x + 25a b x + 15b )\|a \|x +--R / +--R 5 2 4 3 2 +-+ +--R (4a x + 8a b x + 4a b )\|a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +--R 2 2 2 | b \| a +--R (15a x + 30a b x + 15b ) |- - log(------------------------) +--R \| a a x + b +--R + +--R 2 2 2 +-+ +--R (16a x + 50a b x + 30b )\|x +--R / +--R 5 2 4 3 2 +--R 8a x + 16a b x + 8a b +--R , +--R +-+ +-+ +--R 2 2 2 |b \|x 2 2 2 +-+ +--R (- 15a x - 30a b x - 15b ) |- atan(----) + (8a x + 25a b x + 15b )\|x +--R \|a +-+ +--R |b +--R |- +--R \|a +--R ------------------------------------------------------------------------] +--R 5 2 4 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(List(Expression(Integer)),...) +--E 17 + +--S 18 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b +-+ +--R +---+ - 2a |- - \|x + a x - b +-+ +-+ +--R | b +-+ \| a +-+ \|a \|x +--R 15 |- - \|a log(------------------------ + 30\|b atan(--------) +--R \| a a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 18 + +--S 19 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R +-+ |b \|x +-+ \|a \|x +--R - 15\|a |- atan(----) + 15\|b atan(--------) +--R \|a +-+ +-+ +--R |b \|b +--R |- +--R \|a +--R (6) --------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 21 + +)clear all + +--S 22 of 1379 +t0:=1/((a+b/x)^3*x^(3/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1379 +r0:=-1/2*x^(3/2)/(a*(b+a*x)^2)+3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/_ + (a^(5/2)*sqrt(b))-3/4*sqrt(x)/(a^2*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (3a x + 6a b x + 3b )atan(--------) + (- 5a x - 3b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) ---------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4a x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 23 + +--S 24 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (3a x + 6a b x + 3b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (- 10a x - 6b)\|- a b \|x +--R / +--R 4 2 3 2 2 +-----+ +--R (8a x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3a x + 6a b x + 3b )atan(----------) + (- 5a x - 3b)\|a b \|x +--R b +--R ----------------------------------------------------------------] +--R 4 2 3 2 2 +---+ +--R (4a x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 24 + +--S 25 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 25 + +--S 26 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4a \|a \|b \|a b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 28 + +)clear all + +--S 29 of 1379 +t0:=1/((a+b/x)^3*x^(5/2)) +--R +--R +--R x +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1379 +r0:=1/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(a^(3/2)*b^(3/2))-_ + 1/2*sqrt(x)/(a*(b+a*x)^2)+1/4*sqrt(x)/(a*b*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (a x + 2a b x + b )atan(--------) + (a x - b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) ---------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x + 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 30 + +--S 31 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (a x + 2a b x + b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (2a x - 2b)\|- a b \|x +--R / +--R 3 2 2 2 3 +-----+ +--R (8a b x + 16a b x + 8a b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (a x + 2a b x + b )atan(----------) + (a x - b)\|a b \|x +--R b +--R ----------------------------------------------------------] +--R 3 2 2 2 3 +---+ +--R (4a b x + 8a b x + 4a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 31 + +--S 32 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R \|a \|b log(----------------------------) - 2\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) ------------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 8a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 33 + +--S 34 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R \|a \|b atan(----------) - \|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ----------------------------------------------- +--R +-+ +-+ +---+ +--R 4a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1379 +t0:=1/((a+b/x)^3*x^(7/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R 3 3 2 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b )\|x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1379 +r0:=3/4*atan(sqrt(a)*sqrt(x)/sqrt(b))/(b^(5/2)*sqrt(a))+_ + 1/2*sqrt(x)/(b*(b+a*x)^2)+3/4*sqrt(x)/(b^2*(b+a*x)) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|a \|x +-+ +-+ +-+ +--R (3a x + 6a b x + 3b )atan(--------) + (3a x + 5b)\|a \|b \|x +--R +-+ +--R \|b +--R (2) -------------------------------------------------------------- +--R 2 2 2 3 4 +-+ +-+ +--R (4a b x + 8a b x + 4b )\|a \|b +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +-+ +-----+ +--R 2 2 2 2a b\|x + (a x - b)\|- a b +--R (3a x + 6a b x + 3b )log(----------------------------) +--R a x + b +--R + +--R +-----+ +-+ +--R (6a x + 10b)\|- a b \|x +--R / +--R 2 2 2 3 4 +-----+ +--R (8a b x + 16a b x + 8b )\|- a b +--R , +--R +---+ +-+ +--R 2 2 2 \|a b \|x +---+ +-+ +--R (3a x + 6a b x + 3b )atan(----------) + (3a x + 5b)\|a b \|x +--R b +--R --------------------------------------------------------------] +--R 2 2 2 3 4 +---+ +--R (4a b x + 8a b x + 4b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 38 + +--S 39 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +-+ +-----+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (a x - b)\|- a b +-----+ \|a \|x +--R 3\|a \|b log(----------------------------) - 6\|- a b atan(--------) +--R a x + b +-+ +--R \|b +--R (4) -------------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 8b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +--S 41 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +-+ +-+ +--R +-+ +-+ \|a b \|x +---+ \|a \|x +--R 3\|a \|b atan(----------) - 3\|a b atan(--------) +--R b +-+ +--R \|b +--R (6) ------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 4b \|a \|b \|a b +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 42 + +)clear all + +--S 43 of 1379 +t0:=1/((a+b/x)^3*x^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (a x + 3a b x + 3a b x + b x)\|x +--R Type: Expression(Integer) +--E 43 + +--S 44 of 1379 +r0:=-15/4*atan(sqrt(a)*sqrt(x)/sqrt(b))*sqrt(a)/b^(7/2)+_ + (-15/4)/(b^3*sqrt(x))+1/2/(b*(b+a*x)^2*sqrt(x))+5/4/(b^2*(b+a*x)*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|a \|x +--R (- 15a x - 30a b x - 15b )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 2 2 2 +-+ +--R (- 15a x - 25a b x - 8b )\|b +--R / +--R 2 3 2 4 5 +-+ +-+ +--R (4a b x + 8a b x + 4b )\|b \|x +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +--R 2 2 2 | a +-+ \| b +--R (15a x + 30a b x + 15b ) |- - \|x log(------------------------) +--R \| b a x + b +--R + +--R 2 2 2 +--R - 30a x - 50a b x - 16b +--R / +--R 2 3 2 4 5 +-+ +--R (8a b x + 16a b x + 8b )\|x +--R , +--R +-+ +-+ +--R 2 2 2 |a +-+ a\|x 2 2 2 +--R (- 15a x - 30a b x - 15b ) |- \|x atan(-----) - 15a x - 25a b x - 8b +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R -----------------------------------------------------------------------] +--R 2 3 2 4 5 +-+ +--R (4a b x + 8a b x + 4b )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 45 + +--S 46 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 15 |- - \|b log(------------------------ + 30\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R - 15 |- \|b atan(----- + 15\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ---------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 48 + +--S 49 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 49 + +)clear all + +--S 50 of 1379 +t0:=1/((a+b/x)^3*x^(11/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (a x + 3a b x + 3a b x + b x )\|x +--R Type: Expression(Integer) +--E 50 + +--S 51 of 1379 +r0:=(-35/12)/(b^3*x^(3/2))+1/2/(b*x^(3/2)*(b+a*x)^2)+_ + 7/4/(b^2*x^(3/2)*(b+a*x))+35/4*a^(3/2)*atan(sqrt(a)*_ + sqrt(x)/sqrt(b))/b^(9/2)+35/4*a/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|a \|x +--R (105a x + 210a b x + 105a b x)\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 3 3 2 2 2 3 +-+ +--R (105a x + 175a b x + 56a b x - 8b )\|b +--R / +--R 2 4 3 5 2 6 +-+ +-+ +--R (12a b x + 24a b x + 12b x)\|b \|x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +--R 3 3 2 2 2 | a +-+ \| b +--R (105a x + 210a b x + 105a b x) |- - \|x log(----------------------) +--R \| b a x + b +--R + +--R 3 3 2 2 2 3 +--R 210a x + 350a b x + 112a b x - 16b +--R / +--R 2 4 3 5 2 6 +-+ +--R (24a b x + 48a b x + 24b x)\|x +--R , +--R +--R +-+ +-+ +--R 3 3 2 2 2 |a +-+ a\|x 3 3 +--R (105a x + 210a b x + 105a b x) |- \|x atan(-----) + 105a x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 2 2 2 3 +--R 175a b x + 56a b x - 8b +--R / +--R 2 4 3 5 2 6 +-+ +--R (12a b x + 24a b x + 12b x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 52 + +--S 53 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ 2b |- - \|x + a x - b +-+ +-+ +--R | a +-+ \| b +-+ \|a \|x +--R 35a |- - \|b log(----------------------) - 70a\|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) ---------------------------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 53 + +--S 54 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R |a +-+ a\|x +-+ \|a \|x +--R 35a |- \|b atan(-----) - 35a\|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) ---------------------------------------------- +--R 4 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 55 + +--S 56 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 56 + +)clear all + +--S 57 of 1379 +t0:=1/((a+b/x)^3*x^(13/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 6 2 5 2 4 3 3 +-+ +--R (a x + 3a b x + 3a b x + b x )\|x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1379 +r0:=(-63/20)/(b^3*x^(5/2))+21/4*a/(b^4*x^(3/2))+_ + 1/2/(b*x^(5/2)*(b+a*x)^2)+9/4/(b^2*x^(5/2)*(b+a*x))-_ + 63/4*a^(5/2)*atan(sqrt(a)*sqrt(x)/sqrt(b))/b^(11/2)-_ + 63/4*a^2/(b^5*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-+ +--R 4 4 3 3 2 2 2 +-+ +-+ \|a \|x +--R (- 315a x - 630a b x - 315a b x )\|a \|x atan(--------) +--R +-+ +--R \|b +--R + +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (- 315a x - 525a b x - 168a b x + 24a b x - 8b )\|b +--R / +--R 2 5 4 6 3 7 2 +-+ +-+ +--R (20a b x + 40a b x + 20b x )\|b \|x +--R Type: Expression(Integer) +--E 58 + +--S 59 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R 4 4 3 3 2 2 2 | a +-+ +--R (315a x + 630a b x + 315a b x ) |- - \|x +--R \| b +--R * +--R +---+ +--R | a +-+ +--R - 2b |- - \|x + a x - b +--R \| b +--R log(------------------------) +--R a x + b +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 630a x - 1050a b x - 336a b x + 48a b x - 16b +--R / +--R 2 5 4 6 3 7 2 +-+ +--R (40a b x + 80a b x + 40b x )\|x +--R , +--R +--R +-+ +-+ +--R 4 4 3 3 2 2 2 |a +-+ a\|x 4 4 +--R (- 315a x - 630a b x - 315a b x ) |- \|x atan(-----) - 315a x +--R \|b +-+ +--R |a +--R b |- +--R \|b +--R + +--R 3 3 2 2 2 3 4 +--R - 525a b x - 168a b x + 24a b x - 8b +--R / +--R 2 5 4 6 3 7 2 +-+ +--R (20a b x + 40a b x + 20b x )\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 59 + +--S 60 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a +-+ +--R +---+ - 2b |- - \|x + a x - b +-+ +-+ +--R 2 | a +-+ \| b 2 +-+ \|a \|x +--R 63a |- - \|b log(------------------------) + 126a \|a atan(--------) +--R \| b a x + b +-+ +--R \|b +--R (4) --------------------------------------------------------------------- +--R 5 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 60 + +--S 61 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +-+ +-+ +-+ +--R 2 |a +-+ a\|x 2 +-+ \|a \|x +--R - 63a |- \|b atan(-----) + 63a \|a atan(--------) +--R \|b +-+ +-+ +--R |a \|b +--R b |- +--R \|b +--R (6) -------------------------------------------------- +--R 5 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 63 + +)clear all + +--S 64 of 1379 +t0:=(a+b/x)^(1/2)*x^(7/2) +--R +--R +--R +-------+ +--R 3 |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1379 +r0:=-32/315*b^3*(a+b/x)^(3/2)*x^(3/2)/a^4+16/105*b^2*(a+b/x)^(3/2)*_ + x^(5/2)/a^3-4/21*b*(a+b/x)^(3/2)*x^(7/2)/a^2+2/9*(a+b/x)^(3/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------------------- +--R 4 +--R 315a +--R Type: Expression(Integer) +--E 65 + +--S 66 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------------------- +--R 4 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 66 + +--S 67 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 68 + +)clear all + +--S 69 of 1379 +t0:=(a+b/x)^(1/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1379 +r0:=16/105*b^2*(a+b/x)^(3/2)*x^(3/2)/a^3-8/35*b*(a+b/x)^(3/2)*x^(5/2)/_ + a^2+2/7*(a+b/x)^(3/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------ +--R 3 +--R 105a +--R Type: Expression(Integer) +--E 70 + +--S 71 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (30a x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------ +--R 3 +--R 105a +--R Type: Union(Expression(Integer),...) +--E 71 + +--S 72 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 73 + +)clear all + +--S 74 of 1379 +t0:=(a+b/x)^(1/2)*x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1379 +r0:=-4/15*b*(a+b/x)^(3/2)*x^(3/2)/a^2+2/5*(a+b/x)^(3/2)*x^(5/2)/a +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ------------------------------------ +--R 2 +--R 15a +--R Type: Expression(Integer) +--E 75 + +--S 76 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ------------------------------------ +--R 2 +--R 15a +--R Type: Union(Expression(Integer),...) +--E 76 + +--S 77 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 78 + +)clear all + +--S 79 of 1379 +t0:=(a+b/x)^(1/2)*x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1379 +r0:=2/3*(a+b/x)^(3/2)*x^(3/2)/a +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x + 2b) |------- \|x +--R \| x +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x + 2b) |------- \|x +--R \| x +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 81 + +--S 82 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 83 + +)clear all + +--S 84 of 1379 +t0:=(a+b/x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)+2*sqrt(a+b/x)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R (2) - 2\|b atanh(--------------) + 2 |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 85 + +--S 86 of 1379 +--a0:=integrate(t0,x) +--E 86 + +--S 87 of 1379 +--m0:=a0-r0 +--E 87 + +--S 88 of 1379 +--d0:=D(m0,x) +--E 88 + +)clear all + +--S 89 of 1379 +t0:=(a+b/x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1379 +r0:=-a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-sqrt(a+b/x)/sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R - a\|x atanh(--------------) - |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------- +--R +-+ +-+ +--R \|b \|x +--R Type: Expression(Integer) +--E 90 + +--S 91 of 1379 +--a0:=integrate(t0,x) +--E 91 + +--S 92 of 1379 +--m0:=a0-r0 +--E 92 + +--S 93 of 1379 +--d0:=D(m0,x) +--E 93 + +)clear all + +--S 94 of 1379 +t0:=(a+b/x)^(1/2)/x^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1379 +r0:=1/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_ + 1/2*sqrt(a+b/x)/x^(3/2)-1/4*a*sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R a x\|x atanh(--------------) + (- a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------------------- +--R +-+ +-+ +--R 4b x\|b \|x +--R Type: Expression(Integer) +--E 95 + +--S 96 of 1379 +--a0:=integrate(t0,x) +--E 96 + +--S 97 of 1379 +--m0:=a0-r0 +--E 97 + +--S 98 of 1379 +--d0:=D(m0,x) +--E 98 + +)clear all + +--S 99 of 1379 +t0:=(a+b/x)^(1/2)/x^(7/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (1) ---------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1379 +r0:=-1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_ + 1/3*sqrt(a+b/x)/x^(5/2)-1/12*a*sqrt(a+b/x)/(b*x^(3/2))+_ + 1/8*a^2*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 3a x \|x atanh(--------------) + (3a x - 2a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ----------------------------------------------------------------------- +--R 2 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 100 + +--S 101 of 1379 +--a0:=integrate(t0,x) +--E 101 + +--S 102 of 1379 +--m0:=a0-r0 +--E 102 + +--S 103 of 1379 +--d0:=D(m0,x) +--E 103 + +)clear all + +--S 104 of 1379 +t0:=(a+b/x)^(3/2)*x^(9/2) +--R +--R +--R +-------+ +--R 4 3 |a x + b +-+ +--R (1) (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1379 +r0:=-32/1155*b^3*(a+b/x)^(5/2)*x^(5/2)/a^4+16/231*b^2*(a+b/x)^(5/2)*_ + x^(7/2)/a^3-4/33*b*(a+b/x)^(5/2)*x^(9/2)/a^2+_ + 2/11*(a+b/x)^(5/2)*x^(11/2)/a +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 4 +--R 1155a +--R Type: Expression(Integer) +--E 105 + +--S 106 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (210a x + 280a b x + 10a b x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 4 +--R 1155a +--R Type: Union(Expression(Integer),...) +--E 106 + +--S 107 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 108 + +)clear all + +--S 109 of 1379 +t0:=(a+b/x)^(3/2)*x^(7/2) +--R +--R +--R +-------+ +--R 3 2 |a x + b +-+ +--R (1) (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1379 +r0:=16/315*b^2*(a+b/x)^(5/2)*x^(5/2)/a^3-8/63*b*(a+b/x)^(5/2)*_ + x^(7/2)/a^2+2/9*(a+b/x)^(5/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------------------ +--R 3 +--R 315a +--R Type: Expression(Integer) +--E 110 + +--S 111 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x + 100a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------------------ +--R 3 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 111 + +--S 112 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 113 + +)clear all + +--S 114 of 1379 +t0:=(a+b/x)^(3/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 |a x + b +-+ +--R (1) (a x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1379 +r0:=-4/35*b*(a+b/x)^(5/2)*x^(5/2)/a^2+2/7*(a+b/x)^(5/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ------------------------------------------------ +--R 2 +--R 35a +--R Type: Expression(Integer) +--E 115 + +--S 116 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x + 16a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ------------------------------------------------ +--R 2 +--R 35a +--R Type: Union(Expression(Integer),...) +--E 116 + +--S 117 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 118 + +)clear all + +--S 119 of 1379 +t0:=(a+b/x)^(3/2)*x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (1) (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1379 +r0:=2/5*(a+b/x)^(5/2)*x^(5/2)/a +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (2a x + 4a b x + 2b ) |------- \|x +--R \| x +--R (2) ------------------------------------ +--R 5a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (2a x + 4a b x + 2b ) |------- \|x +--R \| x +--R (3) ------------------------------------ +--R 5a +--R Type: Union(Expression(Integer),...) +--E 121 + +--S 122 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 123 + +)clear all + +--S 124 of 1379 +t0:=(a+b/x)^(3/2)*x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1379 +r0:=2/3*(a+b/x)^(3/2)*x^(3/2)-2*b^(3/2)*atanh(sqrt(b)/_ + (sqrt(a+b/x)*sqrt(x)))+2*b*sqrt(a+b/x)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R - 6b\|b atanh(--------------) + (2a x + 8b) |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) --------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 125 + +--S 126 of 1379 +--a0:=integrate(t0,x) +--E 126 + +--S 127 of 1379 +--m0:=a0-r0 +--E 127 + +--S 128 of 1379 +--d0:=D(m0,x) +--E 128 + +)clear all + +--S 129 of 1379 +t0:=(a+b/x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1379 +r0:=-3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_ + 3*b*sqrt(a+b/x)/sqrt(x)+2*(a+b/x)^(3/2)*sqrt(x) +--R +--R +--R +-+ +-------+ +--R +-+ +-+ \|b |a x + b +--R - 3a\|b \|x atanh(--------------) + (2a x - b) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) -------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 130 + +--S 131 of 1379 +--a0:=integrate(t0,x) +--E 131 + +--S 132 of 1379 +--m0:=a0-r0 +--E 132 + +--S 133 of 1379 +--d0:=D(m0,x) +--E 133 + +)clear all + +--S 134 of 1379 +t0:=(a+b/x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1379 +r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_ + 1/2*(a+b/x)^(3/2)/sqrt(x)-3/4*a*sqrt(a+b/x)/sqrt(x) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R - 3a x\|x atanh(--------------) + (- 5a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------------------------- +--R +-+ +-+ +--R 4x\|b \|x +--R Type: Expression(Integer) +--E 135 + +--S 136 of 1379 +--a0:=integrate(t0,x) +--E 136 + +--S 137 of 1379 +--m0:=a0-r0 +--E 137 + +--S 138 of 1379 +--d0:=D(m0,x) +--E 138 + +)clear all + +--S 139 of 1379 +t0:=(a+b/x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R (1) ------------------- +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1379 +r0:=-1/3*(a+b/x)^(3/2)/x^(3/2)+1/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(3/2)-1/4*a*sqrt(a+b/x)/x^(3/2)-1/8*a^2*_ + sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R 3a x \|x atanh(--------------) + (- 3a x - 14a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 140 + +--S 141 of 1379 +--a0:=integrate(t0,x) +--E 141 + +--S 142 of 1379 +--m0:=a0-r0 +--E 142 + +--S 143 of 1379 +--d0:=D(m0,x) +--E 143 + +)clear all + +--S 144 of 1379 +t0:=(a+b/x)^(5/2)*x^(11/2) +--R +--R +--R +-------+ +--R 2 5 4 2 3 |a x + b +-+ +--R (1) (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1379 +r0:=-32/3003*b^3*(a+b/x)^(7/2)*x^(7/2)/a^4+16/429*b^2*(a+b/x)^(7/2)*_ + x^(9/2)/a^3-12/143*b*(a+b/x)^(7/2)*x^(11/2)/a^2+_ + 2/13*(a+b/x)^(7/2)*x^(13/2)/a +--R +--R +--R (2) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b ) +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R / +--R 4 +--R 3003a +--R Type: Expression(Integer) +--E 145 + +--S 146 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 6 5 5 4 2 4 3 3 3 2 4 2 5 6 +--R (462a x + 1134a b x + 742a b x + 10a b x - 12a b x + 16a b x - 32b ) +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R / +--R 4 +--R 3003a +--R Type: Union(Expression(Integer),...) +--E 146 + +--S 147 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 148 + +)clear all + +--S 149 of 1379 +t0:=(a+b/x)^(5/2)*x^(9/2) +--R +--R +--R +-------+ +--R 2 4 3 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1379 +r0:=16/693*b^2*(a+b/x)^(7/2)*x^(7/2)/a^3-8/99*b*(a+b/x)^(7/2)*_ + x^(9/2)/a^2+2/11*(a+b/x)^(7/2)*x^(11/2)/a +--R +--R +--R (2) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R 3 +--R 693a +--R Type: Expression(Integer) +--E 150 + +--S 151 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 5 5 4 4 3 2 3 2 3 2 4 5 |a x + b +-+ +--R (126a x + 322a b x + 226a b x + 6a b x - 8a b x + 16b ) |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R 3 +--R 693a +--R Type: Union(Expression(Integer),...) +--E 151 + +--S 152 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 153 + +)clear all + +--S 154 of 1379 +t0:=(a+b/x)^(5/2)*x^(7/2) +--R +--R +--R +-------+ +--R 2 3 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1379 +r0:=-4/63*b*(a+b/x)^(7/2)*x^(7/2)/a^2+2/9*(a+b/x)^(7/2)*x^(9/2)/a +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (2) ----------------------------------------------------------- +--R 2 +--R 63a +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (14a x + 38a b x + 30a b x + 2a b x - 4b ) |------- \|x +--R \| x +--R (3) ----------------------------------------------------------- +--R 2 +--R 63a +--R Type: Union(Expression(Integer),...) +--E 156 + +--S 157 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 158 + +)clear all + +--S 159 of 1379 +t0:=(a+b/x)^(5/2)*x^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (1) (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1379 +r0:=2/7*(a+b/x)^(7/2)*x^(7/2)/a +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x +--R \| x +--R (2) ---------------------------------------------- +--R 7a +--R Type: Expression(Integer) +--E 160 + +--S 161 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (2a x + 6a b x + 6a b x + 2b ) |------- \|x +--R \| x +--R (3) ---------------------------------------------- +--R 7a +--R Type: Union(Expression(Integer),...) +--E 161 + +--S 162 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 163 + +)clear all + +--S 164 of 1379 +t0:=(a+b/x)^(5/2)*x^(3/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R (1) ---------------------------------- +--R x +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1379 +r0:=2/3*b*(a+b/x)^(3/2)*x^(3/2)+2/5*(a+b/x)^(5/2)*x^(5/2)-2*b^(5/2)*_ + atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))+2*b^2*sqrt(a+b/x)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 30b \|b atanh(--------------) + (6a x + 22a b x + 46b ) |------- \|x +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R 15 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 1379 +--a0:=integrate(t0,x) +--E 166 + +--S 167 of 1379 +--m0:=a0-r0 +--E 167 + +--S 168 of 1379 +--d0:=D(m0,x) +--E 168 + +)clear all + +--S 169 of 1379 +t0:=(a+b/x)^(5/2)*x^(1/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R (1) ---------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1379 +r0:=2/3*(a+b/x)^(5/2)*x^(3/2)-5*a*b^(3/2)*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))-5*b^2*sqrt(a+b/x)/sqrt(x)+10/3*b*(a+b/x)^(3/2)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R +-+ +-+ \|b 2 2 2 |a x + b +--R - 15a b\|b \|x atanh(--------------) + (2a x + 14a b x - 3b ) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------ +--R +-+ +--R 3\|x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1379 +--a0:=integrate(t0,x) +--E 171 + +--S 172 of 1379 +--m0:=a0-r0 +--E 172 + +--S 173 of 1379 +--d0:=D(m0,x) +--E 173 + +)clear all + +--S 174 of 1379 +t0:=(a+b/x)^(5/2)/x^(1/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1379 +r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))*sqrt(b)-_ + 5/2*b*(a+b/x)^(3/2)/sqrt(x)-15/4*a*b*sqrt(a+b/x)/sqrt(x)+_ + 2*(a+b/x)^(5/2)*sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 2 +-+ +-+ \|b 2 2 2 |a x + b +--R - 15a x\|b \|x atanh(--------------) + (8a x - 9a b x - 2b ) |------- +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ----------------------------------------------------------------------- +--R +-+ +--R 4x\|x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1379 +--a0:=integrate(t0,x) +--E 176 + +--S 177 of 1379 +--m0:=a0-r0 +--E 177 + +--S 178 of 1379 +--d0:=D(m0,x) +--E 178 + +)clear all + +--S 179 of 1379 +t0:=(a+b/x)^(5/2)/x^(3/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 3 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1379 +r0:=-5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b)-_ + 5/12*a*(a+b/x)^(3/2)/sqrt(x)-1/3*(a+b/x)^(5/2)/sqrt(x)-_ + 5/8*a^2*sqrt(a+b/x)/sqrt(x) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R - 15a x \|x atanh(--------------) + (- 33a x - 26a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ---------------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 24x \|b \|x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1379 +--a0:=integrate(t0,x) +--E 181 + +--S 182 of 1379 +--m0:=a0-r0 +--E 182 + +--S 183 of 1379 +--d0:=D(m0,x) +--E 183 + +)clear all + +--S 184 of 1379 +t0:=(a+b/x)^(5/2)/x^(5/2) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R (1) ------------------------------ +--R 4 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1379 +r0:=-5/24*a*(a+b/x)^(3/2)/x^(3/2)-1/4*(a+b/x)^(5/2)/x^(3/2)+_ + 5/64*a^4*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-_ + 5/32*a^2*sqrt(a+b/x)/x^(3/2)-5/64*a^3*sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R (2) +--R +-+ +--R 4 3 +-+ \|b +--R 15a x \|x atanh(--------------) +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (- 15a x - 118a b x - 136a b x - 48b ) |------- \|b +--R \| x +--R / +--R 3 +-+ +-+ +--R 192b x \|b \|x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 1379 +--a0:=integrate(t0,x) +--E 186 + +--S 187 of 1379 +--m0:=a0-r0 +--E 187 + +--S 188 of 1379 +--d0:=D(m0,x) +--E 188 + +)clear all + +--S 189 of 1379 +t0:=x^(7/2)/(a+b/x)^(1/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1379 +r0:=-128/315*b^3*x^(3/2)*sqrt(a+b/x)/a^4+32/105*b^2*x^(5/2)*_ + sqrt(a+b/x)/a^3-16/63*b*x^(7/2)*sqrt(a+b/x)/a^2+2/9*x^(9/2)*_ + sqrt(a+b/x)/a+256/315*b^4*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x +--R \| x +--R (2) --------------------------------------------------------------- +--R 5 +--R 315a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 |a x + b +-+ +--R (70a x - 80a b x + 96a b x - 128a b x + 256b ) |------- \|x +--R \| x +--R (3) --------------------------------------------------------------- +--R 5 +--R 315a +--R Type: Union(Expression(Integer),...) +--E 191 + +--S 192 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 193 + +)clear all + +--S 194 of 1379 +t0:=x^(5/2)/(a+b/x)^(1/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1379 +r0:=16/35*b^2*x^(3/2)*sqrt(a+b/x)/a^3-12/35*b*x^(5/2)*sqrt(a+b/x)/a^2+_ + 2/7*x^(7/2)*sqrt(a+b/x)/a-32/35*b^3*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (2) -------------------------------------------------- +--R 4 +--R 35a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 3 3 2 2 2 3 |a x + b +-+ +--R (10a x - 12a b x + 16a b x - 32b ) |------- \|x +--R \| x +--R (3) -------------------------------------------------- +--R 4 +--R 35a +--R Type: Union(Expression(Integer),...) +--E 196 + +--S 197 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 198 + +)clear all + +--S 199 of 1379 +t0:=x^(3/2)/(a+b/x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1379 +r0:=-8/15*b*x^(3/2)*sqrt(a+b/x)/a^2+2/5*x^(5/2)*sqrt(a+b/x)/a+_ + 16/15*b^2*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x - 8a b x + 16b ) |------- \|x +--R \| x +--R (2) ------------------------------------- +--R 3 +--R 15a +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (6a x - 8a b x + 16b ) |------- \|x +--R \| x +--R (3) ------------------------------------- +--R 3 +--R 15a +--R Type: Union(Expression(Integer),...) +--E 201 + +--S 202 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 203 + +)clear all + +--S 204 of 1379 +t0:=x^(1/2)/(a+b/x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (1) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1379 +r0:=2/3*x^(3/2)*sqrt(a+b/x)/a-4/3*b*sqrt(a+b/x)*sqrt(x)/a^2 +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x - 4b) |------- \|x +--R \| x +--R (2) ------------------------- +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 205 + +--S 206 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R (2a x - 4b) |------- \|x +--R \| x +--R (3) ------------------------- +--R 2 +--R 3a +--R Type: Union(Expression(Integer),...) +--E 206 + +--S 207 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 208 + +)clear all + +--S 209 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(1/2)) +--R +--R +--R 1 +--R (1) -------------- +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1379 +r0:=2*sqrt(a+b/x)*sqrt(x)/a +--R +--R +--R +-------+ +--R |a x + b +-+ +--R 2 |------- \|x +--R \| x +--R (2) --------------- +--R a +--R Type: Expression(Integer) +--E 210 + +--S 211 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ +--R 2 |------- \|x +--R \| x +--R (3) --------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 211 + +--S 212 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 213 + +)clear all + +--S 214 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(3/2)) +--R +--R +--R 1 +--R (1) --------------- +--R +-------+ +--R |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R 2atanh(--------------) +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) - ---------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1379 +--a0:=integrate(t0,x) +--E 216 + +--S 217 of 1379 +--m0:=a0-r0 +--E 217 + +--S 218 of 1379 +--d0:=D(m0,x) +--E 218 + +)clear all + +--S 219 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 2 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1379 +r0:=a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)-sqrt(a+b/x)/(b*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R +-+ \|b |a x + b +-+ +--R a\|x atanh(--------------) - |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------- +--R +-+ +-+ +--R b\|b \|x +--R Type: Expression(Integer) +--E 220 + +--S 221 of 1379 +--a0:=integrate(t0,x) +--E 221 + +--S 222 of 1379 +--m0:=a0-r0 +--E 222 + +--S 223 of 1379 +--d0:=D(m0,x) +--E 223 + +)clear all + +--S 224 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 3 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1379 +r0:=-3/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)-_ + 1/2*sqrt(a+b/x)/(b*x^(3/2))+3/4*a*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R +-+ +-------+ +--R 2 +-+ \|b |a x + b +-+ +--R - 3a x\|x atanh(--------------) + (3a x - 2b) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ----------------------------------------------------------- +--R 2 +-+ +-+ +--R 4b x\|b \|x +--R Type: Expression(Integer) +--E 225 + +--S 226 of 1379 +--a0:=integrate(t0,x) +--E 226 + +--S 227 of 1379 +--m0:=a0-r0 +--E 227 + +--S 228 of 1379 +--d0:=D(m0,x) +--E 228 + +)clear all + +--S 229 of 1379 +t0:=1/((a+b/x)^(1/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) ---------------- +--R +-------+ +--R 4 |a x + b +-+ +--R x |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1379 +r0:=5/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)-_ + 1/3*sqrt(a+b/x)/(b*x^(5/2))+5/12*a*sqrt(a+b/x)/(b^2*x^(3/2))-_ + 5/8*a^2*sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-+ +-------+ +--R 3 2 +-+ \|b 2 2 2 |a x + b +-+ +--R 15a x \|x atanh(--------------) + (- 15a x + 10a b x - 8b ) |------- \|b +--R +-------+ \| x +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R -------------------------------------------------------------------------- +--R 3 2 +-+ +-+ +--R 24b x \|b \|x +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1379 +--a0:=integrate(t0,x) +--E 231 + +--S 232 of 1379 +--m0:=a0-r0 +--E 232 + +--S 233 of 1379 +--d0:=D(m0,x) +--E 233 + +)clear all + +--S 234 of 1379 +t0:=x^(5/2)/(a+b/x)^(3/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1379 +r0:=-2*x^(7/2)/(a*sqrt(a+b/x))+128/35*b^2*x^(3/2)*sqrt(a+b/x)/a^4-_ + 96/35*b*x^(5/2)*sqrt(a+b/x)/a^3+16/7*x^(7/2)*sqrt(a+b/x)/a^2-_ + 256/35*b^3*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (10a x - 16a b x + 32a b x - 128a b x - 256b )\|x +--R (2) ----------------------------------------------------- +--R +-------+ +--R 5 |a x + b +--R 35a x |------- +--R \| x +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 5 4 3 2 4 3 2 3 3 2 2 +--R (30a b + 30a )x + (- 48a b - 48a b)x + (96a b + 96a b )x +--R + +--R 4 2 3 5 4 +--R (- 384a b - 384a b )x - 768b - 768a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 5 2 4 3 2 3 4 3 2 +--R 1152a b + (1728a + 128a)b + (432a + 64a )b + (- 72a - 16a )b +--R + +--R 5 4 6 5 +--R (27a + 8a )b - 45a - 5a +--R * +--R x +--R + +--R 6 5 2 4 3 2 3 +--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b +--R + +--R 4 3 2 5 4 +--R (27a + 8a )b + (- 45a - 5a )b +--R / +--R 6 7 5 2 6 +--R (105a b + 105a )x + 105a b + 105a b +--R Type: Union(Expression(Integer),...) +--E 236 + +--S 237 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 2 3 3 2 2 +--R 1152b + (1728a + 128)b + (432a + 64a)b + (- 72a - 16a )b +--R + +--R 4 3 5 4 +--R (27a + 8a )b - 45a - 5a +--R / +--R 5 6 +--R 105a b + 105a +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 238 + +)clear all + +--S 239 of 1379 +t0:=x^(3/2)/(a+b/x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1379 +r0:=-2*x^(5/2)/(a*sqrt(a+b/x))-16/5*b*x^(3/2)*sqrt(a+b/x)/a^3+_ + 12/5*x^(5/2)*sqrt(a+b/x)/a^2+32/5*b^2*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (2a x - 4a b x + 16a b x + 32b )\|x +--R (2) -------------------------------------- +--R +-------+ +--R 4 |a x + b +--R 5a x |------- +--R \| x +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 2 3 2 3 2 2 4 +--R (8a b + 8a )x + (- 16a b - 16a b)x + (64a b + 64a b )x + 128b +--R + +--R 3 +--R 128a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 4 2 3 3 2 2 4 3 5 +--R 256a b + (384a + 16a)b + (96a + 8a )b + (- 16a - 2a )b + 16a +--R + +--R 4 +--R a +--R * +--R x +--R + +--R 5 4 2 3 3 2 2 4 3 +--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + (16a + a )b +--R / +--R 5 6 4 2 5 +--R (20a b + 20a )x + 20a b + 20a b +--R Type: Union(Expression(Integer),...) +--E 241 + +--S 242 of 1379 +m0:=a0-r0 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 256b + (384a + 16)b + (96a + 8a)b + (- 16a - 2a )b + 16a + a +--R (4) ------------------------------------------------------------------- +--R 4 5 +--R 20a b + 20a +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 243 + +)clear all + +--S 244 of 1379 +t0:=x^(1/2)/(a+b/x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (1) ------------------- +--R +-------+ +--R |a x + b +--R (a x + b) |------- +--R \| x +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1379 +r0:=-2*x^(3/2)/(a*sqrt(a+b/x))+8/3*x^(3/2)*sqrt(a+b/x)/a^2-_ + 16/3*b*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R 2 2 2 +-+ +--R (2a x - 8a b x - 16b )\|x +--R (2) --------------------------- +--R +-------+ +--R 3 |a x + b +--R 3a x |------- +--R \| x +--R Type: Expression(Integer) +--E 245 + +--S 246 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 3 2 2 2 3 2 |a x + b +-+ +--R ((6a b + 6a )x + (- 24a b - 24a b)x - 48b - 48a b ) |------- \|x +--R \| x +--R + +--R 3 2 2 3 2 4 3 4 +--R (72a b + (108a + 8a)b + (27a + 4a )b - 9a - a )x + 72b +--R + +--R 3 2 2 3 2 +--R (108a + 8)b + (27a + 4a)b + (- 9a - a )b +--R / +--R 4 5 3 2 4 +--R (9a b + 9a )x + 9a b + 9a b +--R Type: Union(Expression(Integer),...) +--E 246 + +--S 247 of 1379 +m0:=a0-r0 +--R +--R +--R 3 2 2 3 2 +--R 72b + (108a + 8)b + (27a + 4a)b - 9a - a +--R (4) --------------------------------------------- +--R 3 4 +--R 9a b + 9a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 248 + +)clear all + +--S 249 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(1/2)) +--R +--R +--R x +--R (1) ----------------------- +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1379 +r0:=-2*sqrt(x)/(a*sqrt(a+b/x))+4*sqrt(a+b/x)*sqrt(x)/a^2 +--R +--R +--R +-+ +--R (2a x + 4b)\|x +--R (2) --------------- +--R +-------+ +--R 2 |a x + b +--R a x |------- +--R \| x +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 |a x + b +-+ +--R ((10a b + 10a )x + 20b + 20a b) |------- \|x +--R \| x +--R + +--R 2 2 3 2 3 2 2 +--R (50a b + (75a + 2a)b + 25a + a )x + 50b + (75a + 2)b + (25a + a)b +--R / +--R 3 4 2 2 3 +--R (5a b + 5a )x + 5a b + 5a b +--R Type: Union(Expression(Integer),...) +--E 251 + +--S 252 of 1379 +m0:=a0-r0 +--R +--R +--R 2 2 +--R 50b + (75a + 2)b + 25a + a +--R (4) ---------------------------- +--R 2 3 +--R 5a b + 5a +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 253 + +)clear all + +--S 254 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(3/2)) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------+ +--R |a x + b +-+ +--R (a x + b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1379 +r0:=(-2)/(a*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R 2 +--R (2) - --------------- +--R +-------+ +--R |a x + b +-+ +--R a |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 255 + +--S 256 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R |a x + b +-+ 2 2 +--R (- 4b - 4a) |------- \|x + (- 4a b - 4a - a)x - 4b + (- 4a - 1)b +--R \| x +--R (3) ------------------------------------------------------------------- +--R 2 3 2 2 +--R (2a b + 2a )x + 2a b + 2a b +--R Type: Union(Expression(Integer),...) +--E 256 + +--S 257 of 1379 +m0:=a0-r0 +--R +--R +--R - 4b - 4a - 1 +--R (4) ------------- +--R 2 +--R 2a b + 2a +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 258 + +)clear all + +--S 259 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +-------+ +--R 2 |a x + b +-+ +--R (a x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1379 +r0:=-2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(3/2)+2/(b*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R - 2 |------- \|x atanh(-------------- + 2\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ---------------------------------------------- +--R +-------+ +--R |a x + b +-+ +-+ +--R b |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1379 +--a0:=integrate(t0,x) +--E 261 + +--S 262 of 1379 +--m0:=a0-r0 +--E 262 + +--S 263 of 1379 +--d0:=D(m0,x) +--E 263 + +)clear all + +--S 264 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1379 +r0:=3*a*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(5/2)+2/(b*x^(3/2)*_ + sqrt(a+b/x))-3*sqrt(a+b/x)/(b^2*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R 3a x |------- \|x atanh(--------------) + (- 3a x - b)\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ---------------------------------------------------------- +--R +-------+ +--R 2 |a x + b +-+ +-+ +--R b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 265 + +--S 266 of 1379 +--a0:=integrate(t0,x) +--E 266 + +--S 267 of 1379 +--m0:=a0-r0 +--E 267 + +--S 268 of 1379 +--d0:=D(m0,x) +--E 268 + +)clear all + +--S 269 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 4 3 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1379 +r0:=-15/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(7/2)+2/(b*x^(5/2)*_ + sqrt(a+b/x))-5/2*sqrt(a+b/x)/(b^2*x^(3/2))+15/4*a*_ + sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 2 2 |a x + b +-+ \|b 2 2 2 +-+ +--R - 15a x |------- \|x atanh(--------------) + (15a x + 5a b x - 2b )\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R ------------------------------------------------------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +-+ +--R 4b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 270 + +--S 271 of 1379 +--a0:=integrate(t0,x) +--E 271 + +--S 272 of 1379 +--m0:=a0-r0 +--E 272 + +--S 273 of 1379 +--d0:=D(m0,x) +--E 273 + +)clear all + +--S 274 of 1379 +t0:=1/((a+b/x)^(3/2)*x^(11/2)) +--R +--R +--R 1 +--R (1) --------------------------- +--R +-------+ +--R 5 4 |a x + b +-+ +--R (a x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1379 +r0:=35/8*a^3*atanh(sqrt(b)/(sqrt(a+b/x)*sqrt(x)))/b^(9/2)+_ + 2/(b*x^(7/2)*sqrt(a+b/x))-7/3*sqrt(a+b/x)/(b^2*x^(5/2))+_ + 35/12*a*sqrt(a+b/x)/(b^3*x^(3/2))-35/8*a^2*sqrt(a+b/x)/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 3 3 |a x + b +-+ \|b +--R 105a x |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 105a x - 35a b x + 14a b x - 8b )\|b +--R / +--R +-------+ +--R 4 3 |a x + b +-+ +-+ +--R 24b x |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1379 +--a0:=integrate(t0,x) +--E 276 + +--S 277 of 1379 +--m0:=a0-r0 +--E 277 + +--S 278 of 1379 +--d0:=D(m0,x) +--E 278 + +)clear all + +--S 279 of 1379 +t0:=x^(5/2)/(a+b/x)^(5/2) +--R +--R +--R 4 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1379 +r0:=-2/3*x^(7/2)/(a*(a+b/x)^(3/2))-20/3*x^(7/2)/(a^2*sqrt(a+b/x))+_ + 256/21*b^2*x^(3/2)*sqrt(a+b/x)/a^5-64/7*b*x^(5/2)*sqrt(a+b/x)/_ + a^4+160/21*x^(7/2)*sqrt(a+b/x)/a^3-512/21*b^3*sqrt(a+b/x)*sqrt(x)/a^6 +--R +--R +--R 5 5 4 4 3 2 3 2 3 2 4 5 +-+ +--R (6a x - 12a b x + 32a b x - 192a b x - 768a b x - 512b )\|x +--R (2) ---------------------------------------------------------------- +--R +-------+ +--R 7 2 6 |a x + b +--R (21a x + 21a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 7 5 4 3 5 2 6 4 +--R (12a b + 24a b + 12a )x + (- 24a b - 48a b - 24a b)x +--R + +--R 3 4 4 3 5 2 3 2 5 3 4 4 3 2 +--R (64a b + 128a b + 64a b )x + (- 384a b - 768a b - 384a b )x +--R + +--R 6 2 5 3 4 7 6 2 5 +--R (- 1536a b - 3072a b - 1536a b )x - 1024b - 2048a b - 1024a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 6 3 2 5 4 3 4 5 4 3 +--R 1024a b + (2560a + 256a )b + (1920a + 384a )b + (320a + 96a )b +--R + +--R 6 5 2 7 6 8 7 +--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a +--R * +--R 2 +--R x +--R + +--R 7 2 6 3 2 5 4 3 4 +--R 2048a b + (5120a + 512a)b + (3840a + 768a )b + (640a + 192a )b +--R + +--R 5 4 3 6 5 2 7 6 +--R (- 80a - 32a )b + (24a + 12a )b + (- 24a - 6a )b +--R * +--R x +--R + +--R 8 7 2 6 3 2 5 +--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b +--R + +--R 4 3 4 5 4 3 6 5 2 +--R (- 40a - 16a )b + (12a + 6a )b + (- 12a - 3a )b +--R / +--R 8 2 9 10 2 7 3 8 2 9 6 4 +--R (42a b + 84a b + 42a )x + (84a b + 168a b + 84a b)x + 42a b +--R + +--R 7 3 8 2 +--R 84a b + 42a b +--R Type: Union(Expression(Integer),...) +--E 281 + +--S 282 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 5 2 4 3 2 3 +--R 1024b + (2560a + 256)b + (1920a + 384a)b + (320a + 96a )b +--R + +--R 4 3 2 5 4 6 5 +--R (- 40a - 16a )b + (12a + 6a )b - 12a - 3a +--R / +--R 6 2 7 8 +--R 42a b + 84a b + 42a +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 283 + +)clear all + +--S 284 of 1379 +t0:=x^(3/2)/(a+b/x)^(5/2) +--R +--R +--R 3 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1379 +r0:=-2/3*x^(5/2)/(a*(a+b/x)^(3/2))-16/3*x^(5/2)/(a^2*sqrt(a+b/x))-_ + 128/15*b*x^(3/2)*sqrt(a+b/x)/a^4+32/5*x^(5/2)*sqrt(a+b/x)/_ + a^3+256/15*b^2*sqrt(a+b/x)*sqrt(x)/a^5 +--R +--R +--R 4 4 3 3 2 2 2 3 4 +-+ +--R (6a x - 16a b x + 96a b x + 384a b x + 256b )\|x +--R (2) ---------------------------------------------------- +--R +-------+ +--R 6 2 5 |a x + b +--R (15a x + 15a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 5 6 4 3 3 4 2 5 3 +--R (24a b + 48a b + 24a )x + (- 64a b - 128a b - 64a b)x +--R + +--R 2 4 3 3 4 2 2 5 2 4 3 3 +--R (384a b + 768a b + 384a b )x + (1536a b + 3072a b + 1536a b )x +--R + +--R 6 5 2 4 +--R 1024b + 2048a b + 1024a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 5 3 2 4 4 3 3 5 4 2 +--R 2048a b + (5120a + 128a )b + (3840a + 192a )b + (640a + 48a )b +--R + +--R 6 5 7 6 +--R (- 80a - 8a )b + 48a + 3a +--R * +--R 2 +--R x +--R + +--R 6 2 5 3 2 4 +--R 4096a b + (10240a + 256a)b + (7680a + 384a )b +--R + +--R 4 3 3 5 4 2 6 5 +--R (1280a + 96a )b + (- 160a - 16a )b + (96a + 6a )b +--R * +--R x +--R + +--R 7 6 2 5 3 2 4 +--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b +--R + +--R 4 3 3 5 4 2 +--R (- 80a - 8a )b + (48a + 3a )b +--R / +--R 7 2 8 9 2 6 3 7 2 8 5 4 +--R (60a b + 120a b + 60a )x + (120a b + 240a b + 120a b)x + 60a b +--R + +--R 6 3 7 2 +--R 120a b + 60a b +--R Type: Union(Expression(Integer),...) +--E 286 + +--S 287 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4 2 3 3 2 2 +--R 2048b + (5120a + 128)b + (3840a + 192a)b + (640a + 48a )b +--R + +--R 4 3 5 4 +--R (- 80a - 8a )b + 48a + 3a +--R / +--R 5 2 6 7 +--R 60a b + 120a b + 60a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 288 + +)clear all + +--S 289 of 1379 +t0:=x^(1/2)/(a+b/x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (1) ------------------------------ +--R +-------+ +--R 2 2 2 |a x + b +--R (a x + 2a b x + b ) |------- +--R \| x +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1379 +r0:=-2/3*x^(3/2)/(a*(a+b/x)^(3/2))-4*x^(3/2)/(a^2*sqrt(a+b/x))+_ + 16/3*x^(3/2)*sqrt(a+b/x)/a^3-32/3*b*sqrt(a+b/x)*sqrt(x)/a^4 +--R +--R +--R 3 3 2 2 2 3 +-+ +--R (2a x - 12a b x - 48a b x - 32b )\|x +--R (2) --------------------------------------- +--R +-------+ +--R 5 2 4 |a x + b +--R (3a x + 3a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 5 3 2 3 3 2 4 2 +--R (6a b + 12a b + 6a )x + (- 36a b - 72a b - 36a b)x +--R + +--R 4 2 3 3 2 5 4 2 3 +--R (- 144a b - 288a b - 144a b )x - 96b - 192a b - 96a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 4 3 2 3 4 3 2 5 4 6 +--R 144a b + (360a + 16a )b + (270a + 24a )b + (45a + 6a )b - 9a +--R + +--R 5 +--R - a +--R * +--R 2 +--R x +--R + +--R 5 2 4 3 2 3 4 3 2 +--R 288a b + (720a + 32a)b + (540a + 48a )b + (90a + 12a )b +--R + +--R 5 4 +--R (- 18a - 2a )b +--R * +--R x +--R + +--R 6 5 2 4 3 2 3 4 3 2 +--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b + (- 9a - a )b +--R / +--R 6 2 7 8 2 5 3 6 2 7 4 4 5 3 +--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b +--R + +--R 6 2 +--R 9a b +--R Type: Union(Expression(Integer),...) +--E 291 + +--S 292 of 1379 +m0:=a0-r0 +--R +--R +--R 4 3 2 2 3 2 4 3 +--R 144b + (360a + 16)b + (270a + 24a)b + (45a + 6a )b - 9a - a +--R (4) ------------------------------------------------------------------ +--R 4 2 5 6 +--R 9a b + 18a b + 9a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 293 + +)clear all + +--S 294 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(1/2)) +--R +--R +--R 2 +--R x +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1379 +r0:=-2/3*sqrt(x)/(a*(a+b/x)^(3/2))-8/3*sqrt(x)/(a^2*sqrt(a+b/x))+_ + 16/3*sqrt(a+b/x)*sqrt(x)/a^3 +--R +--R +--R 2 2 2 +-+ +--R (6a x + 24a b x + 16b )\|x +--R (2) ---------------------------- +--R +-------+ +--R 4 2 3 |a x + b +--R (3a x + 3a b x) |------- +--R \| x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 4 2 3 2 2 3 4 +--R (30a b + 60a b + 30a )x + (120a b + 240a b + 120a b)x + 80b +--R + +--R 3 2 2 +--R 160a b + 80a b +--R * +--R +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 3 3 2 2 4 3 5 4 2 +--R (200a b + (500a + 8a )b + (375a + 12a )b + 75a + 3a )x +--R + +--R 4 2 3 3 2 2 4 3 5 +--R (400a b + (1000a + 16a)b + (750a + 24a )b + (150a + 6a )b)x + 200b +--R + +--R 4 2 3 3 2 2 +--R (500a + 8)b + (375a + 12a)b + (75a + 3a )b +--R / +--R 5 2 6 7 2 4 3 5 2 6 3 4 4 3 +--R (15a b + 30a b + 15a )x + (30a b + 60a b + 30a b)x + 15a b + 30a b +--R + +--R 5 2 +--R 15a b +--R Type: Union(Expression(Integer),...) +--E 296 + +--S 297 of 1379 +m0:=a0-r0 +--R +--R +--R 3 2 2 3 2 +--R 200b + (500a + 8)b + (375a + 12a)b + 75a + 3a +--R (4) -------------------------------------------------- +--R 3 2 4 5 +--R 15a b + 30a b + 15a +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 298 + +)clear all + +--S 299 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(3/2)) +--R +--R +--R x +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1379 +r0:=(-2/3)/(a*(a+b/x)^(3/2)*sqrt(x))+(-4/3)/(a^2*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R - 6a x - 4b +--R (2) --------------------------- +--R +-------+ +--R 3 2 |a x + b +-+ +--R (3a x + 3a b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 3 3 2 2 |a x + b +-+ +--R ((- 18a b - 36a b - 18a )x - 12b - 24a b - 12a b) |------- \|x +--R \| x +--R + +--R 2 2 3 2 4 3 2 +--R (18a b + (45a + 2a )b + 27a + 3a )x +--R + +--R 3 2 2 3 2 4 3 +--R (36a b + (90a + 4a)b + (54a + 6a )b)x + 18b + (45a + 2)b +--R + +--R 2 2 +--R (27a + 3a)b +--R / +--R 4 2 5 6 2 3 3 4 2 5 2 4 3 3 +--R (9a b + 18a b + 9a )x + (18a b + 36a b + 18a b)x + 9a b + 18a b +--R + +--R 4 2 +--R 9a b +--R Type: Union(Expression(Integer),...) +--E 301 + +--S 302 of 1379 +m0:=a0-r0 +--R +--R +--R 2 2 +--R 18b + (45a + 2)b + 27a + 3a +--R (4) ----------------------------- +--R 2 2 3 4 +--R 9a b + 18a b + 9a +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 303 + +)clear all + +--S 304 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +-------+ +--R 2 2 2 |a x + b +-+ +--R (a x + 2a b x + b ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1379 +r0:=(-2/3)/(a*(a+b/x)^(3/2)*x^(3/2)) +--R +--R +--R 2 +--R (2) - --------------------------- +--R +-------+ +--R 2 |a x + b +-+ +--R (3a x + 3a b) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 305 + +--S 306 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 2 |a x + b +-+ 2 3 2 2 +--R (- 4b - 8a b - 4a ) |------- \|x + (4a b + 4a + a )x +--R \| x +--R + +--R 2 2 3 2 +--R (8a b + (8a + 2a)b)x + 4b + (4a + 1)b +--R / +--R 3 2 4 5 2 2 3 3 2 4 4 2 3 +--R (6a b + 12a b + 6a )x + (12a b + 24a b + 12a b)x + 6a b + 12a b +--R + +--R 3 2 +--R 6a b +--R Type: Union(Expression(Integer),...) +--E 306 + +--S 307 of 1379 +m0:=a0-r0 +--R +--R +--R 4b + 4a + 1 +--R (4) ------------------- +--R 2 2 3 +--R 6a b + 12a b + 6a +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 308 + +)clear all + +--S 309 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(7/2)) +--R +--R +--R 1 +--R (1) ------------------------------------ +--R +-------+ +--R 2 3 2 2 |a x + b +-+ +--R (a x + 2a b x + b x) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(3/2))-2*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(5/2)+2/(b^2*sqrt(a+b/x)*sqrt(x)) +--R +--R +--R +-------+ +-+ +--R |a x + b +-+ \|b +-+ +--R (- 6a x - 6b) |------- \|x atanh(--------------) + (6a x + 8b)\|b +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R (2) ------------------------------------------------------------------ +--R +-------+ +--R 2 3 |a x + b +-+ +-+ +--R (3a b x + 3b ) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1379 +--a0:=integrate(t0,x) +--E 311 + +--S 312 of 1379 +--m0:=a0-r0 +--E 312 + +--S 313 of 1379 +--d0:=D(m0,x) +--E 313 + +)clear all + +--S 314 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(9/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +-------+ +--R 2 4 3 2 2 |a x + b +-+ +--R (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(5/2))+5*a*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(7/2)+10/3/(b^2*x^(3/2)*sqrt(a+b/x))-_ + 5*sqrt(a+b/x)/(b^3*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 2 2 |a x + b +-+ \|b +--R (15a x + 15a b x) |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 2 2 2 +-+ +--R (- 15a x - 20a b x - 3b )\|b +--R / +--R +-------+ +--R 3 2 4 |a x + b +-+ +-+ +--R (3a b x + 3b x) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 315 + +--S 316 of 1379 +--a0:=integrate(t0,x) +--E 316 + +--S 317 of 1379 +--m0:=a0-r0 +--E 317 + +--S 318 of 1379 +--d0:=D(m0,x) +--E 318 + +)clear all + +--S 319 of 1379 +t0:=1/((a+b/x)^(5/2)*x^(11/2)) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R +-------+ +--R 2 5 4 2 3 |a x + b +-+ +--R (a x + 2a b x + b x ) |------- \|x +--R \| x +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1379 +r0:=2/3/(b*(a+b/x)^(3/2)*x^(7/2))-35/4*a^2*atanh(sqrt(b)/(sqrt(a+b/x)*_ + sqrt(x)))/b^(9/2)+14/3/(b^2*x^(5/2)*sqrt(a+b/x))-_ + 35/6*sqrt(a+b/x)/(b^3*x^(3/2))+35/4*a*sqrt(a+b/x)/(b^4*sqrt(x)) +--R +--R +--R (2) +--R +-------+ +-+ +--R 3 3 2 2 |a x + b +-+ \|b +--R (- 105a x - 105a b x ) |------- \|x atanh(--------------) +--R \| x +-------+ +--R |a x + b +-+ +--R |------- \|x +--R \| x +--R + +--R 3 3 2 2 2 3 +-+ +--R (105a x + 140a b x + 21a b x - 6b )\|b +--R / +--R +-------+ +--R 4 3 5 2 |a x + b +-+ +-+ +--R (12a b x + 12b x ) |------- \|b \|x +--R \| x +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1379 +--a0:=integrate(t0,x) +--E 321 + +--S 322 of 1379 +--m0:=a0-r0 +--E 322 + +--S 323 of 1379 +--d0:=D(m0,x) +--E 323 + +)clear all + +--S 324 of 1379 +t0:=(a+b/x^2)*x^6 +--R +--R +--R 6 4 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 324 + +--S 325 of 1379 +r0:=1/5*b*x^5+1/7*a*x^7 +--R +--R +--R 1 7 1 5 +--R (2) - a x + - b x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 325 + +--S 326 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 7 5 +--R 5a x + 7b x +--R (3) ------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 326 + +--S 327 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 328 + +)clear all + +--S 329 of 1379 +t0:=(a+b/x^2)*x^5 +--R +--R +--R 5 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 329 + +--S 330 of 1379 +r0:=1/4*b*x^4+1/6*a*x^6 +--R +--R +--R 1 6 1 4 +--R (2) - a x + - b x +--R 6 4 +--R Type: Polynomial(Fraction(Integer)) +--E 330 + +--S 331 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 6 4 +--R 2a x + 3b x +--R (3) ------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 331 + +--S 332 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 333 + +)clear all + +--S 334 of 1379 +t0:=(a+b/x^2)*x^4 +--R +--R +--R 4 2 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 334 + +--S 335 of 1379 +r0:=1/3*b*x^3+1/5*a*x^5 +--R +--R +--R 1 5 1 3 +--R (2) - a x + - b x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 335 + +--S 336 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 5 3 +--R 3a x + 5b x +--R (3) ------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 336 + +--S 337 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 338 + +)clear all + +--S 339 of 1379 +t0:=(a+b/x^2)*x^3 +--R +--R +--R 3 +--R (1) a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 339 + +--S 340 of 1379 +r0:=1/2*b*x^2+1/4*a*x^4 +--R +--R +--R 1 4 1 2 +--R (2) - a x + - b x +--R 4 2 +--R Type: Polynomial(Fraction(Integer)) +--E 340 + +--S 341 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +--R a x + 2b x +--R (3) ------------ +--R 4 +--R Type: Union(Expression(Integer),...) +--E 341 + +--S 342 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 343 + +)clear all + +--S 344 of 1379 +t0:=(a+b/x^2)*x^2 +--R +--R +--R 2 +--R (1) a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 344 + +--S 345 of 1379 +r0:=b*x+1/3*a*x^3 +--R +--R +--R 1 3 +--R (2) - a x + b x +--R 3 +--R Type: Polynomial(Fraction(Integer)) +--E 345 + +--S 346 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R a x + 3b x +--R (3) ----------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 346 + +--S 347 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 348 + +)clear all + +--S 349 of 1379 +t0:=(a+b/x^2)*x +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 349 + +--S 350 of 1379 +r0:=1/2*a*x^2+b*log(x) +--R +--R +--R 2 +--R 2b log(x) + a x +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2b log(x) + a x +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 351 + +--S 352 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 353 + +)clear all + +--S 354 of 1379 +t0:=a+b/x^2 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 354 + +--S 355 of 1379 +r0:=-b/x+a*x +--R +--R +--R 2 +--R a x - b +--R (2) -------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 355 + +--S 356 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R a x - b +--R (3) -------- +--R x +--R Type: Union(Expression(Integer),...) +--E 356 + +--S 357 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 358 + +)clear all + +--S 359 of 1379 +t0:=(a+b/x^2)/x +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 359 + +--S 360 of 1379 +r0:=-1/2*b/x^2+a*log(x) +--R +--R +--R 2 +--R 2a x log(x) - b +--R (2) --------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 2a x log(x) - b +--R (3) --------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 361 + +--S 362 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 363 + +)clear all + +--S 364 of 1379 +t0:=(a+b/x^2)/x^2 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 364 + +--S 365 of 1379 +r0:=-1/3*b/x^3-a/x +--R +--R +--R 2 1 +--R - a x - - b +--R 3 +--R (2) ------------ +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 365 + +--S 366 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3a x - b +--R (3) ----------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 366 + +--S 367 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 368 + +)clear all + +--S 369 of 1379 +t0:=(a+b/x^2)/x^3 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 369 + +--S 370 of 1379 +r0:=-1/4*b/x^4-1/2*a/x^2 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 2 4 +--R (2) -------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 370 + +--S 371 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2a x - b +--R (3) ----------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 371 + +--S 372 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 373 + +)clear all + +--S 374 of 1379 +t0:=(a+b/x^2)/x^4 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 374 + +--S 375 of 1379 +r0:=-1/5*b/x^5-1/3*a/x^3 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 3 5 +--R (2) -------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 375 + +--S 376 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 5a x - 3b +--R (3) ------------ +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 376 + +--S 377 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 378 + +)clear all + +--S 379 of 1379 +t0:=(a+b/x^2)/x^5 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 379 + +--S 380 of 1379 +r0:=-1/6*b/x^6-1/4*a/x^4 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 4 6 +--R (2) -------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 380 + +--S 381 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 3a x - 2b +--R (3) ------------ +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 381 + +--S 382 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 383 + +)clear all + +--S 384 of 1379 +t0:=(a+b/x^2)/x^6 +--R +--R +--R 2 +--R a x + b +--R (1) -------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 384 + +--S 385 of 1379 +r0:=-1/7*b/x^7-1/5*a/x^5 +--R +--R +--R 1 2 1 +--R - - a x - - b +--R 5 7 +--R (2) -------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 385 + +--S 386 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 7a x - 5b +--R (3) ------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 386 + +--S 387 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 388 + +)clear all + +--S 389 of 1379 +t0:=(a+b/x^2)^2*x^6 +--R +--R +--R 2 6 4 2 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 389 + +--S 390 of 1379 +r0:=1/3*b^2*x^3+2/5*a*b*x^5+1/7*a^2*x^7 +--R +--R +--R 1 2 7 2 5 1 2 3 +--R (2) - a x + - a b x + - b x +--R 7 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 390 + +--S 391 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 7 5 2 3 +--R 15a x + 42a b x + 35b x +--R (3) -------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 391 + +--S 392 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 393 + +)clear all + +--S 394 of 1379 +t0:=(a+b/x^2)^2*x^5 +--R +--R +--R 2 5 3 2 +--R (1) a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 394 + +--S 395 of 1379 +r0:=1/6*(a+b/x^2)^3*x^6/a +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (2) ----------------------------- +--R 6a +--R Type: Fraction(Polynomial(Integer)) +--E 395 + +--S 396 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 6 4 2 2 +--R a x + 3a b x + 3b x +--R (3) ---------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 396 + +--S 397 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R 6a +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 398 + +)clear all + +--S 399 of 1379 +t0:=(a+b/x^2)^2*x^4 +--R +--R +--R 2 4 2 2 +--R (1) a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 399 + +--S 400 of 1379 +r0:=b^2*x+2/3*a*b*x^3+1/5*a^2*x^5 +--R +--R +--R 1 2 5 2 3 2 +--R (2) - a x + - a b x + b x +--R 5 3 +--R Type: Polynomial(Fraction(Integer)) +--E 400 + +--S 401 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3 2 +--R 3a x + 10a b x + 15b x +--R (3) ------------------------ +--R 15 +--R Type: Union(Expression(Integer),...) +--E 401 + +--S 402 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1379 +t0:=(a+b/x^2)^2*x^3 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 404 + +--S 405 of 1379 +r0:=a*b*x^2+1/4*a^2*x^4+b^2*log(x) +--R +--R +--R 2 2 4 2 +--R 4b log(x) + a x + 4a b x +--R (2) -------------------------- +--R 4 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4b log(x) + a x + 4a b x +--R (3) -------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1379 +t0:=(a+b/x^2)^2*x^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 409 + +--S 410 of 1379 +r0:=-b^2/x+2*a*b*x+1/3*a^2*x^3 +--R +--R +--R 2 4 2 2 +--R a x + 6a b x - 3b +--R (2) -------------------- +--R 3x +--R Type: Fraction(Polynomial(Integer)) +--E 410 + +--S 411 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R a x + 6a b x - 3b +--R (3) -------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1379 +t0:=(a+b/x^2)^2*x +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 414 + +--S 415 of 1379 +r0:=-1/2*b^2/x^2+1/2*a^2*x^2+2*a*b*log(x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + a x - b +--R (2) ------------------------- +--R 2 +--R 2x +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 4 2 +--R 4a b x log(x) + a x - b +--R (3) ------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1379 +t0:=(a+b/x^2)^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 419 + +--S 420 of 1379 +r0:=-1/3*b^2/x^3-2*a*b/x+a^2*x +--R +--R +--R 2 4 2 1 2 +--R a x - 2a b x - - b +--R 3 +--R (2) --------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 420 + +--S 421 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 3a x - 6a b x - b +--R (3) -------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1379 +t0:=(a+b/x^2)^2/x +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 424 + +--S 425 of 1379 +r0:=-1/4*b^2/x^4-a*b/x^2+a^2*log(x) +--R +--R +--R 2 4 2 2 +--R 4a x log(x) - 4a b x - b +--R (2) -------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R 4a x log(x) - 4a b x - b +--R (3) -------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1379 +t0:=(a+b/x^2)^2/x^2 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 429 + +--S 430 of 1379 +r0:=-1/5*b^2/x^5-2/3*a*b/x^3-a^2/x +--R +--R +--R 2 4 2 2 1 2 +--R - a x - - a b x - - b +--R 3 5 +--R (2) ------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 430 + +--S 431 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 15a x - 10a b x - 3b +--R (3) ------------------------- +--R 5 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1379 +t0:=(a+b/x^2)^2/x^3 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 434 + +--S 435 of 1379 +r0:=-1/6*(a+b/x^2)^3/b +--R +--R +--R 3 6 2 4 2 2 3 +--R - a x - 3a b x - 3a b x - b +--R (2) ------------------------------- +--R 6 +--R 6b x +--R Type: Fraction(Polynomial(Integer)) +--E 435 + +--S 436 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 3a x - 3a b x - b +--R (3) ---------------------- +--R 6 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R a +--R (4) -- +--R 6b +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1379 +t0:=(a+b/x^2)^2/x^4 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 439 + +--S 440 of 1379 +r0:=-1/7*b^2/x^7-2/5*a*b/x^5-1/3*a^2/x^3 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - a x - - a b x - - b +--R 3 5 7 +--R (2) -------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 440 + +--S 441 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 35a x - 42a b x - 15b +--R (3) -------------------------- +--R 7 +--R 105x +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1379 +t0:=(a+b/x^2)^2/x^5 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 444 + +--S 445 of 1379 +r0:=-1/8*b^2/x^8-1/3*a*b/x^6-1/4*a^2/x^4 +--R +--R +--R 1 2 4 1 2 1 2 +--R - - a x - - a b x - - b +--R 4 3 8 +--R (2) -------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 445 + +--S 446 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 6a x - 8a b x - 3b +--R (3) ----------------------- +--R 8 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1379 +t0:=(a+b/x^2)^2/x^6 +--R +--R +--R 2 4 2 2 +--R a x + 2a b x + b +--R (1) ------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 449 + +--S 450 of 1379 +r0:=-1/9*b^2/x^9-2/7*a*b/x^7-1/5*a^2/x^5 +--R +--R +--R 1 2 4 2 2 1 2 +--R - - a x - - a b x - - b +--R 5 7 9 +--R (2) -------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 450 + +--S 451 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 +--R - 63a x - 90a b x - 35b +--R (3) -------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1379 +t0:=(a+b/x^2)^3*x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R (1) a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 454 + +--S 455 of 1379 +r0:=b^3*x+a*b^2*x^3+3/5*a^2*b*x^5+1/7*a^3*x^7 +--R +--R +--R 1 3 7 3 2 5 2 3 3 +--R (2) - a x + - a b x + a b x + b x +--R 7 5 +--R Type: Polynomial(Fraction(Integer)) +--E 455 + +--S 456 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 7 2 5 2 3 3 +--R 5a x + 21a b x + 35a b x + 35b x +--R (3) ----------------------------------- +--R 35 +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1379 +t0:=(a+b/x^2)^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 459 + +--S 460 of 1379 +r0:=3/2*a*b^2*x^2+3/4*a^2*b*x^4+1/6*a^3*x^6+b^3*log(x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12b log(x) + 2a x + 9a b x + 18a b x +--R (2) --------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 6 2 4 2 2 +--R 12b log(x) + 2a x + 9a b x + 18a b x +--R (3) --------------------------------------- +--R 12 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1379 +t0:=(a+b/x^2)^3*x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 2 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 464 + +--S 465 of 1379 +r0:=-b^3/x+3*a*b^2*x+a^2*b*x^3+1/5*a^3*x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 5a b x + 15a b x - 5b +--R (2) ------------------------------- +--R 5x +--R Type: Fraction(Polynomial(Integer)) +--E 465 + +--S 466 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 5a b x + 15a b x - 5b +--R (3) ------------------------------- +--R 5x +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1379 +t0:=(a+b/x^2)^3*x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 469 + +--S 470 of 1379 +r0:=-1/2*b^3/x^2+3/2*a^2*b*x^2+1/4*a^3*x^4+3*a*b^2*log(x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + a x + 6a b x - 2b +--R (2) ------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 6 2 4 3 +--R 12a b x log(x) + a x + 6a b x - 2b +--R (3) ------------------------------------- +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1379 +t0:=(a+b/x^2)^3*x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 4 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 474 + +--S 475 of 1379 +r0:=-1/3*b^3/x^3-3*a*b^2/x+3*a^2*b*x+1/3*a^3*x^3 +--R +--R +--R 1 3 6 2 4 2 2 1 3 +--R - a x + 3a b x - 3a b x - - b +--R 3 3 +--R (2) --------------------------------- +--R 3 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 475 + +--S 476 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 9a b x - 9a b x - b +--R (3) ----------------------------- +--R 3 +--R 3x +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1379 +t0:=(a+b/x^2)^3*x +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 5 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 479 + +--S 480 of 1379 +r0:=-1/4*b^3/x^4-3/2*a*b^2/x^2+1/2*a^3*x^2+3*a^2*b*log(x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2a x - 6a b x - b +--R (2) ------------------------------------- +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3 6 2 2 3 +--R 12a b x log(x) + 2a x - 6a b x - b +--R (3) ------------------------------------- +--R 4 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1379 +t0:=(a+b/x^2)^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 6 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 484 + +--S 485 of 1379 +r0:=-1/5*b^3/x^5-a*b^2/x^3-3*a^2*b/x+a^3*x +--R +--R +--R 3 6 2 4 2 2 1 3 +--R a x - 3a b x - a b x - - b +--R 5 +--R (2) ------------------------------ +--R 5 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 485 + +--S 486 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 5a x - 15a b x - 5a b x - b +--R (3) ------------------------------- +--R 5 +--R 5x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1379 +t0:=(a+b/x^2)^3/x +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 489 + +--S 490 of 1379 +r0:=-1/6*b^3/x^6-3/4*a*b^2/x^4-3/2*a^2*b/x^2+a^3*log(x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12a x log(x) - 18a b x - 9a b x - 2b +--R (2) --------------------------------------- +--R 6 +--R 12x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R 12a x log(x) - 18a b x - 9a b x - 2b +--R (3) --------------------------------------- +--R 6 +--R 12x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1379 +t0:=(a+b/x^2)^3/x^2 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 8 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 494 + +--S 495 of 1379 +r0:=-1/7*b^3/x^7-3/5*a*b^2/x^5-a^2*b/x^3-a^3/x +--R +--R +--R 3 6 2 4 3 2 2 1 3 +--R - a x - a b x - - a b x - - b +--R 5 7 +--R (2) --------------------------------- +--R 7 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 495 + +--S 496 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 35a x - 35a b x - 21a b x - 5b +--R (3) ------------------------------------ +--R 7 +--R 35x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1379 +t0:=(a+b/x^2)^3/x^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 499 + +--S 500 of 1379 +r0:=-1/8*(a+b/x^2)^4/b +--R +--R +--R 4 8 3 6 2 2 4 3 2 4 +--R - a x - 4a b x - 6a b x - 4a b x - b +--R (2) ----------------------------------------- +--R 8 +--R 8b x +--R Type: Fraction(Polynomial(Integer)) +--E 500 + +--S 501 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 4a x - 6a b x - 4a b x - b +--R (3) -------------------------------- +--R 8 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1379 +m0:=a0-r0 +--R +--R +--R 4 +--R a +--R (4) -- +--R 8b +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1379 +t0:=(a+b/x^2)^3/x^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 504 + +--S 505 of 1379 +r0:=-1/9*b^3/x^9-3/7*a*b^2/x^7-3/5*a^2*b/x^5-1/3*a^3/x^3 +--R +--R +--R 1 3 6 3 2 4 3 2 2 1 3 +--R - - a x - - a b x - - a b x - - b +--R 3 5 7 9 +--R (2) ------------------------------------- +--R 9 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 505 + +--S 506 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 105a x - 189a b x - 135a b x - 35b +--R (3) ---------------------------------------- +--R 9 +--R 315x +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1379 +t0:=(a+b/x^2)^3/x^5 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 509 + +--S 510 of 1379 +r0:=-1/10*b^3/x^10-3/8*a*b^2/x^8-1/2*a^2*b/x^6-1/4*a^3/x^4 +--R +--R +--R 1 3 6 1 2 4 3 2 2 1 3 +--R - - a x - - a b x - - a b x - -- b +--R 4 2 8 10 +--R (2) -------------------------------------- +--R 10 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 510 + +--S 511 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 10a x - 20a b x - 15a b x - 4b +--R (3) ------------------------------------ +--R 10 +--R 40x +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1379 +t0:=(a+b/x^2)^3/x^6 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R (1) ----------------------------- +--R 12 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 514 + +--S 515 of 1379 +r0:=-1/11*b^3/x^11-1/3*a*b^2/x^9-3/7*a^2*b/x^7-1/5*a^3/x^5 +--R +--R +--R 1 3 6 3 2 4 1 2 2 1 3 +--R - - a x - - a b x - - a b x - -- b +--R 5 7 3 11 +--R (2) -------------------------------------- +--R 11 +--R x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 515 + +--S 516 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 4 2 2 3 +--R - 231a x - 495a b x - 385a b x - 105b +--R (3) ----------------------------------------- +--R 11 +--R 1155x +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1379 +t0:=x^6/(a+b/x^2) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 519 + +--S 520 of 1379 +r0:=-b^3*x/a^4+1/3*b^2*x^3/a^3-1/5*b*x^5/a^2+1/7*x^7/a+_ + b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 3 7 2 5 2 3 3 +-+ +--R 105b \|b atan(-----) + (15a x - 21a b x + 35a b x - 105b x)\|a +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------------ +--R 4 +-+ +--R 105a \|a +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 3 | b \| a 3 7 2 5 2 3 +--R 105b |- - log(---------------------) + 30a x - 42a b x + 70a b x +--R \| a 2 +--R a x + b +--R + +--R 3 +--R - 210b x +--R / +--R 4 +--R 210a +--R , +--R +-+ +--R |b +--R +-+ |- +--R 3 |b \|a 3 7 2 5 2 3 3 +--R - 105b |- atan(----) + 15a x - 21a b x + 35a b x - 105b x +--R \|a x +--R -------------------------------------------------------------] +--R 4 +--R 105a +--R Type: Union(List(Expression(Integer)),...) +--E 521 + +--S 522 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R 3 | b +-+ \| a 3 +-+ x\|a +--R b |- - \|a log(---------------------) - 2b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 3 +-+ |b \|a 3 +-+ x\|a +--R - b \|a |- atan(----) - b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 4 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 525 + +)clear all + +--S 526 of 1379 +t0:=x^5/(a+b/x^2) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 526 + +--S 527 of 1379 +r0:=1/2*b^2*x^2/a^3-1/4*b*x^4/a^2+1/6*x^6/a-1/2*b^3*log(b+a*x^2)/a^4 +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (2) ---------------------------------------------- +--R 4 +--R 12a +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 6 2 4 2 2 +--R - 6b log(a x + b) + 2a x - 3a b x + 6a b x +--R (3) ---------------------------------------------- +--R 4 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 528 + +--S 529 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 530 + +)clear all + +--S 531 of 1379 +t0:=x^4/(a+b/x^2) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 531 + +--S 532 of 1379 +r0:=b^2*x/a^3-1/3*b*x^3/a^2+1/5*x^5/a-b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(7/2) +--R +--R +--R +-+ +--R 2 +-+ x\|a 2 5 3 2 +-+ +--R - 15b \|b atan(-----) + (3a x - 5a b x + 15b x)\|a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------- +--R 3 +-+ +--R 15a \|a +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 | b \| a 2 5 3 2 +--R 15b |- - log(-----------------------) + 6a x - 10a b x + 30b x +--R \| a 2 +--R a x + b +--R [-----------------------------------------------------------------, +--R 3 +--R 30a +--R +-+ +--R |b +--R +-+ |- +--R 2 |b \|a 2 5 3 2 +--R 15b |- atan(----) + 3a x - 5a b x + 15b x +--R \|a x +--R --------------------------------------------] +--R 3 +--R 15a +--R Type: Union(List(Expression(Integer)),...) +--E 533 + +--S 534 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R b |- - \|a log(-----------------------) + 2b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R b \|a |- atan(----) + b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 537 + +)clear all + +--S 538 of 1379 +t0:=x^3/(a+b/x^2) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 538 + +--S 539 of 1379 +r0:=-1/2*b*x^2/a^2+1/4*x^4/a+1/2*b^2*log(b+a*x^2)/a^3 +--R +--R +--R 2 2 2 4 2 +--R 2b log(a x + b) + a x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 4a +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 4 2 +--R 2b log(a x + b) + a x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 4a +--R Type: Union(Expression(Integer),...) +--E 540 + +--S 541 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 542 + +)clear all + +--S 543 of 1379 +t0:=x^2/(a+b/x^2) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 543 + +--S 544 of 1379 +r0:=-b*x/a^2+1/3*x^3/a+b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(5/2) +--R +--R +--R +-+ +--R +-+ x\|a 3 +-+ +--R 3b\|b atan(-----) + (a x - 3b x)\|a +--R +-+ +--R \|b +--R (2) ------------------------------------- +--R 2 +-+ +--R 3a \|a +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R | b \| a 3 +--R 3b |- - log(---------------------) + 2a x - 6b x +--R \| a 2 +--R a x + b +--R [-------------------------------------------------, +--R 2 +--R 6a +--R +-+ +--R |b +--R +-+ |- +--R |b \|a 3 +--R - 3b |- atan(----) + a x - 3b x +--R \|a x +--R --------------------------------] +--R 2 +--R 3a +--R Type: Union(List(Expression(Integer)),...) +--E 545 + +--S 546 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R b |- - \|a log(---------------------) - 2b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - b\|a |- atan(----) - b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1379 +t0:=x/(a+b/x^2) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 550 + +--S 551 of 1379 +r0:=1/2*x^2/a-1/2*b*log(b+a*x^2)/a^2 +--R +--R +--R 2 2 +--R - b log(a x + b) + a x +--R (2) ------------------------ +--R 2 +--R 2a +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R - b log(a x + b) + a x +--R (3) ------------------------ +--R 2 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1379 +t0:=1/(a+b/x^2) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 555 + +--S 556 of 1379 +r0:=x/a-atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(3/2) +--R +--R +--R +-+ +--R +-+ x\|a +-+ +--R - \|b atan(-----) + x\|a +--R +-+ +--R \|b +--R (2) ------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | b 2 +-+ +--R +---+ - 2a x |- - + a x - b |b +--R | b \| a +-+ |- +--R |- - log(-----------------------) + 2x |b \|a +--R \| a 2 |- atan(----) + x +--R a x + b \|a x +--R (3) [---------------------------------------,------------------] +--R 2a a +--R Type: Union(List(Expression(Integer)),...) +--E 557 + +--S 558 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R |- - \|a log(-----------------------) + 2\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R \|a |- atan(----) + \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 561 + +)clear all + +--S 562 of 1379 +t0:=1/((a+b/x^2)*x) +--R +--R +--R x +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 562 + +--S 563 of 1379 +r0:=1/2*log(b+a*x^2)/a +--R +--R +--R 2 +--R log(a x + b) +--R (2) ------------- +--R 2a +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(a x + b) +--R (3) ------------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 564 + +--S 565 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 566 + +)clear all + +--S 567 of 1379 +t0:=1/((a+b/x^2)*x^2) +--R +--R +--R 1 +--R (1) -------- +--R 2 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 567 + +--S 568 of 1379 +r0:=atan(x*sqrt(a)/sqrt(b))/(sqrt(a)*sqrt(b)) +--R +--R +--R +-+ +--R x\|a +--R atan(-----) +--R +-+ +--R \|b +--R (2) ----------- +--R +-+ +-+ +--R \|a \|b +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-----+ +--R (a x - b)\|- a b + 2a b x +---+ +--R log(---------------------------) x\|a b +--R 2 atan(-------) +--R a x + b b +--R (3) [--------------------------------,-------------] +--R +-----+ +---+ +--R 2\|- a b \|a b +--R Type: Union(List(Expression(Integer)),...) +--E 569 + +--S 570 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 2\|- a b \|a \|b +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1379 +t0:=1/((a+b/x^2)*x^3) +--R +--R +--R 1 +--R (1) ---------- +--R 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 574 + +--S 575 of 1379 +r0:=-1/2*log(a+b/x^2)/b +--R +--R +--R 2 +--R a x + b +--R log(--------) +--R 2 +--R x +--R (2) - ------------- +--R 2b +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - log(a x + b) + 2log(x) +--R (3) ------------------------- +--R 2b +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1379 +m0:=a0-r0 +--R +--R +--R 2 +--R 2 a x + b +--R - log(a x + b) + 2log(x) + log(--------) +--R 2 +--R x +--R (4) ----------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1379 +t0:=1/((a+b/x^2)*x^4) +--R +--R +--R 1 +--R (1) ----------- +--R 4 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 579 + +--S 580 of 1379 +r0:=(-1)/(b*x)-atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(3/2) +--R +--R +--R +-+ +--R +-+ x\|a +-+ +--R - x\|a atan(-----) - \|b +--R +-+ +--R \|b +--R (2) ------------------------- +--R +-+ +--R b x\|b +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +---+ +--R | a 2 +-+ +--R +---+ - 2b x |- - + a x - b |a +--R | a \| b +-+ b |- +--R x |- - log(-----------------------) - 2 |a \|b +--R \| b 2 x |- atan(-----) - 1 +--R a x + b \|b a x +--R (3) [---------------------------------------,--------------------] +--R 2b x b x +--R Type: Union(List(Expression(Integer)),...) +--E 581 + +--S 582 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R |- - \|b log(-----------------------) + 2\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +--S 584 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R |- \|b atan(-----) + \|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 585 + +)clear all + +--S 586 of 1379 +t0:=1/((a+b/x^2)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 586 + +--S 587 of 1379 +r0:=(-1/2)/(b*x^2)-a*log(x)/b^2+1/2*a*log(b+a*x^2)/b^2 +--R +--R +--R 2 2 2 +--R a x log(a x + b) - 2a x log(x) - b +--R (2) ----------------------------------- +--R 2 2 +--R 2b x +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R a x log(a x + b) - 2a x log(x) - b +--R (3) ----------------------------------- +--R 2 2 +--R 2b x +--R Type: Union(Expression(Integer),...) +--E 588 + +--S 589 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 590 + +)clear all + +--S 591 of 1379 +t0:=1/((a+b/x^2)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 591 + +--S 592 of 1379 +r0:=(-1/3)/(b*x^3)+a/(b^2*x)+a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 2 +-+ +--R 3a x \|a atan(-----) + (3a x - b)\|b +--R +-+ +--R \|b +--R (2) -------------------------------------- +--R 2 3 +-+ +--R 3b x \|b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 3 | a \| b 2 +--R 3a x |- - log(---------------------) + 6a x - 2b +--R \| b 2 +--R a x + b +--R [--------------------------------------------------, +--R 2 3 +--R 6b x +--R +-+ +--R |a +--R +-+ b |- +--R 3 |a \|b 2 +--R - 3a x |- atan(-----) + 3a x - b +--R \|b a x +--R ----------------------------------] +--R 2 3 +--R 3b x +--R Type: Union(List(Expression(Integer)),...) +--E 593 + +--S 594 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R a |- - \|b log(---------------------) - 2a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - a |- \|b atan(-----) - a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 597 + +)clear all + +--S 598 of 1379 +t0:=1/((a+b/x^2)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 5 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 598 + +--S 599 of 1379 +r0:=(-1/4)/(b*x^4)+1/2*a/(b^2*x^2)+a^2*log(x)/b^3-1/2*a^2*log(b+a*x^2)/b^3 +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b +--R (2) ------------------------------------------------- +--R 3 4 +--R 4b x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 4 2 2 +--R - 2a x log(a x + b) + 4a x log(x) + 2a b x - b +--R (3) ------------------------------------------------- +--R 3 4 +--R 4b x +--R Type: Union(Expression(Integer),...) +--E 600 + +--S 601 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 602 + +)clear all + +--S 603 of 1379 +t0:=1/((a+b/x^2)*x^8) +--R +--R +--R 1 +--R (1) ----------- +--R 8 6 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 603 + +--S 604 of 1379 +r0:=(-1/5)/(b*x^5)+1/3*a/(b^2*x^3)-a^2/(b^3*x)-_ + a^(5/2)*atan(x*sqrt(a)/sqrt(b))/b^(7/2) +--R +--R +--R +-+ +--R 2 5 +-+ x\|a 2 4 2 2 +-+ +--R - 15a x \|a atan(-----) + (- 15a x + 5a b x - 3b )\|b +--R +-+ +--R \|b +--R (2) -------------------------------------------------------- +--R 3 5 +-+ +--R 15b x \|b +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 2 5 | a \| b 2 4 2 2 +--R 15a x |- - log(-----------------------) - 30a x + 10a b x - 6b +--R \| b 2 +--R a x + b +--R [------------------------------------------------------------------, +--R 3 5 +--R 30b x +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 |a \|b 2 4 2 2 +--R 15a x |- atan(-----) - 15a x + 5a b x - 3b +--R \|b a x +--R ----------------------------------------------] +--R 3 5 +--R 15b x +--R Type: Union(List(Expression(Integer)),...) +--E 605 + +--S 606 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R 2 | a +-+ \| b 2 +-+ x\|a +--R a |- - \|b log(-----------------------) + 2a \|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R 2 |a +-+ \|b 2 +-+ x\|a +--R a |- \|b atan(-----) + a \|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1379 +t0:=x^6/(a+b/x^2)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 610 + +--S 611 of 1379 +r0:=-9/2*b^3*x/a^5+3/2*b^2*x^3/a^4-9/10*b*x^5/a^3+9/14*x^7/a^2-_ + 1/2*x^9/(a*(b+a*x^2))+9/2*b^(7/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 3 2 4 +-+ x\|a +--R (315a b x + 315b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (10a x - 18a b x + 42a b x - 210a b x - 315b x)\|a +--R / +--R 6 2 5 +-+ +--R (70a x + 70a b)\|a +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 3 2 4 | b \| a 4 9 3 7 +--R (315a b x + 315b ) |- - log(---------------------) + 20a x - 36a b x +--R \| a 2 +--R a x + b +--R + +--R 2 2 5 3 3 4 +--R 84a b x - 420a b x - 630b x +--R / +--R 6 2 5 +--R 140a x + 140a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 3 2 4 |b \|a 4 9 3 7 2 2 5 +--R (- 315a b x - 315b ) |- atan(----) + 10a x - 18a b x + 42a b x +--R \|a x +--R + +--R 3 3 4 +--R - 210a b x - 315b x +--R / +--R 6 2 5 +--R 70a x + 70a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 612 + +--S 613 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R 3 | b +-+ \| a 3 +-+ x\|a +--R 9b |- - \|a log(---------------------) - 18b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------- +--R 5 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 3 +-+ |b \|a 3 +-+ x\|a +--R - 9b \|a |- atan(----) - 9b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 5 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 616 + +)clear all + +--S 617 of 1379 +t0:=x^5/(a+b/x^2)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 617 + +--S 618 of 1379 +r0:=3/2*b^2*x^2/a^4-1/2*b*x^4/a^3+1/6*x^6/a^2-1/2*b^4/(a^5*(b+a*x^2))-_ + 2*b^3*log(b+a*x^2)/a^5 +--R +--R +--R (2) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6a x + 6a b +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 4 2 4 8 3 6 2 2 4 3 2 4 +--R (- 12a b x - 12b )log(a x + b) + a x - 2a b x + 6a b x + 9a b x - 3b +--R --------------------------------------------------------------------------- +--R 6 2 5 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 619 + +--S 620 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1379 +t0:=x^4/(a+b/x^2)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 622 + +--S 623 of 1379 +r0:=7/2*b^2*x/a^4-7/6*b*x^3/a^3+7/10*x^5/a^2-1/2*x^7/(a*(b+a*x^2))-_ + 7/2*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 3 +-+ x\|a +--R (- 105a b x - 105b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6a x - 14a b x + 70a b x + 105b x)\|a +--R / +--R 5 2 4 +-+ +--R (30a x + 30a b)\|a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 2 3 | b \| a 3 7 +--R (105a b x + 105b ) |- - log(-----------------------) + 12a x +--R \| a 2 +--R a x + b +--R + +--R 2 5 2 3 3 +--R - 28a b x + 140a b x + 210b x +--R / +--R 5 2 4 +--R 60a x + 60a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 2 3 |b \|a 3 7 2 5 2 3 3 +--R (105a b x + 105b ) |- atan(----) + 6a x - 14a b x + 70a b x + 105b x +--R \|a x +--R ------------------------------------------------------------------------] +--R 5 2 4 +--R 30a x + 30a b +--R Type: Union(List(Expression(Integer)),...) +--E 624 + +--S 625 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R 7b |- - \|a log(-----------------------) + 14b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R 7b \|a |- atan(----) + 7b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 4 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1379 +t0:=x^3/(a+b/x^2)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 629 + +--S 630 of 1379 +r0:=-b*x^2/a^3+1/4*x^4/a^2+1/2*b^3/(a^4*(b+a*x^2))+3/2*b^2*log(b+a*x^2)/a^4 +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ------------------------------------------------------------- +--R 5 2 4 +--R 4a x + 4a b +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3 2 3 6 2 4 2 2 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ------------------------------------------------------------- +--R 5 2 4 +--R 4a x + 4a b +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1379 +t0:=x^2/(a+b/x^2)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 634 + +--S 635 of 1379 +r0:=-5/2*b*x/a^3+5/6*x^3/a^2-1/2*x^5/(a*(b+a*x^2))+5/2*b^(3/2)*_ + atan(x*sqrt(a)/sqrt(b))/a^(7/2) +--R +--R +--R +-+ +--R 2 2 +-+ x\|a 2 5 3 2 +-+ +--R (15a b x + 15b )\|b atan(-----) + (2a x - 10a b x - 15b x)\|a +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------------- +--R 4 2 3 +-+ +--R (6a x + 6a b)\|a +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 2 | b \| a 2 5 3 2 +--R (15a b x + 15b ) |- - log(---------------------) + 4a x - 20a b x - 30b x +--R \| a 2 +--R a x + b +--R [---------------------------------------------------------------------------- +--R 4 2 3 +--R 12a x + 12a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 2 |b \|a 2 5 3 2 +--R (- 15a b x - 15b ) |- atan(----) + 2a x - 10a b x - 15b x +--R \|a x +--R ------------------------------------------------------------] +--R 4 2 3 +--R 6a x + 6a b +--R Type: Union(List(Expression(Integer)),...) +--E 636 + +--S 637 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 5b |- - \|a log(---------------------) - 10b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +--S 639 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - 5b\|a |- atan(----) - 5b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 640 + +)clear all + +--S 641 of 1379 +t0:=x/(a+b/x^2)^2 +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 641 + +--S 642 of 1379 +r0:=1/2*x^2/a^2-1/2*b^2/(a^3*(b+a*x^2))-b*log(b+a*x^2)/a^3 +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) --------------------------------------------------- +--R 4 2 3 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 2 4 2 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) --------------------------------------------------- +--R 4 2 3 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 643 + +--S 644 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 645 + +)clear all + +--S 646 of 1379 +t0:=1/(a+b/x^2)^2 +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 646 + +--S 647 of 1379 +r0:=3/2*x/a^2-1/2*x^3/(a*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(5/2) +--R +--R +--R +-+ +--R 2 +-+ x\|a 3 +-+ +--R (- 3a x - 3b)\|b atan(-----) + (2a x + 3b x)\|a +--R +-+ +--R \|b +--R (2) -------------------------------------------------- +--R 3 2 2 +-+ +--R (2a x + 2a b)\|a +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 | b \| a 3 +--R (3a x + 3b) |- - log(-----------------------) + 4a x + 6b x +--R \| a 2 +--R a x + b +--R [-------------------------------------------------------------, +--R 3 2 2 +--R 4a x + 4a b +--R +-+ +--R |b +--R +-+ |- +--R 2 |b \|a 3 +--R (3a x + 3b) |- atan(----) + 2a x + 3b x +--R \|a x +--R -----------------------------------------] +--R 3 2 2 +--R 2a x + 2a b +--R Type: Union(List(Expression(Integer)),...) +--E 648 + +--S 649 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 3 |- - \|a log(----------------------- + 6\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R 3\|a |- atan(----) + 3\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 652 + +)clear all + +--S 653 of 1379 +t0:=1/((a+b/x^2)^2*x) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 653 + +--S 654 of 1379 +r0:=1/2*b/(a^2*(b+a*x^2))+1/2*log(b+a*x^2)/a^2 +--R +--R +--R 2 2 +--R (a x + b)log(a x + b) + b +--R (2) --------------------------- +--R 3 2 2 +--R 2a x + 2a b +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 +--R (a x + b)log(a x + b) + b +--R (3) --------------------------- +--R 3 2 2 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 655 + +--S 656 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 657 + +)clear all + +--S 658 of 1379 +t0:=1/((a+b/x^2)^2*x^2) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 658 + +--S 659 of 1379 +r0:=-1/2*x/(a*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 x\|a +-+ +-+ +--R (a x + b)atan(-----) - x\|a \|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a x + 2a b)\|a \|b +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (a x - b)\|- a b + 2a b x +-----+ +--R (a x + b)log(---------------------------) - 2x\|- a b +--R 2 +--R a x + b +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a x + 4a b)\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (a x + b)atan(-------) - x\|a b +--R b +--R ---------------------------------] +--R 2 2 +---+ +--R (2a x + 2a b)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 660 + +--S 661 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4a\|- a b \|a \|b +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2a\|a \|b \|a b +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1379 +t0:=1/((a+b/x^2)^2*x^3) +--R +--R +--R x +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 665 + +--S 666 of 1379 +r0:=1/2/(b*(a+b/x^2)) +--R +--R +--R 2 +--R x +--R (2) ------------- +--R 2 2 +--R 2a b x + 2b +--R Type: Fraction(Polynomial(Integer)) +--E 666 + +--S 667 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 2 +--R 2a x + 2a b +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2a b +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1379 +t0:=1/((a+b/x^2)^2*x^4) +--R +--R +--R 1 +--R (1) ------------------- +--R 2 4 2 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 670 + +--S 671 of 1379 +r0:=1/2*x/(b*(b+a*x^2))+1/2*atan(x*sqrt(a)/sqrt(b))/(b^(3/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 x\|a +-+ +-+ +--R (a x + b)atan(-----) + x\|a \|b +--R +-+ +--R \|b +--R (2) --------------------------------- +--R 2 2 +-+ +-+ +--R (2a b x + 2b )\|a \|b +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ +--R 2 (a x - b)\|- a b + 2a b x +-----+ +--R (a x + b)log(---------------------------) + 2x\|- a b +--R 2 +--R a x + b +--R [-------------------------------------------------------, +--R 2 2 +-----+ +--R (4a b x + 4b )\|- a b +--R +---+ +--R 2 x\|a b +---+ +--R (a x + b)atan(-------) + x\|a b +--R b +--R ---------------------------------] +--R 2 2 +---+ +--R (2a b x + 2b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 672 + +--S 673 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 4b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 673 + +--S 674 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 676 + +)clear all + +--S 677 of 1379 +t0:=1/((a+b/x^2)^2*x^5) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 5 3 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 677 + +--S 678 of 1379 +r0:=1/2/(b*(b+a*x^2))+log(x)/b^2-1/2*log(b+a*x^2)/b^2 +--R +--R +--R 2 2 2 +--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b +--R (2) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2b +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R (- a x - b)log(a x + b) + (2a x + 2b)log(x) + b +--R (3) -------------------------------------------------- +--R 2 2 3 +--R 2a b x + 2b +--R Type: Union(Expression(Integer),...) +--E 679 + +--S 680 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 681 + +)clear all + +--S 682 of 1379 +t0:=1/((a+b/x^2)^2*x^6) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 6 4 2 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 682 + +--S 683 of 1379 +r0:=(-3/2)/(b^2*x)+1/2/(b*x*(b+a*x^2))-3/2*atan(x*sqrt(a)/sqrt(b))*_ + sqrt(a)/b^(5/2) +--R +--R +--R +-+ +--R 3 +-+ x\|a 2 +-+ +--R (- 3a x - 3b x)\|a atan(-----) + (- 3a x - 2b)\|b +--R +-+ +--R \|b +--R (2) ---------------------------------------------------- +--R 2 3 3 +-+ +--R (2a b x + 2b x)\|b +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 3 | a \| b 2 +--R (3a x + 3b x) |- - log(-----------------------) - 6a x - 4b +--R \| b 2 +--R a x + b +--R [-------------------------------------------------------------, +--R 2 3 3 +--R 4a b x + 4b x +--R +-+ +--R |a +--R +-+ b |- +--R 3 |a \|b 2 +--R (3a x + 3b x) |- atan(-----) - 3a x - 2b +--R \|b a x +--R ------------------------------------------] +--R 2 3 3 +--R 2a b x + 2b x +--R Type: Union(List(Expression(Integer)),...) +--E 684 + +--S 685 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 3 |- - \|b log(----------------------- + 6\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 686 + +--S 687 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R 3 |- \|b atan(----- + 3\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) --------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1379 +t0:=1/((a+b/x^2)^2*x^7) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 7 5 2 3 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 689 + +--S 690 of 1379 +r0:=(-1)/(b^2*x^2)+1/2/(b*x^2*(b+a*x^2))-2*a*log(x)/b^3+a*log(b+a*x^2)/b^3 +--R +--R +--R (2) +--R 2 4 2 2 2 4 2 2 2 +--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2b x +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 4 2 2 2 +--R (2a x + 2a b x )log(a x + b) + (- 4a x - 4a b x )log(x) - 2a b x - b +--R ------------------------------------------------------------------------- +--R 3 4 4 2 +--R 2a b x + 2b x +--R Type: Union(Expression(Integer),...) +--E 691 + +--S 692 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 692 + +--S 693 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 693 + +)clear all + +--S 694 of 1379 +t0:=1/((a+b/x^2)^2*x^8) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 8 6 2 4 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 694 + +--S 695 of 1379 +r0:=(-5/6)/(b^2*x^3)+5/2*a/(b^3*x)+1/2/(b*x^3*(b+a*x^2))+5/2*a^(3/2)*_ + atan(x*sqrt(a)/sqrt(b))/b^(7/2) +--R +--R +--R +-+ +--R 2 5 3 +-+ x\|a 2 4 2 2 +-+ +--R (15a x + 15a b x )\|a atan(-----) + (15a x + 10a b x - 2b )\|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------------ +--R 3 5 4 3 +-+ +--R (6a b x + 6b x )\|b +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 2 5 3 | a \| b 2 4 2 +--R (15a x + 15a b x ) |- - log(---------------------) + 30a x + 20a b x +--R \| b 2 +--R a x + b +--R + +--R 2 +--R - 4b +--R / +--R 3 5 4 3 +--R 12a b x + 12b x +--R , +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 3 |a \|b 2 4 2 2 +--R (- 15a x - 15a b x ) |- atan(-----) + 15a x + 10a b x - 2b +--R \|b a x +--R --------------------------------------------------------------] +--R 3 5 4 3 +--R 6a b x + 6b x +--R Type: Union(List(Expression(Integer)),...) +--E 696 + +--S 697 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 5a |- - \|b log(---------------------) - 10a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------- +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - 5a |- \|b atan(-----) - 5a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 700 + +)clear all + +--S 701 of 1379 +t0:=1/((a+b/x^2)^2*x^9) +--R +--R +--R 1 +--R (1) --------------------- +--R 2 9 7 2 5 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 701 + +--S 702 of 1379 +r0:=(-3/4)/(b^2*x^4)+3/2*a/(b^3*x^2)+1/2/(b*x^4*(b+a*x^2))+3*a^2*_ + log(x)/b^4-3/2*a^2*log(b+a*x^2)/b^4 +--R +--R +--R (2) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - b +--R / +--R 4 6 5 4 +--R 4a b x + 4b x +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 3 6 2 4 2 4 +--R (- 6a x - 6a b x )log(a x + b) + (12a x + 12a b x )log(x) + 6a b x +--R + +--R 2 2 3 +--R 3a b x - b +--R / +--R 4 6 5 4 +--R 4a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 703 + +--S 704 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 705 + +)clear all + +--S 706 of 1379 +t0:=x^5/(a+b/x^2)^3 +--R +--R +--R 11 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 706 + +--S 707 of 1379 +r0:=3*b^2*x^2/a^5-3/4*b*x^4/a^4+1/6*x^6/a^3+1/4*b^5/(a^6*(b+a*x^2)^2)-_ + 5/2*b^4/(a^6*(b+a*x^2))-5*b^3*log(b+a*x^2)/a^6 +--R +--R +--R (2) +--R 2 3 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x +--R + +--R 3 2 6 2 3 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27b +--R / +--R 8 4 7 2 6 2 +--R 12a x + 24a b x + 12a b +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 4 4 2 5 2 5 10 4 8 +--R (- 60a b x - 120a b x - 60b )log(a x + b) + 2a x - 5a b x +--R + +--R 3 2 6 2 3 4 4 2 5 +--R 20a b x + 63a b x + 6a b x - 27b +--R / +--R 8 4 7 2 6 2 +--R 12a x + 24a b x + 12a b +--R Type: Union(Expression(Integer),...) +--E 708 + +--S 709 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 710 + +)clear all + +--S 711 of 1379 +t0:=x^4/(a+b/x^2)^3 +--R +--R +--R 10 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 711 + +--S 712 of 1379 +r0:=63/8*b^2*x/a^5-21/8*b*x^3/a^4+63/40*x^5/a^3-1/4*x^9/(a*(b+a*x^2)^2)-_ + 9/8*x^7/(a^2*(b+a*x^2))-63/8*b^(5/2)*atan(x*sqrt(a)/sqrt(b))/a^(11/2) +--R +--R +--R (2) +--R +-+ +--R 2 2 4 3 2 4 +-+ x\|a +--R (- 315a b x - 630a b x - 315b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (8a x - 24a b x + 168a b x + 525a b x + 315b x)\|a +--R / +--R 7 4 6 2 5 2 +-+ +--R (40a x + 80a b x + 40a b )\|a +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 2 4 3 2 4 | b \| a +--R (315a b x + 630a b x + 315b ) |- - log(-----------------------) +--R \| a 2 +--R a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +--R 16a x - 48a b x + 336a b x + 1050a b x + 630b x +--R / +--R 7 4 6 2 5 2 +--R 80a x + 160a b x + 80a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 2 2 4 3 2 4 |b \|a 4 9 3 7 +--R (315a b x + 630a b x + 315b ) |- atan(----) + 8a x - 24a b x +--R \|a x +--R + +--R 2 2 5 3 3 4 +--R 168a b x + 525a b x + 315b x +--R / +--R 7 4 6 2 5 2 +--R 40a x + 80a b x + 40a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 713 + +--S 714 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R 2 | b +-+ \| a 2 +-+ x\|a +--R 63b |- - \|a log(-----------------------) + 126b \|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ----------------------------------------------------------------- +--R 5 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R 2 +-+ |b \|a 2 +-+ x\|a +--R 63b \|a |- atan(----) + 63b \|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 5 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 717 + +)clear all + +--S 718 of 1379 +t0:=x^3/(a+b/x^2)^3 +--R +--R +--R 9 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 718 + +--S 719 of 1379 +r0:=-3/2*b*x^2/a^4+1/4*x^4/a^3-1/4*b^4/(a^5*(b+a*x^2)^2)+2*b^3/_ + (a^5*(b+a*x^2))+3*b^2*log(b+a*x^2)/a^5 +--R +--R +--R (2) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7b +--R / +--R 7 4 6 2 5 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 3 2 4 2 4 8 3 6 2 2 4 +--R (12a b x + 24a b x + 12b )log(a x + b) + a x - 4a b x - 11a b x +--R + +--R 3 2 4 +--R 2a b x + 7b +--R / +--R 7 4 6 2 5 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 720 + +--S 721 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 722 + +)clear all + +--S 723 of 1379 +t0:=x^2/(a+b/x^2)^3 +--R +--R +--R 8 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 723 + +--S 724 of 1379 +r0:=-35/8*b*x/a^4+35/24*x^3/a^3-1/4*x^7/(a*(b+a*x^2)^2)-7/8*x^5/_ + (a^2*(b+a*x^2))+35/8*b^(3/2)*atan(x*sqrt(a)/sqrt(b))/a^(9/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 3 +-+ x\|a +--R (105a b x + 210a b x + 105b )\|b atan(-----) +--R +-+ +--R \|b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (8a x - 56a b x - 175a b x - 105b x)\|a +--R / +--R 6 4 5 2 4 2 +-+ +--R (24a x + 48a b x + 24a b )\|a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +--R 2 4 2 2 3 | b \| a +--R (105a b x + 210a b x + 105b ) |- - log(---------------------) +--R \| a 2 +--R a x + b +--R + +--R 3 7 2 5 2 3 3 +--R 16a x - 112a b x - 350a b x - 210b x +--R / +--R 6 4 5 2 4 2 +--R 48a x + 96a b x + 48a b +--R , +--R +--R +-+ +--R |b +--R +-+ |- +--R 2 4 2 2 3 |b \|a 3 7 2 5 +--R (- 105a b x - 210a b x - 105b ) |- atan(----) + 8a x - 56a b x +--R \|a x +--R + +--R 2 3 3 +--R - 175a b x - 105b x +--R / +--R 6 4 5 2 4 2 +--R 24a x + 48a b x + 24a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 725 + +--S 726 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 35b |- - \|a log(---------------------) - 70b\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R - 35b\|a |- atan(----) - 35b\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) -------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1379 +t0:=x/(a+b/x^2)^3 +--R +--R +--R 7 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 730 + +--S 731 of 1379 +r0:=1/2*x^2/a^3+1/4*b^3/(a^4*(b+a*x^2)^2)-3/2*b^2/(a^4*(b+a*x^2))-_ + 3/2*b*log(b+a*x^2)/a^4 +--R +--R +--R (2) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R --------------------------------------------------------------------------- +--R 6 4 5 2 4 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 3 2 3 6 2 4 2 2 3 +--R (- 6a b x - 12a b x - 6b )log(a x + b) + 2a x + 4a b x - 4a b x - 5b +--R --------------------------------------------------------------------------- +--R 6 4 5 2 4 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 732 + +--S 733 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +)clear all + +--S 735 of 1379 +t0:=1/(a+b/x^2)^3 +--R +--R +--R 6 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 735 + +--S 736 of 1379 +r0:=15/8*x/a^3-1/4*x^5/(a*(b+a*x^2)^2)-5/8*x^3/(a^2*(b+a*x^2))-_ + 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(b)/a^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 4 2 2 +-+ x\|a 2 5 3 2 +-+ +--R (- 15a x - 30a b x - 15b )\|b atan(-----) + (8a x + 25a b x + 15b x)\|a +--R +-+ +--R \|b +--R ---------------------------------------------------------------------------- +--R 5 4 4 2 3 2 +-+ +--R (8a x + 16a b x + 8a b )\|a +--R Type: Expression(Integer) +--E 736 + +--S 737 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +--R 2 4 2 2 | b \| a 2 5 +--R (15a x + 30a b x + 15b ) |- - log(-----------------------) + 16a x +--R \| a 2 +--R a x + b +--R + +--R 3 2 +--R 50a b x + 30b x +--R / +--R 5 4 4 2 3 2 +--R 16a x + 32a b x + 16a b +--R , +--R +-+ +--R |b +--R +-+ |- +--R 2 4 2 2 |b \|a 2 5 3 2 +--R (15a x + 30a b x + 15b ) |- atan(----) + 8a x + 25a b x + 15b x +--R \|a x +--R -------------------------------------------------------------------] +--R 5 4 4 2 3 2 +--R 8a x + 16a b x + 8a b +--R Type: Union(List(Expression(Integer)),...) +--E 737 + +--S 738 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | b 2 +--R +---+ - 2a x |- - + a x - b +-+ +--R | b +-+ \| a +-+ x\|a +--R 15 |- - \|a log(----------------------- + 30\|b atan(-----) +--R \| a 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |b +--R +-+ |- +-+ +--R +-+ |b \|a +-+ x\|a +--R 15\|a |- atan(----) + 15\|b atan(-----) +--R \|a x +-+ +--R \|b +--R (6) ---------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 741 + +)clear all + +--S 742 of 1379 +t0:=1/((a+b/x^2)^3*x) +--R +--R +--R 5 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 742 + +--S 743 of 1379 +r0:=-1/4*b^2/(a^3*(b+a*x^2)^2)+b/(a^3*(b+a*x^2))+1/2*log(b+a*x^2)/a^3 +--R +--R +--R 2 4 2 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (2) ---------------------------------------------------- +--R 5 4 4 2 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Expression(Integer) +--E 743 + +--S 744 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 4 2 2 2 2 2 +--R (2a x + 4a b x + 2b )log(a x + b) + 4a b x + 3b +--R (3) ---------------------------------------------------- +--R 5 4 4 2 3 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 744 + +--S 745 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 746 + +)clear all + +--S 747 of 1379 +t0:=1/((a+b/x^2)^3*x^2) +--R +--R +--R 4 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 747 + +--S 748 of 1379 +r0:=-1/4*x^3/(a*(b+a*x^2)^2)-3/8*x/(a^2*(b+a*x^2))+_ + 3/8*atan(x*sqrt(a)/sqrt(b))/(a^(5/2)*sqrt(b)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (3a x + 6a b x + 3b )atan(-----) + (- 5a x - 3b x)\|a \|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------------- +--R 4 4 3 2 2 2 +-+ +-+ +--R (8a x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (3a x + 6a b x + 3b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (- 10a x - 6b x)\|- a b +--R / +--R 4 4 3 2 2 2 +-----+ +--R (16a x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3a x + 6a b x + 3b )atan(-------) + (- 5a x - 3b x)\|a b +--R b +--R -------------------------------------------------------------] +--R 4 4 3 2 2 2 +---+ +--R (8a x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 749 + +--S 750 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16a \|- a b \|a \|b +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8a \|a \|b \|a b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1379 +t0:=1/((a+b/x^2)^3*x^3) +--R +--R +--R 3 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 754 + +--S 755 of 1379 +r0:=1/4/(b*(a+b/x^2)^2) +--R +--R +--R 4 +--R x +--R (2) ----------------------- +--R 2 4 2 2 3 +--R 4a b x + 8a b x + 4b +--R Type: Fraction(Polynomial(Integer)) +--E 755 + +--S 756 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R - 2a x - b +--R (3) ----------------------- +--R 4 4 3 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R 4a b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1379 +t0:=1/((a+b/x^2)^3*x^4) +--R +--R +--R 2 +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 759 + +--S 760 of 1379 +r0:=-1/4*x/(a*(b+a*x^2)^2)+1/8*x/(a*b*(b+a*x^2))+_ + 1/8*atan(x*sqrt(a)/sqrt(b))/(a^(3/2)*b^(3/2)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (a x + 2a b x + b )atan(-----) + (a x - b x)\|a \|b +--R +-+ +--R \|b +--R (2) ------------------------------------------------------- +--R 3 4 2 2 2 3 +-+ +-+ +--R (8a b x + 16a b x + 8a b )\|a \|b +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (a x + 2a b x + b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (2a x - 2b x)\|- a b +--R / +--R 3 4 2 2 2 3 +-----+ +--R (16a b x + 32a b x + 16a b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (a x + 2a b x + b )atan(-------) + (a x - b x)\|a b +--R b +--R -------------------------------------------------------] +--R 3 4 2 2 2 3 +---+ +--R (8a b x + 16a b x + 8a b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 761 + +--S 762 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R \|a \|b log(---------------------------) - 2\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) --------------------------------------------------------------- +--R +-----+ +-+ +-+ +--R 16a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +--S 764 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R \|a \|b atan(-------) - \|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ----------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 765 + +)clear all + +--S 766 of 1379 +t0:=1/((a+b/x^2)^3*x^5) +--R +--R +--R x +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 766 + +--S 767 of 1379 +r0:=(-1/4)/(a*(a+b/x^2)^2*x^4) +--R +--R +--R 1 +--R (2) - ----------------------- +--R 3 4 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Fraction(Polynomial(Integer)) +--E 767 + +--S 768 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------- +--R 3 4 2 2 2 +--R 4a x + 8a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 768 + +--S 769 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 770 + +)clear all + +--S 771 of 1379 +t0:=1/((a+b/x^2)^3*x^6) +--R +--R +--R 1 +--R (1) ----------------------------- +--R 3 6 2 4 2 2 3 +--R a x + 3a b x + 3a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 771 + +--S 772 of 1379 +r0:=1/4*x/(b*(b+a*x^2)^2)+3/8*x/(b^2*(b+a*x^2))+_ + 3/8*atan(x*sqrt(a)/sqrt(b))/(b^(5/2)*sqrt(a)) +--R +--R +--R +-+ +--R 2 4 2 2 x\|a 3 +-+ +-+ +--R (3a x + 6a b x + 3b )atan(-----) + (3a x + 5b x)\|a \|b +--R +-+ +--R \|b +--R (2) ----------------------------------------------------------- +--R 2 2 4 3 2 4 +-+ +-+ +--R (8a b x + 16a b x + 8b )\|a \|b +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 +-----+ +--R 2 4 2 2 (a x - b)\|- a b + 2a b x +--R (3a x + 6a b x + 3b )log(---------------------------) +--R 2 +--R a x + b +--R + +--R 3 +-----+ +--R (6a x + 10b x)\|- a b +--R / +--R 2 2 4 3 2 4 +-----+ +--R (16a b x + 32a b x + 16b )\|- a b +--R , +--R +---+ +--R 2 4 2 2 x\|a b 3 +---+ +--R (3a x + 6a b x + 3b )atan(-------) + (3a x + 5b x)\|a b +--R b +--R -----------------------------------------------------------] +--R 2 2 4 3 2 4 +---+ +--R (8a b x + 16a b x + 8b )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 773 + +--S 774 of 1379 +m0a:=a0.1-r0 +--R +--R +--R 2 +-----+ +-+ +--R +-+ +-+ (a x - b)\|- a b + 2a b x +-----+ x\|a +--R 3\|a \|b log(---------------------------) - 6\|- a b atan(-----) +--R 2 +-+ +--R a x + b \|b +--R (4) ---------------------------------------------------------------- +--R 2 +-----+ +-+ +-+ +--R 16b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +---+ +-+ +--R +-+ +-+ x\|a b +---+ x\|a +--R 3\|a \|b atan(-------) - 3\|a b atan(-----) +--R b +-+ +--R \|b +--R (6) ------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 777 + +)clear all + +--S 778 of 1379 +t0:=1/((a+b/x^2)^3*x^7) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 7 2 5 2 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 778 + +--S 779 of 1379 +r0:=1/4/(b*(b+a*x^2)^2)+1/2/(b^2*(b+a*x^2))+log(x)/b^3-1/2*log(b+a*x^2)/b^3 +--R +--R +--R (2) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x) +--R + +--R 2 2 +--R 2a b x + 3b +--R / +--R 2 3 4 4 2 5 +--R 4a b x + 8a b x + 4b +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 2 2 2 4 2 2 +--R (- 2a x - 4a b x - 2b )log(a x + b) + (4a x + 8a b x + 4b )log(x) +--R + +--R 2 2 +--R 2a b x + 3b +--R / +--R 2 3 4 4 2 5 +--R 4a b x + 8a b x + 4b +--R Type: Union(Expression(Integer),...) +--E 780 + +--S 781 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 782 + +)clear all + +--S 783 of 1379 +t0:=1/((a+b/x^2)^3*x^8) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 8 2 6 2 4 3 2 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 783 + +--S 784 of 1379 +r0:=(-15/8)/(b^3*x)+1/4/(b*x*(b+a*x^2)^2)+5/8/(b^2*x*(b+a*x^2))-_ + 15/8*atan(x*sqrt(a)/sqrt(b))*sqrt(a)/b^(7/2) +--R +--R +--R (2) +--R +-+ +--R 2 5 3 2 +-+ x\|a +--R (- 15a x - 30a b x - 15b x)\|a atan(-----) +--R +-+ +--R \|b +--R + +--R 2 4 2 2 +-+ +--R (- 15a x - 25a b x - 8b )\|b +--R / +--R 2 3 5 4 3 5 +-+ +--R (8a b x + 16a b x + 8b x)\|b +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +--R 2 5 3 2 | a \| b 2 4 +--R (15a x + 30a b x + 15b x) |- - log(-----------------------) - 30a x +--R \| b 2 +--R a x + b +--R + +--R 2 2 +--R - 50a b x - 16b +--R / +--R 2 3 5 4 3 5 +--R 16a b x + 32a b x + 16b x +--R , +--R +-+ +--R |a +--R +-+ b |- +--R 2 5 3 2 |a \|b 2 4 2 2 +--R (15a x + 30a b x + 15b x) |- atan(-----) - 15a x - 25a b x - 8b +--R \|b a x +--R --------------------------------------------------------------------] +--R 2 3 5 4 3 5 +--R 8a b x + 16a b x + 8b x +--R Type: Union(List(Expression(Integer)),...) +--E 785 + +--S 786 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ - 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 15 |- - \|b log(----------------------- + 30\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 3 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R 15 |- \|b atan(----- + 15\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) ----------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 788 + +--S 789 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 789 + +)clear all + +--S 790 of 1379 +t0:=1/((a+b/x^2)^3*x^9) +--R +--R +--R 1 +--R (1) ------------------------------- +--R 3 9 2 7 2 5 3 3 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 790 + +--S 791 of 1379 +r0:=(-3/2)/(b^3*x^2)+1/4/(b*x^2*(b+a*x^2)^2)+3/4/(b^2*x^2*(b+a*x^2))-_ + 3*a*log(x)/b^4+3/2*a*log(b+a*x^2)/b^4 +--R +--R +--R (2) +--R 3 6 2 4 2 2 2 +--R (6a x + 12a b x + 6a b x )log(a x + b) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 6 5 4 6 2 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 4 2 2 2 +--R (6a x + 12a b x + 6a b x )log(a x + b) +--R + +--R 3 6 2 4 2 2 2 4 2 2 3 +--R (- 12a x - 24a b x - 12a b x )log(x) - 6a b x - 9a b x - 2b +--R / +--R 2 4 6 5 4 6 2 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 792 + +--S 793 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 793 + +--S 794 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 794 + +)clear all + +--S 795 of 1379 +t0:=1/((a+b/x^2)^3*x^10) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 10 2 8 2 6 3 4 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 795 + +--S 796 of 1379 +r0:=(-35/24)/(b^3*x^3)+35/8*a/(b^4*x)+1/4/(b*x^3*(b+a*x^2)^2)+_ + 7/8/(b^2*x^3*(b+a*x^2))+35/8*a^(3/2)*atan(x*sqrt(a)/sqrt(b))/b^(9/2) +--R +--R +--R (2) +--R +-+ +--R 3 7 2 5 2 3 +-+ x\|a +--R (105a x + 210a b x + 105a b x )\|a atan(-----) +--R +-+ +--R \|b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (105a x + 175a b x + 56a b x - 8b )\|b +--R / +--R 2 4 7 5 5 6 3 +-+ +--R (24a b x + 48a b x + 24b x )\|b +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +--R 3 7 2 5 2 3 | a \| b +--R (105a x + 210a b x + 105a b x ) |- - log(---------------------) +--R \| b 2 +--R a x + b +--R + +--R 3 6 2 4 2 2 3 +--R 210a x + 350a b x + 112a b x - 16b +--R / +--R 2 4 7 5 5 6 3 +--R 48a b x + 96a b x + 48b x +--R , +--R +--R +-+ +--R |a +--R +-+ b |- +--R 3 7 2 5 2 3 |a \|b 3 6 +--R (- 105a x - 210a b x - 105a b x ) |- atan(-----) + 105a x +--R \|b a x +--R + +--R 2 4 2 2 3 +--R 175a b x + 56a b x - 8b +--R / +--R 2 4 7 5 5 6 3 +--R 24a b x + 48a b x + 24b x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 797 + +--S 798 of 1379 +m0a:=a0.1-r0 +--R +--R +--R +---+ +--R | a 2 +--R +---+ 2b x |- - + a x - b +-+ +--R | a +-+ \| b +-+ x\|a +--R 35a |- - \|b log(---------------------) - 70a\|a atan(-----) +--R \| b 2 +-+ +--R a x + b \|b +--R (4) ------------------------------------------------------------ +--R 4 +-+ +--R 16b \|b +--R Type: Expression(Integer) +--E 798 + +--S 799 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +-+ +--R |a +--R +-+ b |- +-+ +--R |a +-+ \|b +-+ x\|a +--R - 35a |- \|b atan(-----) - 35a\|a atan(-----) +--R \|b a x +-+ +--R \|b +--R (6) --------------------------------------------- +--R 4 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 801 + +)clear all + +--S 802 of 1379 +t0:=1/((a+b/x^2)^3*x^11) +--R +--R +--R 1 +--R (1) -------------------------------- +--R 3 11 2 9 2 7 3 5 +--R a x + 3a b x + 3a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 802 + +--S 803 of 1379 +r0:=(-3/2)/(b^3*x^4)+3*a/(b^4*x^2)+1/4/(b*x^4*(b+a*x^2)^2)+_ + 1/(b^2*x^4*(b+a*x^2))+6*a^2*log(x)/b^5-3*a^2*log(b+a*x^2)/b^5 +--R +--R +--R (2) +--R 4 8 3 6 2 2 4 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 8 6 6 7 4 +--R 4a b x + 8a b x + 4b x +--R Type: Expression(Integer) +--E 803 + +--S 804 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 8 3 6 2 2 4 2 +--R (- 12a x - 24a b x - 12a b x )log(a x + b) +--R + +--R 4 8 3 6 2 2 4 3 6 2 2 4 3 2 4 +--R (24a x + 48a b x + 24a b x )log(x) + 12a b x + 18a b x + 4a b x - b +--R / +--R 2 5 8 6 6 7 4 +--R 4a b x + 8a b x + 4b x +--R Type: Union(Expression(Integer),...) +--E 804 + +--S 805 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 806 + +)clear all + +--S 807 of 1379 +t0:=(a+b/x^2)^(1/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1379 +r0:=-1/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/8*b*x^2*_ + sqrt(a+b/x^2)/a+1/4*x^4*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 809 + +--S 810 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 14 5 12 4 2 10 3 3 8 +--R - 11a x - 231a b x - 1452a b x - 4048a b x +--R + +--R 2 4 6 5 4 6 2 +--R - 5632a b x - 3840a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 2 5 4 6 2 +--R - 3840a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 5 6 3 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 5 6 3 7 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 2 5 5 6 3 +--R 3840a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x +--R + +--R 2 5 6 6 4 7 2 +--R 7424a b x + 4352a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x +--R + +--R 2 6 4 7 2 +--R 4352a b x + 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 2 6 +--R 3328a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 2 6 +--R - 3840a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (4a b x + 8b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (- a b x - 8a b x - 8b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (- 8a b x - 16b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (2a b x + 16a b x + 16b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1379 +t0:=(a+b/x^2)^(1/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1379 +r0:=1/3*(a+b/x^2)^(3/2)*x^3/a +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + b x) |-------- +--R | 2 +--R \| x +--R (2) ----------------------- +--R 3a +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b +--R (3) ------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 | 2 +--R ((- a x - 5a b x - 4b x) |-------- \|b - 3a b x - 6a b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b +--R (a x + 6a b x + 6a b x )\|b + (3a b x + 7a b x + 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 2 2 +--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 19a b x - 66a b x - 80a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1379 +t0:=(a+b/x^2)^(1/2)*x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (1) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1379 +r0:=1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a)+1/2*x^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 +---+ +--R 4\|- a \|b \|a x + b + (- 2a x - 4b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 821 + +--S 822 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 9 4 7 3 2 5 2 3 3 4 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 5 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 823 + +--S 824 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 +---+ +-+ +--R 4\|- a \|a \|b \|a x + b + (- 2a x - 4b)\|- a \|a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 4a x - 12a b x - 8b x) |-------- \|b - a x - 9a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 16a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 825 + +)clear all + +--S 826 of 1379 +t0:=(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (1) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 826 + +--S 827 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b |a x + b +--R (2) - \|b atanh(------------) + x |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b - b\|b )log(------------------) + a x \|b +--R x +--R (3) -------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression(Integer),...) +--E 828 + +--S 829 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 +-+ \|a x + b - \|b +--R (b\|a x + b - b\|b )log(------------------) +--R x +--R + +--R +--------+ +--R +--------+ +-+ | 2 +--------+ +--R | 2 +-+ \|b |a x + b +-+ | 2 +--R (b\|a x + b - b\|b )atanh(------------) - x |-------- \|b \|a x + b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R a x \|b + b x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x - 7a b x - 4b )\|b + (- a x - 5a b x - 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b x) |-------- \|b + a x + 6a b x + 9a b x + 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ | 2 +--R (3a x + 4b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (- a x - 5a b x - 4b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 830 + +)clear all + +--S 831 of 1379 +t0:=(a+b/x^2)^(1/2)/x +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x |a x + b +--R (2) \|a atanh(-----------) - |-------- +--R +-+ | 2 +--R \|a \| x +--R Type: Expression(Integer) +--E 832 + +--S 833 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R , +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 833 + +--S 834 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R (x\|a \|a x + b - x\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x)\|a +--R / +--R +--------+ +--R | 2 +--R 2 8 6 2 4 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 +-+ +-+ \| x +--R (- x\|a \|a x + b + x\|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 2 +-+ +--R +---+ | 2 +---+ +-+ \|a x + b - \|b +--R (2x\|- a \|a x + b - 2x\|- a \|b )atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R / +--R +--------+ +--R | 2 +-+ +--R x\|a x + b - x\|b +--R Type: Expression(Integer) +--E 836 + +--S 837 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 2a x - 2b x) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 837 + +)clear all + +--S 838 of 1379 +t0:=(a+b/x^2)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1379 +r0:=-1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-1/2*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|b |a x + b +-+ +--R - a x atanh(------------) - |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------- +--R +-+ +--R 2x\|b +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (2a b x \|a x + b + (- a x - 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 4 2 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (2a x \|b \|a x + b - a x - 2a b x )log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 +-+ | 2 2 4 2 \|b +--R (2a x \|b \|a x + b - a x - 2a b x )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 | 2 4 2 +-+ +--R 4b x \|a x + b + (- 2a x - 4b x )\|b +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (5a x + 25a b x + 36a b x + 16b x) |-------- \|b + a x + 14a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 41a b x + 44a b x + 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 842 + +)clear all + +--S 843 of 1379 +t0:=(a+b/x^2)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (- a x - b) |-------- +--R | 2 +--R \| x +--R (2) ----------------------- +--R 2 +--R 3b x +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (3a x + 7a b x + 4b )\|b \|a x + b - a x - 6a b x - 9a b x - 4b +--R ----------------------------------------------------------------------- +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Union(Expression(Integer),...) +--E 845 + +--S 846 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((3a x + 7a b x + 4b )\|b + (a x + 5a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (- 3a x - 7a b x - 4b x) |-------- \|b - a x - 6a b x - 9a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 5 2 3 | 2 5 2 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 6a x - 38a b x - 64a b x - 32b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 19a b x - 66a b x - 80a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (6a x + 44a b x + 102a b x + 96a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 19a b x + 66a b x + 80a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 847 + +)clear all + +--S 848 of 1379 +t0:=(a+b/x^2)^(1/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1379 +r0:=1/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-_ + 1/4*sqrt(a+b/x^2)/x^3-1/8*a*sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 \|b 2 |a x + b +-+ +--R a x atanh(------------) + (- a x - 2b) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 3 +-+ +--R 8b x \|b +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 4 8 3 6 2 2 4 +-+ +--R ((- 4a b x - 8a b x )\|a x + b + (a x + 8a b x + 8a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (a b x + 10a b x + 24a b x + 16b )\|a x + b +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 4a b x - 20a b x - 32a b x - 16b )\|b +--R / +--R +--------+ +--R 2 6 3 4 +-+ | 2 2 2 8 3 6 4 4 +--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x +--R Type: Union(Expression(Integer),...) +--E 850 + +--S 851 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((- 4a x - 8a b x )\|b \|a x + b + a x + 8a b x + 8a b x ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (a x + 10a b x + 24a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (4a b x + 16a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6 +--R (- a x - 10a b x - 24a b x - 16b x) |-------- \|b - 4a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R - 20a b x - 32a b x - 16b +--R / +--R +--------+ +--R 2 6 3 4 | 2 2 8 2 6 3 4 +-+ +--R (32a b x + 64b x )\|a x + b + (- 8a b x - 64a b x - 64b x )\|b +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 9a x - 129a b x - 552a b x - 1008a b x - 832a b x - 256b ) +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x + 960a b x + 256b +--R / +--R +--------+ +--R | 2 +--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 852 + +)clear all + +--S 853 of 1379 +t0:=(a+b/x^2)^(3/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (1) (a x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1379 +r0:=1/4*(a+b/x^2)^(3/2)*x^4+3/8*b^2*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/sqrt(a)+3/8*b*x^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 8\|a +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 21a b x - 56a b x - 40b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|b +--R / +--R +--------+ +--R 2 +---+ +-+ | 2 2 4 2 2 +---+ +--R (32a x + 64b)\|- a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 855 + +--S 856 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 36a b x - 40b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 21a b x - 56a b x - 40b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 21a b x + 56a b x + 40b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +-+ +-+ | 2 2 4 2 2 +-+ +--R (32a x + 64b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64b )\|a +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R - 11a x - 242a b x - 1683a b x - 5500a b x - 9680a b x +--R + +--R 3 5 5 2 6 3 7 +--R - 9472a b x - 4864a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 3 5 6 2 6 4 7 2 +--R - 7424a b x - 4352a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 13872a b x + 11776a b x + 5376a b x + 1024b +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 3 5 6 2 6 4 7 2 +--R 9472a b x + 4864a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 4 5 7 +--R a x + 63a b x + 743a b x + 3653a b x + 9420a b x + 13872a b x +--R + +--R 3 6 5 2 7 3 8 +--R 11776a b x + 5376a b x + 1024a b x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 2 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 3 6 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 3 6 +--R 3840a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 4 6 2 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 857 + +--S 858 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 36a b x - 40b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 21a b x - 56a b x - 40b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 44a b x + 76a b x + 40b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 21a b x + 56a b x + 40b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +---+ +-+ +-+ | 2 +--R (32a x + 64b)\|- a \|a \|b \|a x + b +--R + +--R 2 4 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64b )\|- a \|a +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - a x - 34a b x - 225a b x - 608a b x - 800a b x - 512a b x +--R + +--R 6 +--R - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 8a x + 104a b x + 456a b x + 952a b x + 1040a b x + 576a b x +--R + +--R 6 +--R 128b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 +--R 128b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 3 3 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1379 +t0:=(a+b/x^2)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (1) (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1379 +r0:=1/3*(a+b/x^2)^(3/2)*x^3-b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))+_ + b*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 3 |a x + b +--R - 3b\|b atanh(------------) + (a x + 4b x) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (- 3a b x - 12a b x )\|a x + b + (a x + 9a b x + 12a b x )\|b +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 862 + +--S 863 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 | 2 2 2 3 +-+ +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 2 3 | 2 2 2 3 +-+ \|b +--R ((3a b x + 12b )\|a x + b + (- 9a b x - 12b )\|b )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 +--R ((- a x - 8a b x - 16b x) |-------- \|b - 3a b x - 12a b x ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 +-+ 2 5 2 3 3 |a x + b +--R (a x + 9a b x + 12a b x )\|b + (3a b x + 16a b x + 16b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 8 2 6 2 4 3 2 |a x + b +-+ | 2 +--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1379 +t0:=(a+b/x^2)^(3/2)*x +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1379 +r0:=1/2*(a+b/x^2)^(3/2)*x^2+3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-_ + 3/2*b*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R +-+ \| x 2 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R , +--R +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x - 8b +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 867 + +--S 868 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((3a b x + 12b x)\|a \|a x + b + (- 9a b x - 12b x)\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 3 6 +--R - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 4 6 2 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 4 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 4 6 2 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 5 6 3 7 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 3 7 +--R 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 2 +-+ | 2 3 2 +-+ +-+ +--R ((- 3a b x - 12b x)\|a \|a x + b + (9a b x + 12b x)\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2 +---+ | 2 3 2 +---+ +-+ +--R ((6a b x + 24b x)\|- a \|a x + b + (- 18a b x - 24b x)\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 3a x + 2a b x + 8b )\|b + (- a x - 2a b x + 8b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (3a x - 2a b x - 8b x) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 | 2 3 +-+ +--R (2a x + 8b x)\|a x + b + (- 6a x - 8b x)\|b +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 9 2 7 2 5 3 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 871 + +)clear all + +--S 872 of 1379 +t0:=(a+b/x^2)^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1379 +r0:=-1/2*(a+b/x^2)^(3/2)*x-3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*_ + sqrt(b)+3/2*a*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 2 |a x + b +--R - 3a x\|b atanh(------------) + (2a x - b) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------ +--R 2x +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 4a b x + 3a b x + 4b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + 3a b x - 5a b x - 4b )\|b +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x +--R Type: Union(Expression(Integer),...) +--E 874 + +--S 875 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 2 4 2 2 +-+ +--R ((3a b x + 12a b x )\|a x + b + (- 9a b x - 12a b x )\|b ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3 +--R ((- 2a x - 7a b x + 4b x) |-------- \|b - 4a b x + 3a b x + 4b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + 3a b x - 5a b x - 4b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (6a b x + 5a b x - 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 4 2 +-+ | 2 4 2 2 +--R (2a x + 8b x )\|b \|a x + b - 6a b x - 8b x +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 10 2 8 2 6 3 4 |a x + b +-+ | 2 +--R (7a x + 56a b x + 112a b x + 64b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 876 + +)clear all + +--S 877 of 1379 +t0:=(a+b/x^2)^(3/2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 877 + +--S 878 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)+a^(3/2)*atanh(sqrt(a+b/x^2)/sqrt(a))-a*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 |a x + b +--R 3a x \|a atanh(-----------) + (- 4a x - b) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +--R 3x +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R , +--R +--R +--------+ +--R 2 5 3 +---+ | 2 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 5 3 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 879 + +--S 880 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x +--R | 2 +--R \| x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 3 6 +--R - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 4 6 2 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 4 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 4 6 2 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 5 6 3 7 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 3 7 +--R 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 14 3 12 2 2 10 3 8 4 6 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 5 +--R - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 5 3 +-+ | 2 2 5 3 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 5 3 +---+ | 2 2 5 3 +---+ +-+ +--R ((6a x + 24a b x )\|- a \|a x + b + (- 18a x - 24a b x )\|- a \|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((12a x + 19a b x + 4b )\|b + (4a x + 17a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (- 12a x - 19a b x - 4b x) |-------- \|b - 4a x - 21a b x - 21a b x +--R | 2 +--R \| x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (3a x + 12b x )\|a x + b + (- 9a x - 12b x )\|b +--R Type: Expression(Integer) +--E 882 + +--S 883 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 883 + +)clear all + +--S 884 of 1379 +t0:=(a+b/x^2)^(3/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1379 +r0:=-1/4*(a+b/x^2)^(3/2)/x-3/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_ + sqrt(b)-3/8*a*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 \|b 2 |a x + b +-+ +--R - 3a x atanh(------------) + (- 5a x - 2b) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------------------------- +--R 3 +-+ +--R 8x \|b +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 2 4 | 2 +--R (12a b x + 24a b x )\|a x + b +--R + +--R 4 8 3 6 2 2 4 +-+ +--R (- 3a x - 24a b x - 24a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 2 4 3 2 4 | 2 +--R (5a b x + 42a b x + 56a b x + 16b )\|a x + b +--R + +--R 3 6 2 2 4 3 2 4 +-+ +--R (- 20a b x - 68a b x - 64a b x - 16b )\|b +--R / +--R +--------+ +--R 6 2 4 +-+ | 2 2 8 2 6 3 4 +--R (32a b x + 64b x )\|b \|a x + b - 8a b x - 64a b x - 64b x +--R Type: Union(Expression(Integer),...) +--E 886 + +--S 887 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 6 2 4 +-+ | 2 4 8 3 6 2 2 4 +--R ((12a x + 24a b x )\|b \|a x + b - 3a x - 24a b x - 24a b x ) +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (5a x + 42a b x + 56a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 2 3 3 |a x + b +--R (20a b x + 48a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 3 6 +--R (- 5a x - 42a b x - 56a b x - 16b x) |-------- \|b - 20a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R - 68a b x - 64a b x - 16b +--R / +--R +--------+ +--R 6 2 4 | 2 2 8 6 2 4 +-+ +--R (32a b x + 64b x )\|a x + b + (- 8a x - 64a b x - 64b x )\|b +--R Type: Expression(Integer) +--E 887 + +--S 888 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 2 6 +--R - 1088a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 3 6 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 3 6 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x + 2352a b x +--R + +--R 6 2 7 +--R 1216a b x + 256b +--R / +--R +--------+ +--R | 2 +--R 4 14 3 12 2 2 10 3 8 4 6 |a x + b +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 888 + +)clear all + +--S 889 of 1379 +t0:=(a+b/x^2)^(3/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1379 +r0:=-1/5*(a+b/x^2)^(5/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (- a x - 2a b x - b ) |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------- +--R 4 +--R 5b x +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b \|a x + b - a x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80b x )\|a x + b +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80b x )\|b +--R Type: Union(Expression(Integer),...) +--E 891 + +--S 892 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 14a b x + 41a b x + 44a b x + 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ 5 10 +--R (- 5a x - 30a b x - 61a b x - 52a b x - 16b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 55a b x - 85a b x - 60a b x - 16b +--R / +--R +--------+ +--R 2 9 2 7 3 5 | 2 +--R (5a b x + 60a b x + 80b x )\|a x + b +--R + +--R 2 9 2 7 3 5 +-+ +--R (- 25a b x - 100a b x - 80b x )\|b +--R Type: Expression(Integer) +--E 892 + +--S 893 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x +--R + +--R 5 3 6 +--R - 2048a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 52a b x - 501a b x - 1970a b x - 3920a b x +--R + +--R 2 5 4 6 2 7 +--R - 4192a b x - 2304a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 10a x + 190a b x + 1182a b x + 3530a b x + 5760a b x +--R + +--R 2 5 4 6 2 7 +--R 5280a b x + 2560a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 2 5 5 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x +--R + +--R 6 3 7 +--R 2304a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 893 + +)clear all + +--S 894 of 1379 +t0:=(a+b/x^2)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1379 +r0:=-1/6*(a+b/x^2)^(3/2)/x^3+1/16*a^3*atanh(sqrt(b)/_ + (x*sqrt(a+b/x^2)))/b^(3/2)-1/8*a*sqrt(a+b/x^2)/x^3-1/16*a^2*_ + sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 3 5 \|b 2 4 2 2 |a x + b +-+ +--R 3a x atanh(------------) + (- 3a x - 14a b x - 8b ) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------------------------------- +--R 5 +-+ +--R 48b x \|b +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 4 2 8 3 3 6 | 2 +--R (- 18a b x - 96a b x - 96a b x )\|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 +-+ +--R (3a x + 54a b x + 144a b x + 96a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R (3a b x + 68a b x + 404a b x + 912a b x + 832a b x + 256b ) +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +-+ +--R (- 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b )\|b +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 +-+ | 2 3 2 12 +--R (288a b x + 1536a b x + 1536b x )\|b \|a x + b - 48a b x +--R + +--R 2 3 10 4 8 5 6 +--R - 864a b x - 2304a b x - 1536b x +--R Type: Union(Expression(Integer),...) +--E 896 + +--S 897 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10 +--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x +--R + +--R 4 2 8 3 3 6 +--R 144a b x + 96a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 5 10 +--R (- 18a x - 96a b x - 96a b x )\|b \|a x + b + 3a x + 54a b x +--R + +--R 4 2 8 3 3 6 +--R 144a b x + 96a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (3a x + 68a b x + 404a b x + 912a b x + 832a b x + 256b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (18a b x + 180a b x + 592a b x + 704a b x + 256b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 3a x - 68a b x - 404a b x - 912a b x - 832a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R - 18a b x - 198a b x - 772a b x - 1296a b x - 960a b x - 256b +--R / +--R +--------+ +--R 2 2 10 3 8 4 6 | 2 +--R (288a b x + 1536a b x + 1536b x )\|a x + b +--R + +--R 3 12 2 2 10 3 8 4 6 +-+ +--R (- 48a b x - 864a b x - 2304a b x - 1536b x )\|b +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 13a x - 390a b x - 3653a b x - 16172a b x - 39520a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 56576a b x - 47360a b x - 21504a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 898 + +)clear all + +--S 899 of 1379 +t0:=(a+b/x^2)^(5/2)*x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1379 +r0:=5/8*b*(a+b/x^2)^(3/2)*x^2+1/4*(a+b/x^2)^(5/2)*x^4+_ + 15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))*sqrt(a)-15/8*b^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 4 2 2 |a x + b +--R 15b \|a atanh(-----------) + (2a x + 9a b x - 8b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) --------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240b x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R , +--R +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480b x)\|- a \|a x + b +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480b x)\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 901 + +--S 902 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (15a b x + 180a b x + 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (- 75a b x - 300a b x - 240b x)\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (75a b x + 300a b x + 240b x)\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 6 6 4 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 17 6 15 5 2 13 4 3 11 3 4 9 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 7 6 5 7 3 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 17 6 15 5 2 13 4 3 11 3 4 9 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 7 6 5 7 3 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 8 6 6 7 4 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 5 3 3 4 +-+ | 2 +--R (- 15a b x - 180a b x - 240b x)\|a \|a x + b +--R + +--R 2 2 5 3 3 4 +-+ +-+ +--R (75a b x + 300a b x + 240b x)\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 5 3 3 4 +---+ | 2 +--R (30a b x + 360a b x + 480b x)\|- a \|a x + b +--R + +--R 2 2 5 3 3 4 +---+ +-+ +--R (- 150a b x - 600a b x - 480b x)\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 10a x - 85a b x - 172a b x + 16a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 2a x - 33a b x - 132a b x - 48a b x + 128b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (10a x + 85a b x + 172a b x - 16a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 2a x + 35a b x + 165a b x + 180a b x - 80a b x - 128b +--R / +--R +--------+ +--R 2 5 3 2 | 2 +--R (8a x + 96a b x + 128b x)\|a x + b +--R + +--R 2 5 3 2 +-+ +--R (- 40a x - 160a b x - 128b x)\|b +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 3 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 905 + +)clear all + +--S 906 of 1379 +t0:=(a+b/x^2)^(5/2)*x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1379 +r0:=5/3*b*(a+b/x^2)^(3/2)*x+1/3*(a+b/x^2)^(5/2)*x^3-_ + 5/2*a*b^(3/2)*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))-5/2*b^2*sqrt(a+b/x^2)/x +--R +--R +--R +--------+ +--R +-+ | 2 +--R +-+ \|b 2 4 2 2 |a x + b +--R - 15a b x\|b atanh(------------) + (2a x + 14a b x - 3b ) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------------------------------------- +--R 6x +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 10a b x - 96a b x - 129a b x + 60a b x + 48b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x +--R Type: Union(Expression(Integer),...) +--E 908 + +--S 909 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 3 2 6 2 3 4 4 2 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 3 2 6 2 3 4 4 2 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 2a x - 38a b x - 197a b x - 188a b x + 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 10a b x - 96a b x - 129a b x + 60a b x + 48b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 40a b x + 165a b x + 105a b x - 84a b x - 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (10a b x + 110a b x + 297a b x + 164a b x - 48b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 6 4 2 2 +-+ | 2 2 6 2 4 3 2 +--R (6a x + 72a b x + 96b x )\|b \|a x + b - 30a b x - 120a b x - 96b x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 19152a b x + 14336a b x + 5888a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8 +--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x +--R + +--R 3 6 6 2 7 4 8 2 9 +--R 25648a b x + 17152a b x + 6400a b x + 1024b +--R / +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 910 + +)clear all + +--S 911 of 1379 +t0:=(a+b/x^2)^(5/2)*x +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1379 +r0:=-5/6*b*(a+b/x^2)^(3/2)+1/2*(a+b/x^2)^(5/2)*x^2+5/2*a^(3/2)*b*_ + atanh(sqrt(a+b/x^2)/sqrt(a))-5/2*a*b*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 +-+ \| x 2 4 2 2 |a x + b +--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) -------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R , +--R +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 913 + +--S 914 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 8 6 6 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 9 6 7 7 5 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 7 2 2 5 3 3 +-+ | 2 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 7 2 2 5 3 3 +---+ | 2 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 7 2 2 5 3 3 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 7 5 2 3 | 2 +--R (6a x + 72a b x + 96b x )\|a x + b +--R + +--R 2 7 5 2 3 +-+ +--R (- 30a x - 120a b x - 96b x )\|b +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 5 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 917 + +)clear all + +--S 918 of 1379 +t0:=(a+b/x^2)^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1379 +r0:=-5/8*a*(a+b/x^2)^(3/2)*x-1/4*(a+b/x^2)^(5/2)*x-15/8*a^2*_ + atanh(sqrt(b)/(x*sqrt(a+b/x^2)))*sqrt(b)+15/8*a^2*x*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R 2 3 +-+ \|b 2 4 2 2 |a x + b +--R - 15a x \|b atanh(------------) + (8a x - 9a b x - 2b ) |-------- +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------------------------------- +--R 3 +--R 8x +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 32a b x - 19a b x + 190a b x + 184a b x + 32b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128b x +--R Type: Union(Expression(Integer),...) +--E 920 + +--S 921 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (15a b x + 180a b x + 240a b x )\|a x + b +--R + +--R 4 8 3 2 6 2 3 4 +-+ +--R (- 75a b x - 300a b x - 240a b x )\|b +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 8a x - 87a b x - 18a b x + 168a b x + 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 32a b x - 19a b x + 190a b x + 184a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (8a x + 55a b x - 55a b x - 278a b x - 200a b x - 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (40a b x + 115a b x - 62a b x - 184a b x - 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 8 6 2 4 +-+ | 2 2 8 2 6 +--R (8a x + 96a b x + 128b x )\|b \|a x + b - 40a b x - 160a b x +--R + +--R 3 4 +--R - 128b x +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 11a x - 253a b x - 1925a b x - 7183a b x - 15180a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 19152a b x - 14336a b x - 5888a b x - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R 11a x + 253a b x + 1925a b x + 7183a b x + 15180a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 19152a b x + 14336a b x + 5888a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 4 5 8 +--R a x + 64a b x + 806a b x + 4396a b x + 13073a b x + 23292a b x +--R + +--R 3 6 6 2 7 4 8 2 9 +--R 25648a b x + 17152a b x + 6400a b x + 1024b +--R / +--R 5 16 4 14 3 2 12 2 3 10 4 8 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 6 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 8 6 6 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 922 + +)clear all + +--S 923 of 1379 +t0:=(a+b/x^2)^(5/2)/x +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1379 +r0:=-1/3*a*(a+b/x^2)^(3/2)-1/5*(a+b/x^2)^(5/2)+a^(5/2)*_ + atanh(sqrt(a+b/x^2)/sqrt(a))-a^2*sqrt(a+b/x^2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 4 +-+ \| x 2 4 2 2 |a x + b +--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 4 +--R 15x +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R , +--R +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 925 + +--S 926 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ +-+ 2 +--R (\|b - x\|a )\|a x + b + x\|a \|b - a x - b +--R log(------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 3 9 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 19 8 17 7 2 15 6 3 13 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 3 9 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 2 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 20 8 18 7 2 16 6 3 14 5 4 12 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 10 3 6 8 2 7 6 8 4 9 2 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 2 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 3 10 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 3 10 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 11 6 9 7 7 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 4 9 3 7 2 2 5 +-+ | 2 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 +---+ | 2 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R +---+ +--R x\|- a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 9 7 2 5 | 2 +--R (15a x + 180a b x + 240b x )\|a x + b +--R + +--R 2 9 7 2 5 +-+ +--R (- 75a x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 5 6 3 7 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 17 7 15 6 2 13 5 3 11 4 4 9 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 7 2 6 5 7 3 8 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1379 +t0:=(a+b/x^2)^(5/2)/x^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1379 +r0:=-5/24*a*(a+b/x^2)^(3/2)/x-1/6*(a+b/x^2)^(5/2)/x-_ + 5/16*a^3*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b)-5/16*a^2*_ + sqrt(a+b/x^2)/x +--R +--R +--R (2) +--R +--------+ +--R +-+ | 2 +--R 3 5 \|b 2 4 2 2 |a x + b +-+ +--R - 15a x atanh(------------) + (- 33a x - 26a b x - 8b ) |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R ------------------------------------------------------------------------ +--R 5 +-+ +--R 48x \|b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 10 4 2 8 3 3 6 | 2 +--R (90a b x + 480a b x + 480a b x )\|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 +-+ +--R (- 15a x - 270a b x - 720a b x - 480a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R (33a b x + 620a b x + 2060a b x + 2448a b x + 1216a b x + 256b ) +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x +--R + +--R 6 +--R - 256b +--R * +--R +-+ +--R \|b +--R / +--R +--------+ +--R 2 10 2 8 3 6 +-+ | 2 3 12 +--R (288a b x + 1536a b x + 1536b x )\|b \|a x + b - 48a b x +--R + +--R 2 2 10 3 8 4 6 +--R - 864a b x - 2304a b x - 1536b x +--R Type: Union(Expression(Integer),...) +--E 932 + +--S 933 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 +--R (90a x + 480a b x + 480a b x )\|b \|a x + b - 15a x +--R + +--R 5 10 4 2 8 3 3 6 +--R - 270a b x - 720a b x - 480a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 5 10 4 8 3 2 6 +-+ | 2 6 12 +--R (90a x + 480a b x + 480a b x )\|b \|a x + b - 15a x +--R + +--R 5 10 4 2 8 3 3 6 +--R - 270a b x - 720a b x - 480a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R 33a x + 620a b x + 2060a b x + 2448a b x + 1216a b x +--R + +--R 5 +--R 256b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (198a b x + 1212a b x + 1936a b x + 1088a b x + 256b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 33a x - 620a b x - 2060a b x - 2448a b x - 1216a b x - 256b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 2 8 3 3 6 2 4 4 5 2 6 +--R - 198a b x - 1410a b x - 3148a b x - 3024a b x - 1344a b x - 256b +--R / +--R +--------+ +--R 2 10 2 8 3 6 | 2 +--R (288a b x + 1536a b x + 1536b x )\|a x + b +--R + +--R 3 12 2 10 2 8 3 6 +-+ +--R (- 48a x - 864a b x - 2304a b x - 1536b x )\|b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 9 18 8 16 7 2 14 6 3 12 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 10 4 5 8 3 6 6 2 7 4 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 2 9 +--R - 25600a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 9 19 8 17 7 2 15 6 3 13 5 4 11 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 9 3 6 7 2 7 5 8 3 9 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 19 8 17 7 2 15 6 3 13 5 4 11 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 9 3 6 7 2 7 5 8 3 9 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 9 2 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x + 27648a b x +--R + +--R 10 +--R 4096b +--R / +--R 6 20 5 18 4 2 16 3 3 14 2 4 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 10 6 8 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 12 6 10 7 8 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1379 +t0:=(a+b/x^2)^(5/2)/x^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1379 +r0:=-1/7*(a+b/x^2)^(7/2)/b +--R +--R +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (- a x - 3a b x - 3a b x - b ) |-------- +--R | 2 +--R \| x +--R (2) -------------------------------------------- +--R 6 +--R 7b x +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 7a x + 77a b x + 301a b x + 575a b x + 584a b x + 304a b x +--R + +--R 6 +--R 64b +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R - a x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64b +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448b x )\|a x + b +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b +--R Type: Union(Expression(Integer),...) +--E 937 + +--S 938 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 7a x + 77a b x + 301a b x + 575a b x + 584a b x +--R + +--R 5 2 6 +--R 304a b x + 64b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 27a b x + 155a b x + 377a b x + 456a b x + 272a b x +--R + +--R 6 +--R 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R - 7a x - 77a b x - 301a b x - 575a b x - 584a b x - 304a b x +--R + +--R 6 +--R - 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R - a x - 28a b x - 182a b x - 532a b x - 833a b x - 728a b x +--R + +--R 6 2 7 +--R - 336a b x - 64b +--R / +--R +--------+ +--R 3 13 2 2 11 3 9 4 7 | 2 +--R (7a b x + 168a b x + 560a b x + 448b x )\|a x + b +--R + +--R 3 13 2 2 11 3 9 4 7 +-+ +--R (- 49a b x - 392a b x - 784a b x - 448b x )\|b +--R Type: Expression(Integer) +--E 938 + +--S 939 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 9 19 8 17 7 2 15 6 3 13 +--R - 14a x - 490a b x - 5418a b x - 28814a b x +--R + +--R 5 4 11 4 5 9 3 6 7 2 7 5 +--R - 86784a b x - 159168a b x - 181760a b x - 126464a b x +--R + +--R 8 3 9 +--R - 49152a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R - a x - 101a b x - 1865a b x - 14407a b x - 59906a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R - 149856a b x - 236992a b x - 239360a b x - 150016a b x +--R + +--R 9 2 10 +--R - 53248a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 10 20 9 18 8 2 16 7 3 14 6 4 12 +--R 14a x + 504a b x + 5908a b x + 34232a b x + 115598a b x +--R + +--R 5 5 10 4 6 8 3 7 6 2 8 4 +--R 245952a b x + 340928a b x + 308224a b x + 175616a b x +--R + +--R 9 2 10 +--R 57344a b x + 8192b +--R * +--R +-+ +--R \|b +--R + +--R 10 21 9 19 8 2 17 7 3 15 6 4 13 +--R a x + 101a b x + 1865a b x + 14407a b x + 59906a b x +--R + +--R 5 5 11 4 6 9 3 7 7 2 8 5 +--R 149856a b x + 236992a b x + 239360a b x + 150016a b x +--R + +--R 9 3 10 +--R 53248a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 13 6 11 7 9 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x +--R + +--R 2 5 13 6 11 7 9 +--R - 52736a b x - 32768a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 939 + +)clear all + +--S 940 of 1379 +t0:=(a+b/x^2)^(5/2)/x^4 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1379 +r0:=-5/48*a*(a+b/x^2)^(3/2)/x^3-1/8*(a+b/x^2)^(5/2)/x^3+5/128*a^4*_ + atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-5/64*a^2*_ + sqrt(a+b/x^2)/x^3-5/128*a^3*sqrt(a+b/x^2)/(b*x) +--R +--R +--R (2) +--R +-+ +--R 4 7 \|b +--R 15a x atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 15a x - 118a b x - 136a b x - 48b ) |-------- \|b +--R | 2 +--R \| x +--R / +--R 7 +-+ +--R 384b x \|b +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 7 14 6 2 12 5 3 10 4 4 8 | 2 +--R (- 120a b x - 1200a b x - 2880a b x - 1920a b x )\|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +-+ +--R (15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R 15a b x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 2 6 4 7 2 8 +--R 57600a b x + 29696a b x + 6144b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 2 6 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144b +--R * +--R +-+ +--R \|b +--R / +--R +--------+ +--R 3 2 14 2 3 12 4 10 5 8 +-+ | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152b x )\|b \|a x + b +--R + +--R 4 2 16 3 3 14 2 4 12 5 10 6 8 +--R - 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x +--R Type: Union(Expression(Integer),...) +--E 942 + +--S 943 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 7 14 6 12 5 2 10 4 3 8 +-+ | 2 +--R (- 120a x - 1200a b x - 2880a b x - 1920a b x )\|b \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 7 14 6 12 5 2 10 4 3 8 +-+ | 2 +--R (- 120a x - 1200a b x - 2880a b x - 1920a b x )\|b \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 15a x + 480a b x + 2400a b x + 3840a b x + 1920a b x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 15a x + 598a b x + 6312a b x + 27120a b x + 55424a b x +--R + +--R 2 5 4 6 2 7 +--R 57600a b x + 29696a b x + 6144b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 2 11 4 3 9 3 4 7 +--R 120a b x + 2144a b x + 13408a b x + 35840a b x +--R + +--R 2 5 5 6 3 7 +--R 45056a b x + 26624a b x + 6144b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - 15a x - 598a b x - 6312a b x - 27120a b x - 55424a b x +--R + +--R 2 5 5 6 3 7 +--R - 57600a b x - 29696a b x - 6144b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R - 120a b x - 2264a b x - 15552a b x - 49248a b x - 80896a b x +--R + +--R 2 6 4 7 2 8 +--R - 71680a b x - 32768a b x - 6144b +--R / +--R +--------+ +--R 3 2 14 2 3 12 4 10 5 8 | 2 +--R (3072a b x + 30720a b x + 73728a b x + 49152b x )\|a x + b +--R + +--R 4 16 3 2 14 2 3 12 4 10 5 8 +-+ +--R (- 384a b x - 12288a b x - 61440a b x - 98304a b x - 49152b x )\|b +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 11 22 10 20 9 2 18 8 3 16 +--R - 17a x - 867a b x - 13923a b x - 108545a b x +--R + +--R 7 4 14 6 5 12 5 6 10 4 7 8 +--R - 489872a b x - 1397536a b x - 2635136a b x - 3337984a b x +--R + +--R 3 8 6 2 9 4 10 2 11 +--R - 2816000a b x - 1519616a b x - 475136a b x - 65536b +--R * +--R +-+ +--R \|b +--R + +--R 11 23 10 21 9 2 19 8 3 17 +--R - a x - 147a b x - 3795a b x - 40081a b x +--R + +--R 7 4 15 6 5 13 5 6 11 4 7 9 +--R - 225648a b x - 765088a b x - 1661056a b x - 2369280a b x +--R + +--R 3 8 7 2 9 5 10 3 11 +--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 11 23 10 21 9 2 19 8 3 17 7 4 15 +--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x +--R + +--R 6 5 13 5 6 11 4 7 9 3 8 7 +--R 1397536a b x + 2635136a b x + 3337984a b x + 2816000a b x +--R + +--R 2 9 5 10 3 11 +--R 1519616a b x + 475136a b x + 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 12 24 11 22 10 2 20 9 3 18 8 4 16 +--R a x + 148a b x + 3942a b x + 43876a b x + 265729a b x +--R + +--R 7 5 14 6 6 12 5 7 10 4 8 8 +--R 990736a b x + 2426144a b x + 4030336a b x + 4583168a b x +--R + +--R 3 9 6 2 10 4 11 2 12 +--R 3520512a b x + 1748992a b x + 507904a b x + 65536b +--R / +--R 8 26 7 24 6 2 22 5 3 20 4 4 18 +--R 17a x + 816a b x + 11424a b x + 71808a b x + 239360a b x +--R + +--R 3 5 16 2 6 14 7 12 8 10 +--R 452608a b x + 487424a b x + 278528a b x + 65536b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 28 8 26 7 2 24 6 3 22 5 4 20 +--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x +--R + +--R 4 5 18 3 6 16 2 7 14 8 12 +--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x +--R + +--R 9 10 +--R - 65536b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 944 + +)clear all + +--S 945 of 1379 +t0:=x^3/(a+b/x^2)^(1/2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1379 +r0:=3/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-3/8*b*x^2*_ + sqrt(a+b/x^2)/a^2+1/4*x^4*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 947 + +--S 948 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 4 +--R - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 5 +--R - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 5 6 3 +--R 3328a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 5 6 3 +--R - 3840a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 4 +--R 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 2 6 +--R - 3328a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 2 6 +--R 3840a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 9 2 2 7 3 5 4 3 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 951 + +)clear all + +--S 952 of 1379 +t0:=x/(a+b/x^2)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1379 +r0:=-1/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+1/2*x^2*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 954 + +--S 955 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 +--R - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 2 +---+ +-+ +--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ 2 5 3 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b +--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 958 + +)clear all + +--S 959 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R [-------------------------------------------------------------, +--R +-+ +--R \|a +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R 2atan(------------------------------) +--R a x +--R -------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 961 + +--S 962 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b 2 3 +-+ +--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2 +--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 +---+ | 2 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ a x +--R \|a +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1379 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 |a x + b +--R - \|a x + b + x |-------- +--R | 2 +--R \| x +--R (7) ---------------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R x |-------- \|a x + b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 965 + +)clear all + +--S 966 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^3) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1379 +r0:=-sqrt(a+b/x^2)/b +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R (2) - ----------- +--R b +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | 2 2 +--R \|b \|a x + b - a x - b +--R (3) -------------------------- +--R +--------+ +--R | 2 +-+ +--R b x\|a x + b - b x\|b +--R Type: Union(Expression(Integer),...) +--E 968 + +--S 969 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 2 | 2 +--R \| x \| x +--R (4) -------------------------------------------------------------- +--R +--------+ +--R | 2 +-+ +--R b x\|a x + b - b x\|b +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 5 3 |a x + b | 2 5 3 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 970 + +)clear all + +--S 971 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^5) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 5 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b^2+a*sqrt(a+b/x^2)/b^2 +--R +--R +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (2a x - b) |-------- +--R | 2 +--R \| x +--R (2) ---------------------- +--R 2 2 +--R 3b x +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 2 2 3 +--R (- 6a x - 5a b x + 4b )\|b \|a x + b + 2a x + 9a b x + 3a b x - 4b +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Union(Expression(Integer),...) +--E 973 + +--S 974 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R ((- 6a x - 5a b x + 4b )\|b + (- 2a x - 7a b x + 4b x) |-------- ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 3 +--R (6a x + 5a b x - 4b x) |-------- \|b + 2a x + 9a b x + 3a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 5 3 3 | 2 2 5 3 3 +-+ +--R (3a b x + 12b x )\|a x + b + (- 9a b x - 12b x )\|b +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 11 2 9 2 7 3 5 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 975 + +)clear all + +--S 976 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^7) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 7 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1379 +r0:=2/3*a*(a+b/x^2)^(3/2)/b^3-1/5*(a+b/x^2)^(5/2)/b^3-a^2*sqrt(a+b/x^2)/b^3 +--R +--R +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (- 8a x + 4a b x - 3b ) |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------ +--R 3 4 +--R 15b x +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 5 10 +--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b \|a x + b - 8a x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 100a b x - 175a b x - 55a b x - 20a b x - 48b +--R / +--R +--------+ +--R 2 3 9 4 7 5 5 | 2 +--R (15a b x + 180a b x + 240b x )\|a x + b +--R + +--R 2 3 9 4 7 5 5 +-+ +--R (- 75a b x - 300a b x - 240b x )\|b +--R Type: Union(Expression(Integer),...) +--E 978 + +--S 979 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (40a x + 140a b x + 63a b x - 4a b x + 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (8a x + 92a b x + 83a b x - 28a b x + 48b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 40a x - 140a b x - 63a b x + 4a b x - 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - 8a x - 100a b x - 175a b x - 55a b x - 20a b x - 48b +--R / +--R +--------+ +--R 2 3 9 4 7 5 5 | 2 +--R (15a b x + 180a b x + 240b x )\|a x + b +--R + +--R 2 3 9 4 7 5 5 +-+ +--R (- 75a b x - 300a b x - 240b x )\|b +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b )\|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 17 4 15 3 2 13 2 3 11 4 9 5 7 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 7 +--R - 512b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 980 + +)clear all + +--S 981 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^9) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 9 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1379 +r0:=-a^2*(a+b/x^2)^(3/2)/b^4+3/5*a*(a+b/x^2)^(5/2)/b^4-_ + 1/7*(a+b/x^2)^(7/2)/b^4+a^3*sqrt(a+b/x^2)/b^4 +--R +--R +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (16a x - 8a b x + 6a b x - 5b ) |-------- +--R | 2 +--R \| x +--R (2) --------------------------------------------- +--R 4 6 +--R 35b x +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x +--R + +--R 5 2 6 +--R 176a b x + 320b +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x +--R + +--R 6 2 7 +--R - 336a b x - 320b +--R / +--R +--------+ +--R 3 4 13 2 5 11 6 9 7 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b +--R + +--R 3 4 13 2 5 11 6 9 7 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b +--R Type: Union(Expression(Integer),...) +--E 983 + +--S 984 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 112a x - 840a b x - 1386a b x - 429a b x + 120a b x +--R + +--R 5 2 6 +--R 176a b x + 320b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 16a x - 376a b x - 1094a b x - 523a b x + 152a b x +--R + +--R 5 3 6 +--R 16a b x + 320b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 112a x + 840a b x + 1386a b x + 429a b x - 120a b x +--R + +--R 5 3 6 +--R - 176a b x - 320b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R 16a x + 392a b x + 1470a b x + 1617a b x + 371a b x - 168a b x +--R + +--R 6 2 7 +--R - 336a b x - 320b +--R / +--R +--------+ +--R 3 4 13 2 5 11 6 9 7 7 | 2 +--R (35a b x + 840a b x + 2800a b x + 2240b x )\|a x + b +--R + +--R 3 4 13 2 5 11 6 9 7 7 +-+ +--R (- 245a b x - 1960a b x - 3920a b x - 2240b x )\|b +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 14a x - 448a b x - 4032a b x - 15360a b x - 28160a b x +--R + +--R 5 3 6 +--R - 24576a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x +--R + +--R 2 5 4 6 2 7 +--R - 39424a b x - 28672a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x +--R + +--R 2 5 4 6 2 7 +--R 52736a b x + 32768a b x + 8192b +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 5 6 3 7 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 13 6 11 7 9 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 23 6 21 5 2 19 4 3 17 3 4 15 +--R - 14a x - 462a b x - 4480a b x - 19392a b x - 43520a b x +--R + +--R 2 5 13 6 11 7 9 +--R - 52736a b x - 32768a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 985 + +)clear all + +--S 986 of 1379 +t0:=x^4/(a+b/x^2)^(1/2) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 986 + +--S 987 of 1379 +r0:=8/15*b^2*x*sqrt(a+b/x^2)/a^3-4/15*b*x^3*sqrt(a+b/x^2)/a^2+_ + 1/5*x^5*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (3a x - 4a b x + 8b x) |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------- +--R 3 +--R 15a +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 8 2 6 | 2 2 10 8 2 6 +-+ +--R (- 15a b x - 40b x )\|a x + b + (3a x + 35a b x + 40b x )\|b +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (15a x + 180a b x + 240b )\|b \|a x + b - 75a b x - 300a b x - 240b +--R Type: Union(Expression(Integer),...) +--E 988 + +--S 989 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 3a x - 32a b x - 8a b x - 32a b x - 128b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 +--R - 15a b x - 40a b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 +-+ +--R (3a x + 35a b x + 40a b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (15a b x + 40a b x + 8a b x + 96a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 5 4 4 2 3 2 +-+ | 2 5 4 4 2 2 +--R (15a x + 180a b x + 240a b )\|b \|a x + b - 75a b x - 300a b x +--R + +--R 3 3 +--R - 240a b +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 4 13 3 11 2 2 9 3 7 4 5 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x - 512b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1379 +t0:=x^2/(a+b/x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1379 +r0:=-2/3*b*x*sqrt(a+b/x^2)/a^2+1/3*x^3*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x - 2b x) |-------- +--R | 2 +--R \| x +--R (2) ------------------------ +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3b x \|a x + b + (a x + 3b x )\|b +--R (3) --------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (3a x + 12b)\|b \|a x + b - 9a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 993 + +--S 994 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ 2 4 | 2 +--R ((- a x - 2a b x + 8b x) |-------- \|b - 3a b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 +-+ 2 5 2 3 3 |a x + b +--R (a x + 3a b x )\|b + (3a b x - 2a b x - 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ | 2 3 2 2 2 +--R (3a x + 12a b)\|b \|a x + b - 9a b x - 12a b +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 4 3 2 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 8 2 6 2 4 3 2 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 18a b x + 48a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 995 + +)clear all + +--S 996 of 1379 +t0:=1/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1379 +r0:=x*sqrt(a+b/x^2)/a +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------ +--R a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|b +--R (3) ------------------- +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R Type: Union(Expression(Integer),...) +--E 998 + +--S 999 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 +-+ |a x + b +--R - x |-------- \|b \|a x + b + a x \|b + b x |-------- +--R | 2 | 2 +--R \| x \| x +--R (4) --------------------------------------------------------- +--R +--------+ +--R +-+ | 2 +--R a\|b \|a x + b - a b +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b | 2 2 |a x + b +-+ +--R (a x + 2b) |-------- \|a x + b + (- 2a x - 2b) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1000 + +)clear all + +--S 1001 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) - ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|a x + b - \|b +--R \|b log(------------------) +--R x +--R (3) --------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1003 + +--S 1004 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 2 +-+ +-+ +--R \|a x + b - \|b \|b +--R log(------------------) + atanh(------------) +--R x +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (4) --------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1379 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (5) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b +-+ | 2 4 2 |a x + b +--R x |-------- \|b \|a x + b + (- a x - b x ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1005 + +)clear all + +--S 1006 of 1379 +t0:=1/((a+b/x^2)^(1/2)*x^4) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 2 +--R 4 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1006 + +--S 1007 of 1379 +r0:=1/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)-1/2*sqrt(a+b/x^2)/(b*x) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|b |a x + b +-+ +--R a x atanh(------------) - |-------- \|b +--R +--------+ | 2 +--R | 2 \| x +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------------- +--R +-+ +--R 2b x\|b +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 | 2 2 4 2 +-+ \|a x + b - \|b +--R (- 2a b x \|a x + b + (a x + 2a b x )\|b )log(------------------) +--R x +--R + +--R +--------+ +--R 2 2 | 2 2 2 +-+ +--R (a b x + 2b )\|a x + b + (- 2a b x - 2b )\|b +--R / +--R +--------+ +--R 2 2 +-+ | 2 2 4 3 2 +--R 4b x \|b \|a x + b - 2a b x - 4b x +--R Type: Union(Expression(Integer),...) +--E 1008 + +--S 1009 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +-+ +--R 2 +-+ | 2 2 4 2 \|a x + b - \|b +--R (- 2a x \|b \|a x + b + a x + 2a b x )log(------------------) +--R x +--R + +--R +--------+ +-+ +--R 2 +-+ | 2 2 4 2 \|b +--R (- 2a x \|b \|a x + b + a x + 2a b x )atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b | 2 +--R ((a x + 2b)\|b + 2b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +-+ 2 2 +--R (- a x - 2b x) |-------- \|b - 2a b x - 2b +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 | 2 4 2 2 +-+ +--R 4b x \|a x + b + (- 2a b x - 4b x )\|b +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 2 4 2 2 +-+ +--R (- 5a x - 20a b x - 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (- a x - 12a b x - 16b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (5a x + 20a b x + 16b x) |-------- \|b + a x + 13a b x + 28a b x +--R | 2 +--R \| x +--R + +--R 3 +--R 16b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 8 6 2 4 |a x + b +-+ | 2 +--R (5a x + 20a b x + 16b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1010 + +)clear all + +--S 1011 of 1379 +t0:=1/(x*sqrt(-a+b/x^2)) +--R +--R +--R 1 +--R (1) -------------- +--R +----------+ +--R | 2 +--R |- a x + b +--R x |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1379 +r0:=-atan(sqrt(-a+b/x^2)/sqrt(a))/sqrt(a) +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R atan(-------------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- a +--R +----------+ +--R +-+ +-+ | 2 +-+ +--R \|a \|b - \|- a x + b \|a +--R 2atan(----------------------------) +--R a x +--R -----------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 1013 + +--S 1014 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +-+ +--R \|a +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a +--R + +--R +----------+ +--R | 2 +--R a x\|- a x + b +--R / +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R + +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R +---+ \| x +--R \|- a atan(-------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +----------+ +--R +----------+ | 2 +--R 3 | 2 +---+ 2 4 2 |- a x + b +--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 +---+ 2 3 | 2 +--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b +--R * +--R +-+ +--R \|b +--R + +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 | 2 +---+ 3 5 2 3 2 +--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x +--R / +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +-+ +--R |---------- \|b +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 5 3 2 | 2 +---+ 3 6 2 4 +--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x +--R + +--R 2 2 +--R 4a b x +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1379 +m0b:=a0.2-r0 +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R +----------+ |---------- +--R +-+ +-+ | 2 +-+ | 2 +--R \|a \|b - \|- a x + b \|a \| x +--R 2atan(----------------------------) + atan(-------------) +--R a x +-+ +--R \|a +--R (6) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1016 + +--S 1017 of 1379 +d0b:=D(m0b,x) +--R +--R +--R +----------+ +--R | 2 +----------+ +--R |- a x + b | 2 +--R x |---------- - \|- a x + b +--R | 2 +--R \| x +--R (7) ------------------------------ +--R +----------+ +--R +----------+ | 2 +--R | 2 |- a x + b +--R x\|- a x + b |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1017 + +)clear all + +--S 1018 of 1379 +t0:=1/(x^2*sqrt(2+b/x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R | 2 +--R 2 |2x + b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1018 + +--S 1019 of 1379 +r0:=-asinh(sqrt(b)/(x*sqrt(2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R asinh(-----) +--R +-+ +--R x\|2 +--R (2) - ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (3) -------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 1020 + +--S 1021 of 1379 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +--R \|2x + b - \|b \|b +--R log(-----------------) + asinh(-----) +--R x +-+ +--R x\|2 +--R (4) ------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1021 + +--S 1022 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 1022 + +)clear all + +--S 1023 of 1379 +t0:=1/(x^2*sqrt(2-b/x^2)) +--R +--R +--R 1 +--R (1) ------------ +--R +-------+ +--R | 2 +--R 2 |2x - b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1023 + +--S 1024 of 1379 +r0:=-asin(sqrt(b)/(x*sqrt(2)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R asin(-----) +--R +-+ +--R x\|2 +--R (2) - ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (3) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 1025 + +--S 1026 of 1379 +m0:=a0-r0 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|b +--R - \|- b \|b log(-------------------) + b asin(-----) +--R x +-+ +--R x\|2 +--R (4) ---------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 1027 + +)clear all + +--S 1028 of 1379 +t0:=x^3/(a+b/x^2)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1379 +r0:=15/8*b^2*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(7/2)-x^4/(a*sqrt(a+b/x^2))-_ + 15/8*b*x^2*sqrt(a+b/x^2)/a^3+5/4*x^4*sqrt(a+b/x^2)/a^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 |a x + b \| x 2 4 2 2 +-+ +--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a +--R | 2 +-+ +--R \| x \|a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b +--R 8a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 +--R (75a b x + 300a b x + 240b )\|b \|a x + b - 15a b x +--R + +--R 2 3 4 4 2 5 +--R - 195a b x - 420a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a \|b +--R / +--R +--------+ +--R 5 4 4 2 3 2 +-+ +-+ | 2 +--R (40a x + 160a b x + 128a b )\|a \|b \|a x + b +--R + +--R 6 6 5 4 4 2 2 3 3 +-+ +--R (- 8a x - 104a b x - 224a b x - 128a b )\|a +--R , +--R +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 +--R (150a b x + 600a b x + 480b )\|b \|a x + b - 30a b x +--R + +--R 2 3 4 4 2 5 +--R - 390a b x - 840a b x - 480b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|b +--R / +--R +--------+ +--R 5 4 4 2 3 2 +---+ +-+ | 2 +--R (40a x + 160a b x + 128a b )\|- a \|b \|a x + b +--R + +--R 6 6 5 4 4 2 2 3 3 +---+ +--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1030 + +--S 1031 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 300a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 195a b x - 420a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (- 75a b x - 300a b x - 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (15a b x + 195a b x + 420a b x + 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+ +--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 4 4 2 3 2 +-+ |a x + b +-+ | 2 +--R (40a x + 160a b x + 128a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b +--R (- 8a x - 104a b x - 224a b x - 128a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 18 5 16 4 2 14 3 3 12 +--R 13a x + 364a b x + 2912a b x + 9984a b x +--R + +--R 2 4 10 5 8 6 6 +--R 16640a b x + 13312a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 8 6 6 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 9 6 7 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 9 6 7 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 +--R - 13a x - 377a b x - 3276a b x - 12896a b x +--R + +--R 3 4 11 2 5 9 6 7 7 5 +--R - 26624a b x - 29952a b x - 17408a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 10 2 6 8 7 6 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 3 5 5 2 6 3 7 +--R 29952a b x + 17408a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 +--R - a x - 86a b x - 1289a b x - 7700a b x - 23392a b x +--R + +--R 4 5 7 3 6 5 2 7 3 8 +--R - 39680a b x - 38144a b x - 19456a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 +---+ |a x + b +-+ | 2 +--R (- 75a b x - 300a b x - 240b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 +---+ |a x + b +--R (15a b x + 195a b x + 420a b x + 240b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 +-+ |a x + b +-+ | 2 +--R (150a b x + 600a b x + 480b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 +-+ |a x + b +--R (- 30a b x - 390a b x - 840a b x - 480b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+ +--R (- 10a x - 15a b x + 143a b x + 380a b x + 240b )\|- a \|a \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (- 2a x - 19a b x + 43a b x + 260a b x + 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (10a x + 15a b x - 143a b x - 380a b x - 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+ +--R (2a x + 21a b x - 24a b x - 303a b x - 500a b x - 240b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 4 4 2 3 2 +---+ +-+ |a x + b +-+ | 2 +--R (40a x + 160a b x + 128a b )\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b +--R (- 8a x - 104a b x - 224a b x - 128a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 14 3 12 2 2 10 3 8 4 6 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 51a b x + 450a b x + 1520a b x + 2400a b x + 1792a b x +--R + +--R 6 +--R 512b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 10a x - 180a b x - 1002a b x - 2528a b x - 3232a b x +--R + +--R 5 2 6 +--R - 2048a b x - 512b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1379 +t0:=x/(a+b/x^2)^(3/2) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1035 + +--S 1036 of 1379 +r0:=-3/2*b*atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)-x^2/(a*sqrt(a+b/x^2))+_ + 3/2*x^2*sqrt(a+b/x^2)/a^2 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R |a x + b \| x 2 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 2 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 +-+ |a x + b +--R 2a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (- a x - 7a b x - 12b x)\|a \|a x + b +--R + +--R 2 5 3 2 +-+ +-+ +--R (3a x + 13a b x + 12b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (6a x + 8a b)\|a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|a +--R , +--R +--R +--------+ +--R 2 2 +-+ | 2 2 4 2 2 3 +--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (- a x - 7a b x - 12b x)\|- a \|a x + b +--R + +--R 2 5 3 2 +---+ +-+ +--R (3a x + 13a b x + 12b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 4 4 3 2 2 2 +---+ +--R (6a x + 8a b)\|- a \|b \|a x + b + (- 2a x - 10a b x - 8a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1037 + +--S 1038 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 |a x + b +-+ | 2 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 |a x + b +-+ | 2 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 7a b x - 12b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (a x + 8a b x + 19a b x + 12b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 2 +-+ |a x + b +-+ | 2 +--R (6a x + 8a b)\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 4 3 2 2 2 +-+ |a x + b +--R (- 2a x - 10a b x - 8a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+ +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 3 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +-+ +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 +--R 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x +--R + +--R 5 2 6 +--R 960a b x + 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 2 6 +--R - 1088a b x - 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 2 5 3 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x - 960a b x +--R + +--R 6 +--R - 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 2 +---+ |a x + b +-+ | 2 +--R (9a b x + 12b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 +---+ |a x + b +--R (- 3a b x - 15a b x - 12b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 2 +-+ |a x + b +-+ | 2 +--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 3 +-+ |a x + b +--R (6a b x + 30a b x + 24b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 2 4 2 2 +---+ +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +--R (- a x - 7a b x - 12b x)\|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x)\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +---+ +-+ +--R (a x + 8a b x + 19a b x + 12b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 2 +---+ +-+ |a x + b +-+ | 2 +--R (6a x + 8a b)\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 4 3 2 2 2 +---+ +-+ |a x + b +--R (- 2a x - 10a b x - 8a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 5 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 9 2 7 2 5 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1041 + +)clear all + +--S 1042 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1379 +r0:=atanh(sqrt(a+b/x^2)/sqrt(a))/a^(3/2)+(-1)/(a*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R |a x + b \| x +-+ +--R |-------- atanh(-----------) - \|a +--R | 2 +-+ +--R \| x \|a +--R (2) ------------------------------------ +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R a\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 2 2 +--R (\|b \|a x + b - a x - b) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 2 +-+ +-+ +--R x\|a \|a x + b - x\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R a\|a \|b \|a x + b + (- a x - a b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 \|- a \|a x + b - \|- a \|b +--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------) +--R a x +--R + +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R x\|- a \|a x + b - x\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R a\|- a \|b \|a x + b + (- a x - a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1044 + +--S 1045 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 |a x + b +--R ( |-------- \|b \|a x + b + (- a x - b) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ +--------+ |-------- +--R | 2 +--------+ | 2 | 2 +--R |a x + b +-+ | 2 2 |a x + b \| x +--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------) +--R | 2 | 2 +-+ +--R \| x \| x \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ +-+ +-+ |a x + b | 2 +-+ |a x + b +-+ +--R (\|a \|b + x\|a |-------- )\|a x + b - x\|a |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R + +--R 2 +-+ +--R (- a x - b)\|a +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b +-+ | 2 2 2 +-+ |a x + b +--R a\|a |-------- \|b \|a x + b + (- a x - a b)\|a |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b 3 6 2 4 +--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x +--R | 2 +--R \| x +--R + +--R 2 2 +--R - 16a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (- a x - 12a b x - 16a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (a x + 13a b x + 28a b x + 16b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (5a x + 20a b x + 16a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 3 6 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x + 13a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 +--R 28a b x + 16a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ |a x + b +-+ | 2 2 +---+ |a x + b +--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b +-+ | 2 2 +-+ |a x + b +--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R +---+ +-+ +-+ +---+ +-+ |a x + b | 2 +--R (\|- a \|a \|b + x\|- a \|a |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +-+ 2 +---+ +-+ +--R - x\|- a \|a |-------- \|b + (- a x - b)\|- a \|a +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +---+ +-+ |a x + b +-+ | 2 2 2 +---+ +-+ |a x + b +--R a\|- a \|a |-------- \|b \|a x + b + (- a x - a b)\|- a \|a |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--------+ +--R 2 |a x + b +-+ 3 | 2 3 +-+ +--R (- 2x |-------- \|b - a x - 2b x)\|a x + b + (2a x + 2b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 2 |a x + b +--R (a x + 2b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1048 + +)clear all + +--S 1049 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1049 + +--S 1050 of 1379 +r0:=1/(b*sqrt(a+b/x^2)) +--R +--R +--R 1 +--R (2) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R b |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R - x\|a x + b + x\|b +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R b\|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1051 + +--S 1052 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (4) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 2 |a x + b +--R b |-------- \|b \|a x + b + (- a b x - b ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b | 2 +--R (a x + 3a b x + 2b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1053 + +)clear all + +--S 1054 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^5) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 5 3 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1054 + +--S 1055 of 1379 +r0:=-a/(b^2*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^2 +--R +--R +--R 2 +--R - 2a x - b +--R (2) --------------- +--R +--------+ +--R | 2 +--R 2 2 |a x + b +--R b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 2 +-+ | 2 2 4 2 2 +--R (4a x + 2b)\|b \|a x + b - 2a x - 5a b x - 2b +--R (3) --------------------------------------------------- +--R +--------+ +--R 2 3 3 | 2 2 3 3 +-+ +--R (a b x + 2b x)\|a x + b + (- 2a b x - 2b x)\|b +--R Type: Union(Expression(Integer),...) +--E 1056 + +--S 1057 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((4a x + 2b x) |-------- \|b + 2a x + 5a b x + 2b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (- 4a x - 6a b x - 2b )\|b + (- 2a x - 5a b x - 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 4 3 2 |a x + b | 2 2 4 3 2 |a x + b +-+ +--R (a b x + 2b x ) |-------- \|a x + b + (- 2a b x - 2b x ) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R 3 |a x + b +-+ 2 4 2 2 | 2 +--R ((- 4a x - 8b x) |-------- \|b - a x - 8a b x - 8b )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 +-+ 2 5 3 2 |a x + b +--R (4a x + 12a b x + 8b )\|b + (a x + 8a b x + 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 9 2 7 2 5 3 3 |a x + b | 2 +--R (a x + 9a b x + 16a b x + 8b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +-+ +--R (- 4a x - 16a b x - 20a b x - 8b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1058 + +)clear all + +--S 1059 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 7 5 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1059 + +--S 1060 of 1379 +r0:=-1/3*(a+b/x^2)^(3/2)/b^3+a^2/(b^3*sqrt(a+b/x^2))+2*a*sqrt(a+b/x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R 8a x + 4a b x - b +--R (2) -------------------- +--R +--------+ +--R | 2 +--R 3 4 |a x + b +--R 3b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (- 32a x - 80a b x - 28a b x + 8b )\|b \|a x + b + 8a x + 68a b x +--R + +--R 2 2 4 3 2 4 +--R 95a b x + 24a b x - 8b +--R / +--R +--------+ +--R 2 3 7 4 5 5 3 | 2 +--R (3a b x + 24a b x + 24b x )\|a x + b +--R + +--R 2 3 7 4 5 5 3 +-+ +--R (- 12a b x - 36a b x - 24b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1061 + +--S 1062 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 32a x - 80a b x - 28a b x + 8b x) |-------- \|b - 8a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 68a b x - 95a b x - 24a b x + 8b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (32a x + 112a b x + 108a b x + 20a b x - 8b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (8a x + 68a b x + 95a b x + 24a b x - 8b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 3 8 4 6 5 4 |a x + b | 2 +--R (3a b x + 24a b x + 24b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 3 8 4 6 5 4 |a x + b +-+ +--R (- 12a b x - 36a b x - 24b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 32a b x - 160a b x - 256a b x - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^9) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 9 7 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1379 +r0:=a*(a+b/x^2)^(3/2)/b^4-1/5*(a+b/x^2)^(5/2)/b^4-a^3/(b^4*_ + sqrt(a+b/x^2))-3*a^2*sqrt(a+b/x^2)/b^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R - 16a x - 8a b x + 2a b x - b +--R (2) --------------------------------- +--R +--------+ +--R | 2 +--R 4 6 |a x + b +--R 5b x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x +--R + +--R 6 +--R - 32b +--R / +--R +--------+ +--R 3 4 11 2 5 9 6 7 7 5 | 2 +--R (5a b x + 90a b x + 240a b x + 160b x )\|a x + b +--R + +--R 3 4 11 2 5 9 6 7 7 5 +-+ +--R (- 30a b x - 190a b x - 320a b x - 160b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1066 + +--S 1067 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (96a x + 560a b x + 756a b x + 198a b x - 32a b x + 32b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 16a x + 296a b x + 910a b x + 861a b x + 178a b x - 16a b x +--R + +--R 6 +--R 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 6 +-+ +--R (- 96a x - 656a b x - 1316a b x - 954a b x - 166a b x - 32b )\|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R - 16a x - 296a b x - 910a b x - 861a b x - 178a b x + 16a b x +--R + +--R 6 +--R - 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 4 12 2 5 10 6 8 7 6 |a x + b | 2 +--R (5a b x + 90a b x + 240a b x + 160b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 4 12 2 5 10 6 8 7 6 |a x + b +-+ +--R (- 30a b x - 190a b x - 320a b x - 160b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1067 + +--S 1068 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 2 6 +--R - 6144a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 2 6 +--R 7168a b x + 2048b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x +--R + +--R 6 +--R 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R a x + 73a b x + 912a b x + 4424a b x + 10496a b x +--R + +--R 2 5 11 6 9 7 7 +--R 13056a b x + 8192a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - 12a x - 304a b x - 2364a b x - 8472a b x - 16128a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 16896a b x - 9216a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1068 + +)clear all + +--S 1069 of 1379 +t0:=x^2/(a+b/x^2)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1379 +r0:=-x^3/(a*sqrt(a+b/x^2))-8/3*b*x*sqrt(a+b/x^2)/a^3+4/3*x^3*sqrt(a+b/x^2)/a^2 +--R +--R +--R 2 4 2 2 +--R a x - 4a b x - 8b +--R (2) -------------------- +--R +--------+ +--R | 2 +--R 3 |a x + b +--R 3a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4b x \|a x + b + (a x + 4b x )\|b +--R (3) --------------------------------------------------------------------- +--R +--------+ +--R 2 4 2 2 +-+ | 2 2 4 2 2 3 +--R (3a x + 24a b x + 24b )\|b \|a x + b - 12a b x - 36a b x - 24b +--R Type: Union(Expression(Integer),...) +--E 1071 + +--S 1072 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- a x - 4a b x + 32a b x + 96a b x + 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 |a x + b +--R - 4a b x |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4 +--R (a x + 4a b x ) |-------- \|b + 4a b x - 4a b x - 72a b x +--R | 2 +--R \| x +--R + +--R 4 2 5 +--R - 128a b x - 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 5 5 4 3 3 2 |a x + b +-+ | 2 +--R (3a x + 24a b x + 24a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 5 4 2 3 3 3 |a x + b +--R (- 12a b x - 36a b x - 24a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 10 2 2 8 3 6 4 4 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 8a x - 96a b x - 360a b x - 592a b x - 448a b x - 128b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1073 + +)clear all + +--S 1074 of 1379 +t0:=1/(a+b/x^2)^(3/2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1379 +r0:=-x/(a*sqrt(a+b/x^2))+2*x*sqrt(a+b/x^2)/a^2 +--R +--R +--R 2 +--R a x + 2b +--R (2) -------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ +--R x \|b +--R (3) ------------------------------------------ +--R +--------+ +--R 2 +-+ | 2 2 2 +--R (a x + 2b)\|b \|a x + b - 2a b x - 2b +--R Type: Union(Expression(Integer),...) +--E 1076 + +--S 1077 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +--------+ | 2 +--R 2 4 2 2 +-+ | 2 2 5 |a x + b +-+ 2 4 +--R (- a x - 4a b x - 4b )\|b \|a x + b + a x |-------- \|b + 2a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R 6a b x + 4b +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 3 3 2 |a x + b +-+ | 2 3 3 2 2 |a x + b +--R (a x + 2a b x) |-------- \|b \|a x + b + (- 2a b x - 2a b x) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R 5 3 |a x + b +-+ 2 6 4 2 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ 2 7 5 2 3 |a x + b +--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 4 2 2 3 |a x + b | 2 +--R (a x + 9a b x + 16a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +-+ +--R (- 4a x - 16a b x - 20a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1078 + +)clear all + +--S 1079 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R (a x + b) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1379 +r0:=(-1)/(a*x*sqrt(a+b/x^2)) +--R +--R +--R 1 +--R (2) - -------------- +--R +--------+ +--R | 2 +--R |a x + b +--R a x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R x \|b +--R (3) ------------------------------ +--R +--------+ +--R +-+ | 2 2 2 +--R b\|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1081 + +--S 1082 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 2 +--R +-+ | 2 3 |a x + b +-+ 2 2 +--R b\|b \|a x + b + a x |-------- \|b - a b x - b +--R | 2 +--R \| x +--R (4) --------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 2 3 2 |a x + b +--R a b x |-------- \|b \|a x + b + (- a b x - a b x) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1083 + +)clear all + +--S 1084 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 4 2 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1379 +r0:=-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(3/2)+1/(b*x*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +-+ +--R |a x + b \|b +-+ +--R - x |-------- atanh(------------) + \|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ---------------------------------------- +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1085 + +--S 1086 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +-+ +--R | 2 2 +-+ \|a x + b - \|b 2 +-+ +--R (b\|a x + b + (- a x - b)\|b )log(------------------) - a x \|b +--R x +--R (3) ------------------------------------------------------------------- +--R +--------+ +--R 2 +-+ | 2 2 2 3 +--R b \|b \|a x + b - a b x - b +--R Type: Union(Expression(Integer),...) +--E 1086 + +--S 1087 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 3 |a x + b +--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R |a x + b +-+ | 2 3 |a x + b +--R (x |-------- \|b \|a x + b + (- a x - b x) |-------- ) +--R | 2 | 2 +--R \| x \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R +--------+ | 2 +--R | 2 2 +-+ 3 |a x + b +--R - b\|a x + b + (a x + b)\|b - a x |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b | 2 3 2 |a x + b +-+ +--R b x |-------- \|a x + b + (- a b x - b x) |-------- \|b +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ 2 | 2 2 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (a x + 2b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 6 4 2 2 |a x + b | 2 +--R (a x + 3a b x + 2b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1088 + +)clear all + +--S 1089 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^6) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 6 4 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1379 +r0:=3/2*a*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(5/2)+_ + 1/(b*x^3*sqrt(a+b/x^2))-3/2*sqrt(a+b/x^2)/(b^2*x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 3 |a x + b \|b 2 +-+ +--R 3a x |-------- atanh(------------) + (- 3a x - b)\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 3 |a x + b +-+ +--R 2b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R ((- 9a b x - 12a b x )\|a x + b + (3a x + 15a b x + 12a b x )\|b ) +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (- 3a b x + 5a b x + 4b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (2a x + a b x - 7a b x - 4b )\|b +--R / +--R +--------+ +--R 3 4 4 2 +-+ | 2 2 3 6 4 4 5 2 +--R (6a b x + 8b x )\|b \|a x + b - 2a b x - 10a b x - 8b x +--R Type: Union(Expression(Integer),...) +--E 1091 + +--S 1092 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 |a x + b +-+ | 2 +--R (- 9a x - 12a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (3a x + 15a b x + 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 |a x + b +-+ | 2 +--R (- 9a x - 12a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (3a x + 15a b x + 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 2 4 2 2 3 +--R ((- 3a x + 5a b x + 4b x) |-------- \|b + 9a b x + 15a b x + 4b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3a x - 16a b x - 17a b x - 4b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (2a x + a b x - 7a b x - 4b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 5 4 3 |a x + b | 2 +--R (6a b x + 8b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 2 7 3 5 4 3 |a x + b +-+ +--R (- 2a b x - 10a b x - 8b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 7a x - 56a b x - 112a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 104a b x + 144a b x + 64b +--R / +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1093 + +)clear all + +--S 1094 of 1379 +t0:=1/((a+b/x^2)^(3/2)*x^8) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 2 +--R 8 6 |a x + b +--R (a x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1379 +r0:=-15/8*a^2*atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/b^(7/2)+_ + 1/(b*x^5*sqrt(a+b/x^2))-5/4*sqrt(a+b/x^2)/(b^2*x^3)+_ + 15/8*a*sqrt(a+b/x^2)/(b^3*x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 2 5 |a x + b \|b 2 4 2 2 +-+ +--R - 15a x |-------- atanh(------------) + (15a x + 5a b x - 2b )\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) --------------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 5 |a x + b +-+ +--R 8b x |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1095 + +--S 1096 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 | 2 +--R (75a b x + 300a b x + 240a b x )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 +-+ +--R (- 15a x - 195a b x - 420a b x - 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (25a b x - 25a b x - 170a b x - 56a b x + 32b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b )\|b +--R / +--R +--------+ +--R 2 4 8 5 6 6 4 +-+ | 2 3 4 10 2 5 8 +--R (40a b x + 160a b x + 128b x )\|b \|a x + b - 8a b x - 104a b x +--R + +--R 6 6 7 4 +--R - 224a b x - 128b x +--R Type: Union(Expression(Integer),...) +--E 1096 + +--S 1097 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 |a x + b +-+ | 2 +--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 |a x + b +--R (- 15a x - 195a b x - 420a b x - 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 4 9 3 7 2 2 5 |a x + b +-+ | 2 +--R (75a x + 300a b x + 240a b x ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 |a x + b +--R (- 15a x - 195a b x - 420a b x - 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (25a x - 25a b x - 170a b x - 56a b x + 32b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 75a b x - 325a b x - 330a b x - 40a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (15a x + 200a b x + 483a b x + 354a b x + 24a b x - 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (- 8a x - 29a b x + 101a b x + 202a b x + 40a b x - 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 9 5 7 6 5 |a x + b | 2 +--R (40a b x + 160a b x + 128b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 3 11 2 4 9 5 7 6 5 |a x + b +-+ +--R (- 8a b x - 104a b x - 224a b x - 128b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 +--R - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 +--R - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 +--R 1024b +--R / +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 8 6 6 +--R 3840a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 10 6 8 7 6 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1098 + +)clear all + +--S 1099 of 1379 +t0:=x^3/(a+b/x^2)^(5/2) +--R +--R +--R 7 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1379 +r0:=-1/3*x^4/(a*(a+b/x^2)^(3/2))+35/8*b^2*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/a^(9/2)-7/3*x^4/(a^2*sqrt(a+b/x^2))-35/8*b*x^2*_ + sqrt(a+b/x^2)/a^4+35/12*x^4*sqrt(a+b/x^2)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 2 3 |a x + b \| x +--R (105a b x + 105b ) |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x - 21a b x - 140a b x - 105b )\|a +--R / +--R +--------+ +--R | 2 +--R 5 2 4 +-+ |a x + b +--R (24a x + 24a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1100 + +--S 1101 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 2 8 3 3 6 2 4 4 5 2 6 +-+ +--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R - 105a b x - 2730a b x - 13545a b x - 26040a b x - 21840a b x +--R + +--R 7 +--R - 6720b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R +-+ | 2 +--R \|a \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +-+ +-+ +--R \|a \|b +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +-+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a \|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +-+ +--R \|a +--R , +--R +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b ) +--R * +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R - 210a b x - 5460a b x - 27090a b x - 52080a b x - 43680a b x +--R + +--R 7 +--R - 13440b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R +---+ | 2 +--R \|- a \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +---+ +-+ +--R \|- a \|b +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +---+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +---+ +--R \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1101 + +--S 1102 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (735a b x + 6615a b x + 17640a b x + 18480a b x + 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 +--R - 105a b x - 2730a b x - 13545a b x - 26040a b x +--R + +--R 6 2 7 +--R - 21840a b x - 6720b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x +--R + +--R 7 +--R 6720b +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x +--R + +--R 5 2 6 +--R 20720a b x + 6720b +--R * +--R +-+ +-+ +--R \|a \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x +--R + +--R 2 5 4 6 2 7 +--R - 32424a b x - 24080a b x - 6720b +--R * +--R +-+ +--R \|a +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|a +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 8 24 7 22 6 2 20 5 3 18 +--R 17a x + 816a b x + 11424a b x + 71808a b x +--R + +--R 4 4 16 3 5 14 2 6 12 7 10 +--R 239360a b x + 452608a b x + 487424a b x + 278528a b x +--R + +--R 8 8 +--R 65536b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 9 24 8 22 7 2 20 6 3 18 +--R - 17a x - 816a b x - 11424a b x - 71808a b x +--R + +--R 5 4 16 4 5 14 3 6 12 2 7 10 +--R - 239360a b x - 452608a b x - 487424a b x - 278528a b x +--R + +--R 8 8 +--R - 65536a b x +--R * +--R +-+ +--R \|b +--R + +--R 9 25 8 23 7 2 21 6 3 19 5 4 17 +--R - a x - 144a b x - 3360a b x - 29568a b x - 126720a b x +--R + +--R 4 5 15 3 6 13 2 7 11 8 9 +--R - 292864a b x - 372736a b x - 245760a b x - 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 25 8 23 7 2 21 6 3 19 5 4 17 +--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x +--R + +--R 4 5 15 3 6 13 2 7 11 8 9 +--R 419584a b x + 665600a b x + 618496a b x + 311296a b x +--R + +--R 9 7 +--R 65536b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 25 8 23 7 2 21 6 3 19 +--R 17a x + 816a b x + 11424a b x + 71808a b x +--R + +--R 5 4 17 4 5 15 3 6 13 2 7 11 +--R 239360a b x + 452608a b x + 487424a b x + 278528a b x +--R + +--R 8 9 +--R 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 9 25 8 23 7 2 21 6 3 19 +--R - 17a x - 833a b x - 12240a b x - 83232a b x +--R + +--R 5 4 17 4 5 15 3 6 13 2 7 11 +--R - 311168a b x - 691968a b x - 940032a b x - 765952a b x +--R + +--R 8 9 9 7 +--R - 344064a b x - 65536b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 26 8 24 7 2 22 6 3 20 5 4 18 +--R - a x - 145a b x - 3504a b x - 32928a b x - 156288a b x +--R + +--R 4 5 16 3 6 14 2 7 12 8 10 +--R - 419584a b x - 665600a b x - 618496a b x - 311296a b x +--R + +--R 9 8 +--R - 65536b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 10 26 9 24 8 2 22 7 3 20 6 4 18 +--R a x + 145a b x + 3504a b x + 32928a b x + 156288a b x +--R + +--R 5 5 16 4 6 14 3 7 12 2 8 10 9 8 +--R 419584a b x + 665600a b x + 618496a b x + 311296a b x + 65536a b x +--R / +--R 11 21 10 19 9 2 17 8 3 15 +--R 17a x + 850a b x + 13073a b x + 95472a b x +--R + +--R 7 4 13 6 5 11 5 6 9 4 7 7 +--R 394400a b x + 1003136a b x + 1632000a b x + 1705984a b x +--R + +--R 3 8 5 2 9 3 10 +--R 1110016a b x + 409600a b x + 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 11 22 10 20 9 2 18 8 3 16 +--R - a x - 147a b x - 3795a b x - 40081a b x +--R + +--R 7 4 14 6 5 12 5 6 10 4 7 8 +--R - 225648a b x - 765088a b x - 1661056a b x - 2369280a b x +--R + +--R 3 8 6 2 9 4 10 2 11 +--R - 2213888a b x - 1306624a b x - 442368a b x - 65536b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 11 22 10 20 9 2 18 8 3 16 7 4 14 +--R 17a x + 867a b x + 13923a b x + 108545a b x + 489872a b x +--R + +--R 6 5 12 5 6 10 4 7 8 3 8 6 +--R 1397536a b x + 2635136a b x + 3337984a b x + 2816000a b x +--R + +--R 2 9 4 10 2 11 +--R 1519616a b x + 475136a b x + 65536b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 12 23 11 21 10 2 19 9 3 17 8 4 15 +--R - a x - 147a b x - 3795a b x - 40081a b x - 225648a b x +--R + +--R 7 5 13 6 6 11 5 7 9 4 8 7 +--R - 765088a b x - 1661056a b x - 2369280a b x - 2213888a b x +--R + +--R 3 9 5 2 10 3 11 +--R - 1306624a b x - 442368a b x - 65536a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1103 + +--S 1104 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (- 735a b x - 6615a b x - 17640a b x - 18480a b x - 6720b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R +---+ |a x + b +-+ | 2 +--R \|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 6 2 +--R 105a b x + 2730a b x + 13545a b x + 26040a b x + 21840a b x +--R + +--R 7 +--R 6720b +--R * +--R +--------+ +--R | 2 +--R +---+ |a x + b +--R \|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 2 8 3 3 6 2 4 4 5 2 6 +--R (1470a b x + 13230a b x + 35280a b x + 36960a b x + 13440b ) +--R * +--R +--------+ +--R | 2 +--------+ +--R +-+ |a x + b +-+ | 2 +--R \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 5 2 10 4 3 8 3 4 6 2 5 4 +--R - 210a b x - 5460a b x - 27090a b x - 52080a b x +--R + +--R 6 2 7 +--R - 43680a b x - 13440b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 42a x - 189a b x + 1484a b x + 10543a b x + 22904a b x +--R + +--R 5 2 6 +--R 20720a b x + 6720b +--R * +--R +---+ +-+ +-+ +--R \|- a \|a \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R - 6a x - 123a b x + 164a b x + 4761a b x + 15064a b x +--R + +--R 5 3 6 +--R 17360a b x + 6720b x +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +--R \|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 42a x + 189a b x - 1484a b x - 10543a b x - 22904a b x +--R + +--R 5 3 6 +--R - 20720a b x - 6720b x +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +-+ +--R \|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 6a x + 129a b x - 41a b x - 4925a b x - 19825a b x +--R + +--R 2 5 4 6 2 7 +--R - 32424a b x - 24080a b x - 6720b +--R * +--R +---+ +-+ +--R \|- a \|a +--R / +--R 8 8 7 6 6 2 4 5 3 2 4 4 +---+ +-+ +--R (168a x + 1512a b x + 4032a b x + 4224a b x + 1536a b )\|- a \|a +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 9 10 8 8 7 2 6 6 3 4 5 4 2 +--R - 24a x - 624a b x - 3096a b x - 5952a b x - 4992a b x +--R + +--R 4 5 +--R - 1536a b +--R * +--R +--------+ +--R | 2 +--R +---+ +-+ |a x + b +--R \|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 6 20 5 18 4 2 16 3 3 14 +--R - 14a x - 448a b x - 4032a b x - 15360a b x +--R + +--R 2 4 12 5 10 6 8 +--R - 28160a b x - 24576a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R - a x - 98a b x - 1568a b x - 9408a b x - 26880a b x +--R + +--R 2 5 11 6 9 7 7 +--R - 39424a b x - 28672a b x - 8192b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 21 6 19 5 2 17 4 3 15 3 4 13 +--R 14a x + 462a b x + 4480a b x + 19392a b x + 43520a b x +--R + +--R 2 5 11 6 9 7 7 +--R 52736a b x + 32768a b x + 8192b x +--R * +--R +-+ +--R \|b +--R + +--R 7 22 6 20 5 2 18 4 3 16 3 4 14 +--R a x + 98a b x + 1568a b x + 9408a b x + 26880a b x +--R + +--R 2 5 12 6 10 7 8 +--R 39424a b x + 28672a b x + 8192b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 100a b x + 1765a b x + 12642a b x + 47264a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 102592a b x + 134400a b x + 104960a b x + 45056a b x + 8192b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R - 14a x - 490a b x - 5418a b x - 28814a b x - 86784a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R - 159168a b x - 181760a b x - 126464a b x - 49152a b x - 8192b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1379 +t0:=x/(a+b/x^2)^(5/2) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1379 +r0:=-1/3*x^2/(a*(a+b/x^2)^(3/2))-5/2*b*atanh(sqrt(a+b/x^2)/_ + sqrt(a))/a^(7/2)-5/3*x^2/(a^2*sqrt(a+b/x^2))+5/2*x^2*sqrt(a+b/x^2)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 2 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 2 +-+ +--R \| x \|a +--R + +--R 2 4 2 2 +-+ +--R (3a x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 2 +--R 4 2 3 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +-+ | 2 +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a \|b +--R / +--R +--------+ +--R 6 6 5 4 4 2 2 3 3 +-+ +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|a \|b \|a x + b +--R + +--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+ +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a +--R , +--R +--R +--------+ +--R 3 6 2 2 4 3 2 4 +-+ | 2 +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 4 9 3 7 2 2 5 3 3 4 +---+ | 2 +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|b +--R / +--R +--------+ +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|b \|a x + b +--R + +--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+ +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1108 + +--S 1109 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 3 6 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 +-+ |a x + b +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 6 6 5 4 4 2 2 3 3 +-+ |a x + b +-+ | 2 +--R (30a x + 150a b x + 216a b x + 96a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 7 8 6 6 5 2 4 4 3 2 3 4 +-+ |a x + b +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 18 5 16 4 2 14 3 3 12 +--R - 13a x - 364a b x - 2912a b x - 9984a b x +--R + +--R 2 4 10 5 8 6 6 +--R - 16640a b x - 13312a b x - 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 8 6 6 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 9 6 7 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 9 6 7 7 5 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 9 6 7 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 19 6 17 5 2 15 4 3 13 3 4 11 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 9 6 7 7 5 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 20 6 18 5 2 16 4 3 14 3 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 10 6 8 7 6 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 10 2 6 8 7 6 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 9 17 8 15 7 2 13 6 3 11 5 4 9 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 4 5 7 3 6 5 2 7 3 8 +--R 56576a b x + 47360a b x + 21504a b x + 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 9 18 8 16 7 2 14 6 3 12 5 4 10 +--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x +--R + +--R 4 5 8 3 6 6 2 7 4 8 2 9 +--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 10 19 9 17 8 2 15 7 3 13 6 4 11 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 5 5 9 4 6 7 3 7 5 2 8 3 9 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1110 + +--S 1111 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 +---+ |a x + b +-+ +--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +---+ +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 2 6 2 3 4 4 2 5 +-+ |a x + b +--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 4 8 3 6 2 2 4 3 2 4 +---+ +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a \|b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 9 3 7 2 2 5 3 3 4 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +---+ +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--R 6 6 5 4 4 2 2 3 3 +---+ +-+ |a x + b +-+ +--R (30a x + 150a b x + 216a b x + 96a b )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 7 8 6 6 5 2 4 4 3 2 3 4 +---+ +-+ |a x + b +--R (- 6a x - 84a b x - 246a b x - 264a b x - 96a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 14 3 12 2 2 10 3 8 4 6 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 15 4 13 3 2 11 2 3 9 4 7 5 5 +--R (10a x + 170a b x + 832a b x + 1696a b x + 1536a b x + 512b x ) +--R * +--R +-+ +--R \|b +--R + +--R 5 16 4 14 3 2 12 2 3 10 4 8 5 6 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 2 5 4 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x + 4192a b x +--R + +--R 6 2 7 +--R 2304a b x + 512b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 4 6 2 7 +--R - 5280a b x - 2560a b x - 512b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1112 + +)clear all + +--S 1113 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x) +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2))+atanh(sqrt(a+b/x^2)/sqrt(a))/a^(5/2)+_ + (-1)/(a^2*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ |-------- +--R | 2 | 2 +--R 2 |a x + b \| x 2 +-+ +--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a +--R | 2 +-+ +--R \| x \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 3 2 2 +-+ |a x + b +--R (3a x + 3a b)\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x +--R + +--R 2 2 3 +--R - 27a b x - 12b +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 5 3 2 +-+ | 2 +--R (4a x + 19a b x + 12b x)\|a \|a x + b +--R + +--R 2 5 3 2 +-+ +-+ +--R (- 12a x - 25a b x - 12b x)\|a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +-+ +-+ | 2 +--R (9a x + 21a b x + 12a b )\|a \|b \|a x + b +--R + +--R 5 6 4 4 3 2 2 2 3 +-+ +--R (- 3a x - 18a b x - 27a b x - 12a b )\|a +--R , +--R +--R +--------+ +--R 2 4 2 2 +-+ | 2 3 6 2 4 +--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x +--R + +--R 2 2 3 +--R - 54a b x - 24b +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 2 5 3 2 +---+ | 2 +--R (4a x + 19a b x + 12b x)\|- a \|a x + b +--R + +--R 2 5 3 2 +---+ +-+ +--R (- 12a x - 25a b x - 12b x)\|- a \|b +--R / +--R +--------+ +--R 4 4 3 2 2 2 +---+ +-+ | 2 +--R (9a x + 21a b x + 12a b )\|- a \|b \|a x + b +--R + +--R 5 6 4 4 3 2 2 2 3 +---+ +--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1115 + +--S 1116 of 1379 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b +-+ | 2 +--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 |a x + b +--R (3a x + 18a b x + 27a b x + 12b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 4 2 2 +-+ +-+ +--R (12a x + 25a b x + 12b )\|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (4a x + 19a b x + 12b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 4 3 2 2 2 +-+ |a x + b +-+ | 2 +--R (9a x + 21a b x + 12a b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 6 4 4 3 2 2 2 3 +-+ |a x + b +--R (- 3a x - 18a b x - 27a b x - 12a b )\|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1379 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 5 3 +-+ +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x )\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 13 4 11 3 2 9 2 3 7 4 5 |a x + b +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 5 13 4 11 3 2 9 2 3 7 4 5 +--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x +--R + +--R 5 3 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 14 4 12 3 2 10 2 3 8 4 6 5 4 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 2 5 3 6 +--R 1088a b x + 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 4 6 2 7 +--R - 2352a b x - 1216a b x - 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x +--R + +--R 2 5 4 6 2 7 +--R 2928a b x + 1344a b x + 256b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 8 15 7 13 6 2 11 5 3 9 4 4 7 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 3 5 5 2 6 3 7 +--R - 2352a b x - 1216a b x - 256a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1379 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 +---+ |a x + b +-+ | 2 +--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 +---+ |a x + b +--R (3a x + 18a b x + 27a b x + 12b )\|- a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 +-+ |a x + b +-+ | 2 +--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R 2 4 2 2 +---+ +-+ +-+ +--R (12a x + 25a b x + 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +--R (4a x + 19a b x + 12b x)\|- a \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +---+ +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x)\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 6 2 4 2 2 3 +---+ +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 4 3 2 2 2 +---+ +-+ |a x + b +-+ | 2 +--R (9a x + 21a b x + 12a b )\|- a \|a |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 6 4 4 3 2 2 2 3 +---+ +-+ |a x + b +--R (- 3a x - 18a b x - 27a b x - 12a b )\|- a \|a |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1379 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +-+ 3 9 2 7 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 5 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 9 2 7 2 5 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^3) +--R +--R +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1120 + +--S 1121 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)) +--R +--R +--R 2 +--R x +--R (2) -------------------------- +--R +--------+ +--R | 2 +--R 2 2 |a x + b +--R (3a b x + 3b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 5 3 | 2 5 3 +-+ +--R (- a x - 4b x )\|a x + b + (3a x + 4b x )\|b +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 4 2 +-+ 5 3 |a x + b | 2 +--R ((- 3a x - 4b x )\|b + (- a x - 4b x ) |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 3 |a x + b +-+ 2 6 4 2 2 +--R (3a x + 4b x ) |-------- \|b + a x + 5a b x + 4b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 3 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 2 4 3 2 4 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +-+ 3 7 2 5 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 3 3 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b x)\|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^5) +--R +--R +--R 1 +--R (1) --------------------------------- +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (a x + 2a b x + b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1125 + +--S 1126 of 1379 +r0:=-1/3*a/(b^2*(a+b/x^2)^(3/2))+1/(b^2*sqrt(a+b/x^2)) +--R +--R +--R 2 +--R 2a x + 3b +--R (2) -------------------------- +--R +--------+ +--R | 2 +--R 2 2 3 |a x + b +--R (3a b x + 3b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 5 3 2 | 2 2 5 3 2 +-+ +--R (- 2a x - 11a b x - 12b x)\|a x + b + (6a x + 17a b x + 12b x)\|b +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 2 +-+ +--R (- 6a x - 17a b x - 12b )\|b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +--R (- 2a x - 11a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 2 2 +--R (6a x + 17a b x + 12b x) |-------- \|b + 2a x + 13a b x + 23a b x +--R | 2 +--R \| x +--R + +--R 3 +--R 12b +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 2 4 3 2 4 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 6 2 3 4 4 2 5 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^7) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1130 + +--S 1131 of 1379 +r0:=1/3*a^2/(b^3*(a+b/x^2)^(3/2))-2*a/(b^3*sqrt(a+b/x^2))-sqrt(a+b/x^2)/b^3 +--R +--R +--R 2 4 2 2 +--R - 8a x - 12a b x - 3b +--R (2) ---------------------------- +--R +--------+ +--R | 2 +--R 3 4 4 2 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 4 8 3 6 +--R (32a x + 112a b x + 108a b x + 24b )\|b \|a x + b - 8a x - 76a b x +--R + +--R 2 2 4 3 2 4 +--R - 163a b x - 120a b x - 24b +--R / +--R +--------+ +--R 3 3 7 2 4 5 5 3 6 | 2 +--R (3a b x + 27a b x + 48a b x + 24b x)\|a x + b +--R + +--R 3 3 7 2 4 5 5 3 6 +-+ +--R (- 12a b x - 48a b x - 60a b x - 24b x)\|b +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (32a x + 112a b x + 108a b x + 24b x) |-------- \|b + 8a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R 76a b x + 163a b x + 120a b x + 24b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 32a x - 144a b x - 220a b x - 132a b x - 24b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (- 8a x - 76a b x - 163a b x - 120a b x - 24b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 3 8 2 4 6 5 4 6 2 |a x + b | 2 +--R (3a b x + 27a b x + 48a b x + 24b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 3 8 2 4 6 5 4 6 2 |a x + b +-+ +--R (- 12a b x - 48a b x - 60a b x - 24b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 +--R (- 8a x - 80a b x - 192a b x - 128b x) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 4 +--R - 32a b x - 160a b x - 256a b x - 128b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b )\|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x) |-------- +--R | 2 +--R \| x +--R / +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 5 5 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 3 +--R 128b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x +--R + +--R 5 5 6 3 +--R - 576a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^9) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 9 7 2 5 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1135 + +--S 1136 of 1379 +r0:=-1/3*a^3/(b^4*(a+b/x^2)^(3/2))-1/3*(a+b/x^2)^(3/2)/b^4+_ + 3*a^2/(b^4*sqrt(a+b/x^2))+3*a*sqrt(a+b/x^2)/b^4 +--R +--R +--R 3 6 2 4 2 2 3 +--R 16a x + 24a b x + 6a b x - b +--R (2) -------------------------------- +--R +--------+ +--R | 2 +--R 4 6 5 4 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 96a x - 656a b x - 1316a b x - 954a b x - 160a b x + 32b )\|b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x + 144a b x +--R + +--R 6 +--R - 32b +--R / +--R +--------+ +--R 4 4 11 3 5 9 2 6 7 7 5 8 3 | 2 +--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x )\|a x + b +--R + +--R 4 4 11 3 5 9 2 6 7 7 5 8 3 +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x )\|b +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 96a x - 656a b x - 1316a b x - 954a b x - 160a b x +--R + +--R 5 +--R 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 16a x - 312a b x - 1206a b x - 1771a b x - 1038a b x +--R + +--R 5 2 6 +--R - 144a b x + 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 96a x + 752a b x + 1972a b x + 2270a b x + 1114a b x +--R + +--R 5 2 6 +--R 128a b x - 32b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 +--R 16a x + 312a b x + 1206a b x + 1771a b x + 1038a b x +--R + +--R 5 3 6 +--R 144a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b +--R (3a b x + 57a b x + 198a b x + 240a b x + 96b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 4 12 3 5 10 2 6 8 7 6 8 4 |a x + b +-+ +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 2 6 +--R - 6144a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 2 6 +--R 7168a b x + 2048b +--R * +--R +-+ +--R \|b +--R + +--R 6 13 5 11 4 2 9 3 3 7 2 4 5 5 3 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x + 6144a b x +--R + +--R 6 +--R 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 8 21 7 19 6 2 17 5 3 15 4 4 13 +--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x +--R + +--R 3 5 11 2 6 9 7 7 8 5 +--R 23552a b x + 21248a b x + 10240a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 8 21 7 19 6 2 17 5 3 15 4 4 13 +--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x +--R + +--R 3 5 11 2 6 9 7 7 8 5 +--R - 33024a b x - 26112a b x - 11264a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1379 +t0:=x^2/(a+b/x^2)^(5/2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1140 + +--S 1141 of 1379 +r0:=-1/3*x^3/(a*(a+b/x^2)^(3/2))-2*x^3/(a^2*sqrt(a+b/x^2))-_ + 16/3*b*x*sqrt(a+b/x^2)/a^4+8/3*x^3*sqrt(a+b/x^2)/a^3 +--R +--R +--R 3 6 2 4 2 2 3 +--R a x - 6a b x - 24a b x - 16b +--R (2) -------------------------------- +--R +--------+ +--R | 2 +--R 5 3 4 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 10 2 8 | 2 2 12 10 2 8 +-+ +--R (- 6a b x - 12b x )\|a x + b + (a x + 12a b x + 12b x )\|b +--R / +--R +--------+ +--R 4 8 3 6 2 2 4 3 2 4 +-+ | 2 +--R (3a x + 57a b x + 198a b x + 240a b x + 96b )\|b \|a x + b +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R - 18a b x - 132a b x - 306a b x - 288a b x - 96b +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 12a b x + 84a b x + 704a b x + 1632a b x +--R + +--R 5 2 6 +--R 1536a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 2 9 |a x + b +--R (- 6a b x - 12a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 6 13 5 11 4 2 9 |a x + b +-+ 6 12 5 2 10 +--R (a x + 12a b x + 12a b x ) |-------- \|b + 6a b x + 2a b x +--R | 2 +--R \| x +--R + +--R 4 3 8 3 4 6 2 5 4 6 2 7 +--R - 308a b x - 1360a b x - 2336a b x - 1792a b x - 512b +--R / +--R +--------+ +--R | 2 +--R 8 9 7 7 6 2 5 5 3 3 4 4 |a x + b +-+ +--R (3a x + 57a b x + 198a b x + 240a b x + 96a b x) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 8 9 7 2 7 6 3 5 5 4 3 4 5 |a x + b +--R (- 18a b x - 132a b x - 306a b x - 288a b x - 96a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 17 4 15 3 2 13 2 3 11 4 9 +--R - 12a x - 280a b x - 1792a b x - 4608a b x - 5120a b x +--R + +--R 5 7 +--R - 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R - a x - 72a b x - 840a b x - 3584a b x - 6912a b x +--R + +--R 5 8 6 6 +--R - 6144a b x - 2048b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 18 5 16 4 2 14 3 3 12 2 4 10 +--R 12a x + 292a b x + 2072a b x + 6400a b x + 9728a b x +--R + +--R 5 8 6 6 +--R 7168a b x + 2048b x +--R * +--R +-+ +--R \|b +--R + +--R 6 19 5 17 4 2 15 3 3 13 2 4 11 +--R a x + 72a b x + 840a b x + 3584a b x + 6912a b x +--R + +--R 5 9 6 7 +--R 6144a b x + 2048b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R a x + 74a b x + 985a b x + 5336a b x + 14920a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R 23552a b x + 21248a b x + 10240a b x + 2048b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 +--R - 12a x - 316a b x - 2668a b x - 10836a b x - 24600a b x +--R + +--R 3 5 6 2 6 4 7 2 8 +--R - 33024a b x - 26112a b x - 11264a b x - 2048b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1379 +t0:=1/(a+b/x^2)^(5/2) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1145 + +--S 1146 of 1379 +r0:=-1/3*x/(a*(a+b/x^2)^(3/2))-4/3*x/(a^2*sqrt(a+b/x^2))+_ + 8/3*x*sqrt(a+b/x^2)/a^3 +--R +--R +--R 2 4 2 2 +--R 3a x + 12a b x + 8b +--R (2) --------------------------- +--R +--------+ +--R | 2 +--R 4 3 3 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 6 | 2 8 6 +-+ +--R - 4b x \|a x + b + (3a x + 4b x )\|b +--R / +--R +--------+ +--R 3 6 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (3a x + 27a b x + 48a b x + 24b )\|b \|a x + b - 12a b x - 48a b x +--R + +--R 3 2 4 +--R - 60a b x - 24b +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 8 3 6 2 2 4 3 2 4 +-+ +--R (- 3a x - 36a b x - 128a b x - 160a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 |a x + b +--R - 4a b x |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 |a x + b +-+ 4 8 3 2 6 2 3 4 +--R (3a x + 4a b x ) |-------- \|b + 12a b x + 84a b x + 200a b x +--R | 2 +--R \| x +--R + +--R 4 2 5 +--R 192a b x + 64b +--R / +--R +--------+ +--R | 2 +--------+ +--R 6 7 5 5 4 2 3 3 3 |a x + b +-+ | 2 +--R (3a x + 27a b x + 48a b x + 24a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 6 7 5 2 5 4 3 3 3 4 |a x + b +--R (- 12a b x - 48a b x - 60a b x - 24a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 3 11 2 9 2 7 3 5 |a x + b +-+ 4 12 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 10 2 2 8 3 6 4 4 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 12 3 10 2 2 8 3 6 4 4 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 13 3 11 2 2 9 3 7 4 5 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 34a b x + 225a b x + 608a b x + 800a b x + 512a b x +--R + +--R 6 +--R 128b +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 8a x - 104a b x - 456a b x - 952a b x - 1040a b x +--R + +--R 5 2 6 +--R - 576a b x - 128b +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^2) +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1150 + +--S 1151 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x)+(-2/3)/(a^2*x*sqrt(a+b/x^2)) +--R +--R +--R 2 +--R - 3a x - 2b +--R (2) --------------------------- +--R +--------+ +--R | 2 +--R 3 3 2 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 | 2 6 4 +-+ +--R - 3b x \|a x + b + (2a x + 3b x )\|b +--R / +--R +--------+ +--R 2 4 2 2 3 +-+ | 2 3 6 2 2 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 3 2 4 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 3 +-+ 2 5 |a x + b | 2 +--R ((9a b x + 18a b x + 8b )\|b - 3a b x |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 |a x + b +-+ 3 6 2 2 4 3 2 4 +--R (2a x + 3a b x ) |-------- \|b - 3a b x - 17a b x - 22a b x - 8b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 5 3 2 3 2 3 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 7 4 2 5 3 3 3 2 4 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 7 5 2 3 |a x + b +-+ 3 8 2 6 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 4 3 2 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 8 2 6 2 4 3 2 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 2 +--R 3 9 2 7 2 5 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^4) +--R +--R +--R 1 +--R (1) -------------------------------- +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1155 + +--S 1156 of 1379 +r0:=(-1/3)/(a*(a+b/x^2)^(3/2)*x^3) +--R +--R +--R 1 +--R (2) - --------------------------- +--R +--------+ +--R | 2 +--R 2 3 |a x + b +--R (3a x + 3a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 2 2 | 2 2 6 4 2 2 +-+ +--R (- 3a b x - 6b x )\|a x + b + (a x + 6a b x + 6b x )\|b +--R / +--R +--------+ +--R 2 2 4 3 2 4 +-+ | 2 3 2 6 2 3 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 4 2 5 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 2 3 +-+ 2 5 2 3 |a x + b | 2 +--R ((3a b x + 4b )\|b + (- 3a b x - 6a b x ) |-------- )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +-+ 2 2 4 3 2 4 +--R (a x + 6a b x + 6a b x ) |-------- \|b - a b x - 5a b x - 4b +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 2 5 2 3 3 4 |a x + b +-+ | 2 +--R (9a b x + 21a b x + 12a b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 2 7 3 3 5 2 4 3 5 |a x + b +--R (- 3a b x - 18a b x - 27a b x - 12a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 2 +--R 2 5 3 2 |a x + b +-+ 3 6 2 4 +--R (- 6a x - 32a b x - 32b x) |-------- \|b - a x - 18a b x +--R | 2 +--R \| x +--R + +--R 2 2 3 +--R - 48a b x - 32b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (6a x + 38a b x + 64a b x + 32b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (a x + 18a b x + 48a b x + 32b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 |a x + b +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^6) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 6 4 2 2 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1160 + +--S 1161 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)*x^3)-atanh(sqrt(b)/(x*sqrt(a+b/x^2)))/_ + b^(5/2)+1/(b^2*x*sqrt(a+b/x^2)) +--R +--R +--R +--------+ +--R | 2 +-+ +--R 3 |a x + b \|b 2 +-+ +--R (- 3a x - 3b x) |-------- atanh(------------) + (3a x + 4b)\|b +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R (2) ----------------------------------------------------------------- +--R +--------+ +--R | 2 +--R 2 3 3 |a x + b +-+ +--R (3a b x + 3b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 2 4 2 2 3 | 2 +--R (9a b x + 21a b x + 12b )\|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (- 3a x - 18a b x - 27a b x - 12b )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 2 4 2 2 | 2 3 6 2 4 2 2 +-+ +--R (9a b x + 12a b x )\|a x + b + (- 4a x - 15a b x - 12a b x )\|b +--R / +--R +--------+ +--R 2 3 4 4 2 5 +-+ | 2 3 3 6 2 4 4 +--R (9a b x + 21a b x + 12b )\|b \|a x + b - 3a b x - 18a b x +--R + +--R 5 2 6 +--R - 27a b x - 12b +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 5 3 2 |a x + b +-+ | 2 +--R (9a x + 21a b x + 12b x) |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b x) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 |a x + b +-+ 2 4 2 2 3 +--R ((9a x + 12a b x ) |-------- \|b - 9a b x - 24a b x - 16b ) +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 6 2 4 2 2 3 +-+ +--R (3a x + 19a b x + 32a b x + 16b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 |a x + b +--R (- 4a x - 15a b x - 12a b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 3 5 4 3 5 |a x + b | 2 +--R (9a b x + 21a b x + 12b x) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 2 7 2 3 5 4 3 5 |a x + b +-+ +--R (- 3a b x - 18a b x - 27a b x - 12b x) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 3 6 2 4 2 2 3 +-+ +--R (- 7a x - 56a b x - 112a b x - 64b )\|b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64b x) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 3 7 2 5 2 3 3 |a x + b +-+ 4 8 3 6 +--R (7a x + 56a b x + 112a b x + 64b x) |-------- \|b + a x + 25a b x +--R | 2 +--R \| x +--R + +--R 2 2 4 3 2 4 +--R 104a b x + 144a b x + 64b +--R / +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (7a x + 70a b x + 231a b x + 344a b x + 240a b x + 64b x ) +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 5 4 +--R - a x - 27a b x - 155a b x - 377a b x - 456a b x - 272a b x +--R + +--R 6 2 +--R - 64b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1379 +t0:=1/((a+b/x^2)^(5/2)*x^8) +--R +--R +--R 1 +--R (1) ---------------------------------- +--R +--------+ +--R | 2 +--R 2 8 6 2 4 |a x + b +--R (a x + 2a b x + b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1379 +r0:=1/3/(b*(a+b/x^2)^(3/2)*x^5)+5/2*a*atanh(sqrt(b)/(x*_ + sqrt(a+b/x^2)))/b^(7/2)+5/3/(b^2*x^3*sqrt(a+b/x^2))-_ + 5/2*sqrt(a+b/x^2)/(b^3*x) +--R +--R +--R (2) +--R +--------+ +--R | 2 +-+ +--R 2 5 3 |a x + b \|b +--R (15a x + 15a b x ) |-------- atanh(------------) +--R | 2 +--------+ +--R \| x | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R 2 4 2 2 +-+ +--R (- 15a x - 20a b x - 3b )\|b +--R / +--R +--------+ +--R | 2 +--R 3 5 4 3 |a x + b +-+ +--R (6a b x + 6b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 | 2 +--R (- 75a b x - 375a b x - 540a b x - 240a b x )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +-+ +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x )\|b +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R 4 8 3 2 6 2 3 4 4 2 5 | 2 +--R (- 55a b x - 150a b x - 21a b x + 132a b x + 48b )\|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b )\|b +--R / +--R +--------+ +--R 3 4 8 2 5 6 6 4 7 2 +-+ | 2 4 4 10 +--R (30a b x + 150a b x + 216a b x + 96b x )\|b \|a x + b - 6a b x +--R + +--R 3 5 8 2 6 6 7 4 8 2 +--R - 84a b x - 246a b x - 264a b x - 96b x +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +-+ +--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +-+ +--R \|a x + b - \|b +--R log(------------------) +--R x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +-+ +--R (- 75a x - 375a b x - 540a b x - 240a b x ) |-------- \|b +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 |a x + b +--R (15a x + 210a b x + 615a b x + 660a b x + 240a b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R atanh(------------) +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 4 |a x + b +-+ +--R (- 55a x - 150a b x - 21a b x + 132a b x + 48b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R 4 8 3 2 6 2 3 4 4 2 5 +--R 75a b x + 400a b x + 655a b x + 380a b x + 48b +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 5 +-+ +--R (- 15a x - 215a b x - 683a b x - 839a b x - 404a b x - 48b )\|b +--R + +--R +--------+ +--R | 2 +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 |a x + b +--R (14a x + 121a b x + 174a b x - 39a b x - 156a b x - 48b x) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 3 4 9 2 5 7 6 5 7 3 |a x + b | 2 +--R (30a b x + 150a b x + 216a b x + 96b x ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 3 11 3 4 9 2 5 7 6 5 7 3 |a x + b +-+ +--R (- 6a b x - 84a b x - 246a b x - 264a b x - 96b x ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 +--R - 1024b +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 +--R - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R (11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x + 1024b x) +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 5 2 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 +--R 1024b +--R / +--R 7 18 6 16 5 2 14 4 3 12 3 4 10 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 8 6 6 7 4 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--------+ +--R |a x + b +-+ | 2 +--R |-------- \|b \|a x + b +--R | 2 +--R \| x +--R + +--R 8 20 7 18 6 2 16 5 3 14 4 4 12 +--R - a x - 63a b x - 743a b x - 3653a b x - 9420a b x +--R + +--R 3 5 10 2 6 8 7 6 8 4 +--R - 13872a b x - 11776a b x - 5376a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1379 +t0:=(1+1/x^2)^(1/3)/x^3 +--R +--R +--R +------+ +--R | 2 +--R |x + 1 +--R |------ +--R 3| 2 +--R \| x +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1170 + +--S 1171 of 1379 +r0:=-3/8*(1+1/x^2)^(4/3) +--R +--R +--R +------+ +--R | 2 +--R 2 |x + 1 +--R (- 3x - 3) |------ +--R 3| 2 +--R \| x +--R (2) -------------------- +--R 2 +--R 8x +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +------+ +--R | 2 +--R 2 |x + 1 +--R (- 3x - 3) |------ +--R 3| 2 +--R \| x +--R (3) -------------------- +--R 4 +--R 8x +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1379 +m0:=a0-r0 +--R +--R +--R +------+ +--R | 2 +--R 4 |x + 1 +--R (3x - 3) |------ +--R 3| 2 +--R \| x +--R (4) ------------------ +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1379 +d0:=D(m0,x) +--R +--R +--R 4 2 +--R - x + 6x + 7 +--R (5) -------------- +--R +------+2 +--R | 2 +--R 7 |x + 1 +--R 4x |------ +--R 3| 2 +--R \| x +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1379 +t0:=(1+1/x^2)^(5/3)/x^3 +--R +--R +--R +------+2 +--R | 2 +--R 2 |x + 1 +--R (x + 1) |------ +--R 3| 2 +--R \| x +--R (1) ------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1379 +r0:=-3/16*(1+1/x^2)^(8/3) +--R +--R +--R +------+2 +--R | 2 +--R 4 2 |x + 1 +--R (- 3x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (2) --------------------------- +--R 4 +--R 16x +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +------+2 +--R | 2 +--R 4 2 |x + 1 +--R (- 3x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (3) --------------------------- +--R 8 +--R 16x +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1379 +m0:=a0-r0 +--R +--R +--R +------+2 +--R | 2 +--R 8 6 2 |x + 1 +--R (3x + 6x - 6x - 3) |------ +--R 3| 2 +--R \| x +--R (4) ------------------------------- +--R 8 +--R 16x +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1379 +d0:=D(m0,x) +--R +--R +--R 8 6 4 2 +--R - 4x - 5x + 9x + 17x + 7 +--R (5) ---------------------------- +--R +------+ +--R | 2 +--R 11 |x + 1 +--R 4x |------ +--R 3| 2 +--R \| x +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1379 +t0:=x^5/(a+b/x^3) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1180 + +--S 1181 of 1379 +r0:=-1/3*b*x^3/a^2+1/6*x^6/a+1/3*b^2*log(b+a*x^3)/a^3 +--R +--R +--R 2 3 2 6 3 +--R 2b log(a x + b) + a x - 2a b x +--R (2) --------------------------------- +--R 3 +--R 6a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 3 2 6 3 +--R 2b log(a x + b) + a x - 2a b x +--R (3) --------------------------------- +--R 3 +--R 6a +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1379 +t0:=x^4/(a+b/x^3) +--R +--R +--R 7 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1185 + +--S 1186 of 1379 +r0:=-1/2*b*x^2/a^2+1/5*x^5/a-1/3*b^(5/3)*log(b^(1/3)+a^(1/3)*x)/_ + a^(8/3)+1/6*b^(5/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/_ + a^(8/3)-b^(5/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/_ + (a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R 5b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 3+-+ 3+-+ 3+-+2 \|b - 2x\|a +--R - 10b\|3 \|b log(\|b + x\|a ) - 30b \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 5 2 +-+3+-+2 +--R (6a x - 15b x )\|3 \|a +--R / +--R 2 +-+3+-+2 +--R 30a \|3 \|a +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +--R | 2 | 2 +--R +-+ | b | b +--R 10b\|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b | b | b 2 +--R - 5b\|3 |- -- log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R | b \| a 5 2 +-+ +--R 30b |- -- atan(------------------------ + (6a x - 15b x )\|3 +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+ +--R 30a \|3 +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b +--R 2b\|3 \|b log(\|b + x\|a ) + 2b\|3 |- -- \|a log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 | b | b 2 +--R - b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R | b 3+-+2 \| a 3+-+2 \|b - 2x\|a +--R 6b |- -- \|a atan(------------------------ + 6b \|b atan(-------------) +--R 3| 2 +----+2 +-+3+-+ +--R \| a | 2 \|3 \|b +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 6a \|3 \|a +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1379 +t0:=x^3/(a+b/x^3) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1190 + +--S 1191 of 1379 +r0:=-b*x/a^2+1/4*x^4/a+1/3*b^(4/3)*log(b^(1/3)+a^(1/3)*x)/a^(7/3)-_ + 1/6*b^(4/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(7/3)-_ + b^(4/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R - 2b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ 3+-+ 3+-+ 3+-+ \|b - 2x\|a +--R 4b\|3 \|b log(\|b + x\|a ) - 12b\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 4 +-+3+-+ +--R (3a x - 12b x)\|3 \|a +--R / +--R 2 +-+3+-+ +--R 12a \|3 \|a +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+ |b |b |b 2 +-+ |b |b +--R - 2b\|3 3|- log(3|- - x 3|- + x + 4b\|3 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 +--R |b \|a 4 +-+ +--R - 12b 3|- atan(----------------- + (3a x - 12b x)\|3 +--R \|a +-+ +--R |b +--R 3 3|- +--R \|a +--R / +--R 2 +-+ +--R 12a \|3 +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 2b\|3 \|b log(\|b + x\|a ) +--R + +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b +--R - b\|3 \|a 3|- log(3|- - x 3|- + x + 2b\|3 \|a 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+ +--R 3+-+ |b \|a 3+-+ \|b - 2x\|a +--R - 6b\|a 3|- atan(----------------- + 6b\|b atan(-------------) +--R \|a +-+ +-+3+-+ +--R |b \|3 \|b +--R 3 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 6a \|3 \|a +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1379 +t0:=x^2/(a+b/x^3) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1195 + +--S 1196 of 1379 +r0:=1/3*x^3/a-1/3*b*log(b+a*x^3)/a^2 +--R +--R +--R 3 3 +--R - b log(a x + b) + a x +--R (2) ------------------------ +--R 2 +--R 3a +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R - b log(a x + b) + a x +--R (3) ------------------------ +--R 2 +--R 3a +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1379 +t0:=x/(a+b/x^3) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1200 + +--S 1201 of 1379 +r0:=1/2*x^2/a+1/3*b^(2/3)*log(b^(1/3)+a^(1/3)*x)/a^(5/3)-_ + 1/6*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(5/3)+_ + b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+2 \|b - 2x\|a 2 +-+3+-+2 +--R 6\|b atan(-------------) + 3x \|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |b |b +--R 2\|3 |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |b |b |b 2 +--R - \|3 |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 +--R |b \|a 2 +-+ +--R 6 |-- atan(---------------------- + 3x \|3 +--R 3| 2 +--+2 +--R \|a | 2 +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R +-+ +--R 6a\|3 +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+3+-+2 |b |b +--R 2\|3 \|a |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+3+-+2 |b |b |b 2 +--R - \|3 \|a |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a +--R 6\|a |-- atan(---------------------- - 6\|b atan(-------------) +--R 3| 2 +--+2 +-+3+-+ +--R \|a | 2 \|3 \|b +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R +-+3+-+2 +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1379 +t0:=1/(a+b/x^3) +--R +--R +--R 3 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1205 + +--S 1206 of 1379 +r0:=x/a-1/3*b^(1/3)*log(b^(1/3)+a^(1/3)*x)/a^(4/3)+1/6*b^(1/3)*_ + log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/a^(4/3)+b^(1/3)*_ + atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log(\|b - x\|a \|b + x \|a ) - 2\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +-+3+-+ +--R 6\|b atan(-------------) + 6x\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +---+ +---+ +--R +-+ | b | b | b 2 +-+ | b | b +--R - \|3 3|- - log(3|- - + x 3|- - + x + 2\|3 3|- - log(- 3|- - + x) +--R \| a \| a \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R | b \| a +-+ +--R - 6 3|- - atan(------------------- + 6x\|3 +--R \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R / +--R +-+ +--R 6a\|3 +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - \|3 \|b log(\|b - x\|a \|b + x \|a ) + 2\|3 \|b log(\|b + x\|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - \|3 3|- - \|a log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ +---+ +---+ \|3 3|- - + 2x\|3 +--R +-+ | b 3+-+ | b | b 3+-+ \| a +--R 2\|3 3|- - \|a log(- 3|- - + x - 6 3|- - \|a atan(-------------------) +--R \| a \| a \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +--R - 6\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6a\|3 \|a +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1379 +t0:=1/((a+b/x^3)*x) +--R +--R +--R 2 +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1379 +r0:=1/3*log(b+a*x^3)/a +--R +--R +--R 3 +--R log(a x + b) +--R (2) ------------- +--R 3a +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R log(a x + b) +--R (3) ------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1379 +t0:=1/((a+b/x^3)*x^2) +--R +--R +--R x +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1379 +r0:=-1/3*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(1/3))+1/6*log(b^(2/3)-_ + a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(1/3))-atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+ +--R \|3 log(\|b - x\|a \|b + x \|a ) - 2\|3 log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R \|b - 2x\|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+2 3+-+ +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +-----+2 +--R +-+ 3| 2 2 3| 2 +-+ 3| 2 +--R - \|3 log(x \|- a b + a x \|- a b - a b) + 2\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +--R 2x\|3 \|- a b - a b\|3 +--R - 6atan(-------------------------) +--R 3a b +--R / +--R +-----+ +--R +-+3| 2 +--R 6\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 6\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1379 +t0:=1/((a+b/x^3)*x^3) +--R +--R +--R 1 +--R (1) -------- +--R 3 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1379 +r0:=1/3*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(2/3))-1/6*log(b^(2/3)-_ + a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(2/3))-atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+ 3+-+ 3+-+ +--R - \|3 log(\|b - x\|a \|b + x \|a ) + 2\|3 log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R \|b - 2x\|a +--R - 6atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+3+-+2 +--R 6\|3 \|a \|b +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +----+ +--R +-+ 2 3| 2 3| 2 2 +-+ 3| 2 +--R - \|3 log(x \|a b - b x\|a b + b ) + 2\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +--R 2x\|3 \|a b - b\|3 +--R 6atan(---------------------) +--R 3b +--R / +--R +----+ +--R +-+3| 2 +--R 6\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 6\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1379 +t0:=1/((a+b/x^3)*x^4) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1379 +r0:=-1/3*log(a+b/x^3)/b +--R +--R +--R 3 +--R a x + b +--R log(--------) +--R 3 +--R x +--R (2) - ------------- +--R 3b +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(a x + b) + 3log(x) +--R (3) ------------------------- +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1379 +m0:=a0-r0 +--R +--R +--R 3 +--R 3 a x + b +--R - log(a x + b) + 3log(x) + log(--------) +--R 3 +--R x +--R (4) ----------------------------------------- +--R 3b +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1379 +t0:=1/((a+b/x^3)*x^5) +--R +--R +--R 1 +--R (1) ----------- +--R 5 2 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1379 +r0:=(-1)/(b*x)+1/3*a^(1/3)*log(b^(1/3)+a^(1/3)*x)/b^(4/3)-1/6*a^(1/3)*_ + log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(4/3)+a^(1/3)*_ + atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - x\|3 \|a log(\|b - x\|a \|b + x \|a ) + 2x\|3 \|a log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +-+3+-+ +--R 6x\|a atan(-------------) - 6\|3 \|b +--R +-+3+-+ +--R \|3 \|b +--R / +--R +-+3+-+ +--R 6b x\|3 \|b +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +-+2 +-+ +--R +-+ |a |a +-+ |a |a |a 2 +--R 2x\|3 3|- log(b 3|- + a x - x\|3 3|- log(- b x 3|- + b 3|- + a x ) +--R \|b \|b \|b \|b \|b +--R + +--R +-+2 +--R +-+ |a +-+ +--R +-+ b\|3 3|- - 2a x\|3 +--R |a \|b +-+ +--R 6x 3|- atan(--------------------- - 6\|3 +--R \|b +-+2 +--R |a +--R 3b 3|- +--R \|b +--R / +--R +-+ +--R 6b x\|3 +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R \|3 \|a log(\|b - x\|a \|b + x \|a ) - 2\|3 \|a log(\|b + x\|a ) +--R + +--R +-+ +-+2 +--R +-+ |a 3+-+ |a +--R 2\|3 3|- \|b log(b 3|- + a x) +--R \|b \|b +--R + +--R +-+ +-+2 +-+ +--R +-+ |a 3+-+ |a |a 2 +--R - \|3 3|- \|b log(- b x 3|- + b 3|- + a x ) +--R \|b \|b \|b +--R + +--R +-+2 +--R +-+ |a +-+ +--R +-+ b\|3 3|- - 2a x\|3 3+-+ 3+-+ +--R |a 3+-+ \|b 3+-+ \|b - 2x\|a +--R 6 3|- \|b atan(--------------------- - 6\|a atan(-------------) +--R \|b +-+2 +-+3+-+ +--R |a \|3 \|b +--R 3b 3|- +--R \|b +--R / +--R +-+3+-+ +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1379 +t0:=1/((a+b/x^3)*x^6) +--R +--R +--R 1 +--R (1) ----------- +--R 6 3 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1379 +r0:=(-1/2)/(b*x^2)-1/3*a^(2/3)*log(b^(1/3)+a^(1/3)*x)/b^(5/3)+_ + 1/6*a^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/b^(5/3)+_ + a^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R x \|3 \|a log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 +-+3+-+2 3+-+ 3+-+ 2 3+-+2 \|b - 2x\|a +-+3+-+2 +--R - 2x \|3 \|a log(\|b + x\|a ) + 6x \|a atan(------------- - 3\|3 \|b +--R +-+3+-+ +--R \|3 \|b +--R / +--R 2 +-+3+-+2 +--R 6b x \|3 \|b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 2 +-+ | a 2 | a | a 2 2 +--R - x \|3 |- -- log(b |- -- + a b x |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 +-+ | a | a +--R 2x \|3 |- -- log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 +--R 2 | a \| b +-+ +--R - 6x |- -- atan(----------------------- - 3\|3 +--R 3| 2 +----+ +--R \| b | 2 +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R 2 +-+ +--R 6b x \|3 +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R - \|3 \|a log(\|b - x\|a \|b + x \|a ) + 2\|3 \|a log(\|b + x\|a ) +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | a 3+-+2 2 | a | a 2 2 +--R - \|3 |- -- \|b log(b |- -- + a b x |- -- + a x ) +--R 3| 2 3| 2 3| 2 +--R \| b \| b \| b +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | a 3+-+2 | a +--R 2\|3 |- -- \|b log(- b |- -- + a x) +--R 3| 2 3| 2 +--R \| b \| b +--R + +--R +----+ +--R | 2 +--R +-+ | a +-+ +--R +----+ b\|3 |- -- + 2a x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R | a 3+-+2 \| b 3+-+2 \|b - 2x\|a +--R - 6 |- -- \|b atan(----------------------- - 6\|a atan(-------------) +--R 3| 2 +----+ +-+3+-+ +--R \| b | 2 \|3 \|b +--R | a +--R 3b |- -- +--R 3| 2 +--R \| b +--R / +--R +-+3+-+2 +--R 6b\|3 \|b +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1379 +t0:=1/((a+b/x^3)*x^7) +--R +--R +--R 1 +--R (1) ----------- +--R 7 4 +--R a x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1379 +r0:=(-1/3)/(b*x^3)-a*log(x)/b^2+1/3*a*log(b+a*x^3)/b^2 +--R +--R +--R 3 3 3 +--R a x log(a x + b) - 3a x log(x) - b +--R (2) ----------------------------------- +--R 2 3 +--R 3b x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R a x log(a x + b) - 3a x log(x) - b +--R (3) ----------------------------------- +--R 2 3 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1379 +t0:=x^5/(a+b/x^3)^2 +--R +--R +--R 11 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1379 +r0:=-2/3*b*x^3/a^3+1/6*x^6/a^2+1/3*b^3/(a^4*(b+a*x^3))+b^2*log(b+a*x^3)/a^4 +--R +--R +--R 2 3 3 3 3 9 2 6 2 3 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (2) ------------------------------------------------------------- +--R 5 3 4 +--R 6a x + 6a b +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 3 3 9 2 6 2 3 3 +--R (6a b x + 6b )log(a x + b) + a x - 3a b x - 4a b x + 2b +--R (3) ------------------------------------------------------------- +--R 5 3 4 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1379 +t0:=x^4/(a+b/x^3)^2 +--R +--R +--R 10 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1379 +r0:=-4/3*b*x^2/a^3+8/15*x^5/a^2-1/3*x^8/(a*(b+a*x^3))-8/9*b^(5/3)*_ + log(b^(1/3)+a^(1/3)*x)/a^(11/3)+4/9*b^(5/3)*log(b^(2/3)-a^(1/3)*_ + b^(1/3)*x+a^(2/3)*x^2)/a^(11/3)-8/3*b^(5/3)*atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(11/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 2 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R (20a b x + 20b )\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 2 +-+3+-+2 3+-+ 3+-+ +--R (- 40a b x - 40b )\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 2 3+-+2 \|b - 2x\|a +--R (- 120a b x - 120b )\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 8 5 2 2 +-+3+-+2 +--R (9a x - 36a b x - 60b x )\|3 \|a +--R / +--R 4 3 3 +-+3+-+2 +--R (45a x + 45a b)\|3 \|a +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+2 +--R | 2 | 2 +--R 3 2 +-+ | b | b +--R (40a b x + 40b )\|3 |- -- log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R 3 2 +-+ | b | b | b 2 +--R (- 20a b x - 20b )\|3 |- -- log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R 3 2 | b \| a +--R (120a b x + 120b ) |- -- atan(------------------------) +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 8 5 2 2 +-+ +--R (9a x - 36a b x - 60b x )\|3 +--R / +--R 4 3 3 +-+ +--R (45a x + 45a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - 4b\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +----+2 +--R | 2 | 2 +--R +-+3+-+2 3+-+ 3+-+ +-+ | b 3+-+2 | b +--R 8b\|3 \|b log(\|b + x\|a ) + 8b\|3 |- -- \|a log(a |- -- + b x) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+2 +----+ +--R | 2 | 2 | 2 +--R +-+ | b 3+-+2 | b | b 2 +--R - 4b\|3 |- -- \|a log(- a x |- -- - b |- -- + b x ) +--R 3| 2 3| 2 3| 2 +--R \| a \| a \| a +--R + +--R +----+2 +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- - 2b x\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R 24b |- -- \|a atan(------------------------) +--R 3| 2 +----+2 +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 \|b - 2x\|a +--R 24b \|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 +-+3+-+2 +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1379 +t0:=x^3/(a+b/x^3)^2 +--R +--R +--R 9 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1379 +r0:=-7/3*b*x/a^3+7/12*x^4/a^2-1/3*x^7/(a*(b+a*x^3))+7/9*b^(4/3)*_ + log(b^(1/3)+a^(1/3)*x)/a^(10/3)-7/18*b^(4/3)*log(b^(2/3)-a^(1/3)*_ + b^(1/3)*x+a^(2/3)*x^2)/a^(10/3)-7/3*b^(4/3)*atan((b^(1/3)-_ + 2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(10/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 2 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- 14a b x - 14b )\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 2 +-+3+-+ 3+-+ 3+-+ +--R (28a b x + 28b )\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 2 3+-+ \|b - 2x\|a +--R (- 84a b x - 84b )\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 7 4 2 +-+3+-+ +--R (9a x - 63a b x - 84b x)\|3 \|a +--R / +--R 4 3 3 +-+3+-+ +--R (36a x + 36a b)\|3 \|a +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +-+ +--R 3 2 +-+ |b |b |b 2 +--R (- 14a b x - 14b )\|3 3|- log(3|- - x 3|- + x ) +--R \|a \|a \|a +--R + +--R +-+ +-+ +--R 3 2 +-+ |b |b +--R (28a b x + 28b )\|3 3|- log(3|- + x) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 +--R 3 2 |b \|a +--R (- 84a b x - 84b ) 3|- atan(-----------------) +--R \|a +-+ +--R |b +--R 3 3|- +--R \|a +--R + +--R 2 7 4 2 +-+ +--R (9a x - 63a b x - 84b x)\|3 +--R / +--R 4 3 3 +-+ +--R (36a x + 36a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R 7b\|3 \|b log(\|b - x\|a \|b + x \|a ) - 14b\|3 \|b log(\|b + x\|a ) +--R + +--R +-+ +-+2 +-+ +-+ +-+ +--R +-+3+-+ |b |b |b 2 +-+3+-+ |b |b +--R - 7b\|3 \|a 3|- log(3|- - x 3|- + x + 14b\|3 \|a 3|- log(3|- + x) +--R \|a \|a \|a \|a \|a +--R + +--R +-+ +--R +-+ |b +-+ +--R +-+ \|3 3|- - 2x\|3 3+-+ 3+-+ +--R 3+-+ |b \|a 3+-+ \|b - 2x\|a +--R - 42b\|a 3|- atan(----------------- + 42b\|b atan(-------------) +--R \|a +-+ +-+3+-+ +--R |b \|3 \|b +--R 3 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1379 +t0:=x^2/(a+b/x^3)^2 +--R +--R +--R 8 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1379 +r0:=1/3*x^3/a^2-1/3*b^2/(a^3*(b+a*x^3))-2/3*b*log(b+a*x^3)/a^3 +--R +--R +--R 3 2 3 2 6 3 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (2) --------------------------------------------------- +--R 4 3 3 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 2 3 2 6 3 2 +--R (- 2a b x - 2b )log(a x + b) + a x + a b x - b +--R (3) --------------------------------------------------- +--R 4 3 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1379 +t0:=x/(a+b/x^3)^2 +--R +--R +--R 7 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1379 +r0:=5/6*x^2/a^2-1/3*x^5/(a*(b+a*x^3))+5/9*b^(2/3)*log(b^(1/3)+_ + a^(1/3)*x)/a^(8/3)-5/18*b^(2/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_ + x+a^(2/3)*x^2)/a^(8/3)+5/3*b^(2/3)*atan((b^(1/3)-2*a^(1/3)*x)/_ + (b^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- 5a x - 5b)\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 +-+3+-+2 3+-+ 3+-+ +--R (10a x + 10b)\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+2 \|b - 2x\|a 5 2 +-+3+-+2 +--R (30a x + 30b)\|b atan(-------------) + (9a x + 15b x )\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 3 2 +-+3+-+2 +--R (18a x + 18a b)\|3 \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R 3 +-+ |b |b +--R (10a x + 10b)\|3 |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R 3 +-+ |b |b |b 2 +--R (- 5a x - 5b)\|3 |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 +--R 3 |b \|a 5 2 +-+ +--R (30a x + 30b) |-- atan(---------------------- + (9a x + 15b x )\|3 +--R 3| 2 +--+2 +--R \|a | 2 +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R 3 3 2 +-+ +--R (18a x + 18a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+3+-+2 |b |b +--R 10\|3 \|a |-- log(a |-- + b x) +--R 3| 2 3| 2 +--R \|a \|a +--R + +--R +-+3+-+2 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+2 3+-+ 3+-+ +--R 5\|3 \|b log(\|b - x\|a \|b + x \|a ) - 10\|3 \|b log(\|b + x\|a ) +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+3+-+2 |b |b |b 2 +--R - 5\|3 \|a |-- log(- a x |-- + b |-- + b x ) +--R 3| 2 3| 2 3| 2 +--R \|a \|a \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |b +-+ +--R +--+ a\|3 |-- - 2b x\|3 +--R | 2 3| 2 3+-+ 3+-+ +--R 3+-+2 |b \|a 3+-+2 \|b - 2x\|a +--R 30\|a |-- atan(---------------------- - 30\|b atan(-------------) +--R 3| 2 +--+2 +-+3+-+ +--R \|a | 2 \|3 \|b +--R |b +--R 3a |-- +--R 3| 2 +--R \|a +--R / +--R 2 +-+3+-+2 +--R 18a \|3 \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1379 +t0:=1/(a+b/x^3)^2 +--R +--R +--R 6 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1379 +r0:=4/3*x/a^2-1/3*x^4/(a*(b+a*x^3))-4/9*b^(1/3)*log(b^(1/3)+_ + a^(1/3)*x)/a^(7/3)+2/9*b^(1/3)*log(b^(2/3)-a^(1/3)*b^(1/3)*_ + x+a^(2/3)*x^2)/a^(7/3)+4/3*b^(1/3)*atan((b^(1/3)-2*a^(1/3)*x)/_ + (b^(1/3)*sqrt(3)))/(a^(7/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (2a x + 2b)\|3 \|b log(\|b - x\|a \|b + x \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R (- 4a x - 4b)\|3 \|b log(\|b + x\|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ \|b - 2x\|a 4 +-+3+-+ +--R (12a x + 12b)\|b atan(-------------) + (9a x + 12b x)\|3 \|a +--R +-+3+-+ +--R \|3 \|b +--R / +--R 3 3 2 +-+3+-+ +--R (9a x + 9a b)\|3 \|a +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R 3 +-+ | b | b | b 2 +--R (- 2a x - 2b)\|3 3|- - log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +---+ +--R 3 +-+ | b | b +--R (4a x + 4b)\|3 3|- - log(- 3|- - + x) +--R \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ \|3 3|- - + 2x\|3 +--R 3 | b \| a 4 +-+ +--R (- 12a x - 12b) 3|- - atan(------------------- + (9a x + 12b x)\|3 +--R \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R / +--R 3 3 2 +-+ +--R (9a x + 9a b)\|3 +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 3+-+2 3+-+3+-+ 2 3+-+2 +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log(\|b - x\|a \|b + x \|a ) + 4\|3 \|b log(\|b + x\|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | b 3+-+ | b | b 2 +--R - 2\|3 3|- - \|a log(3|- - + x 3|- - + x ) +--R \| a \| a \| a +--R + +--R +---+ +--R +-+ | b +-+ +--R +---+ +---+ +---+ \|3 3|- - + 2x\|3 +--R +-+ | b 3+-+ | b | b 3+-+ \| a +--R 4\|3 3|- - \|a log(- 3|- - + x - 12 3|- - \|a atan(-------------------) +--R \| a \| a \| a +---+ +--R | b +--R 3 3|- - +--R \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+ \|b - 2x\|a +--R - 12\|b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R 2 +-+3+-+ +--R 9a \|3 \|a +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1379 +t0:=1/((a+b/x^3)^2*x) +--R +--R +--R 5 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1379 +r0:=1/3*b/(a^2*(b+a*x^3))+1/3*log(b+a*x^3)/a^2 +--R +--R +--R 3 3 +--R (a x + b)log(a x + b) + b +--R (2) --------------------------- +--R 3 3 2 +--R 3a x + 3a b +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 +--R (a x + b)log(a x + b) + b +--R (3) --------------------------- +--R 3 3 2 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1379 +t0:=1/((a+b/x^3)^2*x^2) +--R +--R +--R 4 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1379 +r0:=-1/3*x^2/(a*(b+a*x^3))-2/9*log(b^(1/3)+a^(1/3)*x)/(a^(5/3)*b^(1/3))+_ + 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(5/3)*b^(1/3))-_ + 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(5/3)*_ + b^(1/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 +-+3+-+2 3+-+ +--R - 3x \|3 \|a \|b +--R / +--R 2 3 +-+3+-+2 3+-+ +--R (9a x + 9a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6a x - 6b)atan(-------------------------) - 3x \|3 \|- a b +--R 3a b +--R / +--R +-----+ +--R 2 3 +-+3| 2 +--R (9a x + 9a b)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 9a\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1379 +t0:=1/((a+b/x^3)^2*x^3) +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1379 +r0:=-1/3*x/(a*(b+a*x^3))+1/9*log(b^(1/3)+a^(1/3)*x)/(a^(4/3)*b^(2/3))-_ + 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(4/3)*b^(2/3))-_ + 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(4/3)*_ + b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R +-+3+-+3+-+2 +--R - 6x\|3 \|a \|b +--R / +--R 2 3 +-+3+-+3+-+2 +--R (18a x + 18a b)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- a x - b)\|3 log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +----+ +--R 3 2x\|3 \|a b - b\|3 +-+3| 2 +--R (6a x + 6b)atan(---------------------) - 6x\|3 \|a b +--R 3b +--R / +--R +----+ +--R 2 3 +-+3| 2 +--R (18a x + 18a b)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 18a\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1379 +t0:=1/((a+b/x^3)^2*x^4) +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1379 +r0:=1/3/(b*(a+b/x^3)) +--R +--R +--R 3 +--R x +--R (2) ------------- +--R 3 2 +--R 3a b x + 3b +--R Type: Fraction(Polynomial(Integer)) +--E 1291 + +--S 1292 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------ +--R 2 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1379 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 3a b +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1379 +t0:=1/((a+b/x^3)^2*x^5) +--R +--R +--R x +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1379 +r0:=1/3*x^2/(b*(b+a*x^3))-1/9*log(b^(1/3)+a^(1/3)*x)/(a^(2/3)*b^(4/3))+_ + 1/18*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(2/3)*b^(4/3))-_ + 1/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(2/3)*_ + b^(4/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (a x + b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (- 2a x - 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R 2 +-+3+-+2 3+-+ +--R 6x \|3 \|a \|b +--R / +--R 3 2 +-+3+-+2 3+-+ +--R (18a b x + 18b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+2 +-----+ +--R 3 +-+ 3| 2 2 3| 2 +--R (- a x - b)\|3 log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ +--R 3 2x\|3 \|- a b - a b\|3 2 +-+3| 2 +--R (- 6a x - 6b)atan(-------------------------) + 6x \|3 \|- a b +--R 3a b +--R / +--R +-----+ +--R 3 2 +-+3| 2 +--R (18a b x + 18b )\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R - \|3 \|- a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +-----+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log(\|b + x\|a ) +--R + +--R +-----+2 +-----+ +--R +-+3+-+2 3+-+ 3| 2 2 3| 2 +--R - \|3 \|a \|b log(x \|- a b + a x \|- a b - a b) +--R + +--R +-----+2 +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log(x \|- a b + a b) +--R + +--R +-----+2 +--R +-+3| 2 +-+ +-----+ 3+-+ 3+-+ +--R 3+-+2 3+-+ 2x\|3 \|- a b - a b\|3 3| 2 \|b - 2x\|a +--R - 6\|a \|b atan(------------------------- + 6\|- a b atan(-------------) +--R 3a b +-+3+-+ +--R \|3 \|b +--R / +--R +-----+ +--R +-+3| 2 3+-+2 3+-+ +--R 18b\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1379 +t0:=1/((a+b/x^3)^2*x^6) +--R +--R +--R 1 +--R (1) ------------------- +--R 2 6 3 2 +--R a x + 2a b x + b +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1379 +r0:=1/3*x/(b*(b+a*x^3))+2/9*log(b^(1/3)+a^(1/3)*x)/(a^(1/3)*b^(5/3))-_ + 1/9*log(b^(2/3)-a^(1/3)*b^(1/3)*x+a^(2/3)*x^2)/(a^(1/3)*b^(5/3))-_ + 2/3*atan((b^(1/3)-2*a^(1/3)*x)/(b^(1/3)*sqrt(3)))/(a^(1/3)*_ + b^(5/3)*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+ 3+-+2 3+-+3+-+ 2 3+-+2 +--R (- a x - b)\|3 log(\|b - x\|a \|b + x \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 +-+ 3+-+ 3+-+ 3 \|b - 2x\|a +--R (2a x + 2b)\|3 log(\|b + x\|a ) + (- 6a x - 6b)atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R + +--R +-+3+-+3+-+2 +--R 3x\|3 \|a \|b +--R / +--R 3 2 +-+3+-+3+-+2 +--R (9a b x + 9b )\|3 \|a \|b +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+2 +----+ +--R 3 +-+ 2 3| 2 3| 2 2 +--R (- a x - b)\|3 log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R 3 +-+ 3| 2 +--R (2a x + 2b)\|3 log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 +-+ +----+ +--R 3 2x\|3 \|a b - b\|3 +-+3| 2 +--R (6a x + 6b)atan(---------------------) + 3x\|3 \|a b +--R 3b +--R / +--R +----+ +--R 3 2 +-+3| 2 +--R (9a b x + 9b )\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+2 +----+ +--R +-+3+-+3+-+2 2 3| 2 3| 2 2 +--R - \|3 \|a \|b log(x \|a b - b x\|a b + b ) +--R + +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log(x\|a b + b) +--R + +--R +----+ +--R +-+3| 2 3+-+2 3+-+3+-+ 2 3+-+2 +--R \|3 \|a b log(\|b - x\|a \|b + x \|a ) +--R + +--R +----+ +--R +----+ +-+3| 2 +-+ +--R +-+3| 2 3+-+ 3+-+ 3+-+3+-+2 2x\|3 \|a b - b\|3 +--R - 2\|3 \|a b log(\|b + x\|a ) + 6\|a \|b atan(---------------------) +--R 3b +--R + +--R +----+ 3+-+ 3+-+ +--R 3| 2 \|b - 2x\|a +--R 6\|a b atan(-------------) +--R +-+3+-+ +--R \|3 \|b +--R / +--R +----+ +--R +-+3+-+3+-+2 3| 2 +--R 9b\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1379 +t0:=1/((a+b/x^3)^2*x^7) +--R +--R +--R 1 +--R (1) -------------------- +--R 2 7 4 2 +--R a x + 2a b x + b x +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1379 +r0:=1/3/(b*(b+a*x^3))+log(x)/b^2-1/3*log(b+a*x^3)/b^2 +--R +--R +--R 3 3 3 +--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b +--R (2) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3b +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1379 +a0:=integrate(t0,x) +--R +--R +--R 3 3 3 +--R (- a x - b)log(a x + b) + (3a x + 3b)log(x) + b +--R (3) -------------------------------------------------- +--R 2 3 3 +--R 3a b x + 3b +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1379 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1379 +t0:=x^5*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 5 |a x + b +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1310 + +--S 1311 of 1379 +r0:=-1/12*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/12*b*x^3*_ + sqrt(a+b/x^3)/a+1/6*x^6*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R | b 2 2 | b |a x + b 2 3 3 +--R - 2a |---- log(8a x |---- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + b x ) |-------- +--R \| x +--R / +--R 12a +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R +-+ | b 2 2 | b |a x + b 2 3 3 +--R - 2a\|a |---- log(8a x |---- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x - b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R +-+ +--R 12a\|a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--------+ +--R | 4 | 3 | 3 +--R 3 7 2 4 | b 2 7 3 4 |a x + b |a x + b +--R ((- 8a x - 8a b x ) |---- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|16a \| x +--R + +--R +--------+ +----+ +--R | 3 | 4 +--R 3 8 2 5 |a x + b | b 2 2 8 3 5 4 2 +--R (8a x + 8a b x ) |-------- |---- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|16a +--R / +--R +--------+ +----+ +--------+ +--------+ +--R | 3 | 4 | 3 | 3 +--R 2 2 |a x + b | b |a x + b 2 3 3 |a x + b +--R 8a x |-------- |---- |-------- + (2a b x + b ) |-------- +--R | 3 | 3 \| x | 3 +--R \| x \|16a \| x +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1379 +t0:=x^2*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 2 |a x + b +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1315 + +--S 1316 of 1379 +r0:=1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a)+1/3*x^3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 |b |a x + b 3 2 2 |a x + b +--R - |-- log(2a x |-- |-------- - 2a b x - b ) + 2x |-------- +--R \| a \| a \| x \| x +--R (3) ----------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 |b |a x + b 3 2 +--R - \|a |-- log(2a x |-- |-------- - 2a b x - b ) +--R \| a \| a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R - 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6\|a +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 4 |a x + b |b 4 2 |a x + b +--R (- 2a x |-------- |-- - 2a b x - b x) |-------- +--R | 3 \| a \| x +--R \| x +--R + +--R +--+ +--------+ +--R | 2 | 3 +--R 2 5 2 |b 5 2 2 |a x + b +--R (2a x + 2a b x ) |-- + (2a b x + b x ) |-------- +--R \| a | 3 +--R \| x +--R / +--R +--+ +--------+ +--R | 2 | 3 +--R 2 |b |a x + b 3 2 +--R 2a x |-- |-------- - 2a b x - b +--R \| a \| x +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1379 +t0:=sqrt(a+b/x^3)/x +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1320 + +--S 1321 of 1379 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-2/3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x |a x + b +--R 2\|a atanh(-----------) - 2 |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 |a x + b +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4 |-------- +--R \| x \| x +--R (3) ---------------------------------------------------------- +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R +--+ 2 +--+ |a x + b 3 +-+ \| x +--R - x\|4a log(x \|4a |-------- - 2a x - b) - 4x\|a atanh(-----------) +--R \| x +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b +--R - 4 |-------- + 4x |-------- +--R \| x | 3 +--R \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +--+ 5 2 |a x + b |a x + b +--R ((- a x - b x )\|4a + (- 2a x - b x ) |-------- ) |-------- +--R | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +--R 6 3 |a x + b +--+ 2 6 3 2 +--R (a x + b x ) |-------- \|4a + 2a x + 3a b x + b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 | 3 +--R 6 |a x + b +--+ |a x + b 7 4 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1379 +t0:=sqrt(a+b/x^3)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1325 + +--S 1326 of 1379 +r0:=-2/9*(a+b/x^3)^(3/2)/b +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 2a x - 2b) |-------- +--R | 3 +--R \| x +--R (2) ------------------------- +--R 3 +--R 9b x +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 2a x - 2b) |-------- +--R \| x +--R (3) ------------------------- +--R 6 +--R 9b x +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1379 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 6 3 |a x + b +--R (- 2a x - 2b) |-------- + (2a x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------------------------------ +--R 6 +--R 9b x +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1379 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 2 |a x + b 2 6 3 2 |a x + b +--R (- 9a b x - 9b x) |-------- + (4a x + 17a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 8 |a x + b |a x + b +--R 9b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1379 +t0:=sqrt(a+b/x^3)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1330 + +--S 1331 of 1379 +r0:=2/9*a*(a+b/x^3)^(3/2)/b^2-2/15*(a+b/x^3)^(5/2)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (4a x - 2a b x - 6b ) |-------- +--R | 3 +--R \| x +--R (2) ---------------------------------- +--R 2 6 +--R 45b x +--R Type: Expression(Integer) +--E 1331 + +--S 1332 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (4a x - 2a b x - 6b ) |-------- +--R \| x +--R (3) ---------------------------------- +--R 2 9 +--R 45b x +--R Type: Union(Expression(Integer),...) +--E 1332 + +--S 1333 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (4a x - 2a b x - 6b ) |-------- + (- 4a x + 2a b x + 6b x ) |-------- +--R \| x | 3 +--R \| x +--R --------------------------------------------------------------------------- +--R 2 9 +--R 45b x +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 4 3 |a x + b +--R (- 45a b x - 45b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 8a x - 4a b x + 61a b x + 57b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 11 |a x + b |a x + b +--R 45b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1379 +t0:=sqrt(a+b/x^3)/x^10 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 1335 + +--S 1336 of 1379 +r0:=-2/9*a^2*(a+b/x^3)^(3/2)/b^3+4/15*a*(a+b/x^3)^(5/2)/b^3-_ + 2/21*(a+b/x^3)^(7/2)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------ +--R 3 9 +--R 315b x +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 3 12 +--R 315b x +--R Type: Union(Expression(Integer),...) +--E 1337 + +--S 1338 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 16a x + 8a b x - 6a b x - 30b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (16a x - 8a b x + 6a b x + 30b x ) |-------- +--R | 3 +--R \| x +--R / +--R 3 12 +--R 315b x +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 3 4 4 |a x + b +--R (- 315a b x - 315b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (32a x + 16a b x - 4a b x + 387a b x + 375b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 14 |a x + b |a x + b +--R 315b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1379 +t0:=(a+b/x^3)^(3/2)*x^5 +--R +--R +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (1) (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1340 + +--S 1341 of 1379 +r0:=1/6*(a+b/x^3)^(3/2)*x^6+1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/_ + sqrt(a)+1/4*b*x^3*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R +-+ +--R 12\|a +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+ +--------+ +--R | 4 | 4 | 3 +--R |9b 2 |9b |a x + b 2 3 3 +--R - 2 |--- log(8a x |--- |-------- - 6a b x - 3b ) +--R \|16a \|16a \| x +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + 5b x ) |-------- +--R \| x +--R / +--R 12 +--R Type: Union(Expression(Integer),...) +--E 1342 + +--S 1343 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +---+ +---+ +--------+ +--R | 4 | 4 | 3 +--R +-+ |9b 2 |9b |a x + b 2 3 3 +--R - 2\|a |--- log(8a x |--- |-------- - 6a b x - 3b ) +--R \|16a \|16a \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R - 3b atanh(-----------) + (2a x + 5b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x - 5b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R +-+ +--R 12\|a +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--R | 4 +--R 3 8 2 5 2 2 |9b +--R (- 8a x - 16a b x - 8a b x ) |--- +--R \|16a +--R + +--R +--------+ +--R | 3 +--R 2 2 8 3 5 4 2 |a x + b +--R (- 6a b x - 9a b x - 3b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +---+ +--R | 3 | 4 +--R 3 9 2 6 2 3 |a x + b |9b 3 2 9 2 3 6 +--R (8a x + 16a b x + 8a b x ) |-------- |--- + 6a b x + 15a b x +--R | 3 \|16a +--R \| x +--R + +--R 4 3 5 +--R 12a b x + 3b +--R / +--R +--------+ +---+ +--------+ +--------+ +--R | 3 | 4 | 3 | 3 +--R 3 |a x + b |9b |a x + b 2 4 3 |a x + b +--R 8a x |-------- |--- |-------- + (- 6a b x - 3b x) |-------- +--R | 3 \|16a \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1379 +t0:=(a+b/x^3)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 1345 + +--S 1346 of 1379 +r0:=1/3*(a+b/x^3)^(3/2)*x^3+b*atanh(sqrt(a+b/x^3)/sqrt(a))*sqrt(a)-_ + b*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x 3 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-----+ +-----+ | 3 +--R | 2 2 | 2 |a x + b 3 2 +--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b ) +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (2a x - 4b) |-------- +--R \| x +--R / +--R 6x +--R Type: Union(Expression(Integer),...) +--E 1347 + +--S 1348 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +-----+ +-----+ | 3 +--R | 2 2 | 2 |a x + b 3 2 +--R - x\|9a b log(2x \|9a b |-------- - 6a b x - 3b ) +--R \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R +-+ \| x 3 |a x + b +--R - 6b x\|a atanh(-----------) + (2a x - 4b) |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (- 2a x + 4b x) |-------- +--R | 3 +--R \| x +--R / +--R 6x +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----+ +--R 2 8 5 2 2 | 2 +--R (- 2a x - 4a b x - 2b x )\|9a b +--R + +--R +--------+ +--R | 3 +--R 2 8 2 5 3 2 |a x + b +--R (- 6a b x - 9a b x - 3b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +-----+ +--R 2 9 6 2 3 |a x + b | 2 3 9 2 2 6 +--R (2a x + 4a b x + 2b x ) |-------- \|9a b + 6a b x + 15a b x +--R | 3 +--R \| x +--R + +--R 3 3 4 +--R 12a b x + 3b +--R / +--R +--------+ +--------+ +--------+ +--R | 3 +-----+ | 3 | 3 +--R 6 |a x + b | 2 |a x + b 7 2 4 |a x + b +--R 2x |-------- \|9a b |-------- + (- 6a b x - 3b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1349 + +)clear all + +--S 1350 of 1379 +t0:=(a+b/x^3)^(3/2)/x +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1350 + +--S 1351 of 1379 +r0:=-2/9*(a+b/x^3)^(3/2)+2/3*a^(3/2)*atanh(sqrt(a+b/x^3)/sqrt(a))-_ + 2/3*a*sqrt(a+b/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 +-+ \| x 3 |a x + b +--R 6a x \|a atanh(-----------) + (- 8a x - 2b) |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------- +--R 3 +--R 9x +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1379 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +---+ +---+ | 3 +--R 4 | 3 2 | 3 |a x + b 2 3 +--R - 3x \|4a log(x \|4a |-------- - 2a x - a b) +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 16a x - 4b) |-------- +--R \| x +--R / +--R 4 +--R 18x +--R Type: Union(Expression(Integer),...) +--E 1352 + +--S 1353 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R +---+ +---+ | 3 +--R 4 | 3 2 | 3 |a x + b 2 3 +--R - 3x \|4a log(x \|4a |-------- - 2a x - a b) +--R \| x +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 4 +-+ \| x 3 |a x + b +--R - 12a x \|a atanh(-----------) + (- 16a x - 4b) |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (16a x + 4b x) |-------- +--R | 3 +--R \| x +--R / +--R 4 +--R 18x +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--R 2 8 5 2 2 | 3 +--R (- a x - 2a b x - b x )\|4a +--R + +--R +--------+ +--R | 3 +--R 3 8 2 5 2 2 |a x + b +--R (- 2a x - 3a b x - a b x ) |-------- +--R | 3 +--R \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +---+ +--R 2 9 6 2 3 |a x + b | 3 4 9 3 6 2 2 3 3 +--R (a x + 2a b x + b x ) |-------- \|4a + 2a x + 5a b x + 4a b x + a b +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 +---+ | 3 | 3 +--R 9 |a x + b | 3 |a x + b 2 10 7 |a x + b +--R x |-------- \|4a |-------- + (- 2a x - a b x ) |-------- +--R | 3 \| x | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 1354 + +)clear all + +--S 1355 of 1379 +t0:=(a+b/x^3)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 1355 + +--S 1356 of 1379 +r0:=-2/15*(a+b/x^3)^(5/2)/b +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------ +--R 6 +--R 15b x +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- +--R \| x +--R (3) ------------------------------------ +--R 9 +--R 15b x +--R Type: Union(Expression(Integer),...) +--E 1357 + +--S 1358 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (- 2a x - 4a b x - 2b ) |-------- + (2a x + 4a b x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R --------------------------------------------------------------------------- +--R 9 +--R 15b x +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 7 2 4 3 |a x + b +--R (- 15a b x - 30a b x - 15b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x + 27a b x + 42a b x + 19b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 11 |a x + b |a x + b +--R 15b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1359 + +)clear all + +--S 1360 of 1379 +t0:=(a+b/x^3)^(3/2)/x^7 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 1360 + +--S 1361 of 1379 +r0:=2/15*a*(a+b/x^3)^(5/2)/b^2-2/21*(a+b/x^3)^(7/2)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R | 3 +--R \| x +--R (2) ---------------------------------------------- +--R 2 9 +--R 105b x +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R \| x +--R (3) ---------------------------------------------- +--R 2 12 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 1362 + +--S 1363 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (4a x - 2a b x - 16a b x - 10b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (- 4a x + 2a b x + 16a b x + 10b x ) |-------- +--R | 3 +--R \| x +--R / +--R 2 12 +--R 105b x +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 2 7 3 4 4 |a x + b +--R (- 105a b x - 210a b x - 105b x) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 8a x - 4a b x + 141a b x + 262a b x + 125b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 14 |a x + b |a x + b +--R 105b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1379 +t0:=(a+b/x^3)^(3/2)/x^10 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R (1) --------------------- +--R 13 +--R x +--R Type: Expression(Integer) +--E 1365 + +--S 1366 of 1379 +r0:=-2/15*a^2*(a+b/x^3)^(5/2)/b^3+4/21*a*(a+b/x^3)^(7/2)/b^3-_ + 2/27*(a+b/x^3)^(9/2)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------------------- +--R 3 12 +--R 945b x +--R Type: Expression(Integer) +--E 1366 + +--S 1367 of 1379 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R \| x +--R (3) ------------------------------------------------------------- +--R 3 15 +--R 945b x +--R Type: Union(Expression(Integer),...) +--E 1367 + +--S 1368 of 1379 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 16a x + 8a b x - 6a b x - 100a b x - 70b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 15 3 12 2 2 9 3 6 4 3 |a x + b +--R (16a x - 8a b x + 6a b x + 100a b x + 70b x ) |-------- +--R | 3 +--R \| x +--R / +--R 3 15 +--R 945b x +--R Type: Expression(Integer) +--E 1368 + +--S 1369 of 1379 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 2 3 7 4 4 5 |a x + b +--R (- 945a b x - 1890a b x - 945b x) |-------- +--R \| x +--R + +--R 5 15 4 12 3 2 9 2 3 6 4 3 5 +--R (32a x + 16a b x - 4a b x + 1157a b x + 2230a b x + 1085b ) +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 17 |a x + b |a x + b +--R 945b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 1369 + +)clear all + +--S 1370 of 1379 +t0:=x^4*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 4 |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1370 + +--S 1371 of 1379 +--r0:=81/160*x^2*sqrt(8+27/x^3)+1/5*x^5*sqrt(8+27/x^3)+_ +-- 729/160*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 1371 + +--S 1372 of 1379 +--a0:=integrate(t0,x) +--E 1372 + +--S 1373 of 1379 +--m0:=a0-r0 +--E 1373 + +--S 1374 of 1379 +--d0:=D(m0,x) +--E 1374 + +)clear all + +--S 1375 of 1379 +t0:=x*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 1375 + +--S 1376 of 1379 +--r0:=1/2*x^2*sqrt(8+27/x^3)-27/2*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 1376 + +--S 1377 of 1379 +--a0:=integrate(t0,x) +--E 1377 + +--S 1378 of 1379 +--m0:=a0-r0 +--E 1378 + +--S 1379 of 1379 +--d0:=D(m0,x) +--E 1379 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4h.input.pamphlet b/src/input/rich4h.input.pamphlet new file mode 100644 index 0000000..4f31122 --- /dev/null +++ b/src/input/rich4h.input.pamphlet @@ -0,0 +1,24104 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4h.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 255 supplied "optimal results". +\item 173 matching answers. +\item 60 cases where Axiom's results differs from Rubi +\item 25 cases where Axiom supplied 2 results. +\item 4 cases that Axiom failed to integrate. +\item 42 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4h.output +)spool rich4h.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1325 +t0:=sqrt(8+27/x^3)/x^2 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1325 +--r0:=-2/5*sqrt(8+27/x^3)/x-16/5*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+_ +-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_ +-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/_ +-- (3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 2 + +--S 3 of 1325 +--a0:=integrate(t0,x) +--E 3 + +--S 4 of 1325 +--m0:=a0-r0 +--E 4 + +--S 5 of 1325 +--d0:=D(m0,x) +--E 5 + +)clear all + +--S 6 of 1325 +t0:=sqrt(8+27/x^3)/x^5 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1325 +--r0:=-2/11*sqrt(8+27/x^3)/x^4-16/495*sqrt(8+27/x^3)/x+256/1485*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 7 + +--S 8 of 1325 +--a0:=integrate(t0,x) +--E 8 + +--S 9 of 1325 +--m0:=a0-r0 +--E 9 + +--S 10 of 1325 +--d0:=D(m0,x) +--E 10 + +)clear all + +--S 11 of 1325 +t0:=x^3*sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R 3 |8x + 27 +--R (1) x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1325 +--r0:=81/64*x*sqrt(8+27/x^3)+1/4*x^4*sqrt(8+27/x^3)-243/64*(-1)^(1/4)*_ +-- (2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3))))+243/32*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_ +-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 12 + +--S 13 of 1325 +--a0:=integrate(t0,x) +--E 13 + +--S 14 of 1325 +--m0:=a0-r0 +--E 14 + +--S 15 of 1325 +--d0:=D(m0,x) +--E 15 + +)clear all + +--S 16 of 1325 +t0:=sqrt(8+27/x^3) +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R (1) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1325 +--r0:=x*sqrt(8+27/x^3)-9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+_ +-- 1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-_ +-- sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+18*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 17 + +--S 18 of 1325 +--a0:=integrate(t0,x) +--E 18 + +--S 19 of 1325 +--m0:=a0-r0 +--E 19 + +--S 20 of 1325 +--d0:=D(m0,x) +--E 20 + +)clear all + +--S 21 of 1325 +t0:=sqrt(8+27/x^3)/x^3 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1325 +--r0:=-2/7*sqrt(8+27/x^3)/x^2-16/21*(-1)^(1/4)*(2+3/x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3))))+32/21*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 22 + +--S 23 of 1325 +--a0:=integrate(t0,x) +--E 23 + +--S 24 of 1325 +--m0:=a0-r0 +--E 24 + +--S 25 of 1325 +--d0:=D(m0,x) +--E 25 + +)clear all + +--S 26 of 1325 +t0:=sqrt(8+27/x^3)/x^6 +--R +--R +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R (1) ----------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1325 +--r0:=-2/13*sqrt(8+27/x^3)/x^5-16/819*sqrt(8+27/x^3)/x^2+_ +-- 512/7371*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-1024/7371*_ +-- (-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/_ +-- x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 27 + +--S 28 of 1325 +--a0:=integrate(t0,x) +--E 28 + +--S 29 of 1325 +--m0:=a0-r0 +--E 29 + +--S 30 of 1325 +--d0:=D(m0,x) +--E 30 + +)clear all + +--S 31 of 1325 +t0:=x^8/sqrt(a+b/x^3) +--R +--R +--R 8 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1325 +r0:=-5/24*b^3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)+5/24*b^2*x^3*_ + sqrt(a+b/x^3)/a^3-5/36*b*x^6*sqrt(a+b/x^3)/a^2+1/9*x^9*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 \| x 2 9 6 2 3 +-+ |a x + b +--R - 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 3 +-+ +--R 72a \|a +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 6 | 6 | 3 +--R 3 |25b 4 2 |25b |a x + b 3 3 4 +--R - 12a |---- log(16a x |---- |-------- + 10a b x + 5b ) +--R | 7 | 7 \| x +--R \|64a \|64a +--R + +--R +--------+ +--R | 3 +--R 2 8 5 2 2 |a x + b +--R (8a x - 10a b x + 15b x ) |-------- +--R \| x +--R / +--R 3 +--R 72a +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 6 | 6 | 3 +--R 3 +-+ |25b 4 2 |25b |a x + b 3 3 4 +--R - 12a \|a |---- log(16a x |---- |-------- + 10a b x + 5b ) +--R | 7 | 7 \| x +--R \|64a \|64a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 3 \| x 2 8 5 2 2 +-+ |a x + b +--R 15b atanh(-----------) + (8a x - 10a b x + 15b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 2 9 6 2 3 +-+ |a x + b +--R (- 8a x + 10a b x - 15b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R 3 +-+ +--R 72a \|a +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--R | 6 | 3 +--R 5 13 4 10 |25b 3 13 4 10 |a x + b +--R ((- 16a x - 16a b x ) |---- + (10a b x + 5b x ) |-------- ) +--R | 7 | 3 +--R \|64a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +----+ +--R | 3 | 6 +--R 5 14 4 11 |a x + b |25b 2 3 14 4 11 5 8 +--R (16a x + 16a b x ) |-------- |---- - 10a b x - 15a b x - 5b x +--R | 3 | 7 +--R \| x \|64a +--R / +--R +--------+ +----+ +--------+ +--R | 3 | 6 | 3 +--R 5 5 4 2 |a x + b |25b |a x + b +--R (16a x + 16a b x ) |-------- |---- |-------- +--R | 3 | 7 \| x +--R \| x \|64a +--R + +--R +--------+ +--R | 3 +--R 2 3 6 4 3 5 |a x + b +--R (10a b x + 15a b x + 5b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1325 +t0:=x^5/sqrt(a+b/x^3) +--R +--R +--R 5 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1325 +r0:=1/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-1/4*b*x^3*_ + sqrt(a+b/x^3)/a^2+1/6*x^6*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 6 3 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 2 +-+ +--R 12a \|a +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R 2 | 9b 3 2 | 9b |a x + b 2 3 3 +--R - 2a |---- log(8a x |---- |-------- - 6a b x - 3b ) +--R | 5 | 5 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x - 3b x ) |-------- +--R \| x +--R / +--R 2 +--R 12a +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----+ +----+ +--------+ +--R | 4 | 4 | 3 +--R 2 +-+ | 9b 3 2 | 9b |a x + b 2 3 3 +--R - 2a \|a |---- log(8a x |---- |-------- - 6a b x - 3b ) +--R | 5 | 5 \| x +--R \|16a \|16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R 2 \| x 5 2 +-+ |a x + b +--R - 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ \| x +--R \|a +--R + +--R +--------+ +--R | 3 +--R 6 3 +-+ |a x + b +--R (- 2a x + 3b x )\|a |-------- +--R | 3 +--R \| x +--R / +--R 2 +-+ +--R 12a \|a +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----+ +--------+ +--R | 4 | 3 +--R 4 10 3 7 | 9b 2 10 3 7 |a x + b +--R ((- 8a x - 8a b x ) |---- + (- 6a b x - 3b x ) |-------- ) +--R | 5 | 3 +--R \|16a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +----+ +--R | 3 | 4 +--R 4 11 3 8 |a x + b | 9b 2 2 11 3 8 4 5 +--R (8a x + 8a b x ) |-------- |---- + 6a b x + 9a b x + 3b x +--R | 3 | 5 +--R \| x \|16a +--R / +--R +--------+ +----+ +--------+ +--R | 3 | 4 | 3 +--R 4 5 3 2 |a x + b | 9b |a x + b +--R (8a x + 8a b x ) |-------- |---- |-------- +--R | 3 | 5 \| x +--R \| x \|16a +--R + +--R +--------+ +--R | 3 +--R 2 2 6 3 3 4 |a x + b +--R (- 6a b x - 9a b x - 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1325 +t0:=x^2/sqrt(a+b/x^3) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1325 +r0:=-1/3*b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+1/3*x^3*sqrt(a+b/x^3)/a +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--R | 3 | 3 +--R \| x 3 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 3 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 3a\|a +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--+ +--+ +--------+ +--------+ +--R | 2 | 2 | 3 | 3 +--R |b 2 2 |b |a x + b 3 2 2 |a x + b +--R - a |-- log(2a x |-- |-------- + 2a b x + b ) + 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R (3) ------------------------------------------------------------------ +--R 6a +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--+ +--+ +--------+ +--R | 2 | 2 | 3 +--R +-+ |b 2 2 |b |a x + b 3 2 +--R - a\|a |-- log(2a x |-- |-------- + 2a b x + b ) +--R | 3 | 3 \| x +--R \|a \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--------+ +--------+ +--R | 3 | 3 | 3 +--R \| x 2 +-+ |a x + b 3 +-+ |a x + b +--R 2b atanh(-----------) + 2x \|a |-------- - 2x \|a |-------- +--R +-+ \| x | 3 +--R \|a \| x +--R / +--R +-+ +--R 6a\|a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 3 7 2 4 |b 7 2 4 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |-- + (2a b x + b x ) |-------- ) |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--+ +--R | 3 | 2 +--R 3 8 2 5 |a x + b |b 2 8 2 5 3 2 +--R (2a x + 2a b x ) |-------- |-- - 2a b x - 3a b x - b x +--R | 3 | 3 +--R \| x \|a +--R / +--R +--------+ +--+ +--------+ +--R | 3 | 2 | 3 +--R 3 5 2 2 |a x + b |b |a x + b +--R (2a x + 2a b x ) |-------- |-- |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R | 3 +--R 2 6 2 3 3 |a x + b +--R (2a b x + 3a b x + b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1325 +t0:=1/(x*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 3 +--R |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1325 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R | 3 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 3 +--R |1 2 |1 |a x + b 3 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (3) - ----------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 3 | 3 +--R |1 +-+ 2 |1 |a x + b 3 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R +-+ +--R 3\|a +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 3 | 3 +--R 3 |1 |a x + b 3 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 3 \| x +--R \| x +--R + +--R +--------+ +--R | 3 +-+ +--R 4 |a x + b 2 4 |1 +--R (2a x + b x) |-------- + (2a x + 2a b x) |- +--R | 3 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 3 | 3 +-+ | 3 +--R 4 |a x + b |a x + b 2 5 2 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 3 \| x \|a | 3 +--R \| x \| x +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1325 +t0:=1/(x^4*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 4 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1325 +r0:=-2/3*sqrt(a+b/x^3)/b +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R | 3 +--R \| x +--R (2) - ------------ +--R 3b +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R \| x +--R (3) - ------------ +--R 3 +--R 3b x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 2 |-------- + 2x |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------- +--R 3 +--R 3b x +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 3b x |-------- + (4a x + 7b) |-------- +--R \| x | 3 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 |a x + b |a x + b +--R 3b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1325 +t0:=1/(x^7*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 7 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1325 +r0:=-2/9*(a+b/x^3)^(3/2)/b^2+2/3*a*sqrt(a+b/x^3)/b^2 +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (4a x - 2b) |-------- +--R | 3 +--R \| x +--R (2) ----------------------- +--R 2 3 +--R 9b x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (4a x - 2b) |-------- +--R \| x +--R (3) ----------------------- +--R 2 6 +--R 9b x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 6 3 |a x + b +--R (4a x - 2b) |-------- + (- 4a x + 2b x ) |-------- +--R \| x | 3 +--R \| x +--R (4) ------------------------------------------------------ +--R 2 6 +--R 9b x +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 |a x + b 2 6 3 2 |a x + b +--R - 9b x |-------- + (- 8a x - 4a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) --------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 |a x + b |a x + b +--R 9b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1325 +t0:=1/(x^10*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R | 3 +--R 10 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1325 +r0:=4/9*a*(a+b/x^3)^(3/2)/b^3-2/15*(a+b/x^3)^(5/2)/b^3-2/3*a^2*_ + sqrt(a+b/x^3)/b^3 +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------- +--R 3 6 +--R 45b x +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- +--R \| x +--R (3) ------------------------------------- +--R 3 9 +--R 45b x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b 2 9 6 2 3 |a x + b +--R (- 16a x + 8a b x - 6b ) |-------- + (16a x - 8a b x + 6b x ) |-------- +--R \| x | 3 +--R \| x +--R ----------------------------------------------------------------------------- +--R 3 9 +--R 45b x +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b +--R - 45b x |-------- + (32a x + 16a b x - 4a b x + 57b ) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 11 |a x + b |a x + b +--R 45b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1325 +t0:=1/(x^13*sqrt(a+b/x^3)) +--R +--R +--R 1 +--R (1) -------------- +--R +--------+ +--R | 3 +--R 13 |a x + b +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1325 +r0:=-2/3*a^2*(a+b/x^3)^(3/2)/b^4+2/5*a*(a+b/x^3)^(5/2)/b^4-_ + 2/21*(a+b/x^3)^(7/2)/b^4+2/3*a^3*sqrt(a+b/x^3)/b^4 +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R | 3 +--R \| x +--R (2) ------------------------------------------------ +--R 4 9 +--R 105b x +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 4 12 +--R 105b x +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (32a x - 16a b x + 12a b x - 10b ) |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 3 12 2 9 2 6 3 3 |a x + b +--R (- 32a x + 16a b x - 12a b x + 10b x ) |-------- +--R | 3 +--R \| x +--R / +--R 4 12 +--R 105b x +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 4 |a x + b +--R - 105b x |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (- 64a x - 32a b x + 8a b x - 4a b x + 125b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 14 |a x + b |a x + b +--R 105b x |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1325 +t0:=x^5/(a+b/x^3)^(3/2) +--R +--R +--R 8 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1325 +r0:=5/4*b^2*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(7/2)-2/3*x^6/_ + (a*sqrt(a+b/x^3))-5/4*b*x^3*sqrt(a+b/x^3)/a^3+5/6*x^6*sqrt(a+b/x^3)/a^2 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 2 |a x + b \| x 2 6 3 2 +-+ +--R 15b |-------- atanh(-----------) + (2a x - 5a b x - 15b )\|a +--R | 3 +-+ +--R \| x \|a +--R (2) ---------------------------------------------------------------- +--R +--------+ +--R | 3 +--R 3 +-+ |a x + b +--R 12a \|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-----+ +-----+ +--------+ +--R | 4 | 4 | 3 +--R 4 3 3 |225b 4 2 |225b |a x + b 2 3 3 +--R (- 2a x - 2a b) |----- log(8a x |----- |-------- - 30a b x - 15b ) +--R | 7 | 7 \| x +--R \| 16a \| 16a +--R + +--R +--------+ +--R | 3 +--R 2 8 5 2 2 |a x + b +--R (2a x - 5a b x - 15b x ) |-------- +--R \| x +--R / +--R 4 3 3 +--R 12a x + 12a b +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +-----+ +--R | 3 | 4 +--R 4 3 3 +-+ |a x + b |225b +--R (- 2a x - 2a b)\|a |-------- |----- +--R | 3 | 7 +--R \| x \| 16a +--R * +--R +-----+ +--------+ +--R | 4 | 3 +--R 4 2 |225b |a x + b 2 3 3 +--R log(8a x |----- |-------- - 30a b x - 15b ) +--R | 7 \| x +--R \| 16a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 2 3 3 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 5 2 2 +-+ |a x + b |a x + b +--R (2a x - 5a b x - 15b x )\|a |-------- |-------- +--R | 3 \| x +--R \| x +--R + +--R 3 9 2 6 2 3 3 +-+ +--R (- 2a x + 3a b x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 3 +--R 4 3 3 +-+ |a x + b +--R (12a x + 12a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----+ +--------+ +--R | 4 | 3 +--R 5 13 4 10 |225b 2 13 3 10 |a x + b +--R ((- 8a x - 8a b x ) |----- + (- 30a b x - 15b x ) |-------- ) +--R | 7 | 3 +--R \| 16a \| x +--R * +--R +--------+ +--R | 3 +--R |a x + b +--R |-------- +--R \| x +--R + +--R +--------+ +-----+ +--R | 3 | 4 +--R 5 14 4 11 |a x + b |225b 2 2 14 3 11 4 8 +--R (8a x + 8a b x ) |-------- |----- + 30a b x + 45a b x + 15b x +--R | 3 | 7 +--R \| x \| 16a +--R / +--R +--------+ +-----+ +--------+ +--R | 3 | 4 | 3 +--R 6 8 5 5 4 2 2 |a x + b |225b |a x + b +--R (8a x + 16a b x + 8a b x ) |-------- |----- |-------- +--R | 3 | 7 \| x +--R \| x \| 16a +--R + +--R +--------+ +--R | 3 +--R 3 2 9 2 3 6 4 3 5 |a x + b +--R (- 30a b x - 75a b x - 60a b x - 15b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1325 +t0:=x^2/(a+b/x^3)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1325 +r0:=-b*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(5/2)-2/3*x^3/(a*sqrt(a+b/x^3))+_ + x^3*sqrt(a+b/x^3)/a^2 +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R |a x + b \| x 3 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 3 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 3 +--R 2 +-+ |a x + b +--R 3a \|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+ +--------+ +--R | 2 | 2 | 3 +--R 3 3 2 |9b 3 2 |9b |a x + b 3 2 +--R (- a x - a b) |--- log(2a x |--- |-------- + 6a b x + 3b ) +--R | 5 | 5 \| x +--R \| a \| a +--R + +--R +--------+ +--R | 3 +--R 5 2 |a x + b +--R (2a x + 6b x ) |-------- +--R \| x +--R / +--R 3 3 2 +--R 6a x + 6a b +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +---+ +--R | 3 | 2 +--R 3 3 2 +-+ |a x + b |9b +--R (- a x - a b)\|a |-------- |--- +--R | 3 | 5 +--R \| x \| a +--R * +--R +---+ +--------+ +--R | 2 | 3 +--R 3 2 |9b |a x + b 3 2 +--R log(2a x |--- |-------- + 6a b x + 3b ) +--R | 5 \| x +--R \| a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 3 2 |a x + b \| x +--R (6a b x + 6b ) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 +-+ |a x + b |a x + b 2 6 3 2 +-+ +--R (2a x + 6b x )\|a |-------- |-------- + (- 2a x - 8a b x - 6b )\|a +--R | 3 \| x +--R \| x +--R / +--R +--------+ +--R | 3 +--R 3 3 2 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +---+ +--------+ +--------+ +--R | 2 | 3 | 3 +--R 4 10 3 7 |9b 10 2 7 |a x + b |a x + b +--R ((- 2a x - 2a b x ) |--- + (6a b x + 3b x ) |-------- ) |-------- +--R | 5 | 3 \| x +--R \| a \| x +--R + +--R +--------+ +---+ +--R | 3 | 2 +--R 4 11 3 8 |a x + b |9b 2 11 2 8 3 5 +--R (2a x + 2a b x ) |-------- |--- - 6a b x - 9a b x - 3b x +--R | 3 | 5 +--R \| x \| a +--R / +--R +--------+ +---+ +--------+ +--R | 3 | 2 | 3 +--R 5 8 4 5 3 2 2 |a x + b |9b |a x + b +--R (2a x + 4a b x + 2a b x ) |-------- |--- |-------- +--R | 3 | 5 \| x +--R \| x \| a +--R + +--R +--------+ +--R | 3 +--R 3 9 2 2 6 3 3 4 |a x + b +--R (6a b x + 15a b x + 12a b x + 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (a x + b) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1325 +r0:=2/3*atanh(sqrt(a+b/x^3)/sqrt(a))/a^(3/2)+(-2/3)/(a*sqrt(a+b/x^3)) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R |a x + b \| x +-+ +--R 2 |-------- atanh(-----------) - 2\|a +--R | 3 +-+ +--R \| x \|a +--R (2) -------------------------------------- +--R +--------+ +--R | 3 +--R +-+ |a x + b +--R 3a\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R +--+ +--+ | 3 | 3 +--R 2 3 | 1 2 2 | 1 |a x + b 3 2 |a x + b +--R (- a x - a b) |-- log(2a x |-- |-------- - 2a x - b) - 2x |-------- +--R | 3 | 3 \| x \| x +--R \|a \|a +--R -------------------------------------------------------------------------- +--R 2 3 +--R 3a x + 3a b +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R +--+ | 3 +--+ | 3 +--R 2 3 | 1 +-+ |a x + b 2 2 | 1 |a x + b 3 +--R (- a x - a b) |-- \|a |-------- log(2a x |-- |-------- - 2a x - b) +--R | 3 | 3 | 3 \| x +--R \|a \| x \|a +--R + +--R +--------+ +--R | 3 +--R |a x + b +--R +--------+ |-------- +--R | 3 | 3 +--R 3 |a x + b \| x +--R (- 2a x - 2b) |-------- atanh(-----------) +--R | 3 +-+ +--R \| x \|a +--R + +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 +-+ |a x + b |a x + b 3 +-+ +--R - 2x \|a |-------- |-------- + (2a x + 2b)\|a +--R | 3 \| x +--R \| x +--R / +--R +--------+ +--R | 3 +--R 2 3 +-+ |a x + b +--R (3a x + 3a b)\|a |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R | 3 +--+ | 3 +--R 7 4 |a x + b 3 7 2 4 | 1 |a x + b +--R ((- 2a x - b x ) |-------- + (- 2a x - 2a b x ) |-- ) |-------- +--R | 3 | 3 \| x +--R \| x \|a +--R + +--R +--------+ +--R +--+ | 3 +--R 3 8 2 5 | 1 |a x + b 2 8 5 2 2 +--R (2a x + 2a b x ) |-- |-------- + 2a x + 3a b x + b x +--R | 3 | 3 +--R \|a \| x +--R / +--R +--------+ +--------+ +--R +--+ | 3 | 3 +--R 4 8 3 5 2 2 2 | 1 |a x + b |a x + b +--R (2a x + 4a b x + 2a b x ) |-- |-------- |-------- +--R | 3 | 3 \| x +--R \|a \| x +--R + +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 2a x - 5a b x - 4a b x - b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) ----------------------- +--R +--------+ +--R | 3 +--R 4 |a x + b +--R (a x + b x) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1325 +r0:=2/3/(b*sqrt(a+b/x^3)) +--R +--R +--R 2 +--R (2) ------------- +--R +--------+ +--R | 3 +--R |a x + b +--R 3b |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R |a x + b +--R 2 |-------- +--R \| x +--R (3) ------------- +--R 3 2 +--R 3a b x + 3b +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b |a x + b 3 +--R 2 |-------- |-------- - 2a x - 2b +--R | 3 \| x +--R \| x +--R (4) ------------------------------------ +--R +--------+ +--R | 3 +--R 3 2 |a x + b +--R (3a b x + 3b ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R |a x + b 3 |a x + b +--R - 3b x |-------- + (- 4a x - b) |-------- +--R \| x | 3 +--R \| x +--R (5) -------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 5 2 2 |a x + b |a x + b +--R (3a b x + 3b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^7) +--R +--R +--R 1 +--R (1) ------------------------ +--R +--------+ +--R | 3 +--R 7 4 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1325 +r0:=-2/3*a/(b^2*sqrt(a+b/x^3))-2/3*sqrt(a+b/x^3)/b^2 +--R +--R +--R 3 +--R - 4a x - 2b +--R (2) ---------------- +--R +--------+ +--R | 3 +--R 2 3 |a x + b +--R 3b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 |a x + b +--R (- 4a x - 2b) |-------- +--R \| x +--R (3) ------------------------- +--R 2 6 3 3 +--R 3a b x + 3b x +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b |a x + b 2 6 3 2 +--R (- 4a x - 2b) |-------- |-------- + 4a x + 6a b x + 2b +--R | 3 \| x +--R \| x +--R (4) ------------------------------------------------------------ +--R +--------+ +--R | 3 +--R 2 6 3 3 |a x + b +--R (3a b x + 3b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 |a x + b 2 6 3 2 |a x + b +--R - 3b x |-------- + (8a x + 12a b x + 7b ) |-------- +--R \| x | 3 +--R \| x +--R (5) ------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 8 3 5 |a x + b |a x + b +--R (3a b x + 3b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^10) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R | 3 +--R 10 7 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1325 +r0:=-2/9*(a+b/x^3)^(3/2)/b^3+2/3*a^2/(b^3*sqrt(a+b/x^3))+_ + 4/3*a*sqrt(a+b/x^3)/b^3 +--R +--R +--R 2 6 3 2 +--R 16a x + 8a b x - 2b +--R (2) ---------------------- +--R +--------+ +--R | 3 +--R 3 6 |a x + b +--R 9b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 2 6 3 2 |a x + b +--R (16a x + 8a b x - 2b ) |-------- +--R \| x +--R (3) ----------------------------------- +--R 3 9 4 6 +--R 9a b x + 9b x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 2 6 3 2 |a x + b |a x + b 3 9 2 6 +--R (16a x + 8a b x - 2b ) |-------- |-------- - 16a x - 24a b x +--R | 3 \| x +--R \| x +--R + +--R 2 3 3 +--R - 6a b x + 2b +--R / +--R +--------+ +--R | 3 +--R 3 9 4 6 |a x + b +--R (9a b x + 9b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 |a x + b 3 9 2 6 2 3 3 |a x + b +--R - 9b x |-------- + (- 32a x - 48a b x - 12a b x + 13b ) |-------- +--R \| x | 3 +--R \| x +--R (5) ---------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 11 4 8 |a x + b |a x + b +--R (9a b x + 9b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1325 +t0:=1/((a+b/x^3)^(3/2)*x^13) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R | 3 +--R 13 10 |a x + b +--R (a x + b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1325 +r0:=2/3*a*(a+b/x^3)^(3/2)/b^4-2/15*(a+b/x^3)^(5/2)/b^4-_ + 2/3*a^3/(b^4*sqrt(a+b/x^3))-2*a^2*sqrt(a+b/x^3)/b^4 +--R +--R +--R 3 9 2 6 2 3 3 +--R - 32a x - 16a b x + 4a b x - 2b +--R (2) ----------------------------------- +--R +--------+ +--R | 3 +--R 4 9 |a x + b +--R 15b x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 3 +--R 3 9 2 6 2 3 3 |a x + b +--R (- 32a x - 16a b x + 4a b x - 2b ) |-------- +--R \| x +--R (3) ------------------------------------------------ +--R 4 12 5 9 +--R 15a b x + 15b x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 3 | 3 +--R 3 9 2 6 2 3 3 |a x + b |a x + b 4 12 +--R (- 32a x - 16a b x + 4a b x - 2b ) |-------- |-------- + 32a x +--R | 3 \| x +--R \| x +--R + +--R 3 9 2 2 6 3 3 4 +--R 48a b x + 12a b x - 2a b x + 2b +--R / +--R +--------+ +--R | 3 +--R 4 12 5 9 |a x + b +--R (15a b x + 15b x ) |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--R | 3 +--R 4 |a x + b +--R - 15b x |-------- +--R \| x +--R + +--R +--------+ +--R | 3 +--R 4 12 3 9 2 2 6 3 3 4 |a x + b +--R (64a x + 96a b x + 24a b x - 4a b x + 19b ) |-------- +--R | 3 +--R \| x +--R / +--R +--------+ +--------+ +--R | 3 | 3 +--R 4 14 5 11 |a x + b |a x + b +--R (15a b x + 15b x ) |-------- |-------- +--R | 3 \| x +--R \| x +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1325 +t0:=x^4/sqrt(8+27/x^3) +--R +--R +--R 4 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1325 +--r0:=-189/1280*x^2*sqrt(8+27/x^3)+1/40*x^5*sqrt(8+27/x^3)-_ +-- 1701/1280*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 107 + +--S 108 of 1325 +--a0:=integrate(t0,x) +--E 108 + +--S 109 of 1325 +--m0:=a0-r0 +--E 109 + +--S 110 of 1325 +--d0:=D(m0,x) +--E 110 + +)clear all + +--S 111 of 1325 +t0:=x/sqrt(8+27/x^3) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1325 +--r0:=1/16*x^2*sqrt(8+27/x^3)+9/16*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 112 + +--S 113 of 1325 +--a0:=integrate(t0,x) +--E 113 + +--S 114 of 1325 +--m0:=a0-r0 +--E 114 + +--S 115 of 1325 +--d0:=D(m0,x) +--E 115 + +)clear all + +--S 116 of 1325 +t0:=1/(x^2*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 2 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1325 +--r0:=-2/3*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 117 + +--S 118 of 1325 +--a0:=integrate(t0,x) +--E 118 + +--S 119 of 1325 +--m0:=a0-r0 +--E 119 + +--S 120 of 1325 +--d0:=D(m0,x) +--E 120 + +)clear all + +--S 121 of 1325 +t0:=1/(x^5*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 5 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1325 +--r0:=-2/135*sqrt(8+27/x^3)/x+32/405*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 122 + +--S 123 of 1325 +--a0:=integrate(t0,x) +--E 123 + +--S 124 of 1325 +--m0:=a0-r0 +--E 124 + +--S 125 of 1325 +--d0:=D(m0,x) +--E 125 + +)clear all + +--S 126 of 1325 +t0:=x^3/sqrt(8+27/x^3) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1325 +--r0:=-135/512*x*sqrt(8+27/x^3)+1/32*x^4*sqrt(8+27/x^3)+_ +-- 405/512*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))-405/256*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 127 + +--S 128 of 1325 +--a0:=integrate(t0,x) +--E 128 + +--S 129 of 1325 +--m0:=a0-r0 +--E 129 + +--S 130 of 1325 +--d0:=D(m0,x) +--E 130 + +)clear all + +--S 131 of 1325 +t0:=1/sqrt(8+27/x^3) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 3 +--R |8x + 27 +--R |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1325 +--r0:=1/8*x*sqrt(8+27/x^3)-3/8*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),_ +-- -2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*_ +-- sqrt(3))))+3/4*(-1)^(1/4)*elliptic_f(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 132 + +--S 133 of 1325 +--a0:=integrate(t0,x) +--E 133 + +--S 134 of 1325 +--m0:=a0-r0 +--E 134 + +--S 135 of 1325 +--d0:=D(m0,x) +--E 135 + +)clear all + +--S 136 of 1325 +t0:=1/(x^3*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 3 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1325 +--r0:=-2/9*(-1)^(1/4)*(2+3/x)*elliptic_e(%i*asinh((1/2+1/2*%i)*_ +-- sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*_ +-- sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- (sqrt(8+27/x^3)*sqrt((2+3/x)/(3+%i*sqrt(3))))+4/9*(-1)^(1/4)*_ +-- elliptic_f(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*_ +-- sqrt(3))/sqrt(8+27/x^3) +--E 137 + +--S 138 of 1325 +--a0:=integrate(t0,x) +--E 138 + +--S 139 of 1325 +--m0:=a0-r0 +--E 139 + +--S 140 of 1325 +--d0:=D(m0,x) +--E 140 + +)clear all + +--S 141 of 1325 +t0:=1/(x^6*sqrt(8+27/x^3)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 3 +--R 6 |8x + 27 +--R x |-------- +--R | 3 +--R \| x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1325 +--r0:=-2/189*sqrt(8+27/x^3)/x^2+64/1701*(-1)^(1/4)*(2+3/x)*_ +-- elliptic_e(%i*asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/_ +-- 3^(1/4)),-2*sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*_ +-- sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/(sqrt(8+27/x^3)*sqrt((2+_ +-- 3/x)/(3+%i*sqrt(3))))-128/1701*(-1)^(1/4)*elliptic_f(%i*_ +-- asinh((1/2+1/2*%i)*sqrt(1+(-3)/x+%i*sqrt(3))/3^(1/4)),-2*_ +-- sqrt(3)/(3*%i-sqrt(3)))*sqrt(%i*(1+(-3)/x-%i*sqrt(3)))*_ +-- sqrt((2+3/x)/(3+%i*sqrt(3)))*sqrt(1+(-3)/x+%i*sqrt(3))/sqrt(8+27/x^3) +--E 142 + +--S 143 of 1325 +--a0:=integrate(t0,x) +--E 143 + +--S 144 of 1325 +--m0:=a0-r0 +--E 144 + +--S 145 of 1325 +--d0:=D(m0,x) +--E 145 + +)clear all + +--S 146 of 1325 +t0:=1/(a+b/x^4) +--R +--R +--R 4 +--R x +--R (1) -------- +--R 4 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 146 + +--S 147 of 1325 +r0:=x/a+1/2*b^(1/4)*atan(1-a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))-_ + 1/2*b^(1/4)*atan(1+a^(1/4)*x*sqrt(2)/b^(1/4))/(a^(5/4)*sqrt(2))+_ + 1/4*b^(1/4)*log(-a^(1/4)*b^(1/4)*x*sqrt(2)+x^2*sqrt(a)+sqrt(b))/_ + (a^(5/4)*sqrt(2))-1/4*b^(1/4)*log(a^(1/4)*b^(1/4)*x*sqrt(2)+_ + x^2*sqrt(a)+sqrt(b))/(a^(5/4)*sqrt(2)) +--R +--R +--R (2) +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R - \|b log(x\|2 \|a \|b + \|b + x \|a ) +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ 4+-+ \|b + x\|2 \|a +--R \|b log(- x\|2 \|a \|b + \|b + x \|a ) - 2\|b atan(----------------) +--R 4+-+ +--R \|b +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ \|b - x\|2 \|a +-+4+-+ +--R 2\|b atan(----------------) + 4x\|2 \|a +--R 4+-+ +--R \|b +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +-------+ +-------+ +-------+ +--R | b | b | b | b +--R - a |- ----- log(4a |- ----- + x + a |- ----- log(- 4a |- ----- + x) +--R 4| 5 4| 5 4| 5 4| 5 +--R \| 256a \| 256a \| 256a \| 256a +--R + +--R +-------+ +--R | b +--R 4a |- ----- +--R +-------+ 4| 5 +--R | b \| 256a +--R 2a |- ----- atan(------------ + x +--R 4| 5 x +--R \| 256a +--R / +--R a +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R \|b log(x\|2 \|a \|b + \|b + x \|a ) +--R + +--R +-------+ +-------+ +--R +-+ | b 4+-+ | b +--R - 4a\|2 |- ----- \|a log(4a |- ----- + x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R +-------+ +-------+ +--R +-+ | b 4+-+ | b +--R 4a\|2 |- ----- \|a log(- 4a |- ----- + x) +--R 4| 5 4| 5 +--R \| 256a \| 256a +--R + +--R 4+-+ +-+4+-+4+-+ +-+ 2 +-+ +--R - \|b log(- x\|2 \|a \|b + \|b + x \|a ) +--R + +--R +-------+ +--R | b +--R 4a |- ----- +--R +-------+ 4| 5 4+-+ +-+4+-+ +--R +-+ | b 4+-+ \| 256a 4+-+ \|b + x\|2 \|a +--R 8a\|2 |- ----- \|a atan(------------ + 2\|b atan(----------------) +--R 4| 5 x 4+-+ +--R \| 256a \|b +--R + +--R 4+-+ +-+4+-+ +--R 4+-+ \|b - x\|2 \|a +--R - 2\|b atan(----------------) +--R 4+-+ +--R \|b +--R / +--R +-+4+-+ +--R 4a\|2 \|a +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1325 +t0:=(a+b/x^4)^(1/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 3 |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1325 +r0:=1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a)+1/4*x^4*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R \| x 4 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ---------------------------------------- +--R +-+ +--R 4\|a +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 4 +---+ +--R 8\|- a \|b \|a x + b + (- 4a x - 8b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 153 + +--S 154 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +-+ | 4 4 2 \| x +--R (- 2b\|b \|a x + b + a b x + 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4 +--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +-+ +-+ 8 4 +-+ |a x + b +--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 4 4 +-+ +--R 8\|a \|b \|a x + b + (- 4a x - 8b)\|a +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 18 4 14 3 2 10 2 3 6 4 2 +--R - 7a x - 63a b x - 168a b x - 176a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (a x + 26a b x + 129a b x + 248a b x + 208a b x + 64b )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 5 20 4 16 3 2 12 2 3 8 4 4 |a x + b +--R (7a x + 63a b x + 168a b x + 176a b x + 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (- 7a x - 70a b x - 231a b x - 344a b x - 240a b x - 64b )\|a +--R * +--R +-+ +--R \|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (- a x - 26a b x - 129a b x - 248a b x - 208a b x - 64b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 22 5 18 4 2 14 3 3 10 2 4 6 5 2 +--R a x + 26a b x + 129a b x + 248a b x + 208a b x + 64a b x +--R / +--R +--------+ +--R | 4 +--R 4 15 3 11 2 2 7 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 17 3 13 2 2 9 3 5 4 +-+ |a x + b +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 19 4 15 3 2 11 2 3 7 4 3 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 155 + +--S 156 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +---+ +-+ | 4 4 2 +---+ \| x +--R (- 2b\|- a \|b \|a x + b + (a b x + 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 4 4 2 +-+ +--R (4b\|a \|b \|a x + b + (- 2a b x - 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b +--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 4 4 +---+ +-+ +--R 8\|- a \|a \|b \|a x + b + (- 4a x - 8b)\|- a \|a +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 4a x - 12a b x - 8b x ) |-------- \|b - a x - 9a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 16a b x - 8b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (4a x + 16a b x + 20a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 9a b x + 16a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 9 5 2 |a x + b | 4 +--R (a x + 8a b x + 8b x) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b x) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 157 + +)clear all + +--S 158 of 1325 +t0:=(a+b/x^4)^(1/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 158 + +--S 159 of 1325 +--r0:=1/3*x^3*sqrt(a+b/x^4)+2/3*a^(1/4)*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 159 + +--S 160 of 1325 +--a0:=integrate(t0,x) +--E 160 + +--S 161 of 1325 +--m0:=a0-r0 +--E 161 + +--S 162 of 1325 +--d0:=D(m0,x) +--E 162 + +)clear all + +--S 163 of 1325 +t0:=(a+b/x^4)^(1/2)*x +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R (1) x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 163 + +--S 164 of 1325 +r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)+1/2*x^2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R +-+ | 4 +--R +-+ \|b 2 |a x + b +--R - \|b atanh(-------------) + x |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R +-+ - 2\|b \|a x + b + a x + 2b | 4 +--R \|b log(------------------------------) + 2\|a x + b +--R 4 +--R x +--R [------------------------------------------------------, +--R 4 +--R +--------+ +--R | 4 +--------+ +--R +---+ \|a x + b | 4 +--R - \|- b atan(-----------) + \|a x + b +--R +---+ +--R \|- b +--R ---------------------------------------] +--R 2 +--R Type: Union(List(Expression(Integer)),...) +--E 165 + +--S 166 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +-+ +--R +-+ - 2\|b \|a x + b + a x + 2b +-+ \|b +--R \|b log(------------------------------) + 2\|b atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R 2\|a x + b - 2x |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b +-+ 4 | 4 4 +-+ +--R (- 2x |-------- \|b - a x - 2b)\|a x + b + (2a x + 2b)\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +--R (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ | 4 5 +--R 2x\|b \|a x + b - a x - 2b x +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--------+ +--R +-+ \|b +---+ \|a x + b | 4 +--R \|b atanh(-------------) - \|- b atan(-----------) + \|a x + b +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 |a x + b +--R - x |-------- +--R | 4 +--R \| x +--R / +--R 2 +--R Type: Expression(Integer) +--E 168 + +--S 169 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b | 4 4 +--R - x |-------- \|a x + b + a x + b +--R | 4 +--R \| x +--R (7) ------------------------------------- +--R +--------+ +--R | 4 +--R x\|a x + b +--R Type: Expression(Integer) +--E 169 + +)clear all + +--S 170 of 1325 +t0:=(a+b/x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R (1) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 170 + +--S 171 of 1325 +--r0:=x*sqrt(a+b/x^4)+2*a^(3/4)*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-2*a^(3/4)*_ +-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 171 + +--S 172 of 1325 +--a0:=integrate(t0,x) +--E 172 + +--S 173 of 1325 +--m0:=a0-r0 +--E 173 + +--S 174 of 1325 +--d0:=D(m0,x) +--E 174 + +)clear all + +--S 175 of 1325 +t0:=(a+b/x^4)^(1/2)/x +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))*sqrt(a)-1/2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R +-+ \| x |a x + b +--R \|a atanh(-----------) - |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|a \|a x + b - x \|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R , +--R +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b +--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R +-+ | 4 4 +--R \|b \|a x + b - a x - b +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 177 + +--S 178 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R (x \|a \|a x + b - x \|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R 2 +-+ | 4 2 +-+ +-+ \| x +--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 4 | 4 +--R \| x \| x +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R Type: Expression(Integer) +--E 178 + +--S 179 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 14 2 10 2 6 3 2 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 4 +--R \| x +--R + +--R 3 12 2 2 8 3 4 4 +--R 14a b x + 41a b x + 44a b x + 16b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 16 2 12 2 8 3 4 +-+ |a x + b 4 16 +--R (5a x + 25a b x + 36a b x + 16b x )\|a |-------- - 5a x +--R | 4 +--R \| x +--R + +--R 3 12 2 2 8 3 4 4 +--R - 30a b x - 61a b x - 52a b x - 16b +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (a x + 14a b x + 41a b x + 44a b x + 16b x )\|a +--R / +--R +--------+ +--R | 4 +--R 2 15 11 2 7 +-+ |a x + b +-+ +--R (5a x + 20a b x + 16b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +--R (- a x - 13a b x - 28a b x - 16b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 19 2 15 2 11 3 7 +-+ |a x + b +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R 2 +-+ | 4 2 +-+ +-+ \| x +--R (- x \|a \|a x + b + x \|a \|b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +--------+ | 4 +-+ +--R 2 +---+ | 4 2 +---+ +-+ \|a x + b - \|b +--R (2x \|- a \|a x + b - 2x \|- a \|b )atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ 2 |a x + b | 4 2 |a x + b +-+ 4 +--R (\|b + x |-------- )\|a x + b - x |-------- \|b - a x - b +--R | 4 | 4 +--R \| x \| x +--R / +--R +--------+ +--R 2 | 4 2 +-+ +--R 2x \|a x + b - 2x \|b +--R Type: Expression(Integer) +--E 180 + +--S 181 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 6 2 |a x + b +-+ 2 8 4 2 | 4 +--R ((- 2a x - 2b x ) |-------- \|b - a x - 3a b x - 2b )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 +-+ 2 10 6 2 2 |a x + b +--R (2a x + 4a b x + 2b )\|b + (a x + 3a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 9 5 |a x + b | 4 9 5 |a x + b +-+ +--R (a x + 2b x ) |-------- \|a x + b + (- 2a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 181 + +)clear all + +--S 182 of 1325 +t0:=(a+b/x^4)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1325 +--r0:=-1/3*sqrt(a+b/x^4)/x-2/3*a^(5/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 183 + +--S 184 of 1325 +--a0:=integrate(t0,x) +--E 184 + +--S 185 of 1325 +--m0:=a0-r0 +--E 185 + +--S 186 of 1325 +--d0:=D(m0,x) +--E 186 + +)clear all + +--S 187 of 1325 +t0:=(a+b/x^4)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1325 +r0:=-1/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-1/4*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 \|b |a x + b +-+ +--R - a x atanh(-------------) - |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) -------------------------------------------- +--R 2 +-+ +--R 4x \|b +--R Type: Expression(Integer) +--E 188 + +--S 189 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 4 - 2b\|a x + b + (a x + 2b)\|b +-+ | 4 +--R a x log(---------------------------------) - 2\|b \|a x + b +--R 4 +--R x +--R [-------------------------------------------------------------, +--R 4 +-+ +--R 8x \|b +--R +--------+ +--R +---+ | 4 +--------+ +--R 4 \|- b \|a x + b +---+ | 4 +--R - a x atan(-----------------) - \|- b \|a x + b +--R b +--R -------------------------------------------------] +--R 4 +---+ +--R 4x \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 189 + +--S 190 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +-+ +--R 4 - 2b\|a x + b + (a x + 2b)\|b 4 \|b +--R a x log(---------------------------------) + 2a x atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R +-+ | 4 2 |a x + b +-+ +--R - 2\|b \|a x + b + 2x |-------- \|b +--R | 4 +--R \| x +--R / +--R 4 +-+ +--R 8x \|b +--R Type: Expression(Integer) +--E 190 + +--S 191 of 1325 +d0a:=D(m0a,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (5) --------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 4 +---+ \|b 4 +-+ \|- b \|a x + b +--R a x \|- b atanh(-------------) - a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R +---+ +-+ | 4 2 +---+ |a x + b +-+ +--R - \|- b \|b \|a x + b + x \|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 4 +---+ +-+ +--R 4x \|- b \|b +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (7) --------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 193 + +)clear all + +--S 194 of 1325 +t0:=(a+b/x^4)^(1/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R (1) ----------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1325 +--r0:=-1/5*sqrt(a+b/x^4)/x^3-2/5*a^(7/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+_ +-- 2/5*a^(7/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 195 + +--S 196 of 1325 +--a0:=integrate(t0,x) +--E 196 + +--S 197 of 1325 +--m0:=a0-r0 +--E 197 + +--S 198 of 1325 +--d0:=D(m0,x) +--E 198 + +)clear all + +--S 199 of 1325 +t0:=(a+b/x^4)^(3/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1325 +r0:=1/4*(a+b/x^4)^(3/2)*x^4+3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))*_ + sqrt(a)-3/4*b*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R +-+ \| x 4 |a x + b +--R 3b\|a atanh(-----------) + (a x - 2b) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x +--R + +--R 3 +--R - 8b +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R , +--R +--R +--------+ +--R 6 2 2 +---+ | 4 +--R (6a b x + 24b x )\|- a \|a x + b +--R + +--R 6 2 2 +---+ +-+ +--R (- 18a b x - 24b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (- 3a x + 2a b x + 8b )\|b \|a x + b + a x + 3a b x - 6a b x +--R + +--R 3 +--R - 8b +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 201 + +--S 202 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((3a b x + 12b x )\|a \|a x + b + (- 9a b x - 12b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (- 3a x + 2a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 2a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 4 +--R \| x +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 26 5 22 4 2 18 3 3 14 2 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 6 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 6 26 5 22 4 2 18 3 3 14 +--R - 9a x - 138a b x - 681a b x - 1560a b x +--R + +--R 2 4 10 5 6 6 2 +--R - 1840a b x - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 8 6 4 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 8 6 4 7 +--R 2352a b x + 1216a b x + 256b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 8 6 4 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 8 6 4 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R 2352a b x + 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 23 3 19 2 2 15 3 11 4 7 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 5 +--R - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 5 5 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 5 7 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 203 + +--S 204 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 6 2 2 +-+ | 4 6 2 2 +-+ +-+ +--R ((- 3a b x - 12b x )\|a \|a x + b + (9a b x + 12b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 6 2 2 +---+ | 4 6 2 2 +---+ +-+ +--R ((6a b x + 24b x )\|- a \|a x + b + (- 18a b x - 24b x )\|- a \|b ) +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 2 8 4 2 +-+ +--R (- 3a x + 2a b x + 8b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 2a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (3a x - 2a b x - 8b x ) |-------- \|b + a x + 3a b x - 6a b x - 8b +--R | 4 +--R \| x +--R / +--R +--------+ +--R 6 2 | 4 6 2 +-+ +--R (4a x + 16b x )\|a x + b + (- 12a x - 16b x )\|b +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 17 2 13 2 9 3 5 |a x + b | 4 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1325 +t0:=(a+b/x^4)^(3/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1325 +--r0:=1/3*(a+b/x^4)^(3/2)*x^3-2/3*b*sqrt(a+b/x^4)/x+4/3*a^(5/4)*_ +-- (-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 207 + +--S 208 of 1325 +--a0:=integrate(t0,x) +--E 208 + +--S 209 of 1325 +--m0:=a0-r0 +--E 209 + +--S 210 of 1325 +--d0:=D(m0,x) +--E 210 + +)clear all + +--S 211 of 1325 +t0:=(a+b/x^4)^(3/2)*x +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1325 +r0:=1/2*(a+b/x^4)^(3/2)*x^2-3/4*a*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*_ + sqrt(b)-3/4*b*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 +-+ \|b 4 |a x + b +--R - 3a x \|b atanh(-------------) + (2a x - b) |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) -------------------------------------------------------- +--R 2 +--R 4x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ | 4 4 +--------+ +--R 4 +-+ - 2\|b \|a x + b + a x + 2b 4 | 4 +--R 3a x \|b log(------------------------------) + (4a x - 2b)\|a x + b +--R 4 +--R x +--R [----------------------------------------------------------------------, +--R 4 +--R 8x +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ \|a x + b 4 | 4 +--R - 3a x \|- b atan(-----------) + (2a x - b)\|a x + b +--R +---+ +--R \|- b +--R -------------------------------------------------------] +--R 4 +--R 4x +--R Type: Union(List(Expression(Integer)),...) +--E 213 + +--S 214 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +--R 4 +-+ - 2\|b \|a x + b + a x + 2b +--R 3a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 4 +-+ \|b 4 | 4 +--R 6a x \|b atanh(-------------) + (4a x - 2b)\|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +--R (- 4a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R 8x +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 2 8 4 2 +-+ +--R (- 2a x - 4a b x - 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- a x - 3a b x - 2b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 2 4 3 +--R (2a x + 4a b x + 2b x ) |-------- \|b + a x + 4a b x + 5a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 |a x + b +-+ | 4 11 7 |a x + b +--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 215 + +--S 216 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--R 4 +-+ \|b 4 +---+ \|a x + b +--R 3a x \|b atanh(-------------) - 3a x \|- b atan(-----------) +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (2a x - b)\|a x + b + (- 2a x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R 4 +--R 4x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R +--------+ | 4 +--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b +--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |-------- +--R | 4 +--R \| x +--R ------------------------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 7 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 217 + +)clear all + +--S 218 of 1325 +t0:=(a+b/x^4)^(3/2) +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 218 + +--S 219 of 1325 +--r0:=-1/5*(a+b/x^4)^(3/2)*x+6/5*a*x*sqrt(a+b/x^4)+12/5*a^(7/4)*_ +-- (-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/sqrt(a+b/x^4)-12/5*a^(7/4)*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 219 + +--S 220 of 1325 +--a0:=integrate(t0,x) +--E 220 + +--S 221 of 1325 +--m0:=a0-r0 +--E 221 + +--S 222 of 1325 +--d0:=D(m0,x) +--E 222 + +)clear all + +--S 223 of 1325 +t0:=(a+b/x^4)^(3/2)/x +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 223 + +--S 224 of 1325 +r0:=-1/6*(a+b/x^4)^(3/2)+1/2*a^(3/2)*atanh(sqrt(a+b/x^4)/sqrt(a))-_ + 1/2*a*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 4 +-+ \| x 4 |a x + b +--R 3a x \|a atanh(-----------) + (- 4a x - b) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------------------ +--R 4 +--R 6x +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R , +--R +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 10 6 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 2 4 +--R (12a x + 19a b x + 4b )\|b \|a x + b - 4a x - 21a b x - 21a b x +--R + +--R 3 +--R - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 225 + +--S 226 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((3a x + 12a b x )\|a \|a x + b + (- 9a x - 12a b x )\|a \|b ) +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +--R (12a x + 19a b x + 4b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (4a x + 17a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 21a b x - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 26 5 22 4 2 18 3 3 14 2 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 6 6 2 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 6 26 5 22 4 2 18 3 3 14 +--R - 9a x - 138a b x - 681a b x - 1560a b x +--R + +--R 2 4 10 5 6 6 2 +--R - 1840a b x - 1088a b x - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 5 8 6 4 +--R - 960a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 8 6 4 7 +--R 2352a b x + 1216a b x + 256b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 28 5 24 4 2 20 3 3 16 2 4 12 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 5 8 6 4 +--R 1088a b x + 256b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 9a x - 147a b x - 819a b x - 2241a b x - 3400a b x +--R + +--R 2 5 8 6 4 7 +--R - 2928a b x - 1344a b x - 256b +--R * +--R +-+ +--R \|b +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 2352a b x - 1216a b x - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R a x + 43a b x + 363a b x + 1289a b x + 2360a b x +--R + +--R 2 5 10 6 6 7 2 +--R 2352a b x + 1216a b x + 256b x +--R * +--R +-+ +--R \|a +--R / +--R 4 27 3 23 2 2 19 3 15 4 11 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 9 +--R - 256b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (9a x + 129a b x + 552a b x + 1008a b x + 832a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 10 6 +-+ | 4 2 10 6 +-+ +-+ +--R ((- 3a x - 12a b x )\|a \|a x + b + (9a x + 12a b x )\|a \|b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 10 6 +---+ | 4 +--R (6a x + 24a b x )\|- a \|a x + b +--R + +--R 2 10 6 +---+ +-+ +--R (- 18a x - 24a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 2 8 4 2 +-+ +--R (12a x + 19a b x + 4b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (4a x + 17a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 3 12 2 8 +--R (- 12a x - 19a b x - 4b x ) |-------- \|b - 4a x - 21a b x +--R | 4 +--R \| x +--R + +--R 2 4 3 +--R - 21a b x - 4b +--R / +--R +--------+ +--R 10 6 | 4 10 6 +-+ +--R (6a x + 24b x )\|a x + b + (- 18a x - 24b x )\|b +--R Type: Expression(Integer) +--E 228 + +--S 229 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - a x - 20a b x - 85a b x - 146a b x - 112a b x - 32b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (6a x + 50a b x + 146a b x + 198a b x + 128a b x + 32b )\|b +--R + +--R 5 22 4 18 3 2 14 2 3 10 4 6 5 2 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 21 2 17 2 13 3 9 |a x + b | 4 +--R (a x + 18a b x + 48a b x + 32b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +-+ +--R (- 6a x - 38a b x - 64a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 229 + +)clear all + +--S 230 of 1325 +t0:=(a+b/x^4)^(3/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 230 + +--S 231 of 1325 +--r0:=-1/7*(a+b/x^4)^(3/2)/x-2/7*a*sqrt(a+b/x^4)/x-4/7*a^(9/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- ((-b)^(1/4)*sqrt(a+b/x^4)) +--E 231 + +--S 232 of 1325 +--a0:=integrate(t0,x) +--E 232 + +--S 233 of 1325 +--m0:=a0-r0 +--E 233 + +--S 234 of 1325 +--d0:=D(m0,x) +--E 234 + +)clear all + +--S 235 of 1325 +t0:=(a+b/x^4)^(3/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 235 + +--S 236 of 1325 +r0:=-1/8*(a+b/x^4)^(3/2)/x^2-3/16*a^2*atanh(sqrt(b)/(x^2*_ + sqrt(a+b/x^4)))/sqrt(b)-3/16*a*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 6 \|b 4 |a x + b +-+ +--R - 3a x atanh(-------------) + (- 5a x - 2b) |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ----------------------------------------------------------- +--R 6 +-+ +--R 16x \|b +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R | 4 4 +-+ +--------+ +--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 4 +-+ | 4 +--R 3a x log(---------------------------------) + (- 10a x - 4b)\|b \|a x + b +--R 4 +--R x +--R [---------------------------------------------------------------------------- +--R 8 +-+ +--R 32x \|b +--R , +--R +--------+ +--R +---+ | 4 +--------+ +--R 2 8 \|- b \|a x + b 4 +---+ | 4 +--R - 3a x atan(-----------------) + (- 5a x - 2b)\|- b \|a x + b +--R b +--R ----------------------------------------------------------------] +--R 8 +---+ +--R 16x \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 237 + +--S 238 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +-+ +--R 2 8 - 2b\|a x + b + (a x + 2b)\|b 2 8 \|b +--R 3a x log(---------------------------------) + 6a x atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 +-+ | 4 6 2 |a x + b +-+ +--R (- 10a x - 4b)\|b \|a x + b + (10a x + 4b x ) |-------- \|b +--R | 4 +--R \| x +--R / +--R 8 +-+ +--R 32x \|b +--R Type: Expression(Integer) +--E 238 + +--S 239 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ 2 8 2 4 3 +--R ((- a x - 3a b x - 2b x ) |-------- \|b - 2a b x - 4a b x - 2b ) +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (a x + 4a b x + 5a b x + 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 2 10 2 6 3 2 |a x + b +--R (2a b x + 4a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 11 |a x + b | 4 15 11 |a x + b +-+ +--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 2 8 +---+ \|b 2 8 +-+ \|- b \|a x + b +--R 3a x \|- b atanh(-------------) - 3a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R +--------+ | 4 +--R 4 +---+ +-+ | 4 6 2 +---+ |a x + b +-+ +--R (- 5a x - 2b)\|- b \|b \|a x + b + (5a x + 2b x )\|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 8 +---+ +-+ +--R 16x \|- b \|b +--R Type: Expression(Integer) +--E 240 + +--S 241 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R +--------+ | 4 +--R 2 8 4 2 | 4 2 10 6 2 2 |a x + b +--R (- a x - 2a b x - b )\|a x + b + (a x + 2a b x + b x ) |-------- +--R | 4 +--R \| x +--R ------------------------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 11 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 241 + +)clear all + +--S 242 of 1325 +t0:=(a+b/x^4)^(3/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R (1) --------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1325 +--r0:=-1/9*(a+b/x^4)^(3/2)/x^3-2/15*a*sqrt(a+b/x^4)/x^3-4/15*a^(11/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- ((-b)^(3/4)*sqrt(a+b/x^4))+4/15*a^(11/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_ +-- sqrt(a+b/x^4)) +--E 243 + +--S 244 of 1325 +--a0:=integrate(t0,x) +--E 244 + +--S 245 of 1325 +--m0:=a0-r0 +--E 245 + +--S 246 of 1325 +--d0:=D(m0,x) +--E 246 + +)clear all + +--S 247 of 1325 +t0:=(a+b/x^4)^(5/2)*x^3 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1325 +r0:=-5/12*b*(a+b/x^4)^(3/2)+1/4*(a+b/x^4)^(5/2)*x^4+5/4*a^(3/2)*b*_ + atanh(sqrt(a+b/x^4)/sqrt(a))-5/4*a*b*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 4 +-+ \| x 2 8 4 2 |a x + b +--R 15a b x \|a atanh(-----------) + (3a x - 14a b x - 2b ) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) -------------------------------------------------------------------- +--R 4 +--R 12x +--R Type: Expression(Integer) +--E 248 + +--S 249 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R , +--R +--R +--------+ +--R 3 14 2 2 10 3 6 +---+ | 4 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 249 + +--S 250 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (15a b x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (- 75a b x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R Type: Expression(Integer) +--E 250 + +--S 251 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 38 8 34 7 2 30 6 3 26 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 6 9 2 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 9 38 8 34 7 2 30 6 3 26 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 6 9 2 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x +--R + +--R 9 4 +--R - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 4 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x +--R + +--R 9 4 +--R 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 4 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 6 10 2 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 6 10 2 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 35 5 31 4 2 27 3 3 23 2 4 19 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 15 6 11 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 17 6 13 7 9 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 17 6 13 7 9 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 19 6 15 7 11 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 3 14 2 2 10 3 6 +-+ | 4 +--R (- 15a b x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +-+ +-+ +--R (75a b x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 14 2 2 10 3 6 +---+ | 4 +--R (30a b x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 3 14 2 2 10 3 6 +---+ +-+ +--R (- 150a b x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (- 15a x + 10a b x + 242a b x + 264a b x + 32b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 3a x - 22a b x + 122a b x + 248a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +-+ +--R (15a x - 10a b x - 242a b x - 264a b x - 32b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R 3a x + 25a b x - 100a b x - 370a b x - 280a b x - 32b +--R / +--R +--------+ +--R 2 14 10 2 6 | 4 +--R (12a x + 144a b x + 192b x )\|a x + b +--R + +--R 2 14 10 2 6 +-+ +--R (- 60a x - 240a b x - 192b x )\|b +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 34 7 30 6 2 26 5 3 22 4 4 18 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 14 2 6 10 7 6 8 2 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 9 +--R - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 253 + +)clear all + +--S 254 of 1325 +t0:=(a+b/x^4)^(5/2)*x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1325 +--r0:=-10/21*b*(a+b/x^4)^(3/2)/x+1/3*(a+b/x^4)^(5/2)*x^3-20/21*a*b*_ +-- sqrt(a+b/x^4)/x+40/21*a^(9/4)*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4) +--E 255 + +--S 256 of 1325 +--a0:=integrate(t0,x) +--E 256 + +--S 257 of 1325 +--m0:=a0-r0 +--E 257 + +--S 258 of 1325 +--d0:=D(m0,x) +--E 258 + +)clear all + +--S 259 of 1325 +t0:=(a+b/x^4)^(5/2)*x +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1325 +r0:=-5/8*b*(a+b/x^4)^(3/2)/x^2+1/2*(a+b/x^4)^(5/2)*x^2-15/16*a^2*_ + atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))*sqrt(b)-15/16*a*b*sqrt(a+b/x^4)/x^2 +--R +--R +--R +--------+ +--R +-+ | 4 +--R 2 6 +-+ \|b 2 8 4 2 |a x + b +--R - 15a x \|b atanh(-------------) + (8a x - 9a b x - 2b ) |-------- +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) --------------------------------------------------------------------- +--R 6 +--R 16x +--R Type: Expression(Integer) +--E 260 + +--S 261 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b +--R 15a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 | 4 +--R (16a x - 18a b x - 4b )\|a x + b +--R / +--R 8 +--R 32x +--R , +--R +--------+ +--R | 4 +--------+ +--R 2 8 +---+ \|a x + b 2 8 4 2 | 4 +--R - 15a x \|- b atan(-----------) + (8a x - 9a b x - 2b )\|a x + b +--R +---+ +--R \|- b +--R --------------------------------------------------------------------] +--R 8 +--R 16x +--R Type: Union(List(Expression(Integer)),...) +--E 261 + +--S 262 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 +--R 2 8 +-+ - 2\|b \|a x + b + a x + 2b +--R 15a x \|b log(------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 2 8 +-+ \|b 2 8 4 2 | 4 +--R 30a x \|b atanh(-------------) + (16a x - 18a b x - 4b )\|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- 16a x + 18a b x + 4b x ) |-------- +--R | 4 +--R \| x +--R / +--R 8 +--R 32x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 3 12 2 8 2 4 3 +-+ +--R (- 2a x - 6a b x - 6a b x - 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (- a x - 4a b x - 5a b x - 2b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +-+ 4 16 3 12 +--R (2a x + 6a b x + 6a b x + 2b x ) |-------- \|b + a x + 5a b x +--R | 4 +--R \| x +--R + +--R 2 2 8 3 4 4 +--R 9a b x + 7a b x + 2b +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 11 |a x + b +-+ | 4 15 11 |a x + b +--R 2x |-------- \|b \|a x + b + (- a x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 263 + +--S 264 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ | 4 +--R 2 8 +-+ \|b 2 8 +---+ \|a x + b +--R 15a x \|b atanh(-------------) - 15a x \|- b atan(-----------) +--R +--------+ +---+ +--R | 4 \|- b +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R 2 8 4 2 | 4 +--R (8a x - 9a b x - 2b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (- 8a x + 9a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R 8 +--R 16x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (- a x - 3a b x - 3a b x - b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 3a b x + 3a b x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 11 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1325 +t0:=(a+b/x^4)^(5/2) +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 8 +--R x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1325 +--r0:=-2/9*a*(a+b/x^4)^(3/2)*x-1/9*(a+b/x^4)^(5/2)*x+4/3*a^2*x*_ +-- sqrt(a+b/x^4)+8/3*a^(11/4)*(-b)^(1/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/_ +-- sqrt(a+b/x^4)-8/3*a^(11/4)*(-b)^(1/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/sqrt(a+b/x^4) +--E 267 + +--S 268 of 1325 +--a0:=integrate(t0,x) +--E 268 + +--S 269 of 1325 +--m0:=a0-r0 +--E 269 + +--S 270 of 1325 +--d0:=D(m0,x) +--E 270 + +)clear all + +--S 271 of 1325 +t0:=(a+b/x^4)^(5/2)/x +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 9 +--R x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1325 +r0:=-1/6*a*(a+b/x^4)^(3/2)-1/10*(a+b/x^4)^(5/2)+1/2*a^(5/2)*_ + atanh(sqrt(a+b/x^4)/sqrt(a))-1/2*a^2*sqrt(a+b/x^4) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R 2 8 +-+ \| x 2 8 4 2 |a x + b +--R 15a x \|a atanh(-----------) + (- 23a x - 11a b x - 3b ) |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) --------------------------------------------------------------------- +--R 8 +--R 30x +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R , +--R +--R +--------+ +--R 4 18 3 14 2 2 10 +---+ | 4 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R +--------+ +--R 4 16 3 12 2 2 8 3 4 4 +-+ | 4 +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b \|a x + b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 273 + +--S 274 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (15a x + 180a b x + 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (- 75a x - 300a b x - 240a b x )\|a \|b +--R * +--R +--------+ +--R +-+ 2 +-+ | 4 2 +-+ +-+ 4 +--R (\|b - x \|a )\|a x + b + x \|a \|b - a x - b +--R log(--------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 9 38 8 34 7 2 30 6 3 26 +--R 13a x + 403a b x + 4043a b x + 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R 55692a b x + 96096a b x + 103936a b x + 68864a b x +--R + +--R 8 6 9 2 +--R 25600a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 9 38 8 34 7 2 30 6 3 26 +--R - 13a x - 403a b x - 4043a b x - 19825a b x +--R + +--R 5 4 22 4 5 18 3 6 14 2 7 10 +--R - 55692a b x - 96096a b x - 103936a b x - 68864a b x +--R + +--R 8 6 9 2 +--R - 25600a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x +--R + +--R 9 4 +--R - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 4 10 +--R 27648a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 40 8 36 7 2 32 6 3 28 5 4 24 +--R 13a x + 403a b x + 4043a b x + 19825a b x + 55692a b x +--R + +--R 4 5 20 3 6 16 2 7 12 8 8 +--R 96096a b x + 103936a b x + 68864a b x + 25600a b x +--R + +--R 9 4 +--R 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 10 40 9 36 8 2 32 7 3 28 6 4 24 +--R - 13a x - 416a b x - 4446a b x - 23868a b x - 75517a b x +--R + +--R 5 5 20 4 6 16 3 7 12 2 8 8 +--R - 151788a b x - 200032a b x - 172800a b x - 94464a b x +--R + +--R 9 4 10 +--R - 29696a b x - 4096b +--R * +--R +-+ +--R \|b +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R - a x - 88a b x - 1462a b x - 10364a b x - 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R - 94164a b x - 140896a b x - 135424a b x - 81152a b x +--R + +--R 9 6 10 2 +--R - 27648a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 10 42 9 38 8 2 34 7 3 30 6 4 26 +--R a x + 88a b x + 1462a b x + 10364a b x + 40081a b x +--R + +--R 5 5 22 4 6 18 3 7 14 2 8 10 +--R 94164a b x + 140896a b x + 135424a b x + 81152a b x +--R + +--R 9 6 10 2 +--R 27648a b x + 4096b x +--R * +--R +-+ +--R \|a +--R / +--R 6 39 5 35 4 2 31 3 3 27 2 4 23 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 5 19 6 15 +--R 13312a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 21 6 17 7 13 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 21 6 17 7 13 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 43 6 39 5 2 35 4 3 31 3 4 27 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 23 6 19 7 15 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 4 18 3 14 2 2 10 +-+ | 4 +--R (- 15a x - 180a b x - 240a b x )\|a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +-+ +-+ +--R (75a x + 300a b x + 240a b x )\|a \|b +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 4 18 3 14 2 2 10 +---+ | 4 +--R (30a x + 360a b x + 480a b x )\|- a \|a x + b +--R + +--R 4 18 3 14 2 2 10 +---+ +-+ +--R (- 150a x - 600a b x - 480a b x )\|- a \|b +--R * +--R +--------+ +--R | 4 +-+ +--R \|a x + b - \|b +--R atan(------------------) +--R 2 +---+ +--R x \|- a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (115a x + 515a b x + 603a b x + 236a b x + 48b )\|b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (23a x + 287a b x + 503a b x + 212a b x + 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 18 3 14 2 2 10 3 6 4 2 |a x + b +--R (- 115a x - 515a b x - 603a b x - 236a b x - 48b x ) |-------- +--R | 4 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R - 23a x - 310a b x - 790a b x - 715a b x - 260a b x - 48b +--R / +--R +--------+ +--R 2 18 14 2 10 | 4 +--R (30a x + 360a b x + 480b x )\|a x + b +--R + +--R 2 18 14 2 10 +-+ +--R (- 150a x - 600a b x - 480b x )\|b +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 7 30 6 26 5 2 22 4 3 18 3 4 14 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 10 6 6 7 2 +--R - 5280a b x - 2560a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R - a x - 53a b x - 553a b x - 2471a b x - 5890a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R - 8112a b x - 6496a b x - 2816a b x - 512b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 8 32 7 28 6 2 24 5 3 20 4 4 16 +--R 10a x + 200a b x + 1372a b x + 4712a b x + 9290a b x +--R + +--R 3 5 12 2 6 8 7 4 8 +--R 11040a b x + 7840a b x + 3072a b x + 512b +--R * +--R +-+ +--R \|b +--R + +--R 8 34 7 30 6 2 26 5 3 22 4 4 18 +--R a x + 53a b x + 553a b x + 2471a b x + 5890a b x +--R + +--R 3 5 14 2 6 10 7 6 8 2 +--R 8112a b x + 6496a b x + 2816a b x + 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 33 4 29 3 2 25 2 3 21 4 17 +--R - 10a x - 170a b x - 832a b x - 1696a b x - 1536a b x +--R + +--R 5 13 +--R - 512b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 277 + +)clear all + +--S 278 of 1325 +t0:=(a+b/x^4)^(5/2)/x^2 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 10 +--R x +--R Type: Expression(Integer) +--E 278 + +--S 279 of 1325 +--r0:=-10/77*a*(a+b/x^4)^(3/2)/x-1/11*(a+b/x^4)^(5/2)/x-20/77*a^2*_ +-- sqrt(a+b/x^4)/x-40/77*a^(13/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 279 + +--S 280 of 1325 +--a0:=integrate(t0,x) +--E 280 + +--S 281 of 1325 +--m0:=a0-r0 +--E 281 + +--S 282 of 1325 +--d0:=D(m0,x) +--E 282 + +)clear all + +--S 283 of 1325 +t0:=(a+b/x^4)^(5/2)/x^3 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 11 +--R x +--R Type: Expression(Integer) +--E 283 + +--S 284 of 1325 +r0:=-5/48*a*(a+b/x^4)^(3/2)/x^2-1/12*(a+b/x^4)^(5/2)/x^2-5/32*a^3*_ + atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b)-5/32*a^2*sqrt(a+b/x^4)/x^2 +--R +--R +--R (2) +--R +--------+ +--R +-+ | 4 +--R 3 10 \|b 2 8 4 2 |a x + b +-+ +--R - 15a x atanh(-------------) + (- 33a x - 26a b x - 8b ) |-------- \|b +--R +--------+ | 4 +--R | 4 \| x +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R -------------------------------------------------------------------------- +--R 10 +-+ +--R 96x \|b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R | 4 4 +-+ +--R 3 12 - 2b\|a x + b + (a x + 2b)\|b +--R 15a x log(---------------------------------) +--R 4 +--R x +--R + +--R +--------+ +--R 2 8 4 2 +-+ | 4 +--R (- 66a x - 52a b x - 16b )\|b \|a x + b +--R / +--R 12 +-+ +--R 192x \|b +--R , +--R +--R +--------+ +--R +---+ | 4 +--R 3 12 \|- b \|a x + b +--R - 15a x atan(-----------------) +--R b +--R + +--R +--------+ +--R 2 8 4 2 +---+ | 4 +--R (- 33a x - 26a b x - 8b )\|- b \|a x + b +--R / +--R 12 +---+ +--R 96x \|- b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 285 + +--S 286 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 4 +-+ +--R 3 12 - 2b\|a x + b + (a x + 2b)\|b +--R 15a x log(---------------------------------) +--R 4 +--R x +--R + +--R +-+ +--------+ +--R 3 12 \|b 2 8 4 2 +-+ | 4 +--R 30a x atanh(-------------) + (- 66a x - 52a b x - 16b )\|b \|a x + b +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +-+ +--R (66a x + 52a b x + 16b x ) |-------- \|b +--R | 4 +--R \| x +--R / +--R 12 +-+ +--R 192x \|b +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +-+ 3 12 +--R (- a x - 4a b x - 5a b x - 2b x ) |-------- \|b - 2a b x +--R | 4 +--R \| x +--R + +--R 2 2 8 3 4 4 +--R - 6a b x - 6a b x - 2b +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +--R (a x + 5a b x + 9a b x + 7a b x + 2b )\|b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 2 10 3 6 4 2 |a x + b +--R (2a b x + 6a b x + 6a b x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 15 |a x + b | 4 19 15 |a x + b +-+ +--R 2b x |-------- \|a x + b + (- a x - 2b x ) |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R +-+ +---+ | 4 +--R 3 12 +---+ \|b 3 12 +-+ \|- b \|a x + b +--R 15a x \|- b atanh(-------------) - 15a x \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R + +--R +--------+ +--R 2 8 4 2 +---+ +-+ | 4 +--R (- 33a x - 26a b x - 8b )\|- b \|b \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ |a x + b +-+ +--R (33a x + 26a b x + 8b x )\|- b |-------- \|b +--R | 4 +--R \| x +--R / +--R 12 +---+ +-+ +--R 96x \|- b \|b +--R Type: Expression(Integer) +--E 288 + +--S 289 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R 3 12 2 8 2 4 3 | 4 +--R (- a x - 3a b x - 3a b x - b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 14 2 10 2 6 3 2 |a x + b +--R (a x + 3a b x + 3a b x + b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 15 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 289 + +)clear all + +--S 290 of 1325 +t0:=(a+b/x^4)^(5/2)/x^4 +--R +--R +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R (1) -------------------------------- +--R 12 +--R x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 1325 +--r0:=-10/117*a*(a+b/x^4)^(3/2)/x^3-1/13*(a+b/x^4)^(5/2)/x^3-_ +-- 4/39*a^2*sqrt(a+b/x^4)/x^3-8/39*a^(15/4)*elliptic_e(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*_ +-- sqrt(a+b/x^4))+8/39*a^(15/4)*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 291 + +--S 292 of 1325 +--a0:=integrate(t0,x) +--E 292 + +--S 293 of 1325 +--m0:=a0-r0 +--E 293 + +--S 294 of 1325 +--d0:=D(m0,x) +--E 294 + +)clear all + +--S 295 of 1325 +t0:=x^3/(a+b/x^4)^(1/2) +--R +--R +--R 3 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 1325 +r0:=-1/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+1/4*x^4*sqrt(a+b/x^4)/a +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 | 4 +--R \| x 4 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 4 +--R \|a \| x +--R (2) ------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 6 2 +-+ | 4 6 2 +-+ +-+ +--R (- a x - 2b x )\|a \|a x + b + (2a x + 2b x )\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 4 4 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 6 2 +---+ | 4 6 2 +---+ +-+ +--R (- a x - 2b x )\|- a \|a x + b + (2a x + 2b x )\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 8a\|- a \|b \|a x + b + (- 4a x - 8a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 297 + +--S 298 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ | 4 4 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +-+ | 4 4 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ |a x + b +-+ 6 2 +-+ | 4 +--R (- 2x \|a |-------- \|b + (- a x - 2b x )\|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +-+ +-+ 8 4 +-+ |a x + b +--R (2a x + 2b x )\|a \|b + (a x + 2b x )\|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 8a\|a \|b \|a x + b + (- 4a x - 8a b)\|a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 +-+ |a x + b +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- +--R | 4 +--R \| x +--R + +--R 4 17 3 13 2 2 9 3 5 +--R - 7a x - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 19 3 15 2 2 11 3 7 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 19 3 15 2 2 11 3 7 4 3 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 19 3 15 2 2 11 3 7 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 4 19 3 15 2 2 11 3 7 4 3 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 4 21 3 17 2 2 13 3 9 4 5 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 4 +--R \| x +--R + +--R 5 21 4 17 3 2 13 2 3 9 4 5 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 4 +--R 4 14 3 10 2 2 6 3 2 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R +--------+ | 4 +--R +---+ +-+ | 4 4 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 4 4 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 +---+ +-+ |a x + b +-+ 6 2 +---+ +-+ | 4 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x )\|- a \|a )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 +---+ +-+ +-+ 8 4 +---+ +-+ |a x + b +--R (2a x + 2b x )\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 4 2 4 +---+ +-+ +--R 8a\|- a \|a \|b \|a x + b + (- 4a x - 8a b)\|- a \|a +--R Type: Expression(Integer) +--E 300 + +--S 301 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 9 5 |a x + b +-+ 2 11 7 2 3 | 4 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 11 7 2 3 +-+ 2 13 9 2 5 |a x + b +--R (4a x + 12a b x + 8b x )\|b + (a x + 8a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 301 + +)clear all + +--S 302 of 1325 +t0:=x^2/(a+b/x^4)^(1/2) +--R +--R +--R 2 +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1325 +--r0:=1/3*x^3*sqrt(a+b/x^4)/a-1/3*(-b)^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(3/4)*sqrt(a+b/x^4)) +--E 303 + +--S 304 of 1325 +--a0:=integrate(t0,x) +--E 304 + +--S 305 of 1325 +--m0:=a0-r0 +--E 305 + +--S 306 of 1325 +--d0:=D(m0,x) +--E 306 + +)clear all + +--S 307 of 1325 +t0:=x/(a+b/x^4)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1325 +r0:=1/2*x^2*sqrt(a+b/x^4)/a +--R +--R +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) ------------- +--R 2a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 +--R \|a x + b +--R (3) ----------- +--R 2a +--R Type: Union(Expression(Integer),...) +--E 309 + +--S 310 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (4) --------------------------- +--R 2a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 3 |a x + b +--R - x\|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------ +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 311 + +)clear all + +--S 312 of 1325 +t0:=1/(a+b/x^4)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1325 +--r0:=x*sqrt(a+b/x^4)/a+(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4))-_ +-- (-b)^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(1/4)*sqrt(a+b/x^4)) +--E 313 + +--S 314 of 1325 +--a0:=integrate(t0,x) +--E 314 + +--S 315 of 1325 +--m0:=a0-r0 +--E 315 + +--S 316 of 1325 +--d0:=D(m0,x) +--E 316 + +)clear all + +--S 317 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 4 +--R |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------ +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 318 + +--S 319 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R [---------------------------------------------------------------, +--R +-+ +--R 2\|a +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R ------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 319 + +--S 320 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 320 + +--S 321 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 6 2 +-+ |a x + b 2 6 2 +-+ +--R ((3a x + 4b x )\|a |-------- - 3a x - 4a b x )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 |a x + b 2 8 4 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 8 4 |a x + b 2 8 4 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b 3 10 2 6 2 2 +--R (- a x - 5a b x - 4b x )\|a |-------- + a x + 5a b x + 4a b x +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--R 2 7 3 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 9 5 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 11 2 7 2 3 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--------+ +--R | 4 +---+ | 4 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ 2 +--R \|a a x +--R (6) ---------------------------------------------------------------------- +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 323 + +)clear all + +--S 324 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^2) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1325 +--r0:=-a^(1/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(1/4)*sqrt(a+b/x^4)) +--E 325 + +--S 326 of 1325 +--a0:=integrate(t0,x) +--E 326 + +--S 327 of 1325 +--m0:=a0-r0 +--E 327 + +--S 328 of 1325 +--d0:=D(m0,x) +--E 328 + +)clear all + +--S 329 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^3) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 3 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1325 +r0:=-1/2*atanh(sqrt(b)/(x^2*sqrt(a+b/x^4)))/sqrt(b) +--R +--R +--R +-+ +--R \|b +--R atanh(-------------) +--R +--------+ +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (2) - -------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R | 4 4 +-+ +--------+ +--R - 2b\|a x + b + (a x + 2b)\|b +---+ | 4 +--R log(---------------------------------) \|- b \|a x + b +--R 4 atan(-----------------) +--R x b +--R (3) [--------------------------------------,- -----------------------] +--R +-+ +---+ +--R 4\|b 2\|- b +--R Type: Union(List(Expression(Integer)),...) +--E 331 + +--S 332 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +--------+ +--R | 4 4 +-+ +-+ +--R - 2b\|a x + b + (a x + 2b)\|b \|b +--R log(---------------------------------) + 2atanh(-------------) +--R 4 +--------+ +--R x | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (4) -------------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--------+ +--R 4 +-+ 2 |a x + b | 4 +--R ((- a x - 2b)\|b - 2b x |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 6 2 |a x + b +-+ 4 2 +--R (a x + 2b x ) |-------- \|b + 2a b x + 2b +--R | 4 +--R \| x +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R 7 3 |a x + b +-+ | 4 7 2 3 |a x + b +--R (a x + 2b x ) |-------- \|b \|a x + b + (- 2a b x - 2b x ) |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 333 + +--S 334 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +--------+ +--R +-+ +---+ | 4 +--R +---+ \|b +-+ \|- b \|a x + b +--R \|- b atanh(-------------) - \|b atan(-----------------) +--R +--------+ b +--R | 4 +--R 2 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R (6) -------------------------------------------------------- +--R +---+ +-+ +--R 2\|- b \|b +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1325 +d0b:=D(m0b,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R - \|a x + b + x |-------- +--R | 4 +--R \| x +--R (7) ----------------------------- +--R +--------+ +--R | 4 +--------+ +--R 3 |a x + b | 4 +--R x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1325 +t0:=1/((a+b/x^4)^(1/2)*x^4) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1325 +--r0:=-a^(3/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4))+a^(3/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/((-b)^(3/4)*sqrt(a+b/x^4)) +--E 337 + +--S 338 of 1325 +--a0:=integrate(t0,x) +--E 338 + +--S 339 of 1325 +--m0:=a0-r0 +--E 339 + +--S 340 of 1325 +--d0:=D(m0,x) +--E 340 + +)clear all + +--S 341 of 1325 +t0:=x^3/(a+b/x^4)^(3/2) +--R +--R +--R 7 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1325 +r0:=-3/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(5/2)-_ + 1/2*x^4/(a*sqrt(a+b/x^4))+3/4*x^4*sqrt(a+b/x^4)/a^2 +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R |a x + b \| x 4 +-+ +--R - 3b |-------- atanh(-----------) + (a x + 3b)\|a +--R | 4 +-+ +--R \| x \|a +--R (2) --------------------------------------------------- +--R +--------+ +--R | 4 +--R 2 +-+ |a x + b +--R 4a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((9a b x + 12b )\|b \|a x + b - 3a b x - 15a b x - 12b ) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (- a x - 7a b x - 12b x )\|a \|a x + b +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (3a x + 13a b x + 12b x )\|a \|b +--R / +--R +--------+ +--R 3 4 2 +-+ +-+ | 4 4 8 3 4 2 2 +-+ +--R (12a x + 16a b)\|a \|b \|a x + b + (- 4a x - 20a b x - 16a b )\|a +--R , +--R +--R +--------+ +--R 4 2 +-+ | 4 2 8 2 4 3 +--R ((- 18a b x - 24b )\|b \|a x + b + 6a b x + 30a b x + 24b ) +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (- a x - 7a b x - 12b x )\|- a \|a x + b +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (3a x + 13a b x + 12b x )\|- a \|b +--R / +--R +--------+ +--R 3 4 2 +---+ +-+ | 4 +--R (12a x + 16a b)\|- a \|b \|a x + b +--R + +--R 4 8 3 4 2 2 +---+ +--R (- 4a x - 20a b x - 16a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 343 + +--S 344 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 4 2 |a x + b +-+ | 4 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 2 |a x + b +-+ | 4 +--R (9a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 |a x + b +--R (- 3a b x - 15a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +--R (- a x - 7a b x - 12b x )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (a x + 8a b x + 19a b x + 12b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 4 2 +-+ |a x + b +-+ | 4 +--R (12a x + 16a b)\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 8 3 4 2 2 +-+ |a x + b +--R (- 4a x - 20a b x - 16a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 25 3 21 2 2 17 3 13 4 9 +-+ +--R (- 9a x - 120a b x - 432a b x - 576a b x - 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R - a x - 41a b x - 280a b x - 688a b x - 704a b x +--R + +--R 5 7 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 7 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (a x + 41a b x + 280a b x + 688a b x + 704a b x + 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 6 22 5 18 4 2 14 3 3 10 2 4 6 +--R 9a x + 129a b x + 552a b x + 1008a b x + 832a b x +--R + +--R 5 2 +--R 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 6 24 5 20 4 2 16 3 3 12 2 4 8 +--R a x + 42a b x + 321a b x + 968a b x + 1392a b x +--R + +--R 5 4 6 +--R 960a b x + 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 6 24 5 20 4 2 16 3 3 12 2 4 8 +--R - 9a x - 138a b x - 681a b x - 1560a b x - 1840a b x +--R + +--R 5 4 6 +--R - 1088a b x - 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 26 6 22 5 2 18 4 3 14 3 4 10 +--R - a x - 42a b x - 321a b x - 968a b x - 1392a b x +--R + +--R 2 5 6 6 2 +--R - 960a b x - 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--------+ +--R 4 2 +---+ |a x + b +-+ | 4 +--R (9a b x + 12b )\|- a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 +---+ |a x + b +--R (- 3a b x - 15a b x - 12b )\|- a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 4 2 +-+ |a x + b +-+ | 4 +--R (- 18a b x - 24b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 2 4 3 +-+ |a x + b +--R (6a b x + 30a b x + 24b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 2 8 4 2 +---+ +-+ +-+ +--R (- 3a x - 13a b x - 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +--R (- a x - 7a b x - 12b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +-+ +--R (3a x + 13a b x + 12b x )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +---+ +-+ +--R (a x + 8a b x + 19a b x + 12b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 3 4 2 +---+ +-+ |a x + b +-+ | 4 +--R (12a x + 16a b)\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 8 3 4 2 2 +---+ +-+ |a x + b +--R (- 4a x - 20a b x - 16a b )\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 4 +--R \| x +--R + +--R 2 11 3 7 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 19 2 15 2 11 3 7 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 16 3 12 2 2 8 3 4 4 |a x + b | 4 +--R (a x + 19a b x + 66a b x + 80a b x + 32b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 |a x + b +-+ +--R (- 6a x - 44a b x - 102a b x - 96a b x - 32b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 347 + +)clear all + +--S 348 of 1325 +t0:=x^2/(a+b/x^4)^(3/2) +--R +--R +--R 6 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 348 + +--S 349 of 1325 +--r0:=-1/2*x^3/(a*sqrt(a+b/x^4))+5/6*x^3*sqrt(a+b/x^4)/a^2-_ +-- 5/6*(-b)^(3/4)*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(7/4)*sqrt(a+b/x^4)) +--E 349 + +--S 350 of 1325 +--a0:=integrate(t0,x) +--E 350 + +--S 351 of 1325 +--m0:=a0-r0 +--E 351 + +--S 352 of 1325 +--d0:=D(m0,x) +--E 352 + +)clear all + +--S 353 of 1325 +t0:=x/(a+b/x^4)^(3/2) +--R +--R +--R 5 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 353 + +--S 354 of 1325 +r0:=-1/2*x^2/(a*sqrt(a+b/x^4))+x^2*sqrt(a+b/x^4)/a^2 +--R +--R +--R 4 +--R a x + 2b +--R (2) ---------------- +--R +--------+ +--R | 4 +--R 2 2 |a x + b +--R 2a x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R a x + 2b +--R (3) -------------- +--R +--------+ +--R 2 | 4 +--R 2a \|a x + b +--R Type: Union(Expression(Integer),...) +--E 355 + +--S 356 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (- a x - 2b)\|a x + b + (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R (4) ---------------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 2 |a x + b | 4 +--R 2a x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 5 | 4 7 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) -------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 4 |a x + b | 4 +--R (a x + b) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 357 + +)clear all + +--S 358 of 1325 +t0:=1/(a+b/x^4)^(3/2) +--R +--R +--R 4 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 358 + +--S 359 of 1325 +--r0:=-1/2*x/(a*sqrt(a+b/x^4))+3/2*x*sqrt(a+b/x^4)/a^2+_ +-- 3/2*(-b)^(1/4)*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4))-3/2*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*sqrt(a+b/x^4)) +--E 359 + +--S 360 of 1325 +--a0:=integrate(t0,x) +--E 360 + +--S 361 of 1325 +--m0:=a0-r0 +--E 361 + +--S 362 of 1325 +--d0:=D(m0,x) +--E 362 + +)clear all + +--S 363 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x) +--R +--R +--R 3 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 1325 +r0:=1/2*atanh(sqrt(a+b/x^4)/sqrt(a))/a^(3/2)+(-1/2)/(a*sqrt(a+b/x^4)) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R |a x + b \| x +-+ +--R |-------- atanh(-----------) - \|a +--R | 4 +-+ +--R \| x \|a +--R (2) ------------------------------------ +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R 2a\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R +-+ | 4 4 +--R (\|b \|a x + b - a x - b) +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 +-+ | 4 2 +-+ +-+ +--R x \|a \|a x + b - x \|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 4 2 4 +-+ +--R 2a\|a \|b \|a x + b + (- 2a x - 2a b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 4 +---+ +-+ +--R +-+ | 4 4 \|- a \|a x + b - \|- a \|b +--R (2\|b \|a x + b - 2a x - 2b)atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 +---+ | 4 2 +---+ +-+ +--R x \|- a \|a x + b - x \|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 4 2 4 +---+ +--R 2a\|- a \|b \|a x + b + (- 2a x - 2a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 365 + +--S 366 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R |a x + b +-+ | 4 4 |a x + b +--R ( |-------- \|b \|a x + b + (- a x - b) |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ +--------+ |-------- +--R | 4 +--------+ | 4 | 4 +--R |a x + b +-+ | 4 4 |a x + b \| x +--R (- |-------- \|b \|a x + b + (a x + b) |-------- )atanh(-----------) +--R | 4 | 4 +-+ +--R \| x \| x \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ +-+ 2 +-+ |a x + b | 4 2 +-+ |a x + b +-+ +--R (\|a \|b + x \|a |-------- )\|a x + b - x \|a |-------- \|b +--R | 4 | 4 +--R \| x \| x +--R + +--R 4 +-+ +--R (- a x - b)\|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ |a x + b +-+ | 4 2 4 +-+ |a x + b +--R 2a\|a |-------- \|b \|a x + b + (- 2a x - 2a b)\|a |-------- +--R | 4 | 4 +--R \| x \| x +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R +--------+ +--R | 4 +--R 2 13 9 2 5 +-+ |a x + b 3 13 2 9 +--R (5a x + 20a b x + 16b x )\|a |-------- - 5a x - 20a b x +--R | 4 +--R \| x +--R + +--R 2 5 +--R - 16a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 15 2 11 2 7 |a x + b +--R (- a x - 12a b x - 16a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 15 2 11 2 7 3 3 +-+ +--R (a x + 13a b x + 28a b x + 16b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 3 15 2 11 2 7 |a x + b +--R (5a x + 20a b x + 16a b x ) |-------- +--R | 4 +--R \| x +--R + +--R 3 15 2 11 2 7 3 3 +-+ +--R (- 5a x - 25a b x - 36a b x - 16b x )\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 4 +--R 3 17 2 13 2 9 3 5 +-+ |a x + b 4 17 +--R (- a x - 13a b x - 28a b x - 16b x )\|a |-------- + a x +--R | 4 +--R \| x +--R + +--R 3 13 2 2 9 3 5 +--R 13a b x + 28a b x + 16a b x +--R / +--R +--------+ +--R | 4 +--R 4 14 3 10 2 2 6 3 2 |a x + b +-+ +--R (5a x + 25a b x + 36a b x + 16a b x ) |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 4 16 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (5a x + 30a b x + 61a b x + 52a b x + 16b )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 18 4 14 3 2 10 2 3 6 4 2 |a x + b +--R (- a x - 14a b x - 41a b x - 44a b x - 16a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +---+ |a x + b +-+ | 4 4 +---+ |a x + b +--R (- \|- a |-------- \|b \|a x + b + (a x + b)\|- a |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--------+ +--R | 4 +--------+ | 4 +--R +-+ |a x + b +-+ | 4 4 +-+ |a x + b +--R (2\|a |-------- \|b \|a x + b + (- 2a x - 2b)\|a |-------- ) +--R | 4 | 4 +--R \| x \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R | 4 +--------+ +--R +---+ +-+ +-+ 2 +---+ +-+ |a x + b | 4 +--R (\|- a \|a \|b + x \|- a \|a |-------- )\|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 +---+ +-+ |a x + b +-+ 4 +---+ +-+ +--R - x \|- a \|a |-------- \|b + (- a x - b)\|- a \|a +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R +---+ +-+ |a x + b +-+ | 4 +--R 2a\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 4 +---+ +-+ |a x + b +--R (- 2a x - 2a b)\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 368 + +--S 369 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--------+ +--R 5 |a x + b +-+ 7 3 | 4 7 3 +-+ +--R (- 2x |-------- \|b - a x - 2b x )\|a x + b + (2a x + 2b x )\|b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 9 5 |a x + b +--R (a x + 2b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 3a b x + 2b ) |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +-+ +--R (- 2a x - 4a b x - 2b ) |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 369 + +)clear all + +--S 370 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^2) +--R +--R +--R 2 +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 1325 +--r0:=(-1/2)/(a*x*sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(3/4)*(-b)^(1/4)*sqrt(a+b/x^4)) +--E 371 + +--S 372 of 1325 +--a0:=integrate(t0,x) +--E 372 + +--S 373 of 1325 +--m0:=a0-r0 +--E 373 + +--S 374 of 1325 +--d0:=D(m0,x) +--E 374 + +)clear all + +--S 375 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^3) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 375 + +--S 376 of 1325 +r0:=(-1/2)/(a*x^2*sqrt(a+b/x^4)) +--R +--R +--R 1 +--R (2) - ---------------- +--R +--------+ +--R | 4 +--R 2 |a x + b +--R 2a x |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +--------+ +--R | 4 +--R 2a\|a x + b +--R Type: Union(Expression(Integer),...) +--E 377 + +--S 378 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 2 |a x + b +--R \|a x + b - x |-------- +--R | 4 +--R \| x +--R (4) --------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 |a x + b | 4 +--R 2a x |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 378 + +--S 379 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R | 4 3 |a x + b +--R - x\|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) -------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 4 |a x + b | 4 +--R (a x + b) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 379 + +)clear all + +--S 380 of 1325 +t0:=1/((a+b/x^4)^(3/2)*x^4) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R | 4 +--R 4 |a x + b +--R (a x + b) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 380 + +--S 381 of 1325 +--r0:=(-1/2)/(a*x^3*sqrt(a+b/x^4))+1/2*elliptic_e(asin((-b)^(1/4)/_ +-- (a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*_ +-- sqrt(a+b/x^4))-1/2*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(1/4)*(-b)^(3/4)*sqrt(a+b/x^4)) +--E 381 + +--S 382 of 1325 +--a0:=integrate(t0,x) +--E 382 + +--S 383 of 1325 +--m0:=a0-r0 +--E 383 + +--S 384 of 1325 +--d0:=D(m0,x) +--E 384 + +)clear all + +--S 385 of 1325 +t0:=x^3/(a+b/x^4)^(5/2) +--R +--R +--R 11 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 385 + +--S 386 of 1325 +r0:=-1/6*x^4/(a*(a+b/x^4)^(3/2))-5/4*b*atanh(sqrt(a+b/x^4)/sqrt(a))/_ + a^(7/2)-5/6*x^4/(a^2*sqrt(a+b/x^4))+5/4*x^4*sqrt(a+b/x^4)/a^3 +--R +--R +--R (2) +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R 4 2 |a x + b \| x +--R (- 15a b x - 15b ) |-------- atanh(-----------) +--R | 4 +-+ +--R \| x \|a +--R + +--R 2 8 4 2 +-+ +--R (3a x + 20a b x + 15b )\|a +--R / +--R +--------+ +--R | 4 +--R 4 4 3 +-+ |a x + b +--R (12a x + 12a b)\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 3 12 2 2 8 3 4 4 +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b )\|b \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +--R - 15a b x - 210a b x - 615a b x - 660a b x - 240b +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a \|b +--R / +--R +--------+ +--R 6 12 5 8 4 2 4 3 3 +-+ +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|a \|b \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a +--R , +--R +--R +--------+ +--R 3 12 2 2 8 3 4 4 +-+ | 4 +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|b \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +--R 30a b x + 420a b x + 1230a b x + 1320a b x + 480b +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|b +--R / +--R +--------+ +--R 6 12 5 8 4 2 4 3 3 +---+ +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|b \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 387 + +--S 388 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b + a x )\|a x + b - a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 3 12 2 2 8 3 4 4 |a x + b +-+ | 4 +--R (75a b x + 375a b x + 540a b x + 240b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 4 16 3 2 12 2 3 8 4 4 5 |a x + b +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 4 16 3 12 2 2 8 3 4 4 +-+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|a \|b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 6 12 5 8 4 2 4 3 3 +-+ |a x + b +-+ | 4 +--R (60a x + 300a b x + 432a b x + 192a b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 7 16 6 12 5 2 8 4 3 4 3 4 +-+ |a x + b +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 388 + +--S 389 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 6 37 5 33 4 2 29 3 3 25 +--R - 13a x - 364a b x - 2912a b x - 9984a b x +--R + +--R 2 4 21 5 17 6 13 +--R - 16640a b x - 13312a b x - 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 7 37 6 33 5 2 29 4 3 25 3 4 21 +--R - 13a x - 364a b x - 2912a b x - 9984a b x - 16640a b x +--R + +--R 2 5 17 6 13 +--R - 13312a b x - 4096a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 84a b x - 1120a b x - 5376a b x - 11520a b x +--R + +--R 2 5 19 6 15 +--R - 11264a b x - 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R - a x - 85a b x - 1204a b x - 6496a b x - 16896a b x +--R + +--R 2 5 19 6 15 7 11 +--R - 22784a b x - 15360a b x - 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R 13a x + 364a b x + 2912a b x + 9984a b x + 16640a b x +--R + +--R 2 5 19 6 15 +--R 13312a b x + 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 7 39 6 35 5 2 31 4 3 27 3 4 23 +--R 13a x + 377a b x + 3276a b x + 12896a b x + 26624a b x +--R + +--R 2 5 19 6 15 7 11 +--R 29952a b x + 17408a b x + 4096b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 41 6 37 5 2 33 4 3 29 3 4 25 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 2 5 21 6 17 7 13 +--R 22784a b x + 15360a b x + 4096b x +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 8 41 7 37 6 2 33 5 3 29 4 4 25 +--R a x + 85a b x + 1204a b x + 6496a b x + 16896a b x +--R + +--R 3 5 21 2 6 17 7 13 +--R 22784a b x + 15360a b x + 4096a b x +--R / +--R 9 34 8 30 7 2 26 6 3 22 5 4 18 +--R 13a x + 390a b x + 3653a b x + 16172a b x + 39520a b x +--R + +--R 4 5 14 3 6 10 2 7 6 8 2 +--R 56576a b x + 47360a b x + 21504a b x + 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 9 36 8 32 7 2 28 6 3 24 5 4 20 +--R a x + 87a b x + 1375a b x + 8989a b x + 31092a b x +--R + +--R 4 5 16 3 6 12 2 7 8 8 4 9 +--R 63072a b x + 77824a b x + 57600a b x + 23552a b x + 4096b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 9 36 8 32 7 2 28 6 3 24 5 4 20 +--R - 13a x - 403a b x - 4043a b x - 19825a b x - 55692a b x +--R + +--R 4 5 16 3 6 12 2 7 8 8 4 9 +--R - 96096a b x - 103936a b x - 68864a b x - 25600a b x - 4096b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 10 38 9 34 8 2 30 7 3 26 6 4 22 +--R - a x - 87a b x - 1375a b x - 8989a b x - 31092a b x +--R + +--R 5 5 18 4 6 14 3 7 10 2 8 6 9 2 +--R - 63072a b x - 77824a b x - 57600a b x - 23552a b x - 4096a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--R 3 12 2 2 8 3 4 4 +---+ |a x + b +-+ +--R (75a b x + 375a b x + 540a b x + 240b )\|- a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +---+ +--R (- 15a b x - 210a b x - 615a b x - 660a b x - 240b )\|- a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--R 3 12 2 2 8 3 4 4 +-+ |a x + b +-+ +--R (- 150a b x - 750a b x - 1080a b x - 480b )\|a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 16 3 2 12 2 3 8 4 4 5 +-+ +--R (30a b x + 420a b x + 1230a b x + 1320a b x + 480b )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 4 16 3 12 2 2 8 3 4 4 +---+ +-+ +--R (- 15a x - 160a b x - 523a b x - 620a b x - 240b )\|- a \|a +--R * +--R +-+ +--R \|b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (- 3a x - 56a b x - 303a b x - 500a b x - 240b x )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 4 18 3 14 2 2 10 3 6 4 2 +---+ +-+ +--R (15a x + 160a b x + 523a b x + 620a b x + 240b x )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +---+ +-+ +--R (3a x + 59a b x + 359a b x + 803a b x + 740a b x + 240b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--R 6 12 5 8 4 2 4 3 3 +---+ +-+ |a x + b +-+ +--R (60a x + 300a b x + 432a b x + 192a b )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 16 6 12 5 2 8 4 3 4 3 4 +---+ +-+ +--R (- 12a x - 168a b x - 492a b x - 528a b x - 192a b )\|- a \|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 390 + +--S 391 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R 4 29 3 25 2 2 21 3 17 4 13 +--R (- 10a x - 160a b x - 672a b x - 1024a b x - 512b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 5 11 +--R - a x - 50a b x - 400a b x - 1120a b x - 1280a b x - 512b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 31 4 27 3 2 23 2 3 19 4 15 +--R 10a x + 170a b x + 832a b x + 1696a b x + 1536a b x +--R + +--R 5 11 +--R 512b x +--R * +--R +-+ +--R \|b +--R + +--R 5 33 4 29 3 2 25 2 3 21 4 17 5 13 +--R (a x + 50a b x + 400a b x + 1120a b x + 1280a b x + 512b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R / +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R a x + 52a b x + 501a b x + 1970a b x + 3920a b x +--R + +--R 2 5 8 6 4 7 +--R 4192a b x + 2304a b x + 512b +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - 10a x - 190a b x - 1182a b x - 3530a b x - 5760a b x +--R + +--R 2 5 8 6 4 7 +--R - 5280a b x - 2560a b x - 512b +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 391 + +)clear all + +--S 392 of 1325 +t0:=x^2/(a+b/x^4)^(5/2) +--R +--R +--R 10 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1325 +--r0:=-1/6*x^3/(a*(a+b/x^4)^(3/2))-3/4*x^3/(a^2*sqrt(a+b/x^4))+_ +-- 5/4*x^3*sqrt(a+b/x^4)/a^3-5/4*(-b)^(3/4)*elliptic_f(_ +-- asin((-b)^(1/4)/(a^(1/4)*x)),-1)*sqrt((a+b/x^4)/a)/(a^(11/4)*_ +-- sqrt(a+b/x^4)) +--E 393 + +--S 394 of 1325 +--a0:=integrate(t0,x) +--E 394 + +--S 395 of 1325 +--m0:=a0-r0 +--E 395 + +--S 396 of 1325 +--d0:=D(m0,x) +--E 396 + +)clear all + +--S 397 of 1325 +t0:=x/(a+b/x^4)^(5/2) +--R +--R +--R 9 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1325 +r0:=-1/6*x^2/(a*(a+b/x^4)^(3/2))-2/3*x^2/(a^2*sqrt(a+b/x^4))+_ + 4/3*x^2*sqrt(a+b/x^4)/a^3 +--R +--R +--R 2 8 4 2 +--R 3a x + 12a b x + 8b +--R (2) ---------------------------- +--R +--------+ +--R | 4 +--R 4 6 3 2 |a x + b +--R (6a x + 6a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 8 4 2 +--R 3a x + 12a b x + 8b +--R (3) ------------------------- +--R +--------+ +--R 4 4 3 | 4 +--R (6a x + 6a b)\|a x + b +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 8 4 2 | 4 +--R (- 3a x - 12a b x - 8b )\|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 |a x + b +--R (3a x + 12a b x + 8b x ) |-------- +--R | 4 +--R \| x +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 6 3 2 |a x + b | 4 +--R (6a x + 6a b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 9 | 4 11 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 2a b x + b ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 401 + +)clear all + +--S 402 of 1325 +t0:=1/(a+b/x^4)^(5/2) +--R +--R +--R 8 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1325 +--r0:=-1/6*x/(a*(a+b/x^4)^(3/2))-7/12*x/(a^2*sqrt(a+b/x^4))+_ +-- 7/4*x*sqrt(a+b/x^4)/a^3+7/4*(-b)^(1/4)*_ +-- elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4))-7/4*(-b)^(1/4)*_ +-- elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(9/4)*sqrt(a+b/x^4)) +--E 403 + +--S 404 of 1325 +--a0:=integrate(t0,x) +--E 404 + +--S 405 of 1325 +--m0:=a0-r0 +--E 405 + +--S 406 of 1325 +--d0:=D(m0,x) +--E 406 + +)clear all + +--S 407 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x) +--R +--R +--R 7 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1325 +r0:=(-1/6)/(a*(a+b/x^4)^(3/2))+1/2*atanh(sqrt(a+b/x^4)/_ + sqrt(a))/a^(5/2)+(-1/2)/(a^2*sqrt(a+b/x^4)) +--R +--R +--R +--------+ +--R | 4 +--R |a x + b +--R +--------+ |-------- +--R | 4 | 4 +--R 4 |a x + b \| x 4 +-+ +--R (3a x + 3b) |-------- atanh(-----------) + (- 4a x - 3b)\|a +--R | 4 +-+ +--R \| x \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R | 4 +--R 3 4 2 +-+ |a x + b +--R (6a x + 6a b)\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 408 + +--S 409 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 +--R (9a x + 21a b x + 12b )\|b \|a x + b - 3a x - 18a b x +--R + +--R 2 4 3 +--R - 27a b x - 12b +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 10 6 2 2 +-+ | 4 +--R (4a x + 19a b x + 12b x )\|a \|a x + b +--R + +--R 2 10 6 2 2 +-+ +-+ +--R (- 12a x - 25a b x - 12b x )\|a \|b +--R / +--R +--------+ +--R 4 8 3 4 2 2 +-+ +-+ | 4 +--R (18a x + 42a b x + 24a b )\|a \|b \|a x + b +--R + +--R 5 12 4 8 3 2 4 2 3 +-+ +--R (- 6a x - 36a b x - 54a b x - 24a b )\|a +--R , +--R +--R +--------+ +--R 2 8 4 2 +-+ | 4 3 12 2 8 +--R (18a x + 42a b x + 24b )\|b \|a x + b - 6a x - 36a b x +--R + +--R 2 4 3 +--R - 54a b x - 24b +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R +--------+ +--R 2 10 6 2 2 +---+ | 4 +--R (4a x + 19a b x + 12b x )\|- a \|a x + b +--R + +--R 2 10 6 2 2 +---+ +-+ +--R (- 12a x - 25a b x - 12b x )\|- a \|b +--R / +--R +--------+ +--R 4 8 3 4 2 2 +---+ +-+ | 4 +--R (18a x + 42a b x + 24a b )\|- a \|b \|a x + b +--R + +--R 5 12 4 8 3 2 4 2 3 +---+ +--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 409 + +--S 410 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b +-+ | 4 +--R (9a x + 21a b x + 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 |a x + b +--R (- 3a x - 18a b x - 27a b x - 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +-+ +-+ 2 | 4 2 +-+ 4 +-+ +--R (\|a \|b - a x )\|a x + b + a x \|b + (- a x - b)\|a +--R log(----------------------------------------------------------) +--R +--------+ +--R +-+ | 4 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b +-+ | 4 +--R (- 9a x - 21a b x - 12b ) |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 |a x + b +--R (3a x + 18a b x + 27a b x + 12b ) |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 8 4 2 +-+ +-+ +--R (12a x + 25a b x + 12b )\|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +--R (4a x + 19a b x + 12b x )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x )\|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 8 3 4 2 2 +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24a b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 12 4 8 3 2 4 2 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24a b )\|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) +--R 4 25 3 21 2 2 17 3 13 4 9 +-+ +--R (9a x + 120a b x + 432a b x + 576a b x + 256b x )\|a +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 25 4 21 3 2 17 2 3 13 4 9 +--R - 9a x - 120a b x - 432a b x - 576a b x - 256a b x +--R * +--R +-+ +--R \|b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (- a x - 40a b x - 240a b x - 448a b x - 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x +--R + +--R 5 7 +--R 256b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R (9a x + 120a b x + 432a b x + 576a b x + 256a b x ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R + +--R 5 27 4 23 3 2 19 2 3 15 4 11 +--R - 9a x - 129a b x - 552a b x - 1008a b x - 832a b x +--R + +--R 5 7 +--R - 256b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 5 29 4 25 3 2 21 2 3 17 4 13 5 9 +--R (- a x - 41a b x - 280a b x - 688a b x - 704a b x - 256b x ) +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R + +--R 6 29 5 25 4 2 21 3 3 17 2 4 13 5 9 +--R a x + 41a b x + 280a b x + 688a b x + 704a b x + 256a b x +--R / +--R 7 26 6 22 5 2 18 4 3 14 3 4 10 +--R 9a x + 138a b x + 681a b x + 1560a b x + 1840a b x +--R + +--R 2 5 6 6 2 +--R 1088a b x + 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 2 5 8 6 4 7 +--R - 2352a b x - 1216a b x - 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +--R \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 7 28 6 24 5 2 20 4 3 16 3 4 12 +--R 9a x + 147a b x + 819a b x + 2241a b x + 3400a b x +--R + +--R 2 5 8 6 4 7 +--R 2928a b x + 1344a b x + 256b +--R * +--R +--------+ +--R | 4 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 8 30 7 26 6 2 22 5 3 18 4 4 14 +--R - a x - 43a b x - 363a b x - 1289a b x - 2360a b x +--R + +--R 3 5 10 2 6 6 7 2 +--R - 2352a b x - 1216a b x - 256a b x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1325 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 +---+ |a x + b +-+ | 4 +--R (- 9a x - 21a b x - 12b )\|- a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 +---+ |a x + b +--R (3a x + 18a b x + 27a b x + 12b )\|- a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R |a x + b +--R |-------- +--R | 4 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24b )\|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 3 12 2 8 2 4 3 +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24b )\|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R +---+ | 4 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R 2 +--R a x +--R + +--R 2 8 4 2 +---+ +-+ +-+ +--R (12a x + 25a b x + 12b )\|- a \|a \|b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +--R (4a x + 19a b x + 12b x )\|- a \|a |-------- +--R | 4 +--R \| x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R +--------+ +--R | 4 +--R 2 10 6 2 2 +---+ +-+ |a x + b +-+ +--R (- 12a x - 25a b x - 12b x )\|- a \|a |-------- \|b +--R | 4 +--R \| x +--R + +--R 3 12 2 8 2 4 3 +---+ +-+ +--R (- 4a x - 23a b x - 31a b x - 12b )\|- a \|a +--R / +--R +--------+ +--R | 4 +--------+ +--R 4 8 3 4 2 2 +---+ +-+ |a x + b +-+ | 4 +--R (18a x + 42a b x + 24a b )\|- a \|a |-------- \|b \|a x + b +--R | 4 +--R \| x +--R + +--R +--------+ +--R | 4 +--R 5 12 4 8 3 2 4 2 3 +---+ +-+ |a x + b +--R (- 6a x - 36a b x - 54a b x - 24a b )\|- a \|a |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) +--R +--------+ +--R | 4 +--R 2 17 13 2 9 |a x + b +-+ 3 19 2 15 +--R (- 6a x - 32a b x - 32b x ) |-------- \|b - a x - 18a b x +--R | 4 +--R \| x +--R + +--R 2 11 3 7 +--R - 48a b x - 32b x +--R * +--R +--------+ +--R | 4 +--R \|a x + b +--R + +--R 3 19 2 15 2 11 3 7 +-+ +--R (6a x + 38a b x + 64a b x + 32b x )\|b +--R + +--R +--------+ +--R | 4 +--R 3 21 2 17 2 13 3 9 |a x + b +--R (a x + 18a b x + 48a b x + 32b x ) |-------- +--R | 4 +--R \| x +--R / +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R (a x + 20a b x + 85a b x + 146a b x + 112a b x + 32b ) +--R * +--R +--------+ +--R | 4 +--------+ +--R |a x + b | 4 +--R |-------- \|a x + b +--R | 4 +--R \| x +--R + +--R 5 20 4 16 3 2 12 2 3 8 4 4 5 +--R (- 6a x - 50a b x - 146a b x - 198a b x - 128a b x - 32b ) +--R * +--R +--------+ +--R | 4 +--R |a x + b +-+ +--R |-------- \|b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^2) +--R +--R +--R 6 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1325 +--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x)+(-5/12)/(a^2*x*sqrt(a+b/x^4))-_ +-- 5/12*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(7/4)*(-b)^(1/4)*sqrt(a+b/x^4)) +--E 415 + +--S 416 of 1325 +--a0:=integrate(t0,x) +--E 416 + +--S 417 of 1325 +--m0:=a0-r0 +--E 417 + +--S 418 of 1325 +--d0:=D(m0,x) +--E 418 + +)clear all + +--S 419 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^3) +--R +--R +--R 5 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1325 +r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^2)+(-1/3)/(a^2*x^2*sqrt(a+b/x^4)) +--R +--R +--R 4 +--R - 3a x - 2b +--R (2) ---------------------------- +--R +--------+ +--R | 4 +--R 3 6 2 2 |a x + b +--R (6a x + 6a b x ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +--R - 3a x - 2b +--R (3) ------------------------- +--R +--------+ +--R 3 4 2 | 4 +--R (6a x + 6a b)\|a x + b +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 4 | 4 6 2 |a x + b +--R (3a x + 2b)\|a x + b + (- 3a x - 2b x ) |-------- +--R | 4 +--R \| x +--R (4) ------------------------------------------------------ +--R +--------+ +--R | 4 +--------+ +--R 3 6 2 2 |a x + b | 4 +--R (6a x + 6a b x ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1325 +d0:=D(m0,x) +--R +--R +--R +--------+ +--R +--------+ | 4 +--R 5 | 4 7 |a x + b +--R - x \|a x + b + x |-------- +--R | 4 +--R \| x +--R (5) ------------------------------------------- +--R +--------+ +--R | 4 +--------+ +--R 2 8 4 2 |a x + b | 4 +--R (a x + 2a b x + b ) |-------- \|a x + b +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1325 +t0:=1/((a+b/x^4)^(5/2)*x^4) +--R +--R +--R 4 +--R x +--R (1) -------------------------------- +--R +--------+ +--R | 4 +--R 2 8 4 2 |a x + b +--R (a x + 2a b x + b ) |-------- +--R | 4 +--R \| x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1325 +--r0:=(-1/6)/(a*(a+b/x^4)^(3/2)*x^3)+(-1/4)/(a^2*x^3*sqrt(a+b/x^4))+_ +-- 1/4*elliptic_e(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4))-_ +-- 1/4*elliptic_f(asin((-b)^(1/4)/(a^(1/4)*x)),-1)*_ +-- sqrt((a+b/x^4)/a)/(a^(5/4)*(-b)^(3/4)*sqrt(a+b/x^4)) +--E 425 + +--S 426 of 1325 +--a0:=integrate(t0,x) +--E 426 + +--S 427 of 1325 +--m0:=a0-r0 +--E 427 + +--S 428 of 1325 +--d0:=D(m0,x) +--E 428 + +)clear all + +--S 429 of 1325 +t0:=1/(a+b/x^5) +--R +--R +--R 5 +--R x +--R (1) -------- +--R 5 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 429 + +--S 430 of 1325 +r0:=x/a-1/5*b^(1/5)*log(b^(1/5)+a^(1/5)*x)/a^(6/5)+1/20*b^(1/5)*_ + log(2*b^(2/5)+2*a^(2/5)*x^2-a^(1/5)*b^(1/5)*x*(1-sqrt(5)))*_ + (1-sqrt(5))/a^(6/5)+1/20*b^(1/5)*log(2*b^(2/5)+2*a^(2/5)*x^2-_ + a^(1/5)*b^(1/5)*x*(1+sqrt(5)))*(1+sqrt(5))/a^(6/5)+1/5*b^(1/5)*_ + atan(1/2*(-4*a^(1/5)*x+b^(1/5)*(1+sqrt(5)))*sqrt(5+sqrt(5))/_ + (b^(1/5)*sqrt(10)))*sqrt(1/2*(5-sqrt(5)))/a^(6/5)+1/5*b^(1/5)*_ + atan((-4*a^(1/5)*x+b^(1/5)*(1-sqrt(5)))/(b^(1/5)*sqrt(2*_ + (5+sqrt(5)))))*sqrt(1/2*(5+sqrt(5)))/a^(6/5) +--R +--R +--R (2) +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (- \|2 \|5 + \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (\|2 \|5 + \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+5+-+ 5+-+ 5+-+ +--R - 4\|2 \|b log(\|b + x\|a ) +--R + +--R +--------+ +--R +----------+ +-+ 5+-+ 5+-+ | +-+ +--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5 +--R 4\|- \|5 + 5 \|b atan(------------------------------------) +--R +--+5+-+ +--R 2\|10 \|b +--R + +--R +--------+ +-+ 5+-+ 5+-+ +--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a +-+5+-+ +--R - 4\|b \|\|5 + 5 atan(-----------------------) + 20x\|2 \|a +--R +----------+ +--R 5+-+ | +-+ +--R \|b \|2\|5 + 10 +--R / +--R +-+5+-+ +--R 20a\|2 \|a +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CZ1 - 5a %%CZ0 - 5|- - +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R - 5a %%CZ1 - 5a %%CZ0 - 5|- - +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R 10a %%CZ1 log(- 5a %%CZ1 + x) + 10a %%CZ0 log(- 5a %%CZ0 + x) +--R + +--R +---+ +---+ +--R | b | b +--R 2 5|- - log(- 5|- - + x + 10x +--R \| a \| a +--R / +--R 10a +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+5+-+ +--R 10a\|2 \|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R +-+5+-+ +-+5+-+ +-+ | b 5+-+ +--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a +--R \| a +--R * +--R log +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R +-+5+-+ +--R 10a\|2 \|a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b 2 2 +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 - 75a %%CZ0 +--R \| a +--R + +--R +---+ +---+2 +--R | b | b +--R - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R +-+5+-+ +-+5+-+ +-+ | b 5+-+ +--R - 10a\|2 \|a %%CZ1 - 10a\|2 \|a %%CZ0 - 2\|2 5|- - \|a +--R \| a +--R * +--R log +--R - +--R 5a +--R * +--R ROOT +--R +---+ +--R 2 2 2 | b +--R - 75a %%CZ1 + (- 50a %%CZ0 - 10a 5|- -)%%CZ1 +--R \| a +--R + +--R +---+ +---+2 +--R 2 2 | b | b +--R - 75a %%CZ0 - 10a 5|- - %%CZ - 3 5|- - +--R \| a \| a +--R / +--R 2 +--R 25a +--R + +--R +---+ +--R | b +--R 5a %%CZ1 + 5a %%CZ0 + 5|- - + 2x +--R \| a +--R + +--R +-+5+-+ +--R 20a\|2 \|a %%CZ1 log(- 5a %%CZ1 + x) +--R + +--R +-+5+-+ +--R 20a\|2 \|a %%CZ0 log(- 5a %%CZ0 + x) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (\|2 \|5 - \|2 )\|b log(2\|b + (x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +-+ +-+ +-+ 5+-+ 5+-+2 +-+ 5+-+5+-+ 2 5+-+2 +--R (- \|2 \|5 - \|2 )\|b log(2\|b + (- x\|5 - x)\|a \|b + 2x \|a ) +--R + +--R +---+ +---+ +--R +-+5+-+ 5+-+ 5+-+ +-+ | b 5+-+ | b +--R 4\|2 \|b log(\|b + x\|a ) + 4\|2 5|- - \|a log(- 5|- - + x) +--R \| a \| a +--R + +--R +--------+ +--R +----------+ +-+ 5+-+ 5+-+ | +-+ +--R | +-+ 5+-+ ((\|5 + 1)\|b - 4x\|a )\|\|5 + 5 +--R - 4\|- \|5 + 5 \|b atan(------------------------------------) +--R +--+5+-+ +--R 2\|10 \|b +--R + +--R +--------+ +-+ 5+-+ 5+-+ +--R 5+-+ | +-+ (\|5 - 1)\|b + 4x\|a +--R 4\|b \|\|5 + 5 atan(-----------------------) +--R +----------+ +--R 5+-+ | +-+ +--R \|b \|2\|5 + 10 +--R / +--R +-+5+-+ +--R 20a\|2 \|a +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-+ +-+ +-+ 5+-+4 +-+ +-+ +-+ 5+-+5+-+3 +--R (\|2 \|5 + 5\|2 )\|b + (- 3x\|2 \|5 - 5x\|2 )\|a \|b +--R + +--R 2 +-+ +-+ 2 +-+ 5+-+2 5+-+2 +--R (x \|2 \|5 + 5x \|2 )\|a \|b +--R * +--R +--------+ +----------+ +--R | +-+ | +-+ +--R \|\|5 + 5 \|2\|5 + 10 +--R + +--R +----------+ +--R +-+ +--+ | +-+ 5+-+4 +--R 2\|2 \|10 \|- \|5 + 5 \|b +--R + +--R +----------+ +--R +-+ +-+ +-+ +--+ | +-+ 5+-+5+-+3 +--R (x\|2 \|5 - x\|2 )\|10 \|- \|5 + 5 \|a \|b +--R + +--R +----------+ +--R 2 +-+ +--+ | +-+ 5+-+2 5+-+2 +--R 2x \|2 \|10 \|- \|5 + 5 \|a \|b +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R +-+ 5+-+4 +-+ 5+-+5+-+3 +--R (- 20\|5 - 100)\|b + (20x\|5 + 100x)\|a \|b +--R + +--R 2 +-+ 2 5+-+2 5+-+2 +--R (- 20x \|5 - 100x )\|a \|b +--R / +--R +-+ 5+-+4 +-+ 5+-+5+-+3 +--R (40a\|5 + 200a)\|b + (- 40a x\|5 - 200a x)\|a \|b +--R + +--R 2 +-+ 2 5+-+2 5+-+2 3 +-+ 3 5+-+3 5+-+ +--R (40a x \|5 + 200a x )\|a \|b + (- 40a x \|5 - 200a x )\|a \|b +--R + +--R 4 +-+ 4 5+-+4 +--R (40a x \|5 + 200a x )\|a +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1325 +t0:=1/(x*sqrt(a+b/x^5)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | 5 +--R |a x + b +--R x |-------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1325 +r0:=2/5*atanh(sqrt(a+b/x^5)/sqrt(a))/sqrt(a) +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R |-------- +--R | 5 +--R \| x +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) ------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ +-+ | 5 +--R |1 3 |1 |a x + b 5 +--R |- log(2a x |- |-------- - 2a x - b) +--R \|a \|a \| x +--R (3) - ----------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1325 +m0:=a0-r0 +--R +--R +--R +--------+ +--R | 5 +--R |a x + b +--R +--------+ |-------- +--R +-+ +-+ | 5 | 5 +--R |1 +-+ 3 |1 |a x + b 5 \| x +--R - |- \|a log(2a x |- |-------- - 2a x - b) - 2atanh(-----------) +--R \|a \|a \| x +-+ +--R \|a +--R (4) --------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +--------+ +--------+ +--R +-+ | 5 | 5 +--R 5 |1 |a x + b 5 |a x + b +--R (- 2a x |- |-------- - 2a x - b) |-------- +--R \|a | 5 \| x +--R \| x +--R + +--R +--------+ +--R | 5 +-+ +--R 7 2 |a x + b 2 7 2 |1 +--R (2a x + b x ) |-------- + (2a x + 2a b x ) |- +--R | 5 \|a +--R \| x +--R / +--R +--------+ +--------+ +--------+ +--R | 5 | 5 +-+ | 5 +--R 6 |a x + b |a x + b 2 8 3 |1 |a x + b +--R (2a x + b x) |-------- |-------- + (- 2a x - 2a b x ) |- |-------- +--R | 5 \| x \|a | 5 +--R \| x \| x +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1325 +t0:=1/(x*sqrt(-a+b/x^5)) +--R +--R +--R 1 +--R (1) -------------- +--R +----------+ +--R | 5 +--R |- a x + b +--R x |---------- +--R | 5 +--R \| x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1325 +r0:=-2/5*atan(sqrt(-a+b/x^5)/sqrt(a))/sqrt(a) +--R +--R +--R +----------+ +--R | 5 +--R |- a x + b +--R |---------- +--R | 5 +--R \| x +--R 2atan(-------------) +--R +-+ +--R \|a +--R (2) - -------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +----------+ +--R +---+ | 5 +---+ +--R | 1 3 |- a x + b | 1 5 +--R |- - log(2a x |---------- |- - - 2a x + b) +--R \| a \| x \| a +--R (3) - ----------------------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------+ +--R | 5 +--R |- a x + b +--R +----------+ |---------- +--R +---+ | 5 +---+ | 5 +--R | 1 +-+ 3 |- a x + b | 1 5 \| x +--R - |- - \|a log(2a x |---------- |- - - 2a x + b) + 2atan(-------------) +--R \| a \| x \| a +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +-+ +--R 5\|a +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) +--R +----------+ +----------+ +--R | 5 | 5 +---+ +--R 5 |- a x + b |- a x + b 2 7 2 | 1 +--R (- 2a x |---------- |---------- - 2a x + 2a b x ) |- - +--R \| x | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 7 2 |- a x + b 5 |- a x + b +--R (2a x - b x ) |---------- + (- 2a x + b) |---------- +--R | 5 \| x +--R \| x +--R / +--R +----------+ +--R | 5 +---+ +--R 2 8 3 |- a x + b | 1 +--R (2a x - 2a b x ) |---------- |- - +--R | 5 \| a +--R \| x +--R + +--R +----------+ +----------+ +--R | 5 | 5 +--R 6 |- a x + b |- a x + b +--R (2a x - b x) |---------- |---------- +--R \| x | 5 +--R \| x +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1325 +t0:=1/(a+b/x^6) +--R +--R +--R 6 +--R x +--R (1) -------- +--R 6 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 444 + +--S 445 of 1325 +r0:=x/a-1/3*b^(1/6)*atan(a^(1/6)*x/b^(1/6))/a^(7/6)-1/3*atan(a^(1/6)*x*_ + sqrt(2)/sqrt(-b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(-b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2))-1/3*atanh(a^(1/6)*x*_ + sqrt(2)/sqrt(b^(1/3)+sqrt(3)*sqrt(-b^(2/3))))*sqrt(b^(1/3)+_ + sqrt(3)*sqrt(-b^(2/3)))/(a^(7/6)*sqrt(2)) +--R +--R +--R (2) +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R - \|\|3 \|- \|b + \|b atanh(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R - \|\|3 \|- \|b - \|b atan(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b +--R + +--R 6+-+ +--R +-+6+-+ x\|a +-+6+-+ +--R - \|2 \|b atan(-----) + 3x\|2 \|a +--R 6+-+ +--R \|b +--R / +--R +-+6+-+ +--R 3a\|2 \|a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R - a |- ------- log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R | b 2 | b | b 2 +--R a |- ------- log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R - 2a |- ------- log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R | b | b +--R 2a |- ------- log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R - 2a\|3 |- ------- atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ | b \| 46656a +--R 2a\|3 |- ------- atan(------------------ + 2x +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R 2a +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R 2\|\|3 \|- \|b + \|b atanh(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b + \|b +--R + +--R +---------------------+ +--R | +-------+ +-+6+-+ +--R | +-+ | 3+-+2 3+-+ x\|2 \|a +--R 2\|\|3 \|- \|b - \|b atan(------------------------) +--R +---------------------+ +--R | +-------+ +--R | +-+ | 3+-+2 3+-+ +--R \|\|3 \|- \|b - \|b +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | b 6+-+ 2 | b | b 2 +--R - 3a\|2 |- ------- \|a log(36a |- ------- + 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+2 +---------+ +--R +-+ | b 6+-+ 2 | b | b 2 +--R 3a\|2 |- ------- \|a log(36a |- ------- - 6a x |- ------- + x ) +--R 6| 7 6| 7 6| 7 +--R \| 46656a \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R +-+ | b 6+-+ | b +--R - 6a\|2 |- ------- \|a log(6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +---------+ +--R +-+ | b 6+-+ | b +--R 6a\|2 |- ------- \|a log(- 6a |- ------- + x) +--R 6| 7 6| 7 +--R \| 46656a \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 +--R +-+ +-+ | b 6+-+ \| 46656a +--R - 6a\|2 \|3 |- ------- \|a atan(------------------) +--R 6| 7 +---------+ +--R \| 46656a | b +--R 3a |- ------- - x +--R 6| 7 +--R \| 46656a +--R + +--R +---------+ +--R +-+ | b +--R 3a\|3 |- ------- +--R +---------+ 6| 7 6+-+ +--R +-+ +-+ | b 6+-+ \| 46656a +-+6+-+ x\|a +--R 6a\|2 \|3 |- ------- \|a atan(------------------ + 2\|2 \|b atan(-----) +--R 6| 7 +---------+ 6+-+ +--R \| 46656a | b \|b +--R 3a |- ------- + x +--R 6| 7 +--R \| 46656a +--R / +--R +-+6+-+ +--R 6a\|2 \|a +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1325 +t0:=1/(a+b/x^8) +--R +--R +--R 8 +--R x +--R (1) -------- +--R 8 +--R a x + b +--R Type: Fraction(Polynomial(Integer)) +--E 449 + +--S 450 of 1325 +r0:=x/a-1/4*(-b)^(1/8)*atan(a^(1/8)*x/(-b)^(1/8))/a^(9/8)-1/4*(-b)^(1/8)*_ + atanh(a^(1/8)*x/(-b)^(1/8))/a^(9/8)+1/4*(-b)^(1/8)*atan(1-a^(1/8)*_ + x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))-1/4*(-b)^(1/8)*atan(1+_ + a^(1/8)*x*sqrt(2)/(-b)^(1/8))/(a^(9/8)*sqrt(2))+1/8*(-b)^(1/8)*_ + log((-b)^(1/4)+a^(1/4)*x^2-a^(1/8)*(-b)^(1/8)*x*sqrt(2))/(a^(9/8)*_ + sqrt(2))-1/8*(-b)^(1/8)*log((-b)^(1/4)+a^(1/4)*x^2+a^(1/8)*_ + (-b)^(1/8)*x*sqrt(2))/(a^(9/8)*sqrt(2)) +--R +--R +--R (2) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- b log(x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R 8+-+ +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +-+8+---+ x\|a +--R \|- b log(- x\|2 \|- b \|a + x \|a + \|- b ) - 2\|2 \|- b atanh(------) +--R 8+---+ +--R \|- b +--R + +--R +-+8+-+ 8+---+ +-+8+-+ 8+---+ +--R 8+---+ x\|2 \|a + \|- b 8+---+ x\|2 \|a - \|- b +--R - 2\|- b atan(------------------) - 2\|- b atan(------------------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R 8+-+ +--R +-+8+---+ x\|a +-+8+-+ +--R - 2\|2 \|- b atan(------) + 8x\|2 \|a +--R 8+---+ +--R \|- b +--R / +--R +-+8+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +------------+ +--R | b +--R a |- ---------- +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- + 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+2 +------------+ +--R | b 2 | b +-+ | b 2 +--R a |- ---------- log(64a |- ---------- - 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 8| 9 +--R \| 16777216a \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b | b +--R - a\|2 |- ---------- log(8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b | b +--R a\|2 |- ---------- log(- 8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b \| 16777216a +--R 2a\|2 |- ---------- atan(-----------------) +--R 8| 9 x +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +--R - 2a |- ---------- atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b \| 16777216a +-+ +--R 2a |- ---------- atan(------------------------- + x\|2 +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+ +--R a\|2 +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R \|- b log(x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R - +--R +------------+ +--R | b 8+-+ +--R 8a |- ---------- \|a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- + 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +--R | b 8+-+ +--R 8a |- ---------- \|a +--R 8| 9 +--R \| 16777216a +--R * +--R +------------+2 +------------+ +--R 2 | b +-+ | b 2 +--R log(64a |- ---------- - 8a x\|2 |- ---------- + x ) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b 8+-+ | b +--R - 8a\|2 |- ---------- \|a log(8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R +------------+ +------------+ +--R +-+ | b 8+-+ | b +--R 8a\|2 |- ---------- \|a log(- 8a |- ---------- + x) +--R 8| 9 8| 9 +--R \| 16777216a \| 16777216a +--R + +--R 8+---+ +-+8+---+8+-+ 2 4+-+ 4+---+ +--R - \|- b log(- x\|2 \|- b \|a + x \|a + \|- b ) +--R + +--R 8+-+ +-+8+-+ 8+---+ +--R +-+8+---+ x\|a 8+---+ x\|2 \|a + \|- b +--R 2\|2 \|- b atanh(------) + 2\|- b atan(------------------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R +-+8+-+ 8+---+ 8+-+ +--R 8+---+ x\|2 \|a - \|- b +-+8+---+ x\|a +--R 2\|- b atan(------------------) + 2\|2 \|- b atan(------) +--R 8+---+ 8+---+ +--R \|- b \|- b +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R +-+ | b 8+-+ \| 16777216a +--R 16a\|2 |- ---------- \|a atan(-----------------) +--R 8| 9 x +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b 8+-+ \| 16777216a +--R - 16a |- ---------- \|a atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- - x\|2 +--R 8| 9 +--R \| 16777216a +--R + +--R +------------+ +--R | b +--R 8a |- ---------- +--R +------------+ 8| 9 +--R | b 8+-+ \| 16777216a +--R 16a |- ---------- \|a atan(-------------------------) +--R 8| 9 +------------+ +--R \| 16777216a | b +-+ +--R 8a |- ---------- + x\|2 +--R 8| 9 +--R \| 16777216a +--R / +--R +-+8+-+ +--R 8a\|2 \|a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1325 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1325 +t0:=x^m*(a+b*sqrt(x))^p +--R +--R +--R m +-+ p +--R (1) x (b\|x + a) +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1325 +--r0:=2*x^(1/2*(1+2*m))*(a+b*sqrt(x))^(1+p)/(b*(2+2*m+p))-_ +-- 2*a*(1+2*m)*x^m*hypergeometric(-2*m,1+p,2+p,(a+b*sqrt(x))/a)*_ +-- (a+b*sqrt(x))^(1+p)/(b^2*(1+p)*(2+2*m+p)*(-b*sqrt(x)/a)^(2*m)) +--E 455 + +--S 456 of 1325 +--a0:=integrate(t0,x) +--E 456 + +--S 457 of 1325 +--m0:=a0-r0 +--E 457 + +--S 458 of 1325 +--d0:=D(m0,x) +--E 458 + +)clear all + +--S 459 of 1325 +t0:=x^m*(a+b*sqrt(x)) +--R +--R +--R m +-+ m +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1325 +r0:=a*x^(1+m)/(1+m)+2*b*x^(3/2+m)/(3+2*m) +--R +--R +--R 2m + 3 +--R ------ +--R 2 m + 1 +--R (2b m + 2b)x + (2a m + 3a)x +--R (2) -------------------------------------- +--R 2 +--R 2m + 5m + 3 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ m log(x) +--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e +--R (3) ------------------------------------------- +--R 2 +--R 2m + 5m + 3 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 2m + 3 +--R ------ +--R +-+ m log(x) 2 +--R ((2b m + 2b)x\|x + (2a m + 3a)x)%e + (- 2b m - 2b)x +--R + +--R m + 1 +--R (- 2a m - 3a)x +--R / +--R 2 +--R 2m + 5m + 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1325 +t0:=x^4*(a+b*sqrt(x)) +--R +--R +--R 4 +-+ 4 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1325 +r0:=1/5*a*x^5+2/11*b*x^(11/2) +--R +--R +--R 5 +-+ 5 +--R 10b x \|x + 11a x +--R (2) ------------------- +--R 55 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ 5 +--R 10b x \|x + 11a x +--R (3) ------------------- +--R 55 +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1325 +t0:=x^3*(a+b*sqrt(x)) +--R +--R +--R 3 +-+ 3 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1325 +r0:=1/4*a*x^4+2/9*b*x^(9/2) +--R +--R +--R 4 +-+ 4 +--R 8b x \|x + 9a x +--R (2) ----------------- +--R 36 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ 4 +--R 8b x \|x + 9a x +--R (3) ----------------- +--R 36 +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1325 +t0:=x^2*(a+b*sqrt(x)) +--R +--R +--R 2 +-+ 2 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1325 +r0:=1/3*a*x^3+2/7*b*x^(7/2) +--R +--R +--R 3 +-+ 3 +--R 6b x \|x + 7a x +--R (2) ----------------- +--R 21 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 +--R 6b x \|x + 7a x +--R (3) ----------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1325 +t0:=x*(a+b*sqrt(x)) +--R +--R +--R +-+ +--R (1) b x\|x + a x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1325 +r0:=1/2*a*x^2+2/5*b*x^(5/2) +--R +--R +--R 2 +-+ 2 +--R 4b x \|x + 5a x +--R (2) ----------------- +--R 10 +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 +--R 4b x \|x + 5a x +--R (3) ----------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1325 +t0:=a+b*sqrt(x) +--R +--R +--R +-+ +--R (1) b\|x + a +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1325 +r0:=a*x+2/3*b*x^(3/2) +--R +--R +--R +-+ +--R 2b x\|x + 3a x +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2b x\|x + 3a x +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1325 +t0:=(a+b*sqrt(x))/x +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1325 +r0:=a*log(x)+2*b*sqrt(x) +--R +--R +--R +-+ +--R (2) 2b\|x + a log(x) +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) 2a log(\|x ) + 2b\|x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1325 +t0:=(a+b*sqrt(x))/x^2 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1325 +r0:=-a/x-2*b/sqrt(x) +--R +--R +--R +-+ +--R - a\|x - 2b x +--R (2) -------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 2b\|x - a +--R (3) ------------ +--R x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1325 +t0:=(a+b*sqrt(x))/x^3 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1325 +r0:=-1/2*a/x^2-2/3*b/x^(3/2) +--R +--R +--R +-+ +--R - 3a\|x - 4b x +--R (2) --------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 4b\|x - 3a +--R (3) ------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1325 +t0:=(a+b*sqrt(x))/x^4 +--R +--R +--R +-+ +--R b\|x + a +--R (1) --------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1325 +r0:=-1/3*a/x^3-2/5*b/x^(5/2) +--R +--R +--R +-+ +--R - 5a\|x - 6b x +--R (2) --------------- +--R 3 +-+ +--R 15x \|x +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 6b\|x - 5a +--R (3) ------------- +--R 3 +--R 15x +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1325 +t0:=x^m*(a+b*sqrt(x))^2 +--R +--R +--R m +-+ 2 2 m +--R (1) 2a b x \|x + (b x + a )x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1325 +r0:=a^2*x^(1+m)/(1+m)+4*a*b*x^(3/2+m)/(3+2*m)+b^2*x^(2+m)/(2+m) +--R +--R +--R (2) +--R 2m + 3 +--R ------ +--R 2 2 2 2 m + 2 2 2 +--R (2b m + 5b m + 3b )x + (4a b m + 12a b m + 8a b)x +--R + +--R 2 2 2 2 m + 1 +--R (2a m + 7a m + 6a )x +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 2 2 2 2 +--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x +--R + +--R 2 2 2 2 +--R (2a m + 7a m + 6a )x +--R * +--R m log(x) +--R %e +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 +-+ 2 2 2 2 2 +--R (4a b m + 12a b m + 8a b)x\|x + (2b m + 5b m + 3b )x +--R + +--R 2 2 2 2 +--R (2a m + 7a m + 6a )x +--R * +--R m log(x) +--R %e +--R + +--R 2m + 3 +--R ------ +--R 2 2 2 2 m + 2 2 2 +--R (- 2b m - 5b m - 3b )x + (- 4a b m - 12a b m - 8a b)x +--R + +--R 2 2 2 2 m + 1 +--R (- 2a m - 7a m - 6a )x +--R / +--R 3 2 +--R 2m + 9m + 13m + 6 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1325 +t0:=x^4*(a+b*sqrt(x))^2 +--R +--R +--R 4 +-+ 2 5 2 4 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1325 +r0:=1/5*a^2*x^5+4/11*a*b*x^(11/2)+1/6*b^2*x^6 +--R +--R +--R 5 +-+ 2 6 2 5 +--R 120a b x \|x + 55b x + 66a x +--R (2) ------------------------------- +--R 330 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 +-+ 2 6 2 5 +--R 120a b x \|x + 55b x + 66a x +--R (3) ------------------------------- +--R 330 +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1325 +t0:=x^3*(a+b*sqrt(x))^2 +--R +--R +--R 3 +-+ 2 4 2 3 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1325 +r0:=1/4*a^2*x^4+4/9*a*b*x^(9/2)+1/5*b^2*x^5 +--R +--R +--R 4 +-+ 2 5 2 4 +--R 80a b x \|x + 36b x + 45a x +--R (2) ------------------------------ +--R 180 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 +-+ 2 5 2 4 +--R 80a b x \|x + 36b x + 45a x +--R (3) ------------------------------ +--R 180 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1325 +t0:=x^2*(a+b*sqrt(x))^2 +--R +--R +--R 2 +-+ 2 3 2 2 +--R (1) 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1325 +r0:=1/3*a^2*x^3+4/7*a*b*x^(7/2)+1/4*b^2*x^4 +--R +--R +--R 3 +-+ 2 4 2 3 +--R 48a b x \|x + 21b x + 28a x +--R (2) ------------------------------ +--R 84 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 2 4 2 3 +--R 48a b x \|x + 21b x + 28a x +--R (3) ------------------------------ +--R 84 +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1325 +t0:=x*(a+b*sqrt(x))^2 +--R +--R +--R +-+ 2 2 2 +--R (1) 2a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1325 +r0:=1/2*a^2*x^2+4/5*a*b*x^(5/2)+1/3*b^2*x^3 +--R +--R +--R 2 +-+ 2 3 2 2 +--R 24a b x \|x + 10b x + 15a x +--R (2) ------------------------------ +--R 30 +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 3 2 2 +--R 24a b x \|x + 10b x + 15a x +--R (3) ------------------------------ +--R 30 +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 533 + +)clear all + +--S 534 of 1325 +t0:=(a+b*sqrt(x))^2 +--R +--R +--R +-+ 2 2 +--R (1) 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1325 +r0:=a^2*x+4/3*a*b*x^(3/2)+1/2*b^2*x^2 +--R +--R +--R +-+ 2 2 2 +--R 8a b x\|x + 3b x + 6a x +--R (2) ------------------------- +--R 6 +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 2 +--R 8a b x\|x + 3b x + 6a x +--R (3) ------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1325 +t0:=(a+b*sqrt(x))^2/x +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1325 +r0:=b^2*x+a^2*log(x)+4*a*b*sqrt(x) +--R +--R +--R +-+ 2 2 +--R (2) 4a b\|x + a log(x) + b x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +-+ 2 +--R (3) 2a log(\|x ) + 4a b\|x + b x +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1325 +t0:=(a+b*sqrt(x))^2/x^2 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1325 +r0:=-a^2/x+b^2*log(x)-4*a*b/sqrt(x) +--R +--R +--R 2 2 +-+ +--R (b x log(x) - a )\|x - 4a b x +--R (2) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +-+ 2 +--R 2b x log(\|x ) - 4a b\|x - a +--R (3) ------------------------------ +--R x +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 2b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 548 + +)clear all + +--S 549 of 1325 +t0:=(a+b*sqrt(x))^2/x^3 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1325 +r0:=-1/2*a^2/x^2-4/3*a*b/x^(3/2)-b^2/x +--R +--R +--R 2 2 +-+ +--R (- 6b x - 3a )\|x - 8a b x +--R (2) --------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 8a b\|x - 6b x - 3a +--R (3) ----------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 551 + +--S 552 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 1325 +t0:=(a+b*sqrt(x))^2/x^4 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1325 +r0:=-1/3*a^2/x^3-4/5*a*b/x^(5/2)-1/2*b^2/x^2 +--R +--R +--R 2 2 +-+ +--R (- 15b x - 10a )\|x - 24a b x +--R (2) ------------------------------ +--R 3 +-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 24a b\|x - 15b x - 10a +--R (3) -------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 556 + +--S 557 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1325 +t0:=(a+b*sqrt(x))^2/x^5 +--R +--R +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R (1) ------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1325 +r0:=-1/4*a^2/x^4-4/7*a*b/x^(7/2)-1/3*b^2/x^3 +--R +--R +--R 2 2 +-+ +--R (- 28b x - 21a )\|x - 48a b x +--R (2) ------------------------------ +--R 4 +-+ +--R 84x \|x +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 2 +--R - 48a b\|x - 28b x - 21a +--R (3) -------------------------- +--R 4 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 561 + +--S 562 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 563 + +)clear all + +--S 564 of 1325 +t0:=x^m*(a+b*sqrt(x))^3 +--R +--R +--R 3 2 m +-+ 2 3 m +--R (1) (b x + 3a b)x \|x + (3a b x + a )x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1325 +r0:=a^3*x^(1+m)/(1+m)+6*a^2*b*x^(3/2+m)/(3+2*m)+3*a*b^2*x^(2+m)/(2+m)+_ + 2*b^3*x^(5/2+m)/(5+2*m) +--R +--R +--R (2) +--R 2m + 5 +--R ------ +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 2m + 3 +--R ------ +--R 2 3 2 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (4a m + 24a m + 47a m + 30a )x +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R * +--R +-+ +--R \|x +--R + +--R 2 3 2 2 2 2 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 3 3 3 2 3 3 +--R (4a m + 24a m + 47a m + 30a )x +--R * +--R m log(x) +--R %e +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Union(Expression(Integer),...) +--E 566 + +--S 567 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 3 2 3 3 2 +--R (4b m + 18b m + 26b m + 12b )x +--R + +--R 2 3 2 2 2 2 +--R (12a b m + 66a b m + 114a b m + 60a b)x +--R * +--R +-+ +--R \|x +--R + +--R 2 3 2 2 2 2 2 +--R (12a b m + 60a b m + 93a b m + 45a b )x +--R + +--R 3 3 3 2 3 3 +--R (4a m + 24a m + 47a m + 30a )x +--R * +--R m log(x) +--R %e +--R + +--R 2m + 5 +--R ------ +--R 3 3 3 2 3 3 2 +--R (- 4b m - 18b m - 26b m - 12b )x +--R + +--R 2 3 2 2 2 2 m + 2 +--R (- 12a b m - 60a b m - 93a b m - 45a b )x +--R + +--R 2m + 3 +--R ------ +--R 2 3 2 2 2 2 2 +--R (- 12a b m - 66a b m - 114a b m - 60a b)x +--R + +--R 3 3 3 2 3 3 m + 1 +--R (- 4a m - 24a m - 47a m - 30a )x +--R / +--R 4 3 2 +--R 4m + 28m + 71m + 77m + 30 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 568 + +)clear all + +--S 569 of 1325 +t0:=x^4*(a+b*sqrt(x))^3 +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1325 +r0:=1/5*a^3*x^5+6/11*a^2*b*x^(11/2)+1/2*a*b^2*x^6+2/13*b^3*x^(13/2) +--R +--R +--R 3 6 2 5 +-+ 2 6 3 5 +--R (220b x + 780a b x )\|x + 715a b x + 286a x +--R (2) ----------------------------------------------- +--R 1430 +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 6 2 5 +-+ 2 6 3 5 +--R (220b x + 780a b x )\|x + 715a b x + 286a x +--R (3) ----------------------------------------------- +--R 1430 +--R Type: Union(Expression(Integer),...) +--E 571 + +--S 572 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1325 +t0:=x^3*(a+b*sqrt(x))^3 +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1325 +r0:=1/4*a^3*x^4+2/3*a^2*b*x^(9/2)+3/5*a*b^2*x^5+2/11*b^3*x^(11/2) +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (120b x + 440a b x )\|x + 396a b x + 165a x +--R (2) ----------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 5 2 4 +-+ 2 5 3 4 +--R (120b x + 440a b x )\|x + 396a b x + 165a x +--R (3) ----------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1325 +t0:=x^2*(a+b*sqrt(x))^3 +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (1) (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1325 +r0:=1/3*a^3*x^3+6/7*a^2*b*x^(7/2)+3/4*a*b^2*x^4+2/9*b^3*x^(9/2) +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (56b x + 216a b x )\|x + 189a b x + 84a x +--R (2) --------------------------------------------- +--R 252 +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 +-+ 2 4 3 3 +--R (56b x + 216a b x )\|x + 189a b x + 84a x +--R (3) --------------------------------------------- +--R 252 +--R Type: Union(Expression(Integer),...) +--E 581 + +--S 582 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +)clear all + +--S 584 of 1325 +t0:=x*(a+b*sqrt(x))^3 +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (1) (b x + 3a b x)\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1325 +r0:=1/2*a^3*x^2+6/5*a^2*b*x^(5/2)+a*b^2*x^3+2/7*b^3*x^(7/2) +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (20b x + 84a b x )\|x + 70a b x + 35a x +--R (2) ------------------------------------------- +--R 70 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 +-+ 2 3 3 2 +--R (20b x + 84a b x )\|x + 70a b x + 35a x +--R (3) ------------------------------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 586 + +--S 587 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1325 +t0:=(a+b*sqrt(x))^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (1) (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1325 +r0:=-1/2*a*(a+b*sqrt(x))^4/b^2+2/5*(a+b*sqrt(x))^5/b^2 +--R +--R +--R 5 2 2 3 +-+ 4 2 3 2 5 +--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a +--R (2) ----------------------------------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (4b x + 20a b x)\|x + 15a b x + 10a x +--R (3) ---------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 591 + +--S 592 of 1325 +m0:=a0-r0 +--R +--R +--R 5 +--R a +--R (4) ---- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 1325 +t0:=(a+b*sqrt(x))^3/x +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R x +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1325 +r0:=3*a*b^2*x+2/3*b^3*x^(3/2)+a^3*log(x)+6*a^2*b*sqrt(x) +--R +--R +--R 3 2 +-+ 3 2 +--R (2b x + 18a b)\|x + 3a log(x) + 9a b x +--R (2) --------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R 6a log(\|x ) + (2b x + 18a b)\|x + 9a b x +--R (3) ------------------------------------------ +--R 3 +--R Type: Union(Expression(Integer),...) +--E 596 + +--S 597 of 1325 +m0:=a0-r0 +--R +--R +--R 3 +-+ 3 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1325 +t0:=(a+b*sqrt(x))^3/x^2 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1325 +r0:=-a^3/x+3*a*b^2*log(x)-6*a^2*b/sqrt(x)+2*b^3*sqrt(x) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (3a b x log(x) - a )\|x + 2b x - 6a b x +--R (2) ----------------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 3 2 +-+ 3 +--R 6a b x log(\|x ) + (2b x - 6a b)\|x - a +--R (3) ----------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R (4) 6a b log(\|x ) - 3a b log(x) +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1325 +t0:=(a+b*sqrt(x))^3/x^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1325 +r0:=-1/2*(a+b*sqrt(x))^4/(a*x^2) +--R +--R +--R 3 3 +-+ 4 2 2 2 4 +--R (- 4a b x - 4a b)\|x - b x - 6a b x - a +--R (2) ------------------------------------------ +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 4b x - 4a b)\|x - 6a b x - a +--R (3) --------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +--R b +--R (4) -- +--R 2a +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1325 +t0:=(a+b*sqrt(x))^3/x^4 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 4 +--R x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1325 +r0:=-1/3*a^3/x^3-6/5*a^2*b/x^(5/2)-3/2*a*b^2/x^2-2/3*b^3/x^(3/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 45a b x - 10a )\|x - 20b x - 36a b x +--R (2) ----------------------------------------- +--R 3 +-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 20b x - 36a b)\|x - 45a b x - 10a +--R (3) -------------------------------------- +--R 3 +--R 30x +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1325 +t0:=(a+b*sqrt(x))^3/x^5 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 5 +--R x +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1325 +r0:=-1/4*a^3/x^4-6/7*a^2*b/x^(7/2)-a*b^2/x^3-2/5*b^3/x^(5/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 140a b x - 35a )\|x - 56b x - 120a b x +--R (2) ------------------------------------------- +--R 4 +-+ +--R 140x \|x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 56b x - 120a b)\|x - 140a b x - 35a +--R (3) ---------------------------------------- +--R 4 +--R 140x +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1325 +t0:=(a+b*sqrt(x))^3/x^6 +--R +--R +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R (1) ------------------------------ +--R 6 +--R x +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1325 +r0:=-1/5*a^3/x^5-2/3*a^2*b/x^(9/2)-3/4*a*b^2/x^4-2/7*b^3/x^(7/2) +--R +--R +--R 2 3 +-+ 3 2 2 +--R (- 315a b x - 84a )\|x - 120b x - 280a b x +--R (2) -------------------------------------------- +--R 5 +-+ +--R 420x \|x +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 2 +-+ 2 3 +--R (- 120b x - 280a b)\|x - 315a b x - 84a +--R (3) ----------------------------------------- +--R 5 +--R 420x +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1325 +t0:=x^m*(a+b*sqrt(x))^5 +--R +--R +--R 5 2 2 3 4 m +-+ 4 2 3 2 5 m +--R (1) (b x + 10a b x + 5a b)x \|x + (5a b x + 10a b x + a )x +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1325 +r0:=a^5*x^(1+m)/(1+m)+10*a^4*b*x^(3/2+m)/(3+2*m)+10*a^3*_ + b^2*x^(2+m)/(2+m)+20*a^2*b^3*x^(5/2+m)/(5+2*m)+5*a*_ + b^4*x^(3+m)/(3+m)+2*b^5*x^(7/2+m)/(7+2*m) +--R +--R +--R (2) +--R 2m + 7 +--R ------ +--R 5 5 5 4 5 3 5 2 5 5 2 +--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m + 1050a b ) +--R * +--R m + 3 +--R x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 2 3 +--R (80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m + 2520a b ) +--R * +--R 2m + 5 +--R ------ +--R 2 +--R x +--R + +--R 3 2 5 3 2 4 3 2 3 3 2 2 3 2 3 2 +--R (80a b m + 920a b m + 4060a b m + 8530a b m + 8460a b m + 3150a b ) +--R * +--R m + 2 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 4 +--R (40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m + 2100a b) +--R * +--R 2m + 3 +--R ------ +--R 2 +--R x +--R + +--R 5 5 5 4 5 3 5 2 5 5 m + 1 +--R (8a m + 100a m + 490a m + 1175a m + 1377a m + 630a )x +--R / +--R 6 5 4 3 2 +--R 8m + 108m + 590m + 1665m + 2552m + 2007m + 630 +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 5 4 5 3 5 2 5 5 3 +--R (8b m + 80b m + 310b m + 580b m + 522b m + 180b )x +--R + +--R 2 3 5 2 3 4 2 3 3 2 3 2 2 3 +--R 80a b m + 880a b m + 3700a b m + 7400a b m + 7020a b m +--R + +--R 2 3 +--R 2520a b +--R * +--R 2 +--R x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 480a b m + 2230a b m + 4980a b m + 5290a b m +--R + +--R 4 +--R 2100a b +--R * +--R x +--R * +--R +-+ +--R \|x +--R + +--R 4 5 4 4 4 3 4 2 4 +--R 40a b m + 420a b m + 1690a b m + 3255a b m + 2995a b m +--R + +--R 4 +--R 1050a b 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5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1325 +r0:=-1/2*a^5/x^2-10/3*a^4*b/x^(3/2)-10*a^3*b^2/x+5*a*b^4*log(x)-_ + 20*a^2*b^3/sqrt(x)+2*b^5*sqrt(x) +--R +--R +--R 4 2 3 2 5 +-+ 5 3 2 3 2 4 +--R (30a b x log(x) - 60a b x - 3a )\|x + 12b x - 120a b x - 20a b x +--R (2) ------------------------------------------------------------------- +--R 2 +-+ +--R 6x \|x +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 2 +-+ 5 2 2 3 4 +-+ 3 2 5 +--R 60a b x log(\|x ) + (12b x - 120a b x - 20a b)\|x - 60a b x - 3a +--R (3) ------------------------------------------------------------------- +--R 2 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R (4) 10a b log(\|x ) - 5a b log(x) +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1325 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x - 700a b)\|x - 1050a b x - 1575a b x - 126a +--R (3) --------------------------------------------------------------------- +--R 5 +--R 630x +--R Type: Union(Expression(Integer),...) +--E 681 + +--S 682 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 682 + +--S 683 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 683 + +)clear all + +--S 684 of 1325 +t0:=(a+b*sqrt(x))^5/x^7 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R (1) ---------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1325 +r0:=-1/6*a^5/x^6-10/11*a^4*b/x^(11/2)-2*a^3*b^2/x^5-_ + 20/9*a^2*b^3/x^(9/2)-5/4*a*b^4/x^4-2/7*b^5/x^(7/2) +--R +--R +--R (2) +--R 4 2 3 2 5 +-+ 5 3 2 3 2 4 +--R (- 3465a b x - 5544a b x - 462a )\|x - 792b x - 6160a b x - 2520a b x +--R ------------------------------------------------------------------------- +--R 6 +-+ +--R 2772x \|x 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1679600a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 10 2 8 9 4 6 8 6 4 7 +--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x +--R + +--R 8 2 6 10 5 +--R 6928350a b x + 184756a x +--R / +--R 923780 +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 9 3 7 8 5 5 7 7 3 6 +--R 972400a b x + 13041600a b x + 31039008a b x + 17054400a b x +--R + +--R 9 5 +--R 1679600a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 10 2 8 9 4 6 8 6 4 7 +--R 92378b x + 4618900a b x + 24249225a b x + 27713400a b x +--R + +--R 8 2 6 10 5 +--R 6928350a b x + 184756a x +--R / +--R 923780 +--R Type: Union(Expression(Integer),...) +--E 696 + +--S 697 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 697 + +--S 698 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 698 + +)clear all + +--S 699 of 1325 +t0:=x^3*(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 7 3 7 6 5 5 5 7 3 4 9 3 +-+ 10 8 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x +--R + +--R 2 8 7 4 6 6 6 4 5 8 2 4 10 3 +--R 45a b x + 210a b x + 210a b x + 45a b x + a x +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1325 +r0:=1/4*a^10*x^4+20/9*a^9*b*x^(9/2)+9*a^8*b^2*x^5+240/11*a^7*b^3*_ + x^(11/2)+35*a^6*b^4*x^6+504/13*a^5*b^5*x^(13/2)+30*a^4*b^6*_ + x^7+16*a^3*b^7*x^(15/2)+45/8*a^2*b^8*x^8+20/17*a*b^9*x^(17/2)+_ + 1/9*b^10*x^9 +--R +--R +--R (2) +--R 9 8 3 7 7 5 5 6 7 3 5 +--R 205920a b x + 2800512a b x + 6785856a b x + 3818880a b x +--R + +--R 9 4 +--R 388960a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 9 2 8 8 4 6 7 6 4 6 8 2 5 +--R 19448b x + 984555a b x + 5250960a b x + 6126120a b x + 1575288a b x +--R + +--R 10 4 +--R 43758a x +--R / +--R 175032 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 8 3 7 7 5 5 6 7 3 5 +--R 205920a b x + 2800512a b x + 6785856a b x + 3818880a b x +--R + +--R 9 4 +--R 388960a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 9 2 8 8 4 6 7 6 4 6 8 2 5 +--R 19448b x + 984555a b x + 5250960a b x + 6126120a b x + 1575288a b x +--R + +--R 10 4 +--R 43758a x +--R / +--R 175032 +--R Type: Union(Expression(Integer),...) +--E 701 + +--S 702 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 702 + +--S 703 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 703 + +)clear all + +--S 704 of 1325 +t0:=x^2*(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 6 3 7 5 5 5 4 7 3 3 9 2 +-+ 10 7 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x )\|x + b x +--R + +--R 2 8 6 4 6 5 6 4 4 8 2 3 10 2 +--R 45a b x + 210a b x + 210a b x + 45a b x + a x +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1325 +r0:=-2/11*a^5*(a+b*sqrt(x))^11/b^6+5/6*a^4*(a+b*sqrt(x))^12/b^6-_ + 20/13*a^3*(a+b*sqrt(x))^13/b^6+10/7*a^2*(a+b*sqrt(x))^14/b^6-_ + 2/3*a*(a+b*sqrt(x))^15/b^6+1/8*(a+b*sqrt(x))^16/b^6 +--R +--R +--R (2) +--R 15 7 3 13 6 5 11 5 7 9 4 +--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x +--R + +--R 9 7 3 +--R 68640a b x +--R * +--R +-+ +--R \|x +--R + +--R 16 8 2 14 7 4 12 6 6 10 5 8 8 4 +--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x +--R + +--R 10 6 3 16 +--R 8008a b x - a +--R / +--R 6 +--R 24024b +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 7 3 7 6 5 5 5 7 3 4 +--R 32032a b x + 443520a b x + 1100736a b x + 640640a b x +--R + +--R 9 3 +--R 68640a b x +--R * +--R +-+ +--R \|x +--R + +--R 10 8 2 8 7 4 6 6 6 4 5 8 2 4 +--R 3003b x + 154440a b x + 840840a b x + 1009008a b x + 270270a b x +--R + +--R 10 3 +--R 8008a x +--R / +--R 24024 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1325 +m0:=a0-r0 +--R +--R +--R 16 +--R a +--R (4) ------- +--R 6 +--R 24024b +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1325 +t0:=x*(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 5 3 7 4 5 5 3 7 3 2 9 +-+ 10 6 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b x)\|x + b x +--R + +--R 2 8 5 4 6 4 6 4 3 8 2 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a x +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1325 +r0:=-2/11*a^3*(a+b*sqrt(x))^11/b^4+1/2*a^2*(a+b*sqrt(x))^12/b^4-_ + 6/13*a*(a+b*sqrt(x))^13/b^4+1/7*(a+b*sqrt(x))^14/b^4 +--R +--R +--R (2) +--R 13 6 3 11 5 5 9 4 7 7 3 9 5 2 +--R (3080a b x + 43680a b x + 112112a b x + 68640a b x + 8008a b x ) +--R * +--R +-+ +--R \|x +--R + +--R 14 7 2 12 6 4 10 5 6 8 4 8 6 3 +--R 286b x + 15015a b x + 84084a b x + 105105a b x + 30030a b x +--R + +--R 10 4 2 14 +--R 1001a b x - a +--R / +--R 4 +--R 2002b +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 6 3 7 5 5 5 4 7 3 3 9 2 +-+ +--R (3080a b x + 43680a b x + 112112a b x + 68640a b x + 8008a b x )\|x +--R + +--R 10 7 2 8 6 4 6 5 6 4 4 8 2 3 +--R 286b x + 15015a b x + 84084a b x + 105105a b x + 30030a b x +--R + +--R 10 2 +--R 1001a x +--R / +--R 2002 +--R Type: Union(Expression(Integer),...) +--E 711 + +--S 712 of 1325 +m0:=a0-r0 +--R +--R +--R 14 +--R a +--R (4) ------ +--R 4 +--R 2002b +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +)clear all + +--S 714 of 1325 +t0:=(a+b*sqrt(x))^10 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1325 +r0:=-2/11*a*(a+b*sqrt(x))^11/b^2+1/6*(a+b*sqrt(x))^12/b^2 +--R +--R +--R (2) +--R 11 5 3 9 4 5 7 3 7 5 2 9 3 +-+ +--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x +--R + +--R 12 6 2 10 5 4 8 4 6 6 3 8 4 2 10 2 +--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a b x +--R + +--R 12 +--R - a +--R / +--R 2 +--R 66b +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 5 3 7 4 5 5 3 7 3 2 9 +-+ +--R (120a b x + 1760a b x + 4752a b x + 3168a b x + 440a b x)\|x +--R + +--R 10 6 2 8 5 4 6 4 6 4 3 8 2 2 10 +--R 11b x + 594a b x + 3465a b x + 4620a b x + 1485a b x + 66a x +--R / +--R 66 +--R Type: Union(Expression(Integer),...) +--E 716 + +--S 717 of 1325 +m0:=a0-r0 +--R +--R +--R 12 +--R a +--R (4) ---- +--R 2 +--R 66b +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 718 + +)clear all + +--S 719 of 1325 +t0:=(a+b*sqrt(x))^10/x +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1325 +r0:=45*a^8*b^2*x+80*a^7*b^3*x^(3/2)+105*a^6*b^4*x^2+504/5*a^5*b^5*_ + x^(5/2)+70*a^4*b^6*x^3+240/7*a^3*b^7*x^(7/2)+45/4*a^2*b^8*x^4+_ + 20/9*a*b^9*x^(9/2)+1/5*b^10*x^5+a^10*log(x)+20*a^9*b*sqrt(x) +--R +--R +--R (2) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (2800a b x + 43200a b x + 127008a b x + 100800a b x + 25200a b)\|x +--R + +--R 10 10 5 2 8 4 4 6 3 6 4 2 +--R 1260a log(x) + 252b x + 14175a b x + 88200a b x + 132300a b x +--R + +--R 8 2 +--R 56700a b x +--R / +--R 1260 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 +-+ +--R 2520a log(\|x ) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (2800a b x + 43200a b x + 127008a b x + 100800a b x + 25200a b)\|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 8 2 +--R 252b x + 14175a b x + 88200a b x + 132300a b x + 56700a b x +--R / +--R 1260 +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1325 +m0:=a0-r0 +--R +--R +--R 10 +-+ 10 +--R (4) 2a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1325 +t0:=(a+b*sqrt(x))^10/x^2 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1325 +r0:=-a^10/x+210*a^6*b^4*x+168*a^5*b^5*x^(3/2)+105*a^4*b^6*x^2+_ + 48*a^3*b^7*x^(5/2)+15*a^2*b^8*x^3+20/7*a*b^9*x^(7/2)+_ + 1/4*b^10*x^4+45*a^8*b^2*log(x)-20*a^9*b/sqrt(x)+240*a^7*b^3*sqrt(x) +--R +--R +--R (2) +--R 8 2 10 5 2 8 4 4 6 3 6 4 2 +--R 1260a b x log(x) + 7b x + 420a b x + 2940a b x + 5880a b x +--R + +--R 10 +--R - 28a +--R * +--R +-+ +--R \|x +--R + +--R 9 5 3 7 4 5 5 3 7 3 2 9 +--R 80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b x +--R / +--R +-+ +--R 28x\|x +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 +-+ +--R 2520a b x log(\|x ) +--R + +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (80a b x + 1344a b x + 4704a b x + 6720a b x - 560a b)\|x + 7b x +--R + +--R 2 8 4 4 6 3 6 4 2 10 +--R 420a b x + 2940a b x + 5880a b x - 28a +--R / +--R 28x +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1325 +m0:=a0-r0 +--R +--R +--R 8 2 +-+ 8 2 +--R (4) 90a b log(\|x ) - 45a b log(x) +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1325 +t0:=(a+b*sqrt(x))^10/x^3 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 3 +--R x +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1325 +r0:=-1/2*a^10/x^2-20/3*a^9*b/x^(3/2)-45*a^8*b^2/x+210*a^4*b^6*x+_ + 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3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (40a b x + 1440a b x - 3024a b x - 480a b x - 24a b)\|x + 3b x +--R + +--R 2 8 4 6 4 2 8 2 10 +--R 270a b x - 1260a b x - 135a b x - 2a +--R / +--R 3 +--R 6x +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1325 +m0:=a0-r0 +--R +--R +--R 4 6 +-+ 4 6 +--R (4) 420a b log(\|x ) - 210a b log(x) +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 1325 +t0:=(a+b*sqrt(x))^10/x^5 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 5 +--R x +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1325 +r0:=-1/4*a^10/x^4-20/7*a^9*b/x^(7/2)-15*a^8*b^2/x^3-48*a^7*b^3/x^(5/2)-_ + 105*a^6*b^4/x^2-168*a^5*b^5/x^(3/2)-210*a^4*b^6/x+b^10*x+45*_ + 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2 7 3 9 +-+ +--R (- 25200a b x - 100800a b x - 127008a b x - 43200a b x - 2800a b)\|x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R - 56700a b x - 132300a b x - 88200a b x - 14175a b x - 252a +--R / +--R 5 +--R 1260x +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1325 +m0:=a0-r0 +--R +--R +--R 10 +-+ 10 +--R (4) 2b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1325 +t0:=(a+b*sqrt(x))^10/x^7 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 7 +--R x +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1325 +r0:=-1/6*(a+b*sqrt(x))^11/(a*x^6)+1/66*b*(a+b*sqrt(x))^11/(a^2*x^(11/2)) +--R +--R +--R (2) +--R 12 6 2 10 5 4 8 4 6 6 3 8 4 2 10 2 +--R b x - 66a b x - 1485a b x - 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+--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 8 +--R x +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1325 +r0:=-1/7*(a+b*sqrt(x))^11/(a*x^7)+3/91*b*(a+b*sqrt(x))^11/(a^2*x^(13/2))-_ + 1/182*b^2*(a+b*sqrt(x))^11/(a^3*x^6)+_ + 1/2002*b^3*(a+b*sqrt(x))^11/(a^4*x^(11/2)) +--R +--R +--R (2) +--R 14 7 4 10 5 6 8 4 8 6 3 10 4 2 +--R b x - 1001a b x - 30030a b x - 105105a b x - 84084a b x +--R + +--R 12 2 14 +--R - 15015a b x - 286a +--R * +--R +-+ +--R \|x +--R + +--R 5 9 5 7 7 4 9 5 3 11 3 2 13 +--R - 8008a b x - 68640a b x - 112112a b x - 43680a b x - 3080a b x +--R / +--R 4 7 +-+ +--R 2002a x \|x +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ +--R (- 8008a b x - 68640a b x - 112112a b x - 43680a b x - 3080a b)\|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 8 2 +--R - 1001b x - 30030a b x - 105105a b x - 84084a b x - 15015a b x +--R + +--R 10 +--R - 286a +--R 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+--R + +--R 9 +--R - 205920a b +--R * +--R +-+ +--R \|x +--R + +--R 10 5 2 8 4 4 6 3 6 4 2 +--R - 43758b x - 1575288a b x - 6126120a b x - 5250960a b x +--R + +--R 8 2 10 +--R - 984555a b x - 19448a +--R / +--R 9 +--R 175032x +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 768 + +)clear all + +--S 769 of 1325 +t0:=(a+b*sqrt(x))^10/x^11 +--R +--R +--R (1) +--R 9 4 3 7 3 5 5 2 7 3 9 +-+ 10 5 +--R (10a b x + 120a b x + 252a b x + 120a b x + 10a b)\|x + b x +--R + +--R 2 8 4 4 6 3 6 4 2 8 2 10 +--R 45a b x + 210a b x + 210a b x + 45a b x + a +--R / +--R 11 +--R x +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1325 +r0:=-1/10*a^10/x^10-20/19*a^9*b/x^(19/2)-5*a^8*b^2/x^9-240/17*a^7*_ + b^3/x^(17/2)-105/4*a^6*b^4/x^8-168/5*a^5*b^5/x^(15/2)-_ + 30*a^4*b^6/x^7-240/13*a^3*b^7/x^(13/2)-15/2*a^2*b^8/x^6-_ + 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-------------------------------------------------------------------------- +--R 6 +--R 30b +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 +-+ 5 2 2 3 4 +-+ 4 2 3 2 +--R - 60a log(b\|x + a) + (12b x + 20a b x + 60a b)\|x - 15a b x - 30a b x +--R -------------------------------------------------------------------------- +--R 6 +--R 30b +--R Type: Union(Expression(Integer),...) +--E 896 + +--S 897 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 897 + +--S 898 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 898 + +)clear all + +--S 899 of 1325 +t0:=x/(a+b*sqrt(x)) +--R +--R +--R x +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1325 +r0:=-a*x/b^2+2/3*x^(3/2)/b-2*a^3*log(a+b*sqrt(x))/b^4+2*a^2*sqrt(x)/b^3 +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x +--R (2) ------------------------------------------------ +--R 4 +--R 3b +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 +-+ 3 2 +-+ 2 +--R - 6a log(b\|x + a) + (2b x + 6a b)\|x - 3a b x +--R (3) ------------------------------------------------ +--R 4 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 901 + +--S 902 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1325 +t0:=1/(a+b*sqrt(x)) +--R +--R +--R 1 +--R (1) --------- +--R +-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1325 +r0:=-2*a*log(a+b*sqrt(x))/b^2+2*sqrt(x)/b +--R +--R +--R +-+ +-+ +--R - 2a log(b\|x + a) + 2b\|x +--R (2) ---------------------------- +--R 2 +--R b +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R - 2a log(b\|x + a) + 2b\|x +--R (3) ---------------------------- +--R 2 +--R b +--R Type: Union(Expression(Integer),...) +--E 906 + +--S 907 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 907 + +--S 908 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 908 + +)clear all + +--S 909 of 1325 +t0:=1/(x*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------- +--R +-+ +--R b x\|x + a x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1325 +r0:=log(x)/a-2*log(a+b*sqrt(x))/a +--R +--R +--R +-+ +--R - 2log(b\|x + a) + log(x) +--R (2) -------------------------- +--R a +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R - 2log(b\|x + a) + 2log(\|x ) +--R (3) ------------------------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 911 + +--S 912 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R a +--R Type: Expression(Integer) +--E 912 + +--S 913 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 913 + +)clear all + +--S 914 of 1325 +t0:=1/(x*(2+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------ +--R +-+ +--R b x\|x + 2x +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1325 +r0:=-2*atanh(1+b*sqrt(x)) +--R +--R +--R +-+ +--R (2) - 2atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) - log(b\|x + 2) + log(\|x ) +--R Type: Union(Expression(Integer),...) +--E 916 + +--S 917 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +-+ +-+ +--R (4) - log(b\|x + 2) + log(\|x ) + 2atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 917 + +--S 918 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 918 + +)clear all + +--S 919 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 2 +-+ 2 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1325 +r0:=(-1)/(a*x)+b^2*log(x)/a^3-2*b^2*log(a+b*sqrt(x))/a^3+2*b/(a^2*sqrt(x)) +--R +--R +--R 2 +-+ +-+ 2 2 +-+ +--R - 2b x\|x log(b\|x + a) + (b x log(x) - a )\|x + 2a b x +--R (2) --------------------------------------------------------- +--R 3 +-+ +--R a x\|x +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 2 +-+ +-+ 2 +--R - 2b x log(b\|x + a) + 2b x log(\|x ) + 2a b\|x - a +--R (3) ------------------------------------------------------ +--R 3 +--R a x +--R Type: Union(Expression(Integer),...) +--E 921 + +--S 922 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 922 + +--S 923 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 923 + +)clear all + +--S 924 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 3 +-+ 3 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1325 +r0:=(-1/2)/(a*x^2)+2/3*b/(a^2*x^(3/2))-b^2/(a^3*x)+b^4*log(x)/a^5-_ + 2*b^4*log(a+b*sqrt(x))/a^5+2*b^3/(a^4*sqrt(x)) +--R +--R +--R (2) +--R 4 2 +-+ +-+ 4 2 2 2 4 +-+ 3 2 +--R - 12b x \|x log(b\|x + a) + (6b x log(x) - 6a b x - 3a )\|x + 12a b x +--R + +--R 3 +--R 4a b x +--R / +--R 5 2 +-+ +--R 6a x \|x +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 2 +-+ 4 2 +-+ 3 3 +-+ 2 2 +--R - 12b x log(b\|x + a) + 12b x log(\|x ) + (12a b x + 4a b)\|x - 6a b x +--R + +--R 4 +--R - 3a +--R / +--R 5 2 +--R 6a x +--R Type: Union(Expression(Integer),...) +--E 926 + +--S 927 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 927 + +--S 928 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 928 + +)clear all + +--S 929 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) --------------- +--R 4 +-+ 4 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1325 +r0:=(-1/3)/(a*x^3)+2/5*b/(a^2*x^(5/2))-1/2*b^2/(a^3*x^2)+2/3*_ + b^3/(a^4*x^(3/2))-b^4/(a^5*x)+b^6*log(x)/a^7-2*b^6*log(a+b*_ + sqrt(x))/a^7+2*b^5/(a^6*sqrt(x)) +--R +--R +--R (2) +--R 6 3 +-+ +-+ +--R - 60b x \|x log(b\|x + a) +--R + +--R 6 3 2 4 2 4 2 6 +-+ 5 3 3 3 2 +--R (30b x log(x) - 30a b x - 15a b x - 10a )\|x + 60a b x + 20a b x +--R + +--R 5 +--R 12a b x +--R / +--R 7 3 +-+ +--R 30a x \|x +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3 +-+ 6 3 +-+ +--R - 60b x log(b\|x + a) + 60b x log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 2 4 2 4 2 6 +--R (60a b x + 20a b x + 12a b)\|x - 30a b x - 15a b x - 10a +--R / +--R 7 3 +--R 30a x +--R Type: Union(Expression(Integer),...) +--E 931 + +--S 932 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 2b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +)clear all + +--S 934 of 1325 +t0:=x^3/(a+b*sqrt(x))^2 +--R +--R +--R 3 +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1325 +r0:=5*a^4*x/b^6-8/3*a^3*x^(3/2)/b^5+3/2*a^2*x^2/b^4-4/5*a*x^(5/2)/b^3+_ + 1/3*x^3/b^2+14*a^6*log(a+b*sqrt(x))/b^8-12*a^5*sqrt(x)/b^7+_ + 2*a^7/(b^8*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 +-+ 7 +-+ +--R (420a b\|x + 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x +--R + +--R 5 2 7 +--R - 210a b x + 60a +--R / +--R 9 +-+ 8 +--R 30b \|x + 30a b +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 7 +-+ +--R (420a b\|x + 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (10b x + 21a b x + 70a b x - 360a b)\|x - 14a b x - 35a b x +--R + +--R 5 2 7 +--R - 210a b x + 60a +--R / +--R 9 +-+ 8 +--R 30b \|x + 30a b +--R Type: Union(Expression(Integer),...) +--E 936 + +--S 937 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 938 + +)clear all + +--S 939 of 1325 +t0:=x^2/(a+b*sqrt(x))^2 +--R +--R +--R 2 +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1325 +r0:=3*a^2*x/b^4-4/3*a*x^(3/2)/b^3+1/2*x^2/b^2+10*a^4*log(a+b*sqrt(x))/b^6-_ + 8*a^3*sqrt(x)/b^5+2*a^5/(b^6*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+ +--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x +--R + +--R 4 2 3 2 5 +--R - 5a b x - 30a b x + 12a +--R / +--R 7 +-+ 6 +--R 6b \|x + 6a b +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ 5 +-+ 5 2 2 3 4 +-+ +--R (60a b\|x + 60a )log(b\|x + a) + (3b x + 10a b x - 48a b)\|x +--R + +--R 4 2 3 2 5 +--R - 5a b x - 30a b x + 12a +--R / +--R 7 +-+ 6 +--R 6b \|x + 6a b +--R Type: Union(Expression(Integer),...) +--E 941 + +--S 942 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 942 + +--S 943 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 943 + +)clear all + +--S 944 of 1325 +t0:=x/(a+b*sqrt(x))^2 +--R +--R +--R x +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1325 +r0:=x/b^2+6*a^2*log(a+b*sqrt(x))/b^4-4*a*sqrt(x)/b^3+2*a^3/(b^4*(a+b*sqrt(x))) +--R +--R +--R 2 +-+ 3 +-+ 3 2 +-+ 2 3 +--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a +--R (2) ---------------------------------------------------------------- +--R 5 +-+ 4 +--R b \|x + a b +--R Type: Expression(Integer) +--E 945 + +--S 946 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ 3 +-+ 3 2 +-+ 2 3 +--R (6a b\|x + 6a )log(b\|x + a) + (b x - 4a b)\|x - 3a b x + 2a +--R (3) ---------------------------------------------------------------- +--R 5 +-+ 4 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 946 + +--S 947 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 947 + +--S 948 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 948 + +)clear all + +--S 949 of 1325 +t0:=1/(a+b*sqrt(x))^2 +--R +--R +--R 1 +--R (1) ------------------- +--R +-+ 2 2 +--R 2a b\|x + b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1325 +r0:=2*log(a+b*sqrt(x))/b^2+2*a/(b^2*(a+b*sqrt(x))) +--R +--R +--R +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) + 2a +--R (2) -------------------------------- +--R 3 +-+ 2 +--R b \|x + a b +--R Type: Expression(Integer) +--E 950 + +--S 951 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (2b\|x + 2a)log(b\|x + a) + 2a +--R (3) -------------------------------- +--R 3 +-+ 2 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 951 + +--S 952 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 952 + +--S 953 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 953 + +)clear all + +--S 954 of 1325 +t0:=1/(x*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-+ 2 2 2 +--R 2a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1325 +r0:=log(x)/a^2-2*log(a+b*sqrt(x))/a^2+2/(a*(a+b*sqrt(x))) +--R +--R +--R +-+ +-+ +-+ +--R (- 2b\|x - 2a)log(b\|x + a) + b log(x)\|x + a log(x) + 2a +--R (2) ------------------------------------------------------------ +--R 2 +-+ 3 +--R a b\|x + a +--R Type: Expression(Integer) +--E 955 + +--S 956 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +-+ +-+ +--R (- 2b\|x - 2a)log(b\|x + a) + (2b\|x + 2a)log(\|x ) + 2a +--R (3) ----------------------------------------------------------- +--R 2 +-+ 3 +--R a b\|x + a +--R Type: Union(Expression(Integer),...) +--E 956 + +--S 957 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 957 + +--S 958 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 958 + +)clear all + +--S 959 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 2 +-+ 2 3 2 2 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1325 +r0:=(-3)/(a^2*x)+3*b^2*log(x)/a^4-6*b^2*log(a+b*sqrt(x))/a^4+_ + 6*b/(a^3*sqrt(x))+2/(a*x*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 2 +-+ 3 2 +-+ 2 2 3 +-+ +--R (- 6a b x\|x - 6b x )log(b\|x + a) + (3a b x log(x) + 6a b x - a )\|x +--R + +--R 3 2 2 +--R 3b x log(x) + 3a b x +--R / +--R 5 +-+ 4 2 +--R a x\|x + a b x +--R Type: Expression(Integer) +--E 960 + +--S 961 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 2 +-+ 3 +-+ 2 +-+ +--R (- 6b x\|x - 6a b x)log(b\|x + a) + (6b x\|x + 6a b x)log(\|x ) +--R + +--R 2 +-+ 2 3 +--R 3a b\|x + 6a b x - a +--R / +--R 4 +-+ 5 +--R a b x\|x + a x +--R Type: Union(Expression(Integer),...) +--E 961 + +--S 962 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 6b log(\|x ) - 3b log(x) +--R (4) ------------------------ +--R 4 +--R a +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 963 + +)clear all + +--S 964 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 3 +-+ 2 4 2 3 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1325 +r0:=(-5/2)/(a^2*x^2)+10/3*b/(a^3*x^(3/2))-5*b^2/(a^4*x)+_ + 5*b^4*log(x)/a^6-10*b^4*log(a+b*sqrt(x))/a^6+10*b^3/(a^5*_ + sqrt(x))+2/(a*x^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 2 +-+ 5 3 +-+ +--R (- 60a b x \|x - 60b x )log(b\|x + a) +--R + +--R 4 2 4 2 3 2 5 +-+ 5 3 2 3 2 +--R (30a b x log(x) + 60a b x - 10a b x - 3a )\|x + 30b x log(x) + 30a b x +--R + +--R 4 +--R 5a b x +--R / +--R 7 2 +-+ 6 3 +--R 6a x \|x + 6a b x +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 +-+ 4 2 +-+ +--R (- 60b x \|x - 60a b x )log(b\|x + a) +--R + +--R 5 2 +-+ 4 2 +-+ 2 3 4 +-+ 4 2 +--R (60b x \|x + 60a b x )log(\|x ) + (30a b x + 5a b)\|x + 60a b x +--R + +--R 3 2 5 +--R - 10a b x - 3a +--R / +--R 6 2 +-+ 7 2 +--R 6a b x \|x + 6a x +--R Type: Union(Expression(Integer),...) +--E 966 + +--S 967 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 10b log(\|x ) - 5b log(x) +--R (4) ------------------------- +--R 6 +--R a +--R Type: Expression(Integer) +--E 967 + +--S 968 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 968 + +)clear all + +--S 969 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))^2) +--R +--R +--R 1 +--R (1) ------------------------- +--R 4 +-+ 2 5 2 4 +--R 2a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1325 +r0:=(-7/3)/(a^2*x^3)+14/5*b/(a^3*x^(5/2))-7/2*b^2/(a^4*x^2)+_ + 14/3*b^3/(a^5*x^(3/2))-7*b^4/(a^6*x)+7*b^6*log(x)/a^8-_ + 14*b^6*log(a+b*sqrt(x))/a^8+14*b^5/(a^7*sqrt(x))+2/(a*x^3*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 3 +-+ 7 4 +-+ +--R (- 420a b x \|x - 420b x )log(b\|x + a) +--R + +--R 6 3 6 3 3 4 2 5 2 7 +-+ +--R (210a b x log(x) + 420a b x - 70a b x - 21a b x - 10a )\|x +--R + +--R 7 4 2 5 3 4 3 2 6 +--R 210b x log(x) + 210a b x + 35a b x + 14a b x +--R / +--R 9 3 +-+ 8 4 +--R 30a x \|x + 30a b x +--R Type: Expression(Integer) +--E 970 + +--S 971 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 +-+ 6 3 +-+ +--R (- 420b x \|x - 420a b x )log(b\|x + a) +--R + +--R 7 3 +-+ 6 3 +-+ 2 5 2 4 3 6 +-+ +--R (420b x \|x + 420a b x )log(\|x ) + (210a b x + 35a b x + 14a b)\|x +--R + +--R 6 3 3 4 2 5 2 7 +--R 420a b x - 70a b x - 21a b x - 10a +--R / +--R 8 3 +-+ 9 3 +--R 30a b x \|x + 30a x +--R Type: Union(Expression(Integer),...) +--E 971 + +--S 972 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 14b log(\|x ) - 7b log(x) +--R (4) ------------------------- +--R 8 +--R a +--R Type: Expression(Integer) +--E 972 + +--S 973 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 973 + +)clear all + +--S 974 of 1325 +t0:=x^3/(a+b*sqrt(x))^3 +--R +--R +--R 3 +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1325 +r0:=-10*a^3*x/b^6+4*a^2*x^(3/2)/b^5-3/2*a*x^2/b^4+2/5*x^(5/2)/b^3-_ + 42*a^5*log(a+b*sqrt(x))/b^8+30*a^4*sqrt(x)/b^7+_ + a^7/(b^8*(a+b*sqrt(x))^2)-14*a^6/(b^8*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 5 3 7 +-+ 6 2 8 +-+ +--R ((- 420a b x - 1260a b)\|x - 1260a b x - 420a )log(b\|x + a) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3 +--R (- 3a b x - 21a b x + 640a b x + 30a b)\|x + 4b x + 7a b x +--R + +--R 4 4 2 6 2 8 +--R 105a b x + 660a b x - 130a +--R / +--R 11 2 9 +-+ 10 3 8 +--R (10b x + 30a b )\|x + 30a b x + 10a b +--R Type: Expression(Integer) +--E 975 + +--S 976 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 +-+ 5 2 7 +-+ +--R (- 840a b\|x - 420a b x - 420a )log(b\|x + a) +--R + +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 +--R (4b x + 14a b x + 140a b x + 160a b)\|x - 7a b x - 35a b x +--R + +--R 5 2 7 +--R 500a b x - 130a +--R / +--R 9 +-+ 10 2 8 +--R 20a b \|x + 10b x + 10a b +--R Type: Union(Expression(Integer),...) +--E 976 + +--S 977 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 977 + +--S 978 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 978 + +)clear all + +--S 979 of 1325 +t0:=x^2/(a+b*sqrt(x))^3 +--R +--R +--R 2 +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1325 +r0:=-3*a*x/b^4+2/3*x^(3/2)/b^3-20*a^3*log(a+b*sqrt(x))/b^6+_ + 12*a^2*sqrt(x)/b^5+a^5/(b^6*(a+b*sqrt(x))^2)-10*a^4/(b^6*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 3 5 +-+ 4 2 6 +-+ +--R ((- 60a b x - 180a b)\|x - 180a b x - 60a )log(b\|x + a) +--R + +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (- 3a b x + 83a b x - 21a b)\|x + 2b x + 15a b x + 69a b x - 27a +--R / +--R 9 2 7 +-+ 8 3 6 +--R (3b x + 9a b )\|x + 9a b x + 3a b +--R Type: Expression(Integer) +--E 980 + +--S 981 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 +-+ 3 2 5 +-+ +--R (- 120a b\|x - 60a b x - 60a )log(b\|x + a) +--R + +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (2b x + 20a b x + 6a b)\|x - 5a b x + 63a b x - 27a +--R / +--R 7 +-+ 8 2 6 +--R 6a b \|x + 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 981 + +--S 982 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 982 + +--S 983 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 983 + +)clear all + +--S 984 of 1325 +t0:=x/(a+b*sqrt(x))^3 +--R +--R +--R x +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1325 +r0:=-6*a*log(a+b*sqrt(x))/b^4+2*sqrt(x)/b^3+a^3/(b^4*(a+b*sqrt(x))^2)-_ + 6*a^2/(b^4*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 3 +-+ 2 2 4 +-+ +--R ((- 6a b x - 18a b)\|x - 18a b x - 6a )log(b\|x + a) +--R + +--R 3 3 +-+ 4 2 4 +--R (6a b x - 9a b)\|x + 2b x - 5a +--R / +--R 7 2 5 +-+ 6 3 4 +--R (b x + 3a b )\|x + 3a b x + a b +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-+ 2 3 +-+ 3 2 +-+ 2 3 +--R (- 12a b\|x - 6a b x - 6a )log(b\|x + a) + (2b x - 4a b)\|x + 4a b x - 5a +--R ----------------------------------------------------------------------------- +--R 5 +-+ 6 2 4 +--R 2a b \|x + b x + a b +--R Type: Union(Expression(Integer),...) +--E 986 + +--S 987 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 988 + +)clear all + +--S 989 of 1325 +t0:=1/(a+b*sqrt(x))^3 +--R +--R +--R 1 +--R (1) ------------------------------ +--R 3 2 +-+ 2 3 +--R (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1325 +r0:=x/(a*(a+b*sqrt(x))^2) +--R +--R +--R x +--R (2) --------------------- +--R 2 +-+ 2 3 +--R 2a b\|x + a b x + a +--R Type: Expression(Integer) +--E 990 + +--S 991 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R - 2b\|x - a +--R (3) ---------------------- +--R 3 +-+ 4 2 2 +--R 2a b \|x + b x + a b +--R Type: Union(Expression(Integer),...) +--E 991 + +--S 992 of 1325 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - ---- +--R 2 +--R a b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 993 + +)clear all + +--S 994 of 1325 +t0:=1/(x*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 2 2 +-+ 2 2 3 +--R (b x + 3a b x)\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1325 +r0:=log(x)/a^3-2*log(a+b*sqrt(x))/a^3+1/(a*(a+b*sqrt(x))^2)+_ + 2/(a^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 3 2 +-+ 2 3 +-+ +--R ((- 2b x - 6a b)\|x - 6a b x - 2a )log(b\|x + a) +--R + +--R 3 2 2 +-+ 2 3 2 3 +--R ((b x + 3a b)log(x) + 5a b)\|x + (3a b x + a )log(x) + 2a b x + 3a +--R / +--R 3 3 5 +-+ 4 2 6 +--R (a b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 2 2 +-+ +--R (- 4a b\|x - 2b x - 2a )log(b\|x + a) +--R + +--R +-+ 2 2 +-+ +-+ 2 +--R (4a b\|x + 2b x + 2a )log(\|x ) + 2a b\|x + 3a +--R / +--R 4 +-+ 3 2 5 +--R 2a b\|x + a b x + a +--R Type: Union(Expression(Integer),...) +--E 996 + +--S 997 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R 2log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1325 +t0:=1/(x^2*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 3 2 2 +-+ 2 3 3 2 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1325 +r0:=(-6)/(a^3*x)+6*b^2*log(x)/a^5-12*b^2*log(a+b*sqrt(x))/a^5+_ + 12*b/(a^4*sqrt(x))+1/(a*x*(a+b*sqrt(x))^2)+4/(a^2*x*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 4 2 3 2 +-+ 5 3 2 3 2 +-+ +--R ((- 36a b x - 12a b x)\|x - 12b x - 36a b x )log(b\|x + a) +--R + +--R 4 2 3 2 4 2 3 2 5 +-+ +--R ((18a b x + 6a b x)log(x) + 12a b x + 22a b x - a )\|x +--R + +--R 5 3 2 3 2 2 3 2 4 +--R (6b x + 18a b x )log(x) + 30a b x + 3a b x +--R / +--R 6 2 2 8 +-+ 5 3 3 7 2 +--R (3a b x + a x)\|x + a b x + 3a b x +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 +-+ 4 2 2 2 +-+ +--R (- 24a b x\|x - 12b x - 12a b x)log(b\|x + a) +--R + +--R 3 +-+ 4 2 2 2 +-+ 3 3 +-+ +--R (24a b x\|x + 12b x + 12a b x)log(\|x ) + (12a b x + 4a b)\|x +--R + +--R 2 2 4 +--R 18a b x - a +--R / +--R 6 +-+ 5 2 2 7 +--R 2a b x\|x + a b x + a x +--R Type: Union(Expression(Integer),...) +--E 1001 + +--S 1002 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +-+ 2 +--R 12b log(\|x ) - 6b log(x) +--R (4) ------------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 1002 + +--S 1003 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1003 + +)clear all + +--S 1004 of 1325 +t0:=1/(x^3*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 4 2 3 +-+ 2 4 3 3 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1325 +r0:=(-15/2)/(a^3*x^2)+10*b/(a^4*x^(3/2))-15*b^2/(a^5*x)+15*b^4*_ + log(x)/a^7-30*b^4*log(a+b*sqrt(x))/a^7+30*b^3/(a^6*sqrt(x))+_ + 1/(a*x^2*(a+b*sqrt(x))^2)+6/(a^2*x^2*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 6 3 3 4 2 +-+ 7 4 2 5 3 +-+ +--R ((- 180a b x - 60a b x )\|x - 60b x - 180a b x )log(b\|x + a) +--R + +--R 6 3 3 4 2 6 3 3 4 2 5 2 7 +-+ +--R ((90a b x + 30a b x )log(x) + 60a b x + 110a b x - 3a b x - a )\|x +--R + +--R 7 4 2 5 3 2 5 3 4 3 2 6 +--R (30b x + 90a b x )log(x) + 150a b x + 15a b x + a b x +--R / +--R 8 2 3 10 2 +-+ 7 3 4 9 3 +--R (6a b x + 2a x )\|x + 2a b x + 6a b x +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 +-+ 6 3 2 4 2 +-+ +--R (- 120a b x \|x - 60b x - 60a b x )log(b\|x + a) +--R + +--R 5 2 +-+ 6 3 2 4 2 +-+ +--R (120a b x \|x + 60b x + 60a b x )log(\|x ) +--R + +--R 5 2 3 3 5 +-+ 2 4 2 4 2 6 +--R (60a b x + 20a b x + 2a b)\|x + 90a b x - 5a b x - a +--R / +--R 8 2 +-+ 7 2 3 9 2 +--R 4a b x \|x + 2a b x + 2a x +--R Type: Union(Expression(Integer),...) +--E 1006 + +--S 1007 of 1325 +m0:=a0-r0 +--R +--R +--R 4 +-+ 4 +--R 30b log(\|x ) - 15b log(x) +--R (4) -------------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1008 + +)clear all + +--S 1009 of 1325 +t0:=1/(x^4*(a+b*sqrt(x))^3) +--R +--R +--R 1 +--R (1) ------------------------------------- +--R 3 5 2 4 +-+ 2 5 3 4 +--R (b x + 3a b x )\|x + 3a b x + a x +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1325 +r0:=(-28/3)/(a^3*x^3)+56/5*b/(a^4*x^(5/2))-14*b^2/(a^5*x^2)+_ + 56/3*b^3/(a^6*x^(3/2))-28*b^4/(a^7*x)+28*b^6*log(x)/a^9-_ + 56*b^6*log(a+b*sqrt(x))/a^9+56*b^5/(a^8*sqrt(x))+_ + 1/(a*x^3*(a+b*sqrt(x))^2)+8/(a^2*x^3*(a+b*sqrt(x))) +--R +--R +--R (2) +--R 8 4 3 6 3 +-+ 9 5 2 7 4 +-+ +--R ((- 2520a b x - 840a b x )\|x - 840b x - 2520a b x )log(b\|x + a) +--R + +--R 8 4 3 6 3 8 4 3 6 3 5 4 2 +--R (1260a b x + 420a b x )log(x) + 840a b x + 1540a b x - 42a b x +--R + +--R 7 2 9 +--R - 6a b x - 5a +--R * +--R +-+ +--R \|x +--R + +--R 9 5 2 7 4 2 7 4 4 5 3 6 3 2 8 +--R (420b x + 1260a b x )log(x) + 2100a b x + 210a b x + 14a b x + 3a b x +--R / +--R 10 2 4 12 3 +-+ 9 3 5 11 4 +--R (45a b x + 15a x )\|x + 15a b x + 45a b x +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 +-+ 8 4 2 6 3 +-+ +--R (- 1680a b x \|x - 840b x - 840a b x )log(b\|x + a) +--R + +--R 7 3 +-+ 8 4 2 6 3 +-+ +--R (1680a b x \|x + 840b x + 840a b x )log(\|x ) +--R + +--R 7 3 3 5 2 5 3 7 +-+ 2 6 3 4 4 2 +--R (840a b x + 280a b x + 28a b x + 8a b)\|x + 1260a b x - 70a b x +--R + +--R 6 2 8 +--R - 14a b x - 5a +--R / +--R 10 3 +-+ 9 2 4 11 3 +--R 30a b x \|x + 15a b x + 15a x +--R Type: Union(Expression(Integer),...) +--E 1011 + +--S 1012 of 1325 +m0:=a0-r0 +--R +--R +--R 6 +-+ 6 +--R 56b log(\|x ) - 28b log(x) +--R (4) -------------------------- +--R 9 +--R a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1013 + +)clear all + +--S 1014 of 1325 +t0:=x^2*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R 2 | +-+ +--R (1) x \|b\|x + a +--R Type: Expression(Integer) +--E 1014 + +--S 1015 of 1325 +r0:=-4/3*a^5*(a+b*sqrt(x))^(3/2)/b^6+4*a^4*(a+b*sqrt(x))^(5/2)/b^6-_ + 40/7*a^3*(a+b*sqrt(x))^(7/2)/b^6+40/9*a^2*(a+_ + b*sqrt(x))^(9/2)/b^6-20/11*a*(a+b*sqrt(x))^(11/2)/b^6+_ + 4/13*(a+b*sqrt(x))^(13/2)/b^6 +--R +--R +--R (2) +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (252a b x + 320a b x + 512a b)\|x + 2772b x - 280a b x - 384a b x +--R + +--R 6 +--R - 1024a +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 9009b +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 +--R (252a b x + 320a b x + 512a b)\|x + 2772b x - 280a b x - 384a b x +--R + +--R 6 +--R - 1024a +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 9009b +--R Type: Union(Expression(Integer),...) +--E 1016 + +--S 1017 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1017 + +--S 1018 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1018 + +)clear all + +--S 1019 of 1325 +t0:=x*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R (1) x\|b\|x + a +--R Type: Expression(Integer) +--E 1019 + +--S 1020 of 1325 +r0:=-4/3*a^3*(a+b*sqrt(x))^(3/2)/b^4+12/5*a^2*(a+b*sqrt(x))^(5/2)/b^4-_ + 12/7*a*(a+b*sqrt(x))^(7/2)/b^4+4/9*(a+b*sqrt(x))^(9/2)/b^4 +--R +--R +--R +---------+ +--R 3 3 +-+ 4 2 2 2 4 | +-+ +--R ((20a b x + 32a b)\|x + 140b x - 24a b x - 64a )\|b\|x + a +--R (2) -------------------------------------------------------------- +--R 4 +--R 315b +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3 3 +-+ 4 2 2 2 4 | +-+ +--R ((20a b x + 32a b)\|x + 140b x - 24a b x - 64a )\|b\|x + a +--R (3) -------------------------------------------------------------- +--R 4 +--R 315b +--R Type: Union(Expression(Integer),...) +--E 1021 + +--S 1022 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1022 + +--S 1023 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1023 + +)clear all + +--S 1024 of 1325 +t0:=sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R (1) \|b\|x + a +--R Type: Expression(Integer) +--E 1024 + +--S 1025 of 1325 +r0:=-4/3*a*(a+b*sqrt(x))^(3/2)/b^2+4/5*(a+b*sqrt(x))^(5/2)/b^2 +--R +--R +--R +---------+ +--R +-+ 2 2 | +-+ +--R (4a b\|x + 12b x - 8a )\|b\|x + a +--R (2) ------------------------------------ +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +-+ 2 2 | +-+ +--R (4a b\|x + 12b x - 8a )\|b\|x + a +--R (3) ------------------------------------ +--R 2 +--R 15b +--R Type: Union(Expression(Integer),...) +--E 1026 + +--S 1027 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1027 + +--S 1028 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1028 + +)clear all + +--S 1029 of 1325 +t0:=sqrt(a+b*sqrt(x))/x +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R x +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1325 +r0:=-4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))*sqrt(a)+4*sqrt(a+b*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R +-+ \|b\|x + a | +-+ +--R (2) - 4\|a atanh(------------) + 4\|b\|x + a +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R +-+ | +-+ +-+ +---------+ +--R +-+ - 2\|a \|b\|x + a + b\|x + 2a | +-+ +--R [2\|a log(--------------------------------) + 4\|b\|x + a , +--R +-+ +--R \|x +--R +---------+ +--R | +-+ +---------+ +--R +---+ \|b\|x + a | +-+ +--R - 4\|- a atan(------------) + 4\|b\|x + a ] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1031 + +--S 1032 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R +-+ | +-+ +-+ | +-+ +--R +-+ - 2\|a \|b\|x + a + b\|x + 2a +-+ \|b\|x + a +--R (4) 2\|a log(--------------------------------) + 4\|a atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ | +-+ +--R +-+ \|b\|x + a +---+ \|b\|x + a +--R (6) 4\|a atanh(------------) - 4\|- a atan(------------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 1034 + +--S 1035 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1035 + +)clear all + +--S 1036 of 1325 +t0:=sqrt(a+b*sqrt(x))/x^2 +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R 2 +--R x +--R Type: Expression(Integer) +--E 1036 + +--S 1037 of 1325 +r0:=1/2*b^2*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(3/2)-sqrt(a+b*sqrt(x))/x-_ + 1/2*b*sqrt(a+b*sqrt(x))/(a*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R 2 +-+ \|b\|x + a +-+ +-+ +-+ | +-+ +--R b x\|x atanh(------------) + (- 2a\|a \|x - b x\|a )\|b\|x + a +--R +-+ +--R \|a +--R (2) ----------------------------------------------------------------- +--R +-+ +-+ +--R 2a x\|a \|x +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 2 2a\|b\|x + a + b\|a \|x + 2a\|a +--R b x log(-----------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R +-+ +-+ +-+ | +-+ +--R (- 2b\|a \|x - 4a\|a )\|b\|x + a +--R / +--R +-+ +--R 4a x\|a +--R , +--R +---------+ +--R +---+ | +-+ +---------+ +--R 2 \|- a \|b\|x + a +---+ +-+ +---+ | +-+ +--R b x atan(------------------) + (- b\|- a \|x - 2a\|- a )\|b\|x + a +--R a +--R ---------------------------------------------------------------------] +--R +---+ +--R 2a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1038 + +--S 1039 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 2 2a\|b\|x + a + b\|a \|x + 2a\|a 2 \|b\|x + a +--R b log(-----------------------------------) - 2b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ------------------------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 1039 + +--S 1040 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1040 + +--S 1041 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 2 +---+ \|b\|x + a 2 +-+ \|- a \|b\|x + a +--R - b \|- a atanh(------------) + b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 1041 + +--S 1042 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1042 + +)clear all + +--S 1043 of 1325 +t0:=sqrt(a+b*sqrt(x))/x^3 +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R (1) ------------ +--R 3 +--R x +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1325 +r0:=5/32*b^4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(7/2)-_ + 1/2*sqrt(a+b*sqrt(x))/x^2-1/12*b*sqrt(a+b*sqrt(x))/(a*x^(3/2))+_ + 5/48*b^2*sqrt(a+b*sqrt(x))/(a^2*x)-5/32*b^3*_ + sqrt(a+b*sqrt(x))/(a^3*sqrt(x)) +--R +--R +--R (2) +--R +---------+ +--R | +-+ +--R 4 2 +-+ \|b\|x + a +--R 15b x \|x atanh(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 2 3 +-+ +-+ 3 2 2 +-+ | +-+ +--R ((10a b x - 48a )\|a \|x + (- 15b x - 8a b x)\|a )\|b\|x + a +--R / +--R 3 2 +-+ +-+ +--R 96a x \|a \|x +--R Type: Expression(Integer) +--E 1044 + +--S 1045 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 4 2 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 15b x log(-----------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R 3 2 +-+ +-+ 2 3 +-+ | +-+ +--R ((- 30b x - 16a b)\|a \|x + (20a b x - 96a )\|a )\|b\|x + a +--R / +--R 3 2 +-+ +--R 192a x \|a +--R , +--R +--R +---------+ +--R +---+ | +-+ +--R 4 2 \|- a \|b\|x + a +--R 15b x atan(------------------) +--R a +--R + +--R +---------+ +--R 3 2 +---+ +-+ 2 3 +---+ | +-+ +--R ((- 15b x - 8a b)\|- a \|x + (10a b x - 48a )\|- a )\|b\|x + a +--R / +--R 3 2 +---+ +--R 96a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1045 + +--S 1046 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 4 2a\|b\|x + a + b\|a \|x + 2a\|a 4 \|b\|x + a +--R 5b log(-----------------------------------) - 10b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) --------------------------------------------------------------------- +--R 3 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 4 +---+ \|b\|x + a 4 +-+ \|- a \|b\|x + a +--R - 5b \|- a atanh(------------) + 5b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------------- +--R 3 +---+ +-+ +--R 32a \|- a \|a +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1325 +t0:=x^2/sqrt(a+b*sqrt(x)) +--R +--R +--R 2 +--R x +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1325 +r0:=512/693*a^4*(a+b*sqrt(x))^(3/2)/b^6-512/231*a^5*sqrt(a+b*sqrt(x))/_ + b^6-128/231*a^3*x*sqrt(a+b*sqrt(x))/b^4+320/693*a^2*x^(3/2)*_ + sqrt(a+b*sqrt(x))/b^3-40/99*a*x^2*sqrt(a+b*sqrt(x))/b^2+_ + 4/11*x^(5/2)*sqrt(a+b*sqrt(x))/b +--R +--R +--R (2) +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R ((252b x + 320a b x + 512a b)\|x - 280a b x - 384a b x - 1024a ) +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 693b +--R Type: Expression(Integer) +--E 1051 + +--S 1052 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R ((252b x + 320a b x + 512a b)\|x - 280a b x - 384a b x - 1024a ) +--R * +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R / +--R 6 +--R 693b +--R Type: Union(Expression(Integer),...) +--E 1052 + +--S 1053 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1053 + +--S 1054 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1054 + +)clear all + +--S 1055 of 1325 +t0:=x/sqrt(a+b*sqrt(x)) +--R +--R +--R x +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1325 +r0:=32/35*a^2*(a+b*sqrt(x))^(3/2)/b^4-96/35*a^3*sqrt(a+b*sqrt(x))/b^4-_ + 24/35*a*x*sqrt(a+b*sqrt(x))/b^2+4/7*x^(3/2)*sqrt(a+b*sqrt(x))/b +--R +--R +--R +---------+ +--R 3 2 +-+ 2 3 | +-+ +--R ((20b x + 32a b)\|x - 24a b x - 64a )\|b\|x + a +--R (2) -------------------------------------------------- +--R 4 +--R 35b +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3 2 +-+ 2 3 | +-+ +--R ((20b x + 32a b)\|x - 24a b x - 64a )\|b\|x + a +--R (3) -------------------------------------------------- +--R 4 +--R 35b +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1325 +t0:=1/sqrt(a+b*sqrt(x)) +--R +--R +--R 1 +--R (1) ------------ +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1325 +r0:=4/3*(a+b*sqrt(x))^(3/2)/b^2-4*a*sqrt(a+b*sqrt(x))/b^2 +--R +--R +--R +---------+ +--R +-+ | +-+ +--R (4b\|x - 8a)\|b\|x + a +--R (2) ------------------------- +--R 2 +--R 3b +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R +-+ | +-+ +--R (4b\|x - 8a)\|b\|x + a +--R (3) ------------------------- +--R 2 +--R 3b +--R Type: Union(Expression(Integer),...) +--E 1062 + +--S 1063 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1063 + +--S 1064 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1064 + +)clear all + +--S 1065 of 1325 +t0:=1/(x*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) ------------- +--R +---------+ +--R | +-+ +--R x\|b\|x + a +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1325 +r0:=-4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/sqrt(a) +--R +--R +--R +---------+ +--R | +-+ +--R \|b\|x + a +--R 4atanh(------------) +--R +-+ +--R \|a +--R (2) - -------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +-+ +-+ +-+ +---------+ +--R - 2a\|b\|x + a + b\|a \|x + 2a\|a +---+ | +-+ +--R 2log(-------------------------------------) \|- a \|b\|x + a +--R +-+ 4atan(------------------) +--R \|x a +--R [-------------------------------------------,- -------------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1067 + +--S 1068 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R - 2a\|b\|x + a + b\|a \|x + 2a\|a \|b\|x + a +--R 2log(-------------------------------------) + 4atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ------------------------------------------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R +---+ \|b\|x + a +-+ \|- a \|b\|x + a +--R 4\|- a atanh(------------) - 4\|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1071 + +)clear all + +--S 1072 of 1325 +t0:=1/(x^2*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 2 | +-+ +--R x \|b\|x + a +--R Type: Expression(Integer) +--E 1072 + +--S 1073 of 1325 +r0:=-3/2*b^2*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(5/2)-_ + sqrt(a+b*sqrt(x))/(a*x)+3/2*b*sqrt(a+b*sqrt(x))/(a^2*sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +---------+ +--R 2 +-+ \|b\|x + a +-+ +-+ +-+ | +-+ +--R - 3b x\|x atanh(------------) + (- 2a\|a \|x + 3b x\|a )\|b\|x + a +--R +-+ +--R \|a +--R (2) --------------------------------------------------------------------- +--R 2 +-+ +-+ +--R 2a x\|a \|x +--R Type: Expression(Integer) +--E 1073 + +--S 1074 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 3b x log(-------------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R +-+ +-+ +-+ | +-+ +--R (6b\|a \|x - 4a\|a )\|b\|x + a +--R / +--R 2 +-+ +--R 4a x\|a +--R , +--R +---------+ +--R +---+ | +-+ +---------+ +--R 2 \|- a \|b\|x + a +---+ +-+ +---+ | +-+ +--R - 3b x atan(------------------) + (3b\|- a \|x - 2a\|- a )\|b\|x + a +--R a +--R -----------------------------------------------------------------------] +--R 2 +---+ +--R 2a x\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1074 + +--S 1075 of 1325 +m0a:=a0.1-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a 2 \|b\|x + a +--R 3b log(-------------------------------------) + 6b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R (4) ---------------------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 1075 + +--S 1076 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1076 + +--S 1077 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 2 +---+ \|b\|x + a 2 +-+ \|- a \|b\|x + a +--R 3b \|- a atanh(------------) - 3b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) -------------------------------------------------------------- +--R 2 +---+ +-+ +--R 2a \|- a \|a +--R Type: Expression(Integer) +--E 1077 + +--S 1078 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1078 + +)clear all + +--S 1079 of 1325 +t0:=1/(x^3*sqrt(a+b*sqrt(x))) +--R +--R +--R 1 +--R (1) -------------- +--R +---------+ +--R 3 | +-+ +--R x \|b\|x + a +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1325 +r0:=-35/32*b^4*atanh(sqrt(a+b*sqrt(x))/sqrt(a))/a^(9/2)-_ + 1/2*sqrt(a+b*sqrt(x))/(a*x^2)+7/12*b*sqrt(a+b*sqrt(x))/_ + (a^2*x^(3/2))-35/48*b^2*sqrt(a+b*sqrt(x))/(a^3*x)+35/32*b^3*_ + sqrt(a+b*sqrt(x))/(a^4*sqrt(x)) +--R +--R +--R (2) +--R +---------+ +--R | +-+ +--R 4 2 +-+ \|b\|x + a +--R - 105b x \|x atanh(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 2 3 +-+ +-+ 3 2 2 +-+ | +-+ +--R ((- 70a b x - 48a )\|a \|x + (105b x + 56a b x)\|a )\|b\|x + a +--R / +--R 4 2 +-+ +-+ +--R 96a x \|a \|x +--R Type: Expression(Integer) +--E 1080 + +--S 1081 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +---------+ +--R | +-+ +-+ +-+ +-+ +--R 4 2 - 2a\|b\|x + a + b\|a \|x + 2a\|a +--R 105b x log(-------------------------------------) +--R +-+ +--R \|x +--R + +--R +---------+ +--R 3 2 +-+ +-+ 2 3 +-+ | +-+ +--R ((210b x + 112a b)\|a \|x + (- 140a b x - 96a )\|a )\|b\|x + a +--R / +--R 4 2 +-+ +--R 192a x \|a +--R , +--R +--R +---------+ +--R +---+ | +-+ +--R 4 2 \|- a \|b\|x + a +--R - 105b x atan(------------------) +--R a +--R + +--R +---------+ +--R 3 2 +---+ +-+ 2 3 +---+ | +-+ +--R ((105b x + 56a b)\|- a \|x + (- 70a b x - 48a )\|- a )\|b\|x + a +--R / +--R 4 2 +---+ +--R 96a x \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1081 + +--S 1082 of 1325 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +---------+ +---------+ +--R | +-+ +-+ +-+ +-+ | +-+ +--R 4 - 2a\|b\|x + a + b\|a \|x + 2a\|a 4 \|b\|x + a +--R 35b log(-------------------------------------) + 70b atanh(------------) +--R +-+ +-+ +--R \|x \|a +--R ------------------------------------------------------------------------ +--R 4 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 1082 + +--S 1083 of 1325 +d0a:=D(m0a,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1083 + +--S 1084 of 1325 +m0b:=a0.2-r0 +--R +--R +--R +---------+ +---------+ +--R | +-+ +---+ | +-+ +--R 4 +---+ \|b\|x + a 4 +-+ \|- a \|b\|x + a +--R 35b \|- a atanh(------------) - 35b \|a atan(------------------) +--R +-+ a +--R \|a +--R (6) ---------------------------------------------------------------- +--R 4 +---+ +-+ +--R 32a \|- a \|a +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1325 +d0b:=D(m0b,x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1085 + +)clear all + +--S 1086 of 1325 +t0:=sqrt(x)*(a+b*sqrt(x))^n +--R +--R +--R +-+ +-+ n +--R (1) \|x (b\|x + a) +--R Type: Expression(Integer) +--E 1086 + +--S 1087 of 1325 +r0:=2*a^2*(a+b*sqrt(x))^(1+n)/(b^3*(1+n))-4*a*(a+b*sqrt(x))^(2+n)/_ + (b^3*(2+n))+2*(a+b*sqrt(x))^(3+n)/(b^3*(3+n)) +--R +--R +--R (2) +--R 2 +-+ n + 3 2 +-+ n + 2 +--R (2n + 6n + 4)(b\|x + a) + (- 4a n - 16a n - 12a)(b\|x + a) +--R + +--R 2 2 2 2 +-+ n + 1 +--R (2a n + 10a n + 12a )(b\|x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 1087 + +--S 1088 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 +-+ 2 2 2 3 +--R (((2b n + 6b n + 4b )x - 4a b n)\|x + (2a b n + 2a b n)x + 4a ) +--R * +--R +-+ +--R n log(b\|x + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Union(Expression(Integer),...) +--E 1088 + +--S 1089 of 1325 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 +-+ 2 2 2 3 +--R (((2b n + 6b n + 4b )x - 4a b n)\|x + (2a b n + 2a b n)x + 4a ) +--R * +--R +-+ +--R n log(b\|x + a) +--R %e +--R + +--R 2 +-+ n + 3 2 +-+ n + 2 +--R (- 2n - 6n - 4)(b\|x + a) + (4a n + 16a n + 12a)(b\|x + a) +--R + +--R 2 2 2 2 +-+ n + 1 +--R (- 2a n - 10a n - 12a )(b\|x + a) +--R / +--R 3 3 3 2 3 3 +--R b n + 6b n + 11b n + 6b +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1090 + +)clear all + +--S 1091 of 1325 +t0:=(a+b*sqrt(x))^n/sqrt(x) +--R +--R +--R +-+ n +--R (b\|x + a) +--R (1) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1091 + +--S 1092 of 1325 +r0:=2*(a+b*sqrt(x))^(1+n)/(b*(1+n)) +--R +--R +--R +-+ n + 1 +--R 2(b\|x + a) +--R (2) ----------------- +--R b n + b +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R +-+ n log(b\|x + a) +--R (2b\|x + 2a)%e +--R (3) ------------------------------- +--R b n + b +--R Type: Union(Expression(Integer),...) +--E 1093 + +--S 1094 of 1325 +m0:=a0-r0 +--R +--R +--R +-+ +--R +-+ n log(b\|x + a) +-+ n + 1 +--R (2b\|x + 2a)%e - 2(b\|x + a) +--R (4) --------------------------------------------------- +--R b n + b +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1325 +t0:=(1+sqrt(x))/sqrt(x) +--R +--R +--R +-+ +--R \|x + 1 +--R (1) -------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1325 +r0:=x+2*sqrt(x) +--R +--R +--R +-+ +--R (2) 2\|x + x +--R Type: Expression(Integer) +--E 1097 + +--S 1098 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (3) 2\|x + x +--R Type: Union(Expression(Integer),...) +--E 1098 + +--S 1099 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1099 + +--S 1100 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1100 + +)clear all + +--S 1101 of 1325 +t0:=(1+sqrt(x))^2/sqrt(x) +--R +--R +--R +-+ +--R 2\|x + x + 1 +--R (1) ------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1325 +r0:=2/3*(1+sqrt(x))^3 +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x + 2 +--R (2) --------------------- +--R 3 +--R Type: Expression(Integer) +--E 1102 + +--S 1103 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (2x + 6)\|x + 6x +--R (3) ----------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1103 + +--S 1104 of 1325 +m0:=a0-r0 +--R +--R +--R 2 +--R (4) - - +--R 3 +--R Type: Expression(Integer) +--E 1104 + +--S 1105 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1105 + +)clear all + +--S 1106 of 1325 +t0:=(1+sqrt(x))^3/sqrt(x) +--R +--R +--R +-+ +--R (x + 3)\|x + 3x + 1 +--R (1) -------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1325 +r0:=1/2*(1+sqrt(x))^4 +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x + 1 +--R (2) -------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1107 + +--S 1108 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ 2 +--R (4x + 4)\|x + x + 6x +--R (3) ---------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1108 + +--S 1109 of 1325 +m0:=a0-r0 +--R +--R +--R 1 +--R (4) - - +--R 2 +--R Type: Expression(Integer) +--E 1109 + +--S 1110 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1110 + +)clear all + +--S 1111 of 1325 +t0:=sqrt(x)/(1+sqrt(x)) +--R +--R +--R +-+ +--R \|x +--R (1) -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1325 +r0:=x+2*log(1+sqrt(x))-2*sqrt(x) +--R +--R +--R +-+ +-+ +--R (2) 2log(\|x + 1) - 2\|x + x +--R Type: Expression(Integer) +--E 1112 + +--S 1113 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +-+ +--R (3) 2log(\|x + 1) - 2\|x + x +--R Type: Union(Expression(Integer),...) +--E 1113 + +--S 1114 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1114 + +--S 1115 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1115 + +)clear all + +--S 1116 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))) +--R +--R +--R 1 +--R (1) -------- +--R +-+ +--R \|x + x +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1325 +r0:=2*log(1+sqrt(x)) +--R +--R +--R +-+ +--R (2) 2log(\|x + 1) +--R Type: Expression(Integer) +--E 1117 + +--S 1118 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R (3) 2log(\|x + 1) +--R Type: Union(Expression(Integer),...) +--E 1118 + +--S 1119 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1119 + +--S 1120 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1120 + +)clear all + +--S 1121 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))^2) +--R +--R +--R 1 +--R (1) ---------------- +--R +-+ +--R (x + 1)\|x + 2x +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1325 +r0:=(-2)/(1+sqrt(x)) +--R +--R +--R 2 +--R (2) - -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1122 + +--S 1123 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - -------- +--R +-+ +--R \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 1123 + +--S 1124 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1124 + +--S 1125 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1125 + +)clear all + +--S 1126 of 1325 +t0:=1/(sqrt(x)*(1+sqrt(x))^3) +--R +--R +--R 1 +--R (1) ---------------------- +--R +-+ 2 +--R (3x + 1)\|x + x + 3x +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1325 +r0:=(-1)/(1+sqrt(x))^2 +--R +--R +--R 1 +--R (2) - ------------- +--R +-+ +--R 2\|x + x + 1 +--R Type: Expression(Integer) +--E 1127 + +--S 1128 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R +-+ +--R 2\|x + x + 1 +--R Type: Union(Expression(Integer),...) +--E 1128 + +--S 1129 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1129 + +--S 1130 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1130 + +)clear all + +--S 1131 of 1325 +t0:=sqrt(x)*sqrt(1+sqrt(x)) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (1) \|x \|\|x + 1 +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1325 +r0:=4/3*(1+sqrt(x))^(3/2)-8/5*(1+sqrt(x))^(5/2)+4/7*(1+sqrt(x))^(7/2) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R ((60x - 16)\|x + 12x + 32)\|\|x + 1 +--R (2) -------------------------------------- +--R 105 +--R Type: Expression(Integer) +--E 1132 + +--S 1133 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R ((60x - 16)\|x + 12x + 32)\|\|x + 1 +--R (3) -------------------------------------- +--R 105 +--R Type: Union(Expression(Integer),...) +--E 1133 + +--S 1134 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1134 + +--S 1135 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1135 + +)clear all + +--S 1136 of 1325 +t0:=sqrt(1+sqrt(x))/sqrt(x) +--R +--R +--R +--------+ +--R | +-+ +--R \|\|x + 1 +--R (1) ----------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1325 +r0:=4/3*(1+sqrt(x))^(3/2) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (4\|x + 4)\|\|x + 1 +--R (2) ---------------------- +--R 3 +--R Type: Expression(Integer) +--E 1137 + +--S 1138 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R +-+ | +-+ +--R (4\|x + 4)\|\|x + 1 +--R (3) ---------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1138 + +--S 1139 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1139 + +--S 1140 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1140 + +)clear all + +--S 1141 of 1325 +t0:=x^(1/3)/(1+sqrt(x)) +--R +--R +--R 3+-+ +--R \|x +--R (1) -------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1325 +r0:=-3*x^(1/3)+6/5*x^(5/6)-2*log(1+x^(1/6))+log(1-x^(1/6)+x^(1/3))-_ + 2*atan((1-2*x^(1/6))/sqrt(3))*sqrt(3) +--R +--R +--R (2) +--R 6+-+ +--R 6+-+ 6+-+ 3+-+ +-+ 2\|x - 1 +--R - 10log(\|x + 1) + 5log(- \|x + \|x + 1) + 10\|3 atan(---------) +--R +-+ +--R \|3 +--R + +--R 6+-+5 3+-+ +--R 6\|x - 15\|x +--R / +--R 5 +--R Type: Expression(Integer) +--E 1142 + +--S 1143 of 1325 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6+-+ +--R 6+-+2 6+-+ 6+-+ +-+ 2\|x - 1 6+-+5 +--R 5log(\|x - \|x + 1) - 10log(\|x + 1) + 10\|3 atan(---------) + 6\|x +--R +-+ +--R \|3 +--R + +--R 6+-+2 +--R - 15\|x +--R / +--R 5 +--R Type: Union(Expression(Integer),...) +--E 1143 + +--S 1144 of 1325 +m0:=a0-r0 +--R +--R +--R 6+-+2 6+-+ 6+-+ 3+-+ 6+-+2 3+-+ +--R (4) log(\|x - \|x + 1) - log(- \|x + \|x + 1) - 3\|x + 3\|x +--R Type: Expression(Integer) +--E 1144 + +--S 1145 of 1325 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1145 + +)clear all + +--S 1146 of 1325 +t0:=x^4/(a+b*x^(3/2))^(2/3) +--R +--R +--R 4 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1325 +--r0:=-7/20*a*x^2*(a+b*x^(3/2))^(1/3)/b^2+1/4*x^(7/2)*(a+b*x^(3/2))^(1/3)/_ +-- b+7/10*a^2*(a+b*x^(3/2))^(1/3)*sqrt(x)/b^3-7/10*a^3*((a+b*_ +-- x^(3/2))/a)^(2/3)*hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*_ +-- sqrt(x)/(b^3*(a+b*x^(3/2))^(2/3)) +--E 1147 + +--S 1148 of 1325 +--a0:=integrate(t0,x) +--E 1148 + +--S 1149 of 1325 +--m0:=a0-r0 +--E 1149 + +--S 1150 of 1325 +--d0:=D(m0,x) +--E 1150 + +)clear all + +--S 1151 of 1325 +t0:=x^3/(a+b*x^(3/2))^(2/3) +--R +--R +--R 3 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1325 +r0:=-5/9*a*x*(a+b*x^(3/2))^(1/3)/b^2+1/3*x^(5/2)*(a+b*x^(3/2))^(1/3)/b-_ + 10/27*a^2*log(1-b^(1/3)*sqrt(x)/(a+b*x^(3/2))^(1/3))/b^(8/3)+_ + 5/27*a^2*log(1+b^(2/3)*x/(a+b*x^(3/2))^(2/3)+b^(1/3)*sqrt(x)/_ + (a+b*x^(3/2))^(1/3))/b^(8/3)-10/9*a^2*atan((1+2*b^(1/3)*sqrt(x)/_ + (a+b*x^(3/2))^(1/3))/sqrt(3))/(b^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 3| +-+ 3+-+ +-+3| +-+ 3+-+2 +--R 2 +-+ \|b x\|x + a + \|b \|x \|b x\|x + a + x \|b +--R 5a \|3 log(--------------------------------------------------) +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +-+ +--R 2 +-+ \|b x\|x + a - \|b \|x +--R - 10a \|3 log(-------------------------) +--R +-----------+ +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +-+ +--R 2 \|b x\|x + a + 2\|b \|x +--R - 30a atan(--------------------------) +--R +-----------+ +--R +-+3| +-+ +--R \|3 \|b x\|x + a +--R + +--R +-----------+ +--R 2 +-+3+-+2 +-+ +-+3+-+2 3| +-+ +--R (9b x \|3 \|b \|x - 15a x\|3 \|b )\|b x\|x + a +--R / +--R 2 +-+3+-+2 +--R 27b \|3 \|b +--R Type: Expression(Integer) +--E 1152 + +--S 1153 of 1325 +--a0:=integrate(t0,x) +--E 1153 + +--S 1154 of 1325 +--m0:=a0-r0 +--E 1154 + +--S 1155 of 1325 +--d0:=D(m0,x) +--E 1155 + +)clear all + +--S 1156 of 1325 +t0:=x^2/(a+b*x^(3/2))^(2/3) +--R +--R +--R 2 +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1156 + +--S 1157 of 1325 +r0:=-3/2*a*(a+b*x^(3/2))^(1/3)/b^2+1/2*x^(3/2)*(a+b*x^(3/2))^(1/3)/b +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (b x\|x - 3a)\|b x\|x + a +--R (2) ---------------------------- +--R 2 +--R 2b +--R Type: Expression(Integer) +--E 1157 + +--S 1158 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (b x\|x - 3a)\|b x\|x + a +--R (3) ---------------------------- +--R 2 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 1158 + +--S 1159 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1160 + +)clear all + +--S 1161 of 1325 +t0:=x/(a+b*x^(3/2))^(2/3) +--R +--R +--R x +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1325 +--r0:=(a+b*x^(3/2))^(1/3)*sqrt(x)/b-a*((a+b*x^(3/2))/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*sqrt(x)/(b*(a+b*x^(3/2))^(2/3)) +--E 1162 + +--S 1163 of 1325 +--a0:=integrate(t0,x) +--E 1163 + +--S 1164 of 1325 +--m0:=a0-r0 +--E 1164 + +--S 1165 of 1325 +--d0:=D(m0,x) +--E 1165 + +)clear all + +--S 1166 of 1325 +t0:=1/(a+b*x^(3/2))^(2/3) +--R +--R +--R 1 +--R (1) --------------- +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1325 +r0:=-2/3*log(1-b^(1/3)*sqrt(x)/(a+b*x^(3/2))^(1/3))/b^(2/3)+1/3*_ + log(1+b^(2/3)*x/(a+b*x^(3/2))^(2/3)+b^(1/3)*sqrt(x)/(a+_ + b*x^(3/2))^(1/3))/b^(2/3)-2*atan((1+2*b^(1/3)*sqrt(x)/(a+_ + b*x^(3/2))^(1/3))/sqrt(3))/(b^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 3| +-+ 3+-+ +-+3| +-+ 3+-+2 +--R +-+ \|b x\|x + a + \|b \|x \|b x\|x + a + x \|b +--R \|3 log(--------------------------------------------------) +--R +-----------+2 +--R 3| +-+ +--R \|b x\|x + a +--R + +--R +-----------+ +-----------+ +--R 3| +-+ 3+-+ +-+ 3| +-+ 3+-+ +-+ +--R +-+ \|b x\|x + a - \|b \|x \|b x\|x + a + 2\|b \|x +--R - 2\|3 log(-------------------------) - 6atan(--------------------------) +--R +-----------+ +-----------+ +--R 3| +-+ +-+3| +-+ +--R \|b x\|x + a \|3 \|b x\|x + a +--R / +--R +-+3+-+2 +--R 3\|3 \|b +--R Type: Expression(Integer) +--E 1167 + +--S 1168 of 1325 +--a0:=integrate(t0,x) +--E 1168 + +--S 1169 of 1325 +--m0:=a0-r0 +--E 1169 + +--S 1170 of 1325 +--d0:=D(m0,x) +--E 1170 + +)clear all + +--S 1171 of 1325 +t0:=1/(x*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1325 +r0:=2/3*log(a^(1/3)-(a+b*x^(3/2))^(1/3))/a^(2/3)-1/3*log(a^(2/3)+_ + a^(1/3)*(a+b*x^(3/2))^(1/3)+(a+b*x^(3/2))^(2/3))/a^(2/3)-_ + 2*atan((a^(1/3)+2*(a+b*x^(3/2))^(1/3))/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R +-+ 3| +-+ 3+-+3| +-+ 3+-+2 +--R - \|3 log(\|b x\|x + a + \|a \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R +-----------+ 3| +-+ 3+-+ +--R +-+ 3| +-+ 3+-+ 2\|b x\|x + a + \|a +--R 2\|3 log(- \|b x\|x + a + \|a ) - 6atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+2 +--R 3\|3 \|a +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1325 +--a0:=integrate(t0,x) +--E 1173 + +--S 1174 of 1325 +--m0:=a0-r0 +--E 1174 + +--S 1175 of 1325 +--d0:=D(m0,x) +--E 1175 + +)clear all + +--S 1176 of 1325 +t0:=1/(x^2*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 2 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1325 +--r0:=-(a+b*x^(3/2))^(1/3)/(a*x)-b*((a+b*x^(3/2))/a)^(2/3)*_ +-- hypergeometric(1/3,2/3,4/3,-b*x^(3/2)/a)*sqrt(x)/(a*(a+b*x^(3/2))^(2/3)) +--E 1177 + +--S 1178 of 1325 +--a0:=integrate(t0,x) +--E 1178 + +--S 1179 of 1325 +--m0:=a0-r0 +--E 1179 + +--S 1180 of 1325 +--d0:=D(m0,x) +--E 1180 + +)clear all + +--S 1181 of 1325 +t0:=1/(x^3*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 3 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1325 +r0:=-1/2*(a+b*x^(3/2))^(1/3)/(a*x^2)+3/2*b*(a+b*x^(3/2))^(1/3)/(a^2*sqrt(x)) +--R +--R +--R +-----------+ +--R +-+ 2 3| +-+ +--R (- a\|x + 3b x )\|b x\|x + a +--R (2) ------------------------------- +--R 2 2 +-+ +--R 2a x \|x +--R Type: Expression(Integer) +--E 1182 + +--S 1183 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-----------+ +--R +-+ 3| +-+ +--R (3b x\|x - a)\|b x\|x + a +--R (3) ---------------------------- +--R 2 2 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 1183 + +--S 1184 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1184 + +--S 1185 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1185 + +)clear all + +--S 1186 of 1325 +t0:=1/(x^4*(a+b*x^(3/2))^(2/3)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-----------+2 +--R 4 3| +-+ +--R x \|b x\|x + a +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1325 +r0:=-1/3*(a+b*x^(3/2))^(1/3)/(a*x^3)+5/9*b*(a+b*x^(3/2))^(1/3)/_ + (a^2*x^(3/2))+10/27*b^2*log(a^(1/3)-(a+b*x^(3/2))^(1/3))/a^(8/3)-_ + 5/27*b^2*log(a^(2/3)+a^(1/3)*(a+b*x^(3/2))^(1/3)+(a+b*_ + x^(3/2))^(2/3))/a^(8/3)-10/9*b^2*atan((a^(1/3)+2*(a+b*_ + x^(3/2))^(1/3))/(a^(1/3)*sqrt(3)))/(a^(8/3)*sqrt(3)) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R 2 3 +-+ +-+ 3| +-+ 3+-+3| +-+ 3+-+2 +--R - 5b x \|3 \|x log(\|b x\|x + a + \|a \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R 2 3 +-+ +-+ 3| +-+ 3+-+ +--R 10b x \|3 \|x log(- \|b x\|x + a + \|a ) +--R + +--R +-----------+ +--R 3| +-+ 3+-+ +--R 2 3 +-+ 2\|b x\|x + a + \|a +--R - 30b x \|x atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-----------+ +--R +-+3+-+2 +-+ 2 +-+3+-+2 3| +-+ +--R (- 9a\|3 \|a \|x + 15b x \|3 \|a )\|b x\|x + a +--R / +--R 2 3 +-+3+-+2 +-+ +--R 27a x \|3 \|a \|x +--R Type: Expression(Integer) +--E 1187 + +--S 1188 of 1325 +--a0:=integrate(t0,x) +--E 1188 + +--S 1189 of 1325 +--m0:=a0-r0 +--E 1189 + +--S 1190 of 1325 +--d0:=D(m0,x) +--E 1190 + +)clear all + +--S 1191 of 1325 +t0:=sqrt(x)/(1+x^(3/2)) +--R +--R +--R +-+ +--R \|x +--R (1) --------- +--R +-+ +--R x\|x + 1 +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1325 +r0:=2/3*log(1+x^(3/2)) +--R +--R +--R +-+ +--R 2log(x\|x + 1) +--R (2) --------------- +--R 3 +--R Type: Expression(Integer) +--E 1192 + +--S 1193 of 1325 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R 2log(x\|x + 1) +--R (3) --------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 1193 + +--S 1194 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1194 + +--S 1195 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1195 + +)clear all + +--S 1196 of 1325 +t0:=(a+b*x^(1/3))*x^4 +--R +--R +--R 4 3+-+ 4 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1325 +r0:=1/5*a*x^5+3/16*b*x^(16/3) +--R +--R +--R 5 3+-+ 5 +--R 15b x \|x + 16a x +--R (2) ------------------- +--R 80 +--R Type: Expression(Integer) +--E 1197 + +--S 1198 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 5 3+-+ 5 +--R 15b x \|x + 16a x +--R (3) ------------------- +--R 80 +--R Type: Union(Expression(Integer),...) +--E 1198 + +--S 1199 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1199 + +--S 1200 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1200 + +)clear all + +--S 1201 of 1325 +t0:=(a+b*x^(1/3))*x^3 +--R +--R +--R 3 3+-+ 3 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1325 +r0:=1/4*a*x^4+3/13*b*x^(13/3) +--R +--R +--R 4 3+-+ 4 +--R 12b x \|x + 13a x +--R (2) ------------------- +--R 52 +--R Type: Expression(Integer) +--E 1202 + +--S 1203 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+ 4 +--R 12b x \|x + 13a x +--R (3) ------------------- +--R 52 +--R Type: Union(Expression(Integer),...) +--E 1203 + +--S 1204 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1204 + +--S 1205 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1205 + +)clear all + +--S 1206 of 1325 +t0:=(a+b*x^(1/3))*x^2 +--R +--R +--R 2 3+-+ 2 +--R (1) b x \|x + a x +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1325 +r0:=1/3*a*x^3+3/10*b*x^(10/3) +--R +--R +--R 3 3+-+ 3 +--R 9b x \|x + 10a x +--R (2) ------------------ +--R 30 +--R Type: Expression(Integer) +--E 1207 + +--S 1208 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3 +--R 9b x \|x + 10a x +--R (3) ------------------ +--R 30 +--R Type: Union(Expression(Integer),...) +--E 1208 + +--S 1209 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1209 + +--S 1210 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1210 + +)clear all + +--S 1211 of 1325 +t0:=(a+b*x^(1/3))*x +--R +--R +--R 3+-+ +--R (1) b x\|x + a x +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1325 +r0:=1/2*a*x^2+3/7*b*x^(7/3) +--R +--R +--R 2 3+-+ 2 +--R 6b x \|x + 7a x +--R (2) ----------------- +--R 14 +--R Type: Expression(Integer) +--E 1212 + +--S 1213 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 +--R 6b x \|x + 7a x +--R (3) ----------------- +--R 14 +--R Type: Union(Expression(Integer),...) +--E 1213 + +--S 1214 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1214 + +--S 1215 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1215 + +)clear all + +--S 1216 of 1325 +t0:=a+b*x^(1/3) +--R +--R +--R 3+-+ +--R (1) b\|x + a +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1325 +r0:=a*x+3/4*b*x^(4/3) +--R +--R +--R 3+-+ +--R 3b x\|x + 4a x +--R (2) --------------- +--R 4 +--R Type: Expression(Integer) +--E 1217 + +--S 1218 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R 3b x\|x + 4a x +--R (3) --------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 1218 + +--S 1219 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1219 + +--S 1220 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1220 + +)clear all + +--S 1221 of 1325 +t0:=(a+b*x^(1/3))/x +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1325 +r0:=3*b*x^(1/3)+a*log(x) +--R +--R +--R 3+-+ +--R (2) 3b\|x + a log(x) +--R Type: Expression(Integer) +--E 1222 + +--S 1223 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3) 3a log(\|x ) + 3b\|x +--R Type: Union(Expression(Integer),...) +--E 1223 + +--S 1224 of 1325 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1224 + +--S 1225 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1225 + +)clear all + +--S 1226 of 1325 +t0:=(a+b*x^(1/3))/x^2 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1325 +r0:=-a/x-3/2*b/x^(2/3) +--R +--R +--R 3+-+2 +--R - 2a \|x - 3b x +--R (2) ----------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 1227 + +--S 1228 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 3b\|x - 2a +--R (3) ------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1228 + +--S 1229 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1229 + +--S 1230 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1230 + +)clear all + +--S 1231 of 1325 +t0:=(a+b*x^(1/3))/x^3 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1325 +r0:=-1/2*a/x^2-3/5*b/x^(5/3) +--R +--R +--R 3+-+2 +--R - 5a \|x - 6b x +--R (2) ----------------- +--R 2 3+-+2 +--R 10x \|x +--R Type: Expression(Integer) +--E 1232 + +--S 1233 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 6b\|x - 5a +--R (3) ------------- +--R 2 +--R 10x +--R Type: Union(Expression(Integer),...) +--E 1233 + +--S 1234 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1234 + +--S 1235 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1235 + +)clear all + +--S 1236 of 1325 +t0:=(a+b*x^(1/3))/x^4 +--R +--R +--R 3+-+ +--R b\|x + a +--R (1) --------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1325 +r0:=-1/3*a/x^3-3/8*b/x^(8/3) +--R +--R +--R 3+-+2 +--R - 8a \|x - 9b x +--R (2) ----------------- +--R 3 3+-+2 +--R 24x \|x +--R Type: Expression(Integer) +--E 1237 + +--S 1238 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 9b\|x - 8a +--R (3) ------------- +--R 3 +--R 24x +--R Type: Union(Expression(Integer),...) +--E 1238 + +--S 1239 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1239 + +--S 1240 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1240 + +)clear all + +--S 1241 of 1325 +t0:=(a+b*x^(1/3))^2*x^4 +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1325 +r0:=1/5*a^2*x^5+3/8*a*b*x^(16/3)+3/17*b^2*x^(17/3) +--R +--R +--R 2 5 3+-+2 5 3+-+ 2 5 +--R 120b x \|x + 255a b x \|x + 136a x +--R (2) -------------------------------------- +--R 680 +--R Type: Expression(Integer) +--E 1242 + +--S 1243 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3+-+2 5 3+-+ 2 5 +--R 120b x \|x + 255a b x \|x + 136a x +--R (3) -------------------------------------- +--R 680 +--R Type: Union(Expression(Integer),...) +--E 1243 + +--S 1244 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1244 + +--S 1245 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1245 + +)clear all + +--S 1246 of 1325 +t0:=(a+b*x^(1/3))^2*x^3 +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1325 +r0:=1/4*a^2*x^4+6/13*a*b*x^(13/3)+3/14*b^2*x^(14/3) +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R 78b x \|x + 168a b x \|x + 91a x +--R (2) ------------------------------------ +--R 364 +--R Type: Expression(Integer) +--E 1247 + +--S 1248 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R 78b x \|x + 168a b x \|x + 91a x +--R (3) ------------------------------------ +--R 364 +--R Type: Union(Expression(Integer),...) +--E 1248 + +--S 1249 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1249 + +--S 1250 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1250 + +)clear all + +--S 1251 of 1325 +t0:=(a+b*x^(1/3))^2*x^2 +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R (1) b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1325 +r0:=1/3*a^2*x^3+3/5*a*b*x^(10/3)+3/11*b^2*x^(11/3) +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R 45b x \|x + 99a b x \|x + 55a x +--R (2) ----------------------------------- +--R 165 +--R Type: Expression(Integer) +--E 1252 + +--S 1253 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R 45b x \|x + 99a b x \|x + 55a x +--R (3) ----------------------------------- +--R 165 +--R Type: Union(Expression(Integer),...) +--E 1253 + +--S 1254 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1254 + +--S 1255 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1255 + +)clear all + +--S 1256 of 1325 +t0:=(a+b*x^(1/3))^2*x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R (1) b x \|x + 2a b x\|x + a x +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1325 +r0:=1/2*a^2*x^2+6/7*a*b*x^(7/3)+3/8*b^2*x^(8/3) +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R 21b x \|x + 48a b x \|x + 28a x +--R (2) ----------------------------------- +--R 56 +--R Type: Expression(Integer) +--E 1257 + +--S 1258 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R 21b x \|x + 48a b x \|x + 28a x +--R (3) ----------------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 1258 + +--S 1259 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1259 + +--S 1260 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1260 + +)clear all + +--S 1261 of 1325 +t0:=(a+b*x^(1/3))^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R (1) b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1325 +r0:=a^2*x+3/2*a*b*x^(4/3)+3/5*b^2*x^(5/3) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 6b x \|x + 15a b x\|x + 10a x +--R (2) -------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 1262 + +--S 1263 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 6b x \|x + 15a b x\|x + 10a x +--R (3) -------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 1263 + +--S 1264 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1264 + +--S 1265 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1265 + +)clear all + +--S 1266 of 1325 +t0:=(a+b*x^(1/3))^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R x +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1325 +r0:=6*a*b*x^(1/3)+3/2*b^2*x^(2/3)+a^2*log(x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 3b \|x + 12a b\|x + 2a log(x) +--R (2) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1267 + +--S 1268 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(\|x ) + 3b \|x + 12a b\|x +--R (3) ----------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1268 + +--S 1269 of 1325 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1269 + +--S 1270 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1270 + +)clear all + +--S 1271 of 1325 +t0:=(a+b*x^(1/3))^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1325 +r0:=-(a+b*x^(1/3))^3/(a*x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 3a b \|x - 3a b\|x - b x - a +--R (2) ---------------------------------- +--R a x +--R Type: Expression(Integer) +--E 1272 + +--S 1273 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 3b \|x - 3a b\|x - a +--R (3) -------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 1273 + +--S 1274 of 1325 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) -- +--R a +--R Type: Expression(Integer) +--E 1274 + +--S 1275 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1275 + +)clear all + +--S 1276 of 1325 +t0:=(a+b*x^(1/3))^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1325 +r0:=-1/2*a^2/x^2-6/5*a*b/x^(5/3)-3/4*b^2/x^(4/3) +--R +--R +--R 2 3+-+2 2 3+-+ +--R - 10a \|x - 15b x\|x - 24a b x +--R (2) --------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 1277 + +--S 1278 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 15b \|x - 24a b\|x - 10a +--R (3) ------------------------------ +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1278 + +--S 1279 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1279 + +--S 1280 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1280 + +)clear all + +--S 1281 of 1325 +t0:=(a+b*x^(1/3))^2/x^4 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R (1) ----------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1325 +r0:=-1/3*a^2/x^3-3/4*a*b/x^(8/3)-3/7*b^2/x^(7/3) +--R +--R +--R 2 3+-+2 2 3+-+ +--R - 28a \|x - 36b x\|x - 63a b x +--R (2) --------------------------------- +--R 3 3+-+2 +--R 84x \|x +--R Type: Expression(Integer) +--E 1282 + +--S 1283 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 36b \|x - 63a b\|x - 28a +--R (3) ------------------------------ +--R 3 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 1283 + +--S 1284 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1284 + +--S 1285 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1285 + +)clear all + +--S 1286 of 1325 +t0:=(a+b*x^(1/3))^3*x^4 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1325 +r0:=1/5*a^3*x^5+9/16*a^2*b*x^(16/3)+9/17*a*b^2*x^(17/3)+1/6*b^3*x^6 +--R +--R +--R 2 5 3+-+2 2 5 3+-+ 3 6 3 5 +--R 2160a b x \|x + 2295a b x \|x + 680b x + 816a x +--R (2) ---------------------------------------------------- +--R 4080 +--R Type: Expression(Integer) +--E 1287 + +--S 1288 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 5 3+-+2 2 5 3+-+ 3 6 3 5 +--R 2160a b x \|x + 2295a b x \|x + 680b x + 816a x +--R (3) ---------------------------------------------------- +--R 4080 +--R Type: Union(Expression(Integer),...) +--E 1288 + +--S 1289 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1289 + +--S 1290 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1290 + +)clear all + +--S 1291 of 1325 +t0:=(a+b*x^(1/3))^3*x^3 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1325 +r0:=1/4*a^3*x^4+9/13*a^2*b*x^(13/3)+9/14*a*b^2*x^(14/3)+1/5*b^3*x^5 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364b x + 455a x +--R (2) ---------------------------------------------------- +--R 1820 +--R Type: Expression(Integer) +--E 1292 + +--S 1293 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364b x + 455a x +--R (3) ---------------------------------------------------- +--R 1820 +--R Type: Union(Expression(Integer),...) +--E 1293 + +--S 1294 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1294 + +--S 1295 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1295 + +)clear all + +--S 1296 of 1325 +t0:=(a+b*x^(1/3))^3*x^2 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R (1) 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1325 +r0:=1/3*a^3*x^3+9/10*a^2*b*x^(10/3)+9/11*a*b^2*x^(11/3)+1/4*b^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165b x + 220a x +--R (2) -------------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 1297 + +--S 1298 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165b x + 220a x +--R (3) -------------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 1298 + +--S 1299 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1299 + +--S 1300 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1300 + +)clear all + +--S 1301 of 1325 +t0:=(a+b*x^(1/3))^3*x +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R (1) 3a b x \|x + 3a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1325 +r0:=1/2*a^3*x^2+9/7*a^2*b*x^(7/3)+9/8*a*b^2*x^(8/3)+1/3*b^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56b x + 84a x +--R (2) ------------------------------------------------ +--R 168 +--R Type: Expression(Integer) +--E 1302 + +--S 1303 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56b x + 84a x +--R (3) ------------------------------------------------ +--R 168 +--R Type: Union(Expression(Integer),...) +--E 1303 + +--S 1304 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1304 + +--S 1305 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1305 + +)clear all + +--S 1306 of 1325 +t0:=(a+b*x^(1/3))^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R (1) 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1325 +r0:=a^3*x+9/4*a^2*b*x^(4/3)+9/5*a*b^2*x^(5/3)+1/2*b^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10b x + 20a x +--R (2) -------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 1307 + +--S 1308 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10b x + 20a x +--R (3) -------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 1308 + +--S 1309 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1309 + +--S 1310 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1310 + +)clear all + +--S 1311 of 1325 +t0:=(a+b*x^(1/3))^3/x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R x +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1325 +r0:=9*a^2*b*x^(1/3)+9/2*a*b^2*x^(2/3)+b^3*x+a^3*log(x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 9a b \|x + 18a b\|x + 2a log(x) + 2b x +--R (2) ----------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 1312 + +--S 1313 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6a log(\|x ) + 9a b \|x + 18a b\|x + 2b x +--R (3) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1313 + +--S 1314 of 1325 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 1314 + +--S 1315 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1315 + +)clear all + +--S 1316 of 1325 +t0:=(a+b*x^(1/3))^3/x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1325 +r0:=-a^3/x-9/2*a^2*b/x^(2/3)-9*a*b^2/x^(1/3)+b^3*log(x) +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (2b x log(x) - 2a )\|x - 18a b x\|x - 9a b x +--R (2) ----------------------------------------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 1317 + +--S 1318 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b x log(\|x ) - 18a b \|x - 9a b\|x - 2a +--R (3) --------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 1318 + +--S 1319 of 1325 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 1319 + +--S 1320 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1320 + +)clear all + +--S 1321 of 1325 +t0:=(a+b*x^(1/3))^3/x^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1325 +r0:=-1/2*a^3/x^2-9/5*a^2*b/x^(5/3)-9/4*a*b^2/x^(4/3)-b^3/x +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 20b x - 10a )\|x - 45a b x\|x - 36a b x +--R (2) --------------------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 1322 + +--S 1323 of 1325 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 45a b \|x - 36a b\|x - 20b x - 10a +--R (3) ---------------------------------------- +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 1323 + +--S 1324 of 1325 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1324 + +--S 1325 of 1325 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1325 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4i.input.pamphlet b/src/input/rich4i.input.pamphlet new file mode 100644 index 0000000..1160c52 --- /dev/null +++ b/src/input/rich4i.input.pamphlet @@ -0,0 +1,16239 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4i.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 255 integrals in this file. +\item 259 supplied "optimal results". +\item 197 matching answers. +\item 6 cases where Axiom supplied 2 results. +\item 8 cases that Axiom failed to integrate. +\item 55 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +f)set break resume +)sys rm -f rich4i.output +)spool rich4i.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1299 +t0:=(a+b*x^(1/3))^3/x^4 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R (1) -------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1299 +r0:=-1/3*a^3/x^3-9/8*a^2*b/x^(8/3)-9/7*a*b^2/x^(7/3)-1/2*b^3/x^2 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 84b x - 56a )\|x - 216a b x\|x - 189a b x +--R (2) ----------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 216a b \|x - 189a b\|x - 84b x - 56a +--R (3) ------------------------------------------ +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1299 +t0:=(a+b*x^(1/3))^5*x^4 +--R +--R +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ 2 3 5 5 4 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1299 +r0:=1/5*a^5*x^5+15/16*a^4*b*x^(16/3)+30/17*a^3*b^2*x^(17/3)+_ + 5/3*a^2*b^3*x^6+15/19*a*b^4*x^(19/3)+3/20*b^5*x^(20/3) +--R +--R +--R (2) +--R 5 6 3 2 5 3+-+2 4 6 4 5 3+-+ +--R (11628b x + 136800a b x )\|x + (61200a b x + 72675a b x )\|x +--R + +--R 2 3 6 5 5 +--R 129200a b x + 15504a x +--R / +--R 77520 +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 6 3 2 5 3+-+2 4 6 4 5 3+-+ +--R (11628b x + 136800a b x )\|x + (61200a b x + 72675a b x )\|x +--R + +--R 2 3 6 5 5 +--R 129200a b x + 15504a x +--R / +--R 77520 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1299 +t0:=(a+b*x^(1/3))^5*x^3 +--R +--R +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ 2 3 4 5 3 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1299 +r0:=1/4*a^5*x^4+15/13*a^4*b*x^(13/3)+15/7*a^3*b^2*x^(14/3)+2*a^2*b^3*x^5+_ + 15/16*a*b^4*x^(16/3)+3/17*b^5*x^(17/3) +--R +--R +--R (2) +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ +--R (4368b x + 53040a b x )\|x + (23205a b x + 28560a b x )\|x +--R + +--R 2 3 5 5 4 +--R 49504a b x + 6188a x +--R / +--R 24752 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 3 2 4 3+-+2 4 5 4 4 3+-+ +--R (4368b x + 53040a b x )\|x + (23205a b x + 28560a b x )\|x +--R + +--R 2 3 5 5 4 +--R 49504a b x + 6188a x +--R / +--R 24752 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1299 +t0:=(a+b*x^(1/3))^5*x^2 +--R +--R +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 5 2 +--R (1) (b x + 10a b x )\|x + (5a b x + 5a b x )\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1299 +r0:=1/3*a^5*x^3+3/2*a^4*b*x^(10/3)+30/11*a^3*b^2*x^(11/3)+_ + 5/2*a^2*b^3*x^4+15/13*a*b^4*x^(13/3)+3/14*b^5*x^(14/3) +--R +--R +--R (2) +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ +--R (1287b x + 16380a b x )\|x + (6930a b x + 9009a b x )\|x +--R + +--R 2 3 4 5 3 +--R 15015a b x + 2002a x +--R / +--R 6006 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 4 3 2 3 3+-+2 4 4 4 3 3+-+ +--R (1287b x + 16380a b x )\|x + (6930a b x + 9009a b x )\|x +--R + +--R 2 3 4 5 3 +--R 15015a b x + 2002a x +--R / +--R 6006 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1299 +t0:=(a+b*x^(1/3))^5*x +--R +--R +--R 5 2 3 2 3+-+2 4 2 4 3+-+ 2 3 2 5 +--R (1) (b x + 10a b x)\|x + (5a b x + 5a b x)\|x + 10a b x + a x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1299 +r0:=1/2*a^5*x^2+15/7*a^4*b*x^(7/3)+15/4*a^3*b^2*x^(8/3)+10/3*a^2*b^3*_ + x^3+3/2*a*b^4*x^(10/3)+3/11*b^5*x^(11/3) +--R +--R +--R (2) +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 +--R (252b x + 3465a b x )\|x + (1386a b x + 1980a b x )\|x + 3080a b x +--R + +--R 5 2 +--R 462a x +--R / +--R 924 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 3 2 2 3+-+2 4 3 4 2 3+-+ 2 3 3 +--R (252b x + 3465a b x )\|x + (1386a b x + 1980a b x )\|x + 3080a b x +--R + +--R 5 2 +--R 462a x +--R / +--R 924 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1299 +t0:=(a+b*x^(1/3))^5 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (1) (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1299 +r0:=1/2*a^2*(a+b*x^(1/3))^6/b^3-6/7*a*(a+b*x^(1/3))^7/b^3+_ + 3/8*(a+b*x^(1/3))^8/b^3 +--R +--R +--R (2) +--R 8 2 3 5 3+-+2 7 2 4 4 3+-+ 2 6 2 +--R (21b x + 336a b x)\|x + (120a b x + 210a b x)\|x + 280a b x +--R + +--R 5 3 8 +--R 56a b x + a +--R / +--R 3 +--R 56b +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 3 2 3+-+2 4 2 4 3+-+ 2 3 2 5 +--R (21b x + 336a b x)\|x + (120a b x + 210a b x)\|x + 280a b x + 56a x +--R ------------------------------------------------------------------------- +--R 56 +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1299 +m0:=a0-r0 +--R +--R +--R 8 +--R a +--R (4) - ---- +--R 3 +--R 56b +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1299 +t0:=(a+b*x^(1/3))^5/x +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1299 +r0:=15*a^4*b*x^(1/3)+15*a^3*b^2*x^(2/3)+10*a^2*b^3*x+15/4*a*_ + b^4*x^(4/3)+3/5*b^5*x^(5/3)+a^5*log(x) +--R +--R +--R (2) +--R 5 3 2 3+-+2 4 4 3+-+ 5 2 3 +--R (12b x + 300a b )\|x + (75a b x + 300a b)\|x + 20a log(x) + 200a b x +--R ----------------------------------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R 60a log(\|x ) + (12b x + 300a b )\|x + (75a b x + 300a b)\|x + 200a b x +--R -------------------------------------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1299 +m0:=a0-r0 +--R +--R +--R 5 3+-+ 5 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1299 +t0:=(a+b*x^(1/3))^5/x^2 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1299 +r0:=-a^5/x-15/2*a^4*b/x^(2/3)-30*a^3*b^2/x^(1/3)+15*a*b^4*x^(1/3)+_ + 3/2*b^5*x^(2/3)+10*a^2*b^3*log(x) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 4 +--R (20a b x log(x) - 2a )\|x + (3b x - 60a b x)\|x + 30a b x - 15a b x +--R ------------------------------------------------------------------------ +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+ 5 3 2 3+-+2 4 4 3+-+ 5 +--R 60a b x log(\|x ) + (3b x - 60a b )\|x + (30a b x - 15a b)\|x - 2a +--R (3) ---------------------------------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3 3+-+ 2 3 +--R (4) 30a b log(\|x ) - 10a b log(x) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1299 +t0:=(a+b*x^(1/3))^5/x^3 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1299 +r0:=-1/2*(a+b*x^(1/3))^6/(a*x^2) +--R +--R +--R (2) +--R 5 4 2 3+-+2 2 4 5 3+-+ 6 2 3 3 6 +--R (- 6a b x - 15a b )\|x + (- 15a b x - 6a b)\|x - b x - 20a b x - a +--R ----------------------------------------------------------------------- +--R 2 +--R 2a x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 6b x - 15a b )\|x + (- 15a b x - 6a b)\|x - 20a b x - a +--R (3) -------------------------------------------------------------- +--R 2 +--R 2x +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1299 +m0:=a0-r0 +--R +--R +--R 6 +--R b +--R (4) -- +--R 2a +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1299 +t0:=(a+b*x^(1/3))^5/x^4 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1299 +r0:=-1/3*a^5/x^3-15/8*a^4*b/x^(8/3)-30/7*a^3*b^2/x^(7/3)-5*a^2*b^3/x^2-_ + 3*a*b^4/x^(5/3)-3/4*b^5/x^(4/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 4 +--R (- 840a b x - 56a )\|x + (- 126b x - 720a b x)\|x - 504a b x - 315a b x +--R ---------------------------------------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 126b x - 720a b )\|x + (- 504a b x - 315a b)\|x - 840a b x - 56a +--R ----------------------------------------------------------------------- +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1299 +t0:=(a+b*x^(1/3))^5/x^5 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1299 +r0:=-1/4*a^5/x^4-15/11*a^4*b/x^(11/3)-3*a^3*b^2/x^(10/3)-_ + 10/3*a^2*b^3/x^3-15/8*a*b^4/x^(8/3)-3/7*b^5/x^(7/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ 4 2 +--R (- 6160a b x - 462a )\|x + (- 792b x - 5544a b x)\|x - 3465a b x +--R + +--R 4 +--R - 2520a b x +--R / +--R 4 3+-+2 +--R 1848x \|x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (- 792b x - 5544a b )\|x + (- 3465a b x - 2520a b)\|x - 6160a b x - 462a +--R ---------------------------------------------------------------------------- +--R 4 +--R 1848x +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1299 +t0:=(a+b*x^(1/3))^5/x^6 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 6 +--R x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1299 +r0:=-1/5*a^5/x^5-15/14*a^4*b/x^(14/3)-30/13*a^3*b^2/x^(13/3)-_ + 5/2*a^2*b^3/x^4-15/11*a*b^4/x^(11/3)-3/10*b^5/x^(10/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ +--R (- 25025a b x - 2002a )\|x + (- 3003b x - 23100a b x)\|x +--R + +--R 4 2 4 +--R - 13650a b x - 10725a b x +--R / +--R 5 3+-+2 +--R 10010x \|x +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R (- 3003b x - 23100a b )\|x + (- 13650a b x - 10725a b)\|x - 25025a b x +--R + +--R 5 +--R - 2002a +--R / +--R 5 +--R 10010x +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1299 +t0:=(a+b*x^(1/3))^5/x^7 +--R +--R +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 5 +--R (b x + 10a b )\|x + (5a b x + 5a b)\|x + 10a b x + a +--R (1) -------------------------------------------------------- +--R 7 +--R x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1299 +r0:=-1/6*a^5/x^6-15/17*a^4*b/x^(17/3)-15/8*a^3*b^2/x^(16/3)-_ + 2*a^2*b^3/x^5-15/14*a*b^4/x^(14/3)-3/13*b^5/x^(13/3) +--R +--R +--R (2) +--R 2 3 5 3+-+2 5 2 3 2 3+-+ +--R (- 74256a b x - 6188a )\|x + (- 8568b x - 69615a b x)\|x +--R + +--R 4 2 4 +--R - 39780a b x - 32760a b x +--R / +--R 6 3+-+2 +--R 37128x \|x +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3 2 3+-+2 4 4 3+-+ 2 3 +--R (- 8568b x - 69615a b )\|x + (- 39780a b x - 32760a b)\|x - 74256a b x +--R + +--R 5 +--R - 6188a +--R / +--R 6 +--R 37128x +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1299 +t0:=(a+b*x^(1/3))^10*x^4 +--R +--R +--R (1) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ 9 7 4 6 6 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 5 10 4 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1299 +r0:=1/5*a^10*x^5+15/8*a^9*b*x^(16/3)+135/17*a^8*b^2*x^(17/3)+_ + 20*a^7*b^3*x^6+630/19*a^6*b^4*x^(19/3)+189/5*a^5*b^5*x^(20/3)+_ + 30*a^4*b^6*x^7+180/11*a^3*b^7*x^(22/3)+135/23*a^2*b^8*x^(23/3)+_ + 5/4*a*b^9*x^8+3/25*b^10*x^(25/3) +--R +--R +--R (2) +--R 2 8 7 5 5 6 8 2 5 3+-+2 +--R (95931000a b x + 617795640a b x + 129789000a b x )\|x +--R + +--R 10 8 3 7 7 6 4 6 9 5 3+-+ +--R (1961256b x + 267444000a b x + 541926000a b x + 30644625a b x )\|x +--R + +--R 9 8 4 6 7 7 3 6 10 5 +--R 20429750a b x + 490314000a b x + 326876000a b x + 3268760a x +--R / +--R 16343800 +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 7 5 5 6 8 2 5 3+-+2 +--R (95931000a b x + 617795640a b x + 129789000a b x )\|x +--R + +--R 10 8 3 7 7 6 4 6 9 5 3+-+ +--R (1961256b x + 267444000a b x + 541926000a b x + 30644625a b x )\|x +--R + +--R 9 8 4 6 7 7 3 6 10 5 +--R 20429750a b x + 490314000a b x + 326876000a b x + 3268760a x +--R / +--R 16343800 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1299 +t0:=(a+b*x^(1/3))^10*x^3 +--R +--R +--R (1) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ 9 6 4 6 5 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 4 10 3 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1299 +r0:=1/4*a^10*x^4+30/13*a^9*b*x^(13/3)+135/14*a^8*b^2*x^(14/3)+_ + 24*a^7*b^3*x^5+315/8*a^6*b^4*x^(16/3)+756/17*a^5*b^5*x^(17/3)+_ + 35*a^4*b^6*x^6+360/19*a^3*b^7*x^(19/3)+27/4*a^2*b^8*x^(20/3)+_ + 10/7*a*b^9*x^7+3/22*b^10*x^(22/3) +--R +--R +--R (2) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (17459442a b x + 115026912a b x + 24942060a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ +--R (352716b x + 49008960a b x + 101846745a b x + 5969040a b x )\|x +--R + +--R 9 7 4 6 6 7 3 5 10 4 +--R 3695120a b x + 90530440a b x + 62078016a b x + 646646a x +--R / +--R 2586584 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 6 5 5 5 8 2 4 3+-+2 +--R (17459442a b x + 115026912a b x + 24942060a b x )\|x +--R + +--R 10 7 3 7 6 6 4 5 9 4 3+-+ +--R (352716b x + 49008960a b x + 101846745a b x + 5969040a b x )\|x +--R + +--R 9 7 4 6 6 7 3 5 10 4 +--R 3695120a b x + 90530440a b x + 62078016a b x + 646646a x +--R / +--R 2586584 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1299 +t0:=(a+b*x^(1/3))^10*x^2 +--R +--R +--R (1) +--R 2 8 4 5 5 3 8 2 2 3+-+2 +--R (45a b x + 252a b x + 45a b x )\|x +--R + +--R 10 5 3 7 4 6 4 3 9 2 3+-+ 9 5 4 6 4 +--R (b x + 120a b x + 210a b x + 10a b x )\|x + 10a b x + 210a b x +--R + +--R 7 3 3 10 2 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1299 +r0:=1/3*a^10*x^3+3*a^9*b*x^(10/3)+135/11*a^8*b^2*x^(11/3)+_ + 30*a^7*b^3*x^4+630/13*a^6*b^4*x^(13/3)+54*a^5*b^5*x^(14/3)+_ + 42*a^4*b^6*x^5+45/2*a^3*b^7*x^(16/3)+135/17*a^2*b^8*x^(17/3)+_ + 5/3*a*b^9*x^6+3/19*b^10*x^(19/3) +--R +--R +--R (2) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (2200770a b x + 14965236a b x + 3401190a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ +--R (43758b x + 6235515a b x + 13430340a b x + 831402a b x )\|x +--R + +--R 9 6 4 6 5 7 3 4 10 3 +--R 461890a b x + 11639628a b x + 8314020a b x + 92378a x +--R / +--R 277134 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 5 5 5 4 8 2 3 3+-+2 +--R (2200770a b x + 14965236a b x + 3401190a b x )\|x +--R + +--R 10 6 3 7 5 6 4 4 9 3 3+-+ +--R (43758b x + 6235515a b x + 13430340a b x + 831402a b x )\|x +--R + +--R 9 6 4 6 5 7 3 4 10 3 +--R 461890a b x + 11639628a b x + 8314020a b x + 92378a x +--R / +--R 277134 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1299 +t0:=(a+b*x^(1/3))^10*x +--R +--R +--R (1) +--R 2 8 3 5 5 2 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 3+-+ 9 4 4 6 3 +--R (b x + 120a b x + 210a b x + 10a b x)\|x + 10a b x + 210a b x +--R + +--R 7 3 2 10 +--R 120a b x + a x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1299 +r0:=-3/11*a^5*(a+b*x^(1/3))^11/b^6+5/4*a^4*(a+b*x^(1/3))^12/b^6-_ + 30/13*a^3*(a+b*x^(1/3))^13/b^6+15/7*a^2*(a+b*x^(1/3))^14/b^6-_ + a*(a+b*x^(1/3))^15/b^6+3/16*(a+b*x^(1/3))^16/b^6 +--R +--R +--R (2) +--R 2 14 4 5 11 3 8 8 2 3+-+2 +--R (154440a b x + 1100736a b x + 270270a b x )\|x +--R + +--R 16 5 3 13 4 6 10 3 9 7 2 3+-+ +--R (3003b x + 443520a b x + 1009008a b x + 68640a b x )\|x +--R + +--R 15 5 4 12 4 7 9 3 10 6 2 16 +--R 32032a b x + 840840a b x + 640640a b x + 8008a b x - a +--R / +--R 6 +--R 16016b +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 4 5 5 3 8 2 2 3+-+2 +--R (154440a b x + 1100736a b x + 270270a b x )\|x +--R + +--R 10 5 3 7 4 6 4 3 9 2 3+-+ +--R (3003b x + 443520a b x + 1009008a b x + 68640a b x )\|x +--R + +--R 9 5 4 6 4 7 3 3 10 2 +--R 32032a b x + 840840a b x + 640640a b x + 8008a x +--R / +--R 16016 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1299 +m0:=a0-r0 +--R +--R +--R 16 +--R a +--R (4) ------- +--R 6 +--R 16016b +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1299 +t0:=(a+b*x^(1/3))^10 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1299 +r0:=3/11*a^2*(a+b*x^(1/3))^11/b^3-1/2*a*(a+b*x^(1/3))^12/b^3+_ + 3/13*(a+b*x^(1/3))^13/b^3 +--R +--R +--R (2) +--R 2 11 3 5 8 2 8 5 3+-+2 +--R (3510a b x + 27027a b x + 7722a b x)\|x +--R + +--R 13 4 3 10 3 6 7 2 9 4 3+-+ 12 4 +--R (66b x + 10296a b x + 25740a b x + 2145a b x)\|x + 715a b x +--R + +--R 4 9 3 7 6 2 10 3 13 +--R 20020a b x + 17160a b x + 286a b x + a +--R / +--R 3 +--R 286b +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 3 5 5 2 8 2 3+-+2 +--R (3510a b x + 27027a b x + 7722a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 3+-+ 9 4 +--R (66b x + 10296a b x + 25740a b x + 2145a b x)\|x + 715a b x +--R + +--R 4 6 3 7 3 2 10 +--R 20020a b x + 17160a b x + 286a x +--R / +--R 286 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1299 +m0:=a0-r0 +--R +--R +--R 13 +--R a +--R (4) - ----- +--R 3 +--R 286b +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1299 +t0:=(a+b*x^(1/3))^10/x +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1299 +r0:=30*a^9*b*x^(1/3)+135/2*a^8*b^2*x^(2/3)+120*a^7*b^3*x+_ + 315/2*a^6*b^4*x^(4/3)+756/5*a^5*b^5*x^(5/3)+105*a^4*b^6*x^2+_ + 360/7*a^3*b^7*x^(7/3)+135/8*a^2*b^8*x^(8/3)+10/3*a*b^9*x^3+_ + 3/10*b^10*x^(10/3)+a^10*log(x) +--R +--R +--R (2) +--R 2 8 2 5 5 8 2 3+-+2 +--R (14175a b x + 127008a b x + 56700a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 10 +--R (252b x + 43200a b x + 132300a b x + 25200a b)\|x + 840a log(x) +--R + +--R 9 3 4 6 2 7 3 +--R 2800a b x + 88200a b x + 100800a b x +--R / +--R 840 +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a log(\|x ) + (14175a b x + 127008a b x + 56700a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (252b x + 43200a b x + 132300a b x + 25200a b)\|x + 2800a b x +--R + +--R 4 6 2 7 3 +--R 88200a b x + 100800a b x +--R / +--R 840 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1299 +m0:=a0-r0 +--R +--R +--R 10 3+-+ 10 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1299 +t0:=(a+b*x^(1/3))^10/x^2 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1299 +r0:=-a^10/x-15*a^9*b/x^(2/3)-135*a^8*b^2/x^(1/3)+630*a^6*b^4*x^(1/3)+_ + 378*a^5*b^5*x^(2/3)+210*a^4*b^6*x+90*a^3*b^7*x^(4/3)+_ + 27*a^2*b^8*x^(5/3)+5*a*b^9*x^2+3/7*b^10*x^(7/3)+120*a^7*b^3*log(x) +--R +--R +--R (2) +--R 7 3 9 3 4 6 2 10 3+-+2 +--R (840a b x log(x) + 35a b x + 1470a b x - 7a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 6 4 2 +--R (189a b x + 2646a b x - 945a b x)\|x + 3b x + 630a b x + 4410a b x +--R + +--R 9 +--R - 105a b x +--R / +--R 3+-+2 +--R 7x \|x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (189a b x + 2646a b x - 945a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (3b x + 630a b x + 4410a b x - 105a b)\|x + 35a b x + 1470a b x +--R + +--R 10 +--R - 7a +--R / +--R 7x +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1299 +m0:=a0-r0 +--R +--R +--R 7 3 3+-+ 7 3 +--R (4) 360a b log(\|x ) - 120a b log(x) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1299 +t0:=(a+b*x^(1/3))^10/x^3 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 3 +--R x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1299 +r0:=-1/2*a^10/x^2-6*a^9*b/x^(5/3)-135/4*a^8*b^2/x^(4/3)-120*a^7*b^3/x-_ + 315*a^6*b^4/x^(2/3)-756*a^5*b^5/x^(1/3)+360*a^3*b^7*x^(1/3)+_ + 135/2*a^2*b^8*x^(2/3)+10*a*b^9*x+3/4*b^10*x^(4/3)+210*a^4*b^6*log(x) +--R +--R +--R (2) +--R 4 6 2 9 3 7 3 10 3+-+2 +--R (840a b x log(x) + 40a b x - 480a b x - 2a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 +--R (270a b x - 3024a b x - 135a b x)\|x + 3b x + 1440a b x +--R + +--R 6 4 2 9 +--R - 1260a b x - 24a b x +--R / +--R 2 3+-+2 +--R 4x \|x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 6 2 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (270a b x - 3024a b x - 135a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 7 3 10 +--R (3b x + 1440a b x - 1260a b x - 24a b)\|x + 40a b x - 480a b x - 2a +--R / +--R 2 +--R 4x +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1299 +m0:=a0-r0 +--R +--R +--R 4 6 3+-+ 4 6 +--R (4) 630a b log(\|x ) - 210a b log(x) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1299 +t0:=(a+b*x^(1/3))^10/x^4 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 4 +--R x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1299 +r0:=-1/3*a^10/x^3-15/4*a^9*b/x^(8/3)-135/7*a^8*b^2/x^(7/3)-_ + 60*a^7*b^3/x^2-126*a^6*b^4/x^(5/3)-189*a^5*b^5/x^(4/3)-_ + 210*a^4*b^6/x-180*a^3*b^7/x^(2/3)-135*a^2*b^8/x^(1/3)+_ + 3*b^10*x^(1/3)+10*a*b^9*log(x) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (840a b x log(x) - 17640a b x - 5040a b x - 28a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 3 7 3 +--R (- 11340a b x - 15876a b x - 1620a b x)\|x + 252b x - 15120a b x +--R + +--R 6 4 2 9 +--R - 10584a b x - 315a b x +--R / +--R 3 3+-+2 +--R 84x \|x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3 3+-+ 2 8 2 5 5 8 2 3+-+2 +--R 2520a b x log(\|x ) + (- 11340a b x - 15876a b x - 1620a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 4 6 2 +--R (252b x - 15120a b x - 10584a b x - 315a b)\|x - 17640a b x +--R + +--R 7 3 10 +--R - 5040a b x - 28a +--R / +--R 3 +--R 84x +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R (4) 30a b log(\|x ) - 10a b log(x) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1299 +t0:=(a+b*x^(1/3))^10/x^5 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 5 +--R x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1299 +r0:=-1/4*(a+b*x^(1/3))^11/(a*x^4)+1/44*b*(a+b*x^(1/3))^11/(a^2*x^(11/3)) +--R +--R +--R (2) +--R 12 4 3 9 3 6 6 2 9 3 12 3+-+2 +--R (b x - 440a b x - 4620a b x - 1760a b x - 11a )\|x +--R + +--R 4 8 3 7 5 2 10 2 3+-+ 2 10 4 5 7 3 +--R (- 1485a b x - 4752a b x - 594a b x)\|x - 66a b x - 3168a b x +--R + +--R 8 4 2 11 +--R - 3465a b x - 120a b x +--R / +--R 2 4 3+-+2 +--R 44a x \|x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1485a b x - 4752a b x - 594a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 66b x - 3168a b x - 3465a b x - 120a b)\|x - 440a b x +--R + +--R 4 6 2 7 3 10 +--R - 4620a b x - 1760a b x - 11a +--R / +--R 4 +--R 44x +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1299 +m0:=a0-r0 +--R +--R +--R 12 +--R b +--R (4) - ---- +--R 2 +--R 44a +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1299 +t0:=(a+b*x^(1/3))^10/x^6 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 6 +--R x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1299 +r0:=-1/5*(a+b*x^(1/3))^11/(a*x^5)+2/35*b*(a+b*x^(1/3))^11/(a^2*x^(14/3))-_ + 6/455*b^2*(a+b*x^(1/3))^11/(a^3*x^(13/3))+_ + 1/455*b^3*(a+b*x^(1/3))^11/(a^4*x^4)-_ + 1/5005*b^4*(a+b*x^(1/3))^11/(a^5*x^(11/3)) +--R +--R +--R (2) +--R 15 5 6 9 3 9 6 2 12 3 15 3+-+2 +--R (- b x - 25025a b x - 350350a b x - 150150a b x - 1001a )\|x +--R + +--R 7 8 3 10 5 2 13 2 3+-+ 5 10 4 +--R (- 96525a b x - 378378a b x - 51975a b x)\|x - 3003a b x +--R + +--R 8 7 3 11 4 2 14 +--R - 225225a b x - 286650a b x - 10725a b x +--R / +--R 5 5 3+-+2 +--R 5005a x \|x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 96525a b x - 378378a b x - 51975a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 3003b x - 225225a b x - 286650a b x - 10725a b)\|x - 25025a b x +--R + +--R 4 6 2 7 3 10 +--R - 350350a b x - 150150a b x - 1001a +--R / +--R 5 +--R 5005x +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1299 +m0:=a0-r0 +--R +--R +--R 15 +--R b +--R (4) ------ +--R 5 +--R 5005a +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1299 +t0:=(a+b*x^(1/3))^10/x^7 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 7 +--R x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1299 +r0:=-1/6*a^10/x^6-30/17*a^9*b/x^(17/3)-135/16*a^8*b^2/x^(16/3)-_ + 24*a^7*b^3/x^5-45*a^6*b^4/x^(14/3)-756/13*a^5*b^5/x^(13/3)-_ + 105/2*a^4*b^6/x^4-360/11*a^3*b^7/x^(11/3)-27/2*a^2*b^8/x^(10/3)-_ + 10/3*a*b^9/x^3-3/8*b^10/x^(8/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 388960a b x - 6126120a b x - 2800512a b x - 19448a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 1575288a b x - 6785856a b x - 984555a b x)\|x - 43758b x +--R + +--R 3 7 3 6 4 2 9 +--R - 3818880a b x - 5250960a b x - 205920a b x +--R / +--R 6 3+-+2 +--R 116688x \|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1575288a b x - 6785856a b x - 984555a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 43758b x - 3818880a b x - 5250960a b x - 205920a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 388960a b x - 6126120a b x - 2800512a b x - 19448a +--R / +--R 6 +--R 116688x +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1299 +t0:=(a+b*x^(1/3))^10/x^8 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 8 +--R x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1299 +r0:=-1/7*a^10/x^7-3/2*a^9*b/x^(20/3)-135/19*a^8*b^2/x^(19/3)-_ + 20*a^7*b^3/x^6-630/17*a^6*b^4/x^(17/3)-189/4*a^5*b^5/x^(16/3)-_ + 42*a^4*b^6/x^5-180/7*a^3*b^7/x^(14/3)-135/13*a^2*b^8/x^(13/3)-_ + 5/2*a*b^9/x^4-3/11*b^10/x^(11/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 3233230a b x - 54318264a b x - 25865840a b x - 184756a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 13430340a b x - 61108047a b x - 9189180a b x)\|x - 352716b x +--R + +--R 3 7 3 6 4 2 9 +--R - 33256080a b x - 47927880a b x - 1939938a b x +--R / +--R 7 3+-+2 +--R 1293292x \|x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 13430340a b x - 61108047a b x - 9189180a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 352716b x - 33256080a b x - 47927880a b x - 1939938a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 3233230a b x - 54318264a b x - 25865840a b x - 184756a +--R / +--R 7 +--R 1293292x +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1299 +t0:=(a+b*x^(1/3))^10/x^9 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 9 +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1299 +r0:=-1/8*a^10/x^8-30/23*a^9*b/x^(23/3)-135/22*a^8*b^2/x^(22/3)-_ + 120/7*a^7*b^3/x^7-63/2*a^6*b^4/x^(20/3)-756/19*a^5*b^5/x^(19/3)-_ + 35*a^4*b^6/x^6-360/17*a^3*b^7/x^(17/3)-135/16*a^2*b^8/x^(16/3)-_ + 2*a*b^9/x^5-3/14*b^10/x^(14/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 18305056a b x - 320338480a b x - 156900480a b x - 1144066a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ 10 4 +--R (- 77224455a b x - 364174272a b x - 56163240a b x)\|x - 1961256b x +--R + +--R 3 7 3 6 4 2 9 +--R - 193818240a b x - 288304632a b x - 11938080a b x +--R / +--R 8 3+-+2 +--R 9152528x \|x +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 77224455a b x - 364174272a b x - 56163240a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 1961256b x - 193818240a b x - 288304632a b x - 11938080a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 18305056a b x - 320338480a b x - 156900480a b x - 1144066a +--R / +--R 8 +--R 9152528x +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1299 +t0:=(a+b*x^(1/3))^10/x^10 +--R +--R +--R (1) +--R 2 8 2 5 5 8 2 3+-+2 +--R (45a b x + 252a b x + 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 4 6 2 +--R (b x + 120a b x + 210a b x + 10a b)\|x + 10a b x + 210a b x +--R + +--R 7 3 10 +--R 120a b x + a +--R / +--R 10 +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1299 +r0:=-1/9*a^10/x^9-15/13*a^9*b/x^(26/3)-27/5*a^8*b^2/x^(25/3)-_ + 15*a^7*b^3/x^8-630/23*a^6*b^4/x^(23/3)-378/11*a^5*b^5/x^(22/3)-_ + 30*a^4*b^6/x^7-18*a^3*b^7/x^(20/3)-135/19*a^2*b^8/x^(19/3)-_ + 5/3*a*b^9/x^6-3/17*b^10/x^(17/3) +--R +--R +--R (2) +--R 9 3 4 6 2 7 3 10 3+-+2 +--R (- 79676025a b x - 1434168450a b x - 717084225a b x - 5311735a )\|x +--R + +--R 2 8 3 5 5 2 8 2 3+-+ +--R (- 339671475a b x - 1642774770a b x - 258150321a b x)\|x +--R + +--R 10 4 3 7 3 6 4 2 9 +--R - 8436285b x - 860501070a b x - 1309458150a b x - 55160325a b x +--R / +--R 9 3+-+2 +--R 47805615x \|x +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 339671475a b x - 1642774770a b x - 258150321a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ +--R (- 8436285b x - 860501070a b x - 1309458150a b x - 55160325a b)\|x +--R + +--R 9 3 4 6 2 7 3 10 +--R - 79676025a b x - 1434168450a b x - 717084225a b x - 5311735a +--R / +--R 9 +--R 47805615x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1299 +t0:=(a+b*x^(1/3))^15*x^5 +--R +--R +--R (1) +--R 14 9 4 11 8 7 8 7 10 5 6 13 2 5 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 9 5 10 8 8 7 7 11 4 6 14 5 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 10 3 12 9 6 9 8 9 6 7 12 3 6 15 5 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1299 +r0:=1/6*a^15*x^6+45/19*a^14*b*x^(19/3)+63/4*a^13*b^2*x^(20/3)+_ + 65*a^12*b^3*x^7+4095/22*a^11*b^4*x^(22/3)+9009/23*a^10*_ + b^5*x^(23/3)+5005/8*a^9*b^6*x^8+3861/5*a^8*b^7*x^(25/3)+_ + 1485/2*a^7*b^8*x^(26/3)+5005/9*a^6*b^9*x^9+1287/4*a^5*_ + b^10*x^(28/3)+4095/29*a^4*b^11*x^(29/3)+91/2*a^3*b^12*x^10+_ + 315/31*a^2*b^13*x^(31/3)+45/32*a*b^14*x^(32/3)+1/11*b^15*x^11 +--R +--R +--R (2) +--R 14 10 4 11 9 7 8 8 +--R 8751023325a b x + 878723445600a b x + 4620540315600a b x +--R + +--R 10 5 7 13 2 6 +--R 2437502427360a b x + 98011461240a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 10 5 10 9 8 7 8 +--R 63233200800a b x + 2002234136760a b x + 4805361928224a b x +--R + +--R 11 4 7 14 6 +--R 1158317269200a b x + 14738565600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 11 3 12 10 6 9 9 +--R 565722720b x + 283144221360a b x + 3460651594400a b x +--R + +--R 9 6 8 12 3 7 15 6 +--R 3893233043700a b x + 404491744800a b x + 1037158320a x +--R / +--R 6222949920 +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 10 4 11 9 7 8 8 +--R 8751023325a b x + 878723445600a b x + 4620540315600a b x +--R + +--R 10 5 7 13 2 6 +--R 2437502427360a b x + 98011461240a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 10 5 10 9 8 7 8 +--R 63233200800a b x + 2002234136760a b x + 4805361928224a b x +--R + +--R 11 4 7 14 6 +--R 1158317269200a b x + 14738565600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 11 3 12 10 6 9 9 +--R 565722720b x + 283144221360a b x + 3460651594400a b x +--R + +--R 9 6 8 12 3 7 15 6 +--R 3893233043700a b x + 404491744800a b x + 1037158320a x +--R / +--R 6222949920 +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1299 +t0:=(a+b*x^(1/3))^15*x^4 +--R +--R +--R (1) +--R 14 8 4 11 7 7 8 6 10 5 5 13 2 4 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 8 5 10 7 8 7 6 11 4 5 14 4 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 12 3 5 15 4 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1299 +r0:=1/5*a^15*x^5+45/16*a^14*b*x^(16/3)+315/17*a^13*b^2*x^(17/3)+_ + 455/6*a^12*b^3*x^6+4095/19*a^11*b^4*x^(19/3)+9009/20*a^10*_ + b^5*x^(20/3)+715*a^9*b^6*x^7+1755/2*a^8*b^7*x^(22/3)+_ + 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3 4 15 3 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1299 +r0:=1/4*a^15*x^4+45/13*a^14*b*x^(13/3)+45/2*a^13*b^2*x^(14/3)+_ + 91*a^12*b^3*x^5+4095/16*a^11*b^4*x^(16/3)+9009/17*a^10*b^5*_ + x^(17/3)+5005/6*a^9*b^6*x^6+19305/19*a^8*b^7*x^(19/3)+_ + 3861/4*a^7*b^8*x^(20/3)+715*a^6*b^9*x^7+819/2*a^5*b^10*_ + x^(22/3)+4095/23*a^4*b^11*x^(23/3)+455/8*a^3*b^12*x^8+_ + 63/5*a^2*b^13*x^(25/3)+45/26*a*b^14*x^(26/3)+1/9*b^15*x^9 +--R +--R +--R (2) +--R 14 8 4 11 7 7 8 6 +--R 120349800a b x + 12380331600a b x + 67119083460a b x +--R + +--R 10 5 5 13 2 4 +--R 36849692880a b x + 1564547400a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 8 5 10 7 8 7 6 +--R 876146544a b x + 28474762680a b x + 70651666800a b x +--R + +--R 11 4 5 14 4 +--R 17796726675a b x + 240699600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 +--R 7726160b x + 3954828150a b x + 49717839600a b x + 58004146200a b x +--R + +--R 12 3 5 15 4 +--R 6327725040a b x + 17383860a x +--R / +--R 69535440 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 8 4 11 7 7 8 6 +--R 120349800a b x + 12380331600a b x + 67119083460a b x +--R + +--R 10 5 5 13 2 4 +--R 36849692880a b x + 1564547400a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 8 5 10 7 8 7 6 +--R 876146544a b x + 28474762680a b x + 70651666800a b x +--R + +--R 11 4 5 14 4 +--R 17796726675a b x + 240699600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 9 3 12 8 6 9 7 9 6 6 +--R 7726160b x + 3954828150a b x + 49717839600a b x + 58004146200a b x +--R + +--R 12 3 5 15 4 +--R 6327725040a b x + 17383860a x +--R / +--R 69535440 +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1299 +t0:=(a+b*x^(1/3))^15*x^2 +--R +--R +--R (1) +--R 14 6 4 11 5 7 8 4 10 5 3 13 2 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x )\|x +--R + +--R 2 13 6 5 10 5 8 7 4 11 4 3 14 2 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x )\|x +--R + +--R 15 7 3 12 6 6 9 5 9 6 4 12 3 3 15 2 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1299 +r0:=3/16*a^8*(a+b*x^(1/3))^16/b^9-24/17*a^7*(a+b*x^(1/3))^17/b^9+_ + 14/3*a^6*(a+b*x^(1/3))^18/b^9-168/19*a^5*(a+b*x^(1/3))^19/b^9+_ + 21/2*a^4*(a+b*x^(1/3))^20/b^9-8*a^3*(a+b*x^(1/3))^21/b^9+_ + 42/11*a^2*(a+b*x^(1/3))^22/b^9-24/23*a*(a+b*x^(1/3))^23/b^9+_ + 1/8*(a+b*x^(1/3))^24/b^9 +--R +--R +--R (2) +--R 23 7 4 20 6 7 17 5 +--R 7674480a b x + 803134332a b x + 4454358480a b x +--R + +--R 10 14 4 13 11 3 +--R 2524136472a b x + 112326480a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 22 7 5 19 6 8 16 5 +--R 56163240a b x + 1859890032a b x + 4732755885a b x +--R + +--R 11 13 4 14 10 3 +--R 1235591280a b x + 17651304a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 24 8 3 21 7 6 18 6 9 15 5 +--R 490314b x + 254963280a b x + 3272028760a b x + 3926434512a b x +--R + +--R 12 12 4 15 9 3 24 +--R 446185740a b x + 1307504a b x + a +--R / +--R 9 +--R 3922512b +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 7 4 11 6 7 8 5 +--R 7674480a b x + 803134332a b x + 4454358480a b x +--R + +--R 10 5 4 13 2 3 +--R 2524136472a b x + 112326480a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 7 5 10 6 8 7 5 +--R 56163240a b x + 1859890032a b x + 4732755885a b x +--R + +--R 11 4 4 14 3 +--R 1235591280a b x + 17651304a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 8 3 12 7 6 9 6 9 6 5 +--R 490314b x + 254963280a b x + 3272028760a b x + 3926434512a b x +--R + +--R 12 3 4 15 3 +--R 446185740a b x + 1307504a x +--R / +--R 3922512 +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1299 +m0:=a0-r0 +--R +--R +--R 24 +--R a +--R (4) - --------- +--R 9 +--R 3922512b +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1299 +t0:=(a+b*x^(1/3))^15*x +--R +--R +--R (1) +--R 14 5 4 11 4 7 8 3 10 5 2 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b x)\|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 14 3+-+ +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b x)\|x +--R + +--R 15 6 3 12 5 6 9 4 9 6 3 12 3 2 15 +--R b x + 455a b x + 5005a b x + 5005a b x + 455a b x + a x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1299 +r0:=-3/16*a^5*(a+b*x^(1/3))^16/b^6+15/17*a^4*(a+b*x^(1/3))^17/b^6-_ + 5/3*a^3*(a+b*x^(1/3))^18/b^6+30/19*a^2*(a+b*x^(1/3))^19/b^6-_ + 3/4*a*(a+b*x^(1/3))^20/b^6+1/7*(a+b*x^(1/3))^21/b^6 +--R +--R +--R (2) +--R 20 6 4 17 5 7 14 4 10 11 3 +--R 244188a b x + 26142480a b x + 149652360a b x + 88884432a b x +--R + +--R 13 8 2 +--R 4273290a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 19 6 5 16 5 8 13 4 +--R 1799280a b x + 61108047a b x + 161164080a b x +--R + +--R 11 10 3 14 7 2 +--R 44442216a b x + 697680a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 21 7 3 18 6 6 15 5 9 12 4 +--R 15504b x + 8230040a b x + 108636528a b x + 135795660a b x +--R + +--R 12 9 3 15 6 2 21 +--R 16460080a b x + 54264a b x - a +--R / +--R 6 +--R 108528b +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 6 4 11 5 7 8 4 10 5 3 +--R 244188a b x + 26142480a b x + 149652360a b x + 88884432a b x +--R + +--R 13 2 2 +--R 4273290a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 6 5 10 5 8 7 4 11 4 3 +--R 1799280a b x + 61108047a b x + 161164080a b x + 44442216a b x +--R + +--R 14 2 +--R 697680a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 7 3 12 6 6 9 5 9 6 4 +--R 15504b x + 8230040a b x + 108636528a b x + 135795660a b x +--R + +--R 12 3 3 15 2 +--R 16460080a b x + 54264a x +--R / +--R 108528 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1299 +m0:=a0-r0 +--R +--R +--R 21 +--R a +--R (4) -------- +--R 6 +--R 108528b +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1299 +t0:=(a+b*x^(1/3))^15 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1299 +r0:=3/16*a^2*(a+b*x^(1/3))^16/b^3-6/17*a*(a+b*x^(1/3))^17/b^3+_ + 1/6*(a+b*x^(1/3))^18/b^3 +--R +--R +--R (2) +--R 17 5 4 14 4 7 11 3 10 8 2 +--R 2160a b x + 238680a b x + 1432080a b x + 918918a b x +--R + +--R 13 5 +--R 51408a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 16 5 5 13 4 8 10 3 11 7 2 +--R 16065a b x + 565488a b x + 1575288a b x + 477360a b x +--R + +--R 14 4 +--R 9180a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 18 6 3 15 5 6 12 4 9 9 3 12 6 2 +--R 136b x + 74256a b x + 1021020a b x + 1361360a b x + 185640a b x +--R + +--R 15 3 18 +--R 816a b x + a +--R / +--R 3 +--R 816b +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 5 4 11 4 7 8 3 10 5 2 +--R 2160a b x + 238680a b x + 1432080a b x + 918918a b x +--R + +--R 13 2 +--R 51408a b x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 +--R 16065a b x + 565488a b x + 1575288a b x + 477360a b x +--R + +--R 14 +--R 9180a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 15 6 3 12 5 6 9 4 9 6 3 12 3 2 +--R 136b x + 74256a b x + 1021020a b x + 1361360a b x + 185640a b x +--R + +--R 15 +--R 816a x +--R / +--R 816 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1299 +m0:=a0-r0 +--R +--R +--R 18 +--R a +--R (4) - ----- +--R 3 +--R 816b +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1299 +t0:=(a+b*x^(1/3))^15/x +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1299 +r0:=45*a^14*b*x^(1/3)+315/2*a^13*b^2*x^(2/3)+455*a^12*b^3*x+_ + 4095/4*a^11*b^4*x^(4/3)+9009/5*a^10*b^5*x^(5/3)+5005/2*a^9*_ + b^6*x^2+19305/7*a^8*b^7*x^(7/3)+19305/8*a^7*b^8*x^(8/3)+_ + 5005/3*a^6*b^9*x^3+9009/10*a^5*b^10*x^(10/3)+4095/11*a^4*_ + b^11*x^(11/3)+455/4*a^3*b^12*x^4+315/13*a^2*b^13*x^(13/3)+_ + 45/14*a*b^14*x^(14/3)+1/5*b^15*x^5+a^15*log(x) +--R +--R +--R (2) +--R 14 4 4 11 3 7 8 2 10 5 +--R 386100a b x + 44717400a b x + 289864575a b x + 216432216a b x +--R + +--R 13 2 +--R 18918900a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R 2910600a b x + 108216108a b x + 331273800a b x + 122972850a b x +--R + +--R 14 +--R 5405400a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 15 5 3 12 4 6 9 3 +--R 120120a log(x) + 24024b x + 13663650a b x + 200400200a b x +--R + +--R 9 6 2 12 3 +--R 300600300a b x + 54654600a b x +--R / +--R 120120 +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 3+-+ +--R 360360a log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 10 5 +--R 386100a b x + 44717400a b x + 289864575a b x + 216432216a b x +--R + +--R 13 2 +--R 18918900a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R 2910600a b x + 108216108a b x + 331273800a b x + 122972850a b x +--R + +--R 14 +--R 5405400a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 +--R 24024b x + 13663650a b x + 200400200a b x + 300600300a b x +--R + +--R 12 3 +--R 54654600a b x +--R / +--R 120120 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1299 +m0:=a0-r0 +--R +--R +--R 15 3+-+ 15 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1299 +t0:=(a+b*x^(1/3))^15/x^2 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 2 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1299 +r0:=-a^15/x-45/2*a^14*b/x^(2/3)-315*a^13*b^2/x^(1/3)+4095*a^11*_ + b^4*x^(1/3)+9009/2*a^10*b^5*x^(2/3)+5005*a^9*b^6*x+_ + 19305/4*a^8*b^7*x^(4/3)+3861*a^7*b^8*x^(5/3)+5005/2*a^6*_ + 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b x + a +--R / +--R 6 +--R x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1299 +r0:=-1/5*a^15/x^5-45/14*a^14*b/x^(14/3)-315/13*a^13*b^2/x^(13/3)-_ + 455/4*a^12*b^3/x^4-4095/11*a^11*b^4/x^(11/3)-9009/10*a^10*_ + b^5/x^(10/3)-5005/3*a^9*b^6/x^3-19305/8*a^8*b^7/x^(8/3)-_ + 19305/7*a^7*b^8/x^(7/3)-5005/2*a^6*b^9/x^2-9009/5*a^5*_ + b^10/x^(5/3)-4095/4*a^4*b^11/x^(4/3)-455*a^3*b^12/x-_ + 315/2*a^2*b^13/x^(2/3)-45*a*b^14/x^(1/3)+b^15*log(x) +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R 120120b x log(x) - 54654600a b x - 300600300a b x +--R + +--R 9 6 2 12 3 15 +--R - 200400200a b x - 13663650a b x - 24024a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 5405400a b x - 122972850a b x - 331273800a b x +--R + +--R 10 5 2 13 2 +--R - 108216108a b x - 2910600a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 11 4 2 +--R - 18918900a b x - 216432216a b x - 289864575a b x - 44717400a b x +--R + +--R 14 +--R - 386100a b x +--R / +--R 5 3+-+2 +--R 120120x \|x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 15 5 3+-+ +--R 360360b x log(\|x ) +--R + +--R 14 4 4 11 3 7 8 2 +--R - 5405400a b x - 122972850a b x - 331273800a b x +--R + +--R 10 5 13 2 +--R - 108216108a b x - 2910600a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 18918900a b x - 216432216a b x - 289864575a b x +--R + +--R 11 4 14 +--R - 44717400a b x - 386100a b +--R * +--R 3+-+ +--R \|x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 +--R - 54654600a b x - 300600300a b x - 200400200a b x - 13663650a b x +--R + +--R 15 +--R - 24024a +--R / +--R 5 +--R 120120x +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1299 +m0:=a0-r0 +--R +--R +--R 15 3+-+ 15 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1299 +t0:=(a+b*x^(1/3))^15/x^7 +--R +--R +--R (1) +--R 14 4 4 11 3 7 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3+-+2 +--R 816a x \|x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 10 5 +--R - 9180a b x - 477360a b x - 1575288a b x - 565488a b x +--R + +--R 13 2 +--R - 16065a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 +--R - 51408a b x - 918918a b x - 1432080a b x - 238680a b x +--R + +--R 14 +--R - 2160a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 12 3 +--R - 816b x - 185640a b x - 1361360a b x - 1021020a b x - 74256a b x +--R + +--R 15 +--R - 136a +--R / +--R 6 +--R 816x +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1299 +m0:=a0-r0 +--R +--R +--R 18 +--R b +--R (4) ----- +--R 3 +--R 816a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1299 +t0:=(a+b*x^(1/3))^15/x^8 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 8 +--R x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1299 +r0:=-1/7*(a+b*x^(1/3))^16/(a*x^7)+1/28*b*(a+b*x^(1/3))^16/(a^2*x^(20/3))-_ + 1/133*b^2*(a+b*x^(1/3))^16/(a^3*x^(19/3))+1/798*b^3*_ + (a+b*x^(1/3))^16/(a^4*x^6)-1/6783*b^4*(a+b*x^(1/3))^16/_ + (a^5*x^(17/3))+1/108528*b^5*(a+b*x^(1/3))^16/(a^6*x^(16/3)) +--R +--R +--R (2) +--R 21 7 6 15 5 9 12 4 12 9 3 +--R b x - 54264a b x - 16460080a b x - 135795660a b x +--R + +--R 15 6 2 18 3 21 +--R - 108636528a b x - 8230040a b x - 15504a +--R * +--R 3+-+2 +--R \|x +--R + +--R 7 14 5 10 11 4 13 8 3 +--R - 697680a b x - 44442216a b x - 161164080a b x +--R + +--R 16 5 2 19 2 +--R - 61108047a b x - 1799280a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 8 13 5 11 10 4 14 7 3 17 4 2 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Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1299 +t0:=(a+b*x^(1/3))^15/x^9 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 9 +--R x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1299 +r0:=-1/8*(a+b*x^(1/3))^16/(a*x^8)+1/23*b*(a+b*x^(1/3))^16/(a^2*x^(23/3))-_ + 7/506*b^2*(a+b*x^(1/3))^16/(a^3*x^(22/3))+1/253*b^3*_ + (a+b*x^(1/3))^16/(a^4*x^7)-1/1012*b^4*(a+b*x^(1/3))^16/_ + (a^5*x^(20/3))+1/4807*b^5*(a+b*x^(1/3))^16/(a^6*x^(19/3))-_ + 1/28842*b^6*(a+b*x^(1/3))^16/(a^7*x^6)+1/245157*b^7*_ + (a+b*x^(1/3))^16/(a^8*x^(17/3))-1/3922512*b^8*_ + (a+b*x^(1/3))^16/(a^9*x^(16/3)) +--R +--R +--R (2) +--R 24 8 9 15 5 12 12 4 15 9 3 +--R - b x - 1307504a b x - 446185740a b x - 3926434512a b x +--R + +--R 18 6 2 21 3 24 +--R - 3272028760a b x - 254963280a b x - 490314a +--R * +--R 3+-+2 +--R \|x +--R + +--R 10 14 5 13 11 4 16 8 3 +--R - 17651304a b x - 1235591280a b x - 4732755885a b x +--R + +--R 19 5 2 22 2 +--R - 1859890032a b x - 56163240a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 11 13 5 14 10 4 17 7 3 +--R - 112326480a b x - 2524136472a b x - 4454358480a b x +--R + +--R 20 4 2 23 +--R - 803134332a b x - 7674480a b x +--R / +--R 9 8 3+-+2 +--R 3922512a x \|x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 17651304a b x - 1235591280a b x - 4732755885a b x +--R + +--R 10 5 13 2 +--R - 1859890032a b x - 56163240a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 112326480a b x - 2524136472a b x - 4454358480a b x +--R + +--R 11 4 14 +--R - 803134332a b x - 7674480a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 9 6 2 +--R - 1307504b x - 446185740a b x - 3926434512a b x - 3272028760a b x +--R + +--R 12 3 15 +--R - 254963280a b x - 490314a +--R / +--R 8 +--R 3922512x +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1299 +m0:=a0-r0 +--R +--R +--R 24 +--R b +--R (4) --------- +--R 9 +--R 3922512a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1299 +t0:=(a+b*x^(1/3))^15/x^10 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 10 +--R x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1299 +r0:=-1/9*a^15/x^9-45/26*a^14*b/x^(26/3)-63/5*a^13*b^2/x^(25/3)-_ + 455/8*a^12*b^3/x^8-4095/23*a^11*b^4/x^(23/3)-819/2*a^10*_ + b^5/x^(22/3)-715*a^9*b^6/x^7-3861/4*a^8*b^7/x^(20/3)-_ + 19305/19*a^7*b^8/x^(19/3)-5005/6*a^6*b^9/x^6-9009/17*a^5*_ + b^10/x^(17/3)-4095/16*a^4*b^11/x^(16/3)-91*a^3*b^12/x^5-_ + 45/2*a^2*b^13/x^(14/3)-45/13*a*b^14/x^(13/3)-1/4*b^15/x^4 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 17383860b x - 6327725040a b x - 58004146200a b x +--R + +--R 9 6 2 12 3 15 +--R - 49717839600a b x - 3954828150a b x - 7726160a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 240699600a b x - 17796726675a b x - 70651666800a b x +--R + +--R 10 5 2 13 2 +--R - 28474762680a b x - 876146544a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 1564547400a b x - 36849692880a b x - 67119083460a b x +--R + +--R 11 4 2 14 +--R - 12380331600a b x - 120349800a b x +--R / +--R 9 3+-+2 +--R 69535440x \|x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 240699600a b x - 17796726675a b x - 70651666800a b x +--R + +--R 10 5 13 2 +--R - 28474762680a b x - 876146544a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 1564547400a b x - 36849692880a b x - 67119083460a b x +--R + +--R 11 4 14 +--R - 12380331600a b x - 120349800a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 17383860b x - 6327725040a b x - 58004146200a b x +--R + +--R 9 6 2 12 3 15 +--R - 49717839600a b x - 3954828150a b x - 7726160a +--R / +--R 9 +--R 69535440x +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1299 +t0:=(a+b*x^(1/3))^15/x^11 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 11 +--R x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1299 +r0:=-1/10*a^15/x^10-45/29*a^14*b/x^(29/3)-45/4*a^13*b^2/x^(28/3)-_ + 455/9*a^12*b^3/x^9-315/2*a^11*b^4/x^(26/3)-9009/25*a^10*_ + b^5/x^(25/3)-5005/8*a^9*b^6/x^8-19305/23*a^8*b^7/x^(23/3)-_ + 1755/2*a^7*b^8/x^(22/3)-715*a^6*b^9/x^7-9009/20*a^5*b^10/_ + x^(20/3)-4095/19*a^4*b^11/x^(19/3)-455/6*a^3*b^12/x^6-_ + 315/17*a^2*b^13/x^(17/3)-45/16*a*b^14/x^(16/3)-1/5*b^15/x^5 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 155117520b x - 58815393000a b x - 554545134000a b x +--R + +--R 9 6 2 12 3 15 +--R - 485226992250a b x - 39210262000a b x - 77558760a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 2181340125a b x - 167159538000a b x - 680578119000a b x +--R + +--R 10 5 2 13 2 +--R - 279490747536a b x - 8725360500a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 14371182000a b x - 349363434420a b x - 650987766000a b x +--R + +--R 11 4 2 14 +--R - 122155047000a b x - 1203498000a b x +--R / +--R 10 3+-+2 +--R 775587600x \|x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 2181340125a b x - 167159538000a b x - 680578119000a b x +--R + +--R 10 5 13 2 +--R - 279490747536a b x - 8725360500a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 14371182000a b x - 349363434420a b x - 650987766000a b x +--R + +--R 11 4 14 +--R - 122155047000a b x - 1203498000a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 155117520b x - 58815393000a b x - 554545134000a b x +--R + +--R 9 6 2 12 3 15 +--R - 485226992250a b x - 39210262000a b x - 77558760a +--R / +--R 10 +--R 775587600x +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1299 +t0:=(a+b*x^(1/3))^15/x^12 +--R +--R +--R (1) +--R 14 4 4 11 3 7 8 2 10 5 13 2 3+-+2 +--R (15a b x + 1365a b x + 6435a b x + 3003a b x + 105a b )\|x +--R + +--R 2 13 4 5 10 3 8 7 2 11 4 14 3+-+ 15 5 +--R (105a b x + 3003a b x + 6435a b x + 1365a b x + 15a b)\|x + b x +--R + +--R 3 12 4 6 9 3 9 6 2 12 3 15 +--R 455a b x + 5005a b x + 5005a b x + 455a b x + a +--R / +--R 12 +--R x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1299 +r0:=-1/11*a^15/x^11-45/32*a^14*b/x^(32/3)-315/31*a^13*b^2/x^(31/3)-_ + 91/2*a^12*b^3/x^10-4095/29*a^11*b^4/x^(29/3)-1287/4*_ + a^10*b^5/x^(28/3)-5005/9*a^9*b^6/x^9-1485/2*a^8*b^7/x^(26/3)-_ + 3861/5*a^7*b^8/x^(25/3)-5005/8*a^6*b^9/x^8-9009/23*a^5*b^10/_ + x^(23/3)-4095/22*a^4*b^11/x^(22/3)-65*a^3*b^12/x^7-_ + 63/4*a^2*b^13/x^(20/3)-45/19*a*b^14/x^(19/3)-1/6*b^15/x^6 +--R +--R +--R (2) +--R 15 5 3 12 4 6 9 3 +--R - 1037158320b x - 404491744800a b x - 3893233043700a b x +--R + +--R 9 6 2 12 3 15 +--R - 3460651594400a b x - 283144221360a b x - 565722720a +--R * +--R 3+-+2 +--R \|x +--R + +--R 14 5 4 11 4 7 8 3 +--R - 14738565600a b x - 1158317269200a b x - 4805361928224a b x +--R + +--R 10 5 2 13 2 +--R - 2002234136760a b x - 63233200800a b x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 13 5 5 10 4 8 7 3 +--R - 98011461240a b x - 2437502427360a b x - 4620540315600a b x +--R + +--R 11 4 2 14 +--R - 878723445600a b x - 8751023325a b x +--R / +--R 11 3+-+2 +--R 6222949920x \|x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 14 4 4 11 3 7 8 2 +--R - 14738565600a b x - 1158317269200a b x - 4805361928224a b x +--R + +--R 10 5 13 2 +--R - 2002234136760a b x - 63233200800a b +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 13 4 5 10 3 8 7 2 +--R - 98011461240a b x - 2437502427360a b x - 4620540315600a b x +--R + +--R 11 4 14 +--R - 878723445600a b x - 8751023325a b +--R * +--R 3+-+ +--R \|x +--R + +--R 15 5 3 12 4 6 9 3 +--R - 1037158320b x - 404491744800a b x - 3893233043700a b x +--R + +--R 9 6 2 12 3 15 +--R - 3460651594400a b x - 283144221360a b x - 565722720a +--R / +--R 11 +--R 6222949920x +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1299 +t0:=x^3/(a+b*x^(1/3)) +--R +--R +--R 3 +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1299 +r0:=3*a^10*x^(1/3)/b^11-3/2*a^9*x^(2/3)/b^10+a^8*x/b^9-3/4*a^7*_ + x^(4/3)/b^8+3/5*a^6*x^(5/3)/b^7-1/2*a^5*x^2/b^6+3/7*a^4*_ + x^(7/3)/b^5-3/8*a^3*x^(8/3)/b^4+1/3*a^2*x^3/b^3-3/10*a*_ + x^(10/3)/b^2+3/11*x^(11/3)/b-3*a^11*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 11 3+-+ +--R - 27720a log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (2520b x - 3465a b x + 5544a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 2772a b x + 3960a b x - 6930a b x + 27720a b)\|x + 3080a b x +--R + +--R 5 6 2 8 3 +--R - 4620a b x + 9240a b x +--R / +--R 12 +--R 9240b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3+-+ +--R - 27720a log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (2520b x - 3465a b x + 5544a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 2772a b x + 3960a b x - 6930a b x + 27720a b)\|x + 3080a b x +--R + +--R 5 6 2 8 3 +--R - 4620a b x + 9240a b x +--R / +--R 12 +--R 9240b +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1299 +t0:=x^2/(a+b*x^(1/3)) +--R +--R +--R 2 +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1299 +r0:=-3*a^7*x^(1/3)/b^8+3/2*a^6*x^(2/3)/b^7-a^5*x/b^6+3/4*a^4*_ + x^(4/3)/b^5-3/5*a^3*x^(5/3)/b^4+1/2*a^2*x^2/b^3-3/7*_ + a*x^(7/3)/b^2+3/8*x^(8/3)/b+3*a^8*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R 840a log(b\|x + a) + (105b x - 168a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 +--R (- 120a b x + 210a b x - 840a b)\|x + 140a b x - 280a b x +--R / +--R 9 +--R 280b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R 840a log(b\|x + a) + (105b x - 168a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 +--R (- 120a b x + 210a b x - 840a b)\|x + 140a b x - 280a b x +--R / +--R 9 +--R 280b +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1299 +t0:=x/(a+b*x^(1/3)) +--R +--R +--R x +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1299 +r0:=3*a^4*x^(1/3)/b^5-3/2*a^3*x^(2/3)/b^4+a^2*x/b^3-3/4*a*_ + x^(4/3)/b^2+3/5*x^(5/3)/b-3*a^5*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ +--R - 60a log(b\|x + a) + (12b x - 30a b )\|x + (- 15a b x + 60a b)\|x +--R + +--R 2 3 +--R 20a b x +--R / +--R 6 +--R 20b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+ 5 3 2 3+-+2 4 4 3+-+ +--R - 60a log(b\|x + a) + (12b x - 30a b )\|x + (- 15a b x + 60a b)\|x +--R + +--R 2 3 +--R 20a b x +--R / +--R 6 +--R 20b +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1299 +t0:=1/(a+b*x^(1/3)) +--R +--R +--R 1 +--R (1) --------- +--R 3+-+ +--R b\|x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1299 +r0:=-3*a*x^(1/3)/b^2+3/2*x^(2/3)/b+3*a^2*log(a+b*x^(1/3))/b^3 +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(b\|x + a) + 3b \|x - 6a b\|x +--R (2) --------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+ 2 3+-+2 3+-+ +--R 6a log(b\|x + a) + 3b \|x - 6a b\|x +--R (3) --------------------------------------- +--R 3 +--R 2b +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1299 +t0:=1/((a+b*x^(1/3))*x) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-+ +--R b x\|x + a x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1299 +r0:=-3*log(a+b*x^(1/3))/a+log(x)/a +--R +--R +--R 3+-+ +--R - 3log(b\|x + a) + log(x) +--R (2) -------------------------- +--R a +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R - 3log(b\|x + a) + 3log(\|x ) +--R (3) ------------------------------ +--R a +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1299 +t0:=1/((2+b*x^(1/3))*x) +--R +--R +--R 1 +--R (1) ------------ +--R 3+-+ +--R b x\|x + 2x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1299 +r0:=-3*atanh(1+b*x^(1/3)) +--R +--R +--R 3+-+ +--R (2) - 3atanh(b\|x + 1) +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R - 3log(b\|x + 2) + 3log(\|x ) +--R (3) ------------------------------ +--R 2 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R - 3log(b\|x + 2) + 3log(\|x ) + 6atanh(b\|x + 1) +--R (4) -------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1299 +t0:=1/((a+b*x^(1/3))*x^2) +--R +--R +--R 1 +--R (1) --------------- +--R 2 3+-+ 2 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1299 +r0:=(-1)/(a*x)+3/2*b/(a^2*x^(2/3))-3*b^2/(a^3*x^(1/3))+3*b^3*_ + log(a+b*x^(1/3))/a^4-b^3*log(x)/a^4 +--R +--R +--R (2) +--R 3 3+-+2 3+-+ 3 3 3+-+2 2 3+-+ 2 +--R 6b x \|x log(b\|x + a) + (- 2b x log(x) - 2a )\|x - 6a b x\|x + 3a b x +--R --------------------------------------------------------------------------- +--R 4 3+-+2 +--R 2a x \|x +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b x log(b\|x + a) - 6b x log(\|x ) - 6a b \|x + 3a b\|x - 2a +--R (3) ------------------------------------------------------------------ +--R 4 +--R 2a x +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 3b log(\|x ) + b log(x) +--R (4) ------------------------- +--R 4 +--R a +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1299 +t0:=1/((a+b*x^(1/3))*x^3) +--R +--R +--R 1 +--R (1) --------------- +--R 3 3+-+ 3 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1299 +r0:=(-1/2)/(a*x^2)+3/5*b/(a^2*x^(5/3))-3/4*b^2/(a^3*x^(4/3))+_ + b^3/(a^4*x)-3/2*b^4/(a^5*x^(2/3))+3*b^5/(a^6*x^(1/3))-_ + 3*b^6*log(a+b*x^(1/3))/a^7+b^6*log(x)/a^7 +--R +--R +--R (2) +--R 6 2 3+-+2 3+-+ 6 2 3 3 6 3+-+2 +--R - 60b x \|x log(b\|x + a + (20b x log(x) + 20a b x - 10a )\|x +--R + +--R 5 2 4 2 3+-+ 2 4 2 5 +--R (60a b x - 15a b x)\|x - 30a b x + 12a b x +--R / +--R 7 2 3+-+2 +--R 20a x \|x +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 3+-+ 6 2 3+-+ 5 4 2 3+-+2 +--R - 60b x log(b\|x + a) + 60b x log(\|x ) + (60a b x - 15a b )\|x +--R + +--R 2 4 5 3+-+ 3 3 6 +--R (- 30a b x + 12a b)\|x + 20a b x - 10a +--R / +--R 7 2 +--R 20a x +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 3b log(\|x ) - b log(x) +--R (4) ----------------------- +--R 7 +--R a +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1299 +t0:=1/((a+b*x^(1/3))*x^4) +--R +--R +--R 1 +--R (1) --------------- +--R 4 3+-+ 4 +--R b x \|x + a x +--R Type: Expression(Integer) +--E 266 + +--S 267 of 1299 +r0:=(-1/3)/(a*x^3)+3/8*b/(a^2*x^(8/3))-3/7*b^2/(a^3*x^(7/3))+_ + 1/2*b^3/(a^4*x^2)-3/5*b^4/(a^5*x^(5/3))+3/4*b^5/(a^6*x^(4/3))-_ + b^6/(a^7*x)+3/2*b^7/(a^8*x^(2/3))-3*b^8/(a^9*x^(1/3))+_ + 3*b^9*log(a+b*x^(1/3))/a^10-b^9*log(x)/a^10 +--R +--R +--R (2) +--R 9 3 3+-+2 3+-+ +--R 2520b x \|x log(b\|x + a) +--R + +--R 9 3 3 6 2 6 3 9 3+-+2 +--R (- 840b x log(x) - 840a b x + 420a b x - 280a )\|x +--R + +--R 8 3 4 5 2 7 2 3+-+ 2 7 3 5 4 2 +--R (- 2520a b x + 630a b x - 360a b x)\|x + 1260a b x - 504a b x +--R + +--R 8 +--R 315a b x +--R / +--R 10 3 3+-+2 +--R 840a x \|x +--R Type: Expression(Integer) +--E 267 + +--S 268 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3 3+-+ 9 3 3+-+ +--R 2520b x log(b\|x + a) - 2520b x log(\|x ) +--R + +--R 8 2 4 5 7 2 3+-+2 +--R (- 2520a b x + 630a b x - 360a b )\|x +--R + +--R 2 7 2 5 4 8 3+-+ 3 6 2 6 3 9 +--R (1260a b x - 504a b x + 315a b)\|x - 840a b x + 420a b x - 280a +--R / +--R 10 3 +--R 840a x +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 3b log(\|x ) + b log(x) +--R (4) ------------------------- +--R 10 +--R a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 270 + +)clear all + +--S 271 of 1299 +t0:=x^3/(a+b*x^(1/3))^2 +--R +--R +--R 3 +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 271 + +--S 272 of 1299 +r0:=3*a^11/(b^12*(a+b*x^(1/3)))-30*a^9*x^(1/3)/b^11+27/2*a^8*_ + x^(2/3)/b^10-8*a^7*x/b^9+21/4*a^6*x^(4/3)/b^8-18/5*a^5*_ + x^(5/3)/b^7+5/2*a^4*x^2/b^6-12/7*a^3*x^(7/3)/b^5+9/8*a^2*_ + x^(8/3)/b^4-2/3*a*x^3/b^3+3/10*x^(10/3)/b^2+33*a^10*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 10 3+-+ 11 3+-+ +--R (27720a b\|x + 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (252b x - 495a b x + 1386a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 308a b x + 660a b x - 2310a b x - 25200a b)\|x + 385a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 4620a b x + 2520a +--R / +--R 13 3+-+ 12 +--R 840b \|x + 840a b +--R Type: Expression(Integer) +--E 272 + +--S 273 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3+-+ 11 3+-+ +--R (27720a b\|x + 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (252b x - 495a b x + 1386a b x - 13860a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 308a b x + 660a b x - 2310a b x - 25200a b)\|x + 385a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 4620a b x + 2520a +--R / +--R 13 3+-+ 12 +--R 840b \|x + 840a b +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 275 + +)clear all + +--S 276 of 1299 +t0:=x^2/(a+b*x^(1/3))^2 +--R +--R +--R 2 +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 276 + +--S 277 of 1299 +r0:=-3*a^8/(b^9*(a+b*x^(1/3)))+21*a^6*x^(1/3)/b^8-9*a^5*x^(2/3)/b^7+_ + 5*a^4*x/b^6-3*a^3*x^(4/3)/b^5+9/5*a^2*x^(5/3)/b^4-a*x^2/b^3+_ + 3/7*x^(7/3)/b^2-24*a^7*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 7 3+-+ 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R (- 840a b\|x - 840a )log(b\|x + a) + (15b x - 42a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 8 +--R (- 20a b x + 70a b x + 735a b)\|x + 28a b x - 140a b x - 105a +--R / +--R 10 3+-+ 9 +--R 35b \|x + 35a b +--R Type: Expression(Integer) +--E 277 + +--S 278 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 3+-+ 8 3+-+ 8 2 3 5 6 2 3+-+2 +--R (- 840a b\|x - 840a )log(b\|x + a) + (15b x - 42a b x + 420a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 2 6 2 5 3 8 +--R (- 20a b x + 70a b x + 735a b)\|x + 28a b x - 140a b x - 105a +--R / +--R 10 3+-+ 9 +--R 35b \|x + 35a b +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 280 + +)clear all + +--S 281 of 1299 +t0:=x/(a+b*x^(1/3))^2 +--R +--R +--R x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1299 +r0:=3*a^5/(b^6*(a+b*x^(1/3)))-12*a^3*x^(1/3)/b^5+9/2*a^2*x^(2/3)/b^4-_ + 2*a*x/b^3+3/4*x^(4/3)/b^2+15*a^4*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (60a b\|x + 60a )log(b\|x + a) + (3b x - 30a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x - 48a b)\|x + 10a b x + 12a +--R / +--R 7 3+-+ 6 +--R 4b \|x + 4a b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (60a b\|x + 60a )log(b\|x + a) + (3b x - 30a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x - 48a b)\|x + 10a b x + 12a +--R / +--R 7 3+-+ 6 +--R 4b \|x + 4a b +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1299 +t0:=1/(a+b*x^(1/3))^2 +--R +--R +--R 1 +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R b \|x + 2a b\|x + a +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1299 +r0:=-3*a^2/(b^3*(a+b*x^(1/3)))+3*x^(1/3)/b^2-6*a*log(a+b*x^(1/3))/b^3 +--R +--R +--R 3+-+ 2 3+-+ 2 3+-+2 3+-+ 2 +--R (- 6a b\|x - 6a )log(b\|x + a) + 3b \|x + 3a b\|x - 3a +--R (2) ------------------------------------------------------------ +--R 4 3+-+ 3 +--R b \|x + a b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 2 3+-+ 2 3+-+2 3+-+ 2 +--R (- 6a b\|x - 6a )log(b\|x + a) + 3b \|x + 3a b\|x - 3a +--R (3) ------------------------------------------------------------ +--R 4 3+-+ 3 +--R b \|x + a b +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1299 +t0:=1/((a+b*x^(1/3))^2*x) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 3+-+2 3+-+ 2 +--R b x \|x + 2a b x\|x + a x +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1299 +r0:=3/(a*(a+b*x^(1/3)))-3*log(a+b*x^(1/3))/a^2+log(x)/a^2 +--R +--R +--R 3+-+ 3+-+ 3+-+ +--R (- 3b\|x - 3a)log(b\|x + a) + b log(x)\|x + a log(x) + 3a +--R (2) ------------------------------------------------------------ +--R 2 3+-+ 3 +--R a b\|x + a +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ 3+-+ 3+-+ +--R (- 3b\|x - 3a)log(b\|x + a) + (3b\|x + 3a)log(\|x ) + 3a +--R (3) ----------------------------------------------------------- +--R 2 3+-+ 3 +--R a b\|x + a +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 2 +--R a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^2) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 2 3+-+2 2 3+-+ 2 2 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1299 +r0:=(-4)/(a^2*x)+3/(a*(a+b*x^(1/3))*x)+6*b/(a^3*x^(2/3))-_ + 12*b^2/(a^4*x^(1/3))+12*b^3*log(a+b*x^(1/3))/a^5-4*b^3*log(x)/a^5 +--R +--R +--R (2) +--R 4 3+-+ 3 3+-+ 2 2 3+-+2 +--R (12b x\|x + 12a b x)log(b\|x + a) - 6a b \|x +--R + +--R 4 3 3+-+ 3 3 4 +--R (- 4b x log(x) + 2a b)\|x - 4a b x log(x) - 12a b x - a +--R / +--R 5 3+-+ 6 +--R a b x\|x + a x +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3+-+ 3 3+-+ 4 3+-+ 3 3+-+ +--R (12b x\|x + 12a b x)log(b\|x + a) + (- 12b x\|x - 12a b x)log(\|x ) +--R + +--R 2 2 3+-+2 3 3+-+ 3 4 +--R - 6a b \|x + 2a b\|x - 12a b x - a +--R / +--R 5 3+-+ 6 +--R a b x\|x + a x +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 12b log(\|x ) + 4b log(x) +--R (4) --------------------------- +--R 5 +--R a +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^3) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 3 3+-+2 3 3+-+ 2 3 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1299 +r0:=(-7/2)/(a^2*x^2)+3/(a*(a+b*x^(1/3))*x^2)+21/5*b/(a^3*x^(5/3))-_ + 21/4*b^2/(a^4*x^(4/3))+7*b^3/(a^5*x)-21/2*b^4/(a^6*x^(2/3))+_ + 21*b^5/(a^7*x^(1/3))-21*b^6*log(a+b*x^(1/3))/a^8+7*b^6*log(x)/a^8 +--R +--R +--R (2) +--R 7 2 3+-+ 6 2 3+-+ 2 5 5 2 3+-+2 +--R (- 420b x \|x - 420a b x )log(b\|x + a) + (210a b x - 21a b )\|x +--R + +--R 7 2 3 4 6 3+-+ 6 2 6 2 +--R (140b x log(x) - 70a b x + 14a b)\|x + 140a b x log(x) + 420a b x +--R + +--R 4 3 7 +--R 35a b x - 10a +--R / +--R 8 2 3+-+ 9 2 +--R 20a b x \|x + 20a x +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 7 2 3+-+ 6 2 3+-+ +--R (- 420b x \|x - 420a b x )log(b\|x + a) +--R + +--R 7 2 3+-+ 6 2 3+-+ 2 5 5 2 3+-+2 +--R (420b x \|x + 420a b x )log(\|x ) + (210a b x - 21a b )\|x +--R + +--R 3 4 6 3+-+ 6 2 4 3 7 +--R (- 70a b x + 14a b)\|x + 420a b x + 35a b x - 10a +--R / +--R 8 2 3+-+ 9 2 +--R 20a b x \|x + 20a x +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 21b log(\|x ) - 7b log(x) +--R (4) ------------------------- +--R 8 +--R a +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1299 +t0:=1/((a+b*x^(1/3))^2*x^4) +--R +--R +--R 1 +--R (1) ------------------------------ +--R 2 4 3+-+2 4 3+-+ 2 4 +--R b x \|x + 2a b x \|x + a x +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1299 +r0:=(-10/3)/(a^2*x^3)+3/(a*(a+b*x^(1/3))*x^3)+15/4*b/(a^3*x^(8/3))-_ + 30/7*b^2/(a^4*x^(7/3))+5*b^3/(a^5*x^2)-6*b^4/(a^6*x^(5/3))+_ + 15/2*b^5/(a^7*x^(4/3))-10*b^6/(a^8*x)+15*b^7/(a^9*x^(2/3))-_ + 30*b^8/(a^10*x^(1/3))+30*b^9*log(a+b*x^(1/3))/a^11-10*b^9*log(x)/a^11 +--R +--R +--R (2) +--R 10 3 3+-+ 9 3 3+-+ +--R (2520b x \|x + 2520a b x )log(b\|x + a) +--R + +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1260a b x + 126a b x - 45a b )\|x +--R + +--R 10 3 3 7 2 6 4 9 3+-+ 9 3 +--R (- 840b x log(x) + 420a b x - 84a b x + 35a b)\|x - 840a b x log(x) +--R + +--R 9 3 4 6 2 7 3 10 +--R - 2520a b x - 210a b x + 60a b x - 28a +--R / +--R 11 3 3+-+ 12 3 +--R 84a b x \|x + 84a x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 10 3 3+-+ 9 3 3+-+ +--R (2520b x \|x + 2520a b x )log(b\|x + a) +--R + +--R 10 3 3+-+ 9 3 3+-+ +--R (- 2520b x \|x - 2520a b x )log(\|x ) +--R + +--R 2 8 2 5 5 8 2 3+-+2 +--R (- 1260a b x + 126a b x - 45a b )\|x +--R + +--R 3 7 2 6 4 9 3+-+ 9 3 4 6 2 7 3 +--R (420a b x - 84a b x + 35a b)\|x - 2520a b x - 210a b x + 60a b x +--R + +--R 10 +--R - 28a +--R / +--R 11 3 3+-+ 12 3 +--R 84a b x \|x + 84a x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 30b log(\|x ) + 10b log(x) +--R (4) ---------------------------- +--R 11 +--R a +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1299 +t0:=x^3/(a+b*x^(1/3))^3 +--R +--R +--R 3 +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1299 +r0:=3/2*a^11/(b^12*(a+b*x^(1/3))^2)-33*a^10/(b^12*(a+b*x^(1/3)))+_ + 135*a^8*x^(1/3)/b^11-54*a^7*x^(2/3)/b^10+28*a^6*x/b^9-_ + 63/4*a^5*x^(4/3)/b^8+9*a^4*x^(5/3)/b^7-5*a^3*x^2/b^6+_ + 18/7*a^2*x^(7/3)/b^5-9/8*a*x^(8/3)/b^4+1/3*x^3/b^3-_ + 165*a^9*log(a+b*x^(1/3))/b^12 +--R +--R +--R (2) +--R 9 2 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b\|x - 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (56b x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b)\|x + 110a b x +--R + +--R 5 6 2 8 3 11 +--R - 462a b x + 9240a b x - 5292a +--R / +--R 14 3+-+2 13 3+-+ 2 12 +--R 168b \|x + 336a b \|x + 168a b +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 2 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b\|x - 27720a )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (56b x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b)\|x + 110a b x +--R + +--R 5 6 2 8 3 11 +--R - 462a b x + 9240a b x - 5292a +--R / +--R 14 3+-+2 13 3+-+ 2 12 +--R 168b \|x + 336a b \|x + 168a b +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1299 +t0:=x^2/(a+b*x^(1/3))^3 +--R +--R +--R 2 +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1299 +r0:=-3/2*a^8/(b^9*(a+b*x^(1/3))^2)+24*a^7/(b^9*(a+b*x^(1/3)))-_ + 63*a^5*x^(1/3)/b^8+45/2*a^4*x^(2/3)/b^7-10*a^3*x/b^6+_ + 9/2*a^2*x^(4/3)/b^5-9/5*a*x^(5/3)/b^4+1/2*x^2/b^3+_ + 84*a^6*log(a+b*x^(1/3))/b^9 +--R +--R +--R (2) +--R 6 2 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b\|x + 840a )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ +--R (5b x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b)\|x +--R + +--R 2 6 2 5 3 8 +--R 14a b x - 280a b x + 225a +--R / +--R 11 3+-+2 10 3+-+ 2 9 +--R 10b \|x + 20a b \|x + 10a b +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 2 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b\|x + 840a )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ +--R (5b x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b)\|x +--R + +--R 2 6 2 5 3 8 +--R 14a b x - 280a b x + 225a +--R / +--R 11 3+-+2 10 3+-+ 2 9 +--R 10b \|x + 20a b \|x + 10a b +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1299 +t0:=x/(a+b*x^(1/3))^3 +--R +--R +--R x +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1299 +r0:=3/2*a^5/(b^6*(a+b*x^(1/3))^2)-15*a^4/(b^6*(a+b*x^(1/3)))+_ + 18*a^2*x^(1/3)/b^5-9/2*a*x^(2/3)/b^4+x/b^3-30*a^3*log(a+b*x^(1/3))/b^6 +--R +--R +--R (2) +--R 3 2 3+-+2 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (- 60a b \|x - 120a b\|x - 60a )log(b\|x + a) + (2b x + 63a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x + 6a b)\|x + 20a b x - 27a +--R / +--R 8 3+-+2 7 3+-+ 2 6 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3+-+2 4 3+-+ 5 3+-+ 5 3 2 3+-+2 +--R (- 60a b \|x - 120a b\|x - 60a )log(b\|x + a) + (2b x + 63a b )\|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 5a b x + 6a b)\|x + 20a b x - 27a +--R / +--R 8 3+-+2 7 3+-+ 2 6 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1299 +t0:=1/(a+b*x^(1/3))^3 +--R +--R +--R 1 +--R (1) -------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b\|x + b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1299 +r0:=-3/2*a^2/(b^3*(a+b*x^(1/3))^2)+6*a/(b^3*(a+b*x^(1/3)))+_ + 3*log(a+b*x^(1/3))/b^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(b\|x + a) + 12a b\|x + 9a +--R (2) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 2 3 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(b\|x + a) + 12a b\|x + 9a +--R (3) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 2 3 +--R 2b \|x + 4a b \|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1299 +t0:=1/((a+b*x^(1/3))^3*x) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 3a b x \|x + 3a b x\|x + b x + a x +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1299 +r0:=3/2/(a*(a+b*x^(1/3))^2)+3/(a^2*(a+b*x^(1/3)))-_ + 3*log(a+b*x^(1/3))/a^3+log(x)/a^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 2 3+-+ 2 3+-+2 +--R (- 6b \|x - 12a b\|x - 6a )log(b\|x + a) + 2b log(x)\|x +--R + +--R 3+-+ 2 2 +--R (4a b log(x) + 6a b)\|x + 2a log(x) + 9a +--R / +--R 3 2 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b\|x + 2a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 2 3+-+ +--R (- 6b \|x - 12a b\|x - 6a )log(b\|x + a) +--R + +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6b \|x + 12a b\|x + 6a )log(\|x ) + 6a b\|x + 9a +--R / +--R 3 2 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b\|x + 2a +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^2) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1299 +r0:=(-10)/(a^3*x)+3/2/(a*(a+b*x^(1/3))^2*x)+15/2/(a^2*(a+b*x^(1/3))*x)+_ + 15*b/(a^4*x^(2/3))-30*b^2/(a^5*x^(1/3))+30*b^3*log(a+b*x^(1/3))/a^6-_ + 10*b^3*log(x)/a^6 +--R +--R +--R (2) +--R 5 3+-+2 4 3+-+ 2 3 3+-+ +--R (60b x \|x + 120a b x\|x + 60a b x)log(b\|x + a) +--R + +--R 5 3 2 3+-+2 4 4 4 3+-+ +--R (- 20b x log(x) - 20a b )\|x + (- 40a b x log(x) - 60a b x + 5a b)\|x +--R + +--R 2 3 2 3 5 +--R - 20a b x log(x) - 90a b x - 2a +--R / +--R 6 2 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2a x +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 2 3 3+-+ +--R (60b x \|x + 120a b x\|x + 60a b x)log(b\|x + a) +--R + +--R 5 3+-+2 4 3+-+ 2 3 3+-+ 3 2 3+-+2 +--R (- 60b x \|x - 120a b x\|x - 60a b x)log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 2 3 5 +--R (- 60a b x + 5a b)\|x - 90a b x - 2a +--R / +--R 6 2 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2a x +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 30b log(\|x ) + 10b log(x) +--R (4) ---------------------------- +--R 6 +--R a +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1299 +r0:=(-14)/(a^3*x^2)+3/2/(a*(a+b*x^(1/3))^2*x^2)+12/(a^2*(a+b*x^(1/3))*x^2)+_ + 84/5*b/(a^4*x^(5/3))-21*b^2/(a^5*x^(4/3))+28*b^3/(a^6*x)-_ + 42*b^4/(a^7*x^(2/3))+84*b^5/(a^8*x^(1/3))-_ + 84*b^6*log(a+b*x^(1/3))/a^9+28*b^6*log(x)/a^9 +--R +--R +--R (2) +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (- 840b x \|x - 1680a b x \|x - 840a b x )log(b\|x + a) +--R + +--R 8 2 3 5 6 2 3+-+2 +--R (280b x log(x) + 280a b x - 14a b )\|x +--R + +--R 7 2 7 2 4 4 7 3+-+ 2 6 2 +--R (560a b x log(x) + 840a b x - 70a b x + 8a b)\|x + 280a b x log(x) +--R + +--R 2 6 2 5 3 8 +--R 1260a b x + 28a b x - 5a +--R / +--R 9 2 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10a x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (- 840b x \|x - 1680a b x \|x - 840a b x )log(b\|x + a) +--R + +--R 8 2 3+-+2 7 2 3+-+ 2 6 2 3+-+ +--R (840b x \|x + 1680a b x \|x + 840a b x )log(\|x ) +--R + +--R 3 5 6 2 3+-+2 7 2 4 4 7 3+-+ 2 6 2 +--R (280a b x - 14a b )\|x + (840a b x - 70a b x + 8a b)\|x + 1260a b x +--R + +--R 5 3 8 +--R 28a b x - 5a +--R / +--R 9 2 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10a x +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 84b log(\|x ) - 28b log(x) +--R (4) -------------------------- +--R 9 +--R a +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1299 +t0:=1/((a+b*x^(1/3))^3*x^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 3a b x \|x + 3a b x \|x + b x + a x +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1299 +r0:=(-55/3)/(a^3*x^3)+3/2/(a*(a+b*x^(1/3))^2*x^3)+33/2/(a^2*_ + (a+b*x^(1/3))*x^3)+165/8*b/(a^4*x^(8/3))-165/7*b^2/_ + (a^5*x^(7/3))+55/2*b^3/(a^6*x^2)-33*b^4/(a^7*x^(5/3))+_ + 165/4*b^5/(a^8*x^(4/3))-55*b^6/(a^9*x)+165/2*b^7/(a^10*x^(2/3))-_ + 165*b^8/(a^11*x^(1/3))+165*b^9*log(a+b*x^(1/3))/a^12-55*b^9*log(x)/a^12 +--R +--R +--R (2) +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (27720b x \|x + 55440a b x \|x + 27720a b x )log(b\|x + a) +--R + +--R 11 3 3 8 2 6 5 9 2 3+-+2 +--R (- 9240b x log(x) - 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 10 3 4 7 2 7 4 10 +--R (- 18480a b x log(x) - 27720a b x + 2310a b x - 264a b x + 77a b) +--R * +--R 3+-+ +--R \|x +--R + +--R 2 9 3 2 9 3 5 6 2 8 3 11 +--R - 9240a b x log(x) - 41580a b x - 924a b x + 165a b x - 56a +--R / +--R 12 2 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168a x +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (27720b x \|x + 55440a b x \|x + 27720a b x )log(b\|x + a) +--R + +--R 11 3 3+-+2 10 3 3+-+ 2 9 3 3+-+ +--R (- 27720b x \|x - 55440a b x \|x - 27720a b x )log(\|x ) +--R + +--R 3 8 2 6 5 9 2 3+-+2 +--R (- 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 4 7 2 7 4 10 3+-+ 2 9 3 +--R (- 27720a b x + 2310a b x - 264a b x + 77a b)\|x - 41580a b x +--R + +--R 5 6 2 8 3 11 +--R - 924a b x + 165a b x - 56a +--R / +--R 12 2 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168a x +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 165b log(\|x ) + 55b log(x) +--R (4) ----------------------------- +--R 12 +--R a +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1299 +t0:=1/sqrt(1+x^(1/3)) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R |3+-+ +--R \|\|x + 1 +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1299 +r0:=-4*(1+x^(1/3))^(3/2)+6/5*(1+x^(1/3))^(5/2)+6*sqrt(1+x^(1/3)) +--R +--R +--R +--------+ +--R 3+-+2 3+-+ |3+-+ +--R (6\|x - 8\|x + 16)\|\|x + 1 +--R (2) -------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +--------+ +--R 3+-+2 3+-+ |3+-+ +--R (6\|x - 8\|x + 16)\|\|x + 1 +--R (3) -------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1299 +t0:=1/((1+x^(1/3))*x^(3/2)) +--R +--R +--R 1 +--R (1) ----------------- +--R +-+3+-+ +-+ +--R x\|x \|x + x\|x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1299 +r0:=6/x^(1/6)+6*atan(x^(1/6))+(-2)/sqrt(x) +--R +--R +--R +-+6+-+ 6+-+ 6+-+ +-+ +--R 6\|x \|x atan(\|x ) - 2\|x + 6\|x +--R (2) ----------------------------------- +--R +-+6+-+ +--R \|x \|x +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 6+-+3 6+-+ 6+-+2 +--R 6\|x atan(\|x ) + 6\|x - 2 +--R (3) ----------------------------- +--R 6+-+3 +--R \|x +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1299 +m0:=a0-r0 +--R +--R +--R 6+-+3 +-+ +--R 2\|x - 2\|x +--R (4) -------------- +--R +-+6+-+3 +--R \|x \|x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1299 +t0:=x^(2/3)/(1+x^(1/3)) +--R +--R +--R 3+-+2 +--R \|x +--R (1) -------- +--R 3+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1299 +r0:=-3*x^(1/3)+3/2*x^(2/3)-x+3/4*x^(4/3)+3*log(1+x^(1/3)) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 12log(\|x + 1) + 6\|x + (3x - 12)\|x - 4x +--R (2) --------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+2 3+-+ +--R 12log(\|x + 1) + 6\|x + (3x - 12)\|x - 4x +--R (3) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1299 +t0:=1/(1+x^(2/3)) +--R +--R +--R 1 +--R (1) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1299 +r0:=3*x^(1/3)-3*atan(x^(1/3)) +--R +--R +--R 3+-+ 3+-+ +--R (2) - 3atan(\|x ) + 3\|x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3) - 3atan(\|x ) + 3\|x +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1299 +t0:=1/((1+x^(2/3))*x^(1/3)) +--R +--R +--R 1 +--R (1) -------- +--R 3+-+ +--R \|x + x +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1299 +r0:=3/2*log(1+x^(2/3)) +--R +--R +--R 3+-+2 +--R 3log(\|x + 1) +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 +--R 3log(\|x + 1) +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1299 +t0:=1/((1+x^(2/3))*x^(2/3)) +--R +--R +--R 1 +--R (1) ------------- +--R 3+-+2 3+-+ +--R \|x + x\|x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1299 +r0:=3*atan(x^(1/3)) +--R +--R +--R 3+-+ +--R (2) 3atan(\|x ) +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R (3) 3atan(\|x ) +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1299 +t0:=sqrt(-1+x^(2/3))/x^(1/3) +--R +--R +--R +---------+ +--R |3+-+2 +--R \|\|x - 1 +--R (1) ------------ +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1299 +r0:=(-1+x^(2/3))^(3/2) +--R +--R +--R +---------+ +--R 3+-+2 |3+-+2 +--R (2) (\|x - 1)\|\|x - 1 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 3+-+2 3+-+ 2 +--R (4x \|x + 3\|x - 7x)\|\|x - 1 + 6\|x - 9x\|x + 4x - 1 +--R (3) --------------------------------------------------------------- +--R +---------+ +--R 3+-+2 |3+-+2 3+-+ +--R (4\|x - 1)\|\|x - 1 - 3\|x + 4x +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1299 +t0:=(1+x^(2/3))^(3/2)/x^(1/3) +--R +--R +--R +---------+ +--R 3+-+2 |3+-+2 +--R (\|x + 1)\|\|x + 1 +--R (1) ----------------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1299 +r0:=3/5*(1+x^(2/3))^(5/2) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 +--R (6\|x + 3x\|x + 3)\|\|x + 1 +--R (2) --------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +---------+ +--R 3+-+2 3+-+ |3+-+2 +--R (6\|x + 3x\|x + 3)\|\|x + 1 +--R (3) --------------------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1299 +t0:=sqrt(x)/(1+x^(2/3)) +--R +--R +--R +-+ +--R \|x +--R (1) --------- +--R 3+-+2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1299 +r0:=-6*x^(1/6)+6/5*x^(5/6)-3*atan(1-x^(1/6)*sqrt(2))/sqrt(2)+_ + 3*atan(1+x^(1/6)*sqrt(2))/sqrt(2)-3/2*log(1+x^(1/3)-_ + x^(1/6)*sqrt(2))/sqrt(2)+3/2*log(1+x^(1/3)+x^(1/6)*sqrt(2))/sqrt(2) +--R +--R +--R (2) +--R +-+6+-+ 3+-+ +-+6+-+ 3+-+ +--R 15log(\|2 \|x + \|x + 1) - 15log(- \|2 \|x + \|x + 1) +--R + +--R +-+6+-+ +-+6+-+ +-+6+-+5 +-+6+-+ +--R 30atan(\|2 \|x + 1) + 30atan(\|2 \|x - 1) + 12\|2 \|x - 60\|2 \|x +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ 6+-+2 +-+6+-+ +-+ 6+-+2 +-+6+-+ +--R 15\|2 log(\|x + \|2 \|x + 1) - 15\|2 log(\|x - \|2 \|x + 1) +--R + +--R +-+ 1 +-+ 1 6+-+5 6+-+ +--R - 30\|2 atan(------------) - 30\|2 atan(------------) + 24\|x - 120\|x +--R +-+6+-+ +-+6+-+ +--R \|2 \|x - 1 \|2 \|x + 1 +--R / +--R 20 +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 6+-+2 +-+6+-+ 6+-+2 +-+6+-+ +--R 3log(\|x + \|2 \|x + 1) - 3log(\|x - \|2 \|x + 1) +--R + +--R +-+6+-+ 3+-+ +-+6+-+ 3+-+ +--R - 3log(\|2 \|x + \|x + 1) + 3log(- \|2 \|x + \|x + 1) +--R + +--R +-+6+-+ +-+6+-+ 1 +--R - 6atan(\|2 \|x + 1) - 6atan(\|2 \|x - 1) - 6atan(------------) +--R +-+6+-+ +--R \|2 \|x - 1 +--R + +--R 1 +--R - 6atan(------------) +--R +-+6+-+ +--R \|2 \|x + 1 +--R / +--R +-+ +--R 2\|2 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1299 +t0:=x^(1/3)/(-1+x^(5/6)) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------- +--R 6+-+5 +--R \|x - 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1299 +r0a:=6/5*log(1-x^(1/6))-3/10*log(2+2*x^(1/3)+x^(1/6)*(1+sqrt(5)))*_ + (1-sqrt(5))-3/10*log(2+2*x^(1/3)+x^(1/6)*(1-sqrt(5)))*(1+sqrt(5))+_ + 2*sqrt(x)+3/5*atan((1+4*x^(1/6)-sqrt(5))/sqrt(10+2*sqrt(5)))*_ + sqrt(10-2*sqrt(5))-3/5*atan((1+4*x^(1/6)+sqrt(5))/sqrt(10-2*_ + sqrt(5)))*sqrt(10+2*sqrt(5)) +--R +--R +--R (2) +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (3\|5 - 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(- \|x + 1) +--R + +--R +-+ +-+ 6+-+ 3+-+ +--R (- 3\|5 - 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x + \|5 + 1 +--R - 6\|2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+ +--R 6\|- 2\|5 + 10 atan(----------------) + 20\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1299 +r0b:=6/5*log(1-x^(1/6))-3/10*log(2+2*_ + x^(1/3)+x^(1/6)*(1+sqrt(5)))*(1-sqrt(5))-3/10*log(2+2*x^(1/3)+_ + x^(1/6)*(1-sqrt(5)))*(1+sqrt(5))+2*sqrt(x)+6*atan((1+4*x^(1/6)-_ + sqrt(5))/sqrt(2*(5+sqrt(5))))*sqrt(2/5/(5+sqrt(5)))-3/5*_ + atan(1/2*(1+4*x^(1/6)+sqrt(5))*sqrt(1/10*(5+sqrt(5))))*sqrt(2*(5+sqrt(5))) +--R +--R +--R (3) +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (3\|2 \|5 - 3\|2 )log((\|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 6+-+ +--R 12\|2 log(- \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (- 3\|2 \|5 - 3\|2 )log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +--------+ +--R +----------+ 6+-+ +-+ | +-+ +--R +-+ | +-+ (4\|x + \|5 + 1)\|\|5 + 5 +--R - 6\|2 \|2\|5 + 10 atan(-----------------------------) +--R +--+ +--R 2\|10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+ +-+ +--R 12\|- \|5 + 5 atan(----------------) + 20\|2 \|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 398 + +--S 399 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (4) +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R 2 6+-+ 6+-+ +--R 10%%BJ1 log(- 25%%BJ1 + 36\|x ) + 12log(\|x - 1) +--R + +--R 2 6+-+ 6+-+3 +--R 10%%BJ0 log(- 25%%BJ0 + 36\|x ) + 20\|x +--R / +--R 10 +--R Type: Union(Expression(Integer),...) +--E 399 + +--S 400 of 1299 +m0a:=a0-r0a +--R +--R +--R (5) +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-------------------------------------------------------------+ +--R | 2 2 +--R - \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R - 5%%BJ1 - 5%%BJ0 - 6 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R 2 6+-+ +--R 10%%BJ1 log(- 25%%BJ1 + 36\|x ) +--R + +--R +-+ +-+ 6+-+ 3+-+ 6+-+ +--R (- 3\|5 + 3)log((\|5 + 1)\|x + 2\|x + 2) + 12log(\|x - 1) +--R + +--R 6+-+ +-+ +-+ 6+-+ 3+-+ +--R - 12log(- \|x + 1) + (3\|5 + 3)log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +----------+ 6+-+ +-+ +--R 2 6+-+ | +-+ 4\|x + \|5 + 1 +--R 10%%BJ0 log(- 25%%BJ0 + 36\|x ) + 6\|2\|5 + 10 atan(----------------) +--R +------------+ +--R | +-+ +--R \|- 2\|5 + 10 +--R + +--R +------------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 6+-+3 +-+ +--R - 6\|- 2\|5 + 10 atan(----------------) + 20\|x - 20\|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R 10 +--R Type: Expression(Integer) +--E 400 + +--S 401 of 1299 +d0a:=D(m0a,x) +--R +--R +--R (6) +--R +------------+ +--R +-+ | +-+ +-+3+-+6+-+4 +--R x\|5 \|- 2\|5 + 10 \|x \|x \|x +--R + +--R +------------+ +--R +-+ | +-+ +-+3+-+2 +--R - x\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+ +--R (- x - 2x)\|5 \|- 2\|5 + 10 \|x \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+2 +--R (x - x)\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ | +-+ +-+3+-+ 2 +-+ | +-+ +-+ +--R 2x \|5 \|- 2\|5 + 10 \|x \|x - x \|5 \|- 2\|5 + 10 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +------------+ +--R 2 +-+ | +-+ +-+3+-+2 +--R (x + 2x)\|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +------------+ +--R +-+ | +-+ +-+3+-+ 3 2 +-+ | +-+ +-+ +--R x\|5 \|- 2\|5 + 10 \|x \|x + (x + x )\|5 \|- 2\|5 + 10 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +------------+ +------------+ +--R 2 +-+ | +-+ +-+3+-+2 2 +-+ | +-+ +-+3+-+ +--R - 2x \|5 \|- 2\|5 + 10 \|x \|x - x \|5 \|- 2\|5 + 10 \|x \|x +--R + +--R +------------+ +--R 3 +-+ | +-+ +-+ +--R - x \|5 \|- 2\|5 + 10 \|x +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ 2 3+-+2 +--R ((40x - 8)\|x - 80x + 80x)\|x +--R + +--R 2 +-+ 3 2 3+-+ 2 +-+ 2 +--R ((- 4x - 8x)\|x - 40x - 80x + 40x)\|x + (8x - 8x)\|x + 40x +--R * +--R 6+-+5 +--R \|x +--R + +--R 2 +-+ 3 2 3+-+2 +--R ((- 8x - 8x)\|x + 40x - 160x )\|x +--R + +--R 2 +-+ 3 2 3+-+ 2 +-+ 3 +--R ((8x - 8x)\|x + 40x - 80x )\|x + 8x \|x - 80x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ 3 3+-+2 2 +-+ 3 3+-+ +--R ((16x - 24x)\|x + 80x )\|x + ((- 32x - 8x)\|x + 40x )\|x +--R + +--R 2 +-+ 4 +--R - 8x \|x + 40x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ 3 2 +-+ +--R ((64x - 24x)\|x \|x + (40x + 48x - 8x)\|x \|x + (8x - 8x )\|x ) +--R * +--R 6+-+2 +--R \|x +--R + +--R 3 2 +-+3+-+2 +--R (- 40x + 104x - 24x)\|x \|x +--R + +--R 3 2 +-+ 2 3+-+ 3 2 +-+ +--R ((- 40x + 48x - 12x)\|x - 40x )\|x + (48x - 8x )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 3 2 +-+ 2 3+-+2 +--R ((- 80x + 24x - 32x)\|x + 40x )\|x +--R + +--R 3 2 +-+ 3 2 3+-+ 4 3 2 +-+ +--R ((- 40x + 16x )\|x + 80x + 40x )\|x + (- 40x + 8x - 8x )\|x +--R / +--R 2 +-+3+-+2 3 2 +-+3+-+ 2 +-+ 6+-+5 +--R ((80x - 80x)\|x \|x + (40x + 80x - 40x)\|x \|x - 40x \|x )\|x +--R + +--R 3 2 +-+3+-+2 3 2 +-+3+-+ 3 +-+ 6+-+4 +--R ((- 40x + 160x )\|x \|x + (- 40x + 80x )\|x \|x + 80x \|x )\|x +--R + +--R 3 +-+3+-+2 3 +-+3+-+ 4 +-+ 6+-+3 2 +-+3+-+6+-+ +--R (- 80x \|x \|x - 40x \|x \|x - 40x \|x )\|x + 40x \|x \|x \|x +--R + +--R 2 +-+3+-+2 3 2 +-+3+-+ +--R - 40x \|x \|x + (- 80x - 40x )\|x \|x +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1299 +m0b:=a0-r0b +--R +--R +--R (7) +--R +-------------------------------------------------------------+ +--R +-+ | 2 2 +--R \|2 \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R +-+ +-+ +-+ +--R - 5\|2 %%BJ1 - 5\|2 %%BJ0 - 6\|2 +--R * +--R log +--R (5%%BJ1 + 5%%BJ0 + 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R - +--R +-+ +--R \|2 +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R +-+ +-+ +-+ +--R - 5\|2 %%BJ1 - 5\|2 %%BJ0 - 6\|2 +--R * +--R log +--R (- 5%%BJ1 - 5%%BJ0 - 6) +--R * +--R +-------------------------------------------------------------+ +--R | 2 2 +--R \|- 75%%BJ1 + (- 50%%BJ0 - 60)%%BJ1 - 75%%BJ0 - 60%%BJ0 - 108 +--R + +--R 2 2 6+-+ +--R 25%%BJ1 + 25%%BJ0 + 72\|x + 36 +--R + +--R +-+ 2 6+-+ +--R 10\|2 %%BJ1 log(- 25%%BJ1 + 36\|x ) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (- 3\|2 \|5 + 3\|2 )log((\|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 6+-+ +-+ 6+-+ +--R 12\|2 log(\|x - 1) - 12\|2 log(- \|x + 1) +--R + +--R +-+ +-+ +-+ +-+ 6+-+ 3+-+ +--R (3\|2 \|5 + 3\|2 )log((- \|5 + 1)\|x + 2\|x + 2) +--R + +--R +-+ 2 6+-+ +--R 10\|2 %%BJ0 log(- 25%%BJ0 + 36\|x ) +--R + +--R +--------+ +--R +----------+ 6+-+ +-+ | +-+ +--R +-+ | +-+ (4\|x + \|5 + 1)\|\|5 + 5 +--R 6\|2 \|2\|5 + 10 atan(-----------------------------) +--R +--+ +--R 2\|10 +--R + +--R +----------+ 6+-+ +-+ +--R | +-+ 4\|x - \|5 + 1 +-+6+-+3 +-+ +-+ +--R - 12\|- \|5 + 5 atan(----------------) + 20\|2 \|x - 20\|2 \|x +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R / +--R +-+ +--R 10\|2 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1299 +d0b:=D(m0b,x) +--R +--R +--R (8) +--R +--+ +-+3+-+2 2 +--+ +-+ 6+-+5 +--R (4x\|10 \|x \|x + 2x \|10 \|x )\|x +--R + +--R +--+ +-+3+-+2 +-+ 2 +--+ +-+3+-+ 6+-+4 +--R (2x\|10 \|x \|x + (x\|5 + 2x + 3x)\|10 \|x \|x )\|x +--R + +--R +-+ 2 +--+ +-+3+-+2 +--R (- x\|5 - 2x + 3x)\|10 \|x \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+ 2 +--+ +-+ +--R ((- x - 2x)\|5 - 3x )\|10 \|x \|x + 2x \|10 \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+2 +--R ((x - x)\|5 - 3x - x)\|10 \|x \|x +--R + +--R 2 +-+ +--+ +-+3+-+ 2 +-+ 3 2 +--+ +-+ +--R (2x \|5 + 2x)\|10 \|x \|x + (- x \|5 - 2x - x )\|10 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+2 +--R ((x + 2x)\|5 + x )\|10 \|x \|x +--R + +--R +-+ 2 +--+ +-+3+-+ +--R (x\|5 - 2x - x)\|10 \|x \|x +--R + +--R 3 2 +-+ 3 2 +--+ +-+ +--R ((x + x )\|5 + x + x )\|10 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R 2 +-+ +--+ +-+3+-+2 +--R (- 2x \|5 - 4x)\|10 \|x \|x +--R + +--R 2 +-+ 2 +--+ +-+3+-+ 3 +-+ 3 2 +--+ +-+ +--R (- x \|5 + x - 2x)\|10 \|x \|x + (- x \|5 - x - 2x )\|10 \|x +--R * +--R +--------+ +--R | +-+ +--R \|\|5 + 5 +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ +-+3+-+2 +--R (- 2x\|2 \|5 - 10x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R (- x \|2 \|5 - 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+5 +--R \|x +--R + +--R +----------+ +--R +-+ +-+ +-+ | +-+ +-+3+-+2 +--R (- x\|2 \|5 - 5x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- x + x)\|2 \|5 + (- 5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R * +--R 6+-+4 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((x - 4x)\|2 \|5 + (5x - 10x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- x - 5x)\|2 \|5 + (5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R (- x \|2 \|5 - 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+3 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((4x - 2x)\|2 \|5 + 10x \|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((5x - x)\|2 \|5 + (5x - 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ 3 +-+ | +-+ +-+ +--R ((x - 2x )\|2 \|5 + 5x \|2 )\|- \|5 + 5 \|x +--R * +--R 6+-+2 +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ +-+ | +-+ +-+3+-+2 +--R ((2x + 5x)\|2 \|5 + 5x\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((x + 3x)\|2 \|5 + (5x + 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ | +-+ +-+ +--R (2x + 2x )\|2 \|5 \|- \|5 + 5 \|x +--R * +--R 6+-+ +--R \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+2 +--R ((- 5x + 2x)\|2 \|5 + (- 5x + 10x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 2 +-+ +-+ 2 +-+ | +-+ +-+3+-+ +--R ((- 3x + x)\|2 \|5 + (- 5x + 5x)\|2 )\|- \|5 + 5 \|x \|x +--R + +--R +----------+ +--R 3 2 +-+ +-+ 2 +-+ | +-+ +-+ +--R ((- 2x + x )\|2 \|5 + 5x \|2 )\|- \|5 + 5 \|x +--R * +--R +----------+ +--R | +-+ +--R \|2\|5 + 10 +--R + +--R +-+ +-+ 2 +-+ 2 +--R ((40x - 8)\|5 + 200x - 40)\|x + (- 80x + 80x)\|5 - 400x +--R + +--R 400x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ +--R ((- 4x - 8x)\|5 - 20x - 40x)\|x + (- 40x - 80x + 40x)\|5 +--R + +--R 3 2 +--R - 200x - 400x + 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 2 +-+ 2 +-+ 2 +--R ((8x - 8x)\|5 + 40x - 40x)\|x + 40x \|5 + 200x +--R * +--R 6+-+5 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ 3 +--R ((- 8x - 8x)\|5 - 40x - 40x)\|x + (40x - 160x )\|5 + 200x +--R + +--R 2 +--R - 800x +--R * +--R 3+-+2 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 2 +-+ 3 +--R ((8x - 8x)\|5 + 40x - 40x)\|x + (40x - 80x )\|5 + 200x +--R + +--R 2 +--R - 400x +--R * +--R 3+-+ +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 +--R (8x \|5 + 40x )\|x - 80x \|5 - 400x +--R * +--R 6+-+4 +--R \|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 3+-+2 +--R (((16x - 24x)\|5 + 80x - 120x)\|x + 80x \|5 + 400x )\|x +--R + +--R 2 +-+ 2 +-+ 3 +-+ 3 3+-+ +--R (((- 32x - 8x)\|5 - 160x - 40x)\|x + 40x \|5 + 200x )\|x +--R + +--R 2 +-+ 2 +-+ 4 +-+ 4 +--R (- 8x \|5 - 40x )\|x + 40x \|5 + 200x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +-+3+-+2 +--R ((64x - 24x)\|5 + 320x - 120x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((40x + 48x - 8x)\|5 + 200x + 240x - 40x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((8x - 8x )\|5 + 40x - 40x )\|x +--R * +--R 6+-+2 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+2 +--R ((- 40x + 104x - 24x)\|5 - 200x + 520x - 120x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+ 2 +-+ +--R ((- 40x + 48x - 12x)\|5 - 200x + 240x - 60x)\|x - 40x \|5 +--R + +--R 2 +--R - 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ +--R ((48x - 8x )\|5 + 240x - 40x )\|x +--R * +--R 6+-+ +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ 2 +-+ +--R ((- 80x + 24x - 32x)\|5 - 400x + 120x - 160x)\|x + 40x \|5 +--R + +--R 2 +--R 200x +--R * +--R 3+-+2 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+ 3 2 +-+ 3 +--R ((- 40x + 16x )\|5 - 200x + 80x )\|x + (80x + 40x )\|5 + 400x +--R + +--R 2 +--R 200x +--R * +--R 3+-+ +--R \|x +--R + +--R 4 3 2 +-+ 4 3 2 +-+ +--R ((- 40x + 8x - 8x )\|5 - 200x + 40x - 40x )\|x +--R / +--R 2 +-+ 2 +-+3+-+2 +--R ((80x - 80x)\|5 + 400x - 400x)\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((40x + 80x - 40x)\|5 + 200x + 400x - 200x)\|x \|x +--R + +--R 2 +-+ 2 +-+ +--R (- 40x \|5 - 200x )\|x +--R * +--R 6+-+5 +--R \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+2 +--R ((- 40x + 160x )\|5 - 200x + 800x )\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ 3 +-+ 3 +-+ +--R ((- 40x + 80x )\|5 - 200x + 400x )\|x \|x + (80x \|5 + 400x )\|x +--R * +--R 6+-+4 +--R \|x +--R + +--R 3 +-+ 3 +-+3+-+2 3 +-+ 3 +-+3+-+ +--R (- 80x \|5 - 400x )\|x \|x + (- 40x \|5 - 200x )\|x \|x +--R + +--R 4 +-+ 4 +-+ +--R (- 40x \|5 - 200x )\|x +--R * +--R 6+-+3 +--R \|x +--R + +--R 2 +-+ 2 +-+3+-+6+-+ 2 +-+ 2 +-+3+-+2 +--R (40x \|5 + 200x )\|x \|x \|x + (- 40x \|5 - 200x )\|x \|x +--R + +--R 3 2 +-+ 3 2 +-+3+-+ +--R ((- 80x - 40x )\|5 - 400x - 200x )\|x \|x +--R Type: Expression(Integer) +--E 403 + +)clear all + +--S 404 of 1299 +t0:=sqrt(3+(-1)/sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R (1) |--------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1299 +r0:=-1/6*atanh(sqrt(3+(-1)/sqrt(x))/sqrt(3))/sqrt(3)+_ + x*sqrt(3+(-1)/sqrt(x))-1/6*sqrt(x)*sqrt(3+(-1)/sqrt(x)) +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R |--------- +---------+ +--R | +-+ | +-+ +--R \| \|x +-+ +-+ +-+ |3\|x - 1 +--R - atanh(------------) + (- \|3 \|x + 6x\|3 ) |--------- +--R +-+ | +-+ +--R \|3 \| \|x +--R (2) --------------------------------------------------------- +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 405 + +--S 406 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------+ +--R | +-+ +--R +-+ +-+ |3\|x - 1 +-+ +-+ +-+ +--R \|x log(6\|x |--------- - 6\|3 \|x + \|3 ) +--R | +-+ +--R \| \|x +--R + +--R +---------+ +--R | +-+ +--R +-+ +-+ +-+ |3\|x - 1 +--R (12x\|3 \|x - 2x\|3 ) |--------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +-+ +--R 12\|3 \|x +--R Type: Union(Expression(Integer),...) +--E 406 + +--S 407 of 1299 +m0:=a0-r0 +--R +--R +--R +---------+ +--R | +-+ +--R |3\|x - 1 +--R +---------+ |--------- +--R | +-+ | +-+ +--R +-+ |3\|x - 1 +-+ +-+ +-+ \| \|x +--R log(6\|x |--------- - 6\|3 \|x + \|3 ) + 2atanh(------------) +--R | +-+ +-+ +--R \| \|x \|3 +--R (4) ---------------------------------------------------------------- +--R +-+ +--R 12\|3 +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 408 + +)clear all + +--S 409 of 1299 +t0:=1/sqrt(1+1/sqrt(x)) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | +-+ +--R |\|x + 1 +--R |-------- +--R | +-+ +--R \| \|x +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1299 +r0:=3/2*atanh(sqrt(1+1/sqrt(x)))+x*sqrt(1+1/sqrt(x))-_ + 3/2*sqrt(x)*sqrt(1+1/sqrt(x)) +--R +--R +--R +--------+ +--------+ +--R | +-+ | +-+ +--R |\|x + 1 +-+ |\|x + 1 +--R 3atanh( |-------- ) + (- 3\|x + 2x) |-------- +--R | +-+ | +-+ +--R \| \|x \| \|x +--R (2) ----------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 410 + +--S 411 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--------+ +--------+ +--R | +-+ | +-+ +--R +-+ |\|x + 1 +-+ |\|x + 1 +--R 3\|x log( |-------- + 1) - 3\|x log( |-------- - 1) +--R | +-+ | +-+ +--R \| \|x \| \|x +--R + +--R +--------+ +--R | +-+ +--R +-+ |\|x + 1 +--R (4x\|x - 6x) |-------- +--R | +-+ +--R \| \|x +--R / +--R +-+ +--R 4\|x +--R Type: Union(Expression(Integer),...) +--E 411 + +--S 412 of 1299 +m0:=a0-r0 +--R +--R +--R +--------+ +--------+ +--------+ +--R | +-+ | +-+ | +-+ +--R |\|x + 1 |\|x + 1 |\|x + 1 +--R 3log( |-------- + 1) - 3log( |-------- - 1) - 6atanh( |-------- ) +--R | +-+ | +-+ | +-+ +--R \| \|x \| \|x \| \|x +--R (4) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 413 + +)clear all + +--S 414 of 1299 +t0:=(a+b/x^(1/3))*x^4 +--R +--R +--R 4 3+-+ 4 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1299 +r0:=3/14*b*x^(14/3)+1/5*a*x^5 +--R +--R +--R 4 3+-+2 5 +--R 15b x \|x + 14a x +--R (2) -------------------- +--R 70 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+2 5 +--R 15b x \|x + 14a x +--R (3) -------------------- +--R 70 +--R Type: Union(Expression(Integer),...) +--E 416 + +--S 417 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 418 + +)clear all + +--S 419 of 1299 +t0:=(a+b/x^(1/3))*x^3 +--R +--R +--R 3 3+-+ 3 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1299 +r0:=3/11*b*x^(11/3)+1/4*a*x^4 +--R +--R +--R 3 3+-+2 4 +--R 12b x \|x + 11a x +--R (2) -------------------- +--R 44 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+2 4 +--R 12b x \|x + 11a x +--R (3) -------------------- +--R 44 +--R Type: Union(Expression(Integer),...) +--E 421 + +--S 422 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 423 + +)clear all + +--S 424 of 1299 +t0:=(a+b/x^(1/3))*x^2 +--R +--R +--R 2 3+-+ 2 +--R a x \|x + b x +--R (1) --------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1299 +r0:=3/8*b*x^(8/3)+1/3*a*x^3 +--R +--R +--R 2 3+-+2 3 +--R 9b x \|x + 8a x +--R (2) ------------------ +--R 24 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3 +--R 9b x \|x + 8a x +--R (3) ------------------ +--R 24 +--R Type: Union(Expression(Integer),...) +--E 426 + +--S 427 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 428 + +)clear all + +--S 429 of 1299 +t0:=(a+b/x^(1/3))*x +--R +--R +--R 3+-+ +--R a x\|x + b x +--R (1) ------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1299 +r0:=3/5*b*x^(5/3)+1/2*a*x^2 +--R +--R +--R 3+-+2 2 +--R 6b x \|x + 5a x +--R (2) ------------------ +--R 10 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 +--R 6b x \|x + 5a x +--R (3) ------------------ +--R 10 +--R Type: Union(Expression(Integer),...) +--E 431 + +--S 432 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 433 + +)clear all + +--S 434 of 1299 +t0:=a+b/x^(1/3) +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1299 +r0:=3/2*b*x^(2/3)+a*x +--R +--R +--R 3+-+2 +--R 3b \|x + 2a x +--R (2) --------------- +--R 2 +--R Type: Expression(Integer) +--E 435 + +--S 436 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 +--R 3b \|x + 2a x +--R (3) --------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 436 + +--S 437 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 438 + +)clear all + +--S 439 of 1299 +t0:=(a+b/x^(1/3))/x +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3+-+ +--R x\|x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1299 +r0:=-3*b/x^(1/3)+a*log(x) +--R +--R +--R 3+-+ +--R a log(x)\|x - 3b +--R (2) ----------------- +--R 3+-+ +--R \|x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R 3a\|x log(\|x ) - 3b +--R (3) -------------------- +--R 3+-+ +--R \|x +--R Type: Union(Expression(Integer),...) +--E 441 + +--S 442 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 443 + +)clear all + +--S 444 of 1299 +t0:=(a+b/x^(1/3))/x^2 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 2 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1299 +r0:=-3/4*b/x^(4/3)-a/x +--R +--R +--R 3+-+ +--R - 4a\|x - 3b +--R (2) ------------- +--R 3+-+ +--R 4x\|x +--R Type: Expression(Integer) +--E 445 + +--S 446 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 4a\|x - 3b +--R (3) ------------- +--R 3+-+ +--R 4x\|x +--R Type: Union(Expression(Integer),...) +--E 446 + +--S 447 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 448 + +)clear all + +--S 449 of 1299 +t0:=(a+b/x^(1/3))/x^3 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 3 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1299 +r0:=-3/7*b/x^(7/3)-1/2*a/x^2 +--R +--R +--R 3+-+ +--R - 7a\|x - 6b +--R (2) ------------- +--R 2 3+-+ +--R 14x \|x +--R Type: Expression(Integer) +--E 450 + +--S 451 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 7a\|x - 6b +--R (3) ------------- +--R 2 3+-+ +--R 14x \|x +--R Type: Union(Expression(Integer),...) +--E 451 + +--S 452 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 453 + +)clear all + +--S 454 of 1299 +t0:=(a+b/x^(1/3))/x^4 +--R +--R +--R 3+-+ +--R a\|x + b +--R (1) --------- +--R 4 3+-+ +--R x \|x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1299 +r0:=-3/10*b/x^(10/3)-1/3*a/x^3 +--R +--R +--R 3+-+ +--R - 10a\|x - 9b +--R (2) -------------- +--R 3 3+-+ +--R 30x \|x +--R Type: Expression(Integer) +--E 455 + +--S 456 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R - 10a\|x - 9b +--R (3) -------------- +--R 3 3+-+ +--R 30x \|x +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 458 + +)clear all + +--S 459 of 1299 +t0:=(a+b/x^(1/3))^2*x^4 +--R +--R +--R 2 4 3+-+2 4 3+-+ 2 4 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1299 +r0:=3/13*b^2*x^(13/3)+3/7*a*b*x^(14/3)+1/5*a^2*x^5 +--R +--R +--R 4 3+-+2 2 4 3+-+ 2 5 +--R 195a b x \|x + 105b x \|x + 91a x +--R (2) ------------------------------------- +--R 455 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 3+-+2 2 4 3+-+ 2 5 +--R 195a b x \|x + 105b x \|x + 91a x +--R (3) ------------------------------------- +--R 455 +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 463 + +)clear all + +--S 464 of 1299 +t0:=(a+b/x^(1/3))^2*x^3 +--R +--R +--R 2 3 3+-+2 3 3+-+ 2 3 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1299 +r0:=3/10*b^2*x^(10/3)+6/11*a*b*x^(11/3)+1/4*a^2*x^4 +--R +--R +--R 3 3+-+2 2 3 3+-+ 2 4 +--R 120a b x \|x + 66b x \|x + 55a x +--R (2) ------------------------------------ +--R 220 +--R Type: Expression(Integer) +--E 465 + +--S 466 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+2 2 3 3+-+ 2 4 +--R 120a b x \|x + 66b x \|x + 55a x +--R (3) ------------------------------------ +--R 220 +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 468 + +)clear all + +--S 469 of 1299 +t0:=(a+b/x^(1/3))^2*x^2 +--R +--R +--R 2 2 3+-+2 2 3+-+ 2 2 +--R a x \|x + 2a b x \|x + b x +--R (1) ------------------------------ +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1299 +r0:=3/7*b^2*x^(7/3)+3/4*a*b*x^(8/3)+1/3*a^2*x^3 +--R +--R +--R 2 3+-+2 2 2 3+-+ 2 3 +--R 63a b x \|x + 36b x \|x + 28a x +--R (2) ----------------------------------- +--R 84 +--R Type: Expression(Integer) +--E 470 + +--S 471 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 2 3+-+ 2 3 +--R 63a b x \|x + 36b x \|x + 28a x +--R (3) ----------------------------------- +--R 84 +--R Type: Union(Expression(Integer),...) +--E 471 + +--S 472 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 473 + +)clear all + +--S 474 of 1299 +t0:=(a+b/x^(1/3))^2*x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a x \|x + 2a b x\|x + b x +--R (1) ---------------------------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1299 +r0:=3/4*b^2*x^(4/3)+6/5*a*b*x^(5/3)+1/2*a^2*x^2 +--R +--R +--R 3+-+2 2 3+-+ 2 2 +--R 24a b x \|x + 15b x\|x + 10a x +--R (2) ---------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 3+-+ 2 2 +--R 24a b x \|x + 15b x\|x + 10a x +--R (3) ---------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 476 + +--S 477 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 478 + +)clear all + +--S 479 of 1299 +t0:=(a+b/x^(1/3))^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3+-+2 +--R \|x +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1299 +r0:=(b+a*x^(1/3))^3/a +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (2) --------------------------------- +--R a +--R Type: Expression(Integer) +--E 480 + +--S 481 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+2 2 3+-+ 2 +--R (3) 3a b \|x + 3b \|x + a x +--R Type: Union(Expression(Integer),...) +--E 481 + +--S 482 of 1299 +m0:=a0-r0 +--R +--R +--R 3 +--R b +--R (4) - -- +--R a +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 483 + +)clear all + +--S 484 of 1299 +t0:=(a+b/x^(1/3))^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1299 +r0:=-3/2*b^2/x^(2/3)-6*a*b/x^(1/3)+a^2*log(x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R 2a log(x)\|x - 12a b\|x - 3b +--R (2) -------------------------------- +--R 3+-+2 +--R 2\|x +--R Type: Expression(Integer) +--E 485 + +--S 486 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 3+-+ 2 +--R 6a \|x log(\|x - 12a b\|x - 3b +--R (3) ----------------------------------- +--R 3+-+2 +--R 2\|x +--R Type: Union(Expression(Integer),...) +--E 486 + +--S 487 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 488 + +)clear all + +--S 489 of 1299 +t0:=(a+b/x^(1/3))^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 2 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1299 +r0:=-3/5*b^2/x^(5/3)-3/2*a*b/x^(4/3)-a^2/x +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 10a \|x - 15a b\|x - 6b +--R (2) ----------------------------- +--R 3+-+2 +--R 10x \|x +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 10a \|x - 15a b\|x - 6b +--R (3) ----------------------------- +--R 3+-+2 +--R 10x \|x +--R Type: Union(Expression(Integer),...) +--E 491 + +--S 492 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 492 + +--S 493 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 493 + +)clear all + +--S 494 of 1299 +t0:=(a+b/x^(1/3))^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 3 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 494 + +--S 495 of 1299 +r0:=-3/8*b^2/x^(8/3)-6/7*a*b/x^(7/3)-1/2*a^2/x^2 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 28a \|x - 48a b\|x - 21b +--R (2) ------------------------------ +--R 2 3+-+2 +--R 56x \|x +--R Type: Expression(Integer) +--E 495 + +--S 496 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 28a \|x - 48a b\|x - 21b +--R (3) ------------------------------ +--R 2 3+-+2 +--R 56x \|x +--R Type: Union(Expression(Integer),...) +--E 496 + +--S 497 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 497 + +--S 498 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 498 + +)clear all + +--S 499 of 1299 +t0:=(a+b/x^(1/3))^2/x^4 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R (1) ----------------------- +--R 4 3+-+2 +--R x \|x +--R Type: Expression(Integer) +--E 499 + +--S 500 of 1299 +r0:=-3/11*b^2/x^(11/3)-3/5*a*b/x^(10/3)-1/3*a^2/x^3 +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 55a \|x - 99a b\|x - 45b +--R (2) ------------------------------ +--R 3 3+-+2 +--R 165x \|x +--R Type: Expression(Integer) +--E 500 + +--S 501 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 +--R - 55a \|x - 99a b\|x - 45b +--R (3) ------------------------------ +--R 3 3+-+2 +--R 165x \|x +--R Type: Union(Expression(Integer),...) +--E 501 + +--S 502 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 502 + +--S 503 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 503 + +)clear all + +--S 504 of 1299 +t0:=(a+b/x^(1/3))^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R (1) 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1299 +r0:=1/4*b^3*x^4+9/13*a*b^2*x^(13/3)+9/14*a^2*b*x^(14/3)+1/5*a^3*x^5 +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364a x + 455b x +--R (2) ---------------------------------------------------- +--R 1820 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 1170a b x \|x + 1260a b x \|x + 364a x + 455b x +--R (3) ---------------------------------------------------- +--R 1820 +--R Type: Union(Expression(Integer),...) +--E 506 + +--S 507 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 507 + +--S 508 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 508 + +)clear all + +--S 509 of 1299 +t0:=(a+b/x^(1/3))^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R (1) 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1299 +r0:=1/3*b^3*x^3+9/10*a*b^2*x^(10/3)+9/11*a^2*b*x^(11/3)+1/4*a^3*x^4 +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165a x + 220b x +--R (2) -------------------------------------------------- +--R 660 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 540a b x \|x + 594a b x \|x + 165a x + 220b x +--R (3) -------------------------------------------------- +--R 660 +--R Type: Union(Expression(Integer),...) +--E 511 + +--S 512 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 513 + +)clear all + +--S 514 of 1299 +t0:=(a+b/x^(1/3))^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R (1) 3a b x \|x + 3a b x\|x + a x + b x +--R Type: Expression(Integer) +--E 514 + +--S 515 of 1299 +r0:=1/2*b^3*x^2+9/7*a*b^2*x^(7/3)+9/8*a^2*b*x^(8/3)+1/3*a^3*x^3 +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56a x + 84b x +--R (2) ------------------------------------------------ +--R 168 +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 189a b x \|x + 216a b x \|x + 56a x + 84b x +--R (3) ------------------------------------------------ +--R 168 +--R Type: Union(Expression(Integer),...) +--E 516 + +--S 517 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 517 + +--S 518 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 518 + +)clear all + +--S 519 of 1299 +t0:=(a+b/x^(1/3))^3*x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R (1) 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 519 + +--S 520 of 1299 +r0:=b^3*x+9/4*a*b^2*x^(4/3)+9/5*a^2*b*x^(5/3)+1/2*a^3*x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10a x + 20b x +--R (2) -------------------------------------------- +--R 20 +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 36a b x \|x + 45a b x\|x + 10a x + 20b x +--R (3) -------------------------------------------- +--R 20 +--R Type: Union(Expression(Integer),...) +--E 521 + +--S 522 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 522 + +--S 523 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 523 + +)clear all + +--S 524 of 1299 +t0:=(a+b/x^(1/3))^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R x +--R Type: Expression(Integer) +--E 524 + +--S 525 of 1299 +r0:=9*a*b^2*x^(1/3)+9/2*a^2*b*x^(2/3)+a^3*x+b^3*log(x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 9a b \|x + 18a b \|x + 2b log(x) + 2a x +--R (2) ------------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6b log(\|x ) + 9a b \|x + 18a b \|x + 2a x +--R (3) --------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 526 + +--S 527 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3b log(\|x ) - b log(x) +--R Type: Expression(Integer) +--E 527 + +--S 528 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 528 + +)clear all + +--S 529 of 1299 +t0:=(a+b/x^(1/3))^3/x +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 529 + +--S 530 of 1299 +r0:=-b^3/x-9/2*a*b^2/x^(2/3)-9*a^2*b/x^(1/3)+a^3*log(x) +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (2a x log(x) - 2b )\|x - 18a b x\|x - 9a b x +--R (2) ----------------------------------------------- +--R 3+-+2 +--R 2x \|x +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R 6a x log(\|x ) - 18a b \|x - 9a b \|x - 2b +--R (3) ---------------------------------------------- +--R 2x +--R Type: Union(Expression(Integer),...) +--E 531 + +--S 532 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R (4) 3a log(\|x ) - a log(x) +--R Type: Expression(Integer) +--E 532 + +--S 533 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 533 + +)clear all + +--S 534 of 1299 +t0:=(a+b/x^(1/3))^3/x^2 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 534 + +--S 535 of 1299 +r0:=-1/2*b^3/x^2-9/5*a*b^2/x^(5/3)-9/4*a^2*b/x^(4/3)-a^3/x +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 20a x - 10b )\|x - 45a b x\|x - 36a b x +--R (2) --------------------------------------------- +--R 2 3+-+2 +--R 20x \|x +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 45a b \|x - 36a b \|x - 20a x - 10b +--R (3) ----------------------------------------- +--R 2 +--R 20x +--R Type: Union(Expression(Integer),...) +--E 536 + +--S 537 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 537 + +--S 538 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 538 + +)clear all + +--S 539 of 1299 +t0:=(a+b/x^(1/3))^3/x^3 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 4 +--R x +--R Type: Expression(Integer) +--E 539 + +--S 540 of 1299 +r0:=-1/3*b^3/x^3-9/8*a*b^2/x^(8/3)-9/7*a^2*b/x^(7/3)-1/2*a^3/x^2 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 84a x - 56b )\|x - 216a b x\|x - 189a b x +--R (2) ----------------------------------------------- +--R 3 3+-+2 +--R 168x \|x +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 216a b \|x - 189a b \|x - 84a x - 56b +--R (3) ------------------------------------------- +--R 3 +--R 168x +--R Type: Union(Expression(Integer),...) +--E 541 + +--S 542 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 542 + +--S 543 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 543 + +)clear all + +--S 544 of 1299 +t0:=(a+b/x^(1/3))^3/x^4 +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R (1) --------------------------------- +--R 5 +--R x +--R Type: Expression(Integer) +--E 544 + +--S 545 of 1299 +r0:=-1/4*b^3/x^4-9/11*a*b^2/x^(11/3)-9/10*a^2*b/x^(10/3)-1/3*a^3/x^3 +--R +--R +--R 3 3 3+-+2 2 3+-+ 2 +--R (- 220a x - 165b )\|x - 594a b x\|x - 540a b x +--R (2) ------------------------------------------------- +--R 4 3+-+2 +--R 660x \|x +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 2 3+-+ 3 3 +--R - 594a b \|x - 540a b \|x - 220a x - 165b +--R (3) --------------------------------------------- +--R 4 +--R 660x +--R Type: Union(Expression(Integer),...) +--E 546 + +--S 547 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 547 + +--S 548 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 548 + +)clear all + +--S 549 of 1299 +t0:=x^2/(a+b/x^(1/3)) +--R +--R +--R 2 3+-+ +--R x \|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 549 + +--S 550 of 1299 +r0:=3*b^8*x^(1/3)/a^9-3/2*b^7*x^(2/3)/a^8+b^6*x/a^7-3/4*b^5*x^(4/3)/_ + a^6+3/5*b^4*x^(5/3)/a^5-1/2*b^3*x^2/a^4+3/7*b^2*x^(7/3)/a^3-_ + 3/8*b*x^(8/3)/a^2+1/3*x^3/a-3*b^9*log(b+a*x^(1/3))/a^10 +--R +--R +--R (2) +--R 9 3+-+ 8 2 5 4 2 7 3+-+2 +--R - 2520b log(a\|x + b) + (- 315a b x + 504a b x - 1260a b )\|x +--R + +--R 7 2 2 4 5 8 3+-+ 9 3 6 3 2 3 6 +--R (360a b x - 630a b x + 2520a b )\|x + 280a x - 420a b x + 840a b x +--R / +--R 10 +--R 840a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3+-+ 8 2 5 4 2 7 3+-+2 +--R - 2520b log(a\|x + b) + (- 315a b x + 504a b x - 1260a b )\|x +--R + +--R 7 2 2 4 5 8 3+-+ 9 3 6 3 2 3 6 +--R (360a b x - 630a b x + 2520a b )\|x + 280a x - 420a b x + 840a b x +--R / +--R 10 +--R 840a +--R Type: Union(Expression(Integer),...) +--E 551 + +--S 552 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 552 + +--S 553 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 553 + +)clear all + +--S 554 of 1299 +t0:=x/(a+b/x^(1/3)) +--R +--R +--R 3+-+ +--R x\|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 554 + +--S 555 of 1299 +r0:=-3*b^5*x^(1/3)/a^6+3/2*b^4*x^(2/3)/a^5-b^3*x/a^4+_ + 3/4*b^2*x^(4/3)/a^3-3/5*b*x^(5/3)/a^2+1/2*x^2/a+3*b^6*_ + log(b+a*x^(1/3))/a^7 +--R +--R +--R (2) +--R 6 3+-+ 5 2 4 3+-+2 4 2 5 3+-+ +--R 60b log(a\|x + b) + (- 12a b x + 30a b )\|x + (15a b x - 60a b )\|x +--R + +--R 6 2 3 3 +--R 10a x - 20a b x +--R / +--R 7 +--R 20a +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3+-+ 5 2 4 3+-+2 4 2 5 3+-+ +--R 60b log(a\|x + b) + (- 12a b x + 30a b )\|x + (15a b x - 60a b )\|x +--R + +--R 6 2 3 3 +--R 10a x - 20a b x +--R / +--R 7 +--R 20a +--R Type: Union(Expression(Integer),...) +--E 556 + +--S 557 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 557 + +--S 558 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 558 + +)clear all + +--S 559 of 1299 +t0:=1/(a+b/x^(1/3)) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------- +--R 3+-+ +--R a\|x + b +--R Type: Expression(Integer) +--E 559 + +--S 560 of 1299 +r0:=3*b^2*x^(1/3)/a^3-3/2*b*x^(2/3)/a^2+x/a-3*b^3*log(b+a*x^(1/3))/a^4 +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R - 6b log(a\|x + b) - 3a b \|x + 6a b \|x + 2a x +--R (2) --------------------------------------------------- +--R 4 +--R 2a +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 2 3+-+2 2 3+-+ 3 +--R - 6b log(a\|x + b) - 3a b \|x + 6a b \|x + 2a x +--R (3) --------------------------------------------------- +--R 4 +--R 2a +--R Type: Union(Expression(Integer),...) +--E 561 + +--S 562 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 562 + +--S 563 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 563 + +)clear all + +--S 564 of 1299 +t0:=1/((a+b/x^(1/3))*x) +--R +--R +--R 3+-+ +--R \|x +--R (1) ------------- +--R 3+-+ +--R a x\|x + b x +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1299 +r0:=3*log(b+a*x^(1/3))/a +--R +--R +--R 3+-+ +--R 3log(a\|x + b) +--R (2) --------------- +--R a +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ +--R 3log(a\|x + b) +--R (3) --------------- +--R a +--R Type: Union(Expression(Integer),...) +--E 566 + +--S 567 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 568 + +)clear all + +--S 569 of 1299 +t0:=1/((a+b/x^(1/3))*x^2) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 2 3+-+ 2 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 569 + +--S 570 of 1299 +r0:=(-3/2)/(b*x^(2/3))+3*a/(b^2*x^(1/3))-3*a^2*log(b+a*x^(1/3))/b^3+_ + a^2*log(x)/b^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+2 3+-+ 2 +--R - 6a \|x log(a\|x + b + 2a log(x)\|x + 6a b\|x - 3b +--R (2) ---------------------------------------------------------- +--R 3 3+-+2 +--R 2b \|x +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+2 3+-+ 3+-+ 2 +--R - 6a \|x log(a\|x + b + 6a \|x log(\|x + 6a b\|x - 3b +--R (3) ------------------------------------------------------------- +--R 3 3+-+2 +--R 2b \|x +--R Type: Union(Expression(Integer),...) +--E 571 + +--S 572 of 1299 +m0:=a0-r0 +--R +--R +--R 2 3+-+ 2 +--R 3a log(\|x ) - a log(x) +--R (4) ----------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1299 +t0:=1/((a+b/x^(1/3))*x^3) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 3 3+-+ 3 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1299 +r0:=(-3/5)/(b*x^(5/3))+3/4*a/(b^2*x^(4/3))-a^2/(b^3*x)+_ + 3/2*a^3/(b^4*x^(2/3))-3*a^4/(b^5*x^(1/3))+_ + 3*a^5*log(b+a*x^(1/3))/b^6-a^5*log(x)/b^6 +--R +--R +--R (2) +--R 5 3+-+2 3+-+ 5 2 3 3+-+2 +--R 60a x \|x log(a\|x + b) + (- 20a x log(x) - 20a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 15a b )\|x + 30a b x - 12b +--R / +--R 6 3+-+2 +--R 20b x \|x +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 3+-+ 5 3+-+2 3+-+ 2 3 3+-+2 +--R 60a x \|x log(a\|x + b) - 60a x \|x log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 15a b )\|x + 30a b x - 12b +--R / +--R 6 3+-+2 +--R 20b x \|x +--R Type: Union(Expression(Integer),...) +--E 576 + +--S 577 of 1299 +m0:=a0-r0 +--R +--R +--R 5 3+-+ 5 +--R - 3a log(\|x ) + a log(x) +--R (4) ------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +)clear all + +--S 579 of 1299 +t0:=1/((a+b/x^(1/3))*x^4) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 4 3+-+ 4 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1299 +r0:=(-3/8)/(b*x^(8/3))+3/7*a/(b^2*x^(7/3))-1/2*a^2/(b^3*x^2)+_ + 3/5*a^3/(b^4*x^(5/3))-3/4*a^4/(b^5*x^(4/3))+a^5/(b^6*x)-_ + 3/2*a^6/(b^7*x^(2/3))+3*a^7/(b^8*x^(1/3))-_ + 3*a^8*log(b+a*x^(1/3))/b^9+a^8*log(x)/b^9 +--R +--R +--R (2) +--R 8 2 3+-+2 3+-+ 8 2 5 3 2 6 3+-+2 +--R - 840a x \|x log(a\|x + b + (280a x log(x) + 280a b x - 140a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 6 2 2 3 5 8 +--R (840a b x - 210a b x + 120a b )\|x - 420a b x + 168a b x - 105b +--R / +--R 9 2 3+-+2 +--R 280b x \|x +--R Type: Expression(Integer) +--E 580 + +--S 581 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 3+-+ 8 2 3+-+2 3+-+ +--R - 840a x \|x log(a\|x + b + 840a x \|x log(\|x ) +--R + +--R 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (280a b x - 140a b )\|x + (840a b x - 210a b x + 120a b )\|x +--R + +--R 6 2 2 3 5 8 +--R - 420a b x + 168a b x - 105b +--R / +--R 9 2 3+-+2 +--R 280b x \|x +--R Type: Union(Expression(Integer),...) +--E 581 + +--S 582 of 1299 +m0:=a0-r0 +--R +--R +--R 8 3+-+ 8 +--R 3a log(\|x ) - a log(x) +--R (4) ----------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 583 + +)clear all + +--S 584 of 1299 +t0:=1/((a+b/x^(1/3))*x^5) +--R +--R +--R 3+-+ +--R \|x +--R (1) --------------- +--R 5 3+-+ 5 +--R a x \|x + b x +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1299 +r0:=(-3/11)/(b*x^(11/3))+3/10*a/(b^2*x^(10/3))-1/3*a^2/(b^3*x^3)+_ + 3/8*a^3/(b^4*x^(8/3))-3/7*a^4/(b^5*x^(7/3))+1/2*a^5/(b^6*x^2)-_ + 3/5*a^6/(b^7*x^(5/3))+3/4*a^7/(b^8*x^(4/3))-a^8/(b^9*x)+_ + 3/2*a^9/(b^10*x^(2/3))-3*a^10/(b^11*x^(1/3))+_ + 3*a^11*log(b+a*x^(1/3))/b^12-a^11*log(x)/b^12 +--R +--R +--R (2) +--R 11 3 3+-+2 3+-+ +--R 27720a x \|x log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a x log(x) - 9240a b x + 4620a b x - 3080a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 6930a b x - 3960a b x + 2772a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 5544a b x + 3465a b x - 2520b +--R / +--R 12 3 3+-+2 +--R 9240b x \|x +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 3+-+ 11 3 3+-+2 3+-+ +--R 27720a x \|x log(a\|x + b - 27720a x \|x log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a b x + 4620a b x - 3080a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 6930a b x - 3960a b x + 2772a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 5544a b x + 3465a b x - 2520b +--R / +--R 12 3 3+-+2 +--R 9240b x \|x +--R Type: Union(Expression(Integer),...) +--E 586 + +--S 587 of 1299 +m0:=a0-r0 +--R +--R +--R 11 3+-+ 11 +--R - 3a log(\|x ) + a log(x) +--R (4) --------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 587 + +--S 588 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 588 + +)clear all + +--S 589 of 1299 +t0:=x^2/(a+b/x^(1/3))^2 +--R +--R +--R 2 3+-+2 +--R x \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1299 +r0:=-3*b^10/(a^11*(b+a*x^(1/3)))+27*b^8*x^(1/3)/a^10-12*b^7*x^(2/3)/a^9+_ + 7*b^6*x/a^8-9/2*b^5*x^(4/3)/a^7+3*b^4*x^(5/3)/a^6-2*b^3*x^2/a^5+_ + 9/7*b^2*x^(7/3)/a^4-3/4*b*x^(8/3)/a^3+1/3*x^3/a^2-_ + 30*b^9*log(b+a*x^(1/3))/a^11 +--R +--R +--R (2) +--R 9 3+-+ 10 3+-+ +--R (- 2520a b \|x - 2520b )log(a\|x + b) +--R + +--R 8 2 2 5 5 2 8 3+-+2 +--R (45a b x - 126a b x + 1260a b )\|x +--R + +--R 10 3 7 3 2 4 6 9 3+-+ 9 3 6 4 2 +--R (28a x - 60a b x + 210a b x + 2268a b )\|x - 35a b x + 84a b x +--R + +--R 3 7 10 +--R - 420a b x - 252b +--R / +--R 12 3+-+ 11 +--R 84a \|x + 84a b +--R Type: Expression(Integer) +--E 590 + +--S 591 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 9 3+-+ 10 3+-+ +--R (- 2520a b \|x - 2520b )log(a\|x + b) +--R + +--R 8 2 2 5 5 2 8 3+-+2 +--R (45a b x - 126a b x + 1260a b )\|x +--R + +--R 10 3 7 3 2 4 6 9 3+-+ 9 3 6 4 2 +--R (28a x - 60a b x + 210a b x + 2268a b )\|x - 35a b x + 84a b x +--R + +--R 3 7 10 +--R - 420a b x - 252b +--R / +--R 12 3+-+ 11 +--R 84a \|x + 84a b +--R Type: Union(Expression(Integer),...) +--E 591 + +--S 592 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 593 + +)clear all + +--S 594 of 1299 +t0:=x/(a+b/x^(1/3))^2 +--R +--R +--R 3+-+2 +--R x \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 594 + +--S 595 of 1299 +r0:=3*b^7/(a^8*(b+a*x^(1/3)))-18*b^5*x^(1/3)/a^7+15/2*b^4*x^(2/3)/a^6-_ + 4*b^3*x/a^5+9/4*b^2*x^(4/3)/a^4-6/5*b*x^(5/3)/a^3+1/2*x^2/a^2+_ + 21*b^6*log(b+a*x^(1/3))/a^8 +--R +--R +--R (2) +--R 6 3+-+ 7 3+-+ 5 2 2 5 3+-+2 +--R (420a b \|x + 420b )log(a\|x + b) + (21a b x - 210a b )\|x +--R + +--R 7 2 4 3 6 3+-+ 6 2 3 4 7 +--R (10a x - 35a b x - 360a b )\|x - 14a b x + 70a b x + 60b +--R / +--R 9 3+-+ 8 +--R 20a \|x + 20a b +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 6 3+-+ 7 3+-+ 5 2 2 5 3+-+2 +--R (420a b \|x + 420b )log(a\|x + b) + (21a b x - 210a b )\|x +--R + +--R 7 2 4 3 6 3+-+ 6 2 3 4 7 +--R (10a x - 35a b x - 360a b )\|x - 14a b x + 70a b x + 60b +--R / +--R 9 3+-+ 8 +--R 20a \|x + 20a b +--R Type: Union(Expression(Integer),...) +--E 596 + +--S 597 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 597 + +--S 598 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 598 + +)clear all + +--S 599 of 1299 +t0:=1/(a+b/x^(1/3))^2 +--R +--R +--R 3+-+2 +--R \|x +--R (1) ----------------------- +--R 2 3+-+2 3+-+ 2 +--R a \|x + 2a b\|x + b +--R Type: Expression(Integer) +--E 599 + +--S 600 of 1299 +r0:=-3*b^4/(a^5*(b+a*x^(1/3)))+9*b^2*x^(1/3)/a^4-3*b*x^(2/3)/a^3+_ + x/a^2-12*b^3*log(b+a*x^(1/3))/a^5 +--R +--R +--R (2) +--R 3 3+-+ 4 3+-+ 2 2 3+-+2 4 3 3+-+ +--R (- 12a b \|x - 12b )log(a\|x + b) + 6a b \|x + (a x + 9a b )\|x +--R + +--R 3 4 +--R - 2a b x - 3b +--R / +--R 6 3+-+ 5 +--R a \|x + a b +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3+-+ 4 3+-+ 2 2 3+-+2 4 3 3+-+ +--R (- 12a b \|x - 12b )log(a\|x + b) + 6a b \|x + (a x + 9a b )\|x +--R + +--R 3 4 +--R - 2a b x - 3b +--R / +--R 6 3+-+ 5 +--R a \|x + a b +--R Type: Union(Expression(Integer),...) +--E 601 + +--S 602 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 602 + +--S 603 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 603 + +)clear all + +--S 604 of 1299 +t0:=1/((a+b/x^(1/3))^2*x) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ---------------------------- +--R 2 3+-+2 3+-+ 2 +--R a x \|x + 2a b x\|x + b x +--R Type: Expression(Integer) +--E 604 + +--S 605 of 1299 +r0:=3*b/(a^2*(b+a*x^(1/3)))+3*log(b+a*x^(1/3))/a^2 +--R +--R +--R 3+-+ 3+-+ +--R (3a\|x + 3b)log(a\|x + b) + 3b +--R (2) -------------------------------- +--R 3 3+-+ 2 +--R a \|x + a b +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3+-+ 3+-+ +--R (3a\|x + 3b)log(a\|x + b) + 3b +--R (3) -------------------------------- +--R 3 3+-+ 2 +--R a \|x + a b +--R Type: Union(Expression(Integer),...) +--E 606 + +--S 607 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 607 + +--S 608 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 608 + +)clear all + +--S 609 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^2) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 2 3+-+2 2 3+-+ 2 2 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 609 + +--S 610 of 1299 +r0:=(-6)/(b^2*x^(1/3))+3/(b*(b+a*x^(1/3))*x^(1/3))+_ + 6*a*log(b+a*x^(1/3))/b^3-2*a*log(x)/b^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 3+-+ 2 3+-+2 +--R (6a \|x + 6a b\|x )log(a\|x + b) - 2a log(x)\|x +--R + +--R 3+-+ 2 +--R (- 2a b log(x) - 6a b)\|x - 3b +--R / +--R 3 3+-+2 4 3+-+ +--R a b \|x + b \|x +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 3+-+ 2 3+-+2 3+-+ 3+-+ +--R (6a \|x + 6a b\|x )log(a\|x + b) + (- 6a \|x - 6a b\|x )log(\|x ) +--R + +--R 3+-+ 2 +--R - 6a b\|x - 3b +--R / +--R 3 3+-+2 4 3+-+ +--R a b \|x + b \|x +--R Type: Union(Expression(Integer),...) +--E 611 + +--S 612 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R - 6a log(\|x ) + 2a log(x) +--R (4) -------------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 612 + +--S 613 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 613 + +)clear all + +--S 614 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^3) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 3 3+-+2 3 3+-+ 2 3 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 614 + +--S 615 of 1299 +r0:=(-15/4)/(b^2*x^(4/3))+3/(b*(b+a*x^(1/3))*x^(4/3))+_ + 5*a/(b^3*x)-15/2*a^2/(b^4*x^(2/3))+15*a^3/(b^5*x^(1/3))-_ + 15*a^4*log(b+a*x^(1/3))/b^6+5*a^4*log(x)/b^6 +--R +--R +--R (2) +--R 5 2 3+-+ 4 2 3+-+ 3 2 5 3+-+2 +--R (- 60a x \|x - 60a b x )log(a\|x + b) + (30a b x - 3b )\|x +--R + +--R 5 2 2 3 3+-+ 4 2 4 2 4 +--R (20a x log(x) - 10a b x)\|x + 20a b x log(x) + 60a b x + 5a b x +--R / +--R 6 2 3+-+ 7 2 +--R 4a b x \|x + 4b x +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 3+-+ +--R (- 60a x \|x - 60a b x\|x )log(a\|x + b) +--R + +--R 5 3+-+2 4 3+-+ 3+-+ 2 3 3+-+2 +--R (60a x \|x + 60a b x\|x )log(\|x ) - 10a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (60a b x + 5a b )\|x + 30a b x - 3b +--R / +--R 6 3+-+2 7 3+-+ +--R 4a b x \|x + 4b x\|x +--R Type: Union(Expression(Integer),...) +--E 616 + +--S 617 of 1299 +m0:=a0-r0 +--R +--R +--R 4 3+-+ 4 +--R 15a log(\|x ) - 5a log(x) +--R (4) ------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 617 + +--S 618 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 618 + +)clear all + +--S 619 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^4) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 4 3+-+2 4 3+-+ 2 4 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1299 +r0:=(-24/7)/(b^2*x^(7/3))+3/(b*(b+a*x^(1/3))*x^(7/3))+4*a/(b^3*x^2)-_ + 24/5*a^2/(b^4*x^(5/3))+6*a^3/(b^5*x^(4/3))-8*a^4/(b^6*x)+_ + 12*a^5/(b^7*x^(2/3))-24*a^6/(b^8*x^(1/3))+_ + 24*a^7*log(b+a*x^(1/3))/b^9-8*a^7*log(x)/b^9 +--R +--R +--R (2) +--R 8 3 3+-+ 7 3 3+-+ +--R (840a x \|x + 840a b x )log(a\|x + b) +--R + +--R 6 2 2 3 5 8 3+-+2 +--R (- 420a b x + 42a b x - 15b )\|x +--R + +--R 8 3 5 3 2 2 6 3+-+ 7 3 7 3 +--R (- 280a x log(x) + 140a b x - 28a b x)\|x - 280a b x log(x) - 840a b x +--R + +--R 4 4 2 7 +--R - 70a b x + 20a b x +--R / +--R 9 3 3+-+ 10 3 +--R 35a b x \|x + 35b x +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 3+-+ +--R (840a x \|x + 840a b x \|x)log(a\|x + b) +--R + +--R 8 2 3+-+2 7 2 3+-+ 3+-+ 5 3 2 6 3+-+2 +--R (- 840a x \|x - 840a b x \|x)log(\|x ) + (140a b x - 28a b )\|x +--R + +--R 7 2 4 4 7 3+-+ 6 2 2 3 5 8 +--R (- 840a b x - 70a b x + 20a b )\|x - 420a b x + 42a b x - 15b +--R / +--R 9 2 3+-+2 10 2 3+-+ +--R 35a b x \|x + 35b x \|x +--R Type: Union(Expression(Integer),...) +--E 621 + +--S 622 of 1299 +m0:=a0-r0 +--R +--R +--R 7 3+-+ 7 +--R - 24a log(\|x ) + 8a log(x) +--R (4) --------------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 623 + +)clear all + +--S 624 of 1299 +t0:=1/((a+b/x^(1/3))^2*x^5) +--R +--R +--R 3+-+2 +--R \|x +--R (1) ------------------------------ +--R 2 5 3+-+2 5 3+-+ 2 5 +--R a x \|x + 2a b x \|x + b x +--R Type: Expression(Integer) +--E 624 + +--S 625 of 1299 +r0:=(-33/10)/(b^2*x^(10/3))+3/(b*(b+a*x^(1/3))*x^(10/3))+_ + 11/3*a/(b^3*x^3)-33/8*a^2/(b^4*x^(8/3))+33/7*a^3/(b^5*x^(7/3))-_ + 11/2*a^4/(b^6*x^2)+33/5*a^5/(b^7*x^(5/3))-33/4*a^6/(b^8*x^(4/3))+_ + 11*a^7/(b^9*x)-33/2*a^8/(b^10*x^(2/3))+_ + 33*a^9/(b^11*x^(1/3))-33*a^10*log(b+a*x^(1/3))/b^12+11*a^10*log(x)/b^12 +--R +--R +--R (2) +--R 11 4 3+-+ 10 4 3+-+ +--R (- 27720a x \|x - 27720a b x )log(a\|x + b) +--R + +--R 9 2 3 6 5 2 3 8 11 3+-+2 +--R (13860a b x - 1386a b x + 495a b x - 252b )\|x +--R + +--R 11 4 8 3 3 5 6 2 2 9 3+-+ +--R (9240a x log(x) - 4620a b x + 924a b x - 385a b x)\|x +--R + +--R 10 4 10 4 7 4 3 4 7 2 10 +--R 9240a b x log(x) + 27720a b x + 2310a b x - 660a b x + 308a b x +--R / +--R 12 4 3+-+ 13 4 +--R 840a b x \|x + 840b x +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 3+-+ +--R (- 27720a x \|x - 27720a b x \|x)log(a\|x + b) +--R + +--R 11 3 3+-+2 10 3 3+-+ 3+-+ +--R (27720a x \|x + 27720a b x \|x)log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 4620a b x + 924a b x - 385a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (27720a b x + 2310a b x - 660a b x + 308a b )\|x + 13860a b x +--R + +--R 6 5 2 3 8 11 +--R - 1386a b x + 495a b x - 252b +--R / +--R 12 3 3+-+2 13 3 3+-+ +--R 840a b x \|x + 840b x \|x +--R Type: Union(Expression(Integer),...) +--E 626 + +--S 627 of 1299 +m0:=a0-r0 +--R +--R +--R 10 3+-+ 10 +--R 33a log(\|x ) - 11a log(x) +--R (4) ---------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1299 +t0:=x^2/(a+b/x^(1/3))^3 +--R +--R +--R 3 +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1299 +r0:=3/2*b^11/(a^12*(b+a*x^(1/3))^2)-33*b^10/(a^12*(b+a*x^(1/3)))+_ + 135*b^8*x^(1/3)/a^11-54*b^7*x^(2/3)/a^10+28*b^6*x/a^9-_ + 63/4*b^5*x^(4/3)/a^8+9*b^4*x^(5/3)/a^7-5*b^3*x^2/a^6+_ + 18/7*b^2*x^(7/3)/a^5-9/8*b*x^(8/3)/a^4+1/3*x^3/a^3-_ + 165*b^9*log(b+a*x^(1/3))/a^12 +--R +--R +--R (2) +--R 2 9 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b \|x - 27720b )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (56a x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b )\|x + 110a b x +--R + +--R 6 5 2 3 8 11 +--R - 462a b x + 9240a b x - 5292b +--R / +--R 14 3+-+2 13 3+-+ 12 2 +--R 168a \|x + 336a b\|x + 168a b +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 9 3+-+2 10 3+-+ 11 3+-+ +--R (- 27720a b \|x - 55440a b \|x - 27720b )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (56a x - 165a b x + 924a b x + 36288a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 77a b x + 264a b x - 2310a b x + 17136a b )\|x + 110a b x +--R + +--R 6 5 2 3 8 11 +--R - 462a b x + 9240a b x - 5292b +--R / +--R 14 3+-+2 13 3+-+ 12 2 +--R 168a \|x + 336a b\|x + 168a b +--R Type: Union(Expression(Integer),...) +--E 631 + +--S 632 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +)clear all + +--S 634 of 1299 +t0:=x/(a+b/x^(1/3))^3 +--R +--R +--R 2 +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1299 +r0:=-3/2*b^8/(a^9*(b+a*x^(1/3))^2)+24*b^7/(a^9*(b+a*x^(1/3)))-_ + 63*b^5*x^(1/3)/a^8+45/2*b^4*x^(2/3)/a^7-10*b^3*x/a^6+_ + 9/2*b^2*x^(4/3)/a^5-9/5*b*x^(5/3)/a^4+1/2*x^2/a^3+_ + 84*b^6*log(b+a*x^(1/3))/a^9 +--R +--R +--R (2) +--R 2 6 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b \|x + 840b )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (5a x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b )\|x +--R + +--R 6 2 2 3 5 8 +--R 14a b x - 280a b x + 225b +--R / +--R 11 3+-+2 10 3+-+ 9 2 +--R 10a \|x + 20a b\|x + 10a b +--R Type: Expression(Integer) +--E 635 + +--S 636 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3+-+2 7 3+-+ 8 3+-+ +--R (840a b \|x + 1680a b \|x + 840b )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ +--R (5a x - 28a b x - 1035a b )\|x + (- 8a b x + 70a b x - 390a b )\|x +--R + +--R 6 2 2 3 5 8 +--R 14a b x - 280a b x + 225b +--R / +--R 11 3+-+2 10 3+-+ 9 2 +--R 10a \|x + 20a b\|x + 10a b +--R Type: Union(Expression(Integer),...) +--E 636 + +--S 637 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 638 + +)clear all + +--S 639 of 1299 +t0:=1/(a+b/x^(1/3))^3 +--R +--R +--R x +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1299 +r0:=3/2*b^5/(a^6*(b+a*x^(1/3))^2)-15*b^4/(a^6*(b+a*x^(1/3)))+_ + 18*b^2*x^(1/3)/a^5-9/2*b*x^(2/3)/a^4+x/a^3-30*b^3*log(b+a*x^(1/3))/a^6 +--R +--R +--R (2) +--R 2 3 3+-+2 4 3+-+ 5 3+-+ 5 2 3 3+-+2 +--R (- 60a b \|x - 120a b \|x - 60b )log(a\|x + b) + (2a x + 63a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 5a b x + 6a b )\|x + 20a b x - 27b +--R / +--R 8 3+-+2 7 3+-+ 6 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3 3+-+2 4 3+-+ 5 3+-+ 5 2 3 3+-+2 +--R (- 60a b \|x - 120a b \|x - 60b )log(a\|x + b) + (2a x + 63a b )\|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 5a b x + 6a b )\|x + 20a b x - 27b +--R / +--R 8 3+-+2 7 3+-+ 6 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 641 + +--S 642 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 642 + +--S 643 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 643 + +)clear all + +--S 644 of 1299 +t0:=1/((a+b/x^(1/3))^3*x) +--R +--R +--R 1 +--R (1) --------------------------------- +--R 2 3+-+2 2 3+-+ 3 3 +--R 3a b \|x + 3a b \|x + a x + b +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1299 +r0:=-3/2*b^2/(a^3*(b+a*x^(1/3))^2)+6*b/(a^3*(b+a*x^(1/3)))+_ + 3*log(b+a*x^(1/3))/a^3 +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(a\|x + b) + 12a b\|x + 9b +--R (2) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 3 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Expression(Integer) +--E 645 + +--S 646 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(a\|x + b) + 12a b\|x + 9b +--R (3) ------------------------------------------------------------ +--R 5 3+-+2 4 3+-+ 3 2 +--R 2a \|x + 4a b\|x + 2a b +--R Type: Union(Expression(Integer),...) +--E 646 + +--S 647 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 648 + +)clear all + +--S 649 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^2) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R 2 3+-+2 2 3+-+ 3 2 3 +--R 3a b x \|x + 3a b x\|x + a x + b x +--R Type: Expression(Integer) +--E 649 + +--S 650 of 1299 +r0:=3/2/(b*(b+a*x^(1/3))^2)+3/(b^2*(b+a*x^(1/3)))-_ + 3*log(b+a*x^(1/3))/b^3+log(x)/b^3 +--R +--R +--R (2) +--R 2 3+-+2 3+-+ 2 3+-+ 2 3+-+2 +--R (- 6a \|x - 12a b\|x - 6b )log(a\|x + b) + 2a log(x)\|x +--R + +--R 3+-+ 2 2 +--R (4a b log(x) + 6a b)\|x + 2b log(x) + 9b +--R / +--R 2 3 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b \|x + 2b +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 3+-+2 3+-+ 2 3+-+ +--R (- 6a \|x - 12a b\|x - 6b )log(a\|x + b) +--R + +--R 2 3+-+2 3+-+ 2 3+-+ 3+-+ 2 +--R (6a \|x + 12a b\|x + 6b )log(\|x ) + 6a b\|x + 9b +--R / +--R 2 3 3+-+2 4 3+-+ 5 +--R 2a b \|x + 4a b \|x + 2b +--R Type: Union(Expression(Integer),...) +--E 651 + +--S 652 of 1299 +m0:=a0-r0 +--R +--R +--R 3+-+ +--R 3log(\|x ) - log(x) +--R (4) ------------------- +--R 3 +--R b +--R Type: Expression(Integer) +--E 652 + +--S 653 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 653 + +)clear all + +--S 654 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^3) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 2 3+-+2 2 2 3+-+ 3 3 3 2 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 654 + +--S 655 of 1299 +r0:=(-10)/(b^3*x)+3/2/(b*(b+a*x^(1/3))^2*x)+15/2/(b^2*(b+a*x^(1/3))*x)+_ + 15*a/(b^4*x^(2/3))-30*a^2/(b^5*x^(1/3))+30*a^3*_ + log(b+a*x^(1/3))/b^6-10*a^3*log(x)/b^6 +--R +--R +--R (2) +--R 5 3+-+2 4 3+-+ 3 2 3+-+ +--R (60a x \|x + 120a b x\|x + 60a b x)log(a\|x + b) +--R + +--R 5 2 3 3+-+2 4 4 4 3+-+ +--R (- 20a x log(x) - 20a b )\|x + (- 40a b x log(x) - 60a b x + 5a b )\|x +--R + +--R 3 2 3 2 5 +--R - 20a b x log(x) - 90a b x - 2b +--R / +--R 2 6 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2b x +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 3+-+2 4 3+-+ 3 2 3+-+ +--R (60a x \|x + 120a b x\|x + 60a b x)log(a\|x + b) +--R + +--R 5 3+-+2 4 3+-+ 3 2 3+-+ 2 3 3+-+2 +--R (- 60a x \|x - 120a b x\|x - 60a b x)log(\|x ) - 20a b \|x +--R + +--R 4 4 3+-+ 3 2 5 +--R (- 60a b x + 5a b )\|x - 90a b x - 2b +--R / +--R 2 6 3+-+2 7 3+-+ 8 +--R 2a b x \|x + 4a b x\|x + 2b x +--R Type: Union(Expression(Integer),...) +--E 656 + +--S 657 of 1299 +m0:=a0-r0 +--R +--R +--R 3 3+-+ 3 +--R - 30a log(\|x ) + 10a log(x) +--R (4) ---------------------------- +--R 6 +--R b +--R Type: Expression(Integer) +--E 657 + +--S 658 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 658 + +)clear all + +--S 659 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^4) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 3 3+-+2 2 3 3+-+ 3 4 3 3 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 659 + +--S 660 of 1299 +r0:=(-14)/(b^3*x^2)+3/2/(b*(b+a*x^(1/3))^2*x^2)+12/(b^2*_ + (b+a*x^(1/3))*x^2)+84/5*a/(b^4*x^(5/3))-21*a^2/(b^5*x^(4/3))+_ + 28*a^3/(b^6*x)-42*a^4/(b^7*x^(2/3))+84*a^5/(b^8*x^(1/3))-_ + 84*a^6*log(b+a*x^(1/3))/b^9+28*a^6*log(x)/b^9 +--R +--R +--R (2) +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (- 840a x \|x - 1680a b x \|x - 840a b x )log(a\|x + b) +--R + +--R 8 2 5 3 2 6 3+-+2 +--R (280a x log(x) + 280a b x - 14a b )\|x +--R + +--R 7 2 7 2 4 4 7 3+-+ 6 2 2 +--R (560a b x log(x) + 840a b x - 70a b x + 8a b )\|x + 280a b x log(x) +--R + +--R 6 2 2 3 5 8 +--R 1260a b x + 28a b x - 5b +--R / +--R 2 9 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10b x +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (- 840a x \|x - 1680a b x \|x - 840a b x )log(a\|x + b) +--R + +--R 8 2 3+-+2 7 2 3+-+ 6 2 2 3+-+ +--R (840a x \|x + 1680a b x \|x + 840a b x )log(\|x ) +--R + +--R 5 3 2 6 3+-+2 7 2 4 4 7 3+-+ 6 2 2 +--R (280a b x - 14a b )\|x + (840a b x - 70a b x + 8a b )\|x + 1260a b x +--R + +--R 3 5 8 +--R 28a b x - 5b +--R / +--R 2 9 2 3+-+2 10 2 3+-+ 11 2 +--R 10a b x \|x + 20a b x \|x + 10b x +--R Type: Union(Expression(Integer),...) +--E 661 + +--S 662 of 1299 +m0:=a0-r0 +--R +--R +--R 6 3+-+ 6 +--R 84a log(\|x ) - 28a log(x) +--R (4) -------------------------- +--R 9 +--R b +--R Type: Expression(Integer) +--E 662 + +--S 663 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 663 + +)clear all + +--S 664 of 1299 +t0:=1/((a+b/x^(1/3))^3*x^5) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R 2 4 3+-+2 2 4 3+-+ 3 5 3 4 +--R 3a b x \|x + 3a b x \|x + a x + b x +--R Type: Expression(Integer) +--E 664 + +--S 665 of 1299 +r0:=(-55/3)/(b^3*x^3)+3/2/(b*(b+a*x^(1/3))^2*x^3)+33/2/(b^2*(b+_ + a*x^(1/3))*x^3)+165/8*a/(b^4*x^(8/3))-165/7*a^2/(b^5*x^(7/3))+_ + 55/2*a^3/(b^6*x^2)-33*a^4/(b^7*x^(5/3))+165/4*a^5/(b^8*x^(4/3))-_ + 55*a^6/(b^9*x)+165/2*a^7/(b^10*x^(2/3))-165*a^8/(b^11*x^(1/3))+_ + 165*a^9*log(b+a*x^(1/3))/b^12-55*a^9*log(x)/b^12 +--R +--R +--R (2) +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (27720a x \|x + 55440a b x \|x + 27720a b x )log(a\|x + b) +--R + +--R 11 3 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a x log(x) - 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 10 3 7 4 2 4 7 10 +--R (- 18480a b x log(x) - 27720a b x + 2310a b x - 264a b x + 77a b ) +--R * +--R 3+-+ +--R \|x +--R + +--R 9 2 3 9 2 3 6 5 2 3 8 11 +--R - 9240a b x log(x) - 41580a b x - 924a b x + 165a b x - 56b +--R / +--R 2 12 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168b x +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (27720a x \|x + 55440a b x \|x + 27720a b x )log(a\|x + b) +--R + +--R 11 3 3+-+2 10 3 3+-+ 9 2 3 3+-+ +--R (- 27720a x \|x - 55440a b x \|x - 27720a b x )log(\|x ) +--R + +--R 8 3 2 5 6 2 9 3+-+2 +--R (- 9240a b x + 462a b x - 110a b )\|x +--R + +--R 10 3 7 4 2 4 7 10 3+-+ 9 2 3 +--R (- 27720a b x + 2310a b x - 264a b x + 77a b )\|x - 41580a b x +--R + +--R 6 5 2 3 8 11 +--R - 924a b x + 165a b x - 56b +--R / +--R 2 12 3 3+-+2 13 3 3+-+ 14 3 +--R 168a b x \|x + 336a b x \|x + 168b x +--R Type: Union(Expression(Integer),...) +--E 666 + +--S 667 of 1299 +m0:=a0-r0 +--R +--R +--R 9 3+-+ 9 +--R - 165a log(\|x ) + 55a log(x) +--R (4) ----------------------------- +--R 12 +--R b +--R Type: Expression(Integer) +--E 667 + +--S 668 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 668 + +)clear all + +--S 669 of 1299 +t0:=1/(1+b/x^(1/3)) +--R +--R +--R 3+-+ +--R \|x +--R (1) -------- +--R 3+-+ +--R \|x + b +--R Type: Expression(Integer) +--E 669 + +--S 670 of 1299 +r0:=3*b^2*x^(1/3)-3/2*b*x^(2/3)+x-3*b^3*log(b+x^(1/3)) +--R +--R +--R 3 3+-+ 3+-+2 2 3+-+ +--R - 6b log(\|x + b) - 3b \|x + 6b \|x + 2x +--R (2) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 3+-+ 3+-+2 2 3+-+ +--R - 6b log(\|x + b) - 3b \|x + 6b \|x + 2x +--R (3) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 671 + +--S 672 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 672 + +--S 673 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 673 + +)clear all + +--S 674 of 1299 +t0:=x^(2/3)*(1+x^(5/3))^(2/3) +--R +--R +--R +-----------+2 +--R 3+-+2 3| 3+-+2 +--R (1) \|x \|x \|x + 1 +--R Type: Expression(Integer) +--E 674 + +--S 675 of 1299 +r0:=9/25*(1+x^(5/3))^(5/3) +--R +--R +--R +-----------+2 +--R 3+-+2 3| 3+-+2 +--R (9x \|x + 9)\|x \|x + 1 +--R (2) ----------------------------- +--R 25 +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1299 +--a0:=integrate(t0,x) +--E 676 + +--S 677 of 1299 +--m0:=a0-r0 +--E 677 + +--S 678 of 1299 +--d0:=D(m0,x) +--E 678 + +)clear all + +--S 679 of 1299 +t0:=x^(7/3)*(a^(10/3)-x^(10/3))^(19/7) +--R +--R +--R +-----------------+5 +--R 3 5 3+-+3+-+2 6 2 3+-+2 3+-+ 9 7| 3 3+-+ 3 3+-+ +--R (1) (- 2a x \|a \|x + a x \|a \| + x )\|- x \|x + a \|a +--R Type: Expression(Integer) +--E 679 + +--S 680 of 1299 +r0:=-21/260*(a^(10/3)-x^(10/3))^(26/7) +--R +--R +--R (2) +--R +-----------------+5 +--R 3 6 3+-+3+-+2 6 3 3+-+2 3+-+ 10 10 7| 3 3+-+ 3 3+-+ +--R (- 63a x \|a \|x + 63a x \|a \| + 21x - 21a )\|- x \|x + a \|a +--R -------------------------------------------------------------------------- +--R 260 +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1299 +--a0:=integrate(t0,x) +--E 681 + +--S 682 of 1299 +--m0:=a0-r0 +--E 682 + +--S 683 of 1299 +--d0:=D(m0,x) +--E 683 + +)clear all + +--S 684 of 1299 +t0:=1/(1+x^(1/5)) +--R +--R +--R 1 +--R (1) -------- +--R 5+-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 684 + +--S 685 of 1299 +r0:=-5*x^(1/5)+5/2*x^(2/5)-5/3*x^(3/5)+5/4*x^(4/5)+5*log(1+x^(1/5)) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (2) ------------------------------------------------------ +--R 12 +--R Type: Expression(Integer) +--E 685 + +--S 686 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 5+-+ 5+-+4 5+-+3 5+-+2 5+-+ +--R 60log(\|x + 1) + 15\|x - 20\|x + 30\|x - 60\|x +--R (3) ------------------------------------------------------ +--R 12 +--R Type: Union(Expression(Integer),...) +--E 686 + +--S 687 of 1299 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 687 + +--S 688 of 1299 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 688 + +)clear all + +--S 689 of 1299 +t0:=1/(x^(1/5)*sqrt(1+x^(4/5))) +--R +--R +--R 1 +--R (1) ---------------- +--R +---------+ +--R 5+-+ |5+-+4 +--R \|x \|\|x + 1 +--R Type: Expression(Integer) +--E 689 + +--S 690 of 1299 +r0:=5/2*sqrt(1+x^(4/5)) +--R +--R +--R +---------+ +--R |5+-+4 +--R 5\|\|x + 1 +--R (2) ------------- +--R 2 +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1299 +--a0:=integrate(t0,x) +--E 691 + +--S 692 of 1299 +--m0:=a0-r0 +--E 692 + +--S 693 of 1299 +--d0:=D(m0,x) +--E 693 + +)clear all + +--S 694 of 1299 +t0:=(a+b/x^(3/5))^(2/3) +--R +--R +--R +-----------+2 +--R | 5+-+3 +--R |a \|x + b +--R (1) |----------- +--R 3| 5+-+3 +--R \| \|x +--R Type: Expression(Integer) +--E 694 + +--S 695 of 1299 +r0:=(a+b/x^(3/5))^(5/3)*x/a +--R +--R +--R +-----------+2 +--R | 5+-+3 +--R 5+-+3 |a \|x + b +--R (a x \|x + b x) |----------- +--R 3| 5+-+3 +--R \| \|x +--R (2) -------------------------------- +--R 5+-+3 +--R a \|x +--R Type: Expression(Integer) +--E 695 + +--S 696 of 1299 +--a0:=integrate(t0,x) +--E 696 + +--S 697 of 1299 +--m0:=a0-r0 +--E 697 + +--S 698 of 1299 +--d0:=D(m0,x) +--E 698 + +)clear all + +--S 699 of 1299 +t0:=(a+b/x^(3/2))^(2/3) +--R +--R +--R +-----------+2 +--R | +-+ +--R |a x\|x + b +--R (1) |----------- +--R 3| +-+ +--R \| x\|x +--R Type: Expression(Integer) +--E 699 + +--S 700 of 1299 +r0:=(a+b/x^(3/2))^(2/3)*x+2/3*b^(2/3)*log(1-b^(1/3)/((a+_ + b/x^(3/2))^(1/3)*sqrt(x)))-1/3*b^(2/3)*log(1+b^(2/3)/_ + ((a+b/x^(3/2))^(2/3)*x)+b^(1/3)/((a+b/x^(3/2))^(1/3)*sqrt(x)))-_ + 2*b^(2/3)*atan((1+2*b^(1/3)/((a+b/x^(3/2))^(1/3)*sqrt(x)))/_ + sqrt(3))/sqrt(3) +--R +--R +--R (2) +--R +-----------+2 +-----------+ +--R | +-+ | +-+ +--R +-+ |a x\|x + b 3+-+ |a x\|x + b 3+-+2 +-+ +--R x\|x |----------- + x\|b |----------- + \|b \|x +--R 3| +-+ 3| +-+ +--R +-+3+-+2 \| x\|x \| x\|x +--R - \|3 \|b log(------------------------------------------------------) +--R +-----------+2 +--R | +-+ +--R +-+ |a x\|x + b +--R x\|x |----------- +--R 3| +-+ +--R \| x\|x +--R + +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b 3+-+ +--R \|x |----------- - \|b +--R 3| +-+ +--R +-+3+-+2 \| x\|x +--R 2\|3 \|b log(-------------------------) +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b +--R \|x |----------- +--R 3| +-+ +--R \| x\|x +--R + +--R +-----------+ +--R | +-+ +--R +-+ |a x\|x + b 3+-+ +--R \|x |----------- + 2\|b +-----------+2 +--R 3| +-+ | +-+ +--R 3+-+2 \| x\|x +-+ |a x\|x + b +--R - 6\|b atan(--------------------------) + 3x\|3 |----------- +--R +-----------+ 3| +-+ +--R | +-+ \| x\|x +--R +-+ +-+ |a x\|x + b +--R \|3 \|x |----------- +--R 3| +-+ +--R \| x\|x +--R / +--R +-+ +--R 3\|3 +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1299 +--a0:=integrate(t0,x) +--E 701 + +--S 702 of 1299 +--m0:=a0-r0 +--E 702 + +--S 703 of 1299 +--d0:=D(m0,x) +--E 703 + +)clear all + +--S 704 of 1299 +t0:=x^m*(a+b*x^n) +--R +--R +--R m n m +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 704 + +--S 705 of 1299 +r0:=a*x^(1+m)/(1+m)+b*x^(1+m+n)/(1+m+n) +--R +--R +--R n + m + 1 m + 1 +--R (b m + b)x + (a n + a m + a)x +--R (2) ------------------------------------------- +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1299 +a0:=integrate(t0,x) +--R +--R +--R m log(x) n log(x) m log(x) +--R (b m + b)x %e %e + (a n + a m + a)x %e +--R (3) ------------------------------------------------------------- +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Union(Expression(Integer),...) +--E 706 + +--S 707 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R m log(x) n log(x) m log(x) +--R (b m + b)x %e %e + (a n + a m + a)x %e +--R + +--R n + m + 1 m + 1 +--R (- b m - b)x + (- a n - a m - a)x +--R / +--R 2 +--R (m + 1)n + m + 2m + 1 +--R Type: Expression(Integer) +--E 707 + +--S 708 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 708 + +)clear all + +--S 709 of 1299 +t0:=x^3*(a+b*x^n) +--R +--R +--R 3 n 3 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 709 + +--S 710 of 1299 +r0:=1/4*a*x^4+b*x^(4+n)/(4+n) +--R +--R +--R n + 4 4 +--R 4b x + (a n + 4a)x +--R (2) ------------------------ +--R 4n + 16 +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 4 n log(x) 4 +--R 4b x %e + (a n + 4a)x +--R (3) ------------------------------ +--R 4n + 16 +--R Type: Union(Expression(Integer),...) +--E 711 + +--S 712 of 1299 +m0:=a0-r0 +--R +--R +--R 4 n log(x) n + 4 +--R b x %e - b x +--R (4) ------------------------- +--R n + 4 +--R Type: Expression(Integer) +--E 712 + +--S 713 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 713 + +)clear all + +--S 714 of 1299 +t0:=x^2*(a+b*x^n) +--R +--R +--R 2 n 2 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 714 + +--S 715 of 1299 +r0:=1/3*a*x^3+b*x^(3+n)/(3+n) +--R +--R +--R n + 3 3 +--R 3b x + (a n + 3a)x +--R (2) ------------------------ +--R 3n + 9 +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 +--R 3b x %e + (a n + 3a)x +--R (3) ------------------------------ +--R 3n + 9 +--R Type: Union(Expression(Integer),...) +--E 716 + +--S 717 of 1299 +m0:=a0-r0 +--R +--R +--R 3 n log(x) n + 3 +--R b x %e - b x +--R (4) ------------------------- +--R n + 3 +--R Type: Expression(Integer) +--E 717 + +--S 718 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 718 + +)clear all + +--S 719 of 1299 +t0:=x*(a+b*x^n) +--R +--R +--R n +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 719 + +--S 720 of 1299 +r0:=1/2*a*x^2+b*x^(2+n)/(2+n) +--R +--R +--R n + 2 2 +--R 2b x + (a n + 2a)x +--R (2) ------------------------ +--R 2n + 4 +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 +--R 2b x %e + (a n + 2a)x +--R (3) ------------------------------ +--R 2n + 4 +--R Type: Union(Expression(Integer),...) +--E 721 + +--S 722 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) n + 2 +--R b x %e - b x +--R (4) ------------------------- +--R n + 2 +--R Type: Expression(Integer) +--E 722 + +--S 723 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 723 + +)clear all + +--S 724 of 1299 +t0:=a+b*x^n +--R +--R +--R n +--R (1) b x + a +--R Type: Expression(Integer) +--E 724 + +--S 725 of 1299 +r0:=a*x+b*x^(1+n)/(1+n) +--R +--R +--R n + 1 +--R b x + (a n + a)x +--R (2) --------------------- +--R n + 1 +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b x %e + (a n + a)x +--R (3) --------------------------- +--R n + 1 +--R Type: Union(Expression(Integer),...) +--E 726 + +--S 727 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n + 1 +--R b x %e - b x +--R (4) ------------------------- +--R n + 1 +--R Type: Expression(Integer) +--E 727 + +--S 728 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 728 + +)clear all + +--S 729 of 1299 +t0:=(a+b*x^n)/x +--R +--R +--R n +--R b x + a +--R (1) -------- +--R x +--R Type: Expression(Integer) +--E 729 + +--S 730 of 1299 +r0:=b*x^n/n+a*log(x) +--R +--R +--R n +--R b x + a n log(x) +--R (2) ----------------- +--R n +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e + a n log(x) +--R (3) ------------------------- +--R n +--R Type: Union(Expression(Integer),...) +--E 731 + +--S 732 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R b %e - b x +--R (4) ------------------- +--R n +--R Type: Expression(Integer) +--E 732 + +--S 733 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 733 + +)clear all + +--S 734 of 1299 +t0:=(a+b*x^n)/x^2 +--R +--R +--R n +--R b x + a +--R (1) -------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1299 +r0:=-a/x-b*x^(-1+n)/(1-n) +--R +--R +--R n - 1 +--R b x x - a n + a +--R (2) -------------------- +--R (n - 1)x +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e - a n + a +--R (3) ---------------------- +--R (n - 1)x +--R Type: Union(Expression(Integer),...) +--E 736 + +--S 737 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n - 1 +--R b %e - b x x +--R (4) ------------------------- +--R (n - 1)x +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 738 + +)clear all + +--S 739 of 1299 +t0:=(a+b*x^n)/x^3 +--R +--R +--R n +--R b x + a +--R (1) -------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 739 + +--S 740 of 1299 +r0:=-1/2*a/x^2-b*x^(-2+n)/(2-n) +--R +--R +--R 2 n - 2 +--R 2b x x - a n + 2a +--R (2) ---------------------- +--R 2 +--R (2n - 4)x +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R 2b %e - a n + 2a +--R (3) ------------------------ +--R 2 +--R (2n - 4)x +--R Type: Union(Expression(Integer),...) +--E 741 + +--S 742 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 2 n - 2 +--R b %e - b x x +--R (4) ------------------------- +--R 2 +--R (n - 2)x +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1299 +t0:=x^m*(a+b*x^n)^2 +--R +--R +--R 2 m n 2 m n 2 m +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1299 +r0:=a^2*x^(1+m)/(1+m)+2*a*b*x^(1+m+n)/(1+m+n)+b^2*x^(1+m+2*n)/(1+m+2*n) +--R +--R +--R (2) +--R 2 2 2 2 2 2 2n + m + 1 +--R ((b m + b )n + b m + 2b m + b )x +--R + +--R 2 n + m + 1 +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x +--R + +--R 2 2 2 2 2 2 2 2 m + 1 +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 2 2 2 m log(x) n log(x) 2 +--R ((b m + b )n + b m + 2b m + b )x %e (%e ) +--R + +--R 2 m log(x) n log(x) +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x %e %e +--R + +--R 2 2 2 2 2 2 2 2 m log(x) +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x %e +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Union(Expression(Integer),...) +--E 746 + +--S 747 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 2 2 2 m log(x) n log(x) 2 +--R ((b m + b )n + b m + 2b m + b )x %e (%e ) +--R + +--R 2 m log(x) n log(x) +--R ((4a b m + 4a b)n + 2a b m + 4a b m + 2a b)x %e %e +--R + +--R 2 2 2 2 2 2 2 2 m log(x) +--R (2a n + (3a m + 3a )n + a m + 2a m + a )x %e +--R + +--R 2 2 2 2 2 2 2n + m + 1 +--R ((- b m - b )n - b m - 2b m - b )x +--R + +--R 2 n + m + 1 +--R ((- 4a b m - 4a b)n - 2a b m - 4a b m - 2a b)x +--R + +--R 2 2 2 2 2 2 2 2 m + 1 +--R (- 2a n + (- 3a m - 3a )n - a m - 2a m - a )x +--R / +--R 2 2 3 2 +--R (2m + 2)n + (3m + 6m + 3)n + m + 3m + 3m + 1 +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +)clear all + +--S 749 of 1299 +t0:=x^3*(a+b*x^n)^2 +--R +--R +--R 2 3 n 2 3 n 2 3 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1299 +r0:=1/4*a^2*x^4+1/2*b^2*x^(2*(2+n))/(2+n)+2*a*b*x^(4+n)/(4+n) +--R +--R +--R 2 2 2n + 4 n + 4 2 2 2 2 4 +--R (2b n + 8b )x + (8a b n + 16a b)x + (a n + 6a n + 8a )x +--R (2) -------------------------------------------------------------------- +--R 2 +--R 4n + 24n + 32 +--R Type: Expression(Integer) +--E 750 + +--S 751 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 4 n log(x) 2 4 n log(x) +--R (2b n + 8b )x (%e ) + (8a b n + 16a b)x %e +--R + +--R 2 2 2 2 4 +--R (a n + 6a n + 8a )x +--R / +--R 2 +--R 4n + 24n + 32 +--R Type: Union(Expression(Integer),...) +--E 751 + +--S 752 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 4 n log(x) 2 4 n log(x) +--R (b n + 4b )x (%e ) + (4a b n + 8a b)x %e +--R + +--R 2 2 2n + 4 n + 4 +--R (- b n - 4b )x + (- 4a b n - 8a b)x +--R / +--R 2 +--R 2n + 12n + 16 +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 753 + +)clear all + +--S 754 of 1299 +t0:=x^2*(a+b*x^n)^2 +--R +--R +--R 2 2 n 2 2 n 2 2 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 754 + +--S 755 of 1299 +r0:=1/3*a^2*x^3+2*a*b*x^(3+n)/(3+n)+b^2*x^(3+2*n)/(3+2*n) +--R +--R +--R 2 2 2n + 3 n + 3 2 2 2 2 3 +--R (3b n + 9b )x + (12a b n + 18a b)x + (2a n + 9a n + 9a )x +--R (2) ---------------------------------------------------------------------- +--R 2 +--R 6n + 27n + 27 +--R Type: Expression(Integer) +--E 755 + +--S 756 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 3 n log(x) 2 3 n log(x) +--R (3b n + 9b )x (%e ) + (12a b n + 18a b)x %e +--R + +--R 2 2 2 2 3 +--R (2a n + 9a n + 9a )x +--R / +--R 2 +--R 6n + 27n + 27 +--R Type: Union(Expression(Integer),...) +--E 756 + +--S 757 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 3 n log(x) 2 3 n log(x) +--R (b n + 3b )x (%e ) + (4a b n + 6a b)x %e +--R + +--R 2 2 2n + 3 n + 3 +--R (- b n - 3b )x + (- 4a b n - 6a b)x +--R / +--R 2 +--R 2n + 9n + 9 +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 758 + +)clear all + +--S 759 of 1299 +t0:=x*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 759 + +--S 760 of 1299 +r0:=1/2*a^2*x^2+1/2*b^2*x^(2*(1+n))/(1+n)+2*a*b*x^(2+n)/(2+n) +--R +--R +--R 2 2 2n + 2 n + 2 2 2 2 2 2 +--R (b n + 2b )x + (4a b n + 4a b)x + (a n + 3a n + 2a )x +--R (2) ------------------------------------------------------------------ +--R 2 +--R 2n + 6n + 4 +--R Type: Expression(Integer) +--E 760 + +--S 761 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 2 n log(x) 2 2 n log(x) +--R (b n + 2b )x (%e ) + (4a b n + 4a b)x %e +--R + +--R 2 2 2 2 2 +--R (a n + 3a n + 2a )x +--R / +--R 2 +--R 2n + 6n + 4 +--R Type: Union(Expression(Integer),...) +--E 761 + +--S 762 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 n log(x) 2 2 n log(x) +--R (b n + 2b )x (%e ) + (4a b n + 4a b)x %e +--R + +--R 2 2 2n + 2 n + 2 +--R (- b n - 2b )x + (- 4a b n - 4a b)x +--R / +--R 2 +--R 2n + 6n + 4 +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 763 + +)clear all + +--S 764 of 1299 +t0:=(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 +--R (1) b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 764 + +--S 765 of 1299 +r0:=a^2*x+2*a*b*x^(1+n)/(1+n)+b^2*x^(1+2*n)/(1+2*n) +--R +--R +--R 2 2 2n + 1 n + 1 2 2 2 2 +--R (b n + b )x + (4a b n + 2a b)x + (2a n + 3a n + a )x +--R (2) ---------------------------------------------------------------- +--R 2 +--R 2n + 3n + 1 +--R Type: Expression(Integer) +--E 765 + +--S 766 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) +--R (b n + b )x (%e ) + (4a b n + 2a b)x %e +--R + +--R 2 2 2 2 +--R (2a n + 3a n + a )x +--R / +--R 2 +--R 2n + 3n + 1 +--R Type: Union(Expression(Integer),...) +--E 766 + +--S 767 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) +--R (b n + b )x (%e ) + (4a b n + 2a b)x %e +--R + +--R 2 2 2n + 1 n + 1 +--R (- b n - b )x + (- 4a b n - 2a b)x +--R / +--R 2 +--R 2n + 3n + 1 +--R Type: Expression(Integer) +--E 767 + +--S 768 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 768 + +)clear all + +--S 769 of 1299 +t0:=(a+b*x^n)^2/x +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 769 + +--S 770 of 1299 +r0:=2*a*b*x^n/n+1/2*b^2*x^(2*n)/n+a^2*log(x) +--R +--R +--R 2 2n n 2 +--R b x + 4a b x + 2a n log(x) +--R (2) ----------------------------- +--R 2n +--R Type: Expression(Integer) +--E 770 + +--S 771 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 4a b %e + 2a n log(x) +--R (3) ----------------------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 771 + +--S 772 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) 2 n log(x) 2 2n n +--R b (%e ) + 4a b %e - b x - 4a b x +--R (4) --------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 773 + +)clear all + +--S 774 of 1299 +t0:=(a+b*x^n)^2/x^2 +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1299 +r0:=-a^2/x-2*a*b*x^(-1+n)/(1-n)-b^2*x^(-1+2*n)/(1-2*n) +--R +--R +--R 2 2 2n - 1 n - 1 2 2 2 2 +--R (b n - b )x x + (4a b n - 2a b)x x - 2a n + 3a n - a +--R (2) ----------------------------------------------------------------- +--R 2 +--R (2n - 3n + 1)x +--R Type: Expression(Integer) +--E 775 + +--S 776 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) 2 2 2 2 +--R (b n - b )(%e ) + (4a b n - 2a b)%e - 2a n + 3a n - a +--R ----------------------------------------------------------------------- +--R 2 +--R (2n - 3n + 1)x +--R Type: Union(Expression(Integer),...) +--E 776 + +--S 777 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) +--R (b n - b )(%e ) + (4a b n - 2a b)%e +--R + +--R 2 2 2n - 1 n - 1 +--R (- b n + b )x x + (- 4a b n + 2a b)x x +--R / +--R 2 +--R (2n - 3n + 1)x +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 778 + +)clear all + +--S 779 of 1299 +t0:=(a+b*x^n)^2/x^3 +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1299 +r0:=-1/2*a^2/x^2-1/2*b^2/((1-n)*x^(2*(1-n)))-2*a*b*x^(-2+n)/(2-n) +--R +--R +--R (2) +--R 2 - 2n + 2 n - 2 2 2 2 2 - 2n + 2 +--R (4a b n - 4a b)x x x + (- a n + 3a n - 2a )x +--R + +--R 2 2 2 +--R (b n - 2b )x +--R / +--R 2 2 - 2n + 2 +--R (2n - 6n + 4)x x +--R Type: Expression(Integer) +--E 780 + +--S 781 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 2 n log(x) 2 n log(x) 2 2 2 2 +--R (b n - 2b )(%e ) + (4a b n - 4a b)%e - a n + 3a n - 2a +--R ------------------------------------------------------------------------ +--R 2 2 +--R (2n - 6n + 4)x +--R Type: Union(Expression(Integer),...) +--E 781 + +--S 782 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 - 2n + 2 n log(x) 2 - 2n + 2 n log(x) +--R (b n - 2b )x (%e ) + (4a b n - 4a b)x %e +--R + +--R 2 - 2n + 2 n - 2 2 2 2 +--R (- 4a b n + 4a b)x x x + (- b n + 2b )x +--R / +--R 2 2 - 2n + 2 +--R (2n - 6n + 4)x x +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 783 + +)clear all + +--S 784 of 1299 +t0:=x^m*(a+b*x^n)^3 +--R +--R +--R 3 m n 3 2 m n 2 2 m n 3 m +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1299 +r0:=a^3*x^(1+m)/(1+m)+3*a^2*b*x^(1+m+n)/(1+m+n)+_ + 3*a*b^2*x^(1+m+2*n)/(1+m+2*n)+b^3*x^(1+m+3*n)/(1+m+3*n) +--R +--R +--R (2) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b ) +--R * +--R 3n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R 2n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R n + m + 1 +--R x +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m + 1 +--R x +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Expression(Integer) +--E 785 + +--S 786 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b )x +--R * +--R m log(x) n log(x) 3 +--R %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) 2 +--R x %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) +--R x %e %e +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m log(x) +--R x %e +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Union(Expression(Integer),...) +--E 786 + +--S 787 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((2b m + 2b )n + (3b m + 6b m + 3b )n + b m + 3b m + 3b m + b )x +--R * +--R m log(x) n log(x) 3 +--R %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (9a b m + 9a b )n + (12a b m + 24a b m + 12a b )n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) 2 +--R x %e (%e ) +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (18a b m + 18a b)n + (15a b m + 30a b m + 15a b)n + 3a b m +--R + +--R 2 2 2 2 +--R 9a b m + 9a b m + 3a b +--R * +--R m log(x) n log(x) +--R x %e %e +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 3 2 +--R 6a n + (11a m + 11a )n + (6a m + 12a m + 6a )n + a m + 3a m +--R + +--R 3 3 +--R 3a m + a +--R * +--R m log(x) +--R x %e +--R + +--R 3 3 2 3 2 3 3 3 3 3 2 3 3 +--R ((- 2b m - 2b )n + (- 3b m - 6b m - 3b )n - b m - 3b m - 3b m - b ) +--R * +--R 3n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (- 9a b m - 9a b )n + (- 12a b m - 24a b m - 12a b )n - 3a b m +--R + +--R 2 2 2 2 +--R - 9a b m - 9a b m - 3a b +--R * +--R 2n + m + 1 +--R x +--R + +--R 2 2 2 2 2 2 2 2 3 +--R (- 18a b m - 18a b)n + (- 15a b m - 30a b m - 15a b)n - 3a b m +--R + +--R 2 2 2 2 +--R - 9a b m - 9a b m - 3a b +--R * +--R n + m + 1 +--R x +--R + +--R 3 3 3 3 2 3 2 3 3 3 3 +--R - 6a n + (- 11a m - 11a )n + (- 6a m - 12a m - 6a )n - a m +--R + +--R 3 2 3 3 +--R - 3a m - 3a m - a +--R * +--R m + 1 +--R x +--R / +--R 3 2 2 3 2 4 3 +--R (6m + 6)n + (11m + 22m + 11)n + (6m + 18m + 18m + 6)n + m + 4m +--R + +--R 2 +--R 6m + 4m + 1 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 788 + +)clear all + +--S 789 of 1299 +t0:=x^3*(a+b*x^n)^3 +--R +--R +--R 3 3 n 3 2 3 n 2 2 3 n 3 3 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1299 +r0:=1/4*a^3*x^4+3/2*a*b^2*x^(2*(2+n))/(2+n)+3*a^2*b*x^(4+n)/(4+n)+_ + b^3*x^(4+3*n)/(4+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 4 2 2 2 2 2n + 4 +--R (4b n + 24b n + 32b )x + (18a b n + 96a b n + 96a b )x +--R + +--R 2 2 2 2 n + 4 3 3 3 2 3 3 4 +--R (36a b n + 120a b n + 96a b)x + (3a n + 22a n + 48a n + 32a )x +--R / +--R 3 2 +--R 12n + 88n + 192n + 128 +--R Type: Expression(Integer) +--E 790 + +--S 791 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 4 n log(x) 3 +--R (4b n + 24b n + 32b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) 2 +--R (18a b n + 96a b n + 96a b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) +--R (36a b n + 120a b n + 96a b)x %e +--R + +--R 3 3 3 2 3 3 4 +--R (3a n + 22a n + 48a n + 32a )x +--R / +--R 3 2 +--R 12n + 88n + 192n + 128 +--R Type: Union(Expression(Integer),...) +--E 791 + +--S 792 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 4 n log(x) 3 +--R (2b n + 12b n + 16b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) 2 +--R (9a b n + 48a b n + 48a b )x (%e ) +--R + +--R 2 2 2 2 4 n log(x) +--R (18a b n + 60a b n + 48a b)x %e +--R + +--R 3 2 3 3 3n + 4 2 2 2 2 2n + 4 +--R (- 2b n - 12b n - 16b )x + (- 9a b n - 48a b n - 48a b )x +--R + +--R 2 2 2 2 n + 4 +--R (- 18a b n - 60a b n - 48a b)x +--R / +--R 3 2 +--R 6n + 44n + 96n + 64 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 793 + +)clear all + +--S 794 of 1299 +t0:=x^2*(a+b*x^n)^3 +--R +--R +--R 3 2 n 3 2 2 n 2 2 2 n 3 2 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1299 +r0:=1/3*a^3*x^3+1/3*b^3*x^(3*(1+n))/(1+n)+3*a^2*b*x^(3+n)/(3+n)+_ + 3*a*b^2*x^(3+2*n)/(3+2*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 3 2 2 2 2 2n + 3 +--R (2b n + 9b n + 9b )x + (9a b n + 36a b n + 27a b )x +--R + +--R 2 2 2 2 n + 3 3 3 3 2 3 3 3 +--R (18a b n + 45a b n + 27a b)x + (2a n + 11a n + 18a n + 9a )x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Expression(Integer) +--E 795 + +--S 796 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 3 n log(x) 3 +--R (2b n + 9b n + 9b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 2 +--R (9a b n + 36a b n + 27a b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 3 3 3 2 3 3 3 +--R (18a b n + 45a b n + 27a b)x %e + (2a n + 11a n + 18a n + 9a )x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Union(Expression(Integer),...) +--E 796 + +--S 797 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 3 n log(x) 3 +--R (2b n + 9b n + 9b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 2 +--R (9a b n + 36a b n + 27a b )x (%e ) +--R + +--R 2 2 2 2 3 n log(x) 3 2 3 3 3n + 3 +--R (18a b n + 45a b n + 27a b)x %e + (- 2b n - 9b n - 9b )x +--R + +--R 2 2 2 2 2n + 3 +--R (- 9a b n - 36a b n - 27a b )x +--R + +--R 2 2 2 2 n + 3 +--R (- 18a b n - 45a b n - 27a b)x +--R / +--R 3 2 +--R 6n + 33n + 54n + 27 +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 798 + +)clear all + +--S 799 of 1299 +t0:=x*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1299 +r0:=1/2*a^3*x^2+3/2*a*b^2*x^(2*(1+n))/(1+n)+3*a^2*b*x^(2+n)/(2+n)+_ + b^3*x^(2+3*n)/(2+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 2 2 2 2 2 2n + 2 +--R (2b n + 6b n + 4b )x + (9a b n + 24a b n + 12a b )x +--R + +--R 2 2 2 2 n + 2 3 3 3 2 3 3 2 +--R (18a b n + 30a b n + 12a b)x + (3a n + 11a n + 12a n + 4a )x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Expression(Integer) +--E 800 + +--S 801 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 2 n log(x) 3 +--R (2b n + 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 +--R (9a b n + 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 3 3 3 2 3 3 2 +--R (18a b n + 30a b n + 12a b)x %e + (3a n + 11a n + 12a n + 4a )x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Union(Expression(Integer),...) +--E 801 + +--S 802 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 2 n log(x) 3 +--R (2b n + 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 +--R (9a b n + 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 2 n log(x) 3 2 3 3 3n + 2 +--R (18a b n + 30a b n + 12a b)x %e + (- 2b n - 6b n - 4b )x +--R + +--R 2 2 2 2 2n + 2 +--R (- 9a b n - 24a b n - 12a b )x +--R + +--R 2 2 2 2 n + 2 +--R (- 18a b n - 30a b n - 12a b)x +--R / +--R 3 2 +--R 6n + 22n + 24n + 8 +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 803 + +)clear all + +--S 804 of 1299 +t0:=(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R (1) b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1299 +r0:=a^3*x+3*a^2*b*x^(1+n)/(1+n)+3*a*b^2*x^(1+2*n)/(1+2*n)+b^3*x^(1+3*n)/(1+3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n + 1 2 2 2 2 2n + 1 +--R (2b n + 3b n + b )x + (9a b n + 12a b n + 3a b )x +--R + +--R 2 2 2 2 n + 1 3 3 3 2 3 3 +--R (18a b n + 15a b n + 3a b)x + (6a n + 11a n + 6a n + a )x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Expression(Integer) +--E 805 + +--S 806 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n + 3b n + b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n + 12a b n + 3a b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n + 15a b n + 3a b)x %e + (6a n + 11a n + 6a n + a )x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Union(Expression(Integer),...) +--E 806 + +--S 807 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 +--R (2b n + 3b n + b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n + 12a b n + 3a b )x (%e ) +--R + +--R 2 2 2 2 n log(x) 3 2 3 3 3n + 1 +--R (18a b n + 15a b n + 3a b)x %e + (- 2b n - 3b n - b )x +--R + +--R 2 2 2 2 2n + 1 2 2 2 2 n + 1 +--R (- 9a b n - 12a b n - 3a b )x + (- 18a b n - 15a b n - 3a b)x +--R / +--R 3 2 +--R 6n + 11n + 6n + 1 +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 808 + +)clear all + +--S 809 of 1299 +t0:=(a+b*x^n)^3/x +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 809 + +--S 810 of 1299 +r0:=3*a^2*b*x^n/n+3/2*a*b^2*x^(2*n)/n+1/3*b^3*x^(3*n)/n+a^3*log(x) +--R +--R +--R 3 3n 2 2n 2 n 3 +--R 2b x + 9a b x + 18a b x + 6a n log(x) +--R (2) ------------------------------------------ +--R 6n +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 9a b (%e ) + 18a b %e + 6a n log(x) +--R (3) ---------------------------------------------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 811 + +--S 812 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 3n +--R 2b (%e ) + 9a b (%e ) + 18a b %e - 2b x +--R + +--R 2 2n 2 n +--R - 9a b x - 18a b x +--R / +--R 6n +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1299 +t0:=(a+b*x^n)^3/x^2 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1299 +r0:=-a^3/x-3*a^2*b*x^(-1+n)/(1-n)-3*a*b^2*x^(-1+2*n)/(1-2*n)-_ + b^3*x^(-1+3*n)/(1-3*n) +--R +--R +--R (2) +--R 3 2 3 3 3n - 1 2 2 2 2 2n - 1 +--R (2b n - 3b n + b )x x + (9a b n - 12a b n + 3a b )x x +--R + +--R 2 2 2 2 n - 1 3 3 3 2 3 3 +--R (18a b n - 15a b n + 3a b)x x - 6a n + 11a n - 6a n + a +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 3b n + b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 12a b n + 3a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n - 15a b n + 3a b)%e - 6a n + 11a n - 6a n + a +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 3b n + b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 12a b n + 3a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 2 3 3 3n - 1 +--R (18a b n - 15a b n + 3a b)%e + (- 2b n + 3b n - b )x x +--R + +--R 2 2 2 2 2n - 1 +--R (- 9a b n + 12a b n - 3a b )x x +--R + +--R 2 2 2 2 n - 1 +--R (- 18a b n + 15a b n - 3a b)x x +--R / +--R 3 2 +--R (6n - 11n + 6n - 1)x +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1299 +t0:=(a+b*x^n)^3/x^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1299 +r0:=-1/2*a^3/x^2-3/2*a*b^2/((1-n)*x^(2*(1-n)))-_ + 3*a^2*b*x^(-2+n)/(2-n)-b^3*x^(-2+3*n)/(2-3*n) +--R +--R +--R (2) +--R 3 2 3 3 2 - 2n + 2 3n - 2 +--R (2b n - 6b n + 4b )x x x +--R + +--R 2 2 2 2 2 - 2n + 2 n - 2 +--R (18a b n - 30a b n + 12a b)x x x +--R + +--R 3 3 3 2 3 3 - 2n + 2 2 2 2 2 2 +--R (- 3a n + 11a n - 12a n + 4a )x + (9a b n - 24a b n + 12a b )x +--R / +--R 3 2 2 - 2n + 2 +--R (6n - 22n + 24n - 8)x x +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 +--R (2b n - 6b n + 4b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 +--R (9a b n - 24a b n + 12a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 3 3 3 2 3 3 +--R (18a b n - 30a b n + 12a b)%e - 3a n + 11a n - 12a n + 4a +--R / +--R 3 2 2 +--R (6n - 22n + 24n - 8)x +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 - 2n + 2 n log(x) 3 +--R (2b n - 6b n + 4b )x (%e ) +--R + +--R 2 2 2 2 - 2n + 2 n log(x) 2 +--R (9a b n - 24a b n + 12a b )x (%e ) +--R + +--R 2 2 2 2 - 2n + 2 n log(x) +--R (18a b n - 30a b n + 12a b)x %e +--R + +--R 3 2 3 3 2 - 2n + 2 3n - 2 +--R (- 2b n + 6b n - 4b )x x x +--R + +--R 2 2 2 2 2 - 2n + 2 n - 2 +--R (- 18a b n + 30a b n - 12a b)x x x +--R + +--R 2 2 2 2 2 +--R (- 9a b n + 24a b n - 12a b )x +--R / +--R 3 2 2 - 2n + 2 +--R (6n - 22n + 24n - 8)x x +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1299 +t0:=x^m/(a+b*x^n) +--R +--R +--R m +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1299 +--r0:=x^(1+m)*hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a*(1+m)) +--E 825 + +--S 826 of 1299 +--a0:=integrate(t0,x) +--E 826 + +--S 827 of 1299 +--m0:=a0-r0 +--E 827 + +--S 828 of 1299 +--d0:=D(m0,x) +--E 828 + +)clear all + +--S 829 of 1299 +t0:=x/(a+b*x^n) +--R +--R +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1299 +--r0:=1/2*x^2*hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/a +--E 830 + +--S 831 of 1299 +--a0:=integrate(t0,x) +--E 831 + +--S 832 of 1299 +--m0:=a0-r0 +--E 832 + +--S 833 of 1299 +--d0:=D(m0,x) +--E 833 + +)clear all + +--S 834 of 1299 +t0:=1/(a+b*x^n) +--R +--R +--R 1 +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1299 +--r0:=x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/a +--E 835 + +--S 836 of 1299 +--a0:=integrate(t0,x) +--E 836 + +--S 837 of 1299 +--m0:=a0-r0 +--E 837 + +--S 838 of 1299 +--d0:=D(m0,x) +--E 838 + +)clear all + +--S 839 of 1299 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1299 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 840 + +--S 841 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 841 + +--S 842 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 843 + +)clear all + +--S 844 of 1299 +t0:=1/(x^2*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------- +--R 2 n 2 +--R b x x + a x +--R Type: Expression(Integer) +--E 844 + +--S 845 of 1299 +--r0:=-hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a*x) +--E 845 + +--S 846 of 1299 +--a0:=integrate(t0,x) +--E 846 + +--S 847 of 1299 +--m0:=a0-r0 +--E 847 + +--S 848 of 1299 +--d0:=D(m0,x) +--E 848 + +)clear all + +--S 849 of 1299 +t0:=1/(x^3*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------- +--R 3 n 3 +--R b x x + a x +--R Type: Expression(Integer) +--E 849 + +--S 850 of 1299 +--r0:=-1/2*hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a*x^2) +--E 850 + +--S 851 of 1299 +--a0:=integrate(t0,x) +--E 851 + +--S 852 of 1299 +--m0:=a0-r0 +--E 852 + +--S 853 of 1299 +--d0:=D(m0,x) +--E 853 + +)clear all + +--S 854 of 1299 +t0:=x^m/(a+b*x^n)^2 +--R +--R +--R m +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 854 + +--S 855 of 1299 +--r0:=x^(1+m)/(a*n*(a+b*x^n))-(1+m-n)*x^(1+m)*_ +-- hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a^2*(1+m)*n) +--E 855 + +--S 856 of 1299 +--a0:=integrate(t0,x) +--E 856 + +--S 857 of 1299 +--m0:=a0-r0 +--E 857 + +--S 858 of 1299 +--d0:=D(m0,x) +--E 858 + +)clear all + +--S 859 of 1299 +t0:=x/(a+b*x^n)^2 +--R +--R +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 859 + +--S 860 of 1299 +--r0:=x^2/(a*n*(a+b*x^n))-1/2*(2-n)*x^2*_ +-- hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/(a^2*n) +--E 860 + +--S 861 of 1299 +--a0:=integrate(t0,x) +--E 861 + +--S 862 of 1299 +--m0:=a0-r0 +--E 862 + +--S 863 of 1299 +--d0:=D(m0,x) +--E 863 + +)clear all + +--S 864 of 1299 +t0:=1/(a+b*x^n)^2 +--R +--R +--R 1 +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 864 + +--S 865 of 1299 +--r0:=x/(a*n*(a+b*x^n))-(1-n)*x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/(a^2*n) +--E 865 + +--S 866 of 1299 +--a0:=integrate(t0,x) +--E 866 + +--S 867 of 1299 +--m0:=a0-r0 +--E 867 + +--S 868 of 1299 +--d0:=D(m0,x) +--E 868 + +)clear all + +--S 869 of 1299 +t0:=1/(x*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 n 2 n 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 869 + +--S 870 of 1299 +r0:=1/(a*n*(a+b*x^n))+log(x)/a^2-log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R (- b x - a)log(b x + a) + b n log(x)x + a n log(x) + a +--R (2) --------------------------------------------------------- +--R 2 n 3 +--R a b n x + a n +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) n log(x) n log(x) +--R (- b %e - a)log(b %e + a) + b n log(x)%e +--R + +--R a n log(x) + a +--R / +--R 2 n log(x) 3 +--R a b n %e + a n +--R Type: Union(Expression(Integer),...) +--E 871 + +--S 872 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((- b x - a b)%e - a b x - a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((b x + a b)%e + a b x + a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 2 2 n 3 n log(x) 3 n 4 +--R (a b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 872 + +--S 873 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 873 + +)clear all + +--S 874 of 1299 +t0:=1/(x^2*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 2 n 2 2 n 2 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 874 + +--S 875 of 1299 +--r0:=1/(a*n*x*(a+b*x^n))-(1+n)*_ +-- hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a^2*n*x) +--E 875 + +--S 876 of 1299 +--a0:=integrate(t0,x) +--E 876 + +--S 877 of 1299 +--m0:=a0-r0 +--E 877 + +--S 878 of 1299 +--d0:=D(m0,x) +--E 878 + +)clear all + +--S 879 of 1299 +t0:=1/(x^3*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) ---------------------------- +--R 2 3 n 2 3 n 2 3 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 879 + +--S 880 of 1299 +--r0:=1/(a*n*x^2*(a+b*x^n))-1/2*(2+n)*_ +-- hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a^2*n*x^2) +--E 880 + +--S 881 of 1299 +--a0:=integrate(t0,x) +--E 881 + +--S 882 of 1299 +--m0:=a0-r0 +--E 882 + +--S 883 of 1299 +--d0:=D(m0,x) +--E 883 + +)clear all + +--S 884 of 1299 +t0:=x^m/(a+b*x^n)^3 +--R +--R +--R m +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 884 + +--S 885 of 1299 +--r0:=1/2*x^(1+m)/(a*n*(a+b*x^n)^2)-1/2*(1+m-2*n)*x^(1+m)/_ +-- (a^2*n^2*(a+b*x^n))+1/2*(1+m-2*n)*(1+m-n)*x^(1+m)*_ +-- hypergeometric(1,(1+m)/n,(1+m+n)/n,-b*x^n/a)/(a^3*(1+m)*n^2) +--E 885 + +--S 886 of 1299 +--a0:=integrate(t0,x) +--E 886 + +--S 887 of 1299 +--m0:=a0-r0 +--E 887 + +--S 888 of 1299 +--d0:=D(m0,x) +--E 888 + +)clear all + +--S 889 of 1299 +t0:=x/(a+b*x^n)^3 +--R +--R +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 889 + +--S 890 of 1299 +--r0:=1/2*x^2/(a*n*(a+b*x^n)^2)-(1-n)*x^2/(a^2*n^2*(a+b*x^n))+_ +-- 1/2*(1-n)*(2-n)*x^2*hypergeometric(1,2/n,(2+n)/n,-b*x^n/a)/(a^3*n^2) +--E 890 + +--S 891 of 1299 +--a0:=integrate(t0,x) +--E 891 + +--S 892 of 1299 +--m0:=a0-r0 +--E 892 + +--S 893 of 1299 +--d0:=D(m0,x) +--E 893 + +)clear all + +--S 894 of 1299 +t0:=1/(a+b*x^n)^3 +--R +--R +--R 1 +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 894 + +--S 895 of 1299 +--r0:=1/2*x/(a*n*(a+b*x^n)^2)-1/2*(1-2*n)*x/(a^2*n^2*(a+b*x^n))+_ +-- 1/2*(1-2*n)*(1-n)*x*hypergeometric(1,1/n,1+1/n,-b*x^n/a)/(a^3*n^2) +--E 895 + +--S 896 of 1299 +--a0:=integrate(t0,x) +--E 896 + +--S 897 of 1299 +--m0:=a0-r0 +--E 897 + +--S 898 of 1299 +--d0:=D(m0,x) +--E 898 + +)clear all + +--S 899 of 1299 +t0:=1/(x*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------ +--R 3 n 3 2 n 2 2 n 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 899 + +--S 900 of 1299 +r0:=1/2/(a*n*(a+b*x^n)^2)+1/(a^2*n*(a+b*x^n))+log(x)/a^3-log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n 2 n 2 n 2 +--R (- 2b (x ) - 4a b x - 2a )log(b x + a) + 2b n log(x)(x ) +--R + +--R n 2 2 +--R (4a b n log(x) + 2a b)x + 2a n log(x) + 3a +--R / +--R 3 2 n 2 4 n 5 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (- 2b (%e ) - 4a b %e - 2a )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) + (4a b n log(x) + 2a b)%e + 2a n log(x) +--R + +--R 2 +--R 3a +--R / +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 2a b n (%e ) + 4a b n %e + 2a n +--R Type: Union(Expression(Integer),...) +--E 901 + +--S 902 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 2a b x - 3a b )(%e ) + (2a b (x ) - 4a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 4a b x +--R / +--R 3 4 n 2 4 3 n 5 2 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 4 3 n 2 5 2 n 6 n log(x) 5 2 n 2 6 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 7 +--R 2a n +--R Type: Expression(Integer) +--E 902 + +--S 903 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 903 + +)clear all + +--S 904 of 1299 +t0:=1/(x^2*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 2 n 3 2 2 n 2 2 2 n 3 2 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 904 + +--S 905 of 1299 +--r0:=1/2/(a*n*x*(a+b*x^n)^2)+1/2*(1+2*n)/(a^2*n^2*x*(a+b*x^n))-_ +-- 1/2*(1+n)*(1+2*n)*hypergeometric(1,(-1)/n,(-1+n)/n,-b*x^n/a)/(a^3*n^2*x) +--E 905 + +--S 906 of 1299 +--a0:=integrate(t0,x) +--E 906 + +--S 907 of 1299 +--m0:=a0-r0 +--E 907 + +--S 908 of 1299 +--d0:=D(m0,x) +--E 908 + +)clear all + +--S 909 of 1299 +t0:=1/(x^3*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------- +--R 3 3 n 3 2 3 n 2 2 3 n 3 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 909 + +--S 910 of 1299 +--r0:=1/2/(a*n*x^2*(a+b*x^n)^2)+(1+n)/(a^2*n^2*x^2*(a+b*x^n))-_ +-- 1/2*(1+n)*(2+n)*hypergeometric(1,(-2)/n,(-2+n)/n,-b*x^n/a)/(a^3*n^2*x^2) +--E 910 + +--S 911 of 1299 +--a0:=integrate(t0,x) +--E 911 + +--S 912 of 1299 +--m0:=a0-r0 +--E 912 + +--S 913 of 1299 +--d0:=D(m0,x) +--E 913 + +)clear all + +--S 914 of 1299 +t0:=x^m*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R m | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 914 + +--S 915 of 1299 +--r0:=2*x^(1+m)*sqrt(a+b*x^n)/(2+2*m+n)+a*n*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*sqrt(a+b*x^n)) +--E 915 + +--S 916 of 1299 +--a0:=integrate(t0,x) +--E 916 + +--S 917 of 1299 +--m0:=a0-r0 +--E 917 + +--S 918 of 1299 +--d0:=D(m0,x) +--E 918 + +)clear all + +--S 919 of 1299 +t0:=x*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R | n +--R (1) x\|b x + a +--R Type: Expression(Integer) +--E 919 + +--S 920 of 1299 +--r0:=2*x^2*sqrt(a+b*x^n)/(4+n)+1/2*a*n*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((4+n)*sqrt(a+b*x^n)) +--E 920 + +--S 921 of 1299 +--a0:=integrate(t0,x) +--E 921 + +--S 922 of 1299 +--m0:=a0-r0 +--E 922 + +--S 923 of 1299 +--d0:=D(m0,x) +--E 923 + +)clear all + +--S 924 of 1299 +t0:=(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R | n +--R (1) \|b x + a +--R Type: Expression(Integer) +--E 924 + +--S 925 of 1299 +--r0:=2*x*sqrt(a+b*x^n)/(2+n)+a*n*x*_ +-- hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((2+n)*sqrt(a+b*x^n)) +--E 925 + +--S 926 of 1299 +--a0:=integrate(t0,x) +--E 926 + +--S 927 of 1299 +--m0:=a0-r0 +--E 927 + +--S 928 of 1299 +--d0:=D(m0,x) +--E 928 + +)clear all + +--S 929 of 1299 +t0:=(a+b*x^n)^(1/2)/x +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 929 + +--S 930 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))*sqrt(a)/n+2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 931 + +--S 932 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--------+ +--R | n log(x) +-+ \|b x + a | n +--R 2\|b %e + a + 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 932 + +--S 933 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R + +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 934 + +--S 935 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 935 + +)clear all + +--S 936 of 1299 +t0:=(a+b*x^n)^(1/2)/x^2 +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1299 +--r0:=-2*sqrt(a+b*x^n)/((2-n)*x)+a*n*_ +-- hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- ((2-n)*x*sqrt(a+b*x^n)) +--E 937 + +--S 938 of 1299 +--a0:=integrate(t0,x) +--E 938 + +--S 939 of 1299 +--m0:=a0-r0 +--E 939 + +--S 940 of 1299 +--d0:=D(m0,x) +--E 940 + +)clear all + +--S 941 of 1299 +t0:=(a+b*x^n)^(1/2)/x^3 +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1299 +--r0:=-2*sqrt(a+b*x^n)/((4-n)*x^2)+1/2*a*n*_ +-- hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4-n)*x^2*sqrt(a+b*x^n)) +--E 942 + +--S 943 of 1299 +--a0:=integrate(t0,x) +--E 943 + +--S 944 of 1299 +--m0:=a0-r0 +--E 944 + +--S 945 of 1299 +--d0:=D(m0,x) +--E 945 + +)clear all + +--S 946 of 1299 +t0:=x^m*(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R m n m | n +--R (1) (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1299 +--r0:=2*x^(1+m)*(a+b*x^n)^(3/2)/(2+2*m+3*n)+6*a*n*x^(1+m)*_ +-- sqrt(a+b*x^n)/((2+2*m+n)*(2+2*m+3*n))+3*a^2*n^2*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*(2+2*m+3*n)*sqrt(a+b*x^n)) +--E 947 + +--S 948 of 1299 +--a0:=integrate(t0,x) +--E 948 + +--S 949 of 1299 +--m0:=a0-r0 +--E 949 + +--S 950 of 1299 +--d0:=D(m0,x) +--E 950 + +)clear all + +--S 951 of 1299 +t0:=x*(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R n | n +--R (1) (b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1299 +--r0:=2*x^2*(a+b*x^n)^(3/2)/(4+3*n)+6*a*n*x^2*sqrt(a+b*x^n)/_ +-- ((4+n)*(4+3*n))+3/2*a^2*n^2*x^2*hypergeometric(1/2,2/n,_ +-- (2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((4+n)*(4+3*n)*sqrt(a+b*x^n)) +--E 952 + +--S 953 of 1299 +--a0:=integrate(t0,x) +--E 953 + +--S 954 of 1299 +--m0:=a0-r0 +--E 954 + +--S 955 of 1299 +--d0:=D(m0,x) +--E 955 + +)clear all + +--S 956 of 1299 +t0:=(a+b*x^n)^(3/2) +--R +--R +--R +--------+ +--R n | n +--R (1) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1299 +--r0:=2*x*(a+b*x^n)^(3/2)/(2+3*n)+6*a*n*x*sqrt(a+b*x^n)/(4+8*n+3*n^2)+_ +-- 3*a^2*n^2*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4+8*n+3*n^2)*sqrt(a+b*x^n)) +--E 957 + +--S 958 of 1299 +--a0:=integrate(t0,x) +--E 958 + +--S 959 of 1299 +--m0:=a0-r0 +--E 959 + +--S 960 of 1299 +--d0:=D(m0,x) +--E 960 + +)clear all + +--S 961 of 1299 +t0:=(a+b*x^n)^(3/2)/x +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R x +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1299 +r0:=2/3*(a+b*x^n)^(3/2)/n-2*a^(3/2)*atanh(sqrt(a+b*x^n)/sqrt(a))/n+2*a*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a n | n +--R - 6a\|a atanh(-----------) + (2b x + 8a)\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------- +--R 3n +--R Type: Expression(Integer) +--E 962 + +--S 963 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R 3a\|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 8a)\|b %e + a +--R / +--R 3n +--R , +--R +--R +----------------+ +--R | n log(x) +--R +---+ \|b %e + a +--R - 6a\|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 8a)\|b %e + a +--R / +--R 3n +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 963 + +--S 964 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R 3a\|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n log(x) | n log(x) +-+ \|b x + a +--R (2b %e + 8a)\|b %e + a + 6a\|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R n | n +--R (- 2b x - 8a)\|b x + a +--R / +--R 3n +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 965 + +--S 966 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +--R +---+ \|b %e + a +--R - 6a\|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +--------+ +--R +----------------+ | n +--R n log(x) | n log(x) +-+ \|b x + a +--R (2b %e + 8a)\|b %e + a + 6a\|a atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R n | n +--R (- 2b x - 8a)\|b x + a +--R / +--R 3n +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1299 +t0:=(a+b*x^n)^(3/2)/x^2 +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1299 +--r0:=-2*(a+b*x^n)^(3/2)/((2-3*n)*x)+6*a*n*sqrt(a+b*x^n)/_ +-- ((4-8*n+3*n^2)*x)-3*a^2*n^2*hypergeometric(1/2,(-1)/n,_ +-- (-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((4-8*n+3*n^2)*x*sqrt(a+b*x^n)) +--E 969 + +--S 970 of 1299 +--a0:=integrate(t0,x) +--E 970 + +--S 971 of 1299 +--m0:=a0-r0 +--E 971 + +--S 972 of 1299 +--d0:=D(m0,x) +--E 972 + +)clear all + +--S 973 of 1299 +t0:=(a+b*x^n)^(3/2)/x^3 +--R +--R +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R (1) --------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1299 +--r0:=-2*(a+b*x^n)^(3/2)/((4-3*n)*x^2)+6*a*n*sqrt(a+b*x^n)/_ +-- ((16-16*n+3*n^2)*x^2)-3/2*a^2*n^2*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/((16-16*n+3*n^2)*x^2*sqrt(a+b*x^n)) +--E 974 + +--S 975 of 1299 +--a0:=integrate(t0,x) +--E 975 + +--S 976 of 1299 +--m0:=a0-r0 +--E 976 + +--S 977 of 1299 +--d0:=D(m0,x) +--E 977 + +)clear all + +--S 978 of 1299 +t0:=x^m*(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 m n 2 m n 2 m | n +--R (1) (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1299 +--r0:=10*a*n*x^(1+m)*(a+b*x^n)^(3/2)/((2+2*m+3*n)*(2+2*m+5*n))+_ +-- 2*x^(1+m)*(a+b*x^n)^(5/2)/(2+2*m+5*n)+30*a^2*n^2*x^(1+m)*_ +-- sqrt(a+b*x^n)/((2+2*m+n)*(2+2*m+3*n)*(2+2*m+5*n))+15*a^3*n^3*_ +-- x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*(2+2*m+n)*(2+2*m+3*n)*_ +-- (2+2*m+5*n)*sqrt(a+b*x^n)) +--E 979 + +--S 980 of 1299 +--a0:=integrate(t0,x) +--E 980 + +--S 981 of 1299 +--m0:=a0-r0 +--E 981 + +--S 982 of 1299 +--d0:=D(m0,x) +--E 982 + +)clear all + +--S 983 of 1299 +t0:=x*(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (1) (b x (x ) + 2a b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1299 +--r0:=10*a*n*x^2*(a+b*x^n)^(3/2)/(16+32*n+15*n^2)+2*x^2*(a+_ +-- b*x^n)^(5/2)/(4+5*n)+30*a^2*n^2*x^2*sqrt(a+b*x^n)/((4+n)*_ +-- (4+3*n)*(4+5*n))+15/2*a^3*n^3*x^2*hypergeometric(1/2,2/n,(2+n)/n,_ +-- -b*x^n/a)*sqrt((a+b*x^n)/a)/((4+n)*(4+3*n)*(4+5*n)*sqrt(a+b*x^n)) +--E 984 + +--S 985 of 1299 +--a0:=integrate(t0,x) +--E 985 + +--S 986 of 1299 +--m0:=a0-r0 +--E 986 + +--S 987 of 1299 +--d0:=D(m0,x) +--E 987 + +)clear all + +--S 988 of 1299 +t0:=(a+b*x^n)^(5/2) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (1) (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1299 +--r0:=10*a*n*x*(a+b*x^n)^(3/2)/(4+16*n+15*n^2)+2*x*(a+b*x^n)^(5/2)/_ +-- (2+5*n)+30*a^2*n^2*x*sqrt(a+b*x^n)/(8+36*n+46*n^2+15*n^3)+_ +-- 15*a^3*n^3*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((8+36*n+46*n^2+15*n^3)*sqrt(a+b*x^n)) +--E 989 + +--S 990 of 1299 +--a0:=integrate(t0,x) +--E 990 + +--S 991 of 1299 +--m0:=a0-r0 +--E 991 + +--S 992 of 1299 +--d0:=D(m0,x) +--E 992 + +)clear all + +--S 993 of 1299 +t0:=(a+b*x^n)^(5/2)/x +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1299 +r0:=2/3*a*(a+b*x^n)^(3/2)/n+2/5*(a+b*x^n)^(5/2)/n-2*a^(5/2)*atanh(sqrt(a+b*x^n)/sqrt(a))/n+2*a^2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R - 30a \|a atanh(-----------) + (6b (x ) + 22a b x + 46a )\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------------------------------------- +--R 15n +--R Type: Expression(Integer) +--E 994 + +--S 995 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R 2 +-+ - 2\|a \|b %e + a + b %e + 2a +--R 15a \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R / +--R 15n +--R , +--R +--R +----------------+ +--R | n log(x) +--R 2 +---+ \|b %e + a +--R - 30a \|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R / +--R 15n +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 995 + +--S 996 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R 2 +-+ - 2\|a \|b %e + a + b %e + 2a +--R 15a \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R 30a \|a atanh(-----------) + (- 6b (x ) - 22a b x - 46a )\|b x + a +--R +-+ +--R \|a +--R / +--R 15n +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1299 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +--R 2 +---+ \|b %e + a +--R - 30a \|- a atan(-------------------) +--R +---+ +--R \|- a +--R + +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 22a b %e + 46a )\|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R 2 +-+ \|b x + a 2 n 2 n 2 | n +--R 30a \|a atanh(-----------) + (- 6b (x ) - 22a b x - 46a )\|b x + a +--R +-+ +--R \|a +--R / +--R 15n +--R Type: Expression(Integer) +--E 998 + +--S 999 of 1299 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 999 + +)clear all + +--S 1000 of 1299 +t0:=(a+b*x^n)^(5/2)/x^2 +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1299 +--r0:=10*a*n*(a+b*x^n)^(3/2)/((4-16*n+15*n^2)*x)-2*(a+b*x^n)^(5/2)/_ +-- ((2-5*n)*x)-30*a^2*n^2*sqrt(a+b*x^n)/((2-5*n)*(4-8*n+3*n^2)*x)+_ +-- 15*a^3*n^3*hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((2-5*n)*(4-8*n+3*n^2)*x*sqrt(a+b*x^n)) +--E 1001 + +--S 1002 of 1299 +--a0:=integrate(t0,x) +--E 1002 + +--S 1003 of 1299 +--m0:=a0-r0 +--E 1003 + +--S 1004 of 1299 +--d0:=D(m0,x) +--E 1004 + +)clear all + +--S 1005 of 1299 +t0:=(a+b*x^n)^(5/2)/x^3 +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R (1) ----------------------------------- +--R 3 +--R x +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1299 +--r0:=10*a*n*(a+b*x^n)^(3/2)/((16-32*n+15*n^2)*x^2)-2*(a+b*x^n)^(5/2)/_ +-- ((4-5*n)*x^2)-30*a^2*n^2*sqrt(a+b*x^n)/((4-5*n)*(16-16*n+3*n^2)*_ +-- x^2)+15/2*a^3*n^3*hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((4-5*n)*(16-16*n+3*n^2)*x^2*sqrt(a+b*x^n)) +--E 1006 + +--S 1007 of 1299 +--a0:=integrate(t0,x) +--E 1007 + +--S 1008 of 1299 +--m0:=a0-r0 +--E 1008 + +--S 1009 of 1299 +--d0:=D(m0,x) +--E 1009 + +)clear all + +--S 1010 of 1299 +t0:=x^m/(a+b*x^n)^(1/2) +--R +--R +--R m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1010 + +--S 1011 of 1299 +--r0:=x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/((1+m)*sqrt(a+b*x^n)) +--E 1011 + +--S 1012 of 1299 +--a0:=integrate(t0,x) +--E 1012 + +--S 1013 of 1299 +--m0:=a0-r0 +--E 1013 + +--S 1014 of 1299 +--d0:=D(m0,x) +--E 1014 + +)clear all + +--S 1015 of 1299 +t0:=x/(a+b*x^n)^(1/2) +--R +--R +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1015 + +--S 1016 of 1299 +--r0:=1/2*x^2*hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/sqrt(a+b*x^n) +--E 1016 + +--S 1017 of 1299 +--a0:=integrate(t0,x) +--E 1017 + +--S 1018 of 1299 +--m0:=a0-r0 +--E 1018 + +--S 1019 of 1299 +--d0:=D(m0,x) +--E 1019 + +)clear all + +--S 1020 of 1299 +t0:=1/(a+b*x^n)^(1/2) +--R +--R +--R 1 +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1020 + +--S 1021 of 1299 +--r0:=x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/sqrt(a+b*x^n) +--E 1021 + +--S 1022 of 1299 +--a0:=integrate(t0,x) +--E 1022 + +--S 1023 of 1299 +--m0:=a0-r0 +--E 1023 + +--S 1024 of 1299 +--d0:=D(m0,x) +--E 1024 + +)clear all + +--S 1025 of 1299 +t0:=1/(x*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | n +--R x\|b x + a +--R Type: Expression(Integer) +--E 1025 + +--S 1026 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a)) +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 1026 + +--S 1027 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R [-------------------------------------------------------, +--R +-+ +--R n\|a +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R 2atan(-------------------------) +--R a +--R - --------------------------------] +--R +---+ +--R n\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 1027 + +--S 1028 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--------+ +--R | n log(x) +-+ n log(x) +-+ | n +--R - 2a\|b %e + a + b\|a %e + 2a\|a \|b x + a +--R log(--------------------------------------------------) + 2atanh(-----------) +--R n log(x) +-+ +--R %e \|a +--R ----------------------------------------------------------------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 1028 + +--S 1029 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1029 + +--S 1030 of 1299 +m0b:=a0.2-r0 +--R +--R +--R +----------------+ +--------+ +--R +---+ | n log(x) | n +--R +-+ \|- a \|b %e + a +---+ \|b x + a +--R - 2\|a atan(-------------------------) + 2\|- a atanh(-----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------------------------ +--R +---+ +-+ +--R n\|- a \|a +--R Type: Expression(Integer) +--E 1030 + +--S 1031 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1031 + +)clear all + +--S 1032 of 1299 +t0:=1/(x^2*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 2 | n +--R x \|b x + a +--R Type: Expression(Integer) +--E 1032 + +--S 1033 of 1299 +--r0:=-hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(x*sqrt(a+b*x^n)) +--E 1033 + +--S 1034 of 1299 +--a0:=integrate(t0,x) +--E 1034 + +--S 1035 of 1299 +--m0:=a0-r0 +--E 1035 + +--S 1036 of 1299 +--d0:=D(m0,x) +--E 1036 + +)clear all + +--S 1037 of 1299 +t0:=1/(x^3*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------- +--R +--------+ +--R 3 | n +--R x \|b x + a +--R Type: Expression(Integer) +--E 1037 + +--S 1038 of 1299 +--r0:=-1/2*hypergeometric(1/2,(-2)/n,(-2+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(x^2*sqrt(a+b*x^n)) +--E 1038 + +--S 1039 of 1299 +--a0:=integrate(t0,x) +--E 1039 + +--S 1040 of 1299 +--m0:=a0-r0 +--E 1040 + +--S 1041 of 1299 +--d0:=D(m0,x) +--E 1041 + +)clear all + +--S 1042 of 1299 +t0:=x^m/(a+b*x^n)^(3/2) +--R +--R +--R m +--R x +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1042 + +--S 1043 of 1299 +--r0:=2*x^(1+m)/(a*n*sqrt(a+b*x^n))-(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a*(1+m)*n*sqrt(a+b*x^n)) +--E 1043 + +--S 1044 of 1299 +--a0:=integrate(t0,x) +--E 1044 + +--S 1045 of 1299 +--m0:=a0-r0 +--E 1045 + +--S 1046 of 1299 +--d0:=D(m0,x) +--E 1046 + +)clear all + +--S 1047 of 1299 +t0:=x/(a+b*x^n)^(3/2) +--R +--R +--R x +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1047 + +--S 1048 of 1299 +--r0:=2*x^2/(a*n*sqrt(a+b*x^n))-1/2*(4-n)*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*n*sqrt(a+b*x^n)) +--E 1048 + +--S 1049 of 1299 +--a0:=integrate(t0,x) +--E 1049 + +--S 1050 of 1299 +--m0:=a0-r0 +--E 1050 + +--S 1051 of 1299 +--d0:=D(m0,x) +--E 1051 + +)clear all + +--S 1052 of 1299 +t0:=1/(a+b*x^n)^(3/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +--------+ +--R n | n +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1052 + +--S 1053 of 1299 +--r0:=2*x/(a*n*sqrt(a+b*x^n))-(2-n)*x*_ +-- hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*n*sqrt(a+b*x^n)) +--E 1053 + +--S 1054 of 1299 +--a0:=integrate(t0,x) +--E 1054 + +--S 1055 of 1299 +--m0:=a0-r0 +--E 1055 + +--S 1056 of 1299 +--d0:=D(m0,x) +--E 1056 + +)clear all + +--S 1057 of 1299 +t0:=1/(x*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) ------------------------- +--R +--------+ +--R n | n +--R (b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1057 + +--S 1058 of 1299 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)+2/(a*n*sqrt(a+b*x^n)) +--R +--R +--R +--------+ +--R +--------+ | n +--R | n \|b x + a +-+ +--R - 2\|b x + a atanh(-----------) + 2\|a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R +--------+ +--R +-+ | n +--R a n\|a \|b x + a +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +-+ +--R 2\|a +--R / +--R +----------------+ +--R +-+ | n log(x) +--R a n\|a \|b %e + a +--R , +--R +----------------+ +--R +----------------+ +---+ | n log(x) +--R | n log(x) \|- a \|b %e + a +---+ +--R - 2\|b %e + a atan(-------------------------) + 2\|- a +--R a +--R ---------------------------------------------------------------] +--R +----------------+ +--R +---+ | n log(x) +--R a n\|- a \|b %e + a +--R Type: Union(List(Expression(Integer)),...) +--E 1059 + +--S 1060 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +----------------+ +--R | n | n log(x) +--R \|b x + a \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +--------+ | n +----------------+ +--R | n \|b x + a +-+ | n log(x) +--R (2\|b x + a atanh(-----------) - 2\|a )\|b %e + a +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ | n +--R 2\|a \|b x + a +--R / +--R +--------+ +----------------+ +--R +-+ | n | n log(x) +--R a n\|a \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1061 + +--S 1062 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +--------+ +----------------+ +---+ | n log(x) +--R +-+ | n | n log(x) \|- a \|b %e + a +--R - 2\|a \|b x + a \|b %e + a atan(-------------------------) +--R a +--R + +--R +--------+ +--R +--------+ | n +----------------+ +--R +---+ | n \|b x + a +---+ +-+ | n log(x) +--R (2\|- a \|b x + a atanh(-----------) - 2\|- a \|a )\|b %e + a +--R +-+ +--R \|a +--R + +--R +--------+ +--R +---+ +-+ | n +--R 2\|- a \|a \|b x + a +--R / +--R +--------+ +----------------+ +--R +---+ +-+ | n | n log(x) +--R a n\|- a \|a \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1062 + +--S 1063 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1063 + +)clear all + +--S 1064 of 1299 +t0:=1/(x^2*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R 2 n 2 | n +--R (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1064 + +--S 1065 of 1299 +--r0:=2/(a*n*x*sqrt(a+b*x^n))-(2+n)*hypergeometric(1/2,(-1)/n,_ +-- (-1+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a*n*x*sqrt(a+b*x^n)) +--E 1065 + +--S 1066 of 1299 +--a0:=integrate(t0,x) +--E 1066 + +--S 1067 of 1299 +--m0:=a0-r0 +--E 1067 + +--S 1068 of 1299 +--d0:=D(m0,x) +--E 1068 + +)clear all + +--S 1069 of 1299 +t0:=1/(x^3*(a+b*x^n)^(3/2)) +--R +--R +--R 1 +--R (1) -------------------------- +--R +--------+ +--R 3 n 3 | n +--R (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1069 + +--S 1070 of 1299 +--r0:=2/(a*n*x^2*sqrt(a+b*x^n))-1/2*(4+n)*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a*n*x^2*sqrt(a+b*x^n)) +--E 1070 + +--S 1071 of 1299 +--a0:=integrate(t0,x) +--E 1071 + +--S 1072 of 1299 +--m0:=a0-r0 +--E 1072 + +--S 1073 of 1299 +--d0:=D(m0,x) +--E 1073 + +)clear all + +--S 1074 of 1299 +t0:=x^m/(a+b*x^n)^(5/2) +--R +--R +--R m +--R x +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1074 + +--S 1075 of 1299 +--r0:=2/3*x^(1+m)/(a*n*(a+b*x^n)^(3/2))-2/3*(2+2*m-3*n)*x^(1+m)/_ +-- (a^2*n^2*sqrt(a+b*x^n))+1/3*(2+2*m-3*n)*(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*(1+m)*n^2*sqrt(a+b*x^n)) +--E 1075 + +--S 1076 of 1299 +--a0:=integrate(t0,x) +--E 1076 + +--S 1077 of 1299 +--m0:=a0-r0 +--E 1077 + +--S 1078 of 1299 +--d0:=D(m0,x) +--E 1078 + +)clear all + +--S 1079 of 1299 +t0:=x/(a+b*x^n)^(5/2) +--R +--R +--R x +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1079 + +--S 1080 of 1299 +--r0:=2/3*x^2/(a*n*(a+b*x^n)^(3/2))-2/3*(4-3*n)*x^2/(a^2*n^2*_ +-- sqrt(a+b*x^n))+1/6*(4-3*n)*(4-n)*x^2*_ +-- hypergeometric(1/2,2/n,(2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a^2*n^2*sqrt(a+b*x^n)) +--E 1080 + +--S 1081 of 1299 +--a0:=integrate(t0,x) +--E 1081 + +--S 1082 of 1299 +--m0:=a0-r0 +--E 1082 + +--S 1083 of 1299 +--d0:=D(m0,x) +--E 1083 + +)clear all + +--S 1084 of 1299 +t0:=1/(a+b*x^n)^(5/2) +--R +--R +--R 1 +--R (1) ----------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 1084 + +--S 1085 of 1299 +--r0:=2/3*x/(a*n*(a+b*x^n)^(3/2))-2/3*(2-3*n)*x/(a^2*n^2*sqrt(a+b*x^n))+_ +-- 1/3*(2-3*n)*(2-n)*x*hypergeometric(1/2,1/n,1+1/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*n^2*sqrt(a+b*x^n)) +--E 1085 + +--S 1086 of 1299 +--a0:=integrate(t0,x) +--E 1086 + +--S 1087 of 1299 +--m0:=a0-r0 +--E 1087 + +--S 1088 of 1299 +--d0:=D(m0,x) +--E 1088 + +)clear all + +--S 1089 of 1299 +t0:=1/(x*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ---------------------------------------- +--R +--------+ +--R 2 n 2 n 2 | n +--R (b x (x ) + 2a b x x + a x)\|b x + a +--R Type: Expression(Integer) +--E 1089 + +--S 1090 of 1299 +r0:=2/3/(a*n*(a+b*x^n)^(3/2))-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)+2/(a^2*n*sqrt(a+b*x^n)) +--R +--R +--R +--------+ +--R +--------+ | n +--R n | n \|b x + a n +-+ +--R (- 6b x - 6a)\|b x + a atanh(-----------) + (6b x + 8a)\|a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R +--------+ +--R 2 n 3 +-+ | n +--R (3a b n x + 3a n)\|a \|b x + a +--R Type: Expression(Integer) +--E 1090 + +--S 1091 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R n log(x) | n log(x) +--R (3b %e + 3a)\|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +-+ n log(x) +-+ +--R 6b\|a %e + 8a\|a +--R / +--R +----------------+ +--R 2 +-+ n log(x) 3 +-+ | n log(x) +--R (3a b n\|a %e + 3a n\|a )\|b %e + a +--R , +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (- 6b %e - 6a)\|b %e + a +--R * +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R atan(-------------------------) +--R a +--R + +--R +---+ n log(x) +---+ +--R 6b\|- a %e + 8a\|- a +--R / +--R +----------------+ +--R 2 +---+ n log(x) 3 +---+ | n log(x) +--R (3a b n\|- a %e + 3a n\|- a )\|b %e + a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 1091 + +--S 1092 of 1299 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((3b x + 3a b)%e + 3a b x + 3a )\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R 2 n n log(x) n 2 | n +--R ((6b x + 6a b)%e + 6a b x + 6a )\|b x + a +--R * +--R +--------+ +--R | n +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 n +-+ n log(x) n 2 +-+ +--R (- 6b x - 8a b)\|a %e + (- 6a b x - 8a )\|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 2 n +-+ n log(x) n 2 +-+ | n +--R ((6b x + 6a b)\|a %e + (8a b x + 8a )\|a )\|b x + a +--R / +--R +--------+ +--R 2 2 n 3 +-+ n log(x) 3 n 4 +-+ | n +--R ((3a b n x + 3a b n)\|a %e + (3a b n x + 3a n)\|a )\|b x + a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R Type: Expression(Integer) +--E 1092 + +--S 1093 of 1299 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1093 + +--S 1094 of 1299 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +--------+ +--R 2 n +-+ n log(x) n 2 +-+ | n +--R ((- 6b x - 6a b)\|a %e + (- 6a b x - 6a )\|a )\|b x + a +--R * +--R +----------------+ +--R +----------------+ +---+ | n log(x) +--R | n log(x) \|- a \|b %e + a +--R \|b %e + a atan(-------------------------) +--R a +--R + +--R +--------+ +--R 2 n +---+ n log(x) n 2 +---+ | n +--R ((6b x + 6a b)\|- a %e + (6a b x + 6a )\|- a )\|b x + a +--R * +--R +--------+ +--R | n +--R \|b x + a +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R 2 n +---+ +-+ n log(x) n 2 +---+ +-+ +--R (- 6b x - 8a b)\|- a \|a %e + (- 6a b x - 8a )\|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 2 n +---+ +-+ n log(x) n 2 +---+ +-+ | n +--R ((6b x + 6a b)\|- a \|a %e + (8a b x + 8a )\|- a \|a )\|b x + a +--R / +--R 2 2 n 3 +---+ +-+ n log(x) 3 n 4 +---+ +-+ +--R ((3a b n x + 3a b n)\|- a \|a %e + (3a b n x + 3a n)\|- a \|a ) +--R * +--R +--------+ +----------------+ +--R | n | n log(x) +--R \|b x + a \|b %e + a +--R Type: Expression(Integer) +--E 1094 + +--S 1095 of 1299 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1095 + +)clear all + +--S 1096 of 1299 +t0:=1/(x^2*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R +--------+ +--R 2 2 n 2 2 n 2 2 | n +--R (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1096 + +--S 1097 of 1299 +--r0:=2/3/(a*n*x*(a+b*x^n)^(3/2))+2/3*(2+3*n)/(a^2*n^2*x*sqrt(a+b*x^n))-_ +-- 1/3*(2+n)*(2+3*n)*hypergeometric(1/2,(-1)/n,(-1+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a^2*n^2*x*sqrt(a+b*x^n)) +--E 1097 + +--S 1098 of 1299 +--a0:=integrate(t0,x) +--E 1098 + +--S 1099 of 1299 +--m0:=a0-r0 +--E 1099 + +--S 1100 of 1299 +--d0:=D(m0,x) +--E 1100 + +)clear all + +--S 1101 of 1299 +t0:=1/(x^3*(a+b*x^n)^(5/2)) +--R +--R +--R 1 +--R (1) ----------------------------------------- +--R +--------+ +--R 2 3 n 2 3 n 2 3 | n +--R (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 1101 + +--S 1102 of 1299 +--r0:=2/3/(a*n*x^2*(a+b*x^n)^(3/2))+2/3*(4+3*n)/(a^2*n^2*x^2*_ +-- sqrt(a+b*x^n))-1/6*(4+n)*(4+3*n)*hypergeometric(1/2,(-2)/n,_ +-- (-2+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a^2*n^2*x^2*sqrt(a+b*x^n)) +--E 1102 + +--S 1103 of 1299 +--a0:=integrate(t0,x) +--E 1103 + +--S 1104 of 1299 +--m0:=a0-r0 +--E 1104 + +--S 1105 of 1299 +--d0:=D(m0,x) +--E 1105 + +)clear all + +--S 1106 of 1299 +t0:=x^(3+2*n)/sqrt(a+b*x^n) +--R +--R +--R 2n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1299 +--r0:=-4*a*(4+n)*x^4*sqrt(a+b*x^n)/(b^2*(8+n)*(8+3*n))+2*x^(4+n)*_ +-- sqrt(a+b*x^n)/(b*(8+3*n))+4*a^2*(4+n)*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (b^2*(8+n)*(8+3*n)*sqrt(a+b*x^n)) +--E 1107 + +--S 1108 of 1299 +--a0:=integrate(t0,x) +--E 1108 + +--S 1109 of 1299 +--m0:=a0-r0 +--E 1109 + +--S 1110 of 1299 +--d0:=D(m0,x) +--E 1110 + +)clear all + +--S 1111 of 1299 +t0:=x^(3+n)/sqrt(a+b*x^n) +--R +--R +--R n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1299 +--r0:=2*x^4*sqrt(a+b*x^n)/(b*(8+n))-2*a*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b*(8+n)*sqrt(a+b*x^n)) +--E 1112 + +--S 1113 of 1299 +--a0:=integrate(t0,x) +--E 1113 + +--S 1114 of 1299 +--m0:=a0-r0 +--E 1114 + +--S 1115 of 1299 +--d0:=D(m0,x) +--E 1115 + +)clear all + +--S 1116 of 1299 +t0:=x^(3-n)/sqrt(a+b*x^n) +--R +--R +--R - n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1299 +--r0:=x^(4-n)*sqrt(a+b*x^n)/(a*(4-n))-1/8*b*(8-n)*x^4*_ +-- hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a*(4-n)*sqrt(a+b*x^n)) +--E 1117 + +--S 1118 of 1299 +--a0:=integrate(t0,x) +--E 1118 + +--S 1119 of 1299 +--m0:=a0-r0 +--E 1119 + +--S 1120 of 1299 +--d0:=D(m0,x) +--E 1120 + +)clear all + +--S 1121 of 1299 +t0:=x^(3-2*n)/sqrt(a+b*x^n) +--R +--R +--R - 2n + 3 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1299 +--r0:=1/2*x^(4-2*n)*sqrt(a+b*x^n)/(a*(2-n))-1/4*b*(8-3*n)*x^(4-n)*_ +-- sqrt(a+b*x^n)/(a^2*(2-n)*(4-n))+1/32*b^2*(8-3*n)*(8-n)*_ +-- x^4*hypergeometric(1/2,4/n,(4+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/_ +-- (a^2*(2-n)*(4-n)*sqrt(a+b*x^n)) +--E 1122 + +--S 1123 of 1299 +--a0:=integrate(t0,x) +--E 1123 + +--S 1124 of 1299 +--m0:=a0-r0 +--E 1124 + +--S 1125 of 1299 +--d0:=D(m0,x) +--E 1125 + +)clear all + +--S 1126 of 1299 +t0:=x^(m+2*n)/sqrt(a+b*x^n) +--R +--R +--R 2n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1299 +--r0:=-4*a*(1+m+n)*x^(1+m)*sqrt(a+b*x^n)/(b^2*(2+2*m+n)*(2+2*m+3*n))+_ +-- 2*x^(1+m+n)*sqrt(a+b*x^n)/(b*(2+2*m+3*n))+4*a^2*(1+m+n)*_ +-- x^(1+m)*hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b^2*(2+2*m+n)*(2+2*m+3*n)*sqrt(a+b*x^n)) +--E 1127 + +--S 1128 of 1299 +--a0:=integrate(t0,x) +--E 1128 + +--S 1129 of 1299 +--m0:=a0-r0 +--E 1129 + +--S 1130 of 1299 +--d0:=D(m0,x) +--E 1130 + +)clear all + +--S 1131 of 1299 +t0:=x^(m+n)/sqrt(a+b*x^n) +--R +--R +--R n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1299 +--r0:=2*x^(1+m)*sqrt(a+b*x^n)/(b*(2+2*m+n))-2*a*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(b*(2+2*m+n)*sqrt(a+b*x^n)) +--E 1132 + +--S 1133 of 1299 +--a0:=integrate(t0,x) +--E 1133 + +--S 1134 of 1299 +--m0:=a0-r0 +--E 1134 + +--S 1135 of 1299 +--d0:=D(m0,x) +--E 1135 + +)clear all + +--S 1136 of 1299 +t0:=x^(m-n)/sqrt(a+b*x^n) +--R +--R +--R - n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1299 +--r0:=x^(1+m-n)*sqrt(a+b*x^n)/(a*(1+m-n))-1/2*b*(2+2*m-n)*x^(1+m)*_ +-- hypergeometric(1/2,(1+m)/n,(1+m+n)/n,-b*x^n/a)*_ +-- sqrt((a+b*x^n)/a)/(a*(1+m)*(1+m-n)*sqrt(a+b*x^n)) +--E 1137 + +--S 1138 of 1299 +--a0:=integrate(t0,x) +--E 1138 + +--S 1139 of 1299 +--m0:=a0-r0 +--E 1139 + +--S 1140 of 1299 +--d0:=D(m0,x) +--E 1140 + +)clear all + +--S 1141 of 1299 +t0:=x^(m-2*n)/sqrt(a+b*x^n) +--R +--R +--R - 2n + m +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1299 +--r0:=x^(1+m-2*n)*sqrt(a+b*x^n)/(a*(1+m-2*n))-1/2*b*(2+2*m-3*n)*_ +-- x^(1+m-n)*sqrt(a+b*x^n)/(a^2*(1+m-2*n)*(1+m-n))+1/4*b^2*_ +-- (2+2*m-3*n)*(2+2*m-n)*x^(1+m)*hypergeometric(1/2,(1+m)/n,_ +-- (1+m+n)/n,-b*x^n/a)*sqrt((a+b*x^n)/a)/(a^2*(1+m)*(1+m-2*n)*_ +-- (1+m-n)*sqrt(a+b*x^n)) +--E 1142 + +--S 1143 of 1299 +--a0:=integrate(t0,x) +--E 1143 + +--S 1144 of 1299 +--m0:=a0-r0 +--E 1144 + +--S 1145 of 1299 +--d0:=D(m0,x) +--E 1145 + +)clear all + +--S 1146 of 1299 +t0:=-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^n) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (1) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1299 +r0a:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1147 + +--S 1148 of 1299 +r0b:=-b*x^(m+n)/(a*sqrt(a+b*x^n))+x^m*sqrt(a+b*x^n)/a +--R +--R +--R n + m m n m +--R - b x + b x x + a x +--R (3) -------------------------- +--R +--------+ +--R | n +--R a\|b x + a +--R Type: Expression(Integer) +--E 1148 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1149 of 1299 +--a0:=integrate(t0,x) +--E 1149 + +--S 1150 of 1299 +--m0a:=a0-r0a +--E 1150 + +--S 1151 of 1299 +--d0a:=D(m0a,x) +--E 1151 + +--S 1152 of 1299 +--m0b:=a0-r0b +--E 1152 + +--S 1153 of 1299 +--d0b:=D(m0b,x) +--E 1153 + +)clear all + +--S 1154 of 1299 +t0:=x^m/sqrt(a+b*x^(-2+m)) +--R +--R +--R m +--R x +--R (1) --------------- +--R +------------+ +--R | m - 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1154 + +--S 1155 of 1299 +--r0:=2*x^(1+m)*hypergeometric(1/2,1/2*(4+m)/(2-m),1/2*(8-m)/(2-m),_ +-- -a*x^(2-m)/b)*sqrt((b+a*x^(2-m))/b)/((4+m)*sqrt(a+b*x^(-2+m))) +--E 1155 + +--S 1156 of 1299 +--a0:=integrate(t0,x) +--E 1156 + +--S 1157 of 1299 +--m0:=a0-r0 +--E 1157 + +--S 1158 of 1299 +--d0:=D(m0,x) +--E 1158 + +)clear all + +--S 1159 of 1299 +t0:=x^m/sqrt(a+b*x^(2-m)) +--R +--R +--R m +--R x +--R (1) ----------------- +--R +--------------+ +--R | - m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 1159 + +--S 1160 of 1299 +--r0:=x^(1+m)*sqrt(a+b*x^(2-m))/(a*(1+m))-1/6*b*(4+m)*x^3*_ +-- hypergeometric(1/2,3/(2-m),(5-m)/(2-m),-b*x^(2-m)/a)*_ +-- sqrt((a+b*x^(2-m))/a)/(a*(1+m)*sqrt(a+b*x^(2-m))) +--E 1160 + +--S 1161 of 1299 +--a0:=integrate(t0,x) +--E 1161 + +--S 1162 of 1299 +--m0:=a0-r0 +--E 1162 + +--S 1163 of 1299 +--d0:=D(m0,x) +--E 1163 + +)clear all + +--S 1164 of 1299 +t0:=6*a*x^2/(b*(4+m)*sqrt(a+b*x^(-2+m)))+x^m/sqrt(a+b*x^(-2+m)) +--R +--R +--R m 2 +--R (b m + 4b)x + 6a x +--R (1) ------------------------- +--R +------------+ +--R | m - 2 +--R (b m + 4b)\|b x + a +--R Type: Expression(Integer) +--E 1164 + +--S 1165 of 1299 +r0a:=2*x^3*sqrt(a+b*x^(-2+m))/(b*(4+m)) +--R +--R +--R +------------+ +--R 3 | m - 2 +--R 2x \|b x + a +--R (2) ------------------ +--R b m + 4b +--R Type: Expression(Integer) +--E 1165 + +--S 1166 of 1299 +r0b:=2*x^(1+m)*(b+a*x^(2-m))/(b*(4+m)*sqrt(a+b*x^(-2+m))) +--R +--R +--R - m + 2 m + 1 +--R (2a x + 2b)x +--R (3) ------------------------- +--R +------------+ +--R | m - 2 +--R (b m + 4b)\|b x + a +--R Type: Expression(Integer) +--E 1166 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1167 of 1299 +--a0:=integrate(t0,x) +--E 1167 + +--S 1168 of 1299 +--m0a:=a0-r0a +--E 1168 + +--S 1169 of 1299 +--d0a:=D(m0a,x) +--E 1169 + +--S 1170 of 1299 +--m0b:=a0-r0b +--E 1170 + +--S 1171 of 1299 +--d0b:=D(m0b,x) +--E 1171 + +)clear all + +--S 1172 of 1299 +t0:=1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(a+b*x^n)^(3/2) +--R +--R +--R m - 1 n m - 1 +--R (- b n + 2b m)x x + 2a m x +--R (1) ------------------------------------ +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1172 + +--S 1173 of 1299 +r0:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1299 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R (m - 1)log(x) | n log(x) +--R x %e \|b %e + a +--R (3) ------------------------------------ +--R n log(x) +--R b %e + a +--R Type: Union(Expression(Integer),...) +--E 1174 + +--S 1175 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------+ +----------------+ +--R (m - 1)log(x) | n | n log(x) m n log(x) m +--R x %e \|b x + a \|b %e + a - b x %e - a x +--R ----------------------------------------------------------------------- +--R +--------+ +--R n log(x) | n +--R (b %e + a)\|b x + a +--R Type: Expression(Integer) +--E 1175 + +--S 1176 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1176 + +)clear all + +--S 1177 of 1299 +t0:=-1/2*b*n*x^(-1+m+n)/(a+b*x^n)^(3/2)+m*x^(-1+m)/sqrt(a+b*x^n) +--R +--R +--R n + m - 1 m - 1 n m - 1 +--R - b n x + 2b m x x + 2a m x +--R (1) ---------------------------------------------- +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R Type: Expression(Integer) +--E 1177 + +--S 1178 of 1299 +r0a:=x^m/sqrt(a+b*x^n) +--R +--R +--R m +--R x +--R (2) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1299 +r0b:=-b*x^(m+n)/(a*sqrt(a+b*x^n))+x^m*sqrt(a+b*x^n)/a +--R +--R +--R n + m m n m +--R - b x + b x x + a x +--R (3) -------------------------- +--R +--------+ +--R | n +--R a\|b x + a +--R Type: Expression(Integer) +--E 1179 + +-- TPDHERE integrate: implementation incomplete (constant residues) +--S 1180 of 1299 +--a0:=integrate(t0,x) +--E 1180 + +--S 1181 of 1299 +--m0a:=a0-r0a +--E 1181 + +--S 1182 of 1299 +--d0a:=D(m0a,x) +--E 1182 + +--S 1183 of 1299 +--m0b:=a0-r0b +--E 1183 + +--S 1184 of 1299 +--d0b:=D(m0b,x) +--E 1184 + +)clear all + +--S 1185 of 1299 +t0:=(a+b*x^n)^(1/3)/x +--R +--R +--R +--------+ +--R 3| n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 1185 + +--S 1186 of 1299 +r0:=3*(a+b*x^n)^(1/3)/n+a^(1/3)*log(a^(1/3)-(a+b*x^n)^(1/3))/n-_ + 1/2*a^(1/3)*log(a^(2/3)+a^(1/3)*(a+b*x^n)^(1/3)+(a+b*x^n)^(2/3))/n-_ + a^(1/3)*atan((a^(1/3)+2*(a+b*x^n)^(1/3))/(a^(1/3)*sqrt(3)))*sqrt(3)/n +--R +--R +--R (2) +--R +--------+2 +--------+ +--R 3+-+ 3| n 3+-+3| n 3+-+2 +--R - \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| n 3+-+ +--R 3+-+ 3| n 3+-+ +-+3+-+ 2\|b x + a + \|a +--R 2\|a log(- \|b x + a + \|a ) - 2\|3 \|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R 3| n +--R 6\|b x + a +--R / +--R 2n +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+2 +----------------+ +--R 3+-+ 3| n log(x) 3+-+3| n log(x) 3+-+2 +--R - \|a log(\|b %e + a + \|a \|b %e + a + \|a ) +--R + +--R +----------------+ +--R 3+-+ 3| n log(x) 3+-+ +--R 2\|a log(\|b %e + a - \|a ) +--R + +--R +----------------+ +--R 3| n log(x) 3+-+ +----------------+ +--R +-+3+-+ 2\|b %e + a + \|a 3| n log(x) +--R - 2\|3 \|a atan(---------------------------) + 6\|b %e + a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+2 +----------------+ +--R 3+-+ 3| n log(x) 3+-+3| n log(x) 3+-+2 +--R - \|a log(\|b %e + a + \|a \|b %e + a + \|a ) +--R + +--R +----------------+ +--R 3+-+ 3| n log(x) 3+-+ +--R 2\|a log(\|b %e + a - \|a ) +--R + +--R +----------------+ +--R 3| n log(x) 3+-+ +----------------+ +--R +-+3+-+ 2\|b %e + a + \|a 3| n log(x) +--R - 2\|3 \|a atan(---------------------------) + 6\|b %e + a +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+2 +--------+ +--R 3+-+ 3| n 3+-+3| n 3+-+2 +--R \|a log(\|b x + a + \|a \|b x + a + \|a ) +--R + +--R +--------+ +--R +--------+ 3| n 3+-+ +--R 3+-+ 3| n 3+-+ +-+3+-+ 2\|b x + a + \|a +--R - 2\|a log(- \|b x + a + \|a ) + 2\|3 \|a atan(-------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--------+ +--R 3| n +--R - 6\|b x + a +--R / +--R 2n +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n) +--R +--R +--R n 4n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1190 + +--S 1191 of 1299 +r0:=1/4*a*x^(4*n)/n+1/5*b*x^(5*n)/n +--R +--R +--R 5n 4n +--R 4b x + 5a x +--R (2) --------------- +--R 20n +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 5 n log(x) 4 +--R 4b (%e ) + 5a (%e ) +--R (3) ----------------------------------- +--R 20n +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 5 n log(x) 4 5n 4n +--R 4b (%e ) + 5a (%e ) - 4b x - 5a x +--R (4) ----------------------------------------------------- +--R 20n +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1299 +t0:=x^(-1+3*n)*(a+b*x^n) +--R +--R +--R n 3n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1195 + +--S 1196 of 1299 +r0:=1/3*a*x^(3*n)/n+1/4*b*x^(4*n)/n +--R +--R +--R 4n 3n +--R 3b x + 4a x +--R (2) --------------- +--R 12n +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 4 n log(x) 3 +--R 3b (%e ) + 4a (%e ) +--R (3) ----------------------------------- +--R 12n +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 4 n log(x) 3 4n 3n +--R 3b (%e ) + 4a (%e ) - 3b x - 4a x +--R (4) ----------------------------------------------------- +--R 12n +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1299 +t0:=x^(-1+2*n)*(a+b*x^n) +--R +--R +--R n 2n - 1 +--R (1) (b x + a)x +--R Type: Expression(Integer) +--E 1200 + +--S 1201 of 1299 +r0:=1/2*a*x^(2*n)/n+1/3*b*x^(3*n)/n +--R +--R +--R 3n 2n +--R 2b x + 3a x +--R (2) --------------- +--R 6n +--R Type: Expression(Integer) +--E 1201 + +--S 1202 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 3 n log(x) 2 +--R 2b (%e ) + 3a (%e ) +--R (3) ----------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 3 n log(x) 2 3n 2n +--R 2b (%e ) + 3a (%e ) - 2b x - 3a x +--R (4) ----------------------------------------------------- +--R 6n +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1299 +t0:=x^(-1+n)*(a+b*x^n) +--R +--R +--R n - 1 n n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1205 + +--S 1206 of 1299 +r0:=a*x^n/n+1/2*b*x^(2*n)/n +--R +--R +--R 2n n +--R b x + 2a x +--R (2) ------------- +--R 2n +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 2 n log(x) +--R b (%e ) + 2a %e +--R (3) ------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) 2 n log(x) 2n n +--R b (%e ) + 2a %e - b x - 2a x +--R (4) ----------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1299 +t0:=(a+b*x^n)/x +--R +--R +--R n +--R b x + a +--R (1) -------- +--R x +--R Type: Expression(Integer) +--E 1210 + +--S 1211 of 1299 +r0:=b*x^n/n+a*log(x) +--R +--R +--R n +--R b x + a n log(x) +--R (2) ----------------- +--R n +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b %e + a n log(x) +--R (3) ------------------------- +--R n +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R b %e - b x +--R (4) ------------------- +--R n +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1299 +t0:=x^(-1-n)*(a+b*x^n) +--R +--R +--R - n - 1 n - n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1215 + +--S 1216 of 1299 +r0:=-a/(n*x^n)+b*log(x) +--R +--R +--R n +--R b n log(x)x - a +--R (2) ---------------- +--R n +--R n x +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R b n log(x)%e - a +--R (3) ------------------------ +--R n log(x) +--R n %e +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1299 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R a %e - a x +--R (4) ------------------- +--R n n log(x) +--R n x %e +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1299 +t0:=x^(-1-2*n)*(a+b*x^n) +--R +--R +--R - 2n - 1 n - 2n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1220 + +--S 1221 of 1299 +r0:=-1/2*a/(n*x^(2*n))-b/(n*x^n) +--R +--R +--R 2n n +--R - 2b x - a x +--R (2) --------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 2b %e - a +--R (3) ------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1299 +m0:=a0-r0 +--R +--R +--R 2n n n log(x) 2 n 2n n log(x) n 2n +--R (2b x + a x )(%e ) - 2b x x %e - a x x +--R (4) ----------------------------------------------------------- +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1299 +t0:=x^(-1-3*n)*(a+b*x^n) +--R +--R +--R - 3n - 1 n - 3n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1225 + +--S 1226 of 1299 +r0:=-1/3*a/(n*x^(3*n))-1/2*b/(n*x^(2*n)) +--R +--R +--R 3n 2n +--R - 3b x - 2a x +--R (2) ----------------- +--R 2n 3n +--R 6n x x +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 3b %e - 2a +--R (3) -------------------- +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1299 +m0:=a0-r0 +--R +--R +--R 3n 2n n log(x) 3 2n 3n n log(x) 2n 3n +--R (3b x + 2a x )(%e ) - 3b x x %e - 2a x x +--R (4) ---------------------------------------------------------------- +--R 2n 3n n log(x) 3 +--R 6n x x (%e ) +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1299 +t0:=x^(-1-4*n)*(a+b*x^n) +--R +--R +--R - 4n - 1 n - 4n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1230 + +--S 1231 of 1299 +r0:=-1/4*a/(n*x^(4*n))-1/3*b/(n*x^(3*n)) +--R +--R +--R 4n 3n +--R - 4b x - 3a x +--R (2) ----------------- +--R 3n 4n +--R 12n x x +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 4b %e - 3a +--R (3) -------------------- +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1299 +m0:=a0-r0 +--R +--R +--R 4n 3n n log(x) 4 3n 4n n log(x) 3n 4n +--R (4b x + 3a x )(%e ) - 4b x x %e - 3a x x +--R (4) ---------------------------------------------------------------- +--R 3n 4n n log(x) 4 +--R 12n x x (%e ) +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1299 +t0:=x^(-1-5*n)*(a+b*x^n) +--R +--R +--R - 5n - 1 n - 5n - 1 +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 1235 + +--S 1236 of 1299 +r0:=-1/5*a/(n*x^(5*n))-1/4*b/(n*x^(4*n)) +--R +--R +--R 5n 4n +--R - 5b x - 4a x +--R (2) ----------------- +--R 4n 5n +--R 20n x x +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1299 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 5b %e - 4a +--R (3) -------------------- +--R n log(x) 5 +--R 20n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1299 +m0:=a0-r0 +--R +--R +--R 5n 4n n log(x) 5 4n 5n n log(x) 4n 5n +--R (5b x + 4a x )(%e ) - 5b x x %e - 4a x x +--R (4) ---------------------------------------------------------------- +--R 4n 5n n log(x) 5 +--R 20n x x (%e ) +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 4n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1240 + +--S 1241 of 1299 +r0:=1/4*a^2*x^(4*n)/n+2/5*a*b*x^(5*n)/n+1/6*b^2*x^(6*n)/n +--R +--R +--R 2 6n 5n 2 4n +--R 10b x + 24a b x + 15a x +--R (2) ----------------------------- +--R 60n +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 6 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 24a b (%e ) + 15a (%e ) +--R (3) ----------------------------------------------------------- +--R 60n +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 6 n log(x) 5 2 n log(x) 4 2 6n +--R 10b (%e ) + 24a b (%e ) + 15a (%e ) - 10b x +--R + +--R 5n 2 4n +--R - 24a b x - 15a x +--R / +--R 60n +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1299 +t0:=x^(-1+3*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 3n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1245 + +--S 1246 of 1299 +r0:=1/3*a^2*x^(3*n)/n+1/2*a*b*x^(4*n)/n+1/5*b^2*x^(5*n)/n +--R +--R +--R 2 5n 4n 2 3n +--R 6b x + 15a b x + 10a x +--R (2) ---------------------------- +--R 30n +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 5 n log(x) 4 2 n log(x) 3 +--R 6b (%e ) + 15a b (%e ) + 10a (%e ) +--R (3) ---------------------------------------------------------- +--R 30n +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 5 n log(x) 4 2 n log(x) 3 2 5n +--R 6b (%e ) + 15a b (%e ) + 10a (%e ) - 6b x +--R + +--R 4n 2 3n +--R - 15a b x - 10a x +--R / +--R 30n +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1299 +t0:=x^(-1+2*n)*(a+b*x^n)^2 +--R +--R +--R 2 n 2 n 2 2n - 1 +--R (1) (b (x ) + 2a b x + a )x +--R Type: Expression(Integer) +--E 1250 + +--S 1251 of 1299 +r0:=1/2*a^2*x^(2*n)/n+2/3*a*b*x^(3*n)/n+1/4*b^2*x^(4*n)/n +--R +--R +--R 2 4n 3n 2 2n +--R 3b x + 8a b x + 6a x +--R (2) -------------------------- +--R 12n +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 4 n log(x) 3 2 n log(x) 2 +--R 3b (%e ) + 8a b (%e ) + 6a (%e ) +--R (3) -------------------------------------------------------- +--R 12n +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 4 n log(x) 3 2 n log(x) 2 2 4n +--R 3b (%e ) + 8a b (%e ) + 6a (%e ) - 3b x +--R + +--R 3n 2 2n +--R - 8a b x - 6a x +--R / +--R 12n +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1299 +t0:=x^(-1+n)*(a+b*x^n)^2 +--R +--R +--R 2 n - 1 n 2 n - 1 n 2 n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1255 + +--S 1256 of 1299 +r0:=1/3*(a+b*x^n)^3/(b*n) +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (2) ----------------------------------- +--R 3b n +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 3 n log(x) 2 2 n log(x) +--R b (%e ) + 3a b (%e ) + 3a %e +--R (3) ---------------------------------------------------- +--R 3n +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 n 3 +--R b (%e ) + 3a b (%e ) + 3a b %e - b (x ) +--R + +--R 2 n 2 2 n 3 +--R - 3a b (x ) - 3a b x - a +--R / +--R 3b n +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1299 +t0:=(a+b*x^n)^2/x +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R (1) ---------------------- +--R x +--R Type: Expression(Integer) +--E 1260 + +--S 1261 of 1299 +r0:=2*a*b*x^n/n+1/2*b^2*x^(2*n)/n+a^2*log(x) +--R +--R +--R 2 2n n 2 +--R b x + 4a b x + 2a n log(x) +--R (2) ----------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 4a b %e + 2a n log(x) +--R (3) ----------------------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n log(x) 2 n log(x) 2 2n n +--R b (%e ) + 4a b %e - b x - 4a b x +--R (4) --------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1299 +t0:=x^(-1-n)*(a+b*x^n)^2 +--R +--R +--R 2 - n - 1 n 2 - n - 1 n 2 - n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1265 + +--S 1266 of 1299 +r0:=-a^2/(n*x^n)+b^2*x^n/n+2*a*b*log(x) +--R +--R +--R 2 n 2 n 2 +--R b (x ) + 2a b n log(x)x - a +--R (2) ------------------------------ +--R n +--R n x +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R b (%e ) + 2a b n log(x)%e - a +--R (3) ---------------------------------------------- +--R n log(x) +--R n %e +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1299 +m0:=a0-r0 +--R +--R +--R 2 n n log(x) 2 2 n 2 2 n log(x) 2 n +--R b x (%e ) + (- b (x ) + a )%e - a x +--R (4) ----------------------------------------------------- +--R n n log(x) +--R n x %e +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1299 +t0:=x^(-1-2*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 2n - 1 n 2 - 2n - 1 n 2 - 2n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1270 + +--S 1271 of 1299 +r0:=-1/2*a^2/(n*x^(2*n))-2*a*b/(n*x^n)+b^2*log(x) +--R +--R +--R 2 n 2n 2 n +--R (2b n log(x)x - 4a b)x - a x +--R (2) -------------------------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) - 4a b %e - a +--R (3) ----------------------------------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1299 +m0:=a0-r0 +--R +--R +--R 2n 2 n n log(x) 2 n 2n n log(x) 2 n 2n +--R (4a b x + a x )(%e ) - 4a b x x %e - a x x +--R (4) --------------------------------------------------------------- +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1299 +t0:=x^(-1-3*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 3n - 1 n 2 - 3n - 1 n 2 - 3n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1275 + +--S 1276 of 1299 +r0:=-1/3*(a+b*x^n)^3/(a*n*x^(3*n)) +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R - b (x ) - 3a b (x ) - 3a b x - a +--R (2) ------------------------------------- +--R 3n +--R 3a n x +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 3b (%e ) - 3a b %e - a +--R (3) ----------------------------------------- +--R n log(x) 3 +--R 3n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 3 2 n 2 2 n 3 n log(x) 3 +--R (b (x ) + 3a b (x ) + 3a b x + a )(%e ) +--R + +--R 2 3n n log(x) 2 2 3n n log(x) 3 3n +--R - 3a b x (%e ) - 3a b x %e - a x +--R / +--R 3n n log(x) 3 +--R 3a n x (%e ) +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1299 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1299 +t0:=x^(-1-4*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 4n - 1 n 2 - 4n - 1 n 2 - 4n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1280 + +--S 1281 of 1299 +r0:=-1/4*a^2/(n*x^(4*n))-2/3*a*b/(n*x^(3*n))-1/2*b^2/(n*x^(2*n)) +--R +--R +--R 2 3n 2n 4n 2 2n 3n +--R (- 6b x - 8a b x )x - 3a x x +--R (2) ------------------------------------ +--R 2n 3n 4n +--R 12n x x x +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 6b (%e ) - 8a b %e - 3a +--R (3) ------------------------------------------ +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3n 2n 4n 2 2n 3n n log(x) 4 +--R ((6b x + 8a b x )x + 3a x x )(%e ) +--R + +--R 2 2n 3n 4n n log(x) 2 2n 3n 4n n log(x) 2 2n 3n 4n +--R - 6b x x x (%e ) - 8a b x x x %e - 3a x x x +--R / +--R 2n 3n 4n n log(x) 4 +--R 12n x x x (%e ) +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1299 +t0:=x^(-1-5*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 5n - 1 n 2 - 5n - 1 n 2 - 5n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1285 + +--S 1286 of 1299 +r0:=-1/5*a^2/(n*x^(5*n))-1/2*a*b/(n*x^(4*n))-1/3*b^2/(n*x^(3*n)) +--R +--R +--R 2 4n 3n 5n 2 3n 4n +--R (- 10b x - 15a b x )x - 6a x x +--R (2) -------------------------------------- +--R 3n 4n 5n +--R 30n x x x +--R Type: Expression(Integer) +--E 1286 + +--S 1287 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 10b (%e ) - 15a b %e - 6a +--R (3) -------------------------------------------- +--R n log(x) 5 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4n 3n 5n 2 3n 4n n log(x) 5 +--R ((10b x + 15a b x )x + 6a x x )(%e ) +--R + +--R 2 3n 4n 5n n log(x) 2 3n 4n 5n n log(x) 2 3n 4n 5n +--R - 10b x x x (%e ) - 15a b x x x %e - 6a x x x +--R / +--R 3n 4n 5n n log(x) 5 +--R 30n x x x (%e ) +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1299 +t0:=x^(-1-6*n)*(a+b*x^n)^2 +--R +--R +--R 2 - 6n - 1 n 2 - 6n - 1 n 2 - 6n - 1 +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 1290 + +--S 1291 of 1299 +r0:=-1/6*a^2/(n*x^(6*n))-2/5*a*b/(n*x^(5*n))-1/4*b^2/(n*x^(4*n)) +--R +--R +--R 2 5n 4n 6n 2 4n 5n +--R (- 15b x - 24a b x )x - 10a x x +--R (2) --------------------------------------- +--R 4n 5n 6n +--R 60n x x x +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1299 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 +--R - 15b (%e ) - 24a b %e - 10a +--R (3) --------------------------------------------- +--R n log(x) 6 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5n 4n 6n 2 4n 5n n log(x) 6 +--R ((15b x + 24a b x )x + 10a x x )(%e ) +--R + +--R 2 4n 5n 6n n log(x) 2 4n 5n 6n n log(x) 2 4n 5n 6n +--R - 15b x x x (%e ) - 24a b x x x %e - 10a x x x +--R / +--R 4n 5n 6n n log(x) 6 +--R 60n x x x (%e ) +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1299 +t0:=x^(-1+4*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 4n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 1295 + +--S 1296 of 1299 +r0:=1/4*a^3*x^(4*n)/n+3/5*a^2*b*x^(5*n)/n+1/2*a*b^2*x^(6*n)/n+1/7*b^3*x^(7*n)/n +--R +--R +--R 3 7n 2 6n 2 5n 3 4n +--R 20b x + 70a b x + 84a b x + 35a x +--R (2) ----------------------------------------- +--R 140n +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1299 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 7 2 n log(x) 6 2 n log(x) 5 +--R 20b (%e ) + 70a b (%e ) + 84a b (%e ) +--R + +--R 3 n log(x) 4 +--R 35a (%e ) +--R / +--R 140n +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1299 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 7 2 n log(x) 6 2 n log(x) 5 +--R 20b (%e ) + 70a b (%e ) + 84a b (%e ) +--R + +--R 3 n log(x) 4 3 7n 2 6n 2 5n 3 4n +--R 35a (%e ) - 20b x - 70a b x - 84a b x - 35a x +--R / +--R 140n +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1299 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} diff --git a/src/input/rich4j.input.pamphlet b/src/input/rich4j.input.pamphlet new file mode 100644 index 0000000..c5f485c --- /dev/null +++ b/src/input/rich4j.input.pamphlet @@ -0,0 +1,26659 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input rich4j.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\verb|x^m (a+b x^n)^p| +There are: +\begin{itemize} +\item 268 integrals in this file. +\item 276 supplied "optimal results". +\item 239 matching answers. +\item 15 cases where Axiom supplied 2 results. +\item 10 cases that Axiom failed to integrate. +\item 3 that contain expressions Axiom does not recognize. +\end{itemize} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f rich4j.output +)spool rich4j.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 3n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 1 + +--S 2 of 1394 +r0:=1/3*a^3*x^(3*n)/n+3/4*a^2*b*x^(4*n)/n+3/5*a*b^2*x^(5*n)/n+1/6*b^3*x^(6*n)/n +--R +--R +--R 3 6n 2 5n 2 4n 3 3n +--R 10b x + 36a b x + 45a b x + 20a x +--R (2) ----------------------------------------- +--R 60n +--R Type: Expression(Integer) +--E 2 + +--S 3 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 6 2 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 36a b (%e ) + 45a b (%e ) +--R + +--R 3 n log(x) 3 +--R 20a (%e ) +--R / +--R 60n +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 6 2 n log(x) 5 2 n log(x) 4 +--R 10b (%e ) + 36a b (%e ) + 45a b (%e ) +--R + +--R 3 n log(x) 3 3 6n 2 5n 2 4n 3 3n +--R 20a (%e ) - 10b x - 36a b x - 45a b x - 20a x +--R / +--R 60n +--R Type: Expression(Integer) +--E 4 + +--S 5 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +)clear all + +--S 6 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^3 +--R +--R +--R 3 n 3 2 n 2 2 n 3 2n - 1 +--R (1) (b (x ) + 3a b (x ) + 3a b x + a )x +--R Type: Expression(Integer) +--E 6 + +--S 7 of 1394 +r0:=-1/4*a*(a+b*x^n)^4/(b^2*n)+1/5*(a+b*x^n)^5/(b^2*n) +--R +--R +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 5 +--R 4b (x ) + 15a b (x ) + 20a b (x ) + 10a b (x ) - a +--R (2) ------------------------------------------------------- +--R 2 +--R 20b n +--R Type: Expression(Integer) +--E 7 + +--S 8 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 5 2 n log(x) 4 2 n log(x) 3 +--R 4b (%e ) + 15a b (%e ) + 20a b (%e ) +--R + +--R 3 n log(x) 2 +--R 10a (%e ) +--R / +--R 20n +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 4b (%e ) + 15a b (%e ) + 20a b (%e ) +--R + +--R 3 2 n log(x) 2 5 n 5 4 n 4 2 3 n 3 3 2 n 2 +--R 10a b (%e ) - 4b (x ) - 15a b (x ) - 20a b (x ) - 10a b (x ) +--R + +--R 5 +--R a +--R / +--R 2 +--R 20b n +--R Type: Expression(Integer) +--E 9 + +--S 10 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 10 + +)clear all + +--S 11 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^3 +--R +--R +--R 3 n - 1 n 3 2 n - 1 n 2 2 n - 1 n 3 n - 1 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 1394 +r0:=1/4*(a+b*x^n)^4/(b*n) +--R +--R +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R b (x ) + 4a b (x ) + 6a b (x ) + 4a b x + a +--R (2) ------------------------------------------------ +--R 4b n +--R Type: Expression(Integer) +--E 12 + +--S 13 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 4 2 n log(x) 3 2 n log(x) 2 3 n log(x) +--R b (%e ) + 4a b (%e ) + 6a b (%e ) + 4a %e +--R ------------------------------------------------------------------------- +--R 4n +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R b (%e ) + 4a b (%e ) + 6a b (%e ) +--R + +--R 3 n log(x) 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R 4a b %e - b (x ) - 4a b (x ) - 6a b (x ) - 4a b x - a +--R / +--R 4b n +--R Type: Expression(Integer) +--E 14 + +--S 15 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 15 + +)clear all + +--S 16 of 1394 +t0:=(a+b*x^n)^3/x +--R +--R +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R (1) ----------------------------------- +--R x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 1394 +r0:=3*a^2*b*x^n/n+3/2*a*b^2*x^(2*n)/n+1/3*b^3*x^(3*n)/n+a^3*log(x) +--R +--R +--R 3 3n 2 2n 2 n 3 +--R 2b x + 9a b x + 18a b x + 6a n log(x) +--R (2) ------------------------------------------ +--R 6n +--R Type: Expression(Integer) +--E 17 + +--S 18 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 9a b (%e ) + 18a b %e + 6a n log(x) +--R (3) ---------------------------------------------------------------------- +--R 6n +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 3n +--R 2b (%e ) + 9a b (%e ) + 18a b %e - 2b x +--R + +--R 2 2n 2 n +--R - 9a b x - 18a b x +--R / +--R 6n +--R Type: Expression(Integer) +--E 19 + +--S 20 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 20 + +)clear all + +--S 21 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^3 +--R +--R +--R 3 - n - 1 n 3 2 - n - 1 n 2 2 - n - 1 n 3 - n - 1 +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 21 + +--S 22 of 1394 +r0:=-a^3/(n*x^n)+3*a*b^2*x^n/n+1/2*b^3*x^(2*n)/n+3*a^2*b*log(x) +--R +--R +--R 3 n 2n 2 n 2 2 n 3 +--R b x x + 6a b (x ) + 6a b n log(x)x - 2a +--R (2) -------------------------------------------- +--R n +--R 2n x +--R Type: Expression(Integer) +--E 22 + +--S 23 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R b (%e ) + 6a b (%e ) + 6a b n log(x)%e - 2a +--R (3) -------------------------------------------------------------------- +--R n log(x) +--R 2n %e +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n n log(x) 3 2 n n log(x) 2 +--R b x (%e ) + 6a b x (%e ) +--R + +--R 3 n 2n 2 n 2 3 n log(x) 3 n +--R (- b x x - 6a b (x ) + 2a )%e - 2a x +--R / +--R n n log(x) +--R 2n x %e +--R Type: Expression(Integer) +--E 24 + +--S 25 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 25 + +)clear all + +--S 26 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 2n - 1 n 3 2 - 2n - 1 n 2 2 - 2n - 1 n 3 - 2n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 26 + +--S 27 of 1394 +r0:=-1/2*a^3/(n*x^(2*n))-3*a^2*b/(n*x^n)+b^3*x^n/n+3*a*b^2*log(x) +--R +--R +--R 3 n 2 2 n 2 2n 3 n +--R (2b (x ) + 6a b n log(x)x - 6a b)x - a x +--R (2) --------------------------------------------- +--R n 2n +--R 2n x x +--R Type: Expression(Integer) +--E 27 + +--S 28 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 6a b n log(x)(%e ) - 6a b %e - a +--R (3) -------------------------------------------------------------------- +--R n log(x) 2 +--R 2n (%e ) +--R Type: Union(Expression(Integer),...) +--E 28 + +--S 29 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n n log(x) 3 3 n 2 2 2n 3 n n log(x) 2 +--R 2b x x (%e ) + ((- 2b (x ) + 6a b)x + a x )(%e ) +--R + +--R 2 n 2n n log(x) 3 n 2n +--R - 6a b x x %e - a x x +--R / +--R n 2n n log(x) 2 +--R 2n x x (%e ) +--R Type: Expression(Integer) +--E 29 + +--S 30 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 30 + +)clear all + +--S 31 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 3n - 1 n 3 2 - 3n - 1 n 2 2 - 3n - 1 n 3 - 3n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 31 + +--S 32 of 1394 +r0:=-1/3*a^3/(n*x^(3*n))-3/2*a^2*b/(n*x^(2*n))-3*a*b^2/(n*x^n)+b^3*log(x) +--R +--R +--R 3 n 2 2n 2 n 3n 3 n 2n +--R ((6b n log(x)x - 18a b )x - 9a b x )x - 2a x x +--R (2) ----------------------------------------------------- +--R n 2n 3n +--R 6n x x x +--R Type: Expression(Integer) +--E 32 + +--S 33 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 6b n log(x)(%e ) - 18a b (%e ) - 9a b %e - 2a +--R (3) ---------------------------------------------------------------------- +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((18a b x + 9a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 18a b x x x (%e ) - 9a b x x x %e - 2a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 6n x x x (%e ) +--R Type: Expression(Integer) +--E 34 + +--S 35 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 35 + +)clear all + +--S 36 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 4n - 1 n 3 2 - 4n - 1 n 2 2 - 4n - 1 n 3 - 4n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 36 + +--S 37 of 1394 +r0:=-1/4*(a+b*x^n)^4/(a*n*x^(4*n)) +--R +--R +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 +--R - b (x ) - 4a b (x ) - 6a b (x ) - 4a b x - a +--R (2) -------------------------------------------------- +--R 4n +--R 4a n x +--R Type: Expression(Integer) +--E 37 + +--S 38 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 4b (%e ) - 6a b (%e ) - 4a b %e - a +--R (3) -------------------------------------------------------------- +--R n log(x) 4 +--R 4n (%e ) +--R Type: Union(Expression(Integer),...) +--E 38 + +--S 39 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 n log(x) 4 +--R (b (x ) + 4a b (x ) + 6a b (x ) + 4a b x + a )(%e ) +--R + +--R 3 4n n log(x) 3 2 2 4n n log(x) 2 3 4n n log(x) +--R - 4a b x (%e ) - 6a b x (%e ) - 4a b x %e +--R + +--R 4 4n +--R - a x +--R / +--R 4n n log(x) 4 +--R 4a n x (%e ) +--R Type: Expression(Integer) +--E 39 + +--S 40 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 40 + +)clear all + +--S 41 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 5n - 1 n 3 2 - 5n - 1 n 2 2 - 5n - 1 n 3 - 5n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 41 + +--S 42 of 1394 +r0:=-1/5*a^3/(n*x^(5*n))-3/4*a^2*b/(n*x^(4*n))-a*b^2/(n*x^(3*n))-_ + 1/2*b^3/(n*x^(2*n)) +--R +--R +--R 3 3n 2 2n 4n 2 2n 3n 5n 3 2n 3n 4n +--R ((- 10b x - 20a b x )x - 15a b x x )x - 4a x x x +--R (2) ------------------------------------------------------------- +--R 2n 3n 4n 5n +--R 20n x x x x +--R Type: Expression(Integer) +--E 42 + +--S 43 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 10b (%e ) - 20a b (%e ) - 15a b %e - 4a +--R (3) ------------------------------------------------------------------ +--R n log(x) 5 +--R 20n (%e ) +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3n 2 2n 4n 2 2n 3n 5n 3 2n 3n 4n +--R (((10b x + 20a b x )x + 15a b x x )x + 4a x x x ) +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 3 2n 3n 4n 5n n log(x) 3 2 2n 3n 4n 5n n log(x) 2 +--R - 10b x x x x (%e ) - 20a b x x x x (%e ) +--R + +--R 2 2n 3n 4n 5n n log(x) 3 2n 3n 4n 5n +--R - 15a b x x x x %e - 4a x x x x +--R / +--R 2n 3n 4n 5n n log(x) 5 +--R 20n x x x x (%e ) +--R Type: Expression(Integer) +--E 44 + +--S 45 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 45 + +)clear all + +--S 46 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 6n - 1 n 3 2 - 6n - 1 n 2 2 - 6n - 1 n 3 - 6n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 46 + +--S 47 of 1394 +r0:=-1/6*a^3/(n*x^(6*n))-3/5*a^2*b/(n*x^(5*n))-3/4*a*b^2/(n*x^(4*n))-_ + 1/3*b^3/(n*x^(3*n)) +--R +--R +--R 3 4n 2 3n 5n 2 3n 4n 6n 3 3n 4n 5n +--R ((- 20b x - 45a b x )x - 36a b x x )x - 10a x x x +--R (2) -------------------------------------------------------------- +--R 3n 4n 5n 6n +--R 60n x x x x +--R Type: Expression(Integer) +--E 47 + +--S 48 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 20b (%e ) - 45a b (%e ) - 36a b %e - 10a +--R (3) ------------------------------------------------------------------- +--R n log(x) 6 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 4n 2 3n 5n 2 3n 4n 6n 3 3n 4n 5n +--R (((20b x + 45a b x )x + 36a b x x )x + 10a x x x ) +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 3 3n 4n 5n 6n n log(x) 3 2 3n 4n 5n 6n n log(x) 2 +--R - 20b x x x x (%e ) - 45a b x x x x (%e ) +--R + +--R 2 3n 4n 5n 6n n log(x) 3 3n 4n 5n 6n +--R - 36a b x x x x %e - 10a x x x x +--R / +--R 3n 4n 5n 6n n log(x) 6 +--R 60n x x x x (%e ) +--R Type: Expression(Integer) +--E 49 + +--S 50 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 50 + +)clear all + +--S 51 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^3 +--R +--R +--R (1) +--R 3 - 7n - 1 n 3 2 - 7n - 1 n 2 2 - 7n - 1 n 3 - 7n - 1 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 51 + +--S 52 of 1394 +r0:=-1/7*a^3/(n*x^(7*n))-1/2*a^2*b/(n*x^(6*n))-3/5*a*b^2/(n*x^(5*n))-_ + 1/4*b^3/(n*x^(4*n)) +--R +--R +--R 3 5n 2 4n 6n 2 4n 5n 7n 3 4n 5n 6n +--R ((- 35b x - 84a b x )x - 70a b x x )x - 20a x x x +--R (2) -------------------------------------------------------------- +--R 4n 5n 6n 7n +--R 140n x x x x +--R Type: Expression(Integer) +--E 52 + +--S 53 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R - 35b (%e ) - 84a b (%e ) - 70a b %e - 20a +--R (3) ------------------------------------------------------------------- +--R n log(x) 7 +--R 140n (%e ) +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 5n 2 4n 6n 2 4n 5n 7n 3 4n 5n 6n +--R (((35b x + 84a b x )x + 70a b x x )x + 20a x x x ) +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 3 4n 5n 6n 7n n log(x) 3 2 4n 5n 6n 7n n log(x) 2 +--R - 35b x x x x (%e ) - 84a b x x x x (%e ) +--R + +--R 2 4n 5n 6n 7n n log(x) 3 4n 5n 6n 7n +--R - 70a b x x x x %e - 20a x x x x +--R / +--R 4n 5n 6n 7n n log(x) 7 +--R 140n x x x x (%e ) +--R Type: Expression(Integer) +--E 54 + +--S 55 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 55 + +)clear all + +--S 56 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 4n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 56 + +--S 57 of 1394 +r0:=1/4*a^5*x^(4*n)/n+a^4*b*x^(5*n)/n+5/3*a^3*b^2*x^(6*n)/n+_ + 10/7*a^2*b^3*x^(7*n)/n+5/8*a*b^4*x^(8*n)/n+1/9*b^5*x^(9*n)/n +--R +--R +--R 5 9n 4 8n 2 3 7n 3 2 6n 4 5n 5 4n +--R 56b x + 315a b x + 720a b x + 840a b x + 504a b x + 126a x +--R (2) ---------------------------------------------------------------------- +--R 504n +--R Type: Expression(Integer) +--E 57 + +--S 58 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 9 4 n log(x) 8 2 3 n log(x) 7 +--R 56b (%e ) + 315a b (%e ) + 720a b (%e ) +--R + +--R 3 2 n log(x) 6 4 n log(x) 5 5 n log(x) 4 +--R 840a b (%e ) + 504a b (%e ) + 126a (%e ) +--R / +--R 504n +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 9 4 n log(x) 8 2 3 n log(x) 7 +--R 56b (%e ) + 315a b (%e ) + 720a b (%e ) +--R + +--R 3 2 n log(x) 6 4 n log(x) 5 5 n log(x) 4 +--R 840a b (%e ) + 504a b (%e ) + 126a (%e ) +--R + +--R 5 9n 4 8n 2 3 7n 3 2 6n 4 5n 5 4n +--R - 56b x - 315a b x - 720a b x - 840a b x - 504a b x - 126a x +--R / +--R 504n +--R Type: Expression(Integer) +--E 59 + +--S 60 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 60 + +)clear all + +--S 61 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 3n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 61 + +--S 62 of 1394 +r0:=1/6*a^2*(a+b*x^n)^6/(b^3*n)-2/7*a*(a+b*x^n)^7/(b^3*n)+_ + 1/8*(a+b*x^n)^8/(b^3*n) +--R +--R +--R (2) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R 21b (x ) + 120a b (x ) + 280a b (x ) + 336a b (x ) + 210a b (x ) +--R + +--R 5 3 n 3 8 +--R 56a b (x ) + a +--R / +--R 3 +--R 168b n +--R Type: Expression(Integer) +--E 62 + +--S 63 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 8 4 n log(x) 7 2 3 n log(x) 6 +--R 21b (%e ) + 120a b (%e ) + 280a b (%e ) +--R + +--R 3 2 n log(x) 5 4 n log(x) 4 5 n log(x) 3 +--R 336a b (%e ) + 210a b (%e ) + 56a (%e ) +--R / +--R 168n +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 21b (%e ) + 120a b (%e ) + 280a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 336a b (%e ) + 210a b (%e ) + 56a b (%e ) +--R + +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R - 21b (x ) - 120a b (x ) - 280a b (x ) - 336a b (x ) - 210a b (x ) +--R + +--R 5 3 n 3 8 +--R - 56a b (x ) - a +--R / +--R 3 +--R 168b n +--R Type: Expression(Integer) +--E 64 + +--S 65 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 65 + +)clear all + +--S 66 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 2n - 1 +--R (b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a )x +--R Type: Expression(Integer) +--E 66 + +--S 67 of 1394 +r0:=-1/6*a*(a+b*x^n)^6/(b^2*n)+1/7*(a+b*x^n)^7/(b^2*n) +--R +--R +--R (2) +--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R 6b (x ) + 35a b (x ) + 84a b (x ) + 105a b (x ) + 70a b (x ) +--R + +--R 5 2 n 2 7 +--R 21a b (x ) - a +--R / +--R 2 +--R 42b n +--R Type: Expression(Integer) +--E 67 + +--S 68 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 7 4 n log(x) 6 2 3 n log(x) 5 +--R 6b (%e ) + 35a b (%e ) + 84a b (%e ) +--R + +--R 3 2 n log(x) 4 4 n log(x) 3 5 n log(x) 2 +--R 105a b (%e ) + 70a b (%e ) + 21a (%e ) +--R / +--R 42n +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 n log(x) 7 6 n log(x) 6 2 5 n log(x) 5 +--R 6b (%e ) + 35a b (%e ) + 84a b (%e ) +--R + +--R 3 4 n log(x) 4 4 3 n log(x) 3 5 2 n log(x) 2 +--R 105a b (%e ) + 70a b (%e ) + 21a b (%e ) +--R + +--R 7 n 7 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R - 6b (x ) - 35a b (x ) - 84a b (x ) - 105a b (x ) - 70a b (x ) +--R + +--R 5 2 n 2 7 +--R - 21a b (x ) + a +--R / +--R 2 +--R 42b n +--R Type: Expression(Integer) +--E 69 + +--S 70 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 70 + +)clear all + +--S 71 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 n - 1 n 5 4 n - 1 n 4 2 3 n - 1 n 3 3 2 n - 1 n 2 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) + 10a b x (x ) +--R + +--R 4 n - 1 n 5 n - 1 +--R 5a b x x + a x +--R Type: Expression(Integer) +--E 71 + +--S 72 of 1394 +r0:=1/6*(a+b*x^n)^6/(b*n) +--R +--R +--R (2) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 5 n 6 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) + 6a b x + a +--R ----------------------------------------------------------------------------- +--R 6b n +--R Type: Expression(Integer) +--E 72 + +--S 73 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 6 4 n log(x) 5 2 3 n log(x) 4 +--R b (%e ) + 6a b (%e ) + 15a b (%e ) +--R + +--R 3 2 n log(x) 3 4 n log(x) 2 5 n log(x) +--R 20a b (%e ) + 15a b (%e ) + 6a %e +--R / +--R 6n +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n log(x) 6 5 n log(x) 5 2 4 n log(x) 4 +--R b (%e ) + 6a b (%e ) + 15a b (%e ) +--R + +--R 3 3 n log(x) 3 4 2 n log(x) 2 5 n log(x) 6 n 6 +--R 20a b (%e ) + 15a b (%e ) + 6a b %e - b (x ) +--R + +--R 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 5 n 6 +--R - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) - 6a b x - a +--R / +--R 6b n +--R Type: Expression(Integer) +--E 74 + +--S 75 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 75 + +)clear all + +--S 76 of 1394 +t0:=(a+b*x^n)^5/x +--R +--R +--R 5 n 5 4 n 4 2 3 n 3 3 2 n 2 4 n 5 +--R b (x ) + 5a b (x ) + 10a b (x ) + 10a b (x ) + 5a b x + a +--R (1) --------------------------------------------------------------- +--R x +--R Type: Expression(Integer) +--E 76 + +--S 77 of 1394 +r0:=5*a^4*b*x^n/n+5*a^3*b^2*x^(2*n)/n+10/3*a^2*b^3*x^(3*n)/n+_ + 5/4*a*b^4*x^(4*n)/n+1/5*b^5*x^(5*n)/n+a^5*log(x) +--R +--R +--R (2) +--R 5 5n 4 4n 2 3 3n 3 2 2n 4 n 5 +--R 12b x + 75a b x + 200a b x + 300a b x + 300a b x + 60a n log(x) +--R ------------------------------------------------------------------------ +--R 60n +--R Type: Expression(Integer) +--E 77 + +--S 78 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 75a b (%e ) + 200a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 300a b (%e ) + 300a b %e + 60a n log(x) +--R / +--R 60n +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 75a b (%e ) + 200a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 5n 4 4n +--R 300a b (%e ) + 300a b %e - 12b x - 75a b x +--R + +--R 2 3 3n 3 2 2n 4 n +--R - 200a b x - 300a b x - 300a b x +--R / +--R 60n +--R Type: Expression(Integer) +--E 79 + +--S 80 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 80 + +)clear all + +--S 81 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - n - 1 n 5 4 - n - 1 n 4 2 3 - n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - n - 1 n 2 4 - n - 1 n 5 - n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 81 + +--S 82 of 1394 +r0:=-a^5/(n*x^n)+10*a^3*b^2*x^n/n+5*a^2*b^3*x^(2*n)/n+_ + 5/3*a*b^4*x^(3*n)/n+1/4*b^5*x^(4*n)/n+5*a^4*b*log(x) +--R +--R +--R (2) +--R 5 n 4n 4 n 3n 2 3 n 2n 3 2 n 2 4 n 5 +--R 3b x x + 20a b x x + 60a b x x + 120a b (x ) + 60a b n log(x)x - 12a +--R ----------------------------------------------------------------------------- +--R n +--R 12n x +--R Type: Expression(Integer) +--E 82 + +--S 83 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 3b (%e ) + 20a b (%e ) + 60a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 120a b (%e ) + 60a b n log(x)%e - 12a +--R / +--R n log(x) +--R 12n %e +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n n log(x) 5 4 n n log(x) 4 2 3 n n log(x) 3 +--R 3b x (%e ) + 20a b x (%e ) + 60a b x (%e ) +--R + +--R 3 2 n n log(x) 2 +--R 120a b x (%e ) +--R + +--R 5 n 4n 4 n 3n 2 3 n 2n 3 2 n 2 5 n log(x) +--R (- 3b x x - 20a b x x - 60a b x x - 120a b (x ) + 12a )%e +--R + +--R 5 n +--R - 12a x +--R / +--R n n log(x) +--R 12n x %e +--R Type: Expression(Integer) +--E 84 + +--S 85 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 85 + +)clear all + +--S 86 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 2n - 1 n 5 4 - 2n - 1 n 4 2 3 - 2n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 2n - 1 n 2 4 - 2n - 1 n 5 - 2n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 86 + +--S 87 of 1394 +r0:=-1/2*a^5/(n*x^(2*n))-5*a^4*b/(n*x^n)+10*a^2*b^3*x^n/n+_ + 5/2*a*b^4*x^(2*n)/n+1/3*b^5*x^(3*n)/n+10*a^3*b^2*log(x) +--R +--R +--R (2) +--R 5 n 2n 3n 4 n 2n 2 +--R 2b x x x + 15a b x (x ) +--R + +--R 2 3 n 2 3 2 n 4 2n 5 n +--R (60a b (x ) + 60a b n log(x)x - 30a b)x - 3a x +--R / +--R n 2n +--R 6n x x +--R Type: Expression(Integer) +--E 87 + +--S 88 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 2b (%e ) + 15a b (%e ) + 60a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 60a b n log(x)(%e ) - 30a b %e - 3a +--R / +--R n log(x) 2 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n n log(x) 5 4 n 2n n log(x) 4 +--R 2b x x (%e ) + 15a b x x (%e ) +--R + +--R 2 3 n 2n n log(x) 3 +--R 60a b x x (%e ) +--R + +--R 5 n 2n 3n 4 n 2n 2 2 3 n 2 4 2n 5 n +--R (- 2b x x x - 15a b x (x ) + (- 60a b (x ) + 30a b)x + 3a x ) +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 4 n 2n n log(x) 5 n 2n +--R - 30a b x x %e - 3a x x +--R / +--R n 2n n log(x) 2 +--R 6n x x (%e ) +--R Type: Expression(Integer) +--E 89 + +--S 90 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 90 + +)clear all + +--S 91 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 3n - 1 n 5 4 - 3n - 1 n 4 2 3 - 3n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 3n - 1 n 2 4 - 3n - 1 n 5 - 3n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 91 + +--S 92 of 1394 +r0:=-1/3*a^5/(n*x^(3*n))-5/2*a^4*b/(n*x^(2*n))-10*a^3*b^2/(n*x^n)+_ + 5*a*b^4*x^n/n+1/2*b^5*x^(2*n)/n+10*a^2*b^3*log(x) +--R +--R +--R (2) +--R 5 n 2n 2 4 n 2 2 3 n 3 2 2n 4 n +--R (3b x (x ) + (30a b (x ) + 60a b n log(x)x - 60a b )x - 15a b x ) +--R * +--R 3n +--R x +--R + +--R 5 n 2n +--R - 2a x x +--R / +--R n 2n 3n +--R 6n x x x +--R Type: Expression(Integer) +--E 92 + +--S 93 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 3b (%e ) + 30a b (%e ) + 60a b n log(x)(%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 60a b (%e ) - 15a b %e - 2a +--R / +--R n log(x) 3 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n 3n n log(x) 5 4 n 2n 3n n log(x) 4 +--R 3b x x x (%e ) + 30a b x x x (%e ) +--R + +--R 5 n 2n 2 4 n 2 3 2 2n 4 n 3n +--R (- 3b x (x ) + (- 30a b (x ) + 60a b )x + 15a b x )x +--R + +--R 5 n 2n +--R 2a x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 3 2 n 2n 3n n log(x) 2 4 n 2n 3n n log(x) 5 n 2n 3n +--R - 60a b x x x (%e ) - 15a b x x x %e - 2a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 6n x x x (%e ) +--R Type: Expression(Integer) +--E 94 + +--S 95 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 95 + +)clear all + +--S 96 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 4n - 1 n 5 4 - 4n - 1 n 4 2 3 - 4n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 4n - 1 n 2 4 - 4n - 1 n 5 - 4n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 96 + +--S 97 of 1394 +r0:=-1/4*a^5/(n*x^(4*n))-5/3*a^4*b/(n*x^(3*n))-5*a^3*b^2/(n*x^(2*n))-_ + 10*a^2*b^3/(n*x^n)+b^5*x^n/n+5*a*b^4*log(x) +--R +--R +--R (2) +--R 5 n 2 4 n 2 3 2n 3 2 n 3n +--R ((12b (x ) + 60a b n log(x)x - 120a b )x - 60a b x )x +--R + +--R 4 n 2n +--R - 20a b x x +--R * +--R 4n +--R x +--R + +--R 5 n 2n 3n +--R - 3a x x x +--R / +--R n 2n 3n 4n +--R 12n x x x x +--R Type: Expression(Integer) +--E 97 + +--S 98 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 12b (%e ) + 60a b n log(x)(%e ) - 120a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 60a b (%e ) - 20a b %e - 3a +--R / +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2n 3n 4n n log(x) 5 +--R 12b x x x x (%e ) +--R + +--R 5 n 2 2 3 2n 3 2 n 3n 4 n 2n 4n +--R (((- 12b (x ) + 120a b )x + 60a b x )x + 20a b x x )x +--R + +--R 5 n 2n 3n +--R 3a x x x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 2 3 n 2n 3n 4n n log(x) 3 3 2 n 2n 3n 4n n log(x) 2 +--R - 120a b x x x x (%e ) - 60a b x x x x (%e ) +--R + +--R 4 n 2n 3n 4n n log(x) 5 n 2n 3n 4n +--R - 20a b x x x x %e - 3a x x x x +--R / +--R n 2n 3n 4n n log(x) 4 +--R 12n x x x x (%e ) +--R Type: Expression(Integer) +--E 99 + +--S 100 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 100 + +)clear all + +--S 101 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 5n - 1 n 5 4 - 5n - 1 n 4 2 3 - 5n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 5n - 1 n 2 4 - 5n - 1 n 5 - 5n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 1394 +r0:=-1/5*a^5/(n*x^(5*n))-5/4*a^4*b/(n*x^(4*n))-10/3*a^3*b^2/(n*x^(3*n))-_ + 5*a^2*b^3/(n*x^(2*n))-5*a*b^4/(n*x^n)+b^5*log(x) +--R +--R +--R (2) +--R 5 n 4 2n 2 3 n 3n 3 2 n 2n 4n +--R (((60b n log(x)x - 300a b )x - 300a b x )x - 200a b x x )x +--R + +--R 4 n 2n 3n +--R - 75a b x x x +--R * +--R 5n +--R x +--R + +--R 5 n 2n 3n 4n +--R - 12a x x x x +--R / +--R n 2n 3n 4n 5n +--R 60n x x x x x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R 60b n log(x)(%e ) - 300a b (%e ) - 300a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 200a b (%e ) - 75a b %e - 12a +--R / +--R n log(x) 5 +--R 60n (%e ) +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2n 2 3 n 3n 3 2 n 2n 4n 4 n 2n 3n 5n +--R (((300a b x + 300a b x )x + 200a b x x )x + 75a b x x x )x +--R + +--R 5 n 2n 3n 4n +--R 12a x x x x +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 4 n 2n 3n 4n 5n n log(x) 4 2 3 n 2n 3n 4n 5n n log(x) 3 +--R - 300a b x x x x x (%e ) - 300a b x x x x x (%e ) +--R + +--R 3 2 n 2n 3n 4n 5n n log(x) 2 4 n 2n 3n 4n 5n n log(x) +--R - 200a b x x x x x (%e ) - 75a b x x x x x %e +--R + +--R 5 n 2n 3n 4n 5n +--R - 12a x x x x x +--R / +--R n 2n 3n 4n 5n n log(x) 5 +--R 60n x x x x x (%e ) +--R Type: Expression(Integer) +--E 104 + +--S 105 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 105 + +)clear all + +--S 106 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 6n - 1 n 5 4 - 6n - 1 n 4 2 3 - 6n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 6n - 1 n 2 4 - 6n - 1 n 5 - 6n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 1394 +r0:=-1/6*(a+b*x^n)^6/(a*n*x^(6*n)) +--R +--R +--R (2) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) +--R + +--R 5 n 6 +--R - 6a b x - a +--R / +--R 6n +--R 6a n x +--R Type: Expression(Integer) +--E 107 + +--S 108 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 6b (%e ) - 15a b (%e ) - 20a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 15a b (%e ) - 6a b %e - a +--R / +--R n log(x) 6 +--R 6n (%e ) +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n 6 5 n 5 2 4 n 4 3 3 n 3 4 2 n 2 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) +--R + +--R 5 n 6 +--R 6a b x + a +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 5 6n n log(x) 5 2 4 6n n log(x) 4 3 3 6n n log(x) 3 +--R - 6a b x (%e ) - 15a b x (%e ) - 20a b x (%e ) +--R + +--R 4 2 6n n log(x) 2 5 6n n log(x) 6 6n +--R - 15a b x (%e ) - 6a b x %e - a x +--R / +--R 6n n log(x) 6 +--R 6a n x (%e ) +--R Type: Expression(Integer) +--E 109 + +--S 110 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 110 + +)clear all + +--S 111 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 7n - 1 n 5 4 - 7n - 1 n 4 2 3 - 7n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 7n - 1 n 2 4 - 7n - 1 n 5 - 7n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 111 + +--S 112 of 1394 +r0:=-1/7*(a+b*x^n)^6/(a*n*x^(7*n))+1/42*b*(a+b*x^n)^6/(a^2*n*x^(6*n)) +--R +--R +--R (2) +--R 7 n 6 6 n 5 2 5 n 4 3 4 n 3 4 3 n 2 +--R b (x ) + 6a b (x ) + 15a b (x ) + 20a b (x ) + 15a b (x ) +--R + +--R 5 2 n 6 +--R 6a b x + a b +--R * +--R 7n +--R x +--R + +--R 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 5 2 n 2 +--R - 6a b (x ) - 36a b (x ) - 90a b (x ) - 120a b (x ) - 90a b (x ) +--R + +--R 6 n 7 +--R - 36a b x - 6a +--R * +--R 6n +--R x +--R / +--R 2 6n 7n +--R 42a n x x +--R Type: Expression(Integer) +--E 112 + +--S 113 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 21b (%e ) - 70a b (%e ) - 105a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 84a b (%e ) - 35a b %e - 6a +--R / +--R n log(x) 7 +--R 42n (%e ) +--R Type: Union(Expression(Integer),...) +--E 113 + +--S 114 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 n 6 6 n 5 2 5 n 4 3 4 n 3 4 3 n 2 +--R - b (x ) - 6a b (x ) - 15a b (x ) - 20a b (x ) - 15a b (x ) +--R + +--R 5 2 n 6 +--R - 6a b x - a b +--R * +--R 7n +--R x +--R + +--R 6 n 6 2 5 n 5 3 4 n 4 4 3 n 3 +--R 6a b (x ) + 36a b (x ) + 90a b (x ) + 120a b (x ) +--R + +--R 5 2 n 2 6 n 7 +--R 90a b (x ) + 36a b x + 6a +--R * +--R 6n +--R x +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 2 5 6n 7n n log(x) 5 3 4 6n 7n n log(x) 4 +--R - 21a b x x (%e ) - 70a b x x (%e ) +--R + +--R 4 3 6n 7n n log(x) 3 5 2 6n 7n n log(x) 2 +--R - 105a b x x (%e ) - 84a b x x (%e ) +--R + +--R 6 6n 7n n log(x) 7 6n 7n +--R - 35a b x x %e - 6a x x +--R / +--R 2 6n 7n n log(x) 7 +--R 42a n x x (%e ) +--R Type: Expression(Integer) +--E 114 + +--S 115 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 115 + +)clear all + +--S 116 of 1394 +t0:=x^(-1-8*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 8n - 1 n 5 4 - 8n - 1 n 4 2 3 - 8n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 8n - 1 n 2 4 - 8n - 1 n 5 - 8n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 1394 +r0:=-1/8*a^5/(n*x^(8*n))-5/7*a^4*b/(n*x^(7*n))-5/3*a^3*b^2/(n*x^(6*n))-_ + 2*a^2*b^3/(n*x^(5*n))-5/4*a*b^4/(n*x^(4*n))-1/3*b^5/(n*x^(3*n)) +--R +--R +--R (2) +--R 5 4n 4 3n 5n 2 3 3n 4n 6n +--R ((- 56b x - 210a b x )x - 336a b x x )x +--R + +--R 3 2 3n 4n 5n +--R - 280a b x x x +--R * +--R 7n +--R x +--R + +--R 4 3n 4n 5n 6n +--R - 120a b x x x x +--R * +--R 8n +--R x +--R + +--R 5 3n 4n 5n 6n 7n +--R - 21a x x x x x +--R / +--R 3n 4n 5n 6n 7n 8n +--R 168n x x x x x x +--R Type: Expression(Integer) +--E 117 + +--S 118 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 56b (%e ) - 210a b (%e ) - 336a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 280a b (%e ) - 120a b %e - 21a +--R / +--R n log(x) 8 +--R 168n (%e ) +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 4n 4 3n 5n 2 3 3n 4n 6n +--R ((56b x + 210a b x )x + 336a b x x )x +--R + +--R 3 2 3n 4n 5n +--R 280a b x x x +--R * +--R 7n +--R x +--R + +--R 4 3n 4n 5n 6n +--R 120a b x x x x +--R * +--R 8n +--R x +--R + +--R 5 3n 4n 5n 6n 7n +--R 21a x x x x x +--R * +--R n log(x) 8 +--R (%e ) +--R + +--R 5 3n 4n 5n 6n 7n 8n n log(x) 5 +--R - 56b x x x x x x (%e ) +--R + +--R 4 3n 4n 5n 6n 7n 8n n log(x) 4 +--R - 210a b x x x x x x (%e ) +--R + +--R 2 3 3n 4n 5n 6n 7n 8n n log(x) 3 +--R - 336a b x x x x x x (%e ) +--R + +--R 3 2 3n 4n 5n 6n 7n 8n n log(x) 2 +--R - 280a b x x x x x x (%e ) +--R + +--R 4 3n 4n 5n 6n 7n 8n n log(x) 5 3n 4n 5n 6n 7n 8n +--R - 120a b x x x x x x %e - 21a x x x x x x +--R / +--R 3n 4n 5n 6n 7n 8n n log(x) 8 +--R 168n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 119 + +--S 120 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 120 + +)clear all + +--S 121 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 9n - 1 n 5 4 - 9n - 1 n 4 2 3 - 9n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 9n - 1 n 2 4 - 9n - 1 n 5 - 9n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 121 + +--S 122 of 1394 +r0:=-1/9*a^5/(n*x^(9*n))-5/8*a^4*b/(n*x^(8*n))-10/7*a^3*b^2/(n*x^(7*n))-_ + 5/3*a^2*b^3/(n*x^(6*n))-a*b^4/(n*x^(5*n))-1/4*b^5/(n*x^(4*n)) +--R +--R +--R (2) +--R 5 5n 4 4n 6n 2 3 4n 5n 7n +--R ((- 126b x - 504a b x )x - 840a b x x )x +--R + +--R 3 2 4n 5n 6n +--R - 720a b x x x +--R * +--R 8n +--R x +--R + +--R 4 4n 5n 6n 7n +--R - 315a b x x x x +--R * +--R 9n +--R x +--R + +--R 5 4n 5n 6n 7n 8n +--R - 56a x x x x x +--R / +--R 4n 5n 6n 7n 8n 9n +--R 504n x x x x x x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 126b (%e ) - 504a b (%e ) - 840a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 720a b (%e ) - 315a b %e - 56a +--R / +--R n log(x) 9 +--R 504n (%e ) +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5n 4 4n 6n 2 3 4n 5n 7n +--R ((126b x + 504a b x )x + 840a b x x )x +--R + +--R 3 2 4n 5n 6n +--R 720a b x x x +--R * +--R 8n +--R x +--R + +--R 4 4n 5n 6n 7n +--R 315a b x x x x +--R * +--R 9n +--R x +--R + +--R 5 4n 5n 6n 7n 8n +--R 56a x x x x x +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 5 4n 5n 6n 7n 8n 9n n log(x) 5 +--R - 126b x x x x x x (%e ) +--R + +--R 4 4n 5n 6n 7n 8n 9n n log(x) 4 +--R - 504a b x x x x x x (%e ) +--R + +--R 2 3 4n 5n 6n 7n 8n 9n n log(x) 3 +--R - 840a b x x x x x x (%e ) +--R + +--R 3 2 4n 5n 6n 7n 8n 9n n log(x) 2 +--R - 720a b x x x x x x (%e ) +--R + +--R 4 4n 5n 6n 7n 8n 9n n log(x) 5 4n 5n 6n 7n 8n 9n +--R - 315a b x x x x x x %e - 56a x x x x x x +--R / +--R 4n 5n 6n 7n 8n 9n n log(x) 9 +--R 504n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 124 + +--S 125 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 125 + +)clear all + +--S 126 of 1394 +t0:=x^(-1-10*n)*(a+b*x^n)^5 +--R +--R +--R (1) +--R 5 - 10n - 1 n 5 4 - 10n - 1 n 4 2 3 - 10n - 1 n 3 +--R b x (x ) + 5a b x (x ) + 10a b x (x ) +--R + +--R 3 2 - 10n - 1 n 2 4 - 10n - 1 n 5 - 10n - 1 +--R 10a b x (x ) + 5a b x x + a x +--R Type: Expression(Integer) +--E 126 + +--S 127 of 1394 +r0:=-1/10*a^5/(n*x^(10*n))-5/9*a^4*b/(n*x^(9*n))-5/4*a^3*b^2/(n*x^(8*n))-_ + 10/7*a^2*b^3/(n*x^(7*n))-5/6*a*b^4/(n*x^(6*n))-1/5*b^5/(n*x^(5*n)) +--R +--R +--R (2) +--R 5 6n 4 5n 7n 2 3 5n 6n 8n +--R ((- 252b x - 1050a b x )x - 1800a b x x )x +--R + +--R 3 2 5n 6n 7n +--R - 1575a b x x x +--R * +--R 9n +--R x +--R + +--R 4 5n 6n 7n 8n +--R - 700a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 5n 6n 7n 8n 9n +--R - 126a x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n +--R 1260n x x x x x x +--R Type: Expression(Integer) +--E 127 + +--S 128 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 n log(x) 5 4 n log(x) 4 2 3 n log(x) 3 +--R - 252b (%e ) - 1050a b (%e ) - 1800a b (%e ) +--R + +--R 3 2 n log(x) 2 4 n log(x) 5 +--R - 1575a b (%e ) - 700a b %e - 126a +--R / +--R n log(x) 10 +--R 1260n (%e ) +--R Type: Union(Expression(Integer),...) +--E 128 + +--S 129 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 6n 4 5n 7n 2 3 5n 6n 8n +--R ((252b x + 1050a b x )x + 1800a b x x )x +--R + +--R 3 2 5n 6n 7n +--R 1575a b x x x +--R * +--R 9n +--R x +--R + +--R 4 5n 6n 7n 8n +--R 700a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 5n 6n 7n 8n 9n +--R 126a x x x x x +--R * +--R n log(x) 10 +--R (%e ) +--R + +--R 5 5n 6n 7n 8n 9n 10n n log(x) 5 +--R - 252b x x x x x x (%e ) +--R + +--R 4 5n 6n 7n 8n 9n 10n n log(x) 4 +--R - 1050a b x x x x x x (%e ) +--R + +--R 2 3 5n 6n 7n 8n 9n 10n n log(x) 3 +--R - 1800a b x x x x x x (%e ) +--R + +--R 3 2 5n 6n 7n 8n 9n 10n n log(x) 2 +--R - 1575a b x x x x x x (%e ) +--R + +--R 4 5n 6n 7n 8n 9n 10n n log(x) 5 5n 6n 7n 8n 9n 10n +--R - 700a b x x x x x x %e - 126a x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n n log(x) 10 +--R 1260n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 129 + +--S 130 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 130 + +)clear all + +--S 131 of 1394 +t0:=x^(-1+9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 9n - 1 +--R x +--R Type: Expression(Integer) +--E 131 + +--S 132 of 1394 +r0:=1/9*a^8*x^(9*n)/n+4/5*a^7*b*x^(10*n)/n+28/11*a^6*b^2*x^(11*n)/n+_ + 14/3*a^5*b^3*x^(12*n)/n+70/13*a^4*b^4*x^(13*n)/n+_ + 4*a^3*b^5*x^(14*n)/n+28/15*a^2*b^6*x^(15*n)/n+_ + 1/2*a*b^7*x^(16*n)/n+1/17*b^8*x^(17*n)/n +--R +--R +--R (2) +--R 8 17n 7 16n 2 6 15n 3 5 14n +--R 12870b x + 109395a b x + 408408a b x + 875160a b x +--R + +--R 4 4 13n 5 3 12n 6 2 11n 7 10n +--R 1178100a b x + 1021020a b x + 556920a b x + 175032a b x +--R + +--R 8 9n +--R 24310a x +--R / +--R 218790n +--R Type: Expression(Integer) +--E 132 + +--S 133 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 17 7 n log(x) 16 +--R 12870b (%e ) + 109395a b (%e ) +--R + +--R 2 6 n log(x) 15 3 5 n log(x) 14 +--R 408408a b (%e ) + 875160a b (%e ) +--R + +--R 4 4 n log(x) 13 5 3 n log(x) 12 +--R 1178100a b (%e ) + 1021020a b (%e ) +--R + +--R 6 2 n log(x) 11 7 n log(x) 10 8 n log(x) 9 +--R 556920a b (%e ) + 175032a b (%e ) + 24310a (%e ) +--R / +--R 218790n +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 17 7 n log(x) 16 +--R 12870b (%e ) + 109395a b (%e ) +--R + +--R 2 6 n log(x) 15 3 5 n log(x) 14 +--R 408408a b (%e ) + 875160a b (%e ) +--R + +--R 4 4 n log(x) 13 5 3 n log(x) 12 +--R 1178100a b (%e ) + 1021020a b (%e ) +--R + +--R 6 2 n log(x) 11 7 n log(x) 10 +--R 556920a b (%e ) + 175032a b (%e ) +--R + +--R 8 n log(x) 9 8 17n 7 16n 2 6 15n +--R 24310a (%e ) - 12870b x - 109395a b x - 408408a b x +--R + +--R 3 5 14n 4 4 13n 5 3 12n 6 2 11n +--R - 875160a b x - 1178100a b x - 1021020a b x - 556920a b x +--R + +--R 7 10n 8 9n +--R - 175032a b x - 24310a x +--R / +--R 218790n +--R Type: Expression(Integer) +--E 134 + +--S 135 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 135 + +)clear all + +--S 136 of 1394 +t0:=x^(-1+8*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 8n - 1 +--R x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 1394 +r0:=1/8*a^8*x^(8*n)/n+8/9*a^7*b*x^(9*n)/n+14/5*a^6*b^2*x^(10*n)/n+_ + 56/11*a^5*b^3*x^(11*n)/n+35/6*a^4*b^4*x^(12*n)/n+_ + 56/13*a^3*b^5*x^(13*n)/n+2*a^2*b^6*x^(14*n)/n+_ + 8/15*a*b^7*x^(15*n)/n+1/16*b^8*x^(16*n)/n +--R +--R +--R (2) +--R 8 16n 7 15n 2 6 14n 3 5 13n +--R 6435b x + 54912a b x + 205920a b x + 443520a b x +--R + +--R 4 4 12n 5 3 11n 6 2 10n 7 9n +--R 600600a b x + 524160a b x + 288288a b x + 91520a b x +--R + +--R 8 8n +--R 12870a x +--R / +--R 102960n +--R Type: Expression(Integer) +--E 137 + +--S 138 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 16 7 n log(x) 15 2 6 n log(x) 14 +--R 6435b (%e ) + 54912a b (%e ) + 205920a b (%e ) +--R + +--R 3 5 n log(x) 13 4 4 n log(x) 12 +--R 443520a b (%e ) + 600600a b (%e ) +--R + +--R 5 3 n log(x) 11 6 2 n log(x) 10 +--R 524160a b (%e ) + 288288a b (%e ) +--R + +--R 7 n log(x) 9 8 n log(x) 8 +--R 91520a b (%e ) + 12870a (%e ) +--R / +--R 102960n +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 16 7 n log(x) 15 2 6 n log(x) 14 +--R 6435b (%e ) + 54912a b (%e ) + 205920a b (%e ) +--R + +--R 3 5 n log(x) 13 4 4 n log(x) 12 +--R 443520a b (%e ) + 600600a b (%e ) +--R + +--R 5 3 n log(x) 11 6 2 n log(x) 10 +--R 524160a b (%e ) + 288288a b (%e ) +--R + +--R 7 n log(x) 9 8 n log(x) 8 8 16n +--R 91520a b (%e ) + 12870a (%e ) - 6435b x +--R + +--R 7 15n 2 6 14n 3 5 13n 4 4 12n +--R - 54912a b x - 205920a b x - 443520a b x - 600600a b x +--R + +--R 5 3 11n 6 2 10n 7 9n 8 8n +--R - 524160a b x - 288288a b x - 91520a b x - 12870a x +--R / +--R 102960n +--R Type: Expression(Integer) +--E 139 + +--S 140 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 140 + +)clear all + +--S 141 of 1394 +t0:=x^(-1+7*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 7n - 1 +--R x +--R Type: Expression(Integer) +--E 141 + +--S 142 of 1394 +r0:=1/7*a^8*x^(7*n)/n+a^7*b*x^(8*n)/n+28/9*a^6*b^2*x^(9*n)/n+_ + 28/5*a^5*b^3*x^(10*n)/n+70/11*a^4*b^4*x^(11*n)/n+_ + 14/3*a^3*b^5*x^(12*n)/n+28/13*a^2*b^6*x^(13*n)/n+_ + 4/7*a*b^7*x^(14*n)/n+1/15*b^8*x^(15*n)/n +--R +--R +--R (2) +--R 8 15n 7 14n 2 6 13n 3 5 12n +--R 3003b x + 25740a b x + 97020a b x + 210210a b x +--R + +--R 4 4 11n 5 3 10n 6 2 9n 7 8n 8 7n +--R 286650a b x + 252252a b x + 140140a b x + 45045a b x + 6435a x +--R / +--R 45045n +--R Type: Expression(Integer) +--E 142 + +--S 143 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 15 7 n log(x) 14 2 6 n log(x) 13 +--R 3003b (%e ) + 25740a b (%e ) + 97020a b (%e ) +--R + +--R 3 5 n log(x) 12 4 4 n log(x) 11 +--R 210210a b (%e ) + 286650a b (%e ) +--R + +--R 5 3 n log(x) 10 6 2 n log(x) 9 +--R 252252a b (%e ) + 140140a b (%e ) +--R + +--R 7 n log(x) 8 8 n log(x) 7 +--R 45045a b (%e ) + 6435a (%e ) +--R / +--R 45045n +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 15 7 n log(x) 14 2 6 n log(x) 13 +--R 3003b (%e ) + 25740a b (%e ) + 97020a b (%e ) +--R + +--R 3 5 n log(x) 12 4 4 n log(x) 11 +--R 210210a b (%e ) + 286650a b (%e ) +--R + +--R 5 3 n log(x) 10 6 2 n log(x) 9 +--R 252252a b (%e ) + 140140a b (%e ) +--R + +--R 7 n log(x) 8 8 n log(x) 7 8 15n 7 14n +--R 45045a b (%e ) + 6435a (%e ) - 3003b x - 25740a b x +--R + +--R 2 6 13n 3 5 12n 4 4 11n 5 3 10n +--R - 97020a b x - 210210a b x - 286650a b x - 252252a b x +--R + +--R 6 2 9n 7 8n 8 7n +--R - 140140a b x - 45045a b x - 6435a x +--R / +--R 45045n +--R Type: Expression(Integer) +--E 144 + +--S 145 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 145 + +)clear all + +--S 146 of 1394 +t0:=x^(-1+6*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 6n - 1 +--R x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 1394 +r0:=-1/9*a^5*(a+b*x^n)^9/(b^6*n)+1/2*a^4*(a+b*x^n)^10/(b^6*n)-_ + 10/11*a^3*(a+b*x^n)^11/(b^6*n)+5/6*a^2*(a+b*x^n)^12/(b^6*n)-_ + 5/13*a*(a+b*x^n)^13/(b^6*n)+1/14*(a+b*x^n)^14/(b^6*n) +--R +--R +--R (2) +--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11 +--R 1287b (x ) + 11088a b (x ) + 42042a b (x ) + 91728a b (x ) +--R + +--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7 +--R 126126a b (x ) + 112112a b (x ) + 63063a b (x ) + 20592a b (x ) +--R + +--R 8 6 n 6 14 +--R 3003a b (x ) - a +--R / +--R 6 +--R 18018b n +--R Type: Expression(Integer) +--E 147 + +--S 148 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 14 7 n log(x) 13 2 6 n log(x) 12 +--R 1287b (%e ) + 11088a b (%e ) + 42042a b (%e ) +--R + +--R 3 5 n log(x) 11 4 4 n log(x) 10 +--R 91728a b (%e ) + 126126a b (%e ) +--R + +--R 5 3 n log(x) 9 6 2 n log(x) 8 7 n log(x) 7 +--R 112112a b (%e ) + 63063a b (%e ) + 20592a b (%e ) +--R + +--R 8 n log(x) 6 +--R 3003a (%e ) +--R / +--R 18018n +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 14 n log(x) 14 13 n log(x) 13 +--R 1287b (%e ) + 11088a b (%e ) +--R + +--R 2 12 n log(x) 12 3 11 n log(x) 11 +--R 42042a b (%e ) + 91728a b (%e ) +--R + +--R 4 10 n log(x) 10 5 9 n log(x) 9 +--R 126126a b (%e ) + 112112a b (%e ) +--R + +--R 6 8 n log(x) 8 7 7 n log(x) 7 8 6 n log(x) 6 +--R 63063a b (%e ) + 20592a b (%e ) + 3003a b (%e ) +--R + +--R 14 n 14 13 n 13 2 12 n 12 3 11 n 11 +--R - 1287b (x ) - 11088a b (x ) - 42042a b (x ) - 91728a b (x ) +--R + +--R 4 10 n 10 5 9 n 9 6 8 n 8 7 7 n 7 +--R - 126126a b (x ) - 112112a b (x ) - 63063a b (x ) - 20592a b (x ) +--R + +--R 8 6 n 6 14 +--R - 3003a b (x ) + a +--R / +--R 6 +--R 18018b n +--R Type: Expression(Integer) +--E 149 + +--S 150 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 150 + +)clear all + +--S 151 of 1394 +t0:=x^(-1+5*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 5n - 1 +--R x +--R Type: Expression(Integer) +--E 151 + +--S 152 of 1394 +r0:=1/9*a^4*(a+b*x^n)^9/(b^5*n)-2/5*a^3*(a+b*x^n)^10/(b^5*n)+_ + 6/11*a^2*(a+b*x^n)^11/(b^5*n)-1/3*a*(a+b*x^n)^12/(b^5*n)+_ + 1/13*(a+b*x^n)^13/(b^5*n) +--R +--R +--R (2) +--R 13 n 13 12 n 12 2 11 n 11 3 10 n 10 +--R 495b (x ) + 4290a b (x ) + 16380a b (x ) + 36036a b (x ) +--R + +--R 4 9 n 9 5 8 n 8 6 7 n 7 7 6 n 6 +--R 50050a b (x ) + 45045a b (x ) + 25740a b (x ) + 8580a b (x ) +--R + +--R 8 5 n 5 13 +--R 1287a b (x ) + a +--R / +--R 5 +--R 6435b n +--R Type: Expression(Integer) +--E 152 + +--S 153 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 13 7 n log(x) 12 2 6 n log(x) 11 +--R 495b (%e ) + 4290a b (%e ) + 16380a b (%e ) +--R + +--R 3 5 n log(x) 10 4 4 n log(x) 9 5 3 n log(x) 8 +--R 36036a b (%e ) + 50050a b (%e ) + 45045a b (%e ) +--R + +--R 6 2 n log(x) 7 7 n log(x) 6 8 n log(x) 5 +--R 25740a b (%e ) + 8580a b (%e ) + 1287a (%e ) +--R / +--R 6435n +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 n log(x) 13 12 n log(x) 12 2 11 n log(x) 11 +--R 495b (%e ) + 4290a b (%e ) + 16380a b (%e ) +--R + +--R 3 10 n log(x) 10 4 9 n log(x) 9 +--R 36036a b (%e ) + 50050a b (%e ) +--R + +--R 5 8 n log(x) 8 6 7 n log(x) 7 7 6 n log(x) 6 +--R 45045a b (%e ) + 25740a b (%e ) + 8580a b (%e ) +--R + +--R 8 5 n log(x) 5 13 n 13 12 n 12 2 11 n 11 +--R 1287a b (%e ) - 495b (x ) - 4290a b (x ) - 16380a b (x ) +--R + +--R 3 10 n 10 4 9 n 9 5 8 n 8 6 7 n 7 +--R - 36036a b (x ) - 50050a b (x ) - 45045a b (x ) - 25740a b (x ) +--R + +--R 7 6 n 6 8 5 n 5 13 +--R - 8580a b (x ) - 1287a b (x ) - a +--R / +--R 5 +--R 6435b n +--R Type: Expression(Integer) +--E 154 + +--S 155 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 155 + +)clear all + +--S 156 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 4n - 1 +--R x +--R Type: Expression(Integer) +--E 156 + +--S 157 of 1394 +r0:=-1/9*a^3*(a+b*x^n)^9/(b^4*n)+3/10*a^2*(a+b*x^n)^10/(b^4*n)-_ + 3/11*a*(a+b*x^n)^11/(b^4*n)+1/12*(a+b*x^n)^12/(b^4*n) +--R +--R +--R (2) +--R 12 n 12 11 n 11 2 10 n 10 3 9 n 9 +--R 165b (x ) + 1440a b (x ) + 5544a b (x ) + 12320a b (x ) +--R + +--R 4 8 n 8 5 7 n 7 6 6 n 6 7 5 n 5 +--R 17325a b (x ) + 15840a b (x ) + 9240a b (x ) + 3168a b (x ) +--R + +--R 8 4 n 4 12 +--R 495a b (x ) - a +--R / +--R 4 +--R 1980b n +--R Type: Expression(Integer) +--E 157 + +--S 158 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 12 7 n log(x) 11 2 6 n log(x) 10 +--R 165b (%e ) + 1440a b (%e ) + 5544a b (%e ) +--R + +--R 3 5 n log(x) 9 4 4 n log(x) 8 5 3 n log(x) 7 +--R 12320a b (%e ) + 17325a b (%e ) + 15840a b (%e ) +--R + +--R 6 2 n log(x) 6 7 n log(x) 5 8 n log(x) 4 +--R 9240a b (%e ) + 3168a b (%e ) + 495a (%e ) +--R / +--R 1980n +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 n log(x) 12 11 n log(x) 11 2 10 n log(x) 10 +--R 165b (%e ) + 1440a b (%e ) + 5544a b (%e ) +--R + +--R 3 9 n log(x) 9 4 8 n log(x) 8 5 7 n log(x) 7 +--R 12320a b (%e ) + 17325a b (%e ) + 15840a b (%e ) +--R + +--R 6 6 n log(x) 6 7 5 n log(x) 5 8 4 n log(x) 4 +--R 9240a b (%e ) + 3168a b (%e ) + 495a b (%e ) +--R + +--R 12 n 12 11 n 11 2 10 n 10 3 9 n 9 +--R - 165b (x ) - 1440a b (x ) - 5544a b (x ) - 12320a b (x ) +--R + +--R 4 8 n 8 5 7 n 7 6 6 n 6 7 5 n 5 +--R - 17325a b (x ) - 15840a b (x ) - 9240a b (x ) - 3168a b (x ) +--R + +--R 8 4 n 4 12 +--R - 495a b (x ) + a +--R / +--R 4 +--R 1980b n +--R Type: Expression(Integer) +--E 159 + +--S 160 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 160 + +)clear all + +--S 161 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 3n - 1 +--R x +--R Type: Expression(Integer) +--E 161 + +--S 162 of 1394 +r0:=1/9*a^2*(a+b*x^n)^9/(b^3*n)-1/5*a*(a+b*x^n)^10/(b^3*n)+_ + 1/11*(a+b*x^n)^11/(b^3*n) +--R +--R +--R (2) +--R 11 n 11 10 n 10 2 9 n 9 3 8 n 8 +--R 45b (x ) + 396a b (x ) + 1540a b (x ) + 3465a b (x ) +--R + +--R 4 7 n 7 5 6 n 6 6 5 n 5 7 4 n 4 +--R 4950a b (x ) + 4620a b (x ) + 2772a b (x ) + 990a b (x ) +--R + +--R 8 3 n 3 11 +--R 165a b (x ) + a +--R / +--R 3 +--R 495b n +--R Type: Expression(Integer) +--E 162 + +--S 163 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 11 7 n log(x) 10 2 6 n log(x) 9 +--R 45b (%e ) + 396a b (%e ) + 1540a b (%e ) +--R + +--R 3 5 n log(x) 8 4 4 n log(x) 7 5 3 n log(x) 6 +--R 3465a b (%e ) + 4950a b (%e ) + 4620a b (%e ) +--R + +--R 6 2 n log(x) 5 7 n log(x) 4 8 n log(x) 3 +--R 2772a b (%e ) + 990a b (%e ) + 165a (%e ) +--R / +--R 495n +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 n log(x) 11 10 n log(x) 10 2 9 n log(x) 9 +--R 45b (%e ) + 396a b (%e ) + 1540a b (%e ) +--R + +--R 3 8 n log(x) 8 4 7 n log(x) 7 5 6 n log(x) 6 +--R 3465a b (%e ) + 4950a b (%e ) + 4620a b (%e ) +--R + +--R 6 5 n log(x) 5 7 4 n log(x) 4 8 3 n log(x) 3 +--R 2772a b (%e ) + 990a b (%e ) + 165a b (%e ) +--R + +--R 11 n 11 10 n 10 2 9 n 9 3 8 n 8 +--R - 45b (x ) - 396a b (x ) - 1540a b (x ) - 3465a b (x ) +--R + +--R 4 7 n 7 5 6 n 6 6 5 n 5 7 4 n 4 +--R - 4950a b (x ) - 4620a b (x ) - 2772a b (x ) - 990a b (x ) +--R + +--R 8 3 n 3 11 +--R - 165a b (x ) - a +--R / +--R 3 +--R 495b n +--R Type: Expression(Integer) +--E 164 + +--S 165 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 165 + +)clear all + +--S 166 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R * +--R 2n - 1 +--R x +--R Type: Expression(Integer) +--E 166 + +--S 167 of 1394 +r0:=-1/9*a*(a+b*x^n)^9/(b^2*n)+1/10*(a+b*x^n)^10/(b^2*n) +--R +--R +--R (2) +--R 10 n 10 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R 9b (x ) + 80a b (x ) + 315a b (x ) + 720a b (x ) + 1050a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 10 +--R 1008a b (x ) + 630a b (x ) + 240a b (x ) + 45a b (x ) - a +--R / +--R 2 +--R 90b n +--R Type: Expression(Integer) +--E 167 + +--S 168 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 10 7 n log(x) 9 2 6 n log(x) 8 +--R 9b (%e ) + 80a b (%e ) + 315a b (%e ) +--R + +--R 3 5 n log(x) 7 4 4 n log(x) 6 5 3 n log(x) 5 +--R 720a b (%e ) + 1050a b (%e ) + 1008a b (%e ) +--R + +--R 6 2 n log(x) 4 7 n log(x) 3 8 n log(x) 2 +--R 630a b (%e ) + 240a b (%e ) + 45a (%e ) +--R / +--R 90n +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 n log(x) 10 9 n log(x) 9 2 8 n log(x) 8 +--R 9b (%e ) + 80a b (%e ) + 315a b (%e ) +--R + +--R 3 7 n log(x) 7 4 6 n log(x) 6 5 5 n log(x) 5 +--R 720a b (%e ) + 1050a b (%e ) + 1008a b (%e ) +--R + +--R 6 4 n log(x) 4 7 3 n log(x) 3 8 2 n log(x) 2 +--R 630a b (%e ) + 240a b (%e ) + 45a b (%e ) +--R + +--R 10 n 10 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R - 9b (x ) - 80a b (x ) - 315a b (x ) - 720a b (x ) - 1050a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 10 +--R - 1008a b (x ) - 630a b (x ) - 240a b (x ) - 45a b (x ) + a +--R / +--R 2 +--R 90b n +--R Type: Expression(Integer) +--E 169 + +--S 170 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 170 + +)clear all + +--S 171 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 n - 1 n 8 7 n - 1 n 7 2 6 n - 1 n 6 3 5 n - 1 n 5 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) + 56a b x (x ) +--R + +--R 4 4 n - 1 n 4 5 3 n - 1 n 3 6 2 n - 1 n 2 7 n - 1 n +--R 70a b x (x ) + 56a b x (x ) + 28a b x (x ) + 8a b x x +--R + +--R 8 n - 1 +--R a x +--R Type: Expression(Integer) +--E 171 + +--S 172 of 1394 +r0:=1/9*(a+b*x^n)^9/(b*n) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R / +--R 9b n +--R Type: Expression(Integer) +--E 172 + +--S 173 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 9 7 n log(x) 8 2 6 n log(x) 7 +--R b (%e ) + 9a b (%e ) + 36a b (%e ) +--R + +--R 3 5 n log(x) 6 4 4 n log(x) 5 5 3 n log(x) 4 +--R 84a b (%e ) + 126a b (%e ) + 126a b (%e ) +--R + +--R 6 2 n log(x) 3 7 n log(x) 2 8 n log(x) +--R 84a b (%e ) + 36a b (%e ) + 9a %e +--R / +--R 9n +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n log(x) 9 8 n log(x) 8 2 7 n log(x) 7 +--R b (%e ) + 9a b (%e ) + 36a b (%e ) +--R + +--R 3 6 n log(x) 6 4 5 n log(x) 5 5 4 n log(x) 4 +--R 84a b (%e ) + 126a b (%e ) + 126a b (%e ) +--R + +--R 6 3 n log(x) 3 7 2 n log(x) 2 8 n log(x) 9 n 9 +--R 84a b (%e ) + 36a b (%e ) + 9a b %e - b (x ) +--R + +--R 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 5 4 n 4 +--R - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) - 126a b (x ) +--R + +--R 6 3 n 3 7 2 n 2 8 n 9 +--R - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9b n +--R Type: Expression(Integer) +--E 174 + +--S 175 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 175 + +)clear all + +--S 176 of 1394 +t0:=(a+b*x^n)^8/x +--R +--R +--R (1) +--R 8 n 8 7 n 7 2 6 n 6 3 5 n 5 4 4 n 4 +--R b (x ) + 8a b (x ) + 28a b (x ) + 56a b (x ) + 70a b (x ) +--R + +--R 5 3 n 3 6 2 n 2 7 n 8 +--R 56a b (x ) + 28a b (x ) + 8a b x + a +--R / +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 1394 +r0:=8*a^7*b*x^n/n+14*a^6*b^2*x^(2*n)/n+56/3*a^5*b^3*x^(3*n)/n+_ + 35/2*a^4*b^4*x^(4*n)/n+56/5*a^3*b^5*x^(5*n)/n+_ + 14/3*a^2*b^6*x^(6*n)/n+8/7*a*b^7*x^(7*n)/n+1/8*b^8*x^(8*n)/n+a^8*log(x) +--R +--R +--R (2) +--R 8 8n 7 7n 2 6 6n 3 5 5n 4 4 4n +--R 105b x + 960a b x + 3920a b x + 9408a b x + 14700a b x +--R + +--R 5 3 3n 6 2 2n 7 n 8 +--R 15680a b x + 11760a b x + 6720a b x + 840a n log(x) +--R / +--R 840n +--R Type: Expression(Integer) +--E 177 + +--S 178 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 960a b (%e ) + 3920a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 9408a b (%e ) + 14700a b (%e ) + 15680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 11760a b (%e ) + 6720a b %e + 840a n log(x) +--R / +--R 840n +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 960a b (%e ) + 3920a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 9408a b (%e ) + 14700a b (%e ) + 15680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 8n 7 7n +--R 11760a b (%e ) + 6720a b %e - 105b x - 960a b x +--R + +--R 2 6 6n 3 5 5n 4 4 4n 5 3 3n 6 2 2n +--R - 3920a b x - 9408a b x - 14700a b x - 15680a b x - 11760a b x +--R + +--R 7 n +--R - 6720a b x +--R / +--R 840n +--R Type: Expression(Integer) +--E 179 + +--S 180 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 180 + +)clear all + +--S 181 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - n - 1 n 8 7 - n - 1 n 7 2 6 - n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - n - 1 n 5 4 4 - n - 1 n 4 5 3 - n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - n - 1 n 2 7 - n - 1 n 8 - n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 181 + +--S 182 of 1394 +r0:=-a^8/(n*x^n)+28*a^6*b^2*x^n/n+28*a^5*b^3*x^(2*n)/n+_ + 70/3*a^4*b^4*x^(3*n)/n+14*a^3*b^5*x^(4*n)/n+_ + 28/5*a^2*b^6*x^(5*n)/n+4/3*a*b^7*x^(6*n)/n+1/7*b^8*x^(7*n)/n+_ + 8*a^7*b*log(x) +--R +--R +--R (2) +--R 8 n 7n 7 n 6n 2 6 n 5n 3 5 n 4n 4 4 n 3n +--R 15b x x + 140a b x x + 588a b x x + 1470a b x x + 2450a b x x +--R + +--R 5 3 n 2n 6 2 n 2 7 n 8 +--R 2940a b x x + 2940a b (x ) + 840a b n log(x)x - 105a +--R / +--R n +--R 105n x +--R Type: Expression(Integer) +--E 182 + +--S 183 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 15b (%e ) + 140a b (%e ) + 588a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 1470a b (%e ) + 2450a b (%e ) + 2940a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 2940a b (%e ) + 840a b n log(x)%e - 105a +--R / +--R n log(x) +--R 105n %e +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n n log(x) 8 7 n n log(x) 7 2 6 n n log(x) 6 +--R 15b x (%e ) + 140a b x (%e ) + 588a b x (%e ) +--R + +--R 3 5 n n log(x) 5 4 4 n n log(x) 4 +--R 1470a b x (%e ) + 2450a b x (%e ) +--R + +--R 5 3 n n log(x) 3 6 2 n n log(x) 2 +--R 2940a b x (%e ) + 2940a b x (%e ) +--R + +--R 8 n 7n 7 n 6n 2 6 n 5n 3 5 n 4n +--R - 15b x x - 140a b x x - 588a b x x - 1470a b x x +--R + +--R 4 4 n 3n 5 3 n 2n 6 2 n 2 8 +--R - 2450a b x x - 2940a b x x - 2940a b (x ) + 105a +--R * +--R n log(x) +--R %e +--R + +--R 8 n +--R - 105a x +--R / +--R n n log(x) +--R 105n x %e +--R Type: Expression(Integer) +--E 184 + +--S 185 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 185 + +)clear all + +--S 186 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 2n - 1 n 8 7 - 2n - 1 n 7 2 6 - 2n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 2n - 1 n 5 4 4 - 2n - 1 n 4 5 3 - 2n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 2n - 1 n 2 7 - 2n - 1 n 8 - 2n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 186 + +--S 187 of 1394 +r0:=-1/2*a^8/(n*x^(2*n))-8*a^7*b/(n*x^n)+56*a^5*b^3*x^n/n+_ + 35*a^4*b^4*x^(2*n)/n+56/3*a^3*b^5*x^(3*n)/n+_ + 7*a^2*b^6*x^(4*n)/n+8/5*a*b^7*x^(5*n)/n+1/6*b^8*x^(6*n)/n+_ + 28*a^6*b^2*log(x) +--R +--R +--R (2) +--R 8 n 2n 6n 7 n 2n 5n 2 6 n 2n 4n 3 5 n 2n 3n +--R 5b x x x + 48a b x x x + 210a b x x x + 560a b x x x +--R + +--R 4 4 n 2n 2 5 3 n 2 6 2 n 7 2n 8 n +--R 1050a b x (x ) + (1680a b (x ) + 840a b n log(x)x - 240a b)x - 15a x +--R / +--R n 2n +--R 30n x x +--R Type: Expression(Integer) +--E 187 + +--S 188 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 5b (%e ) + 48a b (%e ) + 210a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R 560a b (%e ) + 1050a b (%e ) + 1680a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R 840a b n log(x)(%e ) - 240a b %e - 15a +--R / +--R n log(x) 2 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n n log(x) 8 7 n 2n n log(x) 7 +--R 5b x x (%e ) + 48a b x x (%e ) +--R + +--R 2 6 n 2n n log(x) 6 3 5 n 2n n log(x) 5 +--R 210a b x x (%e ) + 560a b x x (%e ) +--R + +--R 4 4 n 2n n log(x) 4 5 3 n 2n n log(x) 3 +--R 1050a b x x (%e ) + 1680a b x x (%e ) +--R + +--R 8 n 2n 6n 7 n 2n 5n 2 6 n 2n 4n 3 5 n 2n 3n +--R - 5b x x x - 48a b x x x - 210a b x x x - 560a b x x x +--R + +--R 4 4 n 2n 2 5 3 n 2 7 2n 8 n +--R - 1050a b x (x ) + (- 1680a b (x ) + 240a b)x + 15a x +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 7 n 2n n log(x) 8 n 2n +--R - 240a b x x %e - 15a x x +--R / +--R n 2n n log(x) 2 +--R 30n x x (%e ) +--R Type: Expression(Integer) +--E 189 + +--S 190 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 190 + +)clear all + +--S 191 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 3n - 1 n 8 7 - 3n - 1 n 7 2 6 - 3n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 3n - 1 n 5 4 4 - 3n - 1 n 4 5 3 - 3n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 3n - 1 n 2 7 - 3n - 1 n 8 - 3n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 191 + +--S 192 of 1394 +r0:=-1/3*a^8/(n*x^(3*n))-4*a^7*b/(n*x^(2*n))-28*a^6*b^2/(n*x^n)+_ + 70*a^4*b^4*x^n/n+28*a^3*b^5*x^(2*n)/n+28/3*a^2*b^6*x^(3*n)/n+_ + 2*a*b^7*x^(4*n)/n+1/5*b^8*x^(5*n)/n+56*a^5*b^3*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 5n 7 n 2n 3n 4n 2 6 n 2n 3n 2 +--R 3b x x x x + 30a b x x x x + 140a b x x (x ) +--R + +--R 3 5 n 2n 2 4 4 n 2 5 3 n 6 2 2n +--R 420a b x (x ) + (1050a b (x ) + 840a b n log(x)x - 420a b )x +--R + +--R 7 n +--R - 60a b x +--R * +--R 3n +--R x +--R + +--R 8 n 2n +--R - 5a x x +--R / +--R n 2n 3n +--R 15n x x x +--R Type: Expression(Integer) +--E 192 + +--S 193 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 3b (%e ) + 30a b (%e ) + 140a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 420a b (%e ) + 1050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R 840a b n log(x)(%e ) - 420a b (%e ) - 60a b %e +--R + +--R 8 +--R - 5a +--R / +--R n log(x) 3 +--R 15n (%e ) +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n n log(x) 8 7 n 2n 3n n log(x) 7 +--R 3b x x x (%e ) + 30a b x x x (%e ) +--R + +--R 2 6 n 2n 3n n log(x) 6 3 5 n 2n 3n n log(x) 5 +--R 140a b x x x (%e ) + 420a b x x x (%e ) +--R + +--R 4 4 n 2n 3n n log(x) 4 +--R 1050a b x x x (%e ) +--R + +--R 8 n 2n 3n 5n 7 n 2n 3n 4n 2 6 n 2n 3n 2 +--R - 3b x x x x - 30a b x x x x - 140a b x x (x ) +--R + +--R 3 5 n 2n 2 4 4 n 2 6 2 2n 7 n 3n +--R (- 420a b x (x ) + (- 1050a b (x ) + 420a b )x + 60a b x )x +--R + +--R 8 n 2n +--R 5a x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 6 2 n 2n 3n n log(x) 2 7 n 2n 3n n log(x) 8 n 2n 3n +--R - 420a b x x x (%e ) - 60a b x x x %e - 5a x x x +--R / +--R n 2n 3n n log(x) 3 +--R 15n x x x (%e ) +--R Type: Expression(Integer) +--E 194 + +--S 195 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 195 + +)clear all + +--S 196 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 4n - 1 n 8 7 - 4n - 1 n 7 2 6 - 4n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 4n - 1 n 5 4 4 - 4n - 1 n 4 5 3 - 4n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 4n - 1 n 2 7 - 4n - 1 n 8 - 4n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 196 + +--S 197 of 1394 +r0:=-1/4*a^8/(n*x^(4*n))-8/3*a^7*b/(n*x^(3*n))-14*a^6*b^2/(n*x^(2*n))-_ + 56*a^5*b^3/(n*x^n)+56*a^3*b^5*x^n/n+14*a^2*b^6*x^(2*n)/n+_ + 8/3*a*b^7*x^(3*n)/n+1/4*b^8*x^(4*n)/n+70*a^4*b^4*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 4n 2 +--R 3b x x x (x ) +--R + +--R 7 n 2n 3n 2 +--R 32a b x x (x ) +--R + +--R 2 6 n 2n 2 3 5 n 2 4 4 n 5 3 2n +--R 168a b x (x ) + (672a b (x ) + 840a b n log(x)x - 672a b )x +--R + +--R 6 2 n +--R - 168a b x +--R * +--R 3n +--R x +--R + +--R 7 n 2n +--R - 32a b x x +--R * +--R 4n +--R x +--R + +--R 8 n 2n 3n +--R - 3a x x x +--R / +--R n 2n 3n 4n +--R 12n x x x x +--R Type: Expression(Integer) +--E 197 + +--S 198 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 3b (%e ) + 32a b (%e ) + 168a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 672a b (%e ) + 840a b n log(x)(%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) 8 +--R - 672a b (%e ) - 168a b (%e ) - 32a b %e - 3a +--R / +--R n log(x) 4 +--R 12n (%e ) +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n n log(x) 8 7 n 2n 3n 4n n log(x) 7 +--R 3b x x x x (%e ) + 32a b x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n n log(x) 6 3 5 n 2n 3n 4n n log(x) 5 +--R 168a b x x x x (%e ) + 672a b x x x x (%e ) +--R + +--R 8 n 2n 3n 4n 2 +--R - 3b x x x (x ) +--R + +--R 7 n 2n 3n 2 +--R - 32a b x x (x ) +--R + +--R 2 6 n 2n 2 3 5 n 2 5 3 2n 6 2 n +--R (- 168a b x (x ) + (- 672a b (x ) + 672a b )x + 168a b x ) +--R * +--R 3n +--R x +--R + +--R 7 n 2n +--R 32a b x x +--R * +--R 4n +--R x +--R + +--R 8 n 2n 3n +--R 3a x x x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 5 3 n 2n 3n 4n n log(x) 3 6 2 n 2n 3n 4n n log(x) 2 +--R - 672a b x x x x (%e ) - 168a b x x x x (%e ) +--R + +--R 7 n 2n 3n 4n n log(x) 8 n 2n 3n 4n +--R - 32a b x x x x %e - 3a x x x x +--R / +--R n 2n 3n 4n n log(x) 4 +--R 12n x x x x (%e ) +--R Type: Expression(Integer) +--E 199 + +--S 200 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 200 + +)clear all + +--S 201 of 1394 +t0:=x^(-1-5*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 5n - 1 n 8 7 - 5n - 1 n 7 2 6 - 5n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 5n - 1 n 5 4 4 - 5n - 1 n 4 5 3 - 5n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 5n - 1 n 2 7 - 5n - 1 n 8 - 5n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 1394 +r0:=-1/5*a^8/(n*x^(5*n))-2*a^7*b/(n*x^(4*n))-28/3*a^6*b^2/(n*x^(3*n))-_ + 28*a^5*b^3/(n*x^(2*n))-70*a^4*b^4/(n*x^n)+28*a^2*b^6*x^n/n+_ + 4*a*b^7*x^(2*n)/n+1/3*b^8*x^(3*n)/n+56*a^3*b^5*log(x) +--R +--R +--R (2) +--R 8 n 2n 3n 2 +--R 5b x x (x ) +--R + +--R 7 n 2n 2 +--R 60a b x (x ) +--R + +--R 2 6 n 2 3 5 n 4 4 2n 5 3 n +--R (420a b (x ) + 840a b n log(x)x - 1050a b )x - 420a b x +--R * +--R 3n +--R x +--R + +--R 6 2 n 2n +--R - 140a b x x +--R * +--R 4n +--R x +--R + +--R 7 n 2n 3n +--R - 30a b x x x +--R * +--R 5n +--R x +--R + +--R 8 n 2n 3n 4n +--R - 3a x x x x +--R / +--R n 2n 3n 4n 5n +--R 15n x x x x x +--R Type: Expression(Integer) +--E 202 + +--S 203 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 5b (%e ) + 60a b (%e ) + 420a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R 840a b n log(x)(%e ) - 1050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) 8 +--R - 420a b (%e ) - 140a b (%e ) - 30a b %e - 3a +--R / +--R n log(x) 5 +--R 15n (%e ) +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n n log(x) 8 7 n 2n 3n 4n 5n n log(x) 7 +--R 5b x x x x x (%e ) + 60a b x x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n n log(x) 6 +--R 420a b x x x x x (%e ) +--R + +--R 8 n 2n 3n 2 +--R - 5b x x (x ) +--R + +--R 7 n 2n 2 2 6 n 2 4 4 2n +--R - 60a b x (x ) + (- 420a b (x ) + 1050a b )x +--R + +--R 5 3 n +--R 420a b x +--R * +--R 3n +--R x +--R + +--R 6 2 n 2n +--R 140a b x x +--R * +--R 4n +--R x +--R + +--R 7 n 2n 3n +--R 30a b x x x +--R * +--R 5n +--R x +--R + +--R 8 n 2n 3n 4n +--R 3a x x x x +--R * +--R n log(x) 5 +--R (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n n log(x) 4 +--R - 1050a b x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n n log(x) 3 6 2 n 2n 3n 4n 5n n log(x) 2 +--R - 420a b x x x x x (%e ) - 140a b x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n n log(x) 8 n 2n 3n 4n 5n +--R - 30a b x x x x x %e - 3a x x x x x +--R / +--R n 2n 3n 4n 5n n log(x) 5 +--R 15n x x x x x (%e ) +--R Type: Expression(Integer) +--E 204 + +--S 205 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 205 + +)clear all + +--S 206 of 1394 +t0:=x^(-1-6*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 6n - 1 n 8 7 - 6n - 1 n 7 2 6 - 6n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 6n - 1 n 5 4 4 - 6n - 1 n 4 5 3 - 6n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 6n - 1 n 2 7 - 6n - 1 n 8 - 6n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 206 + +--S 207 of 1394 +r0:=-1/6*a^8/(n*x^(6*n))-8/5*a^7*b/(n*x^(5*n))-7*a^6*b^2/(n*x^(4*n))-_ + 56/3*a^5*b^3/(n*x^(3*n))-35*a^4*b^4/(n*x^(2*n))-_ + 56*a^3*b^5/(n*x^n)+8*a*b^7*x^n/n+1/2*b^8*x^(2*n)/n+28*a^2*b^6*log(x) +--R +--R +--R (2) +--R 8 n 2n 2 +--R 15b x (x ) +--R + +--R 7 n 2 2 6 n 3 5 2n +--R (240a b (x ) + 840a b n log(x)x - 1680a b )x +--R + +--R 4 4 n +--R - 1050a b x +--R * +--R 3n +--R x +--R + +--R 5 3 n 2n +--R - 560a b x x +--R * +--R 4n +--R x +--R + +--R 6 2 n 2n 3n +--R - 210a b x x x +--R * +--R 5n +--R x +--R + +--R 7 n 2n 3n 4n +--R - 48a b x x x x +--R * +--R 6n +--R x +--R + +--R 8 n 2n 3n 4n 5n +--R - 5a x x x x x +--R / +--R n 2n 3n 4n 5n 6n +--R 30n x x x x x x +--R Type: Expression(Integer) +--E 207 + +--S 208 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 15b (%e ) + 240a b (%e ) + 840a b n log(x)(%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 1680a b (%e ) - 1050a b (%e ) - 560a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 210a b (%e ) - 48a b %e - 5a +--R / +--R n log(x) 6 +--R 30n (%e ) +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n 6n n log(x) 8 +--R 15b x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n n log(x) 7 +--R 240a b x x x x x x (%e ) +--R + +--R 8 n 2n 2 7 n 2 3 5 2n +--R - 15b x (x ) + (- 240a b (x ) + 1680a b )x +--R + +--R 4 4 n +--R 1050a b x +--R * +--R 3n +--R x +--R + +--R 5 3 n 2n +--R 560a b x x +--R * +--R 4n +--R x +--R + +--R 6 2 n 2n 3n +--R 210a b x x x +--R * +--R 5n +--R x +--R + +--R 7 n 2n 3n 4n +--R 48a b x x x x +--R * +--R 6n +--R x +--R + +--R 8 n 2n 3n 4n 5n +--R 5a x x x x x +--R * +--R n log(x) 6 +--R (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n n log(x) 5 +--R - 1680a b x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n n log(x) 4 +--R - 1050a b x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n n log(x) 3 +--R - 560a b x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n n log(x) 2 +--R - 210a b x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n n log(x) 8 n 2n 3n 4n 5n 6n +--R - 48a b x x x x x x %e - 5a x x x x x x +--R / +--R n 2n 3n 4n 5n 6n n log(x) 6 +--R 30n x x x x x x (%e ) +--R Type: Expression(Integer) +--E 209 + +--S 210 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 210 + +)clear all + +--S 211 of 1394 +t0:=x^(-1-7*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 7n - 1 n 8 7 - 7n - 1 n 7 2 6 - 7n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 7n - 1 n 5 4 4 - 7n - 1 n 4 5 3 - 7n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 7n - 1 n 2 7 - 7n - 1 n 8 - 7n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 211 + +--S 212 of 1394 +r0:=-1/7*a^8/(n*x^(7*n))-4/3*a^7*b/(n*x^(6*n))-28/5*a^6*b^2/(n*x^(5*n))-_ + 14*a^5*b^3/(n*x^(4*n))-70/3*a^4*b^4/(n*x^(3*n))-_ + 28*a^3*b^5/(n*x^(2*n))-28*a^2*b^6/(n*x^n)+b^8*x^n/n+8*a*b^7*log(x) +--R +--R +--R (2) +--R 8 n 2 7 n 2 6 2n +--R (105b (x ) + 840a b n log(x)x - 2940a b )x +--R + +--R 3 5 n +--R - 2940a b x +--R * +--R 3n +--R x +--R + +--R 4 4 n 2n +--R - 2450a b x x +--R * +--R 4n +--R x +--R + +--R 5 3 n 2n 3n +--R - 1470a b x x x +--R * +--R 5n +--R x +--R + +--R 6 2 n 2n 3n 4n +--R - 588a b x x x x +--R * +--R 6n +--R x +--R + +--R 7 n 2n 3n 4n 5n +--R - 140a b x x x x x +--R * +--R 7n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n +--R - 15a x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n +--R 105n x x x x x x x +--R Type: Expression(Integer) +--E 212 + +--S 213 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R 105b (%e ) + 840a b n log(x)(%e ) - 2940a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 2940a b (%e ) - 2450a b (%e ) - 1470a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 588a b (%e ) - 140a b %e - 15a +--R / +--R n log(x) 7 +--R 105n (%e ) +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 n 2n 3n 4n 5n 6n 7n n log(x) 8 +--R 105b x x x x x x x (%e ) +--R + +--R 8 n 2 2 6 2n 3 5 n 3n +--R ((- 105b (x ) + 2940a b )x + 2940a b x )x +--R + +--R 4 4 n 2n +--R 2450a b x x +--R * +--R 4n +--R x +--R + +--R 5 3 n 2n 3n +--R 1470a b x x x +--R * +--R 5n +--R x +--R + +--R 6 2 n 2n 3n 4n +--R 588a b x x x x +--R * +--R 6n +--R x +--R + +--R 7 n 2n 3n 4n 5n +--R 140a b x x x x x +--R * +--R 7n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n +--R 15a x x x x x x +--R * +--R n log(x) 7 +--R (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n 6n 7n n log(x) 6 +--R - 2940a b x x x x x x x (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n 7n n log(x) 5 +--R - 2940a b x x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n 7n n log(x) 4 +--R - 2450a b x x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n 7n n log(x) 3 +--R - 1470a b x x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n 7n n log(x) 2 +--R - 588a b x x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n n log(x) 8 n 2n 3n 4n 5n 6n 7n +--R - 140a b x x x x x x x %e - 15a x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n n log(x) 7 +--R 105n x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 214 + +--S 215 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 215 + +)clear all + +--S 216 of 1394 +t0:=x^(-1-8*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 8n - 1 n 8 7 - 8n - 1 n 7 2 6 - 8n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 8n - 1 n 5 4 4 - 8n - 1 n 4 5 3 - 8n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 8n - 1 n 2 7 - 8n - 1 n 8 - 8n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 216 + +--S 217 of 1394 +r0:=-1/8*a^8/(n*x^(8*n))-8/7*a^7*b/(n*x^(7*n))-14/3*a^6*b^2/(n*x^(6*n))-_ + 56/5*a^5*b^3/(n*x^(5*n))-35/2*a^4*b^4/(n*x^(4*n))-_ + 56/3*a^3*b^5/(n*x^(3*n))-14*a^2*b^6/(n*x^(2*n))-8*a*b^7/(n*x^n)+b^8*log(x) +--R +--R +--R (2) +--R 8 n 7 2n 2 6 n 3n +--R ((840b n log(x)x - 6720a b )x - 11760a b x )x +--R + +--R 3 5 n 2n +--R - 15680a b x x +--R * +--R 4n +--R x +--R + +--R 4 4 n 2n 3n +--R - 14700a b x x x +--R * +--R 5n +--R x +--R + +--R 5 3 n 2n 3n 4n +--R - 9408a b x x x x +--R * +--R 6n +--R x +--R + +--R 6 2 n 2n 3n 4n 5n +--R - 3920a b x x x x x +--R * +--R 7n +--R x +--R + +--R 7 n 2n 3n 4n 5n 6n +--R - 960a b x x x x x x +--R * +--R 8n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n 7n +--R - 105a x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n 8n +--R 840n x x x x x x x x +--R Type: Expression(Integer) +--E 217 + +--S 218 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 +--R 840b n log(x)(%e ) - 6720a b (%e ) +--R + +--R 2 6 n log(x) 6 3 5 n log(x) 5 +--R - 11760a b (%e ) - 15680a b (%e ) +--R + +--R 4 4 n log(x) 4 5 3 n log(x) 3 6 2 n log(x) 2 +--R - 14700a b (%e ) - 9408a b (%e ) - 3920a b (%e ) +--R + +--R 7 n log(x) 8 +--R - 960a b %e - 105a +--R / +--R n log(x) 8 +--R 840n (%e ) +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 2n 2 6 n 3n 3 5 n 2n 4n +--R ((6720a b x + 11760a b x )x + 15680a b x x )x +--R + +--R 4 4 n 2n 3n +--R 14700a b x x x +--R * +--R 5n +--R x +--R + +--R 5 3 n 2n 3n 4n +--R 9408a b x x x x +--R * +--R 6n +--R x +--R + +--R 6 2 n 2n 3n 4n 5n +--R 3920a b x x x x x +--R * +--R 7n +--R x +--R + +--R 7 n 2n 3n 4n 5n 6n +--R 960a b x x x x x x +--R * +--R 8n +--R x +--R + +--R 8 n 2n 3n 4n 5n 6n 7n +--R 105a x x x x x x x +--R * +--R n log(x) 8 +--R (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n 8n n log(x) 7 +--R - 6720a b x x x x x x x x (%e ) +--R + +--R 2 6 n 2n 3n 4n 5n 6n 7n 8n n log(x) 6 +--R - 11760a b x x x x x x x x (%e ) +--R + +--R 3 5 n 2n 3n 4n 5n 6n 7n 8n n log(x) 5 +--R - 15680a b x x x x x x x x (%e ) +--R + +--R 4 4 n 2n 3n 4n 5n 6n 7n 8n n log(x) 4 +--R - 14700a b x x x x x x x x (%e ) +--R + +--R 5 3 n 2n 3n 4n 5n 6n 7n 8n n log(x) 3 +--R - 9408a b x x x x x x x x (%e ) +--R + +--R 6 2 n 2n 3n 4n 5n 6n 7n 8n n log(x) 2 +--R - 3920a b x x x x x x x x (%e ) +--R + +--R 7 n 2n 3n 4n 5n 6n 7n 8n n log(x) 8 n 2n 3n 4n 5n 6n 7n 8n +--R - 960a b x x x x x x x x %e - 105a x x x x x x x x +--R / +--R n 2n 3n 4n 5n 6n 7n 8n n log(x) 8 +--R 840n x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 219 + +--S 220 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 220 + +)clear all + +--S 221 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 9n - 1 n 8 7 - 9n - 1 n 7 2 6 - 9n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 9n - 1 n 5 4 4 - 9n - 1 n 4 5 3 - 9n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 9n - 1 n 2 7 - 9n - 1 n 8 - 9n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 221 + +--S 222 of 1394 +r0:=-1/9*(a+b*x^n)^9/(a*n*x^(9*n)) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R - 126a b (x ) - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9n +--R 9a n x +--R Type: Expression(Integer) +--E 222 + +--S 223 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 9b (%e ) - 36a b (%e ) - 84a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 126a b (%e ) - 126a b (%e ) - 84a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 36a b (%e ) - 9a b %e - a +--R / +--R n log(x) 9 +--R 9n (%e ) +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 8 9n n log(x) 8 2 7 9n n log(x) 7 3 6 9n n log(x) 6 +--R - 9a b x (%e ) - 36a b x (%e ) - 84a b x (%e ) +--R + +--R 4 5 9n n log(x) 5 5 4 9n n log(x) 4 +--R - 126a b x (%e ) - 126a b x (%e ) +--R + +--R 6 3 9n n log(x) 3 7 2 9n n log(x) 2 8 9n n log(x) +--R - 84a b x (%e ) - 36a b x (%e ) - 9a b x %e +--R + +--R 9 9n +--R - a x +--R / +--R 9n n log(x) 9 +--R 9a n x (%e ) +--R Type: Expression(Integer) +--E 224 + +--S 225 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 225 + +)clear all + +--S 226 of 1394 +t0:=x^(-1-10*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 10n - 1 n 8 7 - 10n - 1 n 7 2 6 - 10n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 10n - 1 n 5 4 4 - 10n - 1 n 4 5 3 - 10n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 10n - 1 n 2 7 - 10n - 1 n 8 - 10n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 226 + +--S 227 of 1394 +r0:=-1/10*(a+b*x^n)^9/(a*n*x^(10*n))+1/90*b*(a+b*x^n)^9/(a^2*n*x^(9*n)) +--R +--R +--R (2) +--R 10 n 9 9 n 8 2 8 n 7 3 7 n 6 4 6 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 5 n 4 6 4 n 3 7 3 n 2 8 2 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 n 10 +--R - 81a b x - 9a +--R * +--R 9n +--R x +--R / +--R 2 9n 10n +--R 90a n x x +--R Type: Expression(Integer) +--E 227 + +--S 228 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 45b (%e ) - 240a b (%e ) - 630a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 1008a b (%e ) - 1050a b (%e ) - 720a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 315a b (%e ) - 80a b %e - 9a +--R / +--R n log(x) 10 +--R 90n (%e ) +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 10 n 9 9 n 8 2 8 n 7 3 7 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 6 n 5 5 5 n 4 6 4 n 3 7 3 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 2 n 9 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 9 n 9 2 8 n 8 3 7 n 7 4 6 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 5 n 5 6 4 n 4 7 3 n 3 8 2 n 2 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) + 324a b (x ) +--R + +--R 9 n 10 +--R 81a b x + 9a +--R * +--R 9n +--R x +--R * +--R n log(x) 10 +--R (%e ) +--R + +--R 2 8 9n 10n n log(x) 8 3 7 9n 10n n log(x) 7 +--R - 45a b x x (%e ) - 240a b x x (%e ) +--R + +--R 4 6 9n 10n n log(x) 6 5 5 9n 10n n log(x) 5 +--R - 630a b x x (%e ) - 1008a b x x (%e ) +--R + +--R 6 4 9n 10n n log(x) 4 7 3 9n 10n n log(x) 3 +--R - 1050a b x x (%e ) - 720a b x x (%e ) +--R + +--R 8 2 9n 10n n log(x) 2 9 9n 10n n log(x) 10 9n 10n +--R - 315a b x x (%e ) - 80a b x x %e - 9a x x +--R / +--R 2 9n 10n n log(x) 10 +--R 90a n x x (%e ) +--R Type: Expression(Integer) +--E 229 + +--S 230 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 230 + +)clear all + +--S 231 of 1394 +t0:=x^(-1-11*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 11n - 1 n 8 7 - 11n - 1 n 7 2 6 - 11n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 11n - 1 n 5 4 4 - 11n - 1 n 4 5 3 - 11n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 11n - 1 n 2 7 - 11n - 1 n 8 - 11n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 231 + +--S 232 of 1394 +r0:=-1/11*(a+b*x^n)^9/(a*n*x^(11*n))+1/55*b*(a+b*x^n)^9/(a^2*n*x^(10*n))-_ + 1/495*b^2*(a+b*x^n)^9/(a^3*n*x^(9*n)) +--R +--R +--R (2) +--R 11 n 9 10 n 8 2 9 n 7 3 8 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 7 n 5 5 6 n 4 6 5 n 3 7 4 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 3 n 9 2 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 10 n 9 2 9 n 8 3 8 n 7 4 7 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 6 n 5 6 5 n 4 7 4 n 3 8 3 n 2 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) + 324a b (x ) +--R + +--R 9 2 n 10 +--R 81a b x + 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 9 n 9 3 8 n 8 4 7 n 7 5 6 n 6 +--R - 45a b (x ) - 405a b (x ) - 1620a b (x ) - 3780a b (x ) +--R + +--R 6 5 n 5 7 4 n 4 8 3 n 3 9 2 n 2 +--R - 5670a b (x ) - 5670a b (x ) - 3780a b (x ) - 1620a b (x ) +--R + +--R 10 n 11 +--R - 405a b x - 45a +--R * +--R 9n 10n +--R x x +--R / +--R 3 9n 10n 11n +--R 495a n x x x +--R Type: Expression(Integer) +--E 232 + +--S 233 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 165b (%e ) - 990a b (%e ) - 2772a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 4620a b (%e ) - 4950a b (%e ) - 3465a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 1540a b (%e ) - 396a b %e - 45a +--R / +--R n log(x) 11 +--R 495n (%e ) +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 11 n 9 10 n 8 2 9 n 7 3 8 n 6 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) +--R + +--R 4 7 n 5 5 6 n 4 6 5 n 3 7 4 n 2 +--R 126a b (x ) + 126a b (x ) + 84a b (x ) + 36a b (x ) +--R + +--R 8 3 n 9 2 +--R 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 10 n 9 2 9 n 8 3 8 n 7 4 7 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 6 n 5 6 5 n 4 7 4 n 3 8 3 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 2 n 10 +--R - 81a b x - 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 9 n 9 3 8 n 8 4 7 n 7 5 6 n 6 +--R 45a b (x ) + 405a b (x ) + 1620a b (x ) + 3780a b (x ) +--R + +--R 6 5 n 5 7 4 n 4 8 3 n 3 9 2 n 2 +--R 5670a b (x ) + 5670a b (x ) + 3780a b (x ) + 1620a b (x ) +--R + +--R 10 n 11 +--R 405a b x + 45a +--R * +--R 9n 10n +--R x x +--R * +--R n log(x) 11 +--R (%e ) +--R + +--R 3 8 9n 10n 11n n log(x) 8 4 7 9n 10n 11n n log(x) 7 +--R - 165a b x x x (%e ) - 990a b x x x (%e ) +--R + +--R 5 6 9n 10n 11n n log(x) 6 6 5 9n 10n 11n n log(x) 5 +--R - 2772a b x x x (%e ) - 4620a b x x x (%e ) +--R + +--R 7 4 9n 10n 11n n log(x) 4 8 3 9n 10n 11n n log(x) 3 +--R - 4950a b x x x (%e ) - 3465a b x x x (%e ) +--R + +--R 9 2 9n 10n 11n n log(x) 2 10 9n 10n 11n n log(x) +--R - 1540a b x x x (%e ) - 396a b x x x %e +--R + +--R 11 9n 10n 11n +--R - 45a x x x +--R / +--R 3 9n 10n 11n n log(x) 11 +--R 495a n x x x (%e ) +--R Type: Expression(Integer) +--E 234 + +--S 235 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 235 + +)clear all + +--S 236 of 1394 +t0:=x^(-1-12*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 12n - 1 n 8 7 - 12n - 1 n 7 2 6 - 12n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 12n - 1 n 5 4 4 - 12n - 1 n 4 5 3 - 12n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 12n - 1 n 2 7 - 12n - 1 n 8 - 12n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 236 + +--S 237 of 1394 +r0:=-1/12*(a+b*x^n)^9/(a*n*x^(12*n))+1/44*b*(a+b*x^n)^9/(a^2*n*x^(11*n))-_ + 1/220*b^2*(a+b*x^n)^9/(a^3*n*x^(10*n))+_ + 1/1980*b^3*(a+b*x^n)^9/(a^4*n*x^(9*n)) +--R +--R +--R (2) +--R 12 n 9 11 n 8 2 10 n 7 3 9 n 6 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) +--R + +--R 4 8 n 5 5 7 n 4 6 6 n 3 7 5 n 2 +--R 126a b (x ) + 126a b (x ) + 84a b (x ) + 36a b (x ) +--R + +--R 8 4 n 9 3 +--R 9a b x + a b +--R * +--R 10n +--R x +--R + +--R 11 n 9 2 10 n 8 3 9 n 7 4 8 n 6 +--R - 9a b (x ) - 81a b (x ) - 324a b (x ) - 756a b (x ) +--R + +--R 5 7 n 5 6 6 n 4 7 5 n 3 8 4 n 2 +--R - 1134a b (x ) - 1134a b (x ) - 756a b (x ) - 324a b (x ) +--R + +--R 9 3 n 10 2 +--R - 81a b x - 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 10 n 9 3 9 n 8 4 8 n 7 5 7 n 6 +--R 45a b (x ) + 405a b (x ) + 1620a b (x ) + 3780a b (x ) +--R + +--R 6 6 n 5 7 5 n 4 8 4 n 3 9 3 n 2 +--R 5670a b (x ) + 5670a b (x ) + 3780a b (x ) + 1620a b (x ) +--R + +--R 10 2 n 11 +--R 405a b x + 45a b +--R * +--R 9n 10n +--R x x +--R * +--R 12n +--R x +--R + +--R 3 9 n 9 4 8 n 8 5 7 n 7 6 6 n 6 +--R - 165a b (x ) - 1485a b (x ) - 5940a b (x ) - 13860a b (x ) +--R + +--R 7 5 n 5 8 4 n 4 9 3 n 3 10 2 n 2 +--R - 20790a b (x ) - 20790a b (x ) - 13860a b (x ) - 5940a b (x ) +--R + +--R 11 n 12 +--R - 1485a b x - 165a +--R * +--R 9n 10n 11n +--R x x x +--R / +--R 4 9n 10n 11n 12n +--R 1980a n x x x x +--R Type: Expression(Integer) +--E 237 + +--S 238 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 495b (%e ) - 3168a b (%e ) - 9240a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 15840a b (%e ) - 17325a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 12320a b (%e ) - 5544a b (%e ) - 1440a b %e +--R + +--R 8 +--R - 165a +--R / +--R n log(x) 12 +--R 1980n (%e ) +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 12 n 9 11 n 8 2 10 n 7 3 9 n 6 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) +--R + +--R 4 8 n 5 5 7 n 4 6 6 n 3 7 5 n 2 +--R - 126a b (x ) - 126a b (x ) - 84a b (x ) - 36a b (x ) +--R + +--R 8 4 n 9 3 +--R - 9a b x - a b +--R * +--R 10n +--R x +--R + +--R 11 n 9 2 10 n 8 3 9 n 7 4 8 n 6 +--R 9a b (x ) + 81a b (x ) + 324a b (x ) + 756a b (x ) +--R + +--R 5 7 n 5 6 6 n 4 7 5 n 3 +--R 1134a b (x ) + 1134a b (x ) + 756a b (x ) +--R + +--R 8 4 n 2 9 3 n 10 2 +--R 324a b (x ) + 81a b x + 9a b +--R * +--R 9n +--R x +--R * +--R 11n +--R x +--R + +--R 2 10 n 9 3 9 n 8 4 8 n 7 5 7 n 6 +--R - 45a b (x ) - 405a b (x ) - 1620a b (x ) - 3780a b (x ) +--R + +--R 6 6 n 5 7 5 n 4 8 4 n 3 +--R - 5670a b (x ) - 5670a b (x ) - 3780a b (x ) +--R + +--R 9 3 n 2 10 2 n 11 +--R - 1620a b (x ) - 405a b x - 45a b +--R * +--R 9n 10n +--R x x +--R * +--R 12n +--R x +--R + +--R 3 9 n 9 4 8 n 8 5 7 n 7 6 6 n 6 +--R 165a b (x ) + 1485a b (x ) + 5940a b (x ) + 13860a b (x ) +--R + +--R 7 5 n 5 8 4 n 4 9 3 n 3 10 2 n 2 +--R 20790a b (x ) + 20790a b (x ) + 13860a b (x ) + 5940a b (x ) +--R + +--R 11 n 12 +--R 1485a b x + 165a +--R * +--R 9n 10n 11n +--R x x x +--R * +--R n log(x) 12 +--R (%e ) +--R + +--R 4 8 9n 10n 11n 12n n log(x) 8 +--R - 495a b x x x x (%e ) +--R + +--R 5 7 9n 10n 11n 12n n log(x) 7 +--R - 3168a b x x x x (%e ) +--R + +--R 6 6 9n 10n 11n 12n n log(x) 6 +--R - 9240a b x x x x (%e ) +--R + +--R 7 5 9n 10n 11n 12n n log(x) 5 +--R - 15840a b x x x x (%e ) +--R + +--R 8 4 9n 10n 11n 12n n log(x) 4 +--R - 17325a b x x x x (%e ) +--R + +--R 9 3 9n 10n 11n 12n n log(x) 3 +--R - 12320a b x x x x (%e ) +--R + +--R 10 2 9n 10n 11n 12n n log(x) 2 +--R - 5544a b x x x x (%e ) +--R + +--R 11 9n 10n 11n 12n n log(x) 12 9n 10n 11n 12n +--R - 1440a b x x x x %e - 165a x x x x +--R / +--R 4 9n 10n 11n 12n n log(x) 12 +--R 1980a n x x x x (%e ) +--R Type: Expression(Integer) +--E 239 + +--S 240 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 240 + +)clear all + +--S 241 of 1394 +t0:=x^(-1-13*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 13n - 1 n 8 7 - 13n - 1 n 7 2 6 - 13n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 13n - 1 n 5 4 4 - 13n - 1 n 4 5 3 - 13n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 13n - 1 n 2 7 - 13n - 1 n 8 - 13n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 241 + +--S 242 of 1394 +r0:=-1/13*a^8/(n*x^(13*n))-2/3*a^7*b/(n*x^(12*n))-_ + 28/11*a^6*b^2/(n*x^(11*n))-28/5*a^5*b^3/(n*x^(10*n))-_ + 70/9*a^4*b^4/(n*x^(9*n))-7*a^3*b^5/(n*x^(8*n))-_ + 4*a^2*b^6/(n*x^(7*n))-4/3*a*b^7/(n*x^(6*n))-1/5*b^8/(n*x^(5*n)) +--R +--R +--R (2) +--R 8 6n 7 5n 7n 2 6 5n 6n 8n +--R ((- 1287b x - 8580a b x )x - 25740a b x x )x +--R + +--R 3 5 5n 6n 7n +--R - 45045a b x x x +--R * +--R 9n +--R x +--R + +--R 4 4 5n 6n 7n 8n +--R - 50050a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 3 5n 6n 7n 8n 9n +--R - 36036a b x x x x x +--R * +--R 11n +--R x +--R + +--R 6 2 5n 6n 7n 8n 9n 10n +--R - 16380a b x x x x x x +--R * +--R 12n +--R x +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n +--R - 4290a b x x x x x x x +--R * +--R 13n +--R x +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n +--R - 495a x x x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n 11n 12n 13n +--R 6435n x x x x x x x x x +--R Type: Expression(Integer) +--E 242 + +--S 243 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 1287b (%e ) - 8580a b (%e ) - 25740a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 45045a b (%e ) - 50050a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 36036a b (%e ) - 16380a b (%e ) - 4290a b %e +--R + +--R 8 +--R - 495a +--R / +--R n log(x) 13 +--R 6435n (%e ) +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 6n 7 5n 7n +--R (1287b x + 8580a b x )x +--R + +--R 2 6 5n 6n +--R 25740a b x x +--R * +--R 8n +--R x +--R + +--R 3 5 5n 6n 7n +--R 45045a b x x x +--R * +--R 9n +--R x +--R + +--R 4 4 5n 6n 7n 8n +--R 50050a b x x x x +--R * +--R 10n +--R x +--R + +--R 5 3 5n 6n 7n 8n 9n +--R 36036a b x x x x x +--R * +--R 11n +--R x +--R + +--R 6 2 5n 6n 7n 8n 9n 10n +--R 16380a b x x x x x x +--R * +--R 12n +--R x +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n +--R 4290a b x x x x x x x +--R * +--R 13n +--R x +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n +--R 495a x x x x x x x x +--R * +--R n log(x) 13 +--R (%e ) +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 8 +--R - 1287b x x x x x x x x x (%e ) +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 7 +--R - 8580a b x x x x x x x x x (%e ) +--R + +--R 2 6 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 6 +--R - 25740a b x x x x x x x x x (%e ) +--R + +--R 3 5 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 5 +--R - 45045a b x x x x x x x x x (%e ) +--R + +--R 4 4 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 4 +--R - 50050a b x x x x x x x x x (%e ) +--R + +--R 5 3 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 3 +--R - 36036a b x x x x x x x x x (%e ) +--R + +--R 6 2 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 2 +--R - 16380a b x x x x x x x x x (%e ) +--R + +--R 7 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) +--R - 4290a b x x x x x x x x x %e +--R + +--R 8 5n 6n 7n 8n 9n 10n 11n 12n 13n +--R - 495a x x x x x x x x x +--R / +--R 5n 6n 7n 8n 9n 10n 11n 12n 13n n log(x) 13 +--R 6435n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 244 + +--S 245 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 245 + +)clear all + +--S 246 of 1394 +t0:=x^(-1-14*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 14n - 1 n 8 7 - 14n - 1 n 7 2 6 - 14n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 14n - 1 n 5 4 4 - 14n - 1 n 4 5 3 - 14n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 14n - 1 n 2 7 - 14n - 1 n 8 - 14n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 246 + +--S 247 of 1394 +r0:=-1/14*a^8/(n*x^(14*n))-8/13*a^7*b/(n*x^(13*n))-_ + 7/3*a^6*b^2/(n*x^(12*n))-56/11*a^5*b^3/(n*x^(11*n))-_ + 7*a^4*b^4/(n*x^(10*n))-56/9*a^3*b^5/(n*x^(9*n))-_ + 7/2*a^2*b^6/(n*x^(8*n))-8/7*a*b^7/(n*x^(7*n))-1/6*b^8/(n*x^(6*n)) +--R +--R +--R (2) +--R 8 7n 7 6n 8n 2 6 6n 7n +--R ((- 3003b x - 20592a b x )x - 63063a b x x ) +--R * +--R 9n +--R x +--R + +--R 3 5 6n 7n 8n +--R - 112112a b x x x +--R * +--R 10n +--R x +--R + +--R 4 4 6n 7n 8n 9n +--R - 126126a b x x x x +--R * +--R 11n +--R x +--R + +--R 5 3 6n 7n 8n 9n 10n +--R - 91728a b x x x x x +--R * +--R 12n +--R x +--R + +--R 6 2 6n 7n 8n 9n 10n 11n +--R - 42042a b x x x x x x +--R * +--R 13n +--R x +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n +--R - 11088a b x x x x x x x +--R * +--R 14n +--R x +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n +--R - 1287a x x x x x x x x +--R / +--R 6n 7n 8n 9n 10n 11n 12n 13n 14n +--R 18018n x x x x x x x x x +--R Type: Expression(Integer) +--E 247 + +--S 248 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 3003b (%e ) - 20592a b (%e ) - 63063a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 112112a b (%e ) - 126126a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 91728a b (%e ) - 42042a b (%e ) - 11088a b %e +--R + +--R 8 +--R - 1287a +--R / +--R n log(x) 14 +--R 18018n (%e ) +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 7n 7 6n 8n +--R (3003b x + 20592a b x )x +--R + +--R 2 6 6n 7n +--R 63063a b x x +--R * +--R 9n +--R x +--R + +--R 3 5 6n 7n 8n +--R 112112a b x x x +--R * +--R 10n +--R x +--R + +--R 4 4 6n 7n 8n 9n +--R 126126a b x x x x +--R * +--R 11n +--R x +--R + +--R 5 3 6n 7n 8n 9n 10n +--R 91728a b x x x x x +--R * +--R 12n +--R x +--R + +--R 6 2 6n 7n 8n 9n 10n 11n +--R 42042a b x x x x x x +--R * +--R 13n +--R x +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n +--R 11088a b x x x x x x x +--R * +--R 14n +--R x +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n +--R 1287a x x x x x x x x +--R * +--R n log(x) 14 +--R (%e ) +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 8 +--R - 3003b x x x x x x x x x (%e ) +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 7 +--R - 20592a b x x x x x x x x x (%e ) +--R + +--R 2 6 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 6 +--R - 63063a b x x x x x x x x x (%e ) +--R + +--R 3 5 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 5 +--R - 112112a b x x x x x x x x x (%e ) +--R + +--R 4 4 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 4 +--R - 126126a b x x x x x x x x x (%e ) +--R + +--R 5 3 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 3 +--R - 91728a b x x x x x x x x x (%e ) +--R + +--R 6 2 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 2 +--R - 42042a b x x x x x x x x x (%e ) +--R + +--R 7 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) +--R - 11088a b x x x x x x x x x %e +--R + +--R 8 6n 7n 8n 9n 10n 11n 12n 13n 14n +--R - 1287a x x x x x x x x x +--R / +--R 6n 7n 8n 9n 10n 11n 12n 13n 14n n log(x) 14 +--R 18018n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 249 + +--S 250 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 250 + +)clear all + +--S 251 of 1394 +t0:=x^(-1-15*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 15n - 1 n 8 7 - 15n - 1 n 7 2 6 - 15n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 15n - 1 n 5 4 4 - 15n - 1 n 4 5 3 - 15n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 15n - 1 n 2 7 - 15n - 1 n 8 - 15n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 251 + +--S 252 of 1394 +r0:=-1/15*a^8/(n*x^(15*n))-4/7*a^7*b/(n*x^(14*n))-_ + 28/13*a^6*b^2/(n*x^(13*n))-14/3*a^5*b^3/(n*x^(12*n))-_ + 70/11*a^4*b^4/(n*x^(11*n))-28/5*a^3*b^5/(n*x^(10*n))-_ + 28/9*a^2*b^6/(n*x^(9*n))-a*b^7/(n*x^(8*n))-1/7*b^8/(n*x^(7*n)) +--R +--R +--R (2) +--R 8 8n 7 7n 9n +--R (- 6435b x - 45045a b x )x +--R + +--R 2 6 7n 8n +--R - 140140a b x x +--R * +--R 10n +--R x +--R + +--R 3 5 7n 8n 9n +--R - 252252a b x x x +--R * +--R 11n +--R x +--R + +--R 4 4 7n 8n 9n 10n +--R - 286650a b x x x x +--R * +--R 12n +--R x +--R + +--R 5 3 7n 8n 9n 10n 11n +--R - 210210a b x x x x x +--R * +--R 13n +--R x +--R + +--R 6 2 7n 8n 9n 10n 11n 12n +--R - 97020a b x x x x x x +--R * +--R 14n +--R x +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n +--R - 25740a b x x x x x x x +--R * +--R 15n +--R x +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n +--R - 3003a x x x x x x x x +--R / +--R 7n 8n 9n 10n 11n 12n 13n 14n 15n +--R 45045n x x x x x x x x x +--R Type: Expression(Integer) +--E 252 + +--S 253 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 6435b (%e ) - 45045a b (%e ) - 140140a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 +--R - 252252a b (%e ) - 286650a b (%e ) +--R + +--R 5 3 n log(x) 3 6 2 n log(x) 2 7 n log(x) +--R - 210210a b (%e ) - 97020a b (%e ) - 25740a b %e +--R + +--R 8 +--R - 3003a +--R / +--R n log(x) 15 +--R 45045n (%e ) +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 8 8n 7 7n 9n +--R (6435b x + 45045a b x )x +--R + +--R 2 6 7n 8n +--R 140140a b x x +--R * +--R 10n +--R x +--R + +--R 3 5 7n 8n 9n +--R 252252a b x x x +--R * +--R 11n +--R x +--R + +--R 4 4 7n 8n 9n 10n +--R 286650a b x x x x +--R * +--R 12n +--R x +--R + +--R 5 3 7n 8n 9n 10n 11n +--R 210210a b x x x x x +--R * +--R 13n +--R x +--R + +--R 6 2 7n 8n 9n 10n 11n 12n +--R 97020a b x x x x x x +--R * +--R 14n +--R x +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n +--R 25740a b x x x x x x x +--R * +--R 15n +--R x +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n +--R 3003a x x x x x x x x +--R * +--R n log(x) 15 +--R (%e ) +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 8 +--R - 6435b x x x x x x x x x (%e ) +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 7 +--R - 45045a b x x x x x x x x x (%e ) +--R + +--R 2 6 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 6 +--R - 140140a b x x x x x x x x x (%e ) +--R + +--R 3 5 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 5 +--R - 252252a b x x x x x x x x x (%e ) +--R + +--R 4 4 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 4 +--R - 286650a b x x x x x x x x x (%e ) +--R + +--R 5 3 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 3 +--R - 210210a b x x x x x x x x x (%e ) +--R + +--R 6 2 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 2 +--R - 97020a b x x x x x x x x x (%e ) +--R + +--R 7 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) +--R - 25740a b x x x x x x x x x %e +--R + +--R 8 7n 8n 9n 10n 11n 12n 13n 14n 15n +--R - 3003a x x x x x x x x x +--R / +--R 7n 8n 9n 10n 11n 12n 13n 14n 15n n log(x) 15 +--R 45045n x x x x x x x x x (%e ) +--R Type: Expression(Integer) +--E 254 + +--S 255 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 255 + +)clear all + +--S 256 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^m +--R +--R +--R n - 1 n m +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 256 + +--S 257 of 1394 +r0:=(a+b*x^n)^(1+m)/(b*(1+m)*n) +--R +--R +--R n m + 1 +--R (b x + a) +--R (2) --------------- +--R (b m + b)n +--R Type: Expression(Integer) +--E 257 + +--S 258 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R n log(x) m log(b %e + a) +--R (b %e + a)%e +--R (3) ------------------------------------------- +--R (b m + b)n +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) +--R n log(x) m log(b %e + a) n m + 1 +--R (b %e + a)%e - (b x + a) +--R (4) ------------------------------------------------------------- +--R (b m + b)n +--R Type: Expression(Integer) +--E 259 + +--S 260 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 260 + +)clear all + +--S 261 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^16 +--R +--R +--R (1) +--R 16 n - 1 n 16 15 n - 1 n 15 2 14 n - 1 n 14 +--R b x (x ) + 16a b x (x ) + 120a b x (x ) +--R + +--R 3 13 n - 1 n 13 4 12 n - 1 n 12 5 11 n - 1 n 11 +--R 560a b x (x ) + 1820a b x (x ) + 4368a b x (x ) +--R + +--R 6 10 n - 1 n 10 7 9 n - 1 n 9 8 8 n - 1 n 8 +--R 8008a b x (x ) + 11440a b x (x ) + 12870a b x (x ) +--R + +--R 9 7 n - 1 n 7 10 6 n - 1 n 6 11 5 n - 1 n 5 +--R 11440a b x (x ) + 8008a b x (x ) + 4368a b x (x ) +--R + +--R 12 4 n - 1 n 4 13 3 n - 1 n 3 14 2 n - 1 n 2 +--R 1820a b x (x ) + 560a b x (x ) + 120a b x (x ) +--R + +--R 15 n - 1 n 16 n - 1 +--R 16a b x x + a x +--R Type: Expression(Integer) +--E 261 + +--S 262 of 1394 +r0:=1/17*(a+b*x^n)^17/(b*n) +--R +--R +--R (2) +--R 17 n 17 16 n 16 2 15 n 15 3 14 n 14 +--R b (x ) + 17a b (x ) + 136a b (x ) + 680a b (x ) +--R + +--R 4 13 n 13 5 12 n 12 6 11 n 11 7 10 n 10 +--R 2380a b (x ) + 6188a b (x ) + 12376a b (x ) + 19448a b (x ) +--R + +--R 8 9 n 9 9 8 n 8 10 7 n 7 11 6 n 6 +--R 24310a b (x ) + 24310a b (x ) + 19448a b (x ) + 12376a b (x ) +--R + +--R 12 5 n 5 13 4 n 4 14 3 n 3 15 2 n 2 +--R 6188a b (x ) + 2380a b (x ) + 680a b (x ) + 136a b (x ) +--R + +--R 16 n 17 +--R 17a b x + a +--R / +--R 17b n +--R Type: Expression(Integer) +--E 262 + +--S 263 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 16 n log(x) 17 15 n log(x) 16 2 14 n log(x) 15 +--R b (%e ) + 17a b (%e ) + 136a b (%e ) +--R + +--R 3 13 n log(x) 14 4 12 n log(x) 13 +--R 680a b (%e ) + 2380a b (%e ) +--R + +--R 5 11 n log(x) 12 6 10 n log(x) 11 +--R 6188a b (%e ) + 12376a b (%e ) +--R + +--R 7 9 n log(x) 10 8 8 n log(x) 9 9 7 n log(x) 8 +--R 19448a b (%e ) + 24310a b (%e ) + 24310a b (%e ) +--R + +--R 10 6 n log(x) 7 11 5 n log(x) 6 +--R 19448a b (%e ) + 12376a b (%e ) +--R + +--R 12 4 n log(x) 5 13 3 n log(x) 4 14 2 n log(x) 3 +--R 6188a b (%e ) + 2380a b (%e ) + 680a b (%e ) +--R + +--R 15 n log(x) 2 16 n log(x) +--R 136a b (%e ) + 17a %e +--R / +--R 17n +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 17 n log(x) 17 16 n log(x) 16 2 15 n log(x) 15 +--R b (%e ) + 17a b (%e ) + 136a b (%e ) +--R + +--R 3 14 n log(x) 14 4 13 n log(x) 13 +--R 680a b (%e ) + 2380a b (%e ) +--R + +--R 5 12 n log(x) 12 6 11 n log(x) 11 +--R 6188a b (%e ) + 12376a b (%e ) +--R + +--R 7 10 n log(x) 10 8 9 n log(x) 9 +--R 19448a b (%e ) + 24310a b (%e ) +--R + +--R 9 8 n log(x) 8 10 7 n log(x) 7 +--R 24310a b (%e ) + 19448a b (%e ) +--R + +--R 11 6 n log(x) 6 12 5 n log(x) 5 13 4 n log(x) 4 +--R 12376a b (%e ) + 6188a b (%e ) + 2380a b (%e ) +--R + +--R 14 3 n log(x) 3 15 2 n log(x) 2 16 n log(x) +--R 680a b (%e ) + 136a b (%e ) + 17a b %e +--R + +--R 17 n 17 16 n 16 2 15 n 15 3 14 n 14 +--R - b (x ) - 17a b (x ) - 136a b (x ) - 680a b (x ) +--R + +--R 4 13 n 13 5 12 n 12 6 11 n 11 7 10 n 10 +--R - 2380a b (x ) - 6188a b (x ) - 12376a b (x ) - 19448a b (x ) +--R + +--R 8 9 n 9 9 8 n 8 10 7 n 7 11 6 n 6 +--R - 24310a b (x ) - 24310a b (x ) - 19448a b (x ) - 12376a b (x ) +--R + +--R 12 5 n 5 13 4 n 4 14 3 n 3 15 2 n 2 +--R - 6188a b (x ) - 2380a b (x ) - 680a b (x ) - 136a b (x ) +--R + +--R 16 n 17 +--R - 17a b x - a +--R / +--R 17b n +--R Type: Expression(Integer) +--E 264 + +--S 265 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 265 + +)clear all + +--S 266 of 1394 +t0:=x^12*(a+b*x^13)^12 +--R +--R +--R (1) +--R 12 168 11 155 2 10 142 3 9 129 4 8 116 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 103 6 6 90 7 5 77 8 4 64 9 3 51 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 38 11 25 12 12 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 266 + +--S 267 of 1394 +r0:=1/169*(a+b*x^13)^13/b +--R +--R +--R (2) +--R 1 13 169 1 12 156 6 2 11 143 22 3 10 130 55 4 9 117 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 169 13 13 13 13 +--R + +--R 99 5 8 104 132 6 7 91 132 7 6 78 99 8 5 65 55 9 4 52 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 13 13 13 13 13 +--R + +--R 22 10 3 39 6 11 2 26 1 12 13 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 13 13 13 169 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 267 + +--S 268 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 169 1 11 156 6 2 10 143 22 3 9 130 55 4 8 117 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 169 13 13 13 13 +--R + +--R 99 5 7 104 132 6 6 91 132 7 5 78 99 8 4 65 55 9 3 52 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 13 13 13 13 13 +--R + +--R 22 10 2 39 6 11 26 1 12 13 +--R -- a b x + -- a b x + -- a x +--R 13 13 13 +--R Type: Polynomial(Fraction(Integer)) +--E 268 + +--S 269 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 169 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 269 + +--S 270 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 270 + +)clear all + +--S 271 of 1394 +t0:=x^24*(a+b*x^25)^12 +--R +--R +--R (1) +--R 12 324 11 299 2 10 274 3 9 249 4 8 224 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 199 6 6 174 7 5 149 8 4 124 9 3 99 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 74 11 49 12 24 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 271 + +--S 272 of 1394 +r0:=1/325*(a+b*x^25)^13/b +--R +--R +--R (2) +--R 1 13 325 1 12 300 6 2 11 275 22 3 10 250 11 4 9 225 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 325 25 25 25 5 +--R + +--R 99 5 8 200 132 6 7 175 132 7 6 150 99 8 5 125 11 9 4 100 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 25 25 25 25 5 +--R + +--R 22 10 3 75 6 11 2 50 1 12 25 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 25 25 25 325 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 272 + +--S 273 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 325 1 11 300 6 2 10 275 22 3 9 250 11 4 8 225 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 325 25 25 25 5 +--R + +--R 99 5 7 200 132 6 6 175 132 7 5 150 99 8 4 125 11 9 3 100 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 25 25 25 25 5 +--R + +--R 22 10 2 75 6 11 50 1 12 25 +--R -- a b x + -- a b x + -- a x +--R 25 25 25 +--R Type: Polynomial(Fraction(Integer)) +--E 273 + +--S 274 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 325 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 274 + +--S 275 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 275 + +)clear all + +--S 276 of 1394 +t0:=x^36*(a+b*x^37)^12 +--R +--R +--R (1) +--R 12 480 11 443 2 10 406 3 9 369 4 8 332 +--R b x + 12a b x + 66a b x + 220a b x + 495a b x +--R + +--R 5 7 295 6 6 258 7 5 221 8 4 184 9 3 147 +--R 792a b x + 924a b x + 792a b x + 495a b x + 220a b x +--R + +--R 10 2 110 11 73 12 36 +--R 66a b x + 12a b x + a x +--R Type: Polynomial(Integer) +--E 276 + +--S 277 of 1394 +r0:=1/481*(a+b*x^37)^13/b +--R +--R +--R (2) +--R 1 13 481 1 12 444 6 2 11 407 22 3 10 370 55 4 9 333 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 481 37 37 37 37 +--R + +--R 99 5 8 296 132 6 7 259 132 7 6 222 99 8 5 185 55 9 4 148 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 37 37 37 37 37 +--R + +--R 22 10 3 111 6 11 2 74 1 12 37 1 13 +--R -- a b x + -- a b x + -- a b x + --- a +--R 37 37 37 481 +--R / +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 277 + +--S 278 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 12 481 1 11 444 6 2 10 407 22 3 9 370 55 4 8 333 +--R --- b x + -- a b x + -- a b x + -- a b x + -- a b x +--R 481 37 37 37 37 +--R + +--R 99 5 7 296 132 6 6 259 132 7 5 222 99 8 4 185 55 9 3 148 +--R -- a b x + --- a b x + --- a b x + -- a b x + -- a b x +--R 37 37 37 37 37 +--R + +--R 22 10 2 111 6 11 74 1 12 37 +--R -- a b x + -- a b x + -- a x +--R 37 37 37 +--R Type: Polynomial(Fraction(Integer)) +--E 278 + +--S 279 of 1394 +m0:=a0-r0 +--R +--R +--R 1 13 +--R --- a +--R 481 +--R (4) - ------- +--R b +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 279 + +--S 280 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 280 + +)clear all + +--S 281 of 1394 +t0:=x^(12*m)*(a+b*x^(1+12*m))^12 +--R +--R +--R (1) +--R 12 12m 12m + 1 12 11 12m 12m + 1 11 2 10 12m 12m + 1 10 +--R b x (x ) + 12a b x (x ) + 66a b x (x ) +--R + +--R 3 9 12m 12m + 1 9 4 8 12m 12m + 1 8 5 7 12m 12m + 1 7 +--R 220a b x (x ) + 495a b x (x ) + 792a b x (x ) +--R + +--R 6 6 12m 12m + 1 6 7 5 12m 12m + 1 5 8 4 12m 12m + 1 4 +--R 924a b x (x ) + 792a b x (x ) + 495a b x (x ) +--R + +--R 9 3 12m 12m + 1 3 10 2 12m 12m + 1 2 11 12m 12m + 1 +--R 220a b x (x ) + 66a b x (x ) + 12a b x x +--R + +--R 12 12m +--R a x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 1394 +r0:=1/13*(a+b*x^(1+12*m))^13/(b*(1+12*m)) +--R +--R +--R (2) +--R 13 12m + 1 13 12 12m + 1 12 2 11 12m + 1 11 +--R b (x ) + 13a b (x ) + 78a b (x ) +--R + +--R 3 10 12m + 1 10 4 9 12m + 1 9 5 8 12m + 1 8 +--R 286a b (x ) + 715a b (x ) + 1287a b (x ) +--R + +--R 6 7 12m + 1 7 7 6 12m + 1 6 8 5 12m + 1 5 +--R 1716a b (x ) + 1716a b (x ) + 1287a b (x ) +--R + +--R 9 4 12m + 1 4 10 3 12m + 1 3 11 2 12m + 1 2 +--R 715a b (x ) + 286a b (x ) + 78a b (x ) +--R + +--R 12 12m + 1 13 +--R 13a b x + a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 282 + +--S 283 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 (12m + 1)log(x) 13 11 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 10 (12m + 1)log(x) 11 3 9 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 8 (12m + 1)log(x) 9 5 7 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 6 (12m + 1)log(x) 7 7 5 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 4 (12m + 1)log(x) 5 9 3 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 2 (12m + 1)log(x) 3 11 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) +--R 13a %e +--R / +--R 156m + 13 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 (12m + 1)log(x) 13 12 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 11 (12m + 1)log(x) 11 3 10 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 9 (12m + 1)log(x) 9 5 8 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 7 (12m + 1)log(x) 7 7 6 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 5 (12m + 1)log(x) 5 9 4 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 3 (12m + 1)log(x) 3 11 2 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) 13 12m + 1 13 12 12m + 1 12 +--R 13a b %e - b (x ) - 13a b (x ) +--R + +--R 2 11 12m + 1 11 3 10 12m + 1 10 4 9 12m + 1 9 +--R - 78a b (x ) - 286a b (x ) - 715a b (x ) +--R + +--R 5 8 12m + 1 8 6 7 12m + 1 7 7 6 12m + 1 6 +--R - 1287a b (x ) - 1716a b (x ) - 1716a b (x ) +--R + +--R 8 5 12m + 1 5 9 4 12m + 1 4 10 3 12m + 1 3 +--R - 1287a b (x ) - 715a b (x ) - 286a b (x ) +--R + +--R 11 2 12m + 1 2 12 12m + 1 13 +--R - 78a b (x ) - 13a b x - a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 284 + +--S 285 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 285 + +)clear all + +--S 286 of 1394 +t0:=x^(12+12*(-1+m))*(a+b*x^(1+12*m))^12 +--R +--R +--R (1) +--R 12 12m 12m + 1 12 11 12m 12m + 1 11 2 10 12m 12m + 1 10 +--R b x (x ) + 12a b x (x ) + 66a b x (x ) +--R + +--R 3 9 12m 12m + 1 9 4 8 12m 12m + 1 8 5 7 12m 12m + 1 7 +--R 220a b x (x ) + 495a b x (x ) + 792a b x (x ) +--R + +--R 6 6 12m 12m + 1 6 7 5 12m 12m + 1 5 8 4 12m 12m + 1 4 +--R 924a b x (x ) + 792a b x (x ) + 495a b x (x ) +--R + +--R 9 3 12m 12m + 1 3 10 2 12m 12m + 1 2 11 12m 12m + 1 +--R 220a b x (x ) + 66a b x (x ) + 12a b x x +--R + +--R 12 12m +--R a x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 1394 +r0:=1/13*(a+b*x^(1+12*m))^13/(b*(1+12*m)) +--R +--R +--R (2) +--R 13 12m + 1 13 12 12m + 1 12 2 11 12m + 1 11 +--R b (x ) + 13a b (x ) + 78a b (x ) +--R + +--R 3 10 12m + 1 10 4 9 12m + 1 9 5 8 12m + 1 8 +--R 286a b (x ) + 715a b (x ) + 1287a b (x ) +--R + +--R 6 7 12m + 1 7 7 6 12m + 1 6 8 5 12m + 1 5 +--R 1716a b (x ) + 1716a b (x ) + 1287a b (x ) +--R + +--R 9 4 12m + 1 4 10 3 12m + 1 3 11 2 12m + 1 2 +--R 715a b (x ) + 286a b (x ) + 78a b (x ) +--R + +--R 12 12m + 1 13 +--R 13a b x + a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 287 + +--S 288 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 12 (12m + 1)log(x) 13 11 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 10 (12m + 1)log(x) 11 3 9 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 8 (12m + 1)log(x) 9 5 7 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 6 (12m + 1)log(x) 7 7 5 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 4 (12m + 1)log(x) 5 9 3 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 2 (12m + 1)log(x) 3 11 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) +--R 13a %e +--R / +--R 156m + 13 +--R Type: Union(Expression(Integer),...) +--E 288 + +--S 289 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 13 (12m + 1)log(x) 13 12 (12m + 1)log(x) 12 +--R b (%e ) + 13a b (%e ) +--R + +--R 2 11 (12m + 1)log(x) 11 3 10 (12m + 1)log(x) 10 +--R 78a b (%e ) + 286a b (%e ) +--R + +--R 4 9 (12m + 1)log(x) 9 5 8 (12m + 1)log(x) 8 +--R 715a b (%e ) + 1287a b (%e ) +--R + +--R 6 7 (12m + 1)log(x) 7 7 6 (12m + 1)log(x) 6 +--R 1716a b (%e ) + 1716a b (%e ) +--R + +--R 8 5 (12m + 1)log(x) 5 9 4 (12m + 1)log(x) 4 +--R 1287a b (%e ) + 715a b (%e ) +--R + +--R 10 3 (12m + 1)log(x) 3 11 2 (12m + 1)log(x) 2 +--R 286a b (%e ) + 78a b (%e ) +--R + +--R 12 (12m + 1)log(x) 13 12m + 1 13 12 12m + 1 12 +--R 13a b %e - b (x ) - 13a b (x ) +--R + +--R 2 11 12m + 1 11 3 10 12m + 1 10 4 9 12m + 1 9 +--R - 78a b (x ) - 286a b (x ) - 715a b (x ) +--R + +--R 5 8 12m + 1 8 6 7 12m + 1 7 7 6 12m + 1 6 +--R - 1287a b (x ) - 1716a b (x ) - 1716a b (x ) +--R + +--R 8 5 12m + 1 5 9 4 12m + 1 4 10 3 12m + 1 3 +--R - 1287a b (x ) - 715a b (x ) - 286a b (x ) +--R + +--R 11 2 12m + 1 2 12 12m + 1 13 +--R - 78a b (x ) - 13a b x - a +--R / +--R 156b m + 13b +--R Type: Expression(Integer) +--E 289 + +--S 290 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 290 + +)clear all + +--S 291 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 1394 +r0:=a^2*x^n/(b^3*n)-1/2*a*x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-_ + a^3*log(a+b*x^n)/(b^4*n) +--R +--R +--R 3 n 3 3n 2 2n 2 n +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 292 + +--S 293 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 6a log(b %e + a) + 2b (%e ) - 3a b (%e ) +--R + +--R 2 n log(x) +--R 6a b %e +--R / +--R 4 +--R 6b n +--R Type: Union(Expression(Integer),...) +--E 293 + +--S 294 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 n 3 n log(x) 3 +--R - 6a log(b %e + a) + 6a log(b x + a) + 2b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 3n 2 2n 2 n +--R - 3a b (%e ) + 6a b %e - 2b x + 3a b x - 6a b x +--R / +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 294 + +--S 295 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 295 + +)clear all + +--S 296 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 1394 +r0:=-a*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+a^2*log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 2n n +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 297 + +--S 298 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R 2a log(b %e + a) + b (%e ) - 2a b %e +--R (3) ------------------------------------------------------------ +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 2 n 2 n log(x) 2 +--R 2a log(b %e + a) - 2a log(b x + a) + b (%e ) +--R + +--R n log(x) 2 2n n +--R - 2a b %e - b x + 2a b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 299 + +--S 300 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 300 + +)clear all + +--S 301 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 1394 +r0:=x^n/(b*n)-a*log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R b n +--R Type: Expression(Integer) +--E 302 + +--S 303 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - a log(b %e + a) + b %e +--R (3) ---------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - a log(b %e + a) + a log(b x + a) + b %e - b x +--R (4) ----------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 304 + +--S 305 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 305 + +)clear all + +--S 306 of 1394 +t0:=x^(-1+n)/(a+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 1394 +r0:=log(a+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + a) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 307 + +--S 308 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + a) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + a) - log(b x + a) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 309 + +--S 310 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 310 + +)clear all + +--S 311 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 311 + +--S 312 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 312 + +--S 313 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 314 + +--S 315 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 315 + +)clear all + +--S 316 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 317 + +--S 318 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 319 + +--S 320 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 320 + +)clear all + +--S 321 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 321 + +--S 322 of 1394 +r0:=(-1/2)/(a*n*x^(2*n))+b/(a^2*n*x^n)+b^2*log(x)/a^3-b^2*log(a+b*x^n)/(a^3*n) +--R +--R +--R 2 n 2n n 2 n 2n 2 n +--R - 2b x x log(b x + a) + (2b n log(x)x + 2a b)x - a x +--R (2) ---------------------------------------------------------- +--R 3 n 2n +--R 2a n x x +--R Type: Expression(Integer) +--E 322 + +--S 323 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - 2b (%e ) log(b %e + a) + 2b n log(x)(%e ) +--R + +--R n log(x) 2 +--R 2a b %e - a +--R / +--R 3 n log(x) 2 +--R 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - 2b x x (%e ) log(b %e + a) +--R + +--R 2 n 2n n log(x) 2 n 2n 2 n n log(x) 2 +--R 2b x x (%e ) log(b x + a) + (- 2a b x + a x )(%e ) +--R + +--R n 2n n log(x) 2 n 2n +--R 2a b x x %e - a x x +--R / +--R 3 n 2n n log(x) 2 +--R 2a n x x (%e ) +--R Type: Expression(Integer) +--E 324 + +--S 325 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 325 + +)clear all + +--S 326 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 1394 +r0:=(-1/3)/(a*n*x^(3*n))+1/2*b/(a^2*n*x^(2*n))-b^2/(a^3*n*x^n)-_ + b^3*log(x)/a^4+b^3*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2n 3n n 3 n 2 2n 2 n 3n +--R 6b x x x log(b x + a) + ((- 6b n log(x)x - 6a b )x + 3a b x )x +--R + +--R 3 n 2n +--R - 2a x x +--R / +--R 4 n 2n 3n +--R 6a n x x x +--R Type: Expression(Integer) +--E 327 + +--S 328 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 6b (%e ) log(b %e + a) - 6b n log(x)(%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 6a b (%e ) + 3a b %e - 2a +--R / +--R 4 n log(x) 3 +--R 6a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 6b x x x (%e ) log(b %e + a) +--R + +--R 3 n 2n 3n n log(x) 3 n +--R - 6b x x x (%e ) log(b x + a) +--R + +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((6a b x - 3a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 6a b x x x (%e ) + 3a b x x x %e - 2a x x x +--R / +--R 4 n 2n 3n n log(x) 3 +--R 6a n x x x (%e ) +--R Type: Expression(Integer) +--E 329 + +--S 330 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 330 + +)clear all + +--S 331 of 1394 +t0:=x^(3+4*(-1+n))/(a+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 1394 +r0:=a^2*x^n/(b^3*n)-1/2*a*x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-_ + a^3*log(a+b*x^n)/(b^4*n) +--R +--R +--R 3 n 3 3n 2 2n 2 n +--R - 6a log(b x + a) + 2b x - 3a b x + 6a b x +--R (2) ------------------------------------------------ +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 332 + +--S 333 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 6a log(b %e + a) + 2b (%e ) - 3a b (%e ) +--R + +--R 2 n log(x) +--R 6a b %e +--R / +--R 4 +--R 6b n +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 n 3 n log(x) 3 +--R - 6a log(b %e + a) + 6a log(b x + a) + 2b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 3n 2 2n 2 n +--R - 3a b (%e ) + 6a b %e - 2b x + 3a b x - 6a b x +--R / +--R 4 +--R 6b n +--R Type: Expression(Integer) +--E 334 + +--S 335 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 335 + +)clear all + +--S 336 of 1394 +t0:=x^(2+3*(-1+n))/(a+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 1394 +r0:=-a*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+a^2*log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 2n n +--R 2a log(b x + a) + b x - 2a b x +--R (2) ---------------------------------- +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 337 + +--S 338 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R 2a log(b %e + a) + b (%e ) - 2a b %e +--R (3) ------------------------------------------------------------ +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n log(x) 2 n 2 n log(x) 2 +--R 2a log(b %e + a) - 2a log(b x + a) + b (%e ) +--R + +--R n log(x) 2 2n n +--R - 2a b %e - b x + 2a b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 339 + +--S 340 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 340 + +)clear all + +--S 341 of 1394 +t0:=x^(1+2*(-1+n))/(a+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 1394 +r0:=x^n/(b*n)-a*log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - a log(b x + a) + b x +--R (2) ------------------------ +--R 2 +--R b n +--R Type: Expression(Integer) +--E 342 + +--S 343 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - a log(b %e + a) + b %e +--R (3) ---------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - a log(b %e + a) + a log(b x + a) + b %e - b x +--R (4) ----------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 344 + +--S 345 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 345 + +)clear all + +--S 346 of 1394 +t0:=x^(-1+n)/(a+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 346 + +--S 347 of 1394 +r0:=log(a+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + a) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 347 + +--S 348 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + a) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + a) - log(b x + a) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 349 + +--S 350 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 350 + +)clear all + +--S 351 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 351 + +--S 352 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 352 + +--S 353 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 354 + +--S 355 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 355 + +)clear all + +--S 356 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 357 + +--S 358 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 359 + +--S 360 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 360 + +)clear all + +--S 361 of 1394 +t0:=x^(-3-2*(-1+n))/(a+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 1394 +r0:=(-1/2)/(a*n*x^(2*n))+b/(a^2*n*x^n)+b^2*log(x)/a^3-b^2*log(a+b*x^n)/(a^3*n) +--R +--R +--R 2 n 2n n 2 n 2n 2 n +--R - 2b x x log(b x + a) + (2b n log(x)x + 2a b)x - a x +--R (2) ---------------------------------------------------------- +--R 3 n 2n +--R 2a n x x +--R Type: Expression(Integer) +--E 362 + +--S 363 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - 2b (%e ) log(b %e + a) + 2b n log(x)(%e ) +--R + +--R n log(x) 2 +--R 2a b %e - a +--R / +--R 3 n log(x) 2 +--R 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - 2b x x (%e ) log(b %e + a) +--R + +--R 2 n 2n n log(x) 2 n 2n 2 n n log(x) 2 +--R 2b x x (%e ) log(b x + a) + (- 2a b x + a x )(%e ) +--R + +--R n 2n n log(x) 2 n 2n +--R 2a b x x %e - a x x +--R / +--R 3 n 2n n log(x) 2 +--R 2a n x x (%e ) +--R Type: Expression(Integer) +--E 364 + +--S 365 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 365 + +)clear all + +--S 366 of 1394 +t0:=x^(-4-3*(-1+n))/(a+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 1394 +r0:=(-1/3)/(a*n*x^(3*n))+1/2*b/(a^2*n*x^(2*n))-b^2/(a^3*n*x^n)-_ + b^3*log(x)/a^4+b^3*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2n 3n n 3 n 2 2n 2 n 3n +--R 6b x x x log(b x + a) + ((- 6b n log(x)x - 6a b )x + 3a b x )x +--R + +--R 3 n 2n +--R - 2a x x +--R / +--R 4 n 2n 3n +--R 6a n x x x +--R Type: Expression(Integer) +--E 367 + +--S 368 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 6b (%e ) log(b %e + a) - 6b n log(x)(%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 6a b (%e ) + 3a b %e - 2a +--R / +--R 4 n log(x) 3 +--R 6a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 6b x x x (%e ) log(b %e + a) +--R + +--R 3 n 2n 3n n log(x) 3 n +--R - 6b x x x (%e ) log(b x + a) +--R + +--R 2 2n 2 n 3n 3 n 2n n log(x) 3 +--R ((6a b x - 3a b x )x + 2a x x )(%e ) +--R + +--R 2 n 2n 3n n log(x) 2 2 n 2n 3n n log(x) 3 n 2n 3n +--R - 6a b x x x (%e ) + 3a b x x x %e - 2a x x x +--R / +--R 4 n 2n 3n n log(x) 3 +--R 6a n x x x (%e ) +--R Type: Expression(Integer) +--E 369 + +--S 370 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 370 + +)clear all + +--S 371 of 1394 +t0:=x^(-1+4*n)/(2+b*x^n) +--R +--R +--R 4n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 1394 +r0:=4*x^n/(b^3*n)-x^(2*n)/(b^2*n)+1/3*x^(3*n)/(b*n)-8*log(2+b*x^n)/(b^4*n) +--R +--R +--R n 3 3n 2 2n n +--R - 24log(b x + 2) + b x - 3b x + 12b x +--R (2) ------------------------------------------- +--R 4 +--R 3b n +--R Type: Expression(Integer) +--E 372 + +--S 373 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) 3 n log(x) 3 2 n log(x) 2 +--R - 24log(b %e + 2) + b (%e ) - 3b (%e ) +--R + +--R n log(x) +--R 12b %e +--R / +--R 4 +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) n 3 n log(x) 3 +--R - 24log(b %e + 2) + 24log(b x + 2) + b (%e ) +--R + +--R 2 n log(x) 2 n log(x) 3 3n 2 2n n +--R - 3b (%e ) + 12b %e - b x + 3b x - 12b x +--R / +--R 4 +--R 3b n +--R Type: Expression(Integer) +--E 374 + +--S 375 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 375 + +)clear all + +--S 376 of 1394 +t0:=x^(-1+3*n)/(2+b*x^n) +--R +--R +--R 3n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 1394 +r0:=-2*x^n/(b^2*n)+1/2*x^(2*n)/(b*n)+4*log(2+b*x^n)/(b^3*n) +--R +--R +--R n 2 2n n +--R 8log(b x + 2) + b x - 4b x +--R (2) ------------------------------ +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 377 + +--S 378 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) 2 n log(x) 2 n log(x) +--R 8log(b %e + 2) + b (%e ) - 4b %e +--R (3) -------------------------------------------------------- +--R 3 +--R 2b n +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) n 2 n log(x) 2 n log(x) +--R 8log(b %e + 2) - 8log(b x + 2) + b (%e ) - 4b %e +--R + +--R 2 2n n +--R - b x + 4b x +--R / +--R 3 +--R 2b n +--R Type: Expression(Integer) +--E 379 + +--S 380 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 380 + +)clear all + +--S 381 of 1394 +t0:=x^(-1+2*n)/(2+b*x^n) +--R +--R +--R 2n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 1394 +r0:=x^n/(b*n)-2*log(2+b*x^n)/(b^2*n) +--R +--R +--R n n +--R - 2log(b x + 2) + b x +--R (2) ----------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 382 + +--S 383 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R - 2log(b %e + 2) + b %e +--R (3) --------------------------------------- +--R 2 +--R b n +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n n log(x) n +--R - 2log(b %e + 2) + 2log(b x + 2) + b %e - b x +--R (4) --------------------------------------------------------------- +--R 2 +--R b n +--R Type: Expression(Integer) +--E 384 + +--S 385 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 385 + +)clear all + +--S 386 of 1394 +t0:=x^(-1+n)/(2+b*x^n) +--R +--R +--R n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 386 + +--S 387 of 1394 +r0:=log(2+b*x^n)/(b*n) +--R +--R +--R n +--R log(b x + 2) +--R (2) ------------- +--R b n +--R Type: Expression(Integer) +--E 387 + +--S 388 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(b %e + 2) +--R (3) --------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(b %e + 2) - log(b x + 2) +--R (4) ------------------------------------- +--R b n +--R Type: Expression(Integer) +--E 389 + +--S 390 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 390 + +)clear all + +--S 391 of 1394 +t0:=1/(x*(2+b*x^n)) +--R +--R +--R 1 +--R (1) ----------- +--R n +--R b x x + 2x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 1394 +r0:=-atanh(1+b*x^n)/n +--R +--R +--R n +--R atanh(b x + 1) +--R (2) - --------------- +--R n +--R Type: Expression(Integer) +--E 392 + +--S 393 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + 2) + n log(x) +--R (3) ---------------------------------- +--R 2n +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + 2) + 2atanh(b x + 1) + n log(x) +--R (4) ----------------------------------------------------- +--R 2n +--R Type: Expression(Integer) +--E 394 + +--S 395 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 395 + +)clear all + +--S 396 of 1394 +t0:=x^(-1-n)/(2+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 1394 +r0:=(-1/2)/(n*x^n)+1/2*b*atanh(1+b*x^n)/n +--R +--R +--R n n +--R b x atanh(b x + 1) - 1 +--R (2) ----------------------- +--R n +--R 2n x +--R Type: Expression(Integer) +--E 397 + +--S 398 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + 2) - b n log(x)%e - 2 +--R (3) ------------------------------------------------------------ +--R n log(x) +--R 4n %e +--R Type: Union(Expression(Integer),...) +--E 398 + +--S 399 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) +--R b x %e log(b %e + 2) +--R + +--R n n n n log(x) n +--R (- 2b x atanh(b x + 1) - b n log(x)x + 2)%e - 2x +--R / +--R n n log(x) +--R 4n x %e +--R Type: Expression(Integer) +--E 399 + +--S 400 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 400 + +)clear all + +--S 401 of 1394 +t0:=x^(-1-2*n)/(2+b*x^n) +--R +--R +--R - 2n - 1 +--R x +--R (1) --------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 1394 +r0:=(-1/4)/(n*x^(2*n))+1/4*b/(n*x^n)-1/4*b^2*atanh(1+b*x^n)/n +--R +--R +--R 2 n 2n n 2n n +--R - b x x atanh(b x + 1) + b x - x +--R (2) ------------------------------------- +--R n 2n +--R 4n x x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) 2 +--R - b (%e ) log(b %e + 2) + b n log(x)(%e ) +--R + +--R n log(x) +--R 2b %e - 2 +--R / +--R n log(x) 2 +--R 8n (%e ) +--R Type: Union(Expression(Integer),...) +--E 403 + +--S 404 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 n log(x) +--R - b x x (%e ) log(b %e + 2) +--R + +--R 2 n 2n n 2 n 2n n n log(x) 2 +--R (2b x x atanh(b x + 1) + (b n log(x)x - 2b)x + 2x )(%e ) +--R + +--R n 2n n log(x) n 2n +--R 2b x x %e - 2x x +--R / +--R n 2n n log(x) 2 +--R 8n x x (%e ) +--R Type: Expression(Integer) +--E 404 + +--S 405 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 405 + +)clear all + +--S 406 of 1394 +t0:=x^(-1-3*n)/(2+b*x^n) +--R +--R +--R - 3n - 1 +--R x +--R (1) --------- +--R n +--R b x + 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 1394 +r0:=(-1/6)/(n*x^(3*n))+1/8*b/(n*x^(2*n))-1/8*b^2/(n*x^n)+_ + 1/8*b^3*atanh(1+b*x^n)/n +--R +--R +--R 3 n 2n 3n n 2 2n n 3n n 2n +--R 3b x x x atanh(b x + 1) + (- 3b x + 3b x )x - 4x x +--R (2) ----------------------------------------------------------- +--R n 2n 3n +--R 24n x x x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 n log(x) 3 n log(x) 3 +--R 3b (%e ) log(b %e + 2) - 3b n log(x)(%e ) +--R + +--R 2 n log(x) 2 n log(x) +--R - 6b (%e ) + 6b %e - 8 +--R / +--R n log(x) 3 +--R 48n (%e ) +--R Type: Union(Expression(Integer),...) +--E 408 + +--S 409 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 n log(x) +--R 3b x x x (%e ) log(b %e + 2) +--R + +--R 3 n 2n 3n n +--R - 6b x x x atanh(b x + 1) +--R + +--R 3 n 2 2n n 3n n 2n +--R ((- 3b n log(x)x + 6b )x - 6b x )x + 8x x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 n 2n 3n n log(x) 2 n 2n 3n n log(x) n 2n 3n +--R - 6b x x x (%e ) + 6b x x x %e - 8x x x +--R / +--R n 2n 3n n log(x) 3 +--R 48n x x x (%e ) +--R Type: Expression(Integer) +--E 409 + +--S 410 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 410 + +)clear all + +--S 411 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^2 +--R +--R +--R 4n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 411 + +--S 412 of 1394 +r0:=-2*a*x^n/(b^3*n)+1/2*x^(2*n)/(b^2*n)+a^3/(b^4*n*(a+b*x^n))+_ + 3*a^2*log(a+b*x^n)/(b^4*n) +--R +--R +--R (2) +--R 2 n 3 n 3 n 2 2n 2 n 2 2 n 3 +--R (6a b x + 6a )log(b x + a) + (b x + a b )x - 4a b (x ) - 4a b x + 2a +--R ---------------------------------------------------------------------------- +--R 5 n 4 +--R 2b n x + 2a b n +--R Type: Expression(Integer) +--E 412 + +--S 413 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 3 n log(x) 3 n log(x) 3 +--R (6a b %e + 6a )log(b %e + a) + b (%e ) +--R + +--R 2 n log(x) 2 2 n log(x) 3 +--R - 3a b (%e ) - 4a b %e + 2a +--R / +--R 5 n log(x) 4 +--R 2b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n 3 n log(x) 3 n 4 n log(x) +--R ((6a b x + 6a b)%e + 6a b x + 6a )log(b %e + a) +--R + +--R 2 2 n 3 n log(x) 3 n 4 n +--R ((- 6a b x - 6a b)%e - 6a b x - 6a )log(b x + a) +--R + +--R 4 n 3 n log(x) 3 3 n 2 2 n log(x) 2 +--R (b x + a b )(%e ) + (- 3a b x - 3a b )(%e ) +--R + +--R 4 n 3 2n 3 n 2 3 n log(x) 3 n 2 2 2n +--R ((- b x - a b )x + 4a b (x ) - 6a b)%e + (- a b x - a b )x +--R + +--R 2 2 n 2 3 n +--R 4a b (x ) + 6a b x +--R / +--R 6 n 5 n log(x) 5 n 2 4 +--R (2b n x + 2a b n)%e + 2a b n x + 2a b n +--R Type: Expression(Integer) +--E 414 + +--S 415 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 415 + +)clear all + +--S 416 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^2 +--R +--R +--R 3n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 416 + +--S 417 of 1394 +r0:=x^n/(b^2*n)-a^2/(b^3*n*(a+b*x^n))-2*a*log(a+b*x^n)/(b^3*n) +--R +--R +--R n 2 n 2 n 2 n 2 +--R (- 2a b x - 2a )log(b x + a) + b (x ) + a b x - a +--R (2) ------------------------------------------------------ +--R 4 n 3 +--R b n x + a b n +--R Type: Expression(Integer) +--E 417 + +--S 418 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) 2 n log(x) 2 n log(x) 2 +--R (- 2a b %e - 2a )log(b %e + a) + b (%e ) +--R + +--R n log(x) 2 +--R a b %e - a +--R / +--R 4 n log(x) 3 +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n 2 n log(x) 2 n 3 n log(x) +--R ((- 2a b x - 2a b)%e - 2a b x - 2a )log(b %e + a) +--R + +--R 2 n 2 n log(x) 2 n 3 n +--R ((2a b x + 2a b)%e + 2a b x + 2a )log(b x + a) +--R + +--R 3 n 2 n log(x) 2 3 n 2 2 n log(x) 2 n 2 +--R (b x + a b )(%e ) + (- b (x ) + 2a b)%e - a b (x ) +--R + +--R 2 n +--R - 2a b x +--R / +--R 5 n 4 n log(x) 4 n 2 3 +--R (b n x + a b n)%e + a b n x + a b n +--R Type: Expression(Integer) +--E 419 + +--S 420 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 420 + +)clear all + +--S 421 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^2 +--R +--R +--R 2n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 421 + +--S 422 of 1394 +r0:=a/(b^2*n*(a+b*x^n))+log(a+b*x^n)/(b^2*n) +--R +--R +--R n n +--R (b x + a)log(b x + a) + a +--R (2) --------------------------- +--R 3 n 2 +--R b n x + a b n +--R Type: Expression(Integer) +--E 422 + +--S 423 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) +--R (b %e + a)log(b %e + a) + a +--R (3) ------------------------------------------- +--R 3 n log(x) 2 +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((b x + a b)%e + a b x + a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((- b x - a b)%e - a b x - a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 4 n 3 n log(x) 3 n 2 2 +--R (b n x + a b n)%e + a b n x + a b n +--R Type: Expression(Integer) +--E 424 + +--S 425 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 425 + +)clear all + +--S 426 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^2 +--R +--R +--R n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 426 + +--S 427 of 1394 +r0:=(-1)/(b*n*(a+b*x^n)) +--R +--R +--R 1 +--R (2) - -------------- +--R 2 n +--R b n x + a b n +--R Type: Expression(Integer) +--E 427 + +--S 428 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ---------------------- +--R 2 n log(x) +--R b n %e + a b n +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R %e - x +--R (4) ------------------------------------------- +--R 2 n n log(x) n 2 +--R (b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 429 + +--S 430 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 430 + +)clear all + +--S 431 of 1394 +t0:=1/(x*(a+b*x^n)^2) +--R +--R +--R 1 +--R (1) --------------------------- +--R 2 n 2 n 2 +--R b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 1394 +r0:=1/(a*n*(a+b*x^n))+log(x)/a^2-log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R (- b x - a)log(b x + a) + b n log(x)x + a n log(x) + a +--R (2) --------------------------------------------------------- +--R 2 n 3 +--R a b n x + a n +--R Type: Expression(Integer) +--E 432 + +--S 433 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) n log(x) n log(x) +--R (- b %e - a)log(b %e + a) + b n log(x)%e +--R + +--R a n log(x) + a +--R / +--R 2 n log(x) 3 +--R a b n %e + a n +--R Type: Union(Expression(Integer),...) +--E 433 + +--S 434 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 n n log(x) n 2 n log(x) +--R ((- b x - a b)%e - a b x - a )log(b %e + a) +--R + +--R 2 n n log(x) n 2 n n log(x) +--R ((b x + a b)%e + a b x + a )log(b x + a) - a b %e +--R + +--R n +--R a b x +--R / +--R 2 2 n 3 n log(x) 3 n 4 +--R (a b n x + a b n)%e + a b n x + a n +--R Type: Expression(Integer) +--E 434 + +--S 435 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 435 + +)clear all + +--S 436 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^2 +--R +--R +--R - n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 1394 +r0:=(-2)/(a^2*n*x^n)+1/(a*n*x^n*(a+b*x^n))-2*b*log(x)/a^3+_ + 2*b*log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n n 2 n 2 +--R (2b (x ) + 2a b x )log(b x + a) - 2b n log(x)(x ) +--R + +--R n 2 +--R (- 2a b n log(x) - 2a b)x - a +--R / +--R 3 n 2 4 n +--R a b n (x ) + a n x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) n log(x) +--R (2b (%e ) + 2a b %e )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R - 2b n log(x)(%e ) + (- 2a b n log(x) - 2a b)%e - a +--R / +--R 3 n log(x) 2 4 n log(x) +--R a b n (%e ) + a n %e +--R Type: Union(Expression(Integer),...) +--E 438 + +--S 439 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n 2 2 n n log(x) 2 2 n 2 2 n n log(x) +--R ((2b (x ) + 2a b x )(%e ) + (2a b (x ) + 2a b x )%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 3 n 2 2 n n log(x) 2 +--R (- 2b (x ) - 2a b x )(%e ) +--R + +--R 2 n 2 2 n n log(x) +--R (- 2a b (x ) - 2a b x )%e +--R * +--R n +--R log(b x + a) +--R + +--R 2 n 2 n log(x) 2 2 n 2 3 n log(x) 2 n 2 +--R (2a b x + a b)(%e ) + (- 2a b (x ) + a )%e - a b (x ) +--R + +--R 3 n +--R - a x +--R / +--R 3 2 n 2 4 n n log(x) 2 4 n 2 5 n n log(x) +--R (a b n (x ) + a b n x )(%e ) + (a b n (x ) + a n x )%e +--R Type: Expression(Integer) +--E 439 + +--S 440 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 440 + +)clear all + +--S 441 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^2 +--R +--R +--R - 2n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 1394 +r0:=(-3/2)/(a^2*n*x^(2*n))+3*b/(a^3*n*x^n)+1/(a*n*x^(2*n)*(a+b*x^n))+_ + 3*b^2*log(x)/a^4-3*b^2*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 2 2 n 2n n +--R (- 6b (x ) - 6a b x )x log(b x + a) +--R + +--R 3 n 2 2 2 n 2 2n 2 n 2 +--R (6b n log(x)(x ) + (6a b n log(x) + 6a b )x + 6a b)x - 3a b (x ) +--R + +--R 3 n +--R - a x +--R / +--R 4 n 2 5 n 2n +--R (2a b n (x ) + 2a n x )x +--R Type: Expression(Integer) +--E 442 + +--S 443 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 n log(x) +--R (- 6b (%e ) - 6a b (%e ) )log(b %e + a) +--R + +--R 3 n log(x) 3 2 2 n log(x) 2 +--R 6b n log(x)(%e ) + (6a b n log(x) + 6a b )(%e ) +--R + +--R 2 n log(x) 3 +--R 3a b %e - a +--R / +--R 4 n log(x) 3 5 n log(x) 2 +--R 2a b n (%e ) + 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 443 + +--S 444 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2n n log(x) 3 +--R (- 6b (x ) - 6a b x )x (%e ) +--R + +--R 3 n 2 2 2 n 2n n log(x) 2 +--R (- 6a b (x ) - 6a b x )x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2n n log(x) 3 +--R (6b (x ) + 6a b x )x (%e ) +--R + +--R 3 n 2 2 2 n 2n n log(x) 2 +--R (6a b (x ) + 6a b x )x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 2n 2 2 n 2 3 n n log(x) 3 +--R ((- 6a b x - 6a b )x + 3a b (x ) + a b x )(%e ) +--R + +--R 3 n 2 3 2n 3 n 2 4 n n log(x) 2 +--R ((6a b (x ) - 6a b)x + 3a b (x ) + a x )(%e ) +--R + +--R 2 2 n 2 3 n 2n n log(x) 3 n 2 4 n 2n +--R (3a b (x ) + 3a b x )x %e + (- a b (x ) - a x )x +--R / +--R 4 2 n 2 5 n 2n n log(x) 3 +--R (2a b n (x ) + 2a b n x )x (%e ) +--R + +--R 5 n 2 6 n 2n n log(x) 2 +--R (2a b n (x ) + 2a n x )x (%e ) +--R Type: Expression(Integer) +--E 444 + +--S 445 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 445 + +)clear all + +--S 446 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n)^2 +--R +--R +--R - 3n - 1 +--R x +--R (1) ---------------------- +--R 2 n 2 n 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 446 + +--S 447 of 1394 +r0:=(-4/3)/(a^2*n*x^(3*n))+2*b/(a^3*n*x^(2*n))-4*b^2/(a^4*n*x^n)+_ + 1/(a*n*x^(3*n)*(a+b*x^n))-4*b^3*log(x)/a^5+4*b^3*log(a+b*x^n)/(a^5*n) +--R +--R +--R (2) +--R 4 n 2 3 n 2n 3n n +--R (12b (x ) + 12a b x )x x log(b x + a) +--R + +--R 4 n 2 3 3 n 2 2 2n +--R (- 12b n log(x)(x ) + (- 12a b n log(x) - 12a b )x - 12a b )x +--R + +--R 2 2 n 2 3 n +--R 6a b (x ) + 6a b x +--R * +--R 3n +--R x +--R + +--R 3 n 2 4 n 2n +--R (- 4a b (x ) - a x )x +--R / +--R 5 n 2 6 n 2n 3n +--R (3a b n (x ) + 3a n x )x x +--R Type: Expression(Integer) +--E 447 + +--S 448 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 n log(x) +--R (12b (%e ) + 12a b (%e ) )log(b %e + a) +--R + +--R 4 n log(x) 4 3 3 n log(x) 3 +--R - 12b n log(x)(%e ) + (- 12a b n log(x) - 12a b )(%e ) +--R + +--R 2 2 n log(x) 2 3 n log(x) 4 +--R - 6a b (%e ) + 2a b %e - a +--R / +--R 5 n log(x) 4 6 n log(x) 3 +--R 3a b n (%e ) + 3a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 2 4 n 2n 3n n log(x) 4 +--R (12b (x ) + 12a b x )x x (%e ) +--R + +--R 4 n 2 2 3 n 2n 3n n log(x) 3 +--R (12a b (x ) + 12a b x )x x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 5 n 2 4 n 2n 3n n log(x) 4 +--R (- 12b (x ) - 12a b x )x x (%e ) +--R + +--R 4 n 2 2 3 n 2n 3n n log(x) 3 +--R (- 12a b (x ) - 12a b x )x x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 4 n 2 3 2n 2 3 n 2 3 2 n 3n +--R ((12a b x + 12a b )x - 6a b (x ) - 6a b x )x +--R + +--R 3 2 n 2 4 n 2n +--R (4a b (x ) + a b x )x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 4 n 2 3 2 2n 3 2 n 2 4 n 3n +--R ((- 12a b (x ) + 12a b )x - 6a b (x ) - 6a b x )x +--R + +--R 4 n 2 5 n 2n +--R (4a b (x ) + a x )x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 3 n 2 3 2 n 2n 3n n log(x) 2 +--R (- 6a b (x ) - 6a b x )x x (%e ) +--R + +--R 3 2 n 2 4 n 2n 3n n log(x) 4 n 2 5 n 2n 3n +--R (2a b (x ) + 2a b x )x x %e + (- a b (x ) - a x )x x +--R / +--R 5 2 n 2 6 n 2n 3n n log(x) 4 +--R (3a b n (x ) + 3a b n x )x x (%e ) +--R + +--R 6 n 2 7 n 2n 3n n log(x) 3 +--R (3a b n (x ) + 3a n x )x x (%e ) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 450 + +)clear all + +--S 451 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^3 +--R +--R +--R 4n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 451 + +--S 452 of 1394 +r0:=x^n/(b^3*n)+1/2*a^3/(b^4*n*(a+b*x^n)^2)-3*a^2/(b^4*n*(a+b*x^n))-_ + 3*a*log(a+b*x^n)/(b^4*n) +--R +--R +--R (2) +--R 2 n 2 2 n 3 n 3 n 3 2 n 2 +--R (- 6a b (x ) - 12a b x - 6a )log(b x + a) + 2b (x ) + 4a b (x ) +--R + +--R 2 n 3 +--R - 4a b x - 5a +--R / +--R 6 n 2 5 n 2 4 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 452 + +--S 453 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 2 n log(x) 3 n log(x) +--R (- 6a b (%e ) - 12a b %e - 6a )log(b %e + a) +--R + +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R 2b (%e ) + 4a b (%e ) - 4a b %e - 5a +--R / +--R 6 n log(x) 2 5 n log(x) 2 4 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 2 3 n 3 2 n log(x) 2 +--R (- 6a b (x ) - 12a b x - 6a b )(%e ) +--R + +--R 2 3 n 2 3 2 n 4 n log(x) 3 2 n 2 4 n +--R (- 12a b (x ) - 24a b x - 12a b)%e - 6a b (x ) - 12a b x +--R + +--R 5 +--R - 6a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 2 3 n 3 2 n log(x) 2 +--R (6a b (x ) + 12a b x + 6a b )(%e ) +--R + +--R 2 3 n 2 3 2 n 4 n log(x) 3 2 n 2 4 n +--R (12a b (x ) + 24a b x + 12a b)%e + 6a b (x ) + 12a b x +--R + +--R 5 +--R 6a +--R * +--R n +--R log(b x + a) +--R + +--R 5 n 2 4 n 2 3 n log(x) 3 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 5 n 3 2 3 n 3 2 n log(x) 2 +--R (- 2b (x ) + 12a b x + 9a b )(%e ) +--R + +--R 4 n 3 2 3 n 2 4 n log(x) 2 3 n 3 3 2 n 2 +--R (- 4a b (x ) - 12a b (x ) + 6a b)%e - 2a b (x ) - 9a b (x ) +--R + +--R 4 n +--R - 6a b x +--R / +--R 8 n 2 7 n 2 6 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 7 n 2 2 6 n 3 5 n log(x) 2 6 n 2 3 5 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 4 +--R 2a b n +--R Type: Expression(Integer) +--E 454 + +--S 455 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 455 + +)clear all + +--S 456 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^3 +--R +--R +--R 3n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 456 + +--S 457 of 1394 +r0:=-1/2*a^2/(b^3*n*(a+b*x^n)^2)+2*a/(b^3*n*(a+b*x^n))+log(a+b*x^n)/(b^3*n) +--R +--R +--R 2 n 2 n 2 n n 2 +--R (2b (x ) + 4a b x + 2a )log(b x + a) + 4a b x + 3a +--R (2) ------------------------------------------------------- +--R 5 n 2 4 n 2 3 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 457 + +--S 458 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (2b (%e ) + 4a b %e + 2a )log(b %e + a) +--R + +--R n log(x) 2 +--R 4a b %e + 3a +--R / +--R 5 n log(x) 2 4 n log(x) 2 3 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 4a b x - 3a b )(%e ) + (4a b (x ) - 2a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 2a b x +--R / +--R 7 n 2 6 n 2 5 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 6 n 2 2 5 n 3 4 n log(x) 2 5 n 2 3 4 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 3 +--R 2a b n +--R Type: Expression(Integer) +--E 459 + +--S 460 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 460 + +)clear all + +--S 461 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^3 +--R +--R +--R 2n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 461 + +--S 462 of 1394 +r0:=1/2*x^(2*n)/(a*n*(a+b*x^n)^2) +--R +--R +--R 2n +--R x +--R (2) ------------------------------- +--R 2 n 2 2 n 3 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 462 + +--S 463 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - 2b %e - a +--R (3) ----------------------------------------------- +--R 4 n log(x) 2 3 n log(x) 2 2 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 463 + +--S 464 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 2n n log(x) 2 +--R - b x (%e ) +--R + +--R 3 2n 3 n 2 2 2 n 3 n log(x) 2 2 2n +--R (- 2a b x - 2a b (x ) - 4a b x - 2a b)%e - a b x +--R + +--R 2 2 n 2 3 n 4 +--R - a b (x ) - 2a b x - a +--R / +--R 6 n 2 2 5 n 3 4 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 2 5 n 2 3 4 n 4 3 n log(x) 3 4 n 2 4 3 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 5 2 +--R 2a b n +--R Type: Expression(Integer) +--E 464 + +--S 465 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 465 + +)clear all + +--S 466 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^3 +--R +--R +--R n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 466 + +--S 467 of 1394 +r0:=(-1/2)/(b*n*(a+b*x^n)^2) +--R +--R +--R 1 +--R (2) - ------------------------------- +--R 3 n 2 2 n 2 +--R 2b n (x ) + 4a b n x + 2a b n +--R Type: Expression(Integer) +--E 467 + +--S 468 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ----------------------------------------------- +--R 3 n log(x) 2 2 n log(x) 2 +--R 2b n (%e ) + 4a b n %e + 2a b n +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n log(x) 2 n log(x) n 2 n +--R b (%e ) + 2a %e - b (x ) - 2a x +--R / +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 4 +--R 2a n +--R Type: Expression(Integer) +--E 469 + +--S 470 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 470 + +)clear all + +--S 471 of 1394 +t0:=1/(x*(a+b*x^n)^3) +--R +--R +--R 1 +--R (1) ------------------------------------------ +--R 3 n 3 2 n 2 2 n 3 +--R b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 471 + +--S 472 of 1394 +r0:=1/2/(a*n*(a+b*x^n)^2)+1/(a^2*n*(a+b*x^n))+log(x)/a^3-log(a+b*x^n)/(a^3*n) +--R +--R +--R (2) +--R 2 n 2 n 2 n 2 n 2 +--R (- 2b (x ) - 4a b x - 2a )log(b x + a) + 2b n log(x)(x ) +--R + +--R n 2 2 +--R (4a b n log(x) + 2a b)x + 2a n log(x) + 3a +--R / +--R 3 2 n 2 4 n 5 +--R 2a b n (x ) + 4a b n x + 2a n +--R Type: Expression(Integer) +--E 472 + +--S 473 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 n log(x) 2 n log(x) 2 n log(x) +--R (- 2b (%e ) - 4a b %e - 2a )log(b %e + a) +--R + +--R 2 n log(x) 2 n log(x) 2 +--R 2b n log(x)(%e ) + (4a b n log(x) + 2a b)%e + 2a n log(x) +--R + +--R 2 +--R 3a +--R / +--R 3 2 n log(x) 2 4 n log(x) 5 +--R 2a b n (%e ) + 4a b n %e + 2a n +--R Type: Union(Expression(Integer),...) +--E 473 + +--S 474 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (- 2b (x ) - 4a b x - 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (- 4a b (x ) - 8a b x - 4a b)%e - 2a b (x ) - 4a b x - 2a +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n 2 3 n 2 2 n log(x) 2 +--R (2b (x ) + 4a b x + 2a b )(%e ) +--R + +--R 3 n 2 2 2 n 3 n log(x) 2 2 n 2 3 n 4 +--R (4a b (x ) + 8a b x + 4a b)%e + 2a b (x ) + 4a b x + 2a +--R * +--R n +--R log(b x + a) +--R + +--R 3 n 2 2 n log(x) 2 3 n 2 3 n log(x) +--R (- 2a b x - 3a b )(%e ) + (2a b (x ) - 4a b)%e +--R + +--R 2 2 n 2 3 n +--R 3a b (x ) + 4a b x +--R / +--R 3 4 n 2 4 3 n 5 2 n log(x) 2 +--R (2a b n (x ) + 4a b n x + 2a b n)(%e ) +--R + +--R 4 3 n 2 5 2 n 6 n log(x) 5 2 n 2 6 n +--R (4a b n (x ) + 8a b n x + 4a b n)%e + 2a b n (x ) + 4a b n x +--R + +--R 7 +--R 2a n +--R Type: Expression(Integer) +--E 474 + +--S 475 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 475 + +)clear all + +--S 476 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^3 +--R +--R +--R - n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 476 + +--S 477 of 1394 +r0:=(-3)/(a^3*n*x^n)+1/2/(a*n*x^n*(a+b*x^n)^2)+3/2/(a^2*n*x^n*(a+b*x^n))-_ + 3*b*log(x)/a^4+3*b*log(a+b*x^n)/(a^4*n) +--R +--R +--R (2) +--R 3 n 3 2 n 2 2 n n 3 n 3 +--R (6b (x ) + 12a b (x ) + 6a b x )log(b x + a) - 6b n log(x)(x ) +--R + +--R 2 2 n 2 2 2 n 3 +--R (- 12a b n log(x) - 6a b )(x ) + (- 6a b n log(x) - 9a b)x - 2a +--R / +--R 4 2 n 3 5 n 2 6 n +--R 2a b n (x ) + 4a b n (x ) + 2a n x +--R Type: Expression(Integer) +--E 477 + +--S 478 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) +--R (6b (%e ) + 12a b (%e ) + 6a b %e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 3 n log(x) 3 2 2 n log(x) 2 +--R - 6b n log(x)(%e ) + (- 12a b n log(x) - 6a b )(%e ) +--R + +--R 2 2 n log(x) 3 +--R (- 6a b n log(x) - 9a b)%e - 2a +--R / +--R 4 2 n log(x) 3 5 n log(x) 2 6 n log(x) +--R 2a b n (%e ) + 4a b n (%e ) + 2a n %e +--R Type: Union(Expression(Integer),...) +--E 478 + +--S 479 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 n 3 4 n 2 2 3 n n log(x) 3 +--R (6b (x ) + 12a b (x ) + 6a b x )(%e ) +--R + +--R 4 n 3 2 3 n 2 3 2 n n log(x) 2 +--R (12a b (x ) + 24a b (x ) + 12a b x )(%e ) +--R + +--R 2 3 n 3 3 2 n 2 4 n n log(x) +--R (6a b (x ) + 12a b (x ) + 6a b x )%e +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 5 n 3 4 n 2 2 3 n n log(x) 3 +--R (- 6b (x ) - 12a b (x ) - 6a b x )(%e ) +--R + +--R 4 n 3 2 3 n 2 3 2 n n log(x) 2 +--R (- 12a b (x ) - 24a b (x ) - 12a b x )(%e ) +--R + +--R 2 3 n 3 3 2 n 2 4 n n log(x) +--R (- 6a b (x ) - 12a b (x ) - 6a b x )%e +--R * +--R n +--R log(b x + a) +--R + +--R 4 n 2 2 3 n 3 2 n log(x) 3 +--R (6a b (x ) + 9a b x + 2a b )(%e ) +--R + +--R 4 n 3 3 2 n 4 n log(x) 2 +--R (- 6a b (x ) + 12a b x + 4a b)(%e ) +--R + +--R 2 3 n 3 3 2 n 2 5 n log(x) 3 2 n 3 4 n 2 +--R (- 9a b (x ) - 12a b (x ) + 2a )%e - 2a b (x ) - 4a b (x ) +--R + +--R 5 n +--R - 2a x +--R / +--R 4 4 n 3 5 3 n 2 6 2 n n log(x) 3 +--R (2a b n (x ) + 4a b n (x ) + 2a b n x )(%e ) +--R + +--R 5 3 n 3 6 2 n 2 7 n n log(x) 2 +--R (4a b n (x ) + 8a b n (x ) + 4a b n x )(%e ) +--R + +--R 6 2 n 3 7 n 2 8 n n log(x) +--R (2a b n (x ) + 4a b n (x ) + 2a n x )%e +--R Type: Expression(Integer) +--E 479 + +--S 480 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 480 + +)clear all + +--S 481 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^3 +--R +--R +--R - 2n - 1 +--R x +--R (1) ----------------------------------- +--R 3 n 3 2 n 2 2 n 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 481 + +--S 482 of 1394 +r0:=(-3)/(a^3*n*x^(2*n))+6*b/(a^4*n*x^n)+1/2/(a*n*x^(2*n)*(a+b*x^n)^2)+_ + 2/(a^2*n*x^(2*n)*(a+b*x^n))+6*b^2*log(x)/a^5-6*b^2*log(a+b*x^n)/(a^5*n) +--R +--R +--R (2) +--R 4 n 3 3 n 2 2 2 n 2n n +--R (- 12b (x ) - 24a b (x ) - 12a b x )x log(b x + a) +--R + +--R 4 n 3 3 3 n 2 +--R 12b n log(x)(x ) + (24a b n log(x) + 12a b )(x ) +--R + +--R 2 2 2 2 n 3 +--R (12a b n log(x) + 24a b )x + 12a b +--R * +--R 2n +--R x +--R + +--R 2 2 n 3 3 n 2 4 n +--R - 6a b (x ) - 8a b (x ) - a x +--R / +--R 5 2 n 3 6 n 2 7 n 2n +--R (2a b n (x ) + 4a b n (x ) + 2a n x )x +--R Type: Expression(Integer) +--E 482 + +--S 483 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R (- 12b (%e ) - 24a b (%e ) - 12a b (%e ) ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 4 n log(x) 4 3 3 n log(x) 3 +--R 12b n log(x)(%e ) + (24a b n log(x) + 12a b )(%e ) +--R + +--R 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (12a b n log(x) + 18a b )(%e ) + 4a b %e - a +--R / +--R 5 2 n log(x) 4 6 n log(x) 3 7 n log(x) 2 +--R 2a b n (%e ) + 4a b n (%e ) + 2a n (%e ) +--R Type: Union(Expression(Integer),...) +--E 483 + +--S 484 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 6 n 3 5 n 2 2 4 n 2n n log(x) 4 +--R (- 12b (x ) - 24a b (x ) - 12a b x )x (%e ) +--R + +--R 5 n 3 2 4 n 2 3 3 n 2n n log(x) 3 +--R (- 24a b (x ) - 48a b (x ) - 24a b x )x (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 2n n log(x) 2 +--R (- 12a b (x ) - 24a b (x ) - 12a b x )x (%e ) +--R * +--R n log(x) +--R log(b %e + a) +--R + +--R 6 n 3 5 n 2 2 4 n 2n n log(x) 4 +--R (12b (x ) + 24a b (x ) + 12a b x )x (%e ) +--R + +--R 5 n 3 2 4 n 2 3 3 n 2n n log(x) 3 +--R (24a b (x ) + 48a b (x ) + 24a b x )x (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 2n n log(x) 2 +--R (12a b (x ) + 24a b (x ) + 12a b x )x (%e ) +--R * +--R n +--R log(b x + a) +--R + +--R 5 n 2 2 4 n 3 3 2n 2 4 n 3 3 3 n 2 +--R (- 12a b (x ) - 24a b x - 12a b )x + 6a b (x ) + 8a b (x ) +--R + +--R 4 2 n +--R a b x +--R * +--R n log(x) 4 +--R (%e ) +--R + +--R 5 n 3 3 3 n 4 2 2n 3 3 n 3 4 2 n 2 +--R (12a b (x ) - 36a b x - 24a b )x + 12a b (x ) + 16a b (x ) +--R + +--R 5 n +--R 2a b x +--R * +--R n log(x) 3 +--R (%e ) +--R + +--R 2 4 n 3 3 3 n 2 4 2 n 5 2n 4 2 n 3 +--R (18a b (x ) + 24a b (x ) - 6a b x - 12a b)x + 6a b (x ) +--R + +--R 5 n 2 6 n +--R 8a b (x ) + a x +--R * +--R n log(x) 2 +--R (%e ) +--R + +--R 3 3 n 3 4 2 n 2 5 n 2n n log(x) +--R (4a b (x ) + 8a b (x ) + 4a b x )x %e +--R + +--R 4 2 n 3 5 n 2 6 n 2n +--R (- a b (x ) - 2a b (x ) - a x )x +--R / +--R 5 4 n 3 6 3 n 2 7 2 n 2n n log(x) 4 +--R (2a b n (x ) + 4a b n (x ) + 2a b n x )x (%e ) +--R + +--R 6 3 n 3 7 2 n 2 8 n 2n n log(x) 3 +--R (4a b n (x ) + 8a b n (x ) + 4a b n x )x (%e ) +--R + +--R 7 2 n 3 8 n 2 9 n 2n n log(x) 2 +--R (2a b n (x ) + 4a b n (x ) + 2a n x )x (%e ) +--R Type: Expression(Integer) +--E 484 + +--S 485 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 485 + +)clear all + +--S 486 of 1394 +t0:=x^(-1-1/2*n)/(a+b*x^n) +--R +--R +--R - n - 2 +--R ------- +--R 2 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 486 + +--S 487 of 1394 +r0:=(-2)/(a*n*x^(1/2*n))-2*atan(x^(1/2*n)*sqrt(b)/sqrt(a))*sqrt(b)/(a^(3/2)*n) +--R +--R +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R - 2x \|b atan(------) - 2\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 487 + +--S 488 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R +---+ a x (%e ) + 2a x |- - %e - b +--R | b \| a +--R |- - log(----------------------------------------------------------) +--R \| a (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R (- n - 2)log(x) +--R --------------- +--R 2 +--R - 2x %e +--R / +--R a n +--R , +--R (- n - 2)log(x) +--R --------------- (- n - 2)log(x) +--R +-+ 2 --------------- +--R |b x %e 2 +--R 2 |- atan(------------------- - 2x %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -----------------------------------------------------] +--R a n +--R Type: Union(List(Expression(Integer)),...) +--E 488 + +--S 489 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R n +--R - +---+ +--R 2 | b +-+ +--R x |- - \|a +--R \| a +--R * +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R a x (%e ) + 2a x |- - %e - b +--R \| a +--R log(----------------------------------------------------------) +--R (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R n +--R n (- n - 2)log(x) n - +--R - --------------- - 2 +-+ +--R 2 +-+ 2 2 +-+ x \|b +-+ +--R - 2x x \|a %e + 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 489 + +--S 490 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 490 + +--S 491 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R (- n - 2)log(x) +--R n --------------- n (- n - 2)log(x) +--R - +-+ 2 - --------------- +--R 2 +-+ |b x %e 2 +-+ 2 +--R 2x \|a |- atan(-------------------) - 2x x \|a %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 491 + +--S 492 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 492 + +)clear all + +--S 493 of 1394 +t0:=x^(-1-2/3*n)/(a+b*x^n) +--R +--R +--R - 2n - 3 +--R -------- +--R 3 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 493 + +--S 494 of 1394 +r0:=(-3/2)/(a*n*x^(2/3*n))-b^(2/3)*log(a^(1/3)+b^(1/3)*x^(1/3*n))/_ + (a^(5/3)*n)+1/2*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3*n)+_ + b^(2/3)*x^(2/3*n))/(a^(5/3)*n)+b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(5/3)*n) +--R +--R +--R (2) +--R 2n 2n n 2n n +--R -- -- - -- - +--R 3 3+-+2 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+2 3 3+-+ 3+-+ +--R x \|b log(x \|b - x \|a \|b + \|a - 2x \|b log(x \|b + \|a ) +--R + +--R n +--R 2n - +--R -- 3 3+-+ 3+-+ +--R +-+ 3 3+-+2 2x \|b - \|a 3+-+2 +--R - 2\|3 x \|b atan(-------------- - 3\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2n +--R -- +--R 3 3+-+2 +--R 2a n x \|a +--R Type: Expression(Integer) +--E 494 + +--R +--S 495 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 495 + +--S 496 of 1394 +--m0:=a0-r0 +--E 496 + +--S 497 of 1394 +--d0:=D(m0,x) +--E 497 + +)clear all + +--S 498 of 1394 +t0:=x^(-1-3/4*n)/(a+b*x^n) +--R +--R +--R - 3n - 4 +--R -------- +--R 4 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 498 + +--S 499 of 1394 +r0:=(-4/3)/(a*n*x^(3/4*n))+b^(3/4)*log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+_ + sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(7/4)*n*sqrt(2))-_ + b^(3/4)*log(a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+_ + x^(1/2*n)*sqrt(b))/(a^(7/4)*n*sqrt(2))+b^(3/4)*atan(1-_ + b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(7/4)*n)-_ + b^(3/4)*atan(1+b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(7/4)*n) +--R +--R +--R (2) +--R 3n n n +--R -- - - +--R 4 4+-+3 +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - 3x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R 3n n n +--R -- - - +--R 4 4+-+3 +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R 3x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n +--R 3n - 3n - +--R -- +-+ 4 4+-+ 4+-+ -- +-+ 4 4+-+ 4+-+ +--R 4 4+-+3 \|2 x \|b + \|a 4 4+-+3 \|2 x \|b - \|a +--R - 6x \|b atan(----------------- - 6x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+3 +--R - 4\|2 \|a +--R / +--R 3n +--R -- +--R +-+ 4 4+-+3 +--R 3a n\|2 x \|a +--R Type: Expression(Integer) +--E 499 + +--R +--S 500 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 500 + +--S 501 of 1394 +--m0:=a0-r0 +--E 501 + +--S 502 of 1394 +--d0:=D(m0,x) +--E 502 + +)clear all + +--S 503 of 1394 +t0:=x^(-1-n)/(a+b*x^n) +--R +--R +--R - n - 1 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 503 + +--S 504 of 1394 +r0:=(-1)/(a*n*x^n)-b*log(x)/a^2+b*log(a+b*x^n)/(a^2*n) +--R +--R +--R n n n +--R b x log(b x + a) - b n log(x)x - a +--R (2) ------------------------------------ +--R 2 n +--R a n x +--R Type: Expression(Integer) +--E 504 + +--S 505 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) n log(x) n log(x) +--R b %e log(b %e + a) - b n log(x)%e - a +--R (3) ------------------------------------------------------------ +--R 2 n log(x) +--R a n %e +--R Type: Union(Expression(Integer),...) +--E 505 + +--S 506 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R n n log(x) n log(x) n n log(x) n +--R b x %e log(b %e + a) - b x %e log(b x + a) +--R + +--R n log(x) n +--R a %e - a x +--R / +--R 2 n n log(x) +--R a n x %e +--R Type: Expression(Integer) +--E 506 + +--S 507 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 507 + +)clear all + +--S 508 of 1394 +t0:=x^(-1-1/2*n)/(a+b*x^n) +--R +--R +--R - n - 2 +--R ------- +--R 2 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 508 + +--S 509 of 1394 +r0:=(-2)/(a*n*x^(1/2*n))-2*atan(x^(1/2*n)*sqrt(b)/sqrt(a))*sqrt(b)/(a^(3/2)*n) +--R +--R +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R - 2x \|b atan(------) - 2\|a +--R +-+ +--R \|a +--R (2) ----------------------------- +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 509 + +--S 510 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R +---+ a x (%e ) + 2a x |- - %e - b +--R | b \| a +--R |- - log(----------------------------------------------------------) +--R \| a (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R (- n - 2)log(x) +--R --------------- +--R 2 +--R - 2x %e +--R / +--R a n +--R , +--R (- n - 2)log(x) +--R --------------- (- n - 2)log(x) +--R +-+ 2 --------------- +--R |b x %e 2 +--R 2 |- atan(------------------- - 2x %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R -----------------------------------------------------] +--R a n +--R Type: Union(List(Expression(Integer)),...) +--E 510 + +--S 511 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R n +--R - +---+ +--R 2 | b +-+ +--R x |- - \|a +--R \| a +--R * +--R (- n - 2)log(x) 2 (- n - 2)log(x) +--R --------------- +---+ --------------- +--R 2 2 | b 2 +--R a x (%e ) + 2a x |- - %e - b +--R \| a +--R log(----------------------------------------------------------) +--R (- n - 2)log(x) 2 +--R --------------- +--R 2 2 +--R a x (%e ) + b +--R + +--R n +--R n (- n - 2)log(x) n - +--R - --------------- - 2 +-+ +--R 2 +-+ 2 2 +-+ x \|b +-+ +--R - 2x x \|a %e + 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 511 + +--S 512 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 512 + +--S 513 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R (- n - 2)log(x) +--R n --------------- n (- n - 2)log(x) +--R - +-+ 2 - --------------- +--R 2 +-+ |b x %e 2 +-+ 2 +--R 2x \|a |- atan(-------------------) - 2x x \|a %e +--R \|a +-+ +--R |b +--R |- +--R \|a +--R + +--R n +--R n - +--R - 2 +-+ +--R 2 +-+ x \|b +-+ +--R 2x \|b atan(------) + 2\|a +--R +-+ +--R \|a +--R / +--R n +--R - +--R 2 +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 513 + +--S 514 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 514 + +)clear all + +--S 515 of 1394 +t0:=x^(-1-1/3*n)/(a+b*x^n) +--R +--R +--R - n - 3 +--R ------- +--R 3 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 515 + +--S 516 of 1394 +r0:=(-3)/(a*n*x^(1/3*n))+b^(1/3)*log(a^(1/3)+b^(1/3)*x^(1/3*n))/_ + (a^(4/3)*n)-1/2*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*x^(1/3*n)+_ + b^(2/3)*x^(2/3*n))/(a^(4/3)*n)+b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*sqrt(3)/(a^(4/3)*n) +--R +--R +--R (2) +--R n 2n n n n +--R - -- - - - +--R 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+ 3 3+-+ 3+-+ +--R - x \|b log(x \|b - x \|a \|b + \|a + 2x \|b log(x \|b + \|a ) +--R + +--R n +--R n - +--R - 3 3+-+ 3+-+ +--R +-+ 3 3+-+ 2x \|b - \|a 3+-+ +--R - 2\|3 x \|b atan(-------------- - 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R n +--R - +--R 3 3+-+ +--R 2a n x \|a +--R Type: Expression(Integer) +--E 516 + +--S 517 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- n - 3)log(x) 2 (- n - 3)log(x) +--R --------------- +-+ --------------- +-+2 +--R 2 3 |b 3 |b +--R +-+ x (%e ) - x 3|- %e + 3|- +--R |b \|a \|a +--R - 3|- log(-------------------------------------------------------) +--R \|a 2 +--R x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R 3 |b +--R +-+ x %e + 3|- +--R |b \|a +--R 2 3|- log(--------------------------) +--R \|a x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R 3 |b (- n - 3)log(x) +--R +-+ 2x %e - 3|- --------------- +--R +-+ |b \|a 3 +--R 2\|3 3|- atan(--------------------------- - 6x %e +--R \|a +-+ +--R +-+ |b +--R \|3 3|- +--R \|a +--R / +--R 2a n +--R Type: Union(Expression(Integer),...) +--E 517 + +--S 518 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (- n - 3)log(x) 2 (- n - 3)log(x) +--R --------------- +-+ --------------- +-+2 +--R n 2 3 |b 3 |b +--R - +-+ x (%e ) - x 3|- %e + 3|- +--R 3 3+-+ |b \|a \|a +--R - x \|a 3|- log(-------------------------------------------------------) +--R \|a 2 +--R x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R n 3 |b +--R - +-+ x %e + 3|- +--R 3 3+-+ |b \|a +--R 2x \|a 3|- log(--------------------------) +--R \|a x +--R + +--R (- n - 3)log(x) +--R --------------- +-+ +--R n 3 |b +--R - +-+ 2x %e - 3|- +--R +-+ 3 3+-+ |b \|a +--R 2\|3 x \|a 3|- atan(---------------------------) +--R \|a +-+ +--R +-+ |b +--R \|3 3|- +--R \|a +--R + +--R n 2n n n n +--R - -- - - - +--R 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 3 3+-+ 3 3+-+ 3+-+ +--R x \|b log(x \|b - x \|a \|b + \|a - 2x \|b log(x \|b + \|a ) +--R + +--R n +--R n (- n - 3)log(x) n - +--R - --------------- - 3 3+-+ 3+-+ +--R 3 3+-+ 3 +-+ 3 3+-+ 2x \|b - \|a 3+-+ +--R - 6x x \|a %e + 2\|3 x \|b atan(-------------- + 6\|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R n +--R - +--R 3 3+-+ +--R 2a n x \|a +--R Type: Expression(Integer) +--E 518 + +--S 519 of 1394 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 519 + +)clear all + +--S 520 of 1394 +t0:=x^(-1-1/4*n)/(a+b*x^n) +--R +--R +--R - n - 4 +--R ------- +--R 4 +--R x +--R (1) -------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 520 + +--S 521 of 1394 +r0:=(-4)/(a*n*x^(1/4*n))-b^(1/4)*log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+_ + sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(5/4)*n*sqrt(2))+b^(1/4)*_ + log(a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*sqrt(b))/_ + (a^(5/4)*n*sqrt(2))+b^(1/4)*atan(1-b^(1/4)*x^(1/4*n)*sqrt(2)/_ + a^(1/4))*sqrt(2)/(a^(5/4)*n)-b^(1/4)*atan(1+b^(1/4)*_ + x^(1/4*n)*sqrt(2)/a^(1/4))*sqrt(2)/(a^(5/4)*n) +--R +--R +--R (2) +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n +--R n - n - +--R - +-+ 4 4+-+ 4+-+ - +-+ 4 4+-+ 4+-+ +--R 4 4+-+ \|2 x \|b + \|a 4 4+-+ \|2 x \|b - \|a +--R - 2x \|b atan(----------------- - 2x \|b atan(-----------------) +--R 4+-+ 4+-+ +--R \|a \|a +--R + +--R +-+4+-+ +--R - 4\|2 \|a +--R / +--R n +--R - +--R +-+ 4 4+-+ +--R a n\|2 x \|a +--R Type: Expression(Integer) +--E 521 + +--S 522 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R x %e + a n |- ---- +--R +------+ 4| 5 4 +--R | b \| a n +--R a n |- ---- log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R x %e - a n |- ---- +--R +------+ 4| 5 4 +--R | b \| a n +--R - a n |- ---- log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R +------+ +--R | b +--R a n |- ---- (- n - 4)log(x) +--R +------+ 4| 5 4 --------------- +--R | b \| a n 4 +--R - 2a n |- ---- atan(------------------- - 4x %e +--R 4| 5 4 (- n - 4)log(x) +--R \| a n --------------- +--R 4 +--R x %e +--R / +--R a n +--R Type: Union(Expression(Integer),...) +--E 522 + +--S 523 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R n x %e + a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R a n\|2 x |- ---- \|a log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R (- n - 4)log(x) +--R --------------- +------+ +--R 4 | b +--R n x %e - a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R - a n\|2 x |- ---- \|a log(----------------------------------) +--R 4| 5 4 x +--R \| a n +--R + +--R +------+ +--R | b +--R n a n |- ---- +--R - +------+ 4| 5 4 +--R +-+ 4 | b 4+-+ \| a n +--R - 2a n\|2 x |- ---- \|a atan(-------------------) +--R 4| 5 4 (- n - 4)log(x) +--R \| a n --------------- +--R 4 +--R x %e +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n n n +--R - - - +--R 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n +--R n (- n - 4)log(x) n - +--R - --------------- - +-+ 4 4+-+ 4+-+ +--R +-+ 4 4+-+ 4 4 4+-+ \|2 x \|b + \|a +--R - 4x\|2 x \|a %e + 2x \|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R n +--R n - +--R - +-+ 4 4+-+ 4+-+ +--R 4 4+-+ \|2 x \|b - \|a +-+4+-+ +--R 2x \|b atan(----------------- + 4\|2 \|a +--R 4+-+ +--R \|a +--R / +--R n +--R - +--R +-+ 4 4+-+ +--R a n\|2 x \|a +--R Type: Expression(Integer) +--E 523 + +--S 524 of 1394 +d0:=normalize(D(m0,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 524 + +)clear all + +--S 525 of 1394 +t0:=x^(-1-3/2*n)/(a+b*x^n) +--R +--R +--R - 3n - 2 +--R -------- +--R 2 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 525 + +--S 526 of 1394 +r0:=(-2/3)/(a*n*x^(3/2*n))+2*b/(a^2*n*x^(1/2*n))+2*b^(3/2)*_ + atan(x^(1/2*n)*sqrt(b)/sqrt(a))/(a^(5/2)*n) +--R +--R +--R n +--R n 3n - 3n n +--R - -- 2 +-+ -- - +--R 2 2 +-+ x \|b 2 2 +-+ +--R 6b x x \|b atan(------) + (6b x - 2a x )\|a +--R +-+ +--R \|a +--R (2) ----------------------------------------------- +--R n 3n +--R - -- +--R 2 2 2 +-+ +--R 3a n x x \|a +--R Type: Expression(Integer) +--E 526 + +--R +--S 527 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 527 + +--S 528 of 1394 +--m0:=a0-r0 +--E 528 + +--S 529 of 1394 +--d0:=D(m0,x) +--E 529 + +)clear all + +--S 530 of 1394 +t0:=x^(-1-4/3*n)/(a+b*x^n) +--R +--R +--R - 4n - 3 +--R -------- +--R 3 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 530 + +--S 531 of 1394 +r0:=(-3/4)/(a*n*x^(4/3*n))+3*b/(a^2*n*x^(1/3*n))-b^(4/3)*log(a^(1/3)+_ + b^(1/3)*x^(1/3*n))/(a^(7/3)*n)+1/2*b^(4/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*x^(1/3*n)+b^(2/3)*x^(2/3*n))/(a^(7/3)*n)-_ + b^(4/3)*atan((a^(1/3)-2*b^(1/3)*x^(1/3*n))/(a^(1/3)*sqrt(3)))*_ + sqrt(3)/(a^(7/3)*n) +--R +--R +--R (2) +--R n 4n 2n n +--R - -- -- - +--R 3 3 3+-+ 3 3+-+2 3 3+-+3+-+ 3+-+2 +--R 2b x x \|b log(x \|b - x \|a \|b + \|a ) +--R + +--R n +--R n 4n n n 4n - +--R - -- - - -- 3 3+-+ 3+-+ +--R 3 3 3+-+ 3 3+-+ 3+-+ +-+ 3 3 3+-+ 2x \|b - \|a +--R - 4b x x \|b log(x \|b + \|a + 4b\|3 x x \|b atan(--------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4n n +--R -- - +--R 3 3 3+-+ +--R (12b x - 3a x )\|a +--R / +--R n 4n +--R - -- +--R 2 3 3 3+-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 531 + +--S 532 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 532 + +--S 533 of 1394 +--m0:=a0-r0 +--E 533 + +--S 534 of 1394 +--d0:=D(m0,x) +--E 534 + +)clear all + +--S 535 of 1394 +t0:=x^(-1-5/4*n)/(a+b*x^n) +--R +--R +--R - 5n - 4 +--R -------- +--R 4 +--R x +--R (1) --------- +--R n +--R b x + a +--R Type: Expression(Integer) +--E 535 + +--S 536 of 1394 +r0:=(-4/5)/(a*n*x^(5/4*n))+4*b/(a^2*n*x^(1/4*n))+b^(5/4)*_ + log(-a^(1/4)*b^(1/4)*x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*_ + sqrt(b))/(a^(9/4)*n*sqrt(2))-b^(5/4)*log(a^(1/4)*b^(1/4)*_ + x^(1/4*n)*sqrt(2)+sqrt(a)+x^(1/2*n)*sqrt(b))/(a^(9/4)*n*sqrt(2))-_ + b^(5/4)*atan(1-b^(1/4)*x^(1/4*n)*sqrt(2)/a^(1/4))*_ + sqrt(2)/(a^(9/4)*n)+b^(5/4)*atan(1+b^(1/4)*x^(1/4*n)*_ + sqrt(2)/a^(1/4))*sqrt(2)/(a^(9/4)*n) +--R +--R +--R (2) +--R n 5n n n +--R - -- - - +--R 4 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R - 5b x x \|b log(\|2 x \|a \|b + x \|b + \|a ) +--R + +--R n 5n n n +--R - -- - - +--R 4 4 4+-+ +-+ 4 4+-+4+-+ 2 +-+ +-+ +--R 5b x x \|b log(- \|2 x \|a \|b + x \|b + \|a ) +--R + +--R n +--R n 5n - +--R - -- +-+ 4 4+-+ 4+-+ +--R 4 4 4+-+ \|2 x \|b + \|a +--R 10b x x \|b atan(-----------------) +--R 4+-+ +--R \|a +--R + +--R n +--R n 5n - 5n n +--R - -- +-+ 4 4+-+ 4+-+ -- - +--R 4 4 4+-+ \|2 x \|b - \|a +-+ 4 +-+ 4 4+-+ +--R 10b x x \|b atan(----------------- + (20b\|2 x - 4a\|2 x )\|a +--R 4+-+ +--R \|a +--R / +--R n 5n +--R - -- +--R 2 +-+ 4 4 4+-+ +--R 5a n\|2 x x \|a +--R Type: Expression(Integer) +--E 536 + +--S 537 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 537 + +--S 538 of 1394 +--m0:=a0-r0 +--E 538 + +--S 539 of 1394 +--d0:=D(m0,x) +--E 539 + +)clear all + +--S 540 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 4n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 540 + +--S 541 of 1394 +r0:=-2/3*a^3*(a+b*x^n)^(3/2)/(b^4*n)+6/5*a^2*(a+b*x^n)^(5/2)/(b^4*n)-_ + 6/7*a*(a+b*x^n)^(7/2)/(b^4*n)+2/9*(a+b*x^n)^(9/2)/(b^4*n) +--R +--R +--R +--------+ +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 | n +--R (70b (x ) + 10a b (x ) - 12a b (x ) + 16a b x - 32a )\|b x + a +--R (2) -------------------------------------------------------------------- +--R 4 +--R 315b n +--R Type: Expression(Integer) +--E 541 + +--S 542 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R 70b (%e ) + 10a b (%e ) - 12a b (%e ) +--R + +--R 3 n log(x) 4 +--R 16a b %e - 32a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +--R 315b n +--R Type: Union(Expression(Integer),...) +--E 542 + +--S 543 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 n log(x) 4 3 n log(x) 3 2 2 n log(x) 2 +--R 70b (%e ) + 10a b (%e ) - 12a b (%e ) +--R + +--R 3 n log(x) 4 +--R 16a b %e - 32a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 4 n 4 3 n 3 2 2 n 2 3 n 4 | n +--R (- 70b (x ) - 10a b (x ) + 12a b (x ) - 16a b x + 32a )\|b x + a +--R / +--R 4 +--R 315b n +--R Type: Expression(Integer) +--E 543 + +--S 544 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 544 + +)clear all + +--S 545 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 3n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 545 + +--S 546 of 1394 +r0:=2/3*a^2*(a+b*x^n)^(3/2)/(b^3*n)-4/5*a*(a+b*x^n)^(5/2)/(b^3*n)+_ + 2/7*(a+b*x^n)^(7/2)/(b^3*n) +--R +--R +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (30b (x ) + 6a b (x ) - 8a b x + 16a )\|b x + a +--R (2) ---------------------------------------------------- +--R 3 +--R 105b n +--R Type: Expression(Integer) +--E 546 + +--S 547 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (30b (%e ) + 6a b (%e ) - 8a b %e + 16a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +--R 105b n +--R Type: Union(Expression(Integer),...) +--E 547 + +--S 548 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (30b (%e ) + 6a b (%e ) - 8a b %e + 16a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (- 30b (x ) - 6a b (x ) + 8a b x - 16a )\|b x + a +--R / +--R 3 +--R 105b n +--R Type: Expression(Integer) +--E 548 + +--S 549 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 549 + +)clear all + +--S 550 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R 2n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 550 + +--S 551 of 1394 +r0:=-2/3*a*(a+b*x^n)^(3/2)/(b^2*n)+2/5*(a+b*x^n)^(5/2)/(b^2*n) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (6b (x ) + 2a b x - 4a )\|b x + a +--R (2) ------------------------------------- +--R 2 +--R 15b n +--R Type: Expression(Integer) +--E 551 + +--S 552 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 2a b %e - 4a )\|b %e + a +--R (3) ------------------------------------------------------------- +--R 2 +--R 15b n +--R Type: Union(Expression(Integer),...) +--E 552 + +--S 553 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) + 2a b %e - 4a )\|b %e + a +--R + +--R +--------+ +--R 2 n 2 n 2 | n +--R (- 6b (x ) - 2a b x + 4a )\|b x + a +--R / +--R 2 +--R 15b n +--R Type: Expression(Integer) +--E 553 + +--S 554 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 554 + +)clear all + +--S 555 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 555 + +--S 556 of 1394 +r0:=2/3*(a+b*x^n)^(3/2)/(b*n) +--R +--R +--R +--------+ +--R n | n +--R (2b x + 2a)\|b x + a +--R (2) ----------------------- +--R 3b n +--R Type: Expression(Integer) +--E 556 + +--S 557 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e + 2a)\|b %e + a +--R (3) --------------------------------------- +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 557 + +--S 558 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R n log(x) | n log(x) n | n +--R (2b %e + 2a)\|b %e + a + (- 2b x - 2a)\|b x + a +--R (4) ------------------------------------------------------------------- +--R 3b n +--R Type: Expression(Integer) +--E 558 + +--S 559 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 559 + +)clear all + +--S 560 of 1394 +t0:=(a+b*x^n)^(1/2)/x +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R (1) ----------- +--R x +--R Type: Expression(Integer) +--E 560 + +--S 561 of 1394 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))*sqrt(a)/n+2*sqrt(a+b*x^n)/n +--R +--R +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R - 2\|a atanh(-----------) + 2\|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +--R Type: Expression(Integer) +--E 561 + +--S 562 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R / +--R n +--R , +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R ---------------------------------------------------------] +--R n +--R Type: Union(List(Expression(Integer)),...) +--E 562 + +--S 563 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R +-+ | n log(x) n log(x) +--R +-+ - 2\|a \|b %e + a + b %e + 2a +--R \|a log(----------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--------+ +--R | n log(x) +-+ \|b x + a | n +--R 2\|b %e + a + 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 563 + +--S 564 of 1394 +d0a:=D(normalize(m0a),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 564 + +--S 565 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R | n log(x) +----------------+ +--R +---+ \|b %e + a | n log(x) +--R - 2\|- a atan(-------------------) + 2\|b %e + a +--R +---+ +--R \|- a +--R + +--R +--------+ +--R | n +--------+ +--R +-+ \|b x + a | n +--R 2\|a atanh(-----------) - 2\|b x + a +--R +-+ +--R \|a +--R / +--R n +--R Type: Expression(Integer) +--E 565 + +--S 566 of 1394 +d0b:=D(normalize(m0b),x) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 566 + +)clear all + +--S 567 of 1394 +t0:=x^(-1-n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 567 + +--S 568 of 1394 +r0:=-b*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a))-sqrt(a+b*x^n)/(n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R n \|b x + a +-+ | n +--R - b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------ +--R n +-+ +--R n x \|a +--R Type: Expression(Integer) +--E 568 + +--S 569 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n log(x) - 2a\|b %e + a + b\|a %e + 2a\|a +--R b %e log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ | n log(x) +--R - 2\|a \|b %e + a +--R / +--R +-+ n log(x) +--R 2n\|a %e +--R , +--R +----------------+ +--R +---+ | n log(x) +----------------+ +--R n log(x) \|- a \|b %e + a +---+ | n log(x) +--R - b %e atan(-------------------------) - \|- a \|b %e + a +--R a +--R -------------------------------------------------------------------------] +--R +---+ n log(x) +--R n\|- a %e +--R Type: Union(List(Expression(Integer)),...) +--E 569 + +--S 570 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n n log(x) - 2a\|b %e + a + b\|a %e + 2a\|a +--R b x %e log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n +-+ | n log(x) n n log(x) \|b x + a +--R - 2x \|a \|b %e + a + 2b x %e atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ n log(x) | n +--R 2\|a %e \|b x + a +--R / +--R n +-+ n log(x) +--R 2n x \|a %e +--R Type: Expression(Integer) +--E 570 + +--S 571 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 571 + +--S 572 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R n +-+ n log(x) \|- a \|b %e + a +--R - b x \|a %e atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n +---+ +-+ | n log(x) +--R - x \|- a \|a \|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R n +---+ n log(x) \|b x + a +---+ +-+ n log(x) | n +--R b x \|- a %e atanh(-----------) + \|- a \|a %e \|b x + a +--R +-+ +--R \|a +--R / +--R n +---+ +-+ n log(x) +--R n x \|- a \|a %e +--R Type: Expression(Integer) +--E 572 + +--S 573 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 573 + +)clear all + +--S 574 of 1394 +t0:=x^(-1-2*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 2n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 574 + +--S 575 of 1394 +r0:=1/4*b^2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)-_ + 1/2*sqrt(a+b*x^n)/(n*x^(2*n))-1/4*b*sqrt(a+b*x^n)/(a*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 n 2n \|b x + a 2n n +-+ | n +--R b x x atanh(-----------) + (- b x - 2a x )\|a \|b x + a +--R +-+ +--R \|a +--R (2) ------------------------------------------------------------ +--R n 2n +-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 575 + +--S 576 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n log(x) 2 2a\|b %e + a + b\|a %e + 2a\|a +--R b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ n log(x) +-+ | n log(x) +--R (- 2b\|a %e - 4a\|a )\|b %e + a +--R / +--R +-+ n log(x) 2 +--R 8a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 2 n log(x) 2 \|- a \|b %e + a +--R b (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R +---+ n log(x) +---+ | n log(x) +--R (- b\|- a %e - 2a\|- a )\|b %e + a +--R / +--R +---+ n log(x) 2 +--R 4a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 576 + +--S 577 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n 2n n log(x) 2 2a\|b %e + a + b\|a %e + 2a\|a +--R b x x (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n 2n +-+ n log(x) n 2n +-+ | n log(x) +--R (- 2b x x \|a %e - 4a x x \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n n log(x) 2 \|b x + a +--R - 2b x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +-+ n log(x) 2 | n +--R (2b x + 4a x )\|a (%e ) \|b x + a +--R / +--R n 2n +-+ n log(x) 2 +--R 8a n x x \|a (%e ) +--R Type: Expression(Integer) +--E 577 + +--S 578 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 578 + +--S 579 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 2 n 2n +-+ n log(x) 2 \|- a \|b %e + a +--R b x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n 2n +---+ +-+ n log(x) n 2n +---+ +-+ | n log(x) +--R (- b x x \|- a \|a %e - 2a x x \|- a \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n +---+ n log(x) 2 \|b x + a +--R - b x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +---+ +-+ n log(x) 2 | n +--R (b x + 2a x )\|- a \|a (%e ) \|b x + a +--R / +--R n 2n +---+ +-+ n log(x) 2 +--R 4a n x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 579 + +--S 580 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 580 + +)clear all + +--S 581 of 1394 +t0:=x^(-1-3*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 3n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 581 + +--S 582 of 1394 +r0:=-1/8*b^3*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)-_ + 1/3*sqrt(a+b*x^n)/(n*x^(3*n))-1/12*b*sqrt(a+b*x^n)/_ + (a*n*x^(2*n))+1/8*b^2*sqrt(a+b*x^n)/(a^2*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 3 n 2n 3n \|b x + a +--R - 3b x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ | n +--R ((3b x - 2a b x )x - 8a x x )\|a \|b x + a +--R / +--R 2 n 2n 3n +-+ +--R 24a n x x x \|a +--R Type: Expression(Integer) +--E 582 + +--S 583 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 3 n log(x) 3 - 2a\|b %e + a + b\|a %e + 2a\|a +--R 3b (%e ) log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R 2 +-+ n log(x) 2 +-+ n log(x) 2 +-+ | n log(x) +--R (6b \|a (%e ) - 4a b\|a %e - 16a \|a )\|b %e + a +--R / +--R 2 +-+ n log(x) 3 +--R 48a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 3 n log(x) 3 \|- a \|b %e + a +--R - 3b (%e ) atan(-------------------------) +--R a +--R + +--R 2 +---+ n log(x) 2 +---+ n log(x) 2 +---+ +--R (3b \|- a (%e ) - 2a b\|- a %e - 8a \|- a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 2 +---+ n log(x) 3 +--R 24a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 583 + +--S 584 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 +--R 3b x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 n 2n 3n +-+ n log(x) 2 n 2n 3n +-+ n log(x) +--R 6b x x x \|a (%e ) - 4a b x x x \|a %e +--R + +--R 2 n 2n 3n +-+ +--R - 16a x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n n log(x) 3 \|b x + a +--R 6b x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ n log(x) 3 | n +--R ((- 6b x + 4a b x )x + 16a x x )\|a (%e ) \|b x + a +--R / +--R 2 n 2n 3n +-+ n log(x) 3 +--R 48a n x x x \|a (%e ) +--R Type: Expression(Integer) +--E 584 + +--S 585 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 585 + +--S 586 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 3 n 2n 3n +-+ n log(x) 3 \|- a \|b %e + a +--R - 3b x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 2 n 2n 3n +---+ +-+ n log(x) 2 +--R 3b x x x \|- a \|a (%e ) +--R + +--R n 2n 3n +---+ +-+ n log(x) 2 n 2n 3n +---+ +-+ +--R - 2a b x x x \|- a \|a %e - 8a x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n +---+ n log(x) 3 \|b x + a +--R 3b x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +---+ +-+ n log(x) 3 | n +--R ((- 3b x + 2a b x )x + 8a x x )\|- a \|a (%e ) \|b x + a +--R / +--R 2 n 2n 3n +---+ +-+ n log(x) 3 +--R 24a n x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 586 + +--S 587 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 587 + +)clear all + +--S 588 of 1394 +t0:=x^(-1-4*n)*(a+b*x^n)^(1/2) +--R +--R +--R +--------+ +--R - 4n - 1 | n +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 588 + +--S 589 of 1394 +r0:=5/64*b^4*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(7/2)*n)-_ + 1/4*sqrt(a+b*x^n)/(n*x^(4*n))-1/24*b*sqrt(a+b*x^n)/_ + (a*n*x^(3*n))+5/96*b^2*sqrt(a+b*x^n)/(a^2*n*x^(2*n))-_ + 5/64*b^3*sqrt(a+b*x^n)/(a^3*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 4 n 2n 3n 4n \|b x + a +--R 15b x x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ | n +--R (((- 15b x + 10a b x )x - 8a b x x )x - 48a x x x )\|a \|b x + a +--R / +--R 3 n 2n 3n 4n +-+ +--R 192a n x x x x \|a +--R Type: Expression(Integer) +--E 589 + +--S 590 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 4 n log(x) 4 2a\|b %e + a + b\|a %e + 2a\|a +--R 15b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 +-+ n log(x) 3 2 +-+ n log(x) 2 +--R - 30b \|a (%e ) + 20a b \|a (%e ) +--R + +--R 2 +-+ n log(x) 3 +-+ +--R - 16a b\|a %e - 96a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +-+ n log(x) 4 +--R 384a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 4 n log(x) 4 \|- a \|b %e + a +--R 15b (%e ) atan(-------------------------) +--R a +--R + +--R 3 +---+ n log(x) 3 2 +---+ n log(x) 2 +--R - 15b \|- a (%e ) + 10a b \|- a (%e ) +--R + +--R 2 +---+ n log(x) 3 +---+ +--R - 8a b\|- a %e - 48a \|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +---+ n log(x) 4 +--R 192a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 590 + +--S 591 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 n 2n 3n 4n n log(x) 4 +--R 15b x x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2a\|b %e + a + b\|a %e + 2a\|a +--R log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 n 2n 3n 4n +-+ n log(x) 3 +--R - 30b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 2 2 n 2n 3n 4n +-+ n log(x) +--R 20a b x x x x \|a (%e ) - 16a b x x x x \|a %e +--R + +--R 3 n 2n 3n 4n +-+ +--R - 96a x x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n n log(x) 4 \|b x + a +--R - 30b x x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ +--R (((30b x - 20a b x )x + 16a b x x )x + 96a x x x )\|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 3 n 2n 3n 4n +-+ n log(x) 4 +--R 384a n x x x x \|a (%e ) +--R Type: Expression(Integer) +--E 591 + +--S 592 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 592 + +--S 593 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 4 n 2n 3n 4n +-+ n log(x) 4 \|- a \|b %e + a +--R 15b x x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 3 +--R - 15b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 2 +--R 10a b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 3 n 2n 3n 4n +---+ +-+ +--R - 8a b x x x x \|- a \|a %e - 48a x x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n +---+ n log(x) 4 \|b x + a +--R - 15b x x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +---+ +-+ +--R (((15b x - 10a b x )x + 8a b x x )x + 48a x x x )\|- a \|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 4 +--R 192a n x x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 593 + +--S 594 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 594 + +)clear all + +--S 595 of 1394 +t0:=x^(-1+4*n)/(a+b*x^n)^(1/2) +--R +--R +--R 4n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 595 + +--S 596 of 1394 +r0:=2*a^2*(a+b*x^n)^(3/2)/(b^4*n)-6/5*a*(a+b*x^n)^(5/2)/(b^4*n)+_ + 2/7*(a+b*x^n)^(7/2)/(b^4*n)-2*a^3*sqrt(a+b*x^n)/(b^4*n) +--R +--R +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (10b (x ) - 12a b (x ) + 16a b x - 32a )\|b x + a +--R (2) ------------------------------------------------------ +--R 4 +--R 35b n +--R Type: Expression(Integer) +--E 596 + +--S 597 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (10b (%e ) - 12a b (%e ) + 16a b %e - 32a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +--R 35b n +--R Type: Union(Expression(Integer),...) +--E 597 + +--S 598 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 n log(x) 3 2 n log(x) 2 2 n log(x) 3 +--R (10b (%e ) - 12a b (%e ) + 16a b %e - 32a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R 3 n 3 2 n 2 2 n 3 | n +--R (- 10b (x ) + 12a b (x ) - 16a b x + 32a )\|b x + a +--R / +--R 4 +--R 35b n +--R Type: Expression(Integer) +--E 598 + +--S 599 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 599 + +)clear all + +--S 600 of 1394 +t0:=x^(-1+3*n)/(a+b*x^n)^(1/2) +--R +--R +--R 3n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 600 + +--S 601 of 1394 +r0:=-4/3*a*(a+b*x^n)^(3/2)/(b^3*n)+2/5*(a+b*x^n)^(5/2)/(b^3*n)+_ + 2*a^2*sqrt(a+b*x^n)/(b^3*n) +--R +--R +--R +--------+ +--R 2 n 2 n 2 | n +--R (6b (x ) - 8a b x + 16a )\|b x + a +--R (2) -------------------------------------- +--R 3 +--R 15b n +--R Type: Expression(Integer) +--E 601 + +--S 602 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) - 8a b %e + 16a )\|b %e + a +--R (3) -------------------------------------------------------------- +--R 3 +--R 15b n +--R Type: Union(Expression(Integer),...) +--E 602 + +--S 603 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +----------------+ +--R 2 n log(x) 2 n log(x) 2 | n log(x) +--R (6b (%e ) - 8a b %e + 16a )\|b %e + a +--R + +--R +--------+ +--R 2 n 2 n 2 | n +--R (- 6b (x ) + 8a b x - 16a )\|b x + a +--R / +--R 3 +--R 15b n +--R Type: Expression(Integer) +--E 603 + +--S 604 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 604 + +)clear all + +--S 605 of 1394 +t0:=x^(-1+2*n)/(a+b*x^n)^(1/2) +--R +--R +--R 2n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 605 + +--S 606 of 1394 +r0:=2/3*(a+b*x^n)^(3/2)/(b^2*n)-2*a*sqrt(a+b*x^n)/(b^2*n) +--R +--R +--R +--------+ +--R n | n +--R (2b x - 4a)\|b x + a +--R (2) ----------------------- +--R 2 +--R 3b n +--R Type: Expression(Integer) +--E 606 + +--S 607 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R n log(x) | n log(x) +--R (2b %e - 4a)\|b %e + a +--R (3) --------------------------------------- +--R 2 +--R 3b n +--R Type: Union(Expression(Integer),...) +--E 607 + +--S 608 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R n log(x) | n log(x) n | n +--R (2b %e - 4a)\|b %e + a + (- 2b x + 4a)\|b x + a +--R (4) ------------------------------------------------------------------- +--R 2 +--R 3b n +--R Type: Expression(Integer) +--E 608 + +--S 609 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 609 + +)clear all + +--S 610 of 1394 +t0:=x^(-1+n)/(a+b*x^n)^(1/2) +--R +--R +--R n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 610 + +--S 611 of 1394 +r0:=2*sqrt(a+b*x^n)/(b*n) +--R +--R +--R +--------+ +--R | n +--R 2\|b x + a +--R (2) ------------ +--R b n +--R Type: Expression(Integer) +--E 611 + +--S 612 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +----------------+ +--R | n log(x) +--R 2\|b %e + a +--R (3) -------------------- +--R b n +--R Type: Union(Expression(Integer),...) +--E 612 + +--S 613 of 1394 +m0:=a0-r0 +--R +--R +--R +----------------+ +--------+ +--R | n log(x) | n +--R 2\|b %e + a - 2\|b x + a +--R (4) ----------------------------------- +--R b n +--R Type: Expression(Integer) +--E 613 + +--S 614 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 614 + +)clear all + +--S 615 of 1394 +t0:=1/(x*(a+b*x^n)^(1/2)) +--R +--R +--R 1 +--R (1) ------------ +--R +--------+ +--R | n +--R x\|b x + a +--R Type: Expression(Integer) +--E 615 + +--S 616 of 1394 +r0:=-2*atanh(sqrt(a+b*x^n)/sqrt(a))/(n*sqrt(a)) +--R +--R +--R +--------+ +--R | n +--R \|b x + a +--R 2atanh(-----------) +--R +-+ +--R \|a +--R (2) - ------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 616 + +--S 617 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R [-------------------------------------------------------, +--R +-+ +--R n\|a +--R +----------------+ +--R +---+ | n log(x) +--R \|- a \|b %e + a +--R 2atan(-------------------------) +--R a +--R - --------------------------------] +--R +---+ +--R n\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 617 + +--S 618 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--------+ +--R | n log(x) +-+ n log(x) +-+ | n +--R - 2a\|b %e + a + b\|a %e + 2a\|a \|b x + a +--R log(--------------------------------------------------) + 2atanh(-----------) +--R n log(x) +-+ +--R %e \|a +--R ----------------------------------------------------------------------------- +--R +-+ +--R n\|a +--R Type: Expression(Integer) +--E 618 + +--S 619 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 619 + +--S 620 of 1394 +m0b:=a0.2-r0 +--R +--R +--R +----------------+ +--------+ +--R +---+ | n log(x) | n +--R +-+ \|- a \|b %e + a +---+ \|b x + a +--R - 2\|a atan(-------------------------) + 2\|- a atanh(-----------) +--R a +-+ +--R \|a +--R (6) ------------------------------------------------------------------ +--R +---+ +-+ +--R n\|- a \|a +--R Type: Expression(Integer) +--E 620 + +--S 621 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 621 + +)clear all + +--S 622 of 1394 +t0:=x^(-1-n)/(a+b*x^n)^(1/2) +--R +--R +--R - n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 622 + +--S 623 of 1394 +r0:=b*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(3/2)*n)-sqrt(a+b*x^n)/(a*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R n \|b x + a +-+ | n +--R b x atanh(-----------) - \|a \|b x + a +--R +-+ +--R \|a +--R (2) ---------------------------------------- +--R n +-+ +--R a n x \|a +--R Type: Expression(Integer) +--E 623 + +--S 624 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n log(x) 2a\|b %e + a + b\|a %e + 2a\|a +--R b %e log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ | n log(x) +--R - 2\|a \|b %e + a +--R / +--R +-+ n log(x) +--R 2a n\|a %e +--R , +--R +----------------+ +--R +---+ | n log(x) +----------------+ +--R n log(x) \|- a \|b %e + a +---+ | n log(x) +--R b %e atan(-------------------------) - \|- a \|b %e + a +--R a +--R -----------------------------------------------------------------------] +--R +---+ n log(x) +--R a n\|- a %e +--R Type: Union(List(Expression(Integer)),...) +--E 624 + +--S 625 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R n n log(x) 2a\|b %e + a + b\|a %e + 2a\|a +--R b x %e log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +--------+ +--R +----------------+ | n +--R n +-+ | n log(x) n n log(x) \|b x + a +--R - 2x \|a \|b %e + a - 2b x %e atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ n log(x) | n +--R 2\|a %e \|b x + a +--R / +--R n +-+ n log(x) +--R 2a n x \|a %e +--R Type: Expression(Integer) +--E 625 + +--S 626 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 626 + +--S 627 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R n +-+ n log(x) \|- a \|b %e + a +--R b x \|a %e atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n +---+ +-+ | n log(x) +--R - x \|- a \|a \|b %e + a +--R + +--R +--------+ +--R | n +--------+ +--R n +---+ n log(x) \|b x + a +---+ +-+ n log(x) | n +--R - b x \|- a %e atanh(-----------) + \|- a \|a %e \|b x + a +--R +-+ +--R \|a +--R / +--R n +---+ +-+ n log(x) +--R a n x \|- a \|a %e +--R Type: Expression(Integer) +--E 627 + +--S 628 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 628 + +)clear all + +--S 629 of 1394 +t0:=x^(-1-2*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 2n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 629 + +--S 630 of 1394 +r0:=-3/4*b^2*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(5/2)*n)-_ + 1/2*sqrt(a+b*x^n)/(a*n*x^(2*n))+3/4*b*sqrt(a+b*x^n)/(a^2*n*x^n) +--R +--R +--R +--------+ +--R | n +--------+ +--R 2 n 2n \|b x + a 2n n +-+ | n +--R - 3b x x atanh(-----------) + (3b x - 2a x )\|a \|b x + a +--R +-+ +--R \|a +--R (2) -------------------------------------------------------------- +--R 2 n 2n +-+ +--R 4a n x x \|a +--R Type: Expression(Integer) +--E 630 + +--S 631 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2 n log(x) 2 - 2a\|b %e + a + b\|a %e + 2a\|a +--R 3b (%e ) log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R +-+ n log(x) +-+ | n log(x) +--R (6b\|a %e - 4a\|a )\|b %e + a +--R / +--R 2 +-+ n log(x) 2 +--R 8a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 2 n log(x) 2 \|- a \|b %e + a +--R - 3b (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R +---+ n log(x) +---+ | n log(x) +--R (3b\|- a %e - 2a\|- a )\|b %e + a +--R / +--R 2 +---+ n log(x) 2 +--R 4a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 631 + +--S 632 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 n 2n n log(x) 2 +--R 3b x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R +----------------+ +--R n 2n +-+ n log(x) n 2n +-+ | n log(x) +--R (6b x x \|a %e - 4a x x \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n n log(x) 2 \|b x + a +--R 6b x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +-+ n log(x) 2 | n +--R (- 6b x + 4a x )\|a (%e ) \|b x + a +--R / +--R 2 n 2n +-+ n log(x) 2 +--R 8a n x x \|a (%e ) +--R Type: Expression(Integer) +--E 632 + +--S 633 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 633 + +--S 634 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 2 n 2n +-+ n log(x) 2 \|- a \|b %e + a +--R - 3b x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R +----------------+ +--R n 2n +---+ +-+ n log(x) n 2n +---+ +-+ | n log(x) +--R (3b x x \|- a \|a %e - 2a x x \|- a \|a )\|b %e + a +--R + +--R +--------+ +--R | n +--R 2 n 2n +---+ n log(x) 2 \|b x + a +--R 3b x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2n n +---+ +-+ n log(x) 2 | n +--R (- 3b x + 2a x )\|- a \|a (%e ) \|b x + a +--R / +--R 2 n 2n +---+ +-+ n log(x) 2 +--R 4a n x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 634 + +--S 635 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 635 + +)clear all + +--S 636 of 1394 +t0:=x^(-1-3*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 3n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 636 + +--S 637 of 1394 +r0:=5/8*b^3*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(7/2)*n)-_ + 1/3*sqrt(a+b*x^n)/(a*n*x^(3*n))+5/12*b*sqrt(a+b*x^n)/_ + (a^2*n*x^(2*n))-5/8*b^2*sqrt(a+b*x^n)/(a^3*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 3 n 2n 3n \|b x + a +--R 15b x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ | n +--R ((- 15b x + 10a b x )x - 8a x x )\|a \|b x + a +--R / +--R 3 n 2n 3n +-+ +--R 24a n x x x \|a +--R Type: Expression(Integer) +--E 637 + +--S 638 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 3 n log(x) 3 2a\|b %e + a + b\|a %e + 2a\|a +--R 15b (%e ) log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 +-+ n log(x) 2 +-+ n log(x) 2 +-+ +--R (- 30b \|a (%e ) + 20a b\|a %e - 16a \|a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +-+ n log(x) 3 +--R 48a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 3 n log(x) 3 \|- a \|b %e + a +--R 15b (%e ) atan(-------------------------) +--R a +--R + +--R 2 +---+ n log(x) 2 +---+ n log(x) 2 +---+ +--R (- 15b \|- a (%e ) + 10a b\|- a %e - 8a \|- a ) +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 3 +---+ n log(x) 3 +--R 24a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 638 + +--S 639 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 3 n 2n 3n n log(x) 3 +--R 15b x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R 2a\|b %e + a + b\|a %e + 2a\|a +--R log(------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 2 n 2n 3n +-+ n log(x) 2 n 2n 3n +-+ n log(x) +--R - 30b x x x \|a (%e ) + 20a b x x x \|a %e +--R + +--R 2 n 2n 3n +-+ +--R - 16a x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n n log(x) 3 \|b x + a +--R - 30b x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +-+ n log(x) 3 | n +--R ((30b x - 20a b x )x + 16a x x )\|a (%e ) \|b x + a +--R / +--R 3 n 2n 3n +-+ n log(x) 3 +--R 48a n x x x \|a (%e ) +--R Type: Expression(Integer) +--E 639 + +--S 640 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 640 + +--S 641 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 3 n 2n 3n +-+ n log(x) 3 \|- a \|b %e + a +--R 15b x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 2 n 2n 3n +---+ +-+ n log(x) 2 +--R - 15b x x x \|- a \|a (%e ) +--R + +--R n 2n 3n +---+ +-+ n log(x) 2 n 2n 3n +---+ +-+ +--R 10a b x x x \|- a \|a %e - 8a x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 3 n 2n 3n +---+ n log(x) 3 \|b x + a +--R - 15b x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2n n 3n 2 n 2n +---+ +-+ n log(x) 3 | n +--R ((15b x - 10a b x )x + 8a x x )\|- a \|a (%e ) \|b x + a +--R / +--R 3 n 2n 3n +---+ +-+ n log(x) 3 +--R 24a n x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 641 + +--S 642 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 642 + +)clear all + +--S 643 of 1394 +t0:=x^(-1-4*n)/(a+b*x^n)^(1/2) +--R +--R +--R - 4n - 1 +--R x +--R (1) ----------- +--R +--------+ +--R | n +--R \|b x + a +--R Type: Expression(Integer) +--E 643 + +--S 644 of 1394 +r0:=-35/64*b^4*atanh(sqrt(a+b*x^n)/sqrt(a))/(a^(9/2)*n)-_ + 1/4*sqrt(a+b*x^n)/(a*n*x^(4*n))+7/24*b*sqrt(a+b*x^n)/_ + (a^2*n*x^(3*n))-35/96*b^2*sqrt(a+b*x^n)/(a^3*n*x^(2*n))+_ + 35/64*b^3*sqrt(a+b*x^n)/(a^4*n*x^n) +--R +--R +--R (2) +--R +--------+ +--R | n +--R 4 n 2n 3n 4n \|b x + a +--R - 105b x x x x atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ | n +--R (((105b x - 70a b x )x + 56a b x x )x - 48a x x x )\|a \|b x + a +--R / +--R 4 n 2n 3n 4n +-+ +--R 192a n x x x x \|a +--R Type: Expression(Integer) +--E 644 + +--S 645 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 4 n log(x) 4 +--R 105b (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 +-+ n log(x) 3 2 +-+ n log(x) 2 +--R 210b \|a (%e ) - 140a b \|a (%e ) +--R + +--R 2 +-+ n log(x) 3 +-+ +--R 112a b\|a %e - 96a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +-+ n log(x) 4 +--R 384a n\|a (%e ) +--R , +--R +--R +----------------+ +--R +---+ | n log(x) +--R 4 n log(x) 4 \|- a \|b %e + a +--R - 105b (%e ) atan(-------------------------) +--R a +--R + +--R 3 +---+ n log(x) 3 2 +---+ n log(x) 2 +--R 105b \|- a (%e ) - 70a b \|- a (%e ) +--R + +--R 2 +---+ n log(x) 3 +---+ +--R 56a b\|- a %e - 48a \|- a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R / +--R 4 +---+ n log(x) 4 +--R 192a n\|- a (%e ) +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 645 + +--S 646 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 n 2n 3n 4n n log(x) 4 +--R 105b x x x x (%e ) +--R * +--R +----------------+ +--R | n log(x) +-+ n log(x) +-+ +--R - 2a\|b %e + a + b\|a %e + 2a\|a +--R log(--------------------------------------------------) +--R n log(x) +--R %e +--R + +--R 3 n 2n 3n 4n +-+ n log(x) 3 +--R 210b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 2 +--R - 140a b x x x x \|a (%e ) +--R + +--R 2 n 2n 3n 4n +-+ n log(x) 3 n 2n 3n 4n +-+ +--R 112a b x x x x \|a %e - 96a x x x x \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n n log(x) 4 \|b x + a +--R 210b x x x x (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +-+ +--R (((- 210b x + 140a b x )x - 112a b x x )x + 96a x x x )\|a +--R * +--R +--------+ +--R n log(x) 4 | n +--R (%e ) \|b x + a +--R / +--R 4 n 2n 3n 4n +-+ n log(x) 4 +--R 384a n x x x x \|a (%e ) +--R Type: Expression(Integer) +--E 646 + +--S 647 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 647 + +--S 648 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R +----------------+ +--R +---+ | n log(x) +--R 4 n 2n 3n 4n +-+ n log(x) 4 \|- a \|b %e + a +--R - 105b x x x x \|a (%e ) atan(-------------------------) +--R a +--R + +--R 3 n 2n 3n 4n +---+ +-+ n log(x) 3 +--R 105b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 2 +--R - 70a b x x x x \|- a \|a (%e ) +--R + +--R 2 n 2n 3n 4n +---+ +-+ n log(x) 3 n 2n 3n 4n +---+ +-+ +--R 56a b x x x x \|- a \|a %e - 48a x x x x \|- a \|a +--R * +--R +----------------+ +--R | n log(x) +--R \|b %e + a +--R + +--R +--------+ +--R | n +--R 4 n 2n 3n 4n +---+ n log(x) 4 \|b x + a +--R 105b x x x x \|- a (%e ) atanh(-----------) +--R +-+ +--R \|a +--R + +--R 3 2n 2 n 3n 2 n 2n 4n 3 n 2n 3n +---+ +--R (((- 105b x + 70a b x )x - 56a b x x )x + 48a x x x )\|- a +--R * +--R +--------+ +--R +-+ n log(x) 4 | n +--R \|a (%e ) \|b x + a +--R / +--R 4 n 2n 3n 4n +---+ +-+ n log(x) 4 +--R 192a n x x x x \|- a \|a (%e ) +--R Type: Expression(Integer) +--E 648 + +--S 649 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 649 + +)clear all + +--S 650 of 1394 +t0:=x^(-1+n)*(a+b*x^n)^p +--R +--R +--R n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 650 + +--S 651 of 1394 +r0:=(a+b*x^n)^(1+p)/(b*n*(1+p)) +--R +--R +--R n p + 1 +--R (b x + a) +--R (2) --------------- +--R b n p + b n +--R Type: Expression(Integer) +--E 651 + +--S 652 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R n log(x) p log(b %e + a) +--R (b %e + a)%e +--R (3) ------------------------------------------- +--R b n p + b n +--R Type: Union(Expression(Integer),...) +--E 652 + +--S 653 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) +--R n log(x) p log(b %e + a) n p + 1 +--R (b %e + a)%e - (b x + a) +--R (4) ------------------------------------------------------------- +--R b n p + b n +--R Type: Expression(Integer) +--E 653 + +--S 654 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 654 + +)clear all + +--S 655 of 1394 +t0:=x^(-1+2*n)*(a+b*x^n)^p +--R +--R +--R 2n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 655 + +--S 656 of 1394 +r0:=-a*(a+b*x^n)^(1+p)/(b^2*n*(1+p))+(a+b*x^n)^(2+p)/(b^2*n*(2+p)) +--R +--R +--R n p + 2 n p + 1 +--R (p + 1)(b x + a) + (- a p - 2a)(b x + a) +--R (2) ---------------------------------------------------- +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Expression(Integer) +--E 656 + +--S 657 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R n log(x) +--R 2 2 n log(x) 2 n log(x) 2 p log(b %e + a) +--R ((b p + b )(%e ) + a b p %e - a )%e +--R -------------------------------------------------------------------------- +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Union(Expression(Integer),...) +--E 657 + +--S 658 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 n log(x) 2 n log(x) 2 +--R ((b p + b )(%e ) + a b p %e - a ) +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R n p + 2 n p + 1 +--R (- p - 1)(b x + a) + (a p + 2a)(b x + a) +--R / +--R 2 2 2 2 +--R b n p + 3b n p + 2b n +--R Type: Expression(Integer) +--E 658 + +--S 659 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 659 + +)clear all + +--S 660 of 1394 +t0:=x^(-1+3*n)*(a+b*x^n)^p +--R +--R +--R 3n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 660 + +--S 661 of 1394 +r0:=a^2*(a+b*x^n)^(1+p)/(b^3*n*(1+p))-2*a*(a+b*x^n)^(2+p)/(b^3*n*(2+p))+_ + (a+b*x^n)^(3+p)/(b^3*n*(3+p)) +--R +--R +--R (2) +--R 2 n p + 3 2 n p + 2 +--R (p + 3p + 2)(b x + a) + (- 2a p - 8a p - 6a)(b x + a) +--R + +--R 2 2 2 2 n p + 1 +--R (a p + 5a p + 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Expression(Integer) +--E 661 + +--S 662 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 2 3 3 n log(x) 3 2 2 2 n log(x) 2 +--R (b p + 3b p + 2b )(%e ) + (a b p + a b p)(%e ) +--R + +--R 2 n log(x) 3 +--R - 2a b p %e + 2a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Union(Expression(Integer),...) +--E 662 + +--S 663 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 2 3 3 n log(x) 3 2 2 2 n log(x) 2 +--R (b p + 3b p + 2b )(%e ) + (a b p + a b p)(%e ) +--R + +--R 2 n log(x) 3 +--R - 2a b p %e + 2a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R 2 n p + 3 2 n p + 2 +--R (- p - 3p - 2)(b x + a) + (2a p + 8a p + 6a)(b x + a) +--R + +--R 2 2 2 2 n p + 1 +--R (- a p - 5a p - 6a )(b x + a) +--R / +--R 3 3 3 2 3 3 +--R b n p + 6b n p + 11b n p + 6b n +--R Type: Expression(Integer) +--E 663 + +--S 664 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 664 + +)clear all + +--S 665 of 1394 +t0:=x^(-1+4*n)*(a+b*x^n)^p +--R +--R +--R 4n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 665 + +--S 666 of 1394 +r0:=-a^3*(a+b*x^n)^(1+p)/(b^4*n*(1+p))+3*a^2*(a+b*x^n)^(2+p)/(b^4*n*(2+p))-_ + 3*a*(a+b*x^n)^(3+p)/(b^4*n*(3+p))+(a+b*x^n)^(4+p)/(b^4*n*(4+p)) +--R +--R +--R (2) +--R 3 2 n p + 4 +--R (p + 6p + 11p + 6)(b x + a) +--R + +--R 3 2 n p + 3 +--R (- 3a p - 21a p - 42a p - 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n p + 2 +--R (3a p + 24a p + 57a p + 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n p + 1 +--R (- a p - 9a p - 26a p - 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Expression(Integer) +--E 666 + +--S 667 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 3 4 2 4 4 n log(x) 4 +--R (b p + 6b p + 11b p + 6b )(%e ) +--R + +--R 3 3 3 2 3 n log(x) 3 +--R (a b p + 3a b p + 2a b p)(%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (- 3a b p - 3a b p)(%e ) + 6a b p %e - 6a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Union(Expression(Integer),...) +--E 667 + +--S 668 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 3 4 2 4 4 n log(x) 4 +--R (b p + 6b p + 11b p + 6b )(%e ) +--R + +--R 3 3 3 2 3 n log(x) 3 +--R (a b p + 3a b p + 2a b p)(%e ) +--R + +--R 2 2 2 2 2 n log(x) 2 3 n log(x) 4 +--R (- 3a b p - 3a b p)(%e ) + 6a b p %e - 6a +--R * +--R n log(x) +--R p log(b %e + a) +--R %e +--R + +--R 3 2 n p + 4 +--R (- p - 6p - 11p - 6)(b x + a) +--R + +--R 3 2 n p + 3 +--R (3a p + 21a p + 42a p + 24a)(b x + a) +--R + +--R 2 3 2 2 2 2 n p + 2 +--R (- 3a p - 24a p - 57a p - 36a )(b x + a) +--R + +--R 3 3 3 2 3 3 n p + 1 +--R (a p + 9a p + 26a p + 24a )(b x + a) +--R / +--R 4 4 4 3 4 2 4 4 +--R b n p + 10b n p + 35b n p + 50b n p + 24b n +--R Type: Expression(Integer) +--E 668 + +--S 669 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 669 + +)clear all + +--S 670 of 1394 +t0:=x^(-1-n-n*p)*(a+b*x^n)^p +--R +--R +--R - n p - n - 1 n p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 670 + +--S 671 of 1394 +r0:=-(a+b*x^n)^(1+p)/(a*n*(1+p)*x^(n*(1+p))) +--R +--R +--R n p + 1 +--R (b x + a) +--R (2) - --------------------- +--R n p + n +--R (a n p + a n)x +--R Type: Expression(Integer) +--E 671 + +--S 672 of 1394 +--a0:=integrate(t0,x) +--E 672 + +--S 673 of 1394 +--m0:=a0-r0 +--E 673 + +--S 674 of 1394 +--d0:=D(m0,x) +--E 674 + +)clear all + +--S 675 of 1394 +t0:=x^(-1-9*n)*(a+b*x^n)^8 +--R +--R +--R (1) +--R 8 - 9n - 1 n 8 7 - 9n - 1 n 7 2 6 - 9n - 1 n 6 +--R b x (x ) + 8a b x (x ) + 28a b x (x ) +--R + +--R 3 5 - 9n - 1 n 5 4 4 - 9n - 1 n 4 5 3 - 9n - 1 n 3 +--R 56a b x (x ) + 70a b x (x ) + 56a b x (x ) +--R + +--R 6 2 - 9n - 1 n 2 7 - 9n - 1 n 8 - 9n - 1 +--R 28a b x (x ) + 8a b x x + a x +--R Type: Expression(Integer) +--E 675 + +--S 676 of 1394 +r0:=-1/9*(a+b*x^n)^9/(a*n*x^(9*n)) +--R +--R +--R (2) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R - b (x ) - 9a b (x ) - 36a b (x ) - 84a b (x ) - 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R - 126a b (x ) - 84a b (x ) - 36a b (x ) - 9a b x - a +--R / +--R 9n +--R 9a n x +--R Type: Expression(Integer) +--E 676 + +--S 677 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 n log(x) 8 7 n log(x) 7 2 6 n log(x) 6 +--R - 9b (%e ) - 36a b (%e ) - 84a b (%e ) +--R + +--R 3 5 n log(x) 5 4 4 n log(x) 4 5 3 n log(x) 3 +--R - 126a b (%e ) - 126a b (%e ) - 84a b (%e ) +--R + +--R 6 2 n log(x) 2 7 n log(x) 8 +--R - 36a b (%e ) - 9a b %e - a +--R / +--R n log(x) 9 +--R 9n (%e ) +--R Type: Union(Expression(Integer),...) +--E 677 + +--S 678 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 9 n 9 8 n 8 2 7 n 7 3 6 n 6 4 5 n 5 +--R b (x ) + 9a b (x ) + 36a b (x ) + 84a b (x ) + 126a b (x ) +--R + +--R 5 4 n 4 6 3 n 3 7 2 n 2 8 n 9 +--R 126a b (x ) + 84a b (x ) + 36a b (x ) + 9a b x + a +--R * +--R n log(x) 9 +--R (%e ) +--R + +--R 8 9n n log(x) 8 2 7 9n n log(x) 7 3 6 9n n log(x) 6 +--R - 9a b x (%e ) - 36a b x (%e ) - 84a b x (%e ) +--R + +--R 4 5 9n n log(x) 5 5 4 9n n log(x) 4 +--R - 126a b x (%e ) - 126a b x (%e ) +--R + +--R 6 3 9n n log(x) 3 7 2 9n n log(x) 2 8 9n n log(x) +--R - 84a b x (%e ) - 36a b x (%e ) - 9a b x %e +--R + +--R 9 9n +--R - a x +--R / +--R 9n n log(x) 9 +--R 9a n x (%e ) +--R Type: Expression(Integer) +--E 678 + +--S 679 of 1394 +d0:=D(normalize(m0),x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 679 + +)clear all + +--S 680 of 1394 +t0:=x^(-4-3*p)*(a+b*x^3)^p +--R +--R +--R - 3p - 4 3 p +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 680 + +--S 681 of 1394 +r0:=-1/3*(a+b*x^3)^(1+p)/(a*(1+p)*x^(3*(1+p))) +--R +--R +--R 3 p + 1 +--R (b x + a) +--R (2) - ------------------ +--R 3p + 3 +--R (3a p + 3a)x +--R Type: Expression(Integer) +--E 681 + +--S 682 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R 4 (- 3p - 4)log(x) p log(b x + a) +--R (- b x - a x)%e %e +--R (3) ------------------------------------------------- +--R 3a p + 3a +--R Type: Union(Expression(Integer),...) +--E 682 + +--S 683 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +--R 4 3p + 3 (- 3p - 4)log(x) p log(b x + a) 3 p + 1 +--R (- b x - a x)x %e %e + (b x + a) +--R -------------------------------------------------------------------------- +--R 3p + 3 +--R (3a p + 3a)x +--R Type: Expression(Integer) +--E 683 + +--S 684 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 684 + +)clear all + +--S 685 of 1394 +t0:=(a+b*x^3)^8/x^28 +--R +--R +--R (1) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R b x + 8a b x + 28a b x + 56a b x + 70a b x + 56a b x +--R + +--R 6 2 6 7 3 8 +--R 28a b x + 8a b x + a +--R / +--R 28 +--R x +--R Type: Fraction(Polynomial(Integer)) +--E 685 + +--S 686 of 1394 +r0:=-1/27*(a+b*x^3)^9/(a*x^27) +--R +--R +--R (2) +--R 1 9 27 1 8 24 4 2 7 21 28 3 6 18 14 4 5 15 14 5 4 12 +--R - -- b x - - a b x - - a b x - -- a b x - -- a b x - -- a b x +--R 27 3 3 9 3 3 +--R + +--R 28 6 3 9 4 7 2 6 1 8 3 1 9 +--R - -- a b x - - a b x - - a b x - -- a +--R 9 3 3 27 +--R / +--R 27 +--R a x +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 686 + +--S 687 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 24 7 21 2 6 18 3 5 15 4 4 12 5 3 9 +--R - 9b x - 36a b x - 84a b x - 126a b x - 126a b x - 84a b x +--R + +--R 6 2 6 7 3 8 +--R - 36a b x - 9a b x - a +--R / +--R 27 +--R 27x +--R Type: Union(Expression(Integer),...) +--E 687 + +--S 688 of 1394 +m0:=a0-r0 +--R +--R +--R 9 +--R b +--R (4) --- +--R 27a +--R Type: Expression(Integer) +--E 688 + +--S 689 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 689 + +)clear all + +--S 690 of 1394 +t0:=1/(x*(a+b*x^n)) +--R +--R +--R 1 +--R (1) ------------ +--R n +--R b x x + a x +--R Type: Expression(Integer) +--E 690 + +--S 691 of 1394 +r0:=log(x)/a-log(a+b*x^n)/(a*n) +--R +--R +--R n +--R - log(b x + a) + n log(x) +--R (2) -------------------------- +--R a n +--R Type: Expression(Integer) +--E 691 + +--S 692 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R - log(b %e + a) + n log(x) +--R (3) ---------------------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 692 + +--S 693 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R - log(b %e + a) + log(b x + a) +--R (4) --------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 693 + +--S 694 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 694 + +)clear all + +--S 695 of 1394 +t0:=1/(x*(a+b*x^3)) +--R +--R +--R 1 +--R (1) ---------- +--R 4 +--R b x + a x +--R Type: Fraction(Polynomial(Integer)) +--E 695 + +--S 696 of 1394 +r0:=log(x)/a-1/3*log(a+b*x^3)/a +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (2) ------------------------- +--R 3a +--R Type: Expression(Integer) +--E 696 + +--S 697 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 +--R - log(b x + a) + 3log(x) +--R (3) ------------------------- +--R 3a +--R Type: Union(Expression(Integer),...) +--E 697 + +--S 698 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 698 + +--S 699 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 699 + +)clear all + +--S 700 of 1394 +t0:=1/(x*(a+b/x^n)) +--R +--R +--R n +--R x +--R (1) ------------ +--R n +--R a x x + b x +--R Type: Expression(Integer) +--E 700 + +--S 701 of 1394 +r0:=log(b+a*x^n)/(a*n) +--R +--R +--R n +--R log(a x + b) +--R (2) ------------- +--R a n +--R Type: Expression(Integer) +--E 701 + +--S 702 of 1394 +a0:=integrate(t0,x) +--R +--R +--R n log(x) +--R log(a %e + b) +--R (3) --------------------- +--R a n +--R Type: Union(Expression(Integer),...) +--E 702 + +--S 703 of 1394 +m0:=a0-r0 +--R +--R +--R n log(x) n +--R log(a %e + b) - log(a x + b) +--R (4) ------------------------------------- +--R a n +--R Type: Expression(Integer) +--E 703 + +--S 704 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 704 + +)clear all + +--S 705 of 1394 +t0:=x^m/(a+b*x^(1+m)) +--R +--R +--R m +--R x +--R (1) ------------ +--R m + 1 +--R b x + a +--R Type: Expression(Integer) +--E 705 + +--S 706 of 1394 +r0:=log(a+b*x^(1+m))/(b*(1+m)) +--R +--R +--R m + 1 +--R log(b x + a) +--R (2) ----------------- +--R b m + b +--R Type: Expression(Integer) +--E 706 + +--S 707 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (m + 1)log(x) +--R log(b %e + a) +--R (3) -------------------------- +--R b m + b +--R Type: Union(Expression(Integer),...) +--E 707 + +--S 708 of 1394 +m0:=a0-r0 +--R +--R +--R (m + 1)log(x) m + 1 +--R log(b %e + a) - log(b x + a) +--R (4) ---------------------------------------------- +--R b m + b +--R Type: Expression(Integer) +--E 708 + +--S 709 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 709 + +)clear all + +--S 710 of 1394 +t0:=x^m*(a+b*x^(1+m))^n +--R +--R +--R m m + 1 n +--R (1) x (b x + a) +--R Type: Expression(Integer) +--E 710 + +--S 711 of 1394 +r0:=(a+b*x^(1+m))^(1+n)/(b*(1+m)*(1+n)) +--R +--R +--R m + 1 n + 1 +--R (b x + a) +--R (2) -------------------- +--R (b m + b)n + b m + b +--R Type: Expression(Integer) +--E 711 + +--S 712 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (m + 1)log(x) +--R (m + 1)log(x) n log(b %e + a) +--R (b %e + a)%e +--R (3) ----------------------------------------------------- +--R (b m + b)n + b m + b +--R Type: Union(Expression(Integer),...) +--E 712 + +--S 713 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R (m + 1)log(x) +--R (m + 1)log(x) n log(b %e + a) m + 1 n + 1 +--R (b %e + a)%e - (b x + a) +--R --------------------------------------------------------------------------- +--R (b m + b)n + b m + b +--R Type: Expression(Integer) +--E 713 + +--S 714 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 714 + +)clear all + +--S 715 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^3 +--R +--R +--R 3 m 2m + 2 3 2 m 2m + 2 2 2 m 2m + 2 3 m +--R (1) b x (x ) + 3a b x (x ) + 3a b x x + a x +--R Type: Expression(Integer) +--E 715 + +--S 716 of 1394 +r0:=a^3*x^(1+m)/(1+m)+a^2*b*x^(3*(1+m))/(1+m)+_ + 3/5*a*b^2*x^(5*(1+m))/(1+m)+1/7*b^3*x^(7*(1+m))/(1+m) +--R +--R +--R 3 7m + 7 2 5m + 5 2 3m + 3 3 m + 1 +--R 5b x + 21a b x + 35a b x + 35a x +--R (2) ------------------------------------------------------- +--R 35m + 35 +--R Type: Expression(Integer) +--E 716 + +--S 717 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 7 m log(x) 7 2 5 m log(x) 5 2 3 m log(x) 3 +--R 5b x (%e ) + 21a b x (%e ) + 35a b x (%e ) +--R + +--R 3 m log(x) +--R 35a x %e +--R / +--R 35m + 35 +--R Type: Union(Expression(Integer),...) +--E 717 + +--S 718 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 7 m log(x) 7 2 5 m log(x) 5 2 3 m log(x) 3 +--R 5b x (%e ) + 21a b x (%e ) + 35a b x (%e ) +--R + +--R 3 m log(x) 3 7m + 7 2 5m + 5 2 3m + 3 3 m + 1 +--R 35a x %e - 5b x - 21a b x - 35a b x - 35a x +--R / +--R 35m + 35 +--R Type: Expression(Integer) +--E 718 + +--S 719 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 719 + +)clear all + +--S 720 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^2 +--R +--R +--R 2 m 2m + 2 2 m 2m + 2 2 m +--R (1) b x (x ) + 2a b x x + a x +--R Type: Expression(Integer) +--E 720 + +--S 721 of 1394 +r0:=a^2*x^(1+m)/(1+m)+2/3*a*b*x^(3*(1+m))/(1+m)+1/5*b^2*x^(5*(1+m))/(1+m) +--R +--R +--R 2 5m + 5 3m + 3 2 m + 1 +--R 3b x + 10a b x + 15a x +--R (2) --------------------------------------- +--R 15m + 15 +--R Type: Expression(Integer) +--E 721 + +--S 722 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R 3b x (%e ) + 10a b x (%e ) + 15a x %e +--R (3) ------------------------------------------------------------- +--R 15m + 15 +--R Type: Union(Expression(Integer),...) +--E 722 + +--S 723 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R 3b x (%e ) + 10a b x (%e ) + 15a x %e +--R + +--R 2 5m + 5 3m + 3 2 m + 1 +--R - 3b x - 10a b x - 15a x +--R / +--R 15m + 15 +--R Type: Expression(Integer) +--E 723 + +--S 724 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 724 + +)clear all + +--S 725 of 1394 +t0:=x^m*(a+b*x^(2+2*m)) +--R +--R +--R m 2m + 2 m +--R (1) b x x + a x +--R Type: Expression(Integer) +--E 725 + +--S 726 of 1394 +r0:=a*x^(1+m)/(1+m)+1/3*b*x^(3*(1+m))/(1+m) +--R +--R +--R 3m + 3 m + 1 +--R b x + 3a x +--R (2) --------------------- +--R 3m + 3 +--R Type: Expression(Integer) +--E 726 + +--S 727 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 m log(x) 3 m log(x) +--R b x (%e ) + 3a x %e +--R (3) ----------------------------------- +--R 3m + 3 +--R Type: Union(Expression(Integer),...) +--E 727 + +--S 728 of 1394 +m0:=a0-r0 +--R +--R +--R 3 m log(x) 3 m log(x) 3m + 3 m + 1 +--R b x (%e ) + 3a x %e - b x - 3a x +--R (4) ----------------------------------------------------------- +--R 3m + 3 +--R Type: Expression(Integer) +--E 728 + +--S 729 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 729 + +)clear all + +--S 730 of 1394 +t0:=x^m/(a+b*x^(2+2*m)) +--R +--R +--R m +--R x +--R (1) ------------- +--R 2m + 2 +--R b x + a +--R Type: Expression(Integer) +--E 730 + +--S 731 of 1394 +r0:=atan(x^(1+m)*sqrt(b)/sqrt(a))/((1+m)*sqrt(a)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R (2) ---------------- +--R +-+ +-+ +--R (m + 1)\|a \|b +--R Type: Expression(Integer) +--E 731 + +--S 732 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R [--------------------------------------------------------------, +--R +-----+ +--R (2m + 2)\|- a b +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R -----------------------] +--R +---+ +--R (m + 1)\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 732 + +--S 733 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R +-+ +-+ b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R \|a \|b log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R +-----+ x \|b +--R - 2\|- a b atan(----------) +--R +-+ +--R \|a +--R / +--R +-----+ +-+ +-+ +--R (2m + 2)\|- a b \|a \|b +--R Type: Expression(Integer) +--E 733 + +--S 734 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 734 + +--S 735 of 1394 +m0b:=a0.2-r0 +--R +--R +--R +---+ m log(x) m + 1 +-+ +--R +-+ +-+ x\|a b %e +---+ x \|b +--R \|a \|b atan(-----------------) - \|a b atan(----------) +--R a +-+ +--R \|a +--R (6) -------------------------------------------------------- +--R +-+ +-+ +---+ +--R (m + 1)\|a \|b \|a b +--R Type: Expression(Integer) +--E 735 + +--S 736 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 736 + +)clear all + +--S 737 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^2 +--R +--R +--R m +--R x +--R (1) -------------------------------- +--R 2 2m + 2 2 2m + 2 2 +--R b (x ) + 2a b x + a +--R Type: Expression(Integer) +--E 737 + +--S 738 of 1394 +r0:=1/2*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m))))+_ + 1/2*atan(x^(1+m)*sqrt(b)/sqrt(a))/(a^(3/2)*(1+m)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R 2m + 2 x \|b m + 1 +-+ +-+ +--R (b x + a)atan(----------) + x \|a \|b +--R +-+ +--R \|a +--R (2) ------------------------------------------------ +--R 2m + 2 2 2 +-+ +-+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b +--R Type: Expression(Integer) +--E 738 + +--S 739 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 m log(x) 2 +--R (b x (%e ) + a) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R +-----+ m log(x) +--R 2x\|- a b %e +--R / +--R 2 +-----+ m log(x) 2 2 2 +-----+ +--R (4a b m + 4a b)x \|- a b (%e ) + (4a m + 4a )\|- a b +--R , +--R +---+ m log(x) +--R 2 m log(x) 2 x\|a b %e +---+ m log(x) +--R (b x (%e ) + a)atan(-----------------) + x\|a b %e +--R a +--R ------------------------------------------------------------------] +--R 2 +---+ m log(x) 2 2 2 +---+ +--R (2a b m + 2a b)x \|a b (%e ) + (2a m + 2a )\|a b +--R Type: Union(List(Expression(Integer)),...) +--E 739 + +--S 740 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +-----+ x \|b +--R (- 2b x x - 2a b x )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-----+ +-+ +-+ +--R - 2b x x \|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-----+ +-+ +-+ m log(x) +--R (2b x x + 2a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +-----+ x \|b m + 1 +-----+ +-+ +-+ +--R (- 2a b x - 2a )\|- a b atan(----------) - 2a x \|- a b \|a \|b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-----+ +-+ +-+ +--R ((4a b m + 4a b )x x + (4a b m + 4a b)x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-----+ +-+ +-+ +--R ((4a b m + 4a b)x + 4a m + 4a )\|- a b \|a \|b +--R Type: Expression(Integer) +--E 740 + +--S 741 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 741 + +--S 742 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 2 2 2m + 2 2 +-+ +-+ m log(x) 2 +--R (b x x + a b x )\|a \|b (%e ) +--R + +--R 2m + 2 2 +-+ +-+ +--R (a b x + a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 +---+ x \|b +--R (- b x x - a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 +-+ +-+ +---+ +--R - b x x \|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2m + 2 +-+ +-+ +---+ m log(x) +--R (b x x + a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2m + 2 2 +---+ x \|b m + 1 +-+ +-+ +---+ +--R (- a b x - a )\|a b atan(----------) - a x \|a \|b \|a b +--R +-+ +--R \|a +--R / +--R 2 2 2 2m + 2 2 2 2 +-+ +-+ +---+ +--R ((2a b m + 2a b )x x + (2a b m + 2a b)x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2 2m + 2 3 3 +-+ +-+ +---+ +--R ((2a b m + 2a b)x + 2a m + 2a )\|a \|b \|a b +--R Type: Expression(Integer) +--E 742 + +--S 743 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 743 + +)clear all + +--S 744 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^3 +--R +--R +--R m +--R x +--R (1) -------------------------------------------------- +--R 3 2m + 2 3 2 2m + 2 2 2 2m + 2 3 +--R b (x ) + 3a b (x ) + 3a b x + a +--R Type: Expression(Integer) +--E 744 + +--S 745 of 1394 +r0:=1/4*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^2)+_ + 3/8*x^(1+m)/(a^2*(1+m)*(a+b*x^(2*(1+m))))+_ + 3/8*atan(x^(1+m)*sqrt(b)/sqrt(a))/(a^(5/2)*(1+m)*sqrt(b)) +--R +--R +--R (2) +--R m + 1 +-+ +--R 2 2m + 2 2 2m + 2 2 x \|b +--R (3b (x ) + 6a b x + 3a )atan(----------) +--R +-+ +--R \|a +--R + +--R m + 1 2m + 2 m + 1 +-+ +-+ +--R (3b x x + 5a x )\|a \|b +--R / +--R 2 2 2 2 2m + 2 2 3 3 2m + 2 4 4 +-+ +--R ((8a b m + 8a b )(x ) + (16a b m + 16a b)x + 8a m + 8a )\|a +--R * +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 745 + +--S 746 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R [ +--R 2 4 m log(x) 4 2 m log(x) 2 2 +--R (3b x (%e ) + 6a b x (%e ) + 3a ) +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R 3 +-----+ m log(x) 3 +-----+ m log(x) +--R 6b x \|- a b (%e ) + 10a x\|- a b %e +--R / +--R 2 2 2 2 4 +-----+ m log(x) 4 +--R (16a b m + 16a b )x \|- a b (%e ) +--R + +--R 3 3 2 +-----+ m log(x) 2 4 4 +-----+ +--R (32a b m + 32a b)x \|- a b (%e ) + (16a m + 16a )\|- a b +--R , +--R +--R 2 4 m log(x) 4 2 m log(x) 2 2 +--R (3b x (%e ) + 6a b x (%e ) + 3a ) +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R 3 +---+ m log(x) 3 +---+ m log(x) +--R 3b x \|a b (%e ) + 5a x\|a b %e +--R / +--R 2 2 2 2 4 +---+ m log(x) 4 +--R (8a b m + 8a b )x \|a b (%e ) +--R + +--R 3 3 2 +---+ m log(x) 2 4 4 +---+ +--R (16a b m + 16a b)x \|a b (%e ) + (8a m + 8a )\|a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 746 + +--S 747 of 1394 +m0a:=a0.1-r0 +--R +--R +--R (4) +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-+ +-+ m log(x) 4 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-+ +-+ m log(x) 2 +--R (6a b x (x ) + 12a b x x + 6a b x )\|a \|b (%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 +-+ +-+ +--R (3a b (x ) + 6a b x + 3a )\|a \|b +--R * +--R 2 +-----+ m log(x) 2 m log(x) +-----+ +--R b x \|- a b (%e ) + 2a b x %e - a\|- a b +--R log(---------------------------------------------------------) +--R 2 m log(x) 2 +--R b x (%e ) + a +--R + +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-----+ +--R (- 6b x (x ) - 12a b x x - 6a b x )\|- a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 +-----+ +-+ +-+ +--R (- 6b x x x - 10a b x x )\|- a b \|a \|b +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 3 2m + 2 2 2 3 2m + 2 2 3 +-----+ +-+ +-+ +--R (6b x (x ) + 12a b x x + 6a b x )\|- a b \|a \|b +--R * +--R m log(x) 3 +--R (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-----+ +--R (- 12a b x (x ) - 24a b x x - 12a b x )\|- a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 +-----+ +-+ +-+ +--R (- 12a b x x x - 20a b x x )\|- a b \|a \|b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2m + 2 2 2 2m + 2 3 +-----+ +-+ +-+ m log(x) +--R (10a b x (x ) + 20a b x x + 10a x)\|- a b \|a \|b %e +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 3 2m + 2 4 +-----+ x \|b +--R (- 6a b (x ) - 12a b x - 6a )\|- a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 2m + 2 3 m + 1 +-----+ +-+ +-+ +--R (- 6a b x x - 10a x )\|- a b \|a \|b +--R / +--R 2 4 2 4 4 2m + 2 2 3 3 3 3 4 2m + 2 +--R (16a b m + 16a b )x (x ) + (32a b m + 32a b )x x +--R + +--R 4 2 4 2 4 +--R (16a b m + 16a b )x +--R * +--R +-----+ +-+ +-+ m log(x) 4 +--R \|- a b \|a \|b (%e ) +--R + +--R 3 3 3 3 2 2m + 2 2 4 2 4 2 2 2m + 2 +--R (32a b m + 32a b )x (x ) + (64a b m + 64a b )x x +--R + +--R 5 5 2 +--R (32a b m + 32a b)x +--R * +--R +-----+ +-+ +-+ m log(x) 2 +--R \|- a b \|a \|b (%e ) +--R + +--R 4 2 4 2 2m + 2 2 5 5 2m + 2 6 +--R (16a b m + 16a b )(x ) + (32a b m + 32a b)x + 16a m +--R + +--R 6 +--R 16a +--R * +--R +-----+ +-+ +-+ +--R \|- a b \|a \|b +--R Type: Expression(Integer) +--E 747 + +--S 748 of 1394 +d0a:=normalize(D(m0a,x)) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 748 + +--S 749 of 1394 +m0b:=a0.2-r0 +--R +--R +--R (6) +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +-+ +-+ m log(x) 4 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +-+ +-+ m log(x) 2 +--R (6a b x (x ) + 12a b x x + 6a b x )\|a \|b (%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 +-+ +-+ +--R (3a b (x ) + 6a b x + 3a )\|a \|b +--R * +--R +---+ m log(x) +--R x\|a b %e +--R atan(-----------------) +--R a +--R + +--R m + 1 +-+ +--R 4 4 2m + 2 2 3 4 2m + 2 2 2 4 +---+ x \|b +--R (- 3b x (x ) - 6a b x x - 3a b x )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 +-+ +-+ +---+ +--R (- 3b x x x - 5a b x x )\|a \|b \|a b +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 3 3 2m + 2 2 2 3 2m + 2 2 3 +-+ +-+ +---+ m log(x) 3 +--R (3b x (x ) + 6a b x x + 3a b x )\|a \|b \|a b (%e ) +--R + +--R 3 2 2m + 2 2 2 2 2 2m + 2 3 2 +---+ +--R (- 6a b x (x ) - 12a b x x - 6a b x )\|a b +--R * +--R m + 1 +-+ +--R x \|b +--R atan(----------) +--R +-+ +--R \|a +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 +-+ +-+ +---+ +--R (- 6a b x x x - 10a b x x )\|a \|b \|a b +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 2 2m + 2 2 2 2m + 2 3 +-+ +-+ +---+ m log(x) +--R (5a b x (x ) + 10a b x x + 5a x)\|a \|b \|a b %e +--R + +--R m + 1 +-+ +--R 2 2 2m + 2 2 3 2m + 2 4 +---+ x \|b +--R (- 3a b (x ) - 6a b x - 3a )\|a b atan(----------) +--R +-+ +--R \|a +--R + +--R 2 m + 1 2m + 2 3 m + 1 +-+ +-+ +---+ +--R (- 3a b x x - 5a x )\|a \|b \|a b +--R / +--R 2 4 2 4 4 2m + 2 2 3 3 3 3 4 2m + 2 +--R (8a b m + 8a b )x (x ) + (16a b m + 16a b )x x +--R + +--R 4 2 4 2 4 +--R (8a b m + 8a b )x +--R * +--R +-+ +-+ +---+ m log(x) 4 +--R \|a \|b \|a b (%e ) +--R + +--R 3 3 3 3 2 2m + 2 2 4 2 4 2 2 2m + 2 +--R (16a b m + 16a b )x (x ) + (32a b m + 32a b )x x +--R + +--R 5 5 2 +--R (16a b m + 16a b)x +--R * +--R +-+ +-+ +---+ m log(x) 2 +--R \|a \|b \|a b (%e ) +--R + +--R 4 2 4 2 2m + 2 2 5 5 2m + 2 6 6 +--R ((8a b m + 8a b )(x ) + (16a b m + 16a b)x + 8a m + 8a ) +--R * +--R +-+ +-+ +---+ +--R \|a \|b \|a b +--R Type: Expression(Integer) +--E 749 + +--S 750 of 1394 +d0b:=normalize(D(m0b,x)) +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 750 + +)clear all + +--S 751 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(5/2) +--R +--R +--R +-------------+ +--R 2 m 2m + 2 2 m 2m + 2 2 m | 2m + 2 +--R (1) (b x (x ) + 2a b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 751 + +--S 752 of 1394 +r0:=5/24*a*x^(1+m)*(a+b*x^(2*(1+m)))^(3/2)/(1+m)+_ + 1/6*x^(1+m)*(a+b*x^(2*(1+m)))^(5/2)/(1+m)+_ + 5/16*a^3*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b))+_ + 5/16*a^2*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R (2) +--R m + 1 +-+ +--R 3 x \|b +--R 15a atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R + +--R 2 m + 1 2m + 2 2 m + 1 2m + 2 2 m + 1 +-+ +--R (8b x (x ) + 26a b x x + 33a x )\|b +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R / +--R +-+ +--R (48m + 48)\|b +--R Type: Expression(Integer) +--E 752 + +--S 753 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 753 + +--S 754 of 1394 +--m0:=a0-r0 +--E 754 + +--S 755 of 1394 +--d0:=D(m0,x) +--E 755 + +)clear all + +--S 756 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(3/2) +--R +--R +--R +-------------+ +--R m 2m + 2 m | 2m + 2 +--R (1) (b x x + a x )\|b x + a +--R Type: Expression(Integer) +--E 756 + +--S 757 of 1394 +r0:=1/4*x^(1+m)*(a+b*x^(2*(1+m)))^(3/2)/(1+m)+_ + 3/8*a^2*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*_ + sqrt(b))+3/8*a*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R (2) +--R m + 1 +-+ +--R 2 x \|b +--R 3a atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R + +--R +-------------+ +--R m + 1 2m + 2 m + 1 +-+ | 2m + 2 +--R (2b x x + 5a x )\|b \|b x + a +--R / +--R +-+ +--R (8m + 8)\|b +--R Type: Expression(Integer) +--E 757 + +--S 758 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 758 + +--S 759 of 1394 +--m0:=a0-r0 +--E 759 + +--S 760 of 1394 +--d0:=D(m0,x) +--E 760 + +)clear all + +--S 761 of 1394 +t0:=x^m*(a+b*x^(2+2*m))^(1/2) +--R +--R +--R +-------------+ +--R m | 2m + 2 +--R (1) x \|b x + a +--R Type: Expression(Integer) +--E 761 + +--S 762 of 1394 +r0:=1/2*a*atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b))+_ + 1/2*x^(1+m)*sqrt(a+b*x^(2*(1+m)))/(1+m) +--R +--R +--R m + 1 +-+ +-------------+ +--R x \|b m + 1 +-+ | 2m + 2 +--R a atanh(----------------) + x \|b \|b x + a +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R (2) ------------------------------------------------------ +--R +-+ +--R (2m + 2)\|b +--R Type: Expression(Integer) +--E 762 + +--S 763 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 763 + +--S 764 of 1394 +--m0:=a0-r0 +--E 764 + +--S 765 of 1394 +--d0:=D(m0,x) +--E 765 + +)clear all + +--S 766 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(1/2) +--R +--R +--R m +--R x +--R (1) ---------------- +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 766 + +--S 767 of 1394 +r0:=atanh(x^(1+m)*sqrt(b)/sqrt(a+b*x^(2*(1+m))))/((1+m)*sqrt(b)) +--R +--R +--R m + 1 +-+ +--R x \|b +--R atanh(----------------) +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R (2) ----------------------- +--R +-+ +--R (m + 1)\|b +--R Type: Expression(Integer) +--E 767 + +--R +--S 768 of 1394 (constant residues) +--a0:=integrate(t0,x) +--E 768 + +--S 769 of 1394 +--m0:=a0-r0 +--E 769 + +--S 770 of 1394 +--d0:=D(m0,x) +--E 770 + +)clear all + +--S 771 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(3/2) +--R +--R +--R m +--R x +--R (1) ------------------------------- +--R +-------------+ +--R 2m + 2 | 2m + 2 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 771 + +--S 772 of 1394 +r0:=x^(1+m)/(a*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R m + 1 +--R x +--R (2) ------------------------- +--R +-------------+ +--R | 2m + 2 +--R (a m + a)\|b x + a +--R Type: Expression(Integer) +--E 772 + +--S 773 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +---------------------+ +--R m log(x) | 2 m log(x) 2 +--R x %e \|b x (%e ) + a +--R (3) --------------------------------------- +--R 2 m log(x) 2 2 2 +--R (a b m + a b)x (%e ) + a m + a +--R Type: Union(Expression(Integer),...) +--E 773 + +--S 774 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------------+ +---------------------+ +--R m log(x) | 2m + 2 | 2 m log(x) 2 +--R x %e \|b x + a \|b x (%e ) + a +--R + +--R 2 m + 1 m log(x) 2 m + 1 +--R - b x x (%e ) - a x +--R / +--R +-------------+ +--R 2 m log(x) 2 2 2 | 2m + 2 +--R ((a b m + a b)x (%e ) + a m + a )\|b x + a +--R Type: Expression(Integer) +--E 774 + +--S 775 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 775 + +)clear all + +--S 776 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(5/2) +--R +--R +--R m +--R x +--R (1) -------------------------------------------------- +--R +-------------+ +--R 2 2m + 2 2 2m + 2 2 | 2m + 2 +--R (b (x ) + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 776 + +--S 777 of 1394 +r0:=1/3*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^(3/2))+_ + 2/3*x^(1+m)/(a^2*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R m + 1 2m + 2 m + 1 +--R 2b x x + 3a x +--R (2) ----------------------------------------------------- +--R +-------------+ +--R 2 2 2m + 2 3 3 | 2m + 2 +--R ((3a b m + 3a b)x + 3a m + 3a )\|b x + a +--R Type: Expression(Integer) +--E 777 + +--S 778 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---------------------+ +--R 3 m log(x) 3 m log(x) | 2 m log(x) 2 +--R (2b x (%e ) + 3a x %e )\|b x (%e ) + a +--R ----------------------------------------------------------------------------- +--R 2 2 2 2 4 m log(x) 4 3 3 2 m log(x) 2 4 4 +--R (3a b m + 3a b )x (%e ) + (6a b m + 6a b)x (%e ) + 3a m + 3a +--R Type: Union(Expression(Integer),...) +--E 778 + +--S 779 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 3 2m + 2 3 m log(x) 3 +--R (2b x x + 2a b x )(%e ) +--R + +--R 2m + 2 2 m log(x) +--R (3a b x x + 3a x)%e +--R * +--R +-------------+ +---------------------+ +--R | 2m + 2 | 2 m log(x) 2 +--R \|b x + a \|b x (%e ) + a +--R + +--R 3 4 m + 1 2m + 2 2 4 m + 1 m log(x) 4 +--R (- 2b x x x - 3a b x x )(%e ) +--R + +--R 2 2 m + 1 2m + 2 2 2 m + 1 m log(x) 2 +--R (- 4a b x x x - 6a b x x )(%e ) +--R + +--R 2 m + 1 2m + 2 3 m + 1 +--R - 2a b x x - 3a x +--R / +--R 2 3 2 3 4 2m + 2 3 2 3 2 4 m log(x) 4 +--R ((3a b m + 3a b )x x + (3a b m + 3a b )x )(%e ) +--R + +--R 3 2 3 2 2 2m + 2 4 4 2 m log(x) 2 +--R ((6a b m + 6a b )x x + (6a b m + 6a b)x )(%e ) +--R + +--R 4 4 2m + 2 5 5 +--R (3a b m + 3a b)x + 3a m + 3a +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 779 + +--S 780 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 780 + +)clear all + +--S 781 of 1394 +t0:=x^m/(a+b*x^(2+2*m))^(7/2) +--R +--R +--R m +--R x +--R (1) -------------------------------------------------------------------- +--R +-------------+ +--R 3 2m + 2 3 2 2m + 2 2 2 2m + 2 3 | 2m + 2 +--R (b (x ) + 3a b (x ) + 3a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 781 + +--S 782 of 1394 +r0:=1/5*x^(1+m)/(a*(1+m)*(a+b*x^(2*(1+m)))^(5/2))+_ + 4/15*x^(1+m)/(a^2*(1+m)*(a+b*x^(2*(1+m)))^(3/2))+_ + 8/15*x^(1+m)/(a^3*(1+m)*sqrt(a+b*x^(2*(1+m)))) +--R +--R +--R (2) +--R 2 m + 1 2m + 2 2 m + 1 2m + 2 2 m + 1 +--R 8b x (x ) + 20a b x x + 15a x +--R / +--R 3 2 3 2 2m + 2 2 4 4 2m + 2 5 5 +--R ((15a b m + 15a b )(x ) + (30a b m + 30a b)x + 15a m + 15a ) +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 782 + +--S 783 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 5 m log(x) 5 3 m log(x) 3 2 m log(x) +--R (8b x (%e ) + 20a b x (%e ) + 15a x %e ) +--R * +--R +---------------------+ +--R | 2 m log(x) 2 +--R \|b x (%e ) + a +--R / +--R 3 3 3 3 6 m log(x) 6 4 2 4 2 4 m log(x) 4 +--R (15a b m + 15a b )x (%e ) + (45a b m + 45a b )x (%e ) +--R + +--R 5 5 2 m log(x) 2 6 6 +--R (45a b m + 45a b)x (%e ) + 15a m + 15a +--R Type: Union(Expression(Integer),...) +--E 783 + +--S 784 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 5 2m + 2 2 3 5 2m + 2 2 2 5 m log(x) 5 +--R (8b x (x ) + 16a b x x + 8a b x )(%e ) +--R + +--R 3 3 2m + 2 2 2 2 3 2m + 2 3 3 m log(x) 3 +--R (20a b x (x ) + 40a b x x + 20a b x )(%e ) +--R + +--R 2 2 2m + 2 2 3 2m + 2 4 m log(x) +--R (15a b x (x ) + 30a b x x + 15a x)%e +--R * +--R +-------------+ +---------------------+ +--R | 2m + 2 | 2 m log(x) 2 +--R \|b x + a \|b x (%e ) + a +--R + +--R 5 6 m + 1 2m + 2 2 4 6 m + 1 2m + 2 2 3 6 m + 1 +--R (- 8b x x (x ) - 20a b x x x - 15a b x x ) +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 4 4 m + 1 2m + 2 2 2 3 4 m + 1 2m + 2 3 2 4 m + 1 +--R (- 24a b x x (x ) - 60a b x x x - 45a b x x ) +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 2 3 2 m + 1 2m + 2 2 3 2 2 m + 1 2m + 2 4 2 m + 1 +--R (- 24a b x x (x ) - 60a b x x x - 45a b x x ) +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 3 2 m + 1 2m + 2 2 4 m + 1 2m + 2 5 m + 1 +--R - 8a b x (x ) - 20a b x x - 15a x +--R / +--R 3 5 3 5 6 2m + 2 2 4 4 4 4 6 2m + 2 +--R (15a b m + 15a b )x (x ) + (30a b m + 30a b )x x +--R + +--R 5 3 5 3 6 +--R (15a b m + 15a b )x +--R * +--R m log(x) 6 +--R (%e ) +--R + +--R 4 4 4 4 4 2m + 2 2 5 3 5 3 4 2m + 2 +--R (45a b m + 45a b )x (x ) + (90a b m + 90a b )x x +--R + +--R 6 2 6 2 4 +--R (45a b m + 45a b )x +--R * +--R m log(x) 4 +--R (%e ) +--R + +--R 5 3 5 3 2 2m + 2 2 6 2 6 2 2 2m + 2 +--R (45a b m + 45a b )x (x ) + (90a b m + 90a b )x x +--R + +--R 7 7 2 +--R (45a b m + 45a b)x +--R * +--R m log(x) 2 +--R (%e ) +--R + +--R 6 2 6 2 2m + 2 2 7 7 2m + 2 8 8 +--R (15a b m + 15a b )(x ) + (30a b m + 30a b)x + 15a m + 15a +--R * +--R +-------------+ +--R | 2m + 2 +--R \|b x + a +--R Type: Expression(Integer) +--E 784 + +--S 785 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 785 + +)clear all + +--S 786 of 1394 +t0:=x^n*sqrt(1+x^(1+n)) +--R +--R +--R +----------+ +--R n | n + 1 +--R (1) x \|x + 1 +--R Type: Expression(Integer) +--E 786 + +--S 787 of 1394 +r0:=2/3*(1+x^(1+n))^(3/2)/(1+n) +--R +--R +--R +----------+ +--R n + 1 | n + 1 +--R (2x + 2)\|x + 1 +--R (2) -------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 787 + +--S 788 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------------------+ +--R (n + 1)log(x) | (n + 1)log(x) +--R (2%e + 2)\|%e + 1 +--R (3) -------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 788 + +--S 789 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------------------+ +----------+ +--R (n + 1)log(x) | (n + 1)log(x) n + 1 | n + 1 +--R (2%e + 2)\|%e + 1 + (- 2x - 2)\|x + 1 +--R --------------------------------------------------------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 789 + +--S 790 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 790 + +)clear all + +--S 791 of 1394 +t0:=x^n*sqrt(a^2+x^(1+n)) +--R +--R +--R +-----------+ +--R n | n + 1 2 +--R (1) x \|x + a +--R Type: Expression(Integer) +--E 791 + +--S 792 of 1394 +r0:=2/3*(a^2+x^(1+n))^(3/2)/(1+n) +--R +--R +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (2x + 2a )\|x + a +--R (2) ----------------------------- +--R 3n + 3 +--R Type: Expression(Integer) +--E 792 + +--S 793 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R (3) ----------------------------------------------- +--R 3n + 3 +--R Type: Union(Expression(Integer),...) +--E 793 + +--S 794 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +--------------------+ +--R (n + 1)log(x) 2 | (n + 1)log(x) 2 +--R (2%e + 2a )\|%e + a +--R + +--R +-----------+ +--R n + 1 2 | n + 1 2 +--R (- 2x - 2a )\|x + a +--R / +--R 3n + 3 +--R Type: Expression(Integer) +--E 794 + +--S 795 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 795 + +)clear all + +--S 796 of 1394 +t0:=(c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 796 + +--S 797 of 1394 +r0:=1/6*c^2*(a+b*x)^5*sqrt(c*(a+b*x)^2)/b +--R +--R +--R (2) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R / +--R 6b +--R Type: Expression(Integer) +--E 797 + +--S 798 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 2 6 4 2 5 2 3 2 4 3 2 2 3 4 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a c x)\|c +--R ------------------------------------------------------------------------ +--R 6 +--R Type: Union(Expression(Integer),...) +--E 798 + +--S 799 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (- b c x - 5a b c x - 10a b c x - 10a b c x - 5a b c x - a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x)\|c +--R / +--R 6b +--R Type: Expression(Integer) +--E 799 + +--S 800 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +-+ +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x - 6a b c x +--R + +--R 6 3 +--R - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 800 + +)clear all + +--S 801 of 1394 +t0:=(c*(a+b*x)^2)^(3/2) +--R +--R +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (1) (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 801 + +--S 802 of 1394 +r0:=1/4*c*(a+b*x)^3*sqrt(c*(a+b*x)^2)/b +--R +--R +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 2a b c x + a c +--R (2) --------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 802 + +--S 803 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a c x)\|c +--R (3) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 803 + +--S 804 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + 2a b c x + a c +--R + +--R 4 4 3 3 2 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x)\|c +--R / +--R 4b +--R Type: Expression(Integer) +--E 804 + +--S 805 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------+ +--R 3 3 2 2 2 3 +-+ | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|c \|b c x + 2a b c x + a c +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 805 + +)clear all + +--S 806 of 1394 +t0:=(c*(a+b*x)^2)^(1/2) +--R +--R +--R +-----------------------+ +--R | 2 2 2 +--R (1) \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 806 + +--S 807 of 1394 +r0a:=1/2*(a+b*x)*sqrt(c*(a+b*x)^2)/b +--R +--R +--R +-----------------------+ +--R | 2 2 2 +--R (b x + a)\|b c x + 2a b c x + a c +--R (2) ----------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 807 + +--S 808 of 1394 +r0b:=a*x*sqrt(c*(a+b*x)^2)/(a+b*x)+1/2*b*x^2*sqrt(c*(a+b*x)^2)/(a+b*x) +--R +--R +--R +-----------------------+ +--R 2 | 2 2 2 +--R (b x + 2a x)\|b c x + 2a b c x + a c +--R (3) --------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 808 + +--S 809 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (b x + 2a x)\|c +--R (4) ----------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 809 + +--S 810 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------------------+ +--R | 2 2 2 2 2 +-+ +--R (- b x - a)\|b c x + 2a b c x + a c + (b x + 2a b x)\|c +--R (5) ----------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 810 + +--S 811 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 2 2 2 +--R (b x + a)\|c \|b c x + 2a b c x + a c - b c x - 2a b c x - a c +--R (6) ----------------------------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 811 + +--S 812 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) +--R +-----------------------+ +--R 2 | 2 2 2 2 3 2 2 +-+ +--R (- b x - 2a x)\|b c x + 2a b c x + a c + (b x + 3a b x + 2a x)\|c +--R ----------------------------------------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 812 + +--S 813 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 2 2 2 +--R (b x + a)\|c \|b c x + 2a b c x + a c - b c x - 2a b c x - a c +--R (8) ----------------------------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 813 + +)clear all + +--S 814 of 1394 +t0:=1/(c*(a+b*x)^2)^(1/2) +--R +--R +--R 1 +--R (1) -------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 814 + +--S 815 of 1394 +r0:=(a+b*x)*log(a+b*x)/(b*sqrt(c*(a+b*x)^2)) +--R +--R +--R (b x + a)log(b x + a) +--R (2) --------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R b\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 815 + +--S 816 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(b x + a) +--R (3) ------------ +--R +-+ +--R b\|c +--R Type: Union(Expression(Integer),...) +--E 816 + +--S 817 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------+ +--R | 2 2 2 +-+ +--R log(b x + a)\|b c x + 2a b c x + a c + (- b x - a)log(b x + a)\|c +--R (4) -------------------------------------------------------------------- +--R +-----------------------+ +--R +-+ | 2 2 2 +--R b\|c \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 817 + +--S 818 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R (5) -------------------------------------------- +--R +-----------------------+ +--R | 2 2 2 +--R (b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 818 + +)clear all + +--S 819 of 1394 +t0:=1/(c*(a+b*x)^2)^(3/2) +--R +--R +--R 1 +--R (1) --------------------------------------------------- +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 819 + +--S 820 of 1394 +r0:=(-1/2)/(b*c*(a+b*x)*sqrt(c*(a+b*x)^2)) +--R +--R +--R 1 +--R (2) - ------------------------------------------- +--R +-----------------------+ +--R 2 | 2 2 2 +--R (2b c x + 2a b c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 820 + +--S 821 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------------------- +--R 3 2 2 2 +-+ +--R (2b c x + 4a b c x + 2a b c)\|c +--R Type: Union(Expression(Integer),...) +--E 821 + +--S 822 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------+ +--R | 2 2 2 +-+ +--R - \|b c x + 2a b c x + a c + (b x + a)\|c +--R (4) ----------------------------------------------------------- +--R +-----------------------+ +--R 3 2 2 2 +-+ | 2 2 2 +--R (2b c x + 4a b c x + 2a b c)\|c \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 822 + +--S 823 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R (5) ---------------------------------------------------------------- +--R +-----------------------+ +--R 3 2 3 2 2 2 2 2 3 2 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 823 + +)clear all + +--S 824 of 1394 +t0:=1/(c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R 1 +--R ---------------------------------------------------------------------------- +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 824 + +--S 825 of 1394 +r0:=(-1/4)/(b*c^2*(a+b*x)^3*sqrt(c*(a+b*x)^2)) +--R +--R +--R (2) +--R 1 +--R - ---------------------------------------------------------------------- +--R +-----------------------+ +--R 4 2 3 3 2 2 2 2 2 3 2 | 2 2 2 +--R (4b c x + 12a b c x + 12a b c x + 4a b c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 825 + +--S 826 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------------------- +--R 5 2 4 4 2 3 2 3 2 2 3 2 2 4 2 +-+ +--R (4b c x + 16a b c x + 24a b c x + 16a b c x + 4a b c )\|c +--R Type: Union(Expression(Integer),...) +--E 826 + +--S 827 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------+ +--R | 2 2 2 +-+ +--R - \|b c x + 2a b c x + a c + (b x + a)\|c +--R / +--R 5 2 4 4 2 3 2 3 2 2 3 2 2 4 2 +-+ +--R (4b c x + 16a b c x + 24a b c x + 16a b c x + 4a b c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 827 + +--S 828 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------+ +--R +-+ | 2 2 2 +--R \|c \|b c x + 2a b c x + a c - b c x - a c +--R / +--R 5 3 5 4 3 4 2 3 3 3 3 2 3 2 4 3 5 3 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 828 + +)clear all + +--TPDHERE: factor(25*x^2+30*x+9) = (5*x+3)^2 +--S 829 of 1394 +t0:=sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (1) \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 829 + +--S 830 of 1394 +r0a:=1/10*(3+5*x)*sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R (2) ------------------------- +--R 10 +--R Type: Expression(Integer) +--E 830 + +--S 831 of 1394 +r0b:=3*x*sqrt((3+5*x)^2)/(3+5*x)+5/2*x^2*sqrt((3+5*x)^2)/(3+5*x) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (5x + 6x)\|25x + 30x + 9 +--R (3) --------------------------- +--R 10x + 6 +--R Type: Expression(Integer) +--E 831 + +--S 832 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R 5x + 6x +--R (4) -------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 832 + +--S 833 of 1394 +m0a:=a0-r0a +--R +--R +--R +--------------+ +--R | 2 2 +--R (- 5x - 3)\|25x + 30x + 9 + 25x + 30x +--R (5) ---------------------------------------- +--R 10 +--R Type: Expression(Integer) +--E 833 + +--S 834 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (5x + 3)\|25x + 30x + 9 - 25x - 30x - 9 +--R (6) ------------------------------------------ +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 834 + +--S 835 of 1394 +m0b:=a0-r0b +--R +--R +--R +--------------+ +--R 2 | 2 3 2 +--R (- 5x - 6x)\|25x + 30x + 9 + 25x + 45x + 18x +--R (7) ------------------------------------------------- +--R 10x + 6 +--R Type: Expression(Integer) +--E 835 + +--S 836 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (5x + 3)\|25x + 30x + 9 - 25x - 30x - 9 +--R (8) ------------------------------------------ +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 836 + +)clear all + +--TPDHERE: factor(100*x^2+120*x+36) = 4*(5*x+3)^2 +--TPDHERE: why isn't the sqrt of a perfect square simplified? +--S 837 of 1394 +t0:=sqrt((6+10*x)^2) +--R +--R +--R +-----------------+ +--R | 2 +--R (1) \|100x + 120x + 36 +--R Type: Expression(Integer) +--E 837 + +--S 838 of 1394 +r0a:=1/5*(3+5*x)*sqrt((3+5*x)^2) +--R +--R +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R (2) ------------------------- +--R 5 +--R Type: Expression(Integer) +--E 838 + +--S 839 of 1394 +r0b:=6*x*sqrt((3+5*x)^2)/(3+5*x)+5*x^2*sqrt((3+5*x)^2)/(3+5*x) +--R +--R +--R +--------------+ +--R 2 | 2 +--R (5x + 6x)\|25x + 30x + 9 +--R (3) --------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 839 + +--S 840 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (4) 5x + 6x +--R Type: Union(Expression(Integer),...) +--E 840 + +--S 841 of 1394 +m0a:=a0-r0a +--R +--R +--R +--------------+ +--R | 2 2 +--R (- 5x - 3)\|25x + 30x + 9 + 25x + 30x +--R (5) ---------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 841 + +--S 842 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (10x + 6)\|25x + 30x + 9 - 50x - 60x - 18 +--R (6) -------------------------------------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 842 + +--S 843 of 1394 +m0b:=a0-r0b +--R +--R +--R +--------------+ +--R 2 | 2 3 2 +--R (- 5x - 6x)\|25x + 30x + 9 + 25x + 45x + 18x +--R (7) ------------------------------------------------- +--R 5x + 3 +--R Type: Expression(Integer) +--E 843 + +--S 844 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +--------------+ +--R | 2 2 +--R (10x + 6)\|25x + 30x + 9 - 50x - 60x - 18 +--R (8) -------------------------------------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 844 + +)clear all + +--S 845 of 1394 +t0:=1/sqrt((3+5*x)^2) +--R +--R +--R 1 +--R (1) ----------------- +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 +--R Type: Expression(Integer) +--E 845 + +--S 846 of 1394 +r0:=1/5*(3+5*x)*log(3+5*x)/sqrt((3+5*x)^2) +--R +--R +--R (5x + 3)log(5x + 3) +--R (2) ------------------- +--R +--------------+ +--R | 2 +--R 5\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 846 + +--S 847 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) +--R (3) ----------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 847 + +--S 848 of 1394 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +--R log(5x + 3)\|25x + 30x + 9 + (- 5x - 3)log(5x + 3) +--R (4) ---------------------------------------------------- +--R +--------------+ +--R | 2 +--R 5\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 848 + +--S 849 of 1394 +d0:=D(m0,x) +--R +--R +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 - 5x - 3 +--R (5) -------------------------- +--R +--------------+ +--R | 2 +--R (5x + 3)\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 849 + +)clear all + +--S 850 of 1394 +t0:=1/sqrt((6+10*x)^2) +--R +--R +--R 1 +--R (1) -------------------- +--R +-----------------+ +--R | 2 +--R \|100x + 120x + 36 +--R Type: Expression(Integer) +--E 850 + +--S 851 of 1394 +r0:=1/10*(3+5*x)*log(3+5*x)/sqrt((3+5*x)^2) +--R +--R +--R (5x + 3)log(5x + 3) +--R (2) ------------------- +--R +--------------+ +--R | 2 +--R 10\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 851 + +--S 852 of 1394 +a0:=integrate(t0,x) +--R +--R +--R log(5x + 3) +--R (3) ----------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 852 + +--S 853 of 1394 +m0:=a0-r0 +--R +--R +--R +--------------+ +--R | 2 +--R log(5x + 3)\|25x + 30x + 9 + (- 5x - 3)log(5x + 3) +--R (4) ---------------------------------------------------- +--R +--------------+ +--R | 2 +--R 10\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 853 + +--S 854 of 1394 +d0:=D(m0,x) +--R +--R +--R +--------------+ +--R | 2 +--R \|25x + 30x + 9 - 5x - 3 +--R (5) -------------------------- +--R +--------------+ +--R | 2 +--R (10x + 6)\|25x + 30x + 9 +--R Type: Expression(Integer) +--E 854 + +)clear all + +--S 855 of 1394 +t0:=1/sqrt(-(2+3*x)^2) +--R +--R +--R 1 +--R (1) ------------------ +--R +---------------+ +--R | 2 +--R \|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 855 + +--S 856 of 1394 +r0:=1/3*(2+3*x)*log(2+3*x)/sqrt(-(2+3*x)^2) +--R +--R +--R (3x + 2)log(3x + 2) +--R (2) ------------------- +--R +---------------+ +--R | 2 +--R 3\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 856 + +--S 857 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +---+ 3x + 2 +--R \|- 1 log(------) +--R 3 +--R (3) - ----------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 857 + +--S 858 of 1394 +m0:=a0-r0 +--R +--R +--R +---------------+ +--R +---+ 3x + 2 | 2 +--R - \|- 1 log(------)\|- 9x - 12x - 4 + (- 3x - 2)log(3x + 2) +--R 3 +--R (4) ------------------------------------------------------------- +--R +---------------+ +--R | 2 +--R 3\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 858 + +--S 859 of 1394 +d0:=D(m0,x) +--R +--R +--R +---------------+ +--R +---+ | 2 +--R - \|- 1 \|- 9x - 12x - 4 - 3x - 2 +--R (5) ----------------------------------- +--R +---------------+ +--R | 2 +--R (3x + 2)\|- 9x - 12x - 4 +--R Type: Expression(Integer) +--E 859 + +)clear all + +--S 860 of 1394 +t0:=(c*(a+b*x)^3)^(5/2) +--R +--R +--R (1) +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 2 +--R a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 860 + +--S 861 of 1394 +r0:=2/17*c^2*(a+b*x)^7*sqrt(c*(a+b*x)^3)/b +--R +--R +--R (2) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 +--R 2b c x + 14a b c x + 42a b c x + 70a b c x + 70a b c x +--R + +--R 5 2 2 2 6 2 7 2 +--R 42a b c x + 14a b c x + 2a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R / +--R 17b +--R Type: Expression(Integer) +--E 861 + +--S 862 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 2 8 7 2 7 2 6 2 6 3 5 2 5 4 4 2 4 +--R 2b c x + 16a b c x + 56a b c x + 112a b c x + 140a b c x +--R + +--R 5 3 2 3 6 2 2 2 7 2 8 2 +--R 112a b c x + 56a b c x + 16a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 17b +--R Type: Union(Expression(Integer),...) +--E 862 + +--S 863 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 +--R - 2b c x - 14a b c x - 42a b c x - 70a b c x - 70a b c x +--R + +--R 5 2 2 2 6 2 7 2 +--R - 42a b c x - 14a b c x - 2a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 8 2 8 7 2 7 2 6 2 6 3 5 2 5 4 4 2 4 +--R 2b c x + 16a b c x + 56a b c x + 112a b c x + 140a b c x +--R + +--R 5 3 2 3 6 2 2 2 7 2 8 2 +--R 112a b c x + 56a b c x + 16a b c x + 2a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 17b +--R Type: Expression(Integer) +--E 863 + +--S 864 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 8 3 8 7 3 7 2 6 3 6 3 5 3 5 4 4 3 4 +--R b c x + 8a b c x + 28a b c x + 56a b c x + 70a b c x +--R + +--R 5 3 3 3 6 2 3 2 7 3 8 3 +--R 56a b c x + 28a b c x + 8a b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 9 3 9 8 3 8 2 7 3 7 3 6 3 6 4 5 3 5 +--R - b c x - 9a b c x - 36a b c x - 84a b c x - 126a b c x +--R + +--R 5 4 3 4 6 3 3 3 7 2 3 2 8 3 9 3 +--R - 126a b c x - 84a b c x - 36a b c x - 9a b c x - a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 864 + +)clear all + +--S 865 of 1394 +t0:=(c*(a+b*x)^3)^(3/2) +--R +--R +--R (1) +--R +-----------------------------------+ +--R 3 3 2 2 2 3 | 3 3 2 2 2 3 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 865 + +--S 866 of 1394 +r0:=2/11*c*(a+b*x)^4*sqrt(c*(a+b*x)^3)/b +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (2b c x + 8a b c x + 12a b c x + 8a b c x + 2a c) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R / +--R 11b +--R Type: Expression(Integer) +--E 866 + +--S 867 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b c x + 10a b c x + 20a b c x + 20a b c x + 10a b c x + 2a c) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 11b +--R Type: Union(Expression(Integer),...) +--E 867 + +--S 868 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b c x - 8a b c x - 12a b c x - 8a b c x - 2a c) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b c x + 10a b c x + 20a b c x + 20a b c x + 10a b c x + 2a c) +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R 11b +--R Type: Expression(Integer) +--E 868 + +--S 869 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x +--R + +--R 5 2 6 2 +--R - 6a b c x - a c +--R * +--R +-----------+ +--R \|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 869 + +)clear all + +--S 870 of 1394 +t0:=(c*(a+b*x)^3)^(1/2) +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (1) \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 870 + +--S 871 of 1394 +r0:=2/5*(a+b*x)*sqrt(c*(a+b*x)^3)/b +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (2b x + 2a)\|b c x + 3a b c x + 3a b c x + a c +--R (2) ------------------------------------------------- +--R 5b +--R Type: Expression(Integer) +--E 871 + +--S 872 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R (3) ------------------------------------ +--R 5b +--R Type: Union(Expression(Integer),...) +--E 872 + +--S 873 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R (- 2b x - 2a)\|b c x + 3a b c x + 3a b c x + a c +--R + +--R 2 2 2 +-----------+ +--R (2b x + 4a b x + 2a )\|b c x + a c +--R / +--R 5b +--R Type: Expression(Integer) +--E 873 + +--S 874 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R 2 2 2 | 3 3 2 2 2 3 +--R (b c x + 2a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R + +--R 3 3 2 2 2 3 +-----------+ +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + a c +--R / +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 874 + +)clear all + +--S 875 of 1394 +t0:=1/(c*(a+b*x)^3)^(1/2) +--R +--R +--R 1 +--R (1) -------------------------------------- +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 875 + +--S 876 of 1394 +r0:=-2*(a+b*x)/(b*sqrt(c*(a+b*x)^3)) +--R +--R +--R - 2b x - 2a +--R (2) --------------------------------------- +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R b\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 876 + +--S 877 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - --------------- +--R +-----------+ +--R b\|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 877 + +--S 878 of 1394 +m0:=a0-r0 +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R (4) --------------------------------------------------------------------- +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R b\|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 878 + +--S 879 of 1394 +d0:=D(m0,x) +--R +--R +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R (5) ------------------------------------------------------------------ +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R (b x + a)\|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 879 + +)clear all + +--S 880 of 1394 +t0:=1/(c*(a+b*x)^3)^(3/2) +--R +--R +--R (1) +--R 1 +--R --------------------------------------------------------------------------- +--R +-----------------------------------+ +--R 3 3 2 2 2 3 | 3 3 2 2 2 3 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 880 + +--S 881 of 1394 +r0:=(-2/7)/(b*c*(a+b*x)^2*sqrt(c*(a+b*x)^3)) +--R +--R +--R 2 +--R (2) - -------------------------------------------------------------------- +--R +-----------------------------------+ +--R 3 2 2 2 | 3 3 2 2 2 3 +--R (7b c x + 14a b c x + 7a b c)\|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 881 + +--S 882 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R (3) - --------------------------------------------------------- +--R 4 3 3 2 2 2 3 +-----------+ +--R (7b c x + 21a b c x + 21a b c x + 7a b c)\|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 882 + +--S 883 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R / +--R 4 3 3 2 2 2 3 +-----------+ +--R (7b c x + 21a b c x + 21a b c x + 7a b c)\|b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 883 + +--S 884 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R / +--R 4 4 3 3 2 2 2 3 4 +-----------+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c)\|b c x + a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 884 + +)clear all + +--S 885 of 1394 +t0:=1/(c*(a+b*x)^3)^(5/2) +--R +--R +--R (1) +--R 1 +--R / +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +--R b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x +--R + +--R 6 2 +--R a c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 885 + +--S 886 of 1394 +r0:=(-2/13)/(b*c^2*(a+b*x)^5*sqrt(c*(a+b*x)^3)) +--R +--R +--R (2) +--R - +--R 2 +--R / +--R 6 2 5 5 2 4 2 4 2 3 3 3 2 2 4 2 2 +--R 13b c x + 65a b c x + 130a b c x + 130a b c x + 65a b c x +--R + +--R 5 2 +--R 13a b c +--R * +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +--R \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 886 + +--S 887 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R / +--R 7 2 6 6 2 5 2 5 2 4 3 4 2 3 4 3 2 2 +--R 13b c x + 78a b c x + 195a b c x + 260a b c x + 195a b c x +--R + +--R 5 2 2 6 2 +--R 78a b c x + 13a b c +--R * +--R +-----------+ +--R \|b c x + a c +--R Type: Union(Expression(Integer),...) +--E 887 + +--S 888 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R - 2\|b c x + 3a b c x + 3a b c x + a c + (2b x + 2a)\|b c x + a c +--R / +--R 7 2 6 6 2 5 2 5 2 4 3 4 2 3 4 3 2 2 +--R 13b c x + 78a b c x + 195a b c x + 260a b c x + 195a b c x +--R + +--R 5 2 2 6 2 +--R 78a b c x + 13a b c +--R * +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 888 + +--S 889 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-----------------------------------+ +--R | 3 3 2 2 2 3 +-----------+ +--R \|b c x + 3a b c x + 3a b c x + a c + (- b x - a)\|b c x + a c +--R / +--R 7 2 7 6 2 6 2 5 2 5 3 4 2 4 4 3 2 3 5 2 2 2 +--R b c x + 7a b c x + 21a b c x + 35a b c x + 35a b c x + 21a b c x +--R + +--R 6 2 7 2 +--R 7a b c x + a c +--R * +--R +-----------------------------------+ +--R +-----------+ | 3 3 2 2 2 3 +--R \|b c x + a c \|b c x + 3a b c x + 3a b c x + a c +--R Type: Expression(Integer) +--E 889 + +)clear all + +--S 890 of 1394 +t0:=(c/(a+b*x))^(5/2) +--R +--R +--R +-------+ +--R 2 | c +--R c |------- +--R \|b x + a +--R (1) ------------------ +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 890 + +--S 891 of 1394 +r0:=-2/3*c^2*sqrt(c/(a+b*x))/(b*(a+b*x)) +--R +--R +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R (2) - ------------- +--R 2 +--R 3b x + 3a b +--R Type: Expression(Integer) +--E 891 + +--S 892 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R (3) - ------------- +--R 2 +--R 3b x + 3a b +--R Type: Union(Expression(Integer),...) +--E 892 + +--S 893 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 893 + +--S 894 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 894 + +)clear all + +--S 895 of 1394 +t0:=(c/(a+b*x))^(3/2) +--R +--R +--R +-------+ +--R | c +--R c |------- +--R \|b x + a +--R (1) ----------- +--R b x + a +--R Type: Expression(Integer) +--E 895 + +--S 896 of 1394 +r0:=-2*c*sqrt(c/(a+b*x))/b +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (2) - ------------ +--R b +--R Type: Expression(Integer) +--E 896 + +--S 897 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (3) - ------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 897 + +--S 898 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 898 + +--S 899 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 899 + +)clear all + +--S 900 of 1394 +t0:=(c/(a+b*x))^(1/2) +--R +--R +--R +-------+ +--R | c +--R (1) |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 900 + +--S 901 of 1394 +r0:=2*(a+b*x)*sqrt(c/(a+b*x))/b +--R +--R +--R +-------+ +--R | c +--R (2b x + 2a) |------- +--R \|b x + a +--R (2) --------------------- +--R b +--R Type: Expression(Integer) +--E 901 + +--S 902 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2c +--R (3) ----------- +--R +-------+ +--R | c +--R b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 902 + +--S 903 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 903 + +--S 904 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 904 + +)clear all + +--S 905 of 1394 +t0:=1/(c/(a+b*x))^(1/2) +--R +--R +--R 1 +--R (1) ---------- +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 905 + +--S 906 of 1394 +r0:=2/3*(a+b*x)/(b*sqrt(c/(a+b*x))) +--R +--R +--R 2b x + 2a +--R (2) ------------ +--R +-------+ +--R | c +--R 3b |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 906 + +--S 907 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2b x + 2a +--R (3) ------------ +--R +-------+ +--R | c +--R 3b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 907 + +--S 908 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 908 + +--S 909 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 909 + +)clear all + +--S 910 of 1394 +t0:=1/(c/(a+b*x))^(3/2) +--R +--R +--R b x + a +--R (1) ----------- +--R +-------+ +--R | c +--R c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 910 + +--S 911 of 1394 +r0:=2/5*(a+b*x)^2/(b*c*sqrt(c/(a+b*x))) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (2) -------------------- +--R +-------+ +--R | c +--R 5b c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 911 + +--S 912 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (3) -------------------- +--R +-------+ +--R | c +--R 5b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 912 + +--S 913 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 913 + +--S 914 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 914 + +)clear all + +--S 915 of 1394 +t0:=1/(c/(a+b*x))^(5/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ------------------ +--R +-------+ +--R 2 | c +--R c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 915 + +--S 916 of 1394 +r0:=2/7*(a+b*x)^3/(b*c^2*sqrt(c/(a+b*x))) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 6a b x + 6a b x + 2a +--R (2) ------------------------------ +--R +-------+ +--R 2 | c +--R 7b c |------- +--R \|b x + a +--R Type: Expression(Integer) +--E 916 + +--S 917 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R 2b x + 6a b x + 6a b x + 2a +--R (3) ------------------------------ +--R +-------+ +--R 2 | c +--R 7b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 917 + +--S 918 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 918 + +--S 919 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 919 + +)clear all + +--S 920 of 1394 +t0:=(c/(a+b*x)^2)^(5/2) +--R +--R +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (1) -------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R Type: Expression(Integer) +--E 920 + +--S 921 of 1394 +r0:=-1/4*c^2*sqrt(c/(a+b*x)^2)/(b*(a+b*x)^3) +--R +--R +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) - --------------------------------- +--R 4 3 3 2 2 2 3 +--R 4b x + 12a b x + 12a b x + 4a b +--R Type: Expression(Integer) +--E 921 + +--S 922 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R c \|c +--R (3) - -------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Union(Expression(Integer),...) +--E 922 + +--S 923 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R 2 +-+ 2 2 | c +--R - c \|c + (b c x + a c ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) ---------------------------------------------- +--R 5 4 4 3 2 3 2 3 2 4 +--R 4b x + 16a b x + 24a b x + 16a b x + 4a b +--R Type: Expression(Integer) +--E 923 + +--S 924 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R 2 +-+ 2 2 | c +--R c \|c + (- b c x - a c ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) -------------------------------------------------- +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R Type: Expression(Integer) +--E 924 + +)clear all + +--S 925 of 1394 +t0:=(c/(a+b*x)^2)^(3/2) +--R +--R +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (1) ---------------------- +--R 2 2 2 +--R b x + 2a b x + a +--R Type: Expression(Integer) +--E 925 + +--S 926 of 1394 +r0:=-1/2*c*sqrt(c/(a+b*x)^2)/(b*(a+b*x)) +--R +--R +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) - ---------------------- +--R 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 926 + +--S 927 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R c\|c +--R (3) - --------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Union(Expression(Integer),...) +--E 927 + +--S 928 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-+ | c +--R - c\|c + (b c x + a c) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) -------------------------------------------- +--R 3 2 2 2 +--R 2b x + 4a b x + 2a b +--R Type: Expression(Integer) +--E 928 + +--S 929 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R +-+ | c +--R c\|c + (- b c x - a c) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) -------------------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 929 + +)clear all + +--S 930 of 1394 +t0:=(c/(a+b*x)^2)^(1/2) +--R +--R +--R +------------------+ +--R | c +--R (1) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 930 + +--S 931 of 1394 +r0:=(a+b*x)*log(a+b*x)*sqrt(c/(a+b*x)^2)/b +--R +--R +--R +------------------+ +--R | c +--R (b x + a)log(b x + a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (2) ------------------------------------------ +--R b +--R Type: Expression(Integer) +--E 931 + +--S 932 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-+ +--R log(b x + a)\|c +--R (3) ---------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 932 + +--S 933 of 1394 +m0:=a0-r0 +--R +--R +--R +------------------+ +--R +-+ | c +--R log(b x + a)\|c + (- b x - a)log(b x + a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (4) --------------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 933 + +--S 934 of 1394 +d0:=D(m0,x) +--R +--R +--R +------------------+ +--R | c +-+ +--R (b x + a) |------------------ \|c - c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) ----------------------------------------- +--R +------------------+ +--R 2 2 2 | c +--R (b x + 2a b x + a ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 934 + +)clear all + +--S 935 of 1394 +t0:=1/(c/(a+b*x)^2)^(1/2) +--R +--R +--R 1 +--R (1) --------------------- +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 935 + +--S 936 of 1394 +r0a:=1/2*(a+b*x)/(b*sqrt(c/(a+b*x)^2)) +--R +--R +--R b x + a +--R (2) ----------------------- +--R +------------------+ +--R | c +--R 2b |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 936 + +--S 937 of 1394 +r0b:=a*x/((a+b*x)*sqrt(c/(a+b*x)^2))+1/2*b*x^2/((a+b*x)*sqrt(c/(a+b*x)^2)) +--R +--R +--R 2 +--R b x + 2a x +--R (3) -------------------------------- +--R +------------------+ +--R | c +--R (2b x + 2a) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 937 + +--S 938 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x + 2a x +--R (4) ----------- +--R +-+ +--R 2\|c +--R Type: Union(Expression(Integer),...) +--E 938 + +--S 939 of 1394 +m0a:=a0-r0a +--R +--R +--R +------------------+ +--R +-+ 2 2 | c +--R (- b x - a)\|c + (b x + 2a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (5) ------------------------------------------------------ +--R +------------------+ +--R | c +-+ +--R 2b |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 939 + +--S 940 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +------------------+ +--R | c +-+ +--R (b x + a) |------------------ \|c - c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (6) -------------------------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 940 + +--S 941 of 1394 +m0b:=a0-r0b +--R +--R +--R +------------------+ +--R 2 +-+ 2 3 2 2 | c +--R (- b x - 2a x)\|c + (b x + 3a b x + 2a x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (7) ------------------------------------------------------------------ +--R +------------------+ +--R | c +-+ +--R (2b x + 2a) |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 941 + +--S 942 of 1394 +d0b:=D(m0b,x) +--R +--R +--R +------------------+ +--R +-+ 2 2 2 | c +--R (b x + a)\|c + (- b x - 2a b x - a ) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R (8) ----------------------------------------------------------- +--R c +--R Type: Expression(Integer) +--E 942 + +)clear all + +--S 943 of 1394 +t0:=1/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (1) ---------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 943 + +--S 944 of 1394 +r0:=1/4*(a+b*x)^3/(b*c*sqrt(c/(a+b*x)^2)) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (2) ---------------------------- +--R +------------------+ +--R | c +--R 4b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 944 + +--S 945 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (3) ------------------------------- +--R +-+ +--R 4c\|c +--R Type: Union(Expression(Integer),...) +--E 945 + +--S 946 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 3 2 2 2 3 +-+ +--R (- b x - 3a b x - 3a b x - a )\|c +--R + +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | c +--R (b x + 4a b x + 6a b x + 4a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R | c +-+ +--R 4b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 946 + +--S 947 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +------------------+ +--R 3 3 2 2 2 3 | c +-+ 2 2 +--R (b x + 3a b x + 3a b x + a ) |------------------ \|c - b c x +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 +--R - 2a b c x - a c +--R / +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 947 + +)clear all + +--S 948 of 1394 +t0:=1/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (1) -------------------------------------- +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 948 + +--S 949 of 1394 +r0:=1/6*(a+b*x)^5/(b*c^2*sqrt(c/(a+b*x)^2)) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (2) -------------------------------------------------- +--R +------------------+ +--R 2 | c +--R 6b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 949 + +--S 950 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 5 6 4 5 2 3 4 3 2 3 4 2 5 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a x +--R (3) ------------------------------------------------------ +--R 2 +-+ +--R 6c \|c +--R Type: Union(Expression(Integer),...) +--E 950 + +--S 951 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|c +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x) +--R * +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R 2 | c +-+ +--R 6b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 951 + +--S 952 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a ) +--R * +--R +------------------+ +--R | c +-+ +--R |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +------------------+ +--R 3 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 952 + +)clear all + +--S 953 of 1394 +t0:=(c/(a+b*x)^3)^(5/2) +--R +--R +--R +----------------------------+ +--R 2 | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (1) ------------------------------------------------------------- +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R Type: Expression(Integer) +--E 953 + +--S 954 of 1394 +r0:=-2/13*c^2*sqrt(c/(a+b*x)^3)/(b*(a+b*x)^5) +--R +--R +--R +----------------------------+ +--R 2 | c +--R 2c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) - ----------------------------------------------------------- +--R 6 5 5 4 2 4 3 3 3 2 4 2 5 +--R 13b x + 65a b x + 130a b x + 130a b x + 65a b x + 13a b +--R Type: Expression(Integer) +--E 954 + +--S 955 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-------+ +--R 2 | c +--R 2c |------- +--R \|b x + a +--R - ----------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 13b x + 78a b x + 195a b x + 260a b x + 195a b x + 78a b x + 13a b +--R Type: Union(Expression(Integer),...) +--E 955 + +--S 956 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +----------------------------+ +--R 2 | c 2 2 | c +--R - 2c |------- + (2b c x + 2a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R ----------------------------------------------------------------------- +--R 7 6 6 5 2 5 4 3 4 3 4 3 2 5 2 6 +--R 13b x + 78a b x + 195a b x + 260a b x + 195a b x + 78a b x + 13a b +--R Type: Expression(Integer) +--E 956 + +--S 957 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R 3 | c 3 3 | c +--R - c |------- + (b c x + a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R 9 9 8 8 2 7 7 3 6 6 4 5 5 5 4 4 6 3 3 +--R b x + 9a b x + 36a b x + 84a b x + 126a b x + 126a b x + 84a b x +--R + +--R 7 2 2 8 9 +--R 36a b x + 9a b x + a +--R * +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 957 + +)clear all + +--S 958 of 1394 +t0:=(c/(a+b*x)^3)^(3/2) +--R +--R +--R +----------------------------+ +--R | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (1) -------------------------------- +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 958 + +--S 959 of 1394 +r0:=-2/7*c*sqrt(c/(a+b*x)^3)/(b*(a+b*x)^2) +--R +--R +--R +----------------------------+ +--R | c +--R 2c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) - --------------------------------- +--R 3 2 2 2 +--R 7b x + 14a b x + 7a b +--R Type: Expression(Integer) +--E 959 + +--S 960 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2c |------- +--R \|b x + a +--R (3) - --------------------------------- +--R 4 3 3 2 2 2 3 +--R 7b x + 21a b x + 21a b x + 7a b +--R Type: Union(Expression(Integer),...) +--E 960 + +--S 961 of 1394 +m0:=a0-r0 +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - 2c |------- + (2b c x + 2a c) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (4) --------------------------------------------------------------- +--R 4 3 3 2 2 2 3 +--R 7b x + 21a b x + 21a b x + 7a b +--R Type: Expression(Integer) +--E 961 + +--S 962 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R 2 | c 2 2 | c +--R - c |------- + (b c x + a c ) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a ) +--R * +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 962 + +)clear all + +--S 963 of 1394 +t0:=(c/(a+b*x)^3)^(1/2) +--R +--R +--R +----------------------------+ +--R | c +--R (1) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 963 + +--S 964 of 1394 +r0:=-2*(a+b*x)*sqrt(c/(a+b*x)^3)/b +--R +--R +--R +----------------------------+ +--R | c +--R (- 2b x - 2a) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (2) -------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 964 + +--S 965 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------+ +--R | c +--R 2 |------- +--R \|b x + a +--R (3) - ----------- +--R b +--R Type: Union(Expression(Integer),...) +--E 965 + +--S 966 of 1394 +m0:=a0-r0 +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - 2 |------- + (2b x + 2a) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (4) ---------------------------------------------------------- +--R b +--R Type: Expression(Integer) +--E 966 + +--S 967 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +----------------------------+ +--R | c | c +--R - c |------- + (b c x + a c) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R ----------------------------------------------------------------------- +--R +----------------------------+ +-------+ +--R 3 3 2 2 2 3 | c | c +--R (b x + 3a b x + 3a b x + a ) |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 967 + +)clear all + +--S 968 of 1394 +t0:=1/(c/(a+b*x)^3)^(1/2) +--R +--R +--R 1 +--R (1) ------------------------------- +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 968 + +--S 969 of 1394 +r0:=2/5*(a+b*x)/(b*sqrt(c/(a+b*x)^3)) +--R +--R +--R 2b x + 2a +--R (2) --------------------------------- +--R +----------------------------+ +--R | c +--R 5b |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 969 + +--S 970 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2b x + 4a b x + 2a +--R (3) -------------------- +--R +-------+ +--R | c +--R 5b |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 970 + +--S 971 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R | c +--R (- 2b x - 2a) |------- +--R \|b x + a +--R + +--R +----------------------------+ +--R 2 2 2 | c +--R (2b x + 4a b x + 2a ) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R 5b |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 971 + +--S 972 of 1394 +d0:=D(m0,x) +--R +--R +--R +-------+ +----------------------------+ +--R | c | c +--R - |------- + (b x + a) |---------------------------- +--R \|b x + a | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R (5) ------------------------------------------------------- +--R +----------------------------+ +-------+ +--R | c | c +--R |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 972 + +)clear all + +--S 973 of 1394 +t0:=1/(c/(a+b*x)^3)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (1) -------------------------------- +--R +----------------------------+ +--R | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 973 + +--S 974 of 1394 +r0:=2/11*(a+b*x)^4/(b*c*sqrt(c/(a+b*x)^3)) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R 2b x + 8a b x + 12a b x + 8a b x + 2a +--R (2) ----------------------------------------- +--R +----------------------------+ +--R | c +--R 11b c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 974 + +--S 975 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R 2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a +--R (3) ------------------------------------------------------ +--R +-------+ +--R | c +--R 11b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 975 + +--S 976 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-------+ +--R 4 4 3 3 2 2 2 3 4 | c +--R (- 2b x - 8a b x - 12a b x - 8a b x - 2a ) |------- +--R \|b x + a +--R + +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (2b x + 10a b x + 20a b x + 20a b x + 10a b x + 2a ) +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R 11b c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 976 + +--S 977 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R +-------+ +--R 3 3 2 2 2 3 | c +--R (- b x - 3a b x - 3a b x - a ) |------- +--R \|b x + a +--R + +--R +----------------------------+ +--R 4 4 3 3 2 2 2 3 4 | c +--R (b x + 4a b x + 6a b x + 4a b x + a ) |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R | c | c +--R c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 977 + +)clear all + +--S 978 of 1394 +t0:=1/(c/(a+b*x)^3)^(5/2) +--R +--R +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x + a +--R (1) ------------------------------------------------------------- +--R +----------------------------+ +--R 2 | c +--R c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 978 + +--S 979 of 1394 +r0:=2/17*(a+b*x)^7/(b*c^2*sqrt(c/(a+b*x)^3)) +--R +--R +--R (2) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R 2b x + 14a b x + 42a b x + 70a b x + 70a b x + 42a b x + 14a b x + 2a +--R ---------------------------------------------------------------------------- +--R +----------------------------+ +--R 2 | c +--R 17b c |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 979 + +--S 980 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 2b x + 16a b x + 56a b x + 112a b x + 140a b x + 112a b x +--R + +--R 6 2 2 7 8 +--R 56a b x + 16a b x + 2a +--R / +--R +-------+ +--R 2 | c +--R 17b c |------- +--R \|b x + a +--R Type: Union(Expression(Integer),...) +--E 980 + +--S 981 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 +--R - 2b x - 14a b x - 42a b x - 70a b x - 70a b x - 42a b x +--R + +--R 6 7 +--R - 14a b x - 2a +--R * +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R + +--R 8 8 7 7 2 6 6 3 5 5 4 4 4 5 3 3 +--R 2b x + 16a b x + 56a b x + 112a b x + 140a b x + 112a b x +--R + +--R 6 2 2 7 8 +--R 56a b x + 16a b x + 2a +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R 2 | c | c +--R 17b c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 981 + +--S 982 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- b x - 6a b x - 15a b x - 20a b x - 15a b x - 6a b x - a ) +--R * +--R +-------+ +--R | c +--R |------- +--R \|b x + a +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 +--R b x + 7a b x + 21a b x + 35a b x + 35a b x + 21a b x + 7a b x +--R + +--R 7 +--R a +--R * +--R +----------------------------+ +--R | c +--R |---------------------------- +--R | 3 3 2 2 2 3 +--R \|b x + 3a b x + 3a b x + a +--R / +--R +----------------------------+ +-------+ +--R 2 | c | c +--R c |---------------------------- |------- +--R | 3 3 2 2 2 3 \|b x + a +--R \|b x + 3a b x + 3a b x + a +--R Type: Expression(Integer) +--E 982 + +)clear all + +--S 983 of 1394 +t0:=(c*(a+b*x)^(3/2))^(2/3) +--R +--R +--R +-----------------------+2 +--R 3| +-------+ +--R (1) \|(b c x + a c)\|b x + a +--R Type: Expression(Integer) +--E 983 + +--S 984 of 1394 +r0a:=1/2*(a+b*x)*(c*(a+b*x)^(3/2))^(2/3)/b +--R +--R +--R +-----------------------+2 +--R 3| +-------+ +--R (b x + a)\|(b c x + a c)\|b x + a +--R (2) ------------------------------------ +--R 2b +--R Type: Expression(Integer) +--E 984 + +--S 985 of 1394 +r0b:=a*x*(c*(a+b*x)^(3/2))^(2/3)/(a+b*x)+_ + 1/2*b*x^2*(c*(a+b*x)^(3/2))^(2/3)/(a+b*x) +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R (b x + 2a x)\|(b c x + a c)\|b x + a +--R (3) ---------------------------------------- +--R 2b x + 2a +--R Type: Expression(Integer) +--E 985 + +--S 986 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R (b x + 2a x)\|(b c x + a c)\|b x + a +--R (4) ---------------------------------------- +--R 2b x + 2a +--R Type: Union(Expression(Integer),...) +--E 986 + +--S 987 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------------------+2 +--R 2 3| +-------+ +--R a \|(b c x + a c)\|b x + a +--R (5) - ----------------------------- +--R 2 +--R 2b x + 2a b +--R Type: Expression(Integer) +--E 987 + +--S 988 of 1394 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 988 + +--S 989 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 989 + +--S 990 of 1394 +d0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 990 + +)clear all + +--S 991 of 1394 +t0:=(c*(a+b*x)^(2/3))^(3/2) +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 +--R (1) c \|b x + a \|c \|b x + a +--R Type: Expression(Integer) +--E 991 + +--S 992 of 1394 +r0a:=1/2*c*(a+b*x)^(5/3)*sqrt(c*(a+b*x)^(2/3))/b +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 +--R (b c x + a c)\|b x + a \|c \|b x + a +--R (2) ---------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 992 + +--S 993 of 1394 +r0b:=a*c*x*sqrt(c*(a+b*x)^(2/3))/(a+b*x)^(1/3)+_ + 1/2*b*c*x^2*sqrt(c*(a+b*x)^(2/3))/(a+b*x)^(1/3) +--R +--R +--R +-------------+ +--R 2 | 3+-------+2 +--R (b c x + 2a c x)\|c \|b x + a +--R (3) --------------------------------- +--R 3+-------+ +--R 2\|b x + a +--R Type: Expression(Integer) +--E 993 + +--S 994 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +-+ +--R (b c x + 2a c x)\|c +--R (4) --------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 994 + +--S 995 of 1394 +m0a:=a0-r0a +--R +--R +--R +-------------+ +--R 3+-------+2 | 3+-------+2 2 2 +-+ +--R (- b c x - a c)\|b x + a \|c \|b x + a + (b c x + 2a b c x)\|c +--R (5) -------------------------------------------------------------------- +--R 2b +--R Type: Expression(Integer) +--E 995 + +--S 996 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-------------+ +--R +-+ | 3+-------+2 2 2 3+-------+ +--R (b c x + a c)\|c \|c \|b x + a + (- b c x - a c )\|b x + a +--R (6) -------------------------------------------------------------- +--R +-------------+ +--R | 3+-------+2 +--R \|c \|b x + a +--R Type: Expression(Integer) +--E 996 + +--S 997 of 1394 +m0b:=a0-r0b +--R +--R +--R +-------------+ +--R 2 | 3+-------+2 2 +-+3+-------+ +--R (- b c x - 2a c x)\|c \|b x + a + (b c x + 2a c x)\|c \|b x + a +--R (7) --------------------------------------------------------------------- +--R 3+-------+ +--R 2\|b x + a +--R Type: Expression(Integer) +--E 997 + +--S 998 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R +-------------+ +--R +-+ | 3+-------+2 2 2 3+-------+ +--R (b c x + a c)\|c \|c \|b x + a + (- b c x - a c )\|b x + a +--R (8) -------------------------------------------------------------- +--R +-------------+ +--R | 3+-------+2 +--R \|c \|b x + a +--R Type: Expression(Integer) +--E 998 + +)clear all + +--S 999 of 1394 +t0:=1/(c/(a+b*x)^(3/2))^(2/3) +--R +--R +--R 1 +--R (1) ----------------------- +--R +-------------------+2 +--R | c +--R |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 999 + +--S 1000 of 1394 +r0a:=1/2*(a+b*x)/(b*(c/(a+b*x)^(3/2))^(2/3)) +--R +--R +--R b x + a +--R (2) -------------------------- +--R +-------------------+2 +--R | c +--R 2b |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1000 + +--S 1001 of 1394 +r0b:=a*x/((c/(a+b*x)^(3/2))^(2/3)*(a+b*x))+_ + 1/2*b*x^2/((c/(a+b*x)^(3/2))^(2/3)*(a+b*x)) +--R +--R +--R 2 +--R b x + 2a x +--R (3) ---------------------------------- +--R +-------------------+2 +--R | c +--R (2b x + 2a) |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1001 + +--S 1002 of 1394 +a0:=integrate(t0,x) +--R +--R +--R +-------------------+ +--R 2 3 2 2 | c +--R (b x + 3a b x + 2a x) |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R (4) --------------------------------------------- +--R +-------+ +--R 2c\|b x + a +--R Type: Union(Expression(Integer),...) +--E 1002 + +--S 1003 of 1394 +m0a:=a0-r0a +--R +--R +--R 2 +--R a +--R (5) - ------------------------------------- +--R +-------------------+2 +--R +-------+2 | c +--R 2b \|b x + a |------------------- +--R 3| +-------+ +--R \|(b x + a)\|b x + a +--R Type: Expression(Integer) +--E 1003 + +--S 1004 of 1394 +d0a:=D(m0a,x) +--R +--R +--R (6) 0 +--R Type: Expression(Integer) +--E 1004 + +--S 1005 of 1394 +m0b:=a0-r0b +--R +--R +--R (7) 0 +--R Type: Expression(Integer) +--E 1005 + +--S 1006 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R (8) 0 +--R Type: Expression(Integer) +--E 1006 + +)clear all + +--S 1007 of 1394 +t0:=1/(c/(a+b*x)^(2/3))^(3/2) +--R +--R +--R 3+-------+2 +--R \|b x + a +--R (1) --------------- +--R +-----------+ +--R | c +--R c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1007 + +--S 1008 of 1394 +r0a:=1/2*(a+b*x)^(5/3)/(b*c*sqrt(c/(a+b*x)^(2/3))) +--R +--R +--R 3+-------+2 +--R (b x + a)\|b x + a +--R (2) -------------------- +--R +-----------+ +--R | c +--R 2b c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1008 + +--S 1009 of 1394 +r0b:=a*x/(c*(a+b*x)^(1/3)*sqrt(c/(a+b*x)^(2/3)))+_ + 1/2*b*x^2/(c*(a+b*x)^(1/3)*sqrt(c/(a+b*x)^(2/3))) +--R +--R +--R 2 +--R b x + 2a x +--R (3) -------------------------- +--R +-----------+ +--R 3+-------+ | c +--R 2c\|b x + a |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1009 + +--S 1010 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R b x + 2a x +--R (4) ----------- +--R +-+ +--R 2c\|c +--R Type: Union(Expression(Integer),...) +--E 1010 + +--S 1011 of 1394 +m0a:=a0-r0a +--R +--R +--R +-----------+ +--R 2 2 | c +-+3+-------+2 +--R (b x + 2a b x) |----------- + (- b x - a)\|c \|b x + a +--R |3+-------+2 +--R \|\|b x + a +--R (5) ---------------------------------------------------------- +--R +-----------+ +--R +-+ | c +--R 2b c\|c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1011 + +--S 1012 of 1394 +d0a:=D(m0a,x) +--R +--R +--R +-----------+ +--R +-+ | c 3+-------+2 +--R (b x + a)\|c |----------- - c \|b x + a +--R |3+-------+2 +--R \|\|b x + a +--R (6) ------------------------------------------- +--R +-----------+ +--R 2 | c +--R c |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1012 + +--S 1013 of 1394 +m0b:=a0-r0b +--R +--R +--R +-----------+ +--R 2 3+-------+ | c 2 +-+ +--R (b x + 2a x)\|b x + a |----------- + (- b x - 2a x)\|c +--R |3+-------+2 +--R \|\|b x + a +--R (7) ----------------------------------------------------------- +--R +-----------+ +--R +-+3+-------+ | c +--R 2c\|c \|b x + a |----------- +--R |3+-------+2 +--R \|\|b x + a +--R Type: Expression(Integer) +--E 1013 + +--S 1014 of 1394 +--Rd0b:=D(m0b,x) +--R +--R +--R +-----------+ +--R 3+-------+ | c +-+ +--R (- b x - a)\|b x + a |----------- + (b x + a)\|c +--R |3+-------+2 +--R \|\|b x + a +--R (8) --------------------------------------------------- +--R 2 +--R c +--R Type: Expression(Integer) +--E 1014 + +)clear all + +--S 1015 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2) +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 +--R b d x + 5b c d x + (10b c + a)d x + (10b c + 3a c)d x +--R + +--R 4 2 5 3 +--R (5b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1015 + +--S 1016 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/6*b*(c+d*x)^6/d +--R +--R +--R (2) +--R 1 6 6 5 5 5 2 1 4 4 10 3 3 3 +--R - b d x + b c d x + (- b c + - a)d x + (-- b c + a c)d x +--R 6 2 4 3 +--R + +--R 5 4 3 2 2 2 5 3 1 6 1 4 +--R (- b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 2 6 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1016 + +--S 1017 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 5 6 4 5 5 2 1 3 4 10 3 2 3 +--R - b d x + b c d x + (- b c + - a)d x + (-- b c + a c)d x +--R 6 2 4 3 +--R + +--R 5 4 3 2 2 5 3 +--R (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1017 + +--S 1018 of 1394 +m0:=a0-r0 +--R +--R +--R 1 6 1 4 +--R - - b c - - a c +--R 6 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1018 + +--S 1019 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1019 + +)clear all + +--S 1020 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^2 +--R +--R +--R (1) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d x + 7b c d x + (21b c + 2a b)d x + (35b c + 10a b c)d x +--R + +--R 2 4 2 2 3 3 2 5 3 2 2 2 +--R (35b c + 20a b c + a )d x + (21b c + 20a b c + 3a c)d x +--R + +--R 2 6 4 2 2 2 7 5 2 3 +--R (7b c + 10a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial(Integer) +--E 1020 + +--S 1021 of 1394 +r0:=1/4*a^2*(c+d*x)^4/d+1/3*a*b*(c+d*x)^6/d+1/8*b^2*(c+d*x)^8/d +--R +--R +--R (2) +--R 1 2 8 8 2 7 7 7 2 2 1 6 6 2 3 5 5 +--R - b d x + b c d x + (- b c + - a b)d x + (7b c + 2a b c)d x +--R 8 2 3 +--R + +--R 35 2 4 2 1 2 4 4 2 5 20 3 2 3 3 +--R (-- b c + 5a b c + - a )d x + (7b c + -- a b c + a c)d x +--R 4 4 3 +--R + +--R 7 2 6 4 3 2 2 2 2 2 7 5 2 3 1 2 8 +--R (- b c + 5a b c + - a c )d x + (b c + 2a b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 6 1 2 4 +--R - a b c + - a c +--R 3 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1021 + +--S 1022 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 7 8 2 6 7 7 2 2 1 5 6 2 3 4 5 +--R - b d x + b c d x + (- b c + - a b)d x + (7b c + 2a b c)d x +--R 8 2 3 +--R + +--R 35 2 4 2 1 2 3 4 2 5 20 3 2 2 3 +--R (-- b c + 5a b c + - a )d x + (7b c + -- a b c + a c)d x +--R 4 4 3 +--R + +--R 7 2 6 4 3 2 2 2 2 7 5 2 3 +--R (- b c + 5a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1022 + +--S 1023 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 8 1 6 1 2 4 +--R - - b c - - a b c - - a c +--R 8 3 4 +--R (4) ---------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1023 + +--S 1024 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1024 + +)clear all + +--S 1025 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^3 +--R +--R +--R (1) +--R 3 9 9 3 8 8 3 2 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + (36b c + 3a b )d x + (84b c + 21a b c)d x +--R + +--R 3 4 2 2 2 5 5 3 5 2 3 2 4 4 +--R (126b c + 63a b c + 3a b)d x + (126b c + 105a b c + 15a b c)d x +--R + +--R 3 6 2 4 2 2 3 3 3 +--R (84b c + 105a b c + 30a b c + a )d x +--R + +--R 3 7 2 5 2 3 3 2 2 +--R (36b c + 63a b c + 30a b c + 3a c)d x +--R + +--R 3 8 2 6 2 4 3 2 3 9 2 7 2 5 3 3 +--R (9b c + 21a b c + 15a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial(Integer) +--E 1025 + +--S 1026 of 1394 +r0:=-1/8*a*(a+b*(c+d*x)^2)^4/(b^2*d)+1/10*(a+b*(c+d*x)^2)^5/(b^2*d) +--R +--R +--R (2) +--R 1 5 10 10 5 9 9 9 5 2 3 4 8 8 5 3 4 7 7 +--R -- b d x + b c d x + (- b c + - a b )d x + (12b c + 3a b c)d x +--R 10 2 8 +--R + +--R 5 4 21 4 2 1 2 3 6 6 126 5 5 4 3 2 3 5 5 +--R (21b c + -- a b c + - a b )d x + (--- b c + 21a b c + 3a b c)d x +--R 2 2 5 +--R + +--R 5 6 105 4 4 15 2 3 2 1 3 2 4 4 +--R (21b c + --- a b c + -- a b c + - a b )d x +--R 4 2 4 +--R + +--R 5 7 4 5 2 3 3 3 2 3 3 +--R (12b c + 21a b c + 10a b c + a b c)d x +--R + +--R 9 5 8 21 4 6 15 2 3 4 3 3 2 2 2 2 +--R (- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 5 9 4 7 2 3 5 3 2 3 1 5 10 3 4 8 1 2 3 6 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c + - a b c +--R 10 8 2 +--R + +--R 1 3 2 4 1 5 +--R - a b c - -- a +--R 4 40 +--R / +--R 2 +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1026 + +--S 1027 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 9 10 3 8 9 9 3 2 3 2 7 8 3 3 2 6 7 +--R -- b d x + b c d x + (- b c + - a b )d x + (12b c + 3a b c)d x +--R 10 2 8 +--R + +--R 3 4 21 2 2 1 2 5 6 126 3 5 2 3 2 4 5 +--R (21b c + -- a b c + - a b)d x + (--- b c + 21a b c + 3a b c)d x +--R 2 2 5 +--R + +--R 3 6 105 2 4 15 2 2 1 3 3 4 +--R (21b c + --- a b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 3 7 2 5 2 3 3 2 3 +--R (12b c + 21a b c + 10a b c + a c)d x +--R + +--R 9 3 8 21 2 6 15 2 4 3 3 2 2 +--R (- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 9 2 7 2 5 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1027 + +--S 1028 of 1394 +m0:=a0-r0 +--R +--R +--R 1 5 10 3 4 8 1 2 3 6 1 3 2 4 1 5 +--R - -- b c - - a b c - - a b c - - a b c + -- a +--R 10 8 2 4 40 +--R (4) --------------------------------------------------- +--R 2 +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1028 + +--S 1029 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1029 + +)clear all + +--S 1030 of 1394 +t0:=(2+x)/(1+(2+x)^2) +--R +--R +--R x + 2 +--R (1) ----------- +--R 2 +--R x + 4x + 5 +--R Type: Fraction(Polynomial(Integer)) +--E 1030 + +--S 1031 of 1394 +r0:=1/2*log(1+(2+x)^2) +--R +--R +--R 2 +--R log(x + 4x + 5) +--R (2) ---------------- +--R 2 +--R Type: Expression(Integer) +--E 1031 + +--S 1032 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R log(x + 4x + 5) +--R (3) ---------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 1032 + +--S 1033 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1033 + +--S 1034 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1034 + +)clear all + +--S 1035 of 1394 +t0:=(2+x)/(1+(2+x)^2)^2 +--R +--R +--R x + 2 +--R (1) -------------------------- +--R 4 3 2 +--R x + 8x + 26x + 40x + 25 +--R Type: Fraction(Polynomial(Integer)) +--E 1035 + +--S 1036 of 1394 +r0:=(-1/2)/(1+(2+x)^2) +--R +--R +--R 1 +--R - +--R 2 +--R (2) - ----------- +--R 2 +--R x + 4x + 5 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1036 + +--S 1037 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------- +--R 2 +--R 2x + 8x + 10 +--R Type: Union(Expression(Integer),...) +--E 1037 + +--S 1038 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1038 + +--S 1039 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1039 + +)clear all + +--S 1040 of 1394 +t0:=(2+x)/(1+(2+x)^2)^3 +--R +--R +--R x + 2 +--R (1) --------------------------------------------- +--R 6 5 4 3 2 +--R x + 12x + 63x + 184x + 315x + 300x + 125 +--R Type: Fraction(Polynomial(Integer)) +--E 1040 + +--S 1041 of 1394 +r0:=(-1/4)/(1+(2+x)^2)^2 +--R +--R +--R 1 +--R - +--R 4 +--R (2) - -------------------------- +--R 4 3 2 +--R x + 8x + 26x + 40x + 25 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1041 + +--S 1042 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------- +--R 4 3 2 +--R 4x + 32x + 104x + 160x + 100 +--R Type: Union(Expression(Integer),...) +--E 1042 + +--S 1043 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1043 + +--S 1044 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1044 + +)clear all + +--S 1045 of 1394 +t0:=(c+d*x)^5*(a+b*(c+d*x)^2)^p +--R +--R +--R (1) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (d x + 5c d x + 10c d x + 10c d x + 5c d x + c ) +--R * +--R 2 2 2 p +--R (b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1045 + +--S 1046 of 1394 +r0:=1/2*a^2*(a+b*(c+d*x)^2)^(1+p)/(b^3*d*(1+p))-_ + a*(a+b*(c+d*x)^2)^(2+p)/(b^3*d*(2+p))+1/2*(a+b*(c+d*x)^2)^(3+p)/_ + (b^3*d*(3+p)) +--R +--R +--R (2) +--R 2 2 2 2 p + 3 +--R (p + 3p + 2)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 p + 2 +--R (- 2a p - 8a p - 6a)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 2 2 2 p + 1 +--R (a p + 5a p + 6a )(b d x + 2b c d x + b c + a) +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Expression(Integer) +--E 1046 + +--S 1047 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 6 2 3 6 3 6 6 3 5 2 3 5 3 5 5 +--R (b d p + 3b d p + 2b d )x + (6b c d p + 18b c d p + 12b c d )x +--R + +--R 3 2 2 4 2 3 2 2 4 3 2 4 4 +--R ((15b c + a b )d p + (45b c + a b )d p + 30b c d )x +--R + +--R 3 3 2 3 2 3 3 2 3 3 3 3 3 +--R ((20b c + 4a b c)d p + (60b c + 4a b c)d p + 40b c d )x +--R + +--R 3 4 2 2 2 2 3 4 2 2 2 2 3 4 2 2 +--R ((15b c + 6a b c )d p + (45b c + 6a b c - 2a b)d p + 30b c d )x +--R + +--R 3 5 2 3 2 3 5 2 3 2 3 5 +--R ((6b c + 4a b c )d p + (18b c + 4a b c - 4a b c)d p + 12b c d)x +--R + +--R 3 6 2 4 2 3 6 2 4 2 2 3 6 3 +--R (b c + a b c )p + (3b c + a b c - 2a b c )p + 2b c + 2a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Union(Expression(Integer),...) +--E 1047 + +--S 1048 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 6 2 3 6 3 6 6 3 5 2 3 5 3 5 5 +--R (b d p + 3b d p + 2b d )x + (6b c d p + 18b c d p + 12b c d )x +--R + +--R 3 2 2 4 2 3 2 2 4 3 2 4 4 +--R ((15b c + a b )d p + (45b c + a b )d p + 30b c d )x +--R + +--R 3 3 2 3 2 3 3 2 3 3 3 3 3 +--R ((20b c + 4a b c)d p + (60b c + 4a b c)d p + 40b c d )x +--R + +--R 3 4 2 2 2 2 3 4 2 2 2 2 3 4 2 2 +--R ((15b c + 6a b c )d p + (45b c + 6a b c - 2a b)d p + 30b c d )x +--R + +--R 3 5 2 3 2 3 5 2 3 2 3 5 +--R ((6b c + 4a b c )d p + (18b c + 4a b c - 4a b c)d p + 12b c d)x +--R + +--R 3 6 2 4 2 3 6 2 4 2 2 3 6 3 +--R (b c + a b c )p + (3b c + a b c - 2a b c )p + 2b c + 2a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R + +--R 2 2 2 2 p + 3 +--R (- p - 3p - 2)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 p + 2 +--R (2a p + 8a p + 6a)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 2 2 2 2 p + 1 +--R (- a p - 5a p - 6a )(b d x + 2b c d x + b c + a) +--R / +--R 3 3 3 2 3 3 +--R 2b d p + 12b d p + 22b d p + 12b d +--R Type: Expression(Integer) +--E 1048 + +--S 1049 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1049 + +)clear all + +--S 1050 of 1394 +t0:=(c+d*x)^4*(a+b*(c+d*x)^2)^p +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 2 2 2 p +--R (d x + 4c d x + 6c d x + 4c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1050 + +--S 1051 of 1394 +--r0:=-3*a*(c+d*x)*(a+b*(c+d*x)^2)^(1+p)/(b^2*d*(3+2*p)*(5+2*p))+_ +-- (c+d*x)^3*(a+b*(c+d*x)^2)^(1+p)/(b*d*(5+2*p))+_ +-- 3*a^2*(c+d*x)*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*(c+d*x)^2/a)/(b^2*d*(3+2*p)*(5+2*p)*_ +-- ((a+b*(c+d*x)^2)/a)^p) +--E 1051 + +--S 1052 of 1394 +--a0:=integrate(t0,x) +--E 1052 + +--S 1053 of 1394 +--m0:=a0-r0 +--E 1053 + +--S 1054 of 1394 +--d0:=D(m0,x) +--E 1054 + +)clear all + +--S 1055 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^2)^p +--R +--R +--R 3 3 2 2 2 3 2 2 2 p +--R (1) (d x + 3c d x + 3c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1055 + +--S 1056 of 1394 +r0:=-1/2*a*(a+b*(c+d*x)^2)^(1+p)/(b^2*d*(1+p))+_ + 1/2*(a+b*(c+d*x)^2)^(2+p)/(b^2*d*(2+p)) +--R +--R +--R (2) +--R 2 2 2 p + 2 +--R (p + 1)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 p + 1 +--R (- a p - 2a)(b d x + 2b c d x + b c + a) +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Expression(Integer) +--E 1056 + +--S 1057 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 4 2 4 4 2 3 2 3 3 +--R (b d p + b d )x + (4b c d p + 4b c d )x +--R + +--R 2 2 2 2 2 2 2 2 3 2 3 +--R ((6b c + a b)d p + 6b c d )x + ((4b c + 2a b c)d p + 4b c d)x +--R + +--R 2 4 2 2 4 2 +--R (b c + a b c )p + b c - a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Union(Expression(Integer),...) +--E 1057 + +--S 1058 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 4 2 4 4 2 3 2 3 3 +--R (b d p + b d )x + (4b c d p + 4b c d )x +--R + +--R 2 2 2 2 2 2 2 2 3 2 3 +--R ((6b c + a b)d p + 6b c d )x + ((4b c + 2a b c)d p + 4b c d)x +--R + +--R 2 4 2 2 4 2 +--R (b c + a b c )p + b c - a +--R * +--R 2 2 2 +--R p log(b d x + 2b c d x + b c + a) +--R %e +--R + +--R 2 2 2 p + 2 +--R (- p - 1)(b d x + 2b c d x + b c + a) +--R + +--R 2 2 2 p + 1 +--R (a p + 2a)(b d x + 2b c d x + b c + a) +--R / +--R 2 2 2 2 +--R 2b d p + 6b d p + 4b d +--R Type: Expression(Integer) +--E 1058 + +--S 1059 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1059 + +)clear all + +--S 1060 of 1394 +t0:=(c+d*x)^2*(a+b*(c+d*x)^2)^p +--R +--R +--R 2 2 2 2 2 2 p +--R (1) (d x + 2c d x + c )(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1060 + +--S 1061 of 1394 +--r0:=(c+d*x)*(a+b*(c+d*x)^2)^(1+p)/(b*d*(3+2*p))-_ +-- a*(c+d*x)*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(1/2,-p,3/2,-b*(c+d*x)^2/a)/(b*d*(3+2*p)*_ +-- ((a+b*(c+d*x)^2)/a)^p) +--E 1061 + +--S 1062 of 1394 +--a0:=integrate(t0,x) +--E 1062 + +--S 1063 of 1394 +--m0:=a0-r0 +--E 1063 + +--S 1064 of 1394 +--d0:=D(m0,x) +--E 1064 + +)clear all + +--S 1065 of 1394 +t0:=(c+d*x)*(a+b*(c+d*x)^2)^p +--R +--R +--R 2 2 2 p +--R (1) (d x + c)(b d x + 2b c d x + b c + a) +--R Type: Expression(Integer) +--E 1065 + +--S 1066 of 1394 +r0:=1/2*(a+b*(c+d*x)^2)^(1+p)/(b*d*(1+p)) +--R +--R +--R 2 2 2 p + 1 +--R (b d x + 2b c d x + b c + a) +--R (2) ----------------------------------- +--R 2b d p + 2b d +--R Type: Expression(Integer) +--E 1066 + +--S 1067 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 2 2 +--R 2 2 2 p log(b d x + 2b c d x + b c + a) +--R (b d x + 2b c d x + b c + a)%e +--R (3) ------------------------------------------------------------------- +--R 2b d p + 2b d +--R Type: Union(Expression(Integer),...) +--E 1067 + +--S 1068 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 2 2 2 +--R 2 2 2 p log(b d x + 2b c d x + b c + a) +--R (b d x + 2b c d x + b c + a)%e +--R + +--R 2 2 2 p + 1 +--R - (b d x + 2b c d x + b c + a) +--R / +--R 2b d p + 2b d +--R Type: Expression(Integer) +--E 1068 + +--S 1069 of 1394 +d0:=normalize m0 +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1069 + +)clear all + +--S 1070 of 1394 +t0:=(a+b*(c+d*x)^2)^p/(c+d*x) +--R +--R +--R 2 2 2 p +--R (b d x + 2b c d x + b c + a) +--R (1) ------------------------------- +--R d x + c +--R Type: Expression(Integer) +--E 1070 + +--S 1071 of 1394 +--r0:=1/2*(a+b*(c+d*x)^2)^p*_ +-- hypergeometric(-p,-p,1-p,-a/(b*(c+d*x)^2))/_ +-- (d*p*((a+b*(c+d*x)^2)/(b*(c+d*x)^2))^p) +--E 1071 + +--S 1072 of 1394 +--a0:=integrate(t0,x) +--E 1072 + +--S 1073 of 1394 +--m0:=a0-r0 +--E 1073 + +--S 1074 of 1394 +--d0:=D(m0,x) +--E 1074 + +)clear all + +--S 1075 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (1) +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1075 + +--S 1076 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/7*b*(c+d*x)^7/d +--R +--R +--R (2) +--R 1 7 7 6 6 2 5 5 3 1 4 4 4 3 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 2 6 3 1 7 1 4 +--R (3b c + - a c )d x + (b c + a c )d x + - b c + - a c +--R 2 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1076 + +--S 1077 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 6 7 5 6 2 4 5 3 1 3 4 4 2 3 +--R - b d x + b c d x + 3b c d x + (5b c + - a)d x + (5b c + a c)d x +--R 7 4 +--R + +--R 5 3 2 2 6 3 +--R (3b c + - a c )d x + (b c + a c )x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1077 + +--S 1078 of 1394 +m0:=a0-r0 +--R +--R +--R 1 7 1 4 +--R - - b c - - a c +--R 7 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1078 + +--S 1079 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1079 + +)clear all + +--S 1080 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Polynomial(Integer) +--E 1080 + +--S 1081 of 1394 +r0:=1/4*a^2*(c+d*x)^4/d+2/7*a*b*(c+d*x)^7/d+1/10*b^2*(c+d*x)^10/d +--R +--R +--R (2) +--R 1 2 10 10 2 9 9 9 2 2 8 8 2 3 2 7 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 6 6 126 2 5 2 5 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 4 4 2 7 4 2 3 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 2 9 6 2 3 1 2 10 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )d x + -- b c +--R 2 2 10 +--R + +--R 2 7 1 2 4 +--R - a b c + - a c +--R 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1081 + +--S 1082 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 9 10 2 8 9 9 2 2 7 8 2 3 2 6 7 +--R -- b d x + b c d x + - b c d x + (12b c + - a b)d x +--R 10 2 7 +--R + +--R 2 4 5 6 126 2 5 2 4 5 +--R (21b c + 2a b c)d x + (--- b c + 6a b c )d x +--R 5 +--R + +--R 2 6 3 1 2 3 4 2 7 4 2 2 3 +--R (21b c + 10a b c + - a )d x + (12b c + 10a b c + a c)d x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 2 9 6 2 3 +--R (- b c + 6a b c + - a c )d x + (b c + 2a b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1082 + +--S 1083 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 10 2 7 1 2 4 +--R - -- b c - - a b c - - a c +--R 10 7 4 +--R (4) ------------------------------ +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1083 + +--S 1084 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1084 + +)clear all + +--S 1085 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 3 3 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c + a c +--R Type: Polynomial(Integer) +--E 1085 + +--S 1086 of 1394 +r0:=1/4*a^3*(c+d*x)^4/d+3/7*a^2*b*(c+d*x)^7/d+3/10*a*b^2*(c+d*x)^10/d+_ + 1/13*b^3*(c+d*x)^13/d +--R +--R +--R (2) +--R 1 3 13 13 3 12 12 3 2 11 11 3 3 3 2 10 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 9 9 3 5 27 2 2 8 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 7 7 3 7 2 4 2 6 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 1 3 13 3 2 10 3 2 7 +--R (b c + 3a b c + 3a b c + a c )d x + -- b c + -- a b c + - a b c +--R 13 10 7 +--R + +--R 1 3 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1086 + +--S 1087 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 12 13 3 11 12 3 2 10 11 3 3 3 2 9 10 +--R -- b d x + b c d x + 6b c d x + (22b c + -- a b )d x +--R 13 10 +--R + +--R 3 4 2 8 9 3 5 27 2 2 7 8 +--R (55b c + 3a b c)d x + (99b c + -- a b c )d x +--R 2 +--R + +--R 3 6 2 3 3 2 6 7 3 7 2 4 2 5 6 +--R (132b c + 36a b c + - a b)d x + (132b c + 63a b c + 3a b c)d x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 5 +--R (99b c + --- a b c + 9a b c )d x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 +--R (22b c + 36a b c + 15a b c + a c)d x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 +--R (6b c + -- a b c + 9a b c + - a c )d x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1087 + +--S 1088 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 +--R - -- b c - -- a b c - - a b c - - a c +--R 13 10 7 4 +--R (4) ------------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1088 + +--S 1089 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1089 + +)clear all + +--S 1090 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3) +--R +--R +--R (1) +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + a)d e x +--R + +--R 4 2 3 2 5 2 3 6 3 3 +--R (15b c + 3a c)d e x + (6b c + 3a c )d e x + (b c + a c )e +--R Type: Polynomial(Integer) +--E 1090 + +--S 1091 of 1394 +r0:=1/4*a*e^3*(c+d*x)^4/d+1/7*b*e^3*(c+d*x)^7/d +--R +--R +--R (2) +--R 1 7 3 7 6 3 6 2 5 3 5 3 1 4 3 4 +--R - b d e x + b c d e x + 3b c d e x + (5b c + - a)d e x +--R 7 4 +--R + +--R 4 3 3 3 5 3 2 2 3 2 6 3 3 +--R (5b c + a c)d e x + (3b c + - a c )d e x + (b c + a c )d e x +--R 2 +--R + +--R 1 7 1 4 3 +--R (- b c + - a c )e +--R 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1091 + +--S 1092 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 6 3 7 5 3 6 2 4 3 5 3 1 3 3 4 +--R - b d e x + b c d e x + 3b c d e x + (5b c + - a)d e x +--R 7 4 +--R + +--R 4 2 3 3 5 3 2 3 2 6 3 3 +--R (5b c + a c)d e x + (3b c + - a c )d e x + (b c + a c )e x +--R 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1092 + +--S 1093 of 1394 +m0:=a0-r0 +--R +--R +--R 1 7 1 4 3 +--R (- - b c - - a c )e +--R 7 4 +--R (4) --------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1093 + +--S 1094 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1094 + +)clear all + +--S 1095 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 9 3 9 2 8 3 8 2 2 7 3 7 2 3 6 3 6 +--R b d e x + 9b c d e x + 36b c d e x + (84b c + 2a b)d e x +--R + +--R 2 4 5 3 5 2 5 2 4 3 4 +--R (126b c + 12a b c)d e x + (126b c + 30a b c )d e x +--R + +--R 2 6 3 2 3 3 3 2 7 4 2 2 3 2 +--R (84b c + 40a b c + a )d e x + (36b c + 30a b c + 3a c)d e x +--R + +--R 2 8 5 2 2 3 2 9 6 2 3 3 +--R (9b c + 12a b c + 3a c )d e x + (b c + 2a b c + a c )e +--R Type: Polynomial(Integer) +--E 1095 + +--S 1096 of 1394 +r0:=1/4*a^2*e^3*(c+d*x)^4/d+2/7*a*b*e^3*(c+d*x)^7/d+1/10*b^2*e^3*(c+d*x)^10/d +--R +--R +--R (2) +--R 1 2 10 3 10 2 9 3 9 9 2 2 8 3 8 2 3 2 7 3 7 +--R -- b d e x + b c d e x + - b c d e x + (12b c + - a b)d e x +--R 10 2 7 +--R + +--R 2 4 6 3 6 126 2 5 2 5 3 5 +--R (21b c + 2a b c)d e x + (--- b c + 6a b c )d e x +--R 5 +--R + +--R 2 6 3 1 2 4 3 4 2 7 4 2 3 3 3 +--R (21b c + 10a b c + - a )d e x + (12b c + 10a b c + a c)d e x +--R 4 +--R + +--R 9 2 8 5 3 2 2 2 3 2 2 9 6 2 3 3 +--R (- b c + 6a b c + - a c )d e x + (b c + 2a b c + a c )d e x +--R 2 2 +--R + +--R 1 2 10 2 7 1 2 4 3 +--R (-- b c + - a b c + - a c )e +--R 10 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1096 + +--S 1097 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 9 3 10 2 8 3 9 9 2 2 7 3 8 2 3 2 6 3 7 +--R -- b d e x + b c d e x + - b c d e x + (12b c + - a b)d e x +--R 10 2 7 +--R + +--R 2 4 5 3 6 126 2 5 2 4 3 5 +--R (21b c + 2a b c)d e x + (--- b c + 6a b c )d e x +--R 5 +--R + +--R 2 6 3 1 2 3 3 4 2 7 4 2 2 3 3 +--R (21b c + 10a b c + - a )d e x + (12b c + 10a b c + a c)d e x +--R 4 +--R + +--R 9 2 8 5 3 2 2 3 2 2 9 6 2 3 3 +--R (- b c + 6a b c + - a c )d e x + (b c + 2a b c + a c )e x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1097 + +--S 1098 of 1394 +m0:=a0-r0 +--R +--R +--R 1 2 10 2 7 1 2 4 3 +--R (- -- b c - - a b c - - a c )e +--R 10 7 4 +--R (4) ---------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1098 + +--S 1099 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1099 + +)clear all + +--S 1100 of 1394 +t0:=(c*e+d*e*x)^3*(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 12 3 12 3 11 3 11 3 2 10 3 10 3 3 2 9 3 9 +--R b d e x + 12b c d e x + 66b c d e x + (220b c + 3a b )d e x +--R + +--R 3 4 2 8 3 8 3 5 2 2 7 3 7 +--R (495b c + 27a b c)d e x + (792b c + 108a b c )d e x +--R + +--R 3 6 2 3 2 6 3 6 3 7 2 4 2 5 3 5 +--R (924b c + 252a b c + 3a b)d e x + (792b c + 378a b c + 18a b c)d e x +--R + +--R 3 8 2 5 2 2 4 3 4 +--R (495b c + 378a b c + 45a b c )d e x +--R + +--R 3 9 2 6 2 3 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 3 2 +--R (66b c + 108a b c + 45a b c + 3a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 3 +--R (12b c + 27a b c + 18a b c + 3a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Polynomial(Integer) +--E 1100 + +--S 1101 of 1394 +r0:=1/4*a^3*e^3*(c+d*x)^4/d+3/7*a^2*b*e^3*(c+d*x)^7/d+_ + 3/10*a*b^2*e^3*(c+d*x)^10/d+1/13*b^3*e^3*(c+d*x)^13/d +--R +--R +--R (2) +--R 1 3 13 3 13 3 12 3 12 3 2 11 3 11 3 3 3 2 10 3 10 +--R -- b d e x + b c d e x + 6b c d e x + (22b c + -- a b )d e x +--R 13 10 +--R + +--R 3 4 2 9 3 9 3 5 27 2 2 8 3 8 +--R (55b c + 3a b c)d e x + (99b c + -- a b c )d e x +--R 2 +--R + +--R 3 6 2 3 3 2 7 3 7 3 7 2 4 2 6 3 6 +--R (132b c + 36a b c + - a b)d e x + (132b c + 63a b c + 3a b c)d e x +--R 7 +--R + +--R 3 8 378 2 5 2 2 5 3 5 +--R (99b c + --- a b c + 9a b c )d e x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 4 3 4 +--R (55b c + 63a b c + 15a b c + - a )d e x +--R 4 +--R + +--R 3 10 2 7 2 4 3 3 3 3 +--R (22b c + 36a b c + 15a b c + a c)d e x +--R + +--R 3 11 27 2 8 2 5 3 3 2 2 3 2 +--R (6b c + -- a b c + 9a b c + - a c )d e x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )d e x +--R + +--R 1 3 13 3 2 10 3 2 7 1 3 4 3 +--R (-- b c + -- a b c + - a b c + - a c )e +--R 13 10 7 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1101 + +--S 1102 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 12 3 13 3 11 3 12 3 2 10 3 11 3 3 3 2 9 3 10 +--R -- b d e x + b c d e x + 6b c d e x + (22b c + -- a b )d e x +--R 13 10 +--R + +--R 3 4 2 8 3 9 3 5 27 2 2 7 3 8 +--R (55b c + 3a b c)d e x + (99b c + -- a b c )d e x +--R 2 +--R + +--R 3 6 2 3 3 2 6 3 7 3 7 2 4 2 5 3 6 +--R (132b c + 36a b c + - a b)d e x + (132b c + 63a b c + 3a b c)d e x +--R 7 +--R + +--R 3 8 378 2 5 2 2 4 3 5 +--R (99b c + --- a b c + 9a b c )d e x +--R 5 +--R + +--R 3 9 2 6 2 3 1 3 3 3 4 +--R (55b c + 63a b c + 15a b c + - a )d e x +--R 4 +--R + +--R 3 10 2 7 2 4 3 2 3 3 +--R (22b c + 36a b c + 15a b c + a c)d e x +--R + +--R 3 11 27 2 8 2 5 3 3 2 3 2 +--R (6b c + -- a b c + 9a b c + - a c )d e x +--R 2 2 +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e x +--R Type: Polynomial(Fraction(Integer)) +--E 1102 + +--S 1103 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 13 3 2 10 3 2 7 1 3 4 3 +--R (- -- b c - -- a b c - - a b c - - a c )e +--R 13 10 7 4 +--R (4) ----------------------------------------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1103 + +--S 1104 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1104 + +)clear all + +--S 1105 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1105 + +--S 1106 of 1394 +r0:=1/2*(c+d*x)^2/(b*d)+1/3*a^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(b^(5/3)*d)-1/6*a^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(b^(5/3)*d)+_ + a^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+2 3+-+ 3+-+ 3+-+2 (2d x + 2c)\|b - \|a +--R 2\|3 \|a log((d x + c)\|b + \|a ) - 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+2 +--R (3d x + 6c d x + 3c )\|3 \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1106 + +--S 1107 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a |a +--R 2\|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+ +--+2 +--+ +--R | 2 | 2 | 2 +--R +-+ |a |a |a 2 2 2 +--R - \|3 |-- log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 3| 2 +--R \|b \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a \|b 2 2 +-+ +--R 6 |-- atan(----------------------------------- + (3d x + 6c d x)\|3 +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1107 + +--S 1108 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R - 2\|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R +-+ |a 3+-+2 |a +--R 2\|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R +-+ |a 3+-+2 +--R \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R |a 3+-+2 \|b 2 +-+3+-+2 +--R 6 |-- \|b atan(----------------------------------- - 3c \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1108 + +--S 1109 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1109 + +)clear all + +--S 1110 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1110 + +--S 1111 of 1394 +r0:=x/b-1/3*a^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(b^(4/3)*d)+_ + 1/6*a^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(b^(4/3)*d)+a^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+3+-+ 3+-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2\|3 \|a log((d x + c)\|b + \|a ) - 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+ +--R 6d x\|3 \|b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1111 + +--S 1112 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R +-+ | a | a | a 2 2 2 +--R - \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a | a +--R 2\|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a \| b +-+ +--R - 6 3|- - atan(---------------------------- + 6d x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1112 + +--S 1113 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R 2\|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R +-+ | a 3+-+ | a | a 2 2 2 +--R - \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R +-+ | a 3+-+ | a +--R 2\|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R | a 3+-+ \| b +--R - 6 3|- - \|b atan(----------------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1113 + +--S 1114 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1114 + +)clear all + +--S 1115 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 2 2 +--R d x + 2c d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1115 + +--S 1116 of 1394 +r0:=1/3*log(a+b*(c+d*x)^3)/(b*d) +--R +--R +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R (2) --------------------------------------------- +--R 3b d +--R Type: Expression(Integer) +--E 1116 + +--S 1117 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R (3) --------------------------------------------- +--R 3b d +--R Type: Union(Expression(Integer),...) +--E 1117 + +--S 1118 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1118 + +--S 1119 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1119 + +)clear all + +--S 1120 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3) +--R +--R +--R d x + c +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1120 + +--S 1121 of 1394 +r0:=-1/3*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(2/3)*d)+_ + 1/6*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(1/3)*_ + b^(2/3)*d)-atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2\|3 log((d x + c)\|b + \|a ) + 6atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6d\|3 \|a \|b +--R Type: Expression(Integer) +--E 1121 + +--S 1122 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R \|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1122 + +--S 1123 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1123 + +--S 1124 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1124 + +)clear all + +--S 1125 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)) +--R +--R +--R 1 +--R (1) ------------------------------------------------------------ +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + (4b c + a)d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1125 + +--S 1126 of 1394 +r0:=log(c+d*x)/(a*d)-1/3*log(a+b*(c+d*x)^3)/(a*d) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (2) --------------------------------------------------------------- +--R 3a d +--R Type: Expression(Integer) +--E 1126 + +--S 1127 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (3) --------------------------------------------------------------- +--R 3a d +--R Type: Union(Expression(Integer),...) +--E 1127 + +--S 1128 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1128 + +--S 1129 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1129 + +)clear all + +--S 1130 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 5 5 4 4 2 3 3 3 2 2 4 +--R b d x + 5b c d x + 10b c d x + (10b c + a)d x + (5b c + 2a c)d x +--R + +--R 5 2 +--R b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1130 + +--S 1131 of 1394 +r0:=(-1)/(a*d*(c+d*x))+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*d)-1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(4/3)*d)+b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ +--R (- d x - c)\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R (2d x + 2c)\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +-+3+-+ +--R (- 6d x - 6c)\|b atan(----------------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 +-+3+-+ +--R (6a d x + 6a c d)\|3 \|a +--R Type: Expression(Integer) +--E 1131 + +--S 1132 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+ +--R (6a d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 1132 + +--S 1133 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R +-+3+-+ +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 1133 + +--S 1134 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1134 + +)clear all + +--S 1135 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 +--R b d x + 6b c d x + 15b c d x + (20b c + a)d x + (15b c + 3a c)d x +--R + +--R 5 2 6 3 +--R (6b c + 3a c )d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1135 + +--S 1136 of 1394 +r0:=(-1/2)/(a*d*(c+d*x)^2)-1/3*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(5/3)*d)+1/6*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(5/3)*d)+_ + b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+2 +--R (d x + 2c d x + c )\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 2 2 +-+3+-+2 3+-+ 3+-+ +--R (- 2d x - 4c d x - 2c )\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (2d x + 2c)\|b - \|a +-+3+-+2 +--R (- 6d x - 12c d x - 6c )\|b atan(----------------------) - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 2 2 +-+3+-+2 +--R (6a d x + 12a c d x + 6a c d)\|3 \|a +--R Type: Expression(Integer) +--E 1136 + +--S 1137 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 2 2 2 +-+ +--R (6a d x + 12a c d x + 6a c d)\|3 +--R Type: Union(Expression(Integer),...) +--E 1137 + +--S 1138 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R +-+3+-+2 +--R 6a d\|3 \|a +--R Type: Expression(Integer) +--E 1138 + +--S 1139 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1139 + +)clear all + +--S 1140 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + (35b c + a)d x + (35b c + 4a c)d x +--R + +--R 5 2 2 2 6 3 7 4 +--R (21b c + 6a c )d x + (7b c + 4a c )d x + b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1140 + +--S 1141 of 1394 +r0:=(-1/3)/(a*d*(c+d*x)^3)-b*log(c+d*x)/(a^2*d)+_ + 1/3*b*log(a+b*(c+d*x)^3)/(a^2*d) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3a d x + 9a c d x + 9a c d x + 3a c d +--R Type: Expression(Integer) +--E 1141 + +--S 1142 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3a d x + 9a c d x + 9a c d x + 3a c d +--R Type: Union(Expression(Integer),...) +--E 1142 + +--S 1143 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1143 + +--S 1144 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1144 + +)clear all + +--S 1145 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1145 + +--S 1146 of 1394 +r0:=-1/3*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3))-_ + 2/9*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(5/3)*d)+_ + 1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(1/3)*b^(5/3)*d)-2/3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(1/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d x + 3b c d x + 3b c d x + b c + a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (- 3d x - 6c d x - 3c )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1146 + +--S 1147 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (- 3d x - 6c d x - 3c )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1147 + +--S 1148 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1148 + +--S 1149 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1149 + +)clear all + +--S 1150 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1150 + +--S 1151 of 1394 +r0:=1/3*(-c-d*x)/(b*d*(a+b*(c+d*x)^3))+1/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(2/3)*b^(4/3)*d)-1/18*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(2/3)*b^(4/3)*d)-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*_ + sqrt(3)))/(a^(2/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (- 6d x - 6c)\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1151 + +--S 1152 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (- 6d x - 6c)\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1152 + +--S 1153 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1153 + +--S 1154 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1154 + +)clear all + +--S 1155 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 2 2 +--R d x + 2c d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1155 + +--S 1156 of 1394 +r0:=(-1/3)/(b*d*(a+b*(c+d*x)^3)) +--R +--R +--R 1 +--R - +--R 3 +--R (2) - --------------------------------------------- +--R 2 4 3 2 3 2 2 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1156 + +--S 1157 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - ------------------------------------------------ +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3b d x + 9b c d x + 9b c d x + (3b c + 3a b)d +--R Type: Union(Expression(Integer),...) +--E 1157 + +--S 1158 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1158 + +--S 1159 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1159 + +)clear all + +--S 1160 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R d x + c +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1160 + +--S 1161 of 1394 +r0:=1/3*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3))-1/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(4/3)*b^(2/3)*d)+1/18*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(2/3)*d)-_ + 1/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d x + 3b c d x + 3b c d x + b c + a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d x - 6b c d x - 6b c d x - 2b c - 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (6d x + 12c d x + 6c )\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1161 + +--S 1162 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d x - 18b c d x - 18b c d x - 6b c - 6a) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d x + 12c d x + 6c )\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1162 + +--S 1163 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1163 + +--S 1164 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1164 + +)clear all + +--S 1165 of 1394 +t0:=1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1165 + +--S 1166 of 1394 +r0:=1/3*(c+d*x)/(a*d*(a+b*(c+d*x)^3))+2/9*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(5/3)*b^(1/3)*d)-1/9*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(1/3)*d)-_ + 2/3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (3d x + 3c)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1166 + +--S 1167 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1167 + +--S 1168 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1168 + +--S 1169 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1169 + +)clear all + +--S 1170 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d x + 7b c d x + 21b c d x + (35b c + 2a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (35b c + 8a b c)d x + (21b c + 12a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (7b c + 8a b c + a )d x + b c + 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1170 + +--S 1171 of 1394 +r0:=1/3/(a*d*(a+b*(c+d*x)^3))+log(c+d*x)/(a^2*d)-1/3*log(a+b*(c+d*x)^3)/(a^2*d) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d x + 9a b c d x + 9a b c d x + (3a b c + 3a )d +--R Type: Expression(Integer) +--E 1171 + +--S 1172 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d x + 9a b c d x + 9a b c d x + (3a b c + 3a )d +--R Type: Union(Expression(Integer),...) +--E 1172 + +--S 1173 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1173 + +--S 1174 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1174 + +)clear all + +--S 1175 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R b d x + 8b c d x + 28b c d x + (56b c + 2a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (70b c + 10a b c)d x + (56b c + 20a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 2 8 +--R (28b c + 20a b c + a )d x + (8b c + 10a b c + 2a c)d x + b c +--R + +--R 5 2 2 +--R 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1175 + +--S 1176 of 1394 +r0:=(-4/3)/(a^2*d*(c+d*x))+1/3/(a*d*(c+d*x)*(a+b*(c+d*x)^3))+_ + 4/9*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(7/3)*d)-_ + 2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(7/3)*d)+4/3*b^(1/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(7/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 12b d x - 48b c d x - 72b c d x + (- 48b c - 12a)d x - 12b c +--R + +--R - 12a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 \|a +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1176 + +--S 1177 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 4 2 4 3 2 2 3 2 2 3 3 2 +--R 9a b d x + 36a b c d x + 54a b c d x + (36a b c + 9a )d x +--R + +--R 2 4 3 +--R (9a b c + 9a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1177 + +--S 1178 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 4\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 12\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 9a d\|3 \|a +--R Type: Expression(Integer) +--E 1178 + +--S 1179 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1179 + +)clear all + +--S 1180 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 9 9 2 8 8 2 2 7 7 2 3 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 2a b)d x +--R + +--R 2 4 5 5 2 5 2 4 4 +--R (126b c + 12a b c)d x + (126b c + 30a b c )d x +--R + +--R 2 6 3 2 3 3 2 7 4 2 2 2 +--R (84b c + 40a b c + a )d x + (36b c + 30a b c + 3a c)d x +--R + +--R 2 8 5 2 2 2 9 6 2 3 +--R (9b c + 12a b c + 3a c )d x + b c + 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1180 + +--S 1181 of 1394 +r0:=(-5/6)/(a^2*d*(c+d*x)^2)+1/3/(a*d*(c+d*x)^2*(a+b*(c+d*x)^3))-_ + 5/9*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(8/3)*d)+_ + 5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(8/3)*d)+5/3*b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(8/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 \|a +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1181 + +--S 1182 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 5 2 5 4 2 2 4 3 2 3 3 3 2 +--R 18a b d x + 90a b c d x + 180a b c d x + (180a b c + 18a )d x +--R + +--R 2 4 3 2 2 5 3 2 +--R (90a b c + 36a c)d x + (18a b c + 18a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1182 + +--S 1183 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 30\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 +-+3+-+2 +--R 18a d\|3 \|a +--R Type: Expression(Integer) +--E 1183 + +--S 1184 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1184 + +)clear all + +--S 1185 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 10 10 2 9 9 2 2 8 8 2 3 7 7 +--R b d x + 10b c d x + 45b c d x + (120b c + 2a b)d x +--R + +--R 2 4 6 6 2 5 2 5 5 +--R (210b c + 14a b c)d x + (252b c + 42a b c )d x +--R + +--R 2 6 3 2 4 4 2 7 4 2 3 3 +--R (210b c + 70a b c + a )d x + (120b c + 70a b c + 4a c)d x +--R + +--R 2 8 5 2 2 2 2 2 9 6 2 3 2 10 +--R (45b c + 42a b c + 6a c )d x + (10b c + 14a b c + 4a c )d x + b c +--R + +--R 7 2 4 +--R 2a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1185 + +--S 1186 of 1394 +r0:=(-2/3)/(a^2*d*(c+d*x)^3)+1/3/(a*d*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 2*b*log(c+d*x)/(a^3*d)+2/3*b*log(a+b*(c+d*x)^3)/(a^3*d) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 4 4 3 +--R 3a b d x + 18a b c d x + 45a b c d x + (60a b c + 3a )d x +--R + +--R 3 4 4 3 2 3 5 4 2 2 3 6 4 3 +--R (45a b c + 9a c)d x + (18a b c + 9a c )d x + (3a b c + 3a c )d +--R Type: Expression(Integer) +--E 1186 + +--S 1187 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 4 4 3 +--R 3a b d x + 18a b c d x + 45a b c d x + (60a b c + 3a )d x +--R + +--R 3 4 4 3 2 3 5 4 2 2 3 6 4 3 +--R (45a b c + 9a c)d x + (18a b c + 9a c )d x + (3a b c + 3a c )d +--R Type: Union(Expression(Integer),...) +--E 1187 + +--S 1188 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1188 + +--S 1189 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1189 + +)clear all + +--S 1190 of 1394 +t0:=(c+d*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 4 4 3 3 2 2 2 3 4 +--R d x + 4c d x + 6c d x + 4c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1190 + +--S 1191 of 1394 +r0:=-1/6*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3)^2)+1/9*(c+d*x)^2/_ + (a*b*d*(a+b*(c+d*x)^3))-1/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*b^(5/3)*d)+1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(5/3)*d)-1/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1191 + +--S 1192 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 90b c - 36a b c)d x + (- 36b c - 36a b c )d x - 6b c +--R + +--R 3 2 +--R - 12a b c - 6a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 6b d x + 30b c d x + 60b c d x + (60b c - 3a)d x +--R + +--R 4 5 2 +--R (30b c - 6a c)d x + 6b c - 3a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1192 + +--S 1193 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1193 + +--S 1194 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1194 + +)clear all + +--S 1195 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1195 + +--S 1196 of 1394 +r0:=1/6*(-c-d*x)/(b*d*(a+b*(c+d*x)^3)^2)+1/18*(c+d*x)/_ + (a*b*d*(a+b*(c+d*x)^3))+1/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(4/3)*d)-1/54*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(4/3)*d)-1/9*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1196 + +--S 1197 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - b d x - 6b c d x - 15b c d x + (- 20b c - 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (- 15b c - 6a b c)d x + (- 6b c - 6a b c )d x - b c - 2a b c - a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (3b d x + 12b c d x + 18b c d x + (12b c - 6a)d x + 3b c - 6a c) +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1197 + +--S 1198 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1198 + +--S 1199 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1199 + +)clear all + +--S 1200 of 1394 +t0:=(c+d*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 2 2 2 +--R d x + 2c d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1200 + +--S 1201 of 1394 +r0:=(-1/6)/(b*d*(a+b*(c+d*x)^3)^2) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 6 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 3 6 2 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1201 + +--S 1202 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x +--R + +--R 3 6 2 3 2 +--R (6b c + 12a b c + 6a b)d +--R Type: Union(Expression(Integer),...) +--E 1202 + +--S 1203 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1203 + +--S 1204 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1204 + +)clear all + +--S 1205 of 1394 +t0:=(c+d*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R d x + c +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1205 + +--S 1206 of 1394 +r0:=1/6*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3)^2)+2/9*(c+d*x)^2/(a^2*d*_ + (a+b*(c+d*x)^3))-2/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(7/3)*b^(2/3)*d)+1/27*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(7/3)*b^(2/3)*d)-2/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (30b c + 12a b c)d x + (12b c + 12a b c )d x + 2b c + 4a b c + 2a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d x - 24b c d x - 60b c d x + (- 80b c - 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 60b c - 24a b c)d x + (- 24b c - 24a b c )d x - 4b c - 8a b c +--R + +--R 2 +--R - 4a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 12b d x + 72b c d x + 180b c d x + (240b c + 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (180b c + 72a b c)d x + (72b c + 72a b c )d x + 12b c + 24a b c +--R + +--R 2 +--R 12a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1206 + +--S 1207 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d x + 24b c d x + 60b c d x + (80b c + 8a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (60b c + 24a b c)d x + (24b c + 24a b c )d x + 4b c + 8a b c + 4a +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 12b d x - 72b c d x - 180b c d x + (- 240b c - 24a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 180b c - 72a b c)d x + (- 72b c - 72a b c )d x - 12b c +--R + +--R 3 2 +--R - 24a b c - 12a +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d x + 60b c d x + 120b c d x + (120b c + 21a)d x +--R + +--R 4 5 2 +--R (60b c + 42a c)d x + 12b c + 21a c +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1207 + +--S 1208 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1208 + +--S 1209 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1209 + +)clear all + +--S 1210 of 1394 +t0:=1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1210 + +--S 1211 of 1394 +r0:=1/6*(c+d*x)/(a*d*(a+b*(c+d*x)^3)^2)+5/18*(c+d*x)/_ + (a^2*d*(a+b*(c+d*x)^3))+5/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(8/3)*b^(1/3)*d)-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(8/3)*b^(1/3)*d)-5/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1211 + +--S 1212 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1212 + +--S 1213 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 10\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 30\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1213 + +--S 1214 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1214 + +)clear all + +--S 1215 of 1394 +t0:=1/((c+d*x)*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 10 10 3 9 9 3 2 8 8 3 3 2 7 7 +--R b d x + 10b c d x + 45b c d x + (120b c + 3a b )d x +--R + +--R 3 4 2 6 6 3 5 2 2 5 5 +--R (210b c + 21a b c)d x + (252b c + 63a b c )d x +--R + +--R 3 6 2 3 2 4 4 3 7 2 4 2 3 3 +--R (210b c + 105a b c + 3a b)d x + (120b c + 105a b c + 12a b c)d x +--R + +--R 3 8 2 5 2 2 2 2 +--R (45b c + 63a b c + 18a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 10 2 7 2 4 3 +--R (10b c + 21a b c + 12a b c + a )d x + b c + 3a b c + 3a b c + a c +--R Type: Fraction(Polynomial(Integer)) +--E 1215 + +--S 1216 of 1394 +r0:=1/6/(a*d*(a+b*(c+d*x)^3)^2)+1/3/(a^2*d*(a+b*(c+d*x)^3))+_ + log(c+d*x)/(a^3*d)-1/3*log(a+b*(c+d*x)^3)/(a^3*d) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d x + 36a b c d x + 90a b c d x + (120a b c + 12a b)d x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d x + (36a b c + 36a b c )d x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d +--R Type: Expression(Integer) +--E 1216 + +--S 1217 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d x + 36a b c d x + 90a b c d x + (120a b c + 12a b)d x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d x + (36a b c + 36a b c )d x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d +--R Type: Union(Expression(Integer),...) +--E 1217 + +--S 1218 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1218 + +--S 1219 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1219 + +)clear all + +--S 1220 of 1394 +t0:=1/((c+d*x)^2*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 11 11 3 10 10 3 2 9 9 3 3 2 8 8 +--R b d x + 11b c d x + 55b c d x + (165b c + 3a b )d x +--R + +--R 3 4 2 7 7 3 5 2 2 6 6 +--R (330b c + 24a b c)d x + (462b c + 84a b c )d x +--R + +--R 3 6 2 3 2 5 5 3 7 2 4 2 4 4 +--R (462b c + 168a b c + 3a b)d x + (330b c + 210a b c + 15a b c)d x +--R + +--R 3 8 2 5 2 2 3 3 +--R (165b c + 168a b c + 30a b c )d x +--R + +--R 3 9 2 6 2 3 3 2 2 +--R (55b c + 84a b c + 30a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 11 2 8 2 5 +--R (11b c + 24a b c + 15a b c + 2a c)d x + b c + 3a b c + 3a b c +--R + +--R 3 2 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1220 + +--S 1221 of 1394 +r0:=(-14/9)/(a^3*d*(c+d*x))+1/6/(a*d*(c+d*x)*(a+b*(c+d*x)^3)^2)+_ + 7/18/(a^2*d*(c+d*x)*(a+b*(c+d*x)^3))+14/27*b^(1/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(10/3)*d)-7/27*b^(1/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(10/3)*d)+_ + 14/9*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(10/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 84b d x - 588b c d x - 1764b c d x + (- 2940b c - 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 2940b c - 672a b c)d x + (- 1764b c - 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 588b c - 672a b c - 84a )d x - 84b c - 168a b c - 84a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1221 + +--S 1222 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 7 3 2 7 6 3 2 2 6 5 3 2 3 4 5 4 +--R 54a b d x + 378a b c d x + 1134a b c d x + (1890a b c + 108a b)d x +--R + +--R 3 2 4 4 4 3 3 2 5 4 2 3 2 +--R (1890a b c + 432a b c)d x + (1134a b c + 648a b c )d x +--R + +--R 3 2 6 4 3 5 2 3 2 7 4 4 5 +--R (378a b c + 432a b c + 54a )d x + (54a b c + 108a b c + 54a c)d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1222 + +--S 1223 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 7\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 14\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 42\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 +-+3+-+ +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 1223 + +--S 1224 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1224 + +)clear all + +--S 1225 of 1394 +t0:=1/((c+d*x)^3*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 2 9 9 +--R b d x + 12b c d x + 66b c d x + (220b c + 3a b )d x +--R + +--R 3 4 2 8 8 3 5 2 2 7 7 +--R (495b c + 27a b c)d x + (792b c + 108a b c )d x +--R + +--R 3 6 2 3 2 6 6 3 7 2 4 2 5 5 +--R (924b c + 252a b c + 3a b)d x + (792b c + 378a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 4 4 +--R (495b c + 378a b c + 45a b c )d x +--R + +--R 3 9 2 6 2 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 2 2 +--R (66b c + 108a b c + 45a b c + 3a c)d x +--R + +--R 3 11 2 8 2 5 3 2 3 12 2 9 2 6 +--R (12b c + 27a b c + 18a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1225 + +--S 1226 of 1394 +r0:=(-10/9)/(a^3*d*(c+d*x)^2)+1/6/(a*d*(c+d*x)^2*(a+b*(c+d*x)^3)^2)+_ + 4/9/(a^2*d*(c+d*x)^2*(a+b*(c+d*x)^3))-20/27*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(11/3)*d)+10/27*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(11/3)*d)+_ + 20/9*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(11/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+3+-+2 +--R \|3 \|a +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1226 + +--S 1227 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 8 3 2 8 7 3 2 2 7 6 3 2 3 4 6 5 +--R 54a b d x + 432a b c d x + 1512a b c d x + (3024a b c + 108a b)d x +--R + +--R 3 2 4 4 5 4 3 2 5 4 2 4 3 +--R (3780a b c + 540a b c)d x + (3024a b c + 1080a b c )d x +--R + +--R 3 2 6 4 3 5 3 2 +--R (1512a b c + 1080a b c + 54a )d x +--R + +--R 3 2 7 4 4 5 2 3 2 8 4 5 5 2 +--R (432a b c + 540a b c + 108a c)d x + (54a b c + 108a b c + 54a c )d +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1227 + +--S 1228 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 10\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 20\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 60\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 27a d\|3 \|a +--R Type: Expression(Integer) +--E 1228 + +--S 1229 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1229 + +)clear all + +--S 1230 of 1394 +t0:=1/((c+d*x)^4*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 13 13 3 12 12 3 2 11 11 3 3 2 10 10 +--R b d x + 13b c d x + 78b c d x + (286b c + 3a b )d x +--R + +--R 3 4 2 9 9 3 5 2 2 8 8 +--R (715b c + 30a b c)d x + (1287b c + 135a b c )d x +--R + +--R 3 6 2 3 2 7 7 3 7 2 4 2 6 6 +--R (1716b c + 360a b c + 3a b)d x + (1716b c + 630a b c + 21a b c)d x +--R + +--R 3 8 2 5 2 2 5 5 +--R (1287b c + 756a b c + 63a b c )d x +--R + +--R 3 9 2 6 2 3 3 4 4 +--R (715b c + 630a b c + 105a b c + a )d x +--R + +--R 3 10 2 7 2 4 3 3 3 +--R (286b c + 360a b c + 105a b c + 4a c)d x +--R + +--R 3 11 2 8 2 5 3 2 2 2 +--R (78b c + 135a b c + 63a b c + 6a c )d x +--R + +--R 3 12 2 9 2 6 3 3 3 13 2 10 2 7 +--R (13b c + 30a b c + 21a b c + 4a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 4 +--R a c +--R Type: Fraction(Polynomial(Integer)) +--E 1230 + +--S 1231 of 1394 +r0:=(-1)/(a^3*d*(c+d*x)^3)+1/6/(a*d*(c+d*x)^3*(a+b*(c+d*x)^3)^2)+_ + 1/2/(a^2*d*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 3*b*log(c+d*x)/(a^4*d)+b*log(a+b*(c+d*x)^3)/(a^4*d) +--R +--R +--R (2) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 9 4 2 9 8 4 2 2 8 7 4 2 3 5 7 6 +--R 6a b d x + 54a b c d x + 216a b c d x + (504a b c + 12a b)d x +--R + +--R 4 2 4 5 6 5 4 2 5 5 2 5 4 +--R (756a b c + 72a b c)d x + (756a b c + 180a b c )d x +--R + +--R 4 2 6 5 3 6 4 3 4 2 7 5 4 6 3 2 +--R (504a b c + 240a b c + 6a )d x + (216a b c + 180a b c + 18a c)d x +--R + +--R 4 2 8 5 5 6 2 2 4 2 9 5 6 6 3 +--R (54a b c + 72a b c + 18a c )d x + (6a b c + 12a b c + 6a c )d +--R Type: Expression(Integer) +--E 1231 + +--S 1232 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 9 4 2 9 8 4 2 2 8 7 4 2 3 5 7 6 +--R 6a b d x + 54a b c d x + 216a b c d x + (504a b c + 12a b)d x +--R + +--R 4 2 4 5 6 5 4 2 5 5 2 5 4 +--R (756a b c + 72a b c)d x + (756a b c + 180a b c )d x +--R + +--R 4 2 6 5 3 6 4 3 4 2 7 5 4 6 3 2 +--R (504a b c + 240a b c + 6a )d x + (216a b c + 180a b c + 18a c)d x +--R + +--R 4 2 8 5 5 6 2 2 4 2 9 5 6 6 3 +--R (54a b c + 72a b c + 18a c )d x + (6a b c + 12a b c + 6a c )d +--R Type: Union(Expression(Integer),...) +--E 1232 + +--S 1233 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1233 + +--S 1234 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1234 + +)clear all + +--S 1235 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3) +--R +--R +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R (1) ------------------------------------------------ +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1235 + +--S 1236 of 1394 +r0:=1/2*e^4*(c+d*x)^2/(b*d)+1/3*a^(2/3)*e^4*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (b^(5/3)*d)-1/6*a^(2/3)*e^4*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(b^(5/3)*d)+a^(2/3)*e^4*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 4 +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 +-+3+-+2 3+-+ 3+-+ +--R 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 4 3+-+2 (2d x + 2c)\|b - \|a +--R - 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 4 2 4 2 4 +-+3+-+2 +--R (3d e x + 6c d e x + 3c e )\|3 \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1236 + +--S 1237 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +--+ +--+2 +--R | 2 | 2 +--R 4 +-+ |a |a +--R 2e \|3 |-- log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R 4 +-+ |a +--R e \|3 |-- +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R 4 |a \|b +--R 6e |-- atan(-----------------------------------) +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R + +--R 2 4 2 4 +-+ +--R (3d e x + 6c d e x)\|3 +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1237 + +--S 1238 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 4 +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 +-+3+-+2 3+-+ 3+-+ +--R - 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +--+ +--+2 +--R | 2 | 2 +--R 4 +-+ |a 3+-+2 |a +--R 2e \|3 |-- \|b log(b |-- + a d x + a c) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R - +--R +--+ +--R | 2 +--R 4 +-+ |a 3+-+2 +--R e \|3 |-- \|b +--R 3| 2 +--R \|b +--R * +--R +--+2 +--+ +--R | 2 | 2 +--R |a |a 2 2 2 +--R log((- b d x - b c) |-- + a |-- + a d x + 2a c d x + a c ) +--R 3| 2 3| 2 +--R \|b \|b +--R + +--R 3+-+ 3+-+ +--R 4 3+-+2 (2d x + 2c)\|b - \|a +--R 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +--+2 +--R | 2 +--R +-+ |a +-+ +--R +--+ b\|3 |-- + (- 2a d x - 2a c)\|3 +--R | 2 3| 2 +--R 4 |a 3+-+2 \|b 2 4 +-+3+-+2 +--R 6e |-- \|b atan(----------------------------------- - 3c e \|3 \|b +--R 3| 2 +--+2 +--R \|b | 2 +--R |a +--R 3b |-- +--R 3| 2 +--R \|b +--R / +--R +-+3+-+2 +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1238 + +--S 1239 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1239 + +)clear all + +--S 1240 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3) +--R +--R +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1240 + +--S 1241 of 1394 +r0:=e^3*x/b-1/3*a^(1/3)*e^3*log(a^(1/3)+b^(1/3)*(c+d*x))/(b^(4/3)*d)+_ + 1/6*a^(1/3)*e^3*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*_ + (c+d*x)^2)/(b^(4/3)*d)+a^(1/3)*e^3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R - 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ (2d x + 2c)\|b - \|a 3 +-+3+-+ +--R - 6e \|a atan(---------------------- + 6d e x\|3 \|b +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1241 + +--S 1242 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +---+ +---+2 +---+ +--R 3 +-+ | a | a | a 2 2 2 +--R - e \|3 3|- - log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R 3 +-+ | a | a +--R 2e \|3 3|- - log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R 3 | a \| b 3 +-+ +--R - 6e 3|- - atan(---------------------------- + 6d e x\|3 +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+ +--R 6b d\|3 +--R Type: Union(Expression(Integer),...) +--E 1242 + +--S 1243 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R 3 +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - e \|3 \|a log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 +-+3+-+ 3+-+ 3+-+ +--R 2e \|3 \|a log((d x + c)\|b + \|a ) +--R + +--R +---+ +---+2 +---+ +--R 3 +-+ | a 3+-+ | a | a 2 2 2 +--R - e \|3 3|- - \|b log(3|- - + (d x + c) 3|- - + d x + 2c d x + c ) +--R \| b \| b \| b +--R + +--R +---+ +---+ +--R 3 +-+ | a 3+-+ | a +--R 2e \|3 3|- - \|b log(- 3|- - + d x + c) +--R \| b \| b +--R + +--R 3+-+ 3+-+ +--R 3 3+-+ (2d x + 2c)\|b - \|a +--R 6e \|a atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +---+ +--R +-+ | a +-+ +--R +---+ \|3 3|- - + (2d x + 2c)\|3 +--R 3 | a 3+-+ \| b +--R - 6e 3|- - \|b atan(----------------------------) +--R \| b +---+ +--R | a +--R 3 3|- - +--R \| b +--R / +--R +-+3+-+ +--R 6b d\|3 \|b +--R Type: Expression(Integer) +--E 1243 + +--S 1244 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1244 + +)clear all + +--S 1245 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3) +--R +--R +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1245 + +--S 1246 of 1394 +r0:=1/3*e^2*log(a+b*(c+d*x)^3)/(b*d) +--R +--R +--R 2 3 3 2 2 2 3 +--R e log(b d x + 3b c d x + 3b c d x + b c + a) +--R (2) ----------------------------------------------- +--R 3b d +--R Type: Expression(Integer) +--E 1246 + +--S 1247 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 3 3 2 2 2 3 +--R e log(b d x + 3b c d x + 3b c d x + b c + a) +--R (3) ----------------------------------------------- +--R 3b d +--R Type: Union(Expression(Integer),...) +--E 1247 + +--S 1248 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1248 + +--S 1249 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1249 + +)clear all + +--S 1250 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3) +--R +--R +--R d e x + c e +--R (1) ---------------------------------------- +--R 3 3 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1250 + +--S 1251 of 1394 +r0:=-1/3*e*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(1/3)*b^(2/3)*d)+_ + 1/6*e*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(1/3)*b^(2/3)*d)-e*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(1/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e\|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R +-+ 3+-+ 3+-+ (2d x + 2c)\|b - \|a +--R - 2e\|3 log((d x + c)\|b + \|a ) + 6e atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +-+3+-+3+-+2 +--R 6d\|3 \|a \|b +--R Type: Expression(Integer) +--E 1251 + +--S 1252 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R +-+ +--R e\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+ 3| 2 +--R 2e\|3 log((d x + c)\|- a b + a b) +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 +--R 6d\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1252 + +--S 1253 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 6d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1253 + +--S 1254 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1254 + +)clear all + +--S 1255 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R ----------------------------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d e x + 4b c d e x + 6b c d e x + (4b c + a)d e x + (b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1255 + +--S 1256 of 1394 +r0:=log(c+d*x)/(a*d*e)-1/3*log(a+b*(c+d*x)^3)/(a*d*e) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (2) --------------------------------------------------------------- +--R 3a d e +--R Type: Expression(Integer) +--E 1256 + +--S 1257 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 3 3 2 2 2 3 +--R - log(b d x + 3b c d x + 3b c d x + b c + a) + 3log(d x + c) +--R (3) --------------------------------------------------------------- +--R 3a d e +--R Type: Union(Expression(Integer),...) +--E 1257 + +--S 1258 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1258 + +--S 1259 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1259 + +)clear all + +--S 1260 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 +--R b d e x + 5b c d e x + 10b c d e x + (10b c + a)d e x +--R + +--R 4 2 5 2 2 +--R (5b c + 2a c)d e x + (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1260 + +--S 1261 of 1394 +r0:=(-1)/(a*d*e^2*(c+d*x))+1/3*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*d*e^2)-1/6*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*d*e^2)+b^(1/3)*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R +-+3+-+ +--R (- d x - c)\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R (2d x + 2c)\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +-+3+-+ +--R (- 6d x - 6c)\|b atan(----------------------) - 6\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 2 2 2 +-+3+-+ +--R (6a d e x + 6a c d e )\|3 \|a +--R Type: Expression(Integer) +--E 1261 + +--S 1262 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +-+ +-+2 +--R +-+ |b |b +--R (2d x + 2c)\|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R +-+ +--R +-+ |b +--R (- d x - c)\|3 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +-+ +--R (6d x + 6c) 3|- atan(---------------------------------- - 6\|3 +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 2 2 +-+ +--R (6a d e x + 6a c d e )\|3 +--R Type: Union(Expression(Integer),...) +--E 1262 + +--S 1263 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 2\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R \|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 6\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 +-+3+-+ +--R 6a d e \|3 \|a +--R Type: Expression(Integer) +--E 1263 + +--S 1264 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1264 + +)clear all + +--S 1265 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + a)d e x +--R + +--R 4 2 3 2 5 2 3 6 3 3 +--R (15b c + 3a c)d e x + (6b c + 3a c )d e x + (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1265 + +--S 1266 of 1394 +r0:=(-1/2)/(a*d*e^3*(c+d*x)^2)-1/3*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*d*e^3)+1/6*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*d*e^3)+b^(2/3)*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 2 2 2 +-+3+-+2 +--R (d x + 2c d x + c )\|3 \|b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 2 2 +-+3+-+2 3+-+ 3+-+ +--R (- 2d x - 4c d x - 2c )\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 3+-+ 3+-+ +--R 2 2 2 3+-+2 (2d x + 2c)\|b - \|a +-+3+-+2 +--R (- 6d x - 12c d x - 6c )\|b atan(----------------------) - 3\|3 \|a +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 3 2 2 3 2 3 +-+3+-+2 +--R (6a d e x + 12a c d e x + 6a c d e )\|3 \|a +--R Type: Expression(Integer) +--E 1266 + +--S 1267 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R +----+ +--R | 2 +--R 2 2 2 +-+ | b +--R (- d x - 2c d x - c )\|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R 2 2 2 +-+ | b | b +--R (2d x + 4c d x + 2c )\|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R 2 2 2 | b \| a +--R (- 6d x - 12c d x - 6c ) |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R +-+ +--R - 3\|3 +--R / +--R 3 3 2 2 3 2 3 +-+ +--R (6a d e x + 12a c d e x + 6a c d e )\|3 +--R Type: Union(Expression(Integer),...) +--E 1267 + +--S 1268 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 2\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R \|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 2\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 6\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 6 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 +-+3+-+2 +--R 6a d e \|3 \|a +--R Type: Expression(Integer) +--E 1268 + +--S 1269 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1269 + +)clear all + +--S 1270 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)) +--R +--R +--R (1) +--R 1 +--R / +--R 7 4 7 6 4 6 2 5 4 5 3 4 4 4 +--R b d e x + 7b c d e x + 21b c d e x + (35b c + a)d e x +--R + +--R 4 3 4 3 5 2 2 4 2 6 3 4 +--R (35b c + 4a c)d e x + (21b c + 6a c )d e x + (7b c + 4a c )d e x +--R + +--R 7 4 4 +--R (b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1270 + +--S 1271 of 1394 +r0:=(-1/3)/(a*d*e^4*(c+d*x)^3)-b*log(c+d*x)/(a^2*d*e^4)+_ + 1/3*b*log(a+b*(c+d*x)^3)/(a^2*d*e^4) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 4 3 2 3 4 2 2 2 2 4 2 3 4 +--R 3a d e x + 9a c d e x + 9a c d e x + 3a c d e +--R Type: Expression(Integer) +--E 1271 + +--S 1272 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (b d x + 3b c d x + 3b c d x + b c ) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (- 3b d x - 9b c d x - 9b c d x - 3b c )log(d x + c) - a +--R / +--R 2 4 4 3 2 3 4 2 2 2 2 4 2 3 4 +--R 3a d e x + 9a c d e x + 9a c d e x + 3a c d e +--R Type: Union(Expression(Integer),...) +--E 1272 + +--S 1273 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1273 + +--S 1274 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1274 + +)clear all + +--S 1275 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1275 + +--S 1276 of 1394 +r0:=-1/3*e^4*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3))-2/9*e^4*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(1/3)*b^(5/3)*d)+1/9*e^4*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(1/3)*b^(5/3)*d)-_ + 2/3*e^4*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(1/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (b d e x + 3b c d e x + 3b c d e x + (b c + a)e )\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (- 2b d e x - 6b c d e x - 6b c d e x + (- 2b c - 2a)e )\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 4 2 4 2 4 +-+3+-+3+-+2 +--R (- 3d e x - 6c d e x - 3c e )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+3+-+2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1276 + +--S 1277 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 4 3 2 4 2 2 4 3 4 +--R (- 6b d e x - 18b c d e x - 18b c d e x + (- 6b c - 6a)e ) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 4 2 4 2 4 +-+3| 2 +--R (- 3d e x - 6c d e x - 3c e )\|3 \|- a b +--R / +--R +------+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (9b d x + 27b c d x + 27b c d x + (9b c + 9a b)d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1277 + +--S 1278 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R 4 +-+3| 2 +--R e \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R 4 +-+3| 2 3+-+ 3+-+ +--R 2e \|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R 4 +-+3+-+3+-+2 +--R e \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R 4 +-+3+-+3+-+2 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 4 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 4 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e \|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 9b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1278 + +--S 1279 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1279 + +)clear all + +--S 1280 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1280 + +--S 1281 of 1394 +r0:=-1/3*e^3*(c+d*x)/(b*d*(a+b*(c+d*x)^3))+1/9*e^3*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(2/3)*b^(4/3)*d)-1/18*e^3*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(2/3)*b^(4/3)*d)-_ + 1/3*e^3*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(2/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 +-+3+-+2 3+-+ +--R (- 6d e x - 6c e )\|3 \|a \|b +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3+-+2 3+-+ +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1281 + +--S 1282 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e )\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e )\|3 +--R * +--R +---+ +--R 3| 2 +--R log((d x + c)\|a b + a) +--R + +--R 3 3 3 2 3 2 2 3 3 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e ) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R 3 3 +-+3| 2 +--R (- 6d e x - 6c e )\|3 \|a b +--R / +--R +---+ +--R 2 4 3 2 3 2 2 2 2 2 3 +-+3| 2 +--R (18b d x + 54b c d x + 54b c d x + (18b c + 18a b)d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1282 + +--S 1283 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +-+3+-+2 3+-+ +--R e \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 +-+3+-+2 3+-+ 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R 3 +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R 3 +-+3| 2 3+-+ 3+-+ +--R - 2e \|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6e \|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 18b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1283 + +--S 1284 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1284 + +)clear all + +--S 1285 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1285 + +--S 1286 of 1394 +r0:=-1/3*e^2/(b*d*(a+b*(c+d*x)^3)) +--R +--R +--R 1 2 +--R - e +--R 3 +--R (2) - --------------------------------------------- +--R 2 4 3 2 3 2 2 2 2 2 3 +--R b d x + 3b c d x + 3b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1286 + +--S 1287 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 2 +--R e +--R (3) - ------------------------------------------------ +--R 2 4 3 2 3 2 2 2 2 2 3 +--R 3b d x + 9b c d x + 9b c d x + (3b c + 3a b)d +--R Type: Union(Expression(Integer),...) +--E 1287 + +--S 1288 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1288 + +--S 1289 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1289 + +)clear all + +--S 1290 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R d e x + c e +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1290 + +--S 1291 of 1394 +r0:=1/3*e*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3))-1/9*e*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(4/3)*b^(2/3)*d)+1/18*e*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(2/3)*d)-_ + 1/3*e*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (b d e x + 3b c d e x + 3b c d e x + (b c + a)e)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 2b d e x - 6b c d e x - 6b c d e x + (- 2b c - 2a)e)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d e x + 18b c d e x + 18b c d e x + (6b c + 6a)e) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 2 2 +-+3+-+3+-+2 +--R (6d e x + 12c d e x + 6c e)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+3+-+2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1291 + +--S 1292 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d e x - 3b c d e x - 3b c d e x + (- b c - a)e)\|3 +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d e x + 6b c d e x + 6b c d e x + (2b c + 2a)e)\|3 +--R * +--R +------+2 +--R 3| 2 +--R log((d x + c)\|- a b + a b) +--R + +--R 3 3 2 2 2 3 +--R (- 6b d e x - 18b c d e x - 18b c d e x + (- 6b c - 6a)e) +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R +------+ +--R 2 2 2 +-+3| 2 +--R (6d e x + 12c d e x + 6c e)\|3 \|- a b +--R / +--R +------+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (18a b d x + 54a b c d x + 54a b c d x + (18a b c + 18a )d)\|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1292 + +--S 1293 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 18a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1293 + +--S 1294 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1294 + +)clear all + +--S 1295 of 1394 +t0:=1/(a+b*(c+d*x)^3)^2 +--R +--R +--R (1) +--R 1 +--R / +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1295 + +--S 1296 of 1394 +r0:=1/3*(c+d*x)/(a*d*(a+b*(c+d*x)^3))+2/9*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(1/3)*d)-1/9*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(1/3)*d)-2/3*atan((a^(1/3)-_ + 2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/(a^(5/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 3 3 2 2 2 3 +-+ +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 +--R * +--R 3+-+ 3+-+ +--R log((d x + c)\|b + \|a ) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+3+-+2 3+-+ +--R (3d x + 3c)\|3 \|a \|b +--R / +--R 4 3 3 2 2 2 3 2 +-+3+-+2 3+-+ +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a \|b +--R Type: Expression(Integer) +--E 1296 + +--S 1297 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +-+ +--R (- b d x - 3b c d x - 3b c d x - b c - a)\|3 +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 3 2 2 2 3 +-+ 3| 2 +--R (2b d x + 6b c d x + 6b c d x + 2b c + 2a)\|3 log((d x + c)\|a b + a) +--R + +--R 3 3 2 2 2 3 +--R (6b d x + 18b c d x + 18b c d x + 6b c + 6a) +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R +---+ +--R +-+3| 2 +--R (3d x + 3c)\|3 \|a b +--R / +--R +---+ +--R 4 3 3 2 2 2 3 2 +-+3| 2 +--R (9a b d x + 27a b c d x + 27a b c d x + (9a b c + 9a )d)\|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1297 + +--S 1298 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 2\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 2\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 9a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1298 + +--S 1299 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1299 + +)clear all + +--S 1300 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R b d e x + 7b c d e x + 21b c d e x + (35b c + 2a b)d e x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (35b c + 8a b c)d e x + (21b c + 12a b c )d e x +--R + +--R 2 6 3 2 2 7 4 2 +--R (7b c + 8a b c + a )d e x + (b c + 2a b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1300 + +--S 1301 of 1394 +r0:=1/3/(a*d*e*(a+b*(c+d*x)^3))+log(c+d*x)/(a^2*d*e)-_ + 1/3*log(a+b*(c+d*x)^3)/(a^2*d*e) +--R +--R +--R (2) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d e x + 9a b c d e x + 9a b c d e x + (3a b c + 3a )d e +--R Type: Expression(Integer) +--E 1301 + +--S 1302 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 3 2 2 2 3 +--R (- b d x - 3b c d x - 3b c d x - b c - a) +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 3 2 2 2 3 +--R (3b d x + 9b c d x + 9b c d x + 3b c + 3a)log(d x + c) + a +--R / +--R 2 4 3 2 3 2 2 2 2 2 3 3 +--R 3a b d e x + 9a b c d e x + 9a b c d e x + (3a b c + 3a )d e +--R Type: Union(Expression(Integer),...) +--E 1302 + +--S 1303 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1303 + +--S 1304 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1304 + +)clear all + +--S 1305 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 8 2 8 2 7 2 7 2 2 6 2 6 2 3 5 2 5 +--R b d e x + 8b c d e x + 28b c d e x + (56b c + 2a b)d e x +--R + +--R 2 4 4 2 4 2 5 2 3 2 3 +--R (70b c + 10a b c)d e x + (56b c + 20a b c )d e x +--R + +--R 2 6 3 2 2 2 2 2 7 4 2 2 +--R (28b c + 20a b c + a )d e x + (8b c + 10a b c + 2a c)d e x +--R + +--R 2 8 5 2 2 2 +--R (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1305 + +--S 1306 of 1394 +r0:=(-4/3)/(a^2*d*e^2*(c+d*x))+1/3/(a*d*e^2*(c+d*x)*(a+b*(c+d*x)^3))+_ + 4/9*b^(1/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(7/3)*d*e^2)-_ + 2/9*b^(1/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(7/3)*d*e^2)+4/3*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(7/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - 12b d x - 48b c d x - 72b c d x + (- 48b c - 12a)d x - 12b c +--R + +--R - 12a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 \|a +--R / +--R 2 5 2 4 2 4 2 3 2 2 3 2 2 2 3 3 2 2 +--R 9a b d e x + 36a b c d e x + 54a b c d e x + (36a b c + 9a )d e x +--R + +--R 2 4 3 2 +--R (9a b c + 9a c)d e +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1306 + +--S 1307 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 4 4 3 3 2 2 2 3 4 +--R (4b d x + 16b c d x + 24b c d x + (16b c + 4a)d x + 4b c + 4a c) +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R (- 2b d x - 8b c d x - 12b c d x + (- 8b c - 2a)d x - 2b c - 2a c) +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 12b d x + 48b c d x + 72b c d x + (48b c + 12a)d x + 12b c +--R + +--R 12a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 12b d x - 36b c d x - 36b c d x - 12b c - 9a)\|3 +--R / +--R 2 5 2 4 2 4 2 3 2 2 3 2 2 2 3 3 2 2 +--R 9a b d e x + 36a b c d e x + 54a b c d e x + (36a b c + 9a )d e x +--R + +--R 2 4 3 2 +--R (9a b c + 9a c)d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1307 + +--S 1308 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 2\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 4\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 4\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 2\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 12\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 12\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 2 2 +-+3+-+ +--R 9a d e \|3 \|a +--R Type: Expression(Integer) +--E 1308 + +--S 1309 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1309 + +)clear all + +--S 1310 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 9 3 9 2 8 3 8 2 2 7 3 7 2 3 6 3 6 +--R b d e x + 9b c d e x + 36b c d e x + (84b c + 2a b)d e x +--R + +--R 2 4 5 3 5 2 5 2 4 3 4 +--R (126b c + 12a b c)d e x + (126b c + 30a b c )d e x +--R + +--R 2 6 3 2 3 3 3 2 7 4 2 2 3 2 +--R (84b c + 40a b c + a )d e x + (36b c + 30a b c + 3a c)d e x +--R + +--R 2 8 5 2 2 3 2 9 6 2 3 3 +--R (9b c + 12a b c + 3a c )d e x + (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1310 + +--S 1311 of 1394 +r0:=(-5/6)/(a^2*d*e^3*(c+d*x)^2)+1/3/(a*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3))-_ + 5/9*b^(2/3)*log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(8/3)*d*e^3)+_ + 5/18*b^(2/3)*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(8/3)*d*e^3)+5/3*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(8/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 5 5 4 4 2 3 3 3 2 2 +--R 5b d x + 25b c d x + 50b c d x + (50b c + 5a)d x +--R + +--R 4 5 2 +--R (25b c + 10a c)d x + 5b c + 5a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 10b d x - 50b c d x - 100b c d x + (- 100b c - 10a)d x +--R + +--R 4 5 2 +--R (- 50b c - 20a c)d x - 10b c - 10a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 3 3 2 2 2 3 +-+3+-+2 +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 \|a +--R / +--R 2 6 3 5 2 5 3 4 2 2 4 3 3 +--R 18a b d e x + 90a b c d e x + 180a b c d e x +--R + +--R 2 3 3 3 3 2 2 4 3 2 3 +--R (180a b c + 18a )d e x + (90a b c + 36a c)d e x +--R + +--R 2 5 3 2 3 +--R (18a b c + 18a c )d e +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1311 + +--S 1312 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 5 5 4 4 2 3 3 3 2 2 +--R - 5b d x - 25b c d x - 50b c d x + (- 50b c - 5a)d x +--R + +--R 4 5 2 +--R (- 25b c - 10a c)d x - 5b c - 5a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 10b d x + 50b c d x + 100b c d x + (100b c + 10a)d x +--R + +--R 4 5 2 +--R (50b c + 20a c)d x + 10b c + 10a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R - 30b d x - 150b c d x - 300b c d x + (- 300b c - 30a)d x +--R + +--R 4 5 2 +--R (- 150b c - 60a c)d x - 30b c - 30a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 3 3 2 2 2 3 +-+ +--R (- 15b d x - 45b c d x - 45b c d x - 15b c - 9a)\|3 +--R / +--R 2 6 3 5 2 5 3 4 2 2 4 3 3 +--R 18a b d e x + 90a b c d e x + 180a b c d e x +--R + +--R 2 3 3 3 3 2 2 4 3 2 3 +--R (180a b c + 18a )d e x + (90a b c + 36a c)d e x +--R + +--R 2 5 3 2 3 +--R (18a b c + 18a c )d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1312 + +--S 1313 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 5\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 10\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 5\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 10\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 30\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 30 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 2 3 +-+3+-+2 +--R 18a d e \|3 \|a +--R Type: Expression(Integer) +--E 1313 + +--S 1314 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1314 + +)clear all + +--S 1315 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)^2) +--R +--R +--R (1) +--R 1 +--R / +--R 2 10 4 10 2 9 4 9 2 2 8 4 8 2 3 7 4 7 +--R b d e x + 10b c d e x + 45b c d e x + (120b c + 2a b)d e x +--R + +--R 2 4 6 4 6 2 5 2 5 4 5 +--R (210b c + 14a b c)d e x + (252b c + 42a b c )d e x +--R + +--R 2 6 3 2 4 4 4 2 7 4 2 3 4 3 +--R (210b c + 70a b c + a )d e x + (120b c + 70a b c + 4a c)d e x +--R + +--R 2 8 5 2 2 2 4 2 2 9 6 2 3 4 +--R (45b c + 42a b c + 6a c )d e x + (10b c + 14a b c + 4a c )d e x +--R + +--R 2 10 7 2 4 4 +--R (b c + 2a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1315 + +--S 1316 of 1394 +r0:=(-2/3)/(a^2*d*e^4*(c+d*x)^3)+1/3/(a*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3))-_ + 2*b*log(c+d*x)/(a^3*d*e^4)+2/3*b*log(a+b*(c+d*x)^3)/(a^3*d*e^4) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 4 6 3 6 4 5 3 2 5 4 4 3 3 4 4 4 3 +--R 3a b d e x + 18a b c d e x + 45a b c d e x + (60a b c + 3a )d e x +--R + +--R 3 4 4 3 4 2 3 5 4 2 2 4 3 6 4 3 4 +--R (45a b c + 9a c)d e x + (18a b c + 9a c )d e x + (3a b c + 3a c )d e +--R Type: Expression(Integer) +--E 1316 + +--S 1317 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d x + 12b c d x + 30b c d x + (40b c + 2a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (30b c + 6a b c)d x + (12b c + 6a b c )d x + 2b c + 2a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 6b d x - 36b c d x - 90b c d x + (- 120b c - 6a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 90b c - 18a b c)d x + (- 36b c - 18a b c )d x - 6b c - 6a b c +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R - 2a b d x - 6a b c d x - 6a b c d x - 2a b c - a +--R / +--R 3 7 4 6 3 6 4 5 3 2 5 4 4 3 3 4 4 4 3 +--R 3a b d e x + 18a b c d e x + 45a b c d e x + (60a b c + 3a )d e x +--R + +--R 3 4 4 3 4 2 3 5 4 2 2 4 3 6 4 3 4 +--R (45a b c + 9a c)d e x + (18a b c + 9a c )d e x + (3a b c + 3a c )d e +--R Type: Union(Expression(Integer),...) +--E 1317 + +--S 1318 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1318 + +--S 1319 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1319 + +)clear all + +--S 1320 of 1394 +t0:=(c*e+d*e*x)^4/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 4 4 4 3 4 3 2 2 4 2 3 4 4 4 +--R d e x + 4c d e x + 6c d e x + 4c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1320 + +--S 1321 of 1394 +r0:=-1/6*e^4*(c+d*x)^2/(b*d*(a+b*(c+d*x)^3)^2)+1/9*e^4*(c+d*x)^2/_ + (a*b*d*(a+b*(c+d*x)^3))-1/27*e^4*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(4/3)*b^(5/3)*d)+1/54*e^4*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(4/3)*b^(5/3)*d)-1/9*e^4*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(4/3)*b^(5/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R b d e x + 6b c d e x + 15b c d e x + (20b c + 2a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (15b c + 6a b c)d e x + (6b c + 6a b c )d e x +--R + +--R 2 6 3 2 4 +--R (b c + 2a b c + a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - 2b d e x - 12b c d e x - 30b c d e x + (- 40b c - 4a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 30b c - 12a b c)d e x + (- 12b c - 12a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- 2b c - 4a b c - 2a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 4 +--R (6b c + 12a b c + 6a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 4 5 4 4 4 2 3 4 3 3 2 4 2 +--R 6b d e x + 30b c d e x + 60b c d e x + (60b c - 3a)d e x +--R + +--R 4 4 5 2 4 +--R (30b c - 6a c)d e x + (6b c - 3a c )e +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1321 + +--S 1322 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- b c - 2a b c - a )e +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 4 +--R (2b c + 4a b c + 2a )e +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 4 6 2 5 4 5 2 2 4 4 4 2 3 3 4 3 +--R - 6b d e x - 36b c d e x - 90b c d e x + (- 120b c - 12a b)d e x +--R + +--R 2 4 2 4 2 2 5 2 4 +--R (- 90b c - 36a b c)d e x + (- 36b c - 36a b c )d e x +--R + +--R 2 6 3 2 4 +--R (- 6b c - 12a b c - 6a )e +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 4 5 4 4 4 2 3 4 3 3 2 4 2 +--R 6b d e x + 30b c d e x + 60b c d e x + (60b c - 3a)d e x +--R + +--R 4 4 5 2 4 +--R (30b c - 6a c)d e x + (6b c - 3a c )e +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1322 + +--S 1323 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R 4 +-+3| 2 +--R e \|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R 4 +-+3| 2 3+-+ 3+-+ +--R 2e \|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R 4 +-+3+-+3+-+2 +--R e \|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R 4 +-+3+-+3+-+2 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 4 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 4 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e \|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R +-+3| 2 3+-+3+-+2 +--R 54a b d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1323 + +--S 1324 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1324 + +)clear all + +--S 1325 of 1394 +t0:=(c*e+d*e*x)^3/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 3 3 3 2 3 2 2 3 3 3 +--R d e x + 3c d e x + 3c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1325 + +--S 1326 of 1394 +r0:=-1/6*e^3*(c+d*x)/(b*d*(a+b*(c+d*x)^3)^2)+1/18*e^3*(c+d*x)/_ + (a*b*d*(a+b*(c+d*x)^3))+1/27*e^3*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(5/3)*b^(4/3)*d)-1/54*e^3*log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+_ + b^(2/3)*(c+d*x)^2)/(a^(5/3)*b^(4/3)*d)-1/9*e^3*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(5/3)*b^(4/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 3 +--R (- b c - 2a b c - a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 3 +--R (2b c + 4a b c + 2a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 3 +--R (6b c + 12a b c + 6a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 +--R 3b d e x + 12b c d e x + 18b c d e x + (12b c - 6a)d e x +--R + +--R 4 3 +--R (3b c - 6a c)e +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1326 + +--S 1327 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R - b d e x - 6b c d e x - 15b c d e x + (- 20b c - 2a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (- 15b c - 6a b c)d e x + (- 6b c - 6a b c )d e x +--R + +--R 2 6 3 2 3 +--R (- b c - 2a b c - a )e +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 3 +--R (2b c + 4a b c + 2a )e +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 3 6 2 5 3 5 2 2 4 3 4 2 3 3 3 3 +--R 6b d e x + 36b c d e x + 90b c d e x + (120b c + 12a b)d e x +--R + +--R 2 4 2 3 2 2 5 2 3 +--R (90b c + 36a b c)d e x + (36b c + 36a b c )d e x +--R + +--R 2 6 3 2 3 +--R (6b c + 12a b c + 6a )e +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 3 4 3 3 3 2 2 3 2 3 3 +--R 3b d e x + 12b c d e x + 18b c d e x + (12b c - 6a)d e x +--R + +--R 4 3 +--R (3b c - 6a c)e +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 2 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b )d x +--R + +--R 3 4 2 2 3 2 3 5 2 2 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 3 6 2 2 3 3 +--R (54a b c + 108a b c + 54a b)d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1327 + +--S 1328 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R 3 +-+3+-+2 3+-+ +--R e \|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R 3 +-+3+-+2 3+-+ 3| 2 +--R 2e \|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R 3 +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R e \|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R 3 +-+3| 2 3+-+ 3+-+ +--R - 2e \|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 6e \|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3 3| 2 (2d x + 2c)\|b - \|a +--R - 6e \|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R +-+3+-+2 3+-+3| 2 +--R 54a b d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1328 + +--S 1329 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1329 + +)clear all + +--S 1330 of 1394 +t0:=(c*e+d*e*x)^2/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 2 2 2 2 2 2 +--R d e x + 2c d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1330 + +--S 1331 of 1394 +r0:=-1/6*e^2/(b*d*(a+b*(c+d*x)^3)^2) +--R +--R +--R (2) +--R - +--R 1 2 +--R - e +--R 6 +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R b d x + 6b c d x + 15b c d x + (20b c + 2a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 3 6 2 3 2 +--R (15b c + 6a b c)d x + (6b c + 6a b c )d x + (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1331 + +--S 1332 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 2 +--R e +--R / +--R 3 7 6 3 6 5 3 2 5 4 3 3 2 4 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b )d x +--R + +--R 3 4 2 3 2 3 5 2 2 2 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x +--R + +--R 3 6 2 3 2 +--R (6b c + 12a b c + 6a b)d +--R Type: Union(Expression(Integer),...) +--E 1332 + +--S 1333 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1333 + +--S 1334 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1334 + +)clear all + +--S 1335 of 1394 +t0:=(c*e+d*e*x)/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R d e x + c e +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1335 + +--S 1336 of 1394 +r0:=1/6*e*(c+d*x)^2/(a*d*(a+b*(c+d*x)^3)^2)+2/9*e*(c+d*x)^2/_ + (a^2*d*(a+b*(c+d*x)^3))-2/27*e*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(7/3)*b^(2/3)*d)+1/27*e*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(7/3)*b^(2/3)*d)-2/9*e*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(7/3)*b^(2/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 2b d e x + 12b c d e x + 30b c d e x + (40b c + 4a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (30b c + 12a b c)d e x + (12b c + 12a b c )d e x +--R + +--R 2 6 3 2 +--R (2b c + 4a b c + 2a )e +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 4b d e x - 24b c d e x - 60b c d e x + (- 80b c - 8a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (- 60b c - 24a b c)d e x + (- 24b c - 24a b c )d e x +--R + +--R 2 6 3 2 +--R (- 4b c - 8a b c - 4a )e +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 12b d e x + 72b c d e x + 180b c d e x + (240b c + 24a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (180b c + 72a b c)d e x + (72b c + 72a b c )d e x +--R + +--R 2 6 3 2 +--R (12b c + 24a b c + 12a )e +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d e x + 60b c d e x + 120b c d e x + (120b c + 21a)d e x +--R + +--R 4 5 2 +--R (60b c + 42a c)d e x + (12b c + 21a c )e +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+3+-+2 +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1336 + +--S 1337 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d e x - 12b c d e x - 30b c d e x + (- 40b c - 4a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (- 30b c - 12a b c)d e x + (- 12b c - 12a b c )d e x +--R + +--R 2 6 3 2 +--R (- 2b c - 4a b c - 2a )e +--R * +--R +------+2 +------+ +--R +-+ 3| 2 2 2 2 3| 2 +--R \|3 log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 4b d e x + 24b c d e x + 60b c d e x + (80b c + 8a b)d e x +--R + +--R 2 4 2 2 2 5 2 +--R (60b c + 24a b c)d e x + (24b c + 24a b c )d e x +--R + +--R 2 6 3 2 +--R (4b c + 8a b c + 4a )e +--R * +--R +------+2 +--R +-+ 3| 2 +--R \|3 log((d x + c)\|- a b + a b) +--R + +--R 2 6 6 2 5 5 2 2 4 4 +--R - 12b d e x - 72b c d e x - 180b c d e x +--R + +--R 2 3 3 3 2 4 2 2 +--R (- 240b c - 24a b)d e x + (- 180b c - 72a b c)d e x +--R + +--R 2 5 2 2 6 3 2 +--R (- 72b c - 72a b c )d e x + (- 12b c - 24a b c - 12a )e +--R * +--R +------+2 +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|- a b - a b\|3 +--R atan(-----------------------------------) +--R 3a b +--R + +--R 5 5 4 4 2 3 3 3 2 2 +--R 12b d e x + 60b c d e x + 120b c d e x + (120b c + 21a)d e x +--R + +--R 4 5 2 +--R (60b c + 42a c)d e x + (12b c + 21a c )e +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +------+ +--R +-+3| 2 +--R \|3 \|- a b +--R Type: Union(Expression(Integer),...) +--E 1337 + +--S 1338 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +------+ +--R +-+3| 2 +--R e\|3 \|- a b +--R * +--R 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +------+ +--R +-+3| 2 3+-+ 3+-+ +--R 2e\|3 \|- a b log((d x + c)\|b + \|a ) +--R + +--R - +--R +-+3+-+3+-+2 +--R e\|3 \|a \|b +--R * +--R +------+2 +------+ +--R 3| 2 2 2 2 3| 2 +--R log((d x + c)\|- a b + (b d x + 2b c d x + b c )\|- a b - a b) +--R + +--R +------+2 +--R +-+3+-+3+-+2 3| 2 +--R 2e\|3 \|a \|b log((d x + c)\|- a b + a b) +--R + +--R +------+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 6e\|- a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +------+2 +--R +-+3| 2 +-+ +--R 3+-+3+-+2 (2d x + 2c)\|3 \|- a b - a b\|3 +--R - 6e\|a \|b atan(-----------------------------------) +--R 3a b +--R / +--R +------+ +--R 2 +-+3| 2 3+-+3+-+2 +--R 27a d\|3 \|- a b \|a \|b +--R Type: Expression(Integer) +--E 1338 + +--S 1339 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1339 + +)clear all + +--S 1340 of 1394 +t0:=1/(a+b*(c+d*x)^3)^3 +--R +--R +--R (1) +--R 1 +--R / +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R b d x + 9b c d x + 36b c d x + (84b c + 3a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (126b c + 18a b c)d x + (126b c + 45a b c )d x +--R + +--R 3 6 2 3 2 3 3 3 7 2 4 2 2 2 +--R (84b c + 60a b c + 3a b)d x + (36b c + 45a b c + 9a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 3 +--R (9b c + 18a b c + 9a b c )d x + b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1340 + +--S 1341 of 1394 +r0:=1/6*(c+d*x)/(a*d*(a+b*(c+d*x)^3)^2)+5/18*(c+d*x)/(a^2*d*_ + (a+b*(c+d*x)^3))+5/27*log(a^(1/3)+b^(1/3)*(c+d*x))/_ + (a^(8/3)*b^(1/3)*d)-5/54*log(a^(2/3)-a^(1/3)*b^(1/3)*_ + (c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(8/3)*b^(1/3)*d)-5/9*_ + atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(8/3)*b^(1/3)*d*sqrt(3)) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +-+ 3+-+ 3+-+ +--R \|3 log((d x + c)\|b + \|a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R 3+-+ 3+-+ +--R (2d x + 2c)\|b - \|a +--R atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +-+3+-+2 3+-+ +--R \|3 \|a \|b +--R Type: Expression(Integer) +--E 1341 + +--S 1342 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 5b d x - 30b c d x - 75b c d x + (- 100b c - 10a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 75b c - 30a b c)d x + (- 30b c - 30a b c )d x - 5b c +--R + +--R 3 2 +--R - 10a b c - 5a +--R * +--R +---+2 +---+ +--R +-+ 2 2 2 3| 2 3| 2 2 +--R \|3 log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 10b d x + 60b c d x + 150b c d x + (200b c + 20a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (150b c + 60a b c)d x + (60b c + 60a b c )d x + 10b c + 20a b c +--R + +--R 2 +--R 10a +--R * +--R +---+ +--R +-+ 3| 2 +--R \|3 log((d x + c)\|a b + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 30b d x + 180b c d x + 450b c d x + (600b c + 60a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (450b c + 180a b c)d x + (180b c + 180a b c )d x + 30b c +--R + +--R 3 2 +--R 60a b c + 30a +--R * +--R +---+ +--R +-+3| 2 +-+ +--R (2d x + 2c)\|3 \|a b - a\|3 +--R atan(-----------------------------) +--R 3a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R 15b d x + 60b c d x + 90b c d x + (60b c + 24a)d x + 15b c +--R + +--R 24a c +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R / +--R 2 2 7 6 2 2 6 5 2 2 2 5 4 2 2 3 3 4 3 +--R 54a b d x + 324a b c d x + 810a b c d x + (1080a b c + 108a b)d x +--R + +--R 2 2 4 3 3 2 2 2 5 3 2 2 +--R (810a b c + 324a b c)d x + (324a b c + 324a b c )d x +--R + +--R 2 2 6 3 3 4 +--R (54a b c + 108a b c + 54a )d +--R * +--R +---+ +--R +-+3| 2 +--R \|3 \|a b +--R Type: Union(Expression(Integer),...) +--E 1342 + +--S 1343 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R - +--R +-+3+-+2 3+-+ +--R 5\|3 \|a \|b +--R * +--R +---+2 +---+ +--R 2 2 2 3| 2 3| 2 2 +--R log((d x + 2c d x + c )\|a b + (- a d x - a c)\|a b + a ) +--R + +--R +---+ +--R +-+3+-+2 3+-+ 3| 2 +--R 10\|3 \|a \|b log((d x + c)\|a b + a) +--R + +--R +---+ +--R +-+3| 2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 5\|3 \|a b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 3+-+ 3+-+ +--R - 10\|3 \|a b log((d x + c)\|b + \|a ) +--R + +--R +---+ +--R +-+3| 2 +-+ +--R 3+-+2 3+-+ (2d x + 2c)\|3 \|a b - a\|3 +--R 30\|a \|b atan(-----------------------------) +--R 3a +--R + +--R +---+ 3+-+ 3+-+ +--R 3| 2 (2d x + 2c)\|b - \|a +--R - 30\|a b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R / +--R +---+ +--R 2 +-+3+-+2 3+-+3| 2 +--R 54a d\|3 \|a \|b \|a b +--R Type: Expression(Integer) +--E 1343 + +--S 1344 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1344 + +)clear all + +--S 1345 of 1394 +t0:=1/((c*e+d*e*x)*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 10 10 3 9 9 3 2 8 8 3 3 2 7 7 +--R b d e x + 10b c d e x + 45b c d e x + (120b c + 3a b )d e x +--R + +--R 3 4 2 6 6 3 5 2 2 5 5 +--R (210b c + 21a b c)d e x + (252b c + 63a b c )d e x +--R + +--R 3 6 2 3 2 4 4 +--R (210b c + 105a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 3 3 +--R (120b c + 105a b c + 12a b c)d e x +--R + +--R 3 8 2 5 2 2 2 2 +--R (45b c + 63a b c + 18a b c )d e x +--R + +--R 3 9 2 6 2 3 3 +--R (10b c + 21a b c + 12a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 +--R (b c + 3a b c + 3a b c + a c)e +--R Type: Fraction(Polynomial(Integer)) +--E 1345 + +--S 1346 of 1394 +r0:=1/6/(a*d*e*(a+b*(c+d*x)^3)^2)+1/3/(a^2*d*e*(a+b*(c+d*x)^3))+_ + log(c+d*x)/(a^3*d*e)-1/3*log(a+b*(c+d*x)^3)/(a^3*d*e) +--R +--R +--R (2) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d e x + 36a b c d e x + 90a b c d e x + (120a b c + 12a b)d e x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d e x + (36a b c + 36a b c )d e x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d e +--R Type: Expression(Integer) +--E 1346 + +--S 1347 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 2b d x - 12b c d x - 30b c d x + (- 40b c - 4a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (- 30b c - 12a b c)d x + (- 12b c - 12a b c )d x - 2b c - 4a b c +--R + +--R 2 +--R - 2a +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R 6b d x + 36b c d x + 90b c d x + (120b c + 12a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 3 +--R (90b c + 36a b c)d x + (36b c + 36a b c )d x + 6b c + 12a b c +--R + +--R 2 +--R 6a +--R * +--R log(d x + c) +--R + +--R 3 3 2 2 2 3 2 +--R 2a b d x + 6a b c d x + 6a b c d x + 2a b c + 3a +--R / +--R 3 2 7 6 3 2 6 5 3 2 2 5 4 3 2 3 4 4 3 +--R 6a b d e x + 36a b c d e x + 90a b c d e x + (120a b c + 12a b)d e x +--R + +--R 3 2 4 4 3 2 3 2 5 4 2 2 +--R (90a b c + 36a b c)d e x + (36a b c + 36a b c )d e x +--R + +--R 3 2 6 4 3 5 +--R (6a b c + 12a b c + 6a )d e +--R Type: Union(Expression(Integer),...) +--E 1347 + +--S 1348 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1348 + +--S 1349 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1349 + +)clear all + +--S 1350 of 1394 +t0:=1/((c*e+d*e*x)^2*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 11 2 11 3 10 2 10 3 2 9 2 9 3 3 2 8 2 8 +--R b d e x + 11b c d e x + 55b c d e x + (165b c + 3a b )d e x +--R + +--R 3 4 2 7 2 7 3 5 2 2 6 2 6 +--R (330b c + 24a b c)d e x + (462b c + 84a b c )d e x +--R + +--R 3 6 2 3 2 5 2 5 +--R (462b c + 168a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 4 2 4 +--R (330b c + 210a b c + 15a b c)d e x +--R + +--R 3 8 2 5 2 2 3 2 3 +--R (165b c + 168a b c + 30a b c )d e x +--R + +--R 3 9 2 6 2 3 3 2 2 2 +--R (55b c + 84a b c + 30a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 +--R (11b c + 24a b c + 15a b c + 2a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 2 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1350 + +--S 1351 of 1394 +r0:=(-14/9)/(a^3*d*e^2*(c+d*x))+1/6/(a*d*e^2*(c+d*x)*(a+b*(c+d*x)^3)^2)+_ + 7/18/(a^2*d*e^2*(c+d*x)*(a+b*(c+d*x)^3))+14/27*b^(1/3)*_ + log(a^(1/3)+b^(1/3)*(c+d*x))/(a^(10/3)*d*e^2)-7/27*b^(1/3)*_ + log(a^(2/3)-a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/_ + (a^(10/3)*d*e^2)+14/9*b^(1/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/_ + (a^(1/3)*sqrt(3)))/(a^(10/3)*d*e^2*sqrt(3)) +--R +--R +--R (2) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+3+-+ 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 84b d x - 588b c d x - 1764b c d x + (- 2940b c - 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 2940b c - 672a b c)d x + (- 1764b c - 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 588b c - 672a b c - 84a )d x - 84b c - 168a b c - 84a c +--R * +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+3+-+ +--R \|3 \|a +--R / +--R 3 2 8 2 7 3 2 7 2 6 3 2 2 6 2 5 +--R 54a b d e x + 378a b c d e x + 1134a b c d e x +--R + +--R 3 2 3 4 5 2 4 3 2 4 4 4 2 3 +--R (1890a b c + 108a b)d e x + (1890a b c + 432a b c)d e x +--R + +--R 3 2 5 4 2 3 2 2 3 2 6 4 3 5 2 2 +--R (1134a b c + 648a b c )d e x + (378a b c + 432a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 +--R (54a b c + 108a b c + 54a c)d e +--R * +--R +-+3+-+ +--R \|3 \|a +--R Type: Expression(Integer) +--E 1351 + +--S 1352 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 28b d x + 196b c d x + 588b c d x + (980b c + 56a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (980b c + 224a b c)d x + (588b c + 336a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (196b c + 224a b c + 28a )d x + 28b c + 56a b c + 28a c +--R * +--R +-+ +-+2 +--R +-+ |b |b +--R \|3 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R - 14b d x - 98b c d x - 294b c d x + (- 490b c - 28a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (- 490b c - 112a b c)d x + (- 294b c - 168a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (- 98b c - 112a b c - 14a )d x - 14b c - 28a b c - 14a c +--R * +--R +-+ +-+2 +-+ +--R +-+ |b |b |b 2 2 2 +--R \|3 3|- log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a \|a +--R + +--R 2 7 7 2 6 6 2 2 5 5 2 3 4 4 +--R 84b d x + 588b c d x + 1764b c d x + (2940b c + 168a b)d x +--R + +--R 2 4 3 3 2 5 2 2 2 +--R (2940b c + 672a b c)d x + (1764b c + 1008a b c )d x +--R + +--R 2 6 3 2 2 7 4 2 +--R (588b c + 672a b c + 84a )d x + 84b c + 168a b c + 84a c +--R * +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R |b \|a +--R 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 84b d x - 504b c d x - 1260b c d x + (- 1680b c - 147a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 1260b c - 441a b c)d x + (- 504b c - 441a b c )d x - 84b c +--R + +--R 3 2 +--R - 147a b c - 54a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 8 2 7 3 2 7 2 6 3 2 2 6 2 5 +--R 54a b d e x + 378a b c d e x + 1134a b c d e x +--R + +--R 3 2 3 4 5 2 4 3 2 4 4 4 2 3 +--R (1890a b c + 108a b)d e x + (1890a b c + 432a b c)d e x +--R + +--R 3 2 5 4 2 3 2 2 3 2 6 4 3 5 2 2 +--R (1134a b c + 648a b c )d e x + (378a b c + 432a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 +--R (54a b c + 108a b c + 54a c)d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1352 + +--S 1353 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+ 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R 7\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+ 3+-+ 3+-+ +--R - 14\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R +-+ +-+2 +--R +-+3+-+ |b |b +--R 14\|3 \|a 3|- log(a 3|- + b d x + b c) +--R \|a \|a +--R + +--R - +--R +-+ +--R +-+3+-+ |b +--R 7\|3 \|a 3|- +--R \|a +--R * +--R +-+2 +-+ +--R |b |b 2 2 2 +--R log((- a d x - a c) 3|- + a 3|- + b d x + 2b c d x + b c ) +--R \|a \|a +--R + +--R 3+-+ 3+-+ +--R 3+-+ (2d x + 2c)\|b - \|a +--R 42\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +-+2 +--R +-+ |b +-+ +--R +-+ a\|3 3|- + (- 2b d x - 2b c)\|3 +--R 3+-+ |b \|a +--R 42\|a 3|- atan(----------------------------------) +--R \|a +-+2 +--R |b +--R 3a 3|- +--R \|a +--R / +--R 3 2 +-+3+-+ +--R 27a d e \|3 \|a +--R Type: Expression(Integer) +--E 1353 + +--S 1354 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1354 + +)clear all + +--S 1355 of 1394 +t0:=1/((c*e+d*e*x)^3*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 12 3 12 3 11 3 11 3 2 10 3 10 3 3 2 9 3 9 +--R b d e x + 12b c d e x + 66b c d e x + (220b c + 3a b )d e x +--R + +--R 3 4 2 8 3 8 3 5 2 2 7 3 7 +--R (495b c + 27a b c)d e x + (792b c + 108a b c )d e x +--R + +--R 3 6 2 3 2 6 3 6 +--R (924b c + 252a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 5 3 5 +--R (792b c + 378a b c + 18a b c)d e x +--R + +--R 3 8 2 5 2 2 4 3 4 +--R (495b c + 378a b c + 45a b c )d e x +--R + +--R 3 9 2 6 2 3 3 3 3 3 +--R (220b c + 252a b c + 60a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 2 3 2 +--R (66b c + 108a b c + 45a b c + 3a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 3 +--R (12b c + 27a b c + 18a b c + 3a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 3 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1355 + +--S 1356 of 1394 +r0:=(-10/9)/(a^3*d*e^3*(c+d*x)^2)+1/6/(a*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3)^2)+_ + 4/9/(a^2*d*e^3*(c+d*x)^2*(a+b*(c+d*x)^3))-20/27*b^(2/3)*log(a^(1/3)+_ + b^(1/3)*(c+d*x))/(a^(11/3)*d*e^3)+10/27*b^(2/3)*log(a^(2/3)-_ + a^(1/3)*b^(1/3)*(c+d*x)+b^(2/3)*(c+d*x)^2)/(a^(11/3)*d*e^3)+_ + 20/9*b^(2/3)*atan((a^(1/3)-2*b^(1/3)*(c+d*x))/(a^(1/3)*sqrt(3)))/_ + (a^(11/3)*d*e^3*sqrt(3)) +--R +--R +--R (2) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 20b d x + 160b c d x + 560b c d x + (1120b c + 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (1400b c + 200a b c)d x + (1120b c + 400a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (560b c + 400a b c + 20a )d x + (160b c + 200a b c + 40a c)d x +--R + +--R 2 8 5 2 2 +--R 20b c + 40a b c + 20a c +--R * +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R \|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 40b d x - 320b c d x - 1120b c d x + (- 2240b c - 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 2800b c - 400a b c)d x + (- 2240b c - 800a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 1120b c - 800a b c - 40a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 320b c - 400a b c - 80a c)d x - 40b c - 80a b c - 40a c +--R * +--R +-+3+-+2 3+-+ 3+-+ +--R \|3 \|b log((d x + c)\|b + \|a ) +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R \|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+3+-+2 +--R \|3 \|a +--R / +--R 3 2 9 3 8 3 2 8 3 7 3 2 2 7 3 6 +--R 54a b d e x + 432a b c d e x + 1512a b c d e x +--R + +--R 3 2 3 4 6 3 5 3 2 4 4 5 3 4 +--R (3024a b c + 108a b)d e x + (3780a b c + 540a b c)d e x +--R + +--R 3 2 5 4 2 4 3 3 +--R (3024a b c + 1080a b c )d e x +--R + +--R 3 2 6 4 3 5 3 3 2 +--R (1512a b c + 1080a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 3 +--R (432a b c + 540a b c + 108a c)d e x +--R + +--R 3 2 8 4 5 5 2 3 +--R (54a b c + 108a b c + 54a c )d e +--R * +--R +-+3+-+2 +--R \|3 \|a +--R Type: Expression(Integer) +--E 1356 + +--S 1357 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 20b d x - 160b c d x - 560b c d x + (- 1120b c - 40a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 1400b c - 200a b c)d x + (- 1120b c - 400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 560b c - 400a b c - 20a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 160b c - 200a b c - 40a c)d x - 20b c - 40a b c - 20a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +--R \|3 |- -- +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R 40b d x + 320b c d x + 1120b c d x + (2240b c + 80a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (2800b c + 400a b c)d x + (2240b c + 800a b c )d x +--R + +--R 2 6 3 2 2 2 2 7 4 2 +--R (1120b c + 800a b c + 40a )d x + (320b c + 400a b c + 80a c)d x +--R + +--R 2 8 5 2 2 +--R 40b c + 80a b c + 40a c +--R * +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b | b +--R \|3 |- -- log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 +--R - 120b d x - 960b c d x - 3360b c d x + (- 6720b c - 240a b)d x +--R + +--R 2 4 4 4 2 5 2 3 3 +--R (- 8400b c - 1200a b c)d x + (- 6720b c - 2400a b c )d x +--R + +--R 2 6 3 2 2 2 +--R (- 3360b c - 2400a b c - 120a )d x +--R + +--R 2 7 4 2 2 8 5 2 2 +--R (- 960b c - 1200a b c - 240a c)d x - 120b c - 240a b c - 120a c +--R * +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b \| a +--R |- -- atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 3 3 +--R - 60b d x - 360b c d x - 900b c d x + (- 1200b c - 96a b)d x +--R + +--R 2 4 2 2 2 5 2 2 6 +--R (- 900b c - 288a b c)d x + (- 360b c - 288a b c )d x - 60b c +--R + +--R 3 2 +--R - 96a b c - 27a +--R * +--R +-+ +--R \|3 +--R / +--R 3 2 9 3 8 3 2 8 3 7 3 2 2 7 3 6 +--R 54a b d e x + 432a b c d e x + 1512a b c d e x +--R + +--R 3 2 3 4 6 3 5 3 2 4 4 5 3 4 +--R (3024a b c + 108a b)d e x + (3780a b c + 540a b c)d e x +--R + +--R 3 2 5 4 2 4 3 3 +--R (3024a b c + 1080a b c )d e x +--R + +--R 3 2 6 4 3 5 3 3 2 +--R (1512a b c + 1080a b c + 54a )d e x +--R + +--R 3 2 7 4 4 5 2 3 +--R (432a b c + 540a b c + 108a c)d e x +--R + +--R 3 2 8 4 5 5 2 3 +--R (54a b c + 108a b c + 54a c )d e +--R * +--R +-+ +--R \|3 +--R Type: Union(Expression(Integer),...) +--E 1357 + +--S 1358 of 1394 +m0:=a0-r0 +--R +--R +--R (4) +--R +-+3+-+2 2 2 2 3+-+2 3+-+3+-+ 3+-+2 +--R - 10\|3 \|b log((d x + 2c d x + c )\|b + (- d x - c)\|a \|b + \|a ) +--R + +--R +-+3+-+2 3+-+ 3+-+ +--R 20\|3 \|b log((d x + c)\|b + \|a ) +--R + +--R - +--R +----+ +--R | 2 +--R +-+ | b 3+-+2 +--R 10\|3 |- -- \|a +--R 3| 2 +--R \| a +--R * +--R +----+2 +----+ +--R | 2 | 2 +--R 2 | b | b 2 2 2 2 2 2 +--R log(a |- -- + (a b d x + a b c) |- -- + b d x + 2b c d x + b c ) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R +----+ +----+ +--R | 2 | 2 +--R +-+ | b 3+-+2 | b +--R 20\|3 |- -- \|a log(- a |- -- + b d x + b c) +--R 3| 2 3| 2 +--R \| a \| a +--R + +--R 3+-+ 3+-+ +--R 3+-+2 (2d x + 2c)\|b - \|a +--R 60\|b atan(----------------------) +--R +-+3+-+ +--R \|3 \|a +--R + +--R +----+ +--R | 2 +--R +-+ | b +-+ +--R +----+ a\|3 |- -- + (2b d x + 2b c)\|3 +--R | 2 3| 2 +--R | b 3+-+2 \| a +--R - 60 |- -- \|a atan(----------------------------------) +--R 3| 2 +----+ +--R \| a | 2 +--R | b +--R 3a |- -- +--R 3| 2 +--R \| a +--R / +--R 3 3 +-+3+-+2 +--R 27a d e \|3 \|a +--R Type: Expression(Integer) +--E 1358 + +--S 1359 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1359 + +)clear all + +--S 1360 of 1394 +t0:=1/((c*e+d*e*x)^4*(a+b*(c+d*x)^3)^3) +--R +--R +--R (1) +--R 1 +--R / +--R 3 13 4 13 3 12 4 12 3 2 11 4 11 3 3 2 10 4 10 +--R b d e x + 13b c d e x + 78b c d e x + (286b c + 3a b )d e x +--R + +--R 3 4 2 9 4 9 3 5 2 2 8 4 8 +--R (715b c + 30a b c)d e x + (1287b c + 135a b c )d e x +--R + +--R 3 6 2 3 2 7 4 7 +--R (1716b c + 360a b c + 3a b)d e x +--R + +--R 3 7 2 4 2 6 4 6 +--R (1716b c + 630a b c + 21a b c)d e x +--R + +--R 3 8 2 5 2 2 5 4 5 +--R (1287b c + 756a b c + 63a b c )d e x +--R + +--R 3 9 2 6 2 3 3 4 4 4 +--R (715b c + 630a b c + 105a b c + a )d e x +--R + +--R 3 10 2 7 2 4 3 3 4 3 +--R (286b c + 360a b c + 105a b c + 4a c)d e x +--R + +--R 3 11 2 8 2 5 3 2 2 4 2 +--R (78b c + 135a b c + 63a b c + 6a c )d e x +--R + +--R 3 12 2 9 2 6 3 3 4 +--R (13b c + 30a b c + 21a b c + 4a c )d e x +--R + +--R 3 13 2 10 2 7 3 4 4 +--R (b c + 3a b c + 3a b c + a c )e +--R Type: Fraction(Polynomial(Integer)) +--E 1360 + +--S 1361 of 1394 +r0:=(-1)/(a^3*d*e^4*(c+d*x)^3)+1/6/(a*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3)^2)+_ + 1/2/(a^2*d*e^4*(c+d*x)^3*(a+b*(c+d*x)^3))-3*b*log(c+d*x)/(a^4*d*e^4)+_ + b*log(a+b*(c+d*x)^3)/(a^4*d*e^4) +--R +--R +--R (2) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 4 9 4 2 9 4 8 4 2 2 8 4 7 +--R 6a b d e x + 54a b c d e x + 216a b c d e x +--R + +--R 4 2 3 5 7 4 6 4 2 4 5 6 4 5 +--R (504a b c + 12a b)d e x + (756a b c + 72a b c)d e x +--R + +--R 4 2 5 5 2 5 4 4 4 2 6 5 3 6 4 4 3 +--R (756a b c + 180a b c )d e x + (504a b c + 240a b c + 6a )d e x +--R + +--R 4 2 7 5 4 6 3 4 2 +--R (216a b c + 180a b c + 18a c)d e x +--R + +--R 4 2 8 5 5 6 2 2 4 4 2 9 5 6 6 3 4 +--R (54a b c + 72a b c + 18a c )d e x + (6a b c + 12a b c + 6a c )d e +--R Type: Expression(Integer) +--E 1361 + +--S 1362 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R 6b d x + 54b c d x + 216b c d x + (504b c + 12a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (756b c + 72a b c)d x + (756b c + 180a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (504b c + 240a b c + 6a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (216b c + 180a b c + 18a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (54b c + 72a b c + 18a b c )d x + 6b c + 12a b c + 6a b c +--R * +--R 3 3 2 2 2 3 +--R log(b d x + 3b c d x + 3b c d x + b c + a) +--R + +--R 3 9 9 3 8 8 3 2 7 7 3 3 2 6 6 +--R - 18b d x - 162b c d x - 648b c d x + (- 1512b c - 36a b )d x +--R + +--R 3 4 2 5 5 3 5 2 2 4 4 +--R (- 2268b c - 216a b c)d x + (- 2268b c - 540a b c )d x +--R + +--R 3 6 2 3 2 3 3 +--R (- 1512b c - 720a b c - 18a b)d x +--R + +--R 3 7 2 4 2 2 2 +--R (- 648b c - 540a b c - 54a b c)d x +--R + +--R 3 8 2 5 2 2 3 9 2 6 2 3 +--R (- 162b c - 216a b c - 54a b c )d x - 18b c - 36a b c - 18a b c +--R * +--R log(d x + c) +--R + +--R 2 6 6 2 5 5 2 2 4 4 2 3 2 3 3 +--R - 6a b d x - 36a b c d x - 90a b c d x + (- 120a b c - 9a b)d x +--R + +--R 2 4 2 2 2 2 5 2 2 2 6 +--R (- 90a b c - 27a b c)d x + (- 36a b c - 27a b c )d x - 6a b c +--R + +--R 2 3 3 +--R - 9a b c - 2a +--R / +--R 4 2 10 4 9 4 2 9 4 8 4 2 2 8 4 7 +--R 6a b d e x + 54a b c d e x + 216a b c d e x +--R + +--R 4 2 3 5 7 4 6 4 2 4 5 6 4 5 +--R (504a b c + 12a b)d e x + (756a b c + 72a b c)d e x +--R + +--R 4 2 5 5 2 5 4 4 4 2 6 5 3 6 4 4 3 +--R (756a b c + 180a b c )d e x + (504a b c + 240a b c + 6a )d e x +--R + +--R 4 2 7 5 4 6 3 4 2 +--R (216a b c + 180a b c + 18a c)d e x +--R + +--R 4 2 8 5 5 6 2 2 4 4 2 9 5 6 6 3 4 +--R (54a b c + 72a b c + 18a c )d e x + (6a b c + 12a b c + 6a c )d e +--R Type: Union(Expression(Integer),...) +--E 1362 + +--S 1363 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1363 + +--S 1364 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1364 + +)clear all + +--S 1365 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4) +--R +--R +--R (1) +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 +--R b d x + 7b c d x + 21b c d x + 35b c d x + (35b c + a)d x +--R + +--R 5 2 2 6 2 7 3 +--R (21b c + 3a c)d x + (7b c + 3a c )d x + b c + a c +--R Type: Polynomial(Integer) +--E 1365 + +--S 1366 of 1394 +r0:=1/4*a*(c+d*x)^4/d+1/8*b*(c+d*x)^8/d +--R +--R +--R (2) +--R 1 8 8 7 7 7 2 6 6 3 5 5 35 4 1 4 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 3 3 7 6 3 2 2 2 7 3 1 8 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )d x + - b c +--R 2 2 8 +--R + +--R 1 4 +--R - a c +--R 4 +--R / +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1366 + +--S 1367 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 7 8 6 7 7 2 5 6 3 4 5 35 4 1 3 4 +--R - b d x + b c d x + - b c d x + 7b c d x + (-- b c + - a)d x +--R 8 2 4 4 +--R + +--R 5 2 3 7 6 3 2 2 7 3 +--R (7b c + a c)d x + (- b c + - a c )d x + (b c + a c )x +--R 2 2 +--R Type: Polynomial(Fraction(Integer)) +--E 1367 + +--S 1368 of 1394 +m0:=a0-r0 +--R +--R +--R 1 8 1 4 +--R - - b c - - a c +--R 8 4 +--R (4) ----------------- +--R d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1368 + +--S 1369 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1369 + +)clear all + +--S 1370 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4)^2 +--R +--R +--R (1) +--R 2 11 11 2 10 10 2 2 9 9 2 3 8 8 2 4 7 7 +--R b d x + 11b c d x + 55b c d x + 165b c d x + (330b c + 2a b)d x +--R + +--R 2 5 6 6 2 6 2 5 5 +--R (462b c + 14a b c)d x + (462b c + 42a b c )d x +--R + +--R 2 7 3 4 4 2 8 4 2 3 3 +--R (330b c + 70a b c )d x + (165b c + 70a b c + a )d x +--R + +--R 2 9 5 2 2 2 2 10 6 2 2 2 11 +--R (55b c + 42a b c + 3a c)d x + (11b c + 14a b c + 3a c )d x + b c +--R + +--R 7 2 3 +--R 2a b c + a c +--R Type: Polynomial(Integer) +--E 1370 + +--S 1371 of 1394 +r0:=1/12*(a+b*(c+d*x)^4)^3/(b*d) +--R +--R +--R (2) +--R 1 3 12 12 3 11 11 11 3 2 10 10 55 3 3 9 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 3 4 1 2 8 8 3 5 2 7 7 3 6 2 2 6 6 +--R (--- b c + - a b )d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 3 7 2 3 5 5 165 3 8 35 2 4 1 2 4 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a b)d x +--R 4 2 4 +--R + +--R 55 3 9 2 5 2 3 3 11 3 10 2 6 3 2 2 2 2 +--R (-- b c + 14a b c + a b c)d x + (-- b c + 7a b c + - a b c )d x +--R 3 2 2 +--R + +--R 3 11 2 7 2 3 1 3 12 1 2 8 1 2 4 1 3 +--R (b c + 2a b c + a b c )d x + -- b c + - a b c + - a b c + -- a +--R 12 4 4 12 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1371 + +--S 1372 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 2 11 12 2 10 11 11 2 2 9 10 55 2 3 8 9 +--R -- b d x + b c d x + -- b c d x + -- b c d x +--R 12 2 3 +--R + +--R 165 2 4 1 7 8 2 5 6 7 2 6 2 5 6 +--R (--- b c + - a b)d x + (66b c + 2a b c)d x + (77b c + 7a b c )d x +--R 4 4 +--R + +--R 2 7 3 4 5 165 2 8 35 4 1 2 3 4 +--R (66b c + 14a b c )d x + (--- b c + -- a b c + - a )d x +--R 4 2 4 +--R + +--R 55 2 9 5 2 2 3 11 2 10 6 3 2 2 2 +--R (-- b c + 14a b c + a c)d x + (-- b c + 7a b c + - a c )d x +--R 3 2 2 +--R + +--R 2 11 7 2 3 +--R (b c + 2a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1372 + +--S 1373 of 1394 +m0:=a0-r0 +--R +--R +--R 1 3 12 1 2 8 1 2 4 1 3 +--R - -- b c - - a b c - - a b c - -- a +--R 12 4 4 12 +--R (4) ---------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1373 + +--S 1374 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1374 + +)clear all + +--S 1375 of 1394 +t0:=(c+d*x)^3*(a+b*(c+d*x)^4)^3 +--R +--R +--R (1) +--R 3 15 15 3 14 14 3 2 13 13 3 3 12 12 +--R b d x + 15b c d x + 105b c d x + 455b c d x +--R + +--R 3 4 2 11 11 3 5 2 10 10 +--R (1365b c + 3a b )d x + (3003b c + 33a b c)d x +--R + +--R 3 6 2 2 9 9 3 7 2 3 8 8 +--R (5005b c + 165a b c )d x + (6435b c + 495a b c )d x +--R + +--R 3 8 2 4 2 7 7 3 9 2 5 2 6 6 +--R (6435b c + 990a b c + 3a b)d x + (5005b c + 1386a b c + 21a b c)d x +--R + +--R 3 10 2 6 2 2 5 5 +--R (3003b c + 1386a b c + 63a b c )d x +--R + +--R 3 11 2 7 2 3 4 4 +--R (1365b c + 990a b c + 105a b c )d x +--R + +--R 3 12 2 8 2 4 3 3 3 +--R (455b c + 495a b c + 105a b c + a )d x +--R + +--R 3 13 2 9 2 5 3 2 2 +--R (105b c + 165a b c + 63a b c + 3a c)d x +--R + +--R 3 14 2 10 2 6 3 2 3 15 2 11 2 7 +--R (15b c + 33a b c + 21a b c + 3a c )d x + b c + 3a b c + 3a b c +--R + +--R 3 3 +--R a c +--R Type: Polynomial(Integer) +--E 1375 + +--S 1376 of 1394 +r0:=1/16*(a+b*(c+d*x)^4)^4/(b*d) +--R +--R +--R (2) +--R 1 4 16 16 4 15 15 15 4 2 14 14 4 3 13 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 4 4 1 3 12 12 4 5 3 11 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 4 6 33 3 2 10 10 4 7 3 3 9 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 4 8 495 3 4 3 2 2 8 8 +--R (---- b c + --- a b c + - a b )d x +--R 8 4 8 +--R + +--R 4 9 3 5 2 2 7 7 +--R (715b c + 198a b c + 3a b c)d x +--R + +--R 1001 4 10 3 6 21 2 2 2 6 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 4 11 3 7 2 2 3 5 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 4 12 495 3 8 105 2 2 4 1 3 4 4 +--R (--- b c + --- a b c + --- a b c + - a b)d x +--R 4 4 4 4 +--R + +--R 4 13 3 9 2 2 5 3 3 3 +--R (35b c + 55a b c + 21a b c + a b c)d x +--R + +--R 15 4 14 33 3 10 21 2 2 6 3 3 2 2 2 +--R (-- b c + -- a b c + -- a b c + - a b c )d x +--R 2 2 2 2 +--R + +--R 4 15 3 11 2 2 7 3 3 1 4 16 1 3 12 +--R (b c + 3a b c + 3a b c + a b c )d x + -- b c + - a b c +--R 16 4 +--R + +--R 3 2 2 8 1 3 4 1 4 +--R - a b c + - a b c + -- a +--R 8 4 16 +--R / +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1376 + +--S 1377 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R 1 3 15 16 3 14 15 15 3 2 13 14 3 3 12 13 +--R -- b d x + b c d x + -- b c d x + 35b c d x +--R 16 2 +--R + +--R 455 3 4 1 2 11 12 3 5 2 10 11 +--R (--- b c + - a b )d x + (273b c + 3a b c)d x +--R 4 4 +--R + +--R 1001 3 6 33 2 2 9 10 3 7 2 3 8 9 +--R (---- b c + -- a b c )d x + (715b c + 55a b c )d x +--R 2 2 +--R + +--R 6435 3 8 495 2 4 3 2 7 8 3 9 2 5 2 6 7 +--R (---- b c + --- a b c + - a b)d x + (715b c + 198a b c + 3a b c)d x +--R 8 4 8 +--R + +--R 1001 3 10 2 6 21 2 2 5 6 +--R (---- b c + 231a b c + -- a b c )d x +--R 2 2 +--R + +--R 3 11 2 7 2 3 4 5 +--R (273b c + 198a b c + 21a b c )d x +--R + +--R 455 3 12 495 2 8 105 2 4 1 3 3 4 +--R (--- b c + --- a b c + --- a b c + - a )d x +--R 4 4 4 4 +--R + +--R 3 13 2 9 2 5 3 2 3 +--R (35b c + 55a b c + 21a b c + a c)d x +--R + +--R 15 3 14 33 2 10 21 2 6 3 3 2 2 +--R (-- b c + -- a b c + -- a b c + - a c )d x +--R 2 2 2 2 +--R + +--R 3 15 2 11 2 7 3 3 +--R (b c + 3a b c + 3a b c + a c )x +--R Type: Polynomial(Fraction(Integer)) +--E 1377 + +--S 1378 of 1394 +m0:=a0-r0 +--R +--R +--R 1 4 16 1 3 12 3 2 2 8 1 3 4 1 4 +--R - -- b c - - a b c - - a b c - - a b c - -- a +--R 16 4 8 4 16 +--R (4) ---------------------------------------------------- +--R b d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1378 + +--S 1379 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1379 + +)clear all + +--S 1380 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4) +--R +--R +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R (1) ---------------------------------------------------- +--R 4 4 3 3 2 2 2 3 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1380 + +--S 1381 of 1394 +r0:=1/4*log(a+b*(c+d*x)^4)/(b*d) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R (2) --------------------------------------------------------- +--R 4b d +--R Type: Expression(Integer) +--E 1381 + +--S 1382 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R log(b d x + 4b c d x + 6b c d x + 4b c d x + b c + a) +--R (3) --------------------------------------------------------- +--R 4b d +--R Type: Union(Expression(Integer),...) +--E 1382 + +--S 1383 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1383 + +--S 1384 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1384 + +)clear all + +--S 1385 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4)^2 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 2 8 8 2 7 7 2 2 6 6 2 3 5 5 2 4 4 4 +--R b d x + 8b c d x + 28b c d x + 56b c d x + (70b c + 2a b)d x +--R + +--R 2 5 3 3 2 6 2 2 2 2 7 3 +--R (56b c + 8a b c)d x + (28b c + 12a b c )d x + (8b c + 8a b c )d x +--R + +--R 2 8 4 2 +--R b c + 2a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1385 + +--S 1386 of 1394 +r0:=(-1/4)/(b*d*(a+b*(c+d*x)^4)) +--R +--R +--R 1 +--R - +--R 4 +--R (2) - --------------------------------------------------------- +--R 2 5 4 2 4 3 2 2 3 2 2 3 2 2 4 +--R b d x + 4b c d x + 6b c d x + 4b c d x + (b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1386 + +--S 1387 of 1394 +a0:=integrate(t0,x) +--R +--R +--R 1 +--R (3) - --------------------------------------------------------------- +--R 2 5 4 2 4 3 2 2 3 2 2 3 2 2 4 +--R 4b d x + 16b c d x + 24b c d x + 16b c d x + (4b c + 4a b)d +--R Type: Union(Expression(Integer),...) +--E 1387 + +--S 1388 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1388 + +--S 1389 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1389 + +)clear all + +--S 1390 of 1394 +t0:=(c+d*x)^3/(a+b*(c+d*x)^4)^3 +--R +--R +--R (1) +--R 3 3 2 2 2 3 +--R d x + 3c d x + 3c d x + c +--R / +--R 3 12 12 3 11 11 3 2 10 10 3 3 9 9 +--R b d x + 12b c d x + 66b c d x + 220b c d x +--R + +--R 3 4 2 8 8 3 5 2 7 7 +--R (495b c + 3a b )d x + (792b c + 24a b c)d x +--R + +--R 3 6 2 2 6 6 3 7 2 3 5 5 +--R (924b c + 84a b c )d x + (792b c + 168a b c )d x +--R + +--R 3 8 2 4 2 4 4 3 9 2 5 2 3 3 +--R (495b c + 210a b c + 3a b)d x + (220b c + 168a b c + 12a b c)d x +--R + +--R 3 10 2 6 2 2 2 2 3 11 2 7 2 3 +--R (66b c + 84a b c + 18a b c )d x + (12b c + 24a b c + 12a b c )d x +--R + +--R 3 12 2 8 2 4 3 +--R b c + 3a b c + 3a b c + a +--R Type: Fraction(Polynomial(Integer)) +--E 1390 + +--S 1391 of 1394 +r0:=(-1/8)/(b*d*(a+b*(c+d*x)^4)^2) +--R +--R +--R (2) +--R - +--R 1 +--R - +--R 8 +--R / +--R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 3 4 2 5 4 +--R b d x + 8b c d x + 28b c d x + 56b c d x + (70b c + 2a b )d x +--R + +--R 3 5 2 4 3 3 6 2 2 3 2 3 7 2 3 2 +--R (56b c + 8a b c)d x + (28b c + 12a b c )d x + (8b c + 8a b c )d x +--R + +--R 3 8 2 4 2 +--R (b c + 2a b c + a b)d +--R Type: Fraction(Polynomial(Fraction(Integer))) +--E 1391 + +--S 1392 of 1394 +a0:=integrate(t0,x) +--R +--R +--R (3) +--R - +--R 1 +--R / +--R 3 9 8 3 8 7 3 2 7 6 3 3 6 5 +--R 8b d x + 64b c d x + 224b c d x + 448b c d x +--R + +--R 3 4 2 5 4 3 5 2 4 3 +--R (560b c + 16a b )d x + (448b c + 64a b c)d x +--R + +--R 3 6 2 2 3 2 3 7 2 3 2 +--R (224b c + 96a b c )d x + (64b c + 64a b c )d x +--R + +--R 3 8 2 4 2 +--R (8b c + 16a b c + 8a b)d +--R Type: Union(Expression(Integer),...) +--E 1392 + +--S 1393 of 1394 +m0:=a0-r0 +--R +--R +--R (4) 0 +--R Type: Expression(Integer) +--E 1393 + +--S 1394 of 1394 +d0:=D(m0,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 1394 + +)spool +)lisp (bye) + +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document}